Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [99,2,Mod(8,99)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(99, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("99.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.j (of order \(10\), degree \(4\), 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: | \(0.790518980011\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 62.2 | ||
Root | \(-0.752864 - 0.902863i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 99.62 |
Dual form | 99.2.j.a.8.2 |
$q$-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 \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) |
\(\chi(n)\) | \(e\left(\frac{7}{10}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.205228 | − | 0.149107i | −0.145118 | − | 0.105434i | 0.512857 | − | 0.858474i | \(-0.328587\pi\) |
−0.657975 | + | 0.753039i | \(0.728587\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.598148 | − | 1.84091i | −0.299074 | − | 0.920456i | ||||
\(5\) | −1.71735 | − | 2.36373i | −0.768021 | − | 1.05709i | −0.996504 | − | 0.0835427i | \(-0.973376\pi\) |
0.228483 | − | 0.973548i | \(-0.426624\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.58586 | − | 0.840196i | 0.977363 | − | 0.317564i | 0.223578 | − | 0.974686i | \(-0.428226\pi\) |
0.753785 | + | 0.657122i | \(0.228226\pi\) | |||||||
\(8\) | −0.308515 | + | 0.949513i | −0.109077 | + | 0.335704i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.741170i | 0.234379i | ||||||||
\(11\) | 2.71994 | + | 1.89788i | 0.820092 | + | 0.572232i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.67869 | + | 2.31052i | −0.465586 | + | 0.640824i | −0.975655 | − | 0.219309i | \(-0.929620\pi\) |
0.510070 | + | 0.860133i | \(0.329620\pi\) | |||||||
\(14\) | −0.655969 | − | 0.213137i | −0.175315 | − | 0.0569633i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.92705 | + | 2.12663i | −0.731763 | + | 0.531657i | ||||
\(17\) | 3.60998 | − | 2.62280i | 0.875549 | − | 0.636124i | −0.0565211 | − | 0.998401i | \(-0.518001\pi\) |
0.932070 | + | 0.362278i | \(0.118001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.81761 | − | 0.590579i | −0.416989 | − | 0.135488i | 0.0930053 | − | 0.995666i | \(-0.470353\pi\) |
−0.509995 | + | 0.860178i | \(0.670353\pi\) | |||||||
\(20\) | −3.32418 | + | 4.57534i | −0.743310 | + | 1.02308i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.275220 | − | 0.795058i | −0.0586771 | − | 0.169507i | ||||
\(23\) | − | 0.816370i | − | 0.170225i | −0.996371 | − | 0.0851124i | \(-0.972875\pi\) | ||
0.996371 | − | 0.0851124i | \(-0.0271249\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.09283 | + | 3.36340i | −0.218567 | + | 0.672680i | ||||
\(26\) | 0.689029 | − | 0.223879i | 0.135130 | − | 0.0439063i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.09345 | − | 4.25777i | −0.584608 | − | 0.804644i | ||||
\(29\) | 2.95006 | + | 9.07936i | 0.547813 | + | 1.68599i | 0.714207 | + | 0.699935i | \(0.246788\pi\) |
−0.166394 | + | 0.986059i | \(0.553212\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.84281 | + | 3.51851i | 0.869795 | + | 0.631943i | 0.930532 | − | 0.366211i | \(-0.119345\pi\) |
−0.0607369 | + | 0.998154i | \(0.519345\pi\) | |||||||
\(32\) | 2.91456 | 0.515226 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.13195 | −0.194127 | ||||||||
\(35\) | −6.42681 | − | 4.66935i | −1.08633 | − | 0.789265i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.83750 | + | 5.65524i | 0.302083 | + | 0.929717i | 0.980750 | + | 0.195270i | \(0.0625583\pi\) |
−0.678666 | + | 0.734447i | \(0.737442\pi\) | |||||||
\(38\) | 0.284966 | + | 0.392222i | 0.0462275 | + | 0.0636267i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.77422 | − | 0.901398i | 0.438642 | − | 0.142524i | ||||
\(41\) | 2.60604 | − | 8.02058i | 0.406996 | − | 1.25260i | −0.512221 | − | 0.858853i | \(-0.671177\pi\) |
0.919217 | − | 0.393751i | \(-0.128823\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11.8763i | − | 1.81112i | −0.424214 | − | 0.905562i | \(-0.639450\pi\) | ||
0.424214 | − | 0.905562i | \(-0.360550\pi\) | |||||||
\(44\) | 1.86690 | − | 6.14238i | 0.281446 | − | 0.925998i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.121726 | + | 0.167542i | −0.0179475 | + | 0.0247027i | ||||
\(47\) | −7.34041 | − | 2.38504i | −1.07071 | − | 0.347894i | −0.279945 | − | 0.960016i | \(-0.590316\pi\) |
−0.790764 | + | 0.612122i | \(0.790316\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.317615 | − | 0.230761i | 0.0453735 | − | 0.0329658i | ||||
\(50\) | 0.725785 | − | 0.527314i | 0.102641 | − | 0.0745734i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.25758 | + | 1.70829i | 0.729094 | + | 0.236897i | ||||
\(53\) | −6.14564 | + | 8.45874i | −0.844168 | + | 1.16190i | 0.140950 | + | 0.990017i | \(0.454984\pi\) |
−0.985118 | + | 0.171881i | \(0.945016\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.185009 | − | 9.68851i | −0.0249466 | − | 1.30640i | ||||
\(56\) | 2.71452i | 0.362743i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.748358 | − | 2.30321i | 0.0982642 | − | 0.302426i | ||||
\(59\) | 0.0887332 | − | 0.0288312i | 0.0115521 | − | 0.00375350i | −0.303235 | − | 0.952916i | \(-0.598067\pi\) |
0.314787 | + | 0.949162i | \(0.398067\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.26024 | + | 1.73457i | 0.161357 | + | 0.222089i | 0.882038 | − | 0.471177i | \(-0.156171\pi\) |
−0.720681 | + | 0.693267i | \(0.756171\pi\) | |||||||
\(62\) | −0.469246 | − | 1.44419i | −0.0595943 | − | 0.183412i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.25595 | + | 3.81867i | 0.656994 | + | 0.477334i | ||||
\(65\) | 8.34434 | 1.03499 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.40778 | −0.171988 | −0.0859941 | − | 0.996296i | \(-0.527407\pi\) | ||||
−0.0859941 | + | 0.996296i | \(0.527407\pi\) | |||||||
\(68\) | −6.98766 | − | 5.07683i | −0.847378 | − | 0.615656i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.622728 | + | 1.91656i | 0.0744303 | + | 0.229073i | ||||
\(71\) | −2.12141 | − | 2.91987i | −0.251765 | − | 0.346525i | 0.664363 | − | 0.747410i | \(-0.268703\pi\) |
−0.916128 | + | 0.400885i | \(0.868703\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.67338 | + | 0.543714i | −0.195854 | + | 0.0636369i | −0.405302 | − | 0.914183i | \(-0.632833\pi\) |
0.209447 | + | 0.977820i | \(0.432833\pi\) | |||||||
\(74\) | 0.466129 | − | 1.43460i | 0.0541863 | − | 0.166768i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.69932i | 0.424341i | ||||||||
\(77\) | 8.62796 | + | 2.62237i | 0.983247 | + | 0.298846i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.19260 | + | 5.77063i | −0.471705 | + | 0.649246i | −0.976884 | − | 0.213768i | \(-0.931426\pi\) |
0.505180 | + | 0.863014i | \(0.331426\pi\) | |||||||
\(80\) | 10.0535 | + | 3.26659i | 1.12402 | + | 0.365216i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.73075 | + | 1.25747i | −0.191130 | + | 0.138864i | ||||
\(83\) | −6.33808 | + | 4.60488i | −0.695695 | + | 0.505452i | −0.878527 | − | 0.477692i | \(-0.841473\pi\) |
0.182833 | + | 0.983144i | \(0.441473\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.3992 | − | 4.02874i | −1.34488 | − | 0.436978i | ||||
\(86\) | −1.77084 | + | 2.43735i | −0.190955 | + | 0.262826i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.64120 | + | 1.99709i | −0.281553 | + | 0.212890i | ||||
\(89\) | 2.06830i | 0.219240i | 0.993974 | + | 0.109620i | \(0.0349633\pi\) | ||||
−0.993974 | + | 0.109620i | \(0.965037\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.39957 | + | 7.38512i | −0.251543 | + | 0.774171i | ||||
\(92\) | −1.50286 | + | 0.488310i | −0.156684 | + | 0.0509099i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.15083 | + | 1.58398i | 0.118699 | + | 0.163375i | ||||
\(95\) | 1.72551 | + | 5.31057i | 0.177034 | + | 0.544853i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.35141 | − | 0.981858i | −0.137215 | − | 0.0996926i | 0.517060 | − | 0.855949i | \(-0.327026\pi\) |
−0.654275 | + | 0.756256i | \(0.727026\pi\) | |||||||
\(98\) | −0.0995913 | −0.0100602 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.84540 | 0.684540 | ||||||||
\(101\) | 7.31972 | + | 5.31809i | 0.728339 | + | 0.529170i | 0.889038 | − | 0.457834i | \(-0.151375\pi\) |
−0.160698 | + | 0.987004i | \(0.551375\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.12132 | − | 15.7618i | −0.504618 | − | 1.55306i | −0.801411 | − | 0.598114i | \(-0.795917\pi\) |
0.296793 | − | 0.954942i | \(-0.404083\pi\) | |||||||
\(104\) | −1.67597 | − | 2.30677i | −0.164342 | − | 0.226198i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.52251 | − | 0.819613i | 0.245008 | − | 0.0796079i | ||||
\(107\) | −2.19803 | + | 6.76484i | −0.212492 | + | 0.653982i | 0.786830 | + | 0.617169i | \(0.211721\pi\) |
−0.999322 | + | 0.0368130i | \(0.988279\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.62045i | 0.825690i | 0.910801 | + | 0.412845i | \(0.135465\pi\) | ||||
