Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(49,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.j (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 349.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.349 |
Dual form | 950.2.j.a.49.1 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | −0.228714 | − | 0.973494i | \(-0.573452\pi\) |
0.728714 | + | 0.684819i | \(0.240119\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | 2.00000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | + | 1.73205i | −0.333333 | + | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 5.19615 | + | 3.00000i | 1.44115 | + | 0.832050i | 0.997927 | − | 0.0643593i | \(-0.0205004\pi\) |
0.443227 | + | 0.896410i | \(0.353834\pi\) | |||||||
\(14\) | −1.00000 | − | 1.73205i | −0.267261 | − | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.73205 | − | 1.00000i | 0.420084 | − | 0.242536i | −0.275029 | − | 0.961436i | \(-0.588688\pi\) |
0.695113 | + | 0.718900i | \(0.255354\pi\) | |||||||
\(18\) | − | 2.00000i | − | 0.471405i | ||||||
\(19\) | −3.50000 | + | 2.59808i | −0.802955 | + | 0.596040i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | + | 1.73205i | 0.218218 | + | 0.377964i | ||||
\(22\) | 2.59808 | − | 1.50000i | 0.553912 | − | 0.319801i | ||||
\(23\) | −6.92820 | − | 4.00000i | −1.44463 | − | 0.834058i | −0.446476 | − | 0.894795i | \(-0.647321\pi\) |
−0.998154 | + | 0.0607377i | \(0.980655\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.00000 | −1.17670 | ||||||||
\(27\) | 5.00000i | 0.962250i | ||||||||
\(28\) | 1.73205 | + | 1.00000i | 0.327327 | + | 0.188982i | ||||
\(29\) | −1.00000 | + | 1.73205i | −0.185695 | + | 0.321634i | −0.943811 | − | 0.330487i | \(-0.892787\pi\) |
0.758115 | + | 0.652121i | \(0.226120\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.00000 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −2.59808 | + | 1.50000i | −0.452267 | + | 0.261116i | ||||
\(34\) | −1.00000 | + | 1.73205i | −0.171499 | + | 0.297044i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | + | 1.73205i | 0.166667 | + | 0.288675i | ||||
\(37\) | 8.00000i | 1.31519i | 0.753371 | + | 0.657596i | \(0.228427\pi\) | ||||
−0.753371 | + | 0.657596i | \(0.771573\pi\) | |||||||
\(38\) | 1.73205 | − | 4.00000i | 0.280976 | − | 0.648886i | ||||
\(39\) | 6.00000 | 0.960769 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.50000 | − | 4.33013i | −0.390434 | − | 0.676252i | 0.602072 | − | 0.798441i | \(-0.294342\pi\) |
−0.992507 | + | 0.122189i | \(0.961009\pi\) | |||||||
\(42\) | −1.73205 | − | 1.00000i | −0.267261 | − | 0.154303i | ||||
\(43\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(44\) | −1.50000 | + | 2.59808i | −0.226134 | + | 0.391675i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.00000 | 1.17954 | ||||||||
\(47\) | 5.19615 | + | 3.00000i | 0.757937 | + | 0.437595i | 0.828554 | − | 0.559908i | \(-0.189164\pi\) |
−0.0706177 | + | 0.997503i | \(0.522497\pi\) | |||||||
\(48\) | −0.866025 | − | 0.500000i | −0.125000 | − | 0.0721688i | ||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.00000 | − | 1.73205i | 0.140028 | − | 0.242536i | ||||
\(52\) | 5.19615 | − | 3.00000i | 0.720577 | − | 0.416025i | ||||
\(53\) | 5.19615 | + | 3.00000i | 0.713746 | + | 0.412082i | 0.812447 | − | 0.583036i | \(-0.198135\pi\) |
−0.0987002 | + | 0.995117i | \(0.531468\pi\) | |||||||
\(54\) | −2.50000 | − | 4.33013i | −0.340207 | − | 0.589256i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | −0.267261 | ||||||||
\(57\) | −1.73205 | + | 4.00000i | −0.229416 | + | 0.529813i | ||||
\(58\) | − | 2.00000i | − | 0.262613i | ||||||
\(59\) | 2.50000 | + | 4.33013i | 0.325472 | + | 0.563735i | 0.981608 | − | 0.190909i | \(-0.0611434\pi\) |
−0.656136 | + | 0.754643i | \(0.727810\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.00000 | + | 12.1244i | −0.896258 | + | 1.55236i | −0.0640184 | + | 0.997949i | \(0.520392\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 6.92820 | − | 4.00000i | 0.879883 | − | 0.508001i | ||||
\(63\) | −3.46410 | − | 2.00000i | −0.436436 | − | 0.251976i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.50000 | − | 2.59808i | 0.184637 | − | 0.319801i | ||||
\(67\) | 4.33013 | + | 2.50000i | 0.529009 | + | 0.305424i | 0.740613 | − | 0.671932i | \(-0.234535\pi\) |
−0.211604 | + | 0.977356i | \(0.567869\pi\) | |||||||
\(68\) | − | 2.00000i | − | 0.242536i | ||||||
\(69\) | −8.00000 | −0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00000 | + | 5.19615i | 0.356034 | + | 0.616670i | 0.987294 | − | 0.158901i | \(-0.0507952\pi\) |
−0.631260 | + | 0.775571i | \(0.717462\pi\) | |||||||
\(72\) | −1.73205 | − | 1.00000i | −0.204124 | − | 0.117851i | ||||
\(73\) | 7.79423 | − | 4.50000i | 0.912245 | − | 0.526685i | 0.0310925 | − | 0.999517i | \(-0.490101\pi\) |
0.881153 | + | 0.472831i | \(0.156768\pi\) | |||||||
\(74\) | −4.00000 | − | 6.92820i | −0.464991 | − | 0.805387i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.500000 | + | 4.33013i | 0.0573539 | + | 0.496700i | ||||
\(77\) | − | 6.00000i | − | 0.683763i | ||||||
\(78\) | −5.19615 | + | 3.00000i | −0.588348 | + | 0.339683i | ||||
\(79\) | 4.00000 | + | 6.92820i | 0.450035 | + | 0.779484i | 0.998388 | − | 0.0567635i | \(-0.0180781\pi\) |
−0.548352 | + | 0.836247i | \(0.684745\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 4.33013 | + | 2.50000i | 0.478183 | + | 0.276079i | ||||
\(83\) | 11.0000i | 1.20741i | 0.797209 | + | 0.603703i | \(0.206309\pi\) | ||||
−0.797209 | + | 0.603703i | \(0.793691\pi\) | |||||||
\(84\) | 2.00000 | 0.218218 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.00000i | 0.214423i | ||||||||
\(88\) | − | 3.00000i | − | 0.319801i | ||||||
\(89\) | 7.00000 | − | 12.1244i | 0.741999 | − | 1.28518i | −0.209585 | − | 0.977790i | \(-0.567211\pi\) |
0.951584 | − | 0.307389i | \(-0.0994552\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | + | 10.3923i | −0.628971 | + | 1.08941i | ||||
\(92\) | −6.92820 | + | 4.00000i | −0.722315 | + | 0.417029i | ||||
\(93\) | −6.92820 | + | 4.00000i | −0.718421 | + | 0.414781i | ||||
\(94\) | −6.00000 | −0.618853 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −12.9904 | + | 7.50000i | −1.31897 | + | 0.761510i | −0.983563 | − | 0.180563i | \(-0.942208\pi\) |
−0.335410 | + | 0.942072i | \(0.608875\pi\) | |||||||
\(98\) | −2.59808 | + | 1.50000i | −0.262445 | + | 0.151523i | ||||
\(99\) | 3.00000 | − | 5.19615i | 0.301511 | − | 0.522233i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.00000 | − | 8.66025i | 0.497519 | − | 0.861727i | −0.502477 | − | 0.864590i | \(-0.667578\pi\) |
0.999996 | + | 0.00286291i | \(0.000911295\pi\) | |||||||
\(102\) | 2.00000i | 0.198030i | ||||||||
\(103\) | − | 6.00000i | − | 0.591198i | −0.955312 | − | 0.295599i | \(-0.904481\pi\) | ||
0.955312 | − | 0.295599i | \(-0.0955191\pi\) | |||||||
\(104\) | −3.00000 | + | 5.19615i | −0.294174 | + | 0.509525i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | − | 12.0000i | − | 1.16008i | −0.814587 | − | 0.580042i | \(-0.803036\pi\) | ||
0.814587 | − | 0.580042i | \(-0.196964\pi\) | |||||||
\(108\) | 4.33013 | + | 2.50000i | 0.416667 | + | 0.240563i | ||||
\(109\) | −4.00000 | − | 6.92820i | −0.383131 | − | 0.663602i | 0.608377 | − | 0.793648i | \(-0.291821\pi\) |
−0.991508 | + | 0.130046i | \(0.958487\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | + | 6.92820i | 0.379663 | + | 0.657596i | ||||
\(112\) | 1.73205 | − | 1.00000i | 0.163663 | − | 0.0944911i | ||||
\(113\) | 13.0000i | 1.22294i | 0.791269 | + | 0.611469i | \(0.209421\pi\) | ||||
−0.791269 | + | 0.611469i | \(0.790579\pi\) | |||||||
\(114\) | −0.500000 | − | 4.33013i | −0.0468293 | − | 0.405554i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.00000 | + | 1.73205i | 0.0928477 | + | 0.160817i | ||||
\(117\) | −10.3923 | + | 6.00000i | −0.960769 | + | 0.554700i | ||||
\(118\) | −4.33013 | − | 2.50000i | −0.398621 | − | 0.230144i | ||||
\(119\) | 2.00000 | + | 3.46410i | 0.183340 | + | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | − | 14.0000i | − | 1.26750i | ||||||
\(123\) | −4.33013 | − | 2.50000i | −0.390434 | − | 0.225417i | ||||
\(124\) | −4.00000 | + | 6.92820i | −0.359211 | + | 0.622171i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.00000 | 0.356348 | ||||||||
\(127\) | −5.19615 | − | 3.00000i | −0.461084 | − | 0.266207i | 0.251416 | − | 0.967879i | \(-0.419104\pi\) |
