Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(24,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 16]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.24");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.u (of order \(18\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 24.4 | ||
Character | \(\chi\) | \(=\) | 475.24 |
Dual form | 475.2.u.c.99.4 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{8}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.408399 | + | 1.12207i | 0.288782 | + | 0.793421i | 0.996238 | + | 0.0866635i | \(0.0276205\pi\) |
−0.707456 | + | 0.706757i | \(0.750157\pi\) | |||||||
\(3\) | −2.23864 | − | 0.394733i | −1.29248 | − | 0.227899i | −0.515210 | − | 0.857064i | \(-0.672286\pi\) |
−0.777272 | + | 0.629165i | \(0.783397\pi\) | |||||||
\(4\) | 0.439845 | − | 0.369074i | 0.219923 | − | 0.184537i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.471342 | − | 2.67312i | −0.192425 | − | 1.09129i | ||||
\(7\) | −1.90222 | + | 1.09825i | −0.718970 | + | 0.415098i | −0.814374 | − | 0.580341i | \(-0.802919\pi\) |
0.0954033 | + | 0.995439i | \(0.469586\pi\) | |||||||
\(8\) | 2.66196 | + | 1.53688i | 0.941146 | + | 0.543371i | ||||
\(9\) | 2.03663 | + | 0.741274i | 0.678878 | + | 0.247091i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.41324 | − | 2.44780i | 0.426108 | − | 0.738040i | −0.570415 | − | 0.821356i | \(-0.693218\pi\) |
0.996523 | + | 0.0833161i | \(0.0265511\pi\) | |||||||
\(12\) | −1.13034 | + | 0.652604i | −0.326302 | + | 0.188391i | ||||
\(13\) | 4.01920 | − | 0.708694i | 1.11473 | − | 0.196556i | 0.414202 | − | 0.910185i | \(-0.364061\pi\) |
0.700524 | + | 0.713628i | \(0.252949\pi\) | |||||||
\(14\) | −2.00917 | − | 1.68589i | −0.536972 | − | 0.450573i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.437935 | + | 2.48365i | −0.109484 | + | 0.620913i | ||||
\(17\) | −0.130867 | − | 0.359555i | −0.0317400 | − | 0.0872049i | 0.922810 | − | 0.385254i | \(-0.125886\pi\) |
−0.954550 | + | 0.298049i | \(0.903664\pi\) | |||||||
\(18\) | 2.58797i | 0.609992i | ||||||||
\(19\) | 2.75520 | + | 3.37770i | 0.632087 | + | 0.774898i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.69190 | − | 1.70771i | 1.02386 | − | 0.372653i | ||||
\(22\) | 3.32376 | + | 0.586069i | 0.708628 | + | 0.124950i | ||||
\(23\) | 1.91290 | + | 2.27970i | 0.398867 | + | 0.475351i | 0.927674 | − | 0.373391i | \(-0.121805\pi\) |
−0.528807 | + | 0.848742i | \(0.677361\pi\) | |||||||
\(24\) | −5.35253 | − | 4.49130i | −1.09258 | − | 0.916783i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.43664 | + | 4.22038i | 0.477864 | + | 0.827686i | ||||
\(27\) | 1.63920 | + | 0.946391i | 0.315464 | + | 0.182133i | ||||
\(28\) | −0.431347 | + | 1.18512i | −0.0815170 | + | 0.223966i | ||||
\(29\) | 8.05787 | + | 2.93282i | 1.49631 | + | 0.544612i | 0.955102 | − | 0.296278i | \(-0.0957454\pi\) |
0.541207 | + | 0.840889i | \(0.317968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.34622 | + | 4.06377i | 0.421393 | + | 0.729874i | 0.996076 | − | 0.0885019i | \(-0.0282079\pi\) |
−0.574683 | + | 0.818376i | \(0.694875\pi\) | |||||||
\(32\) | 3.08847 | − | 0.544580i | 0.545969 | − | 0.0962691i | ||||
\(33\) | −4.12997 | + | 4.92191i | −0.718935 | + | 0.856794i | ||||
\(34\) | 0.349999 | − | 0.293684i | 0.0600243 | − | 0.0503663i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.16939 | − | 0.425623i | 0.194898 | − | 0.0709372i | ||||
\(37\) | − | 10.7694i | − | 1.77048i | −0.465131 | − | 0.885242i | \(-0.653993\pi\) | ||
0.465131 | − | 0.885242i | \(-0.346007\pi\) | |||||||
\(38\) | −2.66478 | + | 4.47097i | −0.432285 | + | 0.725287i | ||||
\(39\) | −9.27731 | −1.48556 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.544445 | − | 3.08770i | 0.0850280 | − | 0.482218i | −0.912323 | − | 0.409472i | \(-0.865713\pi\) |
0.997351 | − | 0.0727454i | \(-0.0231760\pi\) | |||||||
\(42\) | 3.83233 | + | 4.56720i | 0.591342 | + | 0.704734i | ||||
\(43\) | 1.29137 | − | 1.53900i | 0.196933 | − | 0.234695i | −0.658537 | − | 0.752549i | \(-0.728824\pi\) |
0.855469 | + | 0.517853i | \(0.173269\pi\) | |||||||
\(44\) | −0.281814 | − | 1.59824i | −0.0424850 | − | 0.240944i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.77675 | + | 3.07743i | −0.261968 | + | 0.453742i | ||||
\(47\) | −3.72722 | + | 10.2405i | −0.543671 | + | 1.49372i | 0.298444 | + | 0.954427i | \(0.403532\pi\) |
−0.842115 | + | 0.539297i | \(0.818690\pi\) | |||||||
\(48\) | 1.96076 | − | 5.38714i | 0.283011 | − | 0.777567i | ||||
\(49\) | −1.08771 | + | 1.88398i | −0.155388 | + | 0.269140i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.151037 | + | 0.856574i | 0.0211494 | + | 0.119944i | ||||
\(52\) | 1.50627 | − | 1.79510i | 0.208882 | − | 0.248936i | ||||
\(53\) | −4.80532 | − | 5.72676i | −0.660062 | − | 0.786631i | 0.327333 | − | 0.944909i | \(-0.393850\pi\) |
−0.987395 | + | 0.158278i | \(0.949406\pi\) | |||||||
\(54\) | −0.392467 | + | 2.22579i | −0.0534080 | + | 0.302892i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.75150 | −0.902208 | ||||||||
\(57\) | −4.83463 | − | 8.64904i | −0.640362 | − | 1.14559i | ||||
\(58\) | 10.2392i | 1.34448i | ||||||||
\(59\) | −12.1961 | + | 4.43900i | −1.58779 | + | 0.577909i | −0.976880 | − | 0.213789i | \(-0.931419\pi\) |
−0.610912 | + | 0.791698i | \(0.709197\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.57784 | − | 3.84126i | 0.586132 | − | 0.491823i | −0.300822 | − | 0.953680i | \(-0.597261\pi\) |
0.886954 | + | 0.461857i | \(0.152817\pi\) | |||||||
\(62\) | −3.60163 | + | 4.29225i | −0.457407 | + | 0.545116i | ||||
\(63\) | −4.68822 | + | 0.826660i | −0.590660 | + | 0.104149i | ||||
\(64\) | 4.39435 | + | 7.61123i | 0.549294 | + | 0.951404i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.20938 | − | 2.62400i | −0.887413 | − | 0.322992i | ||||
\(67\) | 0.358925 | − | 0.986138i | 0.0438496 | − | 0.120476i | −0.915835 | − | 0.401555i | \(-0.868470\pi\) |
0.959685 | + | 0.281079i | \(0.0906922\pi\) | |||||||
\(68\) | −0.190264 | − | 0.109849i | −0.0230729 | − | 0.0133211i | ||||
\(69\) | −3.38242 | − | 5.85853i | −0.407196 | − | 0.705284i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.99626 | − | 5.03146i | −0.711625 | − | 0.597124i | 0.213430 | − | 0.976958i | \(-0.431537\pi\) |
−0.925055 | + | 0.379834i | \(0.875981\pi\) | |||||||
\(72\) | 4.28219 | + | 5.10332i | 0.504661 | + | 0.601432i | ||||
\(73\) | 13.8755 | + | 2.44663i | 1.62401 | + | 0.286357i | 0.910258 | − | 0.414042i | \(-0.135883\pi\) |
0.713752 | + | 0.700399i | \(0.246995\pi\) | |||||||
\(74\) | 12.0840 | − | 4.39822i | 1.40474 | − | 0.511283i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.45848 | + | 0.468792i | 0.282008 | + | 0.0537741i | ||||
\(77\) | 6.20833i | 0.707505i | ||||||||
\(78\) | −3.78884 | − | 10.4098i | −0.429002 | − | 1.17867i | ||||
\(79\) | 2.33355 | − | 13.2342i | 0.262545 | − | 1.48897i | −0.513390 | − | 0.858156i | \(-0.671610\pi\) |
0.775935 | − | 0.630813i | \(-0.217278\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.27685 | − | 6.94510i | −0.919650 | − | 0.771678i | ||||
\(82\) | 3.68695 | − | 0.650110i | 0.407156 | − | 0.0717926i | ||||
\(83\) | 4.81175 | − | 2.77807i | 0.528158 | − | 0.304932i | −0.212108 | − | 0.977246i | \(-0.568033\pi\) |
0.740266 | + | 0.672314i | \(0.234699\pi\) | |||||||
\(84\) | 1.43344 | − | 2.48279i | 0.156401 | − | 0.270894i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.25425 | + | 0.820481i | 0.243082 | + | 0.0884748i | ||||
\(87\) | −16.8810 | − | 9.74626i | −1.80984 | − | 1.04491i | ||||
\(88\) | 7.52398 | − | 4.34397i | 0.802059 | − | 0.463069i | ||||
\(89\) | 1.13984 | + | 6.46435i | 0.120823 | + | 0.685220i | 0.983702 | + | 0.179809i | \(0.0575479\pi\) |
−0.862879 | + | 0.505411i | \(0.831341\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.86708 | + | 5.76216i | −0.719865 | + | 0.604039i | ||||
\(92\) | 1.68276 | + | 0.296716i | 0.175440 | + | 0.0309347i | ||||
\(93\) | −3.64824 | − | 10.0235i | −0.378305 | − | 1.03938i | ||||
\(94\) | −13.0127 | −1.34215 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.12895 | −0.727595 | ||||||||
\(97\) | −4.94091 | − | 13.5750i | −0.501673 | − | 1.37834i | −0.889640 | − | 0.456663i | \(-0.849045\pi\) |
0.387966 | − | 0.921674i | \(-0.373178\pi\) | |||||||
\(98\) | −2.55817 | − | 0.451074i | −0.258414 | − | 0.0455654i | ||||
\(99\) | 4.69275 | − | 3.93768i | 0.471639 | − | 0.395752i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.738074 | + | 4.18582i | 0.0734411 | + | 0.416505i | 0.999257 | + | 0.0385313i | \(0.0122679\pi\) |
−0.925816 | + | 0.377974i | \(0.876621\pi\) | |||||||
\(102\) | −0.899449 | + | 0.519297i | −0.0890587 | + | 0.0514181i | ||||
\(103\) | −12.7051 | − | 7.33528i | −1.25187 | − | 0.722767i | −0.280389 | − | 0.959887i | \(-0.590463\pi\) |
−0.971481 | + | 0.237119i | \(0.923797\pi\) | |||||||
\(104\) | 11.7882 | + | 4.29054i | 1.15592 | + | 0.420722i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.46332 | − | 7.73070i | 0.433516 | − | 0.750872i | ||||
\(107\) | −5.35244 | + | 3.09023i | −0.517439 | + | 0.298744i | −0.735886 | − | 0.677105i | \(-0.763234\pi\) |
0.218447 | + | 0.975849i | \(0.429901\pi\) | |||||||
\(108\) | 1.07028 | − | 0.188720i | 0.102988 | − | 0.0181595i | ||||
\(109\) | −0.577493 | − | 0.484574i | −0.0553138 | − | 0.0464138i | 0.614712 | − | 0.788752i | \(-0.289272\pi\) |
−0.670025 | + | 0.742338i | \(0.733717\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.25105 | + | 24.1089i | −0.403492 | + | 2.28832i | ||||
\(112\) | −1.89461 | − | 5.20540i | −0.179024 | − | 0.491864i | ||||
