Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(218,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.218");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.r (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Relative dimension: | \(34\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 342.5 | ||
Character | \(\chi\) | \(=\) | 403.342 |
Dual form | 403.2.r.a.218.5 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.98176 | − | 1.14417i | −1.40132 | − | 0.809050i | −0.406788 | − | 0.913523i | \(-0.633351\pi\) |
−0.994528 | + | 0.104473i | \(0.966685\pi\) | |||||||
\(3\) | 0.827863 | − | 1.43390i | 0.477967 | − | 0.827863i | −0.521714 | − | 0.853120i | \(-0.674707\pi\) |
0.999681 | + | 0.0252576i | \(0.00804059\pi\) | |||||||
\(4\) | 1.61825 | + | 2.80289i | 0.809124 | + | 1.40144i | ||||
\(5\) | 1.16564i | 0.521288i | 0.965435 | + | 0.260644i | \(0.0839349\pi\) | ||||
−0.965435 | + | 0.260644i | \(0.916065\pi\) | |||||||
\(6\) | −3.28125 | + | 1.89443i | −1.33956 | + | 0.773398i | ||||
\(7\) | −2.58921 | + | 1.49488i | −0.978631 | + | 0.565013i | −0.901857 | − | 0.432036i | \(-0.857796\pi\) |
−0.0767746 | + | 0.997048i | \(0.524462\pi\) | |||||||
\(8\) | − | 2.82952i | − | 1.00039i | ||||||
\(9\) | 0.129286 | + | 0.223931i | 0.0430955 | + | 0.0746436i | ||||
\(10\) | 1.33368 | − | 2.31001i | 0.421748 | − | 0.730489i | ||||
\(11\) | −1.16460 | − | 0.672380i | −0.351139 | − | 0.202730i | 0.314048 | − | 0.949407i | \(-0.398315\pi\) |
−0.665187 | + | 0.746677i | \(0.731648\pi\) | |||||||
\(12\) | 5.35875 | 1.54694 | ||||||||
\(13\) | 3.15059 | − | 1.75322i | 0.873816 | − | 0.486256i | ||||
\(14\) | 6.84160 | 1.82849 | ||||||||
\(15\) | 1.67141 | + | 0.964986i | 0.431555 | + | 0.249158i | ||||
\(16\) | −0.000955288 | 0.00165461i | −0.000238822 | 0.000413652i | ||||||
\(17\) | 3.33708 | + | 5.77999i | 0.809361 | + | 1.40185i | 0.913307 | + | 0.407272i | \(0.133520\pi\) |
−0.103946 | + | 0.994583i | \(0.533147\pi\) | |||||||
\(18\) | − | 0.591702i | − | 0.139466i | ||||||
\(19\) | 2.43890 | − | 1.40810i | 0.559523 | − | 0.323041i | −0.193431 | − | 0.981114i | \(-0.561962\pi\) |
0.752954 | + | 0.658073i | \(0.228628\pi\) | |||||||
\(20\) | −3.26714 | + | 1.88629i | −0.730556 | + | 0.421787i | ||||
\(21\) | 4.95023i | 1.08023i | ||||||||
\(22\) | 1.53863 | + | 2.66499i | 0.328038 | + | 0.568178i | ||||
\(23\) | −1.71975 | + | 2.97870i | −0.358593 | + | 0.621102i | −0.987726 | − | 0.156196i | \(-0.950077\pi\) |
0.629133 | + | 0.777298i | \(0.283410\pi\) | |||||||
\(24\) | −4.05725 | − | 2.34245i | −0.828183 | − | 0.478151i | ||||
\(25\) | 3.64129 | 0.728259 | ||||||||
\(26\) | −8.24969 | − | 0.130344i | −1.61790 | − | 0.0255625i | ||||
\(27\) | 5.39530 | 1.03833 | ||||||||
\(28\) | −8.37998 | − | 4.83818i | −1.58367 | − | 0.914331i | ||||
\(29\) | 0.110886 | − | 0.192060i | 0.0205910 | − | 0.0356647i | −0.855546 | − | 0.517726i | \(-0.826779\pi\) |
0.876137 | + | 0.482062i | \(0.160112\pi\) | |||||||
\(30\) | −2.20822 | − | 3.82474i | −0.403163 | − | 0.698299i | ||||
\(31\) | − | 1.00000i | − | 0.179605i | ||||||
\(32\) | −4.89709 | + | 2.82733i | −0.865691 | + | 0.499807i | ||||
\(33\) | −1.92825 | + | 1.11328i | −0.335666 | + | 0.193797i | ||||
\(34\) | − | 15.2727i | − | 2.61925i | ||||||
\(35\) | −1.74249 | − | 3.01808i | −0.294535 | − | 0.510149i | ||||
\(36\) | −0.418435 | + | 0.724751i | −0.0697392 | + | 0.120792i | ||||
\(37\) | 9.86577 | + | 5.69600i | 1.62192 | + | 0.936417i | 0.986405 | + | 0.164330i | \(0.0525462\pi\) |
0.635517 | + | 0.772087i | \(0.280787\pi\) | |||||||
\(38\) | −6.44443 | −1.04542 | ||||||||
\(39\) | 0.0943101 | − | 5.96906i | 0.0151017 | − | 0.955814i | ||||
\(40\) | 3.29819 | 0.521489 | ||||||||
\(41\) | −4.17402 | − | 2.40987i | −0.651873 | − | 0.376359i | 0.137301 | − | 0.990529i | \(-0.456157\pi\) |
−0.789173 | + | 0.614170i | \(0.789491\pi\) | |||||||
\(42\) | 5.66391 | − | 9.81018i | 0.873960 | − | 1.51374i | ||||
\(43\) | 2.63099 | + | 4.55700i | 0.401222 | + | 0.694936i | 0.993874 | − | 0.110522i | \(-0.0352524\pi\) |
−0.592652 | + | 0.805459i | \(0.701919\pi\) | |||||||
\(44\) | − | 4.35231i | − | 0.656135i | ||||||
\(45\) | −0.261022 | + | 0.150701i | −0.0389108 | + | 0.0224652i | ||||
\(46\) | 6.81627 | − | 3.93538i | 1.00500 | − | 0.580240i | ||||
\(47\) | − | 6.66306i | − | 0.971908i | −0.873984 | − | 0.485954i | \(-0.838472\pi\) | ||
0.873984 | − | 0.485954i | \(-0.161528\pi\) | |||||||
\(48\) | 0.00158169 | + | 0.00273958i | 0.000228298 | + | 0.000395424i | ||||
\(49\) | 0.969355 | − | 1.67897i | 0.138479 | − | 0.239853i | ||||
\(50\) | −7.21617 | − | 4.16626i | −1.02052 | − | 0.589198i | ||||
\(51\) | 11.0506 | 1.54739 | ||||||||
\(52\) | 10.0125 | + | 5.99360i | 1.38849 | + | 0.831163i | ||||
\(53\) | 4.26104 | 0.585299 | 0.292650 | − | 0.956220i | \(-0.405463\pi\) | ||||
0.292650 | + | 0.956220i | \(0.405463\pi\) | |||||||
\(54\) | −10.6922 | − | 6.17314i | −1.45502 | − | 0.840058i | ||||
\(55\) | 0.783750 | − | 1.35750i | 0.105681 | − | 0.183045i | ||||
\(56\) | 4.22980 | + | 7.32623i | 0.565231 | + | 0.979009i | ||||
\(57\) | − | 4.66286i | − | 0.617611i | ||||||
\(58\) | −0.439499 | + | 0.253745i | −0.0577091 | + | 0.0333184i | ||||
\(59\) | −1.92911 | + | 1.11377i | −0.251149 | + | 0.145001i | −0.620290 | − | 0.784372i | \(-0.712985\pi\) |
0.369141 | + | 0.929373i | \(0.379652\pi\) | |||||||
\(60\) | 6.24635i | 0.806400i | ||||||||
\(61\) | −7.53621 | − | 13.0531i | −0.964913 | − | 1.67128i | −0.709848 | − | 0.704354i | \(-0.751237\pi\) |
−0.255065 | − | 0.966924i | \(-0.582097\pi\) | |||||||
\(62\) | −1.14417 | + | 1.98176i | −0.145310 | + | 0.251684i | ||||
\(63\) | −0.669501 | − | 0.386536i | −0.0843492 | − | 0.0486990i | ||||
\(64\) | 12.9436 | 1.61795 | ||||||||
\(65\) | 2.04362 | + | 3.67244i | 0.253480 | + | 0.455510i | ||||
\(66\) | 5.09511 | 0.627165 | ||||||||
\(67\) | 4.16970 | + | 2.40738i | 0.509410 | + | 0.294108i | 0.732591 | − | 0.680669i | \(-0.238311\pi\) |
−0.223181 | + | 0.974777i | \(0.571644\pi\) | |||||||
\(68\) | −10.8004 | + | 18.7069i | −1.30975 | + | 2.26855i | ||||
\(69\) | 2.84744 | + | 4.93191i | 0.342791 | + | 0.593732i | ||||
\(70\) | 7.97481i | 0.953173i | ||||||||
\(71\) | −9.09887 | + | 5.25324i | −1.07984 | + | 0.623444i | −0.930853 | − | 0.365395i | \(-0.880934\pi\) |
−0.148985 | + | 0.988839i | \(0.547601\pi\) | |||||||
\(72\) | 0.633616 | − | 0.365819i | 0.0746724 | − | 0.0431121i | ||||
\(73\) | 13.9653i | 1.63451i | 0.576274 | + | 0.817257i | \(0.304506\pi\) | ||||
−0.576274 | + | 0.817257i | \(0.695494\pi\) | |||||||
\(74\) | −13.0344 | − | 22.5762i | −1.51522 | − | 2.62443i | ||||
\(75\) | 3.01449 | − | 5.22125i | 0.348084 | − | 0.602898i | ||||
\(76\) | 7.89350 | + | 4.55732i | 0.905447 | + | 0.522760i | ||||
\(77\) | 4.02052 | 0.458181 | ||||||||
\(78\) | −7.01651 | + | 11.7213i | −0.794464 | + | 1.32718i | ||||
\(79\) | −5.01179 | −0.563871 | −0.281935 | − | 0.959433i | \(-0.590976\pi\) | ||||
−0.281935 | + | 0.959433i | \(0.590976\pi\) | |||||||
\(80\) | −0.00192867 | − | 0.00111352i | −0.000215632 | − | 0.000124495i | ||||
\(81\) | 4.07871 | − | 7.06453i | 0.453190 | − | 0.784948i | ||||
\(82\) | 5.51461 | + | 9.55158i | 0.608986 | + | 1.05480i | ||||
\(83\) | 3.24122i | 0.355770i | 0.984051 | + | 0.177885i | \(0.0569254\pi\) | ||||
−0.984051 | + | 0.177885i | \(0.943075\pi\) | |||||||
\(84\) | −13.8749 | + | 8.01071i | −1.51388 | + | 0.874040i | ||||
\(85\) | −6.73737 | + | 3.88982i | −0.730770 | + | 0.421910i | ||||
\(86\) | − | 12.0412i | − | 1.29843i | ||||||
\(87\) | −0.183597 | − | 0.317999i | −0.0196837 | − | 0.0340931i | ||||
\(88\) | −1.90251 | + | 3.29525i | −0.202809 | + | 0.351275i | ||||
\(89\) | 7.80700 | + | 4.50737i | 0.827540 | + | 0.477781i | 0.853010 | − | 0.521895i | \(-0.174775\pi\) |
−0.0254695 | + | 0.999676i | \(0.508108\pi\) | |||||||
\(90\) | 0.689709 | 0.0727017 | ||||||||
\(91\) | −5.53669 | + | 9.24923i | −0.580403 | + | 0.969583i | ||||
\(92\) | −11.1319 | −1.16058 | ||||||||
\(93\) | −1.43390 | − | 0.827863i | −0.148689 | − | 0.0858454i | ||||
\(94\) | −7.62367 | + | 13.2046i | −0.786322 | + | 1.36195i | ||||
\(95\) | 1.64133 | + | 2.84287i | 0.168397 | + | 0.291673i | ||||
\(96\) | 9.36258i | 0.955564i | ||||||||
\(97\) | 4.13384 | − | 2.38668i | 0.419728 | − | 0.242330i | −0.275233 | − | 0.961378i | \(-0.588755\pi\) |
0.694961 | + | 0.719047i | \(0.255422\pi\) | |||||||
\(98\) | −3.84206 | + | 2.21821i | −0.388106 | + | 0.224073i | ||||
\(99\) | − | 0.347719i | − | 0.0349470i | ||||||
\(100\) | 5.89251 | + | 10.2061i | 0.589251 | + | 1.02061i | ||||
\(101\) | −1.79500 | + | 3.10902i | −0.178609 | + | 0.309359i | −0.941404 | − | 0.337280i | \(-0.890493\pi\) |
0.762795 | + | 0.646640i | \(0.223826\pi\) | |||||||
\(102\) | −21.8996 | − | 12.6437i | −2.16838 | − | 1.25192i | ||||
\(103\) | −11.0519 | −1.08897 | −0.544486 | − | 0.838770i | \(-0.683275\pi\) | ||||
−0.544486 | + | 0.838770i | \(0.683275\pi\) | |||||||
\(104\) | −4.96078 | − | 8.91466i | −0.486444 | − | 0.874154i | ||||
\(105\) | −5.77017 | −0.563111 | ||||||||
\(106\) | −8.44436 | − | 4.87535i | −0.820189 | − | 0.473536i | ||||
\(107\) | −4.63608 | + | 8.02992i | −0.448186 | + | 0.776282i | −0.998268 | − | 0.0588293i | \(-0.981263\pi\) |
0.550082 | + | 0.835111i | \(0.314597\pi\) | |||||||
\(108\) | 8.73094 | + | 15.1224i | 0.840135 | + | 1.45516i | ||||
\(109\) | 2.45675i | 0.235314i | 0.993054 | + | 0.117657i | \(0.0375384\pi\) | ||||
−0.993054 | + | 0.117657i | \(0.962462\pi\) | |||||||
\(110\) | −3.10641 | + | 1.79349i | −0.296184 | + | 0.171002i | ||||
\(111\) | 16.3350 | − | 9.43102i | 1.55045 | − | 0.895153i | ||||
\(112\) | − | 0.00571218i | − | 0.000539750i | ||||||