−0.712500 | + | 0.701672i | \(0.752437\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.50000 | − | 6.06218i | −0.305796 | − | 0.529655i | 0.671642 | − | 0.740876i | \(-0.265589\pi\) |
−0.977438 | + | 0.211221i | \(0.932256\pi\) | |||||||
\(132\) | 3.00000i | 0.261116i | ||||||||
\(133\) | −5.19615 | − | 7.00000i | −0.450564 | − | 0.606977i | ||||
\(134\) | −5.00000 | −0.431934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.00000 | + | 1.73205i | 0.0857493 | + | 0.148522i | ||||
\(137\) | 2.59808 | + | 1.50000i | 0.221969 | + | 0.128154i | 0.606861 | − | 0.794808i | \(-0.292428\pi\) |
−0.384893 | + | 0.922961i | \(0.625762\pi\) | |||||||
\(138\) | 6.92820 | − | 4.00000i | 0.589768 | − | 0.340503i | ||||
\(139\) | 4.50000 | − | 7.79423i | 0.381685 | − | 0.661098i | −0.609618 | − | 0.792695i | \(-0.708677\pi\) |
0.991303 | + | 0.131597i | \(0.0420106\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | −5.19615 | − | 3.00000i | −0.436051 | − | 0.251754i | ||||
\(143\) | −15.5885 | − | 9.00000i | −1.30357 | − | 0.752618i | ||||
\(144\) | 2.00000 | 0.166667 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.50000 | + | 7.79423i | −0.372423 | + | 0.645055i | ||||
\(147\) | 2.59808 | − | 1.50000i | 0.214286 | − | 0.123718i | ||||
\(148\) | 6.92820 | + | 4.00000i | 0.569495 | + | 0.328798i | ||||
\(149\) | 2.00000 | + | 3.46410i | 0.163846 | + | 0.283790i | 0.936245 | − | 0.351348i | \(-0.114277\pi\) |
−0.772399 | + | 0.635138i | \(0.780943\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(152\) | −2.59808 | − | 3.50000i | −0.210732 | − | 0.283887i | ||||
\(153\) | 4.00000i | 0.323381i | ||||||||
\(154\) | 3.00000 | + | 5.19615i | 0.241747 | + | 0.418718i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.00000 | − | 5.19615i | 0.240192 | − | 0.416025i | ||||
\(157\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(158\) | −6.92820 | − | 4.00000i | −0.551178 | − | 0.318223i | ||||
\(159\) | 6.00000 | 0.475831 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.00000 | − | 13.8564i | 0.630488 | − | 1.09204i | ||||
\(162\) | 0.866025 | + | 0.500000i | 0.0680414 | + | 0.0392837i | ||||
\(163\) | − | 3.00000i | − | 0.234978i | −0.993074 | − | 0.117489i | \(-0.962515\pi\) | ||
0.993074 | − | 0.117489i | \(-0.0374845\pi\) | |||||||
\(164\) | −5.00000 | −0.390434 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.50000 | − | 9.52628i | −0.426883 | − | 0.739383i | ||||
\(167\) | −6.92820 | − | 4.00000i | −0.536120 | − | 0.309529i | 0.207385 | − | 0.978259i | \(-0.433505\pi\) |
−0.743505 | + | 0.668730i | \(0.766838\pi\) | |||||||
\(168\) | −1.73205 | + | 1.00000i | −0.133631 | + | 0.0771517i | ||||
\(169\) | 11.5000 | + | 19.9186i | 0.884615 | + | 1.53220i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | − | 8.66025i | −0.0764719 | − | 0.662266i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.5885 | − | 9.00000i | 1.18517 | − | 0.684257i | 0.227964 | − | 0.973670i | \(-0.426793\pi\) |
0.957205 | + | 0.289412i | \(0.0934598\pi\) | |||||||
\(174\) | −1.00000 | − | 1.73205i | −0.0758098 | − | 0.131306i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.50000 | + | 2.59808i | 0.113067 | + | 0.195837i | ||||
\(177\) | 4.33013 | + | 2.50000i | 0.325472 | + | 0.187912i | ||||
\(178\) | 14.0000i | 1.04934i | ||||||||
\(179\) | −3.00000 | −0.224231 | −0.112115 | − | 0.993695i | \(-0.535763\pi\) | ||||
−0.112115 | + | 0.993695i | \(0.535763\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.00000 | − | 13.8564i | 0.594635 | − | 1.02994i | −0.398963 | − | 0.916967i | \(-0.630630\pi\) |
0.993598 | − | 0.112972i | \(-0.0360369\pi\) | |||||||
\(182\) | − | 12.0000i | − | 0.889499i | ||||||
\(183\) | 14.0000i | 1.03491i | ||||||||
\(184\) | 4.00000 | − | 6.92820i | 0.294884 | − | 0.510754i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.00000 | − | 6.92820i | 0.293294 | − | 0.508001i | ||||
\(187\) | −5.19615 | + | 3.00000i | −0.379980 | + | 0.219382i | ||||
\(188\) | 5.19615 | − | 3.00000i | 0.378968 | − | 0.218797i | ||||
\(189\) | −10.0000 | −0.727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.00000 | −0.289430 | −0.144715 | − | 0.989473i | \(-0.546227\pi\) | ||||
−0.144715 | + | 0.989473i | \(0.546227\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | −8.66025 | + | 5.00000i | −0.623379 | + | 0.359908i | −0.778183 | − | 0.628037i | \(-0.783859\pi\) |
0.154805 | + | 0.987945i | \(0.450525\pi\) | |||||||
\(194\) | 7.50000 | − | 12.9904i | 0.538469 | − | 0.932655i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.50000 | − | 2.59808i | 0.107143 | − | 0.185577i | ||||
\(197\) | 8.00000i | 0.569976i | 0.958531 | + | 0.284988i | \(0.0919897\pi\) | ||||
−0.958531 | + | 0.284988i | \(0.908010\pi\) | |||||||
\(198\) | 6.00000i | 0.426401i | ||||||||
\(199\) | −11.0000 | + | 19.0526i | −0.779769 | + | 1.35060i | 0.152305 | + | 0.988334i | \(0.451330\pi\) |
−0.932075 | + | 0.362267i | \(0.882003\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.00000 | 0.352673 | ||||||||
\(202\) | 10.0000i | 0.703598i | ||||||||
\(203\) | −3.46410 | − | 2.00000i | −0.243132 | − | 0.140372i | ||||
\(204\) | −1.00000 | − | 1.73205i | −0.0700140 | − | 0.121268i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.00000 | + | 5.19615i | 0.209020 | + | 0.362033i | ||||
\(207\) | 13.8564 | − | 8.00000i | 0.963087 | − | 0.556038i | ||||
\(208\) | − | 6.00000i | − | 0.416025i | ||||||
\(209\) | 10.5000 | − | 7.79423i | 0.726300 | − | 0.539138i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | + | 3.46410i | 0.137686 | + | 0.238479i | 0.926620 | − | 0.375999i | \(-0.122700\pi\) |
−0.788935 | + | 0.614477i | \(0.789367\pi\) | |||||||
\(212\) | 5.19615 | − | 3.00000i | 0.356873 | − | 0.206041i | ||||
\(213\) | 5.19615 | + | 3.00000i | 0.356034 | + | 0.205557i | ||||
\(214\) | 6.00000 | + | 10.3923i | 0.410152 | + | 0.710403i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | − | 16.0000i | − | 1.08615i | ||||||
\(218\) | 6.92820 | + | 4.00000i | 0.469237 | + | 0.270914i | ||||
\(219\) | 4.50000 | − | 7.79423i | 0.304082 | − | 0.526685i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | −6.92820 | − | 4.00000i | −0.464991 | − | 0.268462i | ||||
\(223\) | 13.8564 | − | 8.00000i | 0.927894 | − | 0.535720i | 0.0417488 | − | 0.999128i | \(-0.486707\pi\) |
0.886145 | + | 0.463409i | \(0.153374\pi\) | |||||||
\(224\) | −1.00000 | + | 1.73205i | −0.0668153 | + | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.50000 | − | 11.2583i | −0.432374 | − | 0.748893i | ||||
\(227\) | − | 7.00000i | − | 0.464606i | −0.972643 | − | 0.232303i | \(-0.925374\pi\) | ||
0.972643 | − | 0.232303i | \(-0.0746261\pi\) | |||||||
\(228\) | 2.59808 | + | 3.50000i | 0.172062 | + | 0.231793i | ||||
\(229\) | 24.0000 | 1.58596 | 0.792982 | − | 0.609245i | \(-0.208527\pi\) | ||||
0.792982 | + | 0.609245i | \(0.208527\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.00000 | − | 5.19615i | −0.197386 | − | 0.341882i | ||||
\(232\) | −1.73205 | − | 1.00000i | −0.113715 | − | 0.0656532i | ||||
\(233\) | −9.52628 | + | 5.50000i | −0.624087 | + | 0.360317i | −0.778459 | − | 0.627696i | \(-0.783998\pi\) |
0.154371 | + | 0.988013i | \(0.450665\pi\) | |||||||
\(234\) | 6.00000 | − | 10.3923i | 0.392232 | − | 0.679366i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.00000 | 0.325472 | ||||||||
\(237\) | 6.92820 | + | 4.00000i | 0.450035 | + | 0.259828i | ||||
\(238\) | −3.46410 | − | 2.00000i | −0.224544 | − | 0.129641i | ||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.50000 | − | 16.4545i | 0.611949 | − | 1.05993i | −0.378963 | − | 0.925412i | \(-0.623719\pi\) |
0.990912 | − | 0.134515i | \(-0.0429475\pi\) | |||||||
\(242\) | 1.73205 | − | 1.00000i | 0.111340 | − | 0.0642824i | ||||
\(243\) | −13.8564 | − | 8.00000i | −0.888889 | − | 0.513200i | ||||
\(244\) | 7.00000 | + | 12.1244i | 0.448129 | + | 0.776182i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.00000 | 0.318788 | ||||||||
\(247\) | −25.9808 | + | 3.00000i | −1.65312 | + | 0.190885i | ||||
\(248\) | − | 8.00000i | − | 0.508001i | ||||||
\(249\) | 5.50000 | + | 9.52628i | 0.348548 | + | 0.603703i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.50000 | − | 14.7224i | 0.536515 | − | 0.929272i | −0.462573 | − | 0.886581i | \(-0.653074\pi\) |
0.999088 | − | 0.0426905i | \(-0.0135929\pi\) | |||||||
\(252\) | −3.46410 | + | 2.00000i | −0.218218 | + | 0.125988i | ||||
\(253\) | 20.7846 | + | 12.0000i | 1.30672 | + | 0.754434i | ||||
