Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [322,2,Mod(45,322)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(322, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("322.45");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 322 = 2 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 322.g (of order \(6\), degree \(2\), 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: | \(2.57118294509\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 18x^{14} + 226x^{12} + 1434x^{10} + 6585x^{8} + 14406x^{6} + 22423x^{4} + 8085x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 45.6 | ||
Root | \(0.306090 + 0.530164i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 322.45 |
Dual form | 322.2.g.a.229.6 |
$q$-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 \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).
\(n\) | \(185\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 1.05590 | + | 0.609623i | 0.609623 | + | 0.351966i | 0.772818 | − | 0.634628i | \(-0.218847\pi\) |
−0.163195 | + | 0.986594i | \(0.552180\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.23610 | + | 2.14099i | 0.552802 | + | 0.957481i | 0.998071 | + | 0.0620841i | \(0.0197747\pi\) |
−0.445269 | + | 0.895397i | \(0.646892\pi\) | |||||||
\(6\) | − | 1.21925i | − | 0.497755i | ||||||
\(7\) | −1.54219 | + | 2.14980i | −0.582894 | + | 0.812548i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.756718 | − | 1.31067i | −0.252239 | − | 0.436892i | ||||
\(10\) | 1.23610 | − | 2.14099i | 0.390890 | − | 0.677041i | ||||
\(11\) | 1.09791 | + | 0.633878i | 0.331032 | + | 0.191121i | 0.656299 | − | 0.754501i | \(-0.272121\pi\) |
−0.325267 | + | 0.945622i | \(0.605454\pi\) | |||||||
\(12\) | −1.05590 | + | 0.609623i | −0.304812 | + | 0.175983i | ||||
\(13\) | 3.39445i | 0.941451i | 0.882280 | + | 0.470725i | \(0.156008\pi\) | ||||
−0.882280 | + | 0.470725i | \(0.843992\pi\) | |||||||
\(14\) | 2.63288 | + | 0.260678i | 0.703666 | + | 0.0696692i | ||||
\(15\) | 3.01423i | 0.778270i | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.14715 | + | 3.71897i | −0.520760 | + | 0.901983i | 0.478948 | + | 0.877843i | \(0.341018\pi\) |
−0.999709 | + | 0.0241402i | \(0.992315\pi\) | |||||||
\(18\) | −0.756718 | + | 1.31067i | −0.178360 | + | 0.308929i | ||||
\(19\) | 1.23610 | + | 2.14099i | 0.283581 | + | 0.491177i | 0.972264 | − | 0.233885i | \(-0.0751441\pi\) |
−0.688683 | + | 0.725063i | \(0.741811\pi\) | |||||||
\(20\) | −2.47221 | −0.552802 | ||||||||
\(21\) | −2.93897 | + | 1.32981i | −0.641336 | + | 0.290189i | ||||
\(22\) | − | 1.26776i | − | 0.270287i | ||||||
\(23\) | −1.21471 | − | 4.63945i | −0.253284 | − | 0.967392i | ||||
\(24\) | 1.05590 | + | 0.609623i | 0.215534 | + | 0.124439i | ||||
\(25\) | −0.555899 | + | 0.962845i | −0.111180 | + | 0.192569i | ||||
\(26\) | 2.93968 | − | 1.69722i | 0.576518 | − | 0.332853i | ||||
\(27\) | − | 5.50299i | − | 1.05905i | ||||||
\(28\) | −1.09069 | − | 2.41048i | −0.206120 | − | 0.455538i | ||||
\(29\) | 8.99116 | 1.66962 | 0.834808 | − | 0.550541i | \(-0.185579\pi\) | ||||
0.834808 | + | 0.550541i | \(0.185579\pi\) | |||||||
\(30\) | 2.61040 | − | 1.50711i | 0.476591 | − | 0.275160i | ||||
\(31\) | 3.32605 | + | 1.92030i | 0.597377 | + | 0.344896i | 0.768009 | − | 0.640439i | \(-0.221248\pi\) |
−0.170632 | + | 0.985335i | \(0.554581\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0.772854 | + | 1.33862i | 0.134537 | + | 0.233024i | ||||
\(34\) | 4.29430 | 0.736466 | ||||||||
\(35\) | −6.50901 | − | 0.644450i | −1.10022 | − | 0.108932i | ||||
\(36\) | 1.51344 | 0.252239 | ||||||||
\(37\) | 1.24062 | − | 0.716272i | 0.203957 | − | 0.117754i | −0.394543 | − | 0.918877i | \(-0.629097\pi\) |
0.598500 | + | 0.801123i | \(0.295764\pi\) | |||||||
\(38\) | 1.23610 | − | 2.14099i | 0.200522 | − | 0.347315i | ||||
\(39\) | −2.06934 | + | 3.58419i | −0.331359 | + | 0.573930i | ||||
\(40\) | 1.23610 | + | 2.14099i | 0.195445 | + | 0.338521i | ||||
\(41\) | 3.39445i | 0.530124i | 0.964231 | + | 0.265062i | \(0.0853924\pi\) | ||||
−0.964231 | + | 0.265062i | \(0.914608\pi\) | |||||||
\(42\) | 2.62114 | + | 1.88031i | 0.404450 | + | 0.290139i | ||||
\(43\) | − | 12.9877i | − | 1.98060i | −0.138933 | − | 0.990302i | \(-0.544367\pi\) | ||
0.138933 | − | 0.990302i | \(-0.455633\pi\) | |||||||
\(44\) | −1.09791 | + | 0.633878i | −0.165516 | + | 0.0955607i | ||||
\(45\) | 1.87076 | − | 3.24026i | 0.278877 | − | 0.483029i | ||||
\(46\) | −3.41053 | + | 3.37169i | −0.502855 | + | 0.497129i | ||||
\(47\) | −1.43968 | + | 0.831199i | −0.209999 | + | 0.121243i | −0.601311 | − | 0.799015i | \(-0.705355\pi\) |
0.391312 | + | 0.920258i | \(0.372021\pi\) | |||||||
\(48\) | − | 1.21925i | − | 0.175983i | ||||||
\(49\) | −2.24328 | − | 6.63081i | −0.320469 | − | 0.947259i | ||||
\(50\) | 1.11180 | 0.157232 | ||||||||
\(51\) | −4.53435 | + | 2.61791i | −0.634935 | + | 0.366580i | ||||
\(52\) | −2.93968 | − | 1.69722i | −0.407660 | − | 0.235363i | ||||
\(53\) | 7.14474 | + | 4.12502i | 0.981406 | + | 0.566615i | 0.902694 | − | 0.430282i | \(-0.141586\pi\) |
0.0787118 | + | 0.996897i | \(0.474919\pi\) | |||||||
\(54\) | −4.76573 | + | 2.75150i | −0.648534 | + | 0.374431i | ||||
\(55\) | 3.13415i | 0.422609i | ||||||||
\(56\) | −1.54219 | + | 2.14980i | −0.206084 | + | 0.287279i | ||||
\(57\) | 3.01423i | 0.399244i | ||||||||
\(58\) | −4.49558 | − | 7.78657i | −0.590298 | − | 1.02243i | ||||
\(59\) | 8.43785 | + | 4.87160i | 1.09851 | + | 0.634228i | 0.935830 | − | 0.352450i | \(-0.114651\pi\) |
0.162684 | + | 0.986678i | \(0.447985\pi\) | |||||||
\(60\) | −2.61040 | − | 1.50711i | −0.337001 | − | 0.194568i | ||||
\(61\) | −4.61935 | − | 8.00096i | −0.591448 | − | 1.02442i | −0.994038 | − | 0.109037i | \(-0.965223\pi\) |
0.402590 | − | 0.915380i | \(-0.368110\pi\) | |||||||
\(62\) | − | 3.84060i | − | 0.487756i | ||||||
\(63\) | 3.98469 | + | 0.394520i | 0.502024 | + | 0.0497048i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.26749 | + | 4.19589i | −0.901421 | + | 0.520436i | ||||
\(66\) | 0.772854 | − | 1.33862i | 0.0951317 | − | 0.164773i | ||||
\(67\) | −9.87789 | − | 5.70300i | −1.20678 | − | 0.696732i | −0.244722 | − | 0.969593i | \(-0.578697\pi\) |
−0.962054 | + | 0.272861i | \(0.912030\pi\) | |||||||
\(68\) | −2.14715 | − | 3.71897i | −0.260380 | − | 0.450992i | ||||
\(69\) | 1.54571 | − | 5.63930i | 0.186081 | − | 0.678892i | ||||
\(70\) | 2.69640 | + | 5.95920i | 0.322281 | + | 0.712260i | ||||
\(71\) | −10.1030 | −1.19900 | −0.599500 | − | 0.800375i | \(-0.704634\pi\) | ||||
−0.599500 | + | 0.800375i | \(0.704634\pi\) | |||||||
\(72\) | −0.756718 | − | 1.31067i | −0.0891801 | − | 0.154464i | ||||
\(73\) | 3.32605 | + | 1.92030i | 0.389285 | + | 0.224754i | 0.681850 | − | 0.731492i | \(-0.261176\pi\) |
−0.292565 | + | 0.956246i | \(0.594509\pi\) | |||||||
\(74\) | −1.24062 | − | 0.716272i | −0.144219 | − | 0.0832649i | ||||
\(75\) | −1.17395 | + | 0.677778i | −0.135556 | + | 0.0782631i | ||||
\(76\) | −2.47221 | −0.283581 | ||||||||
\(77\) | −3.05590 | + | 1.38272i | −0.348252 | + | 0.157576i | ||||
\(78\) | 4.13867 | 0.468612 | ||||||||
\(79\) | 6.44145 | − | 3.71897i | 0.724720 | − | 0.418417i | −0.0917676 | − | 0.995780i | \(-0.529252\pi\) |
0.816487 | + | 0.577363i | \(0.195918\pi\) | |||||||
\(80\) | 1.23610 | − | 2.14099i | 0.138200 | − | 0.239370i | ||||
\(81\) | 1.08460 | − | 1.87858i | 0.120511 | − | 0.208731i | ||||
\(82\) | 2.93968 | − | 1.69722i | 0.324633 | − | 0.187427i | ||||
\(83\) | −5.21176 | −0.572065 | −0.286033 | − | 0.958220i | \(-0.592337\pi\) | ||||
−0.286033 | + | 0.958220i | \(0.592337\pi\) | |||||||
\(84\) | 0.317831 | − | 3.21013i | 0.0346782 | − | 0.350254i | ||||
\(85\) | −10.6164 | −1.15151 | ||||||||
\(86\) | −11.2477 | + | 6.49384i | −1.21287 | + | 0.700249i | ||||
\(87\) | 9.49375 | + | 5.48122i | 1.01784 | + | 0.587648i | ||||
\(88\) | 1.09791 | + | 0.633878i | 0.117037 | + | 0.0675716i | ||||
\(89\) | −3.43192 | − | 5.94426i | −0.363783 | − | 0.630090i | 0.624797 | − | 0.780787i | \(-0.285182\pi\) |
−0.988580 | + | 0.150697i | \(0.951848\pi\) | |||||||
\(90\) | −3.74153 | −0.394391 | ||||||||
\(91\) | −7.29739 | − | 5.23489i | −0.764974 | − | 0.548766i | ||||
\(92\) | 4.62523 | + | 1.26776i | 0.482214 | + | 0.132173i | ||||
\(93\) | 2.34132 | + | 4.05528i | 0.242783 | + | 0.420513i | ||||
\(94\) | 1.43968 | + | 0.831199i | 0.148492 | + | 0.0857316i | ||||
\(95\) | −3.05590 | + | 5.29297i | −0.313529 | + | 0.543047i | ||||
\(96\) | −1.05590 | + | 0.609623i | −0.107767 | + | 0.0622194i | ||||
\(97\) | −6.49915 | −0.659889 | −0.329944 | − | 0.944000i | \(-0.607030\pi\) | ||||
−0.329944 | + | 0.944000i | \(0.607030\pi\) | |||||||
\(98\) | −4.62081 | + | 5.25815i | −0.466773 | + | 0.531153i | ||||
\(99\) | − | 1.91867i | − | 0.192833i | ||||||
\(100\) | −0.555899 | − | 0.962845i | −0.0555899 | − | 0.0962845i | ||||
\(101\) | 6.16770 | + | 3.56092i | 0.613709 | + | 0.354325i | 0.774416 | − | 0.632677i | \(-0.218044\pi\) |
−0.160707 | + | 0.987002i | \(0.551377\pi\) | |||||||
\(102\) | 4.53435 | + | 2.61791i | 0.448967 | + | 0.259211i | ||||
\(103\) | −6.95337 | − | 12.0436i | −0.685136 | − | 1.18669i | −0.973394 | − | 0.229137i | \(-0.926410\pi\) |
0.288259 | − | 0.957553i | \(-0.406924\pi\) | |||||||
\(104\) | 3.39445i | 0.332853i | ||||||||
\(105\) | −6.47999 | − | 4.64852i | −0.632382 | − | 0.453649i | ||||
\(106\) | − | 8.25004i | − | 0.801315i | ||||||
\(107\) | −5.07809 | + | 2.93183i | −0.490917 | + | 0.283431i | −0.724955 | − | 0.688796i | \(-0.758139\pi\) |
0.234038 | + | 0.972228i | \(0.424806\pi\) | |||||||
\(108\) | 4.76573 | + | 2.75150i | 0.458583 | + | 0.264763i | ||||
\(109\) | 12.3456 | + | 7.12772i | 1.18249 | + | 0.682712i | 0.956590 | − | 0.291438i | \(-0.0941338\pi\) |
0.225902 | + | 0.974150i | \(0.427467\pi\) | |||||||
\(110\) | 2.71426 | − | 1.56708i | 0.258794 | − | 0.149415i | ||||
