Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(277,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 8 x^{10} - 3 x^{9} + 42 x^{8} - 15 x^{7} + 101 x^{6} + 6 x^{5} + 150 x^{4} - 28 x^{3} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 415.5 | ||
Root | \(0.916322 + 1.58712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.415 |
Dual form | 483.2.i.f.277.5 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.916322 | − | 1.58712i | 0.647938 | − | 1.12226i | −0.335677 | − | 0.941977i | \(-0.608965\pi\) |
0.983615 | − | 0.180284i | \(-0.0577016\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.679293 | − | 1.17657i | −0.339646 | − | 0.588285i | ||||
\(5\) | 0.471745 | − | 0.817086i | 0.210971 | − | 0.365412i | −0.741048 | − | 0.671452i | \(-0.765671\pi\) |
0.952019 | + | 0.306040i | \(0.0990042\pi\) | |||||||
\(6\) | 1.83264 | 0.748174 | ||||||||
\(7\) | −1.16166 | − | 2.37709i | −0.439065 | − | 0.898455i | ||||
\(8\) | 1.17548 | 0.415597 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.864540 | − | 1.49743i | −0.273392 | − | 0.473528i | ||||
\(11\) | −1.04340 | − | 1.80722i | −0.314597 | − | 0.544898i | 0.664755 | − | 0.747062i | \(-0.268536\pi\) |
−0.979352 | + | 0.202164i | \(0.935203\pi\) | |||||||
\(12\) | 0.679293 | − | 1.17657i | 0.196095 | − | 0.339646i | ||||
\(13\) | 3.64405 | 1.01068 | 0.505339 | − | 0.862921i | \(-0.331368\pi\) | ||||
0.505339 | + | 0.862921i | \(0.331368\pi\) | |||||||
\(14\) | −4.83717 | − | 0.334494i | −1.29279 | − | 0.0893973i | ||||
\(15\) | 0.943490 | 0.243608 | ||||||||
\(16\) | 2.43571 | − | 4.21877i | 0.608927 | − | 1.05469i | ||||
\(17\) | −0.149720 | − | 0.259323i | −0.0363124 | − | 0.0628950i | 0.847298 | − | 0.531118i | \(-0.178228\pi\) |
−0.883610 | + | 0.468223i | \(0.844894\pi\) | |||||||
\(18\) | 0.916322 | + | 1.58712i | 0.215979 | + | 0.374087i | ||||
\(19\) | 0.289732 | − | 0.501830i | 0.0664690 | − | 0.115128i | −0.830876 | − | 0.556458i | \(-0.812160\pi\) |
0.897345 | + | 0.441330i | \(0.145493\pi\) | |||||||
\(20\) | −1.28181 | −0.286622 | ||||||||
\(21\) | 1.47779 | − | 2.19457i | 0.322480 | − | 0.478894i | ||||
\(22\) | −3.82436 | −0.815357 | ||||||||
\(23\) | 0.500000 | − | 0.866025i | 0.104257 | − | 0.180579i | ||||
\(24\) | 0.587742 | + | 1.01800i | 0.119972 | + | 0.207798i | ||||
\(25\) | 2.05491 | + | 3.55921i | 0.410983 | + | 0.711843i | ||||
\(26\) | 3.33912 | − | 5.78353i | 0.654856 | − | 1.13424i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.00771 | + | 2.98151i | −0.379421 | + | 0.563452i | ||||
\(29\) | −5.89363 | −1.09442 | −0.547210 | − | 0.836995i | \(-0.684310\pi\) | ||||
−0.547210 | + | 0.836995i | \(0.684310\pi\) | |||||||
\(30\) | 0.864540 | − | 1.49743i | 0.157843 | − | 0.273392i | ||||
\(31\) | 3.01194 | + | 5.21683i | 0.540960 | + | 0.936970i | 0.998849 | + | 0.0479608i | \(0.0152723\pi\) |
−0.457889 | + | 0.889009i | \(0.651394\pi\) | |||||||
\(32\) | −3.28830 | − | 5.69551i | −0.581295 | − | 1.00683i | ||||
\(33\) | 1.04340 | − | 1.80722i | 0.181633 | − | 0.314597i | ||||
\(34\) | −0.548767 | −0.0941128 | ||||||||
\(35\) | −2.49029 | − | 0.172206i | −0.420936 | − | 0.0291081i | ||||
\(36\) | 1.35859 | 0.226431 | ||||||||
\(37\) | 0.618718 | − | 1.07165i | 0.101717 | − | 0.176178i | −0.810675 | − | 0.585496i | \(-0.800900\pi\) |
0.912392 | + | 0.409318i | \(0.134233\pi\) | |||||||
\(38\) | −0.530975 | − | 0.919676i | −0.0861356 | − | 0.149191i | ||||
\(39\) | 1.82202 | + | 3.15584i | 0.291757 | + | 0.505339i | ||||
\(40\) | 0.554529 | − | 0.960472i | 0.0876787 | − | 0.151864i | ||||
\(41\) | 8.42024 | 1.31502 | 0.657510 | − | 0.753446i | \(-0.271610\pi\) | ||||
0.657510 | + | 0.753446i | \(0.271610\pi\) | |||||||
\(42\) | −2.12890 | − | 4.35636i | −0.328497 | − | 0.672201i | ||||
\(43\) | −9.08583 | −1.38558 | −0.692788 | − | 0.721142i | \(-0.743618\pi\) | ||||
−0.692788 | + | 0.721142i | \(0.743618\pi\) | |||||||
\(44\) | −1.41755 | + | 2.45527i | −0.213703 | + | 0.370145i | ||||
\(45\) | 0.471745 | + | 0.817086i | 0.0703236 | + | 0.121804i | ||||
\(46\) | −0.916322 | − | 1.58712i | −0.135104 | − | 0.234008i | ||||
\(47\) | −2.53123 | + | 4.38422i | −0.369218 | + | 0.639505i | −0.989444 | − | 0.144919i | \(-0.953708\pi\) |
0.620225 | + | 0.784424i | \(0.287041\pi\) | |||||||
\(48\) | 4.87142 | 0.703128 | ||||||||
\(49\) | −4.30111 | + | 5.52273i | −0.614444 | + | 0.788961i | ||||
\(50\) | 7.53185 | 1.06516 | ||||||||
\(51\) | 0.149720 | − | 0.259323i | 0.0209650 | − | 0.0363124i | ||||
\(52\) | −2.47538 | − | 4.28748i | −0.343273 | − | 0.594566i | ||||
\(53\) | −1.16288 | − | 2.01417i | −0.159734 | − | 0.276668i | 0.775039 | − | 0.631914i | \(-0.217730\pi\) |
−0.934773 | + | 0.355246i | \(0.884397\pi\) | |||||||
\(54\) | −0.916322 | + | 1.58712i | −0.124696 | + | 0.215979i | ||||
\(55\) | −1.96887 | −0.265483 | ||||||||
\(56\) | −1.36551 | − | 2.79423i | −0.182474 | − | 0.373395i | ||||
\(57\) | 0.579464 | 0.0767518 | ||||||||
\(58\) | −5.40047 | + | 9.35388i | −0.709116 | + | 1.22822i | ||||
\(59\) | −1.04007 | − | 1.80146i | −0.135406 | − | 0.234530i | 0.790346 | − | 0.612660i | \(-0.209901\pi\) |
−0.925753 | + | 0.378130i | \(0.876567\pi\) | |||||||
\(60\) | −0.640906 | − | 1.11008i | −0.0827406 | − | 0.143311i | ||||
\(61\) | −6.22701 | + | 10.7855i | −0.797287 | + | 1.38094i | 0.124089 | + | 0.992271i | \(0.460399\pi\) |
−0.921376 | + | 0.388671i | \(0.872934\pi\) | |||||||
\(62\) | 11.0396 | 1.40203 | ||||||||
\(63\) | 2.63945 | + | 0.182520i | 0.332539 | + | 0.0229954i | ||||
\(64\) | −2.30974 | −0.288718 | ||||||||
\(65\) | 1.71906 | − | 2.97750i | 0.213223 | − | 0.369314i | ||||
\(66\) | −1.91218 | − | 3.31200i | −0.235373 | − | 0.407679i | ||||
\(67\) | 2.06882 | + | 3.58330i | 0.252746 | + | 0.437769i | 0.964281 | − | 0.264882i | \(-0.0853329\pi\) |
−0.711535 | + | 0.702651i | \(0.752000\pi\) | |||||||
\(68\) | −0.203407 | + | 0.352312i | −0.0246668 | + | 0.0427241i | ||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | −2.55522 | + | 3.79459i | −0.305407 | + | 0.453540i | ||||
\(71\) | −11.6439 | −1.38188 | −0.690938 | − | 0.722914i | \(-0.742802\pi\) | ||||
−0.690938 | + | 0.722914i | \(0.742802\pi\) | |||||||
\(72\) | −0.587742 | + | 1.01800i | −0.0692661 | + | 0.119972i | ||||
\(73\) | 5.78499 | + | 10.0199i | 0.677082 | + | 1.17274i | 0.975856 | + | 0.218416i | \(0.0700891\pi\) |
−0.298774 | + | 0.954324i | \(0.596578\pi\) | |||||||
\(74\) | −1.13389 | − | 1.96395i | −0.131812 | − | 0.228305i | ||||
\(75\) | −2.05491 | + | 3.55921i | −0.237281 | + | 0.410983i | ||||
\(76\) | −0.787251 | −0.0903039 | ||||||||
\(77\) | −3.08386 | + | 4.57963i | −0.351438 | + | 0.521897i | ||||
\(78\) | 6.67825 | 0.756163 | ||||||||
\(79\) | −8.57920 | + | 14.8596i | −0.965235 | + | 1.67184i | −0.256254 | + | 0.966609i | \(0.582488\pi\) |
−0.708981 | + | 0.705227i | \(0.750845\pi\) | |||||||
\(80\) | −2.29807 | − | 3.98037i | −0.256932 | − | 0.445018i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 7.71565 | − | 13.3639i | 0.852051 | − | 1.47580i | ||||
\(83\) | 10.9740 | 1.20455 | 0.602274 | − | 0.798289i | \(-0.294261\pi\) | ||||
0.602274 | + | 0.798289i | \(0.294261\pi\) | |||||||
\(84\) | −3.58592 | − | 0.247969i | −0.391256 | − | 0.0270556i | ||||
\(85\) | −0.282519 | −0.0306434 | ||||||||
\(86\) | −8.32554 | + | 14.4203i | −0.897766 | + | 1.55498i | ||||
\(87\) | −2.94682 | − | 5.10403i | −0.315932 | − | 0.547210i | ||||
\(88\) | −1.22650 | − | 2.12436i | −0.130745 | − | 0.226458i | ||||
\(89\) | −1.33781 | + | 2.31715i | −0.141807 | + | 0.245617i | −0.928177 | − | 0.372139i | \(-0.878625\pi\) |
0.786370 | + | 0.617756i | \(0.211958\pi\) | |||||||
\(90\) | 1.72908 | 0.182261 | ||||||||
\(91\) | −4.23314 | − | 8.66223i | −0.443753 | − | 0.908048i | ||||
\(92\) | −1.35859 | −0.141642 | ||||||||
\(93\) | −3.01194 | + | 5.21683i | −0.312323 | + | 0.540960i | ||||
\(94\) | 4.63885 | + | 8.03472i | 0.478461 | + | 0.828718i | ||||
\(95\) | −0.273359 | − | 0.473472i | −0.0280460 | − | 0.0485772i | ||||
\(96\) | 3.28830 | − | 5.69551i | 0.335611 | − | 0.581295i | ||||
\(97\) | 0.589843 | 0.0598895 | 0.0299447 | − | 0.999552i | \(-0.490467\pi\) | ||||
0.0299447 | + | 0.999552i | \(0.490467\pi\) | |||||||
\(98\) | 4.82401 | + | 11.8870i | 0.487299 | + | 1.20076i | ||||
\(99\) | 2.08680 | 0.209731 | ||||||||
\(100\) | 2.79178 | − | 4.83550i | 0.279178 | − | 0.483550i | ||||
\(101\) | −3.11417 | − | 5.39390i | −0.309872 | − | 0.536713i | 0.668462 | − | 0.743746i | \(-0.266953\pi\) |
−0.978334 | + | 0.207033i | \(0.933619\pi\) | |||||||
\(102\) | −0.274384 | − | 0.475246i | −0.0271680 | − | 0.0470564i | ||||
\(103\) | 9.32274 | − | 16.1475i | 0.918597 | − | 1.59106i | 0.117049 | − | 0.993126i | \(-0.462656\pi\) |
0.801548 | − | 0.597931i | \(-0.204010\pi\) | |||||||
\(104\) | 4.28352 | 0.420034 | ||||||||
\(105\) | −1.09601 | − | 2.24276i | −0.106960 | − | 0.218871i | ||||
\(106\) | −4.26230 | −0.413992 | ||||||||
\(107\) | 0.324442 | − | 0.561949i | 0.0313650 | − | 0.0543257i | −0.849917 | − | 0.526917i | \(-0.823348\pi\) |
0.881282 | + | 0.472591i | \(0.156681\pi\) | |||||||
\(108\) | 0.679293 | + | 1.17657i | 0.0653650 | + | 0.113215i | ||||
\(109\) | 6.82667 | + | 11.8241i | 0.653876 | + | 1.13255i | 0.982174 | + | 0.187973i | \(0.0601916\pi\) |
−0.328298 | + | 0.944574i | \(0.606475\pi\) | |||||||
\(110\) | −1.80412 | + | 3.12483i | −0.172016 | + | 0.297941i | ||||
\(111\) | 1.23744 | 0.117452 | ||||||||
\(112\) | −12.8579 | − | 0.889131i | −1.21495 | − | 0.0840150i | ||||
\(113\) | 0.547279 | 0.0514836 | 0.0257418 | − | 0.999669i | \(-0.491805\pi\) | ||||
0.0257418 | + | 0.999669i | \(0.491805\pi\) | |||||||
\(114\) | 0.530975 | − | 0.919676i | 0.0497304 | − | 0.0861356i | ||||