\(113\) | − | 0.870003i | − | 0.0818430i | −0.999162 | − | 0.0409215i | \(-0.986971\pi\) | ||
0.999162 | − | 0.0409215i | \(-0.0130294\pi\) | |||||||
\(114\) | 7.73034 | − | 8.95703i | 0.724013 | − | 0.838903i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.62665 | − | 1.68396i | 0.429573 | − | 0.156352i | ||||
\(117\) | 8.71099 | + | 1.53598i | 0.805331 | + | 0.142002i | ||||
\(118\) | −9.96171 | − | 11.8719i | −0.917050 | − | 1.09290i | ||||
\(119\) | 0.643818 | + | 0.540227i | 0.0590187 | + | 0.0495225i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.50551 | + | 2.60762i | 0.136864 | + | 0.237056i | ||||
\(122\) | 6.17973 | + | 3.56787i | 0.559487 | + | 0.323020i | ||||
\(123\) | −2.43764 | + | 6.69735i | −0.219794 | + | 0.603880i | ||||
\(124\) | 2.53180 | + | 0.921502i | 0.227363 | + | 0.0827533i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.84223 | − | 4.92289i | −0.253206 | − | 0.438566i | ||||
\(127\) | 3.39209 | − | 0.598116i | 0.300999 | − | 0.0530743i | −0.0211090 | − | 0.999777i | \(-0.506720\pi\) |
0.322108 | + | 0.946703i | \(0.395609\pi\) | |||||||
\(128\) | −2.71395 | + | 3.23436i | −0.239882 | + | 0.285880i | ||||
\(129\) | −3.49842 | + | 2.93552i | −0.308019 | + | 0.258458i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.67954 | + | 3.52307i | −0.845706 | + | 0.307812i | −0.728288 | − | 0.685271i | \(-0.759684\pi\) |
−0.117418 | + | 0.993083i | \(0.537462\pi\) | |||||||
\(132\) | 3.68914i | 0.321099i | ||||||||
\(133\) | −8.95054 | − | 3.39923i | −0.776110 | − | 0.294751i | ||||
\(134\) | 1.25310 | 0.108251 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.204231 | − | 1.15825i | 0.0175126 | − | 0.0993191i | ||||
\(137\) | 0.943562 | + | 1.12449i | 0.0806140 | + | 0.0960720i | 0.804844 | − | 0.593487i | \(-0.202249\pi\) |
−0.724230 | + | 0.689559i | \(0.757805\pi\) | |||||||
\(138\) | 5.19228 | − | 6.18792i | 0.441996 | − | 0.526750i | ||||
\(139\) | 1.27243 | + | 7.21629i | 0.107926 | + | 0.612078i | 0.990011 | + | 0.140988i | \(0.0450281\pi\) |
−0.882085 | + | 0.471090i | \(0.843861\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.3862 | − | 21.4535i | 1.04310 | − | 1.80671i | ||||
\(142\) | 3.19677 | − | 8.78304i | 0.268267 | − | 0.737057i | ||||
\(143\) | 3.94535 | − | 10.8398i | 0.329927 | − | 0.906467i | ||||
\(144\) | −2.73298 | + | 4.73366i | −0.227748 | + | 0.394472i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.92147 | + | 16.5685i | 0.241783 | + | 1.37122i | ||||
\(147\) | 3.17868 | − | 3.78820i | 0.262173 | − | 0.312445i | ||||
\(148\) | −3.97472 | − | 4.73689i | −0.326720 | − | 0.389370i | ||||
\(149\) | −1.73507 | + | 9.84006i | −0.142142 | + | 0.806129i | 0.827475 | + | 0.561503i | \(0.189777\pi\) |
−0.969617 | + | 0.244627i | \(0.921335\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.0689 | 1.22629 | 0.613144 | − | 0.789971i | \(-0.289905\pi\) | ||||
0.613144 | + | 0.789971i | \(0.289905\pi\) | |||||||
\(152\) | 2.14311 | + | 13.2257i | 0.173829 | + | 1.07275i | ||||
\(153\) | − | 0.829291i | − | 0.0670442i | ||||||
\(154\) | −6.96616 | + | 2.53548i | −0.561349 | + | 0.204314i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.08058 | + | 3.42402i | −0.326708 | + | 0.274141i | ||||
\(157\) | −6.64935 | + | 7.92438i | −0.530676 | + | 0.632435i | −0.963070 | − | 0.269250i | \(-0.913224\pi\) |
0.432395 | + | 0.901684i | \(0.357669\pi\) | |||||||
\(158\) | 15.8027 | − | 2.78645i | 1.25720 | − | 0.221678i | ||||
\(159\) | 8.49687 | + | 14.7170i | 0.673845 | + | 1.16713i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.14242 | − | 2.23566i | −0.484090 | − | 0.176194i | ||||
\(162\) | 4.41261 | − | 12.1235i | 0.346687 | − | 0.952515i | ||||
\(163\) | −5.97565 | − | 3.45005i | −0.468049 | − | 0.270228i | 0.247373 | − | 0.968920i | \(-0.420433\pi\) |
−0.715423 | + | 0.698692i | \(0.753766\pi\) | |||||||
\(164\) | −0.900118 | − | 1.55905i | −0.0702874 | − | 0.121741i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.08229 | + | 4.26455i | 0.394462 | + | 0.330993i | ||||
\(167\) | 7.62476 | + | 9.08683i | 0.590022 | + | 0.703160i | 0.975610 | − | 0.219510i | \(-0.0704460\pi\) |
−0.385589 | + | 0.922671i | \(0.626002\pi\) | |||||||
\(168\) | 15.1142 | + | 2.66504i | 1.16609 | + | 0.205613i | ||||
\(169\) | 3.43575 | − | 1.25051i | 0.264289 | − | 0.0961932i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.10754 | + | 8.92150i | 0.237639 | + | 0.682244i | ||||
\(172\) | − | 1.15353i | − | 0.0879561i | ||||||
\(173\) | 8.68955 | + | 23.8744i | 0.660655 | + | 1.81513i | 0.573935 | + | 0.818901i | \(0.305416\pi\) |
0.0867194 | + | 0.996233i | \(0.472362\pi\) | |||||||
\(174\) | 4.04176 | − | 22.9220i | 0.306405 | − | 1.73771i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.46058 | + | 4.58197i | 0.411607 | + | 0.345379i | ||||
\(177\) | 29.0549 | − | 5.12316i | 2.18390 | − | 0.385080i | ||||
\(178\) | −6.78792 | + | 3.91901i | −0.508776 | + | 0.293742i | ||||
\(179\) | −0.194400 | + | 0.336710i | −0.0145301 | + | 0.0251669i | −0.873199 | − | 0.487364i | \(-0.837959\pi\) |
0.858669 | + | 0.512531i | \(0.171292\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.49536 | − | 1.63618i | −0.334137 | − | 0.121616i | 0.169502 | − | 0.985530i | \(-0.445784\pi\) |
−0.503640 | + | 0.863914i | \(0.668006\pi\) | |||||||
\(182\) | −9.27003 | − | 5.35206i | −0.687141 | − | 0.396721i | ||||
\(183\) | −11.7644 | + | 6.79219i | −0.869651 | + | 0.502093i | ||||
\(184\) | 1.58842 | + | 9.00838i | 0.117100 | + | 0.664107i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.75705 | − | 8.18714i | 0.715422 | − | 0.600310i | ||||
\(187\) | −1.06507 | − | 0.187800i | −0.0778854 | − | 0.0137333i | ||||
\(188\) | 2.14009 | + | 5.87984i | 0.156082 | + | 0.428831i | ||||
\(189\) | −4.15748 | −0.302412 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.8516 | −1.72584 | −0.862921 | − | 0.505338i | \(-0.831368\pi\) | ||||
−0.862921 | + | 0.505338i | \(0.831368\pi\) | |||||||
\(192\) | −6.83297 | − | 18.7734i | −0.493127 | − | 1.35486i | ||||
\(193\) | 11.0554 | + | 1.94937i | 0.795787 | + | 0.140319i | 0.556737 | − | 0.830688i | \(-0.312053\pi\) |
0.239050 | + | 0.971007i | \(0.423164\pi\) | |||||||
\(194\) | 13.2142 | − | 11.0881i | 0.948727 | − | 0.796076i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.216901 | + | 1.23011i | 0.0154929 | + | 0.0878647i | ||||
\(197\) | −14.6122 | + | 8.43639i | −1.04108 | + | 0.601068i | −0.920139 | − | 0.391592i | \(-0.871924\pi\) |
−0.120941 | + | 0.992660i | \(0.538591\pi\) | |||||||
\(198\) | 6.33485 | + | 3.65743i | 0.450198 | + | 0.259922i | ||||
\(199\) | −14.7743 | − | 5.37740i | −1.04732 | − | 0.381194i | −0.239670 | − | 0.970854i | \(-0.577039\pi\) |
−0.807651 | + | 0.589660i | \(0.799262\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.19277 | + | 2.06593i | −0.0841312 | + | 0.145720i | ||||
\(202\) | −4.39534 | + | 2.53765i | −0.309255 | + | 0.178549i | ||||
\(203\) | −18.5488 | + | 3.27065i | −1.30187 | + | 0.229555i | ||||
\(204\) | 0.382572 | + | 0.321016i | 0.0267854 | + | 0.0224756i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.04194 | − | 17.2517i | 0.211942 | − | 1.20198i | ||||
\(207\) | 2.20599 | + | 6.06090i | 0.153327 | + | 0.421262i | ||||
\(208\) | 10.2927i | 0.713668i | ||||||||
\(209\) | 12.1617 | − | 1.97069i | 0.841243 | − | 0.136316i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.72857 | − | 3.17694i | 0.600899 | − | 0.218709i | −0.0236172 | − | 0.999721i | \(-0.507518\pi\) |
0.624517 | + | 0.781012i | \(0.285296\pi\) | |||||||
\(212\) | −4.22720 | − | 0.745369i | −0.290325 | − | 0.0511922i | ||||
\(213\) | 11.4374 | + | 13.6306i | 0.783678 | + | 0.933951i | ||||
\(214\) | −5.65337 | − | 4.74374i | −0.386457 | − | 0.324276i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.90899 | + | 5.03851i | 0.197932 | + | 0.342827i | ||||
\(217\) | −8.92603 | − | 5.15344i | −0.605938 | − | 0.349839i | ||||
\(218\) | 0.307877 | − | 0.845885i | 0.0208521 | − | 0.0572906i | ||||
\(219\) | −30.0966 | − | 10.9543i | −2.03374 | − | 0.740221i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.780797 | − | 1.35238i | −0.0525221 | − | 0.0909710i | ||||
\(222\) | −28.7879 | + | 5.07609i | −1.93212 | + | 0.340685i | ||||
\(223\) | −1.79399 | + | 2.13799i | −0.120134 | + | 0.143170i | −0.822759 | − | 0.568390i | \(-0.807567\pi\) |
0.702625 | + | 0.711560i | \(0.252011\pi\) | |||||||
\(224\) | −5.27685 | + | 4.42781i | −0.352575 | + | 0.295845i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.976201 | − | 0.355308i | 0.0649359 | − | 0.0236347i | ||||
\(227\) | − | 0.844086i | − | 0.0560240i | −0.999608 | − | 0.0280120i | \(-0.991082\pi\) | ||
0.999608 | − | 0.0280120i | \(-0.00891766\pi\) | |||||||
\(228\) | −5.31862 | − | 2.01990i | −0.352235 | − | 0.133771i | ||||
\(229\) | −21.9559 | −1.45089 | −0.725444 | − | 0.688282i | \(-0.758365\pi\) | ||||
−0.725444 | + | 0.688282i | \(0.758365\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.45064 | − | 13.8982i | 0.161240 | − | 0.914438i | ||||
\(232\) | 16.9423 | + | 20.1911i | 1.11232 | + | 1.32561i | ||||
\(233\) | −2.83819 | + | 3.38242i | −0.185936 | + | 0.221590i | −0.850958 | − | 0.525234i | \(-0.823978\pi\) |
0.665022 | + | 0.746824i | \(0.268422\pi\) | |||||||
\(234\) | 1.83408 | + | 10.4016i | 0.119898 | + | 0.679974i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.72606 | + | 6.45373i | −0.242546 | + | 0.420102i | ||||
\(237\) | −10.4480 | + | 28.7056i | −0.678670 | + | 1.86463i | ||||
\(238\) | −0.343236 | + | 0.943034i | −0.0222487 | + | 0.0611278i | ||||
