Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,2,Mod(197,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.197");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.13013575923\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.11534581287092224.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 8x^{10} + 27x^{8} + 14x^{6} + 25x^{4} - 42x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.5 | ||
Root | \(0.707107 - 0.164821i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.197 |
Dual form | 392.2.b.g.197.8 |
$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.321037 | − | 1.37729i | −0.227007 | − | 0.973893i | ||||
\(3\) | − | 2.86877i | − | 1.65628i | −0.560519 | − | 0.828141i | \(-0.689399\pi\) | ||
0.560519 | − | 0.828141i | \(-0.310601\pi\) | |||||||
\(4\) | −1.79387 | + | 0.884323i | −0.896935 | + | 0.442162i | ||||
\(5\) | − | 3.19841i | − | 1.43037i | −0.698934 | − | 0.715186i | \(-0.746342\pi\) | ||
0.698934 | − | 0.715186i | \(-0.253658\pi\) | |||||||
\(6\) | −3.95113 | + | 0.920979i | −1.61304 | + | 0.375988i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.79387 | + | 2.18678i | 0.634229 | + | 0.773145i | ||||
\(9\) | −5.22982 | −1.74327 | ||||||||
\(10\) | −4.40514 | + | 1.02681i | −1.39303 | + | 0.324705i | ||||
\(11\) | − | 1.45212i | − | 0.437832i | −0.975744 | − | 0.218916i | \(-0.929748\pi\) | ||
0.975744 | − | 0.218916i | \(-0.0702521\pi\) | |||||||
\(12\) | 2.53692 | + | 5.14619i | 0.732345 | + | 1.48558i | ||||
\(13\) | 1.14479i | 0.317509i | 0.987318 | + | 0.158754i | \(0.0507478\pi\) | ||||
−0.987318 | + | 0.158754i | \(0.949252\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.17548 | −2.36910 | ||||||||
\(16\) | 2.43594 | − | 3.17272i | 0.608986 | − | 0.793181i | ||||
\(17\) | 5.58002 | 1.35335 | 0.676676 | − | 0.736281i | \(-0.263420\pi\) | ||||
0.676676 | + | 0.736281i | \(0.263420\pi\) | |||||||
\(18\) | 1.67896 | + | 7.20299i | 0.395735 | + | 1.69776i | ||||
\(19\) | − | 1.47444i | − | 0.338259i | −0.985594 | − | 0.169130i | \(-0.945904\pi\) | ||
0.985594 | − | 0.169130i | \(-0.0540956\pi\) | |||||||
\(20\) | 2.82843 | + | 5.73753i | 0.632456 | + | 1.28295i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | + | 0.466185i | −0.426401 | + | 0.0993910i | ||||
\(23\) | 3.28415 | 0.684792 | 0.342396 | − | 0.939556i | \(-0.388762\pi\) | ||||
0.342396 | + | 0.939556i | \(0.388762\pi\) | |||||||
\(24\) | 6.27337 | − | 5.14619i | 1.28055 | − | 1.05046i | ||||
\(25\) | −5.22982 | −1.04596 | ||||||||
\(26\) | 1.57672 | − | 0.367521i | 0.309220 | − | 0.0720768i | ||||
\(27\) | 6.39682i | 1.23107i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.59086i | 0.666806i | 0.942784 | + | 0.333403i | \(0.108197\pi\) | ||||
−0.942784 | + | 0.333403i | \(0.891803\pi\) | |||||||
\(30\) | 2.94567 | + | 12.6373i | 0.537803 | + | 2.30725i | ||||
\(31\) | −1.01237 | −0.181827 | −0.0909134 | − | 0.995859i | \(-0.528979\pi\) | ||||
−0.0909134 | + | 0.995859i | \(0.528979\pi\) | |||||||
\(32\) | −5.15180 | − | 2.33645i | −0.910718 | − | 0.413029i | ||||
\(33\) | −4.16580 | −0.725173 | ||||||||
\(34\) | −1.79139 | − | 7.68532i | −0.307221 | − | 1.31802i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 9.38161 | − | 4.62485i | 1.56360 | − | 0.770808i | ||||
\(37\) | 6.49511i | 1.06779i | 0.845551 | + | 0.533895i | \(0.179272\pi\) | ||||
−0.845551 | + | 0.533895i | \(0.820728\pi\) | |||||||
\(38\) | −2.03073 | + | 0.473349i | −0.329428 | + | 0.0767873i | ||||
\(39\) | 3.28415 | 0.525884 | ||||||||
\(40\) | 6.99423 | − | 5.73753i | 1.10588 | − | 0.907183i | ||||
\(41\) | 7.39608 | 1.15507 | 0.577536 | − | 0.816365i | \(-0.304014\pi\) | ||||
0.577536 | + | 0.816365i | \(0.304014\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.59434i | − | 1.15813i | −0.815283 | − | 0.579063i | \(-0.803419\pi\) | ||
0.815283 | − | 0.579063i | \(-0.196581\pi\) | |||||||
\(44\) | 1.28415 | + | 2.60492i | 0.193592 | + | 0.392707i | ||||
\(45\) | 16.7271i | 2.49353i | ||||||||
\(46\) | −1.05433 | − | 4.52323i | −0.155453 | − | 0.666914i | ||||
\(47\) | −11.9637 | −1.74509 | −0.872544 | − | 0.488535i | \(-0.837531\pi\) | ||||
−0.872544 | + | 0.488535i | \(0.837531\pi\) | |||||||
\(48\) | −9.10180 | − | 6.98815i | −1.31373 | − | 1.00865i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.67896 | + | 7.20299i | 0.237441 | + | 1.01866i | ||||
\(51\) | − | 16.0078i | − | 2.24153i | ||||||
\(52\) | −1.01237 | − | 2.05361i | −0.140390 | − | 0.284785i | ||||
\(53\) | 11.0183i | 1.51349i | 0.653713 | + | 0.756743i | \(0.273210\pi\) | ||||
−0.653713 | + | 0.756743i | \(0.726790\pi\) | |||||||
\(54\) | 8.81029 | − | 2.05361i | 1.19893 | − | 0.279461i | ||||
\(55\) | −4.64449 | −0.626262 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.22982 | −0.560253 | ||||||||
\(58\) | 4.94567 | − | 1.15280i | 0.649398 | − | 0.151370i | ||||
\(59\) | − | 6.31671i | − | 0.822365i | −0.911553 | − | 0.411183i | \(-0.865116\pi\) | ||
0.911553 | − | 0.411183i | \(-0.134884\pi\) | |||||||
\(60\) | 16.4596 | − | 8.11409i | 2.12493 | − | 1.04753i | ||||
\(61\) | − | 3.19841i | − | 0.409514i | −0.978813 | − | 0.204757i | \(-0.934360\pi\) | ||
0.978813 | − | 0.204757i | \(-0.0656404\pi\) | |||||||
\(62\) | 0.325008 | + | 1.39433i | 0.0412760 | + | 0.177080i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.56406 | + | 7.84562i | −0.195507 | + | 0.980702i | ||||
\(65\) | 3.66152 | 0.454156 | ||||||||
\(66\) | 1.33738 | + | 5.73753i | 0.164620 | + | 0.706241i | ||||
\(67\) | − | 2.60492i | − | 0.318242i | −0.987259 | − | 0.159121i | \(-0.949134\pi\) | ||
0.987259 | − | 0.159121i | \(-0.0508660\pi\) | |||||||
\(68\) | −10.0098 | + | 4.93454i | −1.21387 | + | 0.598401i | ||||
\(69\) | − | 9.42145i | − | 1.13421i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.4596 | 1.47869 | 0.739343 | − | 0.673329i | \(-0.235136\pi\) | ||||
0.739343 | + | 0.673329i | \(0.235136\pi\) | |||||||
\(72\) | −9.38161 | − | 11.4365i | −1.10563 | − | 1.34780i | ||||
\(73\) | −9.21213 | −1.07820 | −0.539099 | − | 0.842242i | \(-0.681235\pi\) | ||||
−0.539099 | + | 0.842242i | \(0.681235\pi\) | |||||||
\(74\) | 8.94567 | − | 2.08517i | 1.03991 | − | 0.242396i | ||||
\(75\) | 15.0031i | 1.73241i | ||||||||
\(76\) | 1.30388 | + | 2.64495i | 0.149565 | + | 0.303397i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.05433 | − | 4.52323i | −0.119380 | − | 0.512155i | ||||
\(79\) | −13.8913 | −1.56290 | −0.781449 | − | 0.623970i | \(-0.785519\pi\) | ||||
−0.781449 | + | 0.623970i | \(0.785519\pi\) | |||||||
\(80\) | −10.1477 | − | 7.79114i | −1.13454 | − | 0.871076i | ||||
\(81\) | 2.66152 | 0.295725 | ||||||||
\(82\) | −2.37441 | − | 10.1866i | −0.262210 | − | 1.12492i | ||||
\(83\) | − | 7.87125i | − | 0.863982i | −0.901878 | − | 0.431991i | \(-0.857811\pi\) | ||
0.901878 | − | 0.431991i | \(-0.142189\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 17.8472i | − | 1.93580i | ||||||
\(86\) | −10.4596 | + | 2.43806i | −1.12789 | + | 0.262903i | ||||
\(87\) | 10.3013 | 1.10442 | ||||||||
\(88\) | 3.17548 | − | 2.60492i | 0.338508 | − | 0.277686i | ||||
\(89\) | 3.23027 | 0.342408 | 0.171204 | − | 0.985236i | \(-0.445234\pi\) | ||||
0.171204 | + | 0.985236i | \(0.445234\pi\) | |||||||
\(90\) | 23.0381 | − | 5.37001i | 2.42843 | − | 0.566049i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.89134 | + | 2.90425i | −0.614214 | + | 0.302789i | ||||
\(93\) | 2.90425i | 0.301157i | ||||||||
\(94\) | 3.84080 | + | 16.4776i | 0.396148 | + | 1.69953i | ||||
\(95\) | −4.71585 | −0.483836 | ||||||||
\(96\) | −6.70272 | + | 14.7793i | −0.684093 | + | 1.50841i | ||||
\(97\) | 0.401845 | 0.0408012 | 0.0204006 | − | 0.999792i | \(-0.493506\pi\) | ||||
0.0204006 | + | 0.999792i | \(0.493506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.59434i | 0.763260i | ||||||||
\(100\) | 9.38161 | − | 4.62485i | 0.938161 | − | 0.462485i | ||||
\(101\) | − | 6.22304i | − | 0.619216i | −0.950864 | − | 0.309608i | \(-0.899802\pi\) | ||
0.950864 | − | 0.309608i | \(-0.100198\pi\) | |||||||
\(102\) | −22.0474 | + | 5.13908i | −2.18302 | + | 0.508845i | ||||
\(103\) | 7.31924 | 0.721186 | 0.360593 | − | 0.932723i | \(-0.382574\pi\) | ||||
0.360593 | + | 0.932723i | \(0.382574\pi\) | |||||||
\(104\) | −2.50342 | + | 2.05361i | −0.245480 | + | 0.201373i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 15.1755 | − | 3.53729i | 1.47397 | − | 0.343572i | ||||
\(107\) | 4.46966i | 0.432099i | 0.976382 | + | 0.216049i | \(0.0693172\pi\) | ||||
−0.976382 | + | 0.216049i | \(0.930683\pi\) | |||||||
\(108\) | −5.65685 | − | 11.4751i | −0.544331 | − | 1.10419i | ||||
\(109\) | − | 12.6373i | − | 1.21044i | −0.796060 | − | 0.605218i | \(-0.793086\pi\) | ||
0.796060 | − | 0.605218i | \(-0.206914\pi\) | |||||||
\(110\) | 1.49105 | + | 6.39682i | 0.142166 | + | 0.609913i | ||||