\(115\) | −0.471745 | − | 0.817086i | −0.0439904 | − | 0.0761937i | ||||
\(116\) | 4.00350 | + | 6.93427i | 0.371716 | + | 0.643831i | ||||
\(117\) | −1.82202 | + | 3.15584i | −0.168446 | + | 0.291757i | ||||
\(118\) | −3.81217 | −0.350939 | ||||||||
\(119\) | −0.442510 | + | 0.657142i | −0.0405648 | + | 0.0602401i | ||||
\(120\) | 1.10906 | 0.101243 | ||||||||
\(121\) | 3.32263 | − | 5.75497i | 0.302057 | − | 0.523179i | ||||
\(122\) | 11.4119 | + | 19.7660i | 1.03319 | + | 1.78953i | ||||
\(123\) | 4.21012 | + | 7.29214i | 0.379614 | + | 0.657510i | ||||
\(124\) | 4.09197 | − | 7.08751i | 0.367470 | − | 0.636477i | ||||
\(125\) | 8.59503 | 0.768763 | ||||||||
\(126\) | 2.70827 | − | 4.02186i | 0.241271 | − | 0.358296i | ||||
\(127\) | −1.01278 | −0.0898693 | −0.0449347 | − | 0.998990i | \(-0.514308\pi\) | ||||
−0.0449347 | + | 0.998990i | \(0.514308\pi\) | |||||||
\(128\) | 4.46013 | − | 7.72518i | 0.394224 | − | 0.682816i | ||||
\(129\) | −4.54291 | − | 7.86856i | −0.399981 | − | 0.692788i | ||||
\(130\) | −3.15043 | − | 5.45670i | −0.276311 | − | 0.478584i | ||||
\(131\) | 7.51553 | − | 13.0173i | 0.656635 | − | 1.13733i | −0.324846 | − | 0.945767i | \(-0.605313\pi\) |
0.981481 | − | 0.191558i | \(-0.0613541\pi\) | |||||||
\(132\) | −2.83510 | −0.246764 | ||||||||
\(133\) | −1.52946 | − | 0.105764i | −0.132621 | − | 0.00917087i | ||||
\(134\) | 7.58281 | 0.655055 | ||||||||
\(135\) | −0.471745 | + | 0.817086i | −0.0406013 | + | 0.0703236i | ||||
\(136\) | −0.175994 | − | 0.304830i | −0.0150913 | − | 0.0261389i | ||||
\(137\) | −4.63934 | − | 8.03557i | −0.396365 | − | 0.686525i | 0.596909 | − | 0.802309i | \(-0.296395\pi\) |
−0.993274 | + | 0.115784i | \(0.963062\pi\) | |||||||
\(138\) | 0.916322 | − | 1.58712i | 0.0780025 | − | 0.135104i | ||||
\(139\) | 6.58750 | 0.558744 | 0.279372 | − | 0.960183i | \(-0.409874\pi\) | ||||
0.279372 | + | 0.960183i | \(0.409874\pi\) | |||||||
\(140\) | 1.48903 | + | 3.04698i | 0.125846 | + | 0.257517i | ||||
\(141\) | −5.06246 | −0.426336 | ||||||||
\(142\) | −10.6696 | + | 18.4802i | −0.895370 | + | 1.55083i | ||||
\(143\) | −3.80220 | − | 6.58561i | −0.317956 | − | 0.550716i | ||||
\(144\) | 2.43571 | + | 4.21877i | 0.202976 | + | 0.351564i | ||||
\(145\) | −2.78029 | + | 4.81560i | −0.230890 | + | 0.399914i | ||||
\(146\) | 21.2037 | 1.75483 | ||||||||
\(147\) | −6.93337 | − | 0.963504i | −0.571855 | − | 0.0794685i | ||||
\(148\) | −1.68116 | −0.138191 | ||||||||
\(149\) | 2.94451 | − | 5.10005i | 0.241224 | − | 0.417812i | −0.719839 | − | 0.694141i | \(-0.755784\pi\) |
0.961063 | + | 0.276329i | \(0.0891178\pi\) | |||||||
\(150\) | 3.76593 | + | 6.52278i | 0.307487 | + | 0.532582i | ||||
\(151\) | −6.57693 | − | 11.3916i | −0.535223 | − | 0.927033i | −0.999153 | − | 0.0411608i | \(-0.986894\pi\) |
0.463930 | − | 0.885872i | \(-0.346439\pi\) | |||||||
\(152\) | 0.340575 | − | 0.589894i | 0.0276243 | − | 0.0478467i | ||||
\(153\) | 0.299440 | 0.0242083 | ||||||||
\(154\) | 4.44260 | + | 9.09085i | 0.357995 | + | 0.732562i | ||||
\(155\) | 5.68346 | 0.456507 | ||||||||
\(156\) | 2.47538 | − | 4.28748i | 0.198189 | − | 0.343273i | ||||
\(157\) | 4.21279 | + | 7.29677i | 0.336217 | + | 0.582345i | 0.983718 | − | 0.179720i | \(-0.0575190\pi\) |
−0.647501 | + | 0.762065i | \(0.724186\pi\) | |||||||
\(158\) | 15.7226 | + | 27.2324i | 1.25082 | + | 2.16649i | ||||
\(159\) | 1.16288 | − | 2.01417i | 0.0922227 | − | 0.159734i | ||||
\(160\) | −6.20496 | −0.490545 | ||||||||
\(161\) | −2.63945 | − | 0.182520i | −0.208018 | − | 0.0143846i | ||||
\(162\) | −1.83264 | −0.143986 | ||||||||
\(163\) | −2.07868 | + | 3.60038i | −0.162815 | + | 0.282004i | −0.935877 | − | 0.352326i | \(-0.885391\pi\) |
0.773062 | + | 0.634330i | \(0.218724\pi\) | |||||||
\(164\) | −5.71981 | − | 9.90699i | −0.446642 | − | 0.773606i | ||||
\(165\) | −0.984437 | − | 1.70510i | −0.0766383 | − | 0.132741i | ||||
\(166\) | 10.0557 | − | 17.4170i | 0.780473 | − | 1.35182i | ||||
\(167\) | −3.04445 | −0.235587 | −0.117793 | − | 0.993038i | \(-0.537582\pi\) | ||||
−0.117793 | + | 0.993038i | \(0.537582\pi\) | |||||||
\(168\) | 1.73712 | − | 2.57968i | 0.134022 | − | 0.199027i | ||||
\(169\) | 0.279097 | 0.0214690 | ||||||||
\(170\) | −0.258878 | + | 0.448390i | −0.0198550 | + | 0.0343899i | ||||
\(171\) | 0.289732 | + | 0.501830i | 0.0221563 | + | 0.0383759i | ||||
\(172\) | 6.17194 | + | 10.6901i | 0.470606 | + | 0.815113i | ||||
\(173\) | −8.02715 | + | 13.9034i | −0.610293 | + | 1.05706i | 0.380898 | + | 0.924617i | \(0.375615\pi\) |
−0.991191 | + | 0.132441i | \(0.957719\pi\) | |||||||
\(174\) | −10.8009 | −0.818816 | ||||||||
\(175\) | 6.07347 | − | 9.01930i | 0.459111 | − | 0.681795i | ||||
\(176\) | −10.1657 | −0.766267 | ||||||||
\(177\) | 1.04007 | − | 1.80146i | 0.0781768 | − | 0.135406i | ||||
\(178\) | 2.45172 | + | 4.24651i | 0.183764 | + | 0.318289i | ||||
\(179\) | 2.67255 | + | 4.62898i | 0.199755 | + | 0.345987i | 0.948449 | − | 0.316930i | \(-0.102652\pi\) |
−0.748694 | + | 0.662916i | \(0.769319\pi\) | |||||||
\(180\) | 0.640906 | − | 1.11008i | 0.0477703 | − | 0.0827406i | ||||
\(181\) | −11.6201 | −0.863716 | −0.431858 | − | 0.901942i | \(-0.642142\pi\) | ||||
−0.431858 | + | 0.901942i | \(0.642142\pi\) | |||||||
\(182\) | −17.6269 | − | 1.21891i | −1.30659 | − | 0.0903519i | ||||
\(183\) | −12.4540 | −0.920628 | ||||||||
\(184\) | 0.587742 | − | 1.01800i | 0.0433289 | − | 0.0750479i | ||||
\(185\) | −0.583754 | − | 1.01109i | −0.0429184 | − | 0.0743369i | ||||
\(186\) | 5.51981 | + | 9.56059i | 0.404732 | + | 0.701017i | ||||
\(187\) | −0.312436 | + | 0.541155i | −0.0228476 | + | 0.0395732i | ||||
\(188\) | 6.87779 | 0.501614 | ||||||||
\(189\) | 1.16166 | + | 2.37709i | 0.0844981 | + | 0.172908i | ||||
\(190\) | −1.00194 | −0.0726883 | ||||||||
\(191\) | 8.53757 | − | 14.7875i | 0.617757 | − | 1.06999i | −0.372137 | − | 0.928178i | \(-0.621375\pi\) |
0.989894 | − | 0.141809i | \(-0.0452918\pi\) | |||||||
\(192\) | −1.15487 | − | 2.00030i | −0.0833457 | − | 0.144359i | ||||
\(193\) | 2.32526 | + | 4.02747i | 0.167376 | + | 0.289903i | 0.937496 | − | 0.347995i | \(-0.113137\pi\) |
−0.770121 | + | 0.637898i | \(0.779804\pi\) | |||||||
\(194\) | 0.540486 | − | 0.936149i | 0.0388046 | − | 0.0672116i | ||||
\(195\) | 3.43812 | 0.246209 | ||||||||
\(196\) | 9.41958 | + | 1.30900i | 0.672827 | + | 0.0935002i | ||||
\(197\) | 0.254912 | 0.0181618 | 0.00908088 | − | 0.999959i | \(-0.497109\pi\) | ||||
0.00908088 | + | 0.999959i | \(0.497109\pi\) | |||||||
\(198\) | 1.91218 | − | 3.31200i | 0.135893 | − | 0.235373i | ||||
\(199\) | −2.73799 | − | 4.74233i | −0.194091 | − | 0.336175i | 0.752511 | − | 0.658579i | \(-0.228842\pi\) |
−0.946602 | + | 0.322404i | \(0.895509\pi\) | |||||||
\(200\) | 2.41552 | + | 4.18380i | 0.170803 | + | 0.295840i | ||||
\(201\) | −2.06882 | + | 3.58330i | −0.145923 | + | 0.252746i | ||||
\(202\) | −11.4143 | −0.803110 | ||||||||
\(203\) | 6.84638 | + | 14.0097i | 0.480522 | + | 0.983287i | ||||
\(204\) | −0.406815 | −0.0284827 | ||||||||
\(205\) | 3.97220 | − | 6.88006i | 0.277431 | − | 0.480524i | ||||
\(206\) | −17.0853 | − | 29.5926i | −1.19039 | − | 2.06181i | ||||
\(207\) | 0.500000 | + | 0.866025i | 0.0347524 | + | 0.0601929i | ||||
\(208\) | 8.87584 | − | 15.3734i | 0.615429 | − | 1.06595i | ||||
\(209\) | −1.20923 | −0.0836438 | ||||||||
\(210\) | −4.56382 | − | 0.315592i | −0.314933 | − | 0.0217779i | ||||
\(211\) | −3.18599 | −0.219332 | −0.109666 | − | 0.993968i | \(-0.534978\pi\) | ||||
−0.109666 | + | 0.993968i | \(0.534978\pi\) | |||||||
\(212\) | −1.57988 | + | 2.73643i | −0.108506 | + | 0.187939i | ||||
\(213\) | −5.82195 | − | 10.0839i | −0.398913 | − | 0.690938i | ||||
\(214\) | −0.594586 | − | 1.02985i | −0.0406451 | − | 0.0703993i | ||||
\(215\) | −4.28619 | + | 7.42390i | −0.292316 | + | 0.506306i | ||||
\(216\) | −1.17548 | −0.0799816 | ||||||||
\(217\) | 8.90203 | − | 13.2198i | 0.604309 | − | 0.897419i | ||||
\(218\) | 25.0217 | 1.69468 | ||||||||
\(219\) | −5.78499 | + | 10.0199i | −0.390914 | + | 0.677082i | ||||
\(220\) | 1.33744 | + | 2.31652i | 0.0901703 | + | 0.156180i | ||||
\(221\) | −0.545587 | − | 0.944985i | −0.0367002 | − | 0.0635665i | ||||
\(222\) | 1.13389 | − | 1.96395i | 0.0761017 | − | 0.131812i | ||||
\(223\) | −22.7674 | −1.52462 | −0.762309 | − | 0.647213i | \(-0.775934\pi\) | ||||
−0.762309 | + | 0.647213i | \(0.775934\pi\) | |||||||
\(224\) | −9.71885 | + | 14.4328i | −0.649368 | + | 0.964333i | ||||
\(225\) | −4.10983 | −0.273988 | ||||||||
\(226\) | 0.501484 | − | 0.868595i | 0.0333582 | − | 0.0577781i | ||||
\(227\) | −5.22604 | − | 9.05176i | −0.346864 | − | 0.600787i | 0.638826 | − | 0.769351i | \(-0.279420\pi\) |
−0.985691 | + | 0.168564i | \(0.946087\pi\) | |||||||
\(228\) | −0.393625 | − | 0.681779i | −0.0260685 | − | 0.0451519i | ||||
\(229\) | 5.38392 | − | 9.32522i | 0.355779 | − | 0.616228i | −0.631472 | − | 0.775399i | \(-0.717549\pi\) |
0.987251 | + | 0.159171i | \(0.0508822\pi\) | |||||||
\(230\) | −1.72908 | −0.114012 | ||||||||
\(231\) | −5.50800 | − | 0.380883i | −0.362400 | − | 0.0250602i | ||||
\(232\) | −6.92787 | −0.454837 | ||||||||
\(233\) | −5.87538 | + | 10.1765i | −0.384909 | + | 0.666682i | −0.991757 | − | 0.128136i | \(-0.959100\pi\) |
0.606848 | + | 0.794818i | \(0.292434\pi\) | |||||||
\(234\) | 3.33912 | + | 5.78353i | 0.218285 | + | 0.378081i | ||||
\(235\) | 2.38819 | + | 4.13647i | 0.155788 | + | 0.269833i | ||||
\(236\) | −1.41303 | + | 2.44744i | −0.0919804 | + | 0.159315i | ||||
\(237\) | −17.1584 | −1.11456 | ||||||||
\(238\) | 0.637479 | + | 1.30447i | 0.0413216 | + | 0.0845561i | ||||