−0.910801 | + | 0.412845i | \(0.864535\pi\) | |||||||
\(110\) | −1.40665 | + | 2.01594i | −0.134119 | + | 0.192212i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.78216 | + | 7.95845i | −0.546362 | + | 0.752003i | ||||
\(113\) | −10.8495 | − | 3.52523i | −1.02064 | − | 0.331626i | −0.249556 | − | 0.968360i | \(-0.580285\pi\) |
−0.771083 | + | 0.636735i | \(0.780285\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.92967 | + | 1.40199i | −0.179943 | + | 0.130736i | ||||
\(116\) | 14.9497 | − | 10.8616i | 1.38805 | − | 1.00847i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.0225094 | − | 0.00731376i | −0.00207216 | − | 0.000673286i | ||||
\(119\) | 7.13123 | − | 9.81529i | 0.653719 | − | 0.899767i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.79611 | + | 10.3242i | 0.345101 | + | 0.938566i | ||||
\(122\) | − | 0.543892i | − | 0.0492417i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.58054 | − | 11.0198i | 0.321542 | − | 0.989606i | ||||
\(125\) | −4.06670 | + | 1.32135i | −0.363737 | + | 0.118185i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.69463 | − | 2.33246i | −0.150374 | − | 0.206973i | 0.727184 | − | 0.686443i | \(-0.240829\pi\) |
−0.877558 | + | 0.479470i | \(0.840829\pi\) | |||||||
\(128\) | −2.31057 | − | 7.11122i | −0.204228 | − | 0.628549i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.71249 | − | 1.24420i | −0.150195 | − | 0.109123i | ||||
\(131\) | −2.10155 | −0.183613 | −0.0918067 | − | 0.995777i | \(-0.529264\pi\) | ||||
−0.0918067 | + | 0.995777i | \(0.529264\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.19630 | −0.450576 | ||||||||
\(134\) | 0.288916 | + | 0.209910i | 0.0249586 | + | 0.0181335i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.37665 | + | 4.23690i | 0.118047 | + | 0.363311i | ||||
\(137\) | −2.98245 | − | 4.10498i | −0.254808 | − | 0.350712i | 0.662380 | − | 0.749168i | \(-0.269546\pi\) |
−0.917188 | + | 0.398455i | \(0.869546\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.6282 | − | 5.40283i | 1.41039 | − | 0.458262i | 0.497852 | − | 0.867262i | \(-0.334122\pi\) |
0.912535 | + | 0.409000i | \(0.134122\pi\) | |||||||
\(140\) | −4.75168 | + | 14.6242i | −0.401590 | + | 1.23597i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.915555i | 0.0768317i | ||||||||
\(143\) | −8.95103 | + | 3.09852i | −0.748523 | + | 0.259111i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.3948 | − | 22.5656i | 1.36152 | − | 1.87397i | ||||
\(146\) | 0.424495 | + | 0.137927i | 0.0351315 | + | 0.0114149i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.31171 | − | 6.76535i | 0.765418 | − | 0.556108i | ||||
\(149\) | −4.57623 | + | 3.32483i | −0.374900 | + | 0.272381i | −0.759240 | − | 0.650811i | \(-0.774429\pi\) |
0.384340 | + | 0.923192i | \(0.374429\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.72640 | + | 2.83538i | 0.710145 | + | 0.230740i | 0.641745 | − | 0.766918i | \(-0.278211\pi\) |
0.0683995 | + | 0.997658i | \(0.478211\pi\) | |||||||
\(152\) | 1.12152 | − | 1.54365i | 0.0909677 | − | 0.125206i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.37968 | − | 1.82467i | −0.111178 | − | 0.147036i | ||||
\(155\) | − | 17.4896i | − | 1.40480i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.943653 | + | 2.90426i | −0.0753117 | + | 0.231785i | −0.981625 | − | 0.190821i | \(-0.938885\pi\) |
0.906313 | + | 0.422607i | \(0.138885\pi\) | |||||||
\(158\) | 1.72088 | − | 0.559147i | 0.136906 | − | 0.0444833i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.00531 | − | 6.88922i | −0.395705 | − | 0.544641i | ||||
\(161\) | −0.685911 | − | 2.11102i | −0.0540573 | − | 0.166371i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.39488 | − | 4.64615i | −0.500885 | − | 0.363914i | 0.308470 | − | 0.951234i | \(-0.400183\pi\) |
−0.809355 | + | 0.587320i | \(0.800183\pi\) | |||||||
\(164\) | −16.3240 | −1.27469 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.98737 | 0.154250 | ||||||||
\(167\) | 13.3065 | + | 9.66777i | 1.02969 | + | 0.748115i | 0.968247 | − | 0.249996i | \(-0.0804292\pi\) |
0.0614446 | + | 0.998110i | \(0.480429\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.49672 | + | 4.60642i | 0.115132 | + | 0.354340i | ||||
\(170\) | 1.94394 | + | 2.67561i | 0.149094 | + | 0.205210i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −21.8633 | + | 7.10381i | −1.66706 | + | 0.541660i | ||||
\(173\) | 4.79669 | − | 14.7627i | 0.364686 | − | 1.12239i | −0.585492 | − | 0.810678i | \(-0.699099\pi\) |
0.950178 | − | 0.311709i | \(-0.100901\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.61547i | 0.726861i | ||||||||
\(176\) | −11.9975 | + | 0.229100i | −0.904344 | + | 0.0172691i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.308398 | − | 0.424473i | 0.0231154 | − | 0.0318156i | ||||
\(179\) | 4.93538 | + | 1.60360i | 0.368888 | + | 0.119859i | 0.487594 | − | 0.873071i | \(-0.337875\pi\) |
−0.118706 | + | 0.992929i | \(0.537875\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.29773 | + | 3.12248i | −0.319448 | + | 0.232092i | −0.735940 | − | 0.677047i | \(-0.763259\pi\) |
0.416492 | + | 0.909139i | \(0.363259\pi\) | |||||||
\(182\) | 1.59363 | − | 1.15784i | 0.118128 | − | 0.0858247i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.775154 | + | 0.251863i | 0.0571451 | + | 0.0185676i | ||||
\(185\) | 10.2118 | − | 14.0554i | 0.750788 | − | 1.03337i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.7967 | − | 0.282553i | 1.08204 | − | 0.0206624i | ||||
\(188\) | 14.9396i | 1.08959i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.437719 | − | 1.34716i | 0.0317555 | − | 0.0977334i | ||||
\(191\) | 10.3662 | − | 3.36817i | 0.750069 | − | 0.243712i | 0.0910582 | − | 0.995846i | \(-0.470975\pi\) |
0.659011 | + | 0.752133i | \(0.270975\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.03216 | + | 12.4317i | 0.650149 | + | 0.894853i | 0.999106 | − | 0.0422855i | \(-0.0134639\pi\) |
−0.348956 | + | 0.937139i | \(0.613464\pi\) | |||||||
\(194\) | 0.130946 | + | 0.403009i | 0.00940134 | + | 0.0289344i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.614791 | − | 0.446672i | −0.0439136 | − | 0.0319051i | ||||
\(197\) | −7.24149 | −0.515935 | −0.257967 | − | 0.966154i | \(-0.583053\pi\) | ||||
−0.257967 | + | 0.966154i | \(0.583053\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.3726 | −0.806181 | −0.403090 | − | 0.915160i | \(-0.632064\pi\) | ||||
−0.403090 | + | 0.915160i | \(0.632064\pi\) | |||||||
\(200\) | −2.85643 | − | 2.07532i | −0.201980 | − | 0.146747i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.709247 | − | 2.18284i | −0.0499024 | − | 0.153584i | ||||
\(203\) | 15.2569 | + | 20.9993i | 1.07082 | + | 1.47386i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −23.4339 | + | 7.61415i | −1.63670 | + | 0.531795i | ||||
\(206\) | −1.29915 | + | 3.99838i | −0.0905162 | + | 0.278580i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 10.3330i | − | 0.716463i | ||||||
\(209\) | −3.82295 | − | 5.05595i | −0.264439 | − | 0.349727i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.17376 | + | 2.99193i | −0.149648 | + | 0.205973i | −0.877259 | − | 0.480017i | \(-0.840631\pi\) |
0.727611 | + | 0.685990i | \(0.240631\pi\) | |||||||
\(212\) | 19.2478 | + | 6.25399i | 1.32194 | + | 0.429526i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.45978 | − | 1.06059i | 0.0997885 | − | 0.0725006i | ||||
\(215\) | −28.0724 | + | 20.3958i | −1.91452 | + | 1.39098i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.4791 | + | 5.02946i | 1.05079 | + | 0.341422i | ||||
\(218\) | 1.28537 | − | 1.76916i | 0.0870560 | − | 0.119822i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −17.7250 | + | 6.13575i | −1.19502 | + | 0.413672i | ||||
\(221\) | 12.7438i | 0.857243i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.0875209 | + | 0.269362i | −0.00586083 | + | 0.0180378i | −0.953944 | − | 0.299984i | \(-0.903019\pi\) |
0.948083 | + | 0.318022i | \(0.103019\pi\) | |||||||
\(224\) | 7.53664 | − | 2.44880i | 0.503563 | − | 0.163618i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.70099 | + | 2.34121i | 0.113148 | + | 0.155735i | ||||
\(227\) | −5.64140 | − | 17.3625i | −0.374433 | − | 1.15239i | −0.943860 | − | 0.330345i | \(-0.892835\pi\) |
0.569427 | − | 0.822042i | \(-0.307165\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.3385 | − | 15.5033i | −1.41009 | − | 1.02449i | −0.993310 | − | 0.115479i | \(-0.963160\pi\) |
−0.416777 | − | 0.909009i | \(-0.636840\pi\) | |||||||
\(230\) | 0.605069 | 0.0398971 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.53111 | −0.625748 | ||||||||
\(233\) | 8.73916 | + | 6.34937i | 0.572521 | + | 0.415961i | 0.836020 | − | 0.548699i | \(-0.184877\pi\) |
−0.263499 | + | 0.964660i | \(0.584877\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.96844 | + | 21.4467i | 0.454571 | + | 1.39903i | ||||
\(236\) | −0.106151 | − | 0.146105i | −0.00690986 | − | 0.00951060i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.92705 | + | 0.951057i | −0.189733 | + | 0.0616478i | ||||
