Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [420,2,Mod(391,420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(420, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("420.391");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 420.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.35371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 391.2 | ||
Root | \(-1.39396 + 0.238466i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 420.391 |
Dual form | 420.2.c.b.391.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(241\) | \(281\) | \(337\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.39396 | + | 0.238466i | −0.985681 | + | 0.168621i | ||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.88627 | − | 0.664826i | 0.943134 | − | 0.332413i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | −1.39396 | + | 0.238466i | −0.569083 | + | 0.0973534i | ||||
\(7\) | −2.37694 | − | 1.16196i | −0.898398 | − | 0.439181i | ||||
\(8\) | −2.47085 | + | 1.37655i | −0.873577 | + | 0.486685i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.238466 | − | 1.39396i | −0.0754096 | − | 0.440810i | ||||
\(11\) | 4.86632i | 1.46725i | 0.679554 | + | 0.733626i | \(0.262174\pi\) | ||||
−0.679554 | + | 0.733626i | \(0.737826\pi\) | |||||||
\(12\) | 1.88627 | − | 0.664826i | 0.544519 | − | 0.191919i | ||||
\(13\) | 3.63628i | 1.00852i | 0.863551 | + | 0.504262i | \(0.168235\pi\) | ||||
−0.863551 | + | 0.504262i | \(0.831765\pi\) | |||||||
\(14\) | 3.59045 | + | 1.05292i | 0.959589 | + | 0.281404i | ||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 3.11601 | − | 2.50808i | 0.779003 | − | 0.627020i | ||||
\(17\) | 4.47770i | 1.08600i | 0.839732 | + | 0.543001i | \(0.182712\pi\) | ||||
−0.839732 | + | 0.543001i | \(0.817288\pi\) | |||||||
\(18\) | −1.39396 | + | 0.238466i | −0.328560 | + | 0.0562070i | ||||
\(19\) | 2.70953 | 0.621609 | 0.310804 | − | 0.950474i | \(-0.399402\pi\) | ||||
0.310804 | + | 0.950474i | \(0.399402\pi\) | |||||||
\(20\) | 0.664826 | + | 1.88627i | 0.148660 | + | 0.421782i | ||||
\(21\) | −2.37694 | − | 1.16196i | −0.518691 | − | 0.253561i | ||||
\(22\) | −1.16045 | − | 6.78348i | −0.247410 | − | 1.44624i | ||||
\(23\) | − | 1.68651i | − | 0.351661i | −0.984420 | − | 0.175831i | \(-0.943739\pi\) | ||
0.984420 | − | 0.175831i | \(-0.0562611\pi\) | |||||||
\(24\) | −2.47085 | + | 1.37655i | −0.504360 | + | 0.280988i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −0.867130 | − | 5.06885i | −0.170058 | − | 0.994082i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −5.25605 | − | 0.611525i | −0.993300 | − | 0.115567i | ||||
\(29\) | 8.31929 | 1.54485 | 0.772427 | − | 0.635103i | \(-0.219043\pi\) | ||||
0.772427 | + | 0.635103i | \(0.219043\pi\) | |||||||
\(30\) | −0.238466 | − | 1.39396i | −0.0435378 | − | 0.254502i | ||||
\(31\) | −5.47361 | −0.983090 | −0.491545 | − | 0.870852i | \(-0.663568\pi\) | ||||
−0.491545 | + | 0.870852i | \(0.663568\pi\) | |||||||
\(32\) | −3.74552 | + | 4.23924i | −0.662120 | + | 0.749398i | ||||
\(33\) | 4.86632i | 0.847118i | ||||||||
\(34\) | −1.06778 | − | 6.24175i | −0.183123 | − | 1.07045i | ||||
\(35\) | 1.16196 | − | 2.37694i | 0.196408 | − | 0.401776i | ||||
\(36\) | 1.88627 | − | 0.664826i | 0.314378 | − | 0.110804i | ||||
\(37\) | 7.07032 | 1.16235 | 0.581177 | − | 0.813777i | \(-0.302592\pi\) | ||||
0.581177 | + | 0.813777i | \(0.302592\pi\) | |||||||
\(38\) | −3.77698 | + | 0.646131i | −0.612708 | + | 0.104816i | ||||
\(39\) | 3.63628i | 0.582271i | ||||||||
\(40\) | −1.37655 | − | 2.47085i | −0.217652 | − | 0.390676i | ||||
\(41\) | 11.5568i | 1.80486i | 0.430835 | + | 0.902431i | \(0.358219\pi\) | ||||
−0.430835 | + | 0.902431i | \(0.641781\pi\) | |||||||
\(42\) | 3.59045 | + | 1.05292i | 0.554019 | + | 0.162469i | ||||
\(43\) | − | 7.86152i | − | 1.19887i | −0.800424 | − | 0.599435i | \(-0.795392\pi\) | ||
0.800424 | − | 0.599435i | \(-0.204608\pi\) | |||||||
\(44\) | 3.23526 | + | 9.17919i | 0.487734 | + | 1.38382i | ||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 0.402175 | + | 2.35093i | 0.0592975 | + | 0.346626i | ||||
\(47\) | −4.75086 | −0.692984 | −0.346492 | − | 0.938053i | \(-0.612627\pi\) | ||||
−0.346492 | + | 0.938053i | \(0.612627\pi\) | |||||||
\(48\) | 3.11601 | − | 2.50808i | 0.449758 | − | 0.362010i | ||||
\(49\) | 4.29968 | + | 5.52384i | 0.614240 | + | 0.789120i | ||||
\(50\) | 1.39396 | − | 0.238466i | 0.197136 | − | 0.0337242i | ||||
\(51\) | 4.47770i | 0.627004i | ||||||||
\(52\) | 2.41750 | + | 6.85900i | 0.335246 | + | 0.951173i | ||||
\(53\) | −10.1441 | −1.39340 | −0.696701 | − | 0.717362i | \(-0.745349\pi\) | ||||
−0.696701 | + | 0.717362i | \(0.745349\pi\) | |||||||
\(54\) | −1.39396 | + | 0.238466i | −0.189694 | + | 0.0324511i | ||||
\(55\) | −4.86632 | −0.656175 | ||||||||
\(56\) | 7.47257 | − | 0.400946i | 0.998564 | − | 0.0535786i | ||||
\(57\) | 2.70953 | 0.358886 | ||||||||
\(58\) | −11.5968 | + | 1.98387i | −1.52273 | + | 0.260495i | ||||
\(59\) | 2.97451 | 0.387248 | 0.193624 | − | 0.981076i | \(-0.437976\pi\) | ||||
0.193624 | + | 0.981076i | \(0.437976\pi\) | |||||||
\(60\) | 0.664826 | + | 1.88627i | 0.0858287 | + | 0.243516i | ||||
\(61\) | − | 1.18105i | − | 0.151217i | −0.997138 | − | 0.0756087i | \(-0.975910\pi\) | ||
0.997138 | − | 0.0756087i | \(-0.0240900\pi\) | |||||||
\(62\) | 7.63001 | − | 1.30527i | 0.969013 | − | 0.165770i | ||||
\(63\) | −2.37694 | − | 1.16196i | −0.299466 | − | 0.146394i | ||||
\(64\) | 4.21020 | − | 6.80252i | 0.526275 | − | 0.850315i | ||||
\(65\) | −3.63628 | −0.451025 | ||||||||
\(66\) | −1.16045 | − | 6.78348i | −0.142842 | − | 0.834988i | ||||
\(67\) | 13.1428i | 1.60565i | 0.596215 | + | 0.802825i | \(0.296671\pi\) | ||||
−0.596215 | + | 0.802825i | \(0.703329\pi\) | |||||||
\(68\) | 2.97689 | + | 8.44614i | 0.361001 | + | 1.02425i | ||||
\(69\) | − | 1.68651i | − | 0.203032i | ||||||
\(70\) | −1.05292 | + | 3.59045i | −0.125848 | + | 0.429141i | ||||
\(71\) | − | 14.8383i | − | 1.76098i | −0.474060 | − | 0.880492i | \(-0.657212\pi\) | ||
0.474060 | − | 0.880492i | \(-0.342788\pi\) | |||||||
\(72\) | −2.47085 | + | 1.37655i | −0.291192 | + | 0.162228i | ||||
\(73\) | 1.40398i | 0.164323i | 0.996619 | + | 0.0821615i | \(0.0261823\pi\) | ||||
−0.996619 | + | 0.0821615i | \(0.973818\pi\) | |||||||
\(74\) | −9.85577 | + | 1.68603i | −1.14571 | + | 0.195997i | ||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 5.11090 | − | 1.80137i | 0.586260 | − | 0.206631i | ||||
\(77\) | 5.65450 | − | 11.5670i | 0.644390 | − | 1.31818i | ||||
\(78\) | −0.867130 | − | 5.06885i | −0.0981832 | − | 0.573934i | ||||
\(79\) | 1.01535i | 0.114236i | 0.998367 | + | 0.0571181i | \(0.0181911\pi\) | ||||
−0.998367 | + | 0.0571181i | \(0.981809\pi\) | |||||||
\(80\) | 2.50808 | + | 3.11601i | 0.280412 | + | 0.348381i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.75589 | − | 16.1097i | −0.304338 | − | 1.77902i | ||||
\(83\) | −8.22400 | −0.902701 | −0.451351 | − | 0.892347i | \(-0.649058\pi\) | ||||
−0.451351 | + | 0.892347i | \(0.649058\pi\) | |||||||
\(84\) | −5.25605 | − | 0.611525i | −0.573482 | − | 0.0667229i | ||||
\(85\) | −4.47770 | −0.485675 | ||||||||
\(86\) | 1.87471 | + | 10.9587i | 0.202155 | + | 1.18170i | ||||
\(87\) | 8.31929 | 0.891922 | ||||||||
\(88\) | −6.69876 | − | 12.0240i | −0.714090 | − | 1.28176i | ||||
\(89\) | − | 9.91123i | − | 1.05059i | −0.850921 | − | 0.525294i | \(-0.823955\pi\) | ||
0.850921 | − | 0.525294i | \(-0.176045\pi\) | |||||||
\(90\) | −0.238466 | − | 1.39396i | −0.0251365 | − | 0.146937i | ||||
\(91\) | 4.22523 | − | 8.64322i | 0.442925 | − | 0.906056i | ||||
\(92\) | −1.12123 | − | 3.18121i | −0.116897 | − | 0.331664i | ||||
\(93\) | −5.47361 | −0.567587 | ||||||||
\(94\) | 6.62252 | − | 1.13292i | 0.683061 | − | 0.116852i | ||||
\(95\) | 2.70953i | 0.277992i | ||||||||
\(96\) | −3.74552 | + | 4.23924i | −0.382275 | + | 0.432665i | ||||
\(97\) | − | 13.0383i | − | 1.32384i | −0.749575 | − | 0.661920i | \(-0.769742\pi\) | ||
0.749575 | − | 0.661920i | \(-0.230258\pi\) | |||||||
\(98\) | −7.31084 | − | 6.67470i | −0.738506 | − | 0.674246i | ||||
\(99\) | 4.86632i | 0.489084i | ||||||||
\(100\) | −1.88627 | + | 0.664826i | −0.188627 | + | 0.0664826i | ||||
\(101\) | − | 10.5101i | − | 1.04579i | −0.852396 | − | 0.522897i | \(-0.824851\pi\) | ||
0.852396 | − | 0.522897i | \(-0.175149\pi\) | |||||||
\(102\) | −1.06778 | − | 6.24175i | −0.105726 | − | 0.618026i | ||||
\(103\) | 17.7530 | 1.74926 | 0.874630 | − | 0.484791i | \(-0.161104\pi\) | ||||
0.874630 | + | 0.484791i | \(0.161104\pi\) | |||||||
\(104\) | −5.00554 | − | 8.98471i | −0.490834 | − | 0.881023i | ||||
\(105\) | 1.16196 | − | 2.37694i | 0.113396 | − | 0.231965i | ||||
\(106\) | 14.1405 | − | 2.41903i | 1.37345 | − | 0.234957i | ||||
\(107\) | − | 3.33046i | − | 0.321968i | −0.986957 | − | 0.160984i | \(-0.948533\pi\) | ||
0.986957 | − | 0.160984i | \(-0.0514667\pi\) | |||||||
\(108\) | 1.88627 | − | 0.664826i | 0.181506 | − | 0.0639729i | ||||
\(109\) | −0.497397 | −0.0476420 | −0.0238210 | − | 0.999716i | \(-0.507583\pi\) | ||||
−0.0238210 | + | 0.999716i | \(0.507583\pi\) | |||||||
\(110\) | 6.78348 | − | 1.16045i | 0.646779 | − | 0.110645i | ||||
\(111\) | 7.07032 | 0.671085 | ||||||||
\(112\) | −10.3209 | + | 2.34086i | −0.975231 | + | 0.221190i | ||||