\(239\) | −12.5491 | −0.811734 | −0.405867 | − | 0.913932i | \(-0.633030\pi\) | ||||
−0.405867 | + | 0.913932i | \(0.633030\pi\) | |||||||
\(240\) | 2.29807 | − | 3.98037i | 0.148339 | − | 0.256932i | ||||
\(241\) | 5.31523 | + | 9.20624i | 0.342384 | + | 0.593026i | 0.984875 | − | 0.173267i | \(-0.0554324\pi\) |
−0.642491 | + | 0.766293i | \(0.722099\pi\) | |||||||
\(242\) | −6.08920 | − | 10.5468i | −0.391429 | − | 0.677974i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 16.9199 | 1.08318 | ||||||||
\(245\) | 2.48352 | + | 6.11969i | 0.158666 | + | 0.390973i | ||||
\(246\) | 15.4313 | 0.983864 | ||||||||
\(247\) | 1.05580 | − | 1.82869i | 0.0671788 | − | 0.116357i | ||||
\(248\) | 3.54049 | + | 6.13230i | 0.224821 | + | 0.389402i | ||||
\(249\) | 5.48698 | + | 9.50373i | 0.347723 | + | 0.602274i | ||||
\(250\) | 7.87581 | − | 13.6413i | 0.498110 | − | 0.862752i | ||||
\(251\) | −17.4415 | −1.10090 | −0.550450 | − | 0.834868i | \(-0.685544\pi\) | ||||
−0.550450 | + | 0.834868i | \(0.685544\pi\) | |||||||
\(252\) | −1.57821 | − | 3.22948i | −0.0994179 | − | 0.203438i | ||||
\(253\) | −2.08680 | −0.131196 | ||||||||
\(254\) | −0.928029 | + | 1.60739i | −0.0582297 | + | 0.100857i | ||||
\(255\) | −0.141259 | − | 0.244668i | −0.00884600 | − | 0.0153217i | ||||
\(256\) | −10.4836 | − | 18.1581i | −0.655224 | − | 1.13488i | ||||
\(257\) | −9.36304 | + | 16.2173i | −0.584050 | + | 1.01160i | 0.410943 | + | 0.911661i | \(0.365200\pi\) |
−0.994993 | + | 0.0999435i | \(0.968134\pi\) | |||||||
\(258\) | −16.6511 | −1.03665 | ||||||||
\(259\) | −3.26615 | − | 0.225857i | −0.202948 | − | 0.0140341i | ||||
\(260\) | −4.67098 | −0.289682 | ||||||||
\(261\) | 2.94682 | − | 5.10403i | 0.182403 | − | 0.315932i | ||||
\(262\) | −13.7733 | − | 23.8560i | −0.850917 | − | 1.47383i | ||||
\(263\) | −14.9543 | − | 25.9016i | −0.922121 | − | 1.59716i | −0.796128 | − | 0.605129i | \(-0.793122\pi\) |
−0.125993 | − | 0.992031i | \(-0.540212\pi\) | |||||||
\(264\) | 1.22650 | − | 2.12436i | 0.0754859 | − | 0.130745i | ||||
\(265\) | −2.19434 | −0.134797 | ||||||||
\(266\) | −1.56934 | + | 2.33052i | −0.0962225 | + | 0.142894i | ||||
\(267\) | −2.67561 | −0.163745 | ||||||||
\(268\) | 2.81067 | − | 4.86821i | 0.171689 | − | 0.297374i | ||||
\(269\) | −11.3230 | − | 19.6121i | −0.690378 | − | 1.19577i | −0.971714 | − | 0.236161i | \(-0.924111\pi\) |
0.281336 | − | 0.959609i | \(-0.409222\pi\) | |||||||
\(270\) | 0.864540 | + | 1.49743i | 0.0526143 | + | 0.0911306i | ||||
\(271\) | 6.36818 | − | 11.0300i | 0.386839 | − | 0.670026i | −0.605183 | − | 0.796086i | \(-0.706900\pi\) |
0.992023 | + | 0.126061i | \(0.0402334\pi\) | |||||||
\(272\) | −1.45870 | −0.0884465 | ||||||||
\(273\) | 5.38514 | − | 7.99712i | 0.325924 | − | 0.484008i | ||||
\(274\) | −17.0045 | −1.02728 | ||||||||
\(275\) | 4.28820 | − | 7.42737i | 0.258588 | − | 0.447887i | ||||
\(276\) | −0.679293 | − | 1.17657i | −0.0408886 | − | 0.0708212i | ||||
\(277\) | 14.5063 | + | 25.1257i | 0.871601 | + | 1.50966i | 0.860340 | + | 0.509720i | \(0.170251\pi\) |
0.0112606 | + | 0.999937i | \(0.496416\pi\) | |||||||
\(278\) | 6.03627 | − | 10.4551i | 0.362031 | − | 0.627057i | ||||
\(279\) | −6.02387 | −0.360640 | ||||||||
\(280\) | −2.92730 | − | 0.202425i | −0.174940 | − | 0.0120972i | ||||
\(281\) | −12.4466 | −0.742504 | −0.371252 | − | 0.928532i | \(-0.621071\pi\) | ||||
−0.371252 | + | 0.928532i | \(0.621071\pi\) | |||||||
\(282\) | −4.63885 | + | 8.03472i | −0.276239 | + | 0.478461i | ||||
\(283\) | −4.68198 | − | 8.10943i | −0.278315 | − | 0.482056i | 0.692651 | − | 0.721273i | \(-0.256443\pi\) |
−0.970966 | + | 0.239217i | \(0.923109\pi\) | |||||||
\(284\) | 7.90962 | + | 13.6999i | 0.469349 | + | 0.812937i | ||||
\(285\) | 0.273359 | − | 0.473472i | 0.0161924 | − | 0.0280460i | ||||
\(286\) | −13.9362 | −0.824063 | ||||||||
\(287\) | −9.78143 | − | 20.0157i | −0.577379 | − | 1.18149i | ||||
\(288\) | 6.57660 | 0.387530 | ||||||||
\(289\) | 8.45517 | − | 14.6448i | 0.497363 | − | 0.861458i | ||||
\(290\) | 5.09528 | + | 8.82529i | 0.299205 | + | 0.518239i | ||||
\(291\) | 0.294921 | + | 0.510819i | 0.0172886 | + | 0.0299447i | ||||
\(292\) | 7.85941 | − | 13.6129i | 0.459937 | − | 0.796634i | ||||
\(293\) | 5.69521 | 0.332717 | 0.166359 | − | 0.986065i | \(-0.446799\pi\) | ||||
0.166359 | + | 0.986065i | \(0.446799\pi\) | |||||||
\(294\) | −7.88240 | + | 10.1212i | −0.459711 | + | 0.590280i | ||||
\(295\) | −1.96260 | −0.114267 | ||||||||
\(296\) | 0.727293 | − | 1.25971i | 0.0422731 | − | 0.0732191i | ||||
\(297\) | 1.04340 | + | 1.80722i | 0.0605442 | + | 0.104866i | ||||
\(298\) | −5.39625 | − | 9.34657i | −0.312596 | − | 0.541433i | ||||
\(299\) | 1.82202 | − | 3.15584i | 0.105370 | − | 0.182507i | ||||
\(300\) | 5.58355 | 0.322367 | ||||||||
\(301\) | 10.5546 | + | 21.5978i | 0.608358 | + | 1.24488i | ||||
\(302\) | −24.1063 | −1.38716 | ||||||||
\(303\) | 3.11417 | − | 5.39390i | 0.178904 | − | 0.309872i | ||||
\(304\) | −1.41140 | − | 2.44462i | −0.0809496 | − | 0.140209i | ||||
\(305\) | 5.87512 | + | 10.1760i | 0.336409 | + | 0.582677i | ||||
\(306\) | 0.274384 | − | 0.475246i | 0.0156855 | − | 0.0271680i | ||||
\(307\) | 17.0596 | 0.973642 | 0.486821 | − | 0.873502i | \(-0.338156\pi\) | ||||
0.486821 | + | 0.873502i | \(0.338156\pi\) | |||||||
\(308\) | 7.48309 | + | 0.517462i | 0.426389 | + | 0.0294851i | ||||
\(309\) | 18.6455 | 1.06070 | ||||||||
\(310\) | 5.20788 | − | 9.02032i | 0.295788 | − | 0.512320i | ||||
\(311\) | 8.26214 | + | 14.3104i | 0.468503 | + | 0.811471i | 0.999352 | − | 0.0359958i | \(-0.0114603\pi\) |
−0.530849 | + | 0.847466i | \(0.678127\pi\) | |||||||
\(312\) | 2.14176 | + | 3.70964i | 0.121253 | + | 0.210017i | ||||
\(313\) | 0.746938 | − | 1.29374i | 0.0422195 | − | 0.0731262i | −0.844143 | − | 0.536117i | \(-0.819890\pi\) |
0.886363 | + | 0.462991i | \(0.153224\pi\) | |||||||
\(314\) | 15.4411 | 0.871391 | ||||||||
\(315\) | 1.39428 | − | 2.07055i | 0.0785588 | − | 0.116662i | ||||
\(316\) | 23.3112 | 1.31135 | ||||||||
\(317\) | 9.11172 | − | 15.7820i | 0.511765 | − | 0.886403i | −0.488142 | − | 0.872764i | \(-0.662325\pi\) |
0.999907 | − | 0.0136387i | \(-0.00434146\pi\) | |||||||
\(318\) | −2.13115 | − | 3.69126i | −0.119509 | − | 0.206996i | ||||
\(319\) | 6.14942 | + | 10.6511i | 0.344301 | + | 0.596347i | ||||
\(320\) | −1.08961 | + | 1.88726i | −0.0609111 | + | 0.105501i | ||||
\(321\) | 0.648883 | 0.0362171 | ||||||||
\(322\) | −2.70827 | + | 4.02186i | −0.150926 | + | 0.224130i | ||||
\(323\) | −0.173515 | −0.00965461 | ||||||||
\(324\) | −0.679293 | + | 1.17657i | −0.0377385 | + | 0.0653650i | ||||
\(325\) | 7.48821 | + | 12.9700i | 0.415371 | + | 0.719444i | ||||
\(326\) | 3.80948 | + | 6.59822i | 0.210988 | + | 0.365442i | ||||
\(327\) | −6.82667 | + | 11.8241i | −0.377516 | + | 0.653876i | ||||
\(328\) | 9.89786 | 0.546518 | ||||||||
\(329\) | 13.3621 | + | 0.924001i | 0.736677 | + | 0.0509418i | ||||
\(330\) | −3.60825 | −0.198627 | ||||||||
\(331\) | 11.4774 | − | 19.8795i | 0.630857 | − | 1.09268i | −0.356520 | − | 0.934288i | \(-0.616037\pi\) |
0.987377 | − | 0.158388i | \(-0.0506298\pi\) | |||||||
\(332\) | −7.45453 | − | 12.9116i | −0.409121 | − | 0.708618i | ||||
\(333\) | 0.618718 | + | 1.07165i | 0.0339055 | + | 0.0587261i | ||||
\(334\) | −2.78970 | + | 4.83189i | −0.152645 | + | 0.264390i | ||||
\(335\) | 3.90381 | 0.213288 | ||||||||
\(336\) | −5.65892 | − | 11.5798i | −0.308719 | − | 0.631729i | ||||
\(337\) | 22.2266 | 1.21076 | 0.605381 | − | 0.795936i | \(-0.293021\pi\) | ||||
0.605381 | + | 0.795936i | \(0.293021\pi\) | |||||||
\(338\) | 0.255743 | − | 0.442960i | 0.0139106 | − | 0.0240938i | ||||
\(339\) | 0.273639 | + | 0.473957i | 0.0148620 | + | 0.0257418i | ||||
\(340\) | 0.191913 | + | 0.332403i | 0.0104079 | + | 0.0180271i | ||||
\(341\) | 6.28531 | − | 10.8865i | 0.340369 | − | 0.589536i | ||||
\(342\) | 1.06195 | 0.0574237 | ||||||||
\(343\) | 18.1244 | + | 3.80860i | 0.978627 | + | 0.205645i | ||||
\(344\) | −10.6802 | −0.575840 | ||||||||
\(345\) | 0.471745 | − | 0.817086i | 0.0253979 | − | 0.0439904i | ||||
\(346\) | 14.7109 | + | 25.4800i | 0.790863 | + | 1.36982i | ||||
\(347\) | 2.70421 | + | 4.68383i | 0.145170 | + | 0.251441i | 0.929436 | − | 0.368983i | \(-0.120294\pi\) |
−0.784267 | + | 0.620424i | \(0.786961\pi\) | |||||||
\(348\) | −4.00350 | + | 6.93427i | −0.214610 | + | 0.371716i | ||||
\(349\) | 10.3938 | 0.556369 | 0.278184 | − | 0.960528i | \(-0.410267\pi\) | ||||
0.278184 | + | 0.960528i | \(0.410267\pi\) | |||||||
\(350\) | −8.74943 | − | 17.9039i | −0.467677 | − | 0.957003i | ||||
\(351\) | −3.64405 | −0.194505 | ||||||||
\(352\) | −6.86203 | + | 11.8854i | −0.365747 | + | 0.633493i | ||||
\(353\) | 6.53453 | + | 11.3181i | 0.347798 | + | 0.602404i | 0.985858 | − | 0.167583i | \(-0.0535962\pi\) |
−0.638060 | + | 0.769987i | \(0.720263\pi\) | |||||||
\(354\) | −1.90609 | − | 3.30144i | −0.101307 | − | 0.175469i | ||||
\(355\) | −5.49295 | + | 9.51407i | −0.291535 | + | 0.504954i | ||||
\(356\) | 3.63505 | 0.192657 | ||||||||
\(357\) | −0.790356 | − | 0.0546538i | −0.0418301 | − | 0.00289258i | ||||
\(358\) | 9.79565 | 0.517716 | ||||||||
\(359\) | 9.61160 | − | 16.6478i | 0.507281 | − | 0.878636i | −0.492684 | − | 0.870209i | \(-0.663984\pi\) |
0.999964 | − | 0.00842778i | \(-0.00268268\pi\) | |||||||
\(360\) | 0.554529 | + | 0.960472i | 0.0292262 | + | 0.0506213i | ||||
\(361\) | 9.33211 | + | 16.1637i | 0.491164 | + | 0.850721i | ||||
\(362\) | −10.6478 | + | 18.4425i | −0.559634 | + | 0.969315i | ||||
\(363\) | 6.64526 | 0.348786 | ||||||||
\(364\) | −7.31618 | + | 10.8648i | −0.383472 | + | 0.569469i | ||||
\(365\) | 10.9162 | 0.571378 | ||||||||
