Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(19,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.x (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 80.5 | ||
Character | \(\chi\) | \(=\) | 637.80 |
Dual form | 637.2.x.b.215.6 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.239080 | + | 0.892257i | 0.169055 | + | 0.630921i | 0.997488 | + | 0.0708335i | \(0.0225659\pi\) |
−0.828433 | + | 0.560088i | \(0.810767\pi\) | |||||||
\(3\) | − | 1.14107i | − | 0.658797i | −0.944191 | − | 0.329399i | \(-0.893154\pi\) | ||
0.944191 | − | 0.329399i | \(-0.106846\pi\) | |||||||
\(4\) | 0.993087 | − | 0.573359i | 0.496543 | − | 0.286679i | ||||
\(5\) | 1.02497 | − | 3.82526i | 0.458383 | − | 1.71071i | −0.219566 | − | 0.975598i | \(-0.570464\pi\) |
0.677948 | − | 0.735110i | \(-0.262869\pi\) | |||||||
\(6\) | 1.01813 | − | 0.272807i | 0.415649 | − | 0.111373i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.05537 | + | 2.05537i | 0.726682 | + | 0.726682i | ||||
\(9\) | 1.69796 | 0.565986 | ||||||||
\(10\) | 3.65816 | 1.15681 | ||||||||
\(11\) | 1.48892 | + | 1.48892i | 0.448926 | + | 0.448926i | 0.894997 | − | 0.446071i | \(-0.147177\pi\) |
−0.446071 | + | 0.894997i | \(0.647177\pi\) | |||||||
\(12\) | −0.654243 | − | 1.13318i | −0.188864 | − | 0.327121i | ||||
\(13\) | −3.41094 | + | 1.16855i | −0.946024 | + | 0.324097i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.36489 | − | 1.16957i | −1.12701 | − | 0.301981i | ||||
\(16\) | −0.195801 | + | 0.339138i | −0.0489503 | + | 0.0847845i | ||||
\(17\) | 1.58621 | + | 2.74739i | 0.384712 | + | 0.666341i | 0.991729 | − | 0.128348i | \(-0.0409674\pi\) |
−0.607017 | + | 0.794689i | \(0.707634\pi\) | |||||||
\(18\) | 0.405947 | + | 1.51502i | 0.0956827 | + | 0.357093i | ||||
\(19\) | 0.825689 | + | 0.825689i | 0.189426 | + | 0.189426i | 0.795448 | − | 0.606022i | \(-0.207236\pi\) |
−0.606022 | + | 0.795448i | \(0.707236\pi\) | |||||||
\(20\) | −1.17536 | − | 4.38649i | −0.262818 | − | 0.980849i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.972529 | + | 1.68447i | −0.207344 | + | 0.359130i | ||||
\(23\) | −3.26418 | − | 1.88457i | −0.680628 | − | 0.392961i | 0.119464 | − | 0.992839i | \(-0.461882\pi\) |
−0.800092 | + | 0.599878i | \(0.795216\pi\) | |||||||
\(24\) | 2.34532 | − | 2.34532i | 0.478736 | − | 0.478736i | ||||
\(25\) | −9.25190 | − | 5.34158i | −1.85038 | − | 1.06832i | ||||
\(26\) | −1.85813 | − | 2.76406i | −0.364409 | − | 0.542076i | ||||
\(27\) | − | 5.36070i | − | 1.03167i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.584891 | − | 1.01306i | −0.108612 | − | 0.188121i | 0.806596 | − | 0.591102i | \(-0.201307\pi\) |
−0.915208 | + | 0.402982i | \(0.867974\pi\) | |||||||
\(30\) | − | 4.17422i | − | 0.762106i | ||||||
\(31\) | 4.88736 | − | 1.30956i | 0.877796 | − | 0.235205i | 0.208340 | − | 0.978056i | \(-0.433194\pi\) |
0.669456 | + | 0.742852i | \(0.266527\pi\) | |||||||
\(32\) | 5.26595 | + | 1.41101i | 0.930898 | + | 0.249433i | ||||
\(33\) | 1.69896 | − | 1.69896i | 0.295751 | − | 0.295751i | ||||
\(34\) | −2.07215 | + | 2.07215i | −0.355371 | + | 0.355371i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.68622 | − | 0.973539i | 0.281037 | − | 0.162257i | ||||
\(37\) | −4.26868 | + | 1.14379i | −0.701766 | + | 0.188038i | −0.592022 | − | 0.805922i | \(-0.701670\pi\) |
−0.109745 | + | 0.993960i | \(0.535003\pi\) | |||||||
\(38\) | −0.539321 | + | 0.934132i | −0.0874895 | + | 0.151536i | ||||
\(39\) | 1.33339 | + | 3.89212i | 0.213514 | + | 0.623238i | ||||
\(40\) | 9.96900 | − | 5.75561i | 1.57624 | − | 0.910041i | ||||
\(41\) | −1.85922 | + | 6.93869i | −0.290361 | + | 1.08364i | 0.654472 | + | 0.756087i | \(0.272891\pi\) |
−0.944832 | + | 0.327555i | \(0.893775\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.91410 | − | 1.10511i | −0.291897 | − | 0.168527i | 0.346900 | − | 0.937902i | \(-0.387234\pi\) |
−0.638797 | + | 0.769375i | \(0.720568\pi\) | |||||||
\(44\) | 2.33231 | + | 0.624941i | 0.351609 | + | 0.0942134i | ||||
\(45\) | 1.74036 | − | 6.49513i | 0.259438 | − | 0.968236i | ||||
\(46\) | 0.901126 | − | 3.36305i | 0.132864 | − | 0.495854i | ||||
\(47\) | −11.2261 | − | 3.00801i | −1.63749 | − | 0.438764i | −0.681416 | − | 0.731896i | \(-0.738636\pi\) |
−0.956072 | + | 0.293132i | \(0.905302\pi\) | |||||||
\(48\) | 0.386980 | + | 0.223423i | 0.0558558 | + | 0.0322484i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.55413 | − | 9.53214i | 0.361208 | − | 1.34805i | ||||
\(51\) | 3.13497 | − | 1.80998i | 0.438984 | − | 0.253447i | ||||
\(52\) | −2.71736 | + | 3.11616i | −0.376830 | + | 0.432134i | ||||
\(53\) | −2.44630 | + | 4.23711i | −0.336025 | + | 0.582012i | −0.983681 | − | 0.179921i | \(-0.942416\pi\) |
0.647656 | + | 0.761933i | \(0.275749\pi\) | |||||||
\(54\) | 4.78313 | − | 1.28163i | 0.650901 | − | 0.174408i | ||||
\(55\) | 7.22161 | − | 4.16940i | 0.973762 | − | 0.562202i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.942169 | − | 0.942169i | 0.124793 | − | 0.124793i | ||||
\(58\) | 0.764076 | − | 0.764076i | 0.100328 | − | 0.100328i | ||||
\(59\) | 0.236582 | + | 0.0633920i | 0.0308004 | + | 0.00825293i | 0.274186 | − | 0.961677i | \(-0.411591\pi\) |
−0.243386 | + | 0.969930i | \(0.578258\pi\) | |||||||
\(60\) | −5.00530 | + | 1.34116i | −0.646181 | + | 0.173144i | ||||
\(61\) | 12.3685i | 1.58362i | 0.610767 | + | 0.791811i | \(0.290861\pi\) | ||||
−0.610767 | + | 0.791811i | \(0.709139\pi\) | |||||||
\(62\) | 2.33694 | + | 4.04770i | 0.296791 | + | 0.514058i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.81913i | 0.727392i | ||||||||
\(65\) | 0.973870 | + | 14.2454i | 0.120794 | + | 1.76693i | ||||
\(66\) | 1.92210 | + | 1.10972i | 0.236594 | + | 0.136598i | ||||
\(67\) | 7.28743 | − | 7.28743i | 0.890301 | − | 0.890301i | −0.104250 | − | 0.994551i | \(-0.533244\pi\) |
0.994551 | + | 0.104250i | \(0.0332442\pi\) | |||||||
\(68\) | 3.15048 | + | 1.81893i | 0.382052 | + | 0.220578i | ||||
\(69\) | −2.15043 | + | 3.72465i | −0.258881 | + | 0.448396i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.60477 | + | 5.98907i | 0.190451 | + | 0.710772i | 0.993398 | + | 0.114722i | \(0.0365976\pi\) |
−0.802947 | + | 0.596051i | \(0.796736\pi\) | |||||||
\(72\) | 3.48993 | + | 3.48993i | 0.411292 | + | 0.411292i | ||||
\(73\) | 1.27338 | + | 4.75231i | 0.149037 | + | 0.556216i | 0.999542 | + | 0.0302484i | \(0.00962984\pi\) |
−0.850505 | + | 0.525967i | \(0.823703\pi\) | |||||||
\(74\) | −2.04111 | − | 3.53530i | −0.237274 | − | 0.410971i | ||||
\(75\) | −6.09513 | + | 10.5571i | −0.703804 | + | 1.21903i | ||||
\(76\) | 1.29340 | + | 0.346564i | 0.148363 | + | 0.0397537i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.15399 | + | 2.12026i | −0.357119 | + | 0.240072i | ||||
\(79\) | 1.34840 | + | 2.33549i | 0.151707 | + | 0.262764i | 0.931855 | − | 0.362831i | \(-0.118190\pi\) |
−0.780148 | + | 0.625595i | \(0.784856\pi\) | |||||||
\(80\) | 1.09660 | + | 1.09660i | 0.122603 | + | 0.122603i | ||||
\(81\) | −1.02306 | −0.113674 | ||||||||
\(82\) | −6.63560 | −0.732779 | ||||||||
\(83\) | −3.31162 | − | 3.31162i | −0.363497 | − | 0.363497i | 0.501602 | − | 0.865099i | \(-0.332744\pi\) |
−0.865099 | + | 0.501602i | \(0.832744\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.1353 | − | 3.25165i | 1.31626 | − | 0.352691i | ||||
\(86\) | 0.528416 | − | 1.97208i | 0.0569806 | − | 0.212654i | ||||
\(87\) | −1.15597 | + | 0.667402i | −0.123933 | + | 0.0715530i | ||||
\(88\) | 6.12055i | 0.652453i | ||||||||
\(89\) | 1.80032 | + | 6.71890i | 0.190834 | + | 0.712202i | 0.993306 | + | 0.115512i | \(0.0368510\pi\) |
−0.802472 | + | 0.596690i | \(0.796482\pi\) | |||||||
\(90\) | 6.21141 | 0.654740 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.32215 | −0.450615 | ||||||||
\(93\) | −1.49431 | − | 5.57683i | −0.154952 | − | 0.578290i | ||||
\(94\) | − | 10.7357i | − | 1.10730i | ||||||
\(95\) | 4.00478 | − | 2.31216i | 0.410882 | − | 0.237223i | ||||
\(96\) | 1.61006 | − | 6.00882i | 0.164326 | − | 0.613273i | ||||
\(97\) | 15.8523 | − | 4.24762i | 1.60956 | − | 0.431280i | 0.661649 | − | 0.749814i | \(-0.269857\pi\) |
0.947912 | + | 0.318533i | \(0.103190\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.52812 | + | 2.52812i | 0.254086 | + | 0.254086i | ||||
\(100\) | −12.2506 | −1.22506 | ||||||||
\(101\) | −3.62029 | −0.360233 | −0.180116 | − | 0.983645i | \(-0.557647\pi\) | ||||
−0.180116 | + | 0.983645i | \(0.557647\pi\) | |||||||
\(102\) | 2.36447 | + | 2.36447i | 0.234118 | + | 0.234118i | ||||
\(103\) | −0.795369 | − | 1.37762i | −0.0783700 | − | 0.135741i | 0.824177 | − | 0.566333i | \(-0.191638\pi\) |
−0.902547 | + | 0.430592i | \(0.858305\pi\) | |||||||
\(104\) | −9.41252 | − | 4.60893i | −0.922973 | − | 0.451943i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.36545 | − | 1.16972i | −0.424010 | − | 0.113613i | ||||
\(107\) | 7.44322 | − | 12.8920i | 0.719563 | − | 1.24632i | −0.241610 | − | 0.970373i | \(-0.577676\pi\) |
0.961173 | − | 0.275946i | \(-0.0889911\pi\) | |||||||
\(108\) | −3.07361 | − | 5.32364i | −0.295758 | − | 0.512268i | ||||
\(109\) | −0.868870 | − | 3.24267i | −0.0832226 | − | 0.310591i | 0.911749 | − | 0.410748i | \(-0.134732\pi\) |
−0.994972 | + | 0.100157i | \(0.968066\pi\) | |||||||
\(110\) | 5.44672 | + | 5.44672i | 0.519324 | + | 0.519324i | ||||
\(111\) | 1.30514 | + | 4.87086i | 0.123879 | + | 0.462322i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.88202 | + | 8.45591i | −0.459262 | + | 0.795465i | −0.998922 | − | 0.0464177i | \(-0.985219\pi\) |
0.539660 | + | 0.841883i | \(0.318553\pi\) | |||||||
\(114\) | 1.06591 | + | 0.615404i | 0.0998317 | + | 0.0576378i | ||||
\(115\) | −10.5547 | + | 10.5547i | −0.984228 | + | 0.984228i | ||||