\(113\) | −5.49626 | −0.517045 | −0.258522 | − | 0.966005i | \(-0.583236\pi\) | ||||
−0.258522 | + | 0.966005i | \(0.583236\pi\) | |||||||
\(114\) | −3.77698 | + | 0.646131i | −0.353747 | + | 0.0605157i | ||||
\(115\) | 1.68651 | 0.157268 | ||||||||
\(116\) | 15.6924 | − | 5.53088i | 1.45700 | − | 0.513530i | ||||
\(117\) | 3.63628i | 0.336175i | ||||||||
\(118\) | −4.14635 | + | 0.709319i | −0.381703 | + | 0.0652981i | ||||
\(119\) | 5.20293 | − | 10.6432i | 0.476952 | − | 0.975663i | ||||
\(120\) | −1.37655 | − | 2.47085i | −0.125662 | − | 0.225557i | ||||
\(121\) | −12.6811 | −1.15283 | ||||||||
\(122\) | 0.281640 | + | 1.64634i | 0.0254984 | + | 0.149052i | ||||
\(123\) | 11.5568i | 1.04204i | ||||||||
\(124\) | −10.3247 | + | 3.63900i | −0.927185 | + | 0.326792i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 3.59045 | + | 1.05292i | 0.319863 | + | 0.0938013i | ||||
\(127\) | − | 2.36124i | − | 0.209527i | −0.994497 | − | 0.104763i | \(-0.966592\pi\) | ||
0.994497 | − | 0.104763i | \(-0.0334085\pi\) | |||||||
\(128\) | −4.24669 | + | 10.4864i | −0.375358 | + | 0.926880i | ||||
\(129\) | − | 7.86152i | − | 0.692168i | ||||||
\(130\) | 5.06885 | − | 0.867130i | 0.444567 | − | 0.0760524i | ||||
\(131\) | 1.93713 | 0.169248 | 0.0846239 | − | 0.996413i | \(-0.473031\pi\) | ||||
0.0846239 | + | 0.996413i | \(0.473031\pi\) | |||||||
\(132\) | 3.23526 | + | 9.17919i | 0.281593 | + | 0.798946i | ||||
\(133\) | −6.44039 | − | 3.14838i | −0.558452 | − | 0.272999i | ||||
\(134\) | −3.13411 | − | 18.3206i | −0.270746 | − | 1.58266i | ||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | −6.16380 | − | 11.0637i | −0.528541 | − | 0.948707i | ||||
\(137\) | 15.2841 | 1.30581 | 0.652903 | − | 0.757442i | \(-0.273551\pi\) | ||||
0.652903 | + | 0.757442i | \(0.273551\pi\) | |||||||
\(138\) | 0.402175 | + | 2.35093i | 0.0342354 | + | 0.200125i | ||||
\(139\) | 1.84036 | 0.156097 | 0.0780487 | − | 0.996950i | \(-0.475131\pi\) | ||||
0.0780487 | + | 0.996950i | \(0.475131\pi\) | |||||||
\(140\) | 0.611525 | − | 5.25605i | 0.0516833 | − | 0.444217i | ||||
\(141\) | −4.75086 | −0.400094 | ||||||||
\(142\) | 3.53844 | + | 20.6841i | 0.296939 | + | 1.73577i | ||||
\(143\) | −17.6953 | −1.47976 | ||||||||
\(144\) | 3.11601 | − | 2.50808i | 0.259668 | − | 0.209007i | ||||
\(145\) | 8.31929i | 0.690880i | ||||||||
\(146\) | −0.334801 | − | 1.95709i | −0.0277083 | − | 0.161970i | ||||
\(147\) | 4.29968 | + | 5.52384i | 0.354631 | + | 0.455598i | ||||
\(148\) | 13.3365 | − | 4.70053i | 1.09626 | − | 0.386382i | ||||
\(149\) | −2.97073 | −0.243371 | −0.121686 | − | 0.992569i | \(-0.538830\pi\) | ||||
−0.121686 | + | 0.992569i | \(0.538830\pi\) | |||||||
\(150\) | 1.39396 | − | 0.238466i | 0.113817 | − | 0.0194707i | ||||
\(151\) | 15.8192i | 1.28735i | 0.765300 | + | 0.643674i | \(0.222591\pi\) | ||||
−0.765300 | + | 0.643674i | \(0.777409\pi\) | |||||||
\(152\) | −6.69484 | + | 3.72981i | −0.543023 | + | 0.302528i | ||||
\(153\) | 4.47770i | 0.362001i | ||||||||
\(154\) | −5.12383 | + | 17.4723i | −0.412890 | + | 1.40796i | ||||
\(155\) | − | 5.47361i | − | 0.439651i | ||||||
\(156\) | 2.41750 | + | 6.85900i | 0.193555 | + | 0.549160i | ||||
\(157\) | − | 8.59663i | − | 0.686086i | −0.939320 | − | 0.343043i | \(-0.888542\pi\) | ||
0.939320 | − | 0.343043i | \(-0.111458\pi\) | |||||||
\(158\) | −0.242127 | − | 1.41537i | −0.0192626 | − | 0.112600i | ||||
\(159\) | −10.1441 | −0.804481 | ||||||||
\(160\) | −4.23924 | − | 3.74552i | −0.335141 | − | 0.296109i | ||||
\(161\) | −1.95966 | + | 4.00873i | −0.154443 | + | 0.315932i | ||||
\(162\) | −1.39396 | + | 0.238466i | −0.109520 | + | 0.0187357i | ||||
\(163\) | 1.35767i | 0.106341i | 0.998585 | + | 0.0531703i | \(0.0169326\pi\) | ||||
−0.998585 | + | 0.0531703i | \(0.983067\pi\) | |||||||
\(164\) | 7.68323 | + | 21.7991i | 0.599959 | + | 1.70223i | ||||
\(165\) | −4.86632 | −0.378843 | ||||||||
\(166\) | 11.4640 | − | 1.96115i | 0.889776 | − | 0.152214i | ||||
\(167\) | −2.53862 | −0.196444 | −0.0982220 | − | 0.995165i | \(-0.531316\pi\) | ||||
−0.0982220 | + | 0.995165i | \(0.531316\pi\) | |||||||
\(168\) | 7.47257 | − | 0.400946i | 0.576521 | − | 0.0309336i | ||||
\(169\) | −0.222556 | −0.0171197 | ||||||||
\(170\) | 6.24175 | − | 1.06778i | 0.478721 | − | 0.0818950i | ||||
\(171\) | 2.70953 | 0.207203 | ||||||||
\(172\) | −5.22654 | − | 14.8289i | −0.398520 | − | 1.13069i | ||||
\(173\) | − | 6.99917i | − | 0.532137i | −0.963954 | − | 0.266069i | \(-0.914275\pi\) | ||
0.963954 | − | 0.266069i | \(-0.0857248\pi\) | |||||||
\(174\) | −11.5968 | + | 1.98387i | −0.879150 | + | 0.150397i | ||||
\(175\) | 2.37694 | + | 1.16196i | 0.179680 | + | 0.0878363i | ||||
\(176\) | 12.2051 | + | 15.1635i | 0.919996 | + | 1.14299i | ||||
\(177\) | 2.97451 | 0.223578 | ||||||||
\(178\) | 2.36349 | + | 13.8159i | 0.177151 | + | 1.03554i | ||||
\(179\) | − | 8.98718i | − | 0.671734i | −0.941909 | − | 0.335867i | \(-0.890971\pi\) | ||
0.941909 | − | 0.335867i | \(-0.109029\pi\) | |||||||
\(180\) | 0.664826 | + | 1.88627i | 0.0495532 | + | 0.140594i | ||||
\(181\) | − | 7.23017i | − | 0.537414i | −0.963222 | − | 0.268707i | \(-0.913404\pi\) | ||
0.963222 | − | 0.268707i | \(-0.0865963\pi\) | |||||||
\(182\) | −3.82870 | + | 13.0559i | −0.283802 | + | 0.967769i | ||||
\(183\) | − | 1.18105i | − | 0.0873054i | ||||||
\(184\) | 2.32157 | + | 4.16711i | 0.171148 | + | 0.307203i | ||||
\(185\) | 7.07032i | 0.519820i | ||||||||
\(186\) | 7.63001 | − | 1.30527i | 0.559460 | − | 0.0957071i | ||||
\(187\) | −21.7899 | −1.59344 | ||||||||
\(188\) | −8.96139 | + | 3.15849i | −0.653576 | + | 0.230357i | ||||
\(189\) | −2.37694 | − | 1.16196i | −0.172897 | − | 0.0845205i | ||||
\(190\) | −0.646131 | − | 3.77698i | −0.0468753 | − | 0.274011i | ||||
\(191\) | − | 5.61914i | − | 0.406587i | −0.979118 | − | 0.203293i | \(-0.934835\pi\) | ||
0.979118 | − | 0.203293i | \(-0.0651645\pi\) | |||||||
\(192\) | 4.21020 | − | 6.80252i | 0.303845 | − | 0.490929i | ||||
\(193\) | 5.51737 | 0.397149 | 0.198575 | − | 0.980086i | \(-0.436369\pi\) | ||||
0.198575 | + | 0.980086i | \(0.436369\pi\) | |||||||
\(194\) | 3.10920 | + | 18.1749i | 0.223227 | + | 1.30488i | ||||
\(195\) | −3.63628 | −0.260400 | ||||||||
\(196\) | 11.7827 | + | 7.56090i | 0.841624 | + | 0.540064i | ||||
\(197\) | 6.86110 | 0.488833 | 0.244416 | − | 0.969670i | \(-0.421404\pi\) | ||||
0.244416 | + | 0.969670i | \(0.421404\pi\) | |||||||
\(198\) | −1.16045 | − | 6.78348i | −0.0824698 | − | 0.482081i | ||||
\(199\) | 1.33434 | 0.0945888 | 0.0472944 | − | 0.998881i | \(-0.484940\pi\) | ||||
0.0472944 | + | 0.998881i | \(0.484940\pi\) | |||||||
\(200\) | 2.47085 | − | 1.37655i | 0.174715 | − | 0.0973371i | ||||
\(201\) | 13.1428i | 0.927022i | ||||||||
\(202\) | 2.50630 | + | 14.6507i | 0.176343 | + | 1.03082i | ||||
\(203\) | −19.7745 | − | 9.66672i | −1.38789 | − | 0.678471i | ||||
\(204\) | 2.97689 | + | 8.44614i | 0.208424 | + | 0.591348i | ||||
\(205\) | −11.5568 | −0.807158 | ||||||||
\(206\) | −24.7471 | + | 4.23350i | −1.72421 | + | 0.294962i | ||||
\(207\) | − | 1.68651i | − | 0.117220i | ||||||
\(208\) | 9.12009 | + | 11.3307i | 0.632364 | + | 0.785643i | ||||
\(209\) | 13.1854i | 0.912057i | ||||||||
\(210\) | −1.05292 | + | 3.59045i | −0.0726581 | + | 0.247765i | ||||
\(211\) | 22.2190i | 1.52962i | 0.644256 | + | 0.764810i | \(0.277167\pi\) | ||||
−0.644256 | + | 0.764810i | \(0.722833\pi\) | |||||||
\(212\) | −19.1345 | + | 6.74407i | −1.31416 | + | 0.463185i | ||||
\(213\) | − | 14.8383i | − | 1.01671i | ||||||
\(214\) | 0.794202 | + | 4.64254i | 0.0542905 | + | 0.317357i | ||||
\(215\) | 7.86152 | 0.536151 | ||||||||
\(216\) | −2.47085 | + | 1.37655i | −0.168120 | + | 0.0936627i | ||||
\(217\) | 13.0104 | + | 6.36014i | 0.883206 | + | 0.431755i | ||||
\(218\) | 0.693353 | − | 0.118612i | 0.0469598 | − | 0.00803344i | ||||
\(219\) | 1.40398i | 0.0948719i | ||||||||
\(220\) | −9.17919 | + | 3.23526i | −0.618861 | + | 0.218121i | ||||
\(221\) | −16.2822 | −1.09526 | ||||||||
\(222\) | −9.85577 | + | 1.68603i | −0.661476 | + | 0.113159i | ||||
\(223\) | 28.4530 | 1.90535 | 0.952677 | − | 0.303985i | \(-0.0983174\pi\) | ||||
0.952677 | + | 0.303985i | \(0.0983174\pi\) | |||||||
\(224\) | 13.8287 | − | 5.72425i | 0.923969 | − | 0.382467i | ||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 7.66158 | − | 1.31067i | 0.509641 | − | 0.0871846i | ||||
\(227\) | 20.5963 | 1.36703 | 0.683513 | − | 0.729938i | \(-0.260451\pi\) | ||||
0.683513 | + | 0.729938i | \(0.260451\pi\) | |||||||
\(228\) | 5.11090 | − | 1.80137i | 0.338478 | − | 0.119298i | ||||
\(229\) | − | 10.6828i | − | 0.705937i | −0.935635 | − | 0.352968i | \(-0.885172\pi\) | ||
0.935635 | − | 0.352968i | \(-0.114828\pi\) | |||||||
\(230\) | −2.35093 | + | 0.402175i | −0.155016 | + | 0.0265186i | ||||
\(231\) | 5.65450 | − | 11.5670i | 0.372038 | − | 0.761050i | ||||
\(232\) | −20.5557 | + | 11.4520i | −1.34955 | + | 0.751858i | ||||
\(233\) | 24.6073 | 1.61208 | 0.806038 | − | 0.591864i | \(-0.201608\pi\) | ||||
0.806038 | + | 0.591864i | \(0.201608\pi\) | |||||||
\(234\) | −0.867130 | − | 5.06885i | −0.0566861 | − | 0.331361i | ||||
\(235\) | − | 4.75086i | − | 0.309912i | ||||||
\(236\) | 5.61072 | − | 1.97753i | 0.365226 | − | 0.128726i | ||||
\(237\) | 1.01535i | 0.0659543i | ||||||||
\(238\) | −4.71465 | + | 16.0770i | −0.305605 | + | 1.04212i | ||||
