Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(459,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.459");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.k (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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.58891012706304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 459.1 | ||
Root | \(-1.30089 - 0.554694i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.459 |
Dual form | 637.2.k.h.569.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.10939i | − | 1.49156i | −0.666191 | − | 0.745781i | \(-0.732076\pi\) | ||
0.666191 | − | 0.745781i | \(-0.267924\pi\) | |||||||
\(3\) | −1.13082 | − | 1.95864i | −0.652882 | − | 1.13082i | −0.982420 | − | 0.186682i | \(-0.940227\pi\) |
0.329539 | − | 0.944142i | \(-0.393107\pi\) | |||||||
\(4\) | −2.44952 | −1.22476 | ||||||||
\(5\) | −3.11923 | + | 1.80089i | −1.39496 | + | 0.805382i | −0.993859 | − | 0.110650i | \(-0.964707\pi\) |
−0.401104 | + | 0.916033i | \(0.631373\pi\) | |||||||
\(6\) | −4.13154 | + | 2.38535i | −1.68670 | + | 0.973814i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.948212i | 0.335243i | ||||||||
\(9\) | −1.05753 | + | 1.83169i | −0.352509 | + | 0.610563i | ||||
\(10\) | 3.79878 | + | 6.57967i | 1.20128 | + | 2.08068i | ||||
\(11\) | −0.767631 | + | 0.443192i | −0.231450 | + | 0.133627i | −0.611241 | − | 0.791445i | \(-0.709329\pi\) |
0.379791 | + | 0.925072i | \(0.375996\pi\) | |||||||
\(12\) | 2.76998 | + | 4.79774i | 0.799623 | + | 1.38499i | ||||
\(13\) | −1.17349 | + | 3.40924i | −0.325467 | + | 0.945553i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.05461 | + | 4.07298i | 1.82149 | + | 1.05164i | ||||
\(16\) | −2.89889 | −0.724723 | ||||||||
\(17\) | 4.96016 | 1.20302 | 0.601508 | − | 0.798867i | \(-0.294567\pi\) | ||||
0.601508 | + | 0.798867i | \(0.294567\pi\) | |||||||
\(18\) | 3.86375 | + | 2.23073i | 0.910694 | + | 0.525789i | ||||
\(19\) | −2.06008 | − | 1.18939i | −0.472615 | − | 0.272864i | 0.244719 | − | 0.969594i | \(-0.421304\pi\) |
−0.717334 | + | 0.696730i | \(0.754638\pi\) | |||||||
\(20\) | 7.64062 | − | 4.41132i | 1.70849 | − | 0.986400i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.934864 | + | 1.61923i | 0.199314 | + | 0.345222i | ||||
\(23\) | 3.85851 | 0.804555 | 0.402278 | − | 0.915518i | \(-0.368219\pi\) | ||||
0.402278 | + | 0.915518i | \(0.368219\pi\) | |||||||
\(24\) | 1.85721 | − | 1.07226i | 0.379101 | − | 0.218874i | ||||
\(25\) | 3.98641 | − | 6.90466i | 0.797282 | − | 1.38093i | ||||
\(26\) | 7.19141 | + | 2.47534i | 1.41035 | + | 0.485454i | ||||
\(27\) | −2.00144 | −0.385177 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.640986 | + | 1.11022i | −0.119028 | + | 0.206163i | −0.919383 | − | 0.393364i | \(-0.871311\pi\) |
0.800355 | + | 0.599527i | \(0.204645\pi\) | |||||||
\(30\) | 8.59150 | − | 14.8809i | 1.56859 | − | 2.71687i | ||||
\(31\) | −7.33455 | − | 4.23460i | −1.31732 | − | 0.760557i | −0.334027 | − | 0.942564i | \(-0.608408\pi\) |
−0.983297 | + | 0.182006i | \(0.941741\pi\) | |||||||
\(32\) | 8.01131i | 1.41621i | ||||||||
\(33\) | 1.73611 | + | 1.00234i | 0.302218 | + | 0.174486i | ||||
\(34\) | − | 10.4629i | − | 1.79437i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.59043 | − | 4.48676i | 0.431739 | − | 0.747793i | ||||
\(37\) | 9.63812i | 1.58450i | 0.610198 | + | 0.792249i | \(0.291090\pi\) | ||||
−0.610198 | + | 0.792249i | \(0.708910\pi\) | |||||||
\(38\) | −2.50888 | + | 4.34551i | −0.406994 | + | 0.704935i | ||||
\(39\) | 8.00450 | − | 1.55681i | 1.28175 | − | 0.249289i | ||||
\(40\) | −1.70762 | − | 2.95769i | −0.269999 | − | 0.467652i | ||||
\(41\) | 10.4652 | + | 6.04207i | 1.63438 | + | 0.943612i | 0.982719 | + | 0.185106i | \(0.0592628\pi\) |
0.651666 | + | 0.758506i | \(0.274071\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.82125 | − | 3.15450i | −0.277738 | − | 0.481056i | 0.693084 | − | 0.720856i | \(-0.256251\pi\) |
−0.970822 | + | 0.239800i | \(0.922918\pi\) | |||||||
\(44\) | 1.88033 | − | 1.08561i | 0.283470 | − | 0.163662i | ||||
\(45\) | − | 7.61796i | − | 1.13562i | ||||||
\(46\) | − | 8.13910i | − | 1.20004i | ||||||
\(47\) | −2.58274 | + | 1.49115i | −0.376731 | + | 0.217506i | −0.676395 | − | 0.736539i | \(-0.736459\pi\) |
0.299664 | + | 0.954045i | \(0.403126\pi\) | |||||||
\(48\) | 3.27814 | + | 5.67790i | 0.473158 | + | 0.819535i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −14.5646 | − | 8.40888i | −2.05975 | − | 1.18920i | ||||
\(51\) | −5.60907 | − | 9.71520i | −0.785427 | − | 1.36040i | ||||
\(52\) | 2.87448 | − | 8.35100i | 0.398619 | − | 1.15808i | ||||
\(53\) | −2.46016 | + | 4.26112i | −0.337929 | + | 0.585310i | −0.984043 | − | 0.177931i | \(-0.943060\pi\) |
0.646114 | + | 0.763241i | \(0.276393\pi\) | |||||||
\(54\) | 4.22181i | 0.574516i | ||||||||
\(55\) | 1.59628 | − | 2.76484i | 0.215242 | − | 0.372811i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.37995i | 0.712592i | ||||||||
\(58\) | 2.34189 | + | 1.35209i | 0.307505 | + | 0.177538i | ||||
\(59\) | 7.32746i | 0.953954i | 0.878916 | + | 0.476977i | \(0.158268\pi\) | ||||
−0.878916 | + | 0.476977i | \(0.841732\pi\) | |||||||
\(60\) | −17.2804 | − | 9.97684i | −2.23089 | − | 1.28800i | ||||
\(61\) | 0.769632 | − | 1.33304i | 0.0985412 | − | 0.170678i | −0.812540 | − | 0.582906i | \(-0.801916\pi\) |
0.911081 | + | 0.412227i | \(0.135249\pi\) | |||||||
\(62\) | −8.93242 | + | 15.4714i | −1.13442 | + | 1.96487i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 11.1012 | 1.38765 | ||||||||
\(65\) | −2.47929 | − | 12.7475i | −0.307518 | − | 1.58114i | ||||
\(66\) | 2.11433 | − | 3.66213i | 0.260257 | − | 0.450778i | ||||
\(67\) | −7.29756 | + | 4.21325i | −0.891539 | + | 0.514730i | −0.874445 | − | 0.485124i | \(-0.838775\pi\) |
−0.0170931 | + | 0.999854i | \(0.505441\pi\) | |||||||
\(68\) | −12.1500 | −1.47341 | ||||||||
\(69\) | −4.36330 | − | 7.55745i | −0.525279 | − | 0.909811i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.58490 | + | 3.22444i | −0.662805 | + | 0.382671i | −0.793345 | − | 0.608772i | \(-0.791662\pi\) |
0.130540 | + | 0.991443i | \(0.458329\pi\) | |||||||
\(72\) | −1.73683 | − | 1.00276i | −0.204687 | − | 0.118176i | ||||
\(73\) | −6.19086 | − | 3.57430i | −0.724586 | − | 0.418340i | 0.0918526 | − | 0.995773i | \(-0.470721\pi\) |
−0.816438 | + | 0.577433i | \(0.804054\pi\) | |||||||
\(74\) | 20.3305 | 2.36338 | ||||||||
\(75\) | −18.0317 | −2.08212 | ||||||||
\(76\) | 5.04621 | + | 2.91343i | 0.578840 | + | 0.334193i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.28391 | − | 16.8846i | −0.371830 | − | 1.91180i | ||||
\(79\) | −0.378775 | − | 0.656058i | −0.0426156 | − | 0.0738123i | 0.843931 | − | 0.536452i | \(-0.180236\pi\) |
−0.886546 | + | 0.462640i | \(0.846902\pi\) | |||||||
\(80\) | 9.04232 | − | 5.22059i | 1.01096 | − | 0.583679i | ||||
\(81\) | 5.43585 | + | 9.41518i | 0.603984 | + | 1.04613i | ||||
\(82\) | 12.7451 | − | 22.0751i | 1.40746 | − | 2.43779i | ||||
\(83\) | − | 4.76766i | − | 0.523319i | −0.965160 | − | 0.261659i | \(-0.915730\pi\) | ||
0.965160 | − | 0.261659i | \(-0.0842697\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.4719 | + | 8.93270i | −1.67816 | + | 0.968888i | ||||
\(86\) | −6.65406 | + | 3.84172i | −0.717525 | + | 0.414263i | ||||
\(87\) | 2.89937 | 0.310845 | ||||||||
\(88\) | −0.420240 | − | 0.727877i | −0.0447977 | − | 0.0775919i | ||||
\(89\) | − | 3.61884i | − | 0.383596i | −0.981434 | − | 0.191798i | \(-0.938568\pi\) | ||
0.981434 | − | 0.191798i | \(-0.0614318\pi\) | |||||||
\(90\) | −16.0692 | −1.69385 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.45150 | −0.985387 | ||||||||
\(93\) | 19.1544i | 1.98622i | ||||||||
\(94\) | 3.14541 | + | 5.44800i | 0.324424 | + | 0.561919i | ||||
\(95\) | 8.56783 | 0.879040 | ||||||||
\(96\) | 15.6913 | − | 9.05939i | 1.60149 | − | 0.924620i | ||||
\(97\) | −0.401229 | + | 0.231650i | −0.0407386 | + | 0.0235205i | −0.520231 | − | 0.854026i | \(-0.674154\pi\) |
0.479492 | + | 0.877546i | \(0.340821\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.87475i | − | 0.188419i | ||||||
\(100\) | −9.76479 | + | 16.9131i | −0.976479 | + | 1.69131i | ||||
\(101\) | 2.91152 | + | 5.04289i | 0.289707 | + | 0.501787i | 0.973740 | − | 0.227664i | \(-0.0731089\pi\) |
−0.684033 | + | 0.729451i | \(0.739776\pi\) | |||||||
\(102\) | −20.4931 | + | 11.8317i | −2.02912 | + | 1.17151i | ||||
\(103\) | 4.11944 | + | 7.13508i | 0.405901 | + | 0.703040i | 0.994426 | − | 0.105438i | \(-0.0336246\pi\) |
−0.588525 | + | 0.808479i | \(0.700291\pi\) | |||||||
\(104\) | −3.23268 | − | 1.11271i | −0.316991 | − | 0.109111i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.98837 | + | 5.18944i | 0.873027 | + | 0.504043i | ||||
\(107\) | −3.83260 | −0.370511 | −0.185256 | − | 0.982690i | \(-0.559311\pi\) | ||||
−0.185256 | + | 0.982690i | \(0.559311\pi\) | |||||||
\(108\) | 4.90256 | 0.471749 | ||||||||
\(109\) | 9.02229 | + | 5.20902i | 0.864178 | + | 0.498934i | 0.865409 | − | 0.501066i | \(-0.167058\pi\) |
−0.00123094 | + | 0.999999i | \(0.500392\pi\) | |||||||
\(110\) | −5.83212 | − | 3.36718i | −0.556071 | − | 0.321048i | ||||
\(111\) | 18.8777 | − | 10.8990i | 1.79179 | − | 1.03449i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.45505 | + | 4.25228i | 0.230952 | + | 0.400021i | 0.958089 | − | 0.286472i | \(-0.0924826\pi\) |