\(366\) | −11.4119 | + | 19.7660i | −0.596510 | + | 1.03319i | ||||
\(367\) | 0.887548 | + | 1.53728i | 0.0463296 | + | 0.0802452i | 0.888260 | − | 0.459340i | \(-0.151914\pi\) |
−0.841931 | + | 0.539586i | \(0.818581\pi\) | |||||||
\(368\) | −2.43571 | − | 4.21877i | −0.126970 | − | 0.219919i | ||||
\(369\) | −4.21012 | + | 7.29214i | −0.219170 | + | 0.379614i | ||||
\(370\) | −2.13963 | −0.111234 | ||||||||
\(371\) | −3.43700 | + | 5.10406i | −0.178440 | + | 0.264989i | ||||
\(372\) | 8.18395 | 0.424318 | ||||||||
\(373\) | 3.72011 | − | 6.44341i | 0.192620 | − | 0.333627i | −0.753498 | − | 0.657450i | \(-0.771635\pi\) |
0.946118 | + | 0.323823i | \(0.104968\pi\) | |||||||
\(374\) | 0.572584 | + | 0.991744i | 0.0296076 | + | 0.0512819i | ||||
\(375\) | 4.29751 | + | 7.44351i | 0.221923 | + | 0.384381i | ||||
\(376\) | −2.97542 | + | 5.15359i | −0.153446 | + | 0.265776i | ||||
\(377\) | −21.4767 | −1.10611 | ||||||||
\(378\) | 4.83717 | + | 0.334494i | 0.248797 | + | 0.0172045i | ||||
\(379\) | −4.31050 | −0.221415 | −0.110708 | − | 0.993853i | \(-0.535312\pi\) | ||||
−0.110708 | + | 0.993853i | \(0.535312\pi\) | |||||||
\(380\) | −0.371382 | + | 0.643252i | −0.0190515 | + | 0.0329981i | ||||
\(381\) | −0.506388 | − | 0.877090i | −0.0259430 | − | 0.0449347i | ||||
\(382\) | −15.6463 | − | 27.1002i | −0.800536 | − | 1.38657i | ||||
\(383\) | −17.3457 | + | 30.0437i | −0.886326 | + | 1.53516i | −0.0421400 | + | 0.999112i | \(0.513418\pi\) |
−0.844186 | + | 0.536050i | \(0.819916\pi\) | |||||||
\(384\) | 8.92027 | 0.455211 | ||||||||
\(385\) | 2.28716 | + | 4.68019i | 0.116564 | + | 0.238525i | ||||
\(386\) | 8.52275 | 0.433796 | ||||||||
\(387\) | 4.54291 | − | 7.86856i | 0.230929 | − | 0.399981i | ||||
\(388\) | −0.400676 | − | 0.693991i | −0.0203412 | − | 0.0352321i | ||||
\(389\) | −16.5719 | − | 28.7034i | −0.840230 | − | 1.45532i | −0.889700 | − | 0.456546i | \(-0.849086\pi\) |
0.0494696 | − | 0.998776i | \(-0.484247\pi\) | |||||||
\(390\) | 3.15043 | − | 5.45670i | 0.159528 | − | 0.276311i | ||||
\(391\) | −0.299440 | −0.0151433 | ||||||||
\(392\) | −5.05588 | + | 6.49188i | −0.255361 | + | 0.327889i | ||||
\(393\) | 15.0311 | 0.758217 | ||||||||
\(394\) | 0.233582 | − | 0.404576i | 0.0117677 | − | 0.0203822i | ||||
\(395\) | 8.09439 | + | 14.0199i | 0.407273 | + | 0.705417i | ||||
\(396\) | −1.41755 | − | 2.45527i | −0.0712345 | − | 0.123382i | ||||
\(397\) | 14.2282 | − | 24.6439i | 0.714092 | − | 1.23684i | −0.249217 | − | 0.968448i | \(-0.580173\pi\) |
0.963309 | − | 0.268396i | \(-0.0864935\pi\) | |||||||
\(398\) | −10.0355 | −0.503035 | ||||||||
\(399\) | −0.673138 | − | 1.37744i | −0.0336991 | − | 0.0689581i | ||||
\(400\) | 20.0207 | 1.00103 | ||||||||
\(401\) | 18.9406 | − | 32.8060i | 0.945846 | − | 1.63825i | 0.191798 | − | 0.981434i | \(-0.438568\pi\) |
0.754048 | − | 0.656819i | \(-0.228099\pi\) | |||||||
\(402\) | 3.79141 | + | 6.56691i | 0.189098 | + | 0.327528i | ||||
\(403\) | 10.9756 | + | 19.0104i | 0.546736 | + | 0.946974i | ||||
\(404\) | −4.23087 | + | 7.32808i | −0.210494 | + | 0.364586i | ||||
\(405\) | −0.943490 | −0.0468824 | ||||||||
\(406\) | 28.5085 | + | 1.97139i | 1.41485 | + | 0.0978382i | ||||
\(407\) | −2.58228 | −0.127999 | ||||||||
\(408\) | 0.175994 | − | 0.304830i | 0.00871298 | − | 0.0150913i | ||||
\(409\) | −0.478573 | − | 0.828913i | −0.0236639 | − | 0.0409871i | 0.853951 | − | 0.520354i | \(-0.174200\pi\) |
−0.877615 | + | 0.479366i | \(0.840866\pi\) | |||||||
\(410\) | −7.27964 | − | 12.6087i | −0.359516 | − | 0.622699i | ||||
\(411\) | 4.63934 | − | 8.03557i | 0.228842 | − | 0.396365i | ||||
\(412\) | −25.3315 | −1.24799 | ||||||||
\(413\) | −3.07402 | + | 4.56503i | −0.151263 | + | 0.224630i | ||||
\(414\) | 1.83264 | 0.0900696 | ||||||||
\(415\) | 5.17691 | − | 8.96667i | 0.254124 | − | 0.440157i | ||||
\(416\) | −11.9827 | − | 20.7547i | −0.587502 | − | 1.01758i | ||||
\(417\) | 3.29375 | + | 5.70494i | 0.161296 | + | 0.279372i | ||||
\(418\) | −1.10804 | + | 1.91918i | −0.0541960 | + | 0.0938702i | ||||
\(419\) | −40.7600 | −1.99126 | −0.995628 | − | 0.0934066i | \(-0.970224\pi\) | ||||
−0.995628 | + | 0.0934066i | \(0.970224\pi\) | |||||||
\(420\) | −1.89425 | + | 2.81302i | −0.0924299 | + | 0.137261i | ||||
\(421\) | −26.0184 | −1.26806 | −0.634031 | − | 0.773308i | \(-0.718601\pi\) | ||||
−0.634031 | + | 0.773308i | \(0.718601\pi\) | |||||||
\(422\) | −2.91939 | + | 5.05653i | −0.142114 | + | 0.246148i | ||||
\(423\) | −2.53123 | − | 4.38422i | −0.123073 | − | 0.213168i | ||||
\(424\) | −1.36695 | − | 2.36763i | −0.0663850 | − | 0.114982i | ||||
\(425\) | 0.615323 | − | 1.06577i | 0.0298476 | − | 0.0516975i | ||||
\(426\) | −21.3391 | −1.03388 | ||||||||
\(427\) | 32.8718 | + | 2.27311i | 1.59078 | + | 0.110003i | ||||
\(428\) | −0.881564 | −0.0426120 | ||||||||
\(429\) | 3.80220 | − | 6.58561i | 0.183572 | − | 0.317956i | ||||
\(430\) | 7.85506 | + | 13.6054i | 0.378805 | + | 0.656109i | ||||
\(431\) | 15.7221 | + | 27.2314i | 0.757305 | + | 1.31169i | 0.944220 | + | 0.329315i | \(0.106818\pi\) |
−0.186914 | + | 0.982376i | \(0.559849\pi\) | |||||||
\(432\) | −2.43571 | + | 4.21877i | −0.117188 | + | 0.202976i | ||||
\(433\) | 3.61281 | 0.173621 | 0.0868103 | − | 0.996225i | \(-0.472333\pi\) | ||||
0.0868103 | + | 0.996225i | \(0.472333\pi\) | |||||||
\(434\) | −12.8243 | − | 26.2422i | −0.615584 | − | 1.25966i | ||||
\(435\) | −5.56058 | −0.266609 | ||||||||
\(436\) | 9.27461 | − | 16.0641i | 0.444173 | − | 0.769331i | ||||
\(437\) | −0.289732 | − | 0.501830i | −0.0138598 | − | 0.0240058i | ||||
\(438\) | 10.6018 | + | 18.3629i | 0.506575 | + | 0.877414i | ||||
\(439\) | −9.02553 | + | 15.6327i | −0.430765 | + | 0.746107i | −0.996939 | − | 0.0781784i | \(-0.975090\pi\) |
0.566174 | + | 0.824286i | \(0.308423\pi\) | |||||||
\(440\) | −2.31438 | −0.110334 | ||||||||
\(441\) | −2.63227 | − | 6.48623i | −0.125346 | − | 0.308868i | ||||
\(442\) | −1.99973 | −0.0951177 | ||||||||
\(443\) | 17.6650 | − | 30.5967i | 0.839291 | − | 1.45369i | −0.0511975 | − | 0.998689i | \(-0.516304\pi\) |
0.890488 | − | 0.455006i | \(-0.150363\pi\) | |||||||
\(444\) | −0.840581 | − | 1.45593i | −0.0398922 | − | 0.0690953i | ||||
\(445\) | 1.26221 | + | 2.18620i | 0.0598343 | + | 0.103636i | ||||
\(446\) | −20.8623 | + | 36.1345i | −0.987857 | + | 1.71102i | ||||
\(447\) | 5.88903 | 0.278541 | ||||||||
\(448\) | 2.68313 | + | 5.49047i | 0.126766 | + | 0.259400i | ||||
\(449\) | 5.95593 | 0.281078 | 0.140539 | − | 0.990075i | \(-0.455116\pi\) | ||||
0.140539 | + | 0.990075i | \(0.455116\pi\) | |||||||
\(450\) | −3.76593 | + | 6.52278i | −0.177527 | + | 0.307487i | ||||
\(451\) | −8.78568 | − | 15.2172i | −0.413701 | − | 0.716552i | ||||
\(452\) | −0.371762 | − | 0.643911i | −0.0174862 | − | 0.0302870i | ||||
\(453\) | 6.57693 | − | 11.3916i | 0.309011 | − | 0.535223i | ||||
\(454\) | −19.1549 | −0.898986 | ||||||||
\(455\) | −9.07475 | − | 0.627526i | −0.425431 | − | 0.0294189i | ||||
\(456\) | 0.681151 | 0.0318978 | ||||||||
\(457\) | −15.9837 | + | 27.6846i | −0.747685 | + | 1.29503i | 0.201244 | + | 0.979541i | \(0.435502\pi\) |
−0.948930 | + | 0.315488i | \(0.897832\pi\) | |||||||
\(458\) | −9.86681 | − | 17.0898i | −0.461046 | − | 0.798554i | ||||
\(459\) | 0.149720 | + | 0.259323i | 0.00698833 | + | 0.0121041i | ||||
\(460\) | −0.640906 | + | 1.11008i | −0.0298824 | + | 0.0517578i | ||||
\(461\) | 7.10536 | 0.330930 | 0.165465 | − | 0.986216i | \(-0.447088\pi\) | ||||
0.165465 | + | 0.986216i | \(0.447088\pi\) | |||||||
\(462\) | −5.65161 | + | 8.39283i | −0.262937 | + | 0.390470i | ||||
\(463\) | −42.0816 | −1.95570 | −0.977848 | − | 0.209314i | \(-0.932877\pi\) | ||||
−0.977848 | + | 0.209314i | \(0.932877\pi\) | |||||||
\(464\) | −14.3552 | + | 24.8639i | −0.666422 | + | 1.15428i | ||||
\(465\) | 2.84173 | + | 4.92202i | 0.131782 | + | 0.228253i | ||||
\(466\) | 10.7675 | + | 18.6498i | 0.498794 | + | 0.863936i | ||||
\(467\) | −13.2253 | + | 22.9069i | −0.611995 | + | 1.06001i | 0.378908 | + | 0.925434i | \(0.376300\pi\) |
−0.990904 | + | 0.134573i | \(0.957034\pi\) | |||||||
\(468\) | 4.95075 | 0.228849 | ||||||||
\(469\) | 6.11456 | − | 9.08032i | 0.282344 | − | 0.419290i | ||||
\(470\) | 8.75341 | 0.403765 | ||||||||
\(471\) | −4.21279 | + | 7.29677i | −0.194115 | + | 0.336217i | ||||
\(472\) | −1.22259 | − | 2.11759i | −0.0562743 | − | 0.0974700i | ||||
\(473\) | 9.48015 | + | 16.4201i | 0.435898 | + | 0.754997i | ||||
\(474\) | −15.7226 | + | 27.2324i | −0.722164 | + | 1.25082i | ||||
\(475\) | 2.38150 | 0.109271 | ||||||||
\(476\) | 1.07377 | + | 0.0742518i | 0.0492160 | + | 0.00340333i | ||||
\(477\) | 2.32577 | 0.106490 | ||||||||
\(478\) | −11.4990 | + | 19.9169i | −0.525953 | + | 0.910977i | ||||
\(479\) | 12.6414 | + | 21.8956i | 0.577601 | + | 1.00043i | 0.995754 | + | 0.0920572i | \(0.0293443\pi\) |
−0.418153 | + | 0.908377i | \(0.637322\pi\) | |||||||
\(480\) | −3.10248 | − | 5.37365i | −0.141608 | − | 0.245272i | ||||
\(481\) | 2.25464 | − | 3.90515i | 0.102803 | − | 0.178059i | ||||
\(482\) | 19.4818 | 0.887373 | ||||||||
\(483\) | −1.16166 | − | 2.37709i | −0.0528572 | − | 0.108161i | ||||
\(484\) | −9.02816 | −0.410371 | ||||||||
\(485\) | 0.278255 | − | 0.481952i | 0.0126349 | − | 0.0218843i | ||||
\(486\) | −0.916322 | − | 1.58712i | −0.0415652 | − | 0.0719931i | ||||
\(487\) | −9.98826 | − | 17.3002i | −0.452611 | − | 0.783945i | 0.545936 | − | 0.837827i | \(-0.316174\pi\) |
−0.998547 | + | 0.0538814i | \(0.982841\pi\) | |||||||
\(488\) | −7.31976 | + | 12.6782i | −0.331350 | + | 0.573915i | ||||
\(489\) | −4.15736 | −0.188002 | ||||||||
\(490\) | 11.9884 | + | 1.66598i | 0.541579 | + | 0.0752611i | ||||