\(239\) | 9.20971i | 0.595726i | 0.954609 | + | 0.297863i | \(0.0962739\pi\) | ||||
−0.954609 | + | 0.297863i | \(0.903726\pi\) | |||||||
\(240\) | 2.50808 | + | 3.11601i | 0.161896 | + | 0.201138i | ||||
\(241\) | 11.5159i | 0.741807i | 0.928671 | + | 0.370903i | \(0.120952\pi\) | ||||
−0.928671 | + | 0.370903i | \(0.879048\pi\) | |||||||
\(242\) | 17.6770 | − | 3.02402i | 1.13632 | − | 0.194391i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.785190 | − | 2.22777i | −0.0502667 | − | 0.142618i | ||||
\(245\) | −5.52384 | + | 4.29968i | −0.352905 | + | 0.274696i | ||||
\(246\) | −2.75589 | − | 16.1097i | −0.175709 | − | 1.02712i | ||||
\(247\) | 9.85262i | 0.626907i | ||||||||
\(248\) | 13.5245 | − | 7.53472i | 0.858805 | − | 0.478455i | ||||
\(249\) | −8.22400 | −0.521175 | ||||||||
\(250\) | 0.238466 | + | 1.39396i | 0.0150819 | + | 0.0881620i | ||||
\(251\) | 1.35391 | 0.0854582 | 0.0427291 | − | 0.999087i | \(-0.486395\pi\) | ||||
0.0427291 | + | 0.999087i | \(0.486395\pi\) | |||||||
\(252\) | −5.25605 | − | 0.611525i | −0.331100 | − | 0.0385225i | ||||
\(253\) | 8.20710 | 0.515976 | ||||||||
\(254\) | 0.563077 | + | 3.29149i | 0.0353306 | + | 0.206526i | ||||
\(255\) | −4.47770 | −0.280405 | ||||||||
\(256\) | 3.41907 | − | 15.6304i | 0.213692 | − | 0.976901i | ||||
\(257\) | − | 19.0856i | − | 1.19053i | −0.803531 | − | 0.595263i | \(-0.797048\pi\) | ||
0.803531 | − | 0.595263i | \(-0.202952\pi\) | |||||||
\(258\) | 1.87471 | + | 10.9587i | 0.116714 | + | 0.682257i | ||||
\(259\) | −16.8057 | − | 8.21546i | −1.04426 | − | 0.510484i | ||||
\(260\) | −6.85900 | + | 2.41750i | −0.425377 | + | 0.149927i | ||||
\(261\) | 8.31929 | 0.514951 | ||||||||
\(262\) | −2.70029 | + | 0.461940i | −0.166824 | + | 0.0285387i | ||||
\(263\) | 23.1978i | 1.43044i | 0.698899 | + | 0.715220i | \(0.253674\pi\) | ||||
−0.698899 | + | 0.715220i | \(0.746326\pi\) | |||||||
\(264\) | −6.69876 | − | 12.0240i | −0.412280 | − | 0.740023i | ||||
\(265\) | − | 10.1441i | − | 0.623148i | ||||||
\(266\) | 9.72844 | + | 2.85291i | 0.596489 | + | 0.174923i | ||||
\(267\) | − | 9.91123i | − | 0.606557i | ||||||
\(268\) | 8.73768 | + | 24.7909i | 0.533739 | + | 1.51434i | ||||
\(269\) | 2.77517i | 0.169205i | 0.996415 | + | 0.0846025i | \(0.0269621\pi\) | ||||
−0.996415 | + | 0.0846025i | \(0.973038\pi\) | |||||||
\(270\) | −0.238466 | − | 1.39396i | −0.0145126 | − | 0.0848339i | ||||
\(271\) | −16.6103 | −1.00901 | −0.504503 | − | 0.863410i | \(-0.668324\pi\) | ||||
−0.504503 | + | 0.863410i | \(0.668324\pi\) | |||||||
\(272\) | 11.2304 | + | 13.9526i | 0.680945 | + | 0.845999i | ||||
\(273\) | 4.22523 | − | 8.64322i | 0.255723 | − | 0.523112i | ||||
\(274\) | −21.3054 | + | 3.64473i | −1.28711 | + | 0.220186i | ||||
\(275\) | − | 4.86632i | − | 0.293450i | ||||||
\(276\) | −1.12123 | − | 3.18121i | −0.0674904 | − | 0.191486i | ||||
\(277\) | −3.08317 | −0.185250 | −0.0926250 | − | 0.995701i | \(-0.529526\pi\) | ||||
−0.0926250 | + | 0.995701i | \(0.529526\pi\) | |||||||
\(278\) | −2.56540 | + | 0.438864i | −0.153862 | + | 0.0263213i | ||||
\(279\) | −5.47361 | −0.327697 | ||||||||
\(280\) | 0.400946 | + | 7.47257i | 0.0239611 | + | 0.446571i | ||||
\(281\) | −12.9179 | −0.770617 | −0.385308 | − | 0.922788i | \(-0.625905\pi\) | ||||
−0.385308 | + | 0.922788i | \(0.625905\pi\) | |||||||
\(282\) | 6.62252 | − | 1.13292i | 0.394365 | − | 0.0674643i | ||||
\(283\) | 17.1674 | 1.02050 | 0.510249 | − | 0.860027i | \(-0.329553\pi\) | ||||
0.510249 | + | 0.860027i | \(0.329553\pi\) | |||||||
\(284\) | −9.86490 | − | 27.9890i | −0.585374 | − | 1.66084i | ||||
\(285\) | 2.70953i | 0.160499i | ||||||||
\(286\) | 24.6666 | − | 4.21974i | 1.45857 | − | 0.249518i | ||||
\(287\) | 13.4285 | − | 27.4697i | 0.792661 | − | 1.62148i | ||||
\(288\) | −3.74552 | + | 4.23924i | −0.220707 | + | 0.249799i | ||||
\(289\) | −3.04981 | −0.179401 | ||||||||
\(290\) | −1.98387 | − | 11.5968i | −0.116497 | − | 0.680987i | ||||
\(291\) | − | 13.0383i | − | 0.764319i | ||||||
\(292\) | 0.933400 | + | 2.64827i | 0.0546231 | + | 0.154979i | ||||
\(293\) | − | 1.99319i | − | 0.116443i | −0.998304 | − | 0.0582217i | \(-0.981457\pi\) | ||
0.998304 | − | 0.0582217i | \(-0.0185430\pi\) | |||||||
\(294\) | −7.31084 | − | 6.67470i | −0.426377 | − | 0.389276i | ||||
\(295\) | 2.97451i | 0.173182i | ||||||||
\(296\) | −17.4697 | + | 9.73268i | −1.01541 | + | 0.565701i | ||||
\(297\) | 4.86632i | 0.282373i | ||||||||
\(298\) | 4.14108 | − | 0.708418i | 0.239887 | − | 0.0410375i | ||||
\(299\) | 6.13262 | 0.354659 | ||||||||
\(300\) | −1.88627 | + | 0.664826i | −0.108904 | + | 0.0383838i | ||||
\(301\) | −9.13480 | + | 18.6863i | −0.526521 | + | 1.07706i | ||||
\(302\) | −3.77234 | − | 22.0514i | −0.217074 | − | 1.26891i | ||||
\(303\) | − | 10.5101i | − | 0.603789i | ||||||
\(304\) | 8.44293 | − | 6.79572i | 0.484235 | − | 0.389761i | ||||
\(305\) | 1.18105 | 0.0676265 | ||||||||
\(306\) | −1.06778 | − | 6.24175i | −0.0610409 | − | 0.356817i | ||||
\(307\) | −7.80451 | −0.445427 | −0.222713 | − | 0.974884i | \(-0.571491\pi\) | ||||
−0.222713 | + | 0.974884i | \(0.571491\pi\) | |||||||
\(308\) | 2.97588 | − | 25.5776i | 0.169566 | − | 1.45742i | ||||
\(309\) | 17.7530 | 1.00994 | ||||||||
\(310\) | 1.30527 | + | 7.63001i | 0.0741344 | + | 0.433356i | ||||
\(311\) | −34.9575 | −1.98226 | −0.991130 | − | 0.132897i | \(-0.957572\pi\) | ||||
−0.991130 | + | 0.132897i | \(0.957572\pi\) | |||||||
\(312\) | −5.00554 | − | 8.98471i | −0.283383 | − | 0.508659i | ||||
\(313\) | 17.5160i | 0.990065i | 0.868875 | + | 0.495032i | \(0.164844\pi\) | ||||
−0.868875 | + | 0.495032i | \(0.835156\pi\) | |||||||
\(314\) | 2.05001 | + | 11.9834i | 0.115688 | + | 0.676262i | ||||
\(315\) | 1.16196 | − | 2.37694i | 0.0654693 | − | 0.133925i | ||||
\(316\) | 0.675033 | + | 1.91523i | 0.0379736 | + | 0.107740i | ||||
\(317\) | −9.86500 | −0.554074 | −0.277037 | − | 0.960859i | \(-0.589352\pi\) | ||||
−0.277037 | + | 0.960859i | \(0.589352\pi\) | |||||||
\(318\) | 14.1405 | − | 2.41903i | 0.792961 | − | 0.135652i | ||||
\(319\) | 40.4844i | 2.26669i | ||||||||
\(320\) | 6.80252 | + | 4.21020i | 0.380272 | + | 0.235357i | ||||
\(321\) | − | 3.33046i | − | 0.185888i | ||||||
\(322\) | 1.77575 | − | 6.05533i | 0.0989588 | − | 0.337450i | ||||
\(323\) | 12.1325i | 0.675068i | ||||||||
\(324\) | 1.88627 | − | 0.664826i | 0.104793 | − | 0.0369348i | ||||
\(325\) | − | 3.63628i | − | 0.201705i | ||||||
\(326\) | −0.323757 | − | 1.89254i | −0.0179313 | − | 0.104818i | ||||
\(327\) | −0.497397 | −0.0275061 | ||||||||
\(328\) | −15.9085 | − | 28.5550i | −0.878400 | − | 1.57669i | ||||
\(329\) | 11.2925 | + | 5.52033i | 0.622575 | + | 0.304345i | ||||
\(330\) | 6.78348 | − | 1.16045i | 0.373418 | − | 0.0638809i | ||||
\(331\) | − | 19.7243i | − | 1.08414i | −0.840332 | − | 0.542072i | \(-0.817640\pi\) | ||
0.840332 | − | 0.542072i | \(-0.182360\pi\) | |||||||
\(332\) | −15.5127 | + | 5.46753i | −0.851368 | + | 0.300070i | ||||
\(333\) | 7.07032 | 0.387451 | ||||||||
\(334\) | 3.53874 | − | 0.605374i | 0.193631 | − | 0.0331246i | ||||
\(335\) | −13.1428 | −0.718068 | ||||||||
\(336\) | −10.3209 | + | 2.34086i | −0.563050 | + | 0.127704i | ||||
\(337\) | −13.8674 | −0.755405 | −0.377702 | − | 0.925927i | \(-0.623286\pi\) | ||||
−0.377702 | + | 0.925927i | \(0.623286\pi\) | |||||||
\(338\) | 0.310235 | − | 0.0530720i | 0.0168745 | − | 0.00288674i | ||||
\(339\) | −5.49626 | −0.298516 | ||||||||
\(340\) | −8.44614 | + | 2.97689i | −0.458056 | + | 0.161445i | ||||
\(341\) | − | 26.6364i | − | 1.44244i | ||||||
\(342\) | −3.77698 | + | 0.646131i | −0.204236 | + | 0.0349388i | ||||
\(343\) | −3.80157 | − | 18.1259i | −0.205265 | − | 0.978706i | ||||
\(344\) | 10.8218 | + | 19.4246i | 0.583472 | + | 1.04731i | ||||
\(345\) | 1.68651 | 0.0907985 | ||||||||
\(346\) | 1.66907 | + | 9.75659i | 0.0897295 | + | 0.524517i | ||||
\(347\) | 11.8032i | 0.633631i | 0.948487 | + | 0.316815i | \(0.102614\pi\) | ||||
−0.948487 | + | 0.316815i | \(0.897386\pi\) | |||||||
\(348\) | 15.6924 | − | 5.53088i | 0.841202 | − | 0.296487i | ||||
\(349\) | − | 25.5589i | − | 1.36814i | −0.729417 | − | 0.684069i | \(-0.760209\pi\) | ||
0.729417 | − | 0.684069i | \(-0.239791\pi\) | |||||||
\(350\) | −3.59045 | − | 1.05292i | −0.191918 | − | 0.0562808i | ||||
\(351\) | 3.63628i | 0.194090i | ||||||||
\(352\) | −20.6295 | − | 18.2269i | −1.09956 | − | 0.971496i | ||||
\(353\) | − | 3.70650i | − | 0.197277i | −0.995123 | − | 0.0986386i | \(-0.968551\pi\) | ||
0.995123 | − | 0.0986386i | \(-0.0314488\pi\) | |||||||
\(354\) | −4.14635 | + | 0.709319i | −0.220376 | + | 0.0376999i | ||||
\(355\) | 14.8383 | 0.787536 | ||||||||
\(356\) | −6.58924 | − | 18.6952i | −0.349229 | − | 0.990845i | ||||
\(357\) | 5.20293 | − | 10.6432i | 0.275368 | − | 0.563299i | ||||
\(358\) | 2.14314 | + | 12.5278i | 0.113268 | + | 0.662115i | ||||
\(359\) | − | 15.8922i | − | 0.838758i | −0.907811 | − | 0.419379i | \(-0.862248\pi\) | ||
0.907811 | − | 0.419379i | \(-0.137752\pi\) | |||||||
\(360\) | −1.37655 | − | 2.47085i | −0.0725508 | − | 0.130225i | ||||
\(361\) | −11.6585 | −0.613603 | ||||||||
\(362\) | 1.72415 | + | 10.0786i | 0.0906193 | + | 0.529719i | ||||
\(363\) | −12.6811 | −0.665586 | ||||||||
\(364\) | 2.22368 | − | 19.1125i | 0.116552 | − | 1.00177i | ||||