−0.727136 | + | 0.686493i | \(0.759149\pi\) | |||||||
\(114\) | 11.3484 | 1.06288 | ||||||||
\(115\) | −12.0356 | + | 6.94875i | −1.12233 | + | 0.647975i | ||||
\(116\) | 1.57011 | − | 2.71951i | 0.145781 | − | 0.252500i | ||||
\(117\) | −5.00368 | − | 5.75483i | −0.462590 | − | 0.532034i | ||||
\(118\) | 15.4565 | 1.42288 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.86205 | + | 6.68926i | −0.352555 | + | 0.610643i | ||||
\(121\) | −5.10716 | + | 8.84586i | −0.464287 | + | 0.804169i | ||||
\(122\) | −2.81190 | − | 1.62345i | −0.254578 | − | 0.146980i | ||||
\(123\) | − | 27.3301i | − | 2.46427i | ||||||
\(124\) | 17.9661 | + | 10.3727i | 1.61341 | + | 0.931500i | ||||
\(125\) | 10.7074i | 0.957702i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.15508 | + | 10.6609i | −0.546175 | + | 0.946003i | 0.452357 | + | 0.891837i | \(0.350583\pi\) |
−0.998532 | + | 0.0541658i | \(0.982750\pi\) | |||||||
\(128\) | − | 7.39409i | − | 0.653551i | ||||||
\(129\) | −4.11902 | + | 7.13436i | −0.362660 | + | 0.628145i | ||||
\(130\) | −26.8895 | + | 5.22978i | −2.35837 | + | 0.458682i | ||||
\(131\) | 4.10133 | + | 7.10371i | 0.358335 | + | 0.620654i | 0.987683 | − | 0.156470i | \(-0.0500114\pi\) |
−0.629348 | + | 0.777123i | \(0.716678\pi\) | |||||||
\(132\) | −4.25264 | − | 2.45526i | −0.370145 | − | 0.213703i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.88737 | + | 15.3934i | 0.767752 | + | 1.32979i | ||||
\(135\) | 6.24295 | − | 3.60437i | 0.537308 | − | 0.310215i | ||||
\(136\) | 4.70328i | 0.403303i | ||||||||
\(137\) | 7.45555i | 0.636971i | 0.947928 | + | 0.318485i | \(0.103174\pi\) | ||||
−0.947928 | + | 0.318485i | \(0.896826\pi\) | |||||||
\(138\) | −15.9416 | + | 9.20389i | −1.35704 | + | 0.783487i | ||||
\(139\) | −8.34028 | − | 14.4458i | −0.707413 | − | 1.22528i | −0.965813 | − | 0.259238i | \(-0.916529\pi\) |
0.258400 | − | 0.966038i | \(-0.416805\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.84125 | + | 3.37245i | 0.491922 | + | 0.284011i | ||||
\(142\) | 6.80160 | + | 11.7807i | 0.570778 | + | 0.988616i | ||||
\(143\) | −0.610143 | − | 3.13712i | −0.0510228 | − | 0.262339i | ||||
\(144\) | 3.06566 | − | 5.30987i | 0.255471 | − | 0.442489i | ||||
\(145\) | − | 4.61738i | − | 0.383453i | ||||||
\(146\) | −7.53958 | + | 13.0589i | −0.623980 | + | 1.08076i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 23.6088i | − | 1.94063i | ||||||
\(149\) | 2.18380 | + | 1.26082i | 0.178904 | + | 0.103290i | 0.586777 | − | 0.809748i | \(-0.300396\pi\) |
−0.407874 | + | 0.913038i | \(0.633730\pi\) | |||||||
\(150\) | 38.0359i | 3.10562i | ||||||||
\(151\) | −13.7674 | − | 7.94862i | −1.12038 | − | 0.646849i | −0.178879 | − | 0.983871i | \(-0.557247\pi\) |
−0.941497 | + | 0.337022i | \(0.890580\pi\) | |||||||
\(152\) | 1.12779 | − | 1.95339i | 0.0914760 | − | 0.158441i | ||||
\(153\) | −5.24550 | + | 9.08548i | −0.424074 | + | 0.734517i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 30.5042 | 2.45016 | ||||||||
\(156\) | −19.6072 | + | 3.81343i | −1.56983 | + | 0.305319i | ||||
\(157\) | −6.49155 | + | 11.2437i | −0.518082 | + | 0.897344i | 0.481697 | + | 0.876338i | \(0.340020\pi\) |
−0.999779 | + | 0.0210065i | \(0.993313\pi\) | |||||||
\(158\) | −1.38388 | + | 0.798985i | −0.110096 | + | 0.0635638i | ||||
\(159\) | 11.1280 | 0.882511 | ||||||||
\(160\) | −14.4275 | − | 24.9892i | −1.14059 | − | 1.97557i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 19.8603 | − | 11.4663i | 1.56037 | − | 0.900880i | ||||
\(163\) | 2.00873 | + | 1.15974i | 0.157336 | + | 0.0908378i | 0.576601 | − | 0.817026i | \(-0.304379\pi\) |
−0.419265 | + | 0.907864i | \(0.637712\pi\) | |||||||
\(164\) | −25.6346 | − | 14.8002i | −2.00173 | − | 1.15570i | ||||
\(165\) | −7.22045 | −0.562111 | ||||||||
\(166\) | −10.0569 | −0.780563 | ||||||||
\(167\) | −11.9441 | − | 6.89591i | −0.924260 | − | 0.533622i | −0.0392682 | − | 0.999229i | \(-0.512503\pi\) |
−0.884992 | + | 0.465607i | \(0.845836\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.2459 | − | 8.00140i | −0.788143 | − | 0.615493i | ||||
\(170\) | 18.8425 | + | 32.6362i | 1.44516 | + | 2.50309i | ||||
\(171\) | 4.35718 | − | 2.51562i | 0.333202 | − | 0.192374i | ||||
\(172\) | 4.46118 | + | 7.72700i | 0.340162 | + | 0.589178i | ||||
\(173\) | −1.84216 | + | 3.19071i | −0.140057 | + | 0.242585i | −0.927518 | − | 0.373779i | \(-0.878062\pi\) |
0.787461 | + | 0.616364i | \(0.211395\pi\) | |||||||
\(174\) | − | 6.11590i | − | 0.463645i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.22528 | − | 1.28477i | 0.167737 | − | 0.0968429i | ||||
\(177\) | 14.3519 | − | 8.28607i | 1.07875 | − | 0.622819i | ||||
\(178\) | −7.63353 | −0.572157 | ||||||||
\(179\) | −2.94638 | − | 5.10328i | −0.220223 | − | 0.381437i | 0.734653 | − | 0.678443i | \(-0.237345\pi\) |
−0.954876 | + | 0.297006i | \(0.904012\pi\) | |||||||
\(180\) | 18.6603i | 1.39086i | ||||||||
\(181\) | −2.11543 | −0.157239 | −0.0786193 | − | 0.996905i | \(-0.525051\pi\) | ||||
−0.0786193 | + | 0.996905i | \(0.525051\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.48127 | −0.257343 | ||||||||
\(184\) | 3.65869i | 0.269722i | ||||||||
\(185\) | −17.3572 | − | 30.0635i | −1.27613 | − | 2.21032i | ||||
\(186\) | 40.4040 | 2.96257 | ||||||||
\(187\) | −3.80758 | + | 2.19830i | −0.278437 | + | 0.160756i | ||||
\(188\) | 6.32647 | − | 3.65259i | 0.461406 | − | 0.266393i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 18.0729i | − | 1.31114i | ||||||
\(191\) | 5.68333 | − | 9.84381i | 0.411231 | − | 0.712273i | −0.583794 | − | 0.811902i | \(-0.698432\pi\) |
0.995025 | + | 0.0996290i | \(0.0317656\pi\) | |||||||
\(192\) | −12.5535 | − | 21.7433i | −0.905970 | − | 1.56919i | ||||
\(193\) | −12.2017 | + | 7.04468i | −0.878301 | + | 0.507087i | −0.870098 | − | 0.492879i | \(-0.835945\pi\) |
−0.00820314 | + | 0.999966i | \(0.502611\pi\) | |||||||
\(194\) | 0.488639 | + | 0.846348i | 0.0350823 | + | 0.0607643i | ||||
\(195\) | −22.1643 | + | 19.2713i | −1.58722 | + | 1.38004i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.8815 | − | 11.4786i | −1.41650 | − | 0.817814i | −0.420507 | − | 0.907289i | \(-0.638148\pi\) |
−0.995989 | + | 0.0894753i | \(0.971481\pi\) | |||||||
\(198\) | −3.95458 | −0.281040 | ||||||||
\(199\) | 3.14985 | 0.223287 | 0.111643 | − | 0.993748i | \(-0.464389\pi\) | ||||
0.111643 | + | 0.993748i | \(0.464389\pi\) | |||||||
\(200\) | 6.54708 | + | 3.77996i | 0.462949 | + | 0.267283i | ||||
\(201\) | 16.5045 | + | 9.52888i | 1.16414 | + | 0.672116i | ||||
\(202\) | 10.6374 | − | 6.14152i | 0.748446 | − | 0.432116i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 13.7395 | + | 23.7976i | 0.961959 | + | 1.66616i | ||||
\(205\) | −43.5244 | −3.03987 | ||||||||
\(206\) | 15.0507 | − | 8.68950i | 1.04863 | − | 0.605426i | ||||
\(207\) | −4.08048 | + | 7.06760i | −0.283613 | + | 0.491232i | ||||
\(208\) | 3.40181 | − | 9.88303i | 0.235873 | − | 0.685265i | ||||
\(209\) | 2.10851 | 0.145849 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.43191 | − | 12.8725i | 0.511634 | − | 0.886176i | −0.488275 | − | 0.872690i | \(-0.662374\pi\) |
0.999909 | − | 0.0134864i | \(-0.00429298\pi\) | |||||||
\(212\) | 6.02621 | − | 10.4377i | 0.413882 | − | 0.716865i | ||||
\(213\) | 12.6311 | + | 7.29255i | 0.865467 | + | 0.499678i | ||||
\(214\) | 8.08444i | 0.552641i | ||||||||
\(215\) | 11.3618 | + | 6.55974i | 0.774868 | + | 0.447370i | ||||
\(216\) | − | 1.89779i | − | 0.129128i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.9878 | − | 19.0315i | 0.744191 | − | 1.28898i | ||||
\(219\) | 16.1676i | 1.09251i | ||||||||
\(220\) | −3.91012 | + | 6.77253i | −0.263620 | + | 0.456604i | ||||
\(221\) | −5.82069 | + | 16.9104i | −0.391542 | + | 1.13752i | ||||
\(222\) | −22.9903 | − | 39.8203i | −1.54301 | − | 2.67257i | ||||
\(223\) | 3.79396 | + | 2.19044i | 0.254062 | + | 0.146683i | 0.621623 | − | 0.783317i | \(-0.286474\pi\) |
−0.367561 | + | 0.930000i | \(0.619807\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.43147 | + | 14.6037i | 0.562098 | + | 0.973582i | ||||
\(226\) | 8.96971 | − | 5.17866i | 0.596656 | − | 0.344480i | ||||
\(227\) | 13.5663i | 0.900428i | 0.892921 | + | 0.450214i | \(0.148652\pi\) | ||||
−0.892921 | + | 0.450214i | \(0.851348\pi\) | |||||||
\(228\) | − | 13.1783i | − | 0.872754i | ||||||
\(229\) | −14.3050 | + | 8.25900i | −0.945302 | + | 0.545770i | −0.891618 | − | 0.452788i | \(-0.850429\pi\) |
−0.0536833 | + | 0.998558i | \(0.517096\pi\) | |||||||
\(230\) | 14.6576 | + | 25.3877i | 0.966495 | + | 1.67402i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.05272 | − | 0.607791i | −0.0691147 | − | 0.0399034i | ||||
\(233\) | −8.25131 | − | 14.2917i | −0.540561 | − | 0.936279i | −0.998872 | − | 0.0474874i | \(-0.984879\pi\) |
0.458311 | − | 0.888792i | \(-0.348455\pi\) | |||||||
\(234\) | −12.1392 | + | 10.5547i | −0.793562 | + | 0.689983i | ||||
\(235\) | 5.37078 | − | 9.30246i | 0.350351 | − | 0.606826i | ||||
\(236\) | − | 17.9488i | − | 1.16836i | ||||||
\(237\) | −0.856657 | + | 1.48377i | −0.0556458 | + | 0.0963814i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 30.4210i | 1.96777i | 0.178796 | + | 0.983886i | \(0.442780\pi\) | ||||
−0.178796 | + | 0.983886i | \(0.557220\pi\) | |||||||
