Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [833,2,Mod(344,833)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(833, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("833.344");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 833 = 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 833.g (of order \(4\), 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: | \(6.65153848837\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 62x^{12} + 563x^{8} + 910x^{4} + 289 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 344.5 | ||
Root | \(0.787063 + 0.787063i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 833.344 |
Dual form | 833.2.g.e.540.3 |
$q$-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 \(\left(\mathbb{Z}/833\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.71208i | 1.21062i | 0.795990 | + | 0.605310i | \(0.206951\pi\) | ||||
−0.795990 | + | 0.605310i | \(0.793049\pi\) | |||||||
\(3\) | −0.787063 | + | 0.787063i | −0.454411 | + | 0.454411i | −0.896816 | − | 0.442405i | \(-0.854126\pi\) |
0.442405 | + | 0.896816i | \(0.354126\pi\) | |||||||
\(4\) | −0.931205 | −0.465602 | ||||||||
\(5\) | −2.50697 | + | 2.50697i | −1.12115 | + | 1.12115i | −0.129580 | + | 0.991569i | \(0.541363\pi\) |
−0.991569 | + | 0.129580i | \(0.958637\pi\) | |||||||
\(6\) | −1.34751 | − | 1.34751i | −0.550119 | − | 0.550119i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.82986i | 0.646953i | ||||||||
\(9\) | 1.76106i | 0.587021i | ||||||||
\(10\) | −4.29212 | − | 4.29212i | −1.35729 | − | 1.35729i | ||||
\(11\) | 3.87748 | + | 3.87748i | 1.16911 | + | 1.16911i | 0.982420 | + | 0.186686i | \(0.0597746\pi\) |
0.186686 | + | 0.982420i | \(0.440225\pi\) | |||||||
\(12\) | 0.732917 | − | 0.732917i | 0.211575 | − | 0.211575i | ||||
\(13\) | 3.78474 | 1.04970 | 0.524849 | − | 0.851195i | \(-0.324122\pi\) | ||||
0.524849 | + | 0.851195i | \(0.324122\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 3.94628i | − | 1.01893i | ||||||
\(16\) | −4.99527 | −1.24882 | ||||||||
\(17\) | −3.74726 | + | 1.71990i | −0.908843 | + | 0.417138i | ||||
\(18\) | −3.01508 | −0.710660 | ||||||||
\(19\) | 3.92421i | 0.900276i | 0.892959 | + | 0.450138i | \(0.148625\pi\) | ||||
−0.892959 | + | 0.450138i | \(0.851375\pi\) | |||||||
\(20\) | 2.33450 | − | 2.33450i | 0.522010 | − | 0.522010i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.63855 | + | 6.63855i | −1.41534 | + | 1.41534i | ||||
\(23\) | −0.643281 | − | 0.643281i | −0.134133 | − | 0.134133i | 0.636852 | − | 0.770986i | \(-0.280236\pi\) |
−0.770986 | + | 0.636852i | \(0.780236\pi\) | |||||||
\(24\) | −1.44021 | − | 1.44021i | −0.293983 | − | 0.293983i | ||||
\(25\) | − | 7.56975i | − | 1.51395i | ||||||
\(26\) | 6.47976i | 1.27079i | ||||||||
\(27\) | −3.74726 | − | 3.74726i | −0.721160 | − | 0.721160i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.69227 | − | 1.69227i | 0.314246 | − | 0.314246i | −0.532306 | − | 0.846552i | \(-0.678674\pi\) |
0.846552 | + | 0.532306i | \(0.178674\pi\) | |||||||
\(30\) | 6.75633 | 1.23353 | ||||||||
\(31\) | 6.74493 | − | 6.74493i | 1.21143 | − | 1.21143i | 0.240868 | − | 0.970558i | \(-0.422568\pi\) |
0.970558 | − | 0.240868i | \(-0.0774322\pi\) | |||||||
\(32\) | − | 4.89256i | − | 0.864890i | ||||||
\(33\) | −6.10365 | −1.06251 | ||||||||
\(34\) | −2.94460 | − | 6.41559i | −0.504995 | − | 1.10026i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | − | 1.63991i | − | 0.273318i | ||||||
\(37\) | 7.58956 | − | 7.58956i | 1.24772 | − | 1.24772i | 0.290990 | − | 0.956726i | \(-0.406015\pi\) |
0.956726 | − | 0.290990i | \(-0.0939846\pi\) | |||||||
\(38\) | −6.71855 | −1.08989 | ||||||||
\(39\) | −2.97883 | + | 2.97883i | −0.476994 | + | 0.476994i | ||||
\(40\) | −4.58739 | − | 4.58739i | −0.725331 | − | 0.725331i | ||||
\(41\) | −3.45091 | − | 3.45091i | −0.538941 | − | 0.538941i | 0.384277 | − | 0.923218i | \(-0.374451\pi\) |
−0.923218 | + | 0.384277i | \(0.874451\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.18522i | 0.180744i | 0.995908 | + | 0.0903719i | \(0.0288056\pi\) | ||||
−0.995908 | + | 0.0903719i | \(0.971194\pi\) | |||||||
\(44\) | −3.61073 | − | 3.61073i | −0.544338 | − | 0.544338i | ||||
\(45\) | −4.41493 | − | 4.41493i | −0.658138 | − | 0.658138i | ||||
\(46\) | 1.10135 | − | 1.10135i | 0.162385 | − | 0.162385i | ||||
\(47\) | 2.69502 | 0.393110 | 0.196555 | − | 0.980493i | \(-0.437025\pi\) | ||||
0.196555 | + | 0.980493i | \(0.437025\pi\) | |||||||
\(48\) | 3.93159 | − | 3.93159i | 0.567476 | − | 0.567476i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 12.9600 | 1.83282 | ||||||||
\(51\) | 1.59566 | − | 4.30300i | 0.223436 | − | 0.602540i | ||||
\(52\) | −3.52437 | −0.488742 | ||||||||
\(53\) | 1.33691i | 0.183639i | 0.995776 | + | 0.0918195i | \(0.0292683\pi\) | ||||
−0.995776 | + | 0.0918195i | \(0.970732\pi\) | |||||||
\(54\) | 6.41559 | − | 6.41559i | 0.873051 | − | 0.873051i | ||||
\(55\) | −19.4414 | −2.62148 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.08860 | − | 3.08860i | −0.409096 | − | 0.409096i | ||||
\(58\) | 2.89729 | + | 2.89729i | 0.380433 | + | 0.380433i | ||||
\(59\) | 11.2481i | 1.46437i | 0.681103 | + | 0.732187i | \(0.261500\pi\) | ||||
−0.681103 | + | 0.732187i | \(0.738500\pi\) | |||||||
\(60\) | 3.67479i | 0.474414i | ||||||||
\(61\) | 6.25422 | + | 6.25422i | 0.800771 | + | 0.800771i | 0.983216 | − | 0.182445i | \(-0.0584011\pi\) |
−0.182445 | + | 0.983216i | \(0.558401\pi\) | |||||||
\(62\) | 11.5478 | + | 11.5478i | 1.46658 | + | 1.46658i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.61410 | −0.201763 | ||||||||
\(65\) | −9.48821 | + | 9.48821i | −1.17687 | + | 1.17687i | ||||
\(66\) | − | 10.4499i | − | 1.28630i | ||||||
\(67\) | −0.430248 | −0.0525631 | −0.0262816 | − | 0.999655i | \(-0.508367\pi\) | ||||
−0.0262816 | + | 0.999655i | \(0.508367\pi\) | |||||||
\(68\) | 3.48946 | − | 1.60158i | 0.423160 | − | 0.194220i | ||||
\(69\) | 1.01260 | 0.121903 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.60366 | + | 1.60366i | −0.190320 | + | 0.190320i | −0.795834 | − | 0.605514i | \(-0.792967\pi\) |
0.605514 | + | 0.795834i | \(0.292967\pi\) | |||||||
\(72\) | −3.22250 | −0.379775 | ||||||||
\(73\) | 6.70745 | − | 6.70745i | 0.785048 | − | 0.785048i | −0.195630 | − | 0.980678i | \(-0.562675\pi\) |
0.980678 | + | 0.195630i | \(0.0626752\pi\) | |||||||
\(74\) | 12.9939 | + | 12.9939i | 1.51051 | + | 1.51051i | ||||
\(75\) | 5.95787 | + | 5.95787i | 0.687956 | + | 0.687956i | ||||
\(76\) | − | 3.65425i | − | 0.419171i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.09998 | − | 5.09998i | −0.577459 | − | 0.577459i | ||||
\(79\) | −4.82986 | − | 4.82986i | −0.543402 | − | 0.543402i | 0.381123 | − | 0.924524i | \(-0.375538\pi\) |
−0.924524 | + | 0.381123i | \(0.875538\pi\) | |||||||
\(80\) | 12.5230 | − | 12.5230i | 1.40011 | − | 1.40011i | ||||
\(81\) | 0.615464 | 0.0683848 | ||||||||
\(82\) | 5.90821 | − | 5.90821i | 0.652453 | − | 0.652453i | ||||
\(83\) | − | 3.11707i | − | 0.342143i | −0.985259 | − | 0.171072i | \(-0.945277\pi\) | ||
0.985259 | − | 0.171072i | \(-0.0547229\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.08251 | − | 13.7060i | 0.551275 | − | 1.48662i | ||||
\(86\) | −2.02918 | −0.218812 | ||||||||
\(87\) | 2.66384i | 0.285594i | ||||||||
\(88\) | −7.09525 | + | 7.09525i | −0.756356 | + | 0.756356i | ||||
\(89\) | 2.93381 | 0.310983 | 0.155492 | − | 0.987837i | \(-0.450304\pi\) | ||||
0.155492 | + | 0.987837i | \(0.450304\pi\) | |||||||
\(90\) | 7.55869 | − | 7.55869i | 0.796756 | − | 0.796756i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.599026 | + | 0.599026i | 0.0624528 | + | 0.0624528i | ||||
\(93\) | 10.6174i | 1.10097i | ||||||||
\(94\) | 4.61409i | 0.475907i | ||||||||
\(95\) | −9.83787 | − | 9.83787i | −1.00934 | − | 1.00934i | ||||
\(96\) | 3.85075 | + | 3.85075i | 0.393016 | + | 0.393016i | ||||
\(97\) | −8.64179 | + | 8.64179i | −0.877441 | + | 0.877441i | −0.993269 | − | 0.115828i | \(-0.963048\pi\) |
0.115828 | + | 0.993269i | \(0.463048\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.82850 | + | 6.82850i | −0.686290 | + | 0.686290i | ||||
\(100\) | 7.04899i | 0.704899i | ||||||||
\(101\) | 13.6605 | 1.35927 | 0.679636 | − | 0.733549i | \(-0.262138\pi\) | ||||
0.679636 | + | 0.733549i | \(0.262138\pi\) | |||||||
\(102\) | 7.36706 | + | 2.73188i | 0.729448 | + | 0.270497i | ||||
\(103\) | −3.47099 | −0.342006 | −0.171003 | − | 0.985270i | \(-0.554701\pi\) | ||||
−0.171003 | + | 0.985270i | \(0.554701\pi\) | |||||||
\(104\) | 6.92554i | 0.679105i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.28889 | −0.222317 | ||||||||
\(107\) | 5.99527 | − | 5.99527i | 0.579584 | − | 0.579584i | −0.355204 | − | 0.934789i | \(-0.615589\pi\) |
0.934789 | + | 0.355204i | \(0.115589\pi\) | |||||||