\(365\) | −1.40398 | −0.0734874 | ||||||||
\(366\) | 0.281640 | + | 1.64634i | 0.0147215 | + | 0.0860553i | ||||
\(367\) | 28.7376 | 1.50009 | 0.750046 | − | 0.661385i | \(-0.230031\pi\) | ||||
0.750046 | + | 0.661385i | \(0.230031\pi\) | |||||||
\(368\) | −4.22990 | − | 5.25518i | −0.220499 | − | 0.273945i | ||||
\(369\) | 11.5568i | 0.601620i | ||||||||
\(370\) | −1.68603 | − | 9.85577i | −0.0876526 | − | 0.512377i | ||||
\(371\) | 24.1119 | + | 11.7871i | 1.25183 | + | 0.611956i | ||||
\(372\) | −10.3247 | + | 3.63900i | −0.535311 | + | 0.188673i | ||||
\(373\) | 9.60992 | 0.497583 | 0.248791 | − | 0.968557i | \(-0.419967\pi\) | ||||
0.248791 | + | 0.968557i | \(0.419967\pi\) | |||||||
\(374\) | 30.3744 | − | 5.19616i | 1.57062 | − | 0.268687i | ||||
\(375\) | − | 1.00000i | − | 0.0516398i | ||||||
\(376\) | 11.7387 | − | 6.53981i | 0.605375 | − | 0.337265i | ||||
\(377\) | 30.2513i | 1.55802i | ||||||||
\(378\) | 3.59045 | + | 1.05292i | 0.184673 | + | 0.0541562i | ||||
\(379\) | − | 8.12824i | − | 0.417520i | −0.977967 | − | 0.208760i | \(-0.933057\pi\) | ||
0.977967 | − | 0.208760i | \(-0.0669427\pi\) | |||||||
\(380\) | 1.80137 | + | 5.11090i | 0.0924081 | + | 0.262184i | ||||
\(381\) | − | 2.36124i | − | 0.120970i | ||||||
\(382\) | 1.33997 | + | 7.83288i | 0.0685591 | + | 0.400765i | ||||
\(383\) | 6.56611 | 0.335513 | 0.167756 | − | 0.985828i | \(-0.446348\pi\) | ||||
0.167756 | + | 0.985828i | \(0.446348\pi\) | |||||||
\(384\) | −4.24669 | + | 10.4864i | −0.216713 | + | 0.535134i | ||||
\(385\) | 11.5670 | + | 5.65450i | 0.589507 | + | 0.288180i | ||||
\(386\) | −7.69102 | + | 1.31571i | −0.391462 | + | 0.0669677i | ||||
\(387\) | − | 7.86152i | − | 0.399623i | ||||||
\(388\) | −8.66821 | − | 24.5937i | −0.440062 | − | 1.24856i | ||||
\(389\) | −16.8701 | −0.855349 | −0.427675 | − | 0.903933i | \(-0.640667\pi\) | ||||
−0.427675 | + | 0.903933i | \(0.640667\pi\) | |||||||
\(390\) | 5.06885 | − | 0.867130i | 0.256671 | − | 0.0439089i | ||||
\(391\) | 7.55168 | 0.381905 | ||||||||
\(392\) | −18.2277 | − | 7.72983i | −0.920639 | − | 0.390415i | ||||
\(393\) | 1.93713 | 0.0977152 | ||||||||
\(394\) | −9.56412 | + | 1.63614i | −0.481833 | + | 0.0824275i | ||||
\(395\) | −1.01535 | −0.0510880 | ||||||||
\(396\) | 3.23526 | + | 9.17919i | 0.162578 | + | 0.461272i | ||||
\(397\) | 7.42334i | 0.372567i | 0.982496 | + | 0.186283i | \(0.0596442\pi\) | ||||
−0.982496 | + | 0.186283i | \(0.940356\pi\) | |||||||
\(398\) | −1.86002 | + | 0.318195i | −0.0932344 | + | 0.0159497i | ||||
\(399\) | −6.44039 | − | 3.14838i | −0.322423 | − | 0.157616i | ||||
\(400\) | −3.11601 | + | 2.50808i | −0.155801 | + | 0.125404i | ||||
\(401\) | −11.4462 | −0.571596 | −0.285798 | − | 0.958290i | \(-0.592259\pi\) | ||||
−0.285798 | + | 0.958290i | \(0.592259\pi\) | |||||||
\(402\) | −3.13411 | − | 18.3206i | −0.156315 | − | 0.913748i | ||||
\(403\) | − | 19.9036i | − | 0.991469i | ||||||
\(404\) | −6.98738 | − | 19.8248i | −0.347635 | − | 0.986323i | ||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 29.8701 | + | 8.75952i | 1.48243 | + | 0.434728i | ||||
\(407\) | 34.4065i | 1.70547i | ||||||||
\(408\) | −6.16380 | − | 11.0637i | −0.305154 | − | 0.547736i | ||||
\(409\) | 36.0088i | 1.78052i | 0.455453 | + | 0.890260i | \(0.349477\pi\) | ||||
−0.455453 | + | 0.890260i | \(0.650523\pi\) | |||||||
\(410\) | 16.1097 | − | 2.75589i | 0.795601 | − | 0.136104i | ||||
\(411\) | 15.2841 | 0.753907 | ||||||||
\(412\) | 33.4870 | − | 11.8027i | 1.64979 | − | 0.581477i | ||||
\(413\) | −7.07022 | − | 3.45627i | −0.347903 | − | 0.170072i | ||||
\(414\) | 0.402175 | + | 2.35093i | 0.0197658 | + | 0.115542i | ||||
\(415\) | − | 8.22400i | − | 0.403700i | ||||||
\(416\) | −15.4151 | − | 13.6198i | −0.755786 | − | 0.667763i | ||||
\(417\) | 1.84036 | 0.0901229 | ||||||||
\(418\) | −3.14428 | − | 18.3800i | −0.153792 | − | 0.898997i | ||||
\(419\) | 39.5569 | 1.93248 | 0.966240 | − | 0.257644i | \(-0.0829461\pi\) | ||||
0.966240 | + | 0.257644i | \(0.0829461\pi\) | |||||||
\(420\) | 0.611525 | − | 5.25605i | 0.0298394 | − | 0.256469i | ||||
\(421\) | −16.9601 | −0.826584 | −0.413292 | − | 0.910599i | \(-0.635621\pi\) | ||||
−0.413292 | + | 0.910599i | \(0.635621\pi\) | |||||||
\(422\) | −5.29848 | − | 30.9725i | −0.257926 | − | 1.50772i | ||||
\(423\) | −4.75086 | −0.230995 | ||||||||
\(424\) | 25.0646 | − | 13.9639i | 1.21724 | − | 0.678148i | ||||
\(425\) | − | 4.47770i | − | 0.217200i | ||||||
\(426\) | 3.53844 | + | 20.6841i | 0.171438 | + | 1.00215i | ||||
\(427\) | −1.37233 | + | 2.80727i | −0.0664119 | + | 0.135854i | ||||
\(428\) | −2.21418 | − | 6.28214i | −0.107026 | − | 0.303659i | ||||
\(429\) | −17.6953 | −0.854339 | ||||||||
\(430\) | −10.9587 | + | 1.87471i | −0.528474 | + | 0.0904063i | ||||
\(431\) | 19.0357i | 0.916918i | 0.888716 | + | 0.458459i | \(0.151598\pi\) | ||||
−0.888716 | + | 0.458459i | \(0.848402\pi\) | |||||||
\(432\) | 3.11601 | − | 2.50808i | 0.149919 | − | 0.120670i | ||||
\(433\) | − | 28.8960i | − | 1.38865i | −0.719660 | − | 0.694326i | \(-0.755702\pi\) | ||
0.719660 | − | 0.694326i | \(-0.244298\pi\) | |||||||
\(434\) | −19.6528 | − | 5.76326i | −0.943363 | − | 0.276645i | ||||
\(435\) | 8.31929i | 0.398880i | ||||||||
\(436\) | −0.938224 | + | 0.330683i | −0.0449328 | + | 0.0158368i | ||||
\(437\) | − | 4.56964i | − | 0.218596i | ||||||
\(438\) | −0.334801 | − | 1.95709i | −0.0159974 | − | 0.0935134i | ||||
\(439\) | −22.6953 | −1.08319 | −0.541593 | − | 0.840641i | \(-0.682179\pi\) | ||||
−0.541593 | + | 0.840641i | \(0.682179\pi\) | |||||||
\(440\) | 12.0240 | − | 6.69876i | 0.573220 | − | 0.319351i | ||||
\(441\) | 4.29968 | + | 5.52384i | 0.204747 | + | 0.263040i | ||||
\(442\) | 22.6968 | − | 3.88275i | 1.07958 | − | 0.184684i | ||||
\(443\) | 28.4930i | 1.35374i | 0.736102 | + | 0.676871i | \(0.236664\pi\) | ||||
−0.736102 | + | 0.676871i | \(0.763336\pi\) | |||||||
\(444\) | 13.3365 | − | 4.70053i | 0.632923 | − | 0.223077i | ||||
\(445\) | 9.91123 | 0.469837 | ||||||||
\(446\) | −39.6624 | + | 6.78508i | −1.87807 | + | 0.321283i | ||||
\(447\) | −2.97073 | −0.140511 | ||||||||
\(448\) | −17.9117 | + | 11.2771i | −0.846247 | + | 0.532791i | ||||
\(449\) | 17.2001 | 0.811722 | 0.405861 | − | 0.913935i | \(-0.366972\pi\) | ||||
0.405861 | + | 0.913935i | \(0.366972\pi\) | |||||||
\(450\) | 1.39396 | − | 0.238466i | 0.0657121 | − | 0.0112414i | ||||
\(451\) | −56.2389 | −2.64819 | ||||||||
\(452\) | −10.3674 | + | 3.65406i | −0.487642 | + | 0.171872i | ||||
\(453\) | 15.8192i | 0.743250i | ||||||||
\(454\) | −28.7105 | + | 4.91153i | −1.34745 | + | 0.230509i | ||||
\(455\) | 8.64322 | + | 4.22523i | 0.405201 | + | 0.198082i | ||||
\(456\) | −6.69484 | + | 3.72981i | −0.313515 | + | 0.174665i | ||||
\(457\) | 25.6609 | 1.20037 | 0.600183 | − | 0.799862i | \(-0.295094\pi\) | ||||
0.600183 | + | 0.799862i | \(0.295094\pi\) | |||||||
\(458\) | 2.54748 | + | 14.8914i | 0.119036 | + | 0.695828i | ||||
\(459\) | 4.47770i | 0.209001i | ||||||||
\(460\) | 3.18121 | − | 1.12123i | 0.148325 | − | 0.0522778i | ||||
\(461\) | 36.4599i | 1.69811i | 0.528306 | + | 0.849054i | \(0.322827\pi\) | ||||
−0.528306 | + | 0.849054i | \(0.677173\pi\) | |||||||
\(462\) | −5.12383 | + | 17.4723i | −0.238382 | + | 0.812886i | ||||
\(463\) | 26.2427i | 1.21960i | 0.792555 | + | 0.609801i | \(0.208751\pi\) | ||||
−0.792555 | + | 0.609801i | \(0.791249\pi\) | |||||||
\(464\) | 25.9230 | − | 20.8655i | 1.20345 | − | 0.968655i | ||||
\(465\) | − | 5.47361i | − | 0.253833i | ||||||
\(466\) | −34.3016 | + | 5.86800i | −1.58899 | + | 0.271830i | ||||
\(467\) | −8.40283 | −0.388837 | −0.194418 | − | 0.980919i | \(-0.562282\pi\) | ||||
−0.194418 | + | 0.980919i | \(0.562282\pi\) | |||||||
\(468\) | 2.41750 | + | 6.85900i | 0.111749 | + | 0.317058i | ||||
\(469\) | 15.2715 | − | 31.2397i | 0.705171 | − | 1.44251i | ||||
\(470\) | 1.13292 | + | 6.62252i | 0.0522576 | + | 0.305474i | ||||
\(471\) | − | 8.59663i | − | 0.396112i | ||||||
\(472\) | −7.34956 | + | 4.09457i | −0.338291 | + | 0.188468i | ||||
\(473\) | 38.2567 | 1.75904 | ||||||||
\(474\) | −0.242127 | − | 1.41537i | −0.0111213 | − | 0.0650099i | ||||
\(475\) | −2.70953 | −0.124322 | ||||||||
\(476\) | 2.73823 | − | 23.5350i | 0.125506 | − | 1.07873i | ||||
\(477\) | −10.1441 | −0.464467 | ||||||||
\(478\) | −2.19620 | − | 12.8380i | −0.100452 | − | 0.587196i | ||||
\(479\) | 17.6650 | 0.807136 | 0.403568 | − | 0.914950i | \(-0.367770\pi\) | ||||
0.403568 | + | 0.914950i | \(0.367770\pi\) | |||||||
\(480\) | −4.23924 | − | 3.74552i | −0.193494 | − | 0.170959i | ||||
\(481\) | 25.7097i | 1.17226i | ||||||||
\(482\) | −2.74616 | − | 16.0528i | −0.125084 | − | 0.731185i | ||||
\(483\) | −1.95966 | + | 4.00873i | −0.0891677 | + | 0.182403i | ||||
\(484\) | −23.9200 | + | 8.43073i | −1.08727 | + | 0.383215i | ||||
\(485\) | 13.0383 | 0.592039 | ||||||||
\(486\) | −1.39396 | + | 0.238466i | −0.0632315 | + | 0.0108170i | ||||
\(487\) | − | 1.49550i | − | 0.0677675i | −0.999426 | − | 0.0338837i | \(-0.989212\pi\) | ||
0.999426 | − | 0.0338837i | \(-0.0107876\pi\) | |||||||
\(488\) | 1.62577 | + | 2.91819i | 0.0735953 | + | 0.132100i | ||||
\(489\) | 1.35767i | 0.0613958i | ||||||||
\(490\) | 6.67470 | − | 7.31084i | 0.301532 | − | 0.330270i | ||||
\(491\) | − | 3.45902i | − | 0.156103i | −0.996949 | − | 0.0780517i | \(-0.975130\pi\) | ||