\(240\) | −20.4506 | − | 11.8071i | −1.32008 | − | 0.762147i | ||||
\(241\) | − | 29.5143i | − | 1.90119i | −0.310440 | − | 0.950593i | \(-0.600476\pi\) | ||
0.310440 | − | 0.950593i | \(-0.399524\pi\) | |||||||
\(242\) | 18.6594 | + | 10.7730i | 1.19947 | + | 0.692514i | ||||
\(243\) | 9.29184 | − | 16.0939i | 0.596072 | − | 1.03243i | ||||
\(244\) | −1.88523 | + | 3.26531i | −0.120689 | + | 0.209040i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −57.6497 | −3.67561 | ||||||||
\(247\) | 6.47239 | − | 5.62758i | 0.411828 | − | 0.358074i | ||||
\(248\) | 4.01530 | − | 6.95471i | 0.254972 | − | 0.441624i | ||||
\(249\) | −9.33816 | + | 5.39139i | −0.591782 | + | 0.341665i | ||||
\(250\) | 22.5861 | 1.42847 | ||||||||
\(251\) | −6.49134 | − | 11.2433i | −0.409730 | − | 0.709673i | 0.585130 | − | 0.810940i | \(-0.301044\pi\) |
−0.994859 | + | 0.101267i | \(0.967710\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.96191 | + | 1.71006i | −0.186214 | + | 0.107511i | ||||
\(254\) | 22.4880 | + | 12.9835i | 1.41102 | + | 0.814654i | ||||
\(255\) | 34.9920 | + | 20.2026i | 2.19128 | + | 1.26514i | ||||
\(256\) | 6.60537 | 0.412836 | ||||||||
\(257\) | 4.58521 | 0.286018 | 0.143009 | − | 0.989721i | \(-0.454322\pi\) | ||||
0.143009 | + | 0.989721i | \(0.454322\pi\) | |||||||
\(258\) | 15.0491 | + | 8.68862i | 0.936918 | + | 0.540930i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.07307 | + | 31.2253i | 0.376636 | + | 1.93651i | ||||
\(261\) | −1.35572 | − | 2.34818i | −0.0839170 | − | 0.145348i | ||||
\(262\) | 14.9845 | − | 8.65129i | 0.925744 | − | 0.534479i | ||||
\(263\) | 1.33250 | + | 2.30795i | 0.0821652 | + | 0.142314i | 0.904180 | − | 0.427152i | \(-0.140483\pi\) |
−0.822015 | + | 0.569466i | \(0.807150\pi\) | |||||||
\(264\) | −0.950435 | + | 1.64620i | −0.0584952 | + | 0.101317i | ||||
\(265\) | − | 17.7219i | − | 1.08865i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.08801 | + | 4.09227i | −0.433779 | + | 0.250443i | ||||
\(268\) | 17.8755 | − | 10.3204i | 1.09192 | − | 0.630421i | ||||
\(269\) | 11.9256 | 0.727119 | 0.363559 | − | 0.931571i | \(-0.381561\pi\) | ||||
0.363559 | + | 0.931571i | \(0.381561\pi\) | |||||||
\(270\) | −7.60301 | − | 13.1688i | −0.462705 | − | 0.801428i | ||||
\(271\) | 13.0283i | 0.791414i | 0.918377 | + | 0.395707i | \(0.129500\pi\) | ||||
−0.918377 | + | 0.395707i | \(0.870500\pi\) | |||||||
\(272\) | −14.3790 | −0.871853 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.7267 | 0.950082 | ||||||||
\(275\) | 7.06698i | 0.426155i | ||||||||
\(276\) | 10.6880 | + | 18.5121i | 0.643341 | + | 1.11430i | ||||
\(277\) | −21.3649 | −1.28369 | −0.641846 | − | 0.766833i | \(-0.721831\pi\) | ||||
−0.641846 | + | 0.766833i | \(0.721831\pi\) | |||||||
\(278\) | −30.4718 | + | 17.5929i | −1.82758 | + | 1.05515i | ||||
\(279\) | 15.5130 | − | 8.95641i | 0.928737 | − | 0.536206i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 17.2678i | − | 1.03011i | −0.857158 | − | 0.515054i | \(-0.827772\pi\) | ||
0.857158 | − | 0.515054i | \(-0.172228\pi\) | |||||||
\(282\) | 7.11380 | − | 12.3215i | 0.423621 | − | 0.733733i | ||||
\(283\) | −10.6201 | − | 18.3946i | −0.631299 | − | 1.09344i | −0.987286 | − | 0.158952i | \(-0.949189\pi\) |
0.355987 | − | 0.934491i | \(-0.384145\pi\) | |||||||
\(284\) | 13.6803 | − | 7.89833i | 0.811777 | − | 0.468680i | ||||
\(285\) | −9.68870 | − | 16.7813i | −0.573909 | − | 0.994040i | ||||
\(286\) | −6.61741 | + | 1.28703i | −0.391295 | + | 0.0761037i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −14.6742 | − | 8.47218i | −0.864688 | − | 0.499228i | ||||
\(289\) | 7.60320 | 0.447247 | ||||||||
\(290\) | −9.73985 | −0.571944 | ||||||||
\(291\) | 0.907439 | + | 0.523910i | 0.0531950 | + | 0.0307122i | ||||
\(292\) | 15.1646 | + | 8.75531i | 0.887443 | + | 0.512366i | ||||
\(293\) | −0.363782 | + | 0.210030i | −0.0212524 | + | 0.0122701i | −0.510589 | − | 0.859825i | \(-0.670572\pi\) |
0.489336 | + | 0.872095i | \(0.337239\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.1959 | − | 22.8561i | −0.768298 | − | 1.33073i | ||||
\(296\) | −9.13898 | −0.531192 | ||||||||
\(297\) | 1.53637 | − | 0.887022i | 0.0891490 | − | 0.0514702i | ||||
\(298\) | 2.65955 | − | 4.60648i | 0.154064 | − | 0.266846i | ||||
\(299\) | −4.52791 | + | 13.1546i | −0.261856 | + | 0.760750i | ||||
\(300\) | 44.1690 | 2.55010 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −16.7667 | + | 29.0408i | −0.964817 | + | 1.67111i | ||||
\(303\) | 6.58482 | − | 11.4053i | 0.378288 | − | 0.655215i | ||||
\(304\) | 5.97195 | + | 3.44791i | 0.342515 | + | 0.197751i | ||||
\(305\) | 5.54409i | 0.317453i | ||||||||
\(306\) | 19.1648 | + | 11.0648i | 1.09558 | + | 0.632533i | ||||
\(307\) | 14.0807i | 0.803628i | 0.915721 | + | 0.401814i | \(0.131620\pi\) | ||||
−0.915721 | + | 0.401814i | \(0.868380\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.31673 | − | 16.1370i | 0.530010 | − | 0.918004i | ||||
\(310\) | − | 64.3453i | − | 3.65456i | ||||||
\(311\) | 5.19240 | − | 8.99349i | 0.294434 | − | 0.509974i | −0.680419 | − | 0.732823i | \(-0.738202\pi\) |
0.974853 | + | 0.222849i | \(0.0715356\pi\) | |||||||
\(312\) | 1.47618 | + | 7.58996i | 0.0835724 | + | 0.429697i | ||||
\(313\) | −3.42379 | − | 5.93018i | −0.193524 | − | 0.335194i | 0.752892 | − | 0.658145i | \(-0.228658\pi\) |
−0.946416 | + | 0.322951i | \(0.895325\pi\) | |||||||
\(314\) | 23.7173 | + | 13.6932i | 1.33845 | + | 0.772752i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.927818 | + | 1.60703i | 0.0521938 | + | 0.0904024i | ||||
\(317\) | −0.607299 | + | 0.350624i | −0.0341093 | + | 0.0196930i | −0.516958 | − | 0.856011i | \(-0.672936\pi\) |
0.482848 | + | 0.875704i | \(0.339602\pi\) | |||||||
\(318\) | − | 23.4734i | − | 1.31632i | ||||||
\(319\) | − | 1.13632i | − | 0.0636217i | ||||||
\(320\) | −34.6272 | + | 19.9920i | −1.93572 | + | 1.11759i | ||||
\(321\) | 4.33400 | + | 7.50670i | 0.241900 | + | 0.418983i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.2183 | − | 5.89956i | −0.568563 | − | 0.328260i | ||||
\(324\) | −13.3152 | − | 23.0627i | −0.739735 | − | 1.28126i | ||||
\(325\) | 18.8617 | + | 21.6932i | 1.04626 | + | 1.20332i | ||||
\(326\) | 2.44634 | − | 4.23719i | 0.135490 | − | 0.234676i | ||||
\(327\) | − | 23.5619i | − | 1.30298i | ||||||
\(328\) | −5.72916 | + | 9.92319i | −0.316340 | + | 0.547917i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 15.2307i | 0.838424i | ||||||||
\(331\) | −3.63613 | − | 2.09932i | −0.199860 | − | 0.115389i | 0.396730 | − | 0.917935i | \(-0.370145\pi\) |
−0.596590 | + | 0.802546i | \(0.703478\pi\) | |||||||
\(332\) | 11.6785i | 0.640940i | ||||||||
\(333\) | −17.6541 | − | 10.1926i | −0.967436 | − | 0.558550i | ||||
\(334\) | −14.5462 | + | 25.1947i | −0.795930 | + | 1.37859i | ||||
\(335\) | 15.1752 | − | 26.2842i | 0.829109 | − | 1.43606i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.4278 | −1.11278 | −0.556388 | − | 0.830923i | \(-0.687813\pi\) | ||||
−0.556388 | + | 0.830923i | \(0.687813\pi\) | |||||||
\(338\) | −16.8781 | + | 21.6125i | −0.918046 | + | 1.17556i | ||||
\(339\) | 5.55247 | − | 9.61716i | 0.301569 | − | 0.522333i | ||||
\(340\) | 37.8987 | − | 21.8808i | 2.05535 | − | 1.18665i | ||||
\(341\) | 7.50697 | 0.406525 | ||||||||
\(342\) | −5.30642 | − | 9.19098i | −0.286938 | − | 0.496991i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.99113 | − | 1.72693i | 0.161271 | − | 0.0931098i | ||||
\(345\) | 27.2203 | + | 15.7156i | 1.46549 | + | 0.846102i | ||||
\(346\) | 6.73045 | + | 3.88583i | 0.361831 | + | 0.208903i | ||||
\(347\) | 7.97000 | 0.427852 | 0.213926 | − | 0.976850i | \(-0.431375\pi\) | ||||
0.213926 | + | 0.976850i | \(0.431375\pi\) | |||||||
\(348\) | −7.10207 | −0.380711 | ||||||||
\(349\) | 18.7038 | + | 10.7986i | 1.00119 | + | 0.578037i | 0.908600 | − | 0.417668i | \(-0.137152\pi\) |
0.0925892 | + | 0.995704i | \(0.470486\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.34866 | − | 6.82338i | 0.125362 | − | 0.364205i | ||||
\(352\) | −3.55055 | − | 6.14974i | −0.189245 | − | 0.327782i | ||||
\(353\) | −18.7214 | + | 10.8088i | −0.996439 | + | 0.575295i | −0.907193 | − | 0.420715i | \(-0.861779\pi\) |
−0.0892465 | + | 0.996010i | \(0.528446\pi\) | |||||||
\(354\) | −17.4785 | − | 30.2737i | −0.928974 | − | 1.60903i | ||||
\(355\) | 11.6137 | − | 20.1156i | 0.616393 | − | 1.06762i | ||||
\(356\) | 8.86441i | 0.469813i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.7648 | + | 6.21507i | −0.568938 | + | 0.328476i | ||||
\(359\) | −11.8501 | + | 6.84168i | −0.625426 | + | 0.361090i | −0.778979 | − | 0.627051i | \(-0.784262\pi\) |
0.153552 | + | 0.988141i | \(0.450929\pi\) | |||||||
\(360\) | 7.22344 | 0.380708 | ||||||||
\(361\) | −6.67071 | − | 11.5540i | −0.351090 | − | 0.608106i | ||||
\(362\) | 4.46226i | 0.234531i | ||||||||
\(363\) | 23.1012 | 1.21250 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25.7477 | 1.34769 | ||||||||
\(366\) | 7.34335i | 0.383843i | ||||||||
\(367\) | 5.70638 | + | 9.88374i | 0.297871 | + | 0.515927i | 0.975649 | − | 0.219339i | \(-0.0703902\pi\) |
−0.677778 | + | 0.735267i | \(0.737057\pi\) | |||||||
\(368\) | −11.1854 | −0.583080 | ||||||||
\(369\) | −22.1344 | + | 12.7793i | −1.15227 | + | 0.665263i | ||||