\(108\) | 3.48946 | + | 3.48946i | 0.335774 | + | 0.335774i | ||||
\(109\) | −3.74696 | − | 3.74696i | −0.358894 | − | 0.358894i | 0.504511 | − | 0.863405i | \(-0.331673\pi\) |
−0.863405 | + | 0.504511i | \(0.831673\pi\) | |||||||
\(110\) | − | 33.2852i | − | 3.17362i | ||||||
\(111\) | 11.9469i | 1.13395i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.45333 | + | 6.45333i | 0.607078 | + | 0.607078i | 0.942181 | − | 0.335103i | \(-0.108771\pi\) |
−0.335103 | + | 0.942181i | \(0.608771\pi\) | |||||||
\(114\) | 5.28792 | − | 5.28792i | 0.495259 | − | 0.495259i | ||||
\(115\) | 3.22536 | 0.300767 | ||||||||
\(116\) | −1.57585 | + | 1.57585i | −0.146314 | + | 0.146314i | ||||
\(117\) | 6.66517i | 0.616195i | ||||||||
\(118\) | −19.2576 | −1.77280 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 7.22114 | 0.659197 | ||||||||
\(121\) | 19.0698i | 1.73362i | ||||||||
\(122\) | −10.7077 | + | 10.7077i | −0.969430 | + | 0.969430i | ||||
\(123\) | 5.43216 | 0.489801 | ||||||||
\(124\) | −6.28091 | + | 6.28091i | −0.564043 | + | 0.564043i | ||||
\(125\) | 6.44228 | + | 6.44228i | 0.576215 | + | 0.576215i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 0.446266i | − | 0.0395997i | −0.999804 | − | 0.0197999i | \(-0.993697\pi\) | ||
0.999804 | − | 0.0197999i | \(-0.00630290\pi\) | |||||||
\(128\) | − | 12.5486i | − | 1.10915i | ||||||
\(129\) | −0.932840 | − | 0.932840i | −0.0821319 | − | 0.0821319i | ||||
\(130\) | −16.2445 | − | 16.2445i | −1.42474 | − | 1.42474i | ||||
\(131\) | 0.0311801 | − | 0.0311801i | 0.00272422 | − | 0.00272422i | −0.705743 | − | 0.708468i | \(-0.749387\pi\) |
0.708468 | + | 0.705743i | \(0.249387\pi\) | |||||||
\(132\) | 5.68375 | 0.494707 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 0.736617i | − | 0.0636340i | ||||||
\(135\) | 18.7885 | 1.61706 | ||||||||
\(136\) | −3.14718 | − | 6.85695i | −0.269868 | − | 0.587979i | ||||
\(137\) | 1.92414 | 0.164390 | 0.0821951 | − | 0.996616i | \(-0.473807\pi\) | ||||
0.0821951 | + | 0.996616i | \(0.473807\pi\) | |||||||
\(138\) | 1.73366i | 0.147579i | ||||||||
\(139\) | 4.26435 | − | 4.26435i | 0.361698 | − | 0.361698i | −0.502740 | − | 0.864438i | \(-0.667675\pi\) |
0.864438 | + | 0.502740i | \(0.167675\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.12115 | + | 2.12115i | −0.178633 | + | 0.178633i | ||||
\(142\) | −2.74560 | − | 2.74560i | −0.230405 | − | 0.230405i | ||||
\(143\) | 14.6753 | + | 14.6753i | 1.22721 | + | 1.22721i | ||||
\(144\) | − | 8.79698i | − | 0.733082i | ||||||
\(145\) | 8.48492i | 0.704634i | ||||||||
\(146\) | 11.4837 | + | 11.4837i | 0.950395 | + | 0.950395i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.06743 | + | 7.06743i | −0.580939 | + | 0.580939i | ||||
\(149\) | −19.1730 | −1.57072 | −0.785358 | − | 0.619042i | \(-0.787521\pi\) | ||||
−0.785358 | + | 0.619042i | \(0.787521\pi\) | |||||||
\(150\) | −10.2003 | + | 10.2003i | −0.832853 | + | 0.832853i | ||||
\(151\) | 22.3643i | 1.81998i | 0.414626 | + | 0.909992i | \(0.363912\pi\) | ||||
−0.414626 | + | 0.909992i | \(0.636088\pi\) | |||||||
\(152\) | −7.18076 | −0.582436 | ||||||||
\(153\) | −3.02886 | − | 6.59916i | −0.244869 | − | 0.533510i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 33.8186i | 2.71638i | ||||||||
\(156\) | 2.77390 | − | 2.77390i | 0.222090 | − | 0.222090i | ||||
\(157\) | 3.00878 | 0.240127 | 0.120063 | − | 0.992766i | \(-0.461690\pi\) | ||||
0.120063 | + | 0.992766i | \(0.461690\pi\) | |||||||
\(158\) | 8.26909 | − | 8.26909i | 0.657853 | − | 0.657853i | ||||
\(159\) | −1.05223 | − | 1.05223i | −0.0834476 | − | 0.0834476i | ||||
\(160\) | 12.2655 | + | 12.2655i | 0.969671 | + | 0.969671i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.05372i | 0.0827881i | ||||||||
\(163\) | −10.4590 | − | 10.4590i | −0.819215 | − | 0.819215i | 0.166779 | − | 0.985994i | \(-0.446663\pi\) |
−0.985994 | + | 0.166779i | \(0.946663\pi\) | |||||||
\(164\) | 3.21350 | + | 3.21350i | 0.250932 | + | 0.250932i | ||||
\(165\) | 15.3016 | − | 15.3016i | 1.19123 | − | 1.19123i | ||||
\(166\) | 5.33666 | 0.414205 | ||||||||
\(167\) | 9.61691 | − | 9.61691i | 0.744179 | − | 0.744179i | −0.229200 | − | 0.973379i | \(-0.573611\pi\) |
0.973379 | + | 0.229200i | \(0.0736110\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.32426 | 0.101866 | ||||||||
\(170\) | 23.4657 | + | 8.70164i | 1.79974 | + | 0.667385i | ||||
\(171\) | −6.91079 | −0.528481 | ||||||||
\(172\) | − | 1.10368i | − | 0.0841547i | ||||||
\(173\) | 6.11475 | − | 6.11475i | 0.464896 | − | 0.464896i | −0.435360 | − | 0.900256i | \(-0.643379\pi\) |
0.900256 | + | 0.435360i | \(0.143379\pi\) | |||||||
\(174\) | −4.56070 | −0.345746 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −19.3691 | − | 19.3691i | −1.46000 | − | 1.46000i | ||||
\(177\) | −8.85294 | − | 8.85294i | −0.665428 | − | 0.665428i | ||||
\(178\) | 5.02291i | 0.376483i | ||||||||
\(179\) | − | 10.7073i | − | 0.800304i | −0.916449 | − | 0.400152i | \(-0.868957\pi\) | ||
0.916449 | − | 0.400152i | \(-0.131043\pi\) | |||||||
\(180\) | 4.11120 | + | 4.11120i | 0.306431 | + | 0.306431i | ||||
\(181\) | 11.4187 | + | 11.4187i | 0.848747 | + | 0.848747i | 0.989977 | − | 0.141230i | \(-0.0451056\pi\) |
−0.141230 | + | 0.989977i | \(0.545106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.84493 | −0.727758 | ||||||||
\(184\) | 1.17711 | − | 1.17711i | 0.0867779 | − | 0.0867779i | ||||
\(185\) | 38.0535i | 2.79775i | ||||||||
\(186\) | −18.1778 | −1.33286 | ||||||||
\(187\) | −21.1988 | − | 7.86103i | −1.55021 | − | 0.574856i | ||||
\(188\) | −2.50962 | −0.183033 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.8432 | − | 16.8432i | 1.22193 | − | 1.22193i | ||||
\(191\) | −13.8544 | −1.00247 | −0.501235 | − | 0.865311i | \(-0.667121\pi\) | ||||
−0.501235 | + | 0.865311i | \(0.667121\pi\) | |||||||
\(192\) | 1.27040 | − | 1.27040i | 0.0916832 | − | 0.0916832i | ||||
\(193\) | 10.7483 | + | 10.7483i | 0.773681 | + | 0.773681i | 0.978748 | − | 0.205067i | \(-0.0657412\pi\) |
−0.205067 | + | 0.978748i | \(0.565741\pi\) | |||||||
\(194\) | −14.7954 | − | 14.7954i | −1.06225 | − | 1.06225i | ||||
\(195\) | − | 14.9356i | − | 1.06956i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.0288 | − | 16.0288i | −1.14200 | − | 1.14200i | −0.988083 | − | 0.153921i | \(-0.950810\pi\) |
−0.153921 | − | 0.988083i | \(-0.549190\pi\) | |||||||
\(198\) | −11.6909 | − | 11.6909i | −0.830836 | − | 0.830836i | ||||
\(199\) | −8.30316 | + | 8.30316i | −0.588596 | + | 0.588596i | −0.937251 | − | 0.348655i | \(-0.886638\pi\) |
0.348655 | + | 0.937251i | \(0.386638\pi\) | |||||||
\(200\) | 13.8516 | 0.979455 | ||||||||
\(201\) | 0.338632 | − | 0.338632i | 0.0238853 | − | 0.0238853i | ||||
\(202\) | 23.3879i | 1.64556i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.48588 | + | 4.00697i | −0.104033 | + | 0.280544i | ||||
\(205\) | 17.3026 | 1.20847 | ||||||||
\(206\) | − | 5.94259i | − | 0.414040i | ||||||
\(207\) | 1.13286 | − | 1.13286i | 0.0787391 | − | 0.0787391i | ||||
\(208\) | −18.9058 | −1.31088 | ||||||||
\(209\) | −15.2161 | + | 15.2161i | −1.05252 | + | 1.05252i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.4623 | + | 15.4623i | 1.06447 | + | 1.06447i | 0.997773 | + | 0.0666961i | \(0.0212458\pi\) |
0.0666961 | + | 0.997773i | \(0.478754\pi\) | |||||||
\(212\) | − | 1.24494i | − | 0.0855027i | ||||||
\(213\) | − | 2.52437i | − | 0.172967i | ||||||
\(214\) | 10.2644 | + | 10.2644i | 0.701657 | + | 0.701657i | ||||
\(215\) | −2.97130 | − | 2.97130i | −0.202641 | − | 0.202641i | ||||
\(216\) | 6.85695 | − | 6.85695i | 0.466557 | − | 0.466557i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.41508 | − | 6.41508i | 0.434484 | − | 0.434484i | ||||
\(219\) | 10.5584i | 0.713469i | ||||||||
\(220\) | 18.1040 | 1.22057 | ||||||||
\(221\) | −14.1824 | + | 6.50939i | −0.954011 | + | 0.437869i | ||||
\(222\) | −20.4540 | −1.37279 | ||||||||
\(223\) | − | 24.5325i | − | 1.64282i | −0.570341 | − | 0.821408i | \(-0.693189\pi\) | ||
0.570341 | − | 0.821408i | \(-0.306811\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.3308 | 0.888721 | ||||||||
\(226\) | −11.0486 | + | 11.0486i | −0.734942 | + | 0.734942i | ||||
\(227\) | −7.83465 | − | 7.83465i | −0.520004 | − | 0.520004i | 0.397568 | − | 0.917573i | \(-0.369854\pi\) |
−0.917573 | + | 0.397568i | \(0.869854\pi\) | |||||||
\(228\) | 2.87612 | + | 2.87612i | 0.190476 | + | 0.190476i | ||||
\(229\) | 28.4018i | 1.87684i | 0.345493 | + | 0.938421i | \(0.387712\pi\) | ||||
−0.345493 | + | 0.938421i | \(0.612288\pi\) | |||||||
\(230\) | 5.52207i | 0.364114i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.09661 | + | 3.09661i | 0.203303 | + | 0.203303i | ||||
\(233\) | 2.93257 | − | 2.93257i | 0.192119 | − | 0.192119i | −0.604492 | − | 0.796611i | \(-0.706624\pi\) |