\(254\) | 6.00000 | 0.376473 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −2.59808 | − | 1.50000i | −0.162064 | − | 0.0935674i | 0.416775 | − | 0.909010i | \(-0.363160\pi\) |
−0.578838 | + | 0.815442i | \(0.696494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.0000 | −0.994192 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | − | 3.46410i | −0.123797 | − | 0.214423i | ||||
\(262\) | 6.06218 | + | 3.50000i | 0.374523 | + | 0.216231i | ||||
\(263\) | 22.5167 | − | 13.0000i | 1.38844 | − | 0.801614i | 0.395298 | − | 0.918553i | \(-0.370641\pi\) |
0.993139 | + | 0.116939i | \(0.0373081\pi\) | |||||||
\(264\) | −1.50000 | − | 2.59808i | −0.0923186 | − | 0.159901i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.00000 | + | 3.46410i | 0.490511 | + | 0.212398i | ||||
\(267\) | − | 14.0000i | − | 0.856786i | ||||||
\(268\) | 4.33013 | − | 2.50000i | 0.264505 | − | 0.152712i | ||||
\(269\) | −14.0000 | − | 24.2487i | −0.853595 | − | 1.47847i | −0.877942 | − | 0.478766i | \(-0.841084\pi\) |
0.0243472 | − | 0.999704i | \(-0.492249\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.0000 | + | 19.0526i | 0.668202 | + | 1.15736i | 0.978406 | + | 0.206691i | \(0.0662693\pi\) |
−0.310204 | + | 0.950670i | \(0.600397\pi\) | |||||||
\(272\) | −1.73205 | − | 1.00000i | −0.105021 | − | 0.0606339i | ||||
\(273\) | 12.0000i | 0.726273i | ||||||||
\(274\) | −3.00000 | −0.181237 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.00000 | + | 6.92820i | −0.240772 | + | 0.417029i | ||||
\(277\) | − | 14.0000i | − | 0.841178i | −0.907251 | − | 0.420589i | \(-0.861823\pi\) | ||
0.907251 | − | 0.420589i | \(-0.138177\pi\) | |||||||
\(278\) | 9.00000i | 0.539784i | ||||||||
\(279\) | 8.00000 | − | 13.8564i | 0.478947 | − | 0.829561i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.50000 | + | 6.06218i | −0.208792 | + | 0.361639i | −0.951334 | − | 0.308160i | \(-0.900287\pi\) |
0.742542 | + | 0.669800i | \(0.233620\pi\) | |||||||
\(282\) | −5.19615 | + | 3.00000i | −0.309426 | + | 0.178647i | ||||
\(283\) | 25.1147 | − | 14.5000i | 1.49292 | − | 0.861936i | 0.492949 | − | 0.870058i | \(-0.335919\pi\) |
0.999967 | + | 0.00812260i | \(0.00258553\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.0000 | 1.06436 | ||||||||
\(287\) | 8.66025 | − | 5.00000i | 0.511199 | − | 0.295141i | ||||
\(288\) | −1.73205 | + | 1.00000i | −0.102062 | + | 0.0589256i | ||||
\(289\) | −6.50000 | + | 11.2583i | −0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.50000 | + | 12.9904i | −0.439658 | + | 0.761510i | ||||
\(292\) | − | 9.00000i | − | 0.526685i | ||||||
\(293\) | − | 22.0000i | − | 1.28525i | −0.766179 | − | 0.642627i | \(-0.777845\pi\) | ||
0.766179 | − | 0.642627i | \(-0.222155\pi\) | |||||||
\(294\) | −1.50000 | + | 2.59808i | −0.0874818 | + | 0.151523i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.00000 | −0.464991 | ||||||||
\(297\) | − | 15.0000i | − | 0.870388i | ||||||
\(298\) | −3.46410 | − | 2.00000i | −0.200670 | − | 0.115857i | ||||
\(299\) | −24.0000 | − | 41.5692i | −1.38796 | − | 2.40401i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −10.3923 | + | 6.00000i | −0.598010 | + | 0.345261i | ||||
\(303\) | − | 10.0000i | − | 0.574485i | ||||||
\(304\) | 4.00000 | + | 1.73205i | 0.229416 | + | 0.0993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.00000 | − | 3.46410i | −0.114332 | − | 0.198030i | ||||
\(307\) | −4.33013 | + | 2.50000i | −0.247133 | + | 0.142683i | −0.618451 | − | 0.785823i | \(-0.712239\pi\) |
0.371318 | + | 0.928506i | \(0.378906\pi\) | |||||||
\(308\) | −5.19615 | − | 3.00000i | −0.296078 | − | 0.170941i | ||||
\(309\) | −3.00000 | − | 5.19615i | −0.170664 | − | 0.295599i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | 6.00000i | 0.339683i | ||||||||
\(313\) | 11.2583 | + | 6.50000i | 0.636358 | + | 0.367402i | 0.783210 | − | 0.621757i | \(-0.213581\pi\) |
−0.146852 | + | 0.989158i | \(0.546914\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.00000 | 0.450035 | ||||||||
\(317\) | 25.9808 | + | 15.0000i | 1.45922 | + | 0.842484i | 0.998973 | − | 0.0453045i | \(-0.0144258\pi\) |
0.460252 | + | 0.887788i | \(0.347759\pi\) | |||||||
\(318\) | −5.19615 | + | 3.00000i | −0.291386 | + | 0.168232i | ||||
\(319\) | 3.00000 | − | 5.19615i | 0.167968 | − | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.00000 | − | 10.3923i | −0.334887 | − | 0.580042i | ||||
\(322\) | 16.0000i | 0.891645i | ||||||||
\(323\) | −3.46410 | + | 8.00000i | −0.192748 | + | 0.445132i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.50000 | + | 2.59808i | 0.0830773 | + | 0.143894i | ||||
\(327\) | −6.92820 | − | 4.00000i | −0.383131 | − | 0.221201i | ||||
\(328\) | 4.33013 | − | 2.50000i | 0.239091 | − | 0.138039i | ||||
\(329\) | −6.00000 | + | 10.3923i | −0.330791 | + | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.0000 | −0.934405 | −0.467202 | − | 0.884150i | \(-0.654738\pi\) | ||||
−0.467202 | + | 0.884150i | \(0.654738\pi\) | |||||||
\(332\) | 9.52628 | + | 5.50000i | 0.522823 | + | 0.301852i | ||||
\(333\) | −13.8564 | − | 8.00000i | −0.759326 | − | 0.438397i | ||||
\(334\) | 8.00000 | 0.437741 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.00000 | − | 1.73205i | 0.0545545 | − | 0.0944911i | ||||
\(337\) | 16.4545 | − | 9.50000i | 0.896333 | − | 0.517498i | 0.0203242 | − | 0.999793i | \(-0.493530\pi\) |
0.876009 | + | 0.482295i | \(0.160197\pi\) | |||||||
\(338\) | −19.9186 | − | 11.5000i | −1.08343 | − | 0.625518i | ||||
\(339\) | 6.50000 | + | 11.2583i | 0.353032 | + | 0.611469i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.0000 | 1.29967 | ||||||||
\(342\) | 5.19615 | + | 7.00000i | 0.280976 | + | 0.378517i | ||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.00000 | + | 15.5885i | −0.483843 | + | 0.838041i | ||||
\(347\) | −23.3827 | + | 13.5000i | −1.25525 | + | 0.724718i | −0.972147 | − | 0.234372i | \(-0.924697\pi\) |
−0.283101 | + | 0.959090i | \(0.591363\pi\) | |||||||
\(348\) | 1.73205 | + | 1.00000i | 0.0928477 | + | 0.0536056i | ||||
\(349\) | −16.0000 | −0.856460 | −0.428230 | − | 0.903670i | \(-0.640863\pi\) | ||||
−0.428230 | + | 0.903670i | \(0.640863\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.0000 | + | 25.9808i | −0.800641 | + | 1.38675i | ||||
\(352\) | −2.59808 | − | 1.50000i | −0.138478 | − | 0.0799503i | ||||
\(353\) | 21.0000i | 1.11772i | 0.829263 | + | 0.558859i | \(0.188761\pi\) | ||||
−0.829263 | + | 0.558859i | \(0.811239\pi\) | |||||||
\(354\) | −5.00000 | −0.265747 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.00000 | − | 12.1244i | −0.370999 | − | 0.642590i | ||||
\(357\) | 3.46410 | + | 2.00000i | 0.183340 | + | 0.105851i | ||||
\(358\) | 2.59808 | − | 1.50000i | 0.137313 | − | 0.0792775i | ||||
\(359\) | 12.0000 | + | 20.7846i | 0.633336 | + | 1.09697i | 0.986865 | + | 0.161546i | \(0.0516481\pi\) |
−0.353529 | + | 0.935423i | \(0.615019\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | − | 18.1865i | 0.289474 | − | 0.957186i | ||||
\(362\) | 16.0000i | 0.840941i | ||||||||
\(363\) | −1.73205 | + | 1.00000i | −0.0909091 | + | 0.0524864i | ||||
\(364\) | 6.00000 | + | 10.3923i | 0.314485 | + | 0.544705i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.00000 | − | 12.1244i | −0.365896 | − | 0.633750i | ||||
\(367\) | 24.2487 | + | 14.0000i | 1.26577 | + | 0.730794i | 0.974185 | − | 0.225750i | \(-0.0724833\pi\) |
0.291587 | + | 0.956544i | \(0.405817\pi\) | |||||||
\(368\) | 8.00000i | 0.417029i | ||||||||
\(369\) | 10.0000 | 0.520579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.00000 | + | 10.3923i | −0.311504 | + | 0.539542i | ||||
\(372\) | 8.00000i | 0.414781i | ||||||||
\(373\) | 24.0000i | 1.24267i | 0.783544 | + | 0.621336i | \(0.213410\pi\) | ||||
−0.783544 | + | 0.621336i | \(0.786590\pi\) | |||||||
\(374\) | 3.00000 | − | 5.19615i | 0.155126 | − | 0.268687i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00000 | + | 5.19615i | −0.154713 | + | 0.267971i | ||||
\(377\) | −10.3923 | + | 6.00000i | −0.535231 | + | 0.309016i | ||||
\(378\) | 8.66025 | − | 5.00000i | 0.445435 | − | 0.257172i | ||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.00000 | −0.307389 | ||||||||
\(382\) | 3.46410 | − | 2.00000i | 0.177239 | − | 0.102329i | ||||
\(383\) | −5.19615 | + | 3.00000i | −0.265511 | + | 0.153293i | −0.626846 | − | 0.779143i | \(-0.715654\pi\) |
0.361335 | + | 0.932436i | \(0.382321\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.00000 | − | 8.66025i | 0.254493 | − | 0.440795i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 15.0000i | 0.761510i | ||||||||