\(111\) | 1.74662 | 0.165782 | ||||||||
\(112\) | 2.63288 | + | 0.260678i | 0.248784 | + | 0.0246318i | ||||
\(113\) | 15.6954i | 1.47650i | 0.674528 | + | 0.738249i | \(0.264347\pi\) | ||||
−0.674528 | + | 0.738249i | \(0.735653\pi\) | |||||||
\(114\) | 2.61040 | − | 1.50711i | 0.244486 | − | 0.141154i | ||||
\(115\) | 8.43152 | − | 8.33552i | 0.786243 | − | 0.777291i | ||||
\(116\) | −4.49558 | + | 7.78657i | −0.417404 | + | 0.722965i | ||||
\(117\) | 4.44902 | − | 2.56864i | 0.411312 | − | 0.237471i | ||||
\(118\) | − | 9.74319i | − | 0.896934i | ||||||
\(119\) | −4.68373 | − | 10.3513i | −0.429357 | − | 0.948904i | ||||
\(120\) | 3.01423i | 0.275160i | ||||||||
\(121\) | −4.69640 | − | 8.13440i | −0.426945 | − | 0.739491i | ||||
\(122\) | −4.61935 | + | 8.00096i | −0.418217 | + | 0.724373i | ||||
\(123\) | −2.06934 | + | 3.58419i | −0.186586 | + | 0.323176i | ||||
\(124\) | −3.32605 | + | 1.92030i | −0.298688 | + | 0.172448i | ||||
\(125\) | 9.61243 | 0.859762 | ||||||||
\(126\) | −1.65068 | − | 3.64811i | −0.147055 | − | 0.324999i | ||||
\(127\) | 1.99116 | 0.176686 | 0.0883432 | − | 0.996090i | \(-0.471843\pi\) | ||||
0.0883432 | + | 0.996090i | \(0.471843\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 7.91760 | − | 13.7137i | 0.697106 | − | 1.20742i | ||||
\(130\) | 7.26749 | + | 4.19589i | 0.637401 | + | 0.368004i | ||||
\(131\) | 9.81980 | − | 5.66947i | 0.857960 | − | 0.495344i | −0.00536840 | − | 0.999986i | \(-0.501709\pi\) |
0.863329 | + | 0.504642i | \(0.168375\pi\) | |||||||
\(132\) | −1.54571 | −0.134537 | ||||||||
\(133\) | −6.50901 | − | 0.644450i | −0.564403 | − | 0.0558809i | ||||
\(134\) | 11.4060i | 0.985328i | ||||||||
\(135\) | 11.7819 | − | 6.80226i | 1.01402 | − | 0.585446i | ||||
\(136\) | −2.14715 | + | 3.71897i | −0.184117 | + | 0.318899i | ||||
\(137\) | 1.36978 | + | 0.790842i | 0.117028 | + | 0.0675662i | 0.557371 | − | 0.830263i | \(-0.311810\pi\) |
−0.440343 | + | 0.897829i | \(0.645143\pi\) | |||||||
\(138\) | −5.65663 | + | 1.48103i | −0.481525 | + | 0.126074i | ||||
\(139\) | − | 14.1603i | − | 1.20106i | −0.799603 | − | 0.600528i | \(-0.794957\pi\) | ||
0.799603 | − | 0.600528i | \(-0.205043\pi\) | |||||||
\(140\) | 3.81262 | − | 5.31475i | 0.322225 | − | 0.449178i | ||||
\(141\) | −2.02687 | −0.170694 | ||||||||
\(142\) | 5.05148 | + | 8.74941i | 0.423910 | + | 0.734235i | ||||
\(143\) | −2.15167 | + | 3.72680i | −0.179931 | + | 0.311650i | ||||
\(144\) | −0.756718 | + | 1.31067i | −0.0630599 | + | 0.109223i | ||||
\(145\) | 11.1140 | + | 19.2500i | 0.922967 | + | 1.59863i | ||||
\(146\) | − | 3.84060i | − | 0.317850i | ||||||
\(147\) | 1.67362 | − | 8.36903i | 0.138038 | − | 0.690266i | ||||
\(148\) | 1.43254i | 0.117754i | ||||||||
\(149\) | 2.19582 | − | 1.26776i | 0.179888 | − | 0.103859i | −0.407352 | − | 0.913271i | \(-0.633548\pi\) |
0.587240 | + | 0.809413i | \(0.300214\pi\) | |||||||
\(150\) | 1.17395 | + | 0.677778i | 0.0958523 | + | 0.0553403i | ||||
\(151\) | −4.01344 | + | 6.95148i | −0.326609 | + | 0.565703i | −0.981837 | − | 0.189728i | \(-0.939239\pi\) |
0.655228 | + | 0.755431i | \(0.272573\pi\) | |||||||
\(152\) | 1.23610 | + | 2.14099i | 0.100261 | + | 0.173657i | ||||
\(153\) | 6.49915 | 0.525425 | ||||||||
\(154\) | 2.72542 | + | 1.95512i | 0.219621 | + | 0.157548i | ||||
\(155\) | 9.49474i | 0.762636i | ||||||||
\(156\) | −2.06934 | − | 3.58419i | −0.165679 | − | 0.286965i | ||||
\(157\) | −9.60150 | + | 16.6303i | −0.766283 | + | 1.32724i | 0.173282 | + | 0.984872i | \(0.444563\pi\) |
−0.939566 | + | 0.342369i | \(0.888771\pi\) | |||||||
\(158\) | −6.44145 | − | 3.71897i | −0.512454 | − | 0.295866i | ||||
\(159\) | 5.02942 | + | 8.71121i | 0.398859 | + | 0.690844i | ||||
\(160\) | −2.47221 | −0.195445 | ||||||||
\(161\) | 11.8472 | + | 4.54355i | 0.933690 | + | 0.358082i | ||||
\(162\) | −2.16920 | −0.170428 | ||||||||
\(163\) | 1.24328 | + | 2.15343i | 0.0973813 | + | 0.168669i | 0.910600 | − | 0.413289i | \(-0.135620\pi\) |
−0.813219 | + | 0.581958i | \(0.802287\pi\) | |||||||
\(164\) | −2.93968 | − | 1.69722i | −0.229550 | − | 0.132531i | ||||
\(165\) | −1.91065 | + | 3.30935i | −0.148744 | + | 0.257632i | ||||
\(166\) | 2.60588 | + | 4.51352i | 0.202256 | + | 0.350317i | ||||
\(167\) | 8.20178i | 0.634673i | 0.948313 | + | 0.317337i | \(0.102788\pi\) | ||||
−0.948313 | + | 0.317337i | \(0.897212\pi\) | |||||||
\(168\) | −2.93897 | + | 1.32981i | −0.226746 | + | 0.102597i | ||||
\(169\) | 1.47772 | 0.113671 | ||||||||
\(170\) | 5.30819 | + | 9.19406i | 0.407120 | + | 0.705152i | ||||
\(171\) | 1.87076 | − | 3.24026i | 0.143061 | − | 0.247789i | ||||
\(172\) | 11.2477 | + | 6.49384i | 0.857627 | + | 0.495151i | ||||
\(173\) | 15.2173 | − | 8.78574i | 1.15695 | − | 0.667967i | 0.206381 | − | 0.978472i | \(-0.433831\pi\) |
0.950572 | + | 0.310504i | \(0.100498\pi\) | |||||||
\(174\) | − | 10.9624i | − | 0.831060i | ||||||
\(175\) | −1.21262 | − | 2.67996i | −0.0916655 | − | 0.202586i | ||||
\(176\) | − | 1.26776i | − | 0.0955607i | ||||||
\(177\) | 5.93968 | + | 10.2878i | 0.446454 | + | 0.773280i | ||||
\(178\) | −3.43192 | + | 5.94426i | −0.257233 | + | 0.445541i | ||||
\(179\) | −3.25672 | + | 5.64080i | −0.243419 | + | 0.421613i | −0.961686 | − | 0.274154i | \(-0.911602\pi\) |
0.718267 | + | 0.695767i | \(0.244936\pi\) | |||||||
\(180\) | 1.87076 | + | 3.24026i | 0.139438 | + | 0.241514i | ||||
\(181\) | 10.2407 | 0.761184 | 0.380592 | − | 0.924743i | \(-0.375720\pi\) | ||||
0.380592 | + | 0.924743i | \(0.375720\pi\) | |||||||
\(182\) | −0.884859 | + | 8.93717i | −0.0655901 | + | 0.662467i | ||||
\(183\) | − | 11.2643i | − | 0.832679i | ||||||
\(184\) | −1.21471 | − | 4.63945i | −0.0895495 | − | 0.342025i | ||||
\(185\) | 3.06707 | + | 1.77077i | 0.225495 | + | 0.130190i | ||||
\(186\) | 2.34132 | − | 4.05528i | 0.171674 | − | 0.297348i | ||||
\(187\) | −4.71475 | + | 2.72206i | −0.344777 | + | 0.199057i | ||||
\(188\) | − | 1.66240i | − | 0.121243i | ||||||
\(189\) | 11.8303 | + | 8.48668i | 0.860530 | + | 0.617315i | ||||
\(190\) | 6.11180 | 0.443396 | ||||||||
\(191\) | 8.51452 | − | 4.91586i | 0.616089 | − | 0.355699i | −0.159256 | − | 0.987237i | \(-0.550909\pi\) |
0.775345 | + | 0.631538i | \(0.217576\pi\) | |||||||
\(192\) | 1.05590 | + | 0.609623i | 0.0762029 | + | 0.0439958i | ||||
\(193\) | 3.94227 | − | 6.82822i | 0.283771 | − | 0.491506i | −0.688539 | − | 0.725199i | \(-0.741748\pi\) |
0.972310 | + | 0.233693i | \(0.0750811\pi\) | |||||||
\(194\) | 3.24958 | + | 5.62843i | 0.233306 | + | 0.404098i | ||||
\(195\) | −10.2316 | −0.732703 | ||||||||
\(196\) | 6.86409 | + | 1.37267i | 0.490292 | + | 0.0980477i | ||||
\(197\) | −5.96063 | −0.424677 | −0.212339 | − | 0.977196i | \(-0.568108\pi\) | ||||
−0.212339 | + | 0.977196i | \(0.568108\pi\) | |||||||
\(198\) | −1.66162 | + | 0.959334i | −0.118086 | + | 0.0681769i | ||||
\(199\) | 11.6259 | − | 20.1367i | 0.824139 | − | 1.42745i | −0.0784372 | − | 0.996919i | \(-0.524993\pi\) |
0.902576 | − | 0.430531i | \(-0.141674\pi\) | |||||||
\(200\) | −0.555899 | + | 0.962845i | −0.0393080 | + | 0.0680834i | ||||
\(201\) | −6.95337 | − | 12.0436i | −0.490453 | − | 0.849489i | ||||
\(202\) | − | 7.12184i | − | 0.501091i | ||||||
\(203\) | −13.8661 | + | 19.3292i | −0.973209 | + | 1.35664i | ||||
\(204\) | − | 5.23581i | − | 0.366580i | ||||||
\(205\) | −7.26749 | + | 4.19589i | −0.507583 | + | 0.293053i | ||||
\(206\) | −6.95337 | + | 12.0436i | −0.484464 | + | 0.839116i | ||||
\(207\) | −5.16162 | + | 5.10284i | −0.358757 | + | 0.354672i | ||||
\(208\) | 2.93968 | − | 1.69722i | 0.203830 | − | 0.117681i | ||||
\(209\) | 3.13415i | 0.216794i | ||||||||
\(210\) | −0.785744 | + | 7.93610i | −0.0542215 | + | 0.547643i | ||||
\(211\) | −7.62889 | −0.525194 | −0.262597 | − | 0.964906i | \(-0.584579\pi\) | ||||
−0.262597 | + | 0.964906i | \(0.584579\pi\) | |||||||
\(212\) | −7.14474 | + | 4.12502i | −0.490703 | + | 0.283308i | ||||
\(213\) | −10.6677 | − | 6.15900i | −0.730939 | − | 0.422008i | ||||
\(214\) | 5.07809 | + | 2.93183i | 0.347131 | + | 0.200416i | ||||
\(215\) | 27.8065 | − | 16.0541i | 1.89639 | − | 1.09488i | ||||
\(216\) | − | 5.50299i | − | 0.374431i | ||||||
\(217\) | −9.25767 | + | 4.18888i | −0.628452 | + | 0.284360i | ||||
\(218\) | − | 14.2554i | − | 0.965500i | ||||||
\(219\) | 2.34132 | + | 4.05528i | 0.158212 | + | 0.274031i | ||||
\(220\) | −2.71426 | − | 1.56708i | −0.182995 | − | 0.105652i | ||||
\(221\) | −12.6239 | − | 7.28839i | −0.849173 | − | 0.490270i | ||||
\(222\) | −0.873312 | − | 1.51262i | −0.0586129 | − | 0.101520i | ||||
\(223\) | − | 8.38464i | − | 0.561477i | −0.959784 | − | 0.280738i | \(-0.909421\pi\) | ||
0.959784 | − | 0.280738i | \(-0.0905794\pi\) | |||||||
\(224\) | −1.09069 | − | 2.41048i | −0.0728745 | − | 0.161057i | ||||
\(225\) | 1.68264 | 0.112176 | ||||||||
\(226\) | 13.5926 | − | 7.84770i | 0.904167 | − | 0.522021i | ||||
\(227\) | 6.49463 | − | 11.2490i | 0.431064 | − | 0.746625i | −0.565901 | − | 0.824473i | \(-0.691472\pi\) |
0.996965 | + | 0.0778483i | \(0.0248050\pi\) | |||||||
\(228\) | −2.61040 | − | 1.50711i | −0.172878 | − | 0.0998111i | ||||
\(229\) | −1.55022 | − | 2.68507i | −0.102442 | − | 0.177434i | 0.810248 | − | 0.586087i | \(-0.199332\pi\) |
−0.912690 | + | 0.408652i | \(0.865999\pi\) | |||||||
\(230\) | −11.4345 | − | 3.13415i | −0.753970 | − | 0.206660i | ||||
\(231\) | −4.06966 | − | 0.402932i | −0.267764 | − | 0.0265110i | ||||
\(232\) | 8.99116 | 0.590298 | ||||||||
\(233\) | 12.4182 | + | 21.5089i | 0.813541 | + | 1.40909i | 0.910371 | + | 0.413794i | \(0.135796\pi\) |
−0.0968297 | + | 0.995301i | \(0.530870\pi\) | |||||||
\(234\) | −4.44902 | − | 2.56864i | −0.290841 | − | 0.167917i | ||||
\(235\) | −3.55918 | − | 2.05489i | −0.232175 | − | 0.134047i | ||||
\(236\) | −8.43785 | + | 4.87160i | −0.549257 | + | 0.317114i | ||||