\(116\) | −1.16170 | − | 0.670705i | −0.107861 | − | 0.0622734i | ||||
\(117\) | −5.79163 | + | 1.98414i | −0.535436 | + | 0.183434i | ||||
\(118\) | 0.226248i | 0.0208278i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −6.56755 | − | 11.3753i | −0.599533 | − | 1.03842i | ||||
\(121\) | − | 6.56623i | − | 0.596930i | ||||||
\(122\) | −11.0359 | + | 2.95705i | −0.999140 | + | 0.267719i | ||||
\(123\) | 7.91753 | + | 2.12150i | 0.713900 | + | 0.191289i | ||||
\(124\) | 4.10272 | − | 4.10272i | 0.368436 | − | 0.368436i | ||||
\(125\) | −15.9145 | + | 15.9145i | −1.42343 | + | 1.42343i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.81869 | + | 3.93677i | −0.605061 | + | 0.349332i | −0.771030 | − | 0.636799i | \(-0.780258\pi\) |
0.165969 | + | 0.986131i | \(0.446925\pi\) | |||||||
\(128\) | 5.33974 | − | 1.43078i | 0.471971 | − | 0.126464i | ||||
\(129\) | −1.26100 | + | 2.18412i | −0.111025 | + | 0.192301i | ||||
\(130\) | −12.4778 | + | 4.27474i | −1.09437 | + | 0.374919i | ||||
\(131\) | −1.83447 | + | 1.05913i | −0.160279 | + | 0.0925369i | −0.577994 | − | 0.816041i | \(-0.696164\pi\) |
0.417715 | + | 0.908578i | \(0.362831\pi\) | |||||||
\(132\) | 0.713102 | − | 2.66133i | 0.0620676 | − | 0.231639i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.24454 | + | 4.75999i | 0.712220 | + | 0.411200i | ||||
\(135\) | −20.5061 | − | 5.49458i | −1.76488 | − | 0.472898i | ||||
\(136\) | −2.38666 | + | 8.90714i | −0.204654 | + | 0.763781i | ||||
\(137\) | −3.02455 | + | 11.2878i | −0.258405 | + | 0.964380i | 0.707760 | + | 0.706453i | \(0.249706\pi\) |
−0.966164 | + | 0.257927i | \(0.916961\pi\) | |||||||
\(138\) | −3.83747 | − | 1.02825i | −0.326668 | − | 0.0875303i | ||||
\(139\) | 3.88166 | + | 2.24108i | 0.329238 | + | 0.190086i | 0.655503 | − | 0.755193i | \(-0.272457\pi\) |
−0.326265 | + | 0.945278i | \(0.605790\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.43235 | + | 12.8097i | −0.289056 | + | 1.07877i | ||||
\(142\) | −4.96013 | + | 2.86373i | −0.416245 | + | 0.240319i | ||||
\(143\) | −6.81849 | − | 3.33874i | −0.570191 | − | 0.279200i | ||||
\(144\) | −0.332462 | + | 0.575842i | −0.0277052 | + | 0.0479868i | ||||
\(145\) | −4.47472 | + | 1.19900i | −0.371605 | + | 0.0995713i | ||||
\(146\) | −3.93584 | + | 2.27236i | −0.325733 | + | 0.188062i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.58337 | + | 3.58337i | −0.294551 | + | 0.294551i | ||||
\(149\) | 3.22134 | − | 3.22134i | 0.263903 | − | 0.263903i | −0.562735 | − | 0.826638i | \(-0.690251\pi\) |
0.826638 | + | 0.562735i | \(0.190251\pi\) | |||||||
\(150\) | −10.8768 | − | 2.91444i | −0.888090 | − | 0.237963i | ||||
\(151\) | 14.6306 | − | 3.92025i | 1.19062 | − | 0.319026i | 0.391489 | − | 0.920183i | \(-0.371960\pi\) |
0.799131 | + | 0.601157i | \(0.205293\pi\) | |||||||
\(152\) | 3.39418i | 0.275305i | ||||||||
\(153\) | 2.69331 | + | 4.66496i | 0.217742 | + | 0.377140i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 20.0377i | − | 1.60947i | ||||||
\(156\) | 3.55576 | + | 3.10070i | 0.284689 | + | 0.248255i | ||||
\(157\) | −12.1069 | − | 6.98994i | −0.966239 | − | 0.557858i | −0.0681513 | − | 0.997675i | \(-0.521710\pi\) |
−0.898088 | + | 0.439817i | \(0.855043\pi\) | |||||||
\(158\) | −1.76149 | + | 1.76149i | −0.140136 | + | 0.140136i | ||||
\(159\) | 4.83484 | + | 2.79140i | 0.383428 | + | 0.221372i | ||||
\(160\) | 10.7949 | − | 18.6974i | 0.853415 | − | 1.47816i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.244594 | − | 0.912837i | −0.0192171 | − | 0.0717192i | ||||
\(163\) | 16.5003 | + | 16.5003i | 1.29240 | + | 1.29240i | 0.933297 | + | 0.359107i | \(0.116919\pi\) |
0.359107 | + | 0.933297i | \(0.383081\pi\) | |||||||
\(164\) | 2.13200 | + | 7.95672i | 0.166481 | + | 0.621315i | ||||
\(165\) | −4.75758 | − | 8.24037i | −0.370377 | − | 0.641512i | ||||
\(166\) | 2.16307 | − | 3.74655i | 0.167887 | − | 0.290789i | ||||
\(167\) | −10.8156 | − | 2.89803i | −0.836935 | − | 0.224256i | −0.185198 | − | 0.982701i | \(-0.559293\pi\) |
−0.651737 | + | 0.758445i | \(0.725959\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.2690 | − | 7.97168i | 0.789923 | − | 0.613207i | ||||
\(170\) | 5.80261 | + | 10.0504i | 0.445040 | + | 0.770832i | ||||
\(171\) | 1.40198 | + | 1.40198i | 0.107212 | + | 0.107212i | ||||
\(172\) | −2.53449 | −0.193253 | ||||||||
\(173\) | −3.32856 | −0.253066 | −0.126533 | − | 0.991962i | \(-0.540385\pi\) | ||||
−0.126533 | + | 0.991962i | \(0.540385\pi\) | |||||||
\(174\) | −0.871864 | − | 0.871864i | −0.0660959 | − | 0.0660959i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.796482 | + | 0.213417i | −0.0600371 | + | 0.0160869i | ||||
\(177\) | 0.0723347 | − | 0.269957i | 0.00543701 | − | 0.0202912i | ||||
\(178\) | −5.56457 | + | 3.21270i | −0.417082 | + | 0.240802i | ||||
\(179\) | − | 0.255535i | − | 0.0190996i | −0.999954 | − | 0.00954980i | \(-0.996960\pi\) | ||
0.999954 | − | 0.00954980i | \(-0.00303984\pi\) | |||||||
\(180\) | −1.99571 | − | 7.44808i | −0.148751 | − | 0.555147i | ||||
\(181\) | −7.65115 | −0.568705 | −0.284353 | − | 0.958720i | \(-0.591779\pi\) | ||||
−0.284353 | + | 0.958720i | \(0.591779\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.1133 | 1.04329 | ||||||||
\(184\) | −2.83559 | − | 10.5826i | −0.209042 | − | 0.780157i | ||||
\(185\) | 17.5011i | 1.28671i | ||||||||
\(186\) | 4.61871 | − | 2.66661i | 0.338660 | − | 0.195525i | ||||
\(187\) | −1.72891 | + | 6.45239i | −0.126431 | + | 0.471845i | ||||
\(188\) | −12.8731 | + | 3.44934i | −0.938868 | + | 0.251569i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.02050 | + | 3.02050i | 0.219130 | + | 0.219130i | ||||
\(191\) | −14.5107 | −1.04996 | −0.524978 | − | 0.851116i | \(-0.675927\pi\) | ||||
−0.524978 | + | 0.851116i | \(0.675927\pi\) | |||||||
\(192\) | 6.64004 | 0.479204 | ||||||||
\(193\) | 5.69196 | + | 5.69196i | 0.409716 | + | 0.409716i | 0.881639 | − | 0.471924i | \(-0.156440\pi\) |
−0.471924 | + | 0.881639i | \(0.656440\pi\) | |||||||
\(194\) | 7.57994 | + | 13.1288i | 0.544208 | + | 0.942596i | ||||
\(195\) | 16.2551 | − | 1.11125i | 1.16405 | − | 0.0795785i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.28115 | + | 1.68303i | 0.447514 | + | 0.119911i | 0.475536 | − | 0.879696i | \(-0.342254\pi\) |
−0.0280221 | + | 0.999607i | \(0.508921\pi\) | |||||||
\(198\) | −1.65131 | + | 2.86016i | −0.117354 | + | 0.203263i | ||||
\(199\) | −3.53990 | − | 6.13129i | −0.250937 | − | 0.434636i | 0.712847 | − | 0.701320i | \(-0.247405\pi\) |
−0.963784 | + | 0.266684i | \(0.914072\pi\) | |||||||
\(200\) | −8.03712 | − | 29.9949i | −0.568310 | − | 2.12096i | ||||
\(201\) | −8.31547 | − | 8.31547i | −0.586528 | − | 0.586528i | ||||
\(202\) | −0.865539 | − | 3.23023i | −0.0608991 | − | 0.227279i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.07553 | − | 3.59493i | 0.145316 | − | 0.251695i | ||||
\(205\) | 24.6366 | + | 14.2240i | 1.72070 | + | 0.993445i | ||||
\(206\) | 1.03903 | − | 1.03903i | 0.0723929 | − | 0.0723929i | ||||
\(207\) | −5.54243 | − | 3.19993i | −0.385226 | − | 0.222410i | ||||
\(208\) | 0.271568 | − | 1.38558i | 0.0188298 | − | 0.0960728i | ||||
\(209\) | 2.45877i | 0.170077i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.81923 | − | 6.61509i | −0.262926 | − | 0.455402i | 0.704092 | − | 0.710109i | \(-0.251354\pi\) |
−0.967018 | + | 0.254707i | \(0.918021\pi\) | |||||||
\(212\) | 5.61043i | 0.385326i | ||||||||
\(213\) | 6.83395 | − | 1.83115i | 0.468255 | − | 0.125469i | ||||
\(214\) | 13.2825 | + | 3.55904i | 0.907975 | + | 0.243291i | ||||
\(215\) | −6.18921 | + | 6.18921i | −0.422101 | + | 0.422101i | ||||
\(216\) | 11.0182 | − | 11.0182i | 0.749694 | − | 0.749694i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.68556 | − | 1.55051i | 0.181889 | − | 0.105014i | ||||
\(219\) | 5.42272 | − | 1.45301i | 0.366433 | − | 0.0981855i | ||||
\(220\) | 4.78112 | − | 8.28115i | 0.322343 | − | 0.558315i | ||||
\(221\) | −8.62092 | − | 7.51763i | −0.579906 | − | 0.505690i | ||||
\(222\) | −4.03403 | + | 2.32905i | −0.270746 | + | 0.156315i | ||||
\(223\) | −1.74359 | + | 6.50716i | −0.116759 | + | 0.435752i | −0.999413 | − | 0.0342732i | \(-0.989088\pi\) |
0.882653 | + | 0.470025i | \(0.155755\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −15.7093 | − | 9.06979i | −1.04729 | − | 0.604652i | ||||
\(226\) | −8.71204 | − | 2.33438i | −0.579516 | − | 0.155281i | ||||
\(227\) | 4.18872 | − | 15.6325i | 0.278015 | − | 1.03757i | −0.675778 | − | 0.737105i | \(-0.736192\pi\) |
0.953794 | − | 0.300462i | \(-0.0971409\pi\) | |||||||
\(228\) | 0.395455 | − | 1.47586i | 0.0261896 | − | 0.0977410i | ||||
\(229\) | 18.9495 | + | 5.07751i | 1.25222 | + | 0.335531i | 0.823194 | − | 0.567760i | \(-0.192190\pi\) |
0.429027 | + | 0.903292i | \(0.358857\pi\) | |||||||
\(230\) | −11.9409 | − | 6.89408i | −0.787359 | − | 0.454582i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.880046 | − | 3.28438i | 0.0577778 | − | 0.215630i | ||||
\(233\) | −9.61575 | + | 5.55165i | −0.629949 | + | 0.363701i | −0.780732 | − | 0.624866i | \(-0.785154\pi\) |
0.150784 | + | 0.988567i | \(0.451820\pi\) | |||||||
\(234\) | −3.15503 | − | 4.69326i | −0.206251 | − | 0.306808i | ||||
\(235\) | −23.0128 | + | 39.8594i | −1.50119 | + | 2.60014i | ||||
\(236\) | 0.271293 | − | 0.0726927i | 0.0176597 | − | 0.00473189i | ||||
\(237\) | 2.66496 | − | 1.53862i | 0.173108 | − | 0.0999439i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.0241 | + | 18.0241i | −1.16588 | + | 1.16588i | −0.182716 | + | 0.983166i | \(0.558489\pi\) |
−0.983166 | + | 0.182716i | \(0.941511\pi\) | |||||||
\(240\) | 1.25130 | − | 1.25130i | 0.0807708 | − | 0.0807708i | ||||