\(370\) | −63.4157 | + | 36.6131i | −3.29683 | + | 1.90342i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 46.9190i | − | 2.43264i | ||||||
\(373\) | 15.6404 | − | 27.0900i | 0.809830 | − | 1.40267i | −0.103151 | − | 0.994666i | \(-0.532892\pi\) |
0.912981 | − | 0.408002i | \(-0.133774\pi\) | |||||||
\(374\) | 4.63708 | + | 8.03166i | 0.239778 | + | 0.415307i | ||||
\(375\) | 20.9721 | − | 12.1082i | 1.08299 | − | 0.625266i | ||||
\(376\) | −1.41392 | − | 2.44898i | −0.0729175 | − | 0.126297i | ||||
\(377\) | −3.03282 | − | 3.48811i | −0.156198 | − | 0.179647i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.7421 | + | 13.7075i | 1.21955 | + | 0.704108i | 0.964822 | − | 0.262904i | \(-0.0846803\pi\) |
0.254729 | + | 0.967012i | \(0.418014\pi\) | |||||||
\(380\) | −20.9871 | −1.07661 | ||||||||
\(381\) | 27.8412 | 1.42635 | ||||||||
\(382\) | −20.7644 | − | 11.9883i | −1.06240 | − | 0.613377i | ||||
\(383\) | −13.9436 | − | 8.05032i | −0.712483 | − | 0.411352i | 0.0994967 | − | 0.995038i | \(-0.468277\pi\) |
−0.811980 | + | 0.583686i | \(0.801610\pi\) | |||||||
\(384\) | −14.4824 | + | 8.36142i | −0.739052 | + | 0.426692i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.8600 | + | 25.7382i | 0.756353 | + | 1.31004i | ||||
\(387\) | 7.70408 | 0.391620 | ||||||||
\(388\) | 0.982819 | − | 0.567431i | 0.0498951 | − | 0.0288069i | ||||
\(389\) | 10.5690 | − | 18.3060i | 0.535870 | − | 0.928153i | −0.463251 | − | 0.886227i | \(-0.653317\pi\) |
0.999121 | − | 0.0419264i | \(-0.0133495\pi\) | |||||||
\(390\) | 40.6506 | + | 46.7530i | 2.05842 | + | 2.36743i | ||||
\(391\) | 19.1388 | 0.967893 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.27576 | − | 16.0661i | 0.467900 | − | 0.810427i | ||||
\(394\) | −24.2128 | + | 41.9377i | −1.21982 | + | 2.11279i | ||||
\(395\) | 2.36298 | + | 1.36427i | 0.118894 | + | 0.0686437i | ||||
\(396\) | 4.59224i | 0.230769i | ||||||||
\(397\) | −11.3436 | − | 6.54921i | −0.569317 | − | 0.328695i | 0.187560 | − | 0.982253i | \(-0.439942\pi\) |
−0.756876 | + | 0.653558i | \(0.773276\pi\) | |||||||
\(398\) | − | 6.64426i | − | 0.333046i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11.5562 | + | 20.0159i | −0.577808 | + | 1.00079i | ||||
\(401\) | − | 19.4447i | − | 0.971022i | −0.874230 | − | 0.485511i | \(-0.838633\pi\) | ||
0.874230 | − | 0.485511i | \(-0.161367\pi\) | |||||||
\(402\) | 20.1001 | − | 34.8144i | 1.00250 | − | 1.73639i | ||||
\(403\) | 23.0438 | − | 20.0360i | 1.14789 | − | 0.998064i | ||||
\(404\) | −7.13182 | − | 12.3527i | −0.354821 | − | 0.614568i | ||||
\(405\) | −33.9114 | − | 19.5788i | −1.68507 | − | 0.972876i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.27154 | − | 7.39853i | −0.211732 | − | 0.366731i | ||||
\(408\) | 9.21206 | − | 5.31859i | 0.456065 | − | 0.263309i | ||||
\(409\) | 24.0559i | 1.18949i | 0.803916 | + | 0.594743i | \(0.202746\pi\) | ||||
−0.803916 | + | 0.594743i | \(0.797254\pi\) | |||||||
\(410\) | 91.8098i | 4.53416i | ||||||||
\(411\) | 14.6028 | − | 8.43092i | 0.720302 | − | 0.415867i | ||||
\(412\) | −10.0907 | − | 17.4775i | −0.497131 | − | 0.861056i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 14.9083 | + | 8.60732i | 0.732703 | + | 0.423026i | ||||
\(415\) | 8.58603 | + | 14.8714i | 0.421472 | + | 0.730011i | ||||
\(416\) | −27.3125 | − | 9.40118i | −1.33911 | − | 0.460931i | ||||
\(417\) | −18.8628 | + | 32.6713i | −0.923714 | + | 1.59992i | ||||
\(418\) | − | 4.44767i | − | 0.217542i | ||||||
\(419\) | −19.5119 | + | 33.7956i | −0.953218 | + | 1.65102i | −0.214825 | + | 0.976653i | \(0.568918\pi\) |
−0.738394 | + | 0.674370i | \(0.764415\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0284i | 1.07360i | 0.843710 | + | 0.536799i | \(0.180367\pi\) | ||||
−0.843710 | + | 0.536799i | \(0.819633\pi\) | |||||||
\(422\) | −27.1530 | − | 15.6768i | −1.32179 | − | 0.763134i | ||||
\(423\) | − | 6.30771i | − | 0.306691i | ||||||
\(424\) | −4.04045 | − | 2.33275i | −0.196221 | − | 0.113289i | ||||
\(425\) | 19.7732 | − | 34.2482i | 0.959142 | − | 1.66128i | ||||
\(426\) | 15.3828 | − | 26.6438i | 0.745301 | − | 1.29090i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 9.38803 | 0.453787 | ||||||||
\(429\) | −5.45454 | + | 4.74259i | −0.263348 | + | 0.228974i | ||||
\(430\) | 13.8370 | − | 23.9664i | 0.667281 | − | 1.15576i | ||||
\(431\) | 31.0727 | − | 17.9398i | 1.49672 | − | 0.864131i | 0.496726 | − | 0.867907i | \(-0.334535\pi\) |
0.999993 | + | 0.00377645i | \(0.00120209\pi\) | |||||||
\(432\) | 5.80195 | 0.279147 | ||||||||
\(433\) | 6.10678 | + | 10.5773i | 0.293473 | + | 0.508310i | 0.974629 | − | 0.223828i | \(-0.0718555\pi\) |
−0.681155 | + | 0.732139i | \(0.738522\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.04381 | + | 5.22145i | −0.433618 | + | 0.250349i | ||||
\(436\) | −22.1003 | − | 12.7596i | −1.05841 | − | 0.611074i | ||||
\(437\) | −7.94884 | − | 4.58927i | −0.380245 | − | 0.219534i | ||||
\(438\) | 34.1037 | 1.62954 | ||||||||
\(439\) | 15.7553 | 0.751960 | 0.375980 | − | 0.926628i | \(-0.377306\pi\) | ||||
0.375980 | + | 0.926628i | \(0.377306\pi\) | |||||||
\(440\) | 2.62165 | + | 1.51361i | 0.124982 | + | 0.0721586i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 35.6706 | + | 12.2781i | 1.69668 | + | 0.584009i | ||||
\(443\) | 7.53532 | + | 13.0516i | 0.358014 | + | 0.620099i | 0.987629 | − | 0.156809i | \(-0.0501207\pi\) |
−0.629615 | + | 0.776907i | \(0.716787\pi\) | |||||||
\(444\) | −46.2412 | + | 26.6974i | −2.19451 | + | 1.26700i | ||||
\(445\) | 6.51712 | + | 11.2880i | 0.308941 | + | 0.535102i | ||||
\(446\) | 4.62050 | − | 8.00293i | 0.218787 | − | 0.378950i | ||||
\(447\) | − | 5.70305i | − | 0.269745i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.6585 | − | 15.3913i | 1.25809 | − | 0.726360i | 0.285388 | − | 0.958412i | \(-0.407877\pi\) |
0.972703 | + | 0.232052i | \(0.0745441\pi\) | |||||||
\(450\) | 30.8049 | − | 17.7852i | 1.45216 | − | 0.838404i | ||||
\(451\) | −10.7112 | −0.504370 | ||||||||
\(452\) | −6.01371 | − | 10.4160i | −0.282861 | − | 0.489929i | ||||
\(453\) | 35.9540i | 1.68926i | ||||||||
\(454\) | 28.6166 | 1.34304 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.10133 | −0.238892 | ||||||||
\(457\) | 7.75597i | 0.362809i | 0.983409 | + | 0.181405i | \(0.0580643\pi\) | ||||
−0.983409 | + | 0.181405i | \(0.941936\pi\) | |||||||
\(458\) | 17.4214 | + | 30.1748i | 0.814050 | + | 1.40998i | ||||
\(459\) | −9.92745 | −0.463374 | ||||||||
\(460\) | 29.4814 | − | 17.0211i | 1.37458 | − | 0.793613i | ||||
\(461\) | 1.27498 | − | 0.736110i | 0.0593817 | − | 0.0342840i | −0.470015 | − | 0.882658i | \(-0.655752\pi\) |
0.529397 | + | 0.848374i | \(0.322418\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0366i | 0.652335i | 0.945312 | + | 0.326168i | \(0.105757\pi\) | ||||
−0.945312 | + | 0.326168i | \(0.894243\pi\) | |||||||
\(464\) | 1.85815 | − | 3.21841i | 0.0862625 | − | 0.149411i | ||||
\(465\) | −34.4949 | − | 59.7469i | −1.59966 | − | 2.77070i | ||||
\(466\) | −30.1467 | + | 17.4052i | −1.39652 | + | 0.806281i | ||||
\(467\) | 15.6903 | + | 27.1764i | 0.726060 | + | 1.25757i | 0.958536 | + | 0.284971i | \(0.0919841\pi\) |
−0.232476 | + | 0.972602i | \(0.574683\pi\) | |||||||
\(468\) | 12.2566 | + | 14.0966i | 0.566562 | + | 0.651614i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −19.6225 | − | 11.3291i | −0.905119 | − | 0.522571i | ||||
\(471\) | 29.3632 | 1.35298 | ||||||||
\(472\) | −6.94798 | −0.319807 | ||||||||
\(473\) | 2.79610 | + | 1.61433i | 0.128565 | + | 0.0742268i | ||||
\(474\) | 3.12985 | + | 1.80702i | 0.143759 | + | 0.0829993i | ||||
\(475\) | −16.4246 | + | 9.48277i | −0.753614 | + | 0.435099i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.20337 | − | 9.01251i | −0.238246 | − | 0.412654i | ||||
\(478\) | 64.1698 | 2.93506 | ||||||||
\(479\) | −35.6760 | + | 20.5975i | −1.63008 | + | 0.941125i | −0.646009 | + | 0.763330i | \(0.723563\pi\) |
−0.984068 | + | 0.177795i | \(0.943104\pi\) | |||||||
\(480\) | −32.6299 | + | 56.5167i | −1.48935 | + | 2.57962i | ||||
\(481\) | −32.8587 | − | 11.3102i | −1.49823 | − | 0.515701i | ||||
\(482\) | −62.2572 | −2.83574 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.5101 | − | 21.6681i | 0.568641 | − | 0.984914i | ||||
\(485\) | 0.834351 | − | 1.44514i | 0.0378859 | − | 0.0656204i | ||||
\(486\) | −33.9484 | − | 19.6001i | −1.53993 | − | 0.889078i | ||||
\(487\) | 28.3265i | 1.28360i | 0.766874 | + | 0.641798i | \(0.221811\pi\) | ||||
−0.766874 | + | 0.641798i | \(0.778189\pi\) | |||||||
\(488\) | 1.26400 | + | 0.729774i | 0.0572188 | + | 0.0330353i | ||||
\(489\) | − | 5.24584i | − | 0.237225i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.3931 | − | 30.1258i | 0.784941 | − | 1.35956i | −0.144094 | − | 0.989564i | \(-0.546027\pi\) |
0.929034 | − | 0.369993i | \(-0.120640\pi\) | |||||||
\(492\) | 66.9455i | 3.01814i | ||||||||
\(493\) | −3.17940 | + | 5.50687i | −0.143193 | + | 0.248017i | ||||
\(494\) | −11.8707 | − | 13.6528i | −0.534090 | − | 0.614268i | ||||
\(495\) | 3.37622 | + | 5.84778i | 0.151750 | + | 0.262838i | ||||
\(496\) | 21.2621 | + | 12.2757i | 0.954695 | + | 0.551194i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 11.3725 | + | 19.6978i | 0.509615 | + | 0.882680i | ||||
\(499\) | 0.0601788 | − | 0.0347442i | 0.00269397 | − | 0.00155537i | −0.498652 | − | 0.866802i | \(-0.666172\pi\) |