\(239\) | 2.29393 | − | 7.06000i | 0.148382 | − | 0.456673i | −0.849048 | − | 0.528315i | \(-0.822824\pi\) |
0.997430 | + | 0.0716420i | \(0.0228239\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.66873i | 0.171908i | 0.996299 | + | 0.0859539i | \(0.0273938\pi\) | ||||
−0.996299 | + | 0.0859539i | \(0.972606\pi\) | |||||||
\(242\) | 0.760344 | − | 2.68484i | 0.0488767 | − | 0.172588i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.43938 | − | 3.35752i | 0.156165 | − | 0.214943i | ||||
\(245\) | −1.09091 | − | 0.354458i | −0.0696957 | − | 0.0226455i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.41576 | − | 3.20824i | 0.280968 | − | 0.204135i | ||||
\(248\) | −4.83495 | + | 3.51280i | −0.307020 | + | 0.223063i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.03162 | + | 0.335194i | 0.0652455 | + | 0.0211996i | ||||
\(251\) | 14.2630 | − | 19.6313i | 0.900271 | − | 1.23912i | −0.0701107 | − | 0.997539i | \(-0.522335\pi\) |
0.970382 | − | 0.241577i | \(-0.0776647\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.54937 | − | 2.22047i | 0.0974081 | − | 0.139600i | ||||
\(254\) | 0.731367i | 0.0458901i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.42906 | − | 10.5535i | 0.214316 | − | 0.659597i | ||||
\(257\) | −15.9360 | + | 5.17791i | −0.994059 | + | 0.322989i | −0.760489 | − | 0.649351i | \(-0.775041\pi\) |
−0.233570 | + | 0.972340i | \(0.575041\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.50303 | + | 13.0798i | 0.590490 | + | 0.812739i | ||||
\(260\) | −4.99116 | − | 15.3612i | −0.309538 | − | 0.952661i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.431296 | + | 0.313355i | 0.0266456 | + | 0.0193591i | ||||
\(263\) | 10.9146 | 0.673021 | 0.336511 | − | 0.941680i | \(-0.390753\pi\) | ||||
0.336511 | + | 0.941680i | \(0.390753\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 30.5484 | 1.87657 | ||||||||
\(266\) | 1.06642 | + | 0.774802i | 0.0653866 | + | 0.0475062i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.842064 | + | 2.59161i | 0.0514373 | + | 0.158308i | ||||
\(269\) | 9.22041 | + | 12.6908i | 0.562178 | + | 0.773772i | 0.991601 | − | 0.129331i | \(-0.0412830\pi\) |
−0.429423 | + | 0.903103i | \(0.641283\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.76289 | + | 0.897717i | −0.167834 | + | 0.0545324i | −0.391728 | − | 0.920081i | \(-0.628123\pi\) |
0.223895 | + | 0.974613i | \(0.428123\pi\) | |||||||
\(272\) | −4.98887 | + | 15.3542i | −0.302495 | + | 0.930983i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.28716i | 0.0777601i | ||||||||
\(275\) | −9.35577 | + | 7.07416i | −0.564174 | + | 0.426588i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.4111 | − | 17.0824i | 0.745709 | − | 1.02638i | −0.252561 | − | 0.967581i | \(-0.581273\pi\) |
0.998270 | − | 0.0587992i | \(-0.0187272\pi\) | |||||||
\(278\) | −4.21817 | − | 1.37057i | −0.252989 | − | 0.0822011i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.41638 | − | 4.66177i | 0.383452 | − | 0.278594i | ||||
\(281\) | −2.50015 | + | 1.81647i | −0.149147 | + | 0.108361i | −0.659856 | − | 0.751392i | \(-0.729383\pi\) |
0.510709 | + | 0.859753i | \(0.329383\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.3272 | − | 6.92961i | −1.26777 | − | 0.411923i | −0.403512 | − | 0.914975i | \(-0.632211\pi\) |
−0.864256 | + | 0.503052i | \(0.832211\pi\) | |||||||
\(284\) | −4.10631 | + | 5.65185i | −0.243664 | + | 0.335375i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.29901 | + | 0.698757i | 0.135943 | + | 0.0413183i | ||||
\(287\) | − | 22.9297i | − | 1.35350i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.899570 | − | 2.76859i | 0.0529159 | − | 0.162858i | ||||
\(290\) | −6.72935 | + | 2.18650i | −0.395161 | + | 0.128396i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.00186 | + | 2.75532i | 0.117150 | + | 0.161243i | ||||
\(293\) | −6.40930 | − | 19.7258i | −0.374435 | − | 1.15239i | −0.943859 | − | 0.330349i | \(-0.892833\pi\) |
0.569423 | − | 0.822044i | \(-0.307167\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.220535 | − | 0.160228i | −0.0128400 | − | 0.00932883i | ||||
\(296\) | −5.93663 | −0.345059 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.43492 | 0.0831229 | ||||||||
\(299\) | 1.88624 | + | 1.37043i | 0.109084 | + | 0.0792543i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.97845 | − | 30.7105i | −0.575148 | − | 1.77012i | ||||
\(302\) | −1.36813 | − | 1.88306i | −0.0787268 | − | 0.108358i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.57619 | − | 2.13673i | 0.377170 | − | 0.122550i | ||||
\(305\) | 1.93578 | − | 5.95772i | 0.110843 | − | 0.341138i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.0077i | − | 0.856533i | −0.903652 | − | 0.428267i | \(-0.859124\pi\) | ||
0.903652 | − | 0.428267i | \(-0.140876\pi\) | |||||||
\(308\) | −0.333256 | − | 17.4519i | −0.0189890 | − | 0.994413i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.60781 | + | 3.58935i | −0.148114 | + | 0.203861i | ||||
\(311\) | 1.95824 | + | 0.636270i | 0.111042 | + | 0.0360796i | 0.364011 | − | 0.931395i | \(-0.381407\pi\) |
−0.252969 | + | 0.967474i | \(0.581407\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.1223 | − | 14.6197i | 1.13738 | − | 0.826355i | 0.150628 | − | 0.988591i | \(-0.451870\pi\) |
0.986752 | + | 0.162236i | \(0.0518705\pi\) | |||||||
\(314\) | 0.626709 | − | 0.455330i | 0.0353672 | − | 0.0256958i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.1310 | + | 4.26652i | 0.738677 | + | 0.240011i | ||||
\(317\) | −0.254351 | + | 0.350085i | −0.0142858 | + | 0.0196627i | −0.816100 | − | 0.577910i | \(-0.803868\pi\) |
0.801814 | + | 0.597573i | \(0.203868\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.20754 | + | 30.2941i | −0.515523 | + | 1.69615i | ||||
\(320\) | − | 18.9816i | − | 1.06111i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.173999 | + | 0.535513i | −0.00969657 | + | 0.0298430i | ||||
\(323\) | −8.11053 | + | 2.63527i | −0.451282 | + | 0.146630i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.93668 | − | 8.17113i | −0.329308 | − | 0.453253i | ||||
\(326\) | 0.619634 | + | 1.90704i | 0.0343183 | + | 0.105621i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.81164 | + | 4.94895i | 0.376110 | + | 0.273260i | ||||
\(329\) | −20.9852 | −1.15695 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.3090 | −0.951391 | −0.475696 | − | 0.879610i | \(-0.657804\pi\) | ||||
−0.475696 | + | 0.879610i | \(0.657804\pi\) | |||||||
\(332\) | 12.2683 | + | 8.91344i | 0.673310 | + | 0.489189i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.28934 | − | 3.96819i | −0.0705497 | − | 0.217130i | ||||
\(335\) | 2.41766 | + | 3.32762i | 0.132091 | + | 0.181807i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.8381 | − | 7.74548i | 1.29855 | − | 0.421923i | 0.423471 | − | 0.905910i | \(-0.360812\pi\) |
0.875076 | + | 0.483986i | \(0.160812\pi\) | |||||||
\(338\) | 0.379680 | − | 1.16853i | 0.0206519 | − | 0.0635599i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 25.2356i | 1.36859i | ||||||||
\(341\) | 6.49444 | + | 18.7612i | 0.351694 | + | 1.01598i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.5596 | + | 14.5341i | −0.570166 | + | 0.784766i | ||||
\(344\) | 11.2767 | + | 3.66403i | 0.608001 | + | 0.197551i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.18563 | + | 2.31449i | −0.171260 | + | 0.124428i | ||||
\(347\) | 16.8866 | − | 12.2688i | 0.906519 | − | 0.658625i | −0.0336127 | − | 0.999435i | \(-0.510701\pi\) |
0.940132 | + | 0.340810i | \(0.110701\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.1385 | − | 5.56865i | −0.917405 | − | 0.298083i | −0.188003 | − | 0.982168i | \(-0.560202\pi\) |
−0.729402 | + | 0.684085i | \(0.760202\pi\) | |||||||
\(350\) | 1.43373 | − | 1.97336i | 0.0766361 | − | 0.105481i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.92742 | + | 5.53148i | 0.422533 | + | 0.294829i | ||||
\(353\) | 16.2953i | 0.867313i | 0.901078 | + | 0.433656i | \(0.142777\pi\) | ||||
−0.901078 | + | 0.433656i | \(0.857223\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.25858 | + | 10.0289i | −0.172947 | + | 0.532277i | ||||
\(356\) | 3.80756 | − | 1.23715i | 0.201800 | − | 0.0655689i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.773769 | − | 1.06500i | −0.0408949 | − | 0.0562871i | ||||
\(359\) | 7.65875 | + | 23.5712i | 0.404213 | + | 1.24404i | 0.921550 | + | 0.388259i | \(0.126923\pi\) |
−0.517337 | + | 0.855782i | \(0.673077\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.4164 | − | 9.02103i | −0.653494 | − | 0.474791i | ||||
\(362\) | 1.34760 | 0.0708281 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 15.0306 | 0.787820 | ||||||||
\(365\) | 4.15897 | + | 3.02167i | 0.217690 | + | 0.158161i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.76683 | + | 8.51544i | 0.144428 | + | 0.444502i | 0.996937 | − | 0.0782097i | \(-0.0249204\pi\) |