\(113\) | −0.0875022 | − | 0.151558i | −0.00823152 | − | 0.0142574i | 0.861880 | − | 0.507112i | \(-0.169287\pi\) |
−0.870112 | + | 0.492854i | \(0.835954\pi\) | |||||||
\(114\) | −5.33510 | + | 9.24067i | −0.499678 | + | 0.865468i | ||||
\(115\) | −3.47208 | − | 2.00460i | −0.323773 | − | 0.186930i | ||||
\(116\) | 0.717765 | 0.0666428 | ||||||||
\(117\) | 0.799929 | + | 0.478846i | 0.0739534 | + | 0.0442693i | ||||
\(118\) | 5.09738 | 0.469252 | ||||||||
\(119\) | −17.2808 | − | 9.97710i | −1.58413 | − | 0.914599i | ||||
\(120\) | 2.73045 | − | 4.72927i | 0.249255 | − | 0.431722i | ||||
\(121\) | −4.59581 | − | 7.96018i | −0.417801 | − | 0.723652i | ||||
\(122\) | 34.4908i | 3.12265i | ||||||||
\(123\) | −6.91104 | + | 3.99009i | −0.623147 | + | 0.359774i | ||||
\(124\) | 2.80289 | − | 1.61825i | 0.251707 | − | 0.145323i | ||||
\(125\) | 10.0726i | 0.900921i | ||||||||
\(126\) | 0.884526 | + | 1.53204i | 0.0787999 | + | 0.136485i | ||||
\(127\) | 10.3318 | − | 17.8952i | 0.916800 | − | 1.58794i | 0.112556 | − | 0.993645i | \(-0.464096\pi\) |
0.804244 | − | 0.594299i | \(-0.202570\pi\) | |||||||
\(128\) | −15.8570 | − | 9.15502i | −1.40157 | − | 0.809198i | ||||
\(129\) | 8.71238 | 0.767083 | ||||||||
\(130\) | 0.151933 | − | 9.61614i | 0.0133254 | − | 0.843391i | ||||
\(131\) | −1.18334 | −0.103389 | −0.0516945 | − | 0.998663i | \(-0.516462\pi\) | ||||
−0.0516945 | + | 0.998663i | \(0.516462\pi\) | |||||||
\(132\) | −6.24078 | − | 3.60312i | −0.543190 | − | 0.313611i | ||||
\(133\) | −4.20990 | + | 7.29176i | −0.365044 | + | 0.632275i | ||||
\(134\) | −5.50890 | − | 9.54169i | −0.475896 | − | 0.824276i | ||||
\(135\) | 6.28896i | 0.541267i | ||||||||
\(136\) | 16.3546 | − | 9.44234i | 1.40240 | − | 0.809674i | ||||
\(137\) | 9.36968 | − | 5.40959i | 0.800506 | − | 0.462172i | −0.0431422 | − | 0.999069i | \(-0.513737\pi\) |
0.843648 | + | 0.536897i | \(0.180404\pi\) | |||||||
\(138\) | − | 13.0318i | − | 1.10934i | ||||||
\(139\) | 2.95199 | + | 5.11300i | 0.250385 | + | 0.433679i | 0.963632 | − | 0.267234i | \(-0.0861095\pi\) |
−0.713247 | + | 0.700913i | \(0.752776\pi\) | |||||||
\(140\) | 5.63956 | − | 9.76800i | 0.476630 | − | 0.825547i | ||||
\(141\) | −9.55417 | − | 5.51610i | −0.804606 | − | 0.464540i | ||||
\(142\) | 24.0424 | 2.01759 | ||||||||
\(143\) | −4.84800 | − | 0.0765976i | −0.405410 | − | 0.00640541i | ||||
\(144\) | −0.000494023 | 0 | −4.11686e−5 | 0 | ||||||
\(145\) | 0.223873 | + | 0.129253i | 0.0185916 | + | 0.0107339i | ||||
\(146\) | 15.9787 | − | 27.6758i | 1.32240 | − | 2.29047i | ||||
\(147\) | −1.60499 | − | 2.77992i | −0.132377 | − | 0.229284i | ||||
\(148\) | 36.8702i | 3.03071i | ||||||||
\(149\) | 14.3445 | − | 8.28178i | 1.17514 | − | 0.678470i | 0.220258 | − | 0.975442i | \(-0.429310\pi\) |
0.954886 | + | 0.296972i | \(0.0959768\pi\) | |||||||
\(150\) | −11.9480 | + | 6.89818i | −0.975550 | + | 0.563234i | ||||
\(151\) | 13.4220i | 1.09227i | 0.837697 | + | 0.546135i | \(0.183901\pi\) | ||||
−0.837697 | + | 0.546135i | \(0.816099\pi\) | |||||||
\(152\) | −3.98425 | − | 6.90093i | −0.323166 | − | 0.559739i | ||||
\(153\) | −0.862879 | + | 1.49455i | −0.0697596 | + | 0.120827i | ||||
\(154\) | −7.96771 | − | 4.60016i | −0.642056 | − | 0.370691i | ||||
\(155\) | 1.16564 | 0.0936261 | ||||||||
\(156\) | 16.8832 | − | 9.39507i | 1.35174 | − | 0.752208i | ||||
\(157\) | 3.88582 | 0.310122 | 0.155061 | − | 0.987905i | \(-0.450443\pi\) | ||||
0.155061 | + | 0.987905i | \(0.450443\pi\) | |||||||
\(158\) | 9.93217 | + | 5.73434i | 0.790161 | + | 0.456200i | ||||
\(159\) | 3.52756 | − | 6.10991i | 0.279754 | − | 0.484547i | ||||
\(160\) | −3.29564 | − | 5.70822i | −0.260543 | − | 0.451274i | ||||
\(161\) | − | 10.2833i | − | 0.810439i | ||||||
\(162\) | −16.1660 | + | 9.33347i | −1.27012 | + | 0.733307i | ||||
\(163\) | 15.3333 | − | 8.85266i | 1.20099 | − | 0.693394i | 0.240217 | − | 0.970719i | \(-0.422781\pi\) |
0.960776 | + | 0.277326i | \(0.0894480\pi\) | |||||||
\(164\) | − | 15.5991i | − | 1.21808i | ||||||
\(165\) | −1.29768 | − | 2.24764i | −0.101024 | − | 0.174979i | ||||
\(166\) | 3.70850 | − | 6.42331i | 0.287835 | − | 0.498546i | ||||
\(167\) | −0.849295 | − | 0.490341i | −0.0657204 | − | 0.0379437i | 0.466780 | − | 0.884374i | \(-0.345414\pi\) |
−0.532500 | + | 0.846430i | \(0.678747\pi\) | |||||||
\(168\) | 14.0068 | 1.08065 | ||||||||
\(169\) | 6.85243 | − | 11.0474i | 0.527110 | − | 0.849797i | ||||
\(170\) | 17.8025 | 1.36539 | ||||||||
\(171\) | 0.630634 | + | 0.364097i | 0.0482258 | + | 0.0278432i | ||||
\(172\) | −8.51518 | + | 14.7487i | −0.649276 | + | 1.12458i | ||||
\(173\) | 4.72774 | + | 8.18868i | 0.359443 | + | 0.622574i | 0.987868 | − | 0.155297i | \(-0.0496334\pi\) |
−0.628425 | + | 0.777870i | \(0.716300\pi\) | |||||||
\(174\) | 0.840265i | 0.0637003i | ||||||||
\(175\) | −9.42809 | + | 5.44331i | −0.712697 | + | 0.411476i | ||||
\(176\) | 0.00222505 | − | 0.00128463i | 0.000167719 | − | 9.68329e-5i | ||||
\(177\) | 3.68820i | 0.277222i | ||||||||
\(178\) | −10.3144 | − | 17.8651i | −0.773097 | − | 1.33904i | ||||
\(179\) | −4.11732 | + | 7.13140i | −0.307743 | + | 0.533026i | −0.977868 | − | 0.209222i | \(-0.932907\pi\) |
0.670125 | + | 0.742248i | \(0.266240\pi\) | |||||||
\(180\) | −0.844795 | − | 0.487743i | −0.0629673 | − | 0.0363542i | ||||
\(181\) | −5.36382 | −0.398689 | −0.199345 | − | 0.979929i | \(-0.563881\pi\) | ||||
−0.199345 | + | 0.979929i | \(0.563881\pi\) | |||||||
\(182\) | 21.5551 | − | 11.9948i | 1.59777 | − | 0.889117i | ||||
\(183\) | −24.9558 | −1.84479 | ||||||||
\(184\) | 8.42829 | + | 4.86607i | 0.621342 | + | 0.358732i | ||||
\(185\) | −6.63946 | + | 11.4999i | −0.488143 | + | 0.845489i | ||||
\(186\) | 1.89443 | + | 3.28125i | 0.138906 | + | 0.240593i | ||||
\(187\) | − | 8.97515i | − | 0.656328i | ||||||
\(188\) | 18.6758 | − | 10.7825i | 1.36207 | − | 0.786394i | ||||
\(189\) | −13.9696 | + | 8.06535i | −1.01614 | + | 0.586668i | ||||
\(190\) | − | 7.51186i | − | 0.544967i | ||||||
\(191\) | −7.55804 | − | 13.0909i | −0.546881 | − | 0.947225i | −0.998486 | − | 0.0550074i | \(-0.982482\pi\) |
0.451605 | − | 0.892218i | \(-0.350852\pi\) | |||||||
\(192\) | 10.7155 | − | 18.5599i | 0.773327 | − | 1.33944i | ||||
\(193\) | −7.60965 | − | 4.39343i | −0.547754 | − | 0.316246i | 0.200461 | − | 0.979702i | \(-0.435756\pi\) |
−0.748216 | + | 0.663455i | \(0.769089\pi\) | |||||||
\(194\) | −10.9230 | −0.784229 | ||||||||
\(195\) | 6.95775 | + | 0.109931i | 0.498255 | + | 0.00787234i | ||||
\(196\) | 6.27463 | 0.448188 | ||||||||
\(197\) | −18.8837 | − | 10.9025i | −1.34541 | − | 0.776770i | −0.357811 | − | 0.933794i | \(-0.616477\pi\) |
−0.987595 | + | 0.157024i | \(0.949810\pi\) | |||||||
\(198\) | −0.397849 | + | 0.689095i | −0.0282739 | + | 0.0489718i | ||||
\(199\) | 5.82778 | + | 10.0940i | 0.413121 | + | 0.715546i | 0.995229 | − | 0.0975653i | \(-0.0311055\pi\) |
−0.582109 | + | 0.813111i | \(0.697772\pi\) | |||||||
\(200\) | − | 10.3031i | − | 0.728540i | ||||||
\(201\) | 6.90388 | − | 3.98596i | 0.486962 | − | 0.281148i | ||||
\(202\) | 7.11450 | − | 4.10756i | 0.500574 | − | 0.289007i | ||||
\(203\) | 0.663048i | 0.0465368i | ||||||||
\(204\) | 17.8826 | + | 30.9735i | 1.25203 | + | 2.16858i | ||||
\(205\) | 2.80903 | − | 4.86539i | 0.196191 | − | 0.339814i | ||||
\(206\) | 21.9021 | + | 12.6452i | 1.52599 | + | 0.881033i | ||||
\(207\) | −0.889363 | −0.0618150 | ||||||||
\(208\) | −0.000108826 | 0.00688782i | −7.54575e−6 | 0.000477584i | ||||||
\(209\) | −3.78712 | −0.261961 | ||||||||
\(210\) | 11.4351 | + | 6.60205i | 0.789096 | + | 0.455585i | ||||
\(211\) | 0.0302017 | − | 0.0523110i | 0.00207917 | − | 0.00360124i | −0.864984 | − | 0.501800i | \(-0.832672\pi\) |
0.867063 | + | 0.498198i | \(0.166005\pi\) | |||||||
\(212\) | 6.89542 | + | 11.9432i | 0.473580 | + | 0.820264i | ||||
\(213\) | 17.3958i | 1.19194i | ||||||||
\(214\) | 18.3752 | − | 10.6089i | 1.25610 | − | 0.725210i | ||||
\(215\) | −5.31180 | + | 3.06677i | −0.362262 | + | 0.209152i | ||||
\(216\) | − | 15.2661i | − | 1.03873i | ||||||
\(217\) | 1.49488 | + | 2.58921i | 0.101479 | + | 0.175767i | ||||
\(218\) | 2.81094 | − | 4.86869i | 0.190381 | − | 0.329750i | ||||
\(219\) | 20.0248 | + | 11.5613i | 1.35315 | + | 0.781243i | ||||
\(220\) | 5.07321 | 0.342036 | ||||||||
\(221\) | 20.6474 | + | 12.3597i | 1.38889 | + | 0.831406i | ||||
\(222\) | −43.1627 | −2.89689 | ||||||||
\(223\) | −16.5603 | − | 9.56112i | −1.10896 | − | 0.640260i | −0.170402 | − | 0.985375i | \(-0.554507\pi\) |
−0.938560 | + | 0.345115i | \(0.887840\pi\) | |||||||
\(224\) | 8.45307 | − | 14.6411i | 0.564795 | − | 0.978253i | ||||
\(225\) | 0.470770 | + | 0.815397i | 0.0313847 | + | 0.0543598i | ||||
\(226\) | 0.400470i | 0.0266388i | ||||||||
\(227\) | −1.21674 | + | 0.702483i | −0.0807576 | + | 0.0466254i | −0.539835 | − | 0.841771i | \(-0.681513\pi\) |
0.459077 | + | 0.888396i | \(0.348180\pi\) | |||||||
\(228\) | 13.0695 | − | 7.54566i | 0.865547 | − | 0.499724i | ||||
\(229\) | − | 3.13334i | − | 0.207057i | −0.994626 | − | 0.103529i | \(-0.966987\pi\) | ||
0.994626 | − | 0.103529i | \(-0.0330133\pi\) | |||||||
\(230\) | 4.58721 | + | 7.94529i | 0.302472 | + | 0.523897i | ||||
\(231\) | 3.32844 | − | 5.76503i | 0.218995 | − | 0.379311i | ||||
\(232\) | −0.543439 | − | 0.313755i | −0.0356785 | − | 0.0205990i | ||||
\(233\) | −6.45119 | −0.422632 | −0.211316 | − | 0.977418i | \(-0.567775\pi\) | ||||
−0.211316 | + | 0.977418i | \(0.567775\pi\) | |||||||
\(234\) | −1.03739 | − | 1.86421i | −0.0678160 | − | 0.121867i | ||||
\(235\) | 7.76670 | 0.506644 | ||||||||
\(236\) | −6.24356 | − | 3.60472i | −0.406421 | − | 0.234647i | ||||
\(237\) | −4.14908 | + | 7.18641i | −0.269511 | + | 0.466808i | ||||