0.501346 | + | 0.865247i | \(0.332838\pi\) | |||||||
\(500\) | − | 26.2281i | − | 1.17295i | ||||||
\(501\) | 31.1923i | 1.39357i | ||||||||
\(502\) | −23.7165 | + | 13.6928i | −1.05852 | + | 0.611138i | ||||
\(503\) | −12.8686 | − | 22.2891i | −0.573782 | − | 0.993820i | −0.996173 | − | 0.0874060i | \(-0.972142\pi\) |
0.422391 | − | 0.906414i | \(-0.361191\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.1634 | − | 10.4866i | −0.808260 | − | 0.466649i | ||||
\(506\) | 3.60719 | + | 6.24783i | 0.160359 | + | 0.277750i | ||||
\(507\) | −4.08565 | + | 29.1162i | −0.181450 | + | 1.29309i | ||||
\(508\) | 15.0770 | − | 26.1141i | 0.668933 | − | 1.15863i | ||||
\(509\) | 7.04000i | 0.312042i | 0.987754 | + | 0.156021i | \(0.0498668\pi\) | ||||
−0.987754 | + | 0.156021i | \(0.950133\pi\) | |||||||
\(510\) | 42.6152 | − | 73.8117i | 1.88703 | − | 3.26844i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 28.7215i | − | 1.26932i | ||||||
\(513\) | 4.12312 | + | 2.38049i | 0.182040 | + | 0.105101i | ||||
\(514\) | − | 9.67199i | − | 0.426613i | ||||||
\(515\) | −25.6990 | − | 14.8373i | −1.13243 | − | 0.653810i | ||||
\(516\) | 10.0896 | − | 17.4758i | 0.444171 | − | 0.769327i | ||||
\(517\) | 1.32173 | − | 2.28930i | 0.0581295 | − | 0.100683i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.33263 | 0.365762 | ||||||||
\(520\) | 12.0874 | − | 2.35089i | 0.530066 | − | 0.103093i | ||||
\(521\) | −8.16266 | + | 14.1381i | −0.357613 | + | 0.619403i | −0.987561 | − | 0.157234i | \(-0.949742\pi\) |
0.629949 | + | 0.776637i | \(0.283076\pi\) | |||||||
\(522\) | −4.95322 | + | 2.85974i | −0.216796 | + | 0.125167i | ||||
\(523\) | −7.08946 | −0.310000 | −0.155000 | − | 0.987914i | \(-0.549538\pi\) | ||||
−0.155000 | + | 0.987914i | \(0.549538\pi\) | |||||||
\(524\) | −10.0463 | − | 17.4007i | −0.438874 | − | 0.760152i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.86836 | − | 2.81075i | 0.212271 | − | 0.122555i | ||||
\(527\) | −36.3805 | − | 21.0043i | −1.58476 | − | 0.914963i | ||||
\(528\) | −5.03280 | − | 2.90569i | −0.219025 | − | 0.126454i | ||||
\(529\) | −8.11189 | −0.352691 | ||||||||
\(530\) | −37.3824 | −1.62379 | ||||||||
\(531\) | −13.4216 | − | 7.74899i | −0.582449 | − | 0.336277i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −32.8796 | + | 28.5880i | −1.42417 | + | 1.23828i | ||||
\(534\) | 8.63218 | + | 14.9514i | 0.373551 | + | 0.647009i | ||||
\(535\) | 11.9548 | − | 6.90209i | 0.516850 | − | 0.298403i | ||||
\(536\) | −3.99505 | − | 6.91963i | −0.172560 | − | 0.298882i | ||||
\(537\) | −6.66368 | + | 11.5418i | −0.287559 | + | 0.498067i | ||||
\(538\) | − | 25.1558i | − | 1.08454i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −15.2922 | + | 8.82897i | −0.658073 | + | 0.379938i | ||||
\(541\) | 22.0977 | − | 12.7581i | 0.950055 | − | 0.548515i | 0.0569571 | − | 0.998377i | \(-0.481860\pi\) |
0.893098 | + | 0.449862i | \(0.148527\pi\) | |||||||
\(542\) | 27.4818 | 1.18044 | ||||||||
\(543\) | 2.39218 | + | 4.14338i | 0.102658 | + | 0.177809i | ||||
\(544\) | 39.7374i | 1.70373i | ||||||||
\(545\) | −37.5235 | −1.60733 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.3073 | −0.568978 | −0.284489 | − | 0.958679i | \(-0.591824\pi\) | ||||
−0.284489 | + | 0.958679i | \(0.591824\pi\) | |||||||
\(548\) | − | 18.2625i | − | 0.780136i | ||||||
\(549\) | 1.62781 | + | 2.81945i | 0.0694733 | + | 0.120331i | ||||
\(550\) | 14.9070 | 0.635637 | ||||||||
\(551\) | 2.64097 | − | 1.52476i | 0.112509 | − | 0.0649571i | ||||
\(552\) | 7.16607 | − | 4.13733i | 0.305008 | − | 0.176096i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 45.0669i | 1.91471i | ||||||||
\(555\) | −39.2559 | + | 67.9932i | −1.66632 | + | 2.88615i | ||||
\(556\) | 20.4297 | + | 35.3852i | 0.866412 | + | 1.50067i | ||||
\(557\) | 14.7285 | − | 8.50353i | 0.624069 | − | 0.360306i | −0.154383 | − | 0.988011i | \(-0.549339\pi\) |
0.778451 | + | 0.627705i | \(0.216006\pi\) | |||||||
\(558\) | −18.8926 | − | 32.7229i | −0.799786 | − | 1.38527i | ||||
\(559\) | 12.8916 | − | 2.50732i | 0.545259 | − | 0.106048i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.61140 | + | 4.97179i | 0.363573 | + | 0.209909i | ||||
\(562\) | −36.4244 | −1.53647 | ||||||||
\(563\) | 24.9193 | 1.05022 | 0.525111 | − | 0.851034i | \(-0.324024\pi\) | ||||
0.525111 | + | 0.851034i | \(0.324024\pi\) | |||||||
\(564\) | −14.3083 | − | 8.26088i | −0.602486 | − | 0.347846i | ||||
\(565\) | −15.3158 | − | 8.84257i | −0.644340 | − | 0.372010i | ||||
\(566\) | −38.8013 | + | 22.4019i | −1.63094 | + | 0.941623i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.05745 | − | 5.29566i | −0.128288 | − | 0.222201i | ||||
\(569\) | −5.88129 | −0.246557 | −0.123278 | − | 0.992372i | \(-0.539341\pi\) | ||||
−0.123278 | + | 0.992372i | \(0.539341\pi\) | |||||||
\(570\) | −35.3983 | + | 20.4372i | −1.48267 | + | 0.856022i | ||||
\(571\) | 4.46311 | − | 7.73034i | 0.186775 | − | 0.323504i | −0.757398 | − | 0.652954i | \(-0.773530\pi\) |
0.944173 | + | 0.329449i | \(0.106863\pi\) | |||||||
\(572\) | 1.49456 | + | 7.68444i | 0.0624906 | + | 0.321303i | ||||
\(573\) | −25.7074 | −1.07394 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.3816 | − | 26.6417i | 0.641457 | − | 1.11104i | ||||
\(576\) | −11.7398 | + | 20.3339i | −0.489158 | + | 0.847247i | ||||
\(577\) | 31.3443 | + | 18.0967i | 1.30488 | + | 0.753374i | 0.981237 | − | 0.192804i | \(-0.0617583\pi\) |
0.323645 | + | 0.946179i | \(0.395092\pi\) | |||||||
\(578\) | − | 16.0381i | − | 0.667097i | ||||||
\(579\) | 27.5961 | + | 15.9326i | 1.14685 | + | 0.662136i | ||||
\(580\) | 11.3104i | 0.469638i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.10513 | − | 1.91414i | 0.0458091 | − | 0.0793437i | ||||
\(583\) | − | 4.36130i | − | 0.180626i | ||||||
\(584\) | 3.38919 | − | 5.87025i | 0.140246 | − | 0.242913i | ||||
\(585\) | 25.9715 | + | 8.93958i | 1.07379 | + | 0.369606i | ||||
\(586\) | 0.443035 | + | 0.767358i | 0.0183016 | + | 0.0316993i | ||||
\(587\) | 31.6008 | + | 18.2447i | 1.30431 | + | 0.753041i | 0.981139 | − | 0.193301i | \(-0.0619195\pi\) |
0.323166 | + | 0.946342i | \(0.395253\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.0732 | + | 17.4472i | 0.415058 | + | 0.718901i | ||||
\(590\) | −48.2123 | + | 27.8354i | −1.98487 | + | 1.14596i | ||||
\(591\) | 51.9210i | 2.13574i | ||||||||
\(592\) | − | 27.9399i | − | 1.14832i | ||||||
\(593\) | 30.3048 | − | 17.4965i | 1.24447 | − | 0.718495i | 0.274468 | − | 0.961596i | \(-0.411498\pi\) |
0.970001 | + | 0.243102i | \(0.0781649\pi\) | |||||||
\(594\) | −1.87107 | − | 3.24079i | −0.0767711 | − | 0.132971i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.34926 | − | 3.08839i | −0.219114 | − | 0.126506i | ||||
\(597\) | −3.56193 | − | 6.16944i | −0.145780 | − | 0.252498i | ||||
\(598\) | 27.7482 | + | 9.55113i | 1.13471 | + | 0.390575i | ||||
\(599\) | 16.2526 | − | 28.1503i | 0.664062 | − | 1.15019i | −0.315476 | − | 0.948934i | \(-0.602164\pi\) |
0.979539 | − | 0.201256i | \(-0.0645025\pi\) | |||||||
\(600\) | − | 17.0979i | − | 0.698018i | ||||||
\(601\) | −10.0390 | + | 17.3881i | −0.409500 | + | 0.709275i | −0.994834 | − | 0.101518i | \(-0.967630\pi\) |
0.585334 | + | 0.810792i | \(0.300963\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 17.8225i | − | 0.725788i | ||||||
\(604\) | 33.7235 | + | 19.4703i | 1.37219 | + | 0.792235i | ||||
\(605\) | − | 36.7897i | − | 1.49572i | ||||||
\(606\) | −24.0581 | − | 13.8900i | −0.977294 | − | 0.564241i | ||||
\(607\) | −4.85800 | + | 8.41431i | −0.197180 | + | 0.341526i | −0.947613 | − | 0.319420i | \(-0.896512\pi\) |
0.750433 | + | 0.660947i | \(0.229845\pi\) | |||||||
\(608\) | 9.52856 | − | 16.5039i | 0.386434 | − | 0.669323i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.6946 | 0.473502 | ||||||||
\(611\) | −2.05286 | − | 10.5550i | −0.0830500 | − | 0.427011i | ||||
\(612\) | 12.8490 | − | 22.2551i | 0.519389 | − | 0.899607i | ||||
\(613\) | 10.2898 | − | 5.94080i | 0.415600 | − | 0.239947i | −0.277593 | − | 0.960699i | \(-0.589537\pi\) |
0.693193 | + | 0.720752i | \(0.256203\pi\) | |||||||
\(614\) | 29.7017 | 1.19866 | ||||||||
\(615\) | 49.2184 | + | 85.2488i | 1.98468 | + | 3.43756i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.3105 | + | 9.99422i | −0.696895 | + | 0.402352i | −0.806190 | − | 0.591657i | \(-0.798474\pi\) |
0.109295 | + | 0.994009i | \(0.465141\pi\) | |||||||
\(618\) | −34.0393 | − | 19.6526i | −1.36926 | − | 0.790543i | ||||
\(619\) | −36.1285 | − | 20.8588i | −1.45213 | − | 0.838386i | −0.453525 | − | 0.891244i | \(-0.649834\pi\) |
−0.998602 | + | 0.0528581i | \(0.983167\pi\) | |||||||
\(620\) | −74.7207 | −3.00086 | ||||||||
\(621\) | −7.72257 | −0.309896 | ||||||||
\(622\) | −18.9708 | − | 10.9528i | −0.760659 | − | 0.439166i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −23.2042 | + | 4.51302i | −0.928911 | + | 0.180665i | ||||
\(625\) | 0.649140 | + | 1.12434i | 0.0259656 | + | 0.0449737i | ||||
\(626\) | −12.5091 | + | 7.22211i | −0.499963 | + | 0.288654i | ||||
\(627\) | −2.38435 | − | 4.12982i | −0.0952219 | − | 0.164929i | ||||
\(628\) | 15.9012 | − | 27.5416i | 0.634526 | − | 1.09903i | ||||
\(629\) | 47.8066i | 1.90618i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.2780 | − | 8.82074i | 0.608206 | − | 0.351148i | −0.164057 | − | 0.986451i | \(-0.552458\pi\) |