\(241\) | 24.5725 | + | 6.58419i | 1.58286 | + | 0.424125i | 0.939809 | − | 0.341701i | \(-0.111003\pi\) |
0.643048 | + | 0.765826i | \(0.277670\pi\) | |||||||
\(242\) | 5.85877 | − | 1.56985i | 0.376616 | − | 0.100914i | ||||
\(243\) | − | 14.9147i | − | 0.956779i | ||||||
\(244\) | 7.09158 | + | 12.2830i | 0.453992 | + | 0.786337i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.57168i | 0.482753i | ||||||||
\(247\) | −3.78123 | − | 1.85152i | −0.240594 | − | 0.117809i | ||||
\(248\) | 12.7370 | + | 7.35368i | 0.808797 | + | 0.466959i | ||||
\(249\) | −3.77879 | + | 3.77879i | −0.239471 | + | 0.239471i | ||||
\(250\) | −18.0046 | − | 10.3950i | −1.13871 | − | 0.657437i | ||||
\(251\) | −3.01219 | + | 5.21727i | −0.190128 | + | 0.329311i | −0.945292 | − | 0.326224i | \(-0.894224\pi\) |
0.755165 | + | 0.655535i | \(0.227557\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.05412 | − | 7.66608i | −0.129141 | − | 0.481962i | ||||
\(254\) | −5.14282 | − | 5.14282i | −0.322689 | − | 0.322689i | ||||
\(255\) | −3.71036 | − | 13.8472i | −0.232352 | − | 0.867148i | ||||
\(256\) | 8.37238 | + | 14.5014i | 0.523274 | + | 0.906337i | ||||
\(257\) | 12.2067 | − | 21.1426i | 0.761434 | − | 1.31884i | −0.180678 | − | 0.983542i | \(-0.557829\pi\) |
0.942112 | − | 0.335300i | \(-0.108838\pi\) | |||||||
\(258\) | −2.25028 | − | 0.602960i | −0.140096 | − | 0.0375387i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 9.13489 | + | 13.5886i | 0.566522 | + | 0.842728i | ||||
\(261\) | −0.993120 | − | 1.72014i | −0.0614726 | − | 0.106474i | ||||
\(262\) | −1.38360 | − | 1.38360i | −0.0854794 | − | 0.0854794i | ||||
\(263\) | −15.1408 | −0.933624 | −0.466812 | − | 0.884357i | \(-0.654597\pi\) | ||||
−0.466812 | + | 0.884357i | \(0.654597\pi\) | |||||||
\(264\) | 6.98398 | 0.429834 | ||||||||
\(265\) | 13.7007 | + | 13.7007i | 0.841624 | + | 0.841624i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.66674 | − | 2.05430i | 0.469197 | − | 0.125721i | ||||
\(268\) | 3.05874 | − | 11.4154i | 0.186842 | − | 0.697304i | ||||
\(269\) | −3.06678 | + | 1.77061i | −0.186985 | + | 0.107956i | −0.590570 | − | 0.806986i | \(-0.701097\pi\) |
0.403585 | + | 0.914942i | \(0.367764\pi\) | |||||||
\(270\) | − | 19.6103i | − | 1.19345i | ||||||
\(271\) | 0.195709 | + | 0.730396i | 0.0118885 | + | 0.0443684i | 0.971615 | − | 0.236567i | \(-0.0760221\pi\) |
−0.959727 | + | 0.280935i | \(0.909355\pi\) | |||||||
\(272\) | −1.24233 | −0.0753271 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.7947 | −0.652133 | ||||||||
\(275\) | −5.82214 | − | 21.7285i | −0.351088 | − | 1.31028i | ||||
\(276\) | 4.93187i | 0.296864i | ||||||||
\(277\) | 9.03071 | − | 5.21388i | 0.542603 | − | 0.313272i | −0.203530 | − | 0.979069i | \(-0.565242\pi\) |
0.746133 | + | 0.665797i | \(0.231908\pi\) | |||||||
\(278\) | −1.07159 | + | 3.99923i | −0.0642698 | + | 0.239858i | ||||
\(279\) | 8.29854 | − | 2.22359i | 0.496820 | − | 0.133123i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.1394 | − | 18.1394i | −1.08211 | − | 1.08211i | −0.996313 | − | 0.0857959i | \(-0.972657\pi\) |
−0.0857959 | − | 0.996313i | \(-0.527343\pi\) | |||||||
\(282\) | −12.2502 | −0.729487 | ||||||||
\(283\) | −0.0492199 | −0.00292582 | −0.00146291 | − | 0.999999i | \(-0.500466\pi\) | ||||
−0.00146291 | + | 0.999999i | \(0.500466\pi\) | |||||||
\(284\) | 5.02756 | + | 5.02756i | 0.298331 | + | 0.298331i | ||||
\(285\) | −2.63834 | − | 4.56974i | −0.156282 | − | 0.270688i | ||||
\(286\) | 1.34885 | − | 6.88207i | 0.0797594 | − | 0.406945i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 8.94137 | + | 2.39583i | 0.526875 | + | 0.141176i | ||||
\(289\) | 3.46789 | − | 6.00656i | 0.203993 | − | 0.353327i | ||||
\(290\) | −2.13963 | − | 3.70594i | −0.125643 | − | 0.217621i | ||||
\(291\) | −4.84683 | − | 18.0886i | −0.284126 | − | 1.06037i | ||||
\(292\) | 3.98935 | + | 3.98935i | 0.233459 | + | 0.233459i | ||||
\(293\) | 4.26864 | + | 15.9308i | 0.249377 | + | 0.930686i | 0.971133 | + | 0.238539i | \(0.0766685\pi\) |
−0.721756 | + | 0.692147i | \(0.756665\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.484981 | − | 0.840012i | 0.0282367 | − | 0.0489074i | ||||
\(296\) | −11.1246 | − | 6.42279i | −0.646604 | − | 0.373317i | ||||
\(297\) | 7.98166 | − | 7.98166i | 0.463143 | − | 0.463143i | ||||
\(298\) | 3.64443 | + | 2.10411i | 0.211116 | + | 0.121888i | ||||
\(299\) | 13.3361 | + | 2.61382i | 0.771247 | + | 0.151161i | ||||
\(300\) | 13.9788i | 0.807065i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.99575 | + | 12.1170i | 0.402560 | + | 0.697255i | ||||
\(303\) | 4.13101i | 0.237320i | ||||||||
\(304\) | −0.441693 | + | 0.118351i | −0.0253328 | + | 0.00678791i | ||||
\(305\) | 47.3126 | + | 12.6774i | 2.70911 | + | 0.725905i | ||||
\(306\) | −3.51843 | + | 3.51843i | −0.201135 | + | 0.201135i | ||||
\(307\) | 13.8117 | − | 13.8117i | 0.788274 | − | 0.788274i | −0.192937 | − | 0.981211i | \(-0.561801\pi\) |
0.981211 | + | 0.192937i | \(0.0618012\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.57196 | + | 0.907572i | −0.0894257 | + | 0.0516300i | ||||
\(310\) | 17.8788 | − | 4.79060i | 1.01545 | − | 0.272088i | ||||
\(311\) | −2.25556 | + | 3.90675i | −0.127901 | + | 0.221531i | −0.922863 | − | 0.385128i | \(-0.874157\pi\) |
0.794962 | + | 0.606659i | \(0.207491\pi\) | |||||||
\(312\) | −5.25912 | + | 10.7403i | −0.297739 | + | 0.608052i | ||||
\(313\) | −26.8350 | + | 15.4932i | −1.51681 | + | 0.875728i | −0.517000 | + | 0.855985i | \(0.672951\pi\) |
−0.999805 | + | 0.0197427i | \(0.993715\pi\) | |||||||
\(314\) | 3.34231 | − | 12.4737i | 0.188617 | − | 0.703929i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.67815 | + | 1.54623i | 0.150658 | + | 0.0869823i | ||||
\(317\) | −5.92099 | − | 1.58652i | −0.332556 | − | 0.0891081i | 0.0886774 | − | 0.996060i | \(-0.471736\pi\) |
−0.421233 | + | 0.906952i | \(0.638403\pi\) | |||||||
\(318\) | −1.33473 | + | 4.98129i | −0.0748481 | + | 0.279337i | ||||
\(319\) | 0.637511 | − | 2.37922i | 0.0356938 | − | 0.133211i | ||||
\(320\) | 22.2597 | + | 5.96447i | 1.24435 | + | 0.333424i | ||||
\(321\) | −14.7107 | − | 8.49323i | −0.821072 | − | 0.474046i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.958777 | + | 3.57820i | −0.0533478 | + | 0.199097i | ||||
\(324\) | −1.01599 | + | 0.586583i | −0.0564440 | + | 0.0325879i | ||||
\(325\) | 37.7995 | + | 7.40854i | 2.09674 | + | 0.410952i | ||||
\(326\) | −10.7776 | + | 18.6674i | −0.596918 | + | 1.03389i | ||||
\(327\) | −3.70011 | + | 0.991442i | −0.204617 | + | 0.0548268i | ||||
\(328\) | −18.0829 | + | 10.4402i | −0.998462 | + | 0.576462i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.21509 | − | 6.21509i | 0.342129 | − | 0.342129i | ||||
\(331\) | 11.8222 | − | 11.8222i | 0.649807 | − | 0.649807i | −0.303139 | − | 0.952946i | \(-0.598035\pi\) |
0.952946 | + | 0.303139i | \(0.0980348\pi\) | |||||||
\(332\) | −5.18747 | − | 1.38998i | −0.284699 | − | 0.0762849i | ||||
\(333\) | −7.24804 | + | 1.94211i | −0.397190 | + | 0.106427i | ||||
\(334\) | − | 10.3431i | − | 0.565952i | ||||||
\(335\) | −20.4069 | − | 35.3457i | −1.11495 | − | 1.93114i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.4651i | 0.679017i | 0.940603 | + | 0.339508i | \(0.110261\pi\) | ||||
−0.940603 | + | 0.339508i | \(0.889739\pi\) | |||||||
\(338\) | 9.56790 | + | 7.25672i | 0.520425 | + | 0.394713i | ||||
\(339\) | 9.64879 | + | 5.57073i | 0.524050 | + | 0.302561i | ||||
\(340\) | 10.1871 | − | 10.1871i | 0.552471 | − | 0.552471i | ||||
\(341\) | 9.22673 | + | 5.32706i | 0.499656 | + | 0.288476i | ||||
\(342\) | −0.915745 | + | 1.58612i | −0.0495178 | + | 0.0857674i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.66278 | − | 6.20557i | −0.0896509 | − | 0.334582i | ||||
\(345\) | 12.0436 | + | 12.0436i | 0.648407 | + | 0.648407i | ||||
\(346\) | −0.795792 | − | 2.96994i | −0.0427820 | − | 0.159665i | ||||
\(347\) | −13.1263 | − | 22.7355i | −0.704659 | − | 1.22050i | −0.966815 | − | 0.255479i | \(-0.917767\pi\) |
0.262156 | − | 0.965026i | \(-0.415566\pi\) | |||||||
\(348\) | −0.765322 | + | 1.32558i | −0.0410256 | + | 0.0710583i | ||||
\(349\) | 7.06951 | + | 1.89427i | 0.378422 | + | 0.101398i | 0.443016 | − | 0.896514i | \(-0.353908\pi\) |
−0.0645937 | + | 0.997912i | \(0.520575\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.26423 | + | 18.2850i | 0.334360 | + | 0.975982i | ||||
\(352\) | 5.73971 | + | 9.94146i | 0.305927 | + | 0.529882i | ||||
\(353\) | 19.2744 | + | 19.2744i | 1.02587 | + | 1.02587i | 0.999656 | + | 0.0262143i | \(0.00834524\pi\) |
0.0262143 | + | 0.999656i | \(0.491655\pi\) | |||||||
\(354\) | 0.258165 | 0.0137213 | ||||||||
\(355\) | 24.5546 | 1.30322 | ||||||||
\(356\) | 5.64022 | + | 5.64022i | 0.298931 | + | 0.298931i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.228003 | − | 0.0610933i | 0.0120503 | − | 0.00322888i | ||||
\(359\) | −8.04040 | + | 30.0072i | −0.424356 | + | 1.58372i | 0.340969 | + | 0.940074i | \(0.389245\pi\) |
−0.765325 | + | 0.643644i | \(0.777422\pi\) | |||||||
\(360\) | 16.9269 | − | 9.77278i | 0.892128 | − | 0.515071i | ||||
\(361\) | − | 17.6365i | − | 0.928236i | ||||||
\(362\) | −1.82923 | − | 6.82679i | −0.0961424 | − | 0.358808i | ||||
\(363\) | −7.49254 | −0.393256 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.4840 | 1.01984 | ||||||||
\(366\) | 3.37420 | + | 12.5927i | 0.176372 | + | 0.658231i | ||||
\(367\) | − | 25.1296i | − | 1.31175i | −0.754867 | − | 0.655877i | \(-0.772299\pi\) | ||
0.754867 | − | 0.655877i | \(-0.227701\pi\) | |||||||
\(368\) | 1.27826 | − | 0.738004i | 0.0666339 | − | 0.0384711i | ||||
\(369\) | −3.15687 | + | 11.7816i | −0.164340 | + | 0.613326i | ||||