−0.852509 | + | 0.522712i | \(0.824920\pi\) | |||||||
\(368\) | 1.73611 | + | 2.38956i | 0.0905012 | + | 0.124564i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.19150 | + | 1.36190i | −0.217906 | + | 0.0708018i | ||||
\(371\) | −8.78474 | + | 27.0367i | −0.456081 | + | 1.40367i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.9007i | 0.875088i | 0.899197 | + | 0.437544i | \(0.144152\pi\) | ||||
−0.899197 | + | 0.437544i | \(0.855848\pi\) | |||||||
\(374\) | −3.07882 | − | 2.14830i | −0.159202 | − | 0.111086i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.52926 | − | 6.23399i | 0.233579 | − | 0.321493i | ||||
\(377\) | −25.9303 | − | 8.42527i | −1.33548 | − | 0.433923i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.9625 | + | 11.5975i | −0.819940 | + | 0.595722i | −0.916695 | − | 0.399587i | \(-0.869154\pi\) |
0.0967550 | + | 0.995308i | \(0.469154\pi\) | |||||||
\(380\) | 8.74419 | − | 6.35302i | 0.448567 | − | 0.325903i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.62964 | − | 0.854422i | −0.134544 | − | 0.0437160i | ||||
\(383\) | −2.93889 | + | 4.04503i | −0.150170 | + | 0.206691i | −0.877474 | − | 0.479624i | \(-0.840773\pi\) |
0.727304 | + | 0.686315i | \(0.240773\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.61865 | − | 24.8977i | −0.439247 | − | 1.26890i | ||||
\(386\) | − | 3.89808i | − | 0.198407i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.999169 | + | 3.07513i | −0.0507251 | + | 0.156116i | ||||
\(389\) | 9.37115 | − | 3.04487i | 0.475136 | − | 0.154381i | −0.0616527 | − | 0.998098i | \(-0.519637\pi\) |
0.536789 | + | 0.843716i | \(0.319637\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.14118 | − | 2.94708i | −0.108284 | − | 0.149040i | ||||
\(392\) | 0.121121 | + | 0.372773i | 0.00611754 | + | 0.0188279i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.48615 | + | 1.07975i | 0.0748714 | + | 0.0543972i | ||||
\(395\) | 20.8403 | 1.04859 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.0245 | −0.954812 | −0.477406 | − | 0.878683i | \(-0.658423\pi\) | ||||
−0.477406 | + | 0.878683i | \(0.658423\pi\) | |||||||
\(398\) | 2.33397 | + | 1.69573i | 0.116991 | + | 0.0849991i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.95391 | − | 12.1689i | −0.197696 | − | 0.608445i | ||||
\(401\) | −18.0482 | − | 24.8413i | −0.901286 | − | 1.24051i | −0.970056 | − | 0.242881i | \(-0.921907\pi\) |
0.0687699 | − | 0.997633i | \(-0.478093\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.2592 | + | 5.28293i | −0.809928 | + | 0.263162i | ||||
\(404\) | 5.41185 | − | 16.6560i | 0.269250 | − | 0.828665i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 6.58454i | − | 0.326785i | ||||||
\(407\) | −5.73509 | + | 18.8693i | −0.284278 | + | 0.935315i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.97905 | + | 9.60583i | −0.345092 | + | 0.474978i | −0.945920 | − | 0.324400i | \(-0.894838\pi\) |
0.600828 | + | 0.799378i | \(0.294838\pi\) | |||||||
\(410\) | 5.94461 | + | 1.93152i | 0.293584 | + | 0.0953911i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −25.9528 | + | 18.8558i | −1.27860 | + | 0.928958i | ||||
\(413\) | 0.205228 | − | 0.149107i | 0.0100986 | − | 0.00733706i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21.7694 | + | 7.07330i | 1.06862 | + | 0.347215i | ||||
\(416\) | −4.89265 | + | 6.73416i | −0.239882 | + | 0.330169i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.0306992 | + | 1.60765i | 0.00150155 | + | 0.0786326i | ||||
\(419\) | 10.0629i | 0.491606i | 0.969320 | + | 0.245803i | \(0.0790516\pi\) | ||||
−0.969320 | + | 0.245803i | \(0.920948\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.93337 | + | 5.95029i | −0.0942265 | + | 0.289999i | −0.987051 | − | 0.160405i | \(-0.948720\pi\) |
0.892825 | + | 0.450404i | \(0.148720\pi\) | |||||||
\(422\) | 0.892232 | − | 0.289904i | 0.0434332 | − | 0.0141123i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.13566 | − | 8.44502i | −0.297974 | − | 0.410126i | ||||
\(425\) | 4.87643 | + | 15.0081i | 0.236541 | + | 0.728000i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.71618 | + | 3.42651i | 0.228232 | + | 0.165820i | ||||
\(428\) | 13.7682 | 0.665512 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.80238 | 0.424489 | ||||||||
\(431\) | −15.8885 | − | 11.5436i | −0.765321 | − | 0.556038i | 0.135217 | − | 0.990816i | \(-0.456827\pi\) |
−0.900538 | + | 0.434778i | \(0.856827\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.66882 | + | 29.7576i | 0.464654 | + | 1.43006i | 0.859418 | + | 0.511274i | \(0.170826\pi\) |
−0.394764 | + | 0.918783i | \(0.629174\pi\) | |||||||
\(434\) | −2.42681 | − | 3.34022i | −0.116491 | − | 0.160335i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.8695 | − | 5.15631i | 0.760011 | − | 0.246942i | ||||
\(437\) | −0.482131 | + | 1.48385i | −0.0230634 | + | 0.0709820i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 20.1935i | − | 0.963782i | −0.876231 | − | 0.481891i | \(-0.839950\pi\) | ||
0.876231 | − | 0.481891i | \(-0.160050\pi\) | |||||||
\(440\) | 9.25644 | + | 2.81339i | 0.441283 | + | 0.134123i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.90019 | − | 2.61539i | 0.0903828 | − | 0.124401i | ||||
\(443\) | 23.1752 | + | 7.53009i | 1.10109 | + | 0.357765i | 0.802521 | − | 0.596624i | \(-0.203491\pi\) |
0.298567 | + | 0.954389i | \(0.403491\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.88890 | − | 3.55199i | 0.231756 | − | 0.168381i | ||||
\(446\) | 0.0581253 | − | 0.0422305i | 0.00275231 | − | 0.00199967i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16.7996 | + | 5.45852i | 0.793706 | + | 0.257891i | ||||
\(449\) | 1.94082 | − | 2.67131i | 0.0915930 | − | 0.126067i | −0.760761 | − | 0.649032i | \(-0.775174\pi\) |
0.852354 | + | 0.522965i | \(0.175174\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.3104 | − | 16.8695i | 1.05055 | − | 0.794354i | ||||
\(452\) | 22.0817i | 1.03863i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.43109 | + | 4.40443i | −0.0671642 | + | 0.206710i | ||||
\(455\) | 21.5773 | − | 7.01089i | 1.01156 | − | 0.328675i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.17968 | − | 12.6347i | −0.429407 | − | 0.591028i | 0.538410 | − | 0.842683i | \(-0.319025\pi\) |
−0.967817 | + | 0.251655i | \(0.919025\pi\) | |||||||
\(458\) | 2.06760 | + | 6.36342i | 0.0966126 | + | 0.297343i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.73517 | + | 2.71376i | 0.174153 | + | 0.126530i | ||||
\(461\) | −36.5685 | −1.70316 | −0.851582 | − | 0.524221i | \(-0.824356\pi\) | ||||
−0.851582 | + | 0.524221i | \(0.824356\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.45531 | 0.207056 | 0.103528 | − | 0.994627i | \(-0.466987\pi\) | ||||
0.103528 | + | 0.994627i | \(0.466987\pi\) | |||||||
\(464\) | −27.9434 | − | 20.3021i | −1.29724 | − | 0.942499i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.846784 | − | 2.60613i | −0.0392265 | − | 0.120727i | ||||
\(467\) | −24.4676 | − | 33.6768i | −1.13223 | − | 1.55838i | −0.783769 | − | 0.621052i | \(-0.786706\pi\) |
−0.348458 | − | 0.937325i | \(-0.613294\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.64033 | + | 1.18282i | −0.168095 | + | 0.0546173i | ||||
\(470\) | 1.76772 | − | 5.44049i | 0.0815390 | − | 0.250951i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.0931482i | 0.00428749i | ||||||||
\(473\) | 22.5398 | − | 32.3029i | 1.03638 | − | 1.48529i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.97270 | − | 5.46796i | 0.182280 | − | 0.250887i | ||||
\(476\) | −22.3346 | − | 7.25696i | −1.02371 | − | 0.332622i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.52347 | + | 1.10687i | −0.0696819 | + | 0.0506269i | ||||
\(479\) | 2.84896 | − | 2.06989i | 0.130172 | − | 0.0945756i | −0.520794 | − | 0.853682i | \(-0.674364\pi\) |
0.650966 | + | 0.759107i | \(0.274364\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.1512 | − | 5.24783i | −0.736430 | − | 0.239281i | ||||
\(482\) | 0.397925 | − | 0.547696i | 0.0181250 | − | 0.0249469i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.7353 | − | 13.1637i | 0.760697 | − | 0.598351i | ||||
\(485\) | 4.88056i | 0.221615i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.85775 | − | 30.3390i | 0.446697 | − | 1.37479i | −0.433914 | − | 0.900954i | \(-0.642868\pi\) |
0.880611 | − | 0.473839i | \(-0.157132\pi\) | |||||||
\(488\) | −2.03580 | + | 0.661472i | −0.0921564 | + | 0.0299434i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.171033 | + | 0.235407i | 0.00772648 | + | 0.0106346i | ||||
\(491\) | 7.54595 | + | 23.2241i | 0.340544 | + | 1.04809i | 0.963926 | + | 0.266170i | \(0.0857581\pi\) |
−0.623382 | + | 0.781917i | \(0.714242\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 34.4630 | + | 25.0389i | 1.55214 | + | 1.12769i | ||||
\(494\) | −1.38461 | −0.0622964 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21.6577 | −0.972460 | ||||||||