0.796611 | + | 0.604492i | \(0.206624\pi\) | |||||||
\(234\) | −11.4113 | −0.745979 | ||||||||
\(235\) | −6.75633 | + | 6.75633i | −0.440734 | + | 0.440734i | ||||
\(236\) | − | 10.4743i | − | 0.681816i | ||||||
\(237\) | 7.60281 | 0.493855 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.2805 | 1.11778 | 0.558890 | − | 0.829242i | \(-0.311227\pi\) | ||||
0.558890 | + | 0.829242i | \(0.311227\pi\) | |||||||
\(240\) | 19.7127i | 1.27245i | ||||||||
\(241\) | 0.265171 | − | 0.265171i | 0.0170811 | − | 0.0170811i | −0.698515 | − | 0.715596i | \(-0.746155\pi\) |
0.715596 | + | 0.698515i | \(0.246155\pi\) | |||||||
\(242\) | −32.6489 | −2.09875 | ||||||||
\(243\) | 10.7574 | − | 10.7574i | 0.690085 | − | 0.690085i | ||||
\(244\) | −5.82396 | − | 5.82396i | −0.372841 | − | 0.372841i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.30027i | 0.592964i | ||||||||
\(247\) | 14.8521i | 0.945019i | ||||||||
\(248\) | 12.3423 | + | 12.3423i | 0.783736 | + | 0.783736i | ||||
\(249\) | 2.45333 | + | 2.45333i | 0.155474 | + | 0.155474i | ||||
\(250\) | −11.0297 | + | 11.0297i | −0.697578 | + | 0.697578i | ||||
\(251\) | 15.6012 | 0.984737 | 0.492369 | − | 0.870387i | \(-0.336131\pi\) | ||||
0.492369 | + | 0.870387i | \(0.336131\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.98862i | − | 0.313632i | ||||||
\(254\) | 0.764041 | 0.0479402 | ||||||||
\(255\) | 6.78722 | + | 14.7877i | 0.425032 | + | 0.926043i | ||||
\(256\) | 18.2559 | 1.14100 | ||||||||
\(257\) | 21.0927i | 1.31573i | 0.753138 | + | 0.657863i | \(0.228539\pi\) | ||||
−0.753138 | + | 0.657863i | \(0.771461\pi\) | |||||||
\(258\) | 1.59709 | − | 1.59709i | 0.0994306 | − | 0.0994306i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 8.83547 | − | 8.83547i | 0.547953 | − | 0.547953i | ||||
\(261\) | 2.98019 | + | 2.98019i | 0.184469 | + | 0.184469i | ||||
\(262\) | 0.0533827 | + | 0.0533827i | 0.00329799 | + | 0.00329799i | ||||
\(263\) | 10.6033i | 0.653826i | 0.945054 | + | 0.326913i | \(0.106008\pi\) | ||||
−0.945054 | + | 0.326913i | \(0.893992\pi\) | |||||||
\(264\) | − | 11.1688i | − | 0.687393i | ||||||
\(265\) | −3.35159 | − | 3.35159i | −0.205887 | − | 0.205887i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.30909 | + | 2.30909i | −0.141314 | + | 0.141314i | ||||
\(268\) | 0.400649 | 0.0244735 | ||||||||
\(269\) | −19.7552 | + | 19.7552i | −1.20450 | + | 1.20450i | −0.231711 | + | 0.972785i | \(0.574432\pi\) |
−0.972785 | + | 0.231711i | \(0.925568\pi\) | |||||||
\(270\) | 32.1673i | 1.95764i | ||||||||
\(271\) | −2.88043 | −0.174974 | −0.0874868 | − | 0.996166i | \(-0.527884\pi\) | ||||
−0.0874868 | + | 0.996166i | \(0.527884\pi\) | |||||||
\(272\) | 18.7186 | − | 8.59137i | 1.13498 | − | 0.520928i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.29427i | 0.199014i | ||||||||
\(275\) | 29.3516 | − | 29.3516i | 1.76997 | − | 1.76997i | ||||
\(276\) | −0.942942 | −0.0567584 | ||||||||
\(277\) | −5.07016 | + | 5.07016i | −0.304636 | + | 0.304636i | −0.842825 | − | 0.538188i | \(-0.819109\pi\) |
0.538188 | + | 0.842825i | \(0.319109\pi\) | |||||||
\(278\) | 7.30089 | + | 7.30089i | 0.437879 | + | 0.437879i | ||||
\(279\) | 11.8783 | + | 11.8783i | 0.711133 | + | 0.711133i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.3361i | − | 1.21315i | −0.795026 | − | 0.606575i | \(-0.792543\pi\) | ||
0.795026 | − | 0.606575i | \(-0.207457\pi\) | |||||||
\(282\) | −3.63158 | − | 3.63158i | −0.216257 | − | 0.216257i | ||||
\(283\) | −2.18423 | − | 2.18423i | −0.129839 | − | 0.129839i | 0.639201 | − | 0.769040i | \(-0.279265\pi\) |
−0.769040 | + | 0.639201i | \(0.779265\pi\) | |||||||
\(284\) | 1.49334 | − | 1.49334i | 0.0886134 | − | 0.0886134i | ||||
\(285\) | 15.4860 | 0.917314 | ||||||||
\(286\) | −25.1252 | + | 25.1252i | −1.48568 | + | 1.48568i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 8.61611 | 0.507709 | ||||||||
\(289\) | 11.0839 | − | 12.8898i | 0.651992 | − | 0.758226i | ||||
\(290\) | −14.5268 | −0.853044 | ||||||||
\(291\) | − | 13.6033i | − | 0.797438i | ||||||
\(292\) | −6.24601 | + | 6.24601i | −0.365520 | + | 0.365520i | ||||
\(293\) | 20.4376 | 1.19398 | 0.596989 | − | 0.802249i | \(-0.296364\pi\) | ||||
0.596989 | + | 0.802249i | \(0.296364\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.1985 | − | 28.1985i | −1.64178 | − | 1.64178i | ||||
\(296\) | 13.8878 | + | 13.8878i | 0.807214 | + | 0.807214i | ||||
\(297\) | − | 29.0599i | − | 1.68622i | ||||||
\(298\) | − | 32.8257i | − | 1.90154i | ||||||
\(299\) | −2.43465 | − | 2.43465i | −0.140799 | − | 0.140799i | ||||
\(300\) | −5.54800 | − | 5.54800i | −0.320314 | − | 0.320314i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −38.2894 | −2.20331 | ||||||||
\(303\) | −10.7517 | + | 10.7517i | −0.617669 | + | 0.617669i | ||||
\(304\) | − | 19.6025i | − | 1.12428i | ||||||
\(305\) | −31.3582 | −1.79557 | ||||||||
\(306\) | 11.2983 | − | 5.18564i | 0.645879 | − | 0.296443i | ||||
\(307\) | −24.4776 | −1.39701 | −0.698504 | − | 0.715606i | \(-0.746151\pi\) | ||||
−0.698504 | + | 0.715606i | \(0.746151\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.73188 | − | 2.73188i | 0.155411 | − | 0.155411i | ||||
\(310\) | −57.9001 | −3.28850 | ||||||||
\(311\) | 0.318553 | − | 0.318553i | 0.0180635 | − | 0.0180635i | −0.698017 | − | 0.716081i | \(-0.745934\pi\) |
0.716081 | + | 0.698017i | \(0.245934\pi\) | |||||||
\(312\) | −5.45084 | − | 5.45084i | −0.308593 | − | 0.308593i | ||||
\(313\) | −12.0045 | − | 12.0045i | −0.678534 | − | 0.678534i | 0.281135 | − | 0.959668i | \(-0.409289\pi\) |
−0.959668 | + | 0.281135i | \(0.909289\pi\) | |||||||
\(314\) | 5.15126i | 0.290702i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.49759 | + | 4.49759i | 0.253009 | + | 0.253009i | ||||
\(317\) | 3.31101 | + | 3.31101i | 0.185965 | + | 0.185965i | 0.793949 | − | 0.607984i | \(-0.208022\pi\) |
−0.607984 | + | 0.793949i | \(0.708022\pi\) | |||||||
\(318\) | 1.80150 | − | 1.80150i | 0.101023 | − | 0.101023i | ||||
\(319\) | 13.1235 | 0.734774 | ||||||||
\(320\) | 4.04650 | − | 4.04650i | 0.226206 | − | 0.226206i | ||||
\(321\) | 9.43731i | 0.526739i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.74927 | − | 14.7050i | −0.375539 | − | 0.818210i | ||||
\(324\) | −0.573122 | −0.0318401 | ||||||||
\(325\) | − | 28.6496i | − | 1.58919i | ||||||
\(326\) | 17.9067 | − | 17.9067i | 0.991758 | − | 0.991758i | ||||
\(327\) | 5.89819 | 0.326170 | ||||||||
\(328\) | 6.31467 | − | 6.31467i | 0.348669 | − | 0.348669i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 26.1976 | + | 26.1976i | 1.44213 | + | 1.44213i | ||||
\(331\) | − | 34.5038i | − | 1.89650i | −0.317521 | − | 0.948251i | \(-0.602850\pi\) | ||
0.317521 | − | 0.948251i | \(-0.397150\pi\) | |||||||
\(332\) | 2.90263i | 0.159303i | ||||||||
\(333\) | 13.3657 | + | 13.3657i | 0.732436 | + | 0.732436i | ||||
\(334\) | 16.4649 | + | 16.4649i | 0.900919 | + | 0.900919i | ||||
\(335\) | 1.07862 | − | 1.07862i | 0.0589311 | − | 0.0589311i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.0302 | + | 19.0302i | −1.03664 | + | 1.03664i | −0.0373355 | + | 0.999303i | \(0.511887\pi\) |
−0.999303 | + | 0.0373355i | \(0.988113\pi\) | |||||||
\(338\) | 2.26724i | 0.123322i | ||||||||
\(339\) | −10.1584 | −0.551726 | ||||||||
\(340\) | −4.73285 | + | 12.7631i | −0.256675 | + | 0.692175i | ||||
\(341\) | 52.3068 | 2.83257 | ||||||||
\(342\) | − | 11.8318i | − | 0.639790i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.16878 | −0.116933 | ||||||||
\(345\) | −2.53857 | + | 2.53857i | −0.136672 | + | 0.136672i | ||||
\(346\) | 10.4689 | + | 10.4689i | 0.562812 | + | 0.562812i | ||||
\(347\) | −11.6966 | − | 11.6966i | −0.627907 | − | 0.627907i | 0.319634 | − | 0.947541i | \(-0.396440\pi\) |
−0.947541 | + | 0.319634i | \(0.896440\pi\) | |||||||
\(348\) | − | 2.48058i | − | 0.132973i | ||||||
\(349\) | − | 10.1340i | − | 0.542461i | −0.962514 | − | 0.271231i | \(-0.912569\pi\) | ||
0.962514 | − | 0.271231i | \(-0.0874306\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.1824 | − | 14.1824i | −0.757000 | − | 0.757000i | ||||
\(352\) | 18.9708 | − | 18.9708i | 1.01115 | − | 1.01115i | ||||
\(353\) | 0.797547 | 0.0424491 | 0.0212246 | − | 0.999775i | \(-0.493244\pi\) | ||||
0.0212246 | + | 0.999775i | \(0.493244\pi\) | |||||||
\(354\) | 15.1569 | − | 15.1569i | 0.805581 | − | 0.805581i | ||||
\(355\) | − | 8.04067i | − | 0.426754i | ||||||
\(356\) | −2.73198 | −0.144795 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.3318 | 0.968865 | ||||||||
\(359\) | 20.7329i | 1.09424i | 0.837055 | + | 0.547119i | \(0.184276\pi\) | ||||
−0.837055 | + | 0.547119i | \(0.815724\pi\) | |||||||
\(360\) | 8.07869 | − | 8.07869i | 0.425784 | − | 0.425784i | ||||
\(361\) | 3.60055 | 0.189502 | ||||||||
\(362\) | −19.5497 | + | 19.5497i | −1.02751 | + | 1.02751i | ||||