0.996949 | − | 0.0780517i | \(-0.0248699\pi\) | |||||||
\(492\) | 7.68323 | + | 21.7991i | 0.346387 | + | 0.982780i | ||||
\(493\) | 37.2513i | 1.67771i | ||||||||
\(494\) | −2.34952 | − | 13.7342i | −0.105710 | − | 0.617930i | ||||
\(495\) | −4.86632 | −0.218725 | ||||||||
\(496\) | −17.0558 | + | 13.7283i | −0.765830 | + | 0.616417i | ||||
\(497\) | −17.2416 | + | 35.2698i | −0.773392 | + | 1.58207i | ||||
\(498\) | 11.4640 | − | 1.96115i | 0.513712 | − | 0.0878810i | ||||
\(499\) | − | 16.3100i | − | 0.730135i | −0.930981 | − | 0.365067i | \(-0.881046\pi\) | ||
0.930981 | − | 0.365067i | \(-0.118954\pi\) | |||||||
\(500\) | −0.664826 | − | 1.88627i | −0.0297319 | − | 0.0843565i | ||||
\(501\) | −2.53862 | −0.113417 | ||||||||
\(502\) | −1.88731 | + | 0.322862i | −0.0842346 | + | 0.0144101i | ||||
\(503\) | −27.5175 | −1.22694 | −0.613472 | − | 0.789716i | \(-0.710228\pi\) | ||||
−0.613472 | + | 0.789716i | \(0.710228\pi\) | |||||||
\(504\) | 7.47257 | − | 0.400946i | 0.332855 | − | 0.0178595i | ||||
\(505\) | 10.5101 | 0.467693 | ||||||||
\(506\) | −11.4404 | + | 1.95711i | −0.508587 | + | 0.0870043i | ||||
\(507\) | −0.222556 | −0.00988405 | ||||||||
\(508\) | −1.56982 | − | 4.45394i | −0.0696494 | − | 0.197612i | ||||
\(509\) | 7.28185i | 0.322762i | 0.986892 | + | 0.161381i | \(0.0515949\pi\) | ||||
−0.986892 | + | 0.161381i | \(0.948405\pi\) | |||||||
\(510\) | 6.24175 | − | 1.06778i | 0.276389 | − | 0.0472821i | ||||
\(511\) | 1.63137 | − | 3.33716i | 0.0721675 | − | 0.147627i | ||||
\(512\) | −1.03873 | + | 22.6036i | −0.0459058 | + | 0.998946i | ||||
\(513\) | 2.70953 | 0.119629 | ||||||||
\(514\) | 4.55127 | + | 26.6046i | 0.200748 | + | 1.17348i | ||||
\(515\) | 17.7530i | 0.782293i | ||||||||
\(516\) | −5.22654 | − | 14.8289i | −0.230086 | − | 0.652807i | ||||
\(517\) | − | 23.1192i | − | 1.01678i | ||||||
\(518\) | 25.3857 | + | 7.44446i | 1.11538 | + | 0.327091i | ||||
\(519\) | − | 6.99917i | − | 0.307229i | ||||||
\(520\) | 8.98471 | − | 5.00554i | 0.394006 | − | 0.219508i | ||||
\(521\) | 5.22603i | 0.228957i | 0.993426 | + | 0.114478i | \(0.0365196\pi\) | ||||
−0.993426 | + | 0.114478i | \(0.963480\pi\) | |||||||
\(522\) | −11.5968 | + | 1.98387i | −0.507578 | + | 0.0868316i | ||||
\(523\) | 18.0840 | 0.790756 | 0.395378 | − | 0.918518i | \(-0.370614\pi\) | ||||
0.395378 | + | 0.918518i | \(0.370614\pi\) | |||||||
\(524\) | 3.65394 | − | 1.28785i | 0.159623 | − | 0.0562602i | ||||
\(525\) | 2.37694 | + | 1.16196i | 0.103738 | + | 0.0507123i | ||||
\(526\) | −5.53190 | − | 32.3369i | −0.241202 | − | 1.40996i | ||||
\(527\) | − | 24.5092i | − | 1.06764i | ||||||
\(528\) | 12.2051 | + | 15.1635i | 0.531160 | + | 0.659908i | ||||
\(529\) | 20.1557 | 0.876334 | ||||||||
\(530\) | 2.41903 | + | 14.1405i | 0.105076 | + | 0.614225i | ||||
\(531\) | 2.97451 | 0.129083 | ||||||||
\(532\) | −14.2414 | − | 1.65695i | −0.617444 | − | 0.0718377i | ||||
\(533\) | −42.0236 | −1.82024 | ||||||||
\(534\) | 2.36349 | + | 13.8159i | 0.102278 | + | 0.597872i | ||||
\(535\) | 3.33046 | 0.143988 | ||||||||
\(536\) | −18.0918 | − | 32.4739i | −0.781446 | − | 1.40266i | ||||
\(537\) | − | 8.98718i | − | 0.387826i | ||||||
\(538\) | −0.661784 | − | 3.86848i | −0.0285315 | − | 0.166782i | ||||
\(539\) | −26.8808 | + | 20.9236i | −1.15784 | + | 0.901244i | ||||
\(540\) | 0.664826 | + | 1.88627i | 0.0286096 | + | 0.0811720i | ||||
\(541\) | 24.4454 | 1.05099 | 0.525494 | − | 0.850797i | \(-0.323880\pi\) | ||||
0.525494 | + | 0.850797i | \(0.323880\pi\) | |||||||
\(542\) | 23.1542 | − | 3.96101i | 0.994559 | − | 0.170140i | ||||
\(543\) | − | 7.23017i | − | 0.310276i | ||||||
\(544\) | −18.9820 | − | 16.7713i | −0.813848 | − | 0.719063i | ||||
\(545\) | − | 0.497397i | − | 0.0213062i | ||||||
\(546\) | −3.82870 | + | 13.0559i | −0.163853 | + | 0.558741i | ||||
\(547\) | − | 19.9093i | − | 0.851258i | −0.904898 | − | 0.425629i | \(-0.860053\pi\) | ||
0.904898 | − | 0.425629i | \(-0.139947\pi\) | |||||||
\(548\) | 28.8298 | − | 10.1612i | 1.23155 | − | 0.434067i | ||||
\(549\) | − | 1.18105i | − | 0.0504058i | ||||||
\(550\) | 1.16045 | + | 6.78348i | 0.0494819 | + | 0.289248i | ||||
\(551\) | 22.5414 | 0.960295 | ||||||||
\(552\) | 2.32157 | + | 4.16711i | 0.0988126 | + | 0.177364i | ||||
\(553\) | 1.17980 | − | 2.41343i | 0.0501704 | − | 0.102630i | ||||
\(554\) | 4.29783 | − | 0.735233i | 0.182597 | − | 0.0312370i | ||||
\(555\) | 7.07032i | 0.300118i | ||||||||
\(556\) | 3.47142 | − | 1.22352i | 0.147221 | − | 0.0518888i | ||||
\(557\) | 19.7547 | 0.837034 | 0.418517 | − | 0.908209i | \(-0.362550\pi\) | ||||
0.418517 | + | 0.908209i | \(0.362550\pi\) | |||||||
\(558\) | 7.63001 | − | 1.30527i | 0.323004 | − | 0.0552565i | ||||
\(559\) | 28.5867 | 1.20909 | ||||||||
\(560\) | −2.34086 | − | 10.3209i | −0.0989193 | − | 0.436136i | ||||
\(561\) | −21.7899 | −0.919972 | ||||||||
\(562\) | 18.0071 | − | 3.08048i | 0.759582 | − | 0.129942i | ||||
\(563\) | 8.92016 | 0.375940 | 0.187970 | − | 0.982175i | \(-0.439809\pi\) | ||||
0.187970 | + | 0.982175i | \(0.439809\pi\) | |||||||
\(564\) | −8.96139 | + | 3.15849i | −0.377342 | + | 0.132997i | ||||
\(565\) | − | 5.49626i | − | 0.231229i | ||||||
\(566\) | −23.9308 | + | 4.09385i | −1.00589 | + | 0.172078i | ||||
\(567\) | −2.37694 | − | 1.16196i | −0.0998221 | − | 0.0487979i | ||||
\(568\) | 20.4258 | + | 36.6633i | 0.857046 | + | 1.53836i | ||||
\(569\) | 8.00467 | 0.335573 | 0.167787 | − | 0.985823i | \(-0.446338\pi\) | ||||
0.167787 | + | 0.985823i | \(0.446338\pi\) | |||||||
\(570\) | −0.646131 | − | 3.77698i | −0.0270635 | − | 0.158200i | ||||
\(571\) | − | 32.6423i | − | 1.36604i | −0.730401 | − | 0.683019i | \(-0.760667\pi\) | ||
0.730401 | − | 0.683019i | \(-0.239333\pi\) | |||||||
\(572\) | −33.3781 | + | 11.7643i | −1.39561 | + | 0.491891i | ||||
\(573\) | − | 5.61914i | − | 0.234743i | ||||||
\(574\) | −12.1683 | + | 41.4940i | −0.507895 | + | 1.73193i | ||||
\(575\) | 1.68651i | 0.0703323i | ||||||||
\(576\) | 4.21020 | − | 6.80252i | 0.175425 | − | 0.283438i | ||||
\(577\) | 34.5773i | 1.43947i | 0.694247 | + | 0.719737i | \(0.255737\pi\) | ||||
−0.694247 | + | 0.719737i | \(0.744263\pi\) | |||||||
\(578\) | 4.25133 | − | 0.727277i | 0.176832 | − | 0.0302507i | ||||
\(579\) | 5.51737 | 0.229294 | ||||||||
\(580\) | 5.53088 | + | 15.6924i | 0.229657 | + | 0.651592i | ||||
\(581\) | 19.5479 | + | 9.55600i | 0.810986 | + | 0.396450i | ||||
\(582\) | 3.10920 | + | 18.1749i | 0.128880 | + | 0.753375i | ||||
\(583\) | − | 49.3646i | − | 2.04447i | ||||||
\(584\) | −1.93265 | − | 3.46901i | −0.0799736 | − | 0.143549i | ||||
\(585\) | −3.63628 | −0.150342 | ||||||||
\(586\) | 0.475309 | + | 2.77844i | 0.0196348 | + | 0.114776i | ||||
\(587\) | −38.2214 | −1.57757 | −0.788783 | − | 0.614672i | \(-0.789288\pi\) | ||||
−0.788783 | + | 0.614672i | \(0.789288\pi\) | |||||||
\(588\) | 11.7827 | + | 7.56090i | 0.485912 | + | 0.311806i | ||||
\(589\) | −14.8309 | −0.611097 | ||||||||
\(590\) | −0.709319 | − | 4.14635i | −0.0292022 | − | 0.170703i | ||||
\(591\) | 6.86110 | 0.282228 | ||||||||
\(592\) | 22.0312 | − | 17.7329i | 0.905477 | − | 0.728819i | ||||
\(593\) | − | 28.7500i | − | 1.18062i | −0.807176 | − | 0.590311i | \(-0.799005\pi\) | ||
0.807176 | − | 0.590311i | \(-0.200995\pi\) | |||||||
\(594\) | −1.16045 | − | 6.78348i | −0.0476140 | − | 0.278329i | ||||
\(595\) | 10.6432 | + | 5.20293i | 0.436330 | + | 0.213299i | ||||
\(596\) | −5.60359 | + | 1.97502i | −0.229532 | + | 0.0808998i | ||||
\(597\) | 1.33434 | 0.0546109 | ||||||||
\(598\) | −8.54865 | + | 1.46242i | −0.349580 | + | 0.0598029i | ||||
\(599\) | − | 13.1500i | − | 0.537296i | −0.963238 | − | 0.268648i | \(-0.913423\pi\) | ||
0.963238 | − | 0.268648i | \(-0.0865769\pi\) | |||||||
\(600\) | 2.47085 | − | 1.37655i | 0.100872 | − | 0.0561976i | ||||
\(601\) | − | 32.8895i | − | 1.34159i | −0.741643 | − | 0.670794i | \(-0.765953\pi\) | ||
0.741643 | − | 0.670794i | \(-0.234047\pi\) | |||||||
\(602\) | 8.27752 | − | 28.2264i | 0.337366 | − | 1.15042i | ||||
\(603\) | 13.1428i | 0.535217i | ||||||||
\(604\) | 10.5170 | + | 29.8392i | 0.427931 | + | 1.21414i | ||||
\(605\) | − | 12.6811i | − | 0.515560i | ||||||
\(606\) | 2.50630 | + | 14.6507i | 0.101812 | + | 0.595143i | ||||
\(607\) | −26.5553 | −1.07785 | −0.538923 | − | 0.842355i | \(-0.681169\pi\) | ||||
−0.538923 | + | 0.842355i | \(0.681169\pi\) | |||||||
\(608\) | −10.1486 | + | 11.4863i | −0.411579 | + | 0.465832i | ||||
\(609\) | −19.7745 | − | 9.66672i | −0.801301 | − | 0.391715i | ||||
\(610\) | −1.64634 | + | 0.281640i | −0.0666582 | + | 0.0114033i | ||||
\(611\) | − | 17.2755i | − | 0.698890i | ||||||
\(612\) | 2.97689 | + | 8.44614i | 0.120334 | + | 0.341415i | ||||
\(613\) | −37.0669 | −1.49712 | −0.748558 | − | 0.663069i | \(-0.769254\pi\) | ||||
−0.748558 | + | 0.663069i | \(0.769254\pi\) | |||||||
\(614\) | 10.8792 | − | 1.86111i | 0.439049 | − | 0.0751083i | ||||
\(615\) | −11.5568 | −0.466013 | ||||||||
\(616\) | 1.95113 | + | 36.3639i | 0.0786134 | + | 1.46514i | ||||
\(617\) | −3.72176 | −0.149832 | −0.0749162 | − | 0.997190i | \(-0.523869\pi\) | ||||
−0.0749162 | + | 0.997190i | \(0.523869\pi\) | |||||||
\(618\) | −24.7471 | + | 4.23350i | −0.995474 | + | 0.170296i | ||||
\(619\) | −45.7106 | −1.83726 | −0.918632 | − | 0.395113i | \(-0.870705\pi\) | ||||