\(389\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 3.00000i | 0.151523i | ||||||||
\(393\) | −6.06218 | − | 3.50000i | −0.305796 | − | 0.176552i | ||||
\(394\) | −4.00000 | − | 6.92820i | −0.201517 | − | 0.349038i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.00000 | − | 5.19615i | −0.150756 | − | 0.261116i | ||||
\(397\) | 13.8564 | − | 8.00000i | 0.695433 | − | 0.401508i | −0.110211 | − | 0.993908i | \(-0.535153\pi\) |
0.805644 | + | 0.592400i | \(0.201819\pi\) | |||||||
\(398\) | − | 22.0000i | − | 1.10276i | ||||||
\(399\) | −8.00000 | − | 3.46410i | −0.400501 | − | 0.173422i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.50000 | + | 2.59808i | 0.0749064 | + | 0.129742i | 0.901046 | − | 0.433724i | \(-0.142801\pi\) |
−0.826139 | + | 0.563466i | \(0.809468\pi\) | |||||||
\(402\) | −4.33013 | + | 2.50000i | −0.215967 | + | 0.124689i | ||||
\(403\) | −41.5692 | − | 24.0000i | −2.07071 | − | 1.19553i | ||||
\(404\) | −5.00000 | − | 8.66025i | −0.248759 | − | 0.430864i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.00000 | 0.198517 | ||||||||
\(407\) | − | 24.0000i | − | 1.18964i | ||||||
\(408\) | 1.73205 | + | 1.00000i | 0.0857493 | + | 0.0495074i | ||||
\(409\) | −9.50000 | + | 16.4545i | −0.469745 | + | 0.813622i | −0.999402 | − | 0.0345902i | \(-0.988987\pi\) |
0.529657 | + | 0.848212i | \(0.322321\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.00000 | 0.147979 | ||||||||
\(412\) | −5.19615 | − | 3.00000i | −0.255996 | − | 0.147799i | ||||
\(413\) | −8.66025 | + | 5.00000i | −0.426143 | + | 0.246034i | ||||
\(414\) | −8.00000 | + | 13.8564i | −0.393179 | + | 0.681005i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.00000 | + | 5.19615i | 0.147087 | + | 0.254762i | ||||
\(417\) | − | 9.00000i | − | 0.440732i | ||||||
\(418\) | −5.19615 | + | 12.0000i | −0.254152 | + | 0.586939i | ||||
\(419\) | −28.0000 | −1.36789 | −0.683945 | − | 0.729534i | \(-0.739737\pi\) | ||||
−0.683945 | + | 0.729534i | \(0.739737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.00000 | + | 6.92820i | 0.194948 | + | 0.337660i | 0.946883 | − | 0.321577i | \(-0.104213\pi\) |
−0.751935 | + | 0.659237i | \(0.770879\pi\) | |||||||
\(422\) | −3.46410 | − | 2.00000i | −0.168630 | − | 0.0973585i | ||||
\(423\) | −10.3923 | + | 6.00000i | −0.505291 | + | 0.291730i | ||||
\(424\) | −3.00000 | + | 5.19615i | −0.145693 | + | 0.252347i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.00000 | −0.290701 | ||||||||
\(427\) | −24.2487 | − | 14.0000i | −1.17348 | − | 0.677507i | ||||
\(428\) | −10.3923 | − | 6.00000i | −0.502331 | − | 0.290021i | ||||
\(429\) | −18.0000 | −0.869048 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.00000 | − | 5.19615i | 0.144505 | − | 0.250290i | −0.784683 | − | 0.619897i | \(-0.787174\pi\) |
0.929188 | + | 0.369607i | \(0.120508\pi\) | |||||||
\(432\) | 4.33013 | − | 2.50000i | 0.208333 | − | 0.120281i | ||||
\(433\) | 25.9808 | + | 15.0000i | 1.24856 | + | 0.720854i | 0.970821 | − | 0.239804i | \(-0.0770831\pi\) |
0.277734 | + | 0.960658i | \(0.410416\pi\) | |||||||
\(434\) | 8.00000 | + | 13.8564i | 0.384012 | + | 0.665129i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.00000 | −0.383131 | ||||||||
\(437\) | 34.6410 | − | 4.00000i | 1.65710 | − | 0.191346i | ||||
\(438\) | 9.00000i | 0.430037i | ||||||||
\(439\) | −4.00000 | − | 6.92820i | −0.190910 | − | 0.330665i | 0.754642 | − | 0.656136i | \(-0.227810\pi\) |
−0.945552 | + | 0.325471i | \(0.894477\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | + | 5.19615i | −0.142857 | + | 0.247436i | ||||
\(442\) | −10.3923 | + | 6.00000i | −0.494312 | + | 0.285391i | ||||
\(443\) | −7.79423 | − | 4.50000i | −0.370315 | − | 0.213801i | 0.303281 | − | 0.952901i | \(-0.401918\pi\) |
−0.673596 | + | 0.739100i | \(0.735251\pi\) | |||||||
\(444\) | 8.00000 | 0.379663 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.00000 | + | 13.8564i | −0.378811 | + | 0.656120i | ||||
\(447\) | 3.46410 | + | 2.00000i | 0.163846 | + | 0.0945968i | ||||
\(448\) | − | 2.00000i | − | 0.0944911i | ||||||
\(449\) | −29.0000 | −1.36859 | −0.684297 | − | 0.729203i | \(-0.739891\pi\) | ||||
−0.684297 | + | 0.729203i | \(0.739891\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.50000 | + | 12.9904i | 0.353161 | + | 0.611693i | ||||
\(452\) | 11.2583 | + | 6.50000i | 0.529547 | + | 0.305734i | ||||
\(453\) | 10.3923 | − | 6.00000i | 0.488273 | − | 0.281905i | ||||
\(454\) | 3.50000 | + | 6.06218i | 0.164263 | + | 0.284512i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.00000 | − | 1.73205i | −0.187317 | − | 0.0811107i | ||||
\(457\) | 13.0000i | 0.608114i | 0.952654 | + | 0.304057i | \(0.0983414\pi\) | ||||
−0.952654 | + | 0.304057i | \(0.901659\pi\) | |||||||
\(458\) | −20.7846 | + | 12.0000i | −0.971201 | + | 0.560723i | ||||
\(459\) | 5.00000 | + | 8.66025i | 0.233380 | + | 0.404226i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.0000 | + | 19.0526i | 0.512321 | + | 0.887366i | 0.999898 | + | 0.0142861i | \(0.00454755\pi\) |
−0.487577 | + | 0.873080i | \(0.662119\pi\) | |||||||
\(462\) | 5.19615 | + | 3.00000i | 0.241747 | + | 0.139573i | ||||
\(463\) | − | 34.0000i | − | 1.58011i | −0.613033 | − | 0.790057i | \(-0.710051\pi\) | ||
0.613033 | − | 0.790057i | \(-0.289949\pi\) | |||||||
\(464\) | 2.00000 | 0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.50000 | − | 9.52628i | 0.254783 | − | 0.441296i | ||||
\(467\) | 7.00000i | 0.323921i | 0.986797 | + | 0.161961i | \(0.0517818\pi\) | ||||
−0.986797 | + | 0.161961i | \(0.948218\pi\) | |||||||
\(468\) | 12.0000i | 0.554700i | ||||||||
\(469\) | −5.00000 | + | 8.66025i | −0.230879 | + | 0.399893i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.33013 | + | 2.50000i | −0.199310 | + | 0.115072i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −8.00000 | −0.367452 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.00000 | 0.183340 | ||||||||
\(477\) | −10.3923 | + | 6.00000i | −0.475831 | + | 0.274721i | ||||
\(478\) | 10.3923 | − | 6.00000i | 0.475333 | − | 0.274434i | ||||
\(479\) | 6.00000 | − | 10.3923i | 0.274147 | − | 0.474837i | −0.695773 | − | 0.718262i | \(-0.744938\pi\) |
0.969920 | + | 0.243426i | \(0.0782712\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.0000 | + | 41.5692i | −1.09431 | + | 1.89539i | ||||
\(482\) | 19.0000i | 0.865426i | ||||||||
\(483\) | − | 16.0000i | − | 0.728025i | ||||||
\(484\) | −1.00000 | + | 1.73205i | −0.0454545 | + | 0.0787296i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 16.0000 | 0.725775 | ||||||||
\(487\) | 4.00000i | 0.181257i | 0.995885 | + | 0.0906287i | \(0.0288876\pi\) | ||||
−0.995885 | + | 0.0906287i | \(0.971112\pi\) | |||||||
\(488\) | −12.1244 | − | 7.00000i | −0.548844 | − | 0.316875i | ||||
\(489\) | −1.50000 | − | 2.59808i | −0.0678323 | − | 0.117489i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.0000 | − | 17.3205i | −0.451294 | − | 0.781664i | 0.547173 | − | 0.837020i | \(-0.315704\pi\) |
−0.998467 | + | 0.0553560i | \(0.982371\pi\) | |||||||
\(492\) | −4.33013 | + | 2.50000i | −0.195217 | + | 0.112709i | ||||
\(493\) | 4.00000i | 0.180151i | ||||||||
\(494\) | 21.0000 | − | 15.5885i | 0.944835 | − | 0.701358i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.00000 | + | 6.92820i | 0.179605 | + | 0.311086i | ||||
\(497\) | −10.3923 | + | 6.00000i | −0.466159 | + | 0.269137i | ||||
\(498\) | −9.52628 | − | 5.50000i | −0.426883 | − | 0.246461i | ||||
\(499\) | 16.5000 | + | 28.5788i | 0.738641 | + | 1.27936i | 0.953107 | + | 0.302633i | \(0.0978656\pi\) |
−0.214466 | + | 0.976732i | \(0.568801\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.00000 | −0.357414 | ||||||||
\(502\) | 17.0000i | 0.758747i | ||||||||
\(503\) | 3.46410 | + | 2.00000i | 0.154457 | + | 0.0891756i | 0.575236 | − | 0.817987i | \(-0.304910\pi\) |
−0.420780 | + | 0.907163i | \(0.638243\pi\) | |||||||
\(504\) | 2.00000 | − | 3.46410i | 0.0890871 | − | 0.154303i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −24.0000 | −1.06693 | ||||||||
\(507\) | 19.9186 | + | 11.5000i | 0.884615 | + | 0.510733i | ||||
\(508\) | −5.19615 | + | 3.00000i | −0.230542 | + | 0.133103i | ||||
\(509\) | 6.00000 | − | 10.3923i | 0.265945 | − | 0.460631i | −0.701866 | − | 0.712309i | \(-0.747649\pi\) |
0.967811 | + | 0.251679i | \(0.0809826\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.00000 | + | 15.5885i | 0.398137 | + | 0.689593i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −12.9904 | − | 17.5000i | −0.573539 | − | 0.772644i | ||||