\(239\) | 9.91358 | − | 17.1708i | 0.641256 | − | 1.11069i | −0.343896 | − | 0.939008i | \(-0.611747\pi\) |
0.985153 | − | 0.171681i | \(-0.0549198\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.62651 | − | 20.5670i | −0.233604 | − | 1.32484i | −0.845533 | − | 0.533923i | \(-0.820717\pi\) |
0.611929 | − | 0.790913i | \(-0.290394\pi\) | |||||||
\(242\) | −2.31107 | + | 2.75423i | −0.148561 | + | 0.177049i | ||||
\(243\) | 12.1375 | + | 14.4649i | 0.778620 | + | 0.927923i | ||||
\(244\) | 0.595830 | − | 3.37912i | 0.0381441 | − | 0.216326i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.51040 | −0.542603 | ||||||||
\(247\) | 13.4675 | + | 11.6231i | 0.856915 | + | 0.739558i | ||||
\(248\) | 14.4235i | 0.915891i | ||||||||
\(249\) | −11.8684 | + | 4.31974i | −0.752129 | + | 0.273753i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.25499 | − | 3.57036i | 0.268573 | − | 0.225359i | −0.498548 | − | 0.866862i | \(-0.666133\pi\) |
0.767121 | + | 0.641503i | \(0.221689\pi\) | |||||||
\(252\) | −1.75699 | + | 2.09390i | −0.110680 | + | 0.131904i | ||||
\(253\) | 8.28364 | − | 1.46063i | 0.520788 | − | 0.0918290i | ||||
\(254\) | 2.05645 | + | 3.56188i | 0.129033 | + | 0.223492i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.7798 | + | 4.28750i | 0.736237 | + | 0.267969i | ||||
\(257\) | 6.88036 | − | 18.9036i | 0.429185 | − | 1.17918i | −0.517123 | − | 0.855911i | \(-0.672997\pi\) |
0.946308 | − | 0.323266i | \(-0.104781\pi\) | |||||||
\(258\) | −4.72260 | − | 2.72659i | −0.294016 | − | 0.169750i | ||||
\(259\) | 11.8275 | + | 20.4858i | 0.734924 | + | 1.27293i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.2369 | + | 11.9462i | 0.881242 | + | 0.739450i | ||||
\(262\) | −7.90623 | − | 9.42228i | −0.488448 | − | 0.582110i | ||||
\(263\) | −11.5304 | − | 2.03312i | −0.710995 | − | 0.125368i | −0.193558 | − | 0.981089i | \(-0.562003\pi\) |
−0.517437 | + | 0.855721i | \(0.673114\pi\) | |||||||
\(264\) | −18.5582 | + | 6.75464i | −1.14218 | + | 0.415719i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.158773 | − | 11.4313i | 0.00973499 | − | 0.700900i | ||||
\(267\) | − | 14.9213i | − | 0.913169i | ||||||
\(268\) | −0.206086 | − | 0.566218i | −0.0125887 | − | 0.0345873i | ||||
\(269\) | 2.23756 | − | 12.6898i | 0.136426 | − | 0.773712i | −0.837429 | − | 0.546545i | \(-0.815943\pi\) |
0.973856 | − | 0.227167i | \(-0.0729463\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.8097 | − | 9.90953i | −0.717389 | − | 0.601961i | 0.209273 | − | 0.977857i | \(-0.432890\pi\) |
−0.926662 | + | 0.375896i | \(0.877335\pi\) | |||||||
\(272\) | 0.950321 | − | 0.167567i | 0.0576217 | − | 0.0101603i | ||||
\(273\) | 17.6475 | − | 10.1888i | 1.06807 | − | 0.616652i | ||||
\(274\) | −0.876407 | + | 1.51798i | −0.0529457 | + | 0.0917046i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.64997 | − | 1.32848i | −0.219703 | − | 0.0799652i | ||||
\(277\) | −4.58742 | − | 2.64855i | −0.275632 | − | 0.159136i | 0.355813 | − | 0.934557i | \(-0.384204\pi\) |
−0.631444 | + | 0.775421i | \(0.717537\pi\) | |||||||
\(278\) | −7.57750 | + | 4.37487i | −0.454468 | + | 0.262387i | ||||
\(279\) | 1.76602 | + | 10.0156i | 0.105729 | + | 0.599618i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.12384 | + | 3.46031i | −0.246008 | + | 0.206425i | −0.757451 | − | 0.652892i | \(-0.773555\pi\) |
0.511443 | + | 0.859317i | \(0.329111\pi\) | |||||||
\(282\) | 29.1307 | + | 5.13653i | 1.73471 | + | 0.305876i | ||||
\(283\) | 6.04576 | + | 16.6106i | 0.359383 | + | 0.987397i | 0.979244 | + | 0.202685i | \(0.0649668\pi\) |
−0.619861 | + | 0.784712i | \(0.712811\pi\) | |||||||
\(284\) | −4.49441 | −0.266694 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.7742 | 0.814487 | ||||||||
\(287\) | 2.35540 | + | 6.47141i | 0.139035 | + | 0.381995i | ||||
\(288\) | 6.69377 | + | 1.18029i | 0.394434 | + | 0.0695494i | ||||
\(289\) | 12.9106 | − | 10.8333i | 0.759447 | − | 0.637252i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.70242 | + | 32.3400i | 0.334282 | + | 1.89581i | ||||
\(292\) | 7.00608 | − | 4.04496i | 0.410000 | − | 0.236714i | ||||
\(293\) | 4.07939 | + | 2.35524i | 0.238320 | + | 0.137594i | 0.614405 | − | 0.788991i | \(-0.289396\pi\) |
−0.376084 | + | 0.926586i | \(0.622730\pi\) | |||||||
\(294\) | 5.54878 | + | 2.01959i | 0.323611 | + | 0.117785i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 16.5514 | − | 28.6678i | 0.962029 | − | 1.66628i | ||||
\(297\) | 4.63316 | − | 2.67495i | 0.268843 | − | 0.155217i | ||||
\(298\) | −11.7498 | + | 2.07181i | −0.680648 | + | 0.120017i | ||||
\(299\) | 9.30394 | + | 7.80693i | 0.538061 | + | 0.451486i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.766273 | + | 4.34575i | −0.0441673 | + | 0.250485i | ||||
\(302\) | 6.15411 | + | 16.9083i | 0.354129 | + | 0.972962i | ||||
\(303\) | − | 9.66191i | − | 0.555062i | ||||||
\(304\) | −9.59563 | + | 5.36375i | −0.550347 | + | 0.307632i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.930520 | − | 0.338681i | 0.0531943 | − | 0.0193611i | ||||
\(307\) | 11.6265 | + | 2.05006i | 0.663557 | + | 0.117003i | 0.495275 | − | 0.868736i | \(-0.335067\pi\) |
0.168281 | + | 0.985739i | \(0.446178\pi\) | |||||||
\(308\) | 2.29134 | + | 2.73071i | 0.130561 | + | 0.155596i | ||||
\(309\) | 25.5467 | + | 21.4362i | 1.45330 | + | 1.21946i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.47006 | + | 7.74236i | 0.253474 | + | 0.439029i | 0.964480 | − | 0.264157i | \(-0.0850936\pi\) |
−0.711006 | + | 0.703186i | \(0.751760\pi\) | |||||||
\(312\) | −24.6959 | − | 14.2582i | −1.39813 | − | 0.807209i | ||||
\(313\) | 4.59349 | − | 12.6205i | 0.259639 | − | 0.713353i | −0.739550 | − | 0.673101i | \(-0.764962\pi\) |
0.999190 | − | 0.0402519i | \(-0.0128160\pi\) | |||||||
\(314\) | −11.6073 | − | 4.22470i | −0.655036 | − | 0.238414i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.85801 | − | 6.68227i | −0.217030 | − | 0.375907i | ||||
\(317\) | 10.8896 | − | 1.92013i | 0.611622 | − | 0.107845i | 0.140747 | − | 0.990046i | \(-0.455049\pi\) |
0.470875 | + | 0.882200i | \(0.343938\pi\) | |||||||
\(318\) | −13.0433 | + | 15.5445i | −0.731435 | + | 0.871690i | ||||
\(319\) | 18.5667 | − | 15.5793i | 1.03953 | − | 0.872273i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.2020 | − | 4.80514i | 0.736865 | − | 0.268197i | ||||
\(322\) | − | 7.80524i | − | 0.434969i | ||||||
\(323\) | 0.853903 | − | 1.43268i | 0.0475124 | − | 0.0797163i | ||||
\(324\) | −6.20379 | −0.344655 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.43073 | − | 8.11408i | 0.0792408 | − | 0.449397i | ||||
\(327\) | 1.10152 | + | 1.31275i | 0.0609144 | + | 0.0725950i | ||||
\(328\) | 6.19473 | − | 7.38259i | 0.342047 | − | 0.407635i | ||||
\(329\) | −4.15655 | − | 23.5730i | −0.229158 | − | 1.29962i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.42273 | − | 2.46424i | 0.0782003 | − | 0.135447i | −0.824273 | − | 0.566192i | \(-0.808416\pi\) |
0.902473 | + | 0.430745i | \(0.141749\pi\) | |||||||
\(332\) | 1.09111 | − | 2.99781i | 0.0598827 | − | 0.164526i | ||||
\(333\) | 7.98310 | − | 21.9334i | 0.437471 | − | 1.20194i | ||||
\(334\) | −7.08209 | + | 12.2665i | −0.387515 | + | 0.671195i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.18661 | + | 12.4009i | 0.119290 | + | 0.676525i | ||||
\(337\) | −4.11760 | + | 4.90717i | −0.224300 | + | 0.267311i | −0.866445 | − | 0.499273i | \(-0.833600\pi\) |
0.642145 | + | 0.766584i | \(0.278045\pi\) | |||||||
\(338\) | 2.80632 | + | 3.34444i | 0.152643 | + | 0.181913i | ||||
\(339\) | −0.343419 | + | 1.94763i | −0.0186520 | + | 0.105781i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.2631 | 0.718235 | ||||||||
\(342\) | −8.74140 | + | 7.13040i | −0.472681 | + | 0.385568i | ||||
\(343\) | − | 20.1537i | − | 1.08820i | ||||||
\(344\) | 5.80285 | − | 2.11206i | 0.312869 | − | 0.113875i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −23.2398 | + | 19.5005i | −1.24938 | + | 1.04835i | ||||
\(347\) | −10.1579 | + | 12.1057i | −0.545305 | + | 0.649869i | −0.966368 | − | 0.257162i | \(-0.917213\pi\) |
0.421063 | + | 0.907031i | \(0.361657\pi\) | |||||||
\(348\) | −11.0221 | + | 1.94350i | −0.590848 | + | 0.104182i | ||||
\(349\) | −13.7825 | − | 23.8721i | −0.737763 | − | 1.27784i | −0.953501 | − | 0.301391i | \(-0.902549\pi\) |
0.215738 | − | 0.976451i | \(-0.430784\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.25897 | + | 2.64205i | 0.387455 | + | 0.141022i | ||||
\(352\) | 3.03172 | − | 8.32959i | 0.161591 | − | 0.443968i | ||||
\(353\) | −3.66228 | − | 2.11442i | −0.194924 | − | 0.112539i | 0.399362 | − | 0.916793i | \(-0.369232\pi\) |
−0.594285 | + | 0.804254i | \(0.702565\pi\) | |||||||
\(354\) | 17.6145 | + | 30.5092i | 0.936200 | + | 1.62155i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.88718 | + | 2.42263i | 0.153020 | + | 0.128399i | ||||
\(357\) | −1.22803 | − | 1.46351i | −0.0649944 | − | 0.0774573i | ||||
\(358\) | −0.457204 | − | 0.0806174i | −0.0241640 | − | 0.00426076i | ||||
\(359\) | 5.38553 | − | 1.96017i | 0.284237 | − | 0.103454i | −0.195967 | − | 0.980610i | \(-0.562785\pi\) |
0.480205 | + | 0.877157i | \(0.340562\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.81772 | + | 18.6125i | −0.200932 | + | 0.979605i | ||||
\(362\) | − | 5.71231i | − | 0.300232i | ||||||
\(363\) | −2.34099 | − | 6.43180i | −0.122870 | − | 0.337582i | ||||
\(364\) | −0.893788 | + | 5.06892i | −0.0468472 | + | 0.265684i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −12.4259 | − | 10.4265i | −0.649510 | − | 0.545004i | ||||
\(367\) | 0.931253 | − | 0.164205i | 0.0486110 | − | 0.00857143i | −0.149290 | − | 0.988793i | \(-0.547699\pi\) |