\(237\) | 9.06869 | 0.589075 | ||||||||
\(238\) | −6.62264 | + | 9.23189i | −0.429282 | + | 0.598414i | ||||
\(239\) | −24.6701 | −1.59578 | −0.797889 | − | 0.602804i | \(-0.794050\pi\) | ||||
−0.797889 | + | 0.602804i | \(0.794050\pi\) | |||||||
\(240\) | 2.61040 | − | 1.50711i | 0.168500 | − | 0.0972838i | ||||
\(241\) | −10.0757 | + | 17.4516i | −0.649032 | + | 1.12416i | 0.334323 | + | 0.942459i | \(0.391492\pi\) |
−0.983355 | + | 0.181697i | \(0.941841\pi\) | |||||||
\(242\) | −4.69640 | + | 8.13440i | −0.301896 | + | 0.522899i | ||||
\(243\) | −12.0067 | + | 6.93210i | −0.770233 | + | 0.444694i | ||||
\(244\) | 9.23871 | 0.591448 | ||||||||
\(245\) | 11.4236 | − | 12.9992i | 0.729827 | − | 0.830489i | ||||
\(246\) | 4.13867 | 0.263872 | ||||||||
\(247\) | −7.26749 | + | 4.19589i | −0.462419 | + | 0.266978i | ||||
\(248\) | 3.32605 | + | 1.92030i | 0.211205 | + | 0.121939i | ||||
\(249\) | −5.50310 | − | 3.17721i | −0.348744 | − | 0.201348i | ||||
\(250\) | −4.80622 | − | 8.32461i | −0.303972 | − | 0.526495i | ||||
\(251\) | −29.3772 | −1.85427 | −0.927137 | − | 0.374721i | \(-0.877738\pi\) | ||||
−0.927137 | + | 0.374721i | \(0.877738\pi\) | |||||||
\(252\) | −2.33401 | + | 3.25359i | −0.147029 | + | 0.204957i | ||||
\(253\) | 1.60721 | − | 5.86367i | 0.101044 | − | 0.368646i | ||||
\(254\) | −0.995578 | − | 1.72439i | −0.0624681 | − | 0.108198i | ||||
\(255\) | −11.2098 | − | 6.47200i | −0.701987 | − | 0.405292i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 3.93918 | − | 2.27429i | 0.245720 | − | 0.141866i | −0.372083 | − | 0.928199i | \(-0.621356\pi\) |
0.617803 | + | 0.786333i | \(0.288023\pi\) | |||||||
\(258\) | −15.8352 | −0.985856 | ||||||||
\(259\) | −0.373433 | + | 3.77171i | −0.0232040 | + | 0.234363i | ||||
\(260\) | − | 8.39177i | − | 0.520436i | ||||||
\(261\) | −6.80377 | − | 11.7845i | −0.421143 | − | 0.729441i | ||||
\(262\) | −9.81980 | − | 5.66947i | −0.606670 | − | 0.350261i | ||||
\(263\) | −4.94893 | − | 2.85726i | −0.305164 | − | 0.176186i | 0.339596 | − | 0.940571i | \(-0.389710\pi\) |
−0.644760 | + | 0.764385i | \(0.723043\pi\) | |||||||
\(264\) | 0.772854 | + | 1.33862i | 0.0475659 | + | 0.0823865i | ||||
\(265\) | 20.3958i | 1.25290i | ||||||||
\(266\) | 2.69640 | + | 5.95920i | 0.165327 | + | 0.365382i | ||||
\(267\) | − | 8.36872i | − | 0.512157i | ||||||
\(268\) | 9.87789 | − | 5.70300i | 0.603388 | − | 0.348366i | ||||
\(269\) | −7.17395 | − | 4.14188i | −0.437403 | − | 0.252535i | 0.265092 | − | 0.964223i | \(-0.414598\pi\) |
−0.702496 | + | 0.711688i | \(0.747931\pi\) | |||||||
\(270\) | −11.7819 | − | 6.80226i | −0.717022 | − | 0.413973i | ||||
\(271\) | 0.343470 | − | 0.198302i | 0.0208643 | − | 0.0120460i | −0.489532 | − | 0.871986i | \(-0.662832\pi\) |
0.510396 | + | 0.859940i | \(0.329499\pi\) | |||||||
\(272\) | 4.29430 | 0.260380 | ||||||||
\(273\) | −4.51399 | − | 9.97618i | −0.273199 | − | 0.603786i | ||||
\(274\) | − | 1.58168i | − | 0.0955531i | ||||||
\(275\) | −1.22065 | + | 0.704744i | −0.0736081 | + | 0.0424977i | ||||
\(276\) | 4.11093 | + | 4.15827i | 0.247449 | + | 0.250299i | ||||
\(277\) | 8.75948 | − | 15.1719i | 0.526306 | − | 0.911589i | −0.473224 | − | 0.880942i | \(-0.656910\pi\) |
0.999530 | − | 0.0306472i | \(-0.00975682\pi\) | |||||||
\(278\) | −12.2631 | + | 7.08013i | −0.735494 | + | 0.424638i | ||||
\(279\) | − | 5.81250i | − | 0.347985i | ||||||
\(280\) | −6.50901 | − | 0.644450i | −0.388988 | − | 0.0385133i | ||||
\(281\) | 20.4451i | 1.21965i | 0.792536 | + | 0.609826i | \(0.208761\pi\) | ||||
−0.792536 | + | 0.609826i | \(0.791239\pi\) | |||||||
\(282\) | 1.01344 | + | 1.75532i | 0.0603493 | + | 0.104528i | ||||
\(283\) | −7.00655 | + | 12.1357i | −0.416496 | + | 0.721393i | −0.995584 | − | 0.0938724i | \(-0.970075\pi\) |
0.579088 | + | 0.815265i | \(0.303409\pi\) | |||||||
\(284\) | 5.05148 | − | 8.74941i | 0.299750 | − | 0.519182i | ||||
\(285\) | −6.45344 | + | 3.72590i | −0.382269 | + | 0.220703i | ||||
\(286\) | 4.30333 | 0.254461 | ||||||||
\(287\) | −7.29739 | − | 5.23489i | −0.430751 | − | 0.309006i | ||||
\(288\) | 1.51344 | 0.0891801 | ||||||||
\(289\) | −0.720506 | − | 1.24795i | −0.0423827 | − | 0.0734090i | ||||
\(290\) | 11.1140 | − | 19.2500i | 0.652636 | − | 1.13040i | ||||
\(291\) | −6.86245 | − | 3.96204i | −0.402284 | − | 0.232259i | ||||
\(292\) | −3.32605 | + | 1.92030i | −0.194643 | + | 0.112377i | ||||
\(293\) | 4.28527 | 0.250348 | 0.125174 | − | 0.992135i | \(-0.460051\pi\) | ||||
0.125174 | + | 0.992135i | \(0.460051\pi\) | |||||||
\(294\) | −8.08460 | + | 2.73511i | −0.471503 | + | 0.159515i | ||||
\(295\) | 24.0872i | 1.40241i | ||||||||
\(296\) | 1.24062 | − | 0.716272i | 0.0721095 | − | 0.0416325i | ||||
\(297\) | 3.48823 | − | 6.04179i | 0.202407 | − | 0.350580i | ||||
\(298\) | −2.19582 | − | 1.26776i | −0.127200 | − | 0.0734391i | ||||
\(299\) | 15.7484 | − | 4.12326i | 0.910752 | − | 0.238455i | ||||
\(300\) | − | 1.35556i | − | 0.0782631i | ||||||
\(301\) | 27.9209 | + | 20.0295i | 1.60934 | + | 1.15448i | ||||
\(302\) | 8.02687 | 0.461895 | ||||||||
\(303\) | 4.34164 | + | 7.51995i | 0.249421 | + | 0.432010i | ||||
\(304\) | 1.23610 | − | 2.14099i | 0.0708953 | − | 0.122794i | ||||
\(305\) | 11.4200 | − | 19.7800i | 0.653907 | − | 1.13260i | ||||
\(306\) | −3.24958 | − | 5.62843i | −0.185766 | − | 0.321756i | ||||
\(307\) | 29.9300i | 1.70820i | 0.520111 | + | 0.854098i | \(0.325890\pi\) | ||||
−0.520111 | + | 0.854098i | \(0.674110\pi\) | |||||||
\(308\) | 0.330476 | − | 3.33785i | 0.0188306 | − | 0.190192i | ||||
\(309\) | − | 16.9557i | − | 0.964578i | ||||||
\(310\) | 8.22269 | − | 4.74737i | 0.467017 | − | 0.269633i | ||||
\(311\) | 4.83673 | + | 2.79248i | 0.274266 | + | 0.158347i | 0.630825 | − | 0.775926i | \(-0.282717\pi\) |
−0.356559 | + | 0.934273i | \(0.616050\pi\) | |||||||
\(312\) | −2.06934 | + | 3.58419i | −0.117153 | + | 0.202915i | ||||
\(313\) | −4.42798 | − | 7.66948i | −0.250284 | − | 0.433505i | 0.713320 | − | 0.700839i | \(-0.247191\pi\) |
−0.963604 | + | 0.267334i | \(0.913857\pi\) | |||||||
\(314\) | 19.2030 | 1.08369 | ||||||||
\(315\) | 4.08083 | + | 9.01887i | 0.229929 | + | 0.508156i | ||||
\(316\) | 7.43795i | 0.418417i | ||||||||
\(317\) | −9.52428 | − | 16.4965i | −0.534937 | − | 0.926538i | −0.999166 | − | 0.0408228i | \(-0.987002\pi\) |
0.464230 | − | 0.885715i | \(-0.346331\pi\) | |||||||
\(318\) | 5.02942 | − | 8.71121i | 0.282036 | − | 0.488500i | ||||
\(319\) | 9.87147 | + | 5.69930i | 0.552696 | + | 0.319099i | ||||
\(320\) | 1.23610 | + | 2.14099i | 0.0691002 | + | 0.119685i | ||||
\(321\) | −7.14926 | −0.399033 | ||||||||
\(322\) | −1.98878 | − | 12.5318i | −0.110830 | − | 0.698367i | ||||
\(323\) | −10.6164 | −0.590712 | ||||||||
\(324\) | 1.08460 | + | 1.87858i | 0.0602555 | + | 0.104366i | ||||
\(325\) | −3.26833 | − | 1.88697i | −0.181294 | − | 0.104670i | ||||
\(326\) | 1.24328 | − | 2.15343i | 0.0688590 | − | 0.119267i | ||||
\(327\) | 8.69045 | + | 15.0523i | 0.480583 | + | 0.832394i | ||||
\(328\) | 3.39445i | 0.187427i | ||||||||
\(329\) | 0.433351 | − | 4.37689i | 0.0238914 | − | 0.241306i | ||||
\(330\) | 3.82131 | 0.210356 | ||||||||
\(331\) | −1.30101 | − | 2.25341i | −0.0715098 | − | 0.123859i | 0.828053 | − | 0.560649i | \(-0.189448\pi\) |
−0.899563 | + | 0.436791i | \(0.856115\pi\) | |||||||
\(332\) | 2.60588 | − | 4.51352i | 0.143016 | − | 0.247712i | ||||
\(333\) | −1.87760 | − | 1.08403i | −0.102892 | − | 0.0594046i | ||||
\(334\) | 7.10295 | − | 4.10089i | 0.388656 | − | 0.224391i | ||||
\(335\) | − | 28.1980i | − | 1.54062i | ||||||
\(336\) | 2.62114 | + | 1.88031i | 0.142995 | + | 0.102580i | ||||
\(337\) | − | 5.37754i | − | 0.292934i | −0.989216 | − | 0.146467i | \(-0.953210\pi\) | ||
0.989216 | − | 0.146467i | \(-0.0467901\pi\) | |||||||
\(338\) | −0.738859 | − | 1.27974i | −0.0401886 | − | 0.0696088i | ||||
\(339\) | −9.56828 | + | 16.5728i | −0.519678 | + | 0.900108i | ||||
\(340\) | 5.30819 | − | 9.19406i | 0.287877 | − | 0.498618i | ||||
\(341\) | 2.43447 | + | 4.21663i | 0.131834 | + | 0.228343i | ||||
\(342\) | −3.74153 | −0.202319 | ||||||||
\(343\) | 17.7145 | + | 5.40339i | 0.956493 | + | 0.291755i | ||||
\(344\) | − | 12.9877i | − | 0.700249i | ||||||
\(345\) | 13.9844 | − | 3.66141i | 0.752893 | − | 0.197124i | ||||
\(346\) | −15.2173 | − | 8.78574i | −0.818090 | − | 0.472324i | ||||
\(347\) | −6.84623 | + | 11.8580i | −0.367525 | + | 0.636572i | −0.989178 | − | 0.146721i | \(-0.953128\pi\) |
0.621653 | + | 0.783293i | \(0.286461\pi\) | |||||||
\(348\) | −9.49375 | + | 5.48122i | −0.508918 | + | 0.293824i | ||||
\(349\) | 23.2774i | 1.24601i | 0.782217 | + | 0.623006i | \(0.214089\pi\) | ||||
−0.782217 | + | 0.623006i | \(0.785911\pi\) | |||||||
\(350\) | −1.71461 | + | 2.39014i | −0.0916496 | + | 0.127759i | ||||
\(351\) | 18.6796 | 0.997045 | ||||||||
\(352\) | −1.09791 | + | 0.633878i | −0.0585187 | + | 0.0337858i | ||||
\(353\) | −27.4228 | − | 15.8325i | −1.45957 | − | 0.842681i | −0.460576 | − | 0.887620i | \(-0.652357\pi\) |
−0.998990 | + | 0.0449392i | \(0.985691\pi\) | |||||||
\(354\) | 5.93968 | − | 10.2878i | 0.315690 | − | 0.546792i | ||||
\(355\) | −12.4883 | − | 21.6303i | −0.662809 | − | 1.14802i | ||||
\(356\) | 6.86384 | 0.363783 | ||||||||
\(357\) | 1.36486 | − | 13.7853i | 0.0722362 | − | 0.729593i | ||||
\(358\) | 6.51344 | 0.344246 | ||||||||
\(359\) | 30.4661 | − | 17.5896i | 1.60794 | − | 0.928345i | 0.618110 | − | 0.786092i | \(-0.287899\pi\) |
0.989830 | − | 0.142253i | \(-0.0454346\pi\) | |||||||
\(360\) | 1.87076 | − | 3.24026i | 0.0985979 | − | 0.170777i | ||||
\(361\) | 6.44410 | − | 11.1615i | 0.339163 | − | 0.587448i | ||||
\(362\) | −5.12034 | − | 8.86869i | −0.269119 | − | 0.466128i | ||||
\(363\) | − | 11.4521i | − | 0.601081i | ||||||
\(364\) | 8.18225 | − | 3.70227i | 0.428866 | − | 0.194052i | ||||