\(514\) | 3.00000 | 0.132324 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.5885 | − | 9.00000i | −0.685580 | − | 0.395820i | ||||
\(518\) | 13.8564 | − | 8.00000i | 0.608816 | − | 0.351500i | ||||
\(519\) | 9.00000 | − | 15.5885i | 0.395056 | − | 0.684257i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.0000 | 0.920027 | 0.460013 | − | 0.887912i | \(-0.347845\pi\) | ||||
0.460013 | + | 0.887912i | \(0.347845\pi\) | |||||||
\(522\) | 3.46410 | + | 2.00000i | 0.151620 | + | 0.0875376i | ||||
\(523\) | 6.92820 | + | 4.00000i | 0.302949 | + | 0.174908i | 0.643767 | − | 0.765222i | \(-0.277371\pi\) |
−0.340818 | + | 0.940129i | \(0.610704\pi\) | |||||||
\(524\) | −7.00000 | −0.305796 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.0000 | + | 22.5167i | −0.566827 | + | 0.981773i | ||||
\(527\) | −13.8564 | + | 8.00000i | −0.603595 | + | 0.348485i | ||||
\(528\) | 2.59808 | + | 1.50000i | 0.113067 | + | 0.0652791i | ||||
\(529\) | 20.5000 | + | 35.5070i | 0.891304 | + | 1.54378i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.0000 | −0.433963 | ||||||||
\(532\) | −8.66025 | + | 1.00000i | −0.375470 | + | 0.0433555i | ||||
\(533\) | − | 30.0000i | − | 1.29944i | ||||||
\(534\) | 7.00000 | + | 12.1244i | 0.302920 | + | 0.524672i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.50000 | + | 4.33013i | −0.107984 | + | 0.187033i | ||||
\(537\) | −2.59808 | + | 1.50000i | −0.112115 | + | 0.0647298i | ||||
\(538\) | 24.2487 | + | 14.0000i | 1.04544 | + | 0.603583i | ||||
\(539\) | −9.00000 | −0.387657 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.00000 | + | 6.92820i | −0.171973 | + | 0.297867i | −0.939110 | − | 0.343617i | \(-0.888348\pi\) |
0.767136 | + | 0.641484i | \(0.221681\pi\) | |||||||
\(542\) | −19.0526 | − | 11.0000i | −0.818377 | − | 0.472490i | ||||
\(543\) | − | 16.0000i | − | 0.686626i | ||||||
\(544\) | 2.00000 | 0.0857493 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −6.00000 | − | 10.3923i | −0.256776 | − | 0.444750i | ||||
\(547\) | 6.92820 | + | 4.00000i | 0.296229 | + | 0.171028i | 0.640747 | − | 0.767752i | \(-0.278625\pi\) |
−0.344519 | + | 0.938779i | \(0.611958\pi\) | |||||||
\(548\) | 2.59808 | − | 1.50000i | 0.110984 | − | 0.0640768i | ||||
\(549\) | −14.0000 | − | 24.2487i | −0.597505 | − | 1.03491i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.00000 | − | 8.66025i | −0.0426014 | − | 0.368939i | ||||
\(552\) | − | 8.00000i | − | 0.340503i | ||||||
\(553\) | −13.8564 | + | 8.00000i | −0.589234 | + | 0.340195i | ||||
\(554\) | 7.00000 | + | 12.1244i | 0.297402 | + | 0.515115i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.50000 | − | 7.79423i | −0.190843 | − | 0.330549i | ||||
\(557\) | 34.6410 | + | 20.0000i | 1.46779 | + | 0.847427i | 0.999349 | − | 0.0360693i | \(-0.0114837\pi\) |
0.468438 | + | 0.883497i | \(0.344817\pi\) | |||||||
\(558\) | 16.0000i | 0.677334i | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.00000 | + | 5.19615i | −0.126660 | + | 0.219382i | ||||
\(562\) | − | 7.00000i | − | 0.295277i | ||||||
\(563\) | 23.0000i | 0.969334i | 0.874699 | + | 0.484667i | \(0.161059\pi\) | ||||
−0.874699 | + | 0.484667i | \(0.838941\pi\) | |||||||
\(564\) | 3.00000 | − | 5.19615i | 0.126323 | − | 0.218797i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −14.5000 | + | 25.1147i | −0.609480 | + | 1.05565i | ||||
\(567\) | 1.73205 | − | 1.00000i | 0.0727393 | − | 0.0419961i | ||||
\(568\) | −5.19615 | + | 3.00000i | −0.218026 | + | 0.125877i | ||||
\(569\) | −34.0000 | −1.42535 | −0.712677 | − | 0.701492i | \(-0.752517\pi\) | ||||
−0.712677 | + | 0.701492i | \(0.752517\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.0000 | −1.21361 | −0.606806 | − | 0.794850i | \(-0.707550\pi\) | ||||
−0.606806 | + | 0.794850i | \(0.707550\pi\) | |||||||
\(572\) | −15.5885 | + | 9.00000i | −0.651786 | + | 0.376309i | ||||
\(573\) | −3.46410 | + | 2.00000i | −0.144715 | + | 0.0835512i | ||||
\(574\) | −5.00000 | + | 8.66025i | −0.208696 | + | 0.361472i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | − | 1.73205i | 0.0416667 | − | 0.0721688i | ||||
\(577\) | 7.00000i | 0.291414i | 0.989328 | + | 0.145707i | \(0.0465456\pi\) | ||||
−0.989328 | + | 0.145707i | \(0.953454\pi\) | |||||||
\(578\) | − | 13.0000i | − | 0.540729i | ||||||
\(579\) | −5.00000 | + | 8.66025i | −0.207793 | + | 0.359908i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.0000 | −0.912714 | ||||||||
\(582\) | − | 15.0000i | − | 0.621770i | ||||||
\(583\) | −15.5885 | − | 9.00000i | −0.645608 | − | 0.372742i | ||||
\(584\) | 4.50000 | + | 7.79423i | 0.186211 | + | 0.322527i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.0000 | + | 19.0526i | 0.454406 | + | 0.787054i | ||||
\(587\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(588\) | − | 3.00000i | − | 0.123718i | ||||||
\(589\) | 28.0000 | − | 20.7846i | 1.15372 | − | 0.856415i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.00000 | + | 6.92820i | 0.164538 | + | 0.284988i | ||||
\(592\) | 6.92820 | − | 4.00000i | 0.284747 | − | 0.164399i | ||||
\(593\) | −11.2583 | − | 6.50000i | −0.462324 | − | 0.266923i | 0.250697 | − | 0.968066i | \(-0.419340\pi\) |
−0.713021 | + | 0.701143i | \(0.752674\pi\) | |||||||
\(594\) | 7.50000 | + | 12.9904i | 0.307729 | + | 0.533002i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.00000 | 0.163846 | ||||||||
\(597\) | 22.0000i | 0.900400i | ||||||||
\(598\) | 41.5692 | + | 24.0000i | 1.69989 | + | 0.981433i | ||||
\(599\) | 24.0000 | − | 41.5692i | 0.980613 | − | 1.69847i | 0.320607 | − | 0.947212i | \(-0.396113\pi\) |
0.660006 | − | 0.751260i | \(-0.270554\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.0000 | −1.50926 | −0.754631 | − | 0.656150i | \(-0.772184\pi\) | ||||
−0.754631 | + | 0.656150i | \(0.772184\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.66025 | + | 5.00000i | −0.352673 | + | 0.203616i | ||||
\(604\) | 6.00000 | − | 10.3923i | 0.244137 | − | 0.422857i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.00000 | + | 8.66025i | 0.203111 | + | 0.351799i | ||||
\(607\) | − | 14.0000i | − | 0.568242i | −0.958788 | − | 0.284121i | \(-0.908298\pi\) | ||
0.958788 | − | 0.284121i | \(-0.0917018\pi\) | |||||||
\(608\) | −4.33013 | + | 0.500000i | −0.175610 | + | 0.0202777i | ||||
\(609\) | −4.00000 | −0.162088 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.0000 | + | 31.1769i | 0.728202 | + | 1.26128i | ||||
\(612\) | 3.46410 | + | 2.00000i | 0.140028 | + | 0.0808452i | ||||
\(613\) | 29.4449 | − | 17.0000i | 1.18927 | − | 0.686624i | 0.231127 | − | 0.972924i | \(-0.425759\pi\) |
0.958140 | + | 0.286300i | \(0.0924254\pi\) | |||||||
\(614\) | 2.50000 | − | 4.33013i | 0.100892 | − | 0.174750i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.00000 | 0.241747 | ||||||||
\(617\) | −16.4545 | − | 9.50000i | −0.662433 | − | 0.382456i | 0.130771 | − | 0.991413i | \(-0.458255\pi\) |
−0.793203 | + | 0.608957i | \(0.791588\pi\) | |||||||
\(618\) | 5.19615 | + | 3.00000i | 0.209020 | + | 0.120678i | ||||
\(619\) | −40.0000 | −1.60774 | −0.803868 | − | 0.594808i | \(-0.797228\pi\) | ||||
−0.803868 | + | 0.594808i | \(0.797228\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.0000 | − | 34.6410i | 0.802572 | − | 1.39010i | ||||
\(622\) | 20.7846 | − | 12.0000i | 0.833387 | − | 0.481156i | ||||
\(623\) | 24.2487 | + | 14.0000i | 0.971504 | + | 0.560898i | ||||
\(624\) | −3.00000 | − | 5.19615i | −0.120096 | − | 0.208013i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −13.0000 | −0.519584 | ||||||||
\(627\) | 5.19615 | − | 12.0000i | 0.207514 | − | 0.479234i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.00000 | + | 13.8564i | 0.318981 | + | 0.552491i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.0000 | − | 25.9808i | 0.597141 | − | 1.03428i | −0.396100 | − | 0.918207i | \(-0.629637\pi\) |
0.993241 | − | 0.116071i | \(-0.0370299\pi\) | |||||||
\(632\) | −6.92820 | + | 4.00000i | −0.275589 | + | 0.159111i | ||||
\(633\) | 3.46410 | + | 2.00000i | 0.137686 | + | 0.0794929i | ||||
\(634\) | −30.0000 | −1.19145 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.00000 | − | 5.19615i | 0.118958 | − | 0.206041i | ||||
\(637\) | 15.5885 | + | 9.00000i | 0.617637 | + | 0.356593i | ||||
\(638\) | 6.00000i | 0.237542i | ||||||||