\(111\) | 18.6329 | 1.76856 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.2298 | −0.962340 | −0.481170 | − | 0.876627i | \(-0.659788\pi\) | ||||
−0.481170 | + | 0.876627i | \(0.659788\pi\) | |||||||
\(114\) | 1.35793 | + | 5.82569i | 0.127181 | + | 0.545626i | ||||
\(115\) | − | 10.5040i | − | 0.979507i | ||||||
\(116\) | −3.17548 | − | 6.44154i | −0.294836 | − | 0.598082i | ||||
\(117\) | − | 5.98706i | − | 0.553504i | ||||||
\(118\) | −8.69995 | + | 2.02790i | −0.800896 | + | 0.186683i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −16.4596 | − | 20.0648i | −1.50255 | − | 1.83166i | ||||
\(121\) | 8.89134 | 0.808303 | ||||||||
\(122\) | −4.40514 | + | 1.02681i | −0.398823 | + | 0.0929627i | ||||
\(123\) | − | 21.2176i | − | 1.91313i | ||||||
\(124\) | 1.81606 | − | 0.895261i | 0.163087 | − | 0.0803968i | ||||
\(125\) | 0.735042i | 0.0657442i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.0668 | 1.33696 | 0.668482 | − | 0.743728i | \(-0.266944\pi\) | ||||
0.668482 | + | 0.743728i | \(0.266944\pi\) | |||||||
\(128\) | 11.3078 | − | 0.364570i | 0.999481 | − | 0.0322237i | ||||
\(129\) | −21.7864 | −1.91818 | ||||||||
\(130\) | −1.17548 | − | 5.04299i | −0.103097 | − | 0.442299i | ||||
\(131\) | − | 4.92238i | − | 0.430070i | −0.976606 | − | 0.215035i | \(-0.931013\pi\) | ||
0.976606 | − | 0.215035i | \(-0.0689866\pi\) | |||||||
\(132\) | 7.47291 | − | 3.68392i | 0.650434 | − | 0.320644i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.58774 | + | 0.836276i | −0.309934 | + | 0.0722433i | ||||
\(135\) | 20.4596 | 1.76088 | ||||||||
\(136\) | 10.0098 | + | 12.2023i | 0.858336 | + | 1.04634i | ||||
\(137\) | 18.3510 | 1.56783 | 0.783914 | − | 0.620869i | \(-0.213220\pi\) | ||||
0.783914 | + | 0.620869i | \(0.213220\pi\) | |||||||
\(138\) | −12.9761 | + | 3.02463i | −1.10460 | + | 0.257474i | ||||
\(139\) | 17.0567i | 1.44673i | 0.690464 | + | 0.723366i | \(0.257406\pi\) | ||||
−0.690464 | + | 0.723366i | \(0.742594\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 34.3211i | 2.89036i | ||||||||
\(142\) | −4.00000 | − | 17.1606i | −0.335673 | − | 1.44008i | ||||
\(143\) | 1.66238 | 0.139016 | ||||||||
\(144\) | −12.7395 | + | 16.5928i | −1.06163 | + | 1.38273i | ||||
\(145\) | 11.4850 | 0.953781 | ||||||||
\(146\) | 2.95743 | + | 12.6878i | 0.244759 | + | 1.05005i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.74378 | − | 11.6514i | −0.472136 | − | 0.957738i | ||||
\(149\) | 20.3985i | 1.67111i | 0.549405 | + | 0.835556i | \(0.314854\pi\) | ||||
−0.549405 | + | 0.835556i | \(0.685146\pi\) | |||||||
\(150\) | 20.6637 | − | 4.81655i | 1.68718 | − | 0.393270i | ||||
\(151\) | 4.71585 | 0.383771 | 0.191885 | − | 0.981417i | \(-0.438540\pi\) | ||||
0.191885 | + | 0.981417i | \(0.438540\pi\) | |||||||
\(152\) | 3.22428 | − | 2.64495i | 0.261523 | − | 0.214534i | ||||
\(153\) | −29.1825 | −2.35926 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.23797i | 0.260080i | ||||||||
\(156\) | −5.89134 | + | 2.90425i | −0.471684 | + | 0.232526i | ||||
\(157\) | 9.01170i | 0.719212i | 0.933104 | + | 0.359606i | \(0.117089\pi\) | ||||
−0.933104 | + | 0.359606i | \(0.882911\pi\) | |||||||
\(158\) | 4.45963 | + | 19.1324i | 0.354789 | + | 1.52209i | ||||
\(159\) | 31.6090 | 2.50676 | ||||||||
\(160\) | −7.47291 | + | 16.4776i | −0.590786 | + | 1.30266i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.854446 | − | 3.66569i | −0.0671316 | − | 0.288004i | ||||
\(163\) | − | 4.69009i | − | 0.367356i | −0.982986 | − | 0.183678i | \(-0.941200\pi\) | ||
0.982986 | − | 0.183678i | \(-0.0588004\pi\) | |||||||
\(164\) | −13.2676 | + | 6.54052i | −1.03603 | + | 0.510729i | ||||
\(165\) | 13.3239i | 1.03727i | ||||||||
\(166\) | −10.8410 | + | 2.52696i | −0.841426 | + | 0.196130i | ||||
\(167\) | −13.9885 | −1.08246 | −0.541230 | − | 0.840875i | \(-0.682041\pi\) | ||||
−0.541230 | + | 0.840875i | \(0.682041\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.6894 | 0.899188 | ||||||||
\(170\) | −24.5808 | + | 5.72960i | −1.88526 | + | 0.439440i | ||||
\(171\) | 7.71104i | 0.589678i | ||||||||
\(172\) | 6.71585 | + | 13.6233i | 0.512079 | + | 1.03876i | ||||
\(173\) | 7.54161i | 0.573378i | 0.958024 | + | 0.286689i | \(0.0925546\pi\) | ||||
−0.958024 | + | 0.286689i | \(0.907445\pi\) | |||||||
\(174\) | −3.30711 | − | 14.1880i | −0.250711 | − | 1.07559i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.60719 | − | 3.53729i | −0.347280 | − | 0.266634i | ||||
\(177\) | −18.1212 | −1.36207 | ||||||||
\(178\) | −1.03704 | − | 4.44903i | −0.0777292 | − | 0.333469i | ||||
\(179\) | 14.8894i | 1.11288i | 0.830887 | + | 0.556441i | \(0.187834\pi\) | ||||
−0.830887 | + | 0.556441i | \(0.812166\pi\) | |||||||
\(180\) | −14.7922 | − | 30.0062i | −1.10254 | − | 2.23653i | ||||
\(181\) | − | 16.4911i | − | 1.22577i | −0.790170 | − | 0.612887i | \(-0.790008\pi\) | ||
0.790170 | − | 0.612887i | \(-0.209992\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.17548 | −0.678271 | ||||||||
\(184\) | 5.89134 | + | 7.18172i | 0.434315 | + | 0.529444i | ||||
\(185\) | 20.7740 | 1.52734 | ||||||||
\(186\) | 4.00000 | − | 0.932371i | 0.293294 | − | 0.0683647i | ||||
\(187\) | − | 8.10288i | − | 0.592541i | ||||||
\(188\) | 21.4614 | − | 10.5798i | 1.56523 | − | 0.771611i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.51396 | + | 6.49511i | 0.109834 | + | 0.471205i | ||||
\(191\) | 2.35097 | 0.170110 | 0.0850550 | − | 0.996376i | \(-0.472893\pi\) | ||||
0.0850550 | + | 0.996376i | \(0.472893\pi\) | |||||||
\(192\) | 22.5072 | + | 4.48691i | 1.62432 | + | 0.323815i | ||||
\(193\) | −9.55286 | −0.687630 | −0.343815 | − | 0.939037i | \(-0.611719\pi\) | ||||
−0.343815 | + | 0.939037i | \(0.611719\pi\) | |||||||
\(194\) | −0.129007 | − | 0.553458i | −0.00926216 | − | 0.0397360i | ||||
\(195\) | − | 10.5040i | − | 0.752210i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 12.0578i | − | 0.859086i | −0.903046 | − | 0.429543i | \(-0.858675\pi\) | ||
0.903046 | − | 0.429543i | \(-0.141325\pi\) | |||||||
\(198\) | 10.4596 | − | 2.43806i | 0.743334 | − | 0.173266i | ||||
\(199\) | 3.99447 | 0.283160 | 0.141580 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141580 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(200\) | −9.38161 | − | 11.4365i | −0.663380 | − | 0.808681i | ||||
\(201\) | −7.47291 | −0.527099 | ||||||||
\(202\) | −8.57095 | + | 1.99782i | −0.603050 | + | 0.140566i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 14.1560 | + | 28.7159i | 0.991121 | + | 2.01051i | ||||
\(205\) | − | 23.6557i | − | 1.65218i | ||||||
\(206\) | −2.34974 | − | 10.0807i | −0.163714 | − | 0.702358i | ||||
\(207\) | −17.1755 | −1.19378 | ||||||||
\(208\) | 3.63212 | + | 2.78866i | 0.251842 | + | 0.193359i | ||||
\(209\) | −2.14107 | −0.148101 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.44154i | 0.443454i | 0.975109 | + | 0.221727i | \(0.0711694\pi\) | ||||
−0.975109 | + | 0.221727i | \(0.928831\pi\) | |||||||
\(212\) | −9.74378 | − | 19.7655i | −0.669205 | − | 1.35750i | ||||
\(213\) | − | 35.7438i | − | 2.44912i | ||||||
\(214\) | 6.15604 | − | 1.43493i | 0.420818 | − | 0.0980896i | ||||
\(215\) | −24.2898 | −1.65655 | ||||||||
\(216\) | −13.9885 | + | 11.4751i | −0.951794 | + | 0.780779i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −17.4053 | + | 4.05705i | −1.17884 | + | 0.274778i | ||||
\(219\) | 26.4275i | 1.78580i | ||||||||
\(220\) | 8.33161 | − | 4.10723i | 0.561717 | − | 0.276909i | ||||
\(221\) | 6.38797i | 0.429702i | ||||||||
\(222\) | −5.98186 | − | 25.6630i | −0.401476 | − | 1.72239i | ||||
\(223\) | −19.2830 | −1.29128 | −0.645641 | − | 0.763641i | \(-0.723410\pi\) | ||||
−0.645641 | + | 0.763641i | \(0.723410\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 27.3510 | 1.82340 | ||||||||
\(226\) | 3.28415 | + | 14.0895i | 0.218458 | + | 0.937216i | ||||
\(227\) | 9.68889i | 0.643074i | 0.946897 | + | 0.321537i | \(0.104200\pi\) | ||||
−0.946897 | + | 0.321537i | \(0.895800\pi\) | |||||||
\(228\) | 7.58774 | − | 3.74052i | 0.502510 | − | 0.247722i | ||||
\(229\) | 9.35925i | 0.618477i | 0.950985 | + | 0.309238i | \(0.100074\pi\) | ||||
−0.950985 | + | 0.309238i | \(0.899926\pi\) | |||||||
\(230\) | −14.4671 | + | 3.37218i | −0.953935 | + | 0.222355i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.85244 | + | 6.44154i | −0.515538 | + | 0.422908i | ||||
\(233\) | 16.9193 | 1.10842 | 0.554209 | − | 0.832378i | \(-0.313021\pi\) | ||||
0.554209 | + | 0.832378i | \(0.313021\pi\) | |||||||
\(234\) | −8.24594 | + | 1.92207i | −0.539054 | + | 0.125650i | ||||
\(235\) | 38.2649i | 2.49613i | ||||||||
\(236\) | 5.58601 | + | 11.3314i | 0.363618 | + | 0.737608i | ||||
\(237\) | 39.8510i | 2.58860i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.71585 | −0.305043 | −0.152522 | − | 0.988300i | \(-0.548739\pi\) | ||||
−0.152522 | + | 0.988300i | \(0.548739\pi\) | |||||||