\(370\) | −15.6155 | + | 4.18417i | −0.811813 | + | 0.217525i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.68150 | − | 4.68150i | −0.242724 | − | 0.242724i | ||||
\(373\) | −3.10820 | −0.160937 | −0.0804683 | − | 0.996757i | \(-0.525642\pi\) | ||||
−0.0804683 | + | 0.996757i | \(0.525642\pi\) | |||||||
\(374\) | −6.17054 | −0.319071 | ||||||||
\(375\) | 18.1595 | + | 18.1595i | 0.937755 | + | 0.937755i | ||||
\(376\) | −16.8911 | − | 29.2562i | −0.871091 | − | 1.50877i | ||||
\(377\) | 3.17884 | + | 2.77202i | 0.163718 | + | 0.142766i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.35536 | − | 1.16702i | −0.223720 | − | 0.0599456i | 0.145218 | − | 0.989400i | \(-0.453612\pi\) |
−0.368938 | + | 0.929454i | \(0.620278\pi\) | |||||||
\(380\) | 2.65140 | − | 4.59235i | 0.136014 | − | 0.235583i | ||||
\(381\) | 4.49213 | + | 7.78060i | 0.230139 | + | 0.398612i | ||||
\(382\) | −3.46921 | − | 12.9473i | −0.177500 | − | 0.662440i | ||||
\(383\) | −23.7683 | − | 23.7683i | −1.21450 | − | 1.21450i | −0.969530 | − | 0.244974i | \(-0.921221\pi\) |
−0.244974 | − | 0.969530i | \(-0.578779\pi\) | |||||||
\(384\) | −1.63262 | − | 6.09302i | −0.0833143 | − | 0.310933i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.71786 | + | 6.43952i | −0.189234 | + | 0.327763i | ||||
\(387\) | −3.25006 | − | 1.87642i | −0.165210 | − | 0.0953839i | ||||
\(388\) | 13.3073 | − | 13.3073i | 0.675577 | − | 0.675577i | ||||
\(389\) | −17.8940 | − | 10.3311i | −0.907263 | − | 0.523809i | −0.0277136 | − | 0.999616i | \(-0.508823\pi\) |
−0.879550 | + | 0.475807i | \(0.842156\pi\) | |||||||
\(390\) | 4.87778 | + | 14.2380i | 0.246996 | + | 0.720970i | ||||
\(391\) | − | 11.9573i | − | 0.604707i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.20855 | + | 2.09326i | 0.0609631 | + | 0.105591i | ||||
\(394\) | 6.00678i | 0.302617i | ||||||||
\(395\) | 10.3159 | − | 2.76415i | 0.519051 | − | 0.139079i | ||||
\(396\) | 3.96017 | + | 1.06112i | 0.199006 | + | 0.0533235i | ||||
\(397\) | 5.19736 | − | 5.19736i | 0.260848 | − | 0.260848i | −0.564550 | − | 0.825399i | \(-0.690950\pi\) |
0.825399 | + | 0.564550i | \(0.190950\pi\) | |||||||
\(398\) | 4.62437 | − | 4.62437i | 0.231799 | − | 0.231799i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.62307 | − | 2.09178i | 0.181153 | − | 0.104589i | ||||
\(401\) | −1.38785 | + | 0.371875i | −0.0693062 | + | 0.0185705i | −0.293306 | − | 0.956019i | \(-0.594755\pi\) |
0.223999 | + | 0.974589i | \(0.428089\pi\) | |||||||
\(402\) | 5.43148 | − | 9.40760i | 0.270898 | − | 0.469208i | ||||
\(403\) | −15.1402 | + | 10.1780i | −0.754187 | + | 0.507000i | ||||
\(404\) | −3.59527 | + | 2.07573i | −0.178871 | + | 0.103271i | ||||
\(405\) | −1.04862 | + | 3.91348i | −0.0521061 | + | 0.194463i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.05873 | − | 4.65271i | −0.399457 | − | 0.230626i | ||||
\(408\) | 10.1637 | + | 2.72335i | 0.503177 | + | 0.134826i | ||||
\(409\) | −1.78773 | + | 6.67192i | −0.0883978 | + | 0.329905i | −0.995936 | − | 0.0900646i | \(-0.971293\pi\) |
0.907538 | + | 0.419970i | \(0.137959\pi\) | |||||||
\(410\) | −6.80132 | + | 25.3829i | −0.335893 | + | 1.25357i | ||||
\(411\) | 12.8802 | + | 3.45123i | 0.635331 | + | 0.170236i | ||||
\(412\) | −1.57974 | − | 0.912063i | −0.0778282 | − | 0.0449341i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.53007 | − | 5.71031i | 0.0751990 | − | 0.280647i | ||||
\(415\) | −16.0621 | + | 9.27346i | −0.788458 | + | 0.455216i | ||||
\(416\) | −19.6107 | + | 1.34066i | −0.961492 | + | 0.0657310i | ||||
\(417\) | 2.55723 | − | 4.42925i | 0.125228 | − | 0.216901i | ||||
\(418\) | −2.19385 | + | 0.587842i | −0.107305 | + | 0.0287523i | ||||
\(419\) | 7.98102 | − | 4.60785i | 0.389899 | − | 0.225108i | −0.292218 | − | 0.956352i | \(-0.594393\pi\) |
0.682116 | + | 0.731244i | \(0.261060\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.26432 | − | 9.26432i | 0.451515 | − | 0.451515i | −0.444342 | − | 0.895857i | \(-0.646562\pi\) |
0.895857 | + | 0.444342i | \(0.146562\pi\) | |||||||
\(422\) | 4.98927 | − | 4.98927i | 0.242874 | − | 0.242874i | ||||
\(423\) | −19.0614 | − | 5.10748i | −0.926795 | − | 0.248334i | ||||
\(424\) | −13.7369 | + | 3.68078i | −0.667120 | + | 0.178754i | ||||
\(425\) | − | 33.8915i | − | 1.64398i | ||||||
\(426\) | 3.26772 | + | 5.65985i | 0.158321 | + | 0.274221i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 17.0705i | − | 0.825136i | ||||||
\(429\) | −3.80974 | + | 7.78038i | −0.183936 | + | 0.375640i | ||||
\(430\) | −7.00209 | − | 4.04266i | −0.337671 | − | 0.194954i | ||||
\(431\) | 4.60076 | − | 4.60076i | 0.221611 | − | 0.221611i | −0.587566 | − | 0.809176i | \(-0.699914\pi\) |
0.809176 | + | 0.587566i | \(0.199914\pi\) | |||||||
\(432\) | 1.81802 | + | 1.04963i | 0.0874694 | + | 0.0505005i | ||||
\(433\) | −12.5684 | + | 21.7691i | −0.604000 | + | 1.04616i | 0.388209 | + | 0.921571i | \(0.373094\pi\) |
−0.992209 | + | 0.124587i | \(0.960239\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.36814 | + | 5.10597i | 0.0655973 | + | 0.244812i | ||||
\(436\) | −2.72207 | − | 2.72207i | −0.130364 | − | 0.130364i | ||||
\(437\) | −1.13912 | − | 4.25126i | −0.0544916 | − | 0.203365i | ||||
\(438\) | 2.59292 | + | 4.49107i | 0.123895 | + | 0.214592i | ||||
\(439\) | 8.84493 | − | 15.3199i | 0.422145 | − | 0.731177i | −0.574004 | − | 0.818853i | \(-0.694610\pi\) |
0.996149 | + | 0.0876754i | \(0.0279438\pi\) | |||||||
\(440\) | 23.4127 | + | 6.27341i | 1.11616 | + | 0.299073i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.64657 | − | 9.48939i | 0.221015 | − | 0.451364i | ||||
\(443\) | 7.16955 | + | 12.4180i | 0.340635 | + | 0.589998i | 0.984551 | − | 0.175099i | \(-0.0560245\pi\) |
−0.643915 | + | 0.765097i | \(0.722691\pi\) | |||||||
\(444\) | 4.08887 | + | 4.08887i | 0.194049 | + | 0.194049i | ||||
\(445\) | 27.5468 | 1.30584 | ||||||||
\(446\) | −6.22292 | −0.294664 | ||||||||
\(447\) | −3.67578 | − | 3.67578i | −0.173858 | − | 0.173858i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.82768 | + | 0.757676i | −0.133447 | + | 0.0357569i | −0.324924 | − | 0.945740i | \(-0.605339\pi\) |
0.191477 | + | 0.981497i | \(0.438672\pi\) | |||||||
\(450\) | 4.33680 | − | 16.1852i | 0.204439 | − | 0.762976i | ||||
\(451\) | −13.0994 | + | 7.56293i | −0.616826 | + | 0.356124i | ||||
\(452\) | 11.1966i | 0.526644i | ||||||||
\(453\) | −4.47329 | − | 16.6945i | −0.210173 | − | 0.784378i | ||||
\(454\) | 14.9497 | 0.701623 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.87300 | 0.181370 | ||||||||
\(457\) | −6.30680 | − | 23.5373i | −0.295020 | − | 1.10103i | −0.941202 | − | 0.337845i | \(-0.890302\pi\) |
0.646182 | − | 0.763183i | \(-0.276365\pi\) | |||||||
\(458\) | 18.1218i | 0.846776i | ||||||||
\(459\) | 14.7280 | − | 8.50319i | 0.687442 | − | 0.396895i | ||||
\(460\) | −4.43009 | + | 16.5333i | −0.206554 | + | 0.770870i | ||||
\(461\) | −20.1416 | + | 5.39694i | −0.938090 | + | 0.251360i | −0.695301 | − | 0.718719i | \(-0.744729\pi\) |
−0.242789 | + | 0.970079i | \(0.578062\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.98662 | + | 8.98662i | 0.417644 | + | 0.417644i | 0.884391 | − | 0.466747i | \(-0.154574\pi\) |
−0.466747 | + | 0.884391i | \(0.654574\pi\) | |||||||
\(464\) | 0.458090 | 0.0212663 | ||||||||
\(465\) | −22.8644 | −1.06031 | ||||||||
\(466\) | −7.25243 | − | 7.25243i | −0.335963 | − | 0.335963i | ||||
\(467\) | 11.5521 | + | 20.0088i | 0.534566 | + | 0.925895i | 0.999184 | + | 0.0403838i | \(0.0128581\pi\) |
−0.464619 | + | 0.885511i | \(0.653809\pi\) | |||||||
\(468\) | −4.61396 | + | 5.29111i | −0.213281 | + | 0.244582i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −41.0668 | − | 11.0038i | −1.89427 | − | 0.507568i | ||||
\(471\) | −7.97602 | + | 13.8149i | −0.367516 | + | 0.636556i | ||||
\(472\) | 0.355969 | + | 0.616557i | 0.0163848 | + | 0.0283793i | ||||
\(473\) | −1.20453 | − | 4.49535i | −0.0553842 | − | 0.206697i | ||||
\(474\) | 2.00998 | + | 2.00998i | 0.0923215 | + | 0.0923215i | ||||
\(475\) | −3.22870 | − | 12.0497i | −0.148143 | − | 0.552877i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.15371 | + | 7.19444i | −0.190185 | + | 0.329411i | ||||
\(478\) | −20.3913 | − | 11.7729i | −0.932678 | − | 0.538482i | ||||
\(479\) | −7.82481 | + | 7.82481i | −0.357525 | + | 0.357525i | −0.862900 | − | 0.505375i | \(-0.831354\pi\) |
0.505375 | + | 0.862900i | \(0.331354\pi\) | |||||||
\(480\) | −21.3350 | − | 12.3178i | −0.973807 | − | 0.562227i | ||||
\(481\) | 13.2236 | − | 8.88955i | 0.602945 | − | 0.405328i | ||||
\(482\) | 23.4992i | 1.07036i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.76481 | − | 6.52084i | −0.171128 | − | 0.296402i | ||||
\(485\) | − | 64.9930i | − | 2.95118i | ||||||
\(486\) | 13.3078 | − | 3.56580i | 0.603652 | − | 0.161748i | ||||
\(487\) | −30.1548 | − | 8.07996i | −1.36644 | − | 0.366138i | −0.500266 | − | 0.865872i | \(-0.666764\pi\) |
−0.866179 | + | 0.499734i | \(0.833431\pi\) | |||||||
\(488\) | −25.4217 | + | 25.4217i | −1.15079 | + | 1.15079i | ||||
\(489\) | 18.8280 | − | 18.8280i | 0.851432 | − | 0.851432i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.5025 | − | 11.2598i | 0.880137 | − | 0.508147i | 0.00943333 | − | 0.999956i | \(-0.496997\pi\) |
0.870704 | + | 0.491808i | \(0.163664\pi\) | |||||||
\(492\) | 9.07918 | − | 2.43276i | 0.409321 | − | 0.109677i | ||||
\(493\) | 1.85552 | − | 3.21385i | 0.0835683 | − | 0.144745i | ||||
\(494\) | 0.748014 | − | 3.81649i | 0.0336547 | − | 0.171712i | ||||
\(495\) | 12.2620 | − | 7.07946i | 0.551135 | − | 0.318198i | ||||
\(496\) | −0.512829 | + | 1.91390i | −0.0230267 | + | 0.0859368i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.27508 | − | 2.46822i | −0.191571 | − | 0.110604i | ||||