\(639\) | −12.0000 | −0.474713 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.5000 | − | 18.1865i | −0.414725 | − | 0.718325i | 0.580674 | − | 0.814136i | \(-0.302789\pi\) |
−0.995400 | + | 0.0958109i | \(0.969456\pi\) | |||||||
\(642\) | 10.3923 | + | 6.00000i | 0.410152 | + | 0.236801i | ||||
\(643\) | 4.33013 | − | 2.50000i | 0.170764 | − | 0.0985904i | −0.412182 | − | 0.911101i | \(-0.635233\pi\) |
0.582946 | + | 0.812511i | \(0.301900\pi\) | |||||||
\(644\) | −8.00000 | − | 13.8564i | −0.315244 | − | 0.546019i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.00000 | − | 8.66025i | −0.0393445 | − | 0.340733i | ||||
\(647\) | 6.00000i | 0.235884i | 0.993020 | + | 0.117942i | \(0.0376297\pi\) | ||||
−0.993020 | + | 0.117942i | \(0.962370\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | −7.50000 | − | 12.9904i | −0.294401 | − | 0.509917i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.00000 | − | 13.8564i | −0.313545 | − | 0.543075i | ||||
\(652\) | −2.59808 | − | 1.50000i | −0.101749 | − | 0.0587445i | ||||
\(653\) | 36.0000i | 1.40879i | 0.709809 | + | 0.704394i | \(0.248781\pi\) | ||||
−0.709809 | + | 0.704394i | \(0.751219\pi\) | |||||||
\(654\) | 8.00000 | 0.312825 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.50000 | + | 4.33013i | −0.0976086 | + | 0.169063i | ||||
\(657\) | 18.0000i | 0.702247i | ||||||||
\(658\) | − | 12.0000i | − | 0.467809i | ||||||
\(659\) | −6.00000 | + | 10.3923i | −0.233727 | + | 0.404827i | −0.958902 | − | 0.283738i | \(-0.908425\pi\) |
0.725175 | + | 0.688565i | \(0.241759\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.0000 | − | 19.0526i | 0.427850 | − | 0.741059i | −0.568831 | − | 0.822454i | \(-0.692604\pi\) |
0.996682 | + | 0.0813955i | \(0.0259377\pi\) | |||||||
\(662\) | 14.7224 | − | 8.50000i | 0.572204 | − | 0.330362i | ||||
\(663\) | 10.3923 | − | 6.00000i | 0.403604 | − | 0.233021i | ||||
\(664\) | −11.0000 | −0.426883 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16.0000 | 0.619987 | ||||||||
\(667\) | 13.8564 | − | 8.00000i | 0.536522 | − | 0.309761i | ||||
\(668\) | −6.92820 | + | 4.00000i | −0.268060 | + | 0.154765i | ||||
\(669\) | 8.00000 | − | 13.8564i | 0.309298 | − | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.0000 | − | 36.3731i | 0.810696 | − | 1.40417i | ||||
\(672\) | 2.00000i | 0.0771517i | ||||||||
\(673\) | − | 26.0000i | − | 1.00223i | −0.865382 | − | 0.501113i | \(-0.832924\pi\) | ||
0.865382 | − | 0.501113i | \(-0.167076\pi\) | |||||||
\(674\) | −9.50000 | + | 16.4545i | −0.365926 | + | 0.633803i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.0000 | 0.884615 | ||||||||
\(677\) | − | 2.00000i | − | 0.0768662i | −0.999261 | − | 0.0384331i | \(-0.987763\pi\) | ||
0.999261 | − | 0.0384331i | \(-0.0122367\pi\) | |||||||
\(678\) | −11.2583 | − | 6.50000i | −0.432374 | − | 0.249631i | ||||
\(679\) | −15.0000 | − | 25.9808i | −0.575647 | − | 0.997050i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.50000 | − | 6.06218i | −0.134120 | − | 0.232303i | ||||
\(682\) | −20.7846 | + | 12.0000i | −0.795884 | + | 0.459504i | ||||
\(683\) | 36.0000i | 1.37750i | 0.724998 | + | 0.688751i | \(0.241841\pi\) | ||||
−0.724998 | + | 0.688751i | \(0.758159\pi\) | |||||||
\(684\) | −8.00000 | − | 3.46410i | −0.305888 | − | 0.132453i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10.0000 | − | 17.3205i | −0.381802 | − | 0.661300i | ||||
\(687\) | 20.7846 | − | 12.0000i | 0.792982 | − | 0.457829i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.0000 | + | 31.1769i | 0.685745 | + | 1.18775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.0000 | 1.06517 | 0.532585 | − | 0.846376i | \(-0.321221\pi\) | ||||
0.532585 | + | 0.846376i | \(0.321221\pi\) | |||||||
\(692\) | − | 18.0000i | − | 0.684257i | ||||||
\(693\) | 10.3923 | + | 6.00000i | 0.394771 | + | 0.227921i | ||||
\(694\) | 13.5000 | − | 23.3827i | 0.512453 | − | 0.887595i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.00000 | −0.0758098 | ||||||||
\(697\) | −8.66025 | − | 5.00000i | −0.328031 | − | 0.189389i | ||||
\(698\) | 13.8564 | − | 8.00000i | 0.524473 | − | 0.302804i | ||||
\(699\) | −5.50000 | + | 9.52628i | −0.208029 | + | 0.360317i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.0000 | + | 36.3731i | 0.793159 | + | 1.37379i | 0.924002 | + | 0.382389i | \(0.124898\pi\) |
−0.130843 | + | 0.991403i | \(0.541768\pi\) | |||||||
\(702\) | − | 30.0000i | − | 1.13228i | ||||||
\(703\) | −20.7846 | − | 28.0000i | −0.783906 | − | 1.05604i | ||||
\(704\) | 3.00000 | 0.113067 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.5000 | − | 18.1865i | −0.395173 | − | 0.684459i | ||||
\(707\) | 17.3205 | + | 10.0000i | 0.651405 | + | 0.376089i | ||||
\(708\) | 4.33013 | − | 2.50000i | 0.162736 | − | 0.0939558i | ||||
\(709\) | 10.0000 | − | 17.3205i | 0.375558 | − | 0.650485i | −0.614852 | − | 0.788642i | \(-0.710784\pi\) |
0.990410 | + | 0.138157i | \(0.0441178\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.0000 | −0.600047 | ||||||||
\(712\) | 12.1244 | + | 7.00000i | 0.454379 | + | 0.262336i | ||||
\(713\) | 55.4256 | + | 32.0000i | 2.07571 | + | 1.19841i | ||||
\(714\) | −4.00000 | −0.149696 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.50000 | + | 2.59808i | −0.0560576 | + | 0.0970947i | ||||
\(717\) | −10.3923 | + | 6.00000i | −0.388108 | + | 0.224074i | ||||
\(718\) | −20.7846 | − | 12.0000i | −0.775675 | − | 0.447836i | ||||
\(719\) | 25.0000 | + | 43.3013i | 0.932343 | + | 1.61486i | 0.779305 | + | 0.626644i | \(0.215572\pi\) |
0.153037 | + | 0.988220i | \(0.451094\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000 | 0.446903 | ||||||||
\(722\) | 4.33013 | + | 18.5000i | 0.161151 | + | 0.688499i | ||||
\(723\) | − | 19.0000i | − | 0.706618i | ||||||
\(724\) | −8.00000 | − | 13.8564i | −0.297318 | − | 0.514969i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.00000 | − | 1.73205i | 0.0371135 | − | 0.0642824i | ||||
\(727\) | 6.92820 | − | 4.00000i | 0.256953 | − | 0.148352i | −0.365991 | − | 0.930618i | \(-0.619270\pi\) |
0.622944 | + | 0.782267i | \(0.285937\pi\) | |||||||
\(728\) | −10.3923 | − | 6.00000i | −0.385164 | − | 0.222375i | ||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 12.1244 | + | 7.00000i | 0.448129 | + | 0.258727i | ||||
\(733\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(734\) | −28.0000 | −1.03350 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.00000 | − | 6.92820i | −0.147442 | − | 0.255377i | ||||
\(737\) | −12.9904 | − | 7.50000i | −0.478507 | − | 0.276266i | ||||
\(738\) | −8.66025 | + | 5.00000i | −0.318788 | + | 0.184053i | ||||
\(739\) | 2.50000 | + | 4.33013i | 0.0919640 | + | 0.159286i | 0.908337 | − | 0.418238i | \(-0.137352\pi\) |
−0.816373 | + | 0.577524i | \(0.804019\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.0000 | + | 15.5885i | −0.771454 | + | 0.572656i | ||||
\(742\) | − | 12.0000i | − | 0.440534i | ||||||
\(743\) | −3.46410 | + | 2.00000i | −0.127086 | + | 0.0733729i | −0.562195 | − | 0.827005i | \(-0.690043\pi\) |
0.435110 | + | 0.900378i | \(0.356710\pi\) | |||||||
\(744\) | −4.00000 | − | 6.92820i | −0.146647 | − | 0.254000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −12.0000 | − | 20.7846i | −0.439351 | − | 0.760979i | ||||
\(747\) | −19.0526 | − | 11.0000i | −0.697097 | − | 0.402469i | ||||
\(748\) | 6.00000i | 0.219382i | ||||||||
\(749\) | 24.0000 | 0.876941 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.0000 | − | 32.9090i | 0.693320 | − | 1.20087i | −0.277424 | − | 0.960748i | \(-0.589481\pi\) |
0.970744 | − | 0.240118i | \(-0.0771860\pi\) | |||||||
\(752\) | − | 6.00000i | − | 0.218797i | ||||||
\(753\) | − | 17.0000i | − | 0.619514i | ||||||
\(754\) | 6.00000 | − | 10.3923i | 0.218507 | − | 0.378465i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.00000 | + | 8.66025i | −0.181848 | + | 0.314970i | ||||
\(757\) | 29.4449 | − | 17.0000i | 1.07019 | − | 0.617876i | 0.141958 | − | 0.989873i | \(-0.454660\pi\) |
0.928234 | + | 0.371997i | \(0.121327\pi\) | |||||||
\(758\) | −24.2487 | + | 14.0000i | −0.880753 | + | 0.508503i | ||||
\(759\) | 24.0000 | 0.871145 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.00000 | −0.108750 | −0.0543750 | − | 0.998521i | \(-0.517317\pi\) | ||||
−0.0543750 | + | 0.998521i | \(0.517317\pi\) | |||||||
\(762\) | 5.19615 | − | 3.00000i | 0.188237 | − | 0.108679i | ||||
\(763\) | 13.8564 | − | 8.00000i | 0.501636 | − | 0.289619i | ||||
\(764\) | −2.00000 | + | 3.46410i | −0.0723575 | + | 0.125327i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.00000 | − | 5.19615i | 0.108394 | − | 0.187745i | ||||