\(363\) | −15.0091 | − | 15.0091i | −0.787774 | − | 0.787774i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 33.6307i | 1.76031i | ||||||||
\(366\) | − | 16.8553i | − | 0.881039i | ||||||
\(367\) | −3.45988 | − | 3.45988i | −0.180604 | − | 0.180604i | 0.611015 | − | 0.791619i | \(-0.290762\pi\) |
−0.791619 | + | 0.611015i | \(0.790762\pi\) | |||||||
\(368\) | 3.21336 | + | 3.21336i | 0.167508 | + | 0.167508i | ||||
\(369\) | 6.07727 | − | 6.07727i | 0.316370 | − | 0.316370i | ||||
\(370\) | −65.1505 | −3.38702 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 9.88695i | − | 0.512614i | ||||||
\(373\) | 6.65171 | 0.344412 | 0.172206 | − | 0.985061i | \(-0.444910\pi\) | ||||
0.172206 | + | 0.985061i | \(0.444910\pi\) | |||||||
\(374\) | 13.4587 | − | 36.2940i | 0.695932 | − | 1.87672i | ||||
\(375\) | −10.1410 | −0.523677 | ||||||||
\(376\) | 4.93151i | 0.254323i | ||||||||
\(377\) | 6.40480 | − | 6.40480i | 0.329864 | − | 0.329864i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.33788 | + | 4.33788i | −0.222822 | + | 0.222822i | −0.809686 | − | 0.586864i | \(-0.800362\pi\) |
0.586864 | + | 0.809686i | \(0.300362\pi\) | |||||||
\(380\) | 9.16107 | + | 9.16107i | 0.469953 | + | 0.469953i | ||||
\(381\) | 0.351240 | + | 0.351240i | 0.0179945 | + | 0.0179945i | ||||
\(382\) | − | 23.7198i | − | 1.21361i | ||||||
\(383\) | − | 28.9723i | − | 1.48041i | −0.672379 | − | 0.740207i | \(-0.734727\pi\) | ||
0.672379 | − | 0.740207i | \(-0.265273\pi\) | |||||||
\(384\) | 9.87652 | + | 9.87652i | 0.504009 | + | 0.504009i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.4019 | + | 18.4019i | −0.936634 | + | 0.936634i | ||||
\(387\) | −2.08724 | −0.106100 | ||||||||
\(388\) | 8.04728 | − | 8.04728i | 0.408539 | − | 0.408539i | ||||
\(389\) | 10.2248i | 0.518420i | 0.965821 | + | 0.259210i | \(0.0834621\pi\) | ||||
−0.965821 | + | 0.259210i | \(0.916538\pi\) | |||||||
\(390\) | 25.5710 | 1.29484 | ||||||||
\(391\) | 3.51692 | + | 1.30416i | 0.177858 | + | 0.0659541i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.0490814i | 0.00247583i | ||||||||
\(394\) | 27.4425 | − | 27.4425i | 1.38253 | − | 1.38253i | ||||
\(395\) | 24.2166 | 1.21847 | ||||||||
\(396\) | 6.35873 | − | 6.35873i | 0.319538 | − | 0.319538i | ||||
\(397\) | 3.33631 | + | 3.33631i | 0.167445 | + | 0.167445i | 0.785855 | − | 0.618411i | \(-0.212223\pi\) |
−0.618411 | + | 0.785855i | \(0.712223\pi\) | |||||||
\(398\) | −14.2156 | − | 14.2156i | −0.712566 | − | 0.712566i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 37.8129i | 1.89065i | ||||||||
\(401\) | −5.33652 | − | 5.33652i | −0.266493 | − | 0.266493i | 0.561192 | − | 0.827685i | \(-0.310343\pi\) |
−0.827685 | + | 0.561192i | \(0.810343\pi\) | |||||||
\(402\) | 0.579764 | + | 0.579764i | 0.0289160 | + | 0.0289160i | ||||
\(403\) | 25.5278 | − | 25.5278i | 1.27163 | − | 1.27163i | ||||
\(404\) | −12.7207 | −0.632880 | ||||||||
\(405\) | −1.54295 | + | 1.54295i | −0.0766696 | + | 0.0766696i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 58.8568 | 2.91742 | ||||||||
\(408\) | 7.87388 | + | 2.91983i | 0.389815 | + | 0.144553i | ||||
\(409\) | 11.3008 | 0.558791 | 0.279395 | − | 0.960176i | \(-0.409866\pi\) | ||||
0.279395 | + | 0.960176i | \(0.409866\pi\) | |||||||
\(410\) | 29.6234i | 1.46299i | ||||||||
\(411\) | −1.51442 | + | 1.51442i | −0.0747007 | + | 0.0747007i | ||||
\(412\) | 3.23220 | 0.159239 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.93954 | + | 1.93954i | 0.0953232 | + | 0.0953232i | ||||
\(415\) | 7.81439 | + | 7.81439i | 0.383593 | + | 0.383593i | ||||
\(416\) | − | 18.5171i | − | 0.907874i | ||||||
\(417\) | 6.71263i | 0.328719i | ||||||||
\(418\) | −26.0511 | − | 26.0511i | −1.27420 | − | 1.27420i | ||||
\(419\) | −20.0293 | − | 20.0293i | −0.978497 | − | 0.978497i | 0.0212763 | − | 0.999774i | \(-0.493227\pi\) |
−0.999774 | + | 0.0212763i | \(0.993227\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.8374 | 1.74661 | 0.873304 | − | 0.487176i | \(-0.161973\pi\) | ||||
0.873304 | + | 0.487176i | \(0.161973\pi\) | |||||||
\(422\) | −26.4727 | + | 26.4727i | −1.28867 | + | 1.28867i | ||||
\(423\) | 4.74611i | 0.230764i | ||||||||
\(424\) | −2.44636 | −0.118806 | ||||||||
\(425\) | 13.0192 | + | 28.3658i | 0.631526 | + | 1.37594i | ||||
\(426\) | 4.32191 | 0.209397 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.58282 | + | 5.58282i | −0.269856 | + | 0.269856i | ||||
\(429\) | −23.1007 | −1.11531 | ||||||||
\(430\) | 5.08708 | − | 5.08708i | 0.245321 | − | 0.245321i | ||||
\(431\) | 3.91140 | + | 3.91140i | 0.188405 | + | 0.188405i | 0.795006 | − | 0.606601i | \(-0.207467\pi\) |
−0.606601 | + | 0.795006i | \(0.707467\pi\) | |||||||
\(432\) | 18.7186 | + | 18.7186i | 0.900597 | + | 0.900597i | ||||
\(433\) | 2.97397i | 0.142920i | 0.997443 | + | 0.0714599i | \(0.0227658\pi\) | ||||
−0.997443 | + | 0.0714599i | \(0.977234\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.67816 | − | 6.67816i | −0.320193 | − | 0.320193i | ||||
\(436\) | 3.48919 | + | 3.48919i | 0.167102 | + | 0.167102i | ||||
\(437\) | 2.52437 | − | 2.52437i | 0.120757 | − | 0.120757i | ||||
\(438\) | −18.0767 | −0.863740 | ||||||||
\(439\) | 1.26188 | − | 1.26188i | 0.0602261 | − | 0.0602261i | −0.676352 | − | 0.736578i | \(-0.736440\pi\) |
0.736578 | + | 0.676352i | \(0.236440\pi\) | |||||||
\(440\) | − | 35.5751i | − | 1.69598i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.1446 | − | 24.2813i | −0.530093 | − | 1.15495i | ||||
\(443\) | −8.70125 | −0.413409 | −0.206704 | − | 0.978403i | \(-0.566274\pi\) | ||||
−0.206704 | + | 0.978403i | \(0.566274\pi\) | |||||||
\(444\) | − | 11.1250i | − | 0.527971i | ||||||
\(445\) | −7.35496 | + | 7.35496i | −0.348659 | + | 0.348659i | ||||
\(446\) | 42.0015 | 1.98883 | ||||||||
\(447\) | 15.0904 | − | 15.0904i | 0.713750 | − | 0.713750i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.5684 | − | 12.5684i | −0.593139 | − | 0.593139i | 0.345339 | − | 0.938478i | \(-0.387764\pi\) |
−0.938478 | + | 0.345339i | \(0.887764\pi\) | |||||||
\(450\) | 22.8234i | 1.07590i | ||||||||
\(451\) | − | 26.7617i | − | 1.26016i | ||||||
\(452\) | −6.00937 | − | 6.00937i | −0.282657 | − | 0.282657i | ||||
\(453\) | −17.6021 | − | 17.6021i | −0.827021 | − | 0.827021i | ||||
\(454\) | 13.4135 | − | 13.4135i | 0.629528 | − | 0.629528i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.65171 | − | 5.65171i | 0.264666 | − | 0.264666i | ||||
\(457\) | 22.4208i | 1.04880i | 0.851472 | + | 0.524400i | \(0.175710\pi\) | ||||
−0.851472 | + | 0.524400i | \(0.824290\pi\) | |||||||
\(458\) | −48.6260 | −2.27214 | ||||||||
\(459\) | 20.4869 | + | 7.59702i | 0.956244 | + | 0.354598i | ||||
\(460\) | −3.00347 | −0.140038 | ||||||||
\(461\) | 24.0555i | 1.12038i | 0.828365 | + | 0.560189i | \(0.189271\pi\) | ||||
−0.828365 | + | 0.560189i | \(0.810729\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.665002 | −0.0309053 | −0.0154526 | − | 0.999881i | \(-0.504919\pi\) | ||||
−0.0154526 | + | 0.999881i | \(0.504919\pi\) | |||||||
\(464\) | −8.45333 | + | 8.45333i | −0.392436 | + | 0.392436i | ||||
\(465\) | −26.6174 | − | 26.6174i | −1.23435 | − | 1.23435i | ||||
\(466\) | 5.02078 | + | 5.02078i | 0.232583 | + | 0.232583i | ||||
\(467\) | 20.5935i | 0.952954i | 0.879187 | + | 0.476477i | \(0.158086\pi\) | ||||
−0.879187 | + | 0.476477i | \(0.841914\pi\) | |||||||
\(468\) | − | 6.20664i | − | 0.286902i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −11.5674 | − | 11.5674i | −0.533562 | − | 0.533562i | ||||
\(471\) | −2.36810 | + | 2.36810i | −0.109116 | + | 0.109116i | ||||
\(472\) | −20.5824 | −0.947381 | ||||||||
\(473\) | −4.59566 | + | 4.59566i | −0.211308 | + | 0.211308i | ||||
\(474\) | 13.0166i | 0.597871i | ||||||||
\(475\) | 29.7053 | 1.36297 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.35439 | −0.107800 | ||||||||
\(478\) | 29.5855i | 1.35321i | ||||||||
\(479\) | 6.54363 | − | 6.54363i | 0.298986 | − | 0.298986i | −0.541631 | − | 0.840617i | \(-0.682193\pi\) |
0.840617 | + | 0.541631i | \(0.182193\pi\) | |||||||
\(480\) | −19.3074 | −0.881258 | ||||||||
\(481\) | 28.7245 | − | 28.7245i | 1.30973 | − | 1.30973i | ||||
\(482\) | 0.453992 | + | 0.453992i | 0.0206788 | + | 0.0206788i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 17.7579i | − | 0.807175i | ||||||
\(485\) | − | 43.3294i | − | 1.96748i | ||||||
\(486\) | 18.4174 | + | 18.4174i | 0.835431 | + | 0.835431i | ||||
\(487\) | 1.08588 | + | 1.08588i | 0.0492058 | + | 0.0492058i | 0.731282 | − | 0.682076i | \(-0.238923\pi\) |
−0.682076 | + | 0.731282i | \(0.738923\pi\) | |||||||
\(488\) | −11.4443 | + | 11.4443i | −0.518061 | + | 0.518061i | ||||
\(489\) | 16.4638 | 0.744521 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14.6140i | − | 0.659521i | −0.944065 | − | 0.329760i | \(-0.893032\pi\) | ||