−0.918632 | + | 0.395113i | \(0.870705\pi\) | |||||||
\(620\) | −3.63900 | − | 10.3247i | −0.146146 | − | 0.414650i | ||||
\(621\) | − | 1.68651i | − | 0.0676772i | ||||||
\(622\) | 48.7295 | − | 8.33619i | 1.95388 | − | 0.334251i | ||||
\(623\) | −11.5165 | + | 23.5584i | −0.461399 | + | 0.943847i | ||||
\(624\) | 9.12009 | + | 11.3307i | 0.365096 | + | 0.453591i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −4.17698 | − | 24.4167i | −0.166946 | − | 0.975888i | ||||
\(627\) | 13.1854i | 0.526576i | ||||||||
\(628\) | −5.71526 | − | 16.2155i | −0.228064 | − | 0.647071i | ||||
\(629\) | 31.6588i | 1.26232i | ||||||||
\(630\) | −1.05292 | + | 3.59045i | −0.0419492 | + | 0.143047i | ||||
\(631\) | 11.1088i | 0.442235i | 0.975247 | + | 0.221117i | \(0.0709704\pi\) | ||||
−0.975247 | + | 0.221117i | \(0.929030\pi\) | |||||||
\(632\) | −1.39769 | − | 2.50879i | −0.0555971 | − | 0.0997941i | ||||
\(633\) | 22.2190i | 0.883126i | ||||||||
\(634\) | 13.7515 | − | 2.35247i | 0.546140 | − | 0.0934285i | ||||
\(635\) | 2.36124 | 0.0937031 | ||||||||
\(636\) | −19.1345 | + | 6.74407i | −0.758733 | + | 0.267420i | ||||
\(637\) | −20.0862 | + | 15.6348i | −0.795846 | + | 0.619475i | ||||
\(638\) | −9.65415 | − | 56.4337i | −0.382212 | − | 2.23423i | ||||
\(639\) | − | 14.8383i | − | 0.586995i | ||||||
\(640\) | −10.4864 | − | 4.24669i | −0.414513 | − | 0.167865i | ||||
\(641\) | −9.74294 | −0.384823 | −0.192412 | − | 0.981314i | \(-0.561631\pi\) | ||||
−0.192412 | + | 0.981314i | \(0.561631\pi\) | |||||||
\(642\) | 0.794202 | + | 4.64254i | 0.0313446 | + | 0.183226i | ||||
\(643\) | 9.82459 | 0.387444 | 0.193722 | − | 0.981056i | \(-0.437944\pi\) | ||||
0.193722 | + | 0.981056i | \(0.437944\pi\) | |||||||
\(644\) | −1.03134 | + | 8.86437i | −0.0406406 | + | 0.349305i | ||||
\(645\) | 7.86152 | 0.309547 | ||||||||
\(646\) | −2.89318 | − | 16.9122i | −0.113831 | − | 0.665402i | ||||
\(647\) | 43.7691 | 1.72074 | 0.860370 | − | 0.509671i | \(-0.170233\pi\) | ||||
0.860370 | + | 0.509671i | \(0.170233\pi\) | |||||||
\(648\) | −2.47085 | + | 1.37655i | −0.0970641 | + | 0.0540762i | ||||
\(649\) | 14.4749i | 0.568190i | ||||||||
\(650\) | 0.867130 | + | 5.06885i | 0.0340117 | + | 0.198816i | ||||
\(651\) | 13.0104 | + | 6.36014i | 0.509919 | + | 0.249274i | ||||
\(652\) | 0.902612 | + | 2.56092i | 0.0353490 | + | 0.100293i | ||||
\(653\) | 6.78003 | 0.265323 | 0.132661 | − | 0.991161i | \(-0.457648\pi\) | ||||
0.132661 | + | 0.991161i | \(0.457648\pi\) | |||||||
\(654\) | 0.693353 | − | 0.118612i | 0.0271123 | − | 0.00463811i | ||||
\(655\) | 1.93713i | 0.0756899i | ||||||||
\(656\) | 28.9853 | + | 36.0110i | 1.13168 | + | 1.40599i | ||||
\(657\) | 1.40398i | 0.0547743i | ||||||||
\(658\) | −17.0577 | − | 5.00225i | −0.664980 | − | 0.195008i | ||||
\(659\) | 16.7430i | 0.652214i | 0.945333 | + | 0.326107i | \(0.105737\pi\) | ||||
−0.945333 | + | 0.326107i | \(0.894263\pi\) | |||||||
\(660\) | −9.17919 | + | 3.23526i | −0.357300 | + | 0.125932i | ||||
\(661\) | − | 33.0783i | − | 1.28660i | −0.765616 | − | 0.643298i | \(-0.777566\pi\) | ||
0.765616 | − | 0.643298i | \(-0.222434\pi\) | |||||||
\(662\) | 4.70357 | + | 27.4949i | 0.182810 | + | 1.06862i | ||||
\(663\) | −16.2822 | −0.632348 | ||||||||
\(664\) | 20.3203 | − | 11.3208i | 0.788579 | − | 0.439332i | ||||
\(665\) | 3.14838 | − | 6.44039i | 0.122089 | − | 0.249747i | ||||
\(666\) | −9.85577 | + | 1.68603i | −0.381903 | + | 0.0653324i | ||||
\(667\) | − | 14.0306i | − | 0.543265i | ||||||
\(668\) | −4.78851 | + | 1.68774i | −0.185273 | + | 0.0653006i | ||||
\(669\) | 28.4530 | 1.10006 | ||||||||
\(670\) | 18.3206 | − | 3.13411i | 0.707786 | − | 0.121081i | ||||
\(671\) | 5.74735 | 0.221874 | ||||||||
\(672\) | 13.8287 | − | 5.72425i | 0.533454 | − | 0.220818i | ||||
\(673\) | 51.0877 | 1.96929 | 0.984643 | − | 0.174578i | \(-0.0558560\pi\) | ||||
0.984643 | + | 0.174578i | \(0.0558560\pi\) | |||||||
\(674\) | 19.3306 | − | 3.30690i | 0.744588 | − | 0.127377i | ||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −0.419800 | + | 0.147961i | −0.0161461 | + | 0.00569080i | ||||
\(677\) | − | 46.6750i | − | 1.79387i | −0.442165 | − | 0.896934i | \(-0.645789\pi\) | ||
0.442165 | − | 0.896934i | \(-0.354211\pi\) | |||||||
\(678\) | 7.66158 | − | 1.31067i | 0.294241 | − | 0.0503360i | ||||
\(679\) | −15.1501 | + | 30.9913i | −0.581406 | + | 1.18934i | ||||
\(680\) | 11.0637 | − | 6.16380i | 0.424275 | − | 0.236371i | ||||
\(681\) | 20.5963 | 0.789253 | ||||||||
\(682\) | 6.35187 | + | 37.1301i | 0.243226 | + | 1.42179i | ||||
\(683\) | − | 9.64514i | − | 0.369061i | −0.982827 | − | 0.184530i | \(-0.940924\pi\) | ||
0.982827 | − | 0.184530i | \(-0.0590764\pi\) | |||||||
\(684\) | 5.11090 | − | 1.80137i | 0.195420 | − | 0.0688769i | ||||
\(685\) | 15.2841i | 0.583974i | ||||||||
\(686\) | 9.62166 | + | 24.3603i | 0.367357 | + | 0.930080i | ||||
\(687\) | − | 10.6828i | − | 0.407573i | ||||||
\(688\) | −19.7173 | − | 24.4966i | −0.751715 | − | 0.933923i | ||||
\(689\) | − | 36.8869i | − | 1.40528i | ||||||
\(690\) | −2.35093 | + | 0.402175i | −0.0894984 | + | 0.0153105i | ||||
\(691\) | 7.87711 | 0.299659 | 0.149830 | − | 0.988712i | \(-0.452127\pi\) | ||||
0.149830 | + | 0.988712i | \(0.452127\pi\) | |||||||
\(692\) | −4.65323 | − | 13.2023i | −0.176889 | − | 0.501877i | ||||
\(693\) | 5.65450 | − | 11.5670i | 0.214797 | − | 0.439392i | ||||
\(694\) | −2.81467 | − | 16.4533i | −0.106843 | − | 0.624558i | ||||
\(695\) | 1.84036i | 0.0698089i | ||||||||
\(696\) | −20.5557 | + | 11.4520i | −0.779163 | + | 0.434085i | ||||
\(697\) | −51.7477 | −1.96008 | ||||||||
\(698\) | 6.09494 | + | 35.6282i | 0.230697 | + | 1.34855i | ||||
\(699\) | 24.6073 | 0.930733 | ||||||||
\(700\) | 5.25605 | + | 0.611525i | 0.198660 | + | 0.0231135i | ||||
\(701\) | 41.7864 | 1.57825 | 0.789125 | − | 0.614233i | \(-0.210535\pi\) | ||||
0.789125 | + | 0.614233i | \(0.210535\pi\) | |||||||
\(702\) | −0.867130 | − | 5.06885i | −0.0327277 | − | 0.191311i | ||||
\(703\) | 19.1572 | 0.722529 | ||||||||
\(704\) | 33.1033 | + | 20.4882i | 1.24763 | + | 0.772177i | ||||
\(705\) | − | 4.75086i | − | 0.178928i | ||||||
\(706\) | 0.883875 | + | 5.16673i | 0.0332651 | + | 0.194452i | ||||
\(707\) | −12.2124 | + | 24.9818i | −0.459293 | + | 0.939539i | ||||
\(708\) | 5.61072 | − | 1.97753i | 0.210864 | − | 0.0743201i | ||||
\(709\) | −29.4303 | −1.10528 | −0.552639 | − | 0.833421i | \(-0.686379\pi\) | ||||
−0.552639 | + | 0.833421i | \(0.686379\pi\) | |||||||
\(710\) | −20.6841 | + | 3.53844i | −0.776260 | + | 0.132795i | ||||
\(711\) | 1.01535i | 0.0380787i | ||||||||
\(712\) | 13.6433 | + | 24.4892i | 0.511306 | + | 0.917770i | ||||
\(713\) | 9.23129i | 0.345715i | ||||||||
\(714\) | −4.71465 | + | 16.0770i | −0.176441 | + | 0.601666i | ||||
\(715\) | − | 17.6953i | − | 0.661768i | ||||||
\(716\) | −5.97491 | − | 16.9522i | −0.223293 | − | 0.633535i | ||||
\(717\) | 9.20971i | 0.343943i | ||||||||
\(718\) | 3.78975 | + | 22.1531i | 0.141432 | + | 0.826748i | ||||
\(719\) | 27.0792 | 1.00988 | 0.504942 | − | 0.863153i | \(-0.331514\pi\) | ||||
0.504942 | + | 0.863153i | \(0.331514\pi\) | |||||||
\(720\) | 2.50808 | + | 3.11601i | 0.0934706 | + | 0.116127i | ||||
\(721\) | −42.1979 | − | 20.6284i | −1.57153 | − | 0.768242i | ||||
\(722\) | 16.2515 | − | 2.78015i | 0.604816 | − | 0.103466i | ||||
\(723\) | 11.5159i | 0.428282i | ||||||||
\(724\) | −4.80680 | − | 13.6380i | −0.178643 | − | 0.506853i | ||||
\(725\) | −8.31929 | −0.308971 | ||||||||
\(726\) | 17.6770 | − | 3.02402i | 0.656055 | − | 0.112232i | ||||
\(727\) | −40.2389 | −1.49238 | −0.746189 | − | 0.665734i | \(-0.768118\pi\) | ||||
−0.746189 | + | 0.665734i | \(0.768118\pi\) | |||||||
\(728\) | 1.45795 | + | 27.1724i | 0.0540353 | + | 1.00707i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.95709 | − | 0.334801i | 0.0724352 | − | 0.0123915i | ||||
\(731\) | 35.2015 | 1.30198 | ||||||||
\(732\) | −0.785190 | − | 2.22777i | −0.0290215 | − | 0.0823407i | ||||
\(733\) | 12.5147i | 0.462242i | 0.972925 | + | 0.231121i | \(0.0742394\pi\) | ||||
−0.972925 | + | 0.231121i | \(0.925761\pi\) | |||||||
\(734\) | −40.0592 | + | 6.85296i | −1.47861 | + | 0.252947i | ||||
\(735\) | −5.52384 | + | 4.29968i | −0.203750 | + | 0.158596i | ||||
\(736\) | 7.14951 | + | 6.31684i | 0.263534 | + | 0.232842i | ||||
\(737\) | −63.9572 | −2.35589 | ||||||||
\(738\) | −2.75589 | − | 16.1097i | −0.101446 | − | 0.593006i | ||||
\(739\) | − | 25.5637i | − | 0.940377i | −0.882566 | − | 0.470188i | \(-0.844186\pi\) | ||
0.882566 | − | 0.470188i | \(-0.155814\pi\) | |||||||
\(740\) | 4.70053 | + | 13.3365i | 0.172795 | + | 0.490260i | ||||
\(741\) | 9.85262i | 0.361945i | ||||||||
\(742\) | −36.4220 | − | 10.6809i | −1.33709 | − | 0.392108i | ||||
\(743\) | − | 18.2745i | − | 0.670425i | −0.942143 | − | 0.335212i | \(-0.891192\pi\) | ||
0.942143 | − | 0.335212i | \(-0.108808\pi\) | |||||||
\(744\) | 13.5245 | − | 7.53472i | 0.495831 | − | 0.276236i | ||||
\(745\) | − | 2.97073i | − | 0.108839i | ||||||
\(746\) | −13.3959 | + | 2.29164i | −0.490458 | + | 0.0839029i | ||||
\(747\) | −8.22400 | −0.300900 | ||||||||
\(748\) | −41.1017 | + | 14.4865i | −1.50283 | + | 0.529680i | ||||
\(749\) | −3.86988 | + | 7.91630i | −0.141402 | + | 0.289255i | ||||
\(750\) | 0.238466 | + | 1.39396i | 0.00870755 | + | 0.0509003i | ||||