\(240\) | −22.3510 | + | 29.1113i | −1.44275 | + | 1.87912i | ||||
\(241\) | 8.88713 | 0.572470 | 0.286235 | − | 0.958159i | \(-0.407596\pi\) | ||||
0.286235 | + | 0.958159i | \(0.407596\pi\) | |||||||
\(242\) | −2.85445 | − | 12.2460i | −0.183491 | − | 0.787201i | ||||
\(243\) | 11.5552i | 0.741265i | ||||||||
\(244\) | 2.82843 | + | 5.73753i | 0.181071 | + | 0.367308i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −29.2229 | + | 6.81163i | −1.86318 | + | 0.434294i | ||||
\(247\) | 1.68793 | 0.107400 | ||||||||
\(248\) | −1.81606 | − | 2.21383i | −0.115320 | − | 0.140578i | ||||
\(249\) | −22.5808 | −1.43100 | ||||||||
\(250\) | 1.01237 | − | 0.235976i | 0.0640278 | − | 0.0149244i | ||||
\(251\) | − | 16.3974i | − | 1.03500i | −0.855684 | − | 0.517499i | \(-0.826863\pi\) | ||
0.855684 | − | 0.517499i | \(-0.173137\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.76899i | − | 0.299824i | ||||||
\(254\) | −4.83700 | − | 20.7514i | −0.303501 | − | 1.30206i | ||||
\(255\) | −51.1994 | −3.20623 | ||||||||
\(256\) | −4.13235 | − | 15.4572i | −0.258272 | − | 0.966072i | ||||
\(257\) | 12.7279 | 0.793946 | 0.396973 | − | 0.917830i | \(-0.370061\pi\) | ||||
0.396973 | + | 0.917830i | \(0.370061\pi\) | |||||||
\(258\) | 6.99423 | + | 30.0062i | 0.435442 | + | 1.86811i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6.56829 | + | 3.23797i | −0.407348 | + | 0.200810i | ||||
\(261\) | − | 18.7795i | − | 1.16242i | ||||||
\(262\) | −6.77956 | + | 1.58026i | −0.418842 | + | 0.0976291i | ||||
\(263\) | 21.8913 | 1.34988 | 0.674939 | − | 0.737874i | \(-0.264170\pi\) | ||||
0.674939 | + | 0.737874i | \(0.264170\pi\) | |||||||
\(264\) | −7.47291 | − | 9.10972i | −0.459926 | − | 0.560664i | ||||
\(265\) | 35.2412 | 2.16485 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 9.26689i | − | 0.567125i | ||||||
\(268\) | 2.30359 | + | 4.67289i | 0.140714 | + | 0.285442i | ||||
\(269\) | 18.5176i | 1.12904i | 0.825420 | + | 0.564519i | \(0.190938\pi\) | ||||
−0.825420 | + | 0.564519i | \(0.809062\pi\) | |||||||
\(270\) | −6.56829 | − | 28.1789i | −0.399734 | − | 1.71491i | ||||
\(271\) | 13.9335 | 0.846397 | 0.423199 | − | 0.906037i | \(-0.360907\pi\) | ||||
0.423199 | + | 0.906037i | \(0.360907\pi\) | |||||||
\(272\) | 13.5926 | − | 17.7039i | 0.824173 | − | 1.07345i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.89134 | − | 25.2747i | −0.355909 | − | 1.52690i | ||||
\(275\) | 7.59434i | 0.457956i | ||||||||
\(276\) | 8.33161 | + | 16.9009i | 0.501504 | + | 1.01731i | ||||
\(277\) | − | 13.9226i | − | 0.836527i | −0.908326 | − | 0.418264i | \(-0.862639\pi\) | ||
0.908326 | − | 0.418264i | \(-0.137361\pi\) | |||||||
\(278\) | 23.4921 | − | 5.47584i | 1.40896 | − | 0.328419i | ||||
\(279\) | 5.29450 | 0.316973 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.43171 | 0.0854084 | 0.0427042 | − | 0.999088i | \(-0.486403\pi\) | ||||
0.0427042 | + | 0.999088i | \(0.486403\pi\) | |||||||
\(282\) | 47.2702 | − | 11.0183i | 2.81490 | − | 0.656133i | ||||
\(283\) | − | 4.49907i | − | 0.267442i | −0.991019 | − | 0.133721i | \(-0.957307\pi\) | ||
0.991019 | − | 0.133721i | \(-0.0426926\pi\) | |||||||
\(284\) | −22.3510 | + | 11.0183i | −1.32629 | + | 0.653818i | ||||
\(285\) | 13.5287i | 0.801370i | ||||||||
\(286\) | −0.533686 | − | 2.28959i | −0.0315575 | − | 0.135386i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 26.9429 | + | 12.2192i | 1.58763 | + | 0.720023i | ||||
\(289\) | 14.1366 | 0.831564 | ||||||||
\(290\) | −3.68712 | − | 15.8183i | −0.216515 | − | 0.928880i | ||||
\(291\) | − | 1.15280i | − | 0.0675783i | ||||||
\(292\) | 16.5254 | − | 8.14651i | 0.967075 | − | 0.476738i | ||||
\(293\) | 8.04068i | 0.469741i | 0.972027 | + | 0.234871i | \(0.0754667\pi\) | ||||
−0.972027 | + | 0.234871i | \(0.924533\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.2034 | −1.17629 | ||||||||
\(296\) | −14.2034 | + | 11.6514i | −0.825556 | + | 0.677223i | ||||
\(297\) | 9.28897 | 0.539001 | ||||||||
\(298\) | 28.0947 | − | 6.54868i | 1.62748 | − | 0.379355i | ||||
\(299\) | 3.75967i | 0.217428i | ||||||||
\(300\) | −13.2676 | − | 26.9136i | −0.766005 | − | 1.55386i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.51396 | − | 6.49511i | −0.0871187 | − | 0.373752i | ||||
\(303\) | −17.8524 | −1.02560 | ||||||||
\(304\) | −4.67798 | − | 3.59165i | −0.268301 | − | 0.205995i | ||||
\(305\) | −10.2298 | −0.585758 | ||||||||
\(306\) | 9.36864 | + | 40.1928i | 0.535570 | + | 2.29767i | ||||
\(307\) | 11.9785i | 0.683648i | 0.939764 | + | 0.341824i | \(0.111045\pi\) | ||||
−0.939764 | + | 0.341824i | \(0.888955\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 20.9972i | − | 1.19449i | ||||||
\(310\) | 4.45963 | − | 1.03951i | 0.253290 | − | 0.0590400i | ||||
\(311\) | 21.6701 | 1.22880 | 0.614398 | − | 0.788996i | \(-0.289399\pi\) | ||||
0.614398 | + | 0.788996i | \(0.289399\pi\) | |||||||
\(312\) | 5.89134 | + | 7.18172i | 0.333531 | + | 0.406585i | ||||
\(313\) | 9.42081 | 0.532496 | 0.266248 | − | 0.963905i | \(-0.414216\pi\) | ||||
0.266248 | + | 0.963905i | \(0.414216\pi\) | |||||||
\(314\) | 12.4117 | − | 2.89309i | 0.700435 | − | 0.163266i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.9193 | − | 12.2844i | 1.40182 | − | 0.691053i | ||||
\(317\) | − | 9.15360i | − | 0.514117i | −0.966396 | − | 0.257059i | \(-0.917247\pi\) | ||
0.966396 | − | 0.257059i | \(-0.0827534\pi\) | |||||||
\(318\) | −10.1477 | − | 43.5349i | −0.569053 | − | 2.44132i | ||||
\(319\) | 5.21438 | 0.291949 | ||||||||
\(320\) | 25.0935 | + | 5.00249i | 1.40277 | + | 0.279648i | ||||
\(321\) | 12.8224 | 0.715678 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 8.22739i | − | 0.457784i | ||||||
\(324\) | −4.77442 | + | 2.35364i | −0.265246 | + | 0.130758i | ||||
\(325\) | − | 5.98706i | − | 0.332103i | ||||||
\(326\) | −6.45963 | + | 1.50569i | −0.357766 | + | 0.0833926i | ||||
\(327\) | −36.2535 | −2.00482 | ||||||||
\(328\) | 13.2676 | + | 16.1736i | 0.732581 | + | 0.893039i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 18.3510 | − | 4.27748i | 1.01019 | − | 0.235467i | ||||
\(331\) | − | 19.8788i | − | 1.09264i | −0.837578 | − | 0.546318i | \(-0.816029\pi\) | ||
0.837578 | − | 0.546318i | \(-0.183971\pi\) | |||||||
\(332\) | 6.96073 | + | 14.1200i | 0.382020 | + | 0.774936i | ||||
\(333\) | − | 33.9682i | − | 1.86145i | ||||||
\(334\) | 4.49081 | + | 19.2662i | 0.245726 | + | 1.05420i | ||||
\(335\) | −8.33161 | −0.455204 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.5529 | −1.06511 | −0.532556 | − | 0.846395i | \(-0.678768\pi\) | ||||
−0.532556 | + | 0.846395i | \(0.678768\pi\) | |||||||
\(338\) | −3.75274 | − | 16.0998i | −0.204122 | − | 0.875713i | ||||
\(339\) | 29.3469i | 1.59391i | ||||||||
\(340\) | 15.7827 | + | 32.0155i | 0.855936 | + | 1.73629i | ||||
\(341\) | 1.47008i | 0.0796096i | ||||||||
\(342\) | 10.6204 | − | 2.47553i | 0.574283 | − | 0.133861i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 16.6072 | − | 13.6233i | 0.895400 | − | 0.734517i | ||||
\(345\) | −30.1336 | −1.62234 | ||||||||
\(346\) | 10.3870 | − | 2.42113i | 0.558409 | − | 0.130161i | ||||
\(347\) | − | 31.0043i | − | 1.66440i | −0.554479 | − | 0.832198i | \(-0.687082\pi\) | ||
0.554479 | − | 0.832198i | \(-0.312918\pi\) | |||||||
\(348\) | −18.4793 | + | 9.10972i | −0.990593 | + | 0.488332i | ||||
\(349\) | − | 14.6735i | − | 0.785453i | −0.919655 | − | 0.392726i | \(-0.871532\pi\) | ||
0.919655 | − | 0.392726i | \(-0.128468\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.32304 | −0.390875 | ||||||||
\(352\) | −3.39281 | + | 7.48105i | −0.180837 | + | 0.398741i | ||||
\(353\) | 25.6667 | 1.36610 | 0.683049 | − | 0.730372i | \(-0.260653\pi\) | ||||
0.683049 | + | 0.730372i | \(0.260653\pi\) | |||||||
\(354\) | 5.81756 | + | 24.9581i | 0.309200 | + | 1.32651i | ||||
\(355\) | − | 39.8510i | − | 2.11507i | ||||||
\(356\) | −5.79469 | + | 2.85661i | −0.307118 | + | 0.151400i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.5070 | − | 4.78003i | 1.08383 | − | 0.252633i | ||||
\(359\) | −4.20341 | −0.221847 | −0.110924 | − | 0.993829i | \(-0.535381\pi\) | ||||
−0.110924 | + | 0.993829i | \(0.535381\pi\) | |||||||
\(360\) | −36.5785 | + | 30.0062i | −1.92786 | + | 1.58147i | ||||
\(361\) | 16.8260 | 0.885581 | ||||||||
\(362\) | −22.7131 | + | 5.29425i | −1.19377 | + | 0.278260i | ||||
\(363\) | − | 25.5072i | − | 1.33878i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 29.4642i | 1.54222i | ||||||||
\(366\) | 2.94567 | + | 12.6373i | 0.153973 | + | 0.660564i | ||||
\(367\) | −35.6035 | −1.85849 | −0.929244 | − | 0.369467i | \(-0.879540\pi\) | ||||
−0.929244 | + | 0.369467i | \(0.879540\pi\) | |||||||
\(368\) | 8.00000 | − | 10.4197i | 0.417029 | − | 0.543164i | ||||
\(369\) | −38.6801 | −2.01361 | ||||||||