\(499\) | −22.0367 | − | 5.90470i | −0.986496 | − | 0.264331i | −0.270718 | − | 0.962659i | \(-0.587261\pi\) |
−0.715778 | + | 0.698328i | \(0.753928\pi\) | |||||||
\(500\) | −6.67975 | + | 24.9292i | −0.298728 | + | 1.11487i | ||||
\(501\) | −3.30686 | + | 12.3414i | −0.147739 | + | 0.551371i | ||||
\(502\) | −5.37530 | − | 1.44031i | −0.239911 | − | 0.0642841i | ||||
\(503\) | 3.72935 | + | 2.15314i | 0.166283 | + | 0.0960037i | 0.580832 | − | 0.814023i | \(-0.302727\pi\) |
−0.414549 | + | 0.910027i | \(0.636061\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.71071 | + | 13.8486i | −0.165124 | + | 0.616253i | ||||
\(506\) | 6.34901 | − | 3.66561i | 0.282248 | − | 0.162956i | ||||
\(507\) | −9.09625 | − | 11.7176i | −0.403979 | − | 0.520399i | ||||
\(508\) | −4.51437 | + | 7.81911i | −0.200293 | + | 0.346917i | ||||
\(509\) | 26.1818 | − | 7.01539i | 1.16049 | − | 0.310952i | 0.373327 | − | 0.927700i | \(-0.378217\pi\) |
0.787161 | + | 0.616748i | \(0.211550\pi\) | |||||||
\(510\) | 11.4682 | − | 6.62119i | 0.507822 | − | 0.293191i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −3.11938 | + | 3.11938i | −0.137858 | + | 0.137858i | ||||
\(513\) | 4.42627 | − | 4.42627i | 0.195425 | − | 0.195425i | ||||
\(514\) | 21.7831 | + | 5.83675i | 0.960809 | + | 0.257448i | ||||
\(515\) | −6.08498 | + | 1.63047i | −0.268136 | + | 0.0718469i | ||||
\(516\) | 2.89203i | 0.127314i | ||||||||
\(517\) | −12.2360 | − | 21.1934i | −0.538139 | − | 0.932084i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.79813i | 0.166719i | ||||||||
\(520\) | −27.2779 | + | 31.2813i | −1.19622 | + | 1.37177i | ||||
\(521\) | −12.0981 | − | 6.98482i | −0.530026 | − | 0.306011i | 0.211001 | − | 0.977486i | \(-0.432328\pi\) |
−0.741027 | + | 0.671475i | \(0.765661\pi\) | |||||||
\(522\) | 1.29737 | − | 1.29737i | 0.0567843 | − | 0.0567843i | ||||
\(523\) | −35.9424 | − | 20.7514i | −1.57165 | − | 0.907394i | −0.995967 | − | 0.0897221i | \(-0.971402\pi\) |
−0.575685 | − | 0.817672i | \(-0.695265\pi\) | |||||||
\(524\) | −1.21453 | + | 2.10362i | −0.0530569 | + | 0.0918972i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.61986 | − | 13.5095i | −0.157834 | − | 0.589043i | ||||
\(527\) | 11.3503 | + | 11.3503i | 0.494425 | + | 0.494425i | ||||
\(528\) | 0.243523 | + | 0.908842i | 0.0105980 | + | 0.0395523i | ||||
\(529\) | −4.39677 | − | 7.61543i | −0.191164 | − | 0.331106i | ||||
\(530\) | −8.94896 | + | 15.5001i | −0.388718 | + | 0.673279i | ||||
\(531\) | 0.401707 | + | 0.107637i | 0.0174326 | + | 0.00467105i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.76652 | − | 25.8400i | −0.0765163 | − | 1.11926i | ||||
\(534\) | 3.66592 | + | 6.34956i | 0.158640 | + | 0.274773i | ||||
\(535\) | −41.6862 | − | 41.6862i | −1.80225 | − | 1.80225i | ||||
\(536\) | 29.9567 | 1.29393 | ||||||||
\(537\) | −0.291584 | −0.0125828 | ||||||||
\(538\) | −2.31304 | − | 2.31304i | −0.0997223 | − | 0.0997223i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −23.5147 | + | 6.30074i | −1.01191 | + | 0.271141i | ||||
\(541\) | −1.61721 | + | 6.03551i | −0.0695292 | + | 0.259487i | −0.991937 | − | 0.126730i | \(-0.959552\pi\) |
0.922408 | + | 0.386217i | \(0.126218\pi\) | |||||||
\(542\) | −0.604911 | + | 0.349246i | −0.0259832 | + | 0.0150014i | ||||
\(543\) | 8.73050i | 0.374661i | ||||||||
\(544\) | 4.47630 | + | 16.7058i | 0.191920 | + | 0.716255i | ||||
\(545\) | −13.2946 | −0.569478 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.9633 | −1.11011 | −0.555055 | − | 0.831814i | \(-0.687303\pi\) | ||||
−0.555055 | + | 0.831814i | \(0.687303\pi\) | |||||||
\(548\) | 3.46831 | + | 12.9439i | 0.148159 | + | 0.552936i | ||||
\(549\) | 21.0012i | 0.896308i | ||||||||
\(550\) | 17.9955 | − | 10.3897i | 0.767330 | − | 0.443018i | ||||
\(551\) | 0.353535 | − | 1.31941i | 0.0150611 | − | 0.0562088i | ||||
\(552\) | −12.0755 | + | 3.23561i | −0.513965 | + | 0.137717i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6.81118 | + | 6.81118i | 0.289379 | + | 0.289379i | ||||
\(555\) | 19.9700 | 0.847681 | ||||||||
\(556\) | 5.13976 | 0.217975 | ||||||||
\(557\) | 21.7708 | + | 21.7708i | 0.922458 | + | 0.922458i | 0.997203 | − | 0.0747448i | \(-0.0238142\pi\) |
−0.0747448 | + | 0.997203i | \(0.523814\pi\) | |||||||
\(558\) | 3.96802 | + | 6.87282i | 0.167980 | + | 0.290950i | ||||
\(559\) | 7.82024 | + | 1.53273i | 0.330761 | + | 0.0648276i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.36263 | + | 1.97281i | 0.310850 | + | 0.0832921i | ||||
\(562\) | 11.8483 | − | 20.5218i | 0.499790 | − | 0.865661i | ||||
\(563\) | 16.1301 | + | 27.9382i | 0.679804 | + | 1.17745i | 0.975040 | + | 0.222030i | \(0.0712683\pi\) |
−0.295236 | + | 0.955424i | \(0.595398\pi\) | |||||||
\(564\) | 3.93594 | + | 14.6891i | 0.165733 | + | 0.618524i | ||||
\(565\) | 27.3421 | + | 27.3421i | 1.15029 | + | 1.15029i | ||||
\(566\) | −0.0117675 | − | 0.0439168i | −0.000494624 | − | 0.00184596i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.01135 | + | 15.6081i | −0.378108 | + | 0.654902i | ||||
\(569\) | −3.82034 | − | 2.20567i | −0.160157 | − | 0.0924666i | 0.417779 | − | 0.908548i | \(-0.362808\pi\) |
−0.577936 | + | 0.816082i | \(0.696142\pi\) | |||||||
\(570\) | 3.44661 | − | 3.44661i | 0.144363 | − | 0.144363i | ||||
\(571\) | −30.0822 | − | 17.3680i | −1.25890 | − | 0.726826i | −0.286039 | − | 0.958218i | \(-0.592339\pi\) |
−0.972861 | + | 0.231392i | \(0.925672\pi\) | |||||||
\(572\) | −8.68565 | + | 0.593782i | −0.363165 | + | 0.0248273i | ||||
\(573\) | 16.5577i | 0.691709i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.1332 | + | 34.8717i | 0.839613 | + | 1.45425i | ||||
\(576\) | 9.88065i | 0.411694i | ||||||||
\(577\) | −32.6785 | + | 8.75618i | −1.36042 | + | 0.364524i | −0.863972 | − | 0.503540i | \(-0.832031\pi\) |
−0.496452 | + | 0.868064i | \(0.665364\pi\) | |||||||
\(578\) | 6.18850 | + | 1.65820i | 0.257408 | + | 0.0689721i | ||||
\(579\) | 6.49492 | − | 6.49492i | 0.269920 | − | 0.269920i | ||||
\(580\) | −3.75633 | + | 3.75633i | −0.155973 | + | 0.155973i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 14.9809 | − | 8.64925i | 0.620980 | − | 0.358523i | ||||
\(583\) | −9.95106 | + | 2.66638i | −0.412131 | + | 0.110430i | ||||
\(584\) | −7.15047 | + | 12.3850i | −0.295889 | + | 0.512494i | ||||
\(585\) | 1.65359 | + | 24.1882i | 0.0683675 | + | 1.00006i | ||||
\(586\) | −13.1938 | + | 7.61745i | −0.545031 | + | 0.314674i | ||||
\(587\) | 4.46785 | − | 16.6742i | 0.184408 | − | 0.688219i | −0.810349 | − | 0.585948i | \(-0.800722\pi\) |
0.994757 | − | 0.102271i | \(-0.0326109\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.11673 | + | 2.95415i | 0.210831 | + | 0.121723i | ||||
\(590\) | 0.865456 | + | 0.231898i | 0.0356303 | + | 0.00954710i | ||||
\(591\) | 1.92046 | − | 7.16724i | 0.0789970 | − | 0.294821i | ||||
\(592\) | 0.447911 | − | 1.67163i | 0.0184090 | − | 0.0687034i | ||||
\(593\) | −24.2880 | − | 6.50794i | −0.997387 | − | 0.267249i | −0.277037 | − | 0.960859i | \(-0.589352\pi\) |
−0.720351 | + | 0.693610i | \(0.756019\pi\) | |||||||
\(594\) | 9.02994 | + | 5.21344i | 0.370503 | + | 0.213910i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.35209 | − | 5.04606i | 0.0553837 | − | 0.206695i | ||||
\(597\) | −6.99624 | + | 4.03928i | −0.286337 | + | 0.165317i | ||||
\(598\) | 0.856196 | + | 12.5242i | 0.0350125 | + | 0.512151i | ||||
\(599\) | 0.438119 | − | 0.758845i | 0.0179011 | − | 0.0310056i | −0.856936 | − | 0.515423i | \(-0.827635\pi\) |
0.874837 | + | 0.484417i | \(0.160968\pi\) | |||||||
\(600\) | −34.2263 | + | 9.17092i | −1.39728 | + | 0.374401i | ||||
\(601\) | −19.6980 | + | 11.3726i | −0.803496 | + | 0.463899i | −0.844692 | − | 0.535252i | \(-0.820217\pi\) |
0.0411960 | + | 0.999151i | \(0.486883\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.3737 | − | 12.3737i | 0.503898 | − | 0.503898i | ||||
\(604\) | 12.2817 | − | 12.2817i | 0.499737 | − | 0.499737i | ||||
\(605\) | −25.1175 | − | 6.73022i | −1.02117 | − | 0.273622i | ||||
\(606\) | −3.68593 | + | 0.987641i | −0.149730 | + | 0.0401202i | ||||
\(607\) | 30.8708i | 1.25301i | 0.779418 | + | 0.626504i | \(0.215515\pi\) | ||||
−0.779418 | + | 0.626504i | \(0.784485\pi\) | |||||||
\(608\) | 3.18298 | + | 5.51309i | 0.129087 | + | 0.223585i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 45.2459i | 1.83195i | ||||||||
\(611\) | 41.8064 | − | 2.85803i | 1.69130 | − | 0.115624i | ||||
\(612\) | 5.34939 | + | 3.08847i | 0.216236 | + | 0.124844i | ||||
\(613\) | 33.2772 | − | 33.2772i | 1.34405 | − | 1.34405i | 0.452071 | − | 0.891982i | \(-0.350685\pi\) |
0.891982 | − | 0.452071i | \(-0.149315\pi\) | |||||||
\(614\) | 15.6257 | + | 9.02148i | 0.630601 | + | 0.364077i | ||||
\(615\) | 16.2305 | − | 28.1121i | 0.654479 | − | 1.13359i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.88092 | − | 7.01970i | −0.0757231 | − | 0.282602i | 0.917673 | − | 0.397336i | \(-0.130065\pi\) |
−0.993396 | + | 0.114734i | \(0.963399\pi\) | |||||||
\(618\) | −1.18561 | − | 1.18561i | −0.0476923 | − | 0.0476923i | ||||
\(619\) | −5.34817 | − | 19.9596i | −0.214961 | − | 0.802246i | −0.986180 | − | 0.165676i | \(-0.947019\pi\) |
0.771219 | − | 0.636570i | \(-0.219647\pi\) | |||||||
\(620\) | −11.4888 | − | 19.8992i | −0.461401 | − | 0.799170i | ||||
\(621\) | −10.1026 | + | 17.4983i | −0.405405 | + | 0.702182i | ||||
\(622\) | −4.02508 | − | 1.07852i | −0.161391 | − | 0.0432446i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.58105 | − | 0.309878i | −0.0632925 | − | 0.0124050i | ||||
\(625\) | 17.8571 | + | 30.9295i | 0.714285 | + | 1.23718i | ||||
\(626\) | −20.2396 | − | 20.2396i | −0.808939 | − | 0.808939i | ||||
\(627\) | 2.80563 | 0.112046 | ||||||||