\(497\) | −7.93893 | − | 5.76797i | −0.356110 | − | 0.258729i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.19057 | − | 22.1303i | −0.321894 | − | 0.990689i | −0.972823 | − | 0.231550i | \(-0.925620\pi\) |
0.650929 | − | 0.759139i | \(-0.274380\pi\) | |||||||
\(500\) | 4.86498 | + | 6.69608i | 0.217569 | + | 0.299458i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.85431 | + | 1.90218i | −0.261291 | + | 0.0848985i | ||||
\(503\) | 11.2856 | − | 34.7334i | 0.503199 | − | 1.54869i | −0.300579 | − | 0.953757i | \(-0.597180\pi\) |
0.803778 | − | 0.594930i | \(-0.202820\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 26.4348i | − | 1.17633i | ||||||
\(506\) | −0.649061 | + | 0.224681i | −0.0288543 | + | 0.00998829i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.28022 | + | 4.51483i | −0.145536 | + | 0.200313i | ||||
\(509\) | −23.6347 | − | 7.67938i | −1.04759 | − | 0.340383i | −0.265868 | − | 0.964009i | \(-0.585659\pi\) |
−0.781722 | + | 0.623627i | \(0.785659\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.87030 | + | 2.81193i | −0.171212 | + | 0.124393i | ||||
\(512\) | −14.3757 | + | 10.4445i | −0.635321 | + | 0.461588i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.04257 | + | 1.31351i | 0.178310 | + | 0.0579364i | ||||
\(515\) | −28.4615 | + | 39.1739i | −1.25416 | + | 1.72621i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.4389 | − | 20.4184i | −0.679003 | − | 0.897999i | ||||
\(518\) | − | 4.10130i | − | 0.180201i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.57436 | + | 7.92306i | −0.112893 | + | 0.347449i | ||||
\(521\) | 9.26334 | − | 3.00984i | 0.405834 | − | 0.131864i | −0.0989844 | − | 0.995089i | \(-0.531559\pi\) |
0.504819 | + | 0.863225i | \(0.331559\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.5526 | + | 26.9118i | 0.854975 | + | 1.17677i | 0.982744 | + | 0.184968i | \(0.0592182\pi\) |
−0.127769 | + | 0.991804i | \(0.540782\pi\) | |||||||
\(524\) | 1.25704 | + | 3.86877i | 0.0549140 | + | 0.169008i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.23997 | − | 1.62743i | −0.0976674 | − | 0.0709595i | ||||
\(527\) | 26.7108 | 1.16354 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.3335 | 0.971023 | ||||||||
\(530\) | −6.26937 | − | 4.55496i | −0.272324 | − | 0.197855i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.10816 | + | 9.56592i | 0.134756 | + | 0.414735i | ||||
\(533\) | 14.1570 | + | 19.4854i | 0.613207 | + | 0.844007i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.7650 | − | 6.42205i | 0.854517 | − | 0.277649i | ||||
\(536\) | 0.434323 | − | 1.33671i | 0.0187599 | − | 0.0577371i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 3.97933i | − | 0.171561i | ||||||
\(539\) | 1.30185 | − | 0.0248597i | 0.0560746 | − | 0.00107078i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.85075 | + | 9.42925i | −0.294537 | + | 0.405395i | −0.930481 | − | 0.366340i | \(-0.880611\pi\) |
0.635944 | + | 0.771735i | \(0.280611\pi\) | |||||||
\(542\) | 0.700877 | + | 0.227729i | 0.0301052 | + | 0.00978178i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.5215 | − | 7.64432i | 0.451106 | − | 0.327748i | ||||
\(545\) | 20.3764 | − | 14.8043i | 0.872829 | − | 0.634147i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.773004 | + | 0.251164i | 0.0330513 | + | 0.0107390i | 0.325496 | − | 0.945543i | \(-0.394469\pi\) |
−0.292445 | + | 0.956282i | \(0.594469\pi\) | |||||||
\(548\) | −5.77297 | + | 7.94581i | −0.246609 | + | 0.339428i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.97487 | − | 0.0568072i | 0.126849 | − | 0.00242227i | ||||
\(551\) | − | 18.2450i | − | 0.777264i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.99302 | + | 18.4446i | −0.254849 | + | 0.784345i | ||||
\(554\) | −5.09419 | + | 1.65520i | −0.216431 | + | 0.0703228i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19.8923 | − | 27.3794i | −0.843620 | − | 1.16114i | ||||
\(557\) | 2.14843 | + | 6.61219i | 0.0910320 | + | 0.280168i | 0.986199 | − | 0.165563i | \(-0.0529440\pi\) |
−0.895167 | + | 0.445730i | \(0.852944\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.4405 | + | 19.9367i | 1.16061 | + | 0.843233i | ||||
\(560\) | 28.7416 | 1.21455 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.783948 | 0.0330689 | ||||||||
\(563\) | −23.2654 | − | 16.9033i | −0.980519 | − | 0.712388i | −0.0226941 | − | 0.999742i | \(-0.507224\pi\) |
−0.957824 | + | 0.287354i | \(0.907224\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.2998 | + | 31.6994i | 0.433314 | + | 1.33360i | ||||
\(566\) | 3.34367 | + | 4.60217i | 0.140545 | + | 0.193444i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.42694 | − | 1.11348i | 0.143791 | − | 0.0467207i | ||||
\(569\) | −3.22890 | + | 9.93752i | −0.135362 | + | 0.416602i | −0.995646 | − | 0.0932129i | \(-0.970286\pi\) |
0.860284 | + | 0.509815i | \(0.170286\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.2530i | 0.889409i | 0.895677 | + | 0.444704i | \(0.146691\pi\) | ||||
−0.895677 | + | 0.444704i | \(0.853309\pi\) | |||||||
\(572\) | 11.0581 | + | 14.6247i | 0.462364 | + | 0.611489i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.41897 | + | 4.70580i | −0.142705 | + | 0.196416i | ||||
\(575\) | 2.74578 | + | 0.892157i | 0.114507 | + | 0.0372055i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.6856 | + | 9.21665i | −0.528110 | + | 0.383694i | −0.819650 | − | 0.572864i | \(-0.805832\pi\) |
0.291541 | + | 0.956558i | \(0.405832\pi\) | |||||||
\(578\) | −0.597432 | + | 0.434060i | −0.0248499 | + | 0.0180545i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −51.3477 | − | 16.6839i | −2.13210 | − | 0.692761i | ||||
\(581\) | −12.5204 | + | 17.2328i | −0.519432 | + | 0.714937i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −32.7694 | + | 11.3436i | −1.35717 | + | 0.469803i | ||||
\(584\) | − | 1.75664i | − | 0.0726903i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.62588 | + | 5.00395i | −0.0671646 | + | 0.206711i | ||||
\(587\) | −19.1691 | + | 6.22843i | −0.791195 | + | 0.257075i | −0.676613 | − | 0.736339i | \(-0.736553\pi\) |
−0.114582 | + | 0.993414i | \(0.536553\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.72441 | − | 9.25536i | −0.277075 | − | 0.381360i | ||||
\(590\) | 0.0213688 | + | 0.0657664i | 0.000879739 | + | 0.00270756i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −17.4051 | − | 12.6455i | −0.715343 | − | 0.519727i | ||||
\(593\) | 40.5694 | 1.66599 | 0.832993 | − | 0.553284i | \(-0.186626\pi\) | ||||
0.832993 | + | 0.553284i | \(0.186626\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −35.4475 | −1.45320 | ||||||||
\(596\) | 8.85798 | + | 6.43570i | 0.362837 | + | 0.263617i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.182768 | − | 0.562502i | −0.00747394 | − | 0.0230024i | ||||
\(599\) | −6.42889 | − | 8.84861i | −0.262678 | − | 0.361545i | 0.657223 | − | 0.753696i | \(-0.271731\pi\) |
−0.919901 | + | 0.392151i | \(0.871731\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.5556 | − | 5.05433i | 0.634527 | − | 0.206170i | 0.0259478 | − | 0.999663i | \(-0.491740\pi\) |
0.608580 | + | 0.793493i | \(0.291740\pi\) | |||||||
\(602\) | −2.53129 | + | 7.79050i | −0.103168 | + | 0.317517i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 17.7605i | − | 0.722665i | ||||||
\(605\) | 17.8844 | − | 26.7032i | 0.727104 | − | 1.08564i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.0272 | + | 19.3068i | −0.569348 | + | 0.783641i | −0.992477 | − | 0.122429i | \(-0.960932\pi\) |
0.423129 | + | 0.906069i | \(0.360932\pi\) | |||||||
\(608\) | −5.29755 | − | 1.72128i | −0.214844 | − | 0.0698070i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.28561 | + | 0.934052i | −0.0520529 | + | 0.0378187i | ||||
\(611\) | 17.8330 | − | 12.9564i | 0.721445 | − | 0.524161i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.0461533 | + | 0.0149961i | 0.00186411 | + | 0.000605687i | 0.309949 | − | 0.950753i | \(-0.399688\pi\) |
−0.308085 | + | 0.951359i | \(0.599688\pi\) | |||||||
\(614\) | −2.23774 | + | 3.07999i | −0.0903080 | + | 0.124298i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.15183 | + | 7.38332i | −0.207573 | + | 0.297482i | ||||
\(617\) | 8.24561i | 0.331956i | 0.986129 | + | 0.165978i | \(0.0530780\pi\) | ||||
−0.986129 | + | 0.165978i | \(0.946922\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.537464 | + | 1.65414i | −0.0216025 | + | 0.0664857i | −0.961277 | − | 0.275585i | \(-0.911128\pi\) |
0.939674 | + | 0.342071i | \(0.111128\pi\) | |||||||
\(620\) | −32.1968 | + | 10.4614i | −1.29305 | + | 0.420139i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.307013 | − | 0.422567i | −0.0123101 | − | 0.0169434i | ||||
\(623\) | 1.73778 | + | 5.34834i | 0.0696227 | + | 0.214277i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.4126 | + | 17.7368i | 0.976506 | + | 0.709473i | ||||
\(626\) | −6.30955 | −0.252180 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.91094 | 0.235872 | ||||||||