\(365\) | 9.49474i | 0.496977i | ||||||||
\(366\) | −9.75514 | + | 5.63213i | −0.509910 | + | 0.294396i | ||||
\(367\) | −6.62379 | + | 11.4727i | −0.345759 | + | 0.598873i | −0.985491 | − | 0.169725i | \(-0.945712\pi\) |
0.639732 | + | 0.768598i | \(0.279045\pi\) | |||||||
\(368\) | −3.41053 | + | 3.37169i | −0.177786 | + | 0.175762i | ||||
\(369\) | 4.44902 | − | 2.56864i | 0.231607 | − | 0.133718i | ||||
\(370\) | − | 3.54154i | − | 0.184116i | ||||||
\(371\) | −19.8865 | + | 8.99820i | −1.03246 | + | 0.467163i | ||||
\(372\) | −4.68264 | −0.242783 | ||||||||
\(373\) | −31.6868 | + | 18.2944i | −1.64068 | + | 0.947246i | −0.660086 | + | 0.751190i | \(0.729480\pi\) |
−0.980593 | + | 0.196056i | \(0.937186\pi\) | |||||||
\(374\) | 4.71475 | + | 2.72206i | 0.243794 | + | 0.140755i | ||||
\(375\) | 10.1498 | + | 5.85997i | 0.524131 | + | 0.302607i | ||||
\(376\) | −1.43968 | + | 0.831199i | −0.0742458 | + | 0.0428658i | ||||
\(377\) | 30.5200i | 1.57186i | ||||||||
\(378\) | 1.43451 | − | 14.4887i | 0.0737833 | − | 0.745219i | ||||
\(379\) | − | 1.29081i | − | 0.0663045i | −0.999450 | − | 0.0331523i | \(-0.989445\pi\) | ||
0.999450 | − | 0.0331523i | \(-0.0105546\pi\) | |||||||
\(380\) | −3.05590 | − | 5.29297i | −0.156764 | − | 0.271524i | ||||
\(381\) | 2.10246 | + | 1.21386i | 0.107712 | + | 0.0621877i | ||||
\(382\) | −8.51452 | − | 4.91586i | −0.435641 | − | 0.251517i | ||||
\(383\) | 2.42354 | + | 4.19769i | 0.123837 | + | 0.214492i | 0.921278 | − | 0.388905i | \(-0.127147\pi\) |
−0.797441 | + | 0.603397i | \(0.793813\pi\) | |||||||
\(384\) | − | 1.21925i | − | 0.0622194i | ||||||
\(385\) | −6.73780 | − | 4.83347i | −0.343390 | − | 0.246336i | ||||
\(386\) | −7.88455 | −0.401313 | ||||||||
\(387\) | −17.0226 | + | 9.82802i | −0.865309 | + | 0.499586i | ||||
\(388\) | 3.24958 | − | 5.62843i | 0.164972 | − | 0.285740i | ||||
\(389\) | −12.3624 | − | 7.13745i | −0.626800 | − | 0.361883i | 0.152712 | − | 0.988271i | \(-0.451199\pi\) |
−0.779512 | + | 0.626388i | \(0.784533\pi\) | |||||||
\(390\) | 5.11582 | + | 8.86086i | 0.259050 | + | 0.448687i | ||||
\(391\) | 19.8621 | + | 5.44413i | 1.00447 | + | 0.275321i | ||||
\(392\) | −2.24328 | − | 6.63081i | −0.113303 | − | 0.334907i | ||||
\(393\) | 13.8250 | 0.697377 | ||||||||
\(394\) | 2.98031 | + | 5.16206i | 0.150146 | + | 0.260061i | ||||
\(395\) | 15.9246 | + | 9.19406i | 0.801253 | + | 0.462604i | ||||
\(396\) | 1.66162 | + | 0.959334i | 0.0834993 | + | 0.0482084i | ||||
\(397\) | −27.4857 | + | 15.8689i | −1.37947 | + | 0.796435i | −0.992095 | − | 0.125488i | \(-0.959950\pi\) |
−0.387371 | + | 0.921924i | \(0.626617\pi\) | |||||||
\(398\) | −23.2518 | −1.16551 | ||||||||
\(399\) | −6.47999 | − | 4.64852i | −0.324405 | − | 0.232717i | ||||
\(400\) | 1.11180 | 0.0555899 | ||||||||
\(401\) | −3.68834 | + | 2.12946i | −0.184187 | + | 0.106340i | −0.589258 | − | 0.807945i | \(-0.700580\pi\) |
0.405071 | + | 0.914285i | \(0.367247\pi\) | |||||||
\(402\) | −6.95337 | + | 12.0436i | −0.346802 | + | 0.600679i | ||||
\(403\) | −6.51835 | + | 11.2901i | −0.324702 | + | 0.562401i | ||||
\(404\) | −6.16770 | + | 3.56092i | −0.306854 | + | 0.177162i | ||||
\(405\) | 5.36270 | 0.266475 | ||||||||
\(406\) | 23.6726 | + | 2.34380i | 1.17485 | + | 0.116321i | ||||
\(407\) | 1.81612 | 0.0900215 | ||||||||
\(408\) | −4.53435 | + | 2.61791i | −0.224484 | + | 0.129606i | ||||
\(409\) | −6.42276 | − | 3.70818i | −0.317585 | − | 0.183358i | 0.332731 | − | 0.943022i | \(-0.392030\pi\) |
−0.650316 | + | 0.759664i | \(0.725363\pi\) | |||||||
\(410\) | 7.26749 | + | 4.19589i | 0.358916 | + | 0.207220i | ||||
\(411\) | 0.964232 | + | 1.67010i | 0.0475621 | + | 0.0823799i | ||||
\(412\) | 13.9067 | 0.685136 | ||||||||
\(413\) | −23.4858 | + | 10.6268i | −1.15566 | + | 0.522908i | ||||
\(414\) | 7.00000 | + | 1.91867i | 0.344031 | + | 0.0942974i | ||||
\(415\) | −6.44227 | − | 11.1583i | −0.316239 | − | 0.547742i | ||||
\(416\) | −2.93968 | − | 1.69722i | −0.144130 | − | 0.0832133i | ||||
\(417\) | 8.63242 | − | 14.9518i | 0.422732 | − | 0.732192i | ||||
\(418\) | 2.71426 | − | 1.56708i | 0.132759 | − | 0.0766482i | ||||
\(419\) | 33.1406 | 1.61903 | 0.809513 | − | 0.587102i | \(-0.199731\pi\) | ||||
0.809513 | + | 0.587102i | \(0.199731\pi\) | |||||||
\(420\) | 7.26573 | − | 3.28757i | 0.354531 | − | 0.160417i | ||||
\(421\) | − | 28.6831i | − | 1.39793i | −0.715157 | − | 0.698964i | \(-0.753645\pi\) | ||
0.715157 | − | 0.698964i | \(-0.246355\pi\) | |||||||
\(422\) | 3.81444 | + | 6.60681i | 0.185684 | + | 0.321615i | ||||
\(423\) | 2.17886 | + | 1.25797i | 0.105940 | + | 0.0611644i | ||||
\(424\) | 7.14474 | + | 4.12502i | 0.346979 | + | 0.200329i | ||||
\(425\) | −2.38720 | − | 4.13475i | −0.115796 | − | 0.200565i | ||||
\(426\) | 12.3180i | 0.596809i | ||||||||
\(427\) | 24.3244 | + | 2.40833i | 1.17714 | + | 0.116547i | ||||
\(428\) | − | 5.86367i | − | 0.283431i | ||||||
\(429\) | −4.54388 | + | 2.62341i | −0.219381 | + | 0.126660i | ||||
\(430\) | −27.8065 | − | 16.0541i | −1.34095 | − | 0.774198i | ||||
\(431\) | 21.2811 | + | 12.2866i | 1.02507 | + | 0.591827i | 0.915570 | − | 0.402159i | \(-0.131740\pi\) |
0.109505 | + | 0.993986i | \(0.465074\pi\) | |||||||
\(432\) | −4.76573 | + | 2.75150i | −0.229291 | + | 0.132381i | ||||
\(433\) | −24.3265 | −1.16906 | −0.584528 | − | 0.811374i | \(-0.698720\pi\) | ||||
−0.584528 | + | 0.811374i | \(0.698720\pi\) | |||||||
\(434\) | 8.25651 | + | 5.92294i | 0.396325 | + | 0.284310i | ||||
\(435\) | 27.1014i | 1.29941i | ||||||||
\(436\) | −12.3456 | + | 7.12772i | −0.591246 | + | 0.341356i | ||||
\(437\) | 8.43152 | − | 8.33552i | 0.403334 | − | 0.398742i | ||||
\(438\) | 2.34132 | − | 4.05528i | 0.111872 | − | 0.193769i | ||||
\(439\) | 3.93526 | − | 2.27202i | 0.187820 | − | 0.108438i | −0.403142 | − | 0.915138i | \(-0.632082\pi\) |
0.590961 | + | 0.806700i | \(0.298749\pi\) | |||||||
\(440\) | 3.13415i | 0.149415i | ||||||||
\(441\) | −6.99331 | + | 7.95787i | −0.333015 | + | 0.378946i | ||||
\(442\) | 14.5768i | 0.693347i | ||||||||
\(443\) | 10.2326 | + | 17.7234i | 0.486166 | + | 0.842064i | 0.999874 | − | 0.0159012i | \(-0.00506171\pi\) |
−0.513708 | + | 0.857965i | \(0.671728\pi\) | |||||||
\(444\) | −0.873312 | + | 1.51262i | −0.0414456 | + | 0.0717858i | ||||
\(445\) | 8.48441 | − | 14.6954i | 0.402200 | − | 0.696630i | ||||
\(446\) | −7.26131 | + | 4.19232i | −0.343833 | + | 0.198512i | ||||
\(447\) | 3.09142 | 0.146219 | ||||||||
\(448\) | −1.54219 | + | 2.14980i | −0.0728618 | + | 0.101569i | ||||
\(449\) | −31.4921 | −1.48620 | −0.743102 | − | 0.669178i | \(-0.766646\pi\) | ||||
−0.743102 | + | 0.669178i | \(0.766646\pi\) | |||||||
\(450\) | −0.841318 | − | 1.45721i | −0.0396601 | − | 0.0686933i | ||||
\(451\) | −2.15167 | + | 3.72680i | −0.101318 | + | 0.175488i | ||||
\(452\) | −13.5926 | − | 7.84770i | −0.639343 | − | 0.369125i | ||||
\(453\) | −8.47557 | + | 4.89337i | −0.398217 | + | 0.229911i | ||||
\(454\) | −12.9893 | −0.609617 | ||||||||
\(455\) | 2.18755 | − | 22.0945i | 0.102554 | − | 1.03581i | ||||
\(456\) | 3.01423i | 0.141154i | ||||||||
\(457\) | 9.36053 | − | 5.40430i | 0.437867 | − | 0.252803i | −0.264825 | − | 0.964296i | \(-0.585314\pi\) |
0.702692 | + | 0.711494i | \(0.251981\pi\) | |||||||
\(458\) | −1.55022 | + | 2.68507i | −0.0724372 | + | 0.125465i | ||||
\(459\) | 20.4655 | + | 11.8158i | 0.955247 | + | 0.551512i | ||||
\(460\) | 3.00301 | + | 11.4697i | 0.140016 | + | 0.534776i | ||||
\(461\) | 36.3796i | 1.69437i | 0.531299 | + | 0.847185i | \(0.321704\pi\) | ||||
−0.531299 | + | 0.847185i | \(0.678296\pi\) | |||||||
\(462\) | 1.68588 | + | 3.72590i | 0.0784343 | + | 0.173344i | ||||
\(463\) | 25.6344 | 1.19133 | 0.595666 | − | 0.803232i | \(-0.296888\pi\) | ||||
0.595666 | + | 0.803232i | \(0.296888\pi\) | |||||||
\(464\) | −4.49558 | − | 7.78657i | −0.208702 | − | 0.361482i | ||||
\(465\) | −5.78822 | + | 10.0255i | −0.268422 | + | 0.464921i | ||||
\(466\) | 12.4182 | − | 21.5089i | 0.575260 | − | 0.996380i | ||||
\(467\) | −18.2010 | − | 31.5251i | −0.842243 | − | 1.45881i | −0.887994 | − | 0.459855i | \(-0.847901\pi\) |
0.0457505 | − | 0.998953i | \(-0.485432\pi\) | |||||||
\(468\) | 5.13728i | 0.237471i | ||||||||
\(469\) | 27.4939 | − | 12.4404i | 1.26955 | − | 0.574442i | ||||
\(470\) | 4.10979i | 0.189570i | ||||||||
\(471\) | −20.2764 | + | 11.7066i | −0.934288 | + | 0.539412i | ||||
\(472\) | 8.43785 | + | 4.87160i | 0.388384 | + | 0.224233i | ||||
\(473\) | 8.23261 | − | 14.2593i | 0.378536 | − | 0.655643i | ||||
\(474\) | −4.53435 | − | 7.85372i | −0.208269 | − | 0.360733i | ||||
\(475\) | −2.74859 | −0.126114 | ||||||||
\(476\) | 11.3064 | + | 1.11943i | 0.518227 | + | 0.0513090i | ||||
\(477\) | − | 12.4859i | − | 0.571691i | ||||||
\(478\) | 12.3351 | + | 21.3650i | 0.564193 | + | 0.977211i | ||||
\(479\) | −1.95577 | + | 3.38750i | −0.0893615 | + | 0.154779i | −0.907241 | − | 0.420610i | \(-0.861816\pi\) |
0.817880 | + | 0.575389i | \(0.195149\pi\) | |||||||
\(480\) | −2.61040 | − | 1.50711i | −0.119148 | − | 0.0687900i | ||||
\(481\) | 2.43135 | + | 4.21122i | 0.110860 | + | 0.192015i | ||||
\(482\) | 20.1514 | 0.917869 | ||||||||
\(483\) | 9.73960 | + | 12.0199i | 0.443167 | + | 0.546922i | ||||
\(484\) | 9.39279 | 0.426945 | ||||||||
\(485\) | −8.03362 | − | 13.9146i | −0.364788 | − | 0.631831i | ||||
\(486\) | 12.0067 | + | 6.93210i | 0.544637 | + | 0.314446i | ||||
\(487\) | 15.1951 | − | 26.3186i | 0.688554 | − | 1.19261i | −0.283752 | − | 0.958898i | \(-0.591579\pi\) |
0.972306 | − | 0.233713i | \(-0.0750876\pi\) | |||||||
\(488\) | −4.61935 | − | 8.00096i | −0.209108 | − | 0.362186i | ||||
\(489\) | 3.03173i | 0.137100i | ||||||||
\(490\) | −16.9694 | − | 3.39352i | −0.766601 | − | 0.153303i | ||||
\(491\) | −20.2990 | −0.916082 | −0.458041 | − | 0.888931i | \(-0.651449\pi\) | ||||