0.772263 | + | 0.635303i | \(0.219125\pi\) | |||||||
\(632\) | 0.622082 | − | 0.359159i | 0.0247451 | − | 0.0142866i | ||||
\(633\) | −33.6168 | −1.33615 | ||||||||
\(634\) | 0.739603 | + | 1.28103i | 0.0293734 | + | 0.0508762i | ||||
\(635\) | − | 44.3385i | − | 1.75952i | ||||||
\(636\) | −27.2584 | −1.08086 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.39694 | −0.0948958 | ||||||||
\(639\) | − | 13.6397i | − | 0.539580i | ||||||
\(640\) | 13.3159 | + | 23.0639i | 0.526359 | + | 0.911680i | ||||
\(641\) | 10.9202 | 0.431324 | 0.215662 | − | 0.976468i | \(-0.430809\pi\) | ||||
0.215662 | + | 0.976468i | \(0.430809\pi\) | |||||||
\(642\) | 15.8346 | − | 9.14208i | 0.624940 | − | 0.360809i | ||||
\(643\) | 15.2725 | − | 8.81757i | 0.602288 | − | 0.347731i | −0.167653 | − | 0.985846i | \(-0.553619\pi\) |
0.769941 | + | 0.638115i | \(0.220286\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 29.6716i | − | 1.16832i | ||||||
\(646\) | −12.4445 | + | 21.5544i | −0.489620 | + | 0.848048i | ||||
\(647\) | 8.33632 | + | 14.4389i | 0.327735 | + | 0.567653i | 0.982062 | − | 0.188558i | \(-0.0603815\pi\) |
−0.654327 | + | 0.756211i | \(0.727048\pi\) | |||||||
\(648\) | −8.92758 | + | 5.15434i | −0.350708 | + | 0.202482i | ||||
\(649\) | −3.24747 | − | 5.62479i | −0.127474 | − | 0.220792i | ||||
\(650\) | 45.7593 | − | 39.7866i | 1.79483 | − | 1.56056i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.92042 | − | 2.84080i | −0.192698 | − | 0.111254i | ||||
\(653\) | −6.77329 | −0.265059 | −0.132530 | − | 0.991179i | \(-0.542310\pi\) | ||||
−0.132530 | + | 0.991179i | \(0.542310\pi\) | |||||||
\(654\) | −49.7013 | −1.94347 | ||||||||
\(655\) | −25.5860 | − | 14.7721i | −0.999727 | − | 0.577193i | ||||
\(656\) | −30.3374 | − | 17.5153i | −1.18448 | − | 0.683858i | ||||
\(657\) | 13.0940 | − | 7.55983i | 0.510846 | − | 0.294937i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.7680 | − | 29.0431i | −0.653190 | − | 1.13136i | −0.982344 | − | 0.187082i | \(-0.940097\pi\) |
0.329154 | − | 0.944276i | \(-0.393236\pi\) | |||||||
\(660\) | 17.6866 | 0.688451 | ||||||||
\(661\) | 21.7945 | − | 12.5830i | 0.847707 | − | 0.489424i | −0.0121696 | − | 0.999926i | \(-0.503874\pi\) |
0.859876 | + | 0.510502i | \(0.170540\pi\) | |||||||
\(662\) | −4.42829 | + | 7.67002i | −0.172110 | + | 0.298104i | ||||
\(663\) | 39.7036 | − | 7.72202i | 1.54196 | − | 0.299898i | ||||
\(664\) | 4.52075 | 0.175439 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −21.5001 | + | 37.2393i | −0.833112 | + | 1.44299i | ||||
\(667\) | −2.47325 | + | 4.28380i | −0.0957647 | + | 0.165869i | ||||
\(668\) | 29.2572 | + | 16.8917i | 1.13200 | + | 0.653558i | ||||
\(669\) | − | 9.90802i | − | 0.383066i | ||||||
\(670\) | −55.4436 | − | 32.0104i | −2.14197 | − | 1.23667i | ||||
\(671\) | 1.36438i | 0.0526713i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.927341 | + | 1.60620i | −0.0357464 | + | 0.0619145i | −0.883345 | − | 0.468723i | \(-0.844714\pi\) |
0.847599 | + | 0.530638i | \(0.178048\pi\) | |||||||
\(674\) | 43.0902i | 1.65977i | ||||||||
\(675\) | −7.97855 | + | 13.8193i | −0.307094 | + | 0.531903i | ||||
\(676\) | 25.0974 | + | 19.5996i | 0.965286 | + | 0.753831i | ||||
\(677\) | 7.36044 | + | 12.7487i | 0.282885 | + | 0.489971i | 0.972094 | − | 0.234592i | \(-0.0753753\pi\) |
−0.689209 | + | 0.724562i | \(0.742042\pi\) | |||||||
\(678\) | −20.2863 | − | 11.7123i | −0.779092 | − | 0.449809i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −8.47009 | − | 14.6706i | −0.324813 | − | 0.562593i | ||||
\(681\) | 26.5716 | − | 15.3411i | 1.01823 | − | 0.587873i | ||||
\(682\) | − | 15.8351i | − | 0.606358i | ||||||
\(683\) | 7.94353i | 0.303951i | 0.988384 | + | 0.151975i | \(0.0485634\pi\) | ||||
−0.988384 | + | 0.151975i | \(0.951437\pi\) | |||||||
\(684\) | −10.6730 | + | 6.16206i | −0.408092 | + | 0.235612i | ||||
\(685\) | −13.4266 | − | 23.2556i | −0.513005 | − | 0.888551i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 32.3529 | + | 18.6790i | 1.23434 | + | 0.712647i | ||||
\(688\) | 5.27960 | + | 9.14454i | 0.201283 | + | 0.348632i | ||||
\(689\) | −11.6402 | − | 13.3877i | −0.443458 | − | 0.510029i | ||||
\(690\) | 33.1504 | − | 57.4182i | 1.26201 | − | 2.18587i | ||||
\(691\) | − | 10.2307i | − | 0.389193i | −0.980883 | − | 0.194597i | \(-0.937660\pi\) | ||
0.980883 | − | 0.194597i | \(-0.0623397\pi\) | |||||||
\(692\) | 4.51240 | − | 7.81571i | 0.171536 | − | 0.297109i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 16.8118i | − | 0.638168i | ||||||
\(695\) | 52.0306 | + | 30.0399i | 1.97363 | + | 1.13948i | ||||
\(696\) | 2.74922i | 0.104209i | ||||||||
\(697\) | 51.9089 | + | 29.9696i | 1.96619 | + | 1.13518i | ||||
\(698\) | 22.7785 | − | 39.4535i | 0.862178 | − | 1.49334i | ||||
\(699\) | −18.6616 | + | 32.3228i | −0.705845 | + | 1.22256i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.5978 | −0.626891 | −0.313445 | − | 0.949606i | \(-0.601483\pi\) | ||||
−0.313445 | + | 0.949606i | \(0.601483\pi\) | |||||||
\(702\) | −14.3932 | − | 4.95424i | −0.543235 | − | 0.186986i | ||||
\(703\) | 11.4635 | − | 19.8553i | 0.432353 | − | 0.748857i | ||||
\(704\) | −8.52162 | + | 4.91996i | −0.321171 | + | 0.185428i | ||||
\(705\) | −24.2936 | −0.914951 | ||||||||
\(706\) | 22.8000 | + | 39.4907i | 0.858088 | + | 1.48625i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −35.1552 | + | 20.2969i | −1.32121 | + | 0.762804i | ||||
\(709\) | −41.4531 | − | 23.9329i | −1.55680 | − | 0.898820i | −0.997560 | − | 0.0698158i | \(-0.977759\pi\) |
−0.559242 | − | 0.829004i | \(-0.688908\pi\) | |||||||
\(710\) | −42.4316 | − | 24.4979i | −1.59243 | − | 0.919389i | ||||
\(711\) | 1.60226 | 0.0600895 | ||||||||
\(712\) | 3.43142 | 0.128598 | ||||||||
\(713\) | −28.3004 | − | 16.3393i | −1.05986 | − | 0.611910i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.55279 | + | 8.68661i | 0.282458 | + | 0.324861i | ||||
\(716\) | 7.21722 | + | 12.5006i | 0.269720 | + | 0.467169i | ||||
\(717\) | 59.5840 | − | 34.4008i | 2.22520 | − | 1.28472i | ||||
\(718\) | 14.4318 | + | 24.9965i | 0.538588 | + | 0.932862i | ||||
\(719\) | −19.0461 | + | 32.9888i | −0.710300 | + | 1.23028i | 0.254444 | + | 0.967087i | \(0.418107\pi\) |
−0.964744 | + | 0.263188i | \(0.915226\pi\) | |||||||
\(720\) | 22.0836i | 0.823009i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −24.3719 | + | 14.0711i | −0.907028 | + | 0.523673i | ||||
\(723\) | −57.8081 | + | 33.3755i | −2.14991 | + | 1.24125i | ||||
\(724\) | 5.18179 | 0.192580 | ||||||||
\(725\) | 5.11047 | + | 8.85159i | 0.189798 | + | 0.328740i | ||||
\(726\) | − | 48.7294i | − | 1.80852i | ||||||
\(727\) | 15.4059 | 0.571374 | 0.285687 | − | 0.958323i | \(-0.407778\pi\) | ||||
0.285687 | + | 0.958323i | \(0.407778\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.41460 | −0.348689 | ||||||||
\(730\) | − | 54.3118i | − | 2.01017i | ||||||
\(731\) | −9.03369 | − | 15.6468i | −0.334123 | − | 0.578718i | ||||
\(732\) | 8.52744 | 0.315183 | ||||||||
\(733\) | 10.0717 | − | 5.81490i | 0.372007 | − | 0.214778i | −0.302328 | − | 0.953204i | \(-0.597764\pi\) |
0.674335 | + | 0.738426i | \(0.264430\pi\) | |||||||
\(734\) | 20.8487 | − | 12.0370i | 0.769538 | − | 0.444293i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 30.9117i | 1.13942i | ||||||||
\(737\) | 3.73456 | − | 6.46844i | 0.137564 | − | 0.238268i | ||||
\(738\) | 26.9565 | + | 46.6900i | 0.992282 | + | 1.71868i | ||||
\(739\) | −2.32875 | + | 1.34451i | −0.0856645 | + | 0.0494584i | −0.542220 | − | 0.840236i | \(-0.682416\pi\) |
0.456556 | + | 0.889695i | \(0.349083\pi\) | |||||||
\(740\) | 42.5168 | + | 73.6413i | 1.56295 | + | 2.70711i | ||||
\(741\) | −18.3416 | − | 6.31331i | −0.673794 | − | 0.231925i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.13665 | − | 1.23360i | −0.0783862 | − | 0.0452563i | 0.460295 | − | 0.887766i | \(-0.347744\pi\) |
−0.538681 | + | 0.842510i | \(0.681077\pi\) | |||||||
\(744\) | −18.1624 | −0.665866 | ||||||||
\(745\) | −9.08236 | −0.332752 | ||||||||
\(746\) | −57.1433 | − | 32.9917i | −2.09217 | − | 1.20791i | ||||
\(747\) | 8.73288 | + | 5.04193i | 0.319519 | + | 0.184475i | ||||
\(748\) | 9.32673 | − | 5.38479i | 0.341019 | − | 0.196887i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −25.5409 | − | 44.2382i | −0.932623 | − | 1.61535i | ||||
\(751\) | 37.9185 | 1.38366 | 0.691832 | − | 0.722058i | \(-0.256804\pi\) | ||||
0.691832 | + | 0.722058i | \(0.256804\pi\) | |||||||
\(752\) | 7.48709 | − | 4.32267i | 0.273026 | − | 0.157632i | ||||
\(753\) | −14.6811 | + | 25.4285i | −0.535010 | + | 0.926664i | ||||
\(754\) | −7.35777 | + | 6.39740i | −0.267954 | + | 0.232980i | ||||
\(755\) | 57.2583 | 2.08384 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.3225 | + | 30.0035i | −0.629598 | + | 1.09050i | 0.358034 | + | 0.933709i | \(0.383447\pi\) |
−0.987632 | + | 0.156788i | \(0.949886\pi\) | |||||||
\(758\) | 28.9145 | − | 50.0814i | 1.05022 | − | 1.81904i | ||||
\(759\) | 6.69881 | + | 3.86756i | 0.243151 | + | 0.140384i | ||||
\(760\) | 8.12411i | 0.294692i | ||||||||
\(761\) | −19.7969 | − | 11.4297i | −0.717636 | − | 0.414328i | 0.0962458 | − | 0.995358i | \(-0.469317\pi\) |
−0.813882 | + | 0.581030i | \(0.802650\pi\) | |||||||