0.197901 | + | 0.980222i | \(0.436588\pi\) | |||||||
\(368\) | −6.49971 | + | 3.75261i | −0.338821 | + | 0.195618i | ||||
\(369\) | 3.39767 | − | 5.88493i | 0.176876 | − | 0.306357i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.4302 | + | 5.61612i | 0.801094 | + | 0.291574i | ||||
\(372\) | −5.30406 | − | 3.06230i | −0.275003 | − | 0.158773i | ||||
\(373\) | −0.583094 | + | 0.336649i | −0.0301915 | + | 0.0174310i | −0.515020 | − | 0.857178i | \(-0.672215\pi\) |
0.484828 | + | 0.874609i | \(0.338882\pi\) | |||||||
\(374\) | −0.224248 | − | 1.27177i | −0.0115956 | − | 0.0657618i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −25.6601 | + | 21.5314i | −1.32332 | + | 1.11040i | ||||
\(377\) | 34.4647 | + | 6.07706i | 1.77502 | + | 0.312984i | ||||
\(378\) | −1.69791 | − | 4.66497i | −0.0873310 | − | 0.239940i | ||||
\(379\) | 34.7701 | 1.78602 | 0.893010 | − | 0.450037i | \(-0.148589\pi\) | ||||
0.893010 | + | 0.450037i | \(0.148589\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.82977 | −0.401131 | ||||||||
\(382\) | −9.74097 | − | 26.7631i | −0.498392 | − | 1.36932i | ||||
\(383\) | −26.8426 | − | 4.73308i | −1.37159 | − | 0.241849i | −0.561174 | − | 0.827698i | \(-0.689650\pi\) |
−0.810420 | + | 0.585849i | \(0.800761\pi\) | |||||||
\(384\) | 7.35229 | − | 6.16930i | 0.375195 | − | 0.314826i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.32770 | + | 13.2010i | 0.118477 | + | 0.671916i | ||||
\(387\) | 3.77088 | − | 2.17712i | 0.191684 | − | 0.110669i | ||||
\(388\) | −7.18343 | − | 4.14736i | −0.364684 | − | 0.210550i | ||||
\(389\) | 34.2998 | + | 12.4841i | 1.73907 | + | 0.632969i | 0.999208 | − | 0.0397915i | \(-0.0126694\pi\) |
0.739860 | + | 0.672761i | \(0.234892\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.569343 | − | 0.986131i | 0.0287929 | − | 0.0498708i | ||||
\(392\) | −5.79091 | + | 3.34338i | −0.292485 | + | 0.168866i | ||||
\(393\) | 23.0597 | − | 4.06605i | 1.16321 | − | 0.205105i | ||||
\(394\) | −15.4338 | − | 12.9505i | −0.777544 | − | 0.652437i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.610786 | − | 3.46394i | 0.0306932 | − | 0.174070i | ||||
\(397\) | 4.73209 | + | 13.0013i | 0.237497 | + | 0.652517i | 0.999985 | + | 0.00551465i | \(0.00175538\pi\) |
−0.762488 | + | 0.647002i | \(0.776022\pi\) | |||||||
\(398\) | − | 18.7739i | − | 0.941048i | ||||||
\(399\) | 18.6953 | + | 11.1427i | 0.935934 | + | 0.557835i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.8095 | + | 8.30199i | −1.13905 | + | 0.414582i | −0.841572 | − | 0.540145i | \(-0.818369\pi\) |
−0.297482 | + | 0.954727i | \(0.596147\pi\) | |||||||
\(402\) | −2.80524 | − | 0.494639i | −0.139912 | − | 0.0246703i | ||||
\(403\) | 12.3099 | + | 14.6704i | 0.613200 | + | 0.730783i | ||||
\(404\) | 1.86952 | + | 1.56871i | 0.0930120 | + | 0.0780463i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.2452 | − | 19.4772i | −0.558089 | − | 0.966638i | ||||
\(407\) | −26.3614 | − | 15.2198i | −1.30669 | − | 0.754417i | ||||
\(408\) | −0.914400 | + | 2.51229i | −0.0452695 | + | 0.124377i | ||||
\(409\) | −31.8875 | − | 11.6061i | −1.57674 | − | 0.573885i | −0.602245 | − | 0.798311i | \(-0.705727\pi\) |
−0.974491 | + | 0.224426i | \(0.927949\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.66842 | − | 2.88980i | −0.0822973 | − | 0.142543i | ||||
\(412\) | −8.29554 | + | 1.46273i | −0.408692 | + | 0.0720634i | ||||
\(413\) | 18.3244 | − | 21.8382i | 0.901686 | − | 1.07459i | ||||
\(414\) | −5.89981 | + | 4.95053i | −0.289960 | + | 0.243305i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 12.0272 | − | 4.37756i | 0.589684 | − | 0.214628i | ||||
\(417\) | − | 16.6570i | − | 0.815696i | ||||||
\(418\) | 7.17807 | + | 12.8414i | 0.351091 | + | 0.628094i | ||||
\(419\) | −21.4325 | −1.04705 | −0.523523 | − | 0.852012i | \(-0.675382\pi\) | ||||
−0.523523 | + | 0.852012i | \(0.675382\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.27528 | + | 7.23247i | −0.0621533 | + | 0.352489i | 0.937832 | + | 0.347089i | \(0.112830\pi\) |
−0.999985 | + | 0.00539967i | \(0.998281\pi\) | |||||||
\(422\) | 7.12947 | + | 8.49657i | 0.347057 | + | 0.413607i | ||||
\(423\) | −15.1820 | + | 18.0932i | −0.738173 | + | 0.879720i | ||||
\(424\) | −3.99022 | − | 22.6297i | −0.193782 | − | 1.09899i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10.6234 | + | 18.4002i | −0.514704 | + | 0.891494i | ||||
\(427\) | −4.48939 | + | 12.3345i | −0.217257 | + | 0.596908i | ||||
\(428\) | −1.21372 | + | 3.33467i | −0.0586674 | + | 0.161187i | ||||
\(429\) | −13.1111 | + | 22.7090i | −0.633008 | + | 1.09640i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.0219443 | + | 0.124452i | 0.00105702 | + | 0.00599466i | 0.985332 | − | 0.170650i | \(-0.0545868\pi\) |
−0.984275 | + | 0.176645i | \(0.943476\pi\) | |||||||
\(432\) | −3.06837 | + | 3.65674i | −0.147627 | + | 0.175935i | ||||
\(433\) | −3.73982 | − | 4.45694i | −0.179724 | − | 0.214187i | 0.668660 | − | 0.743569i | \(-0.266868\pi\) |
−0.848384 | + | 0.529382i | \(0.822424\pi\) | |||||||
\(434\) | 2.13713 | − | 12.1203i | 0.102585 | − | 0.581791i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.432852 | −0.0207298 | ||||||||
\(437\) | −2.42973 | + | 12.7422i | −0.116230 | + | 0.609544i | ||||
\(438\) | − | 38.2441i | − | 1.82738i | ||||||
\(439\) | 17.3872 | − | 6.32841i | 0.829844 | − | 0.302039i | 0.108049 | − | 0.994146i | \(-0.465540\pi\) |
0.721795 | + | 0.692107i | \(0.243317\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.61182 | + | 3.03068i | −0.171992 | + | 0.144318i | ||||
\(442\) | 1.19858 | − | 1.42842i | 0.0570108 | − | 0.0679429i | ||||
\(443\) | 21.7891 | − | 3.84201i | 1.03523 | − | 0.182539i | 0.369889 | − | 0.929076i | \(-0.379396\pi\) |
0.665344 | + | 0.746537i | \(0.268285\pi\) | |||||||
\(444\) | 7.02817 | + | 12.1732i | 0.333542 | + | 0.577712i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.13163 | − | 1.13982i | −0.148287 | − | 0.0539720i | ||||
\(447\) | 7.76840 | − | 21.3435i | 0.367433 | − | 1.00951i | ||||
\(448\) | −16.7180 | − | 9.65214i | −0.789851 | − | 0.456021i | ||||
\(449\) | −10.2840 | − | 17.8124i | −0.485331 | − | 0.840617i | 0.514527 | − | 0.857474i | \(-0.327967\pi\) |
−0.999858 | + | 0.0168567i | \(0.994634\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.78865 | − | 5.69635i | −0.319665 | − | 0.268231i | ||||
\(452\) | −0.321096 | − | 0.382667i | −0.0151031 | − | 0.0179991i | ||||
\(453\) | −33.7339 | − | 5.94819i | −1.58495 | − | 0.279470i | ||||
\(454\) | 0.947121 | − | 0.344724i | 0.0444506 | − | 0.0161787i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.422979 | − | 30.4537i | 0.0198078 | − | 1.42612i | ||||
\(457\) | 20.3583i | 0.952323i | 0.879358 | + | 0.476161i | \(0.157972\pi\) | ||||
−0.879358 | + | 0.476161i | \(0.842028\pi\) | |||||||
\(458\) | −8.96676 | − | 24.6360i | −0.418989 | − | 1.15116i | ||||
\(459\) | 0.125762 | − | 0.713233i | 0.00587008 | − | 0.0332909i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.24592 | − | 3.56275i | −0.197752 | − | 0.165934i | 0.538535 | − | 0.842603i | \(-0.318978\pi\) |
−0.736287 | + | 0.676670i | \(0.763423\pi\) | |||||||
\(462\) | 16.5956 | − | 2.92625i | 0.772097 | − | 0.136142i | ||||
\(463\) | −28.2757 | + | 16.3250i | −1.31408 | + | 0.758686i | −0.982770 | − | 0.184835i | \(-0.940825\pi\) |
−0.331313 | + | 0.943521i | \(0.607492\pi\) | |||||||
\(464\) | −10.8129 | + | 18.7286i | −0.501978 | + | 0.869451i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.95442 | − | 1.80326i | −0.229509 | − | 0.0835344i | ||||
\(467\) | −24.8214 | − | 14.3306i | −1.14860 | − | 0.663142i | −0.200051 | − | 0.979785i | \(-0.564111\pi\) |
−0.948545 | + | 0.316643i | \(0.897444\pi\) | |||||||
\(468\) | 4.39838 | − | 2.53941i | 0.203315 | − | 0.117384i | ||||
\(469\) | 0.400268 | + | 2.27003i | 0.0184827 | + | 0.104820i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.0135 | − | 15.1152i | 0.830020 | − | 0.696469i | ||||
\(472\) | −39.2877 | − | 6.92748i | −1.80836 | − | 0.318863i | ||||
\(473\) | −1.94214 | − | 5.33600i | −0.0892999 | − | 0.245350i | ||||
\(474\) | −36.4766 | −1.67542 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.482564 | 0.0221183 | ||||||||
\(477\) | −5.54159 | − | 15.2254i | −0.253732 | − | 0.697123i | ||||
\(478\) | 23.3155 | + | 4.11115i | 1.06643 | + | 0.188040i | ||||
\(479\) | −7.86922 | + | 6.60306i | −0.359554 | + | 0.301701i | −0.804613 | − | 0.593800i | \(-0.797627\pi\) |
0.445059 | + | 0.895501i | \(0.353183\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.63223 | − | 43.2846i | −0.348000 | − | 1.97361i | ||||
\(482\) | 21.5964 | − | 12.4687i | 0.983691 | − | 0.567934i | ||||
\(483\) | 12.8682 | + | 7.42946i | 0.585523 | + | 0.338052i | ||||
\(484\) | 1.62460 | + | 0.591304i | 0.0738453 | + | 0.0268775i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −11.2736 | + | 19.5265i | −0.511382 | + | 0.885740i | ||||
\(487\) | 9.63406 | − | 5.56223i | 0.436561 | − | 0.252049i | −0.265577 | − | 0.964090i | \(-0.585562\pi\) |
0.702138 | + | 0.712041i | \(0.252229\pi\) | |||||||
\(488\) | 18.0896 | − | 3.18968i | 0.818878 | − | 0.144390i | ||||
\(489\) | 12.0155 | + | 10.0822i | 0.543360 | + | 0.455934i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.41105 | − | 13.6738i | 0.108809 | − | 0.617089i | −0.880821 | − | 0.473450i | \(-0.843009\pi\) |
0.989630 | − | 0.143639i | \(-0.0458804\pi\) | |||||||
\(492\) | 1.39964 | + | 3.84547i | 0.0631004 | + | 0.173367i | ||||
\(493\) | − | 3.28106i | − | 0.147771i | ||||||