−0.458041 | + | 0.888931i | \(0.651449\pi\) | |||||||
\(492\) | −2.06934 | − | 3.58419i | −0.0932929 | − | 0.161588i | ||||
\(493\) | −19.3054 | + | 33.4379i | −0.869470 | + | 1.50597i | ||||
\(494\) | 7.26749 | + | 4.19589i | 0.326980 | + | 0.188782i | ||||
\(495\) | 4.10786 | − | 2.37167i | 0.184634 | − | 0.106599i | ||||
\(496\) | − | 3.84060i | − | 0.172448i | ||||||
\(497\) | 15.5807 | − | 21.7193i | 0.698890 | − | 0.974245i | ||||
\(498\) | 6.35443i | 0.284749i | ||||||||
\(499\) | −3.40473 | − | 5.89716i | −0.152417 | − | 0.263993i | 0.779699 | − | 0.626155i | \(-0.215372\pi\) |
−0.932115 | + | 0.362162i | \(0.882039\pi\) | |||||||
\(500\) | −4.80622 | + | 8.32461i | −0.214941 | + | 0.372288i | ||||
\(501\) | −5.00000 | + | 8.66025i | −0.223384 | + | 0.386912i | ||||
\(502\) | 14.6886 | + | 25.4414i | 0.655585 | + | 1.13551i | ||||
\(503\) | 3.19779 | 0.142582 | 0.0712911 | − | 0.997456i | \(-0.477288\pi\) | ||||
0.0712911 | + | 0.997456i | \(0.477288\pi\) | |||||||
\(504\) | 3.98469 | + | 0.394520i | 0.177492 | + | 0.0175733i | ||||
\(505\) | 17.6067i | 0.783486i | ||||||||
\(506\) | −5.88169 | + | 1.53995i | −0.261473 | + | 0.0684593i | ||||
\(507\) | 1.56032 | + | 0.900852i | 0.0692963 | + | 0.0400082i | ||||
\(508\) | −0.995578 | + | 1.72439i | −0.0441716 | + | 0.0765075i | ||||
\(509\) | 7.04396 | − | 4.06683i | 0.312218 | − | 0.180259i | −0.335700 | − | 0.941969i | \(-0.608973\pi\) |
0.647919 | + | 0.761710i | \(0.275640\pi\) | |||||||
\(510\) | 12.9440i | 0.573170i | ||||||||
\(511\) | −9.25767 | + | 4.18888i | −0.409535 | + | 0.185305i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 11.7819 | − | 6.80226i | 0.520182 | − | 0.300327i | ||||
\(514\) | −3.93918 | − | 2.27429i | −0.173750 | − | 0.100315i | ||||
\(515\) | 17.1901 | − | 29.7742i | 0.757488 | − | 1.31201i | ||||
\(516\) | 7.91760 | + | 13.7137i | 0.348553 | + | 0.603711i | ||||
\(517\) | −2.10752 | −0.0926884 | ||||||||
\(518\) | 3.45312 | − | 1.56245i | 0.151721 | − | 0.0686503i | ||||
\(519\) | 21.4240 | 0.940408 | ||||||||
\(520\) | −7.26749 | + | 4.19589i | −0.318700 | + | 0.184002i | ||||
\(521\) | 19.8849 | − | 34.4417i | 0.871175 | − | 1.50892i | 0.0103923 | − | 0.999946i | \(-0.496692\pi\) |
0.860782 | − | 0.508973i | \(-0.169975\pi\) | |||||||
\(522\) | −6.80377 | + | 11.7845i | −0.297793 | + | 0.515793i | ||||
\(523\) | 16.2253 | + | 28.1030i | 0.709483 | + | 1.22886i | 0.965049 | + | 0.262068i | \(0.0844046\pi\) |
−0.255567 | + | 0.966791i | \(0.582262\pi\) | |||||||
\(524\) | 11.3389i | 0.495344i | ||||||||
\(525\) | 0.353364 | − | 3.56901i | 0.0154221 | − | 0.155765i | ||||
\(526\) | 5.71453i | 0.249165i | ||||||||
\(527\) | −14.2831 | + | 8.24634i | −0.622180 | + | 0.359216i | ||||
\(528\) | 0.772854 | − | 1.33862i | 0.0336342 | − | 0.0582561i | ||||
\(529\) | −20.0490 | + | 11.2712i | −0.871694 | + | 0.490050i | ||||
\(530\) | 17.6633 | − | 10.1979i | 0.767244 | − | 0.442968i | ||||
\(531\) | − | 14.7457i | − | 0.639909i | ||||||
\(532\) | 3.81262 | − | 5.31475i | 0.165298 | − | 0.230423i | ||||
\(533\) | −11.5223 | −0.499085 | ||||||||
\(534\) | −7.24752 | + | 4.18436i | −0.313631 | + | 0.181075i | ||||
\(535\) | −12.5541 | − | 7.24810i | −0.542760 | − | 0.313363i | ||||
\(536\) | −9.87789 | − | 5.70300i | −0.426660 | − | 0.246332i | ||||
\(537\) | −6.87753 | + | 3.97074i | −0.296787 | + | 0.171350i | ||||
\(538\) | 8.28376i | 0.357138i | ||||||||
\(539\) | 1.74021 | − | 8.70200i | 0.0749561 | − | 0.374822i | ||||
\(540\) | 13.6045i | 0.585446i | ||||||||
\(541\) | −11.1614 | − | 19.3322i | −0.479868 | − | 0.831156i | 0.519865 | − | 0.854248i | \(-0.325982\pi\) |
−0.999733 | + | 0.0230924i | \(0.992649\pi\) | |||||||
\(542\) | −0.343470 | − | 0.198302i | −0.0147533 | − | 0.00851781i | ||||
\(543\) | 10.8131 | + | 6.24296i | 0.464035 | + | 0.267911i | ||||
\(544\) | −2.14715 | − | 3.71897i | −0.0920583 | − | 0.159450i | ||||
\(545\) | 35.2424i | 1.50962i | ||||||||
\(546\) | −6.38263 | + | 8.89732i | −0.273151 | + | 0.380770i | ||||
\(547\) | −12.9010 | −0.551609 | −0.275804 | − | 0.961214i | \(-0.588944\pi\) | ||||
−0.275804 | + | 0.961214i | \(0.588944\pi\) | |||||||
\(548\) | −1.36978 | + | 0.790842i | −0.0585141 | + | 0.0337831i | ||||
\(549\) | −6.99110 | + | 12.1089i | −0.298373 | + | 0.516797i | ||||
\(550\) | 1.22065 | + | 0.704744i | 0.0520488 | + | 0.0300504i | ||||
\(551\) | 11.1140 | + | 19.2500i | 0.473472 | + | 0.820077i | ||||
\(552\) | 1.54571 | − | 5.63930i | 0.0657897 | − | 0.240025i | ||||
\(553\) | −1.93891 | + | 19.5832i | −0.0824509 | + | 0.832763i | ||||
\(554\) | −17.5190 | −0.744310 | ||||||||
\(555\) | 2.15901 | + | 3.73951i | 0.0916447 | + | 0.158733i | ||||
\(556\) | 12.2631 | + | 7.08013i | 0.520073 | + | 0.300264i | ||||
\(557\) | 1.60885 | + | 0.928870i | 0.0681692 | + | 0.0393575i | 0.533697 | − | 0.845676i | \(-0.320802\pi\) |
−0.465528 | + | 0.885033i | \(0.654136\pi\) | |||||||
\(558\) | −5.03377 | + | 2.90625i | −0.213097 | + | 0.123031i | ||||
\(559\) | 44.0860 | 1.86464 | ||||||||
\(560\) | 2.69640 | + | 5.95920i | 0.113944 | + | 0.251822i | ||||
\(561\) | −6.63773 | −0.280245 | ||||||||
\(562\) | 17.7060 | − | 10.2225i | 0.746881 | − | 0.431212i | ||||
\(563\) | −2.88227 | + | 4.99224i | −0.121473 | + | 0.210398i | −0.920349 | − | 0.391099i | \(-0.872095\pi\) |
0.798876 | + | 0.601496i | \(0.205428\pi\) | |||||||
\(564\) | 1.01344 | − | 1.75532i | 0.0426734 | − | 0.0739125i | ||||
\(565\) | −33.6037 | + | 19.4011i | −1.41372 | + | 0.816211i | ||||
\(566\) | 14.0131 | 0.589015 | ||||||||
\(567\) | 2.36591 | + | 5.22881i | 0.0993590 | + | 0.219589i | ||||
\(568\) | −10.1030 | −0.423910 | ||||||||
\(569\) | 23.8451 | − | 13.7670i | 0.999641 | − | 0.577143i | 0.0914986 | − | 0.995805i | \(-0.470834\pi\) |
0.908142 | + | 0.418662i | \(0.137501\pi\) | |||||||
\(570\) | 6.45344 | + | 3.72590i | 0.270305 | + | 0.156061i | ||||
\(571\) | −26.7378 | − | 15.4371i | −1.11894 | − | 0.646023i | −0.177813 | − | 0.984064i | \(-0.556902\pi\) |
−0.941131 | + | 0.338042i | \(0.890235\pi\) | |||||||
\(572\) | −2.15167 | − | 3.72680i | −0.0899657 | − | 0.155825i | ||||
\(573\) | 11.9873 | 0.500777 | ||||||||
\(574\) | −0.884859 | + | 8.93717i | −0.0369333 | + | 0.373030i | ||||
\(575\) | 5.14233 | + | 1.40949i | 0.214450 | + | 0.0587797i | ||||
\(576\) | −0.756718 | − | 1.31067i | −0.0315299 | − | 0.0546114i | ||||
\(577\) | −35.7439 | − | 20.6367i | −1.48804 | − | 0.859119i | −0.488131 | − | 0.872770i | \(-0.662321\pi\) |
−0.999907 | + | 0.0136513i | \(0.995655\pi\) | |||||||
\(578\) | −0.720506 | + | 1.24795i | −0.0299691 | + | 0.0519080i | ||||
\(579\) | 8.32529 | − | 4.80661i | 0.345987 | − | 0.199756i | ||||
\(580\) | −22.2280 | −0.922967 | ||||||||
\(581\) | 8.03755 | − | 11.2043i | 0.333454 | − | 0.464831i | ||||
\(582\) | 7.92407i | 0.328463i | ||||||||
\(583\) | 5.22952 | + | 9.05779i | 0.216585 | + | 0.375136i | ||||
\(584\) | 3.32605 | + | 1.92030i | 0.137633 | + | 0.0794625i | ||||
\(585\) | 10.9989 | + | 6.35021i | 0.454748 | + | 0.262549i | ||||
\(586\) | −2.14263 | − | 3.71115i | −0.0885114 | − | 0.153306i | ||||
\(587\) | 13.5868i | 0.560787i | 0.959885 | + | 0.280393i | \(0.0904649\pi\) | ||||
−0.959885 | + | 0.280393i | \(0.909535\pi\) | |||||||
\(588\) | 6.41098 | + | 5.63391i | 0.264384 | + | 0.232339i | ||||
\(589\) | 9.49474i | 0.391224i | ||||||||
\(590\) | 20.8601 | − | 12.0436i | 0.858797 | − | 0.495827i | ||||
\(591\) | −6.29382 | − | 3.63374i | −0.258893 | − | 0.149472i | ||||
\(592\) | −1.24062 | − | 0.716272i | −0.0509891 | − | 0.0294386i | ||||
\(593\) | 12.3664 | − | 7.13972i | 0.507826 | − | 0.293193i | −0.224114 | − | 0.974563i | \(-0.571949\pi\) |
0.731939 | + | 0.681370i | \(0.238615\pi\) | |||||||
\(594\) | −6.97645 | −0.286247 | ||||||||
\(595\) | 16.3725 | − | 22.8231i | 0.671208 | − | 0.935657i | ||||
\(596\) | 2.53551i | 0.103859i | ||||||||
\(597\) | 24.5516 | − | 14.1749i | 1.00483 | − | 0.580138i | ||||
\(598\) | −11.4450 | − | 11.5769i | −0.468022 | − | 0.473413i | ||||
\(599\) | −11.6674 | + | 20.2085i | −0.476716 | + | 0.825696i | −0.999644 | − | 0.0266806i | \(-0.991506\pi\) |
0.522928 | + | 0.852377i | \(0.324840\pi\) | |||||||
\(600\) | −1.17395 | + | 0.677778i | −0.0479261 | + | 0.0276702i | ||||
\(601\) | − | 41.8019i | − | 1.70513i | −0.522618 | − | 0.852567i | \(-0.675045\pi\) | ||
0.522618 | − | 0.852567i | \(-0.324955\pi\) | |||||||
\(602\) | 3.38561 | − | 34.1950i | 0.137987 | − | 1.39368i | ||||
\(603\) | 17.2623i | 0.702974i | ||||||||
\(604\) | −4.01344 | − | 6.95148i | −0.163304 | − | 0.282852i | ||||
\(605\) | 11.6105 | − | 20.1099i | 0.472032 | − | 0.817584i | ||||
\(606\) | 4.34164 | − | 7.51995i | 0.176367 | − | 0.305477i | ||||
\(607\) | −6.12191 | + | 3.53448i | −0.248480 | + | 0.143460i | −0.619068 | − | 0.785337i | \(-0.712490\pi\) |
0.370588 | + | 0.928797i | \(0.379156\pi\) | |||||||
\(608\) | −2.47221 | −0.100261 | ||||||||
\(609\) | −26.4247 | + | 11.9566i | −1.07078 | + | 0.484505i | ||||
\(610\) | −22.8400 | −0.924764 | ||||||||
\(611\) | −2.82146 | − | 4.88692i | −0.114144 | − | 0.197703i | ||||
\(612\) | −3.24958 | + | 5.62843i | −0.131356 | + | 0.227516i | ||||
\(613\) | −36.2475 | − | 20.9275i | −1.46402 | − | 0.845254i | −0.464829 | − | 0.885401i | \(-0.653884\pi\) |
−0.999194 | + | 0.0401467i | \(0.987217\pi\) | |||||||
\(614\) | 25.9202 | − | 14.9650i | 1.04605 | − | 0.603939i | ||||
\(615\) | −10.2316 | −0.412580 | ||||||||
\(616\) | −3.05590 | + | 1.38272i | −0.123126 | + | 0.0557115i | ||||
\(617\) | − | 44.8424i | − | 1.80529i | −0.430390 | − | 0.902643i | \(-0.641624\pi\) | ||
0.430390 | − | 0.902643i | \(-0.358376\pi\) | |||||||
\(618\) | −14.6841 | + | 8.47787i | −0.590681 | + | 0.341030i | ||||
\(619\) | 2.13812 | − | 3.70333i | 0.0859382 | − | 0.148849i | −0.819852 | − | 0.572575i | \(-0.805945\pi\) |
0.905791 | + | 0.423726i | \(0.139278\pi\) | |||||||