\(762\) | − | 58.7280i | − | 2.12749i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −13.9214 | + | 24.1126i | −0.503659 | + | 0.872363i | ||||
\(765\) | − | 37.7863i | − | 1.36617i | ||||||
\(766\) | −16.9813 | + | 29.4124i | −0.613558 | + | 1.06271i | ||||
\(767\) | −24.9811 | − | 8.59868i | −0.902015 | − | 0.310480i | ||||
\(768\) | −7.46951 | − | 12.9376i | −0.269533 | − | 0.466844i | ||||
\(769\) | −44.8839 | − | 25.9137i | −1.61855 | − | 0.934473i | −0.987294 | − | 0.158902i | \(-0.949205\pi\) |
−0.631260 | − | 0.775571i | \(-0.717462\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.18507 | − | 8.98080i | −0.186736 | − | 0.323436i | ||||
\(772\) | 29.8884 | − | 17.2561i | 1.07571 | − | 0.621060i | ||||
\(773\) | − | 5.69966i | − | 0.205003i | −0.994733 | − | 0.102501i | \(-0.967315\pi\) | ||
0.994733 | − | 0.102501i | \(-0.0326846\pi\) | |||||||
\(774\) | − | 16.2509i | − | 0.584126i | ||||||
\(775\) | −58.4770 | + | 33.7617i | −2.10056 | + | 1.21276i | ||||
\(776\) | −0.219653 | − | 0.380450i | −0.00788508 | − | 0.0136574i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −38.6146 | − | 22.2941i | −1.38440 | − | 0.799283i | ||||
\(779\) | −14.3727 | − | 24.8943i | −0.514956 | − | 0.891930i | ||||
\(780\) | 54.2918 | − | 47.2054i | 1.94396 | − | 1.69022i | ||||
\(781\) | 2.85809 | − | 4.95037i | 0.102271 | − | 0.177138i | ||||
\(782\) | − | 40.3712i | − | 1.44367i | ||||||
\(783\) | 1.28289 | − | 2.22204i | 0.0458469 | − | 0.0794092i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 46.7622i | − | 1.66902i | ||||||
\(786\) | −33.8896 | − | 19.5662i | −1.20880 | − | 0.697902i | ||||
\(787\) | − | 16.8141i | − | 0.599358i | −0.954040 | − | 0.299679i | \(-0.903120\pi\) | ||
0.954040 | − | 0.299679i | \(-0.0968796\pi\) | |||||||
\(788\) | 48.7000 | + | 28.1170i | 1.73487 | + | 1.00163i | ||||
\(789\) | 3.01364 | − | 5.21977i | 0.107288 | − | 0.185829i | ||||
\(790\) | 2.87777 | − | 4.98444i | 0.102386 | − | 0.177338i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.77766 | 0.0631664 | ||||||||
\(793\) | 3.64151 | + | 4.18817i | 0.129314 | + | 0.148726i | ||||
\(794\) | −13.8148 | + | 23.9280i | −0.490270 | + | 0.849172i | ||||
\(795\) | −34.7109 | + | 20.0404i | −1.23107 | + | 0.710759i | ||||
\(796\) | −7.71562 | −0.273473 | ||||||||
\(797\) | 21.0651 | + | 36.4858i | 0.746163 | + | 1.29239i | 0.949650 | + | 0.313314i | \(0.101439\pi\) |
−0.203487 | + | 0.979078i | \(0.565227\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.8108 | + | 7.39632i | −0.453214 | + | 0.261663i | ||||
\(800\) | 55.3154 | + | 31.9364i | 1.95570 | + | 1.12912i | ||||
\(801\) | 6.62859 | + | 3.82702i | 0.234210 | + | 0.135221i | ||||
\(802\) | −41.0164 | −1.44834 | ||||||||
\(803\) | 6.33640 | 0.223607 | ||||||||
\(804\) | −40.4281 | − | 23.3412i | −1.42579 | − | 0.823180i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −42.2637 | − | 48.6083i | −1.48868 | − | 1.71215i | ||||
\(807\) | −13.4858 | − | 23.3581i | −0.474723 | − | 0.822244i | ||||
\(808\) | −4.78173 | + | 2.76073i | −0.168221 | + | 0.0971223i | ||||
\(809\) | 15.0843 | + | 26.1268i | 0.530336 | + | 0.918569i | 0.999374 | + | 0.0353910i | \(0.0112677\pi\) |
−0.469037 | + | 0.883178i | \(0.655399\pi\) | |||||||
\(810\) | −41.2992 | + | 71.5323i | −1.45111 | + | 2.51339i | ||||
\(811\) | − | 23.7929i | − | 0.835480i | −0.908567 | − | 0.417740i | \(-0.862822\pi\) | ||
0.908567 | − | 0.417740i | \(-0.137178\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.5178 | − | 14.7327i | 0.894950 | − | 0.516699i | ||||
\(814\) | −15.6064 | + | 9.01034i | −0.547003 | + | 0.315812i | ||||
\(815\) | −8.35425 | −0.292637 | ||||||||
\(816\) | 16.2601 | + | 28.1633i | 0.569217 | + | 0.985913i | ||||
\(817\) | 8.66468i | 0.303139i | ||||||||
\(818\) | 50.7432 | 1.77419 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 106.614 | 3.72312 | ||||||||
\(821\) | 35.8847i | 1.25239i | 0.779668 | + | 0.626193i | \(0.215388\pi\) | ||||
−0.779668 | + | 0.626193i | \(0.784612\pi\) | |||||||
\(822\) | −17.7841 | − | 30.8029i | −0.620291 | − | 1.07438i | ||||
\(823\) | 12.2346 | 0.426470 | 0.213235 | − | 0.977001i | \(-0.431600\pi\) | ||||
0.213235 | + | 0.977001i | \(0.431600\pi\) | |||||||
\(824\) | −6.76557 | + | 3.90610i | −0.235690 | + | 0.136076i | ||||
\(825\) | 13.8417 | − | 7.99151i | 0.481906 | − | 0.278229i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.3474i | 0.950962i | 0.879726 | + | 0.475481i | \(0.157726\pi\) | ||||
−0.879726 | + | 0.475481i | \(0.842274\pi\) | |||||||
\(828\) | 9.99521 | − | 17.3122i | 0.347358 | − | 0.601641i | ||||
\(829\) | 11.7869 | + | 20.4155i | 0.409376 | + | 0.709060i | 0.994820 | − | 0.101653i | \(-0.0324132\pi\) |
−0.585444 | + | 0.810713i | \(0.699080\pi\) | |||||||
\(830\) | 31.3697 | − | 18.1113i | 1.08886 | − | 0.628652i | ||||
\(831\) | 24.1599 | + | 41.8463i | 0.838099 | + | 1.45163i | ||||
\(832\) | −13.0271 | + | 37.8466i | −0.451634 | + | 1.31210i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 68.9165 | + | 39.7889i | 2.38638 | + | 1.37778i | ||||
\(835\) | 49.6751 | 1.71908 | ||||||||
\(836\) | −5.16483 | −0.178630 | ||||||||
\(837\) | 14.6796 | + | 8.47530i | 0.507403 | + | 0.292949i | ||||
\(838\) | 71.2880 | + | 41.1582i | 2.46260 | + | 1.42179i | ||||
\(839\) | 9.16975 | − | 5.29416i | 0.316575 | − | 0.182775i | −0.333290 | − | 0.942824i | \(-0.608159\pi\) |
0.649865 | + | 0.760050i | \(0.274825\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.6783 | + | 23.6915i | 0.471665 | + | 0.816947i | ||||
\(842\) | 46.4664 | 1.60134 | ||||||||
\(843\) | −33.8214 | + | 19.5268i | −1.16487 | + | 0.672538i | ||||
\(844\) | −18.2046 | + | 31.5313i | −0.626629 | + | 1.08535i | ||||
\(845\) | 46.3689 | + | 6.50658i | 1.59514 | + | 0.223833i | ||||
\(846\) | −13.3054 | −0.457449 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.13174 | − | 12.3525i | 0.244905 | − | 0.424188i | ||||
\(849\) | −24.0189 | + | 41.6020i | −0.824328 | + | 1.42778i | ||||
\(850\) | −72.2428 | − | 41.7094i | −2.47791 | − | 1.43062i | ||||
\(851\) | 37.1888i | 1.27482i | ||||||||
\(852\) | −30.9401 | − | 17.8633i | −1.05999 | − | 0.611985i | ||||
\(853\) | 21.3925i | 0.732464i | 0.930524 | + | 0.366232i | \(0.119352\pi\) | ||||
−0.930524 | + | 0.366232i | \(0.880648\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.06070 | + | 15.6936i | −0.309870 | + | 0.536710i | ||||
\(856\) | − | 3.63412i | − | 0.124212i | ||||||
\(857\) | 3.61065 | − | 6.25382i | 0.123337 | − | 0.213626i | −0.797744 | − | 0.602996i | \(-0.793974\pi\) |
0.921082 | + | 0.389369i | \(0.127307\pi\) | |||||||
\(858\) | 10.0040 | + | 11.5057i | 0.341529 | + | 0.392800i | ||||
\(859\) | −28.5536 | − | 49.4563i | −0.974238 | − | 1.68743i | −0.682429 | − | 0.730952i | \(-0.739076\pi\) |
−0.291809 | − | 0.956477i | \(-0.594257\pi\) | |||||||
\(860\) | −27.8309 | − | 16.0682i | −0.949027 | − | 0.547921i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −37.8421 | − | 65.5444i | −1.28891 | − | 2.23245i | ||||
\(863\) | −44.4584 | + | 25.6681i | −1.51338 | + | 0.873751i | −0.513503 | + | 0.858088i | \(0.671653\pi\) |
−0.999877 | + | 0.0156631i | \(0.995014\pi\) | |||||||
\(864\) | − | 16.0341i | − | 0.545493i | ||||||
\(865\) | − | 13.2701i | − | 0.451197i | ||||||
\(866\) | 22.3115 | − | 12.8816i | 0.758177 | − | 0.437734i | ||||
\(867\) | −8.59788 | − | 14.8920i | −0.291999 | − | 0.505758i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.581520 | + | 0.335741i | 0.0197267 | + | 0.0113892i | ||||
\(870\) | 11.0141 | + | 19.0769i | 0.373412 | + | 0.646768i | ||||
\(871\) | −5.80039 | − | 29.8233i | −0.196539 | − | 1.01052i | ||||
\(872\) | −4.93925 | + | 8.55504i | −0.167264 | + | 0.289710i | ||||
\(873\) | − | 0.979903i | − | 0.0331647i | ||||||
\(874\) | −9.68055 | + | 16.7672i | −0.327449 | + | 0.567159i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 39.6029i | − | 1.33806i | ||||||
\(877\) | 18.5570 | + | 10.7139i | 0.626624 | + | 0.361781i | 0.779443 | − | 0.626473i | \(-0.215502\pi\) |
−0.152820 | + | 0.988254i | \(0.548835\pi\) | |||||||
\(878\) | − | 33.2341i | − | 1.12160i | ||||||
\(879\) | 0.822748 | + | 0.475014i | 0.0277506 | + | 0.0160218i | ||||
\(880\) | −4.62745 | + | 8.01497i | −0.155991 | + | 0.270185i | ||||
\(881\) | 14.5309 | − | 25.1683i | 0.489560 | − | 0.847943i | −0.510368 | − | 0.859956i | \(-0.670491\pi\) |
0.999928 | + | 0.0120134i | \(0.00382406\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.83594 | 0.162742 | 0.0813711 | − | 0.996684i | \(-0.474070\pi\) | ||||
0.0813711 | + | 0.996684i | \(0.474070\pi\) | |||||||
\(884\) | 14.2579 | − | 41.4223i | 0.479545 | − | 1.39318i | ||||
\(885\) | −29.8446 | + | 51.6924i | −1.00322 | + | 1.73762i | ||||
\(886\) | 27.5308 | − | 15.8949i | 0.924916 | − | 0.534000i | ||||
\(887\) | −24.9898 | −0.839075 | −0.419538 | − | 0.907738i | \(-0.637808\pi\) | ||||
−0.419538 | + | 0.907738i | \(0.637808\pi\) | |||||||
\(888\) | 10.3346 | + | 17.9000i | 0.346806 | + | 0.600685i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 23.8108 | − | 13.7471i | 0.798138 | − | 0.460805i | ||||
\(891\) | −8.34546 | − | 4.81826i | −0.279584 | − | 0.161418i | ||||
\(892\) | −9.29338 | − | 5.36553i | −0.311165 | − | 0.179651i | ||||
\(893\) | 7.09420 | 0.237398 | ||||||||
\(894\) | −12.0299 | −0.402341 | ||||||||