\(629\) | 21.4659 | + | 15.5959i | 0.855903 | + | 0.621850i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.14182 | − | 25.0580i | −0.324121 | − | 0.997541i | −0.971836 | − | 0.235659i | \(-0.924275\pi\) |
0.647715 | − | 0.761883i | \(-0.275725\pi\) | |||||||
\(632\) | −4.18580 | − | 5.76126i | −0.166502 | − | 0.229171i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.104400 | − | 0.0339216i | 0.00414625 | − | 0.00134720i | ||||
\(635\) | −2.60303 | + | 8.01130i | −0.103298 | + | 0.317919i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.12123i | 0.0444249i | ||||||||
\(638\) | 6.40670 | − | 4.84429i | 0.253644 | − | 0.191787i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −12.8409 | + | 17.6740i | −0.507582 | + | 0.698626i | ||||
\(641\) | −8.27017 | − | 2.68714i | −0.326652 | − | 0.106136i | 0.141100 | − | 0.989995i | \(-0.454936\pi\) |
−0.467752 | + | 0.883860i | \(0.654936\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.4877 | − | 12.7055i | 0.689646 | − | 0.501057i | −0.186897 | − | 0.982379i | \(-0.559843\pi\) |
0.876544 | + | 0.481322i | \(0.159843\pi\) | |||||||
\(644\) | −3.47592 | + | 2.52540i | −0.136970 | + | 0.0995148i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.05744 | + | 0.668503i | 0.0809489 | + | 0.0263019i | ||||
\(647\) | −17.2616 | + | 23.7586i | −0.678625 | + | 0.934048i | −0.999916 | − | 0.0129330i | \(-0.995883\pi\) |
0.321291 | + | 0.946980i | \(0.395883\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.296067 | + | 0.0899860i | 0.0116216 | + | 0.00353226i | ||||
\(650\) | 2.56214i | 0.100495i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.72806 | + | 14.5515i | −0.185165 | + | 0.569880i | ||||
\(653\) | −22.5339 | + | 7.32170i | −0.881818 | + | 0.286520i | −0.714712 | − | 0.699419i | \(-0.753442\pi\) |
−0.167106 | + | 0.985939i | \(0.553442\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.60909 | + | 4.96749i | 0.141019 | + | 0.194096i | ||||
\(656\) | 9.42876 | + | 29.0187i | 0.368131 | + | 1.13299i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.30674 | + | 3.12903i | 0.167894 | + | 0.121982i | ||||
\(659\) | 34.5941 | 1.34759 | 0.673797 | − | 0.738916i | \(-0.264662\pi\) | ||||
0.673797 | + | 0.738916i | \(0.264662\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.4913 | 1.38045 | 0.690225 | − | 0.723595i | \(-0.257512\pi\) | ||||
0.690225 | + | 0.723595i | \(0.257512\pi\) | |||||||
\(662\) | 3.55229 | + | 2.58089i | 0.138064 | + | 0.100309i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.41700 | − | 7.43877i | −0.0937979 | − | 0.288680i | ||||
\(665\) | 8.92385 | + | 12.2826i | 0.346052 | + | 0.476300i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.41211 | − | 2.40834i | 0.286998 | − | 0.0932513i | ||||
\(668\) | 9.83822 | − | 30.2789i | 0.380652 | − | 1.17153i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 1.04341i | − | 0.0403104i | ||||||
\(671\) | 0.135765 | + | 7.10971i | 0.00524115 | + | 0.274467i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.2854 | + | 16.9095i | −0.473569 | + | 0.651812i | −0.977253 | − | 0.212076i | \(-0.931978\pi\) |
0.503684 | + | 0.863888i | \(0.331978\pi\) | |||||||
\(674\) | −6.04715 | − | 1.96484i | −0.232928 | − | 0.0756827i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.58475 | − | 5.51064i | 0.291721 | − | 0.211948i | ||||
\(677\) | 19.6090 | − | 14.2468i | 0.753634 | − | 0.547547i | −0.143317 | − | 0.989677i | \(-0.545777\pi\) |
0.896951 | + | 0.442130i | \(0.145777\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.31951 | − | 1.40350i | −0.165768 | − | 0.0538612i | ||||
\(680\) | 7.65068 | − | 10.5303i | 0.293390 | − | 0.403817i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.46458 | − | 4.81868i | 0.0560817 | − | 0.184517i | ||||
\(683\) | − | 17.6311i | − | 0.674636i | −0.941391 | − | 0.337318i | \(-0.890480\pi\) | ||
0.941391 | − | 0.337318i | \(-0.109520\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.58116 | + | 14.0994i | −0.175037 | + | 0.538709i | ||||
\(686\) | 4.33425 | − | 1.40828i | 0.165482 | − | 0.0537685i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 25.2565 | + | 34.7626i | 0.962896 | + | 1.32531i | ||||
\(689\) | −9.22748 | − | 28.3993i | −0.351539 | − | 1.08193i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.5718 | − | 17.1259i | −0.896713 | − | 0.651500i | 0.0409063 | − | 0.999163i | \(-0.486976\pi\) |
−0.937620 | + | 0.347663i | \(0.886976\pi\) | |||||||
\(692\) | −30.0459 | −1.14218 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.29496 | −0.200994 | ||||||||
\(695\) | −41.3272 | − | 30.0260i | −1.56763 | − | 1.13895i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.6286 | − | 35.7893i | −0.440466 | − | 1.35562i | ||||
\(698\) | 2.68698 | + | 3.69831i | 0.101704 | + | 0.139983i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 17.7012 | − | 5.75148i | 0.669044 | − | 0.217385i | ||||
\(701\) | −4.54301 | + | 13.9820i | −0.171587 | + | 0.528091i | −0.999461 | − | 0.0328229i | \(-0.989550\pi\) |
0.827874 | + | 0.560914i | \(0.189550\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 11.3642i | − | 0.428611i | ||||||
\(704\) | 7.04848 | + | 20.3617i | 0.265649 | + | 0.767411i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.42974 | − | 3.34425i | 0.0914445 | − | 0.125863i | ||||
\(707\) | 23.3960 | + | 7.60182i | 0.879897 | + | 0.285896i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.72312 | + | 6.33772i | −0.327604 | + | 0.238018i | −0.739413 | − | 0.673252i | \(-0.764897\pi\) |
0.411810 | + | 0.911270i | \(0.364897\pi\) | |||||||
\(710\) | 2.16412 | − | 1.57233i | 0.0812180 | − | 0.0590083i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.96388 | − | 0.638103i | −0.0735995 | − | 0.0239139i | ||||
\(713\) | 2.87241 | − | 3.95353i | 0.107572 | − | 0.148061i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.6961 | + | 15.8366i | 0.848785 | + | 0.592254i | ||||
\(716\) | − | 10.0448i | − | 0.375391i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.94284 | − | 5.97944i | 0.0725060 | − | 0.223151i | ||||
\(719\) | 30.1960 | − | 9.81128i | 1.12612 | − | 0.365899i | 0.314020 | − | 0.949416i | \(-0.398324\pi\) |
0.812101 | + | 0.583517i | \(0.198324\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.4860 | − | 36.4549i | −0.986390 | − | 1.35765i | ||||
\(722\) | 1.20309 | + | 3.70273i | 0.0447744 | + | 0.137801i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.31889 | + | 6.04403i | 0.309169 | + | 0.224625i | ||||
\(725\) | −33.7614 | −1.25387 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.6418 | 0.876828 | 0.438414 | − | 0.898773i | \(-0.355540\pi\) | ||||
0.438414 | + | 0.898773i | \(0.355540\pi\) | |||||||
\(728\) | −6.27196 | − | 4.55685i | −0.232454 | − | 0.168888i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.402984 | − | 1.24026i | −0.0149151 | − | 0.0459040i | ||||
\(731\) | −31.1493 | − | 42.8733i | −1.15210 | − | 1.58573i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.6206 | − | 5.07543i | 0.576959 | − | 0.187465i | −0.00597872 | − | 0.999982i | \(-0.501903\pi\) |
0.582938 | + | 0.812517i | \(0.301903\pi\) | |||||||
\(734\) | 0.701877 | − | 2.16016i | 0.0259068 | − | 0.0797328i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 2.37936i | − | 0.0877043i | ||||||
\(737\) | −3.82908 | − | 2.67181i | −0.141046 | − | 0.0984172i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.4813 | − | 28.1901i | 0.753417 | − | 1.03699i | −0.244316 | − | 0.969696i | \(-0.578563\pi\) |
0.997733 | − | 0.0672942i | \(-0.0214366\pi\) | |||||||
\(740\) | −31.9829 | − | 10.3919i | −1.17571 | − | 0.382013i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.83422 | − | 4.23881i | 0.214181 | − | 0.155611i | ||||
\(743\) | −42.7101 | + | 31.0307i | −1.56688 | + | 1.13841i | −0.636813 | + | 0.771019i | \(0.719748\pi\) |
−0.930068 | + | 0.367387i | \(0.880252\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.7180 | + | 5.10708i | 0.575862 | + | 0.187109i | ||||
\(746\) | 2.52001 | − | 3.46850i | 0.0922643 | − | 0.126991i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.37077 | − | 27.0704i | −0.342629 | − | 0.989791i | ||||
\(749\) | 19.3397i | 0.706657i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.8766 | − | 48.8631i | 0.579345 | − | 1.78304i | −0.0415382 | − | 0.999137i | \(-0.513226\pi\) |
0.620883 | − | 0.783903i | \(-0.286774\pi\) | |||||||
\(752\) | 26.5578 | − | 8.62917i | 0.968465 | − | 0.314673i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.06535 | + | 5.59548i | 0.148051 | + | 0.203775i | ||||
\(755\) | −8.28421 | − | 25.4962i | −0.301493 | − | 0.927900i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.71877 | + | 4.15493i | 0.207852 | + | 0.151013i | 0.686841 | − | 0.726807i | \(-0.258997\pi\) |
−0.478989 | + | 0.877821i | \(0.658997\pi\) | |||||||
\(758\) | 5.00521 | 0.181797 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.57481 | −0.202219 | ||||||||