\(491\) | −41.0091 | −1.85072 | −0.925358 | − | 0.379095i | \(-0.876235\pi\) | ||||
−0.925358 | + | 0.379095i | \(0.876235\pi\) | |||||||
\(492\) | 5.71981 | − | 9.90699i | 0.257869 | − | 0.446642i | ||||
\(493\) | 0.882395 | + | 1.52835i | 0.0397411 | + | 0.0688335i | ||||
\(494\) | −1.93490 | − | 3.35135i | −0.0870553 | − | 0.150784i | ||||
\(495\) | 0.984437 | − | 1.70510i | 0.0442472 | − | 0.0766383i | ||||
\(496\) | 29.3448 | 1.31762 | ||||||||
\(497\) | 13.5262 | + | 27.6786i | 0.606734 | + | 1.24155i | ||||
\(498\) | 20.1114 | 0.901212 | ||||||||
\(499\) | −7.02344 | + | 12.1650i | −0.314412 | + | 0.544578i | −0.979312 | − | 0.202354i | \(-0.935141\pi\) |
0.664900 | + | 0.746932i | \(0.268474\pi\) | |||||||
\(500\) | −5.83854 | − | 10.1126i | −0.261107 | − | 0.452251i | ||||
\(501\) | −1.52222 | − | 2.63657i | −0.0680080 | − | 0.117793i | ||||
\(502\) | −15.9821 | + | 27.6817i | −0.713314 | + | 1.23550i | ||||
\(503\) | 12.8463 | 0.572787 | 0.286393 | − | 0.958112i | \(-0.407544\pi\) | ||||
0.286393 | + | 0.958112i | \(0.407544\pi\) | |||||||
\(504\) | 3.10263 | + | 0.214549i | 0.138202 | + | 0.00955679i | ||||
\(505\) | −5.87638 | −0.261495 | ||||||||
\(506\) | −1.91218 | + | 3.31200i | −0.0850068 | + | 0.147236i | ||||
\(507\) | 0.139549 | + | 0.241705i | 0.00619757 | + | 0.0107345i | ||||
\(508\) | 0.687971 | + | 1.19160i | 0.0305238 | + | 0.0528687i | ||||
\(509\) | 13.3906 | − | 23.1932i | 0.593528 | − | 1.02802i | −0.400224 | − | 0.916417i | \(-0.631068\pi\) |
0.993753 | − | 0.111604i | \(-0.0355989\pi\) | |||||||
\(510\) | −0.517756 | −0.0229266 | ||||||||
\(511\) | 17.0980 | − | 25.3911i | 0.756372 | − | 1.12324i | ||||
\(512\) | −20.5848 | −0.909730 | ||||||||
\(513\) | −0.289732 | + | 0.501830i | −0.0127920 | + | 0.0221563i | ||||
\(514\) | 17.1591 | + | 29.7205i | 0.756856 | + | 1.31091i | ||||
\(515\) | −8.79591 | − | 15.2350i | −0.387594 | − | 0.671333i | ||||
\(516\) | −6.17194 | + | 10.6901i | −0.271704 | + | 0.470606i | ||||
\(517\) | 10.5644 | 0.464620 | ||||||||
\(518\) | −3.35130 | + | 4.97680i | −0.147248 | + | 0.218668i | ||||
\(519\) | −16.0543 | −0.704705 | ||||||||
\(520\) | 2.02073 | − | 3.50001i | 0.0886149 | − | 0.153485i | ||||
\(521\) | 13.4152 | + | 23.2359i | 0.587732 | + | 1.01798i | 0.994529 | + | 0.104463i | \(0.0333123\pi\) |
−0.406797 | + | 0.913519i | \(0.633354\pi\) | |||||||
\(522\) | −5.40047 | − | 9.35388i | −0.236372 | − | 0.409408i | ||||
\(523\) | 8.04730 | − | 13.9383i | 0.351884 | − | 0.609481i | −0.634696 | − | 0.772762i | \(-0.718875\pi\) |
0.986580 | + | 0.163282i | \(0.0522079\pi\) | |||||||
\(524\) | −20.4210 | −0.892095 | ||||||||
\(525\) | 10.8477 | + | 0.750125i | 0.473431 | + | 0.0327382i | ||||
\(526\) | −54.8118 | −2.38991 | ||||||||
\(527\) | 0.901895 | − | 1.56213i | 0.0392871 | − | 0.0680473i | ||||
\(528\) | −5.08284 | − | 8.80373i | −0.221202 | − | 0.383133i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.0217391 | − | 0.0376533i | ||||
\(530\) | −2.01072 | + | 3.48267i | −0.0873401 | + | 0.151277i | ||||
\(531\) | 2.08015 | 0.0902708 | ||||||||
\(532\) | 0.914516 | + | 1.87137i | 0.0396493 | + | 0.0811340i | ||||
\(533\) | 30.6838 | 1.32906 | ||||||||
\(534\) | −2.45172 | + | 4.24651i | −0.106096 | + | 0.183764i | ||||
\(535\) | −0.306107 | − | 0.530193i | −0.0132342 | − | 0.0229223i | ||||
\(536\) | 2.43186 | + | 4.21211i | 0.105040 | + | 0.181935i | ||||
\(537\) | −2.67255 | + | 4.62898i | −0.115329 | + | 0.199755i | ||||
\(538\) | −41.5022 | −1.78929 | ||||||||
\(539\) | 14.4686 | + | 2.01064i | 0.623205 | + | 0.0866044i | ||||
\(540\) | 1.28181 | 0.0551604 | ||||||||
\(541\) | 0.338479 | − | 0.586263i | 0.0145524 | − | 0.0252054i | −0.858658 | − | 0.512550i | \(-0.828701\pi\) |
0.873210 | + | 0.487344i | \(0.162034\pi\) | |||||||
\(542\) | −11.6706 | − | 20.2141i | −0.501296 | − | 0.868270i | ||||
\(543\) | −5.81006 | − | 10.0633i | −0.249333 | − | 0.431858i | ||||
\(544\) | −0.984649 | + | 1.70546i | −0.0422165 | + | 0.0731211i | ||||
\(545\) | 12.8818 | 0.551795 | ||||||||
\(546\) | −7.75783 | − | 15.8748i | −0.332005 | − | 0.679378i | ||||
\(547\) | −8.38777 | −0.358635 | −0.179318 | − | 0.983791i | \(-0.557389\pi\) | ||||
−0.179318 | + | 0.983791i | \(0.557389\pi\) | |||||||
\(548\) | −6.30293 | + | 10.9170i | −0.269248 | + | 0.466351i | ||||
\(549\) | −6.22701 | − | 10.7855i | −0.265762 | − | 0.460314i | ||||
\(550\) | −7.85874 | − | 13.6117i | −0.335098 | − | 0.580406i | ||||
\(551\) | −1.70757 | + | 2.95760i | −0.0727450 | + | 0.125998i | ||||
\(552\) | 1.17548 | 0.0500320 | ||||||||
\(553\) | 45.2887 | + | 3.13175i | 1.92587 | + | 0.133176i | ||||
\(554\) | 53.1699 | 2.25897 | ||||||||
\(555\) | 0.583754 | − | 1.01109i | 0.0247790 | − | 0.0429184i | ||||
\(556\) | −4.47484 | − | 7.75065i | −0.189775 | − | 0.328701i | ||||
\(557\) | 1.24944 | + | 2.16409i | 0.0529404 | + | 0.0916955i | 0.891281 | − | 0.453451i | \(-0.149807\pi\) |
−0.838341 | + | 0.545147i | \(0.816474\pi\) | |||||||
\(558\) | −5.51981 | + | 9.56059i | −0.233672 | + | 0.404732i | ||||
\(559\) | −33.1092 | −1.40037 | ||||||||
\(560\) | −6.79212 | + | 10.0865i | −0.287019 | + | 0.426234i | ||||
\(561\) | −0.624872 | −0.0263821 | ||||||||
\(562\) | −11.4051 | + | 19.7543i | −0.481097 | + | 0.833284i | ||||
\(563\) | 20.2290 | + | 35.0377i | 0.852551 | + | 1.47666i | 0.878899 | + | 0.477008i | \(0.158279\pi\) |
−0.0263482 | + | 0.999653i | \(0.508388\pi\) | |||||||
\(564\) | 3.43889 | + | 5.95634i | 0.144804 | + | 0.250807i | ||||
\(565\) | 0.258176 | − | 0.447174i | 0.0108615 | − | 0.0188127i | ||||
\(566\) | −17.1608 | −0.721323 | ||||||||
\(567\) | −1.47779 | + | 2.19457i | −0.0620614 | + | 0.0921632i | ||||
\(568\) | −13.6872 | −0.574303 | ||||||||
\(569\) | 6.24012 | − | 10.8082i | 0.261599 | − | 0.453104i | −0.705068 | − | 0.709140i | \(-0.749083\pi\) |
0.966667 | + | 0.256037i | \(0.0824167\pi\) | |||||||
\(570\) | −0.500970 | − | 0.867705i | −0.0209833 | − | 0.0363442i | ||||
\(571\) | 15.4964 | + | 26.8405i | 0.648502 | + | 1.12324i | 0.983481 | + | 0.181013i | \(0.0579377\pi\) |
−0.334978 | + | 0.942226i | \(0.608729\pi\) | |||||||
\(572\) | −5.16562 | + | 8.94711i | −0.215985 | + | 0.374098i | ||||
\(573\) | 17.0751 | 0.713324 | ||||||||
\(574\) | −40.7301 | − | 2.81652i | −1.70004 | − | 0.117559i | ||||
\(575\) | 4.10983 | 0.171392 | ||||||||
\(576\) | 1.15487 | − | 2.00030i | 0.0481197 | − | 0.0833457i | ||||
\(577\) | −5.26512 | − | 9.11945i | −0.219190 | − | 0.379648i | 0.735371 | − | 0.677665i | \(-0.237008\pi\) |
−0.954560 | + | 0.298017i | \(0.903675\pi\) | |||||||
\(578\) | −15.4953 | − | 26.8387i | −0.644520 | − | 1.11634i | ||||
\(579\) | −2.32526 | + | 4.02747i | −0.0966345 | + | 0.167376i | ||||
\(580\) | 7.55452 | 0.313684 | ||||||||
\(581\) | −12.7480 | − | 26.0861i | −0.528875 | − | 1.08223i | ||||
\(582\) | 1.08097 | 0.0448077 | ||||||||
\(583\) | −2.42671 | + | 4.20318i | −0.100504 | + | 0.174078i | ||||
\(584\) | 6.80017 | + | 11.7782i | 0.281393 | + | 0.487387i | ||||
\(585\) | 1.71906 | + | 2.97750i | 0.0710744 | + | 0.123105i | ||||
\(586\) | 5.21864 | − | 9.03895i | 0.215580 | − | 0.373396i | ||||
\(587\) | 7.06244 | 0.291498 | 0.145749 | − | 0.989322i | \(-0.453441\pi\) | ||||
0.145749 | + | 0.989322i | \(0.453441\pi\) | |||||||
\(588\) | 3.57616 | + | 8.81210i | 0.147478 | + | 0.363405i | ||||
\(589\) | 3.49062 | 0.143828 | ||||||||
\(590\) | −1.79837 | + | 3.11487i | −0.0740378 | + | 0.128237i | ||||
\(591\) | 0.127456 | + | 0.220761i | 0.00524285 | + | 0.00908088i | ||||
\(592\) | −3.01403 | − | 5.22046i | −0.123876 | − | 0.214559i | ||||
\(593\) | −19.9462 | + | 34.5479i | −0.819094 | + | 1.41871i | 0.0872571 | + | 0.996186i | \(0.472190\pi\) |
−0.906351 | + | 0.422526i | \(0.861144\pi\) | |||||||
\(594\) | 3.82436 | 0.156916 | ||||||||
\(595\) | 0.328190 | + | 0.671572i | 0.0134545 | + | 0.0275318i | ||||
\(596\) | −8.00075 | −0.327723 | ||||||||
\(597\) | 2.73799 | − | 4.74233i | 0.112058 | − | 0.194091i | ||||
\(598\) | −3.33912 | − | 5.78353i | −0.136547 | − | 0.236506i | ||||
\(599\) | −5.93228 | − | 10.2750i | −0.242386 | − | 0.419826i | 0.719007 | − | 0.695003i | \(-0.244597\pi\) |
−0.961394 | + | 0.275177i | \(0.911264\pi\) | |||||||
\(600\) | −2.41552 | + | 4.18380i | −0.0986132 | + | 0.170803i | ||||
\(601\) | 15.0105 | 0.612290 | 0.306145 | − | 0.951985i | \(-0.400961\pi\) | ||||
0.306145 | + | 0.951985i | \(0.400961\pi\) | |||||||
\(602\) | 43.9497 | + | 3.03916i | 1.79126 | + | 0.123867i | ||||
\(603\) | −4.13763 | −0.168498 | ||||||||
\(604\) | −8.93532 | + | 15.4764i | −0.363573 | + | 0.629727i | ||||
\(605\) | −3.13487 | − | 5.42975i | −0.127451 | − | 0.220751i | ||||
\(606\) | −5.70717 | − | 9.88511i | −0.231838 | − | 0.401555i | ||||
\(607\) | 2.09995 | − | 3.63722i | 0.0852343 | − | 0.147630i | −0.820257 | − | 0.571996i | \(-0.806169\pi\) |
0.905491 | + | 0.424365i | \(0.139503\pi\) | |||||||
\(608\) | −3.81090 | −0.154553 | ||||||||
\(609\) | −8.70955 | + | 12.9340i | −0.352929 | + | 0.524111i | ||||
\(610\) | 21.5340 | 0.871887 | ||||||||
\(611\) | −9.22393 | + | 15.9763i | −0.373160 | + | 0.646333i | ||||
\(612\) | −0.203407 | − | 0.352312i | −0.00822226 | − | 0.0142414i | ||||
\(613\) | −15.4932 | − | 26.8351i | −0.625766 | − | 1.08386i | −0.988392 | − | 0.151924i | \(-0.951453\pi\) |
0.362626 | − | 0.931935i | \(-0.381880\pi\) | |||||||
\(614\) | 15.6321 | − | 27.0755i | 0.630859 | − | 1.09268i | ||||
\(615\) | 7.94441 | 0.320349 | ||||||||
\(616\) | −3.62502 | + | 5.38328i | −0.146056 | + | 0.216899i | ||||
\(617\) | 1.93041 | 0.0777153 | 0.0388577 | − | 0.999245i | \(-0.487628\pi\) | ||||
0.0388577 | + | 0.999245i | \(0.487628\pi\) | |||||||