\(494\) | −7.54176 | + | 19.8583i | −0.339320 | + | 0.893465i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.1205 | + | 4.04752i | −0.499324 | + | 0.181739i | ||||
\(497\) | 16.9320 | + | 2.98556i | 0.759502 | + | 0.133921i | ||||
\(498\) | −9.69408 | − | 11.5530i | −0.434402 | − | 0.517700i | ||||
\(499\) | −9.79608 | − | 8.21989i | −0.438533 | − | 0.367973i | 0.396627 | − | 0.917980i | \(-0.370181\pi\) |
−0.835160 | + | 0.550007i | \(0.814625\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.4822 | − | 23.3519i | −0.602342 | − | 1.04329i | ||||
\(502\) | 5.74392 | + | 3.31625i | 0.256364 | + | 0.148012i | ||||
\(503\) | −3.57906 | + | 9.83338i | −0.159582 | + | 0.438449i | −0.993554 | − | 0.113358i | \(-0.963839\pi\) |
0.833972 | + | 0.551807i | \(0.186061\pi\) | |||||||
\(504\) | −13.7503 | − | 5.00472i | −0.612489 | − | 0.222928i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.02195 | + | 8.69828i | 0.223253 | + | 0.386686i | ||||
\(507\) | −8.18505 | + | 1.44324i | −0.363511 | + | 0.0640968i | ||||
\(508\) | 1.27124 | − | 1.51501i | 0.0564024 | − | 0.0672177i | ||||
\(509\) | −21.4000 | + | 17.9567i | −0.948539 | + | 0.795919i | −0.979051 | − | 0.203616i | \(-0.934731\pi\) |
0.0305117 | + | 0.999534i | \(0.490286\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.0813 | + | 10.5847i | −1.28648 | + | 0.468241i | ||||
\(512\) | 23.4130i | 1.03472i | ||||||||
\(513\) | 1.31970 | + | 8.14422i | 0.0582660 | + | 0.359576i | ||||
\(514\) | 24.0211 | 1.05952 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.455338 | + | 2.58235i | −0.0200451 | + | 0.113682i | ||||
\(517\) | 19.7992 | + | 23.5957i | 0.870766 | + | 1.03774i | ||||
\(518\) | −18.1561 | + | 21.6376i | −0.797733 | + | 0.950701i | ||||
\(519\) | −10.0288 | − | 56.8762i | −0.440216 | − | 2.49659i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.03138 | − | 6.98256i | 0.176618 | − | 0.305912i | −0.764102 | − | 0.645095i | \(-0.776818\pi\) |
0.940720 | + | 0.339184i | \(0.110151\pi\) | |||||||
\(522\) | −7.59008 | + | 20.8536i | −0.332209 | + | 0.912736i | ||||
\(523\) | 3.94751 | − | 10.8457i | 0.172612 | − | 0.474249i | −0.822976 | − | 0.568076i | \(-0.807688\pi\) |
0.995588 | + | 0.0938274i | \(0.0299102\pi\) | |||||||
\(524\) | −2.95723 | + | 5.12207i | −0.129187 | + | 0.223759i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.42771 | − | 13.7682i | −0.105853 | − | 0.600322i | ||||
\(527\) | 1.15411 | − | 1.37541i | 0.0502736 | − | 0.0599138i | ||||
\(528\) | −10.4156 | − | 12.4129i | −0.453283 | − | 0.540201i | ||||
\(529\) | 2.45604 | − | 13.9289i | 0.106784 | − | 0.605605i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −28.1294 | −1.22071 | ||||||||
\(532\) | −5.19142 | + | 1.80828i | −0.225077 | + | 0.0783987i | ||||
\(533\) | − | 12.7959i | − | 0.554254i | ||||||
\(534\) | 16.7427 | − | 6.09385i | 0.724528 | − | 0.263706i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.47102 | − | 2.07343i | 0.106732 | − | 0.0895587i | ||||
\(537\) | 0.568103 | − | 0.677038i | 0.0245154 | − | 0.0292164i | ||||
\(538\) | 15.1526 | − | 2.67182i | 0.653277 | − | 0.115190i | ||||
\(539\) | 3.07440 | + | 5.32502i | 0.132424 | + | 0.229365i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.1819 | − | 11.7133i | −1.38361 | − | 0.503593i | −0.460339 | − | 0.887743i | \(-0.652272\pi\) |
−0.923270 | + | 0.384151i | \(0.874494\pi\) | |||||||
\(542\) | 6.29608 | − | 17.2983i | 0.270440 | − | 0.743027i | ||||
\(543\) | 9.41766 | + | 5.43729i | 0.404150 | + | 0.233336i | ||||
\(544\) | −0.599987 | − | 1.03921i | −0.0257242 | − | 0.0445556i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 18.6397 | + | 15.6405i | 0.797704 | + | 0.669353i | ||||
\(547\) | −17.8017 | − | 21.2152i | −0.761146 | − | 0.907098i | 0.236774 | − | 0.971565i | \(-0.423910\pi\) |
−0.997920 | + | 0.0644666i | \(0.979465\pi\) | |||||||
\(548\) | 0.830043 | + | 0.146359i | 0.0354577 | + | 0.00625214i | ||||
\(549\) | 12.1708 | − | 4.42981i | 0.519437 | − | 0.189060i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.2949 | + | 35.2976i | 0.523779 | + | 1.50373i | ||||
\(552\) | − | 20.7936i | − | 0.885033i | ||||||
\(553\) | 10.0955 | + | 27.7372i | 0.429305 | + | 1.17951i | ||||
\(554\) | 1.09835 | − | 6.22906i | 0.0466645 | − | 0.264647i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.22302 | + | 2.70443i | 0.136686 | + | 0.114694i | ||||
\(557\) | −13.4285 | + | 2.36781i | −0.568985 | + | 0.100327i | −0.450737 | − | 0.892657i | \(-0.648839\pi\) |
−0.118248 | + | 0.992984i | \(0.537728\pi\) | |||||||
\(558\) | −10.5169 | + | 6.07195i | −0.445217 | + | 0.257046i | ||||
\(559\) | 4.09961 | − | 7.10074i | 0.173395 | − | 0.300329i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.31017 | + | 0.840835i | 0.0975356 | + | 0.0355001i | ||||
\(562\) | −5.56687 | − | 3.21403i | −0.234824 | − | 0.135576i | ||||
\(563\) | −33.7910 | + | 19.5093i | −1.42412 | + | 0.822217i | −0.996648 | − | 0.0818108i | \(-0.973930\pi\) |
−0.427474 | + | 0.904028i | \(0.640596\pi\) | |||||||
\(564\) | −2.46992 | − | 14.0076i | −0.104003 | − | 0.589828i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −16.1691 | + | 13.5675i | −0.679638 | + | 0.570284i | ||||
\(567\) | 23.3718 | + | 4.12107i | 0.981522 | + | 0.173069i | ||||
\(568\) | −8.22904 | − | 22.6091i | −0.345283 | − | 0.948657i | ||||
\(569\) | −8.86810 | −0.371770 | −0.185885 | − | 0.982572i | \(-0.559515\pi\) | ||||
−0.185885 | + | 0.982572i | \(0.559515\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.4054 | 1.48167 | 0.740834 | − | 0.671688i | \(-0.234431\pi\) | ||||
0.740834 | + | 0.671688i | \(0.234431\pi\) | |||||||
\(572\) | −2.26533 | − | 6.22395i | −0.0947184 | − | 0.260237i | ||||
\(573\) | 53.3953 | + | 9.41503i | 2.23062 | + | 0.393319i | ||||
\(574\) | −6.29941 | + | 5.28583i | −0.262932 | + | 0.220626i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.30767 | + | 18.7587i | 0.137820 | + | 0.781613i | ||||
\(577\) | −22.5238 | + | 13.0041i | −0.937677 | + | 0.541368i | −0.889231 | − | 0.457458i | \(-0.848760\pi\) |
−0.0484454 | + | 0.998826i | \(0.515427\pi\) | |||||||
\(578\) | 17.4283 | + | 10.0623i | 0.724923 | + | 0.418535i | ||||
\(579\) | −23.9797 | − | 8.72790i | −0.996562 | − | 0.362719i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.10200 | + | 10.5690i | −0.253153 | + | 0.438475i | ||||
\(582\) | −33.9588 | + | 19.6061i | −1.40764 | + | 0.812700i | ||||
\(583\) | −20.8091 | + | 3.66920i | −0.861823 | + | 0.151963i | ||||
\(584\) | 33.1760 | + | 27.8379i | 1.37283 | + | 1.15194i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.976714 | + | 5.53922i | −0.0403477 | + | 0.228823i | ||||
\(587\) | −3.60512 | − | 9.90499i | −0.148799 | − | 0.408823i | 0.842791 | − | 0.538241i | \(-0.180911\pi\) |
−0.991590 | + | 0.129419i | \(0.958689\pi\) | |||||||
\(588\) | − | 2.83939i | − | 0.117094i | ||||||
\(589\) | −7.26189 | + | 19.1213i | −0.299221 | + | 0.787880i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 36.0417 | − | 13.1181i | 1.48256 | − | 0.539607i | ||||
\(592\) | 26.7475 | + | 4.71631i | 1.09932 | + | 0.193839i | ||||
\(593\) | 8.50064 | + | 10.1307i | 0.349080 | + | 0.416017i | 0.911803 | − | 0.410629i | \(-0.134691\pi\) |
−0.562723 | + | 0.826645i | \(0.690246\pi\) | |||||||
\(594\) | 4.89365 | + | 4.10626i | 0.200789 | + | 0.168482i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.86855 | + | 4.96848i | 0.117500 | + | 0.203517i | ||||
\(597\) | 30.9517 | + | 17.8700i | 1.26677 | + | 0.731370i | ||||
\(598\) | −4.96018 | + | 13.6280i | −0.202837 | + | 0.557289i | ||||
\(599\) | −3.49529 | − | 1.27218i | −0.142814 | − | 0.0519800i | 0.269624 | − | 0.962966i | \(-0.413100\pi\) |
−0.412438 | + | 0.910986i | \(0.635323\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.0672 | + | 36.4895i | 0.859349 | + | 1.48844i | 0.872550 | + | 0.488524i | \(0.162465\pi\) |
−0.0132009 | + | 0.999913i | \(0.504202\pi\) | |||||||
\(602\) | −5.18917 | + | 0.914990i | −0.211495 | + | 0.0372922i | ||||
\(603\) | 1.46200 | − | 1.74234i | 0.0595371 | − | 0.0709536i | ||||
\(604\) | 6.62798 | − | 5.56153i | 0.269689 | − | 0.226296i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.8413 | − | 3.94591i | 0.440398 | − | 0.160292i | ||||
\(607\) | − | 27.1082i | − | 1.10029i | −0.835070 | − | 0.550144i | \(-0.814573\pi\) | ||
0.835070 | − | 0.550144i | \(-0.185427\pi\) | |||||||
\(608\) | 10.3488 | + | 8.93149i | 0.419699 | + | 0.362220i | ||||
\(609\) | 42.8151 | 1.73496 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.72311 | + | 43.8000i | −0.312444 | + | 1.77196i | ||||
\(612\) | −0.306070 | − | 0.364760i | −0.0123721 | − | 0.0147445i | ||||
\(613\) | −7.22977 | + | 8.61611i | −0.292008 | + | 0.348001i | −0.892025 | − | 0.451986i | \(-0.850716\pi\) |
0.600017 | + | 0.799987i | \(0.295160\pi\) | |||||||
\(614\) | 2.44793 | + | 13.8829i | 0.0987904 | + | 0.560268i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.54149 | + | 16.5263i | −0.384438 | + | 0.665866i | ||||
\(617\) | 10.4849 | − | 28.8071i | 0.422108 | − | 1.15973i | −0.528391 | − | 0.849001i | \(-0.677204\pi\) |
0.950498 | − | 0.310730i | \(-0.100573\pi\) | |||||||
\(618\) | −13.6196 | + | 37.4196i | −0.547861 | + | 1.50524i | ||||
\(619\) | −20.1384 | + | 34.8807i | −0.809431 | + | 1.40198i | 0.103828 | + | 0.994595i | \(0.466891\pi\) |
−0.913259 | + | 0.407380i | \(0.866442\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.978126 | + | 5.54723i | 0.0392509 | + | 0.222603i | ||||
\(622\) | −6.86188 | + | 8.17767i | −0.275136 | + | 0.327895i | ||||
\(623\) | −9.26766 | − | 11.0448i | −0.371301 | − | 0.442499i | ||||