\(761\) | 23.5688 | + | 17.1238i | 0.854370 | + | 0.620736i | 0.926347 | − | 0.376670i | \(-0.122931\pi\) |
−0.0719775 | + | 0.997406i | \(0.522931\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.24287 | + | 22.2913i | 0.262210 | + | 0.806998i | ||||
\(764\) | −12.4010 | − | 17.0685i | −0.448653 | − | 0.617517i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.20628 | − | 0.391945i | 0.0435847 | − | 0.0141615i | ||||
\(767\) | −0.0823407 | + | 0.253419i | −0.00297315 | + | 0.00915042i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.2408i | 1.59536i | 0.603079 | + | 0.797682i | \(0.293940\pi\) | ||||
−0.603079 | + | 0.797682i | \(0.706060\pi\) | |||||||
\(770\) | −1.94362 | + | 6.39479i | −0.0700432 | + | 0.230452i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.4831 | − | 24.0634i | 0.629230 | − | 0.866061i | ||||
\(773\) | 38.0786 | + | 12.3725i | 1.36959 | + | 0.445007i | 0.899234 | − | 0.437468i | \(-0.144125\pi\) |
0.470358 | + | 0.882476i | \(0.344125\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.1266 | + | 12.4432i | −0.615204 | + | 0.446972i | ||||
\(776\) | 1.34922 | − | 0.980265i | 0.0484341 | − | 0.0351895i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.37723 | − | 0.772409i | −0.0852279 | − | 0.0276922i | ||||
\(779\) | −9.47357 | + | 13.0393i | −0.339426 | + | 0.467180i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.228538 | − | 11.9680i | −0.00817775 | − | 0.428250i | ||||
\(782\) | 0.924086i | 0.0330453i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.438933 | + | 1.35090i | −0.0156762 | + | 0.0482463i | ||||
\(785\) | 8.48547 | − | 2.75709i | 0.302859 | − | 0.0984049i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.6720 | − | 22.9470i | −0.594292 | − | 0.817973i | 0.400878 | − | 0.916131i | \(-0.368705\pi\) |
−0.995171 | + | 0.0981579i | \(0.968705\pi\) | |||||||
\(788\) | 4.33149 | + | 13.3309i | 0.154303 | + | 0.474895i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.27701 | − | 3.10743i | −0.152169 | − | 0.110558i | ||||
\(791\) | −31.0173 | −1.10285 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.12332 | −0.217446 | ||||||||
\(794\) | 3.90435 | + | 2.83668i | 0.138560 | + | 0.100670i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.80249 | + | 20.9359i | 0.241108 | + | 0.742054i | ||||
\(797\) | 8.78371 | + | 12.0897i | 0.311135 | + | 0.428241i | 0.935735 | − | 0.352704i | \(-0.114738\pi\) |
−0.624600 | + | 0.780945i | \(0.714738\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.7542 | + | 10.6425i | −1.15876 | + | 0.376504i | ||||
\(800\) | −3.18513 | + | 9.80283i | −0.112611 | + | 0.346582i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.78923i | 0.275047i | ||||||||
\(803\) | −5.58339 | − | 1.69700i | −0.197034 | − | 0.0598860i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.81192 | + | 5.24666i | −0.134352 | + | 0.184920i | ||||
\(806\) | 4.12456 | + | 1.34015i | 0.145281 | + | 0.0472048i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.30784 | + | 5.30946i | −0.257089 | + | 0.186786i | ||||
\(809\) | 24.0892 | − | 17.5019i | 0.846933 | − | 0.615333i | −0.0773660 | − | 0.997003i | \(-0.524651\pi\) |
0.924299 | + | 0.381670i | \(0.124651\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.9856 | + | 13.6420i | 1.47432 | + | 0.479034i | 0.932409 | − | 0.361405i | \(-0.117703\pi\) |
0.541906 | + | 0.840439i | \(0.317703\pi\) | |||||||
\(812\) | 29.5320 | − | 40.6473i | 1.03637 | − | 1.42644i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.99053 | − | 3.01735i | 0.139868 | − | 0.105758i | ||||
\(815\) | 23.0948i | 0.808975i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.01391 | + | 21.5866i | −0.245386 | + | 0.755220i | ||||
\(818\) | 2.86459 | − | 0.930761i | 0.100158 | − | 0.0325433i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 28.0340 | + | 38.5854i | 0.978988 | + | 1.34746i | ||||
\(821\) | −1.23760 | − | 3.80893i | −0.0431924 | − | 0.132933i | 0.927135 | − | 0.374728i | \(-0.122264\pi\) |
−0.970327 | + | 0.241795i | \(0.922264\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.1262 | − | 24.7941i | −1.18956 | − | 0.864268i | −0.196345 | − | 0.980535i | \(-0.562907\pi\) |
−0.993218 | + | 0.116266i | \(0.962907\pi\) | |||||||
\(824\) | 16.5460 | 0.576409 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.0643512 | −0.00223906 | ||||||||
\(827\) | −21.5183 | − | 15.6340i | −0.748266 | − | 0.543647i | 0.147023 | − | 0.989133i | \(-0.453031\pi\) |
−0.895289 | + | 0.445486i | \(0.853031\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.77976 | + | 11.6329i | 0.131276 | + | 0.404027i | 0.994992 | − | 0.0999518i | \(-0.0318689\pi\) |
−0.863716 | + | 0.503979i | \(0.831869\pi\) | |||||||
\(830\) | −3.41300 | − | 4.69759i | −0.118467 | − | 0.163056i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −17.6463 | + | 5.73362i | −0.611774 | + | 0.198777i | ||||
\(833\) | 0.541343 | − | 1.66608i | 0.0187564 | − | 0.0577264i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 48.0560i | − | 1.66305i | ||||||
\(836\) | −7.02087 | + | 10.0619i | −0.242822 | + | 0.347999i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.50045 | − | 2.06519i | 0.0518321 | − | 0.0713408i | ||||
\(839\) | −9.17434 | − | 2.98092i | −0.316733 | − | 0.102913i | 0.146336 | − | 0.989235i | \(-0.453252\pi\) |
−0.463069 | + | 0.886322i | \(0.653252\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −50.2704 | + | 36.5236i | −1.73346 | + | 1.25943i | ||||
\(842\) | 1.28401 | − | 0.932887i | 0.0442498 | − | 0.0321494i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.80810 | + | 2.21209i | 0.234345 | + | 0.0761432i | ||||
\(845\) | 8.31793 | − | 11.4486i | 0.286146 | − | 0.393846i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.4906 | + | 23.5075i | 0.635344 | + | 0.807727i | ||||
\(848\) | − | 37.8287i | − | 1.29904i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.23703 | − | 3.80718i | 0.0424298 | − | 0.130585i | ||||
\(851\) | 4.61677 | − | 1.50008i | 0.158261 | − | 0.0514221i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.89976 | − | 9.49670i | −0.236243 | − | 0.325161i | 0.674391 | − | 0.738374i | \(-0.264406\pi\) |
−0.910634 | + | 0.413214i | \(0.864406\pi\) | |||||||
\(854\) | −0.456976 | − | 1.40643i | −0.0156374 | − | 0.0481270i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.74518 | − | 4.17412i | −0.196366 | − | 0.142668i | ||||
\(857\) | −48.7738 | −1.66608 | −0.833041 | − | 0.553212i | \(-0.813402\pi\) | ||||
−0.833041 | + | 0.553212i | \(0.813402\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.0880 | −1.06071 | −0.530355 | − | 0.847776i | \(-0.677941\pi\) | ||||
−0.530355 | + | 0.847776i | \(0.677941\pi\) | |||||||
\(860\) | 54.3383 | + | 39.4791i | 1.85292 | + | 1.34623i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.53952 | + | 4.73815i | 0.0524362 | + | 0.161382i | ||||
\(863\) | 30.6459 | + | 42.1805i | 1.04320 | + | 1.43584i | 0.894559 | + | 0.446950i | \(0.147490\pi\) |
0.148641 | + | 0.988891i | \(0.452510\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −43.1325 | + | 14.0146i | −1.46655 | + | 0.476511i | ||||
\(866\) | 2.45274 | − | 7.54876i | 0.0833475 | − | 0.256517i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 31.5040i | − | 1.06931i | ||||||
\(869\) | −22.3556 | + | 7.73868i | −0.758361 | + | 0.262517i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.36324 | − | 3.25272i | 0.0800753 | − | 0.110214i | ||||
\(872\) | −8.18523 | − | 2.65954i | −0.277187 | − | 0.0900635i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.320198 | − | 0.232637i | 0.0108309 | − | 0.00786907i | ||||
\(875\) | −9.40572 | + | 6.83366i | −0.317971 | + | 0.231020i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.1564 | + | 5.24952i | 0.545561 | + | 0.177264i | 0.568814 | − | 0.822466i | \(-0.307402\pi\) |
−0.0232530 | + | 0.999730i | \(0.507402\pi\) | |||||||
\(878\) | −3.01098 | + | 4.14426i | −0.101616 | + | 0.139862i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 21.1454 | + | 27.9653i | 0.712810 | + | 0.942710i | ||||
\(881\) | 50.3115i | 1.69504i | 0.530765 | + | 0.847519i | \(0.321905\pi\) | ||||
−0.530765 | + | 0.847519i | \(0.678095\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.44037 | − | 13.6660i | 0.149430 | − | 0.459899i | −0.848124 | − | 0.529798i | \(-0.822268\pi\) |
0.997554 | + | 0.0698990i | \(0.0222677\pi\) | |||||||
\(884\) | 23.4603 | − | 7.62270i | 0.789054 | − | 0.256379i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.63341 | − | 5.00096i | −0.122067 | − | 0.168011i | ||||
\(887\) | 12.7625 | + | 39.2790i | 0.428523 | + | 1.31886i | 0.899580 | + | 0.436756i | \(0.143873\pi\) |
−0.471057 | + | 0.882103i | \(0.656127\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.34181 | − | 4.60760i | −0.212698 | − | 0.154534i | ||||
\(890\) | −1.53296 | −0.0513851 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.548221 | 0.0183558 | ||||||||