\(751\) | 45.5201i | 1.66105i | 0.556979 | + | 0.830527i | \(0.311960\pi\) | ||||
−0.556979 | + | 0.830527i | \(0.688040\pi\) | |||||||
\(752\) | −14.8037 | + | 11.9155i | −0.539836 | + | 0.434515i | ||||
\(753\) | 1.35391 | 0.0493393 | ||||||||
\(754\) | −7.21391 | − | 42.1692i | −0.262715 | − | 1.53571i | ||||
\(755\) | −15.8192 | −0.575719 | ||||||||
\(756\) | −5.25605 | − | 0.611525i | −0.191161 | − | 0.0222410i | ||||
\(757\) | −0.384669 | −0.0139810 | −0.00699051 | − | 0.999976i | \(-0.502225\pi\) | ||||
−0.00699051 | + | 0.999976i | \(0.502225\pi\) | |||||||
\(758\) | 1.93831 | + | 11.3305i | 0.0704026 | + | 0.411541i | ||||
\(759\) | 8.20710 | 0.297899 | ||||||||
\(760\) | −3.72981 | − | 6.69484i | −0.135295 | − | 0.242847i | ||||
\(761\) | 21.5937i | 0.782771i | 0.920227 | + | 0.391386i | \(0.128004\pi\) | ||||
−0.920227 | + | 0.391386i | \(0.871996\pi\) | |||||||
\(762\) | 0.563077 | + | 3.29149i | 0.0203981 | + | 0.119238i | ||||
\(763\) | 1.18228 | + | 0.577958i | 0.0428015 | + | 0.0209235i | ||||
\(764\) | −3.73575 | − | 10.5992i | −0.135155 | − | 0.383466i | ||||
\(765\) | −4.47770 | −0.161892 | ||||||||
\(766\) | −9.15292 | + | 1.56580i | −0.330709 | + | 0.0565745i | ||||
\(767\) | 10.8161i | 0.390548i | ||||||||
\(768\) | 3.41907 | − | 15.6304i | 0.123375 | − | 0.564014i | ||||
\(769\) | − | 6.41120i | − | 0.231194i | −0.993296 | − | 0.115597i | \(-0.963122\pi\) | ||
0.993296 | − | 0.115597i | \(-0.0368781\pi\) | |||||||
\(770\) | −17.4723 | − | 5.12383i | −0.629659 | − | 0.184650i | ||||
\(771\) | − | 19.0856i | − | 0.687351i | ||||||
\(772\) | 10.4072 | − | 3.66809i | 0.374565 | − | 0.132018i | ||||
\(773\) | − | 20.1678i | − | 0.725385i | −0.931909 | − | 0.362693i | \(-0.881857\pi\) | ||
0.931909 | − | 0.362693i | \(-0.118143\pi\) | |||||||
\(774\) | 1.87471 | + | 10.9587i | 0.0673849 | + | 0.393901i | ||||
\(775\) | 5.47361 | 0.196618 | ||||||||
\(776\) | 17.9479 | + | 32.2157i | 0.644293 | + | 1.15648i | ||||
\(777\) | −16.8057 | − | 8.21546i | −0.602902 | − | 0.294728i | ||||
\(778\) | 23.5163 | − | 4.02295i | 0.843101 | − | 0.144230i | ||||
\(779\) | 31.3134i | 1.12192i | ||||||||
\(780\) | −6.85900 | + | 2.41750i | −0.245592 | + | 0.0865602i | ||||
\(781\) | 72.2081 | 2.58381 | ||||||||
\(782\) | −10.5268 | + | 1.80082i | −0.376436 | + | 0.0643972i | ||||
\(783\) | 8.31929 | 0.297307 | ||||||||
\(784\) | 27.2521 | + | 6.42841i | 0.973288 | + | 0.229586i | ||||
\(785\) | 8.59663 | 0.306827 | ||||||||
\(786\) | −2.70029 | + | 0.461940i | −0.0963160 | + | 0.0164768i | ||||
\(787\) | 22.3873 | 0.798019 | 0.399010 | − | 0.916947i | \(-0.369354\pi\) | ||||
0.399010 | + | 0.916947i | \(0.369354\pi\) | |||||||
\(788\) | 12.9419 | − | 4.56144i | 0.461035 | − | 0.162494i | ||||
\(789\) | 23.1978i | 0.825865i | ||||||||
\(790\) | 1.41537 | − | 0.242127i | 0.0503564 | − | 0.00861450i | ||||
\(791\) | 13.0643 | + | 6.38646i | 0.464512 | + | 0.227076i | ||||
\(792\) | −6.69876 | − | 12.0240i | −0.238030 | − | 0.427253i | ||||
\(793\) | 4.29462 | 0.152506 | ||||||||
\(794\) | −1.77021 | − | 10.3479i | −0.0628226 | − | 0.367232i | ||||
\(795\) | − | 10.1441i | − | 0.359775i | ||||||
\(796\) | 2.51692 | − | 0.887104i | 0.0892099 | − | 0.0314426i | ||||
\(797\) | 2.24576i | 0.0795490i | 0.999209 | + | 0.0397745i | \(0.0126640\pi\) | ||||
−0.999209 | + | 0.0397745i | \(0.987336\pi\) | |||||||
\(798\) | 9.72844 | + | 2.85291i | 0.344383 | + | 0.100992i | ||||
\(799\) | − | 21.2729i | − | 0.752582i | ||||||
\(800\) | 3.74552 | − | 4.23924i | 0.132424 | − | 0.149880i | ||||
\(801\) | − | 9.91123i | − | 0.350196i | ||||||
\(802\) | 15.9556 | − | 2.72953i | 0.563411 | − | 0.0963830i | ||||
\(803\) | −6.83220 | −0.241103 | ||||||||
\(804\) | 8.73768 | + | 24.7909i | 0.308154 | + | 0.874306i | ||||
\(805\) | −4.00873 | − | 1.95966i | −0.141289 | − | 0.0690690i | ||||
\(806\) | 4.74634 | + | 27.7449i | 0.167183 | + | 0.977272i | ||||
\(807\) | 2.77517i | 0.0976906i | ||||||||
\(808\) | 14.4677 | + | 25.9689i | 0.508972 | + | 0.913581i | ||||
\(809\) | −47.6518 | −1.67535 | −0.837674 | − | 0.546170i | \(-0.816085\pi\) | ||||
−0.837674 | + | 0.546170i | \(0.816085\pi\) | |||||||
\(810\) | −0.238466 | − | 1.39396i | −0.00837885 | − | 0.0489789i | ||||
\(811\) | −40.5019 | −1.42222 | −0.711108 | − | 0.703083i | \(-0.751806\pi\) | ||||
−0.711108 | + | 0.703083i | \(0.751806\pi\) | |||||||
\(812\) | −43.7266 | − | 5.08746i | −1.53450 | − | 0.178535i | ||||
\(813\) | −16.6103 | −0.582550 | ||||||||
\(814\) | −8.20478 | − | 47.9614i | −0.287577 | − | 1.68105i | ||||
\(815\) | −1.35767 | −0.0475570 | ||||||||
\(816\) | 11.2304 | + | 13.9526i | 0.393144 | + | 0.488438i | ||||
\(817\) | − | 21.3010i | − | 0.745228i | ||||||
\(818\) | −8.58687 | − | 50.1949i | −0.300233 | − | 1.75502i | ||||
\(819\) | 4.22523 | − | 8.64322i | 0.147642 | − | 0.302019i | ||||
\(820\) | −21.7991 | + | 7.68323i | −0.761258 | + | 0.268310i | ||||
\(821\) | 11.8126 | 0.412263 | 0.206132 | − | 0.978524i | \(-0.433913\pi\) | ||||
0.206132 | + | 0.978524i | \(0.433913\pi\) | |||||||
\(822\) | −21.3054 | + | 3.64473i | −0.743112 | + | 0.127125i | ||||
\(823\) | 14.2178i | 0.495602i | 0.968811 | + | 0.247801i | \(0.0797079\pi\) | ||||
−0.968811 | + | 0.247801i | \(0.920292\pi\) | |||||||
\(824\) | −43.8651 | + | 24.4380i | −1.52811 | + | 0.851339i | ||||
\(825\) | − | 4.86632i | − | 0.169424i | ||||||
\(826\) | 10.6798 | + | 3.13191i | 0.371599 | + | 0.108973i | ||||
\(827\) | 11.5710i | 0.402363i | 0.979554 | + | 0.201182i | \(0.0644781\pi\) | ||||
−0.979554 | + | 0.201182i | \(0.935522\pi\) | |||||||
\(828\) | −1.12123 | − | 3.18121i | −0.0389656 | − | 0.110555i | ||||
\(829\) | − | 22.7146i | − | 0.788910i | −0.918915 | − | 0.394455i | \(-0.870933\pi\) | ||
0.918915 | − | 0.394455i | \(-0.129067\pi\) | |||||||
\(830\) | 1.96115 | + | 11.4640i | 0.0680724 | + | 0.397920i | ||||
\(831\) | −3.08317 | −0.106954 | ||||||||
\(832\) | 24.7359 | + | 15.3095i | 0.857562 | + | 0.530760i | ||||
\(833\) | −24.7341 | + | 19.2527i | −0.856986 | + | 0.667066i | ||||
\(834\) | −2.56540 | + | 0.438864i | −0.0888325 | + | 0.0151966i | ||||
\(835\) | − | 2.53862i | − | 0.0878524i | ||||||
\(836\) | 8.76603 | + | 24.8713i | 0.303180 | + | 0.860191i | ||||
\(837\) | −5.47361 | −0.189196 | ||||||||
\(838\) | −55.1408 | + | 9.43298i | −1.90481 | + | 0.325857i | ||||
\(839\) | 41.1901 | 1.42204 | 0.711020 | − | 0.703172i | \(-0.248234\pi\) | ||||
0.711020 | + | 0.703172i | \(0.248234\pi\) | |||||||
\(840\) | 0.400946 | + | 7.47257i | 0.0138339 | + | 0.257828i | ||||
\(841\) | 40.2107 | 1.38657 | ||||||||
\(842\) | 23.6417 | − | 4.04440i | 0.814748 | − | 0.139379i | ||||
\(843\) | −12.9179 | −0.444916 | ||||||||
\(844\) | 14.7718 | + | 41.9110i | 0.508466 | + | 1.44264i | ||||
\(845\) | − | 0.222556i | − | 0.00765615i | ||||||
\(846\) | 6.62252 | − | 1.13292i | 0.227687 | − | 0.0389505i | ||||
\(847\) | 30.1422 | + | 14.7350i | 1.03570 | + | 0.506301i | ||||
\(848\) | −31.6092 | + | 25.4423i | −1.08546 | + | 0.873691i | ||||
\(849\) | 17.1674 | 0.589185 | ||||||||
\(850\) | 1.06778 | + | 6.24175i | 0.0366246 | + | 0.214090i | ||||
\(851\) | − | 11.9242i | − | 0.408755i | ||||||
\(852\) | −9.86490 | − | 27.9890i | −0.337966 | − | 0.958889i | ||||
\(853\) | − | 13.0933i | − | 0.448305i | −0.974554 | − | 0.224152i | \(-0.928039\pi\) | ||
0.974554 | − | 0.224152i | \(-0.0719613\pi\) | |||||||
\(854\) | 1.24354 | − | 4.24049i | 0.0425532 | − | 0.145107i | ||||
\(855\) | 2.70953i | 0.0926640i | ||||||||
\(856\) | 4.58456 | + | 8.22907i | 0.156697 | + | 0.281264i | ||||
\(857\) | − | 2.06062i | − | 0.0703895i | −0.999380 | − | 0.0351948i | \(-0.988795\pi\) | ||
0.999380 | − | 0.0351948i | \(-0.0112052\pi\) | |||||||
\(858\) | 24.6666 | − | 4.21974i | 0.842105 | − | 0.144059i | ||||
\(859\) | 11.2503 | 0.383856 | 0.191928 | − | 0.981409i | \(-0.438526\pi\) | ||||
0.191928 | + | 0.981409i | \(0.438526\pi\) | |||||||
\(860\) | 14.8289 | − | 5.22654i | 0.505662 | − | 0.178224i | ||||
\(861\) | 13.4285 | − | 27.4697i | 0.457643 | − | 0.936165i | ||||
\(862\) | −4.53937 | − | 26.5351i | −0.154612 | − | 0.903789i | ||||
\(863\) | − | 7.30131i | − | 0.248540i | −0.992248 | − | 0.124270i | \(-0.960341\pi\) | ||
0.992248 | − | 0.124270i | \(-0.0396588\pi\) | |||||||
\(864\) | −3.74552 | + | 4.23924i | −0.127425 | + | 0.144222i | ||||
\(865\) | 6.99917 | 0.237979 | ||||||||
\(866\) | 6.89072 | + | 40.2800i | 0.234156 | + | 1.36877i | ||||
\(867\) | −3.04981 | −0.103577 | ||||||||
\(868\) | 28.7696 | + | 3.34725i | 0.976503 | + | 0.113613i | ||||
\(869\) | −4.94104 | −0.167613 | ||||||||
\(870\) | −1.98387 | − | 11.5968i | −0.0672595 | − | 0.393168i | ||||
\(871\) | −47.7910 | −1.61934 | ||||||||
\(872\) | 1.22899 | − | 0.684694i | 0.0416190 | − | 0.0231867i | ||||
\(873\) | − | 13.0383i | − | 0.441280i | ||||||
\(874\) | 1.08971 | + | 6.36992i | 0.0368598 | + | 0.215466i | ||||
\(875\) | −1.16196 | + | 2.37694i | −0.0392816 | + | 0.0803552i | ||||
\(876\) | 0.933400 | + | 2.64827i | 0.0315367 | + | 0.0894769i | ||||
\(877\) | 16.5634 | 0.559307 | 0.279654 | − | 0.960101i | \(-0.409780\pi\) | ||||
0.279654 | + | 0.960101i | \(0.409780\pi\) | |||||||
\(878\) | 31.6364 | − | 5.41206i | 1.06768 | − | 0.182648i | ||||
\(879\) | − | 1.99319i | − | 0.0672287i | ||||||
\(880\) | −15.1635 | + | 12.2051i | −0.511162 | + | 0.411435i | ||||