\(628\) | −16.0310 | −0.639706 | ||||||||
\(629\) | −9.91345 | − | 9.91345i | −0.395275 | − | 0.395275i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.77115 | − | 1.54637i | 0.229746 | − | 0.0615602i | −0.142109 | − | 0.989851i | \(-0.545388\pi\) |
0.371855 | + | 0.928291i | \(0.378722\pi\) | |||||||
\(632\) | −2.02884 | + | 7.57174i | −0.0807030 | + | 0.301188i | ||||
\(633\) | −7.54829 | + | 4.35801i | −0.300018 | + | 0.173215i | ||||
\(634\) | − | 5.66235i | − | 0.224881i | ||||||
\(635\) | 8.07018 | + | 30.1183i | 0.320255 | + | 1.19521i | ||||
\(636\) | 6.40189 | 0.253852 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.27530 | 0.0900798 | ||||||||
\(639\) | 2.72483 | + | 10.1692i | 0.107793 | + | 0.402287i | ||||
\(640\) | − | 21.8924i | − | 0.865373i | ||||||
\(641\) | −19.3092 | + | 11.1482i | −0.762667 | + | 0.440326i | −0.830253 | − | 0.557387i | \(-0.811804\pi\) |
0.0675854 | + | 0.997713i | \(0.478470\pi\) | |||||||
\(642\) | 4.06112 | − | 15.1563i | 0.160280 | − | 0.598171i | ||||
\(643\) | 19.2524 | − | 5.15868i | 0.759242 | − | 0.203438i | 0.141629 | − | 0.989920i | \(-0.454766\pi\) |
0.617614 | + | 0.786481i | \(0.288099\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.06233 | + | 7.06233i | 0.278079 | + | 0.278079i | ||||
\(646\) | −3.42190 | −0.134633 | ||||||||
\(647\) | 14.8646 | 0.584389 | 0.292195 | − | 0.956359i | \(-0.405615\pi\) | ||||
0.292195 | + | 0.956359i | \(0.405615\pi\) | |||||||
\(648\) | −2.10277 | − | 2.10277i | −0.0826047 | − | 0.0826047i | ||||
\(649\) | 0.257866 | + | 0.446638i | 0.0101221 | + | 0.0175321i | ||||
\(650\) | 2.42678 | + | 35.4981i | 0.0951861 | + | 1.39235i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 25.8468 | + | 6.92564i | 1.01224 | + | 0.271229i | ||||
\(653\) | −16.5493 | + | 28.6642i | −0.647623 | + | 1.12172i | 0.336067 | + | 0.941838i | \(0.390903\pi\) |
−0.983689 | + | 0.179877i | \(0.942430\pi\) | |||||||
\(654\) | −1.76924 | − | 3.06442i | −0.0691828 | − | 0.119828i | ||||
\(655\) | 2.17117 | + | 8.10292i | 0.0848346 | + | 0.316607i | ||||
\(656\) | −1.98914 | − | 1.98914i | −0.0776627 | − | 0.0776627i | ||||
\(657\) | 2.16214 | + | 8.06922i | 0.0843531 | + | 0.314810i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.6093 | − | 40.8925i | 0.919687 | − | 1.59295i | 0.119797 | − | 0.992798i | \(-0.461776\pi\) |
0.799890 | − | 0.600147i | \(-0.204891\pi\) | |||||||
\(660\) | −9.44937 | − | 5.45560i | −0.367816 | − | 0.212359i | ||||
\(661\) | −11.7411 | + | 11.7411i | −0.456675 | + | 0.456675i | −0.897562 | − | 0.440888i | \(-0.854664\pi\) |
0.440888 | + | 0.897562i | \(0.354664\pi\) | |||||||
\(662\) | 13.3749 | + | 7.72200i | 0.519830 | + | 0.300124i | ||||
\(663\) | −8.57814 | + | 9.83707i | −0.333147 | + | 0.382040i | ||||
\(664\) | − | 13.6132i | − | 0.528293i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.46572 | − | 6.00280i | −0.134294 | − | 0.232604i | ||||
\(667\) | 4.40908i | 0.170720i | ||||||||
\(668\) | −12.4024 | + | 3.32322i | −0.479864 | + | 0.128579i | ||||
\(669\) | 7.42513 | + | 1.98956i | 0.287072 | + | 0.0769207i | ||||
\(670\) | 26.6586 | − | 26.6586i | 1.02991 | − | 1.02991i | ||||
\(671\) | −18.4157 | + | 18.4157i | −0.710929 | + | 0.710929i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.5906 | + | 13.0427i | −0.870802 | + | 0.502758i | −0.867615 | − | 0.497237i | \(-0.834348\pi\) |
−0.00318750 | + | 0.999995i | \(0.501015\pi\) | |||||||
\(674\) | −11.1221 | + | 2.98015i | −0.428406 | + | 0.114791i | ||||
\(675\) | −28.6346 | + | 49.5967i | −1.10215 | + | 1.90898i | ||||
\(676\) | 5.62737 | − | 13.8044i | 0.216437 | − | 0.530938i | ||||
\(677\) | 16.8583 | − | 9.73314i | 0.647917 | − | 0.374075i | −0.139741 | − | 0.990188i | \(-0.544627\pi\) |
0.787658 | + | 0.616113i | \(0.211294\pi\) | |||||||
\(678\) | −2.66370 | + | 9.94105i | −0.102299 | + | 0.381784i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 31.6258 | + | 18.2592i | 1.21280 | + | 0.700208i | ||||
\(681\) | −17.8378 | − | 4.77963i | −0.683546 | − | 0.183156i | ||||
\(682\) | −2.54718 | + | 9.50621i | −0.0975366 | + | 0.364012i | ||||
\(683\) | 5.35648 | − | 19.9907i | 0.204960 | − | 0.764921i | −0.784502 | − | 0.620127i | \(-0.787081\pi\) |
0.989462 | − | 0.144794i | \(-0.0462521\pi\) | |||||||
\(684\) | 2.19613 | + | 0.588452i | 0.0839712 | + | 0.0225000i | ||||
\(685\) | 40.0786 | + | 23.1394i | 1.53132 | + | 0.884110i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.79380 | − | 21.6228i | 0.221047 | − | 0.824960i | ||||
\(688\) | 0.749566 | − | 0.432762i | 0.0285769 | − | 0.0164989i | ||||
\(689\) | 3.39290 | − | 17.3111i | 0.129259 | − | 0.659502i | ||||
\(690\) | −7.86663 | + | 13.6254i | −0.299477 | + | 0.518710i | ||||
\(691\) | −13.6373 | + | 3.65409i | −0.518786 | + | 0.139008i | −0.508705 | − | 0.860941i | \(-0.669876\pi\) |
−0.0100808 | + | 0.999949i | \(0.503209\pi\) | |||||||
\(692\) | −3.30555 | + | 1.90846i | −0.125658 | + | 0.0725488i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.1477 | − | 17.1477i | 0.650916 | − | 0.650916i | ||||
\(695\) | 12.5513 | − | 12.5513i | 0.476098 | − | 0.476098i | ||||
\(696\) | −3.74770 | − | 1.00419i | −0.142056 | − | 0.0380639i | ||||
\(697\) | −22.0124 | + | 5.89821i | −0.833779 | + | 0.223411i | ||||
\(698\) | 6.76071i | 0.255896i | ||||||||
\(699\) | 6.33483 | + | 10.9722i | 0.239605 | + | 0.415008i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.8075i | 1.01251i | 0.862385 | + | 0.506253i | \(0.168970\pi\) | ||||
−0.862385 | + | 0.506253i | \(0.831030\pi\) | |||||||
\(702\) | −14.8173 | + | 9.96088i | −0.559243 | + | 0.375949i | ||||
\(703\) | −4.46901 | − | 2.58019i | −0.168552 | − | 0.0973135i | ||||
\(704\) | −8.66423 | + | 8.66423i | −0.326545 | + | 0.326545i | ||||
\(705\) | 45.4824 | + | 26.2593i | 1.71297 | + | 0.988981i | ||||
\(706\) | −12.5896 | + | 21.8058i | −0.473815 | + | 0.820672i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.0829475 | − | 0.309564i | −0.00311736 | − | 0.0116341i | ||||
\(709\) | −20.3216 | − | 20.3216i | −0.763192 | − | 0.763192i | 0.213706 | − | 0.976898i | \(-0.431447\pi\) |
−0.976898 | + | 0.213706i | \(0.931447\pi\) | |||||||
\(710\) | 5.87050 | + | 21.9090i | 0.220316 | + | 0.822231i | ||||
\(711\) | 2.28952 | + | 3.96557i | 0.0858638 | + | 0.148720i | ||||
\(712\) | −10.1095 | + | 17.5101i | −0.378869 | + | 0.656220i | ||||
\(713\) | −18.4212 | − | 4.93594i | −0.689879 | − | 0.184852i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.7603 | + | 22.6603i | −0.738994 | + | 0.847449i | ||||
\(716\) | −0.146513 | − | 0.253769i | −0.00547547 | − | 0.00948378i | ||||
\(717\) | 20.5668 | + | 20.5668i | 0.768080 | + | 0.768080i | ||||
\(718\) | −28.6964 | −1.07094 | ||||||||
\(719\) | −2.91511 | −0.108715 | −0.0543577 | − | 0.998522i | \(-0.517311\pi\) | ||||
−0.0543577 | + | 0.998522i | \(0.517311\pi\) | |||||||
\(720\) | 1.86198 | + | 1.86198i | 0.0693918 | + | 0.0693918i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 15.7363 | − | 4.21652i | 0.585644 | − | 0.156923i | ||||
\(723\) | 7.51303 | − | 28.0390i | 0.279413 | − | 1.04278i | ||||
\(724\) | −7.59825 | + | 4.38685i | −0.282387 | + | 0.163036i | ||||
\(725\) | 12.4970i | 0.464126i | ||||||||
\(726\) | −1.79131 | − | 6.68527i | −0.0664818 | − | 0.248114i | ||||
\(727\) | 26.1967 | 0.971584 | 0.485792 | − | 0.874075i | \(-0.338531\pi\) | ||||
0.485792 | + | 0.874075i | \(0.338531\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.0879 | −0.743998 | ||||||||
\(730\) | 4.65822 | + | 17.3847i | 0.172409 | + | 0.643437i | ||||
\(731\) | − | 7.01171i | − | 0.259337i | ||||||
\(732\) | 14.0157 | − | 8.09199i | 0.518037 | − | 0.299089i | ||||
\(733\) | 1.65037 | − | 6.15927i | 0.0609579 | − | 0.227498i | −0.928726 | − | 0.370767i | \(-0.879095\pi\) |
0.989684 | + | 0.143269i | \(0.0457615\pi\) | |||||||
\(734\) | 22.4221 | − | 6.00798i | 0.827614 | − | 0.221758i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.5299 | − | 14.5299i | −0.535577 | − | 0.535577i | ||||
\(737\) | 21.7008 | 0.799359 | ||||||||
\(738\) | −11.2670 | −0.414743 | ||||||||
\(739\) | 17.7953 | + | 17.7953i | 0.654609 | + | 0.654609i | 0.954099 | − | 0.299490i | \(-0.0968165\pi\) |
−0.299490 | + | 0.954099i | \(0.596817\pi\) | |||||||
\(740\) | 10.0344 | + | 17.3802i | 0.368873 | + | 0.638907i | ||||
\(741\) | −2.11271 | + | 4.31465i | −0.0776124 | + | 0.158503i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.8890 | − | 6.40103i | −0.876401 | − | 0.234831i | −0.207547 | − | 0.978225i | \(-0.566548\pi\) |
−0.668854 | + | 0.743394i | \(0.733215\pi\) | |||||||
\(744\) | 8.39107 | − | 14.5338i | 0.307632 | − | 0.532834i | ||||
\(745\) | −9.02067 | − | 15.6243i | −0.330492 | − | 0.572429i | ||||
\(746\) | −0.743108 | − | 2.77332i | −0.0272071 | − | 0.101538i | ||||
\(747\) | −5.62298 | − | 5.62298i | −0.205734 | − | 0.205734i | ||||
\(748\) | 1.98257 | + | 7.39907i | 0.0724901 | + | 0.270537i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −11.8614 | + | 20.5446i | −0.433118 | + | 0.750182i | ||||
\(751\) | −12.2932 | − | 7.09751i | −0.448587 | − | 0.258992i | 0.258646 | − | 0.965972i | \(-0.416724\pi\) |
−0.707233 | + | 0.706980i | \(0.750057\pi\) | |||||||
\(752\) | 3.21821 | − | 3.21821i | 0.117356 | − | 0.117356i | ||||
\(753\) | 5.95327 | + | 3.43712i | 0.216949 | + | 0.125256i | ||||
\(754\) | −1.71336 | + | 3.49907i | −0.0623967 | + | 0.127429i | ||||
\(755\) | − | 59.9839i | − | 2.18304i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.3674 | − | 21.4210i | −0.449502 | − | 0.778559i | 0.548852 | − | 0.835920i | \(-0.315065\pi\) |
−0.998354 | + | 0.0573601i | \(0.981732\pi\) | |||||||
\(758\) | − | 4.16511i | − | 0.151284i | ||||||