0.944065 | − | 0.329760i | \(-0.106968\pi\) | |||||||
\(492\) | −5.05845 | −0.228053 | ||||||||
\(493\) | −3.43083 | + | 9.25190i | −0.154517 | + | 0.416685i | ||||
\(494\) | −25.4280 | −1.14406 | ||||||||
\(495\) | − | 34.2376i | − | 1.53887i | ||||||
\(496\) | −33.6928 | + | 33.6928i | −1.51285 | + | 1.51285i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.20029 | + | 4.20029i | −0.188220 | + | 0.188220i | ||||
\(499\) | 14.0490 | + | 14.0490i | 0.628919 | + | 0.628919i | 0.947796 | − | 0.318877i | \(-0.103306\pi\) |
−0.318877 | + | 0.947796i | \(0.603306\pi\) | |||||||
\(500\) | −5.99908 | − | 5.99908i | −0.268287 | − | 0.268287i | ||||
\(501\) | 15.1382i | 0.676326i | ||||||||
\(502\) | 26.7104i | 1.19214i | ||||||||
\(503\) | −25.4194 | − | 25.4194i | −1.13339 | − | 1.13339i | −0.989609 | − | 0.143786i | \(-0.954072\pi\) |
−0.143786 | − | 0.989609i | \(-0.545928\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.2465 | + | 34.2465i | −1.52395 | + | 1.52395i | ||||
\(506\) | 8.54090 | 0.379689 | ||||||||
\(507\) | −1.04228 | + | 1.04228i | −0.0462892 | + | 0.0462892i | ||||
\(508\) | 0.415565i | 0.0184377i | ||||||||
\(509\) | −8.06864 | −0.357636 | −0.178818 | − | 0.983882i | \(-0.557227\pi\) | ||||
−0.178818 | + | 0.983882i | \(0.557227\pi\) | |||||||
\(510\) | −25.3177 | + | 11.6202i | −1.12109 | + | 0.514552i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 6.15837i | 0.272164i | ||||||||
\(513\) | 14.7050 | − | 14.7050i | 0.649243 | − | 0.649243i | ||||
\(514\) | −36.1123 | −1.59284 | ||||||||
\(515\) | 8.70164 | − | 8.70164i | 0.383440 | − | 0.383440i | ||||
\(516\) | 0.868664 | + | 0.868664i | 0.0382408 | + | 0.0382408i | ||||
\(517\) | 10.4499 | + | 10.4499i | 0.459587 | + | 0.459587i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.62539i | 0.422508i | ||||||||
\(520\) | −17.3621 | − | 17.3621i | −0.761378 | − | 0.761378i | ||||
\(521\) | 5.42273 | + | 5.42273i | 0.237574 | + | 0.237574i | 0.815845 | − | 0.578271i | \(-0.196272\pi\) |
−0.578271 | + | 0.815845i | \(0.696272\pi\) | |||||||
\(522\) | −5.10232 | + | 5.10232i | −0.223322 | + | 0.223322i | ||||
\(523\) | −32.6947 | −1.42964 | −0.714819 | − | 0.699310i | \(-0.753491\pi\) | ||||
−0.714819 | + | 0.699310i | \(0.753491\pi\) | |||||||
\(524\) | −0.0290350 | + | 0.0290350i | −0.00126840 | + | 0.00126840i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.1536 | −0.791535 | ||||||||
\(527\) | −13.6744 | + | 36.8756i | −0.595665 | + | 1.60633i | ||||
\(528\) | 30.4894 | 1.32688 | ||||||||
\(529\) | − | 22.1724i | − | 0.964017i | ||||||
\(530\) | 5.73818 | − | 5.73818i | 0.249251 | − | 0.249251i | ||||
\(531\) | −19.8086 | −0.859619 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.0608 | − | 13.0608i | −0.565725 | − | 0.565725i | ||||
\(534\) | −3.95335 | − | 3.95335i | −0.171078 | − | 0.171078i | ||||
\(535\) | 30.0599i | 1.29960i | ||||||||
\(536\) | − | 0.787293i | − | 0.0340059i | ||||||
\(537\) | 8.42735 | + | 8.42735i | 0.363667 | + | 0.363667i | ||||
\(538\) | −33.8224 | − | 33.8224i | −1.45819 | − | 1.45819i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −17.4959 | −0.752905 | ||||||||
\(541\) | −14.4440 | + | 14.4440i | −0.620994 | + | 0.620994i | −0.945786 | − | 0.324791i | \(-0.894706\pi\) |
0.324791 | + | 0.945786i | \(0.394706\pi\) | |||||||
\(542\) | − | 4.93151i | − | 0.211827i | ||||||
\(543\) | −17.9745 | −0.771360 | ||||||||
\(544\) | 8.41472 | + | 18.3337i | 0.360778 | + | 0.786050i | ||||
\(545\) | 18.7870 | 0.804746 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.6169 | − | 30.6169i | 1.30908 | − | 1.30908i | 0.387007 | − | 0.922077i | \(-0.373509\pi\) |
0.922077 | − | 0.387007i | \(-0.126491\pi\) | |||||||
\(548\) | −1.79177 | −0.0765405 | ||||||||
\(549\) | −11.0141 | + | 11.0141i | −0.470070 | + | 0.470070i | ||||
\(550\) | 50.2522 | + | 50.2522i | 2.14276 | + | 2.14276i | ||||
\(551\) | 6.64082 | + | 6.64082i | 0.282909 | + | 0.282909i | ||||
\(552\) | 1.85292i | 0.0788657i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −8.68050 | − | 8.68050i | −0.368799 | − | 0.368799i | ||||
\(555\) | −29.9505 | − | 29.9505i | −1.27133 | − | 1.27133i | ||||
\(556\) | −3.97098 | + | 3.97098i | −0.168407 | + | 0.168407i | ||||
\(557\) | 21.2160 | 0.898951 | 0.449476 | − | 0.893293i | \(-0.351611\pi\) | ||||
0.449476 | + | 0.893293i | \(0.351611\pi\) | |||||||
\(558\) | −20.3365 | + | 20.3365i | −0.860912 | + | 0.860912i | ||||
\(559\) | 4.48573i | 0.189726i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 22.8719 | − | 10.4977i | 0.965654 | − | 0.443212i | ||||
\(562\) | 34.8170 | 1.46866 | ||||||||
\(563\) | − | 17.8118i | − | 0.750677i | −0.926888 | − | 0.375339i | \(-0.877526\pi\) | ||
0.926888 | − | 0.375339i | \(-0.122474\pi\) | |||||||
\(564\) | 1.97523 | − | 1.97523i | 0.0831721 | − | 0.0831721i | ||||
\(565\) | −32.3566 | −1.36125 | ||||||||
\(566\) | 3.73957 | − | 3.73957i | 0.157186 | − | 0.157186i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.93448 | − | 2.93448i | −0.123128 | − | 0.123128i | ||||
\(569\) | 20.9185i | 0.876950i | 0.898743 | + | 0.438475i | \(0.144481\pi\) | ||||
−0.898743 | + | 0.438475i | \(0.855519\pi\) | |||||||
\(570\) | 26.5133i | 1.11052i | ||||||||
\(571\) | −19.0298 | − | 19.0298i | −0.796371 | − | 0.796371i | 0.186151 | − | 0.982521i | \(-0.440399\pi\) |
−0.982521 | + | 0.186151i | \(0.940399\pi\) | |||||||
\(572\) | −13.6657 | − | 13.6657i | −0.571391 | − | 0.571391i | ||||
\(573\) | 10.9043 | − | 10.9043i | 0.455533 | − | 0.455533i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.86947 | + | 4.86947i | −0.203071 | + | 0.203071i | ||||
\(576\) | − | 2.84253i | − | 0.118439i | ||||||
\(577\) | −4.09850 | −0.170623 | −0.0853113 | − | 0.996354i | \(-0.527188\pi\) | ||||
−0.0853113 | + | 0.996354i | \(0.527188\pi\) | |||||||
\(578\) | 22.0684 | + | 18.9764i | 0.917923 | + | 0.789315i | ||||
\(579\) | −16.9192 | −0.703138 | ||||||||
\(580\) | − | 7.90119i | − | 0.328079i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 23.2898 | 0.965395 | ||||||||
\(583\) | −5.18385 | + | 5.18385i | −0.214693 | + | 0.214693i | ||||
\(584\) | 12.2737 | + | 12.2737i | 0.507889 | + | 0.507889i | ||||
\(585\) | −16.7094 | − | 16.7094i | −0.690847 | − | 0.690847i | ||||
\(586\) | 34.9908i | 1.44545i | ||||||||
\(587\) | − | 30.1079i | − | 1.24269i | −0.783538 | − | 0.621344i | \(-0.786587\pi\) | ||
0.783538 | − | 0.621344i | \(-0.213413\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.4686 | + | 26.4686i | 1.09062 | + | 1.09062i | ||||
\(590\) | 48.2780 | − | 48.2780i | 1.98758 | − | 1.98758i | ||||
\(591\) | 25.2313 | 1.03788 | ||||||||
\(592\) | −37.9119 | + | 37.9119i | −1.55817 | + | 1.55817i | ||||
\(593\) | − | 16.8436i | − | 0.691683i | −0.938293 | − | 0.345842i | \(-0.887593\pi\) | ||
0.938293 | − | 0.345842i | \(-0.112407\pi\) | |||||||
\(594\) | 49.7527 | 2.04138 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.8540 | 0.731329 | ||||||||
\(597\) | − | 13.0702i | − | 0.534929i | ||||||
\(598\) | 4.16831 | − | 4.16831i | 0.170455 | − | 0.170455i | ||||
\(599\) | −6.37653 | −0.260538 | −0.130269 | − | 0.991479i | \(-0.541584\pi\) | ||||
−0.130269 | + | 0.991479i | \(0.541584\pi\) | |||||||
\(600\) | −10.9021 | + | 10.9021i | −0.445075 | + | 0.445075i | ||||
\(601\) | 22.6980 | + | 22.6980i | 0.925870 | + | 0.925870i | 0.997436 | − | 0.0715659i | \(-0.0227996\pi\) |
−0.0715659 | + | 0.997436i | \(0.522800\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 0.757694i | − | 0.0308557i | ||||||
\(604\) | − | 20.8258i | − | 0.847389i | ||||||
\(605\) | −47.8072 | − | 47.8072i | −1.94364 | − | 1.94364i | ||||
\(606\) | −18.4077 | − | 18.4077i | −0.747762 | − | 0.747762i | ||||
\(607\) | 9.88359 | − | 9.88359i | 0.401163 | − | 0.401163i | −0.477480 | − | 0.878643i | \(-0.658450\pi\) |
0.878643 | + | 0.477480i | \(0.158450\pi\) | |||||||
\(608\) | 19.1994 | 0.778640 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 53.6877i | − | 2.17375i | ||||||
\(611\) | 10.2000 | 0.412646 | ||||||||
\(612\) | 2.82049 | + | 6.14517i | 0.114011 | + | 0.248404i | ||||
\(613\) | −30.9977 | −1.25199 | −0.625993 | − | 0.779828i | \(-0.715306\pi\) | ||||
−0.625993 | + | 0.779828i | \(0.715306\pi\) | |||||||
\(614\) | − | 41.9075i | − | 1.69125i | ||||||
\(615\) | −13.6182 | + | 13.6182i | −0.549140 | + | 0.549140i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.1042 | + | 22.1042i | −0.889883 | + | 0.889883i | −0.994511 | − | 0.104629i | \(-0.966635\pi\) |
0.104629 | + | 0.994511i | \(0.466635\pi\) | |||||||
\(618\) | 4.67719 | + | 4.67719i | 0.188144 | + | 0.188144i | ||||
\(619\) | −4.96117 | − | 4.96117i | −0.199406 | − | 0.199406i | 0.600339 | − | 0.799745i | \(-0.295032\pi\) |
−0.799745 | + | 0.600339i | \(0.795032\pi\) | |||||||