\(624\) | 4.06286 | − | 23.0416i | 0.162644 | − | 0.922403i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.0370 | 0.640968 | ||||||||
\(627\) | −28.0036 | − | 0.388950i | −1.11836 | − | 0.0155332i | ||||
\(628\) | 5.93960i | 0.237016i | ||||||||
\(629\) | −3.87220 | + | 1.40937i | −0.154395 | + | 0.0561951i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.6279 | − | 24.8608i | 1.17947 | − | 0.989692i | 0.179487 | − | 0.983760i | \(-0.442556\pi\) |
0.999982 | − | 0.00593154i | \(-0.00188808\pi\) | |||||||
\(632\) | 26.5513 | − | 31.6426i | 1.05616 | − | 1.25868i | ||||
\(633\) | −20.7942 | + | 3.66658i | −0.826495 | + | 0.145733i | ||||
\(634\) | 6.60183 | + | 11.4347i | 0.262192 | + | 0.454130i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.16897 | + | 3.33723i | 0.363573 | + | 0.132330i | ||||
\(637\) | −3.03658 | + | 8.34295i | −0.120314 | + | 0.330560i | ||||
\(638\) | 25.0636 | + | 14.4705i | 0.992278 | + | 0.572892i | ||||
\(639\) | −8.48250 | − | 14.6921i | −0.335562 | − | 0.581211i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.0725 | − | 27.7511i | −1.30628 | − | 1.09610i | −0.989023 | − | 0.147764i | \(-0.952792\pi\) |
−0.317261 | − | 0.948338i | \(-0.602763\pi\) | |||||||
\(642\) | 10.7834 | + | 12.8511i | 0.425586 | + | 0.507193i | ||||
\(643\) | −4.31238 | − | 0.760389i | −0.170064 | − | 0.0299868i | 0.0879678 | − | 0.996123i | \(-0.471963\pi\) |
−0.258032 | + | 0.966137i | \(0.583074\pi\) | |||||||
\(644\) | −3.52684 | + | 1.28366i | −0.138977 | + | 0.0505834i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.95629 | + | 0.373032i | 0.0769693 | + | 0.0146768i | ||||
\(647\) | − | 16.4916i | − | 0.648351i | −0.945997 | − | 0.324176i | \(-0.894913\pi\) | ||
0.945997 | − | 0.324176i | \(-0.105087\pi\) | |||||||
\(648\) | −11.3588 | − | 31.2081i | −0.446217 | − | 1.22597i | ||||
\(649\) | −6.37015 | + | 36.1269i | −0.250050 | + | 1.41811i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.9480 | + | 15.0601i | 0.703436 | + | 0.590253i | ||||
\(652\) | −3.90169 | + | 0.687973i | −0.152802 | + | 0.0269431i | ||||
\(653\) | −1.40826 | + | 0.813059i | −0.0551095 | + | 0.0318175i | −0.527302 | − | 0.849678i | \(-0.676796\pi\) |
0.472192 | + | 0.881496i | \(0.343463\pi\) | |||||||
\(654\) | −1.02313 | + | 1.77211i | −0.0400074 | + | 0.0692949i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.43034 | + | 2.70442i | 0.290106 | + | 0.105590i | ||||
\(657\) | 26.4458 | + | 15.2685i | 1.03175 | + | 0.595680i | ||||
\(658\) | 24.7529 | − | 14.2911i | 0.964969 | − | 0.557125i | ||||
\(659\) | 0.331134 | + | 1.87796i | 0.0128992 | + | 0.0731548i | 0.990578 | − | 0.136951i | \(-0.0437303\pi\) |
−0.977679 | + | 0.210106i | \(0.932619\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.07136 | − | 4.25538i | 0.197253 | − | 0.165515i | −0.538811 | − | 0.842426i | \(-0.681126\pi\) |
0.736064 | + | 0.676911i | \(0.236682\pi\) | |||||||
\(662\) | 3.34608 | + | 0.590004i | 0.130049 | + | 0.0229312i | ||||
\(663\) | 1.21410 | + | 3.33571i | 0.0471516 | + | 0.129548i | ||||
\(664\) | 17.0783 | 0.662765 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 27.8710 | 1.07998 | ||||||||
\(667\) | 8.72791 | + | 23.9797i | 0.337946 | + | 0.928499i | ||||
\(668\) | 6.70743 | + | 1.18270i | 0.259518 | + | 0.0457601i | ||||
\(669\) | 4.86003 | − | 4.07805i | 0.187900 | − | 0.157667i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.93307 | − | 16.6343i | −0.113230 | − | 0.642158i | ||||
\(672\) | 13.5608 | − | 7.82933i | 0.523119 | − | 0.302023i | ||||
\(673\) | −10.7785 | − | 6.22298i | −0.415482 | − | 0.239878i | 0.277661 | − | 0.960679i | \(-0.410441\pi\) |
−0.693142 | + | 0.720801i | \(0.743774\pi\) | |||||||
\(674\) | −7.18779 | − | 2.61614i | −0.276864 | − | 0.100770i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.04967 | − | 1.81808i | 0.0403719 | − | 0.0699261i | ||||
\(677\) | 4.07556 | − | 2.35303i | 0.156637 | − | 0.0904342i | −0.419633 | − | 0.907694i | \(-0.637841\pi\) |
0.576270 | + | 0.817260i | \(0.304508\pi\) | |||||||
\(678\) | −2.32562 | + | 0.410069i | −0.0893149 | + | 0.0157486i | ||||
\(679\) | 24.3074 | + | 20.3963i | 0.932833 | + | 0.782739i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.333189 | + | 1.88961i | −0.0127678 | + | 0.0724100i | ||||
\(682\) | 5.41662 | + | 14.8820i | 0.207413 | + | 0.569863i | ||||
\(683\) | − | 17.6914i | − | 0.676942i | −0.940977 | − | 0.338471i | \(-0.890090\pi\) | ||
0.940977 | − | 0.338471i | \(-0.109910\pi\) | |||||||
\(684\) | 4.65953 | + | 2.77717i | 0.178162 | + | 0.106188i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 22.6138 | − | 8.23076i | 0.863400 | − | 0.314252i | ||||
\(687\) | 49.1515 | + | 8.66673i | 1.87524 | + | 0.330656i | ||||
\(688\) | 3.25680 | + | 3.88130i | 0.124164 | + | 0.147973i | ||||
\(689\) | −23.3721 | − | 19.6115i | −0.890406 | − | 0.747140i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.0639 | − | 22.6273i | −0.496974 | − | 0.860784i | 0.503020 | − | 0.864275i | \(-0.332222\pi\) |
−0.999994 | + | 0.00349090i | \(0.998889\pi\) | |||||||
\(692\) | 12.6335 | + | 7.29394i | 0.480252 | + | 0.277274i | ||||
\(693\) | −4.60208 | + | 12.6441i | −0.174819 | + | 0.480310i | ||||
\(694\) | −17.7319 | − | 6.45388i | −0.673093 | − | 0.244986i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −29.9578 | − | 51.8883i | −1.13555 | − | 1.96682i | ||||
\(697\) | −1.18145 | + | 0.208321i | −0.0447505 | + | 0.00789073i | ||||
\(698\) | 21.1573 | − | 25.2143i | 0.800814 | − | 0.954374i | ||||
\(699\) | 7.68885 | − | 6.45171i | 0.290819 | − | 0.244026i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.9867 | − | 7.27458i | 0.754889 | − | 0.274757i | 0.0642272 | − | 0.997935i | \(-0.479542\pi\) |
0.690661 | + | 0.723178i | \(0.257320\pi\) | |||||||
\(702\) | 9.22406i | 0.348140i | ||||||||
\(703\) | 36.3759 | − | 29.6720i | 1.37194 | − | 1.11910i | ||||
\(704\) | 24.8411 | 0.936233 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.876847 | − | 4.97285i | 0.0330006 | − | 0.187156i | ||||
\(707\) | −6.00104 | − | 7.15176i | −0.225692 | − | 0.268970i | ||||
\(708\) | 10.8888 | − | 12.9768i | 0.409227 | − | 0.487698i | ||||
\(709\) | −1.84788 | − | 10.4798i | −0.0693985 | − | 0.393578i | −0.999645 | − | 0.0266433i | \(-0.991518\pi\) |
0.930247 | − | 0.366935i | \(-0.119593\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.5628 | − | 25.2235i | 0.546148 | − | 0.945956i | ||||
\(712\) | −6.90075 | + | 18.9597i | −0.258617 | + | 0.710543i | ||||
\(713\) | −4.77611 | + | 13.1222i | −0.178867 | + | 0.491432i | ||||
\(714\) | 1.14063 | − | 1.97563i | 0.0426871 | − | 0.0739361i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.0387652 | + | 0.219848i | 0.00144872 | + | 0.00821612i | ||||
\(717\) | −28.9709 | + | 34.5261i | −1.08194 | + | 1.28940i | ||||
\(718\) | 4.39889 | + | 5.24239i | 0.164165 | + | 0.195644i | ||||
\(719\) | 6.65775 | − | 37.7580i | 0.248292 | − | 1.40813i | −0.564429 | − | 0.825481i | \(-0.690904\pi\) |
0.812721 | − | 0.582653i | \(-0.197985\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.2238 | 1.20008 | ||||||||
\(722\) | −22.4436 | + | 3.31759i | −0.835265 | + | 0.123468i | ||||
\(723\) | 47.4736i | 1.76556i | ||||||||
\(724\) | −2.58113 | + | 0.939456i | −0.0959271 | + | 0.0349146i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6.26086 | − | 5.25348i | 0.232362 | − | 0.194975i | ||||
\(727\) | −4.95353 | + | 5.90339i | −0.183716 | + | 0.218945i | −0.850040 | − | 0.526718i | \(-0.823422\pi\) |
0.666324 | + | 0.745663i | \(0.267867\pi\) | |||||||
\(728\) | −27.1357 | + | 4.78475i | −1.00572 | + | 0.177335i | ||||
\(729\) | −5.25474 | − | 9.10148i | −0.194620 | − | 0.337092i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.722353 | − | 0.262915i | −0.0267172 | − | 0.00972427i | ||||
\(732\) | −2.66770 | + | 7.32946i | −0.0986012 | + | 0.270905i | ||||
\(733\) | 3.53795 | + | 2.04263i | 0.130677 | + | 0.0754464i | 0.563913 | − | 0.825834i | \(-0.309295\pi\) |
−0.433236 | + | 0.901280i | \(0.642628\pi\) | |||||||
\(734\) | 0.564571 | + | 0.977866i | 0.0208387 | + | 0.0360937i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.14941 | + | 5.99906i | 0.263531 | + | 0.221128i | ||||
\(737\) | −1.90662 | − | 2.27223i | −0.0702314 | − | 0.0836985i | ||||
\(738\) | 7.99089 | + | 1.40901i | 0.294149 | + | 0.0518663i | ||||
\(739\) | −23.1521 | + | 8.42669i | −0.851665 | + | 0.309981i | −0.730719 | − | 0.682678i | \(-0.760815\pi\) |
−0.120946 | + | 0.992659i | \(0.538593\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25.5609 | − | 31.3360i | −0.939002 | − | 1.15116i | ||||
\(742\) | 19.6073i | 0.719806i | ||||||||
\(743\) | −8.81599 | − | 24.2217i | −0.323427 | − | 0.888610i | −0.989733 | − | 0.142931i | \(-0.954347\pi\) |
0.666305 | − | 0.745679i | \(-0.267875\pi\) | |||||||
\(744\) | 5.69342 | − | 32.2890i | 0.208731 | − | 1.18377i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.615878 | − | 0.516783i | −0.0225489 | − | 0.0189208i | ||||
\(747\) | 11.8591 | − | 2.09108i | 0.433901 | − | 0.0765085i | ||||
\(748\) | −0.537777 | + | 0.310486i | −0.0196631 | + | 0.0113525i | ||||
\(749\) | 6.78766 | − | 11.7566i | 0.248016 | − | 0.429576i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.5890 | + | 5.30998i | 0.532362 | + | 0.193764i | 0.594193 | − | 0.804323i | \(-0.297472\pi\) |
−0.0618308 | + | 0.998087i | \(0.519694\pi\) | |||||||
\(752\) | −23.8014 | − | 13.7418i | −0.867950 | − | 0.501111i | ||||
\(753\) | −10.9348 | + | 6.31319i | −0.398485 | + | 0.230065i | ||||
\(754\) | 7.25648 | + | 41.1535i | 0.264265 | + | 1.49872i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.82865 | + | 1.53442i | −0.0665073 | + | 0.0558062i | ||||