\(759\) | −8.74753 | + | 2.34389i | −0.317515 | + | 0.0850780i | ||||
\(760\) | 12.9836 | + | 3.47895i | 0.470966 | + | 0.126195i | ||||
\(761\) | −8.21162 | + | 8.21162i | −0.297671 | + | 0.297671i | −0.840101 | − | 0.542430i | \(-0.817504\pi\) |
0.542430 | + | 0.840101i | \(0.317504\pi\) | |||||||
\(762\) | −5.86832 | + | 5.86832i | −0.212587 | + | 0.212587i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −14.4104 | + | 8.31983i | −0.521349 | + | 0.301001i | ||||
\(765\) | 20.6052 | − | 5.52116i | 0.744984 | − | 0.199618i | ||||
\(766\) | 15.5249 | − | 26.8900i | 0.560938 | − | 0.971574i | ||||
\(767\) | −0.881044 | + | 0.0602313i | −0.0318126 | + | 0.00217483i | ||||
\(768\) | 16.5471 | − | 9.55348i | 0.597092 | − | 0.344731i | ||||
\(769\) | 9.18218 | − | 34.2684i | 0.331118 | − | 1.23575i | −0.576899 | − | 0.816815i | \(-0.695737\pi\) |
0.908017 | − | 0.418933i | \(-0.137596\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.1252 | − | 13.9287i | −0.868850 | − | 0.501631i | ||||
\(772\) | 8.91614 | + | 2.38907i | 0.320899 | + | 0.0859846i | ||||
\(773\) | 5.21138 | − | 19.4491i | 0.187440 | − | 0.699536i | −0.806655 | − | 0.591023i | \(-0.798724\pi\) |
0.994095 | − | 0.108513i | \(-0.0346090\pi\) | |||||||
\(774\) | 0.897229 | − | 3.34850i | 0.0322502 | − | 0.120359i | ||||
\(775\) | −52.2125 | − | 13.9903i | −1.87553 | − | 0.502547i | ||||
\(776\) | 41.3128 | + | 23.8519i | 1.48304 | + | 0.856234i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.93992 | − | 18.4360i | 0.177105 | − | 0.660964i | ||||
\(779\) | −7.26433 | + | 4.19406i | −0.260272 | + | 0.150268i | ||||
\(780\) | 15.5055 | − | 10.4236i | 0.555187 | − | 0.373223i | ||||
\(781\) | −6.52788 | + | 11.3066i | −0.233586 | + | 0.404583i | ||||
\(782\) | 10.6690 | − | 2.85875i | 0.381522 | − | 0.102229i | ||||
\(783\) | −5.43072 | + | 3.13543i | −0.194078 | + | 0.112051i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −39.1476 | + | 39.1476i | −1.39724 | + | 1.39724i | ||||
\(786\) | −1.57879 | + | 1.57879i | −0.0563136 | + | 0.0563136i | ||||
\(787\) | 13.7104 | + | 3.67369i | 0.488723 | + | 0.130953i | 0.494762 | − | 0.869029i | \(-0.335255\pi\) |
−0.00603826 | + | 0.999982i | \(0.501922\pi\) | |||||||
\(788\) | 7.20271 | − | 1.92996i | 0.256586 | − | 0.0687520i | ||||
\(789\) | 17.2768i | 0.615069i | ||||||||
\(790\) | 4.93266 | + | 8.54362i | 0.175496 | + | 0.303968i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 10.3924i | 0.369279i | ||||||||
\(793\) | −14.4532 | − | 42.1881i | −0.513247 | − | 1.49814i | ||||
\(794\) | 5.87997 | + | 3.39480i | 0.208672 | + | 0.120477i | ||||
\(795\) | 15.6334 | − | 15.6334i | 0.554460 | − | 0.554460i | ||||
\(796\) | −7.03086 | − | 4.05927i | −0.249202 | − | 0.143877i | ||||
\(797\) | −0.388404 | + | 0.672735i | −0.0137580 | + | 0.0238295i | −0.872822 | − | 0.488038i | \(-0.837713\pi\) |
0.859064 | + | 0.511867i | \(0.171046\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.54267 | − | 35.6137i | −0.337595 | − | 1.25992i | ||||
\(800\) | −41.1830 | − | 41.1830i | −1.45604 | − | 1.45604i | ||||
\(801\) | 3.05687 | + | 11.4084i | 0.108009 | + | 0.403096i | ||||
\(802\) | −0.663616 | − | 1.14942i | −0.0234331 | − | 0.0405873i | ||||
\(803\) | −5.17985 | + | 8.97176i | −0.182793 | + | 0.316607i | ||||
\(804\) | −13.0257 | − | 3.49023i | −0.459382 | − | 0.123091i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.7011 | − | 11.0756i | −0.447376 | − | 0.390122i | ||||
\(807\) | 2.02039 | + | 3.49941i | 0.0711210 | + | 0.123185i | ||||
\(808\) | −7.44103 | − | 7.44103i | −0.261775 | − | 0.261775i | ||||
\(809\) | −32.2608 | −1.13423 | −0.567115 | − | 0.823639i | \(-0.691940\pi\) | ||||
−0.567115 | + | 0.823639i | \(0.691940\pi\) | |||||||
\(810\) | −3.74254 | −0.131499 | ||||||||
\(811\) | −33.8219 | − | 33.8219i | −1.18765 | − | 1.18765i | −0.977716 | − | 0.209930i | \(-0.932676\pi\) |
−0.209930 | − | 0.977716i | \(-0.567324\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.833434 | − | 0.223318i | 0.0292298 | − | 0.00783210i | ||||
\(814\) | 2.22474 | − | 8.30283i | 0.0779770 | − | 0.291014i | ||||
\(815\) | 80.0303 | − | 46.2055i | 2.80334 | − | 1.61851i | ||||
\(816\) | 1.41758i | 0.0496253i | ||||||||
\(817\) | −0.667976 | − | 2.49292i | −0.0233695 | − | 0.0872163i | ||||
\(818\) | −6.38048 | −0.223088 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 32.6217 | 1.13920 | ||||||||
\(821\) | 5.72488 | + | 21.3655i | 0.199800 | + | 0.745663i | 0.990972 | + | 0.134069i | \(0.0428045\pi\) |
−0.791172 | + | 0.611593i | \(0.790529\pi\) | |||||||
\(822\) | 12.3175i | 0.429623i | ||||||||
\(823\) | −12.7603 | + | 7.36718i | −0.444797 | + | 0.256804i | −0.705630 | − | 0.708580i | \(-0.749336\pi\) |
0.260833 | + | 0.965384i | \(0.416003\pi\) | |||||||
\(824\) | 1.19674 | − | 4.46628i | 0.0416903 | − | 0.155590i | ||||
\(825\) | −24.7938 | + | 6.64347i | −0.863209 | + | 0.231296i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.90723 | − | 5.90723i | −0.205415 | − | 0.205415i | 0.596901 | − | 0.802315i | \(-0.296399\pi\) |
−0.802315 | + | 0.596901i | \(0.796399\pi\) | |||||||
\(828\) | −7.33882 | −0.255042 | ||||||||
\(829\) | 46.8750 | 1.62804 | 0.814018 | − | 0.580839i | \(-0.197275\pi\) | ||||
0.814018 | + | 0.580839i | \(0.197275\pi\) | |||||||
\(830\) | −12.1144 | − | 12.1144i | −0.420498 | − | 0.420498i | ||||
\(831\) | −5.94941 | − | 10.3047i | −0.206383 | − | 0.357465i | ||||
\(832\) | −6.79993 | − | 19.8487i | −0.235745 | − | 0.688130i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.56341 | + | 1.22276i | 0.158018 | + | 0.0423408i | ||||
\(835\) | −22.1714 | + | 38.4020i | −0.767273 | + | 1.32896i | ||||
\(836\) | 1.40976 | + | 2.44177i | 0.0487575 | + | 0.0844504i | ||||
\(837\) | −7.02019 | − | 26.1997i | −0.242653 | − | 0.905594i | ||||
\(838\) | 6.01948 | + | 6.01948i | 0.207940 | + | 0.207940i | ||||
\(839\) | −0.889290 | − | 3.31888i | −0.0307017 | − | 0.114580i | 0.948875 | − | 0.315654i | \(-0.102224\pi\) |
−0.979576 | + | 0.201073i | \(0.935557\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.8158 | − | 23.9297i | 0.476407 | − | 0.825161i | ||||
\(842\) | 10.4811 | + | 6.05125i | 0.361201 | + | 0.208540i | ||||
\(843\) | −20.6984 | + | 20.6984i | −0.712890 | + | 0.712890i | ||||
\(844\) | −7.58565 | − | 4.37958i | −0.261109 | − | 0.150751i | ||||
\(845\) | −19.9683 | − | 47.4523i | −0.686930 | − | 1.63241i | ||||
\(846\) | − | 18.2287i | − | 0.626717i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.957977 | − | 1.65926i | −0.0328971 | − | 0.0569794i | ||||
\(849\) | 0.0561634i | 0.00192752i | ||||||||
\(850\) | 30.2399 | − | 8.10276i | 1.03722 | − | 0.277922i | ||||
\(851\) | 16.0893 | + | 4.31111i | 0.551533 | + | 0.147783i | ||||
\(852\) | 5.73680 | − | 5.73680i | 0.196540 | − | 0.196540i | ||||
\(853\) | −13.3798 | + | 13.3798i | −0.458117 | + | 0.458117i | −0.898037 | − | 0.439920i | \(-0.855007\pi\) |
0.439920 | + | 0.898037i | \(0.355007\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.79995 | − | 3.92595i | 0.232553 | − | 0.134265i | ||||
\(856\) | 41.7964 | − | 11.1993i | 1.42857 | − | 0.382784i | ||||
\(857\) | 9.65574 | − | 16.7242i | 0.329834 | − | 0.571289i | −0.652645 | − | 0.757664i | \(-0.726341\pi\) |
0.982479 | + | 0.186375i | \(0.0596740\pi\) | |||||||
\(858\) | −7.85293 | − | 1.53914i | −0.268095 | − | 0.0525453i | ||||
\(859\) | 49.4177 | − | 28.5313i | 1.68611 | − | 0.973477i | 0.728662 | − | 0.684873i | \(-0.240142\pi\) |
0.957449 | − | 0.288604i | \(-0.0931910\pi\) | |||||||
\(860\) | −2.59779 | + | 9.69507i | −0.0885837 | + | 0.330599i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.20501 | + | 3.00511i | 0.177283 | + | 0.102355i | ||||
\(863\) | 9.07665 | + | 2.43208i | 0.308973 | + | 0.0827890i | 0.409974 | − | 0.912097i | \(-0.365538\pi\) |
−0.101001 | + | 0.994886i | \(0.532205\pi\) | |||||||
\(864\) | 7.56399 | − | 28.2292i | 0.257332 | − | 0.960377i | ||||
\(865\) | −3.41169 | + | 12.7326i | −0.116001 | + | 0.432922i | ||||
\(866\) | −22.4285 | − | 6.00971i | −0.762153 | − | 0.204218i | ||||
\(867\) | −6.85391 | − | 3.95710i | −0.232771 | − | 0.134390i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.46971 | + | 5.48502i | −0.0498564 | + | 0.186067i | ||||
\(870\) | −4.22874 | + | 2.44147i | −0.143368 | + | 0.0827735i | ||||
\(871\) | −16.3413 | + | 33.3727i | −0.553703 | + | 1.13079i | ||||
\(872\) | 4.87902 | − | 8.45071i | 0.165224 | − | 0.286177i | ||||
\(873\) | 26.9166 | − | 7.21228i | 0.910989 | − | 0.244099i | ||||
\(874\) | 3.52088 | − | 2.03278i | 0.119096 | − | 0.0687598i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.55213 | − | 4.55213i | 0.153802 | − | 0.153802i | ||||
\(877\) | −11.1516 | + | 11.1516i | −0.376563 | + | 0.376563i | −0.869861 | − | 0.493297i | \(-0.835791\pi\) |
0.493297 | + | 0.869861i | \(0.335791\pi\) | |||||||
\(878\) | 15.7839 | + | 4.22928i | 0.532681 | + | 0.142731i | ||||
\(879\) | 18.1781 | − | 4.87082i | 0.613134 | − | 0.164289i | ||||
\(880\) | 3.26549i | 0.110080i | ||||||||
\(881\) | 20.1922 | + | 34.9739i | 0.680293 | + | 1.17830i | 0.974891 | + | 0.222681i | \(0.0714807\pi\) |
−0.294599 | + | 0.955621i | \(0.595186\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 29.9282i | − | 1.00716i | −0.863947 | − | 0.503582i | \(-0.832015\pi\) | ||
0.863947 | − | 0.503582i | \(-0.167985\pi\) | |||||||
\(884\) | −12.8716 | − | 2.52278i | −0.432919 | − | 0.0848502i | ||||
\(885\) | −0.958513 | − | 0.553398i | −0.0322201 | − | 0.0186023i | ||||
\(886\) | −9.36597 | + | 9.36597i | −0.314656 | + | 0.314656i | ||||
\(887\) | −21.0340 | − | 12.1440i | −0.706254 | − | 0.407756i | 0.103418 | − | 0.994638i | \(-0.467022\pi\) |
−0.809673 | + | 0.586882i | \(0.800355\pi\) | |||||||