\(618\) | 17.0853 | − | 29.5926i | 0.687270 | − | 1.19039i | ||||
\(619\) | −16.6422 | − | 28.8251i | −0.668907 | − | 1.15858i | −0.978210 | − | 0.207617i | \(-0.933429\pi\) |
0.309304 | − | 0.950963i | \(-0.399904\pi\) | |||||||
\(620\) | −3.86073 | − | 6.68699i | −0.155051 | − | 0.268556i | ||||
\(621\) | −0.500000 | + | 0.866025i | −0.0200643 | + | 0.0347524i | ||||
\(622\) | 30.2831 | 1.21424 | ||||||||
\(623\) | 7.06214 | + | 0.488353i | 0.282939 | + | 0.0195654i | ||||
\(624\) | 17.7517 | 0.710636 | ||||||||
\(625\) | −6.21991 | + | 10.7732i | −0.248796 | + | 0.430928i | ||||
\(626\) | −1.36887 | − | 2.37096i | −0.0547112 | − | 0.0947625i | ||||
\(627\) | −0.604613 | − | 1.04722i | −0.0241459 | − | 0.0418219i | ||||
\(628\) | 5.72343 | − | 9.91328i | 0.228390 | − | 0.395583i | ||||
\(629\) | −0.370538 | −0.0147743 | ||||||||
\(630\) | −2.00860 | − | 4.11018i | −0.0800245 | − | 0.163753i | ||||
\(631\) | 4.49815 | 0.179068 | 0.0895342 | − | 0.995984i | \(-0.471462\pi\) | ||||
0.0895342 | + | 0.995984i | \(0.471462\pi\) | |||||||
\(632\) | −10.0847 | + | 17.4672i | −0.401149 | + | 0.694810i | ||||
\(633\) | −1.59299 | − | 2.75914i | −0.0633158 | − | 0.109666i | ||||
\(634\) | −16.6985 | − | 28.9227i | −0.663184 | − | 1.14867i | ||||
\(635\) | −0.477772 | + | 0.827525i | −0.0189598 | + | 0.0328393i | ||||
\(636\) | −3.15975 | −0.125292 | ||||||||
\(637\) | −15.6734 | + | 20.1251i | −0.621004 | + | 0.797385i | ||||
\(638\) | 22.5394 | 0.892343 | ||||||||
\(639\) | 5.82195 | − | 10.0839i | 0.230313 | − | 0.398913i | ||||
\(640\) | −4.20809 | − | 7.28863i | −0.166339 | − | 0.288108i | ||||
\(641\) | 13.4105 | + | 23.2276i | 0.529681 | + | 0.917435i | 0.999401 | + | 0.0346188i | \(0.0110217\pi\) |
−0.469720 | + | 0.882816i | \(0.655645\pi\) | |||||||
\(642\) | 0.594586 | − | 1.02985i | 0.0234664 | − | 0.0406451i | ||||
\(643\) | −21.1912 | −0.835701 | −0.417850 | − | 0.908516i | \(-0.637216\pi\) | ||||
−0.417850 | + | 0.908516i | \(0.637216\pi\) | |||||||
\(644\) | 1.57821 | + | 3.22948i | 0.0621902 | + | 0.127259i | ||||
\(645\) | −8.57238 | −0.337537 | ||||||||
\(646\) | −0.158995 | + | 0.275388i | −0.00625559 | + | 0.0108350i | ||||
\(647\) | −1.64119 | − | 2.84262i | −0.0645218 | − | 0.111755i | 0.831960 | − | 0.554836i | \(-0.187219\pi\) |
−0.896482 | + | 0.443081i | \(0.853886\pi\) | |||||||
\(648\) | −0.587742 | − | 1.01800i | −0.0230887 | − | 0.0399908i | ||||
\(649\) | −2.17043 | + | 3.75929i | −0.0851967 | + | 0.147565i | ||||
\(650\) | 27.4464 | 1.07654 | ||||||||
\(651\) | 15.8997 | + | 1.09948i | 0.623159 | + | 0.0430919i | ||||
\(652\) | 5.64813 | 0.221198 | ||||||||
\(653\) | −16.3956 | + | 28.3981i | −0.641610 | + | 1.11130i | 0.343463 | + | 0.939166i | \(0.388400\pi\) |
−0.985073 | + | 0.172135i | \(0.944933\pi\) | |||||||
\(654\) | 12.5109 | + | 21.6694i | 0.489213 | + | 0.847342i | ||||
\(655\) | −7.09082 | − | 12.2817i | −0.277061 | − | 0.479884i | ||||
\(656\) | 20.5092 | − | 35.5230i | 0.800751 | − | 1.38694i | ||||
\(657\) | −11.5700 | −0.451388 | ||||||||
\(658\) | 13.7105 | − | 20.3605i | 0.534491 | − | 0.793737i | ||||
\(659\) | 11.1625 | 0.434828 | 0.217414 | − | 0.976079i | \(-0.430238\pi\) | ||||
0.217414 | + | 0.976079i | \(0.430238\pi\) | |||||||
\(660\) | −1.33744 | + | 2.31652i | −0.0520599 | + | 0.0901703i | ||||
\(661\) | −4.19731 | − | 7.26995i | −0.163256 | − | 0.282768i | 0.772778 | − | 0.634676i | \(-0.218866\pi\) |
−0.936035 | + | 0.351908i | \(0.885533\pi\) | |||||||
\(662\) | −21.0341 | − | 36.4321i | −0.817512 | − | 1.41597i | ||||
\(663\) | 0.545587 | − | 0.944985i | 0.0211888 | − | 0.0367002i | ||||
\(664\) | 12.8997 | 0.500606 | ||||||||
\(665\) | −0.807935 | + | 1.19981i | −0.0313304 | + | 0.0465266i | ||||
\(666\) | 2.26778 | 0.0878747 | ||||||||
\(667\) | −2.94682 | + | 5.10403i | −0.114101 | + | 0.197629i | ||||
\(668\) | 2.06807 | + | 3.58201i | 0.0800161 | + | 0.138592i | ||||
\(669\) | −11.3837 | − | 19.7172i | −0.440119 | − | 0.762309i | ||||
\(670\) | 3.57715 | − | 6.19581i | 0.138197 | − | 0.239365i | ||||
\(671\) | 25.9891 | 1.00330 | ||||||||
\(672\) | −17.3586 | − | 1.20036i | −0.669623 | − | 0.0463050i | ||||
\(673\) | 30.3183 | 1.16869 | 0.584343 | − | 0.811507i | \(-0.301352\pi\) | ||||
0.584343 | + | 0.811507i | \(0.301352\pi\) | |||||||
\(674\) | 20.3668 | − | 35.2763i | 0.784498 | − | 1.35879i | ||||
\(675\) | −2.05491 | − | 3.55921i | −0.0790937 | − | 0.136994i | ||||
\(676\) | −0.189589 | − | 0.328377i | −0.00729187 | − | 0.0126299i | ||||
\(677\) | 5.15063 | − | 8.92116i | 0.197955 | − | 0.342868i | −0.749910 | − | 0.661540i | \(-0.769903\pi\) |
0.947865 | + | 0.318672i | \(0.103237\pi\) | |||||||
\(678\) | 1.00297 | 0.0385187 | ||||||||
\(679\) | −0.685195 | − | 1.40211i | −0.0262954 | − | 0.0538080i | ||||
\(680\) | −0.332096 | −0.0127353 | ||||||||
\(681\) | 5.22604 | − | 9.05176i | 0.200262 | − | 0.346864i | ||||
\(682\) | −11.5187 | − | 19.9510i | −0.441075 | − | 0.763965i | ||||
\(683\) | 24.0871 | + | 41.7200i | 0.921666 | + | 1.59637i | 0.796837 | + | 0.604194i | \(0.206505\pi\) |
0.124829 | + | 0.992178i | \(0.460162\pi\) | |||||||
\(684\) | 0.393625 | − | 0.681779i | 0.0150506 | − | 0.0260685i | ||||
\(685\) | −8.75433 | −0.334486 | ||||||||
\(686\) | 22.6525 | − | 25.2757i | 0.864876 | − | 0.965029i | ||||
\(687\) | 10.7678 | 0.410819 | ||||||||
\(688\) | −22.1304 | + | 38.3310i | −0.843714 | + | 1.46136i | ||||
\(689\) | −4.23760 | − | 7.33975i | −0.161440 | − | 0.279622i | ||||
\(690\) | −0.864540 | − | 1.49743i | −0.0329125 | − | 0.0570061i | ||||
\(691\) | 18.3597 | − | 31.8000i | 0.698437 | − | 1.20973i | −0.270571 | − | 0.962700i | \(-0.587212\pi\) |
0.969008 | − | 0.247029i | \(-0.0794543\pi\) | |||||||
\(692\) | 21.8111 | 0.829135 | ||||||||
\(693\) | −2.42415 | − | 4.96051i | −0.0920857 | − | 0.188434i | ||||
\(694\) | 9.91171 | 0.376243 | ||||||||
\(695\) | 3.10762 | − | 5.38255i | 0.117879 | − | 0.204172i | ||||
\(696\) | −3.46394 | − | 5.99971i | −0.131300 | − | 0.227419i | ||||
\(697\) | −1.26068 | − | 2.18356i | −0.0477516 | − | 0.0827082i | ||||
\(698\) | 9.52410 | − | 16.4962i | 0.360492 | − | 0.624391i | ||||
\(699\) | −11.7508 | −0.444455 | ||||||||
\(700\) | −14.7375 | − | 1.01911i | −0.557025 | − | 0.0385187i | ||||
\(701\) | 35.3581 | 1.33546 | 0.667728 | − | 0.744406i | \(-0.267267\pi\) | ||||
0.667728 | + | 0.744406i | \(0.267267\pi\) | |||||||
\(702\) | −3.33912 | + | 5.78353i | −0.126027 | + | 0.218285i | ||||
\(703\) | −0.358524 | − | 0.620983i | −0.0135220 | − | 0.0234208i | ||||
\(704\) | 2.40999 | + | 4.17422i | 0.0908299 | + | 0.157322i | ||||
\(705\) | −2.38819 | + | 4.13647i | −0.0899445 | + | 0.155788i | ||||
\(706\) | 23.9509 | 0.901405 | ||||||||
\(707\) | −9.20419 | + | 13.6685i | −0.346159 | + | 0.514058i | ||||
\(708\) | −2.82606 | −0.106210 | ||||||||
\(709\) | 5.49808 | − | 9.52295i | 0.206485 | − | 0.357642i | −0.744120 | − | 0.668046i | \(-0.767131\pi\) |
0.950605 | + | 0.310404i | \(0.100464\pi\) | |||||||
\(710\) | 10.0666 | + | 17.4359i | 0.377794 | + | 0.654358i | ||||
\(711\) | −8.57920 | − | 14.8596i | −0.321745 | − | 0.557279i | ||||
\(712\) | −1.57257 | + | 2.72377i | −0.0589346 | + | 0.102078i | ||||
\(713\) | 6.02387 | 0.225596 | ||||||||
\(714\) | −0.810963 | + | 1.20431i | −0.0303495 | + | 0.0450701i | ||||
\(715\) | −7.17468 | −0.268318 | ||||||||
\(716\) | 3.63088 | − | 6.28887i | 0.135692 | − | 0.235026i | ||||
\(717\) | −6.27455 | − | 10.8678i | −0.234327 | − | 0.405867i | ||||
\(718\) | −17.6146 | − | 30.5095i | −0.657373 | − | 1.13860i | ||||
\(719\) | 18.2877 | − | 31.6752i | 0.682016 | − | 1.18129i | −0.292348 | − | 0.956312i | \(-0.594437\pi\) |
0.974365 | − | 0.224975i | \(-0.0722300\pi\) | |||||||
\(720\) | 4.59613 | 0.171288 | ||||||||
\(721\) | −49.2138 | − | 3.40317i | −1.83282 | − | 0.126741i | ||||
\(722\) | 34.2049 | 1.27297 | ||||||||
\(723\) | −5.31523 | + | 9.20624i | −0.197675 | + | 0.342384i | ||||
\(724\) | 7.89346 | + | 13.6719i | 0.293358 | + | 0.508111i | ||||
\(725\) | −12.1109 | − | 20.9767i | −0.449788 | − | 0.779055i | ||||
\(726\) | 6.08920 | − | 10.5468i | 0.225991 | − | 0.391429i | ||||
\(727\) | −12.9513 | −0.480337 | −0.240169 | − | 0.970731i | \(-0.577203\pi\) | ||||
−0.240169 | + | 0.970731i | \(0.577203\pi\) | |||||||
\(728\) | −4.97599 | − | 10.1823i | −0.184422 | − | 0.377382i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 10.0027 | − | 17.3252i | 0.370217 | − | 0.641235i | ||||
\(731\) | 1.36033 | + | 2.35616i | 0.0503136 | + | 0.0871457i | ||||
\(732\) | 8.45993 | + | 14.6530i | 0.312688 | + | 0.541592i | ||||
\(733\) | −3.13178 | + | 5.42440i | −0.115675 | + | 0.200355i | −0.918049 | − | 0.396466i | \(-0.870236\pi\) |
0.802374 | + | 0.596821i | \(0.203570\pi\) | |||||||
\(734\) | 3.25312 | 0.120075 | ||||||||
\(735\) | −4.05805 | + | 5.21063i | −0.149683 | + | 0.192197i | ||||
\(736\) | −6.57660 | −0.242417 | ||||||||
\(737\) | 4.31721 | − | 7.47763i | 0.159026 | − | 0.275442i | ||||
\(738\) | 7.71565 | + | 13.3639i | 0.284017 | + | 0.491932i | ||||
\(739\) | −16.2107 | − | 28.0778i | −0.596322 | − | 1.03286i | −0.993359 | − | 0.115057i | \(-0.963295\pi\) |
0.397037 | − | 0.917803i | \(-0.370039\pi\) | |||||||
\(740\) | −0.793079 | + | 1.37365i | −0.0291542 | + | 0.0504965i | ||||
\(741\) | 2.11159 | 0.0775714 | ||||||||
\(742\) | 4.95134 | + | 10.1319i | 0.181769 | + | 0.371953i | ||||
\(743\) | −4.32354 | −0.158615 | −0.0793076 | − | 0.996850i | \(-0.525271\pi\) | ||||
−0.0793076 | + | 0.996850i | \(0.525271\pi\) | |||||||
\(744\) | −3.54049 | + | 6.13230i | −0.129801 | + | 0.224821i | ||||
\(745\) | −2.77812 | − | 4.81184i | −0.101782 | − | 0.176292i | ||||
\(746\) | −6.81763 | − | 11.8085i | −0.249611 | − | 0.432339i | ||||