\(620\) | − | 31.4921i | − | 1.26475i | ||||||
\(621\) | 4.82108i | 0.193463i | ||||||||
\(622\) | 0.545387 | + | 0.545387i | 0.0218680 | + | 0.0218680i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 14.8800 | − | 14.8800i | 0.595679 | − | 0.595679i | ||||
\(625\) | 5.54761 | 0.221904 | ||||||||
\(626\) | 20.5526 | − | 20.5526i | 0.821447 | − | 0.821447i | ||||
\(627\) | − | 23.9520i | − | 0.956552i | ||||||
\(628\) | −2.80179 | −0.111804 | ||||||||
\(629\) | −15.3867 | + | 41.4933i | −0.613509 | + | 1.65445i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.0354i | 0.479123i | 0.970881 | + | 0.239562i | \(0.0770037\pi\) | ||||
−0.970881 | + | 0.239562i | \(0.922996\pi\) | |||||||
\(632\) | 8.83796 | − | 8.83796i | 0.351555 | − | 0.351555i | ||||
\(633\) | −24.3396 | −0.967413 | ||||||||
\(634\) | −5.66870 | + | 5.66870i | −0.225133 | + | 0.225133i | ||||
\(635\) | 1.11877 | + | 1.11877i | 0.0443972 | + | 0.0443972i | ||||
\(636\) | 0.979845 | + | 0.979845i | 0.0388534 | + | 0.0388534i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 22.4684i | 0.889533i | ||||||||
\(639\) | −2.82416 | − | 2.82416i | −0.111722 | − | 0.111722i | ||||
\(640\) | 31.4589 | + | 31.4589i | 1.24352 | + | 1.24352i | ||||
\(641\) | 27.1348 | − | 27.1348i | 1.07176 | − | 1.07176i | 0.0745423 | − | 0.997218i | \(-0.476250\pi\) |
0.997218 | − | 0.0745423i | \(-0.0237496\pi\) | |||||||
\(642\) | −16.1574 | −0.637681 | ||||||||
\(643\) | 4.98124 | − | 4.98124i | 0.196441 | − | 0.196441i | −0.602031 | − | 0.798472i | \(-0.705642\pi\) |
0.798472 | + | 0.602031i | \(0.205642\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.67719 | 0.184164 | ||||||||
\(646\) | 25.1761 | − | 11.5553i | 0.990542 | − | 0.454635i | ||||
\(647\) | −45.4370 | −1.78631 | −0.893156 | − | 0.449747i | \(-0.851514\pi\) | ||||
−0.893156 | + | 0.449747i | \(0.851514\pi\) | |||||||
\(648\) | 1.12621i | 0.0442418i | ||||||||
\(649\) | −43.6142 | + | 43.6142i | −1.71201 | + | 1.71201i | ||||
\(650\) | 49.0502 | 1.92391 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.73950 | + | 9.73950i | 0.381428 | + | 0.381428i | ||||
\(653\) | 2.02405 | + | 2.02405i | 0.0792074 | + | 0.0792074i | 0.745601 | − | 0.666393i | \(-0.232163\pi\) |
−0.666393 | + | 0.745601i | \(0.732163\pi\) | |||||||
\(654\) | 10.0981i | 0.394869i | ||||||||
\(655\) | 0.156335i | 0.00610850i | ||||||||
\(656\) | 17.2382 | + | 17.2382i | 0.673039 | + | 0.673039i | ||||
\(657\) | 11.8122 | + | 11.8122i | 0.460840 | + | 0.460840i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.39527 | −0.132261 | −0.0661305 | − | 0.997811i | \(-0.521065\pi\) | ||||
−0.0661305 | + | 0.997811i | \(0.521065\pi\) | |||||||
\(660\) | −14.2490 | + | 14.2490i | −0.554640 | + | 0.554640i | ||||
\(661\) | − | 15.0572i | − | 0.585656i | −0.956165 | − | 0.292828i | \(-0.905404\pi\) | ||
0.956165 | − | 0.292828i | \(-0.0945963\pi\) | |||||||
\(662\) | 59.0732 | 2.29595 | ||||||||
\(663\) | 6.03914 | − | 16.2857i | 0.234541 | − | 0.632486i | ||||
\(664\) | 5.70380 | 0.221350 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −22.8831 | + | 22.8831i | −0.886702 | + | 0.886702i | ||||
\(667\) | −2.17721 | −0.0843018 | ||||||||
\(668\) | −8.95531 | + | 8.95531i | −0.346492 | + | 0.346492i | ||||
\(669\) | 19.3086 | + | 19.3086i | 0.746514 | + | 0.746514i | ||||
\(670\) | 1.84667 | + | 1.84667i | 0.0713432 | + | 0.0713432i | ||||
\(671\) | 48.5013i | 1.87237i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.6305 | + | 16.6305i | 0.641060 | + | 0.641060i | 0.950816 | − | 0.309756i | \(-0.100247\pi\) |
−0.309756 | + | 0.950816i | \(0.600247\pi\) | |||||||
\(674\) | −32.5811 | − | 32.5811i | −1.25498 | − | 1.25498i | ||||
\(675\) | −28.3658 | + | 28.3658i | −1.09180 | + | 1.09180i | ||||
\(676\) | −1.23316 | −0.0474292 | ||||||||
\(677\) | −26.7743 | + | 26.7743i | −1.02902 | + | 1.02902i | −0.0294529 | + | 0.999566i | \(0.509376\pi\) |
−0.999566 | + | 0.0294529i | \(0.990624\pi\) | |||||||
\(678\) | − | 17.3919i | − | 0.667931i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 25.0800 | + | 9.30027i | 0.961775 | + | 0.356649i | ||||
\(681\) | 12.3327 | 0.472591 | ||||||||
\(682\) | 89.5531i | 3.42917i | ||||||||
\(683\) | 16.6107 | − | 16.6107i | 0.635592 | − | 0.635592i | −0.313873 | − | 0.949465i | \(-0.601627\pi\) |
0.949465 | + | 0.313873i | \(0.101627\pi\) | |||||||
\(684\) | 6.43536 | 0.246062 | ||||||||
\(685\) | −4.82375 | + | 4.82375i | −0.184306 | + | 0.184306i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22.3540 | − | 22.3540i | −0.852858 | − | 0.852858i | ||||
\(688\) | − | 5.92047i | − | 0.225716i | ||||||
\(689\) | 5.05986i | 0.192765i | ||||||||
\(690\) | −4.34622 | − | 4.34622i | −0.165458 | − | 0.165458i | ||||
\(691\) | −6.03978 | − | 6.03978i | −0.229764 | − | 0.229764i | 0.582830 | − | 0.812594i | \(-0.301945\pi\) |
−0.812594 | + | 0.582830i | \(0.801945\pi\) | |||||||
\(692\) | −5.69408 | + | 5.69408i | −0.216457 | + | 0.216457i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.0255 | − | 20.0255i | 0.760157 | − | 0.760157i | ||||
\(695\) | 21.3812i | 0.811034i | ||||||||
\(696\) | −4.87446 | −0.184766 | ||||||||
\(697\) | 18.8667 | + | 6.99621i | 0.714626 | + | 0.265000i | ||||
\(698\) | 17.3502 | 0.656715 | ||||||||
\(699\) | 4.61623i | 0.174602i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.16499 | −0.346157 | −0.173078 | − | 0.984908i | \(-0.555371\pi\) | ||||
−0.173078 | + | 0.984908i | \(0.555371\pi\) | |||||||
\(702\) | 24.2813 | − | 24.2813i | 0.916440 | − | 0.916440i | ||||
\(703\) | 29.7831 | + | 29.7831i | 1.12329 | + | 1.12329i | ||||
\(704\) | −6.25865 | − | 6.25865i | −0.235882 | − | 0.235882i | ||||
\(705\) | − | 10.6353i | − | 0.400549i | ||||||
\(706\) | 1.36546i | 0.0513898i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 8.24390 | + | 8.24390i | 0.309825 | + | 0.309825i | ||||
\(709\) | 1.04370 | − | 1.04370i | 0.0391971 | − | 0.0391971i | −0.687237 | − | 0.726434i | \(-0.741176\pi\) |
0.726434 | + | 0.687237i | \(0.241176\pi\) | |||||||
\(710\) | 13.7662 | 0.516637 | ||||||||
\(711\) | 8.50569 | − | 8.50569i | 0.318988 | − | 0.318988i | ||||
\(712\) | 5.36846i | 0.201192i | ||||||||
\(713\) | −8.67777 | −0.324985 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −73.5808 | −2.75177 | ||||||||
\(716\) | 9.97073i | 0.372624i | ||||||||
\(717\) | −13.6008 | + | 13.6008i | −0.507932 | + | 0.507932i | ||||
\(718\) | −35.4962 | −1.32471 | ||||||||
\(719\) | −7.89648 | + | 7.89648i | −0.294489 | + | 0.294489i | −0.838851 | − | 0.544362i | \(-0.816772\pi\) |
0.544362 | + | 0.838851i | \(0.316772\pi\) | |||||||
\(720\) | 22.0537 | + | 22.0537i | 0.821894 | + | 0.821894i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.16441i | 0.229416i | ||||||||
\(723\) | 0.417412i | 0.0155237i | ||||||||
\(724\) | −10.6332 | − | 10.6332i | −0.395179 | − | 0.395179i | ||||
\(725\) | −12.8101 | − | 12.8101i | −0.475753 | − | 0.475753i | ||||
\(726\) | 25.6967 | − | 25.6967i | 0.953695 | − | 0.953695i | ||||
\(727\) | 29.4789 | 1.09331 | 0.546656 | − | 0.837357i | \(-0.315901\pi\) | ||||
0.546656 | + | 0.837357i | \(0.315901\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.7798i | 0.695549i | ||||||||
\(730\) | −57.5783 | −2.13107 | ||||||||
\(731\) | −2.03846 | − | 4.44131i | −0.0753950 | − | 0.164268i | ||||
\(732\) | 9.16765 | 0.338846 | ||||||||
\(733\) | − | 14.4608i | − | 0.534123i | −0.963679 | − | 0.267062i | \(-0.913947\pi\) | ||
0.963679 | − | 0.267062i | \(-0.0860527\pi\) | |||||||
\(734\) | 5.92358 | − | 5.92358i | 0.218643 | − | 0.218643i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.14729 | + | 3.14729i | −0.116011 | + | 0.116011i | ||||
\(737\) | −1.66828 | − | 1.66828i | −0.0614518 | − | 0.0614518i | ||||
\(738\) | 10.4047 | + | 10.4047i | 0.383004 | + | 0.383004i | ||||
\(739\) | 18.0495i | 0.663963i | 0.943286 | + | 0.331982i | \(0.107717\pi\) | ||||
−0.943286 | + | 0.331982i | \(0.892283\pi\) | |||||||
\(740\) | − | 35.4356i | − | 1.30264i | ||||||
\(741\) | −11.6896 | − | 11.6896i | −0.429427 | − | 0.429427i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.5374 | − | 22.5374i | 0.826816 | − | 0.826816i | −0.160259 | − | 0.987075i | \(-0.551233\pi\) |
0.987075 | + | 0.160259i | \(0.0512331\pi\) | |||||||
\(744\) | −19.4283 | −0.712276 | ||||||||
\(745\) | 48.0661 | − | 48.0661i | 1.76101 | − | 1.76101i | ||||
\(746\) | 11.3882i | 0.416953i | ||||||||
\(747\) | 5.48936 | 0.200845 | ||||||||
\(748\) | 19.7404 | + | 7.32023i | 0.721782 | + | 0.267654i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 17.3621i | − | 0.633974i | ||||||
\(751\) | −27.9002 | + | 27.9002i | −1.01809 | + | 1.01809i | −0.0182586 | + | 0.999833i | \(0.505812\pi\) |
−0.999833 | + | 0.0182586i | \(0.994188\pi\) | |||||||
\(752\) | −13.4624 | −0.490922 | ||||||||