\(881\) | − | 47.9064i | − | 1.61401i | −0.590546 | − | 0.807004i | \(-0.701088\pi\) | ||
0.590546 | − | 0.807004i | \(-0.298912\pi\) | |||||||
\(882\) | −7.31084 | − | 6.67470i | −0.246169 | − | 0.224749i | ||||
\(883\) | − | 27.5910i | − | 0.928511i | −0.885701 | − | 0.464255i | \(-0.846322\pi\) | ||
0.885701 | − | 0.464255i | \(-0.153678\pi\) | |||||||
\(884\) | −30.7126 | + | 10.8248i | −1.03298 | + | 0.364078i | ||||
\(885\) | 2.97451i | 0.0999869i | ||||||||
\(886\) | −6.79461 | − | 39.7181i | −0.228269 | − | 1.33436i | ||||
\(887\) | −37.5247 | −1.25996 | −0.629978 | − | 0.776613i | \(-0.716936\pi\) | ||||
−0.629978 | + | 0.776613i | \(0.716936\pi\) | |||||||
\(888\) | −17.4697 | + | 9.73268i | −0.586245 | + | 0.326607i | ||||
\(889\) | −2.74368 | + | 5.61253i | −0.0920201 | + | 0.188238i | ||||
\(890\) | −13.8159 | + | 2.36349i | −0.463110 | + | 0.0792244i | ||||
\(891\) | 4.86632i | 0.163028i | ||||||||
\(892\) | 53.6700 | − | 18.9163i | 1.79700 | − | 0.633364i | ||||
\(893\) | −12.8726 | −0.430765 | ||||||||
\(894\) | 4.14108 | − | 0.708418i | 0.138499 | − | 0.0236930i | ||||
\(895\) | 8.98718 | 0.300408 | ||||||||
\(896\) | 22.2790 | − | 19.9911i | 0.744289 | − | 0.667857i | ||||
\(897\) | 6.13262 | 0.204762 | ||||||||
\(898\) | −23.9763 | + | 4.10164i | −0.800099 | + | 0.136873i | ||||
\(899\) | −45.5366 | −1.51873 | ||||||||
\(900\) | −1.88627 | + | 0.664826i | −0.0628756 | + | 0.0221609i | ||||
\(901\) | − | 45.4223i | − | 1.51324i | ||||||
\(902\) | 78.3950 | − | 13.4111i | 2.61027 | − | 0.446540i | ||||
\(903\) | −9.13480 | + | 18.6863i | −0.303987 | + | 0.621842i | ||||
\(904\) | 13.5804 | − | 7.56590i | 0.451678 | − | 0.251638i | ||||
\(905\) | 7.23017 | 0.240339 | ||||||||
\(906\) | −3.77234 | − | 22.0514i | −0.125328 | − | 0.732608i | ||||
\(907\) | − | 53.8990i | − | 1.78969i | −0.446381 | − | 0.894843i | \(-0.647288\pi\) | ||
0.446381 | − | 0.894843i | \(-0.352712\pi\) | |||||||
\(908\) | 38.8502 | − | 13.6930i | 1.28929 | − | 0.454417i | ||||
\(909\) | − | 10.5101i | − | 0.348598i | ||||||
\(910\) | −13.0559 | − | 3.82870i | −0.432799 | − | 0.126920i | ||||
\(911\) | 10.7104i | 0.354851i | 0.984134 | + | 0.177425i | \(0.0567768\pi\) | ||||
−0.984134 | + | 0.177425i | \(0.943223\pi\) | |||||||
\(912\) | 8.44293 | − | 6.79572i | 0.279573 | − | 0.225029i | ||||
\(913\) | − | 40.0207i | − | 1.32449i | ||||||
\(914\) | −35.7704 | + | 6.11926i | −1.18318 | + | 0.202407i | ||||
\(915\) | 1.18105 | 0.0390442 | ||||||||
\(916\) | −7.10218 | − | 20.1505i | −0.234663 | − | 0.665793i | ||||
\(917\) | −4.60444 | − | 2.25088i | −0.152052 | − | 0.0743304i | ||||
\(918\) | −1.06778 | − | 6.24175i | −0.0352420 | − | 0.206009i | ||||
\(919\) | − | 19.2285i | − | 0.634289i | −0.948377 | − | 0.317145i | \(-0.897276\pi\) | ||
0.948377 | − | 0.317145i | \(-0.102724\pi\) | |||||||
\(920\) | −4.16711 | + | 2.32157i | −0.137385 | + | 0.0765399i | ||||
\(921\) | −7.80451 | −0.257167 | ||||||||
\(922\) | −8.69446 | − | 50.8238i | −0.286337 | − | 1.67379i | ||||
\(923\) | 53.9563 | 1.77599 | ||||||||
\(924\) | 2.97588 | − | 25.5776i | 0.0978992 | − | 0.841442i | ||||
\(925\) | −7.07032 | −0.232471 | ||||||||
\(926\) | −6.25799 | − | 36.5814i | −0.205650 | − | 1.20214i | ||||
\(927\) | 17.7530 | 0.583087 | ||||||||
\(928\) | −31.1600 | + | 35.2674i | −1.02288 | + | 1.15771i | ||||
\(929\) | − | 29.2671i | − | 0.960221i | −0.877208 | − | 0.480110i | \(-0.840597\pi\) | ||
0.877208 | − | 0.480110i | \(-0.159403\pi\) | |||||||
\(930\) | 1.30527 | + | 7.63001i | 0.0428015 | + | 0.250198i | ||||
\(931\) | 11.6501 | + | 14.9670i | 0.381817 | + | 0.490524i | ||||
\(932\) | 46.4159 | − | 16.3596i | 1.52040 | − | 0.535875i | ||||
\(933\) | −34.9575 | −1.14446 | ||||||||
\(934\) | 11.7132 | − | 2.00379i | 0.383269 | − | 0.0655661i | ||||
\(935\) | − | 21.7899i | − | 0.712607i | ||||||
\(936\) | −5.00554 | − | 8.98471i | −0.163611 | − | 0.293674i | ||||
\(937\) | 23.8800i | 0.780127i | 0.920788 | + | 0.390063i | \(0.127547\pi\) | ||||
−0.920788 | + | 0.390063i | \(0.872453\pi\) | |||||||
\(938\) | −13.8383 | + | 47.1887i | −0.451836 | + | 1.54076i | ||||
\(939\) | 17.5160i | 0.571614i | ||||||||
\(940\) | −3.15849 | − | 8.96139i | −0.103019 | − | 0.292288i | ||||
\(941\) | − | 56.0030i | − | 1.82565i | −0.408355 | − | 0.912823i | \(-0.633897\pi\) | ||
0.408355 | − | 0.912823i | \(-0.366103\pi\) | |||||||
\(942\) | 2.05001 | + | 11.9834i | 0.0667928 | + | 0.390440i | ||||
\(943\) | 19.4906 | 0.634700 | ||||||||
\(944\) | 9.26860 | − | 7.46030i | 0.301667 | − | 0.242812i | ||||
\(945\) | 1.16196 | − | 2.37694i | 0.0377987 | − | 0.0773218i | ||||
\(946\) | −53.3284 | + | 9.12292i | −1.73386 | + | 0.296612i | ||||
\(947\) | 6.51797i | 0.211806i | 0.994376 | + | 0.105903i | \(0.0337733\pi\) | ||||
−0.994376 | + | 0.105903i | \(0.966227\pi\) | |||||||
\(948\) | 0.675033 | + | 1.91523i | 0.0219241 | + | 0.0622037i | ||||
\(949\) | −5.10525 | −0.165724 | ||||||||
\(950\) | 3.77698 | − | 0.646131i | 0.122542 | − | 0.0209633i | ||||
\(951\) | −9.86500 | −0.319895 | ||||||||
\(952\) | 1.79532 | + | 33.4599i | 0.0581865 | + | 1.08444i | ||||
\(953\) | −36.4257 | −1.17994 | −0.589972 | − | 0.807424i | \(-0.700861\pi\) | ||||
−0.589972 | + | 0.807424i | \(0.700861\pi\) | |||||||
\(954\) | 14.1405 | − | 2.41903i | 0.457817 | − | 0.0783189i | ||||
\(955\) | 5.61914 | 0.181831 | ||||||||
\(956\) | 6.12285 | + | 17.3720i | 0.198027 | + | 0.561850i | ||||
\(957\) | 40.4844i | 1.30867i | ||||||||
\(958\) | −24.6244 | + | 4.21251i | −0.795579 | + | 0.136100i | ||||
\(959\) | −36.3293 | − | 17.7595i | −1.17313 | − | 0.573485i | ||||
\(960\) | 6.80252 | + | 4.21020i | 0.219550 | + | 0.135884i | ||||
\(961\) | −1.03957 | −0.0335345 | ||||||||
\(962\) | −6.13089 | − | 35.8384i | −0.197668 | − | 1.15548i | ||||
\(963\) | − | 3.33046i | − | 0.107323i | ||||||
\(964\) | 7.65609 | + | 21.7221i | 0.246586 | + | 0.699623i | ||||
\(965\) | 5.51737i | 0.177611i | ||||||||
\(966\) | 1.77575 | − | 6.05533i | 0.0571339 | − | 0.194827i | ||||
\(967\) | 33.7820i | 1.08636i | 0.839618 | + | 0.543178i | \(0.182779\pi\) | ||||
−0.839618 | + | 0.543178i | \(0.817221\pi\) | |||||||
\(968\) | 31.3331 | − | 17.4562i | 1.00708 | − | 0.561065i | ||||
\(969\) | 12.1325i | 0.389751i | ||||||||
\(970\) | −18.1749 | + | 3.10920i | −0.583562 | + | 0.0998302i | ||||
\(971\) | 29.8443 | 0.957749 | 0.478875 | − | 0.877883i | \(-0.341045\pi\) | ||||
0.478875 | + | 0.877883i | \(0.341045\pi\) | |||||||
\(972\) | 1.88627 | − | 0.664826i | 0.0605021 | − | 0.0213243i | ||||
\(973\) | −4.37443 | − | 2.13844i | −0.140238 | − | 0.0685551i | ||||
\(974\) | 0.356626 | + | 2.08467i | 0.0114270 | + | 0.0667971i | ||||
\(975\) | − | 3.63628i | − | 0.116454i | ||||||
\(976\) | −2.96216 | − | 3.68015i | −0.0948164 | − | 0.117799i | ||||
\(977\) | −14.9298 | −0.477646 | −0.238823 | − | 0.971063i | \(-0.576762\pi\) | ||||
−0.238823 | + | 0.971063i | \(0.576762\pi\) | |||||||
\(978\) | −0.323757 | − | 1.89254i | −0.0103526 | − | 0.0605166i | ||||
\(979\) | 48.2313 | 1.54148 | ||||||||
\(980\) | −7.56090 | + | 11.7827i | −0.241524 | + | 0.376386i | ||||
\(981\) | −0.497397 | −0.0158807 | ||||||||
\(982\) | 0.824859 | + | 4.82174i | 0.0263223 | + | 0.153868i | ||||
\(983\) | −4.50914 | −0.143819 | −0.0719096 | − | 0.997411i | \(-0.522909\pi\) | ||||
−0.0719096 | + | 0.997411i | \(0.522909\pi\) | |||||||
\(984\) | −15.9085 | − | 28.5550i | −0.507144 | − | 0.910300i | ||||
\(985\) | 6.86110i | 0.218613i | ||||||||
\(986\) | −8.88318 | − | 51.9270i | −0.282898 | − | 1.65369i | ||||
\(987\) | 11.2925 | + | 5.52033i | 0.359444 | + | 0.175714i | ||||
\(988\) | 6.55028 | + | 18.5847i | 0.208392 | + | 0.591257i | ||||
\(989\) | −13.2585 | −0.421596 | ||||||||
\(990\) | 6.78348 | − | 1.16045i | 0.215593 | − | 0.0368816i | ||||
\(991\) | 44.9341i | 1.42738i | 0.700463 | + | 0.713689i | \(0.252977\pi\) | ||||
−0.700463 | + | 0.713689i | \(0.747023\pi\) | |||||||
\(992\) | 20.5015 | − | 23.2039i | 0.650923 | − | 0.736726i | ||||
\(993\) | − | 19.7243i | − | 0.625931i | ||||||
\(994\) | 15.6235 | − | 53.2763i | 0.495548 | − | 1.68982i | ||||
\(995\) | 1.33434i | 0.0423014i | ||||||||
\(996\) | −15.5127 | + | 5.46753i | −0.491538 | + | 0.173245i | ||||
\(997\) | 24.1118i | 0.763628i | 0.924239 | + | 0.381814i | \(0.124700\pi\) | ||||
−0.924239 | + | 0.381814i | \(0.875300\pi\) | |||||||
\(998\) | 3.88938 | + | 22.7355i | 0.123116 | + | 0.719680i | ||||
\(999\) | 7.07032 | 0.223695 |
(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 | 420.2.c.b.391.2 | yes | 16 | |
3.2 | odd | 2 | 1260.2.c.e.811.15 | 16 | |||
4.3 | odd | 2 | 420.2.c.a.391.1 | ✓ | 16 | ||
7.6 | odd | 2 | 420.2.c.a.391.2 | yes | 16 | ||
12.11 | even | 2 | 1260.2.c.d.811.16 | 16 | |||
21.20 | even | 2 | 1260.2.c.d.811.15 | 16 | |||
28.27 | even | 2 | inner | 420.2.c.b.391.1 | yes | 16 | |
84.83 | odd | 2 | 1260.2.c.e.811.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.c.a.391.1 | ✓ | 16 | 4.3 | odd | 2 | ||
420.2.c.a.391.2 | yes | 16 | 7.6 | odd | 2 | ||
420.2.c.b.391.1 | yes | 16 | 28.27 | even | 2 | inner | |
420.2.c.b.391.2 | yes | 16 | 1.1 | even | 1 | trivial | |
1260.2.c.d.811.15 | 16 | 21.20 | even | 2 | |||
1260.2.c.d.811.16 | 16 | 12.11 | even | 2 | |||
1260.2.c.e.811.15 | 16 | 3.2 | odd | 2 | |||
1260.2.c.e.811.16 | 16 | 84.83 | odd | 2 |