\(370\) | −6.66922 | − | 28.6119i | −0.346716 | − | 1.48746i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.56829 | − | 5.20985i | −0.133160 | − | 0.270118i | ||||
\(373\) | − | 9.97884i | − | 0.516684i | −0.966053 | − | 0.258342i | \(-0.916824\pi\) | ||
0.966053 | − | 0.258342i | \(-0.0831762\pi\) | |||||||
\(374\) | −11.1600 | + | 2.60132i | −0.577072 | + | 0.134511i | ||||
\(375\) | 2.10866 | 0.108891 | ||||||||
\(376\) | −21.4614 | − | 26.1621i | −1.10679 | − | 1.34921i | ||||
\(377\) | −4.11080 | −0.211717 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.5283i | 1.25993i | 0.776622 | + | 0.629967i | \(0.216932\pi\) | ||||
−0.776622 | + | 0.629967i | \(0.783068\pi\) | |||||||
\(380\) | 8.45963 | − | 4.17034i | 0.433970 | − | 0.213934i | ||||
\(381\) | − | 43.2232i | − | 2.21439i | ||||||
\(382\) | −0.754747 | − | 3.23797i | −0.0386162 | − | 0.165669i | ||||
\(383\) | 8.63896 | 0.441430 | 0.220715 | − | 0.975338i | \(-0.429161\pi\) | ||||
0.220715 | + | 0.975338i | \(0.429161\pi\) | |||||||
\(384\) | −1.04587 | − | 32.4395i | −0.0533716 | − | 1.65542i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.06682 | + | 13.1571i | 0.156097 | + | 0.669678i | ||||
\(387\) | 39.7170i | 2.01893i | ||||||||
\(388\) | −0.720858 | + | 0.355361i | −0.0365960 | + | 0.0180407i | ||||
\(389\) | − | 12.6373i | − | 0.640738i | −0.947293 | − | 0.320369i | \(-0.896193\pi\) | ||
0.947293 | − | 0.320369i | \(-0.103807\pi\) | |||||||
\(390\) | −14.4671 | + | 3.37218i | −0.732572 | + | 0.170757i | ||||
\(391\) | 18.3256 | 0.926765 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.1212 | −0.712318 | ||||||||
\(394\) | −16.6072 | + | 3.87101i | −0.836658 | + | 0.195019i | ||||
\(395\) | 44.4302i | 2.23552i | ||||||||
\(396\) | −6.71585 | − | 13.6233i | −0.337484 | − | 0.684595i | ||||
\(397\) | 1.87984i | 0.0943463i | 0.998887 | + | 0.0471732i | \(0.0150213\pi\) | ||||
−0.998887 | + | 0.0471732i | \(0.984979\pi\) | |||||||
\(398\) | −1.28237 | − | 5.50156i | −0.0642795 | − | 0.275768i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.7395 | + | 16.5928i | −0.636977 | + | 0.829638i | ||||
\(401\) | 14.5808 | 0.728129 | 0.364065 | − | 0.931374i | \(-0.381389\pi\) | ||||
0.364065 | + | 0.931374i | \(0.381389\pi\) | |||||||
\(402\) | 2.39908 | + | 10.2924i | 0.119655 | + | 0.513338i | ||||
\(403\) | − | 1.15895i | − | 0.0577316i | ||||||
\(404\) | 5.50318 | + | 11.1633i | 0.273793 | + | 0.555396i | ||||
\(405\) | − | 8.51263i | − | 0.422996i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.43171 | 0.467512 | ||||||||
\(408\) | 35.0055 | − | 28.7159i | 1.73303 | − | 1.42165i | ||||
\(409\) | −30.1948 | −1.49304 | −0.746519 | − | 0.665364i | \(-0.768276\pi\) | ||||
−0.746519 | + | 0.665364i | \(0.768276\pi\) | |||||||
\(410\) | −32.5808 | + | 7.59434i | −1.60905 | + | 0.375058i | ||||
\(411\) | − | 52.6446i | − | 2.59677i | ||||||
\(412\) | −13.1298 | + | 6.47257i | −0.646857 | + | 0.318881i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.51396 | + | 23.6557i | 0.270996 | + | 1.16261i | ||||
\(415\) | −25.1755 | −1.23582 | ||||||||
\(416\) | 2.67475 | − | 5.89775i | 0.131141 | − | 0.289161i | ||||
\(417\) | 48.9317 | 2.39620 | ||||||||
\(418\) | 0.687361 | + | 2.94887i | 0.0336199 | + | 0.144234i | ||||
\(419\) | − | 7.28773i | − | 0.356029i | −0.984028 | − | 0.178014i | \(-0.943033\pi\) | ||
0.984028 | − | 0.178014i | \(-0.0569673\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 2.30560i | − | 0.112368i | −0.998420 | − | 0.0561840i | \(-0.982107\pi\) | ||
0.998420 | − | 0.0561840i | \(-0.0178933\pi\) | |||||||
\(422\) | 8.87189 | − | 2.06797i | 0.431877 | − | 0.100667i | ||||
\(423\) | 62.5681 | 3.04216 | ||||||||
\(424\) | −24.0947 | + | 19.7655i | −1.17014 | + | 0.959897i | ||||
\(425\) | −29.1825 | −1.41556 | ||||||||
\(426\) | −49.2296 | + | 11.4751i | −2.38518 | + | 0.555969i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.95263 | − | 8.01800i | −0.191058 | − | 0.387565i | ||||
\(429\) | − | 4.76899i | − | 0.230249i | ||||||
\(430\) | 7.79792 | + | 33.4542i | 0.376049 | + | 1.61330i | ||||
\(431\) | −2.36489 | −0.113913 | −0.0569563 | − | 0.998377i | \(-0.518140\pi\) | ||||
−0.0569563 | + | 0.998377i | \(0.518140\pi\) | |||||||
\(432\) | 20.2953 | + | 15.5823i | 0.976460 | + | 0.749703i | ||||
\(433\) | −11.0832 | −0.532624 | −0.266312 | − | 0.963887i | \(-0.585805\pi\) | ||||
−0.266312 | + | 0.963887i | \(0.585805\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 32.9479i | − | 1.57973i | ||||||
\(436\) | 11.1755 | + | 22.6697i | 0.535209 | + | 1.08568i | ||||
\(437\) | − | 4.84227i | − | 0.231637i | ||||||
\(438\) | 36.3983 | − | 8.48418i | 1.73918 | − | 0.405390i | ||||
\(439\) | −6.66922 | −0.318305 | −0.159152 | − | 0.987254i | \(-0.550876\pi\) | ||||
−0.159152 | + | 0.987254i | \(0.550876\pi\) | |||||||
\(440\) | −8.33161 | − | 10.1565i | −0.397194 | − | 0.484192i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.79811 | − | 2.05077i | 0.418483 | − | 0.0975454i | ||||
\(443\) | 1.33883i | 0.0636098i | 0.999494 | + | 0.0318049i | \(0.0101255\pi\) | ||||
−0.999494 | + | 0.0318049i | \(0.989874\pi\) | |||||||
\(444\) | −33.4251 | + | 16.4776i | −1.58628 | + | 0.781990i | ||||
\(445\) | − | 10.3317i | − | 0.489771i | ||||||
\(446\) | 6.19054 | + | 26.5583i | 0.293131 | + | 1.25757i | ||||
\(447\) | 58.5186 | 2.76783 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.35097 | −0.205335 | −0.102667 | − | 0.994716i | \(-0.532738\pi\) | ||||
−0.102667 | + | 0.994716i | \(0.532738\pi\) | |||||||
\(450\) | −8.78067 | − | 37.6703i | −0.413925 | − | 1.77579i | ||||
\(451\) | − | 10.7400i | − | 0.505728i | ||||||
\(452\) | 18.3510 | − | 9.04646i | 0.863157 | − | 0.425510i | ||||
\(453\) | − | 13.5287i | − | 0.635633i | ||||||
\(454\) | 13.3444 | − | 3.11049i | 0.626286 | − | 0.145983i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.58774 | − | 9.24970i | −0.355329 | − | 0.433157i | ||||
\(457\) | −22.0125 | −1.02970 | −0.514850 | − | 0.857280i | \(-0.672153\pi\) | ||||
−0.514850 | + | 0.857280i | \(0.672153\pi\) | |||||||
\(458\) | 12.8904 | − | 3.00466i | 0.602330 | − | 0.140399i | ||||
\(459\) | 35.6943i | 1.66607i | ||||||||
\(460\) | 9.28897 | + | 18.8429i | 0.433101 | + | 0.878555i | ||||
\(461\) | 6.80657i | 0.317014i | 0.987358 | + | 0.158507i | \(0.0506680\pi\) | ||||
−0.987358 | + | 0.158507i | \(0.949332\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.43171 | 0.0665370 | 0.0332685 | − | 0.999446i | \(-0.489408\pi\) | ||||
0.0332685 | + | 0.999446i | \(0.489408\pi\) | |||||||
\(464\) | 11.3928 | + | 8.74714i | 0.528898 | + | 0.406076i | ||||
\(465\) | 9.28897 | 0.430766 | ||||||||
\(466\) | −5.43171 | − | 23.3028i | −0.251619 | − | 1.07948i | ||||
\(467\) | 33.7974i | 1.56396i | 0.623306 | + | 0.781978i | \(0.285789\pi\) | ||||
−0.623306 | + | 0.781978i | \(0.714211\pi\) | |||||||
\(468\) | 5.29450 | + | 10.7400i | 0.244738 | + | 0.496458i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 52.7019 | − | 12.2844i | 2.43096 | − | 0.566639i | ||||
\(471\) | 25.8524 | 1.19122 | ||||||||
\(472\) | 13.8133 | − | 11.3314i | 0.635808 | − | 0.521568i | ||||
\(473\) | −11.0279 | −0.507065 | ||||||||
\(474\) | 54.8865 | − | 12.7936i | 2.52102 | − | 0.587631i | ||||
\(475\) | 7.71104i | 0.353807i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 57.6239i | − | 2.63842i | ||||||
\(478\) | 1.51396 | + | 6.49511i | 0.0692470 | + | 0.297079i | ||||
\(479\) | 21.9577 | 1.00327 | 0.501637 | − | 0.865078i | \(-0.332731\pi\) | ||||
0.501637 | + | 0.865078i | \(0.332731\pi\) | |||||||
\(480\) | 47.2702 | + | 21.4380i | 2.15758 | + | 0.978508i | ||||
\(481\) | −7.43557 | −0.339033 | ||||||||
\(482\) | −2.85309 | − | 12.2402i | −0.129955 | − | 0.557525i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −15.9499 | + | 7.86282i | −0.724996 | + | 0.357401i | ||||
\(485\) | − | 1.28526i | − | 0.0583608i | ||||||
\(486\) | 15.9149 | − | 3.70964i | 0.721912 | − | 0.168272i | ||||
\(487\) | −37.1227 | −1.68219 | −0.841094 | − | 0.540888i | \(-0.818088\pi\) | ||||
−0.841094 | + | 0.540888i | \(0.818088\pi\) | |||||||
\(488\) | 6.99423 | − | 5.73753i | 0.316614 | − | 0.259726i | ||||
\(489\) | −13.4548 | −0.608446 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3.31071i | − | 0.149410i | −0.997206 | − | 0.0747051i | \(-0.976198\pi\) | ||
0.997206 | − | 0.0747051i | \(-0.0238016\pi\) | |||||||
\(492\) | 18.7632 | + | 38.0616i | 0.845911 | + | 1.71595i | ||||
\(493\) | 20.0371i | 0.902424i | ||||||||
\(494\) | −0.541887 | − | 2.32477i | −0.0243807 | − | 0.104596i | ||||
\(495\) | 24.2898 | 1.09175 | ||||||||
\(496\) | −2.46607 | + | 3.21197i | −0.110730 | + | 0.144222i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.24926 | + | 31.1003i | 0.324847 | + | 1.39364i | ||||
\(499\) | 24.5345i | 1.09831i | 0.835719 | + | 0.549157i | \(0.185051\pi\) | ||||
−0.835719 | + | 0.549157i | \(0.814949\pi\) | |||||||