\(757\) | −21.3440 | − | 3.76351i | −0.775759 | − | 0.136787i | −0.228268 | − | 0.973598i | \(-0.573306\pi\) |
−0.547492 | + | 0.836811i | \(0.684417\pi\) | |||||||
\(758\) | 14.2001 | + | 39.0143i | 0.515769 | + | 1.41706i | ||||
\(759\) | −19.1207 | −0.694037 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.91229 | 0.0693204 | 0.0346602 | − | 0.999399i | \(-0.488965\pi\) | ||||
0.0346602 | + | 0.999399i | \(0.488965\pi\) | |||||||
\(762\) | −3.19767 | − | 8.78552i | −0.115839 | − | 0.318266i | ||||
\(763\) | 1.63070 | + | 0.287536i | 0.0590353 | + | 0.0104095i | ||||
\(764\) | −10.4910 | + | 8.80302i | −0.379552 | + | 0.318482i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.65167 | − | 32.0522i | −0.204203 | − | 1.15809i | ||||
\(767\) | −45.8726 | + | 26.4845i | −1.65636 | + | 0.956301i | ||||
\(768\) | −24.6784 | − | 14.2481i | −0.890504 | − | 0.514133i | ||||
\(769\) | 23.4461 | + | 8.53369i | 0.845489 | + | 0.307733i | 0.728200 | − | 0.685365i | \(-0.240357\pi\) |
0.117289 | + | 0.993098i | \(0.462580\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.8646 | + | 39.6026i | −0.823448 | + | 1.42625i | ||||
\(772\) | 5.58214 | − | 3.22285i | 0.200906 | − | 0.115993i | ||||
\(773\) | −17.1974 | + | 3.03236i | −0.618547 | + | 0.109067i | −0.474136 | − | 0.880451i | \(-0.657240\pi\) |
−0.144410 | + | 0.989518i | \(0.546129\pi\) | |||||||
\(774\) | 3.98289 | + | 3.34204i | 0.143162 | + | 0.120127i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.71075 | − | 43.7298i | 0.276800 | − | 1.56981i | ||||
\(777\) | −18.3911 | − | 50.5291i | −0.659777 | − | 1.81272i | ||||
\(778\) | 43.5851i | 1.56260i | ||||||||
\(779\) | 11.9294 | − | 6.66827i | 0.427414 | − | 0.238915i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.7902 | + | 7.56700i | −0.743931 | + | 0.270769i | ||||
\(782\) | 1.33902 | + | 0.236106i | 0.0478834 | + | 0.00844313i | ||||
\(783\) | 10.4328 | + | 12.4334i | 0.372839 | + | 0.444333i | ||||
\(784\) | −4.20279 | − | 3.52656i | −0.150100 | − | 0.125949i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 13.9799 | + | 24.2140i | 0.498648 | + | 0.863684i | ||||
\(787\) | 42.5745 | + | 24.5804i | 1.51762 | + | 0.876196i | 0.999785 | + | 0.0207128i | \(0.00659357\pi\) |
0.517831 | + | 0.855483i | \(0.326740\pi\) | |||||||
\(788\) | −3.31348 | + | 9.10371i | −0.118038 | + | 0.324306i | ||||
\(789\) | 25.0099 | + | 9.10287i | 0.890377 | + | 0.324071i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.955477 | + | 1.65493i | 0.0339728 | + | 0.0588427i | ||||
\(792\) | 18.5437 | − | 3.26975i | 0.658921 | − | 0.116185i | ||||
\(793\) | 15.6770 | − | 18.6831i | 0.556706 | − | 0.663456i | ||||
\(794\) | −12.6558 | + | 10.6194i | −0.449136 | + | 0.376870i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.48306 | + | 3.08758i | −0.300674 | + | 0.109436i | ||||
\(797\) | − | 35.4304i | − | 1.25501i | −0.778613 | − | 0.627505i | \(-0.784076\pi\) | ||
0.778613 | − | 0.627505i | \(-0.215924\pi\) | |||||||
\(798\) | −4.86777 | + | 25.5280i | −0.172317 | + | 0.903682i | ||||
\(799\) | 4.16978 | 0.147516 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.47042 | + | 14.0105i | −0.0872880 | + | 0.495035i | ||||
\(802\) | −18.6308 | − | 22.2033i | −0.657876 | − | 0.784026i | ||||
\(803\) | 25.5983 | − | 30.5069i | 0.903346 | − | 1.07657i | ||||
\(804\) | 0.237849 | + | 1.34891i | 0.00838829 | + | 0.0475724i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11.4338 | + | 19.8039i | −0.402738 | + | 0.697562i | ||||
\(807\) | −10.0182 | + | 27.5248i | −0.352657 | + | 0.968917i | ||||
\(808\) | −4.46840 | + | 12.2768i | −0.157198 | + | 0.431898i | ||||
\(809\) | −18.1503 | + | 31.4373i | −0.638131 | + | 1.10528i | 0.347711 | + | 0.937602i | \(0.386959\pi\) |
−0.985842 | + | 0.167674i | \(0.946374\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.04633 | − | 5.93406i | −0.0367418 | − | 0.208373i | 0.960910 | − | 0.276860i | \(-0.0892939\pi\) |
−0.997652 | + | 0.0684872i | \(0.978183\pi\) | |||||||
\(812\) | −6.95148 | + | 8.28445i | −0.243949 | + | 0.290727i | ||||
\(813\) | 22.5261 | + | 26.8456i | 0.790026 | + | 0.941516i | ||||
\(814\) | 6.31163 | − | 35.7950i | 0.221223 | − | 1.25462i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.19357 | −0.0767905 | ||||||||
\(817\) | 8.75627 | + | 0.121618i | 0.306343 | + | 0.00425488i | ||||
\(818\) | − | 40.5198i | − | 1.41674i | ||||||
\(819\) | −18.2571 | + | 6.64503i | −0.637954 | + | 0.232196i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.0570 | + | 23.5426i | −0.979196 | + | 0.821643i | −0.983968 | − | 0.178345i | \(-0.942926\pi\) |
0.00477169 | + | 0.999989i | \(0.498481\pi\) | |||||||
\(822\) | 2.56116 | − | 3.05227i | 0.0893307 | − | 0.106460i | ||||
\(823\) | −15.0754 | + | 2.65820i | −0.525495 | + | 0.0926590i | −0.430101 | − | 0.902781i | \(-0.641522\pi\) |
−0.0953939 | + | 0.995440i | \(0.530411\pi\) | |||||||
\(824\) | −22.5470 | − | 39.0525i | −0.785461 | − | 1.36046i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 31.9876 | + | 11.6425i | 1.11299 | + | 0.405096i | ||||
\(827\) | 7.21472 | − | 19.8223i | 0.250880 | − | 0.689288i | −0.748769 | − | 0.662831i | \(-0.769355\pi\) |
0.999650 | − | 0.0264579i | \(-0.00842279\pi\) | |||||||
\(828\) | 3.20722 | + | 1.85169i | 0.111458 | + | 0.0643506i | ||||
\(829\) | 20.0967 | + | 34.8085i | 0.697987 | + | 1.20895i | 0.969163 | + | 0.246419i | \(0.0792539\pi\) |
−0.271177 | + | 0.962530i | \(0.587413\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.22414 | + | 7.73997i | 0.319982 | + | 0.268497i | ||||
\(832\) | 23.0558 | + | 27.4769i | 0.799317 | + | 0.952589i | ||||
\(833\) | 0.819740 | + | 0.144542i | 0.0284023 | + | 0.00500809i | ||||
\(834\) | 18.6902 | − | 6.80269i | 0.647190 | − | 0.235558i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.62194 | − | 5.35537i | 0.159853 | − | 0.185219i | ||||
\(837\) | 8.88176i | 0.306998i | ||||||||
\(838\) | −8.75300 | − | 24.0487i | −0.302367 | − | 0.830747i | ||||
\(839\) | −4.84143 | + | 27.4571i | −0.167145 | + | 0.947925i | 0.779681 | + | 0.626177i | \(0.215381\pi\) |
−0.946825 | + | 0.321748i | \(0.895730\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.1125 | + | 28.6238i | 1.17629 | + | 0.987027i | ||||
\(842\) | −8.63613 | + | 1.52278i | −0.297621 | + | 0.0524786i | ||||
\(843\) | 10.5977 | − | 6.11859i | 0.365004 | − | 0.210735i | ||||
\(844\) | 2.66669 | − | 4.61885i | 0.0917914 | − | 0.158987i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −26.5021 | − | 9.64596i | −0.911159 | − | 0.331635i | ||||
\(847\) | −5.72761 | − | 3.30684i | −0.196803 | − | 0.113624i | ||||
\(848\) | 16.3277 | − | 9.42680i | 0.560696 | − | 0.323718i | ||||
\(849\) | −6.97755 | − | 39.5717i | −0.239469 | − | 1.35810i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.5511 | − | 20.6008i | 0.841601 | − | 0.706187i | ||||
\(852\) | 10.0614 | + | 1.77409i | 0.344697 | + | 0.0607794i | ||||
\(853\) | 6.88015 | + | 18.9031i | 0.235572 | + | 0.647228i | 0.999997 | + | 0.00251570i | \(0.000800774\pi\) |
−0.764425 | + | 0.644713i | \(0.776977\pi\) | |||||||
\(854\) | −15.6736 | −0.536339 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18.9973 | −0.649315 | ||||||||
\(857\) | 1.48855 | + | 4.08976i | 0.0508480 | + | 0.139704i | 0.962517 | − | 0.271222i | \(-0.0874278\pi\) |
−0.911669 | + | 0.410926i | \(0.865206\pi\) | |||||||
\(858\) | −30.8356 | − | 5.43715i | −1.05271 | − | 0.185621i | ||||
\(859\) | 4.22949 | − | 3.54896i | 0.144308 | − | 0.121089i | −0.567776 | − | 0.823183i | \(-0.692196\pi\) |
0.712084 | + | 0.702094i | \(0.247751\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.71842 | − | 15.4169i | −0.0926435 | − | 0.525408i | ||||
\(862\) | −0.130682 | + | 0.0754492i | −0.00445104 | + | 0.00256981i | ||||
\(863\) | 31.0093 | + | 17.9032i | 1.05557 | + | 0.609433i | 0.924203 | − | 0.381901i | \(-0.124730\pi\) |
0.131366 | + | 0.991334i | \(0.458064\pi\) | |||||||
\(864\) | 5.57800 | + | 2.03022i | 0.189767 | + | 0.0690697i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.47365 | − | 6.01653i | 0.118039 | − | 0.204450i | ||||
\(867\) | −33.1785 | + | 19.1556i | −1.12680 | + | 0.650559i | ||||
\(868\) | −5.82808 | + | 1.02765i | −0.197818 | + | 0.0348806i | ||||
\(869\) | −29.0969 | − | 24.4152i | −0.987046 | − | 0.828230i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.743722 | − | 4.21786i | 0.0252001 | − | 0.142917i | ||||
\(872\) | −0.792530 | − | 2.17746i | −0.0268385 | − | 0.0737381i | ||||
\(873\) | − | 31.3100i | − | 1.05968i | ||||||
\(874\) | −15.2899 | + | 2.47759i | −0.517190 | + | 0.0838059i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −17.2808 | + | 6.28970i | −0.583864 | + | 0.212509i | ||||
\(877\) | −24.1462 | − | 4.25763i | −0.815360 | − | 0.143770i | −0.249610 | − | 0.968347i | \(-0.580302\pi\) |
−0.565750 | + | 0.824577i | \(0.691413\pi\) | |||||||
\(878\) | 14.2018 | + | 16.9250i | 0.479288 | + | 0.571193i | ||||
\(879\) | −8.20261 | − | 6.88280i | −0.276667 | − | 0.232151i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.7421 | + | 25.5341i | 0.496675 | + | 0.860266i | 0.999993 | − | 0.00383530i | \(-0.00122082\pi\) |
−0.503318 | + | 0.864101i | \(0.667887\pi\) | |||||||
\(882\) | −4.87569 | − | 2.81498i | −0.164173 | − | 0.0947853i | ||||
\(883\) | 2.74594 | − | 7.54441i | 0.0924083 | − | 0.253890i | −0.884874 | − | 0.465830i | \(-0.845756\pi\) |
0.977283 | + | 0.211940i | \(0.0679782\pi\) | |||||||
\(884\) | −0.842559 | − | 0.306666i | −0.0283383 | − | 0.0103143i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.2096 | + | 22.8798i | 0.443787 | + | 0.768661i | ||||