\(238\) | 22.8310 | + | 39.5444i | 1.47991 | + | 2.56328i | ||||
\(239\) | − | 16.2114i | − | 1.04863i | −0.851524 | − | 0.524315i | \(-0.824321\pi\) | ||
0.851524 | − | 0.524315i | \(-0.175679\pi\) | |||||||
\(240\) | −0.00319335 | + | 0.00184368i | −0.000206130 | + | 0.000119009i | ||||
\(241\) | 3.17424 | − | 1.83265i | 0.204471 | − | 0.118051i | −0.394268 | − | 0.918995i | \(-0.629002\pi\) |
0.598739 | + | 0.800944i | \(0.295669\pi\) | |||||||
\(242\) | 21.0335i | 1.35209i | ||||||||
\(243\) | 1.33973 | + | 2.32048i | 0.0859436 | + | 0.148859i | ||||
\(244\) | 24.3909 | − | 42.2463i | 1.56147 | − | 2.70454i | ||||
\(245\) | 1.95707 | + | 1.12991i | 0.125033 | + | 0.0721876i | ||||
\(246\) | 18.2614 | 1.16430 | ||||||||
\(247\) | 5.21527 | − | 8.71229i | 0.331840 | − | 0.554350i | ||||
\(248\) | −2.82952 | −0.179675 | ||||||||
\(249\) | 4.64758 | + | 2.68328i | 0.294528 | + | 0.170046i | ||||
\(250\) | 11.5248 | − | 19.9615i | 0.728890 | − | 1.26247i | ||||
\(251\) | −15.4041 | − | 26.6808i | −0.972301 | − | 1.68407i | −0.688569 | − | 0.725171i | \(-0.741761\pi\) |
−0.283731 | − | 0.958904i | \(-0.591572\pi\) | |||||||
\(252\) | − | 2.50205i | − | 0.157614i | ||||||
\(253\) | 4.00564 | − | 2.31265i | 0.251832 | − | 0.145395i | ||||
\(254\) | −40.9503 | + | 23.6427i | −2.56945 | + | 1.48347i | ||||
\(255\) | 12.8810i | 0.806636i | ||||||||
\(256\) | 8.00618 | + | 13.8671i | 0.500386 | + | 0.866695i | ||||
\(257\) | −2.53629 | + | 4.39299i | −0.158210 | + | 0.274027i | −0.934223 | − | 0.356689i | \(-0.883905\pi\) |
0.776014 | + | 0.630716i | \(0.217239\pi\) | |||||||
\(258\) | −17.2658 | − | 9.96844i | −1.07492 | − | 0.620608i | ||||
\(259\) | −34.0595 | −2.11635 | ||||||||
\(260\) | −6.98635 | + | 11.6709i | −0.433275 | + | 0.723801i | ||||
\(261\) | 0.0573443 | 0.00354952 | ||||||||
\(262\) | 2.34510 | + | 1.35394i | 0.144880 | + | 0.0836468i | ||||
\(263\) | −5.47171 | + | 9.47729i | −0.337400 | + | 0.584395i | −0.983943 | − | 0.178483i | \(-0.942881\pi\) |
0.646543 | + | 0.762878i | \(0.276214\pi\) | |||||||
\(264\) | 3.15004 | + | 5.45603i | 0.193872 | + | 0.335795i | ||||
\(265\) | 4.96682i | 0.305109i | ||||||||
\(266\) | 16.6860 | − | 9.63367i | 1.02308 | − | 0.590678i | ||||
\(267\) | 12.9262 | − | 7.46297i | 0.791074 | − | 0.456727i | ||||
\(268\) | 15.5829i | 0.951879i | ||||||||
\(269\) | −1.75681 | − | 3.04289i | −0.107115 | − | 0.185528i | 0.807485 | − | 0.589888i | \(-0.200828\pi\) |
−0.914600 | + | 0.404359i | \(0.867495\pi\) | |||||||
\(270\) | 7.19563 | − | 12.4632i | 0.437912 | − | 0.758486i | ||||
\(271\) | −16.9716 | − | 9.79854i | −1.03095 | − | 0.595219i | −0.113693 | − | 0.993516i | \(-0.536268\pi\) |
−0.917257 | + | 0.398297i | \(0.869601\pi\) | |||||||
\(272\) | −0.0127515 | −0.000773173 | ||||||||
\(273\) | 8.67886 | + | 15.5962i | 0.525268 | + | 0.943922i | ||||
\(274\) | −24.7579 | −1.49568 | ||||||||
\(275\) | −4.24064 | − | 2.44833i | −0.255720 | − | 0.147640i | ||||
\(276\) | −9.21572 | + | 15.9621i | −0.554721 | + | 0.960805i | ||||
\(277\) | −5.42456 | − | 9.39562i | −0.325930 | − | 0.564528i | 0.655770 | − | 0.754961i | \(-0.272344\pi\) |
−0.981700 | + | 0.190433i | \(0.939011\pi\) | |||||||
\(278\) | − | 13.5103i | − | 0.810295i | ||||||
\(279\) | 0.223931 | − | 0.129286i | 0.0134064 | − | 0.00774018i | ||||
\(280\) | −8.53972 | + | 4.93041i | −0.510346 | + | 0.294648i | ||||
\(281\) | 5.18454i | 0.309284i | 0.987971 | + | 0.154642i | \(0.0494224\pi\) | ||||
−0.987971 | + | 0.154642i | \(0.950578\pi\) | |||||||
\(282\) | 12.6227 | + | 21.8632i | 0.751672 | + | 1.30193i | ||||
\(283\) | 8.55608 | − | 14.8196i | 0.508606 | − | 0.880932i | −0.491344 | − | 0.870966i | \(-0.663494\pi\) |
0.999950 | − | 0.00996632i | \(-0.00317243\pi\) | |||||||
\(284\) | −29.4485 | − | 17.0021i | −1.74744 | − | 1.00889i | ||||
\(285\) | 5.43520 | 0.321953 | ||||||||
\(286\) | 9.51993 | + | 5.69873i | 0.562925 | + | 0.336973i | ||||
\(287\) | 14.4099 | 0.850591 | ||||||||
\(288\) | −1.26625 | − | 0.731072i | −0.0746147 | − | 0.0430788i | ||||
\(289\) | −13.7722 | + | 23.8542i | −0.810131 | + | 1.40319i | ||||
\(290\) | −0.295774 | − | 0.512296i | −0.0173685 | − | 0.0300831i | ||||
\(291\) | − | 7.90336i | − | 0.463303i | ||||||
\(292\) | −39.1431 | + | 22.5993i | −2.29068 | + | 1.32252i | ||||
\(293\) | −15.7413 | + | 9.08826i | −0.919618 | + | 0.530942i | −0.883513 | − | 0.468406i | \(-0.844828\pi\) |
−0.0361048 | + | 0.999348i | \(0.511495\pi\) | |||||||
\(294\) | 7.34550i | 0.428398i | ||||||||
\(295\) | −1.29825 | − | 2.24864i | −0.0755872 | − | 0.130921i | ||||
\(296\) | 16.1170 | − | 27.9154i | 0.936779 | − | 1.62255i | ||||
\(297\) | −6.28335 | − | 3.62769i | −0.364597 | − | 0.210500i | ||||
\(298\) | −37.9030 | −2.19566 | ||||||||
\(299\) | −0.195914 | + | 12.3998i | −0.0113300 | + | 0.717097i | ||||
\(300\) | 19.5128 | 1.12657 | ||||||||
\(301\) | −13.6244 | − | 7.86604i | −0.785296 | − | 0.453391i | ||||
\(302\) | 15.3571 | − | 26.5992i | 0.883701 | − | 1.53061i | ||||
\(303\) | 2.97202 | + | 5.14769i | 0.170738 | + | 0.295727i | ||||
\(304\) | 0.00538057i | 0.000308597i | ||||||||
\(305\) | 15.2152 | − | 8.78448i | 0.871218 | − | 0.502998i | ||||
\(306\) | 3.42004 | − | 1.97456i | 0.195510 | − | 0.112878i | ||||
\(307\) | − | 2.69825i | − | 0.153998i | −0.997031 | − | 0.0769988i | \(-0.975466\pi\) | ||
0.997031 | − | 0.0769988i | \(-0.0245338\pi\) | |||||||
\(308\) | 6.50620 | + | 11.2691i | 0.370725 | + | 0.642115i | ||||
\(309\) | −9.14943 | + | 15.8473i | −0.520493 | + | 0.901520i | ||||
\(310\) | −2.31001 | − | 1.33368i | −0.131200 | − | 0.0757482i | ||||
\(311\) | 32.1030 | 1.82039 | 0.910197 | − | 0.414176i | \(-0.135930\pi\) | ||||
0.910197 | + | 0.414176i | \(0.135930\pi\) | |||||||
\(312\) | −16.8896 | − | 0.266852i | −0.956184 | − | 0.0151075i | ||||
\(313\) | −27.5752 | −1.55864 | −0.779320 | − | 0.626626i | \(-0.784435\pi\) | ||||
−0.779320 | + | 0.626626i | \(0.784435\pi\) | |||||||
\(314\) | −7.70075 | − | 4.44603i | −0.434579 | − | 0.250904i | ||||
\(315\) | 0.450561 | − | 0.780394i | 0.0253862 | − | 0.0439702i | ||||
\(316\) | −8.11032 | − | 14.0475i | −0.456241 | − | 0.790233i | ||||
\(317\) | − | 31.8275i | − | 1.78761i | −0.448456 | − | 0.893805i | \(-0.648026\pi\) | ||
0.448456 | − | 0.893805i | \(-0.351974\pi\) | |||||||
\(318\) | −13.9815 | + | 8.07225i | −0.784046 | + | 0.452669i | ||||
\(319\) | −0.258275 | + | 0.149115i | −0.0144606 | + | 0.00834886i | ||||
\(320\) | 15.0875i | 0.843419i | ||||||||
\(321\) | 7.67607 | + | 13.2953i | 0.428436 | + | 0.742074i | ||||
\(322\) | −11.7659 | + | 20.3791i | −0.655686 | + | 1.13568i | ||||
\(323\) | 16.2776 | + | 9.39790i | 0.905712 | + | 0.522913i | ||||
\(324\) | 26.4015 | 1.46675 | ||||||||
\(325\) | 11.4722 | − | 6.38400i | 0.636364 | − | 0.354120i | ||||
\(326\) | −40.5158 | −2.24396 | ||||||||
\(327\) | 3.52274 | + | 2.03385i | 0.194808 | + | 0.112472i | ||||
\(328\) | −6.81878 | + | 11.8105i | −0.376504 | + | 0.652125i | ||||
\(329\) | 9.96051 | + | 17.2521i | 0.549140 | + | 0.951139i | ||||
\(330\) | 5.93904i | 0.326933i | ||||||||
\(331\) | 14.0536 | − | 8.11386i | 0.772456 | − | 0.445978i | −0.0612938 | − | 0.998120i | \(-0.519523\pi\) |
0.833750 | + | 0.552142i | \(0.186189\pi\) | |||||||
\(332\) | −9.08476 | + | 5.24509i | −0.498591 | + | 0.287862i | ||||
\(333\) | 2.94566i | 0.161421i | ||||||||
\(334\) | 1.12207 | + | 1.94348i | 0.0613967 | + | 0.106342i | ||||
\(335\) | −2.80612 | + | 4.86035i | −0.153315 | + | 0.265549i | ||||
\(336\) | −0.00819069 | − | 0.00472890i | −0.000446839 | − | 0.000257983i | ||||
\(337\) | −35.8683 | −1.95387 | −0.976936 | − | 0.213533i | \(-0.931503\pi\) | ||||
−0.976936 | + | 0.213533i | \(0.931503\pi\) | |||||||
\(338\) | −26.2199 | + | 14.0529i | −1.42618 | + | 0.764376i | ||||
\(339\) | −0.289759 | −0.0157376 | ||||||||
\(340\) | −21.8055 | − | 12.5894i | −1.18257 | − | 0.682755i | ||||
\(341\) | −0.672380 | + | 1.16460i | −0.0364114 | + | 0.0630664i | ||||
\(342\) | −0.833177 | − | 1.44311i | −0.0450531 | − | 0.0780342i | ||||
\(343\) | − | 15.1321i | − | 0.817056i | ||||||
\(344\) | 12.8941 | − | 7.44443i | 0.695205 | − | 0.401377i | ||||
\(345\) | −5.74881 | + | 3.31907i | −0.309505 | + | 0.178693i | ||||
\(346\) | − | 21.6373i | − | 1.16323i | ||||||
\(347\) | −11.9179 | − | 20.6423i | −0.639784 | − | 1.10814i | −0.985480 | − | 0.169792i | \(-0.945690\pi\) |
0.345695 | − | 0.938347i | \(-0.387643\pi\) | |||||||
\(348\) | 0.594211 | − | 1.02920i | 0.0318531 | − | 0.0551711i | ||||
\(349\) | −30.5271 | − | 17.6248i | −1.63408 | − | 0.943435i | −0.982817 | − | 0.184580i | \(-0.940907\pi\) |
−0.651260 | − | 0.758855i | \(-0.725759\pi\) | |||||||
\(350\) | 24.9123 | 1.33162 | ||||||||
\(351\) | 16.9984 | − | 9.45916i | 0.907307 | − | 0.504893i | ||||
\(352\) | 7.60417 | 0.405304 | ||||||||
\(353\) | 18.3030 | + | 10.5672i | 0.974171 | + | 0.562438i | 0.900505 | − | 0.434845i | \(-0.143197\pi\) |
0.0736655 | + | 0.997283i | \(0.476530\pi\) | |||||||
\(354\) | 4.21993 | − | 7.30913i | 0.224287 | − | 0.388476i | ||||
\(355\) | −6.12336 | − | 10.6060i | −0.324994 | − | 0.562906i | ||||
\(356\) | 29.1762i | 1.54633i | ||||||||
\(357\) | −28.6123 | + | 16.5193i | −1.51433 | + | 0.874296i | ||||
\(358\) | 16.3191 | − | 9.42182i | 0.862490 | − | 0.497959i | ||||
\(359\) | 12.7307i | 0.671901i | 0.941880 | + | 0.335950i | \(0.109057\pi\) | ||||
−0.941880 | + | 0.335950i | \(0.890943\pi\) | |||||||
\(360\) | 0.426411 | + | 0.738566i | 0.0224738 | + | 0.0389258i | ||||
\(361\) | −5.53450 | + | 9.58603i | −0.291289 | + | 0.504528i | ||||
\(362\) | 10.6298 | + | 6.13712i | 0.558690 | + | 0.322560i | ||||
\(363\) | −15.2188 | −0.798780 | ||||||||