\(500\) | −0.650015 | − | 1.31857i | −0.0290696 | − | 0.0589683i | ||||
\(501\) | 40.1296i | 1.79286i | ||||||||
\(502\) | −22.5841 | + | 5.26418i | −1.00798 | + | 0.234952i | ||||
\(503\) | −3.68712 | −0.164401 | −0.0822003 | − | 0.996616i | \(-0.526195\pi\) | ||||
−0.0822003 | + | 0.996616i | \(0.526195\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.9038 | −0.885708 | ||||||||
\(506\) | −6.56829 | + | 1.53102i | −0.291996 | + | 0.0680622i | ||||
\(507\) | − | 33.5343i | − | 1.48931i | ||||||
\(508\) | −27.0279 | + | 13.3239i | −1.19917 | + | 0.591154i | ||||
\(509\) | − | 29.7567i | − | 1.31894i | −0.751730 | − | 0.659471i | \(-0.770780\pi\) | ||
0.751730 | − | 0.659471i | \(-0.229220\pi\) | |||||||
\(510\) | 16.4369 | + | 70.5165i | 0.727837 | + | 3.12252i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −19.9624 | + | 10.6538i | −0.882221 | + | 0.470835i | ||||
\(513\) | 9.43171 | 0.416420 | ||||||||
\(514\) | −4.08613 | − | 17.5301i | −0.180232 | − | 0.773218i | ||||
\(515\) | − | 23.4099i | − | 1.03156i | ||||||
\(516\) | 39.0820 | − | 19.2662i | 1.72049 | − | 0.848147i | ||||
\(517\) | 17.3728i | 0.764055i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.6351 | 0.949676 | ||||||||
\(520\) | 6.56829 | + | 8.00696i | 0.288039 | + | 0.351128i | ||||
\(521\) | −30.1948 | −1.32286 | −0.661430 | − | 0.750007i | \(-0.730050\pi\) | ||||
−0.661430 | + | 0.750007i | \(0.730050\pi\) | |||||||
\(522\) | −25.8649 | + | 6.02892i | −1.13208 | + | 0.263879i | ||||
\(523\) | 42.5324i | 1.85981i | 0.367796 | + | 0.929906i | \(0.380112\pi\) | ||||
−0.367796 | + | 0.929906i | \(0.619888\pi\) | |||||||
\(524\) | 4.35297 | + | 8.83011i | 0.190161 | + | 0.385745i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.02792 | − | 30.1508i | −0.306432 | − | 1.31464i | ||||
\(527\) | −5.64903 | −0.246076 | ||||||||
\(528\) | −10.1477 | + | 13.2169i | −0.441620 | + | 0.575194i | ||||
\(529\) | −12.2144 | −0.531060 | ||||||||
\(530\) | −11.3137 | − | 48.5374i | −0.491436 | − | 2.10833i | ||||
\(531\) | 33.0352i | 1.43361i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.46699i | 0.366746i | ||||||||
\(534\) | −12.7632 | + | 2.97501i | −0.552319 | + | 0.128741i | ||||
\(535\) | 14.2958 | 0.618062 | ||||||||
\(536\) | 5.69641 | − | 4.67289i | 0.246047 | − | 0.201838i | ||||
\(537\) | 42.7141 | 1.84325 | ||||||||
\(538\) | 25.5042 | − | 5.94483i | 1.09956 | − | 0.256300i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −36.7019 | + | 18.0929i | −1.57940 | + | 0.778596i | ||||
\(541\) | 5.20985i | 0.223989i | 0.993709 | + | 0.111994i | \(0.0357239\pi\) | ||||
−0.993709 | + | 0.111994i | \(0.964276\pi\) | |||||||
\(542\) | −4.47315 | − | 19.1904i | −0.192138 | − | 0.824300i | ||||
\(543\) | −47.3091 | −2.03023 | ||||||||
\(544\) | −28.7471 | − | 13.0374i | −1.23252 | − | 0.558975i | ||||
\(545\) | −40.4193 | −1.73137 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.1465i | 1.58827i | 0.607743 | + | 0.794134i | \(0.292075\pi\) | ||||
−0.607743 | + | 0.794134i | \(0.707925\pi\) | |||||||
\(548\) | −32.9193 | + | 16.2282i | −1.40624 | + | 0.693234i | ||||
\(549\) | 16.7271i | 0.713895i | ||||||||
\(550\) | 10.4596 | − | 2.43806i | 0.446000 | − | 0.103959i | ||||
\(551\) | 5.29450 | 0.225553 | ||||||||
\(552\) | 20.6027 | − | 16.9009i | 0.876908 | − | 0.719348i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −19.1755 | + | 4.46966i | −0.814688 | + | 0.189898i | ||||
\(555\) | − | 59.5958i | − | 2.52970i | ||||||
\(556\) | −15.0837 | − | 30.5976i | −0.639690 | − | 1.29763i | ||||
\(557\) | 30.8182i | 1.30581i | 0.757440 | + | 0.652905i | \(0.226450\pi\) | ||||
−0.757440 | + | 0.652905i | \(0.773550\pi\) | |||||||
\(558\) | −1.69973 | − | 7.29208i | −0.0719553 | − | 0.308698i | ||||
\(559\) | 8.69396 | 0.367715 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23.2453 | −0.981415 | ||||||||
\(562\) | −0.459630 | − | 1.97188i | −0.0193883 | − | 0.0831786i | ||||
\(563\) | 20.4289i | 0.860976i | 0.902596 | + | 0.430488i | \(0.141659\pi\) | ||||
−0.902596 | + | 0.430488i | \(0.858341\pi\) | |||||||
\(564\) | −30.3510 | − | 61.5676i | −1.27801 | − | 2.59247i | ||||
\(565\) | 32.7191i | 1.37650i | ||||||||
\(566\) | −6.19654 | + | 1.44437i | −0.260460 | + | 0.0607113i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 22.3510 | + | 27.2465i | 0.937826 | + | 1.14324i | ||||
\(569\) | 28.0125 | 1.17434 | 0.587172 | − | 0.809462i | \(-0.300241\pi\) | ||||
0.587172 | + | 0.809462i | \(0.300241\pi\) | |||||||
\(570\) | 18.6329 | − | 4.34320i | 0.780448 | − | 0.181917i | ||||
\(571\) | 14.5618i | 0.609392i | 0.952450 | + | 0.304696i | \(0.0985549\pi\) | ||||
−0.952450 | + | 0.304696i | \(0.901445\pi\) | |||||||
\(572\) | −2.98210 | + | 1.47008i | −0.124688 | + | 0.0614673i | ||||
\(573\) | − | 6.74437i | − | 0.281750i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.1755 | −0.716267 | ||||||||
\(576\) | 8.17972 | − | 41.0311i | 0.340822 | − | 1.70963i | ||||
\(577\) | −20.3172 | −0.845815 | −0.422907 | − | 0.906173i | \(-0.638990\pi\) | ||||
−0.422907 | + | 0.906173i | \(0.638990\pi\) | |||||||
\(578\) | −4.53837 | − | 19.4702i | −0.188771 | − | 0.809854i | ||||
\(579\) | 27.4049i | 1.13891i | ||||||||
\(580\) | −20.6027 | + | 10.1565i | −0.855480 | + | 0.421725i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.58774 | + | 0.370091i | −0.0658140 | + | 0.0153408i | ||||
\(583\) | 16.0000 | 0.662652 | ||||||||
\(584\) | −16.5254 | − | 20.1450i | −0.683825 | − | 0.833604i | ||||
\(585\) | −19.1491 | −0.791717 | ||||||||
\(586\) | 11.0744 | − | 2.58135i | 0.457478 | − | 0.106635i | ||||
\(587\) | − | 8.05859i | − | 0.332614i | −0.986074 | − | 0.166307i | \(-0.946816\pi\) | ||
0.986074 | − | 0.166307i | \(-0.0531842\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.49267i | 0.0615046i | ||||||||
\(590\) | 6.48604 | + | 27.8260i | 0.267026 | + | 1.14558i | ||||
\(591\) | −34.5911 | −1.42289 | ||||||||
\(592\) | 20.6072 | + | 15.8217i | 0.846950 | + | 0.650269i | ||||
\(593\) | −26.0664 | −1.07042 | −0.535209 | − | 0.844720i | \(-0.679767\pi\) | ||||
−0.535209 | + | 0.844720i | \(0.679767\pi\) | |||||||
\(594\) | −2.98210 | − | 12.7936i | −0.122357 | − | 0.524929i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −18.0389 | − | 36.5923i | −0.738902 | − | 1.49888i | ||||
\(597\) | − | 11.4592i | − | 0.468994i | ||||||
\(598\) | 5.17817 | − | 1.20699i | 0.211751 | − | 0.0493576i | ||||
\(599\) | 47.4876 | 1.94029 | 0.970144 | − | 0.242528i | \(-0.0779766\pi\) | ||||
0.970144 | + | 0.242528i | \(0.0779766\pi\) | |||||||
\(600\) | −32.8086 | + | 26.9136i | −1.33940 | + | 1.09874i | ||||
\(601\) | 2.00922 | 0.0819580 | 0.0409790 | − | 0.999160i | \(-0.486952\pi\) | ||||
0.0409790 | + | 0.999160i | \(0.486952\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.6233i | 0.554782i | ||||||||
\(604\) | −8.45963 | + | 4.17034i | −0.344217 | + | 0.169689i | ||||
\(605\) | − | 28.4381i | − | 1.15617i | ||||||
\(606\) | 5.73129 | + | 24.5880i | 0.232818 | + | 0.998821i | ||||
\(607\) | −41.5480 | −1.68638 | −0.843191 | − | 0.537614i | \(-0.819326\pi\) | ||||
−0.843191 | + | 0.537614i | \(0.819326\pi\) | |||||||
\(608\) | −3.44495 | + | 7.59600i | −0.139711 | + | 0.308059i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.28415 | + | 14.0895i | 0.132971 | + | 0.570465i | ||||
\(611\) | − | 13.6960i | − | 0.554081i | ||||||
\(612\) | 52.3496 | − | 25.8067i | 2.11611 | − | 1.04318i | ||||
\(613\) | − | 35.0077i | − | 1.41395i | −0.707239 | − | 0.706974i | \(-0.750060\pi\) | ||
0.707239 | − | 0.706974i | \(-0.249940\pi\) | |||||||
\(614\) | 16.4979 | − | 3.84553i | 0.665800 | − | 0.155193i | ||||
\(615\) | −67.8626 | −2.73648 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.58078 | 0.264932 | 0.132466 | − | 0.991188i | \(-0.457710\pi\) | ||||
0.132466 | + | 0.991188i | \(0.457710\pi\) | |||||||
\(618\) | −28.9193 | + | 6.74087i | −1.16330 | + | 0.271157i | ||||
\(619\) | 0.391842i | 0.0157495i | 0.999969 | + | 0.00787473i | \(0.00250663\pi\) | ||||
−0.999969 | + | 0.00787473i | \(0.997493\pi\) | |||||||
\(620\) | −2.86341 | − | 5.80850i | −0.114997 | − | 0.233275i | ||||
\(621\) | 21.0081i | 0.843025i | ||||||||
\(622\) | −6.95688 | − | 29.8460i | −0.278946 | − | 1.19672i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8.00000 | − | 10.4197i | 0.320256 | − | 0.417121i | ||||
\(625\) | −23.7981 | −0.951924 | ||||||||
\(626\) | −3.02443 | − | 12.9752i | −0.120880 | − | 0.518594i | ||||
\(627\) | 6.14222i | 0.245296i | ||||||||
\(628\) | −7.96925 | − | 16.1658i | −0.318008 | − | 0.645086i | ||||
\(629\) | 36.2428i | 1.44510i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.4876 | 0.935025 | 0.467512 | − | 0.883987i | \(-0.345150\pi\) | ||||
0.467512 | + | 0.883987i | \(0.345150\pi\) | |||||||
\(632\) | −24.9193 | − | 30.3774i | −0.991235 | − | 1.20835i | ||||