\(620\) | −8.22269 | − | 4.74737i | −0.330231 | − | 0.190659i | ||||
\(621\) | −25.5309 | + | 6.68453i | −1.02452 | + | 0.268241i | ||||
\(622\) | − | 5.58497i | − | 0.223937i | ||||||
\(623\) | 18.0717 | + | 1.78925i | 0.724026 | + | 0.0716849i | ||||
\(624\) | 4.13867 | 0.165679 | ||||||||
\(625\) | 14.6614 | + | 25.3944i | 0.586458 | + | 1.01577i | ||||
\(626\) | −4.42798 | + | 7.66948i | −0.176978 | + | 0.306534i | ||||
\(627\) | −1.91065 | + | 3.30935i | −0.0763041 | + | 0.132163i | ||||
\(628\) | −9.60150 | − | 16.6303i | −0.383142 | − | 0.663621i | ||||
\(629\) | 6.15177i | 0.245287i | ||||||||
\(630\) | 5.77016 | − | 8.04353i | 0.229888 | − | 0.320462i | ||||
\(631\) | − | 34.7236i | − | 1.38232i | −0.722700 | − | 0.691162i | \(-0.757099\pi\) | ||
0.722700 | − | 0.691162i | \(-0.242901\pi\) | |||||||
\(632\) | 6.44145 | − | 3.71897i | 0.256227 | − | 0.147933i | ||||
\(633\) | −8.05533 | − | 4.65075i | −0.320171 | − | 0.184851i | ||||
\(634\) | −9.52428 | + | 16.4965i | −0.378257 | + | 0.655161i | ||||
\(635\) | 2.46127 | + | 4.26305i | 0.0976726 | + | 0.169174i | ||||
\(636\) | −10.0588 | −0.398859 | ||||||||
\(637\) | 22.5080 | − | 7.61470i | 0.891798 | − | 0.301706i | ||||
\(638\) | − | 11.3986i | − | 0.451275i | ||||||
\(639\) | 7.64509 | + | 13.2417i | 0.302435 | + | 0.523833i | ||||
\(640\) | 1.23610 | − | 2.14099i | 0.0488612 | − | 0.0846302i | ||||
\(641\) | 6.73329 | + | 3.88746i | 0.265949 | + | 0.153546i | 0.627045 | − | 0.778983i | \(-0.284264\pi\) |
−0.361096 | + | 0.932529i | \(0.617597\pi\) | |||||||
\(642\) | 3.57463 | + | 6.19144i | 0.141079 | + | 0.244357i | ||||
\(643\) | −29.0738 | −1.14656 | −0.573278 | − | 0.819361i | \(-0.694329\pi\) | ||||
−0.573278 | + | 0.819361i | \(0.694329\pi\) | |||||||
\(644\) | −9.85843 | + | 7.98821i | −0.388476 | + | 0.314779i | ||||
\(645\) | 39.1479 | 1.54145 | ||||||||
\(646\) | 5.30819 | + | 9.19406i | 0.208848 | + | 0.361736i | ||||
\(647\) | 0.980757 | + | 0.566241i | 0.0385576 | + | 0.0222612i | 0.519155 | − | 0.854680i | \(-0.326247\pi\) |
−0.480597 | + | 0.876941i | \(0.659580\pi\) | |||||||
\(648\) | 1.08460 | − | 1.87858i | 0.0426071 | − | 0.0737976i | ||||
\(649\) | 6.17600 | + | 10.6971i | 0.242429 | + | 0.419899i | ||||
\(650\) | 3.77394i | 0.148026i | ||||||||
\(651\) | −12.3288 | − | 1.22066i | −0.483204 | − | 0.0478415i | ||||
\(652\) | −2.48656 | −0.0973813 | ||||||||
\(653\) | 11.5471 | + | 20.0001i | 0.451871 | + | 0.782664i | 0.998502 | − | 0.0547097i | \(-0.0174233\pi\) |
−0.546631 | + | 0.837374i | \(0.684090\pi\) | |||||||
\(654\) | 8.69045 | − | 15.0523i | 0.339824 | − | 0.588592i | ||||
\(655\) | 24.2766 | + | 14.0161i | 0.948564 | + | 0.547654i | ||||
\(656\) | 2.93968 | − | 1.69722i | 0.114775 | − | 0.0662655i | ||||
\(657\) | − | 5.81250i | − | 0.226767i | ||||||
\(658\) | −4.00717 | + | 1.81315i | −0.156216 | + | 0.0706840i | ||||
\(659\) | − | 4.27458i | − | 0.166514i | −0.996528 | − | 0.0832569i | \(-0.973468\pi\) | ||
0.996528 | − | 0.0832569i | \(-0.0265322\pi\) | |||||||
\(660\) | −1.91065 | − | 3.30935i | −0.0743721 | − | 0.128816i | ||||
\(661\) | 18.4774 | − | 32.0038i | 0.718688 | − | 1.24480i | −0.242831 | − | 0.970069i | \(-0.578076\pi\) |
0.961520 | − | 0.274736i | \(-0.0885905\pi\) | |||||||
\(662\) | −1.30101 | + | 2.25341i | −0.0505651 | + | 0.0875813i | ||||
\(663\) | −8.88635 | − | 15.3916i | −0.345117 | − | 0.597760i | ||||
\(664\) | −5.21176 | −0.202256 | ||||||||
\(665\) | −6.66605 | − | 14.7324i | −0.258498 | − | 0.571296i | ||||
\(666\) | 2.16806i | 0.0840108i | ||||||||
\(667\) | −10.9216 | − | 41.7140i | −0.422887 | − | 1.61517i | ||||
\(668\) | −7.10295 | − | 4.10089i | −0.274822 | − | 0.158668i | ||||
\(669\) | 5.11147 | − | 8.85333i | 0.197621 | − | 0.342290i | ||||
\(670\) | −24.4202 | + | 14.0990i | −0.943433 | + | 0.544691i | ||||
\(671\) | − | 11.7124i | − | 0.452153i | ||||||
\(672\) | 0.317831 | − | 3.21013i | 0.0122606 | − | 0.123833i | ||||
\(673\) | 16.0507 | 0.618711 | 0.309355 | − | 0.950947i | \(-0.399887\pi\) | ||||
0.309355 | + | 0.950947i | \(0.399887\pi\) | |||||||
\(674\) | −4.65709 | + | 2.68877i | −0.179384 | + | 0.103568i | ||||
\(675\) | 5.29853 | + | 3.05911i | 0.203941 | + | 0.117745i | ||||
\(676\) | −0.738859 | + | 1.27974i | −0.0284177 | + | 0.0492208i | ||||
\(677\) | −2.01347 | − | 3.48744i | −0.0773841 | − | 0.134033i | 0.824736 | − | 0.565517i | \(-0.191323\pi\) |
−0.902121 | + | 0.431484i | \(0.857990\pi\) | |||||||
\(678\) | 19.1366 | 0.734935 | ||||||||
\(679\) | 10.0229 | − | 13.9719i | 0.384645 | − | 0.536191i | ||||
\(680\) | −10.6164 | −0.407120 | ||||||||
\(681\) | 13.7154 | − | 7.91856i | 0.525574 | − | 0.303440i | ||||
\(682\) | 2.43447 | − | 4.21663i | 0.0932207 | − | 0.161463i | ||||
\(683\) | 11.6692 | − | 20.2116i | 0.446509 | − | 0.773377i | −0.551647 | − | 0.834078i | \(-0.686000\pi\) |
0.998156 | + | 0.0607009i | \(0.0193336\pi\) | |||||||
\(684\) | 1.87076 | + | 3.24026i | 0.0715304 | + | 0.123894i | ||||
\(685\) | 3.91025i | 0.149403i | ||||||||
\(686\) | −4.17778 | − | 18.0429i | −0.159508 | − | 0.688881i | ||||
\(687\) | − | 3.78021i | − | 0.144224i | ||||||
\(688\) | −11.2477 | + | 6.49384i | −0.428813 | + | 0.247575i | ||||
\(689\) | −14.0022 | + | 24.2525i | −0.533440 | + | 0.923946i | ||||
\(690\) | −10.1631 | − | 10.2801i | −0.386901 | − | 0.391357i | ||||
\(691\) | −32.7506 | + | 18.9086i | −1.24589 | + | 0.719317i | −0.970288 | − | 0.241954i | \(-0.922212\pi\) |
−0.275605 | + | 0.961271i | \(0.588878\pi\) | |||||||
\(692\) | 17.5715i | 0.667967i | ||||||||
\(693\) | 4.12475 | + | 2.95896i | 0.156686 | + | 0.112402i | ||||
\(694\) | 13.6925 | 0.519759 | ||||||||
\(695\) | 30.3170 | − | 17.5035i | 1.14999 | − | 0.663946i | ||||
\(696\) | 9.49375 | + | 5.48122i | 0.359860 | + | 0.207765i | ||||
\(697\) | −12.6239 | − | 7.28839i | −0.478163 | − | 0.276067i | ||||
\(698\) | 20.1589 | − | 11.6387i | 0.763024 | − | 0.440532i | ||||
\(699\) | 30.2816i | 1.14536i | ||||||||
\(700\) | 2.92723 | + | 0.289821i | 0.110639 | + | 0.0109542i | ||||
\(701\) | − | 26.4771i | − | 1.00003i | −0.866017 | − | 0.500014i | \(-0.833328\pi\) | ||
0.866017 | − | 0.500014i | \(-0.166672\pi\) | |||||||
\(702\) | −9.33982 | − | 16.1770i | −0.352509 | − | 0.610563i | ||||
\(703\) | 3.06707 | + | 1.77077i | 0.115677 | + | 0.0667859i | ||||
\(704\) | 1.09791 | + | 0.633878i | 0.0413790 | + | 0.0238902i | ||||
\(705\) | −2.50542 | − | 4.33952i | −0.0943597 | − | 0.163436i | ||||
\(706\) | 31.6651i | 1.19173i | ||||||||
\(707\) | −17.1670 | + | 7.76769i | −0.645633 | + | 0.292134i | ||||
\(708\) | −11.8794 | −0.446454 | ||||||||
\(709\) | −14.1532 | + | 8.17135i | −0.531534 | + | 0.306882i | −0.741641 | − | 0.670797i | \(-0.765952\pi\) |
0.210107 | + | 0.977678i | \(0.432619\pi\) | |||||||
\(710\) | −12.4883 | + | 21.6303i | −0.468677 | + | 0.811772i | ||||
\(711\) | −9.74873 | − | 5.62843i | −0.365606 | − | 0.211083i | ||||
\(712\) | −3.43192 | − | 5.94426i | −0.128617 | − | 0.222771i | ||||
\(713\) | 4.86894 | − | 17.7637i | 0.182343 | − | 0.665254i | ||||
\(714\) | −12.6208 | + | 5.71062i | −0.472322 | + | 0.213715i | ||||
\(715\) | −10.6387 | −0.397866 | ||||||||
\(716\) | −3.25672 | − | 5.64080i | −0.121709 | − | 0.210807i | ||||
\(717\) | −26.0492 | − | 15.0395i | −0.972824 | − | 0.561660i | ||||
\(718\) | −30.4661 | − | 17.5896i | −1.13699 | − | 0.656439i | ||||
\(719\) | −37.3661 | + | 21.5733i | −1.39352 | + | 0.804549i | −0.993703 | − | 0.112046i | \(-0.964260\pi\) |
−0.399817 | + | 0.916595i | \(0.630926\pi\) | |||||||
\(720\) | −3.74153 | −0.139438 | ||||||||
\(721\) | 36.6147 | + | 3.62518i | 1.36360 | + | 0.135009i | ||||
\(722\) | −12.8882 | −0.479649 | ||||||||
\(723\) | −21.2778 | + | 12.2847i | −0.791330 | + | 0.456875i | ||||
\(724\) | −5.12034 | + | 8.86869i | −0.190296 | + | 0.329602i | ||||
\(725\) | −4.99817 | + | 8.65709i | −0.185627 | + | 0.321516i | ||||
\(726\) | −9.91784 | + | 5.72607i | −0.368086 | + | 0.212514i | ||||
\(727\) | −13.4385 | −0.498405 | −0.249203 | − | 0.968451i | \(-0.580168\pi\) | ||||
−0.249203 | + | 0.968451i | \(0.580168\pi\) | |||||||
\(728\) | −7.29739 | − | 5.23489i | −0.270459 | − | 0.194018i | ||||
\(729\) | −23.4115 | −0.867092 | ||||||||
\(730\) | 8.22269 | − | 4.74737i | 0.304335 | − | 0.175708i | ||||
\(731\) | 48.3009 | + | 27.8865i | 1.78647 | + | 1.03142i | ||||
\(732\) | 9.75514 | + | 5.63213i | 0.360560 | + | 0.208170i | ||||
\(733\) | 15.4206 | + | 26.7093i | 0.569573 | + | 0.986530i | 0.996608 | + | 0.0822949i | \(0.0262249\pi\) |
−0.427035 | + | 0.904235i | \(0.640442\pi\) | |||||||
\(734\) | 13.2476 | 0.488977 | ||||||||
\(735\) | 19.9868 | − | 6.76176i | 0.737224 | − | 0.249411i | ||||
\(736\) | 4.62523 | + | 1.26776i | 0.170488 | + | 0.0467301i | ||||
\(737\) | −7.23001 | − | 12.5228i | −0.266321 | − | 0.461282i | ||||
\(738\) | −4.44902 | − | 2.56864i | −0.163771 | − | 0.0945530i | ||||
\(739\) | −0.993256 | + | 1.72037i | −0.0365375 | + | 0.0632848i | −0.883716 | − | 0.468024i | \(-0.844966\pi\) |
0.847178 | + | 0.531309i | \(0.178300\pi\) | |||||||
\(740\) | −3.06707 | + | 1.77077i | −0.112748 | + | 0.0650948i | ||||
\(741\) | −10.2316 | −0.375869 | ||||||||
\(742\) | 17.7359 | + | 12.7232i | 0.651107 | + | 0.467082i | ||||
\(743\) | − | 1.57808i | − | 0.0578941i | −0.999581 | − | 0.0289471i | \(-0.990785\pi\) | ||
0.999581 | − | 0.0289471i | \(-0.00921543\pi\) | |||||||
\(744\) | 2.34132 | + | 4.05528i | 0.0858369 | + | 0.148674i | ||||
\(745\) | 5.42851 | + | 3.13415i | 0.198885 | + | 0.114826i | ||||
\(746\) | 31.6868 | + | 18.2944i | 1.16014 | + | 0.669804i | ||||
\(747\) | 3.94384 | + | 6.83093i | 0.144297 | + | 0.249931i | ||||
\(748\) | − | 5.44413i | − | 0.199057i | ||||||
\(749\) | 1.52853 | − | 15.4383i | 0.0558513 | − | 0.564104i | ||||
\(750\) | − | 11.7199i | − | 0.427951i | ||||||