\(895\) | 18.3809 | + | 10.6122i | 0.614406 | + | 0.354727i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 30.8855 | − | 6.00696i | 1.03124 | − | 0.200567i | ||||
\(898\) | −32.4662 | − | 56.2331i | −1.08341 | − | 1.87652i | ||||
\(899\) | 9.40269 | − | 5.42865i | 0.313597 | − | 0.181055i | ||||
\(900\) | −20.6530 | − | 35.7721i | −0.688435 | − | 1.19240i | ||||
\(901\) | −12.2028 | + | 21.1359i | −0.406534 | + | 0.704138i | ||||
\(902\) | 22.5940i | 0.752300i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.03206 | + | 2.32791i | −0.134104 | + | 0.0774252i | ||||
\(905\) | 6.59852 | − | 3.80966i | 0.219342 | − | 0.126637i | ||||
\(906\) | 75.8409 | 2.51964 | ||||||||
\(907\) | 7.52060 | + | 13.0261i | 0.249717 | + | 0.432523i | 0.963447 | − | 0.267898i | \(-0.0863290\pi\) |
−0.713730 | + | 0.700421i | \(0.752996\pi\) | |||||||
\(908\) | − | 33.2310i | − | 1.10281i | ||||||
\(909\) | −12.3160 | −0.408497 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.22150 | −0.305522 | −0.152761 | − | 0.988263i | \(-0.548816\pi\) | ||||
−0.152761 | + | 0.988263i | \(0.548816\pi\) | |||||||
\(912\) | − | 15.5959i | − | 0.516432i | ||||||
\(913\) | 2.11299 | + | 3.65981i | 0.0699298 | + | 0.121122i | ||||
\(914\) | 16.3604 | 0.541153 | ||||||||
\(915\) | 10.8589 | − | 6.26939i | 0.358984 | − | 0.207260i | ||||
\(916\) | 35.0404 | − | 20.2306i | 1.15777 | − | 0.668437i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 20.9409i | 0.691151i | ||||||||
\(919\) | 22.5402 | − | 39.0407i | 0.743531 | − | 1.28783i | −0.207346 | − | 0.978268i | \(-0.566483\pi\) |
0.950878 | − | 0.309567i | \(-0.100184\pi\) | |||||||
\(920\) | −6.58889 | − | 11.4123i | −0.217229 | − | 0.376252i | ||||
\(921\) | 27.5791 | − | 15.9228i | 0.908762 | − | 0.524674i | ||||
\(922\) | −1.55274 | − | 2.68943i | −0.0511368 | − | 0.0885716i | ||||
\(923\) | −4.43910 | − | 22.8241i | −0.146115 | − | 0.751265i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 66.5480 | + | 38.4215i | 2.18808 | + | 1.26329i | ||||
\(926\) | 29.6086 | 0.972999 | ||||||||
\(927\) | −17.4257 | −0.572334 | ||||||||
\(928\) | −8.89433 | − | 5.13514i | −0.291971 | − | 0.168569i | ||||
\(929\) | 40.6313 | + | 23.4585i | 1.33307 | + | 0.769647i | 0.985769 | − | 0.168107i | \(-0.0537654\pi\) |
0.347300 | + | 0.937754i | \(0.387099\pi\) | |||||||
\(930\) | −126.030 | + | 72.7632i | −4.13267 | + | 2.38600i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 20.2117 | + | 35.0078i | 0.662058 | + | 1.14672i | ||||
\(933\) | −23.4867 | −0.768921 | ||||||||
\(934\) | 57.3256 | − | 33.0969i | 1.87575 | − | 1.08296i | ||||
\(935\) | 7.91781 | − | 13.7140i | 0.258940 | − | 0.448497i | ||||
\(936\) | 5.45680 | − | 4.74455i | 0.178361 | − | 0.155080i | ||||
\(937\) | −28.3912 | −0.927501 | −0.463750 | − | 0.885966i | \(-0.653497\pi\) | ||||
−0.463750 | + | 0.885966i | \(0.653497\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.74342 | + | 13.4120i | −0.252697 | + | 0.437684i | ||||
\(940\) | −13.1558 | + | 22.7866i | −0.429096 | + | 0.743216i | ||||
\(941\) | 15.4774 | + | 8.93589i | 0.504549 | + | 0.291302i | 0.730590 | − | 0.682816i | \(-0.239245\pi\) |
−0.226041 | + | 0.974118i | \(0.572578\pi\) | |||||||
\(942\) | − | 61.9384i | − | 2.01806i | ||||||
\(943\) | 40.3800 | + | 23.3134i | 1.31495 | + | 0.759188i | ||||
\(944\) | − | 21.2415i | − | 0.691353i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.40524 | − | 5.89805i | 0.110714 | − | 0.191762i | ||||
\(947\) | − | 9.52234i | − | 0.309435i | −0.987959 | − | 0.154717i | \(-0.950553\pi\) | ||
0.987959 | − | 0.154717i | \(-0.0494467\pi\) | |||||||
\(948\) | 2.09840 | − | 3.63453i | 0.0681528 | − | 0.118044i | ||||
\(949\) | 19.4505 | − | 16.9118i | 0.631391 | − | 0.548979i | ||||
\(950\) | 20.0028 | + | 34.6459i | 0.648978 | + | 1.12406i | ||||
\(951\) | 1.37350 | + | 0.792989i | 0.0445387 | + | 0.0257144i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.70900 | − | 11.6203i | −0.217326 | − | 0.376419i | 0.736664 | − | 0.676259i | \(-0.236400\pi\) |
−0.953990 | + | 0.299840i | \(0.903067\pi\) | |||||||
\(954\) | −19.0109 | + | 10.9759i | −0.615500 | + | 0.355359i | ||||
\(955\) | 40.9402i | 1.32479i | ||||||||
\(956\) | − | 74.5169i | − | 2.41005i | ||||||
\(957\) | −2.22565 | + | 1.28498i | −0.0719450 | + | 0.0415375i | ||||
\(958\) | 43.4482 | + | 75.2545i | 1.40375 | + | 2.43136i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 78.3145 | + | 45.2149i | 2.52759 | + | 1.45931i | ||||
\(961\) | 20.3637 | + | 35.2710i | 0.656895 | + | 1.13778i | ||||
\(962\) | −23.8576 | + | 69.3117i | −0.769201 | + | 2.23470i | ||||
\(963\) | 4.05308 | − | 7.02013i | 0.130609 | − | 0.226221i | ||||
\(964\) | 72.2960i | 2.32850i | ||||||||
\(965\) | 25.3734 | − | 43.9480i | 0.816798 | − | 1.41474i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.9316i | 0.415851i | 0.978145 | + | 0.207926i | \(0.0666712\pi\) | ||||
−0.978145 | + | 0.207926i | \(0.933329\pi\) | |||||||
\(968\) | −8.38775 | − | 4.84267i | −0.269593 | − | 0.155649i | ||||
\(969\) | 26.6854i | 0.857260i | ||||||||
\(970\) | −3.04836 | − | 1.75997i | −0.0978769 | − | 0.0565093i | ||||
\(971\) | −23.7607 | + | 41.1547i | −0.762516 | + | 1.32072i | 0.179034 | + | 0.983843i | \(0.442703\pi\) |
−0.941550 | + | 0.336874i | \(0.890630\pi\) | |||||||
\(972\) | −22.7605 | + | 39.4224i | −0.730044 | + | 1.26447i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 59.7515 | 1.91456 | ||||||||
\(975\) | 21.1600 | − | 61.4744i | 0.677662 | − | 1.96876i | ||||
\(976\) | −2.23108 | + | 3.86434i | −0.0714151 | + | 0.123695i | ||||
\(977\) | −31.6049 | + | 18.2471i | −1.01113 | + | 0.583776i | −0.911522 | − | 0.411251i | \(-0.865092\pi\) |
−0.0996074 | + | 0.995027i | \(0.531759\pi\) | |||||||
\(978\) | −11.0655 | −0.353836 | ||||||||
\(979\) | 1.60384 | + | 2.77793i | 0.0512589 | + | 0.0887831i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.0826 | + | 11.0174i | −0.609261 | + | 0.351757i | ||||
\(982\) | −63.5470 | − | 36.6889i | −2.02787 | − | 1.17079i | ||||
\(983\) | 38.2647 | + | 22.0921i | 1.22045 | + | 0.704629i | 0.965015 | − | 0.262196i | \(-0.0844466\pi\) |
0.255439 | + | 0.966825i | \(0.417780\pi\) | |||||||
\(984\) | 25.9147 | 0.826130 | ||||||||
\(985\) | 82.6865 | 2.63461 | ||||||||
\(986\) | 11.6161 | + | 6.70658i | 0.369933 | + | 0.213581i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15.8542 | + | 13.7849i | −0.504391 | + | 0.438555i | ||||
\(989\) | −7.02731 | − | 12.1717i | −0.223455 | − | 0.387036i | ||||
\(990\) | 12.3352 | − | 7.12176i | 0.392040 | − | 0.226344i | ||||
\(991\) | 25.3549 | + | 43.9159i | 0.805424 | + | 1.39504i | 0.916005 | + | 0.401168i | \(0.131396\pi\) |
−0.110581 | + | 0.993867i | \(0.535271\pi\) | |||||||
\(992\) | 33.9247 | − | 58.7594i | 1.07711 | − | 1.86561i | ||||
\(993\) | 9.49586i | 0.301342i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.82511 | + | 5.67253i | −0.311477 | + | 0.179831i | ||||
\(996\) | 22.8740 | − | 13.2063i | 0.724790 | − | 0.418458i | ||||
\(997\) | −50.2768 | −1.59228 | −0.796141 | − | 0.605111i | \(-0.793129\pi\) | ||||
−0.796141 | + | 0.605111i | \(0.793129\pi\) | |||||||
\(998\) | −0.0732891 | − | 0.126940i | −0.00231993 | − | 0.00401823i | ||||
\(999\) | − | 19.2901i | − | 0.610312i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 637.2.k.h.459.1 | 12 | ||
7.2 | even | 3 | 637.2.u.h.30.1 | 12 | |||
7.3 | odd | 6 | 637.2.q.h.589.6 | 12 | |||
7.4 | even | 3 | 91.2.q.a.43.6 | yes | 12 | ||
7.5 | odd | 6 | 637.2.u.i.30.1 | 12 | |||
7.6 | odd | 2 | 637.2.k.g.459.1 | 12 | |||
13.10 | even | 6 | 637.2.u.h.361.1 | 12 | |||
21.11 | odd | 6 | 819.2.ct.a.316.1 | 12 | |||
28.11 | odd | 6 | 1456.2.cc.c.225.5 | 12 | |||
91.4 | even | 6 | 1183.2.c.i.337.11 | 12 | |||
91.10 | odd | 6 | 637.2.q.h.491.6 | 12 | |||
91.23 | even | 6 | inner | 637.2.k.h.569.6 | 12 | ||
91.32 | odd | 12 | 1183.2.a.m.1.2 | 6 | |||
91.45 | even | 12 | 8281.2.a.by.1.2 | 6 | |||
91.46 | odd | 12 | 1183.2.a.p.1.5 | 6 | |||
91.59 | even | 12 | 8281.2.a.ch.1.5 | 6 | |||
91.62 | odd | 6 | 637.2.u.i.361.1 | 12 | |||
91.74 | even | 3 | 1183.2.c.i.337.2 | 12 | |||
91.75 | odd | 6 | 637.2.k.g.569.6 | 12 | |||
91.88 | even | 6 | 91.2.q.a.36.6 | ✓ | 12 | ||
273.179 | odd | 6 | 819.2.ct.a.127.1 | 12 | |||
364.179 | odd | 6 | 1456.2.cc.c.673.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.q.a.36.6 | ✓ | 12 | 91.88 | even | 6 | ||
91.2.q.a.43.6 | yes | 12 | 7.4 | even | 3 | ||
637.2.k.g.459.1 | 12 | 7.6 | odd | 2 | |||
637.2.k.g.569.6 | 12 | 91.75 | odd | 6 | |||
637.2.k.h.459.1 | 12 | 1.1 | even | 1 | trivial | ||
637.2.k.h.569.6 | 12 | 91.23 | even | 6 | inner | ||
637.2.q.h.491.6 | 12 | 91.10 | odd | 6 | |||
637.2.q.h.589.6 | 12 | 7.3 | odd | 6 | |||
637.2.u.h.30.1 | 12 | 7.2 | even | 3 | |||
637.2.u.h.361.1 | 12 | 13.10 | even | 6 | |||
637.2.u.i.30.1 | 12 | 7.5 | odd | 6 | |||
637.2.u.i.361.1 | 12 | 91.62 | odd | 6 | |||
819.2.ct.a.127.1 | 12 | 273.179 | odd | 6 | |||
819.2.ct.a.316.1 | 12 | 21.11 | odd | 6 | |||
1183.2.a.m.1.2 | 6 | 91.32 | odd | 12 | |||
1183.2.a.p.1.5 | 6 | 91.46 | odd | 12 | |||
1183.2.c.i.337.2 | 12 | 91.74 | even | 3 | |||
1183.2.c.i.337.11 | 12 | 91.4 | even | 6 | |||
1456.2.cc.c.225.5 | 12 | 28.11 | odd | 6 | |||
1456.2.cc.c.673.5 | 12 | 364.179 | odd | 6 | |||
8281.2.a.by.1.2 | 6 | 91.45 | even | 12 | |||
8281.2.a.ch.1.5 | 6 | 91.59 | even | 12 |