\(633\) | 18.4793 | 0.734485 | ||||||||
\(634\) | −12.6072 | + | 2.93864i | −0.500695 | + | 0.116708i | ||||
\(635\) | − | 48.1898i | − | 1.91236i | ||||||
\(636\) | −56.7025 | + | 27.9526i | −2.24840 | + | 1.10839i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.67401 | − | 7.18172i | −0.0662746 | − | 0.284327i | ||||
\(639\) | −65.1616 | −2.57775 | ||||||||
\(640\) | −1.16604 | − | 36.1671i | −0.0460919 | − | 1.42963i | ||||
\(641\) | −15.9347 | −0.629383 | −0.314691 | − | 0.949194i | \(-0.601901\pi\) | ||||
−0.314691 | + | 0.949194i | \(0.601901\pi\) | |||||||
\(642\) | −4.11647 | − | 17.6602i | −0.162464 | − | 0.696993i | ||||
\(643\) | 44.8491i | 1.76868i | 0.466847 | + | 0.884338i | \(0.345390\pi\) | ||||
−0.466847 | + | 0.884338i | \(0.654610\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 69.6817i | 2.74372i | ||||||||
\(646\) | −11.3315 | + | 2.64129i | −0.445833 | + | 0.103920i | ||||
\(647\) | −23.9825 | −0.942847 | −0.471424 | − | 0.881907i | \(-0.656260\pi\) | ||||
−0.471424 | + | 0.881907i | \(0.656260\pi\) | |||||||
\(648\) | 4.77442 | + | 5.82017i | 0.187557 | + | 0.228638i | ||||
\(649\) | −9.17264 | −0.360058 | ||||||||
\(650\) | −8.24594 | + | 1.92207i | −0.323432 | + | 0.0753897i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.14756 | + | 8.41342i | 0.162431 | + | 0.329495i | ||||
\(653\) | 9.06564i | 0.354766i | 0.984142 | + | 0.177383i | \(0.0567631\pi\) | ||||
−0.984142 | + | 0.177383i | \(0.943237\pi\) | |||||||
\(654\) | 11.6387 | + | 49.9317i | 0.455110 | + | 1.95248i | ||||
\(655\) | −15.7438 | −0.615160 | ||||||||
\(656\) | 18.0164 | − | 23.4657i | 0.703423 | − | 0.916182i | ||||
\(657\) | 48.1778 | 1.87959 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 21.9578i | − | 0.855354i | −0.903932 | − | 0.427677i | \(-0.859332\pi\) | ||
0.903932 | − | 0.427677i | \(-0.140668\pi\) | |||||||
\(660\) | −11.7827 | − | 23.9014i | −0.458640 | − | 0.930362i | ||||
\(661\) | 26.0641i | 1.01377i | 0.862012 | + | 0.506887i | \(0.169204\pi\) | ||||
−0.862012 | + | 0.506887i | \(0.830796\pi\) | |||||||
\(662\) | −27.3789 | + | 6.38182i | −1.06411 | + | 0.248036i | ||||
\(663\) | 18.3256 | 0.711707 | ||||||||
\(664\) | 17.2127 | − | 14.1200i | 0.667984 | − | 0.547963i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −46.7842 | + | 10.9051i | −1.81285 | + | 0.422562i | ||||
\(667\) | 11.7929i | 0.456624i | ||||||||
\(668\) | 25.0935 | − | 12.3703i | 0.970896 | − | 0.478622i | ||||
\(669\) | 55.3183i | 2.13873i | ||||||||
\(670\) | 2.67475 | + | 11.4751i | 0.103335 | + | 0.443320i | ||||
\(671\) | −4.64449 | −0.179298 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.5683 | 1.17832 | 0.589161 | − | 0.808016i | \(-0.299459\pi\) | ||||
0.589161 | + | 0.808016i | \(0.299459\pi\) | |||||||
\(674\) | 6.27719 | + | 26.9300i | 0.241788 | + | 1.03731i | ||||
\(675\) | − | 33.4542i | − | 1.28765i | ||||||
\(676\) | −20.9694 | + | 10.3372i | −0.806514 | + | 0.397587i | ||||
\(677\) | − | 11.9119i | − | 0.457813i | −0.973448 | − | 0.228906i | \(-0.926485\pi\) | ||
0.973448 | − | 0.228906i | \(-0.0735149\pi\) | |||||||
\(678\) | 40.4193 | − | 9.42145i | 1.55229 | − | 0.361829i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 39.0279 | − | 32.0155i | 1.49665 | − | 1.22774i | ||||
\(681\) | 27.7952 | 1.06511 | ||||||||
\(682\) | 2.02474 | − | 0.471951i | 0.0775312 | − | 0.0180720i | ||||
\(683\) | 18.9402i | 0.724728i | 0.932037 | + | 0.362364i | \(0.118030\pi\) | ||||
−0.932037 | + | 0.362364i | \(0.881970\pi\) | |||||||
\(684\) | −6.81905 | − | 13.8326i | −0.260733 | − | 0.528903i | ||||
\(685\) | − | 58.6939i | − | 2.24258i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.8495 | 1.02437 | ||||||||
\(688\) | −24.0947 | − | 18.4994i | −0.918603 | − | 0.705283i | ||||
\(689\) | −12.6137 | −0.480545 | ||||||||
\(690\) | 9.67401 | + | 41.5028i | 0.368283 | + | 1.57999i | ||||
\(691\) | − | 8.55765i | − | 0.325549i | −0.986663 | − | 0.162774i | \(-0.947956\pi\) | ||
0.986663 | − | 0.162774i | \(-0.0520442\pi\) | |||||||
\(692\) | −6.66922 | − | 13.5287i | −0.253526 | − | 0.514283i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −42.7019 | + | 9.95351i | −1.62094 | + | 0.377830i | ||||
\(695\) | 54.5544 | 2.06937 | ||||||||
\(696\) | 18.4793 | + | 22.5268i | 0.700455 | + | 0.853877i | ||||
\(697\) | 41.2702 | 1.56322 | ||||||||
\(698\) | −20.2097 | + | 4.71072i | −0.764947 | + | 0.178304i | ||||
\(699\) | − | 48.5374i | − | 1.83585i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 3.59086i | − | 0.135625i | −0.997698 | − | 0.0678125i | \(-0.978398\pi\) | ||
0.997698 | − | 0.0678125i | \(-0.0216020\pi\) | |||||||
\(702\) | 2.35097 | + | 10.0860i | 0.0887315 | + | 0.380670i | ||||
\(703\) | 9.57663 | 0.361190 | ||||||||
\(704\) | 11.3928 | + | 2.27120i | 0.429383 | + | 0.0855992i | ||||
\(705\) | 109.773 | 4.13429 | ||||||||
\(706\) | −8.23995 | − | 35.3505i | −0.310114 | − | 1.33043i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 32.5070 | − | 16.0250i | 1.22169 | − | 0.602255i | ||||
\(709\) | 36.8725i | 1.38477i | 0.721526 | + | 0.692387i | \(0.243441\pi\) | ||||
−0.721526 | + | 0.692387i | \(0.756559\pi\) | |||||||
\(710\) | −54.8865 | + | 12.7936i | −2.05985 | + | 0.480136i | ||||
\(711\) | 72.6491 | 2.72455 | ||||||||
\(712\) | 5.79469 | + | 7.06391i | 0.217165 | + | 0.264731i | ||||
\(713\) | −3.32477 | −0.124514 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 5.31698i | − | 0.198844i | ||||||
\(716\) | −13.1670 | − | 26.7096i | −0.492074 | − | 0.998184i | ||||
\(717\) | 13.5287i | 0.505238i | ||||||||
\(718\) | 1.34945 | + | 5.78932i | 0.0503610 | + | 0.216056i | ||||
\(719\) | 43.9901 | 1.64055 | 0.820277 | − | 0.571966i | \(-0.193819\pi\) | ||||
0.820277 | + | 0.571966i | \(0.193819\pi\) | |||||||
\(720\) | 53.0704 | + | 40.7462i | 1.97782 | + | 1.51852i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.40178 | − | 23.1744i | −0.201033 | − | 0.862461i | ||||
\(723\) | − | 25.4951i | − | 0.948172i | ||||||
\(724\) | 14.5835 | + | 29.5829i | 0.541990 | + | 1.09944i | ||||
\(725\) | − | 18.7795i | − | 0.697455i | ||||||
\(726\) | −35.1308 | + | 8.18874i | −1.30383 | + | 0.303913i | ||||
\(727\) | −50.1870 | −1.86133 | −0.930666 | − | 0.365870i | \(-0.880772\pi\) | ||||
−0.930666 | + | 0.365870i | \(0.880772\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 41.1336 | 1.52347 | ||||||||
\(730\) | 40.5808 | − | 9.45908i | 1.50196 | − | 0.350096i | ||||
\(731\) | − | 42.3765i | − | 1.56735i | ||||||
\(732\) | 16.4596 | − | 8.11409i | 0.608365 | − | 0.299906i | ||||
\(733\) | 6.30750i | 0.232973i | 0.993192 | + | 0.116486i | \(0.0371632\pi\) | ||||
−0.993192 | + | 0.116486i | \(0.962837\pi\) | |||||||
\(734\) | 11.4300 | + | 49.0365i | 0.421890 | + | 1.80997i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.9193 | − | 7.67324i | −0.623652 | − | 0.282839i | ||||
\(737\) | −3.78267 | −0.139336 | ||||||||
\(738\) | 12.4177 | + | 53.2738i | 0.457103 | + | 1.96104i | ||||
\(739\) | − | 34.4000i | − | 1.26542i | −0.774387 | − | 0.632712i | \(-0.781942\pi\) | ||
0.774387 | − | 0.632712i | \(-0.218058\pi\) | |||||||
\(740\) | −37.2659 | + | 18.3709i | −1.36992 | + | 0.675329i | ||||
\(741\) | − | 4.84227i | − | 0.177885i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.93023 | −0.364305 | −0.182152 | − | 0.983270i | \(-0.558306\pi\) | ||||
−0.182152 | + | 0.983270i | \(0.558306\pi\) | |||||||
\(744\) | −6.35097 | + | 5.20985i | −0.232838 | + | 0.191002i | ||||
\(745\) | 65.2428 | 2.39031 | ||||||||
\(746\) | −13.7438 | + | 3.20357i | −0.503195 | + | 0.117291i | ||||
\(747\) | 41.1652i | 1.50616i | ||||||||
\(748\) | 7.16556 | + | 14.5355i | 0.261999 | + | 0.531471i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.676959 | − | 2.90425i | −0.0247190 | − | 0.106048i | ||||
\(751\) | 10.7717 | 0.393065 | 0.196532 | − | 0.980497i | \(-0.437032\pi\) | ||||
0.196532 | + | 0.980497i | \(0.437032\pi\) | |||||||
\(752\) | −29.1430 | + | 37.9576i | −1.06273 | + | 1.38417i | ||||
\(753\) | −47.0404 | −1.71425 | ||||||||
\(754\) | 1.31972 | + | 5.66177i | 0.0480613 | + | 0.206190i | ||||
\(755\) | − | 15.0832i | − | 0.548935i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.2090i | 0.589127i | 0.955632 | + | 0.294563i | \(0.0951742\pi\) | ||||
−0.955632 | + | 0.294563i | \(0.904826\pi\) | |||||||
\(758\) | 33.7827 | − | 7.87449i | 1.22704 | − | 0.286014i | ||||
\(759\) | −13.6811 | −0.496593 | ||||||||
\(760\) | −8.45963 | − | 10.3126i | −0.306863 | − | 0.374076i | ||||
\(761\) | −5.37134 | −0.194711 | −0.0973554 | − | 0.995250i | \(-0.531038\pi\) | ||||
−0.0973554 | + | 0.995250i | \(0.531038\pi\) | |||||||
\(762\) | −59.5310 | + | 13.8762i | −2.15658 | + | 0.502683i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.21733 | + | 2.07901i | −0.152578 | + | 0.0752161i | ||||
\(765\) | 93.3374i | 3.37462i | ||||||||