\(364\) | −34.8843 | − | 0.551166i | −1.82843 | − | 0.0288889i | ||||
\(365\) | −16.2784 | −0.852052 | ||||||||
\(366\) | 49.4564 | + | 28.5537i | 2.58513 | + | 1.49252i | ||||
\(367\) | −10.8245 | + | 18.7485i | −0.565033 | + | 0.978665i | 0.432014 | + | 0.901867i | \(0.357803\pi\) |
−0.997047 | + | 0.0767983i | \(0.975530\pi\) | |||||||
\(368\) | −0.00328572 | − | 0.00569103i | −0.000171280 | − | 0.000296665i | ||||
\(369\) | − | 1.24626i | − | 0.0648775i | ||||||
\(370\) | 26.3156 | − | 15.1933i | 1.36809 | − | 0.789864i | ||||
\(371\) | −11.0328 | + | 6.36976i | −0.572792 | + | 0.330702i | ||||
\(372\) | − | 5.35875i | − | 0.277838i | ||||||
\(373\) | 14.1255 | + | 24.4661i | 0.731391 | + | 1.26681i | 0.956289 | + | 0.292424i | \(0.0944618\pi\) |
−0.224898 | + | 0.974382i | \(0.572205\pi\) | |||||||
\(374\) | −10.2691 | + | 17.7866i | −0.531002 | + | 0.919723i | ||||
\(375\) | 14.4431 | + | 8.33873i | 0.745839 | + | 0.430610i | ||||
\(376\) | −18.8533 | −0.972283 | ||||||||
\(377\) | 0.0126322 | − | 0.799512i | 0.000650589 | − | 0.0411769i | ||||
\(378\) | 36.9125 | 1.89857 | ||||||||
\(379\) | 25.5614 | + | 14.7579i | 1.31300 | + | 0.758061i | 0.982592 | − | 0.185777i | \(-0.0594802\pi\) |
0.330408 | + | 0.943838i | \(0.392814\pi\) | |||||||
\(380\) | −5.31217 | + | 9.20095i | −0.272508 | + | 0.471999i | ||||
\(381\) | −17.1066 | − | 29.6296i | −0.876400 | − | 1.51797i | ||||
\(382\) | 34.5907i | 1.76982i | ||||||||
\(383\) | 24.8170 | − | 14.3281i | 1.26809 | − | 0.732130i | 0.293461 | − | 0.955971i | \(-0.405193\pi\) |
0.974626 | + | 0.223841i | \(0.0718595\pi\) | |||||||
\(384\) | −26.2548 | + | 15.1582i | −1.33981 | + | 0.773539i | ||||
\(385\) | 4.68646i | 0.238844i | ||||||||
\(386\) | 10.0537 | + | 17.4135i | 0.511718 | + | 0.886321i | ||||
\(387\) | −0.680302 | + | 1.17832i | −0.0345817 | + | 0.0598972i | ||||
\(388\) | 13.3792 | + | 7.72446i | 0.679224 | + | 0.392150i | ||||
\(389\) | 21.4851 | 1.08934 | 0.544669 | − | 0.838651i | \(-0.316655\pi\) | ||||
0.544669 | + | 0.838651i | \(0.316655\pi\) | |||||||
\(390\) | −13.6628 | − | 8.17870i | −0.691843 | − | 0.414145i | ||||
\(391\) | −22.9558 | −1.16093 | ||||||||
\(392\) | −4.75069 | − | 2.74281i | −0.239946 | − | 0.138533i | ||||
\(393\) | −0.979643 | + | 1.69679i | −0.0494165 | + | 0.0855918i | ||||
\(394\) | 24.9486 | + | 43.2122i | 1.25689 | + | 2.17700i | ||||
\(395\) | − | 5.84192i | − | 0.293939i | ||||||
\(396\) | 0.974616 | − | 0.562695i | 0.0489763 | − | 0.0282765i | ||||
\(397\) | −6.01423 | + | 3.47232i | −0.301846 | + | 0.174271i | −0.643272 | − | 0.765638i | \(-0.722423\pi\) |
0.341426 | + | 0.939909i | \(0.389090\pi\) | |||||||
\(398\) | − | 26.6719i | − | 1.33694i | ||||||
\(399\) | 6.97043 | + | 12.0731i | 0.348958 | + | 0.604413i | ||||
\(400\) | −0.00347848 | + | 0.00602491i | −0.000173924 | + | 0.000301246i | ||||
\(401\) | 29.7572 | + | 17.1803i | 1.48600 | + | 0.857944i | 0.999873 | − | 0.0159430i | \(-0.00507503\pi\) |
0.486129 | + | 0.873887i | \(0.338408\pi\) | |||||||
\(402\) | −18.2424 | −0.909850 | ||||||||
\(403\) | −1.75322 | − | 3.15059i | −0.0873342 | − | 0.156942i | ||||
\(404\) | −11.6190 | −0.578066 | ||||||||
\(405\) | 8.23467 | + | 4.75429i | 0.409184 | + | 0.236243i | ||||
\(406\) | 0.758639 | − | 1.31400i | 0.0376506 | − | 0.0652128i | ||||
\(407\) | −7.65976 | − | 13.2671i | −0.379680 | − | 0.657625i | ||||
\(408\) | − | 31.2678i | − | 1.54799i | ||||||
\(409\) | 18.2613 | − | 10.5432i | 0.902962 | − | 0.521326i | 0.0248023 | − | 0.999692i | \(-0.492104\pi\) |
0.878160 | + | 0.478367i | \(0.158771\pi\) | |||||||
\(410\) | −11.1337 | + | 6.42802i | −0.549852 | + | 0.317457i | ||||
\(411\) | − | 17.9136i | − | 0.883612i | ||||||
\(412\) | −17.8847 | − | 30.9771i | −0.881114 | − | 1.52613i | ||||
\(413\) | 3.32992 | − | 5.76759i | 0.163855 | − | 0.283805i | ||||
\(414\) | 1.76250 | + | 1.01758i | 0.0866223 | + | 0.0500114i | ||||
\(415\) | −3.77808 | −0.185458 | ||||||||
\(416\) | −10.4718 | + | 17.4934i | −0.513420 | + | 0.857687i | ||||
\(417\) | 9.77538 | 0.478702 | ||||||||
\(418\) | 7.50516 | + | 4.33311i | 0.367089 | + | 0.211939i | ||||
\(419\) | 20.2471 | − | 35.0690i | 0.989135 | − | 1.71323i | 0.367255 | − | 0.930120i | \(-0.380298\pi\) |
0.621880 | − | 0.783112i | \(-0.286369\pi\) | |||||||
\(420\) | −9.33756 | − | 16.1731i | −0.455626 | − | 0.789168i | ||||
\(421\) | − | 8.67865i | − | 0.422971i | −0.977381 | − | 0.211486i | \(-0.932170\pi\) | ||
0.977381 | − | 0.211486i | \(-0.0678302\pi\) | |||||||
\(422\) | −0.119705 | + | 0.0691118i | −0.00582716 | + | 0.00336431i | ||||
\(423\) | 1.49206 | − | 0.861444i | 0.0725466 | − | 0.0418848i | ||||
\(424\) | − | 12.0567i | − | 0.585525i | ||||||
\(425\) | 12.1513 | + | 21.0467i | 0.589424 | + | 1.02091i | ||||
\(426\) | 19.9038 | − | 34.4744i | 0.964341 | − | 1.67029i | ||||
\(427\) | 39.0257 | + | 22.5315i | 1.88859 | + | 1.09038i | ||||
\(428\) | −30.0093 | −1.45055 | ||||||||
\(429\) | −4.12331 | + | 6.88813i | −0.199075 | + | 0.332562i | ||||
\(430\) | 14.0356 | 0.676858 | ||||||||
\(431\) | −1.59055 | − | 0.918303i | −0.0766140 | − | 0.0442331i | 0.461204 | − | 0.887294i | \(-0.347418\pi\) |
−0.537818 | + | 0.843061i | \(0.680751\pi\) | |||||||
\(432\) | −0.00515407 | + | 0.00892711i | −0.000247975 | + | 0.000429506i | ||||
\(433\) | −8.18383 | − | 14.1748i | −0.393290 | − | 0.681198i | 0.599591 | − | 0.800306i | \(-0.295330\pi\) |
−0.992881 | + | 0.119108i | \(0.961996\pi\) | |||||||
\(434\) | − | 6.84160i | − | 0.328407i | ||||||
\(435\) | 0.370671 | − | 0.214007i | 0.0177723 | − | 0.0102609i | ||||
\(436\) | −6.88600 | + | 3.97563i | −0.329780 | + | 0.190398i | ||||
\(437\) | 9.68635i | 0.463361i | ||||||||
\(438\) | −26.4563 | − | 45.8236i | −1.26413 | − | 2.18954i | ||||
\(439\) | −10.4651 | + | 18.1260i | −0.499471 | + | 0.865109i | −1.00000 | 0.000611071i | \(-0.999805\pi\) | |
0.500529 | + | 0.865720i | \(0.333139\pi\) | |||||||
\(440\) | −3.84106 | − | 2.21764i | −0.183115 | − | 0.105722i | ||||
\(441\) | 0.501298 | 0.0238713 | ||||||||
\(442\) | −26.7765 | − | 48.1182i | −1.27363 | − | 2.28875i | ||||
\(443\) | −8.09774 | −0.384735 | −0.192368 | − | 0.981323i | \(-0.561617\pi\) | ||||
−0.192368 | + | 0.981323i | \(0.561617\pi\) | |||||||
\(444\) | 52.8682 | + | 30.5234i | 2.50901 | + | 1.44858i | ||||
\(445\) | −5.25395 | + | 9.10012i | −0.249061 | + | 0.431387i | ||||
\(446\) | 21.8791 | + | 37.8957i | 1.03600 | + | 1.79441i | ||||
\(447\) | − | 27.4247i | − | 1.29714i | ||||||
\(448\) | −33.5138 | + | 19.3492i | −1.58338 | + | 0.914164i | ||||
\(449\) | −7.84837 | + | 4.53126i | −0.370387 | + | 0.213843i | −0.673628 | − | 0.739071i | \(-0.735265\pi\) |
0.303240 | + | 0.952914i | \(0.401932\pi\) | |||||||
\(450\) | − | 2.15456i | − | 0.101567i | ||||||
\(451\) | 3.24070 | + | 5.61306i | 0.152599 | + | 0.264309i | ||||
\(452\) | 0.283201 | − | 0.490518i | 0.0133206 | − | 0.0230720i | ||||
\(453\) | 19.2459 | + | 11.1116i | 0.904249 | + | 0.522069i | ||||
\(454\) | 3.21504 | 0.150889 | ||||||||
\(455\) | −10.7812 | − | 6.45376i | −0.505432 | − | 0.302557i | ||||
\(456\) | −13.1937 | −0.617850 | ||||||||
\(457\) | −8.70469 | − | 5.02566i | −0.407188 | − | 0.235090i | 0.282393 | − | 0.959299i | \(-0.408872\pi\) |
−0.689581 | + | 0.724209i | \(0.742205\pi\) | |||||||
\(458\) | −3.58507 | + | 6.20953i | −0.167519 | + | 0.290152i | ||||
\(459\) | 18.0046 | + | 31.1848i | 0.840381 | + | 1.45558i | ||||
\(460\) | − | 12.9758i | − | 0.604999i | ||||||
\(461\) | 5.23441 | − | 3.02209i | 0.243791 | − | 0.140753i | −0.373127 | − | 0.927780i | \(-0.621714\pi\) |
0.616918 | + | 0.787028i | \(0.288381\pi\) | |||||||
\(462\) | −13.1923 | + | 7.61660i | −0.613763 | + | 0.354356i | ||||
\(463\) | − | 31.6378i | − | 1.47034i | −0.677885 | − | 0.735168i | \(-0.737103\pi\) | ||
0.677885 | − | 0.735168i | \(-0.262897\pi\) | |||||||
\(464\) | 0.000211856 | 0 | 0.000366946i | 9.83519e−6 | 0 | 1.70350e-5i | ||||
\(465\) | 0.964986 | − | 1.67141i | 0.0447502 | − | 0.0775096i | ||||
\(466\) | 12.7847 | + | 7.38126i | 0.592241 | + | 0.341930i | ||||
\(467\) | 36.2253 | 1.67631 | 0.838154 | − | 0.545433i | \(-0.183635\pi\) | ||||
0.838154 | + | 0.545433i | \(0.183635\pi\) | |||||||
\(468\) | −0.0476681 | + | 3.01700i | −0.00220346 | + | 0.139461i | ||||
\(469\) | −14.3950 | −0.664699 | ||||||||
\(470\) | −15.3917 | − | 8.88642i | −0.709968 | − | 0.409900i | ||||
\(471\) | 3.21692 | − | 5.57187i | 0.148228 | − | 0.256738i | ||||
\(472\) | 3.15144 | + | 5.45846i | 0.145057 | + | 0.251246i | ||||
\(473\) | − | 7.07609i | − | 0.325359i | ||||||
\(474\) | 16.4449 | − | 9.49449i | 0.755341 | − | 0.436097i | ||||
\(475\) | 8.88077 | − | 5.12731i | 0.407478 | − | 0.235257i | ||||
\(476\) | − | 64.5817i | − | 2.96010i | ||||||
\(477\) | 0.550895 | + | 0.954178i | 0.0252237 | + | 0.0436888i | ||||
\(478\) | −18.5486 | + | 32.1272i | −0.848394 | + | 1.46946i | ||||
\(479\) | −18.8047 | − | 10.8569i | −0.859210 | − | 0.496065i | 0.00453787 | − | 0.999990i | \(-0.498556\pi\) |
−0.863748 | + | 0.503925i | \(0.831889\pi\) | |||||||
\(480\) | −10.9134 | −0.498124 | ||||||||
\(481\) | 41.0693 | + | 0.648889i | 1.87260 | + | 0.0295868i | ||||
\(482\) | −8.38745 | −0.382038 | ||||||||
\(483\) | −14.7453 | − | 8.51318i | −0.670932 | − | 0.387363i | ||||
\(484\) | 14.8743 | − | 25.7631i | 0.676105 | − | 1.17105i | ||||
\(485\) | 2.78199 | + | 4.81855i | 0.126324 | + | 0.218799i | ||||
\(486\) | − | 6.13150i | − | 0.278131i | ||||||
\(487\) | 10.4259 | − | 6.01937i | 0.472440 | − | 0.272764i | −0.244820 | − | 0.969568i | \(-0.578729\pi\) |
0.717261 | + | 0.696805i | \(0.245396\pi\) | |||||||
\(488\) | −36.9340 | + | 21.3239i | −1.67192 | + | 0.965286i | ||||