\(753\) | −12.2791 | + | 12.2791i | −0.447475 | + | 0.447475i | ||||
\(754\) | 10.9655 | + | 10.9655i | 0.399340 | + | 0.399340i | ||||
\(755\) | −56.0666 | − | 56.0666i | −2.04047 | − | 2.04047i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 11.7657i | − | 0.427633i | −0.976874 | − | 0.213816i | \(-0.931411\pi\) | ||
0.976874 | − | 0.213816i | \(-0.0685894\pi\) | |||||||
\(758\) | −7.42678 | − | 7.42678i | −0.269753 | − | 0.269753i | ||||
\(759\) | 3.92636 | + | 3.92636i | 0.142518 | + | 0.142518i | ||||
\(760\) | 18.0019 | − | 18.0019i | 0.652998 | − | 0.652998i | ||||
\(761\) | −26.3966 | −0.956877 | −0.478439 | − | 0.878121i | \(-0.658797\pi\) | ||||
−0.478439 | + | 0.878121i | \(0.658797\pi\) | |||||||
\(762\) | −0.601349 | + | 0.601349i | −0.0217846 | + | 0.0217846i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 12.9013 | 0.466752 | ||||||||
\(765\) | 24.1371 | + | 8.95062i | 0.872679 | + | 0.323610i | ||||
\(766\) | 49.6028 | 1.79222 | ||||||||
\(767\) | 42.5710i | 1.53715i | ||||||||
\(768\) | −14.3686 | + | 14.3686i | −0.518481 | + | 0.518481i | ||||
\(769\) | 14.6383 | 0.527871 | 0.263936 | − | 0.964540i | \(-0.414979\pi\) | ||||
0.263936 | + | 0.964540i | \(0.414979\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.6013 | − | 16.6013i | −0.597880 | − | 0.597880i | ||||
\(772\) | −10.0089 | − | 10.0089i | −0.360228 | − | 0.360228i | ||||
\(773\) | 17.9450i | 0.645438i | 0.946495 | + | 0.322719i | \(0.104597\pi\) | ||||
−0.946495 | + | 0.322719i | \(0.895403\pi\) | |||||||
\(774\) | − | 3.57351i | − | 0.128447i | ||||||
\(775\) | −51.0575 | − | 51.0575i | −1.83404 | − | 1.83404i | ||||
\(776\) | −15.8133 | − | 15.8133i | −0.567663 | − | 0.567663i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17.5057 | −0.627609 | ||||||||
\(779\) | 13.5421 | − | 13.5421i | 0.485196 | − | 0.485196i | ||||
\(780\) | 13.9081i | 0.497991i | ||||||||
\(781\) | −12.4364 | −0.445008 | ||||||||
\(782\) | −2.23282 | + | 6.02123i | −0.0798454 | + | 0.215319i | ||||
\(783\) | −12.6827 | −0.453244 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.54291 | + | 7.54291i | −0.269218 | + | 0.269218i | ||||
\(786\) | −0.0840310 | −0.00299729 | ||||||||
\(787\) | −0.592701 | + | 0.592701i | −0.0211275 | + | 0.0211275i | −0.717592 | − | 0.696464i | \(-0.754756\pi\) |
0.696464 | + | 0.717592i | \(0.254756\pi\) | |||||||
\(788\) | 14.9261 | + | 14.9261i | 0.531720 | + | 0.531720i | ||||
\(789\) | −8.34544 | − | 8.34544i | −0.297106 | − | 0.297106i | ||||
\(790\) | 41.4606i | 1.47510i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −12.4952 | − | 12.4952i | −0.443997 | − | 0.443997i | ||||
\(793\) | 23.6706 | + | 23.6706i | 0.840568 | + | 0.840568i | ||||
\(794\) | −5.71202 | + | 5.71202i | −0.202712 | + | 0.202712i | ||||
\(795\) | 5.27583 | 0.187114 | ||||||||
\(796\) | 7.73194 | − | 7.73194i | 0.274051 | − | 0.274051i | ||||
\(797\) | 17.3052i | 0.612981i | 0.951874 | + | 0.306490i | \(0.0991547\pi\) | ||||
−0.951874 | + | 0.306490i | \(0.900845\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.0989 | + | 4.63518i | −0.357275 | + | 0.163981i | ||||
\(800\) | −37.0355 | −1.30940 | ||||||||
\(801\) | 5.16663i | 0.182554i | ||||||||
\(802\) | 9.13653 | − | 9.13653i | 0.322622 | − | 0.322622i | ||||
\(803\) | 52.0161 | 1.83561 | ||||||||
\(804\) | −0.315336 | + | 0.315336i | −0.0111210 | + | 0.0111210i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 43.7056 | + | 43.7056i | 1.53946 | + | 1.53946i | ||||
\(807\) | − | 31.0972i | − | 1.09467i | ||||||
\(808\) | 24.9968i | 0.879386i | ||||||||
\(809\) | 22.2239 | + | 22.2239i | 0.781352 | + | 0.781352i | 0.980059 | − | 0.198707i | \(-0.0636743\pi\) |
−0.198707 | + | 0.980059i | \(0.563674\pi\) | |||||||
\(810\) | −2.64164 | − | 2.64164i | −0.0928178 | − | 0.0928178i | ||||
\(811\) | −23.4079 | + | 23.4079i | −0.821964 | + | 0.821964i | −0.986389 | − | 0.164426i | \(-0.947423\pi\) |
0.164426 | + | 0.986389i | \(0.447423\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.26708 | − | 2.26708i | 0.0795099 | − | 0.0795099i | ||||
\(814\) | 100.767i | 3.53189i | ||||||||
\(815\) | 52.4409 | 1.83692 | ||||||||
\(816\) | −7.97073 | + | 21.4946i | −0.279031 | + | 0.752463i | ||||
\(817\) | −4.65104 | −0.162719 | ||||||||
\(818\) | 19.3479i | 0.676483i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −16.1123 | −0.562665 | ||||||||
\(821\) | 15.2809 | − | 15.2809i | 0.533307 | − | 0.533307i | −0.388248 | − | 0.921555i | \(-0.626920\pi\) |
0.921555 | + | 0.388248i | \(0.126920\pi\) | |||||||
\(822\) | −2.59280 | − | 2.59280i | −0.0904343 | − | 0.0904343i | ||||
\(823\) | −15.7187 | − | 15.7187i | −0.547920 | − | 0.547920i | 0.377919 | − | 0.925839i | \(-0.376640\pi\) |
−0.925839 | + | 0.377919i | \(0.876640\pi\) | |||||||
\(824\) | − | 6.35141i | − | 0.221262i | ||||||
\(825\) | 46.2031i | 1.60859i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.0315 | + | 31.0315i | 1.07907 | + | 1.07907i | 0.996593 | + | 0.0824786i | \(0.0262836\pi\) |
0.0824786 | + | 0.996593i | \(0.473716\pi\) | |||||||
\(828\) | −1.05492 | + | 1.05492i | −0.0366611 | + | 0.0366611i | ||||
\(829\) | 48.2425 | 1.67553 | 0.837765 | − | 0.546031i | \(-0.183862\pi\) | ||||
0.837765 | + | 0.546031i | \(0.183862\pi\) | |||||||
\(830\) | −13.3788 | + | 13.3788i | −0.464386 | + | 0.464386i | ||||
\(831\) | − | 7.98107i | − | 0.276860i | ||||||
\(832\) | −6.10895 | −0.211790 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −11.4925 | −0.397954 | ||||||||
\(835\) | 48.2185i | 1.66867i | ||||||||
\(836\) | 14.1693 | − | 14.1693i | 0.490055 | − | 0.490055i | ||||
\(837\) | −50.5500 | −1.74726 | ||||||||
\(838\) | 34.2918 | − | 34.2918i | 1.18459 | − | 1.18459i | ||||
\(839\) | −18.6559 | − | 18.6559i | −0.644073 | − | 0.644073i | 0.307482 | − | 0.951554i | \(-0.400514\pi\) |
−0.951554 | + | 0.307482i | \(0.900514\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.2725i | 0.802499i | ||||||||
\(842\) | 61.3563i | 2.11448i | ||||||||
\(843\) | 16.0058 | + | 16.0058i | 0.551269 | + | 0.551269i | ||||
\(844\) | −14.3986 | − | 14.3986i | −0.495619 | − | 0.495619i | ||||
\(845\) | −3.31988 | + | 3.31988i | −0.114207 | + | 0.114207i | ||||
\(846\) | −8.12570 | −0.279367 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 6.67823i | − | 0.229331i | ||||||
\(849\) | 3.43826 | 0.118001 | ||||||||
\(850\) | −48.5644 | + | 22.2899i | −1.66575 | + | 0.764538i | ||||
\(851\) | −9.76443 | −0.334720 | ||||||||
\(852\) | 2.35071i | 0.0805338i | ||||||||
\(853\) | −12.6584 | + | 12.6584i | −0.433415 | + | 0.433415i | −0.889788 | − | 0.456374i | \(-0.849148\pi\) |
0.456374 | + | 0.889788i | \(0.349148\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 17.3251 | − | 17.3251i | 0.592506 | − | 0.592506i | ||||
\(856\) | 10.9705 | + | 10.9705i | 0.374964 | + | 0.374964i | ||||
\(857\) | −16.8061 | − | 16.8061i | −0.574086 | − | 0.574086i | 0.359182 | − | 0.933268i | \(-0.383056\pi\) |
−0.933268 | + | 0.359182i | \(0.883056\pi\) | |||||||
\(858\) | − | 39.5502i | − | 1.35022i | ||||||
\(859\) | − | 42.5275i | − | 1.45102i | −0.688211 | − | 0.725510i | \(-0.741604\pi\) | ||
0.688211 | − | 0.725510i | \(-0.258396\pi\) | |||||||
\(860\) | 2.76688 | + | 2.76688i | 0.0943499 | + | 0.0943499i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.69661 | + | 6.69661i | −0.228087 | + | 0.228087i | ||||
\(863\) | 35.7959 | 1.21851 | 0.609253 | − | 0.792976i | \(-0.291470\pi\) | ||||
0.609253 | + | 0.792976i | \(0.291470\pi\) | |||||||
\(864\) | −18.3337 | + | 18.3337i | −0.623724 | + | 0.623724i | ||||
\(865\) | 30.6589i | 1.04244i | ||||||||
\(866\) | −5.09166 | −0.173022 | ||||||||
\(867\) | 1.42141 | + | 18.8688i | 0.0482735 | + | 0.640819i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 37.4554i | − | 1.27059i | ||||||
\(870\) | 11.4335 | − | 11.4335i | 0.387633 | − | 0.387633i | ||||
\(871\) | −1.62838 | −0.0551754 | ||||||||
\(872\) | 6.85641 | − | 6.85641i | 0.232187 | − | 0.232187i | ||||
\(873\) | −15.2187 | − | 15.2187i | −0.515077 | − | 0.515077i | ||||
\(874\) | 4.32191 | + | 4.32191i | 0.146191 | + | 0.146191i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 9.83200i | − | 0.332193i | ||||||
\(877\) | −15.0886 | − | 15.0886i | −0.509506 | − | 0.509506i | 0.404869 | − | 0.914375i | \(-0.367317\pi\) |
−0.914375 | + | 0.404869i | \(0.867317\pi\) | |||||||
\(878\) | 2.16043 | + | 2.16043i | 0.0729109 | + | 0.0729109i | ||||
\(879\) | −16.0857 | + | 16.0857i | −0.542557 | + | 0.542557i | ||||
\(880\) | 97.1152 | 3.27375 | ||||||||
\(881\) | 24.2562 | − | 24.2562i | 0.817212 | − | 0.817212i | −0.168491 | − | 0.985703i | \(-0.553890\pi\) |
0.985703 | + | 0.168491i | \(0.0538895\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.3180 | 0.852018 | 0.426009 | − | 0.904719i | \(-0.359919\pi\) | ||||
0.426009 | + | 0.904719i | \(0.359919\pi\) | |||||||