\(766\) | −2.77342 | − | 11.8984i | −0.100208 | − | 0.429906i | ||||
\(767\) | 7.23133 | 0.261108 | ||||||||
\(768\) | −44.3430 | + | 11.8547i | −1.60009 | + | 0.427771i | ||||
\(769\) | 10.1872 | 0.367358 | 0.183679 | − | 0.982986i | \(-0.441199\pi\) | ||||
0.183679 | + | 0.982986i | \(0.441199\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 36.5134i | − | 1.31500i | ||||||
\(772\) | 17.1366 | − | 8.44781i | 0.616759 | − | 0.304043i | ||||
\(773\) | 51.3882i | 1.84831i | 0.382022 | + | 0.924153i | \(0.375228\pi\) | ||||
−0.382022 | + | 0.924153i | \(0.624772\pi\) | |||||||
\(774\) | 54.7019 | − | 12.7506i | 1.96622 | − | 0.458312i | ||||
\(775\) | 5.29450 | 0.190184 | ||||||||
\(776\) | 0.720858 | + | 0.878748i | 0.0258773 | + | 0.0315452i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17.4053 | + | 4.05705i | −0.624010 | + | 0.145452i | ||||
\(779\) | − | 10.9051i | − | 0.390714i | ||||||
\(780\) | 9.28897 | + | 18.8429i | 0.332599 | + | 0.674684i | ||||
\(781\) | − | 18.0929i | − | 0.647416i | ||||||
\(782\) | −5.88319 | − | 25.2397i | −0.210382 | − | 0.902570i | ||||
\(783\) | −22.9701 | −0.820884 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.8231 | 1.02874 | ||||||||
\(786\) | 4.53341 | + | 19.4490i | 0.161701 | + | 0.693721i | ||||
\(787\) | − | 45.4326i | − | 1.61950i | −0.586776 | − | 0.809749i | \(-0.699603\pi\) | ||
0.586776 | − | 0.809749i | \(-0.300397\pi\) | |||||||
\(788\) | 10.6630 | + | 21.6302i | 0.379855 | + | 0.770545i | ||||
\(789\) | − | 62.8011i | − | 2.23578i | ||||||
\(790\) | 61.1933 | − | 14.2637i | 2.17716 | − | 0.507480i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −16.6072 | + | 13.6233i | −0.590111 | + | 0.484082i | ||||
\(793\) | 3.66152 | 0.130024 | ||||||||
\(794\) | 2.58909 | − | 0.603497i | 0.0918832 | − | 0.0214173i | ||||
\(795\) | − | 101.099i | − | 3.58560i | ||||||
\(796\) | −7.16556 | + | 3.53240i | −0.253977 | + | 0.125203i | ||||
\(797\) | − | 30.4917i | − | 1.08007i | −0.841642 | − | 0.540036i | \(-0.818410\pi\) | ||
0.841642 | − | 0.540036i | \(-0.181590\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −66.7578 | −2.36172 | ||||||||
\(800\) | 26.9429 | + | 12.2192i | 0.952577 | + | 0.432014i | ||||
\(801\) | −16.8937 | −0.596910 | ||||||||
\(802\) | −4.68097 | − | 20.0820i | −0.165291 | − | 0.709120i | ||||
\(803\) | 13.3772i | 0.472070i | ||||||||
\(804\) | 13.4054 | − | 6.60847i | 0.472773 | − | 0.233063i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.59622 | + | 0.372067i | −0.0562244 | + | 0.0131055i | ||||
\(807\) | 53.1227 | 1.87001 | ||||||||
\(808\) | 13.6084 | − | 11.1633i | 0.478744 | − | 0.392725i | ||||
\(809\) | −18.9068 | −0.664727 | −0.332363 | − | 0.943151i | \(-0.607846\pi\) | ||||
−0.332363 | + | 0.943151i | \(0.607846\pi\) | |||||||
\(810\) | −11.7244 | + | 2.73287i | −0.411953 | + | 0.0960232i | ||||
\(811\) | 34.8800i | 1.22480i | 0.790548 | + | 0.612401i | \(0.209796\pi\) | ||||
−0.790548 | + | 0.612401i | \(0.790204\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 39.9718i | − | 1.40187i | ||||||
\(814\) | −3.02792 | − | 12.9902i | −0.106129 | − | 0.455307i | ||||
\(815\) | −15.0008 | −0.525456 | ||||||||
\(816\) | −50.7882 | − | 38.9940i | −1.77794 | − | 1.36506i | ||||
\(817\) | −11.1974 | −0.391747 | ||||||||
\(818\) | 9.69365 | + | 41.5871i | 0.338931 | + | 1.45406i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.9193 | + | 42.4352i | 0.730532 | + | 1.48190i | ||||
\(821\) | 10.3509i | 0.361249i | 0.983552 | + | 0.180624i | \(0.0578119\pi\) | ||||
−0.983552 | + | 0.180624i | \(0.942188\pi\) | |||||||
\(822\) | −72.5070 | + | 16.9009i | −2.52897 | + | 0.589485i | ||||
\(823\) | 7.32304 | 0.255265 | 0.127633 | − | 0.991822i | \(-0.459262\pi\) | ||||
0.127633 | + | 0.991822i | \(0.459262\pi\) | |||||||
\(824\) | 13.1298 | + | 16.0056i | 0.457397 | + | 0.557581i | ||||
\(825\) | 21.7864 | 0.758504 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.6881i | 1.17145i | 0.810510 | + | 0.585725i | \(0.199190\pi\) | ||||
−0.810510 | + | 0.585725i | \(0.800810\pi\) | |||||||
\(828\) | 30.8106 | − | 15.1887i | 1.07074 | − | 0.527843i | ||||
\(829\) | − | 11.8848i | − | 0.412777i | −0.978470 | − | 0.206388i | \(-0.933829\pi\) | ||
0.978470 | − | 0.206388i | \(-0.0661710\pi\) | |||||||
\(830\) | 8.08226 | + | 34.6740i | 0.280539 | + | 1.20355i | ||||
\(831\) | −39.9406 | −1.38553 | ||||||||
\(832\) | −8.98162 | − | 1.79052i | −0.311382 | − | 0.0620752i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −15.7089 | − | 67.3933i | −0.543954 | − | 2.33364i | ||||
\(835\) | 44.7408i | 1.54832i | ||||||||
\(836\) | 3.84080 | − | 1.89339i | 0.132837 | − | 0.0654844i | ||||
\(837\) | − | 6.47594i | − | 0.223841i | ||||||
\(838\) | −10.0373 | + | 2.33963i | −0.346734 | + | 0.0808211i | ||||
\(839\) | 53.8741 | 1.85994 | 0.929970 | − | 0.367635i | \(-0.119832\pi\) | ||||
0.929970 | + | 0.367635i | \(0.119832\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.1057 | 0.555369 | ||||||||
\(842\) | −3.17548 | + | 0.740182i | −0.109434 | + | 0.0255083i | ||||
\(843\) | − | 4.10723i | − | 0.141460i | ||||||
\(844\) | −5.69641 | − | 11.5553i | −0.196078 | − | 0.397750i | ||||
\(845\) | − | 37.3876i | − | 1.28617i | ||||||
\(846\) | −20.0867 | − | 86.1745i | −0.690593 | − | 2.96274i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 34.9582 | + | 26.8401i | 1.20047 | + | 0.921692i | ||||
\(849\) | −12.9068 | −0.442959 | ||||||||
\(850\) | 9.36864 | + | 40.1928i | 0.321342 | + | 1.37860i | ||||
\(851\) | 21.3309i | 0.731214i | ||||||||
\(852\) | 31.6090 | + | 64.1197i | 1.08291 | + | 2.19670i | ||||
\(853\) | − | 31.6588i | − | 1.08398i | −0.840386 | − | 0.541988i | \(-0.817672\pi\) | ||
0.840386 | − | 0.541988i | \(-0.182328\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 24.6630 | 0.843458 | ||||||||
\(856\) | −9.77419 | + | 8.01800i | −0.334075 | + | 0.274050i | ||||
\(857\) | −3.02159 | −0.103216 | −0.0516078 | − | 0.998667i | \(-0.516435\pi\) | ||||
−0.0516078 | + | 0.998667i | \(0.516435\pi\) | |||||||
\(858\) | −6.56829 | + | 1.53102i | −0.224238 | + | 0.0522682i | ||||
\(859\) | 14.9274i | 0.509315i | 0.967031 | + | 0.254657i | \(0.0819627\pi\) | ||||
−0.967031 | + | 0.254657i | \(0.918037\pi\) | |||||||
\(860\) | 43.5728 | − | 21.4800i | 1.48582 | − | 0.732463i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.759216 | + | 3.25714i | 0.0258590 | + | 0.110939i | ||||
\(863\) | −2.86341 | −0.0974716 | −0.0487358 | − | 0.998812i | \(-0.515519\pi\) | ||||
−0.0487358 | + | 0.998812i | \(0.515519\pi\) | |||||||
\(864\) | 14.9458 | − | 32.9551i | 0.508467 | − | 1.12116i | ||||
\(865\) | 24.1212 | 0.820144 | ||||||||
\(866\) | 3.55811 | + | 15.2648i | 0.120910 | + | 0.518719i | ||||
\(867\) | − | 40.5546i | − | 1.37730i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.1719i | 0.684286i | ||||||||
\(870\) | −45.3789 | + | 10.5775i | −1.53849 | + | 0.358610i | ||||
\(871\) | 2.98210 | 0.101045 | ||||||||
\(872\) | 27.6351 | − | 22.6697i | 0.935843 | − | 0.767694i | ||||
\(873\) | −2.10157 | −0.0711275 | ||||||||
\(874\) | −6.66922 | + | 1.55455i | −0.225590 | + | 0.0525833i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −23.3704 | − | 47.4074i | −0.789613 | − | 1.60175i | ||||
\(877\) | − | 25.6275i | − | 0.865381i | −0.901543 | − | 0.432690i | \(-0.857564\pi\) | ||
0.901543 | − | 0.432690i | \(-0.142436\pi\) | |||||||
\(878\) | 2.14107 | + | 9.18547i | 0.0722575 | + | 0.309995i | ||||
\(879\) | 23.0668 | 0.778024 | ||||||||
\(880\) | −11.3137 | + | 14.7357i | −0.381385 | + | 0.496739i | ||||
\(881\) | 22.1882 | 0.747540 | 0.373770 | − | 0.927521i | \(-0.378065\pi\) | ||||
0.373770 | + | 0.927521i | \(0.378065\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.5063i | 0.892010i | 0.895031 | + | 0.446005i | \(0.147154\pi\) | ||||
−0.895031 | + | 0.446005i | \(0.852846\pi\) | |||||||
\(884\) | −5.64903 | − | 11.4592i | −0.189998 | − | 0.385415i | ||||
\(885\) | 57.9588i | 1.94827i | ||||||||
\(886\) | 1.84396 | − | 0.429814i | 0.0619492 | − | 0.0144399i | ||||
\(887\) | 11.0064 | 0.369557 | 0.184779 | − | 0.982780i | \(-0.440843\pi\) | ||||
0.184779 | + | 0.982780i | \(0.440843\pi\) | |||||||
\(888\) | 33.4251 | + | 40.7462i | 1.12167 | + | 1.36735i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −14.2298 | + | 3.31687i | −0.476984 | + | 0.111182i | ||||
\(891\) | − | 3.86486i | − | 0.129478i | ||||||
\(892\) | 34.5911 | − | 17.0524i | 1.15820 | − | 0.570956i | ||||
\(893\) | 17.6398i | 0.590292i | ||||||||
\(894\) | −18.7866 | − | 80.5972i | −0.628319 | − | 2.69557i | ||||
\(895\) | 47.6222 | 1.59184 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.7856 | 0.360121 | ||||||||
\(898\) | 1.39682 | + | 5.99255i | 0.0466125 | + | 0.199974i | ||||
\(899\) | − | 3.63528i | − | 0.121243i | ||||||
\(900\) | −49.0641 | + | 24.1871i | −1.63547 | + | 0.806237i | ||||