\(767\) | 30.0000i | 1.08324i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −25.0000 | + | 43.3013i | −0.901523 | + | 1.56148i | −0.0760054 | + | 0.997107i | \(0.524217\pi\) |
−0.825518 | + | 0.564376i | \(0.809117\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.00000 | −0.108042 | ||||||||
\(772\) | 10.0000i | 0.359908i | ||||||||
\(773\) | 25.9808 | + | 15.0000i | 0.934463 | + | 0.539513i | 0.888220 | − | 0.459418i | \(-0.151942\pi\) |
0.0462427 | + | 0.998930i | \(0.485275\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.50000 | − | 12.9904i | −0.269234 | − | 0.466328i | ||||
\(777\) | −13.8564 | + | 8.00000i | −0.497096 | + | 0.286998i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.0000 | + | 8.66025i | 0.716574 | + | 0.310286i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.00000 | − | 15.5885i | −0.322045 | − | 0.557799i | ||||
\(782\) | 13.8564 | − | 8.00000i | 0.495504 | − | 0.286079i | ||||
\(783\) | −8.66025 | − | 5.00000i | −0.309492 | − | 0.178685i | ||||
\(784\) | −1.50000 | − | 2.59808i | −0.0535714 | − | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 7.00000 | 0.249682 | ||||||||
\(787\) | − | 1.00000i | − | 0.0356462i | −0.999841 | − | 0.0178231i | \(-0.994326\pi\) | ||
0.999841 | − | 0.0178231i | \(-0.00567356\pi\) | |||||||
\(788\) | 6.92820 | + | 4.00000i | 0.246807 | + | 0.142494i | ||||
\(789\) | 13.0000 | − | 22.5167i | 0.462812 | − | 0.801614i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.0000 | −0.924454 | ||||||||
\(792\) | 5.19615 | + | 3.00000i | 0.184637 | + | 0.106600i | ||||
\(793\) | −72.7461 | + | 42.0000i | −2.58329 | + | 1.49146i | ||||
\(794\) | −8.00000 | + | 13.8564i | −0.283909 | + | 0.491745i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.0000 | + | 19.0526i | 0.389885 | + | 0.675300i | ||||
\(797\) | − | 28.0000i | − | 0.991811i | −0.868377 | − | 0.495905i | \(-0.834836\pi\) | ||
0.868377 | − | 0.495905i | \(-0.165164\pi\) | |||||||
\(798\) | 8.66025 | − | 1.00000i | 0.306570 | − | 0.0353996i | ||||
\(799\) | 12.0000 | 0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.0000 | + | 24.2487i | 0.494666 | + | 0.856786i | ||||
\(802\) | −2.59808 | − | 1.50000i | −0.0917413 | − | 0.0529668i | ||||
\(803\) | −23.3827 | + | 13.5000i | −0.825157 | + | 0.476405i | ||||
\(804\) | 2.50000 | − | 4.33013i | 0.0881682 | − | 0.152712i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 48.0000 | 1.69073 | ||||||||
\(807\) | −24.2487 | − | 14.0000i | −0.853595 | − | 0.492823i | ||||
\(808\) | 8.66025 | + | 5.00000i | 0.304667 | + | 0.175899i | ||||
\(809\) | 51.0000 | 1.79306 | 0.896532 | − | 0.442978i | \(-0.146078\pi\) | ||||
0.896532 | + | 0.442978i | \(0.146078\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.0000 | + | 17.3205i | −0.351147 | + | 0.608205i | −0.986451 | − | 0.164057i | \(-0.947542\pi\) |
0.635303 | + | 0.772263i | \(0.280875\pi\) | |||||||
\(812\) | −3.46410 | + | 2.00000i | −0.121566 | + | 0.0701862i | ||||
\(813\) | 19.0526 | + | 11.0000i | 0.668202 | + | 0.385787i | ||||
\(814\) | 12.0000 | + | 20.7846i | 0.420600 | + | 0.728500i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.00000 | −0.0700140 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 19.0000i | − | 0.664319i | ||||||
\(819\) | −12.0000 | − | 20.7846i | −0.419314 | − | 0.726273i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.00000 | − | 12.1244i | 0.244302 | − | 0.423143i | −0.717633 | − | 0.696421i | \(-0.754775\pi\) |
0.961935 | + | 0.273278i | \(0.0881079\pi\) | |||||||
\(822\) | −2.59808 | + | 1.50000i | −0.0906183 | + | 0.0523185i | ||||
\(823\) | 1.73205 | + | 1.00000i | 0.0603755 | + | 0.0348578i | 0.529884 | − | 0.848070i | \(-0.322235\pi\) |
−0.469508 | + | 0.882928i | \(0.655569\pi\) | |||||||
\(824\) | 6.00000 | 0.209020 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.00000 | − | 8.66025i | 0.173972 | − | 0.301329i | ||||
\(827\) | −23.3827 | − | 13.5000i | −0.813096 | − | 0.469441i | 0.0349341 | − | 0.999390i | \(-0.488878\pi\) |
−0.848030 | + | 0.529949i | \(0.822211\pi\) | |||||||
\(828\) | − | 16.0000i | − | 0.556038i | ||||||
\(829\) | −48.0000 | −1.66711 | −0.833554 | − | 0.552437i | \(-0.813698\pi\) | ||||
−0.833554 | + | 0.552437i | \(0.813698\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.00000 | − | 12.1244i | −0.242827 | − | 0.420589i | ||||
\(832\) | −5.19615 | − | 3.00000i | −0.180144 | − | 0.104006i | ||||
\(833\) | 5.19615 | − | 3.00000i | 0.180036 | − | 0.103944i | ||||
\(834\) | 4.50000 | + | 7.79423i | 0.155822 | + | 0.269892i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.50000 | − | 12.9904i | −0.0518786 | − | 0.449282i | ||||
\(837\) | − | 40.0000i | − | 1.38260i | ||||||
\(838\) | 24.2487 | − | 14.0000i | 0.837658 | − | 0.483622i | ||||
\(839\) | 21.0000 | + | 36.3731i | 0.725001 | + | 1.25574i | 0.958974 | + | 0.283495i | \(0.0914938\pi\) |
−0.233973 | + | 0.972243i | \(0.575173\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.5000 | + | 21.6506i | 0.431034 | + | 0.746574i | ||||
\(842\) | −6.92820 | − | 4.00000i | −0.238762 | − | 0.137849i | ||||
\(843\) | 7.00000i | 0.241093i | ||||||||
\(844\) | 4.00000 | 0.137686 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.00000 | − | 10.3923i | 0.206284 | − | 0.357295i | ||||
\(847\) | − | 4.00000i | − | 0.137442i | ||||||
\(848\) | − | 6.00000i | − | 0.206041i | ||||||
\(849\) | 14.5000 | − | 25.1147i | 0.497639 | − | 0.861936i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32.0000 | − | 55.4256i | 1.09695 | − | 1.89997i | ||||
\(852\) | 5.19615 | − | 3.00000i | 0.178017 | − | 0.102778i | ||||
\(853\) | 8.66025 | − | 5.00000i | 0.296521 | − | 0.171197i | −0.344358 | − | 0.938839i | \(-0.611903\pi\) |
0.640879 | + | 0.767642i | \(0.278570\pi\) | |||||||
\(854\) | 28.0000 | 0.958140 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.0000 | 0.410152 | ||||||||
\(857\) | −12.9904 | + | 7.50000i | −0.443743 | + | 0.256195i | −0.705184 | − | 0.709024i | \(-0.749136\pi\) |
0.261441 | + | 0.965219i | \(0.415802\pi\) | |||||||
\(858\) | 15.5885 | − | 9.00000i | 0.532181 | − | 0.307255i | ||||
\(859\) | 11.5000 | − | 19.9186i | 0.392375 | − | 0.679613i | −0.600387 | − | 0.799709i | \(-0.704987\pi\) |
0.992762 | + | 0.120096i | \(0.0383202\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.00000 | − | 8.66025i | 0.170400 | − | 0.295141i | ||||
\(862\) | 6.00000i | 0.204361i | ||||||||
\(863\) | − | 24.0000i | − | 0.816970i | −0.912765 | − | 0.408485i | \(-0.866057\pi\) | ||
0.912765 | − | 0.408485i | \(-0.133943\pi\) | |||||||
\(864\) | −2.50000 | + | 4.33013i | −0.0850517 | + | 0.147314i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −30.0000 | −1.01944 | ||||||||
\(867\) | 13.0000i | 0.441503i | ||||||||
\(868\) | −13.8564 | − | 8.00000i | −0.470317 | − | 0.271538i | ||||
\(869\) | −12.0000 | − | 20.7846i | −0.407072 | − | 0.705070i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.0000 | + | 25.9808i | 0.508256 | + | 0.880325i | ||||
\(872\) | 6.92820 | − | 4.00000i | 0.234619 | − | 0.135457i | ||||
\(873\) | − | 30.0000i | − | 1.01535i | ||||||
\(874\) | −28.0000 | + | 20.7846i | −0.947114 | + | 0.703050i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.50000 | − | 7.79423i | −0.152041 | − | 0.263343i | ||||
\(877\) | −32.9090 | + | 19.0000i | −1.11126 | + | 0.641584i | −0.939155 | − | 0.343495i | \(-0.888389\pi\) |
−0.172102 | + | 0.985079i | \(0.555056\pi\) | |||||||
\(878\) | 6.92820 | + | 4.00000i | 0.233816 | + | 0.134993i | ||||
\(879\) | −11.0000 | − | 19.0526i | −0.371021 | − | 0.642627i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.0000 | 1.17918 | 0.589590 | − | 0.807703i | \(-0.299289\pi\) | ||||
0.589590 | + | 0.807703i | \(0.299289\pi\) | |||||||
\(882\) | − | 6.00000i | − | 0.202031i | ||||||
\(883\) | 19.9186 | + | 11.5000i | 0.670314 | + | 0.387006i | 0.796196 | − | 0.605039i | \(-0.206843\pi\) |
−0.125882 | + | 0.992045i | \(0.540176\pi\) | |||||||
\(884\) | 6.00000 | − | 10.3923i | 0.201802 | − | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.00000 | 0.302361 | ||||||||
\(887\) | −3.46410 | − | 2.00000i | −0.116313 | − | 0.0671534i | 0.440715 | − | 0.897647i | \(-0.354725\pi\) |
−0.557028 | + | 0.830494i | \(0.688058\pi\) | |||||||
\(888\) | −6.92820 | + | 4.00000i | −0.232495 | + | 0.134231i | ||||
\(889\) | 6.00000 | − | 10.3923i | 0.201234 | − | 0.348547i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.50000 | + | 2.59808i | 0.0502519 | + | 0.0870388i | ||||