\(888\) | −7.32886 | + | 12.6940i | −0.245940 | + | 0.425981i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 6.58588 | + | 24.5788i | 0.220759 | + | 0.823885i | ||||
\(891\) | −1.52326 | − | 1.52326i | −0.0510312 | − | 0.0510312i | ||||
\(892\) | 1.99940 | + | 7.46188i | 0.0669450 | + | 0.249842i | ||||
\(893\) | −6.78554 | − | 11.7529i | −0.227070 | − | 0.393296i | ||||
\(894\) | 2.40094 | − | 4.15855i | 0.0802994 | − | 0.139083i | ||||
\(895\) | −0.977489 | − | 0.261917i | −0.0326738 | − | 0.00875493i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.98255 | − | 15.2174i | 0.0995844 | − | 0.508096i | ||||
\(898\) | −1.35208 | − | 2.34188i | −0.0451196 | − | 0.0781495i | ||||
\(899\) | −4.18524 | − | 4.18524i | −0.139586 | − | 0.139586i | ||||
\(900\) | −20.8010 | −0.693366 | ||||||||
\(901\) | −15.5213 | −0.517091 | ||||||||
\(902\) | −9.87987 | − | 9.87987i | −0.328964 | − | 0.328964i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −27.4143 | + | 7.34565i | −0.911787 | + | 0.244313i | ||||
\(905\) | −7.84223 | + | 29.2676i | −0.260685 | + | 0.972888i | ||||
\(906\) | 13.8263 | − | 7.98265i | 0.459350 | − | 0.265206i | ||||
\(907\) | 26.3763i | 0.875811i | 0.899021 | + | 0.437906i | \(0.144280\pi\) | ||||
−0.899021 | + | 0.437906i | \(0.855720\pi\) | |||||||
\(908\) | −4.80328 | − | 17.9261i | −0.159403 | − | 0.594898i | ||||
\(909\) | −6.14711 | −0.203887 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.3906 | 1.63638 | 0.818192 | − | 0.574945i | \(-0.194977\pi\) | ||||
0.818192 | + | 0.574945i | \(0.194977\pi\) | |||||||
\(912\) | 0.135047 | + | 0.504003i | 0.00447186 | + | 0.0166892i | ||||
\(913\) | − | 9.86146i | − | 0.326367i | ||||||
\(914\) | 19.4935 | − | 11.2546i | 0.644787 | − | 0.372268i | ||||
\(915\) | 14.4658 | − | 53.9870i | 0.478224 | − | 1.78476i | ||||
\(916\) | 21.7298 | − | 5.82247i | 0.717972 | − | 0.192380i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 11.1082 | + | 11.1082i | 0.366625 | + | 0.366625i | ||||
\(919\) | 51.0587 | 1.68427 | 0.842135 | − | 0.539267i | \(-0.181299\pi\) | ||||
0.842135 | + | 0.539267i | \(0.181299\pi\) | |||||||
\(920\) | −43.3874 | −1.43044 | ||||||||
\(921\) | −15.7601 | − | 15.7601i | −0.519313 | − | 0.519313i | ||||
\(922\) | −9.63091 | − | 16.6812i | −0.317177 | − | 0.549367i | ||||
\(923\) | −12.4723 | − | 18.5531i | −0.410530 | − | 0.610683i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 45.6030 | + | 12.2193i | 1.49942 | + | 0.401768i | ||||
\(926\) | −5.86986 | + | 10.1669i | −0.192896 | + | 0.334105i | ||||
\(927\) | −1.35050 | − | 2.33914i | −0.0443563 | − | 0.0768274i | ||||
\(928\) | −1.65057 | − | 6.16002i | −0.0541827 | − | 0.202213i | ||||
\(929\) | 32.1671 | + | 32.1671i | 1.05537 | + | 1.05537i | 0.998374 | + | 0.0569949i | \(0.0181519\pi\) |
0.0569949 | + | 0.998374i | \(0.481848\pi\) | |||||||
\(930\) | −5.46642 | − | 20.4009i | −0.179251 | − | 0.668973i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.36618 | + | 11.0265i | −0.208531 | + | 0.361187i | ||||
\(933\) | 4.45787 | + | 2.57375i | 0.145944 | + | 0.0842609i | ||||
\(934\) | −15.0911 | + | 15.0911i | −0.493796 | + | 0.493796i | ||||
\(935\) | 22.9100 | + | 13.2271i | 0.749235 | + | 0.432571i | ||||
\(936\) | −15.9821 | − | 7.82577i | −0.522390 | − | 0.255793i | ||||
\(937\) | 45.0942i | 1.47316i | 0.676348 | + | 0.736582i | \(0.263561\pi\) | ||||
−0.676348 | + | 0.736582i | \(0.736439\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.6788 | + | 30.6207i | 0.576927 | + | 0.999267i | ||||
\(940\) | 52.7785i | 1.72144i | ||||||||
\(941\) | 2.87139 | − | 0.769386i | 0.0936046 | − | 0.0250813i | −0.211713 | − | 0.977332i | \(-0.567904\pi\) |
0.305317 | + | 0.952251i | \(0.401237\pi\) | |||||||
\(942\) | −14.2333 | − | 3.81381i | −0.463747 | − | 0.124261i | ||||
\(943\) | 19.1453 | − | 19.1453i | 0.623456 | − | 0.623456i | ||||
\(944\) | −0.0678217 | + | 0.0678217i | −0.00220741 | + | 0.00220741i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.72303 | − | 2.14949i | 0.121046 | − | 0.0698861i | ||||
\(947\) | −29.3119 | + | 7.85409i | −0.952508 | + | 0.255224i | −0.701426 | − | 0.712742i | \(-0.747453\pi\) |
−0.251082 | + | 0.967966i | \(0.580786\pi\) | |||||||
\(948\) | 1.76436 | − | 3.05596i | 0.0573037 | − | 0.0992530i | ||||
\(949\) | −9.89671 | − | 14.7218i | −0.321261 | − | 0.477891i | ||||
\(950\) | 9.97949 | − | 5.76166i | 0.323777 | − | 0.186933i | ||||
\(951\) | −1.81034 | + | 6.75627i | −0.0587042 | + | 0.219087i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.1244 | + | 5.84531i | 0.327961 | + | 0.189348i | 0.654935 | − | 0.755685i | \(-0.272696\pi\) |
−0.326975 | + | 0.945033i | \(0.606029\pi\) | |||||||
\(954\) | −7.41236 | − | 1.98614i | −0.239984 | − | 0.0643035i | ||||
\(955\) | −14.8731 | + | 55.5071i | −0.481282 | + | 1.79617i | ||||
\(956\) | −7.56522 | + | 28.2338i | −0.244677 | + | 0.913145i | ||||
\(957\) | −2.71486 | − | 0.727445i | −0.0877590 | − | 0.0235150i | ||||
\(958\) | −8.85250 | − | 5.11099i | −0.286011 | − | 0.165129i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 6.80588 | − | 25.3999i | 0.219659 | − | 0.819777i | ||||
\(961\) | −4.67543 | + | 2.69936i | −0.150820 | + | 0.0870762i | ||||
\(962\) | 11.0933 | + | 9.67357i | 0.357661 | + | 0.311888i | ||||
\(963\) | 12.6383 | − | 21.8901i | 0.407263 | − | 0.705399i | ||||
\(964\) | 28.1778 | − | 7.55021i | 0.907545 | − | 0.243176i | ||||
\(965\) | 27.6073 | − | 15.9391i | 0.888711 | − | 0.513097i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.9273 | + | 14.9273i | −0.480028 | + | 0.480028i | −0.905141 | − | 0.425112i | \(-0.860235\pi\) |
0.425112 | + | 0.905141i | \(0.360235\pi\) | |||||||
\(968\) | 13.4960 | − | 13.4960i | 0.433778 | − | 0.433778i | ||||
\(969\) | 4.08298 | + | 1.09403i | 0.131164 | + | 0.0351454i | ||||
\(970\) | 57.9904 | − | 15.5385i | 1.86196 | − | 0.498911i | ||||
\(971\) | 5.91305i | 0.189759i | 0.995489 | + | 0.0948795i | \(0.0302466\pi\) | ||||
−0.995489 | + | 0.0948795i | \(0.969753\pi\) | |||||||
\(972\) | −8.55149 | − | 14.8116i | −0.274289 | − | 0.475083i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 28.8376i | − | 0.924016i | ||||||
\(975\) | 8.45366 | − | 43.1319i | 0.270734 | − | 1.38133i | ||||
\(976\) | −4.19462 | − | 2.42176i | −0.134266 | − | 0.0775188i | ||||
\(977\) | −39.2539 | + | 39.2539i | −1.25585 | + | 1.25585i | −0.302787 | + | 0.953058i | \(0.597917\pi\) |
−0.953058 | + | 0.302787i | \(0.902083\pi\) | |||||||
\(978\) | 21.3008 | + | 12.2980i | 0.681125 | + | 0.393248i | ||||
\(979\) | −7.32337 | + | 12.6844i | −0.234056 | + | 0.405397i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.47530 | − | 5.50591i | −0.0471028 | − | 0.175790i | ||||
\(982\) | 14.7093 | + | 14.7093i | 0.469392 | + | 0.469392i | ||||
\(983\) | −5.58397 | − | 20.8396i | −0.178101 | − | 0.664682i | −0.996003 | − | 0.0893237i | \(-0.971529\pi\) |
0.817902 | − | 0.575358i | \(-0.195137\pi\) | |||||||
\(984\) | 11.9130 | + | 20.6339i | 0.379772 | + | 0.657784i | ||||
\(985\) | 12.8760 | − | 22.3020i | 0.410265 | − | 0.710600i | ||||
\(986\) | 3.31120 | + | 0.887233i | 0.105450 | + | 0.0282553i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.81667 | + | 0.329285i | −0.153239 | + | 0.0104759i | ||||
\(989\) | 4.16530 | + | 7.21451i | 0.132449 | + | 0.229408i | ||||
\(990\) | 9.24829 | + | 9.24829i | 0.293930 | + | 0.293930i | ||||
\(991\) | 54.7204 | 1.73825 | 0.869125 | − | 0.494592i | \(-0.164683\pi\) | ||||
0.869125 | + | 0.494592i | \(0.164683\pi\) | |||||||
\(992\) | 27.5844 | 0.875807 | ||||||||
\(993\) | −13.4900 | − | 13.4900i | −0.428091 | − | 0.428091i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.0821 | + | 7.25662i | −0.858560 | + | 0.230050i | ||||
\(996\) | −1.58606 | + | 5.91926i | −0.0502563 | + | 0.187559i | ||||
\(997\) | −29.4379 | + | 16.9960i | −0.932308 | + | 0.538268i | −0.887541 | − | 0.460729i | \(-0.847588\pi\) |
−0.0447672 | + | 0.998997i | \(0.514255\pi\) | |||||||
\(998\) | − | 21.0741i | − | 0.667088i | ||||||
\(999\) | 6.13151 | + | 22.8831i | 0.193992 | + | 0.723990i |
(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 | 637.2.x.b.80.5 | 32 | ||
7.2 | even | 3 | 637.2.bb.b.509.6 | 32 | |||
7.3 | odd | 6 | 91.2.bc.a.41.4 | yes | 32 | ||
7.4 | even | 3 | 91.2.bc.a.41.3 | yes | 32 | ||
7.5 | odd | 6 | 637.2.bb.b.509.5 | 32 | |||
7.6 | odd | 2 | inner | 637.2.x.b.80.6 | 32 | ||
13.7 | odd | 12 | 637.2.bb.b.423.5 | 32 | |||
21.11 | odd | 6 | 819.2.fm.g.496.5 | 32 | |||
21.17 | even | 6 | 819.2.fm.g.496.6 | 32 | |||
91.20 | even | 12 | 637.2.bb.b.423.6 | 32 | |||
91.33 | even | 12 | inner | 637.2.x.b.215.6 | 32 | ||
91.46 | odd | 12 | 91.2.bc.a.20.4 | yes | 32 | ||
91.59 | even | 12 | 91.2.bc.a.20.3 | ✓ | 32 | ||
91.72 | odd | 12 | inner | 637.2.x.b.215.5 | 32 | ||
273.59 | odd | 12 | 819.2.fm.g.748.5 | 32 | |||
273.137 | even | 12 | 819.2.fm.g.748.6 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.bc.a.20.3 | ✓ | 32 | 91.59 | even | 12 | ||
91.2.bc.a.20.4 | yes | 32 | 91.46 | odd | 12 | ||
91.2.bc.a.41.3 | yes | 32 | 7.4 | even | 3 | ||
91.2.bc.a.41.4 | yes | 32 | 7.3 | odd | 6 | ||
637.2.x.b.80.5 | 32 | 1.1 | even | 1 | trivial | ||
637.2.x.b.80.6 | 32 | 7.6 | odd | 2 | inner | ||
637.2.x.b.215.5 | 32 | 91.72 | odd | 12 | inner | ||
637.2.x.b.215.6 | 32 | 91.33 | even | 12 | inner | ||
637.2.bb.b.423.5 | 32 | 13.7 | odd | 12 | |||
637.2.bb.b.423.6 | 32 | 91.20 | even | 12 | |||
637.2.bb.b.509.5 | 32 | 7.5 | odd | 6 | |||
637.2.bb.b.509.6 | 32 | 7.2 | even | 3 | |||
819.2.fm.g.496.5 | 32 | 21.11 | odd | 6 | |||
819.2.fm.g.496.6 | 32 | 21.17 | even | 6 | |||
819.2.fm.g.748.5 | 32 | 273.59 | odd | 12 | |||
819.2.fm.g.748.6 | 32 | 273.137 | even | 12 |