\(747\) | −5.48698 | + | 9.50373i | −0.200758 | + | 0.347723i | ||||
\(748\) | 0.848942 | 0.0310404 | ||||||||
\(749\) | −1.71269 | − | 0.118434i | −0.0625805 | − | 0.00432749i | ||||
\(750\) | 15.7516 | 0.575168 | ||||||||
\(751\) | 6.02158 | − | 10.4297i | 0.219730 | − | 0.380584i | −0.734995 | − | 0.678072i | \(-0.762816\pi\) |
0.954726 | + | 0.297488i | \(0.0961489\pi\) | |||||||
\(752\) | 12.3307 | + | 21.3574i | 0.449654 | + | 0.778823i | ||||
\(753\) | −8.72076 | − | 15.1048i | −0.317802 | − | 0.550450i | ||||
\(754\) | −19.6796 | + | 34.0860i | −0.716687 | + | 1.24134i | ||||
\(755\) | −12.4105 | −0.451665 | ||||||||
\(756\) | 2.00771 | − | 2.98151i | 0.0730195 | − | 0.108436i | ||||
\(757\) | 17.8806 | 0.649880 | 0.324940 | − | 0.945735i | \(-0.394656\pi\) | ||||
0.324940 | + | 0.945735i | \(0.394656\pi\) | |||||||
\(758\) | −3.94980 | + | 6.84126i | −0.143463 | + | 0.248486i | ||||
\(759\) | −1.04340 | − | 1.80722i | −0.0378730 | − | 0.0655980i | ||||
\(760\) | −0.321329 | − | 0.556559i | −0.0116558 | − | 0.0201885i | ||||
\(761\) | −13.1480 | + | 22.7730i | −0.476615 | + | 0.825522i | −0.999641 | − | 0.0267950i | \(-0.991470\pi\) |
0.523026 | + | 0.852317i | \(0.324803\pi\) | |||||||
\(762\) | −1.85606 | −0.0672379 | ||||||||
\(763\) | 20.1768 | − | 29.9632i | 0.730448 | − | 1.08474i | ||||
\(764\) | −23.1980 | −0.839276 | ||||||||
\(765\) | 0.141259 | − | 0.244668i | 0.00510724 | − | 0.00884600i | ||||
\(766\) | 31.7886 | + | 55.0594i | 1.14857 | + | 1.98938i | ||||
\(767\) | −3.79008 | − | 6.56462i | −0.136852 | − | 0.237035i | ||||
\(768\) | 10.4836 | − | 18.1581i | 0.378294 | − | 0.655224i | ||||
\(769\) | −32.2632 | −1.16344 | −0.581720 | − | 0.813389i | \(-0.697620\pi\) | ||||
−0.581720 | + | 0.813389i | \(0.697620\pi\) | |||||||
\(770\) | 9.52378 | + | 0.658577i | 0.343213 | + | 0.0237335i | ||||
\(771\) | −18.7261 | −0.674403 | ||||||||
\(772\) | 3.15906 | − | 5.47166i | 0.113697 | − | 0.196929i | ||||
\(773\) | 5.28783 | + | 9.15878i | 0.190190 | + | 0.329419i | 0.945313 | − | 0.326164i | \(-0.105756\pi\) |
−0.755123 | + | 0.655583i | \(0.772423\pi\) | |||||||
\(774\) | −8.32554 | − | 14.4203i | −0.299255 | − | 0.518326i | ||||
\(775\) | −12.3785 | + | 21.4403i | −0.444650 | + | 0.770157i | ||||
\(776\) | 0.693351 | 0.0248899 | ||||||||
\(777\) | −1.43748 | − | 2.94149i | −0.0515692 | − | 0.105526i | ||||
\(778\) | −60.7409 | −2.17767 | ||||||||
\(779\) | 2.43961 | − | 4.22553i | 0.0874081 | − | 0.151395i | ||||
\(780\) | −2.33549 | − | 4.04519i | −0.0836240 | − | 0.144841i | ||||
\(781\) | 12.1492 | + | 21.0431i | 0.434734 | + | 0.752982i | ||||
\(782\) | −0.274384 | + | 0.475246i | −0.00981194 | + | 0.0169948i | ||||
\(783\) | 5.89363 | 0.210621 | ||||||||
\(784\) | 12.8229 | + | 31.5971i | 0.457960 | + | 1.12847i | ||||
\(785\) | 7.94945 | 0.283728 | ||||||||
\(786\) | 13.7733 | − | 23.8560i | 0.491277 | − | 0.850917i | ||||
\(787\) | 13.7617 | + | 23.8360i | 0.490552 | + | 0.849660i | 0.999941 | − | 0.0108760i | \(-0.00346200\pi\) |
−0.509389 | + | 0.860536i | \(0.670129\pi\) | |||||||
\(788\) | −0.173160 | − | 0.299922i | −0.00616857 | − | 0.0106843i | ||||
\(789\) | 14.9543 | − | 25.9016i | 0.532387 | − | 0.922121i | ||||
\(790\) | 29.6683 | 1.05555 | ||||||||
\(791\) | −0.635750 | − | 1.30093i | −0.0226047 | − | 0.0462557i | ||||
\(792\) | 2.45300 | 0.0871636 | ||||||||
\(793\) | −22.6915 | + | 39.3029i | −0.805800 | + | 1.39569i | ||||
\(794\) | −26.0752 | − | 45.1636i | −0.925374 | − | 1.60280i | ||||
\(795\) | −1.09717 | − | 1.90035i | −0.0389126 | − | 0.0673985i | ||||
\(796\) | −3.71979 | + | 6.44286i | −0.131844 | + | 0.228361i | ||||
\(797\) | −43.4629 | −1.53953 | −0.769767 | − | 0.638324i | \(-0.779628\pi\) | ||||
−0.769767 | + | 0.638324i | \(0.779628\pi\) | |||||||
\(798\) | −2.80296 | − | 0.193827i | −0.0992239 | − | 0.00686141i | ||||
\(799\) | 1.51590 | 0.0536288 | ||||||||
\(800\) | 13.5144 | − | 23.4075i | 0.477805 | − | 0.827582i | ||||
\(801\) | −1.33781 | − | 2.31715i | −0.0472691 | − | 0.0818724i | ||||
\(802\) | −34.7113 | − | 60.1217i | −1.22570 | − | 2.12297i | ||||
\(803\) | 12.0721 | − | 20.9095i | 0.426016 | − | 0.737881i | ||||
\(804\) | 5.62133 | 0.198249 | ||||||||
\(805\) | −1.39428 | + | 2.07055i | −0.0491419 | + | 0.0729774i | ||||
\(806\) | 40.2289 | 1.41700 | ||||||||
\(807\) | 11.3230 | − | 19.6121i | 0.398590 | − | 0.690378i | ||||
\(808\) | −3.66066 | − | 6.34045i | −0.128782 | − | 0.223056i | ||||
\(809\) | −21.4072 | − | 37.0784i | −0.752639 | − | 1.30361i | −0.946540 | − | 0.322587i | \(-0.895447\pi\) |
0.193901 | − | 0.981021i | \(-0.437886\pi\) | |||||||
\(810\) | −0.864540 | + | 1.49743i | −0.0303769 | + | 0.0526143i | ||||
\(811\) | 45.2610 | 1.58933 | 0.794664 | − | 0.607049i | \(-0.207647\pi\) | ||||
0.794664 | + | 0.607049i | \(0.207647\pi\) | |||||||
\(812\) | 11.8327 | − | 17.5719i | 0.415245 | − | 0.616653i | ||||
\(813\) | 12.7364 | 0.446684 | ||||||||
\(814\) | −2.36620 | + | 4.09838i | −0.0829353 | + | 0.143648i | ||||
\(815\) | 1.96121 | + | 3.39692i | 0.0686983 | + | 0.118989i | ||||
\(816\) | −0.729349 | − | 1.26327i | −0.0255323 | − | 0.0442233i | ||||
\(817\) | −2.63245 | + | 4.55954i | −0.0920979 | + | 0.159518i | ||||
\(818\) | −1.75411 | −0.0613310 | ||||||||
\(819\) | 9.61828 | + | 0.665112i | 0.336090 | + | 0.0232409i | ||||
\(820\) | −10.7932 | −0.376913 | ||||||||
\(821\) | 18.1607 | − | 31.4552i | 0.633812 | − | 1.09779i | −0.352954 | − | 0.935641i | \(-0.614823\pi\) |
0.986766 | − | 0.162153i | \(-0.0518439\pi\) | |||||||
\(822\) | −8.50225 | − | 14.7263i | −0.296550 | − | 0.513640i | ||||
\(823\) | −26.0501 | − | 45.1200i | −0.908048 | − | 1.57279i | −0.816772 | − | 0.576960i | \(-0.804239\pi\) |
−0.0912763 | − | 0.995826i | \(-0.529095\pi\) | |||||||
\(824\) | 10.9587 | − | 18.9811i | 0.381766 | − | 0.661238i | ||||
\(825\) | 8.57639 | 0.298592 | ||||||||
\(826\) | 4.42844 | + | 9.06187i | 0.154085 | + | 0.315303i | ||||
\(827\) | −21.6989 | −0.754545 | −0.377273 | − | 0.926102i | \(-0.623138\pi\) | ||||
−0.377273 | + | 0.926102i | \(0.623138\pi\) | |||||||
\(828\) | 0.679293 | − | 1.17657i | 0.0236071 | − | 0.0408886i | ||||
\(829\) | 6.78776 | + | 11.7567i | 0.235749 | + | 0.408329i | 0.959490 | − | 0.281743i | \(-0.0909125\pi\) |
−0.723741 | + | 0.690071i | \(0.757579\pi\) | |||||||
\(830\) | −9.48743 | − | 16.4327i | −0.329314 | − | 0.570388i | ||||
\(831\) | −14.5063 | + | 25.1257i | −0.503219 | + | 0.871601i | ||||
\(832\) | −8.41682 | −0.291801 | ||||||||
\(833\) | 2.07613 | + | 0.288512i | 0.0719336 | + | 0.00999634i | ||||
\(834\) | 12.0725 | 0.418038 | ||||||||
\(835\) | −1.43620 | + | 2.48758i | −0.0497018 | + | 0.0860861i | ||||
\(836\) | 0.821418 | + | 1.42274i | 0.0284093 | + | 0.0492064i | ||||
\(837\) | −3.01194 | − | 5.21683i | −0.104108 | − | 0.180320i | ||||
\(838\) | −37.3493 | + | 64.6909i | −1.29021 | + | 2.23471i | ||||
\(839\) | −40.6915 | −1.40483 | −0.702413 | − | 0.711770i | \(-0.747894\pi\) | ||||
−0.702413 | + | 0.711770i | \(0.747894\pi\) | |||||||
\(840\) | −1.28834 | − | 2.63633i | −0.0444521 | − | 0.0909620i | ||||
\(841\) | 5.73489 | 0.197755 | ||||||||
\(842\) | −23.8413 | + | 41.2943i | −0.821625 | + | 1.42310i | ||||
\(843\) | −6.22332 | − | 10.7791i | −0.214343 | − | 0.371252i | ||||
\(844\) | 2.16422 | + | 3.74853i | 0.0744954 | + | 0.129030i | ||||
\(845\) | 0.131663 | − | 0.228046i | 0.00452933 | − | 0.00784503i | ||||
\(846\) | −9.27770 | −0.318974 | ||||||||
\(847\) | −17.5398 | − | 1.21289i | −0.602676 | − | 0.0416755i | ||||
\(848\) | −11.3298 | −0.389066 | ||||||||
\(849\) | 4.68198 | − | 8.10943i | 0.160685 | − | 0.278315i | ||||
\(850\) | −1.12767 | − | 1.95318i | −0.0386787 | − | 0.0669935i | ||||
\(851\) | −0.618718 | − | 1.07165i | −0.0212094 | − | 0.0367357i | ||||
\(852\) | −7.90962 | + | 13.6999i | −0.270979 | + | 0.469349i | ||||
\(853\) | −53.5882 | −1.83482 | −0.917412 | − | 0.397938i | \(-0.869726\pi\) | ||||
−0.917412 | + | 0.397938i | \(0.869726\pi\) | |||||||
\(854\) | 33.7288 | − | 50.0884i | 1.15418 | − | 1.71399i | ||||
\(855\) | 0.546718 | 0.0186974 | ||||||||
\(856\) | 0.381376 | − | 0.660563i | 0.0130352 | − | 0.0225776i | ||||
\(857\) | 7.59264 | + | 13.1508i | 0.259360 | + | 0.449224i | 0.966071 | − | 0.258278i | \(-0.0831552\pi\) |
−0.706711 | + | 0.707502i | \(0.749822\pi\) | |||||||
\(858\) | −6.96808 | − | 12.0691i | −0.237886 | − | 0.412031i | ||||
\(859\) | 18.9692 | − | 32.8557i | 0.647222 | − | 1.12102i | −0.336562 | − | 0.941661i | \(-0.609264\pi\) |
0.983784 | − | 0.179360i | \(-0.0574025\pi\) | |||||||
\(860\) | 11.6463 | 0.397136 | ||||||||
\(861\) | 12.4434 | − | 18.4788i | 0.424068 | − | 0.629756i | ||||
\(862\) | 57.6259 | 1.96275 | ||||||||
\(863\) | −17.4820 | + | 30.2797i | −0.595094 | + | 1.03073i | 0.398440 | + | 0.917195i | \(0.369552\pi\) |
−0.993534 | + | 0.113539i | \(0.963781\pi\) | |||||||
\(864\) | 3.28830 | + | 5.69551i | 0.111870 | + | 0.193765i | ||||
\(865\) | 7.57353 | + | 13.1177i | 0.257508 | + | 0.446016i | ||||
\(866\) | 3.31050 | − | 5.73395i | 0.112495 | − | 0.194848i | ||||
\(867\) | 16.9103 | 0.574305 | ||||||||
\(868\) | −21.6011 | − | 1.49373i | −0.733189 | − | 0.0507006i | ||||
\(869\) | 35.8062 | 1.21464 | ||||||||
\(870\) | −5.09528 | + | 8.82529i | −0.172746 | + | 0.299205i | ||||
\(871\) | 7.53887 | + | 13.0577i | 0.255445 | + | 0.442444i | ||||
\(872\) | 8.02464 | + | 13.8991i | 0.271749 | + | 0.470683i | ||||
\(873\) | −0.294921 | + | 0.510819i | −0.00998158 | + | 0.0172886i | ||||
\(874\) | −1.06195 | −0.0359210 | ||||||||
\(875\) | −9.98447 | − | 20.4311i | −0.337537 | − | 0.690699i | ||||
\(876\) | 15.7188 | 0.531089 | ||||||||