\(893\) | 11.9335 | + | 8.67018i | 0.399339 | + | 0.290136i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.68529 | − | 14.4198i | −0.156612 | − | 0.482002i | ||||
\(896\) | −11.9496 | − | 16.4473i | −0.399209 | − | 0.549465i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.796620 | + | 0.258838i | −0.0265836 | + | 0.00863752i | ||||
\(899\) | −17.6592 | + | 54.3495i | −0.588968 | + | 1.81266i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46.6547i | 1.55429i | ||||||||
\(902\) | −7.09406 | + | 0.135466i | −0.236206 | + | 0.00451053i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.69450 | − | 9.21419i | 0.222656 | − | 0.306460i | ||||
\(905\) | 14.7614 | + | 4.79627i | 0.490685 | + | 0.159433i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.1288 | − | 15.3510i | 0.701571 | − | 0.509721i | −0.178872 | − | 0.983872i | \(-0.557245\pi\) |
0.880444 | + | 0.474151i | \(0.157245\pi\) | |||||||
\(908\) | −28.5883 | + | 20.7706i | −0.948738 | + | 0.689298i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.47363 | − | 1.77849i | −0.181449 | − | 0.0589563i | ||||
\(911\) | 26.6929 | − | 36.7397i | 0.884377 | − | 1.21724i | −0.0908128 | − | 0.995868i | \(-0.528946\pi\) |
0.975189 | − | 0.221372i | \(-0.0710535\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.9787 | + | 0.496082i | −0.859769 | + | 0.0164179i | ||||
\(914\) | 3.96175i | 0.131043i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.7767 | + | 48.5555i | −0.521275 | + | 1.60432i | ||||
\(917\) | −5.43431 | + | 1.76572i | −0.179457 | + | 0.0583091i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.3737 | − | 22.5365i | −0.540119 | − | 0.743410i | 0.448511 | − | 0.893777i | \(-0.351954\pi\) |
−0.988630 | + | 0.150367i | \(0.951954\pi\) | |||||||
\(920\) | −0.735874 | − | 2.26479i | −0.0242610 | − | 0.0746678i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.50486 | + | 5.45260i | 0.247160 | + | 0.179572i | ||||
\(923\) | 10.3076 | 0.339280 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.0289 | −0.691427 | ||||||||
\(926\) | −0.914353 | − | 0.664317i | −0.0300475 | − | 0.0218308i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.59813 | + | 26.4623i | 0.282248 | + | 0.868669i | ||||
\(929\) | 29.2450 | + | 40.2523i | 0.959497 | + | 1.32063i | 0.947178 | + | 0.320710i | \(0.103921\pi\) |
0.0123191 | + | 0.999924i | \(0.496079\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.713584 | + | 0.231857i | −0.0233868 | + | 0.00759882i | ||||
\(932\) | 6.46131 | − | 19.8859i | 0.211647 | − | 0.651384i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.5597i | 0.345524i | ||||||||
\(935\) | −26.0789 | − | 34.4901i | −0.852872 | − | 1.12795i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.9943 | − | 16.5087i | 0.391837 | − | 0.539317i | −0.566835 | − | 0.823831i | \(-0.691832\pi\) |
0.958672 | + | 0.284514i | \(0.0918323\pi\) | |||||||
\(938\) | 0.923462 | + | 0.300051i | 0.0301521 | + | 0.00979702i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 35.3132 | − | 25.6566i | 1.15179 | − | 0.836825i | ||||
\(941\) | 14.1929 | − | 10.3117i | 0.462675 | − | 0.336153i | −0.331904 | − | 0.943313i | \(-0.607691\pi\) |
0.794580 | + | 0.607160i | \(0.207691\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.54776 | − | 2.12750i | −0.213224 | − | 0.0692808i | ||||
\(944\) | −0.198413 | + | 0.273093i | −0.00645781 | + | 0.00888841i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.44237 | + | 3.26860i | −0.306998 | + | 0.106271i | ||||
\(947\) | − | 47.0672i | − | 1.52948i | −0.644340 | − | 0.764739i | \(-0.722868\pi\) | ||
0.644340 | − | 0.764739i | \(-0.277132\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.55283 | − | 4.77911i | 0.0504069 | − | 0.155136i | ||||
\(950\) | −1.63062 | + | 0.529820i | −0.0529042 | + | 0.0171896i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.11966 | + | 9.79937i | 0.230749 | + | 0.317599i | ||||
\(953\) | −15.9545 | − | 49.1029i | −0.516817 | − | 1.59060i | −0.779952 | − | 0.625839i | \(-0.784757\pi\) |
0.263136 | − | 0.964759i | \(-0.415243\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.7637 | − | 18.7185i | −0.833695 | − | 0.605715i | ||||
\(956\) | −14.3689 | −0.464725 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.893318 | −0.0288618 | ||||||||
\(959\) | −11.1612 | − | 8.10907i | −0.360413 | − | 0.261855i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.49341 | + | 4.59623i | 0.0481744 | + | 0.148266i | ||||
\(962\) | 2.53218 | + | 3.48525i | 0.0816408 | + | 0.112369i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.91289 | − | 1.59629i | 0.158233 | − | 0.0514132i | ||||
\(965\) | 13.8738 | − | 42.6991i | 0.446613 | − | 1.37453i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.6964i | 1.08360i | 0.840506 | + | 0.541802i | \(0.182258\pi\) | ||||
−0.840506 | + | 0.541802i | \(0.817742\pi\) | |||||||
\(968\) | −10.9741 | + | 0.419271i | −0.352722 | + | 0.0134759i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.727724 | − | 1.00163i | 0.0233658 | − | 0.0321603i | ||||
\(971\) | 53.1467 | + | 17.2684i | 1.70556 | + | 0.554170i | 0.989584 | − | 0.143955i | \(-0.0459822\pi\) |
0.715976 | + | 0.698125i | \(0.245982\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38.4588 | − | 27.9419i | 1.23293 | − | 0.895777i | ||||
\(974\) | −6.54684 | + | 4.75656i | −0.209774 | + | 0.152410i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.37757 | − | 2.39712i | −0.236150 | − | 0.0767299i | ||||
\(977\) | 12.1432 | − | 16.7137i | 0.388496 | − | 0.534719i | −0.569314 | − | 0.822120i | \(-0.692791\pi\) |
0.957810 | + | 0.287401i | \(0.0927912\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.92539 | + | 5.62565i | −0.125456 | + | 0.179797i | ||||
\(980\) | 2.22029i | 0.0709245i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.91422 | − | 5.89137i | 0.0610853 | − | 0.188001i | ||||
\(983\) | −47.6740 | + | 15.4902i | −1.52056 | + | 0.494061i | −0.945936 | − | 0.324354i | \(-0.894853\pi\) |
−0.574628 | + | 0.818415i | \(0.694853\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.4362 | + | 17.1169i | 0.396249 | + | 0.545390i | ||||
\(986\) | −3.33931 | − | 10.2773i | −0.106345 | − | 0.327297i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.54737 | − | 6.21003i | −0.271928 | − | 0.197567i | ||||
\(989\) | −9.69548 | −0.308298 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.3068 | 1.43922 | 0.719609 | − | 0.694379i | \(-0.244321\pi\) | ||||
0.719609 | + | 0.694379i | \(0.244321\pi\) | |||||||
\(992\) | 14.1147 | + | 10.2549i | 0.448141 | + | 0.325594i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.769246 | + | 2.36750i | 0.0243990 | + | 0.0750924i | ||||
\(995\) | 19.5307 | + | 26.8817i | 0.619164 | + | 0.852206i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.77676 | − | 3.17666i | 0.309633 | − | 0.100606i | −0.150079 | − | 0.988674i | \(-0.547953\pi\) |
0.459712 | + | 0.888068i | \(0.347953\pi\) | |||||||
\(998\) | −1.82407 | + | 5.61392i | −0.0577400 | + | 0.177705i | ||||
\(999\) | 0 | 0 |
(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 | 99.2.j.a.62.2 | yes | 16 | |
3.2 | odd | 2 | inner | 99.2.j.a.62.3 | yes | 16 | |
4.3 | odd | 2 | 1584.2.cd.c.161.2 | 16 | |||
9.2 | odd | 6 | 891.2.u.c.458.3 | 32 | |||
9.4 | even | 3 | 891.2.u.c.755.3 | 32 | |||
9.5 | odd | 6 | 891.2.u.c.755.2 | 32 | |||
9.7 | even | 3 | 891.2.u.c.458.2 | 32 | |||
11.5 | even | 5 | 1089.2.d.g.1088.10 | 16 | |||
11.6 | odd | 10 | 1089.2.d.g.1088.8 | 16 | |||
11.8 | odd | 10 | inner | 99.2.j.a.8.3 | yes | 16 | |
12.11 | even | 2 | 1584.2.cd.c.161.3 | 16 | |||
33.5 | odd | 10 | 1089.2.d.g.1088.7 | 16 | |||
33.8 | even | 10 | inner | 99.2.j.a.8.2 | ✓ | 16 | |
33.17 | even | 10 | 1089.2.d.g.1088.9 | 16 | |||
44.19 | even | 10 | 1584.2.cd.c.305.3 | 16 | |||
99.41 | even | 30 | 891.2.u.c.107.2 | 32 | |||
99.52 | odd | 30 | 891.2.u.c.701.2 | 32 | |||
99.74 | even | 30 | 891.2.u.c.701.3 | 32 | |||
99.85 | odd | 30 | 891.2.u.c.107.3 | 32 | |||
132.107 | odd | 10 | 1584.2.cd.c.305.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.j.a.8.2 | ✓ | 16 | 33.8 | even | 10 | inner | |
99.2.j.a.8.3 | yes | 16 | 11.8 | odd | 10 | inner | |
99.2.j.a.62.2 | yes | 16 | 1.1 | even | 1 | trivial | |
99.2.j.a.62.3 | yes | 16 | 3.2 | odd | 2 | inner | |
891.2.u.c.107.2 | 32 | 99.41 | even | 30 | |||
891.2.u.c.107.3 | 32 | 99.85 | odd | 30 | |||
891.2.u.c.458.2 | 32 | 9.7 | even | 3 | |||
891.2.u.c.458.3 | 32 | 9.2 | odd | 6 | |||
891.2.u.c.701.2 | 32 | 99.52 | odd | 30 | |||
891.2.u.c.701.3 | 32 | 99.74 | even | 30 | |||
891.2.u.c.755.2 | 32 | 9.5 | odd | 6 | |||
891.2.u.c.755.3 | 32 | 9.4 | even | 3 | |||
1089.2.d.g.1088.7 | 16 | 33.5 | odd | 10 | |||
1089.2.d.g.1088.8 | 16 | 11.6 | odd | 10 | |||
1089.2.d.g.1088.9 | 16 | 33.17 | even | 10 | |||
1089.2.d.g.1088.10 | 16 | 11.5 | even | 5 | |||
1584.2.cd.c.161.2 | 16 | 4.3 | odd | 2 | |||
1584.2.cd.c.161.3 | 16 | 12.11 | even | 2 | |||
1584.2.cd.c.305.2 | 16 | 132.107 | odd | 10 | |||
1584.2.cd.c.305.3 | 16 | 44.19 | even | 10 |