\(751\) | −14.9992 | + | 8.65979i | −0.547329 | + | 0.316000i | −0.748044 | − | 0.663649i | \(-0.769007\pi\) |
0.200715 | + | 0.979650i | \(0.435673\pi\) | |||||||
\(752\) | 1.43968 | + | 0.831199i | 0.0524997 | + | 0.0303107i | ||||
\(753\) | −31.0194 | − | 17.9091i | −1.13041 | − | 0.652642i | ||||
\(754\) | 26.4311 | − | 15.2600i | 0.962564 | − | 0.555737i | ||||
\(755\) | −19.8441 | −0.722200 | ||||||||
\(756\) | −13.2648 | + | 6.00203i | −0.482438 | + | 0.218292i | ||||
\(757\) | 29.1470i | 1.05937i | 0.848196 | + | 0.529683i | \(0.177689\pi\) | ||||
−0.848196 | + | 0.529683i | \(0.822311\pi\) | |||||||
\(758\) | −1.11788 | + | 0.645406i | −0.0406031 | + | 0.0234422i | ||||
\(759\) | 5.27168 | − | 5.21165i | 0.191350 | − | 0.189171i | ||||
\(760\) | −3.05590 | + | 5.29297i | −0.110849 | + | 0.191996i | ||||
\(761\) | −16.6464 | + | 9.61082i | −0.603432 | + | 0.348392i | −0.770391 | − | 0.637572i | \(-0.779939\pi\) |
0.166958 | + | 0.985964i | \(0.446605\pi\) | |||||||
\(762\) | − | 2.42771i | − | 0.0879467i | ||||||
\(763\) | −34.3624 | + | 15.5482i | −1.24400 | + | 0.562883i | ||||
\(764\) | 9.83173i | 0.355699i | ||||||||
\(765\) | 8.03362 | + | 13.9146i | 0.290456 | + | 0.503085i | ||||
\(766\) | 2.42354 | − | 4.19769i | 0.0875659 | − | 0.151669i | ||||
\(767\) | −16.5364 | + | 28.6419i | −0.597094 | + | 1.03420i | ||||
\(768\) | −1.05590 | + | 0.609623i | −0.0381015 | + | 0.0219979i | ||||
\(769\) | −32.3533 | −1.16669 | −0.583344 | − | 0.812225i | \(-0.698256\pi\) | ||||
−0.583344 | + | 0.812225i | \(0.698256\pi\) | |||||||
\(770\) | −0.817005 | + | 8.25184i | −0.0294428 | + | 0.297376i | ||||
\(771\) | 5.54584 | 0.199729 | ||||||||
\(772\) | 3.94227 | + | 6.82822i | 0.141886 | + | 0.245753i | ||||
\(773\) | 18.0142 | − | 31.2015i | 0.647925 | − | 1.12224i | −0.335693 | − | 0.941971i | \(-0.608970\pi\) |
0.983618 | − | 0.180267i | \(-0.0576962\pi\) | |||||||
\(774\) | 17.0226 | + | 9.82802i | 0.611866 | + | 0.353261i | ||||
\(775\) | −3.69790 | + | 2.13498i | −0.132832 | + | 0.0766909i | ||||
\(776\) | −6.49915 | −0.233306 | ||||||||
\(777\) | −2.69363 | + | 3.75489i | −0.0966335 | + | 0.134706i | ||||
\(778\) | 14.2749i | 0.511780i | ||||||||
\(779\) | −7.26749 | + | 4.19589i | −0.260385 | + | 0.150333i | ||||
\(780\) | 5.11582 | − | 8.86086i | 0.183176 | − | 0.317270i | ||||
\(781\) | −11.0921 | − | 6.40404i | −0.396907 | − | 0.229155i | ||||
\(782\) | −5.21632 | − | 19.9232i | −0.186535 | − | 0.712452i | ||||
\(783\) | − | 49.4783i | − | 1.76821i | ||||||
\(784\) | −4.62081 | + | 5.25815i | −0.165029 | + | 0.187791i | ||||
\(785\) | −47.4738 | −1.69441 | ||||||||
\(786\) | −6.91248 | − | 11.9728i | −0.246560 | − | 0.427054i | ||||
\(787\) | 14.6732 | − | 25.4147i | 0.523042 | − | 0.905935i | −0.476598 | − | 0.879121i | \(-0.658130\pi\) |
0.999640 | − | 0.0268143i | \(-0.00853627\pi\) | |||||||
\(788\) | 2.98031 | − | 5.16206i | 0.106169 | − | 0.183891i | ||||
\(789\) | −3.48371 | − | 6.03396i | −0.124023 | − | 0.214815i | ||||
\(790\) | − | 18.3881i | − | 0.654220i | ||||||
\(791\) | −33.7420 | − | 24.2053i | −1.19973 | − | 0.860642i | ||||
\(792\) | − | 1.91867i | − | 0.0681769i | ||||||
\(793\) | 27.1588 | − | 15.6802i | 0.964439 | − | 0.556819i | ||||
\(794\) | 27.4857 | + | 15.8689i | 0.975430 | + | 0.563165i | ||||
\(795\) | −12.4338 | + | 21.5359i | −0.440980 | + | 0.763799i | ||||
\(796\) | 11.6259 | + | 20.1367i | 0.412069 | + | 0.713725i | ||||
\(797\) | −23.8046 | −0.843202 | −0.421601 | − | 0.906782i | \(-0.638532\pi\) | ||||
−0.421601 | + | 0.906782i | \(0.638532\pi\) | |||||||
\(798\) | −0.785744 | + | 7.93610i | −0.0278150 | + | 0.280935i | ||||
\(799\) | − | 7.13883i | − | 0.252554i | ||||||
\(800\) | −0.555899 | − | 0.962845i | −0.0196540 | − | 0.0340417i | ||||
\(801\) | −5.19399 | + | 8.99626i | −0.183521 | + | 0.317867i | ||||
\(802\) | 3.68834 | + | 2.12946i | 0.130240 | + | 0.0751940i | ||||
\(803\) | 2.43447 | + | 4.21663i | 0.0859106 | + | 0.148801i | ||||
\(804\) | 13.9067 | 0.490453 | ||||||||
\(805\) | 4.91666 | + | 30.9811i | 0.173290 | + | 1.09194i | ||||
\(806\) | 13.0367 | 0.459198 | ||||||||
\(807\) | −5.04997 | − | 8.74681i | −0.177768 | − | 0.307902i | ||||
\(808\) | 6.16770 | + | 3.56092i | 0.216979 | + | 0.125273i | ||||
\(809\) | 25.5237 | − | 44.2084i | 0.897366 | − | 1.55428i | 0.0665172 | − | 0.997785i | \(-0.478811\pi\) |
0.830849 | − | 0.556498i | \(-0.187855\pi\) | |||||||
\(810\) | −2.68135 | − | 4.64424i | −0.0942131 | − | 0.163182i | ||||
\(811\) | − | 48.7844i | − | 1.71305i | −0.516104 | − | 0.856526i | \(-0.672618\pi\) | ||
0.516104 | − | 0.856526i | \(-0.327382\pi\) | |||||||
\(812\) | −9.80652 | − | 21.6730i | −0.344141 | − | 0.760573i | ||||
\(813\) | 0.483559 | 0.0169591 | ||||||||
\(814\) | −0.908058 | − | 1.57280i | −0.0318274 | − | 0.0551267i | ||||
\(815\) | −3.07365 | + | 5.32371i | −0.107665 | + | 0.186482i | ||||
\(816\) | 4.53435 | + | 2.61791i | 0.158734 | + | 0.0916450i | ||||
\(817\) | 27.8065 | − | 16.0541i | 0.972828 | − | 0.561662i | ||||
\(818\) | 7.41636i | 0.259307i | ||||||||
\(819\) | −1.33918 | + | 13.5258i | −0.0467947 | + | 0.472631i | ||||
\(820\) | − | 8.39177i | − | 0.293053i | ||||||
\(821\) | −0.368516 | − | 0.638289i | −0.0128613 | − | 0.0222764i | 0.859523 | − | 0.511097i | \(-0.170761\pi\) |
−0.872384 | + | 0.488820i | \(0.837427\pi\) | |||||||
\(822\) | 0.964232 | − | 1.67010i | 0.0336315 | − | 0.0582514i | ||||
\(823\) | −25.2931 | + | 43.8089i | −0.881662 | + | 1.52708i | −0.0321698 | + | 0.999482i | \(0.510242\pi\) |
−0.849492 | + | 0.527601i | \(0.823092\pi\) | |||||||
\(824\) | −6.95337 | − | 12.0436i | −0.242232 | − | 0.419558i | ||||
\(825\) | −1.71851 | −0.0598310 | ||||||||
\(826\) | 20.9459 | + | 15.0259i | 0.728802 | + | 0.522817i | ||||
\(827\) | 18.2125i | 0.633310i | 0.948541 | + | 0.316655i | \(0.102560\pi\) | ||||
−0.948541 | + | 0.316655i | \(0.897440\pi\) | |||||||
\(828\) | −1.83838 | − | 7.02151i | −0.0638883 | − | 0.244014i | ||||
\(829\) | 21.2080 | + | 12.2444i | 0.736585 | + | 0.425267i | 0.820826 | − | 0.571178i | \(-0.193513\pi\) |
−0.0842416 | + | 0.996445i | \(0.526847\pi\) | |||||||
\(830\) | −6.44227 | + | 11.1583i | −0.223615 | + | 0.387312i | ||||
\(831\) | 18.4983 | − | 10.6800i | 0.641697 | − | 0.370484i | ||||
\(832\) | 3.39445i | 0.117681i | ||||||||
\(833\) | 29.4765 | + | 5.89465i | 1.02130 | + | 0.204237i | ||||
\(834\) | −17.2648 | −0.597833 | ||||||||
\(835\) | −17.5600 | + | 10.1382i | −0.607687 | + | 0.350848i | ||||
\(836\) | −2.71426 | − | 1.56708i | −0.0938745 | − | 0.0541985i | ||||
\(837\) | 10.5674 | − | 18.3033i | 0.365262 | − | 0.632653i | ||||
\(838\) | −16.5703 | − | 28.7006i | −0.572412 | − | 0.991447i | ||||
\(839\) | 20.0986 | 0.693881 | 0.346940 | − | 0.937887i | \(-0.387221\pi\) | ||||
0.346940 | + | 0.937887i | \(0.387221\pi\) | |||||||
\(840\) | −6.47999 | − | 4.64852i | −0.223581 | − | 0.160389i | ||||
\(841\) | 51.8409 | 1.78762 | ||||||||
\(842\) | −24.8403 | + | 14.3415i | −0.856052 | + | 0.494242i | ||||
\(843\) | −12.4638 | + | 21.5879i | −0.429276 | + | 0.743528i | ||||
\(844\) | 3.81444 | − | 6.60681i | 0.131299 | − | 0.227416i | ||||
\(845\) | 1.82661 | + | 3.16378i | 0.0628373 | + | 0.108837i | ||||
\(846\) | − | 2.51593i | − | 0.0864996i | ||||||
\(847\) | 24.7301 | + | 2.44850i | 0.849736 | + | 0.0841313i | ||||
\(848\) | − | 8.25004i | − | 0.283308i | ||||||
\(849\) | −14.7964 | + | 8.54272i | −0.507812 | + | 0.293185i | ||||
\(850\) | −2.38720 | + | 4.13475i | −0.0818802 | + | 0.141821i | ||||
\(851\) | −4.83010 | − | 4.88573i | −0.165574 | − | 0.167481i | ||||
\(852\) | 10.6677 | − | 6.15900i | 0.365469 | − | 0.211004i | ||||
\(853\) | − | 28.1854i | − | 0.965050i | −0.875882 | − | 0.482525i | \(-0.839720\pi\) | ||
0.875882 | − | 0.482525i | \(-0.160280\pi\) | |||||||
\(854\) | −10.0765 | − | 22.2697i | −0.344812 | − | 0.762054i | ||||
\(855\) | 9.24982 | 0.316337 | ||||||||
\(856\) | −5.07809 | + | 2.93183i | −0.173565 | + | 0.100208i | ||||
\(857\) | −45.4805 | − | 26.2582i | −1.55358 | − | 0.896962i | −0.997846 | − | 0.0656045i | \(-0.979102\pi\) |
−0.555738 | − | 0.831357i | \(-0.687564\pi\) | |||||||
\(858\) | 4.54388 | + | 2.62341i | 0.155126 | + | 0.0895618i | ||||
\(859\) | −8.57908 | + | 4.95314i | −0.292715 | + | 0.168999i | −0.639165 | − | 0.769069i | \(-0.720720\pi\) |
0.346451 | + | 0.938068i | \(0.387387\pi\) | |||||||
\(860\) | 32.1082i | 1.09488i | ||||||||
\(861\) | −4.51399 | − | 9.97618i | −0.153836 | − | 0.339987i | ||||
\(862\) | − | 24.5733i | − | 0.836970i | ||||||
\(863\) | −3.48933 | − | 6.04369i | −0.118778 | − | 0.205730i | 0.800506 | − | 0.599325i | \(-0.204564\pi\) |
−0.919284 | + | 0.393596i | \(0.871231\pi\) | |||||||
\(864\) | 4.76573 | + | 2.75150i | 0.162134 | + | 0.0936078i | ||||
\(865\) | 37.6204 | + | 21.7201i | 1.27913 | + | 0.738507i | ||||
\(866\) | 12.1632 | + | 21.0673i | 0.413323 | + | 0.715897i | ||||
\(867\) | − | 1.75695i | − | 0.0596691i | ||||||
\(868\) | 1.00116 | − | 10.1118i | 0.0339816 | − | 0.343218i | ||||
\(869\) | 9.42950 | 0.319874 | ||||||||
\(870\) | 23.4705 | − | 13.5507i | 0.795724 | − | 0.459412i | ||||
\(871\) | 19.3585 | − | 33.5300i | 0.655939 | − | 1.13612i | ||||
\(872\) | 12.3456 | + | 7.12772i | 0.418074 | + | 0.241375i | ||||
\(873\) | 4.91803 | + | 8.51827i | 0.166450 | + | 0.288300i | ||||
\(874\) | −11.4345 | − | 3.13415i | −0.386779 | − | 0.106014i | ||||
\(875\) | −14.8242 | + | 20.6648i | −0.501150 | + | 0.698598i | ||||
\(876\) | −4.68264 | −0.158212 | ||||||||
\(877\) | 19.5669 | + | 33.8909i | 0.660728 | + | 1.14441i | 0.980425 | + | 0.196894i | \(0.0630855\pi\) |
−0.319697 | + | 0.947520i | \(0.603581\pi\) | |||||||
\(878\) | −3.93526 | − | 2.27202i | −0.132808 | − | 0.0766770i | ||||
\(879\) | 4.52481 | + | 2.61240i | 0.152618 | + | 0.0881140i | ||||
\(880\) | 2.71426 | − | 1.56708i | 0.0914976 | − | 0.0528261i | ||||