\(892\) | − | 16.0000i | − | 0.535720i | ||||||
\(893\) | −25.9808 | + | 3.00000i | −0.869413 | + | 0.100391i | ||||
\(894\) | −4.00000 | −0.133780 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000 | + | 1.73205i | 0.0334077 | + | 0.0578638i | ||||
\(897\) | −41.5692 | − | 24.0000i | −1.38796 | − | 0.801337i | ||||
\(898\) | 25.1147 | − | 14.5000i | 0.838090 | − | 0.483871i | ||||
\(899\) | 8.00000 | − | 13.8564i | 0.266815 | − | 0.462137i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | −12.9904 | − | 7.50000i | −0.432532 | − | 0.249723i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.0000 | −0.432374 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.00000 | + | 10.3923i | −0.199337 | + | 0.345261i | ||||
\(907\) | 40.7032 | − | 23.5000i | 1.35153 | − | 0.780305i | 0.363064 | − | 0.931764i | \(-0.381731\pi\) |
0.988463 | + | 0.151460i | \(0.0483973\pi\) | |||||||
\(908\) | −6.06218 | − | 3.50000i | −0.201180 | − | 0.116152i | ||||
\(909\) | 10.0000 | + | 17.3205i | 0.331679 | + | 0.574485i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.0000 | −1.06021 | −0.530104 | − | 0.847933i | \(-0.677847\pi\) | ||||
−0.530104 | + | 0.847933i | \(0.677847\pi\) | |||||||
\(912\) | 4.33013 | − | 0.500000i | 0.143385 | − | 0.0165567i | ||||
\(913\) | − | 33.0000i | − | 1.09214i | ||||||
\(914\) | −6.50000 | − | 11.2583i | −0.215001 | − | 0.372392i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.0000 | − | 20.7846i | 0.396491 | − | 0.686743i | ||||
\(917\) | 12.1244 | − | 7.00000i | 0.400381 | − | 0.231160i | ||||
\(918\) | −8.66025 | − | 5.00000i | −0.285831 | − | 0.165025i | ||||
\(919\) | −14.0000 | −0.461817 | −0.230909 | − | 0.972975i | \(-0.574170\pi\) | ||||
−0.230909 | + | 0.972975i | \(0.574170\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.50000 | + | 4.33013i | −0.0823778 | + | 0.142683i | ||||
\(922\) | −19.0526 | − | 11.0000i | −0.627463 | − | 0.362266i | ||||
\(923\) | 36.0000i | 1.18495i | ||||||||
\(924\) | −6.00000 | −0.197386 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17.0000 | + | 29.4449i | 0.558655 | + | 0.967618i | ||||
\(927\) | 10.3923 | + | 6.00000i | 0.341328 | + | 0.197066i | ||||
\(928\) | −1.73205 | + | 1.00000i | −0.0568574 | + | 0.0328266i | ||||
\(929\) | −13.5000 | − | 23.3827i | −0.442921 | − | 0.767161i | 0.554984 | − | 0.831861i | \(-0.312724\pi\) |
−0.997905 | + | 0.0646999i | \(0.979391\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.5000 | + | 7.79423i | −0.344124 | + | 0.255446i | ||||
\(932\) | 11.0000i | 0.360317i | ||||||||
\(933\) | −20.7846 | + | 12.0000i | −0.680458 | + | 0.392862i | ||||
\(934\) | −3.50000 | − | 6.06218i | −0.114523 | − | 0.198361i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.00000 | − | 10.3923i | −0.196116 | − | 0.339683i | ||||
\(937\) | −30.3109 | − | 17.5000i | −0.990214 | − | 0.571700i | −0.0848755 | − | 0.996392i | \(-0.527049\pi\) |
−0.905338 | + | 0.424691i | \(0.860383\pi\) | |||||||
\(938\) | − | 10.0000i | − | 0.326512i | ||||||
\(939\) | 13.0000 | 0.424239 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.0000 | + | 32.9090i | −0.619382 | + | 1.07280i | 0.370216 | + | 0.928946i | \(0.379284\pi\) |
−0.989599 | + | 0.143856i | \(0.954050\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40.0000i | 1.30258i | ||||||||
\(944\) | 2.50000 | − | 4.33013i | 0.0813681 | − | 0.140934i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.0333 | + | 26.0000i | −1.46339 | + | 0.844886i | −0.999166 | − | 0.0408333i | \(-0.986999\pi\) |
−0.464220 | + | 0.885720i | \(0.653665\pi\) | |||||||
\(948\) | 6.92820 | − | 4.00000i | 0.225018 | − | 0.129914i | ||||
\(949\) | 54.0000 | 1.75291 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.0000 | 0.972817 | ||||||||
\(952\) | −3.46410 | + | 2.00000i | −0.112272 | + | 0.0648204i | ||||
\(953\) | 6.06218 | − | 3.50000i | 0.196373 | − | 0.113376i | −0.398589 | − | 0.917129i | \(-0.630500\pi\) |
0.594963 | + | 0.803753i | \(0.297167\pi\) | |||||||
\(954\) | 6.00000 | − | 10.3923i | 0.194257 | − | 0.336463i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.00000 | + | 10.3923i | −0.194054 | + | 0.336111i | ||||
\(957\) | − | 6.00000i | − | 0.193952i | ||||||
\(958\) | 12.0000i | 0.387702i | ||||||||
\(959\) | −3.00000 | + | 5.19615i | −0.0968751 | + | 0.167793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | − | 48.0000i | − | 1.54758i | ||||||
\(963\) | 20.7846 | + | 12.0000i | 0.669775 | + | 0.386695i | ||||
\(964\) | −9.50000 | − | 16.4545i | −0.305974 | − | 0.529963i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8.00000 | + | 13.8564i | 0.257396 | + | 0.445823i | ||||
\(967\) | −46.7654 | + | 27.0000i | −1.50387 | + | 0.868261i | −0.503883 | + | 0.863772i | \(0.668096\pi\) |
−0.999990 | + | 0.00448958i | \(0.998571\pi\) | |||||||
\(968\) | − | 2.00000i | − | 0.0642824i | ||||||
\(969\) | 1.00000 | + | 8.66025i | 0.0321246 | + | 0.278207i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.50000 | − | 12.9904i | −0.240686 | − | 0.416881i | 0.720224 | − | 0.693742i | \(-0.244039\pi\) |
−0.960910 | + | 0.276861i | \(0.910706\pi\) | |||||||
\(972\) | −13.8564 | + | 8.00000i | −0.444444 | + | 0.256600i | ||||
\(973\) | 15.5885 | + | 9.00000i | 0.499743 | + | 0.288527i | ||||
\(974\) | −2.00000 | − | 3.46410i | −0.0640841 | − | 0.110997i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.0000 | 0.448129 | ||||||||
\(977\) | 33.0000i | 1.05576i | 0.849318 | + | 0.527882i | \(0.177014\pi\) | ||||
−0.849318 | + | 0.527882i | \(0.822986\pi\) | |||||||
\(978\) | 2.59808 | + | 1.50000i | 0.0830773 | + | 0.0479647i | ||||
\(979\) | −21.0000 | + | 36.3731i | −0.671163 | + | 1.16249i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.0000 | 0.510841 | ||||||||
\(982\) | 17.3205 | + | 10.0000i | 0.552720 | + | 0.319113i | ||||
\(983\) | −31.1769 | + | 18.0000i | −0.994389 | + | 0.574111i | −0.906583 | − | 0.422027i | \(-0.861319\pi\) |
−0.0878058 | + | 0.996138i | \(0.527985\pi\) | |||||||
\(984\) | 2.50000 | − | 4.33013i | 0.0796971 | − | 0.138039i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.00000 | − | 3.46410i | −0.0636930 | − | 0.110319i | ||||
\(987\) | 12.0000i | 0.381964i | ||||||||
\(988\) | −10.3923 | + | 24.0000i | −0.330623 | + | 0.763542i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | − | 27.7128i | −0.508257 | − | 0.880327i | −0.999954 | − | 0.00956046i | \(-0.996957\pi\) |
0.491698 | − | 0.870766i | \(-0.336377\pi\) | |||||||
\(992\) | −6.92820 | − | 4.00000i | −0.219971 | − | 0.127000i | ||||
\(993\) | −14.7224 | + | 8.50000i | −0.467202 | + | 0.269739i | ||||
\(994\) | 6.00000 | − | 10.3923i | 0.190308 | − | 0.329624i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 11.0000 | 0.348548 | ||||||||
\(997\) | −1.73205 | − | 1.00000i | −0.0548546 | − | 0.0316703i | 0.472322 | − | 0.881426i | \(-0.343416\pi\) |
−0.527176 | + | 0.849756i | \(0.676749\pi\) | |||||||
\(998\) | −28.5788 | − | 16.5000i | −0.904647 | − | 0.522298i | ||||
\(999\) | −40.0000 | −1.26554 |
(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 | 950.2.j.a.349.1 | 4 | ||
5.2 | odd | 4 | 950.2.e.a.501.1 | 2 | |||
5.3 | odd | 4 | 190.2.e.b.121.1 | yes | 2 | ||
5.4 | even | 2 | inner | 950.2.j.a.349.2 | 4 | ||
15.8 | even | 4 | 1710.2.l.b.1261.1 | 2 | |||
19.11 | even | 3 | inner | 950.2.j.a.49.2 | 4 | ||
20.3 | even | 4 | 1520.2.q.e.881.1 | 2 | |||
95.49 | even | 6 | inner | 950.2.j.a.49.1 | 4 | ||
95.68 | odd | 12 | 190.2.e.b.11.1 | ✓ | 2 | ||
95.83 | odd | 12 | 3610.2.a.a.1.1 | 1 | |||
95.87 | odd | 12 | 950.2.e.a.201.1 | 2 | |||
95.88 | even | 12 | 3610.2.a.i.1.1 | 1 | |||
285.68 | even | 12 | 1710.2.l.b.1531.1 | 2 | |||
380.163 | even | 12 | 1520.2.q.e.961.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.e.b.11.1 | ✓ | 2 | 95.68 | odd | 12 | ||
190.2.e.b.121.1 | yes | 2 | 5.3 | odd | 4 | ||
950.2.e.a.201.1 | 2 | 95.87 | odd | 12 | |||
950.2.e.a.501.1 | 2 | 5.2 | odd | 4 | |||
950.2.j.a.49.1 | 4 | 95.49 | even | 6 | inner | ||
950.2.j.a.49.2 | 4 | 19.11 | even | 3 | inner | ||
950.2.j.a.349.1 | 4 | 1.1 | even | 1 | trivial | ||
950.2.j.a.349.2 | 4 | 5.4 | even | 2 | inner | ||
1520.2.q.e.881.1 | 2 | 20.3 | even | 4 | |||
1520.2.q.e.961.1 | 2 | 380.163 | even | 12 | |||
1710.2.l.b.1261.1 | 2 | 15.8 | even | 4 | |||
1710.2.l.b.1531.1 | 2 | 285.68 | even | 12 | |||
3610.2.a.a.1.1 | 1 | 95.83 | odd | 12 | |||
3610.2.a.i.1.1 | 1 | 95.88 | even | 12 |