\(489\) | − | 29.3151i | − | 1.32568i | ||||||
\(490\) | −2.58563 | − | 4.47844i | −0.116807 | − | 0.202315i | ||||
\(491\) | −1.96290 | + | 3.39985i | −0.0885846 | + | 0.153433i | −0.906913 | − | 0.421318i | \(-0.861568\pi\) |
0.818328 | + | 0.574751i | \(0.194901\pi\) | |||||||
\(492\) | −22.3675 | − | 12.9139i | −1.00841 | − | 0.582204i | ||||
\(493\) | 1.48014 | 0.0666624 | ||||||||
\(494\) | −20.3037 | + | 11.2985i | −0.913509 | + | 0.508344i | ||||
\(495\) | 0.405313 | 0.0182175 | ||||||||
\(496\) | 0.00165461 | 0.000955288i | 7.42941e−5 | 4.28937e-5i | ||||||
\(497\) | 15.7060 | − | 27.2035i | 0.704508 | − | 1.22024i | ||||
\(498\) | −6.14026 | − | 10.6352i | −0.275152 | − | 0.476576i | ||||
\(499\) | 4.56322i | 0.204278i | 0.994770 | + | 0.102139i | \(0.0325686\pi\) | ||||
−0.994770 | + | 0.102139i | \(0.967431\pi\) | |||||||
\(500\) | −28.2324 | + | 16.3000i | −1.26259 | + | 0.728956i | ||||
\(501\) | −1.40620 | + | 0.811870i | −0.0628244 | + | 0.0362717i | ||||
\(502\) | 70.4998i | 3.14656i | ||||||||
\(503\) | −19.6124 | − | 33.9697i | −0.874474 | − | 1.51463i | −0.857322 | − | 0.514781i | \(-0.827873\pi\) |
−0.0171522 | − | 0.999853i | \(-0.505460\pi\) | |||||||
\(504\) | −1.09371 | + | 1.89437i | −0.0487178 | + | 0.0843817i | ||||
\(505\) | −3.62399 | − | 2.09231i | −0.161265 | − | 0.0931066i | ||||
\(506\) | −10.5843 | −0.470528 | ||||||||
\(507\) | −10.1680 | − | 18.9714i | −0.451575 | − | 0.842549i | ||||
\(508\) | 66.8777 | 2.96722 | ||||||||
\(509\) | −28.4849 | − | 16.4457i | −1.26257 | − | 0.728945i | −0.288998 | − | 0.957330i | \(-0.593322\pi\) |
−0.973571 | + | 0.228385i | \(0.926656\pi\) | |||||||
\(510\) | 14.7380 | − | 25.5270i | 0.652609 | − | 1.13035i | ||||
\(511\) | −20.8765 | − | 36.1591i | −0.923521 | − | 1.59959i | ||||
\(512\) | − | 0.0216157i | − | 0.000955288i | ||||||
\(513\) | 13.1586 | − | 7.59714i | 0.580967 | − | 0.335422i | ||||
\(514\) | 10.0526 | − | 5.80390i | 0.443403 | − | 0.255999i | ||||
\(515\) | − | 12.8824i | − | 0.567668i | ||||||
\(516\) | 14.0988 | + | 24.4198i | 0.620665 | + | 1.07502i | ||||
\(517\) | −4.48011 | + | 7.75978i | −0.197035 | + | 0.341275i | ||||
\(518\) | 67.4976 | + | 38.9698i | 2.96568 | + | 1.71223i | ||||
\(519\) | 15.6557 | 0.687207 | ||||||||
\(520\) | 10.3912 | − | 5.78246i | 0.455686 | − | 0.253578i | ||||
\(521\) | −8.31125 | −0.364122 | −0.182061 | − | 0.983287i | \(-0.558277\pi\) | ||||
−0.182061 | + | 0.983287i | \(0.558277\pi\) | |||||||
\(522\) | −0.113643 | − | 0.0656116i | −0.00497400 | − | 0.00287174i | ||||
\(523\) | 0.0865411 | − | 0.149894i | 0.00378418 | − | 0.00655439i | −0.864127 | − | 0.503274i | \(-0.832129\pi\) |
0.867911 | + | 0.496719i | \(0.165462\pi\) | |||||||
\(524\) | −1.91494 | − | 3.31677i | −0.0836544 | − | 0.144894i | ||||
\(525\) | 18.0253i | 0.786687i | ||||||||
\(526\) | 21.6872 | − | 12.5211i | 0.945609 | − | 0.545947i | ||||
\(527\) | 5.77999 | − | 3.33708i | 0.251781 | − | 0.145366i | ||||
\(528\) | − | 0.00425400i | − | 0.000185132i | ||||||
\(529\) | 5.58490 | + | 9.67334i | 0.242822 | + | 0.420580i | ||||
\(530\) | 5.68289 | − | 9.84305i | 0.246849 | − | 0.427555i | ||||
\(531\) | −0.498816 | − | 0.287991i | −0.0216468 | − | 0.0124978i | ||||
\(532\) | −27.2506 | −1.18146 | ||||||||
\(533\) | −17.3757 | − | 0.274533i | −0.752624 | − | 0.0118913i | ||||
\(534\) | −34.1556 | −1.47806 | ||||||||
\(535\) | −9.35996 | − | 5.40397i | −0.404666 | − | 0.233634i | ||||
\(536\) | 6.81172 | − | 11.7983i | 0.294222 | − | 0.509607i | ||||
\(537\) | 6.81715 | + | 11.8076i | 0.294182 | + | 0.509538i | ||||
\(538\) | 8.04037i | 0.346645i | ||||||||
\(539\) | −2.25782 | + | 1.30355i | −0.0972510 | + | 0.0561479i | ||||
\(540\) | −17.6272 | + | 10.1771i | −0.758555 | + | 0.437952i | ||||
\(541\) | 35.6501i | 1.53272i | 0.642413 | + | 0.766359i | \(0.277934\pi\) | ||||
−0.642413 | + | 0.766359i | \(0.722066\pi\) | |||||||
\(542\) | 22.4224 | + | 38.8367i | 0.963124 | + | 1.66818i | ||||
\(543\) | −4.44050 | + | 7.69118i | −0.190560 | + | 0.330060i | ||||
\(544\) | −32.6840 | − | 18.8701i | −1.40131 | − | 0.809048i | ||||
\(545\) | −2.86368 | −0.122667 | ||||||||
\(546\) | 0.645232 | − | 40.8379i | 0.0276134 | − | 1.74770i | ||||
\(547\) | −29.6538 | −1.26791 | −0.633953 | − | 0.773371i | \(-0.718569\pi\) | ||||
−0.633953 | + | 0.773371i | \(0.718569\pi\) | |||||||
\(548\) | 30.3249 | + | 17.5081i | 1.29542 | + | 0.747909i | ||||
\(549\) | 1.94866 | − | 3.37518i | 0.0831668 | − | 0.144049i | ||||
\(550\) | 5.60262 | + | 9.70402i | 0.238896 | + | 0.413781i | ||||
\(551\) | − | 0.624556i | − | 0.0266070i | ||||||
\(552\) | 13.9549 | − | 8.05688i | 0.593961 | − | 0.342924i | ||||
\(553\) | 12.9766 | − | 7.49205i | 0.551821 | − | 0.318594i | ||||
\(554\) | 24.8265i | 1.05478i | ||||||||
\(555\) | 10.9931 | + | 19.0407i | 0.466632 | + | 0.808231i | ||||
\(556\) | −9.55411 | + | 16.5482i | −0.405185 | + | 0.701800i | ||||
\(557\) | −7.74827 | − | 4.47347i | −0.328305 | − | 0.189547i | 0.326783 | − | 0.945099i | \(-0.394035\pi\) |
−0.655088 | + | 0.755552i | \(0.727369\pi\) | |||||||
\(558\) | −0.591702 | −0.0250488 | ||||||||
\(559\) | 16.2786 | + | 9.74454i | 0.688511 | + | 0.412150i | ||||
\(560\) | 0.00665832 | 0.000281365 | ||||||||
\(561\) | −12.8695 | − | 7.43019i | −0.543350 | − | 0.313703i | ||||
\(562\) | 5.93200 | − | 10.2745i | 0.250226 | − | 0.433404i | ||||
\(563\) | −5.71183 | − | 9.89317i | −0.240725 | − | 0.416948i | 0.720196 | − | 0.693770i | \(-0.244052\pi\) |
−0.960921 | + | 0.276823i | \(0.910718\pi\) | |||||||
\(564\) | − | 35.7057i | − | 1.50348i | ||||||
\(565\) | 0.176662 | − | 0.101996i | 0.00743222 | − | 0.00429099i | ||||
\(566\) | −33.9122 | + | 19.5792i | −1.42544 | + | 0.822976i | ||||
\(567\) | 24.3888i | 1.02423i | ||||||||
\(568\) | 14.8641 | + | 25.7454i | 0.623685 | + | 1.08025i | ||||
\(569\) | −7.00352 | + | 12.1304i | −0.293603 | + | 0.508535i | −0.974659 | − | 0.223696i | \(-0.928188\pi\) |
0.681056 | + | 0.732231i | \(0.261521\pi\) | |||||||
\(570\) | −10.7713 | − | 6.21879i | −0.451158 | − | 0.260476i | ||||
\(571\) | 36.2259 | 1.51601 | 0.758004 | − | 0.652250i | \(-0.226175\pi\) | ||||
0.758004 | + | 0.652250i | \(0.226175\pi\) | |||||||
\(572\) | −7.63057 | − | 13.7123i | −0.319050 | − | 0.573342i | ||||
\(573\) | −25.0281 | −1.04556 | ||||||||
\(574\) | −28.5570 | − | 16.4874i | −1.19195 | − | 0.688170i | ||||
\(575\) | −6.26212 | + | 10.8463i | −0.261149 | + | 0.452323i | ||||
\(576\) | 1.67343 | + | 2.89847i | 0.0697264 | + | 0.120770i | ||||
\(577\) | 34.5709i | 1.43920i | 0.694387 | + | 0.719602i | \(0.255676\pi\) | ||||
−0.694387 | + | 0.719602i | \(0.744324\pi\) | |||||||
\(578\) | 54.5865 | − | 31.5155i | 2.27050 | − | 1.31087i | ||||
\(579\) | −12.5995 | + | 7.27432i | −0.523617 | + | 0.302310i | ||||
\(580\) | 0.836652i | 0.0347401i | ||||||||
\(581\) | −4.84524 | − | 8.39220i | −0.201014 | − | 0.348167i | ||||
\(582\) | −9.04278 | + | 15.6626i | −0.374835 | + | 0.649234i | ||||
\(583\) | −4.96240 | − | 2.86504i | −0.205521 | − | 0.118658i | ||||
\(584\) | 39.5151 | 1.63514 | ||||||||
\(585\) | −0.558160 | + | 0.932425i | −0.0230771 | + | 0.0385510i | ||||
\(586\) | 41.5940 | 1.71823 | ||||||||
\(587\) | 6.53643 | + | 3.77381i | 0.269787 | + | 0.155762i | 0.628791 | − | 0.777574i | \(-0.283550\pi\) |
−0.359004 | + | 0.933336i | \(0.616883\pi\) | |||||||
\(588\) | 5.19453 | − | 8.99719i | 0.214219 | − | 0.371038i | ||||
\(589\) | −1.40810 | − | 2.43890i | −0.0580198 | − | 0.100493i | ||||
\(590\) | 5.94169i | 0.244615i | ||||||||
\(591\) | −31.2662 | + | 18.0515i | −1.28612 | + | 0.742541i | ||||
\(592\) | −0.0188493 | + | 0.0108826i | −0.000774701 | + | 0.000447274i | ||||
\(593\) | − | 26.2214i | − | 1.07678i | −0.842695 | − | 0.538391i | \(-0.819032\pi\) | ||
0.842695 | − | 0.538391i | \(-0.180968\pi\) | |||||||
\(594\) | 8.30139 | + | 14.3784i | 0.340610 | + | 0.589954i | ||||
\(595\) | 11.6297 | − | 20.1432i | 0.476770 | − | 0.825789i | ||||
\(596\) | 46.4258 | + | 26.8039i | 1.90167 | + | 1.09793i | ||||
\(597\) | 19.2984 | 0.789832 | ||||||||
\(598\) | 14.5757 | − | 24.3492i | 0.596044 | − | 0.995712i | ||||
\(599\) | −7.99098 | −0.326503 | −0.163251 | − | 0.986585i | \(-0.552198\pi\) | ||||
−0.163251 | + | 0.986585i | \(0.552198\pi\) | |||||||
\(600\) | −14.7736 | − | 8.52956i | −0.603131 | − | 0.348218i | ||||
\(601\) | 5.55772 | − | 9.62625i | 0.226704 | − | 0.392663i | −0.730125 | − | 0.683313i | \(-0.760538\pi\) |
0.956829 | + | 0.290650i | \(0.0938717\pi\) | |||||||
\(602\) | 18.0002 | + | 31.1772i | 0.733632 | + | 1.27069i | ||||
\(603\) | 1.24497i | 0.0506989i | ||||||||
\(604\) | −37.6204 | + | 21.7202i | −1.53075 | + | 0.883781i | ||||
\(605\) | 9.27866 | − | 5.35704i | 0.377231 | − | 0.217795i | ||||
\(606\) | − | 13.6020i | − | 0.552543i | ||||||
\(607\) | 12.0145 | + | 20.8097i | 0.487652 | + | 0.844638i | 0.999899 | − | 0.0142002i | \(-0.00452023\pi\) |
−0.512247 | + | 0.858838i | \(0.671187\pi\) | |||||||
\(608\) | −7.96235 | + | 13.7912i | −0.322916 | + | 0.559307i | ||||
\(609\) | 0.950744 | + | 0.548913i | 0.0385261 | + | 0.0222431i | ||||
\(610\) | −40.2037 | −1.62780 | ||||||||
\(611\) | −11.6818 | − | 20.9926i | −0.472596 | − | 0.849269i | ||||
\(612\) | −5.58541 | −0.225777 | ||||||||
\(613\) | −6.83888 | − | 3.94843i | −0.276220 | − | 0.159476i | 0.355491 | − | 0.934680i | \(-0.384314\pi\) |
−0.631711 | + | 0.775204i | \(0.717647\pi\) | |||||||
\(614\) | −3.08726 | + | 5.34729i | −0.124592 | + | 0.215799i | ||||
\(615\) | −4.65099 | − | 8.05575i | −0.187546 | − | 0.324839i | ||||
\(616\) | − | 11.3761i | − | 0.458358i | ||||||
\(617\) | 38.0117 | − | 21.9461i | 1.53030 | − | 0.883516i | 0.530947 | − | 0.847405i | \(-0.321836\pi\) |