\(877\) | −19.5214 | + | 33.8120i | −0.659191 | + | 1.14175i | 0.321635 | + | 0.946864i | \(0.395768\pi\) |
−0.980826 | + | 0.194888i | \(0.937566\pi\) | |||||||
\(878\) | 16.5406 | + | 28.6491i | 0.558218 | + | 0.966862i | ||||
\(879\) | 2.84760 | + | 4.93219i | 0.0960473 | + | 0.166359i | ||||
\(880\) | −4.79560 | + | 8.30623i | −0.161660 | + | 0.280003i | ||||
\(881\) | 21.5235 | 0.725145 | 0.362572 | − | 0.931956i | \(-0.381899\pi\) | ||||
0.362572 | + | 0.931956i | \(0.381899\pi\) | |||||||
\(882\) | −12.7064 | − | 1.76576i | −0.427847 | − | 0.0594562i | ||||
\(883\) | −17.0630 | −0.574217 | −0.287109 | − | 0.957898i | \(-0.592694\pi\) | ||||
−0.287109 | + | 0.957898i | \(0.592694\pi\) | |||||||
\(884\) | −0.741227 | + | 1.28384i | −0.0249302 | + | 0.0431803i | ||||
\(885\) | −0.981299 | − | 1.69966i | −0.0329860 | − | 0.0571335i | ||||
\(886\) | −32.3737 | − | 56.0729i | −1.08762 | − | 1.88381i | ||||
\(887\) | −21.5732 | + | 37.3659i | −0.724357 | + | 1.25462i | 0.234882 | + | 0.972024i | \(0.424530\pi\) |
−0.959238 | + | 0.282599i | \(0.908804\pi\) | |||||||
\(888\) | 1.45459 | 0.0488127 | ||||||||
\(889\) | 1.17650 | + | 2.40746i | 0.0394585 | + | 0.0807436i | ||||
\(890\) | 4.62635 | 0.155076 | ||||||||
\(891\) | −1.04340 | + | 1.80722i | −0.0349552 | + | 0.0605442i | ||||
\(892\) | 15.4657 | + | 26.7874i | 0.517831 | + | 0.896910i | ||||
\(893\) | 1.46676 | + | 2.54050i | 0.0490831 | + | 0.0850145i | ||||
\(894\) | 5.39625 | − | 9.34657i | 0.180478 | − | 0.312596i | ||||
\(895\) | 5.04304 | 0.168570 | ||||||||
\(896\) | −23.5446 | − | 1.62813i | −0.786569 | − | 0.0543919i | ||||
\(897\) | 3.64405 | 0.121671 | ||||||||
\(898\) | 5.45755 | − | 9.45276i | 0.182121 | − | 0.315443i | ||||
\(899\) | −17.7512 | − | 30.7461i | −0.592037 | − | 1.02544i | ||||
\(900\) | 2.79178 | + | 4.83550i | 0.0930592 | + | 0.161183i | ||||
\(901\) | −0.348214 | + | 0.603124i | −0.0116007 | + | 0.0200930i | ||||
\(902\) | −32.2020 | −1.07221 | ||||||||
\(903\) | −13.4270 | + | 19.9395i | −0.446821 | + | 0.663544i | ||||
\(904\) | 0.643318 | 0.0213964 | ||||||||
\(905\) | −5.48173 | + | 9.49463i | −0.182219 | + | 0.315612i | ||||
\(906\) | −12.0532 | − | 20.8767i | −0.400440 | − | 0.693582i | ||||
\(907\) | 4.74298 | + | 8.21508i | 0.157488 | + | 0.272777i | 0.933962 | − | 0.357372i | \(-0.116327\pi\) |
−0.776474 | + | 0.630149i | \(0.782994\pi\) | |||||||
\(908\) | −7.10002 | + | 12.2976i | −0.235622 | + | 0.408110i | ||||
\(909\) | 6.22834 | 0.206581 | ||||||||
\(910\) | −9.31135 | + | 13.8277i | −0.308668 | + | 0.458383i | ||||
\(911\) | 17.7773 | 0.588988 | 0.294494 | − | 0.955653i | \(-0.404849\pi\) | ||||
0.294494 | + | 0.955653i | \(0.404849\pi\) | |||||||
\(912\) | 1.41140 | − | 2.44462i | 0.0467363 | − | 0.0809496i | ||||
\(913\) | −11.4502 | − | 19.8324i | −0.378947 | − | 0.656356i | ||||
\(914\) | 29.2924 | + | 50.7360i | 0.968907 | + | 1.67820i | ||||
\(915\) | −5.87512 | + | 10.1760i | −0.194226 | + | 0.336409i | ||||
\(916\) | −14.6290 | −0.483357 | ||||||||
\(917\) | −39.6737 | − | 2.74347i | −1.31014 | − | 0.0905973i | ||||
\(918\) | 0.548767 | 0.0181120 | ||||||||
\(919\) | −1.75335 | + | 3.03689i | −0.0578376 | + | 0.100178i | −0.893494 | − | 0.449074i | \(-0.851754\pi\) |
0.835657 | + | 0.549252i | \(0.185087\pi\) | |||||||
\(920\) | −0.554529 | − | 0.960472i | −0.0182823 | − | 0.0316658i | ||||
\(921\) | 8.52979 | + | 14.7740i | 0.281066 | + | 0.486821i | ||||
\(922\) | 6.51080 | − | 11.2770i | 0.214422 | − | 0.371389i | ||||
\(923\) | −42.4309 | −1.39663 | ||||||||
\(924\) | 3.29341 | + | 6.73928i | 0.108345 | + | 0.221706i | ||||
\(925\) | 5.08565 | 0.167215 | ||||||||
\(926\) | −38.5603 | + | 66.7884i | −1.26717 | + | 2.19480i | ||||
\(927\) | 9.32274 | + | 16.1475i | 0.306199 | + | 0.530352i | ||||
\(928\) | 19.3800 | + | 33.5672i | 0.636181 | + | 1.10190i | ||||
\(929\) | −7.62220 | + | 13.2020i | −0.250076 | + | 0.433145i | −0.963547 | − | 0.267541i | \(-0.913789\pi\) |
0.713470 | + | 0.700686i | \(0.247122\pi\) | |||||||
\(930\) | 10.4158 | 0.341546 | ||||||||
\(931\) | 1.52530 | + | 3.75853i | 0.0499898 | + | 0.123181i | ||||
\(932\) | 15.9644 | 0.522932 | ||||||||
\(933\) | −8.26214 | + | 14.3104i | −0.270490 | + | 0.468503i | ||||
\(934\) | 24.2373 | + | 41.9803i | 0.793070 | + | 1.37364i | ||||
\(935\) | 0.294780 | + | 0.510574i | 0.00964033 | + | 0.0166975i | ||||
\(936\) | −2.14176 | + | 3.70964i | −0.0700057 | + | 0.121253i | ||||
\(937\) | −16.0219 | −0.523414 | −0.261707 | − | 0.965147i | \(-0.584285\pi\) | ||||
−0.261707 | + | 0.965147i | \(0.584285\pi\) | |||||||
\(938\) | −8.80863 | − | 18.0250i | −0.287612 | − | 0.588538i | ||||
\(939\) | 1.49388 | 0.0487508 | ||||||||
\(940\) | 3.24456 | − | 5.61975i | 0.105826 | − | 0.183296i | ||||
\(941\) | 4.14969 | + | 7.18748i | 0.135276 | + | 0.234305i | 0.925703 | − | 0.378251i | \(-0.123475\pi\) |
−0.790427 | + | 0.612556i | \(0.790141\pi\) | |||||||
\(942\) | 7.72055 | + | 13.3724i | 0.251549 | + | 0.435696i | ||||
\(943\) | 4.21012 | − | 7.29214i | 0.137100 | − | 0.237465i | ||||
\(944\) | −10.1333 | −0.329810 | ||||||||
\(945\) | 2.49029 | + | 0.172206i | 0.0810092 | + | 0.00560185i | ||||
\(946\) | 34.7475 | 1.12974 | ||||||||
\(947\) | −24.1605 | + | 41.8472i | −0.785111 | + | 1.35985i | 0.143822 | + | 0.989604i | \(0.454061\pi\) |
−0.928933 | + | 0.370249i | \(0.879273\pi\) | |||||||
\(948\) | 11.6556 | + | 20.1881i | 0.378556 | + | 0.655677i | ||||
\(949\) | 21.0808 | + | 36.5130i | 0.684312 | + | 1.18526i | ||||
\(950\) | 2.18222 | − | 3.77971i | 0.0708005 | − | 0.122630i | ||||
\(951\) | 18.2234 | 0.590935 | ||||||||
\(952\) | −0.520163 | + | 0.772460i | −0.0168586 | + | 0.0250356i | ||||
\(953\) | 12.0181 | 0.389303 | 0.194652 | − | 0.980872i | \(-0.437642\pi\) | ||||
0.194652 | + | 0.980872i | \(0.437642\pi\) | |||||||
\(954\) | 2.13115 | − | 3.69126i | 0.0689986 | − | 0.119509i | ||||
\(955\) | −8.05511 | − | 13.9519i | −0.260657 | − | 0.451472i | ||||
\(956\) | 8.52452 | + | 14.7649i | 0.275703 | + | 0.477531i | ||||
\(957\) | −6.14942 | + | 10.6511i | −0.198782 | + | 0.344301i | ||||
\(958\) | 46.3344 | 1.49700 | ||||||||
\(959\) | −13.7119 | + | 20.3627i | −0.442782 | + | 0.657545i | ||||
\(960\) | −2.17922 | −0.0703340 | ||||||||
\(961\) | −2.64353 | + | 4.57873i | −0.0852752 | + | 0.147701i | ||||
\(962\) | −4.13195 | − | 7.15675i | −0.133219 | − | 0.230743i | ||||
\(963\) | 0.324442 | + | 0.561949i | 0.0104550 | + | 0.0181086i | ||||
\(964\) | 7.22119 | − | 12.5075i | 0.232579 | − | 0.402838i | ||||
\(965\) | 4.38772 | 0.141246 | ||||||||
\(966\) | −4.83717 | − | 0.334494i | −0.155633 | − | 0.0107622i | ||||
\(967\) | 20.9914 | 0.675036 | 0.337518 | − | 0.941319i | \(-0.390413\pi\) | ||||
0.337518 | + | 0.941319i | \(0.390413\pi\) | |||||||
\(968\) | 3.90570 | − | 6.76488i | 0.125534 | − | 0.217431i | ||||
\(969\) | −0.0867573 | − | 0.150268i | −0.00278705 | − | 0.00482731i | ||||
\(970\) | −0.509943 | − | 0.883247i | −0.0163733 | − | 0.0283594i | ||||
\(971\) | 2.64763 | − | 4.58583i | 0.0849665 | − | 0.147166i | −0.820410 | − | 0.571775i | \(-0.806255\pi\) |
0.905377 | + | 0.424609i | \(0.139588\pi\) | |||||||
\(972\) | −1.35859 | −0.0435767 | ||||||||
\(973\) | −7.65241 | − | 15.6591i | −0.245325 | − | 0.502007i | ||||
\(974\) | −36.6098 | −1.17305 | ||||||||
\(975\) | −7.48821 | + | 12.9700i | −0.239815 | + | 0.415371i | ||||
\(976\) | 30.3344 | + | 52.5407i | 0.970980 | + | 1.68179i | ||||
\(977\) | 13.3384 | + | 23.1028i | 0.426733 | + | 0.739124i | 0.996581 | − | 0.0826270i | \(-0.0263310\pi\) |
−0.569847 | + | 0.821751i | \(0.692998\pi\) | |||||||
\(978\) | −3.80948 | + | 6.59822i | −0.121814 | + | 0.210988i | ||||
\(979\) | 5.58347 | 0.178448 | ||||||||
\(980\) | 5.51321 | − | 7.07909i | 0.176113 | − | 0.226133i | ||||
\(981\) | −13.6533 | −0.435917 | ||||||||
\(982\) | −37.5776 | + | 65.0862i | −1.19915 | + | 2.07699i | ||||
\(983\) | −3.31971 | − | 5.74990i | −0.105882 | − | 0.183393i | 0.808216 | − | 0.588886i | \(-0.200433\pi\) |
−0.914098 | + | 0.405493i | \(0.867100\pi\) | |||||||
\(984\) | 4.94893 | + | 8.57180i | 0.157766 | + | 0.273259i | ||||
\(985\) | 0.120254 | − | 0.208285i | 0.00383160 | − | 0.00663652i | ||||
\(986\) | 3.23423 | 0.102999 | ||||||||
\(987\) | 5.88085 | + | 12.0339i | 0.187189 | + | 0.383044i | ||||
\(988\) | −2.86878 | −0.0912681 | ||||||||
\(989\) | −4.54291 | + | 7.86856i | −0.144456 | + | 0.250206i | ||||
\(990\) | −1.80412 | − | 3.12483i | −0.0573388 | − | 0.0993137i | ||||
\(991\) | −15.1721 | − | 26.2789i | −0.481958 | − | 0.834777i | 0.517827 | − | 0.855485i | \(-0.326741\pi\) |
−0.999786 | + | 0.0207088i | \(0.993408\pi\) | |||||||
\(992\) | 19.8083 | − | 34.3090i | 0.628915 | − | 1.08931i | ||||
\(993\) | 22.9549 | 0.728451 | ||||||||
\(994\) | 56.3235 | + | 3.89482i | 1.78647 | + | 0.123536i | ||||
\(995\) | −5.16652 | −0.163790 | ||||||||
\(996\) | 7.45453 | − | 12.9116i | 0.236206 | − | 0.409121i | ||||
\(997\) | −23.4924 | − | 40.6900i | −0.744011 | − | 1.28867i | −0.950655 | − | 0.310249i | \(-0.899588\pi\) |
0.206644 | − | 0.978416i | \(-0.433746\pi\) | |||||||
\(998\) | 12.8715 | + | 22.2940i | 0.407439 | + | 0.705705i | ||||
\(999\) | −0.618718 | + | 1.07165i | −0.0195754 | + | 0.0339055i |
(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 | 483.2.i.f.415.5 | yes | 12 | |
7.2 | even | 3 | 3381.2.a.bc.1.2 | 6 | |||
7.4 | even | 3 | inner | 483.2.i.f.277.5 | ✓ | 12 | |
7.5 | odd | 6 | 3381.2.a.bd.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.f.277.5 | ✓ | 12 | 7.4 | even | 3 | inner | |
483.2.i.f.415.5 | yes | 12 | 1.1 | even | 1 | trivial | |
3381.2.a.bc.1.2 | 6 | 7.2 | even | 3 | |||
3381.2.a.bd.1.2 | 6 | 7.5 | odd | 6 |