\(901\) | 61.4825i | 2.04828i | ||||||||
\(902\) | −14.7922 | + | 3.44794i | −0.492525 | + | 0.114804i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18.3510 | − | 22.3704i | −0.610344 | − | 0.744029i | ||||
\(905\) | −52.7453 | −1.75331 | ||||||||
\(906\) | −18.6329 | + | 4.34320i | −0.619038 | + | 0.144293i | ||||
\(907\) | 57.5895i | 1.91223i | 0.292995 | + | 0.956114i | \(0.405348\pi\) | ||||
−0.292995 | + | 0.956114i | \(0.594652\pi\) | |||||||
\(908\) | −8.56811 | − | 17.3806i | −0.284343 | − | 0.576796i | ||||
\(909\) | 32.5453i | 1.07946i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.77170 | 0.0918306 | 0.0459153 | − | 0.998945i | \(-0.485380\pi\) | ||||
0.0459153 | + | 0.998945i | \(0.485380\pi\) | |||||||
\(912\) | −10.3036 | + | 13.4200i | −0.341186 | + | 0.444382i | ||||
\(913\) | −11.4300 | −0.378279 | ||||||||
\(914\) | 7.06682 | + | 30.3176i | 0.233750 | + | 1.00282i | ||||
\(915\) | 29.3469i | 0.970180i | ||||||||
\(916\) | −8.27660 | − | 16.7893i | −0.273467 | − | 0.554734i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 49.1616 | − | 11.4592i | 1.62257 | − | 0.378210i | ||||
\(919\) | 20.4596 | 0.674901 | 0.337450 | − | 0.941343i | \(-0.390435\pi\) | ||||
0.337450 | + | 0.941343i | \(0.390435\pi\) | |||||||
\(920\) | 22.9701 | − | 18.8429i | 0.757301 | − | 0.621232i | ||||
\(921\) | 34.3635 | 1.13231 | ||||||||
\(922\) | 9.37464 | − | 2.18516i | 0.308737 | − | 0.0719644i | ||||
\(923\) | 14.2637i | 0.469496i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 33.9682i | − | 1.11687i | ||||||
\(926\) | −0.459630 | − | 1.97188i | −0.0151044 | − | 0.0647999i | ||||
\(927\) | −38.2783 | −1.25722 | ||||||||
\(928\) | 8.38986 | − | 18.4994i | 0.275411 | − | 0.607272i | ||||
\(929\) | 11.5442 | 0.378754 | 0.189377 | − | 0.981904i | \(-0.439353\pi\) | ||||
0.189377 | + | 0.981904i | \(0.439353\pi\) | |||||||
\(930\) | −2.98210 | − | 12.7936i | −0.0977870 | − | 0.419520i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −30.3510 | + | 14.9621i | −0.994179 | + | 0.490100i | ||||
\(933\) | − | 62.1663i | − | 2.03523i | ||||||
\(934\) | 46.5489 | − | 10.8502i | 1.52313 | − | 0.355029i | ||||
\(935\) | −25.9163 | −0.847554 | ||||||||
\(936\) | 13.0924 | − | 10.7400i | 0.427939 | − | 0.351049i | ||||
\(937\) | −46.4780 | −1.51837 | −0.759185 | − | 0.650874i | \(-0.774402\pi\) | ||||
−0.759185 | + | 0.650874i | \(0.774402\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 27.0261i | − | 0.881964i | ||||||
\(940\) | −33.8385 | − | 68.6422i | −1.10369 | − | 2.23886i | ||||
\(941\) | − | 39.6772i | − | 1.29344i | −0.762728 | − | 0.646720i | \(-0.776140\pi\) | ||
0.762728 | − | 0.646720i | \(-0.223860\pi\) | |||||||
\(942\) | −8.29959 | − | 35.6064i | −0.270415 | − | 1.16012i | ||||
\(943\) | 24.2898 | 0.790985 | ||||||||
\(944\) | −20.0412 | − | 15.3871i | −0.652284 | − | 0.500809i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.54037 | + | 15.1887i | 0.115107 | + | 0.493827i | ||||
\(947\) | − | 50.2561i | − | 1.63310i | −0.577271 | − | 0.816552i | \(-0.695882\pi\) | ||
0.577271 | − | 0.816552i | \(-0.304118\pi\) | |||||||
\(948\) | −35.2412 | − | 71.4875i | −1.14458 | − | 2.32181i | ||||
\(949\) | − | 10.5460i | − | 0.342338i | ||||||
\(950\) | 10.6204 | − | 2.47553i | 0.344570 | − | 0.0803167i | ||||
\(951\) | −26.2595 | −0.851524 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.4596 | 0.857111 | 0.428556 | − | 0.903515i | \(-0.359023\pi\) | ||||
0.428556 | + | 0.903515i | \(0.359023\pi\) | |||||||
\(954\) | −79.3650 | + | 18.4994i | −2.56954 | + | 0.598940i | ||||
\(955\) | − | 7.51935i | − | 0.243320i | ||||||
\(956\) | 8.45963 | − | 4.17034i | 0.273604 | − | 0.134878i | ||||
\(957\) | − | 14.9588i | − | 0.483550i | ||||||
\(958\) | −7.04923 | − | 30.2422i | −0.227750 | − | 0.977081i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 14.3510 | − | 71.9873i | 0.463175 | − | 2.32338i | ||||
\(961\) | −29.9751 | −0.966939 | ||||||||
\(962\) | 2.38709 | + | 10.2410i | 0.0769629 | + | 0.330182i | ||||
\(963\) | − | 23.3755i | − | 0.753265i | ||||||
\(964\) | −15.9424 | + | 7.85909i | −0.513469 | + | 0.253124i | ||||
\(965\) | 30.5539i | 0.983566i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.98903 | −0.224752 | −0.112376 | − | 0.993666i | \(-0.535846\pi\) | ||||
−0.112376 | + | 0.993666i | \(0.535846\pi\) | |||||||
\(968\) | 15.9499 | + | 19.4434i | 0.512649 | + | 0.624936i | ||||
\(969\) | −23.6024 | −0.758220 | ||||||||
\(970\) | −1.77018 | + | 0.412617i | −0.0568372 | + | 0.0132483i | ||||
\(971\) | 26.3180i | 0.844583i | 0.906460 | + | 0.422292i | \(0.138774\pi\) | ||||
−0.906460 | + | 0.422292i | \(0.861226\pi\) | |||||||
\(972\) | −10.2185 | − | 20.7285i | −0.327759 | − | 0.664866i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11.9177 | + | 51.1288i | 0.381869 | + | 1.63827i | ||||
\(975\) | −17.1755 | −0.550056 | ||||||||
\(976\) | −10.1477 | − | 7.79114i | −0.324819 | − | 0.249388i | ||||
\(977\) | 32.9193 | 1.05318 | 0.526590 | − | 0.850119i | \(-0.323470\pi\) | ||||
0.526590 | + | 0.850119i | \(0.323470\pi\) | |||||||
\(978\) | 4.31948 | + | 18.5312i | 0.138122 | + | 0.592561i | ||||
\(979\) | − | 4.69076i | − | 0.149917i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 66.0909i | 2.11012i | ||||||||
\(982\) | −4.55982 | + | 1.06286i | −0.145510 | + | 0.0339172i | ||||
\(983\) | 26.9646 | 0.860036 | 0.430018 | − | 0.902820i | \(-0.358507\pi\) | ||||
0.430018 | + | 0.902820i | \(0.358507\pi\) | |||||||
\(984\) | 46.3983 | − | 38.0616i | 1.47912 | − | 1.21336i | ||||
\(985\) | −38.5659 | −1.22881 | ||||||||
\(986\) | 27.5969 | − | 6.43264i | 0.878865 | − | 0.204857i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.02792 | + | 1.49267i | −0.0963311 | + | 0.0474883i | ||||
\(989\) | − | 24.9409i | − | 0.793076i | ||||||
\(990\) | −7.79792 | − | 33.4542i | −0.247834 | − | 1.06324i | ||||
\(991\) | −12.4596 | −0.395793 | −0.197897 | − | 0.980223i | \(-0.563411\pi\) | ||||
−0.197897 | + | 0.980223i | \(0.563411\pi\) | |||||||
\(992\) | 5.21552 | + | 2.36535i | 0.165593 | + | 0.0750998i | ||||
\(993\) | −57.0275 | −1.80971 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 12.7759i | − | 0.405025i | ||||||
\(996\) | 40.5070 | − | 19.9687i | 1.28351 | − | 0.632733i | ||||
\(997\) | 44.8670i | 1.42095i | 0.703721 | + | 0.710477i | \(0.251521\pi\) | ||||
−0.703721 | + | 0.710477i | \(0.748479\pi\) | |||||||
\(998\) | 33.7911 | − | 7.87647i | 1.06964 | − | 0.249325i | ||||
\(999\) | −41.5480 | −1.31452 |
(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 | 392.2.b.g.197.5 | ✓ | 12 | |
4.3 | odd | 2 | 1568.2.b.g.785.12 | 12 | |||
7.2 | even | 3 | 392.2.p.h.165.4 | 24 | |||
7.3 | odd | 6 | 392.2.p.h.373.12 | 24 | |||
7.4 | even | 3 | 392.2.p.h.373.11 | 24 | |||
7.5 | odd | 6 | 392.2.p.h.165.3 | 24 | |||
7.6 | odd | 2 | inner | 392.2.b.g.197.6 | yes | 12 | |
8.3 | odd | 2 | 1568.2.b.g.785.1 | 12 | |||
8.5 | even | 2 | inner | 392.2.b.g.197.8 | yes | 12 | |
28.3 | even | 6 | 1568.2.t.h.177.2 | 24 | |||
28.11 | odd | 6 | 1568.2.t.h.177.12 | 24 | |||
28.19 | even | 6 | 1568.2.t.h.753.11 | 24 | |||
28.23 | odd | 6 | 1568.2.t.h.753.1 | 24 | |||
28.27 | even | 2 | 1568.2.b.g.785.2 | 12 | |||
56.3 | even | 6 | 1568.2.t.h.177.11 | 24 | |||
56.5 | odd | 6 | 392.2.p.h.165.12 | 24 | |||
56.11 | odd | 6 | 1568.2.t.h.177.1 | 24 | |||
56.13 | odd | 2 | inner | 392.2.b.g.197.7 | yes | 12 | |
56.19 | even | 6 | 1568.2.t.h.753.2 | 24 | |||
56.27 | even | 2 | 1568.2.b.g.785.11 | 12 | |||
56.37 | even | 6 | 392.2.p.h.165.11 | 24 | |||
56.45 | odd | 6 | 392.2.p.h.373.3 | 24 | |||
56.51 | odd | 6 | 1568.2.t.h.753.12 | 24 | |||
56.53 | even | 6 | 392.2.p.h.373.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
392.2.b.g.197.5 | ✓ | 12 | 1.1 | even | 1 | trivial | |
392.2.b.g.197.6 | yes | 12 | 7.6 | odd | 2 | inner | |
392.2.b.g.197.7 | yes | 12 | 56.13 | odd | 2 | inner | |
392.2.b.g.197.8 | yes | 12 | 8.5 | even | 2 | inner | |
392.2.p.h.165.3 | 24 | 7.5 | odd | 6 | |||
392.2.p.h.165.4 | 24 | 7.2 | even | 3 | |||
392.2.p.h.165.11 | 24 | 56.37 | even | 6 | |||
392.2.p.h.165.12 | 24 | 56.5 | odd | 6 | |||
392.2.p.h.373.3 | 24 | 56.45 | odd | 6 | |||
392.2.p.h.373.4 | 24 | 56.53 | even | 6 | |||
392.2.p.h.373.11 | 24 | 7.4 | even | 3 | |||
392.2.p.h.373.12 | 24 | 7.3 | odd | 6 | |||
1568.2.b.g.785.1 | 12 | 8.3 | odd | 2 | |||
1568.2.b.g.785.2 | 12 | 28.27 | even | 2 | |||
1568.2.b.g.785.11 | 12 | 56.27 | even | 2 | |||
1568.2.b.g.785.12 | 12 | 4.3 | odd | 2 | |||
1568.2.t.h.177.1 | 24 | 56.11 | odd | 6 | |||
1568.2.t.h.177.2 | 24 | 28.3 | even | 6 | |||
1568.2.t.h.177.11 | 24 | 56.3 | even | 6 | |||
1568.2.t.h.177.12 | 24 | 28.11 | odd | 6 | |||
1568.2.t.h.753.1 | 24 | 28.23 | odd | 6 | |||
1568.2.t.h.753.2 | 24 | 56.19 | even | 6 | |||
1568.2.t.h.753.11 | 24 | 28.19 | even | 6 | |||
1568.2.t.h.753.12 | 24 | 56.51 | odd | 6 |