0.999348 | − | 0.0361115i | \(-0.0114972\pi\) | |||||||
\(618\) | 36.2639 | − | 20.9370i | 1.45875 | − | 0.842209i | ||||
\(619\) | 24.5974i | 0.988653i | 0.869276 | + | 0.494326i | \(0.164585\pi\) | ||||
−0.869276 | + | 0.494326i | \(0.835415\pi\) | |||||||
\(620\) | 1.88629 | + | 3.26714i | 0.0757551 | + | 0.131212i | ||||
\(621\) | −9.27858 | + | 16.0710i | −0.372337 | + | 0.644906i | ||||
\(622\) | −63.6204 | − | 36.7313i | −2.55095 | − | 1.47279i | ||||
\(623\) | −26.9520 | −1.07981 | ||||||||
\(624\) | 0.00978635 | + | 0.00585822i | 0.000391768 | + | 0.000234516i | ||||
\(625\) | 6.46549 | 0.258620 | ||||||||
\(626\) | 54.6474 | + | 31.5507i | 2.18415 | + | 1.26102i | ||||
\(627\) | −3.13522 | + | 5.43035i | −0.125208 | + | 0.216867i | ||||
\(628\) | 6.28821 | + | 10.8915i | 0.250927 | + | 0.434618i | ||||
\(629\) | 76.0321i | 3.03160i | ||||||||
\(630\) | −1.78581 | + | 1.03104i | −0.0711482 | + | 0.0410774i | ||||
\(631\) | 18.7540 | − | 10.8276i | 0.746583 | − | 0.431040i | −0.0778749 | − | 0.996963i | \(-0.524813\pi\) |
0.824458 | + | 0.565923i | \(0.191480\pi\) | |||||||
\(632\) | 14.1810i | 0.564089i | ||||||||
\(633\) | −0.0500058 | − | 0.0866126i | −0.00198755 | − | 0.00344254i | ||||
\(634\) | −36.4160 | + | 63.0744i | −1.44627 | + | 2.50501i | ||||
\(635\) | 20.8593 | + | 12.0431i | 0.827776 | + | 0.477917i | ||||
\(636\) | 22.8339 | 0.905421 | ||||||||
\(637\) | 0.110429 | − | 6.98925i | 0.00437535 | − | 0.276924i | ||||
\(638\) | 0.682453 | 0.0270186 | ||||||||
\(639\) | −2.35272 | − | 1.35834i | −0.0930722 | − | 0.0537353i | ||||
\(640\) | 10.6714 | − | 18.4834i | 0.421825 | − | 0.730622i | ||||
\(641\) | −9.16018 | − | 15.8659i | −0.361806 | − | 0.626666i | 0.626453 | − | 0.779460i | \(-0.284506\pi\) |
−0.988258 | + | 0.152794i | \(0.951173\pi\) | |||||||
\(642\) | − | 35.1309i | − | 1.38651i | ||||||
\(643\) | −30.3463 | + | 17.5204i | −1.19674 | + | 0.690938i | −0.959827 | − | 0.280593i | \(-0.909469\pi\) |
−0.236913 | + | 0.971531i | \(0.576136\pi\) | |||||||
\(644\) | 28.8230 | − | 16.6410i | 1.13578 | − | 0.655746i | ||||
\(645\) | 10.1555i | 0.399871i | ||||||||
\(646\) | −21.5056 | − | 37.2488i | −0.846126 | − | 1.46553i | ||||
\(647\) | −7.54305 | + | 13.0649i | −0.296548 | + | 0.513636i | −0.975344 | − | 0.220691i | \(-0.929169\pi\) |
0.678796 | + | 0.734327i | \(0.262502\pi\) | |||||||
\(648\) | −19.9892 | − | 11.5408i | −0.785252 | − | 0.453365i | ||||
\(649\) | 2.99551 | 0.117584 | ||||||||
\(650\) | −30.0396 | − | 0.474620i | −1.17825 | − | 0.0186161i | ||||
\(651\) | 4.95023 | 0.194015 | ||||||||
\(652\) | 49.6260 | + | 28.6516i | 1.94350 | + | 1.12208i | ||||
\(653\) | 0.340523 | − | 0.589803i | 0.0133257 | − | 0.0230808i | −0.859286 | − | 0.511496i | \(-0.829092\pi\) |
0.872611 | + | 0.488415i | \(0.162425\pi\) | |||||||
\(654\) | −4.65415 | − | 8.06122i | −0.181992 | − | 0.315219i | ||||
\(655\) | − | 1.37934i | − | 0.0538954i | ||||||
\(656\) | 0.00797479 | − | 0.00460425i | 0.000311363 | − | 0.000179766i | ||||
\(657\) | −3.12726 | + | 1.80552i | −0.122006 | + | 0.0704401i | ||||
\(658\) | − | 45.5860i | − | 1.77713i | ||||||
\(659\) | −10.3238 | − | 17.8813i | −0.402158 | − | 0.696558i | 0.591828 | − | 0.806064i | \(-0.298406\pi\) |
−0.993986 | + | 0.109506i | \(0.965073\pi\) | |||||||
\(660\) | 4.19992 | − | 7.27447i | 0.163482 | − | 0.283159i | ||||
\(661\) | −22.0214 | − | 12.7141i | −0.856535 | − | 0.494521i | 0.00631539 | − | 0.999980i | \(-0.497990\pi\) |
−0.862850 | + | 0.505459i | \(0.831323\pi\) | |||||||
\(662\) | −37.1345 | −1.44327 | ||||||||
\(663\) | 34.8158 | − | 19.3741i | 1.35214 | − | 0.752429i | ||||
\(664\) | 9.17108 | 0.355907 | ||||||||
\(665\) | −8.49953 | − | 4.90721i | −0.329598 | − | 0.190293i | ||||
\(666\) | 3.37034 | − | 5.83760i | 0.130598 | − | 0.226202i | ||||
\(667\) | 0.381393 | + | 0.660593i | 0.0147676 | + | 0.0255783i | ||||
\(668\) | − | 3.17397i | − | 0.122805i | ||||||
\(669\) | −27.4194 | + | 15.8306i | −1.06009 | + | 0.612046i | ||||
\(670\) | 11.1221 | − | 6.42136i | 0.429685 | − | 0.248079i | ||||
\(671\) | 20.2688i | 0.782468i | ||||||||
\(672\) | −13.9960 | − | 24.2417i | −0.539906 | − | 0.935145i | ||||
\(673\) | −7.53163 | + | 13.0452i | −0.290323 | + | 0.502854i | −0.973886 | − | 0.227037i | \(-0.927096\pi\) |
0.683563 | + | 0.729892i | \(0.260429\pi\) | |||||||
\(674\) | 71.0824 | + | 41.0394i | 2.73799 | + | 1.58078i | ||||
\(675\) | 19.6459 | 0.756170 | ||||||||
\(676\) | 42.0534 | + | 1.32921i | 1.61744 | + | 0.0511233i | ||||
\(677\) | 13.4298 | 0.516150 | 0.258075 | − | 0.966125i | \(-0.416912\pi\) | ||||
0.258075 | + | 0.966125i | \(0.416912\pi\) | |||||||
\(678\) | 0.574233 | + | 0.331534i | 0.0220533 | + | 0.0127325i | ||||
\(679\) | −7.13561 | + | 12.3592i | −0.273839 | + | 0.474304i | ||||
\(680\) | 11.0063 | + | 19.0635i | 0.422073 | + | 0.731052i | ||||
\(681\) | 2.32624i | 0.0891416i | ||||||||
\(682\) | 2.66499 | − | 1.53863i | 0.102048 | − | 0.0589173i | ||||
\(683\) | −19.2876 | + | 11.1357i | −0.738020 | + | 0.426096i | −0.821349 | − | 0.570426i | \(-0.806778\pi\) |
0.0833292 | + | 0.996522i | \(0.473445\pi\) | |||||||
\(684\) | 2.35680i | 0.0901144i | ||||||||
\(685\) | 6.30561 | + | 10.9216i | 0.240925 | + | 0.417294i | ||||
\(686\) | −17.3137 | + | 29.9881i | −0.661039 | + | 1.14495i | ||||
\(687\) | −4.49290 | − | 2.59398i | −0.171415 | − | 0.0989664i | ||||
\(688\) | −0.0100534 | −0.000383282 | ||||||||
\(689\) | 13.4248 | − | 7.47055i | 0.511444 | − | 0.284605i | ||||
\(690\) | 15.1903 | 0.578286 | ||||||||
\(691\) | 15.6005 | + | 9.00694i | 0.593470 | + | 0.342640i | 0.766468 | − | 0.642282i | \(-0.222012\pi\) |
−0.172998 | + | 0.984922i | \(0.555346\pi\) | |||||||
\(692\) | −15.3013 | + | 26.5026i | −0.581668 | + | 1.00748i | ||||
\(693\) | 0.519799 | + | 0.900318i | 0.0197455 | + | 0.0342003i | ||||
\(694\) | 54.5442i | 2.07047i | ||||||||
\(695\) | −5.95990 | + | 3.44095i | −0.226072 | + | 0.130523i | ||||
\(696\) | −0.899786 | + | 0.519492i | −0.0341063 | + | 0.0196913i | ||||
\(697\) | − | 32.1678i | − | 1.21844i | ||||||
\(698\) | 40.3316 | + | 69.8563i | 1.52657 | + | 2.64410i | ||||
\(699\) | −5.34070 | + | 9.25037i | −0.202004 | + | 0.349881i | ||||
\(700\) | −30.5140 | − | 17.6172i | −1.15332 | − | 0.665869i | ||||
\(701\) | −12.1690 | −0.459617 | −0.229809 | − | 0.973236i | \(-0.573810\pi\) | ||||
−0.229809 | + | 0.973236i | \(0.573810\pi\) | |||||||
\(702\) | −44.5096 | − | 0.703244i | −1.67991 | − | 0.0265422i | ||||
\(703\) | 32.0822 | 1.21000 | ||||||||
\(704\) | −15.0741 | − | 8.70303i | −0.568126 | − | 0.328008i | ||||
\(705\) | 6.42976 | − | 11.1367i | 0.242159 | − | 0.419432i | ||||
\(706\) | −24.1814 | − | 41.8835i | −0.910080 | − | 1.57631i | ||||
\(707\) | − | 10.7332i | − | 0.403665i | ||||||
\(708\) | −10.3376 | + | 5.96843i | −0.388512 | + | 0.224307i | ||||
\(709\) | −17.8614 | + | 10.3123i | −0.670800 | + | 0.387287i | −0.796380 | − | 0.604797i | \(-0.793254\pi\) |
0.125579 | + | 0.992084i | \(0.459921\pi\) | |||||||
\(710\) | 28.0246i | 1.05175i | ||||||||
\(711\) | −0.647957 | − | 1.12229i | −0.0243003 | − | 0.0420893i | ||||
\(712\) | 12.7537 | − | 22.0901i | 0.477965 | − | 0.827860i | ||||
\(713\) | 2.97870 | + | 1.71975i | 0.111553 | + | 0.0644052i | ||||
\(714\) | 75.6037 | 2.82940 | ||||||||
\(715\) | 0.0892848 | − | 5.65100i | 0.00333906 | − | 0.211335i | ||||
\(716\) | −26.6514 | −0.996008 | ||||||||
\(717\) | −23.2456 | − | 13.4208i | −0.868122 | − | 0.501210i | ||||
\(718\) | 14.5661 | − | 25.2292i | 0.543601 | − | 0.941545i | ||||
\(719\) | −14.6427 | − | 25.3618i | −0.546079 | − | 0.945837i | −0.998538 | − | 0.0540515i | \(-0.982786\pi\) |
0.452459 | − | 0.891785i | \(-0.350547\pi\) | |||||||
\(720\) | 0 | 0.000575851i | 0 | 2.14607e-5i | ||||||
\(721\) | 28.6157 | − | 16.5213i | 1.06570 | − | 0.615284i | ||||
\(722\) | 21.9361 | − | 12.6648i | 0.816377 | − | 0.471335i | ||||
\(723\) | − | 6.06873i | − | 0.225699i | ||||||
\(724\) | −8.67998 | − | 15.0342i | −0.322589 | − | 0.558741i | ||||
\(725\) | 0.403769 | − | 0.699349i | 0.0149956 | − | 0.0259732i | ||||
\(726\) | 30.1600 | + | 17.4129i | 1.11934 | + | 0.646253i | ||||
\(727\) | 4.82505 | 0.178951 | 0.0894756 | − | 0.995989i | \(-0.471481\pi\) | ||||
0.0894756 | + | 0.995989i | \(0.471481\pi\) | |||||||
\(728\) | 26.1709 | + | 15.6662i | 0.969958 | + | 0.580627i | ||||
\(729\) | 28.9087 | 1.07069 | ||||||||
\(730\) | 32.2599 | + | 18.6253i | 1.19399 | + | 0.689353i | ||||
\(731\) | −17.5596 | + | 30.4142i | −0.649467 | + | 1.12491i | ||||
\(732\) | −40.3847 | − | 69.9483i | −1.49266 | − | 2.58536i | ||||
\(733\) | 5.74059i | 0.212033i | 0.994364 | + | 0.106017i | \(0.0338097\pi\) | ||||
−0.994364 | + | 0.106017i | \(0.966190\pi\) | |||||||
\(734\) | 42.9030 | − | 24.7701i | 1.58358 | − | 0.914279i | ||||
\(735\) | 3.24037 | − | 1.87083i | 0.119523 | − | 0.0690066i | ||||
\(736\) | − | 19.4493i | − | 0.716909i | ||||||
\(737\) | −3.23735 | − | 5.60725i | −0.119249 | − | 0.206546i | ||||
\(738\) | −1.42593 | + | 2.46978i | −0.0524891 | + | 0.0909138i | ||||
\(739\) | 0.304004 | + | 0.175517i | 0.0111830 | + | 0.00645648i | 0.505581 | − | 0.862779i | \(-0.331278\pi\) |
−0.494398 | + | 0.869236i | \(0.664611\pi\) | |||||||
\(740\) | −42.9772 | −1.57987 | ||||||||
\(741\) | −8.17503 | − | 14.6908i | −0.300317 | − | 0.539679i | ||||
\(742\) | 29.1524 | 1.07022 | ||||||||
\(743\) | 43.3990 | + | 25.0564i | 1.59216 | + | 0.919231i | 0.992937 | + | 0.118646i | \(0.0378554\pi\) |
0.599219 | + | 0.800585i | \(0.295478\pi\) | |||||||
\(744\) | −2.34245 | + | 4.05725i | −0.0858785 | + | 0.148746i | ||||
\(745\) | 9.65353 | + | 16.7204i | 0.353678 | + | 0.612589i | ||||