\(881\) | 16.1961 | 0.545660 | 0.272830 | − | 0.962062i | \(-0.412040\pi\) | ||||
0.272830 | + | 0.962062i | \(0.412040\pi\) | |||||||
\(882\) | 10.3884 | + | 2.07745i | 0.349795 | + | 0.0699512i | ||||
\(883\) | 3.29018 | 0.110723 | 0.0553617 | − | 0.998466i | \(-0.482369\pi\) | ||||
0.0553617 | + | 0.998466i | \(0.482369\pi\) | |||||||
\(884\) | 12.6239 | − | 7.28839i | 0.424586 | − | 0.245135i | ||||
\(885\) | −14.6841 | + | 25.4336i | −0.493601 | + | 0.854942i | ||||
\(886\) | 10.2326 | − | 17.7234i | 0.343771 | − | 0.595429i | ||||
\(887\) | −11.9436 | + | 6.89564i | −0.401027 | + | 0.231533i | −0.686927 | − | 0.726726i | \(-0.741041\pi\) |
0.285900 | + | 0.958259i | \(0.407707\pi\) | |||||||
\(888\) | 1.74662 | 0.0586129 | ||||||||
\(889\) | −3.07075 | + | 4.28059i | −0.102990 | + | 0.143566i | ||||
\(890\) | −16.9688 | −0.568796 | ||||||||
\(891\) | 2.38158 | − | 1.37501i | 0.0797860 | − | 0.0460645i | ||||
\(892\) | 7.26131 | + | 4.19232i | 0.243127 | + | 0.140369i | ||||
\(893\) | −3.55918 | − | 2.05489i | −0.119103 | − | 0.0687644i | ||||
\(894\) | −1.54571 | − | 2.67724i | −0.0516962 | − | 0.0895405i | ||||
\(895\) | −16.1026 | −0.538249 | ||||||||
\(896\) | 2.63288 | + | 0.260678i | 0.0879583 | + | 0.00870865i | ||||
\(897\) | 19.1423 | + | 5.24683i | 0.639144 | + | 0.175186i | ||||
\(898\) | 15.7460 | + | 27.2730i | 0.525452 | + | 0.910110i | ||||
\(899\) | 29.9051 | + | 17.2657i | 0.997390 | + | 0.575843i | ||||
\(900\) | −0.841318 | + | 1.45721i | −0.0280439 | + | 0.0485735i | ||||
\(901\) | −30.6817 | + | 17.7141i | −1.02215 | + | 0.590141i | ||||
\(902\) | 4.30333 | 0.143285 | ||||||||
\(903\) | 17.2712 | + | 38.1704i | 0.574750 | + | 1.27023i | ||||
\(904\) | 15.6954i | 0.522021i | ||||||||
\(905\) | 12.6585 | + | 21.9252i | 0.420784 | + | 0.728819i | ||||
\(906\) | 8.47557 | + | 4.89337i | 0.281582 | + | 0.162571i | ||||
\(907\) | −10.0175 | − | 5.78359i | −0.332625 | − | 0.192041i | 0.324381 | − | 0.945926i | \(-0.394844\pi\) |
−0.657006 | + | 0.753885i | \(0.728177\pi\) | |||||||
\(908\) | 6.49463 | + | 11.2490i | 0.215532 | + | 0.373312i | ||||
\(909\) | − | 10.7785i | − | 0.357499i | ||||||
\(910\) | −20.2282 | + | 9.15278i | −0.670558 | + | 0.303412i | ||||
\(911\) | 52.9276i | 1.75357i | 0.480882 | + | 0.876785i | \(0.340317\pi\) | ||||
−0.480882 | + | 0.876785i | \(0.659683\pi\) | |||||||
\(912\) | 2.61040 | − | 1.50711i | 0.0864389 | − | 0.0499055i | ||||
\(913\) | −5.72204 | − | 3.30362i | −0.189372 | − | 0.109334i | ||||
\(914\) | −9.36053 | − | 5.40430i | −0.309619 | − | 0.178758i | ||||
\(915\) | 24.1167 | − | 13.9238i | 0.797274 | − | 0.460306i | ||||
\(916\) | 3.10045 | 0.102442 | ||||||||
\(917\) | −2.95581 | + | 29.8540i | −0.0976095 | + | 0.985867i | ||||
\(918\) | − | 23.6315i | − | 0.779956i | ||||||
\(919\) | −1.20381 | + | 0.695019i | −0.0397100 | + | 0.0229266i | −0.519724 | − | 0.854334i | \(-0.673965\pi\) |
0.480014 | + | 0.877261i | \(0.340632\pi\) | |||||||
\(920\) | 8.43152 | − | 8.33552i | 0.277979 | − | 0.274814i | ||||
\(921\) | −18.2460 | + | 31.6031i | −0.601228 | + | 1.04136i | ||||
\(922\) | 31.5057 | − | 18.1898i | 1.03758 | − | 0.599050i | ||||
\(923\) | − | 34.2940i | − | 1.12880i | ||||||
\(924\) | 2.38378 | − | 3.32296i | 0.0784206 | − | 0.109317i | ||||
\(925\) | 1.59270i | 0.0523676i | ||||||||
\(926\) | −12.8172 | − | 22.2001i | −0.421200 | − | 0.729539i | ||||
\(927\) | −10.5235 | + | 18.2272i | −0.345636 | + | 0.598660i | ||||
\(928\) | −4.49558 | + | 7.78657i | −0.147575 | + | 0.255607i | ||||
\(929\) | 14.2728 | − | 8.24038i | 0.468274 | − | 0.270358i | −0.247243 | − | 0.968953i | \(-0.579525\pi\) |
0.715517 | + | 0.698596i | \(0.246191\pi\) | |||||||
\(930\) | 11.5764 | 0.379606 | ||||||||
\(931\) | 11.4236 | − | 12.9992i | 0.374393 | − | 0.426032i | ||||
\(932\) | −24.8363 | −0.813541 | ||||||||
\(933\) | 3.40473 | + | 5.89716i | 0.111466 | + | 0.193064i | ||||
\(934\) | −18.2010 | + | 31.5251i | −0.595556 | + | 1.03153i | ||||
\(935\) | −11.6558 | − | 6.72950i | −0.381186 | − | 0.220078i | ||||
\(936\) | 4.44902 | − | 2.56864i | 0.145421 | − | 0.0839587i | ||||
\(937\) | 41.9928 | 1.37184 | 0.685922 | − | 0.727675i | \(-0.259399\pi\) | ||||
0.685922 | + | 0.727675i | \(0.259399\pi\) | |||||||
\(938\) | −24.5206 | − | 17.5903i | −0.800627 | − | 0.574342i | ||||
\(939\) | − | 10.7976i | − | 0.352366i | ||||||
\(940\) | 3.55918 | − | 2.05489i | 0.116088 | − | 0.0670233i | ||||
\(941\) | −16.7249 | + | 28.9683i | −0.545216 | + | 0.944341i | 0.453378 | + | 0.891319i | \(0.350219\pi\) |
−0.998593 | + | 0.0530227i | \(0.983114\pi\) | |||||||
\(942\) | 20.2764 | + | 11.7066i | 0.660642 | + | 0.381422i | ||||
\(943\) | 15.7484 | − | 4.12326i | 0.512837 | − | 0.134272i | ||||
\(944\) | − | 9.74319i | − | 0.317114i | ||||||
\(945\) | −3.54640 | + | 35.8191i | −0.115365 | + | 1.16519i | ||||
\(946\) | −16.4652 | −0.535330 | ||||||||
\(947\) | 5.02687 | + | 8.70680i | 0.163351 | + | 0.282933i | 0.936069 | − | 0.351817i | \(-0.114436\pi\) |
−0.772717 | + | 0.634750i | \(0.781103\pi\) | |||||||
\(948\) | −4.53435 | + | 7.85372i | −0.147269 | + | 0.255077i | ||||
\(949\) | −6.51835 | + | 11.2901i | −0.211595 | + | 0.366493i | ||||
\(950\) | 1.37430 | + | 2.38035i | 0.0445880 | + | 0.0772288i | ||||
\(951\) | − | 23.2249i | − | 0.753119i | ||||||
\(952\) | −4.68373 | − | 10.3513i | −0.151801 | − | 0.335488i | ||||
\(953\) | 19.7821i | 0.640806i | 0.947281 | + | 0.320403i | \(0.103818\pi\) | ||||
−0.947281 | + | 0.320403i | \(0.896182\pi\) | |||||||
\(954\) | −10.8131 | + | 6.24296i | −0.350088 | + | 0.202123i | ||||
\(955\) | 21.0496 | + | 12.1530i | 0.681151 | + | 0.393263i | ||||
\(956\) | 12.3351 | − | 21.3650i | 0.398945 | − | 0.690992i | ||||
\(957\) | 6.94885 | + | 12.0358i | 0.224624 | + | 0.389061i | ||||
\(958\) | 3.91154 | 0.126376 | ||||||||
\(959\) | −3.81262 | + | 1.72512i | −0.123116 | + | 0.0557070i | ||||
\(960\) | 3.01423i | 0.0972838i | ||||||||
\(961\) | −8.12491 | − | 14.0728i | −0.262094 | − | 0.453960i | ||||
\(962\) | 2.43135 | − | 4.21122i | 0.0783898 | − | 0.135775i | ||||
\(963\) | 7.68536 | + | 4.43715i | 0.247657 | + | 0.142985i | ||||
\(964\) | −10.0757 | − | 17.4516i | −0.324516 | − | 0.562078i | ||||
\(965\) | 19.4922 | 0.627477 | ||||||||
\(966\) | 5.53970 | − | 14.4447i | 0.178237 | − | 0.464749i | ||||
\(967\) | 39.6200 | 1.27409 | 0.637047 | − | 0.770825i | \(-0.280156\pi\) | ||||
0.637047 | + | 0.770825i | \(0.280156\pi\) | |||||||
\(968\) | −4.69640 | − | 8.13440i | −0.150948 | − | 0.261449i | ||||
\(969\) | −11.2098 | − | 6.47200i | −0.360112 | − | 0.207911i | ||||
\(970\) | −8.03362 | + | 13.9146i | −0.257944 | + | 0.446772i | ||||
\(971\) | −23.8065 | − | 41.2340i | −0.763987 | − | 1.32326i | −0.940781 | − | 0.339016i | \(-0.889906\pi\) |
0.176794 | − | 0.984248i | \(-0.443427\pi\) | |||||||
\(972\) | − | 13.8642i | − | 0.444694i | ||||||
\(973\) | 30.4417 | + | 21.8378i | 0.975916 | + | 0.700089i | ||||
\(974\) | −30.3901 | −0.973763 | ||||||||
\(975\) | −2.30068 | − | 3.98490i | −0.0736808 | − | 0.127619i | ||||
\(976\) | −4.61935 | + | 8.00096i | −0.147862 | + | 0.256104i | ||||
\(977\) | 0.251904 | + | 0.145437i | 0.00805912 | + | 0.00465293i | 0.504024 | − | 0.863690i | \(-0.331852\pi\) |
−0.495965 | + | 0.868342i | \(0.665186\pi\) | |||||||
\(978\) | 2.62556 | − | 1.51587i | 0.0839561 | − | 0.0484721i | ||||
\(979\) | − | 8.70168i | − | 0.278107i | ||||||
\(980\) | 5.54585 | + | 16.3927i | 0.177156 | + | 0.523647i | ||||
\(981\) | − | 21.5747i | − | 0.688828i | ||||||
\(982\) | 10.1495 | + | 17.5795i | 0.323884 | + | 0.560983i | ||||
\(983\) | −15.7179 | + | 27.2242i | −0.501323 | + | 0.868317i | 0.498676 | + | 0.866789i | \(0.333820\pi\) |
−0.999999 | + | 0.00152833i | \(0.999514\pi\) | |||||||
\(984\) | −2.06934 | + | 3.58419i | −0.0659680 | + | 0.114260i | ||||
\(985\) | −7.36795 | − | 12.7617i | −0.234762 | − | 0.406620i | ||||
\(986\) | 38.6107 | 1.22962 | ||||||||
\(987\) | 3.12583 | − | 4.35737i | 0.0994963 | − | 0.138697i | ||||
\(988\) | − | 8.39177i | − | 0.266978i | ||||||
\(989\) | −60.2557 | + | 15.7762i | −1.91602 | + | 0.501656i | ||||
\(990\) | −4.10786 | − | 2.37167i | −0.130556 | − | 0.0753767i | ||||
\(991\) | 6.83645 | − | 11.8411i | 0.217167 | − | 0.376144i | −0.736774 | − | 0.676139i | \(-0.763652\pi\) |
0.953941 | + | 0.299995i | \(0.0969850\pi\) | |||||||
\(992\) | −3.32605 | + | 1.92030i | −0.105602 | + | 0.0609695i | ||||
\(993\) | − | 3.17250i | − | 0.100676i | ||||||
\(994\) | −26.5998 | − | 2.63362i | −0.843696 | − | 0.0835333i | ||||
\(995\) | 57.4832 | 1.82234 | ||||||||
\(996\) | 5.50310 | − | 3.17721i | 0.174372 | − | 0.100674i | ||||
\(997\) | −8.61882 | − | 4.97608i | −0.272961 | − | 0.157594i | 0.357272 | − | 0.934001i | \(-0.383707\pi\) |
−0.630232 | + | 0.776407i | \(0.717040\pi\) | |||||||
\(998\) | −3.40473 | + | 5.89716i | −0.107775 | + | 0.186671i | ||||
\(999\) | −3.94164 | − | 6.82712i | −0.124708 | − | 0.216001i |
(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 | 322.2.g.a.45.6 | yes | 16 | |
7.3 | odd | 6 | 2254.2.c.c.2253.12 | 16 | |||
7.4 | even | 3 | 2254.2.c.c.2253.5 | 16 | |||
7.5 | odd | 6 | inner | 322.2.g.a.229.5 | yes | 16 | |
23.22 | odd | 2 | inner | 322.2.g.a.45.5 | ✓ | 16 | |
161.45 | even | 6 | 2254.2.c.c.2253.11 | 16 | |||
161.68 | even | 6 | inner | 322.2.g.a.229.6 | yes | 16 | |
161.137 | odd | 6 | 2254.2.c.c.2253.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.2.g.a.45.5 | ✓ | 16 | 23.22 | odd | 2 | inner | |
322.2.g.a.45.6 | yes | 16 | 1.1 | even | 1 | trivial | |
322.2.g.a.229.5 | yes | 16 | 7.5 | odd | 6 | inner | |
322.2.g.a.229.6 | yes | 16 | 161.68 | even | 6 | inner | |
2254.2.c.c.2253.5 | 16 | 7.4 | even | 3 | |||
2254.2.c.c.2253.6 | 16 | 161.137 | odd | 6 | |||
2254.2.c.c.2253.11 | 16 | 161.45 | even | 6 | |||
2254.2.c.c.2253.12 | 16 | 7.3 | odd | 6 |