\(884\) | 13.2067 | − | 6.06157i | 0.444190 | − | 0.203873i | ||||
\(885\) | 44.3880 | 1.49209 | ||||||||
\(886\) | − | 14.8972i | − | 0.500481i | ||||||
\(887\) | 11.9511 | − | 11.9511i | 0.401279 | − | 0.401279i | −0.477405 | − | 0.878684i | \(-0.658422\pi\) |
0.878684 | + | 0.477405i | \(0.158422\pi\) | |||||||
\(888\) | −21.8612 | −0.733613 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12.5923 | − | 12.5923i | −0.422093 | − | 0.422093i | ||||
\(891\) | 2.38645 | + | 2.38645i | 0.0799491 | + | 0.0799491i | ||||
\(892\) | 22.8448i | 0.764899i | ||||||||
\(893\) | 10.5758i | 0.353907i | ||||||||
\(894\) | 25.8359 | + | 25.8359i | 0.864081 | + | 0.864081i | ||||
\(895\) | 26.8429 | + | 26.8429i | 0.897261 | + | 0.897261i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.83245 | 0.127962 | ||||||||
\(898\) | 21.5180 | − | 21.5180i | 0.718066 | − | 0.718066i | ||||
\(899\) | − | 22.8285i | − | 0.761372i | ||||||
\(900\) | −12.4137 | −0.413791 | ||||||||
\(901\) | −2.29936 | − | 5.00975i | −0.0766027 | − | 0.166899i | ||||
\(902\) | 45.8180 | 1.52557 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.8087 | + | 11.8087i | −0.392751 | + | 0.392751i | ||||
\(905\) | −57.2527 | −1.90314 | ||||||||
\(906\) | 30.1362 | − | 30.1362i | 1.00121 | − | 1.00121i | ||||
\(907\) | −20.5548 | − | 20.5548i | −0.682512 | − | 0.682512i | 0.278053 | − | 0.960566i | \(-0.410311\pi\) |
−0.960566 | + | 0.278053i | \(0.910311\pi\) | |||||||
\(908\) | 7.29566 | + | 7.29566i | 0.242115 | + | 0.242115i | ||||
\(909\) | 24.0571i | 0.797922i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.6975 | + | 33.6975i | 1.11645 | + | 1.11645i | 0.992259 | + | 0.124188i | \(0.0396326\pi\) |
0.124188 | + | 0.992259i | \(0.460367\pi\) | |||||||
\(912\) | 15.4284 | + | 15.4284i | 0.510885 | + | 0.510885i | ||||
\(913\) | 12.0864 | − | 12.0864i | 0.400001 | − | 0.400001i | ||||
\(914\) | −38.3861 | −1.26970 | ||||||||
\(915\) | 24.6809 | − | 24.6809i | 0.815926 | − | 0.815926i | ||||
\(916\) | − | 26.4479i | − | 0.873862i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −13.0067 | + | 35.0750i | −0.429284 | + | 1.15765i | ||||
\(919\) | 0.642431 | 0.0211918 | 0.0105959 | − | 0.999944i | \(-0.496627\pi\) | ||||
0.0105959 | + | 0.999944i | \(0.496627\pi\) | |||||||
\(920\) | 5.90196i | 0.194582i | ||||||||
\(921\) | 19.2654 | − | 19.2654i | 0.634816 | − | 0.634816i | ||||
\(922\) | −41.1849 | −1.35635 | ||||||||
\(923\) | −6.06946 | + | 6.06946i | −0.199779 | + | 0.199779i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −57.4511 | − | 57.4511i | −1.88898 | − | 1.88898i | ||||
\(926\) | − | 1.13853i | − | 0.0374146i | ||||||
\(927\) | − | 6.11263i | − | 0.200765i | ||||||
\(928\) | −8.27952 | − | 8.27952i | −0.271789 | − | 0.271789i | ||||
\(929\) | 6.08987 | + | 6.08987i | 0.199802 | + | 0.199802i | 0.799915 | − | 0.600113i | \(-0.204878\pi\) |
−0.600113 | + | 0.799915i | \(0.704878\pi\) | |||||||
\(930\) | 45.5710 | − | 45.5710i | 1.49433 | − | 1.49433i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.73082 | + | 2.73082i | −0.0894510 | + | 0.0894510i | ||||
\(933\) | 0.501443i | 0.0164165i | ||||||||
\(934\) | −35.2577 | −1.15367 | ||||||||
\(935\) | 72.8521 | − | 33.4374i | 2.38252 | − | 1.09352i | ||||
\(936\) | −12.1963 | −0.398649 | ||||||||
\(937\) | 20.8080i | 0.679766i | 0.940468 | + | 0.339883i | \(0.110388\pi\) | ||||
−0.940468 | + | 0.339883i | \(0.889612\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.8966 | 0.616666 | ||||||||
\(940\) | 6.29153 | − | 6.29153i | 0.205207 | − | 0.205207i | ||||
\(941\) | −2.37017 | − | 2.37017i | −0.0772652 | − | 0.0772652i | 0.667418 | − | 0.744683i | \(-0.267399\pi\) |
−0.744683 | + | 0.667418i | \(0.767399\pi\) | |||||||
\(942\) | −4.05437 | − | 4.05437i | −0.132098 | − | 0.132098i | ||||
\(943\) | 4.43980i | 0.144580i | ||||||||
\(944\) | − | 56.1871i | − | 1.82874i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.86811 | − | 7.86811i | −0.255814 | − | 0.255814i | ||||
\(947\) | 8.49486 | − | 8.49486i | 0.276046 | − | 0.276046i | −0.555482 | − | 0.831528i | \(-0.687466\pi\) |
0.831528 | + | 0.555482i | \(0.187466\pi\) | |||||||
\(948\) | −7.07977 | −0.229940 | ||||||||
\(949\) | 25.3860 | − | 25.3860i | 0.824063 | − | 0.824063i | ||||
\(950\) | 50.8578i | 1.65004i | ||||||||
\(951\) | −5.21194 | −0.169009 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.0495 | 0.422716 | 0.211358 | − | 0.977409i | \(-0.432211\pi\) | ||||
0.211358 | + | 0.977409i | \(0.432211\pi\) | |||||||
\(954\) | − | 4.03089i | − | 0.130505i | ||||||
\(955\) | 34.7325 | − | 34.7325i | 1.12392 | − | 1.12392i | ||||
\(956\) | −16.0916 | −0.520441 | ||||||||
\(957\) | −10.3290 | + | 10.3290i | −0.333889 | + | 0.333889i | ||||
\(958\) | 11.2032 | + | 11.2032i | 0.361959 | + | 0.361959i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 6.36969i | 0.205581i | ||||||||
\(961\) | − | 59.9883i | − | 1.93511i | ||||||
\(962\) | 49.1786 | + | 49.1786i | 1.58558 | + | 1.58558i | ||||
\(963\) | 10.5580 | + | 10.5580i | 0.340228 | + | 0.340228i | ||||
\(964\) | −0.246928 | + | 0.246928i | −0.00795302 | + | 0.00795302i | ||||
\(965\) | −53.8913 | −1.73482 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.4078i | 1.04216i | 0.853507 | + | 0.521082i | \(0.174471\pi\) | ||||
−0.853507 | + | 0.521082i | \(0.825529\pi\) | |||||||
\(968\) | −34.8950 | −1.12157 | ||||||||
\(969\) | 16.8859 | + | 6.26169i | 0.542453 | + | 0.201155i | ||||
\(970\) | 74.1832 | 2.38188 | ||||||||
\(971\) | 24.9206i | 0.799740i | 0.916572 | + | 0.399870i | \(0.130945\pi\) | ||||
−0.916572 | + | 0.399870i | \(0.869055\pi\) | |||||||
\(972\) | −10.0173 | + | 10.0173i | −0.321305 | + | 0.321305i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.85911 | + | 1.85911i | −0.0595696 | + | 0.0595696i | ||||
\(975\) | 22.5490 | + | 22.5490i | 0.722146 | + | 0.722146i | ||||
\(976\) | −31.2415 | − | 31.2415i | −1.00002 | − | 1.00002i | ||||
\(977\) | 23.5906i | 0.754731i | 0.926064 | + | 0.377365i | \(0.123170\pi\) | ||||
−0.926064 | + | 0.377365i | \(0.876830\pi\) | |||||||
\(978\) | 28.1873i | 0.901332i | ||||||||
\(979\) | 11.3758 | + | 11.3758i | 0.363572 | + | 0.363572i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.59863 | − | 6.59863i | 0.210678 | − | 0.210678i | ||||
\(982\) | 25.0203 | 0.798430 | ||||||||
\(983\) | −7.34127 | + | 7.34127i | −0.234150 | + | 0.234150i | −0.814422 | − | 0.580272i | \(-0.802946\pi\) |
0.580272 | + | 0.814422i | \(0.302946\pi\) | |||||||
\(984\) | 9.94009i | 0.316879i | ||||||||
\(985\) | 80.3672 | 2.56071 | ||||||||
\(986\) | −15.8400 | − | 5.87384i | −0.504447 | − | 0.187061i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 13.8304i | − | 0.440003i | ||||||
\(989\) | 0.762426 | − | 0.762426i | 0.0242437 | − | 0.0242437i | ||||
\(990\) | 58.6174 | 1.86298 | ||||||||
\(991\) | −16.0590 | + | 16.0590i | −0.510132 | + | 0.510132i | −0.914567 | − | 0.404435i | \(-0.867468\pi\) |
0.404435 | + | 0.914567i | \(0.367468\pi\) | |||||||
\(992\) | −33.0000 | − | 33.0000i | −1.04775 | − | 1.04775i | ||||
\(993\) | 27.1567 | + | 27.1567i | 0.861792 | + | 0.861792i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 41.6315i | − | 1.31981i | ||||||
\(996\) | −2.28455 | − | 2.28455i | −0.0723889 | − | 0.0723889i | ||||
\(997\) | −27.3633 | − | 27.3633i | −0.866605 | − | 0.866605i | 0.125490 | − | 0.992095i | \(-0.459950\pi\) |
−0.992095 | + | 0.125490i | \(0.959950\pi\) | |||||||
\(998\) | −24.0529 | + | 24.0529i | −0.761382 | + | 0.761382i | ||||
\(999\) | −56.8801 | −1.79961 |
(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 | 833.2.g.e.344.5 | ✓ | 16 | |
7.2 | even | 3 | 833.2.o.e.361.5 | 32 | |||
7.3 | odd | 6 | 833.2.o.e.667.3 | 32 | |||
7.4 | even | 3 | 833.2.o.e.667.4 | 32 | |||
7.5 | odd | 6 | 833.2.o.e.361.6 | 32 | |||
7.6 | odd | 2 | inner | 833.2.g.e.344.6 | yes | 16 | |
17.13 | even | 4 | inner | 833.2.g.e.540.3 | yes | 16 | |
119.13 | odd | 4 | inner | 833.2.g.e.540.4 | yes | 16 | |
119.30 | even | 12 | 833.2.o.e.557.4 | 32 | |||
119.47 | odd | 12 | 833.2.o.e.557.3 | 32 | |||
119.81 | even | 12 | 833.2.o.e.30.5 | 32 | |||
119.115 | odd | 12 | 833.2.o.e.30.6 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
833.2.g.e.344.5 | ✓ | 16 | 1.1 | even | 1 | trivial | |
833.2.g.e.344.6 | yes | 16 | 7.6 | odd | 2 | inner | |
833.2.g.e.540.3 | yes | 16 | 17.13 | even | 4 | inner | |
833.2.g.e.540.4 | yes | 16 | 119.13 | odd | 4 | inner | |
833.2.o.e.30.5 | 32 | 119.81 | even | 12 | |||
833.2.o.e.30.6 | 32 | 119.115 | odd | 12 | |||
833.2.o.e.361.5 | 32 | 7.2 | even | 3 | |||
833.2.o.e.361.6 | 32 | 7.5 | odd | 6 | |||
833.2.o.e.557.3 | 32 | 119.47 | odd | 12 | |||
833.2.o.e.557.4 | 32 | 119.30 | even | 12 | |||
833.2.o.e.667.3 | 32 | 7.3 | odd | 6 | |||
833.2.o.e.667.4 | 32 | 7.4 | even | 3 |