\(746\) | − | 64.6479i | − | 2.36693i | ||||||
\(747\) | −0.725808 | + | 0.419045i | −0.0265559 | + | 0.0153321i | ||||
\(748\) | 25.1563 | − | 14.5240i | 0.919807 | − | 0.531051i | ||||
\(749\) | − | 27.7216i | − | 1.01292i | ||||||
\(750\) | −19.0818 | − | 33.0507i | −0.696770 | − | 1.20684i | ||||
\(751\) | −10.1842 | + | 17.6395i | −0.371625 | + | 0.643674i | −0.989816 | − | 0.142355i | \(-0.954533\pi\) |
0.618191 | + | 0.786028i | \(0.287866\pi\) | |||||||
\(752\) | 0.0110248 | + | 0.00636514i | 0.000402031 | + | 0.000232113i | ||||
\(753\) | −51.0101 | −1.85891 | ||||||||
\(754\) | −0.939811 | + | 1.56999i | −0.0342259 | + | 0.0571755i | ||||
\(755\) | −15.6452 | −0.569387 | ||||||||
\(756\) | −45.2125 | − | 26.1035i | −1.64436 | − | 0.949374i | ||||
\(757\) | 4.56723 | − | 7.91068i | 0.165999 | − | 0.287519i | −0.771011 | − | 0.636822i | \(-0.780249\pi\) |
0.937010 | + | 0.349304i | \(0.113582\pi\) | |||||||
\(758\) | −33.7710 | − | 58.4931i | −1.22662 | − | 2.12457i | ||||
\(759\) | − | 7.65824i | − | 0.277977i | ||||||
\(760\) | 8.04397 | − | 4.64419i | 0.291785 | − | 0.168462i | ||||
\(761\) | 27.6201 | − | 15.9465i | 1.00123 | − | 0.578058i | 0.0926156 | − | 0.995702i | \(-0.470477\pi\) |
0.908611 | + | 0.417643i | \(0.137144\pi\) | |||||||
\(762\) | 78.2916i | 2.83621i | ||||||||
\(763\) | −3.67256 | − | 6.36106i | −0.132956 | − | 0.230286i | ||||
\(764\) | 24.4616 | − | 42.3687i | 0.884989 | − | 1.53285i | ||||
\(765\) | −1.74210 | − | 1.00580i | −0.0629858 | − | 0.0363649i | ||||
\(766\) | −65.5750 | −2.36932 | ||||||||
\(767\) | −4.12515 | + | 6.89120i | −0.148950 | + | 0.248827i | ||||
\(768\) | 26.5121 | 0.956672 | ||||||||
\(769\) | −28.5537 | − | 16.4855i | −1.02967 | − | 0.594482i | −0.112782 | − | 0.993620i | \(-0.535976\pi\) |
−0.916891 | + | 0.399138i | \(0.869310\pi\) | |||||||
\(770\) | 5.36211 | − | 9.28744i | 0.193237 | − | 0.334696i | ||||
\(771\) | 4.19940 | + | 7.27358i | 0.151238 | + | 0.261952i | ||||
\(772\) | − | 28.4386i | − | 1.02353i | ||||||
\(773\) | −14.5948 | + | 8.42632i | −0.524939 | + | 0.303074i | −0.738953 | − | 0.673757i | \(-0.764680\pi\) |
0.214014 | + | 0.976831i | \(0.431346\pi\) | |||||||
\(774\) | 2.69639 | − | 1.55676i | 0.0969197 | − | 0.0559566i | ||||
\(775\) | − | 3.64129i | − | 0.130799i | ||||||
\(776\) | −6.75315 | − | 11.6968i | −0.242424 | − | 0.419890i | ||||
\(777\) | −28.1966 | + | 48.8379i | −1.01155 | + | 1.75205i | ||||
\(778\) | −42.5783 | − | 24.5826i | −1.52651 | − | 0.881329i | ||||
\(779\) | −13.5734 | −0.486317 | ||||||||
\(780\) | 10.9512 | + | 19.6797i | 0.392117 | + | 0.704645i | ||||
\(781\) | 14.1287 | 0.505564 | ||||||||
\(782\) | 45.4929 | + | 26.2653i | 1.62682 | + | 0.939247i | ||||
\(783\) | 0.598264 | − | 1.03622i | 0.0213802 | − | 0.0370316i | ||||
\(784\) | 0.00185203 | + | 0.00320780i | 6.61438e−5 | + | 0.000114564i | ||||
\(785\) | 4.52944i | 0.161663i | ||||||||
\(786\) | 3.88283 | − | 2.24176i | 0.138496 | − | 0.0799608i | ||||
\(787\) | 27.8310 | − | 16.0682i | 0.992067 | − | 0.572770i | 0.0861756 | − | 0.996280i | \(-0.472535\pi\) |
0.905892 | + | 0.423510i | \(0.139202\pi\) | |||||||
\(788\) | − | 70.5717i | − | 2.51401i | ||||||
\(789\) | 9.05966 | + | 15.6918i | 0.322532 | + | 0.558642i | ||||
\(790\) | −6.68415 | + | 11.5773i | −0.237811 | + | 0.411901i | ||||
\(791\) | 0.453124 | + | 0.261611i | 0.0161112 | + | 0.00930183i | ||||
\(792\) | −0.983877 | −0.0349605 | ||||||||
\(793\) | −46.6285 | − | 27.9123i | −1.65583 | − | 0.991195i | ||||
\(794\) | 15.8917 | 0.563975 | ||||||||
\(795\) | 7.12193 | + | 4.11185i | 0.252589 | + | 0.145832i | ||||
\(796\) | −18.8616 | + | 32.6692i | −0.668531 | + | 1.15793i | ||||
\(797\) | 9.16399 | + | 15.8725i | 0.324605 | + | 0.562233i | 0.981432 | − | 0.191808i | \(-0.0614352\pi\) |
−0.656827 | + | 0.754041i | \(0.728102\pi\) | |||||||
\(798\) | − | 31.9014i | − | 1.12930i | ||||||
\(799\) | 38.5125 | − | 22.2352i | 1.36247 | − | 0.786624i | ||||
\(800\) | −17.8317 | + | 10.2952i | −0.630447 | + | 0.363989i | ||||
\(801\) | 2.33097i | 0.0823607i | ||||||||
\(802\) | −39.3144 | − | 68.0945i | −1.38824 | − | 2.40450i | ||||
\(803\) | 9.38998 | − | 16.2639i | 0.331365 | − | 0.573941i | ||||
\(804\) | 22.3444 | + | 12.9005i | 0.788025 | + | 0.454967i | ||||
\(805\) | 11.9866 | 0.422472 | ||||||||
\(806\) | −0.130344 | + | 8.24969i | −0.00459116 | + | 0.290583i | ||||
\(807\) | −5.81761 | −0.204789 | ||||||||
\(808\) | 8.79704 | + | 5.07898i | 0.309479 | + | 0.178678i | ||||
\(809\) | 25.3257 | − | 43.8654i | 0.890404 | − | 1.54222i | 0.0510120 | − | 0.998698i | \(-0.483755\pi\) |
0.839392 | − | 0.543527i | \(-0.182911\pi\) | |||||||
\(810\) | −10.8794 | − | 18.8437i | −0.382264 | − | 0.662101i | ||||
\(811\) | − | 15.5125i | − | 0.544716i | −0.962196 | − | 0.272358i | \(-0.912197\pi\) | ||
0.962196 | − | 0.272358i | \(-0.0878035\pi\) | |||||||
\(812\) | −1.85845 | + | 1.07298i | −0.0652187 | + | 0.0376541i | ||||
\(813\) | −28.1003 | + | 16.2237i | −0.985520 | + | 0.568990i | ||||
\(814\) | 35.0563i | 1.22872i | ||||||||
\(815\) | 10.3190 | + | 17.8730i | 0.361458 | + | 0.626063i | ||||
\(816\) | −0.0105565 | + | 0.0182844i | −0.000369551 | + | 0.000640081i | ||||
\(817\) | 12.8334 | + | 7.40939i | 0.448986 | + | 0.259222i | ||||
\(818\) | −48.2526 | −1.68711 | ||||||||
\(819\) | −2.78701 | − | 0.0440342i | −0.0973859 | − | 0.00153868i | ||||
\(820\) | 18.1828 | 0.634973 | ||||||||
\(821\) | 6.23630 | + | 3.60053i | 0.217648 | + | 0.125659i | 0.604861 | − | 0.796331i | \(-0.293229\pi\) |
−0.387213 | + | 0.921990i | \(0.626562\pi\) | |||||||
\(822\) | −20.4962 | + | 35.5004i | −0.714886 | + | 1.23822i | ||||
\(823\) | −17.4515 | − | 30.2269i | −0.608321 | − | 1.05364i | −0.991517 | − | 0.129976i | \(-0.958510\pi\) |
0.383196 | − | 0.923667i | \(-0.374823\pi\) | |||||||
\(824\) | 31.2715i | 1.08939i | ||||||||
\(825\) | −7.02133 | + | 4.05377i | −0.244451 | + | 0.141134i | ||||
\(826\) | −13.1982 | + | 7.61999i | −0.459224 | + | 0.265133i | ||||
\(827\) | 15.2492i | 0.530267i | 0.964212 | + | 0.265134i | \(0.0854161\pi\) | ||||
−0.964212 | + | 0.265134i | \(0.914584\pi\) | |||||||
\(828\) | −1.43921 | − | 2.49278i | −0.0500160 | − | 0.0866302i | ||||
\(829\) | 7.29608 | − | 12.6372i | 0.253403 | − | 0.438907i | −0.711057 | − | 0.703134i | \(-0.751783\pi\) |
0.964461 | + | 0.264227i | \(0.0851167\pi\) | |||||||
\(830\) | 7.48724 | + | 4.32276i | 0.259886 | + | 0.150045i | ||||
\(831\) | −17.9632 | −0.623136 | ||||||||
\(832\) | 40.7800 | − | 22.6930i | 1.41379 | − | 0.786739i | ||||
\(833\) | 12.9393 | 0.448319 | ||||||||
\(834\) | −19.3725 | − | 11.1847i | −0.670813 | − | 0.387294i | ||||
\(835\) | 0.571559 | − | 0.989969i | 0.0197796 | − | 0.0342593i | ||||
\(836\) | −6.12850 | − | 10.6149i | −0.211958 | − | 0.367123i | ||||
\(837\) | − | 5.39530i | − | 0.186489i | ||||||
\(838\) | −80.2498 | + | 46.3322i | −2.77218 | + | 1.60052i | ||||
\(839\) | 7.25814 | − | 4.19049i | 0.250579 | − | 0.144672i | −0.369450 | − | 0.929250i | \(-0.620454\pi\) |
0.620029 | + | 0.784579i | \(0.287121\pi\) | |||||||
\(840\) | 16.3268i | 0.563328i | ||||||||
\(841\) | 14.4754 | + | 25.0721i | 0.499152 | + | 0.864557i | ||||
\(842\) | −9.92984 | + | 17.1990i | −0.342205 | + | 0.592716i | ||||
\(843\) | 7.43412 | + | 4.29209i | 0.256045 | + | 0.147827i | ||||
\(844\) | 0.195496 | 0.00672924 | ||||||||
\(845\) | 12.8772 | + | 7.98743i | 0.442989 | + | 0.274776i | ||||
\(846\) | −3.94255 | −0.135548 | ||||||||
\(847\) | 23.7991 | + | 13.7404i | 0.817746 | + | 0.472126i | ||||
\(848\) | −0.00407052 | + | 0.00705035i | −0.000139782 | + | 0.000242110i | ||||
\(849\) | −14.1665 | − | 24.5371i | −0.486194 | − | 0.842112i | ||||
\(850\) | − | 55.6126i | − | 1.90750i | ||||||
\(851\) | −33.9334 | + | 19.5914i | −1.16322 | + | 0.671586i | ||||
\(852\) | −48.7586 | + | 28.1508i | −1.67044 | + | 0.964429i | ||||
\(853\) | 11.9819i | 0.410253i | 0.978735 | + | 0.205127i | \(0.0657606\pi\) | ||||
−0.978735 | + | 0.205127i | \(0.934239\pi\) | |||||||
\(854\) | −51.5598 | − | 89.3041i | −1.76434 | − | 3.05592i | ||||
\(855\) | −0.424404 | + | 0.735090i | −0.0145143 | + | 0.0251395i | ||||
\(856\) | 22.7208 | + | 13.1179i | 0.776581 | + | 0.448360i | ||||
\(857\) | 47.7544 | 1.63126 | 0.815630 | − | 0.578574i | \(-0.196391\pi\) | ||||
0.815630 | + | 0.578574i | \(0.196391\pi\) | |||||||
\(858\) | 16.0526 | − | 8.93286i | 0.548027 | − | 0.304963i | ||||
\(859\) | −27.3365 | −0.932710 | −0.466355 | − | 0.884598i | \(-0.654433\pi\) | ||||
−0.466355 | + | 0.884598i | \(0.654433\pi\) | |||||||
\(860\) | −17.1916 | − | 9.92559i | −0.586230 | − | 0.338460i | ||||
\(861\) | 11.9294 | − | 20.6624i | 0.406554 | − | 0.704172i | ||||
\(862\) | 2.10139 | + | 3.63971i | 0.0715736 | + | 0.123969i | ||||
\(863\) | 39.1219i | 1.33173i | 0.746074 | + | 0.665863i | \(0.231937\pi\) | ||||
−0.746074 | + | 0.665863i | \(0.768063\pi\) | |||||||
\(864\) | −26.4213 | + | 15.2543i | −0.898870 | + | 0.518963i | ||||
\(865\) | −9.54501 | + | 5.51082i | −0.324540 | + | 0.187373i | ||||
\(866\) | 37.4548i | 1.27276i | ||||||||
\(867\) | 22.8030 | + | 39.4960i | 0.774431 | + | 1.34135i | ||||
\(868\) | −4.83818 | + | 8.37998i | −0.164219 | + | 0.284435i | ||||
\(869\) | 5.83672 | + | 3.36983i | 0.197997 | + | 0.114314i | ||||
\(870\) | −0.979442 | −0.0332062 | ||||||||
\(871\) | 17.3577 | + | 0.274248i | 0.588143 | + | 0.00929255i | ||||
\(872\) | 6.95143 | 0.235405 | ||||||||
\(873\) | 1.06890 | + | 0.617130i | 0.0361768 | + | 0.0208867i | ||||
\(874\) | 11.0828 | − | 19.1960i | 0.374882 | − | 0.649315i | ||||
\(875\) | −15.0574 | − | 26.0801i | −0.509032 | − | 0.881669i | ||||
\(876\) | 74.8364i | 2.52849i | ||||||||