\(887\) | −20.5987 | + | 3.63211i | −0.691638 | + | 0.121954i | −0.508409 | − | 0.861116i | \(-0.669766\pi\) |
−0.183229 | + | 0.983070i | \(0.558655\pi\) | |||||||
\(888\) | −48.3688 | + | 57.6437i | −1.62315 | + | 1.93439i | ||||
\(889\) | −5.79561 | + | 4.86309i | −0.194378 | + | 0.163103i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28.6974 | + | 10.4450i | −0.961399 | + | 0.349921i | ||||
\(892\) | 1.60250i | 0.0536556i | ||||||||
\(893\) | −44.8585 | + | 15.6251i | −1.50113 | + | 0.522874i | ||||
\(894\) | 27.1214 | 0.907077 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.61040 | − | 9.13305i | 0.0537998 | − | 0.305114i | ||||
\(897\) | −17.7465 | − | 21.1495i | −0.592540 | − | 0.706162i | ||||
\(898\) | 15.7867 | − | 18.8138i | 0.526809 | − | 0.627826i | ||||
\(899\) | 6.98720 | + | 39.6264i | 0.233036 | + | 1.32161i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.43023 | + | 2.47723i | −0.0476478 | + | 0.0825283i | ||||
\(902\) | 3.61921 | − | 9.94370i | 0.120506 | − | 0.331089i | ||||
\(903\) | 3.43083 | − | 9.42612i | 0.114171 | − | 0.313682i | ||||
\(904\) | 1.33709 | − | 2.31591i | 0.0444711 | − | 0.0770262i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7.10260 | − | 40.2809i | −0.235968 | − | 1.33824i | ||||
\(907\) | 0.188414 | − | 0.224543i | 0.00625619 | − | 0.00745584i | −0.762907 | − | 0.646508i | \(-0.776229\pi\) |
0.769163 | + | 0.639052i | \(0.220673\pi\) | |||||||
\(908\) | −0.311530 | − | 0.371267i | −0.0103385 | − | 0.0123209i | ||||
\(909\) | −1.59966 | + | 9.07211i | −0.0530573 | + | 0.300903i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.0356 | −0.730073 | −0.365037 | − | 0.930993i | \(-0.618944\pi\) | ||||
−0.365037 | + | 0.930993i | \(0.618944\pi\) | |||||||
\(912\) | 23.5984 | − | 8.21981i | 0.781423 | − | 0.272185i | ||||
\(913\) | − | 15.7043i | − | 0.519736i | ||||||
\(914\) | −22.8434 | + | 8.31432i | −0.755592 | + | 0.275013i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.65720 | + | 8.10336i | −0.319083 | + | 0.267742i | ||||
\(917\) | 14.5434 | − | 17.3321i | 0.480265 | − | 0.572358i | ||||
\(918\) | 0.851656 | − | 0.150170i | 0.0281089 | − | 0.00495635i | ||||
\(919\) | −0.460757 | − | 0.798054i | −0.0151990 | − | 0.0263254i | 0.858326 | − | 0.513105i | \(-0.171505\pi\) |
−0.873525 | + | 0.486780i | \(0.838171\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.2183 | − | 9.17870i | −0.830970 | − | 0.302448i | ||||
\(922\) | 2.26361 | − | 6.21922i | 0.0745481 | − | 0.204819i | ||||
\(923\) | −27.6660 | − | 15.9729i | −0.910636 | − | 0.525756i | ||||
\(924\) | −4.05158 | − | 7.01755i | −0.133287 | − | 0.230860i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −29.8655 | − | 25.0601i | −0.981440 | − | 0.823526i | ||||
\(927\) | −20.4382 | − | 24.3573i | −0.671277 | − | 0.799997i | ||||
\(928\) | 26.4836 | + | 4.66978i | 0.869368 | + | 0.153293i | ||||
\(929\) | −22.0825 | + | 8.03737i | −0.724503 | + | 0.263697i | −0.677836 | − | 0.735213i | \(-0.737082\pi\) |
−0.0466666 | + | 0.998911i | \(0.514860\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.36039 | + | 1.51677i | −0.306774 | + | 0.0497100i | ||||
\(932\) | 2.53525i | 0.0830448i | ||||||||
\(933\) | −6.95069 | − | 19.0969i | −0.227556 | − | 0.625204i | ||||
\(934\) | 5.94289 | − | 33.7038i | 0.194457 | − | 1.10282i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 20.8277 | + | 17.4765i | 0.680774 | + | 0.571238i | ||||
\(937\) | 52.5128 | − | 9.25942i | 1.71552 | − | 0.302492i | 0.772445 | − | 0.635081i | \(-0.219033\pi\) |
0.943072 | + | 0.332589i | \(0.107922\pi\) | |||||||
\(938\) | −2.38366 | + | 1.37621i | −0.0778293 | + | 0.0449348i | ||||
\(939\) | −15.2649 | + | 26.4396i | −0.498152 | + | 0.862824i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.88045 | + | 1.41237i | 0.126499 | + | 0.0460418i | 0.404494 | − | 0.914541i | \(-0.367448\pi\) |
−0.277995 | + | 0.960583i | \(0.589670\pi\) | |||||||
\(942\) | 24.3169 | + | 14.0394i | 0.792288 | + | 0.457428i | ||||
\(943\) | 8.08050 | − | 4.66528i | 0.263137 | − | 0.151922i | ||||
\(944\) | −5.68386 | − | 32.2348i | −0.184994 | − | 1.04915i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.19418 | − | 4.35843i | 0.168877 | − | 0.141705i | ||||
\(947\) | 8.29375 | + | 1.46241i | 0.269511 | + | 0.0475220i | 0.306770 | − | 0.951784i | \(-0.400752\pi\) |
−0.0372596 | + | 0.999306i | \(0.511863\pi\) | |||||||
\(948\) | 5.99900 | + | 16.4821i | 0.194838 | + | 0.535314i | ||||
\(949\) | 57.5025 | 1.86661 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.1359 | −0.815088 | ||||||||
\(952\) | 0.883552 | + | 2.42754i | 0.0286361 | + | 0.0786770i | ||||
\(953\) | 18.6859 | + | 3.29483i | 0.605296 | + | 0.106730i | 0.467893 | − | 0.883785i | \(-0.345013\pi\) |
0.137403 | + | 0.990515i | \(0.456125\pi\) | |||||||
\(954\) | 14.8207 | − | 12.4361i | 0.479838 | − | 0.402632i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.97686 | − | 11.2114i | −0.0639364 | − | 0.362601i | ||||
\(957\) | −47.7138 | + | 27.5476i | −1.54237 | + | 0.890487i | ||||
\(958\) | −10.6229 | − | 6.13311i | −0.343209 | − | 0.198152i | ||||
\(959\) | −3.02983 | − | 1.10277i | −0.0978383 | − | 0.0356102i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.49052 | − | 7.77782i | 0.144856 | − | 0.250897i | ||||
\(962\) | 45.4511 | − | 26.2412i | 1.46540 | − | 0.846051i | ||||
\(963\) | −13.1917 | + | 2.32605i | −0.425095 | + | 0.0749558i | ||||
\(964\) | −9.18584 | − | 7.70784i | −0.295856 | − | 0.248253i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.08099 | + | 17.4732i | −0.0991292 | + | 0.562189i | ||||
\(967\) | 1.28556 | + | 3.53205i | 0.0413408 | + | 0.113583i | 0.958645 | − | 0.284603i | \(-0.0918619\pi\) |
−0.917305 | + | 0.398186i | \(0.869640\pi\) | |||||||
\(968\) | 9.25517i | 0.297473i | ||||||||
\(969\) | −2.47711 | + | 2.87019i | −0.0795763 | + | 0.0922038i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.0598 | + | 4.38940i | −0.387016 | + | 0.140862i | −0.528198 | − | 0.849121i | \(-0.677132\pi\) |
0.141182 | + | 0.989984i | \(0.454910\pi\) | |||||||
\(972\) | 10.6772 | + | 1.88268i | 0.342472 | + | 0.0603871i | ||||
\(973\) | −10.3457 | − | 12.3295i | −0.331668 | − | 0.395266i | ||||
\(974\) | 10.1757 | + | 8.53845i | 0.326051 | + | 0.273590i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.53556 | + | 13.0520i | 0.241207 | + | 0.417783i | ||||
\(977\) | 23.8455 | + | 13.7672i | 0.762887 | + | 0.440453i | 0.830331 | − | 0.557270i | \(-0.188151\pi\) |
−0.0674446 | + | 0.997723i | \(0.521485\pi\) | |||||||
\(978\) | −6.40579 | + | 17.5998i | −0.204835 | + | 0.562779i | ||||
\(979\) | 17.4343 | + | 6.34557i | 0.557203 | + | 0.202805i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.816940 | − | 1.41498i | −0.0260829 | − | 0.0451769i | ||||
\(982\) | 16.3276 | − | 2.87899i | 0.521033 | − | 0.0918722i | ||||
\(983\) | 31.0232 | − | 36.9720i | 0.989486 | − | 1.17922i | 0.00568028 | − | 0.999984i | \(-0.498192\pi\) |
0.983805 | − | 0.179239i | \(-0.0573637\pi\) | |||||||
\(984\) | −16.7819 | + | 14.0817i | −0.534989 | + | 0.448909i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.68157 | − | 1.33998i | 0.117245 | − | 0.0426737i | ||||
\(987\) | 54.4122i | 1.73196i | ||||||||
\(988\) | 10.2134 | + | 0.141856i | 0.324931 | + | 0.00451305i | ||||
\(989\) | 5.97872 | 0.190112 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.57591 | + | 42.9651i | −0.240657 | + | 1.36483i | 0.589710 | + | 0.807615i | \(0.299242\pi\) |
−0.830367 | + | 0.557217i | \(0.811869\pi\) | |||||||
\(992\) | 9.45927 | + | 11.2731i | 0.300332 | + | 0.357922i | ||||
\(993\) | −4.15770 | + | 4.95495i | −0.131941 | + | 0.157241i | ||||
\(994\) | 3.56499 | + | 20.2181i | 0.113075 | + | 0.641279i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.62595 | + | 6.28034i | −0.114893 | + | 0.199000i | ||||
\(997\) | 10.3283 | − | 28.3767i | 0.327099 | − | 0.898698i | −0.661743 | − | 0.749731i | \(-0.730183\pi\) |
0.988842 | − | 0.148967i | \(-0.0475949\pi\) | |||||||
\(998\) | 5.22255 | − | 14.3488i | 0.165317 | − | 0.454205i | ||||
\(999\) | 10.1921 | − | 17.6532i | 0.322464 | − | 0.558523i |
(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 | 475.2.u.c.24.4 | 36 | ||
5.2 | odd | 4 | 475.2.l.b.176.2 | 18 | |||
5.3 | odd | 4 | 95.2.k.b.81.2 | yes | 18 | ||
5.4 | even | 2 | inner | 475.2.u.c.24.3 | 36 | ||
15.8 | even | 4 | 855.2.bs.b.271.2 | 18 | |||
19.4 | even | 9 | inner | 475.2.u.c.99.3 | 36 | ||
95.2 | even | 36 | 9025.2.a.cd.1.4 | 9 | |||
95.4 | even | 18 | inner | 475.2.u.c.99.4 | 36 | ||
95.17 | odd | 36 | 9025.2.a.ce.1.6 | 9 | |||
95.23 | odd | 36 | 95.2.k.b.61.2 | ✓ | 18 | ||
95.42 | odd | 36 | 475.2.l.b.251.2 | 18 | |||
95.78 | even | 36 | 1805.2.a.u.1.6 | 9 | |||
95.93 | odd | 36 | 1805.2.a.t.1.4 | 9 | |||
285.23 | even | 36 | 855.2.bs.b.631.2 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.k.b.61.2 | ✓ | 18 | 95.23 | odd | 36 | ||
95.2.k.b.81.2 | yes | 18 | 5.3 | odd | 4 | ||
475.2.l.b.176.2 | 18 | 5.2 | odd | 4 | |||
475.2.l.b.251.2 | 18 | 95.42 | odd | 36 | |||
475.2.u.c.24.3 | 36 | 5.4 | even | 2 | inner | ||
475.2.u.c.24.4 | 36 | 1.1 | even | 1 | trivial | ||
475.2.u.c.99.3 | 36 | 19.4 | even | 9 | inner | ||
475.2.u.c.99.4 | 36 | 95.4 | even | 18 | inner | ||
855.2.bs.b.271.2 | 18 | 15.8 | even | 4 | |||
855.2.bs.b.631.2 | 18 | 285.23 | even | 36 | |||
1805.2.a.t.1.4 | 9 | 95.93 | odd | 36 | |||
1805.2.a.u.1.6 | 9 | 95.78 | even | 36 | |||
9025.2.a.cd.1.4 | 9 | 95.2 | even | 36 | |||
9025.2.a.ce.1.6 | 9 | 95.17 | odd | 36 |