\(877\) | −18.0910 | + | 10.4448i | −0.610890 | + | 0.352698i | −0.773314 | − | 0.634024i | \(-0.781402\pi\) |
0.162424 | + | 0.986721i | \(0.448069\pi\) | |||||||
\(878\) | 41.4785 | − | 23.9476i | 1.39983 | − | 0.808194i | ||||
\(879\) | 30.0953i | 1.01509i | ||||||||
\(880\) | 0.00149741 | + | 0.00259360i | 5.04778e−5 | + | 8.74302e-5i | ||||
\(881\) | −3.25288 | + | 5.63416i | −0.109592 | + | 0.189820i | −0.915605 | − | 0.402079i | \(-0.868288\pi\) |
0.806013 | + | 0.591898i | \(0.201621\pi\) | |||||||
\(882\) | −0.993452 | − | 0.573570i | −0.0334513 | − | 0.0193131i | ||||
\(883\) | −10.5474 | −0.354948 | −0.177474 | − | 0.984126i | \(-0.556793\pi\) | ||||
−0.177474 | + | 0.984126i | \(0.556793\pi\) | |||||||
\(884\) | −1.23039 | + | 77.8734i | −0.0413824 | + | 2.61917i | ||||
\(885\) | −4.29910 | −0.144513 | ||||||||
\(886\) | 16.0478 | + | 9.26519i | 0.539136 | + | 0.311270i | ||||
\(887\) | −23.0050 | + | 39.8457i | −0.772431 | + | 1.33789i | 0.163797 | + | 0.986494i | \(0.447626\pi\) |
−0.936227 | + | 0.351395i | \(0.885707\pi\) | |||||||
\(888\) | −26.6853 | − | 46.2202i | −0.895499 | − | 1.55105i | ||||
\(889\) | 61.7794i | 2.07202i | ||||||||
\(890\) | 20.8241 | − | 12.0228i | 0.698027 | − | 0.403006i | ||||
\(891\) | −9.50011 | + | 5.48489i | −0.318266 | + | 0.183751i | ||||
\(892\) | − | 61.8890i | − | 2.07220i | ||||||
\(893\) | −9.38227 | − | 16.2506i | −0.313966 | − | 0.543805i | ||||
\(894\) | −31.3785 | + | 54.3492i | −1.04945 | + | 1.81771i | ||||
\(895\) | −8.31262 | − | 4.79929i | −0.277860 | − | 0.160423i | ||||
\(896\) | 54.7428 | 1.82883 | ||||||||
\(897\) | 17.6178 | + | 10.5462i | 0.588242 | + | 0.352128i | ||||
\(898\) | 20.7381 | 0.692040 | ||||||||
\(899\) | −0.192060 | − | 0.110886i | −0.00640558 | − | 0.00369826i | ||||
\(900\) | −1.52364 | + | 2.63903i | −0.0507881 | + | 0.0879677i | ||||
\(901\) | 14.2194 | + | 24.6288i | 0.473718 | + | 0.820504i | ||||
\(902\) | − | 14.8316i | − | 0.493840i | ||||||
\(903\) | −22.5582 | + | 13.0240i | −0.750691 | + | 0.433412i | ||||
\(904\) | −0.428837 | + | 0.247589i | −0.0142629 | + | 0.00823470i | ||||
\(905\) | − | 6.25226i | − | 0.207832i | ||||||
\(906\) | −25.4271 | − | 44.0411i | −0.844759 | − | 1.46317i | ||||
\(907\) | −29.3569 | + | 50.8477i | −0.974781 | + | 1.68837i | −0.294124 | + | 0.955767i | \(0.595028\pi\) |
−0.680657 | + | 0.732602i | \(0.738305\pi\) | |||||||
\(908\) | −3.93796 | − | 2.27358i | −0.130686 | − | 0.0754514i | ||||
\(909\) | −0.928274 | −0.0307889 | ||||||||
\(910\) | 13.9816 | + | 25.1254i | 0.463486 | + | 0.832898i | ||||
\(911\) | 37.5292 | 1.24340 | 0.621700 | − | 0.783256i | \(-0.286442\pi\) | ||||
0.621700 | + | 0.783256i | \(0.286442\pi\) | |||||||
\(912\) | 0.00771520 | + | 0.00445437i | 0.000255476 | + | 0.000147499i | ||||
\(913\) | 2.17933 | − | 3.77471i | 0.0721253 | − | 0.124925i | ||||
\(914\) | 11.5004 | + | 19.9193i | 0.380400 | + | 0.658871i | ||||
\(915\) | − | 29.0894i | − | 0.961665i | ||||||
\(916\) | 8.78240 | − | 5.07052i | 0.290179 | − | 0.167535i | ||||
\(917\) | 3.06392 | − | 1.76896i | 0.101180 | − | 0.0584161i | ||||
\(918\) | − | 82.4011i | − | 2.71964i | ||||||
\(919\) | −7.10814 | − | 12.3117i | −0.234476 | − | 0.406124i | 0.724644 | − | 0.689123i | \(-0.242004\pi\) |
−0.959120 | + | 0.282999i | \(0.908671\pi\) | |||||||
\(920\) | −5.67207 | + | 9.82431i | −0.187003 | + | 0.323898i | ||||
\(921\) | −3.86903 | − | 2.23378i | −0.127489 | − | 0.0736057i | ||||
\(922\) | −13.8311 | −0.455503 | ||||||||
\(923\) | −19.4567 | + | 32.5031i | −0.640426 | + | 1.06985i | ||||
\(924\) | 21.5450 | 0.708777 | ||||||||
\(925\) | 35.9242 | + | 20.7408i | 1.18118 | + | 0.681954i | ||||
\(926\) | −36.1990 | + | 62.6986i | −1.18957 | + | 2.06040i | ||||
\(927\) | −1.42886 | − | 2.47485i | −0.0469298 | − | 0.0812848i | ||||
\(928\) | 1.25405i | 0.0411662i | ||||||||
\(929\) | 31.8850 | − | 18.4088i | 1.04611 | − | 0.603973i | 0.124553 | − | 0.992213i | \(-0.460250\pi\) |
0.921558 | + | 0.388240i | \(0.126917\pi\) | |||||||
\(930\) | −3.82474 | + | 2.20822i | −0.125418 | + | 0.0724102i | ||||
\(931\) | − | 5.45980i | − | 0.178938i | ||||||
\(932\) | −10.4396 | − | 18.0820i | −0.341961 | − | 0.592295i | ||||
\(933\) | 26.5769 | − | 46.0325i | 0.870088 | − | 1.50704i | ||||
\(934\) | −71.7899 | − | 41.4479i | −2.34904 | − | 1.35622i | ||||
\(935\) | 10.4618 | 0.342136 | ||||||||
\(936\) | 1.35490 | − | 2.26341i | 0.0442864 | − | 0.0739820i | ||||
\(937\) | 14.1542 | 0.462398 | 0.231199 | − | 0.972907i | \(-0.425735\pi\) | ||||
0.231199 | + | 0.972907i | \(0.425735\pi\) | |||||||
\(938\) | 28.5274 | + | 16.4703i | 0.931454 | + | 0.537775i | ||||
\(939\) | −22.8285 | + | 39.5400i | −0.744978 | + | 1.29034i | ||||
\(940\) | 12.5684 | + | 21.7692i | 0.409938 | + | 0.710033i | ||||
\(941\) | 42.0386i | 1.37042i | 0.728346 | + | 0.685210i | \(0.240290\pi\) | ||||
−0.728346 | + | 0.685210i | \(0.759710\pi\) | |||||||
\(942\) | −12.7503 | + | 7.36141i | −0.415428 | + | 0.239848i | ||||
\(943\) | 14.3566 | − | 8.28877i | 0.467514 | − | 0.269919i | ||||
\(944\) | − | 0.00425589i | − | 0.000138518i | ||||||
\(945\) | −9.40126 | − | 16.2835i | −0.305823 | − | 0.529701i | ||||
\(946\) | −8.09625 | + | 14.0231i | −0.263232 | + | 0.455931i | ||||
\(947\) | −13.6226 | − | 7.86501i | −0.442675 | − | 0.255579i | 0.262057 | − | 0.965053i | \(-0.415599\pi\) |
−0.704732 | + | 0.709474i | \(0.748933\pi\) | |||||||
\(948\) | −26.8569 | −0.872273 | ||||||||
\(949\) | 24.4842 | + | 43.9989i | 0.794792 | + | 1.42826i | ||||
\(950\) | −23.4661 | −0.761340 | ||||||||
\(951\) | −45.6374 | − | 26.3488i | −1.47990 | − | 0.854418i | ||||
\(952\) | −28.2304 | + | 48.8965i | −0.914953 | + | 1.58474i | ||||
\(953\) | 4.98311 | + | 8.63101i | 0.161419 | + | 0.279586i | 0.935378 | − | 0.353650i | \(-0.115060\pi\) |
−0.773959 | + | 0.633236i | \(0.781726\pi\) | |||||||
\(954\) | − | 2.52127i | − | 0.0816291i | ||||||
\(955\) | 15.2592 | − | 8.80992i | 0.493777 | − | 0.285082i | ||||
\(956\) | 45.4388 | − | 26.2341i | 1.46960 | − | 0.848472i | ||||
\(957\) | 0.493788i | 0.0159619i | ||||||||
\(958\) | 24.8443 | + | 43.0316i | 0.802683 | + | 1.39029i | ||||
\(959\) | −16.1734 | + | 28.0132i | −0.522267 | + | 0.904592i | ||||
\(960\) | 21.6340 | + | 12.4904i | 0.698235 | + | 0.403126i | ||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | −80.6471 | − | 48.2762i | −2.60017 | − | 1.55649i | ||||
\(963\) | −2.39753 | −0.0772592 | ||||||||
\(964\) | 10.2734 | + | 5.93136i | 0.330885 | + | 0.191036i | ||||
\(965\) | 5.12114 | − | 8.87007i | 0.164855 | − | 0.285538i | ||||
\(966\) | 19.4810 | + | 33.7421i | 0.626792 | + | 1.08564i | ||||
\(967\) | 23.4245i | 0.753282i | 0.926359 | + | 0.376641i | \(0.122921\pi\) | ||||
−0.926359 | + | 0.376641i | \(0.877079\pi\) | |||||||
\(968\) | −22.5235 | + | 13.0039i | −0.723932 | + | 0.417962i | ||||
\(969\) | 26.9513 | − | 15.5603i | 0.865801 | − | 0.499870i | ||||
\(970\) | − | 12.7323i | − | 0.408809i | ||||||
\(971\) | −23.2109 | − | 40.2025i | −0.744874 | − | 1.29016i | −0.950254 | − | 0.311477i | \(-0.899176\pi\) |
0.205380 | − | 0.978682i | \(-0.434157\pi\) | |||||||
\(972\) | −4.33602 | + | 7.51021i | −0.139078 | + | 0.240890i | ||||
\(973\) | −15.2867 | − | 8.82577i | −0.490069 | − | 0.282941i | ||||
\(974\) | −27.5487 | −0.882718 | ||||||||
\(975\) | 0.343411 | − | 21.7351i | 0.0109980 | − | 0.696080i | ||||
\(976\) | 0.0287970 | 0.000921770 | ||||||||
\(977\) | 4.05911 | + | 2.34353i | 0.129862 | + | 0.0749761i | 0.563524 | − | 0.826100i | \(-0.309445\pi\) |
−0.433661 | + | 0.901076i | \(0.642779\pi\) | |||||||
\(978\) | −33.5415 | + | 58.0956i | −1.07254 | + | 1.85769i | ||||
\(979\) | −6.06134 | − | 10.4985i | −0.193721 | − | 0.335535i | ||||
\(980\) | 7.31393i | 0.233635i | ||||||||
\(981\) | −0.550142 | + | 0.317625i | −0.0175647 | + | 0.0101410i | ||||
\(982\) | 7.78001 | − | 4.49179i | 0.248270 | − | 0.143339i | ||||
\(983\) | − | 12.3743i | − | 0.394679i | −0.980335 | − | 0.197339i | \(-0.936770\pi\) | ||
0.980335 | − | 0.197339i | \(-0.0632301\pi\) | |||||||
\(984\) | 11.2900 | + | 19.5549i | 0.359913 | + | 0.623388i | ||||
\(985\) | 12.7083 | − | 22.0115i | 0.404921 | − | 0.701344i | ||||
\(986\) | −2.93329 | − | 1.69354i | −0.0934150 | − | 0.0539332i | ||||
\(987\) | 32.9837 | 1.04988 | ||||||||
\(988\) | 32.8592 | + | 0.519169i | 1.04539 | + | 0.0165170i | ||||
\(989\) | −18.0986 | −0.575501 | ||||||||
\(990\) | −0.803233 | − | 0.463747i | −0.0255284 | − | 0.0147388i | ||||
\(991\) | −1.68797 | + | 2.92365i | −0.0536201 | + | 0.0928727i | −0.891590 | − | 0.452844i | \(-0.850409\pi\) |
0.837970 | + | 0.545717i | \(0.183743\pi\) | |||||||
\(992\) | 2.82733 | + | 4.89709i | 0.0897679 | + | 0.155483i | ||||
\(993\) | − | 26.8686i | − | 0.852650i | ||||||
\(994\) | −62.2508 | + | 35.9405i | −1.97448 | + | 1.13996i | ||||
\(995\) | −11.7659 | + | 6.79307i | −0.373005 | + | 0.215355i | ||||
\(996\) | 17.3689i | 0.550353i | ||||||||
\(997\) | 5.32742 | + | 9.22736i | 0.168721 | + | 0.292233i | 0.937970 | − | 0.346715i | \(-0.112703\pi\) |
−0.769249 | + | 0.638949i | \(0.779370\pi\) | |||||||
\(998\) | 5.22109 | − | 9.04320i | 0.165271 | − | 0.286257i | ||||
\(999\) | 53.2288 | + | 30.7317i | 1.68408 | + | 0.972307i |
(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 | 403.2.r.a.342.5 | yes | 68 | |
13.6 | odd | 12 | 5239.2.a.r.1.29 | 34 | |||
13.7 | odd | 12 | 5239.2.a.q.1.6 | 34 | |||
13.10 | even | 6 | inner | 403.2.r.a.218.5 | ✓ | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.r.a.218.5 | ✓ | 68 | 13.10 | even | 6 | inner | |
403.2.r.a.342.5 | yes | 68 | 1.1 | even | 1 | trivial | |
5239.2.a.q.1.6 | 34 | 13.7 | odd | 12 | |||
5239.2.a.r.1.29 | 34 | 13.6 | odd | 12 |