Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(37,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.y (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 37.13 | ||
Character | \(\chi\) | \(=\) | 432.37 |
Dual form | 432.2.y.e.397.13 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.812713 | + | 1.15737i | 0.574675 | + | 0.818382i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.678997 | + | 1.88121i | −0.339498 | + | 0.940607i | ||||
\(5\) | 2.69708 | − | 0.722679i | 1.20617 | − | 0.323192i | 0.400911 | − | 0.916117i | \(-0.368694\pi\) |
0.805258 | + | 0.592925i | \(0.202027\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.89314 | + | 1.67035i | −1.09350 | + | 0.631334i | −0.934507 | − | 0.355945i | \(-0.884159\pi\) |
−0.158996 | + | 0.987279i | \(0.550826\pi\) | |||||||
\(8\) | −2.72908 | + | 0.743037i | −0.964877 | + | 0.262703i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.02835 | + | 2.53418i | 0.957649 | + | 0.801377i | ||||
\(11\) | −1.23365 | + | 4.60405i | −0.371960 | + | 1.38817i | 0.485777 | + | 0.874083i | \(0.338537\pi\) |
−0.857737 | + | 0.514089i | \(0.828130\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.398486 | + | 1.48717i | 0.110520 | + | 0.412467i | 0.998913 | − | 0.0466175i | \(-0.0148442\pi\) |
−0.888393 | + | 0.459084i | \(0.848178\pi\) | |||||||
\(14\) | −4.28450 | − | 1.99090i | −1.14508 | − | 0.532092i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.07793 | − | 2.55468i | −0.769482 | − | 0.638669i | ||||
\(17\) | 6.47719 | 1.57095 | 0.785475 | − | 0.618894i | \(-0.212419\pi\) | ||||
0.785475 | + | 0.618894i | \(0.212419\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.957336 | − | 0.957336i | 0.219628 | − | 0.219628i | −0.588714 | − | 0.808342i | \(-0.700365\pi\) |
0.808342 | + | 0.588714i | \(0.200365\pi\) | |||||||
\(20\) | −0.471792 | + | 5.56447i | −0.105496 | + | 1.24425i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.33117 | + | 2.31398i | −1.34981 | + | 0.493342i | ||||
\(23\) | 3.70277 | + | 2.13780i | 0.772081 | + | 0.445761i | 0.833617 | − | 0.552343i | \(-0.186266\pi\) |
−0.0615352 | + | 0.998105i | \(0.519600\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.42183 | − | 1.39824i | 0.484365 | − | 0.279648i | ||||
\(26\) | −1.39735 | + | 1.66984i | −0.274042 | + | 0.327482i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.17786 | − | 6.57677i | −0.222595 | − | 1.24289i | ||||
\(29\) | 1.07893 | + | 0.289099i | 0.200353 | + | 0.0536843i | 0.357600 | − | 0.933875i | \(-0.383595\pi\) |
−0.157247 | + | 0.987559i | \(0.550262\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.89670 | − | 3.28518i | 0.340657 | − | 0.590036i | −0.643898 | − | 0.765112i | \(-0.722684\pi\) |
0.984555 | + | 0.175076i | \(0.0560171\pi\) | |||||||
\(32\) | 0.455227 | − | 5.63851i | 0.0804734 | − | 0.996757i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.26409 | + | 7.49649i | 0.902785 | + | 1.28564i | ||||
\(35\) | −6.59588 | + | 6.59588i | −1.11491 | + | 1.11491i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.14639 | − | 6.14639i | −1.01046 | − | 1.01046i | −0.999945 | − | 0.0105160i | \(-0.996653\pi\) |
−0.0105160 | − | 0.999945i | \(-0.503347\pi\) | |||||||
\(38\) | 1.88603 | + | 0.329950i | 0.305954 | + | 0.0535249i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.82357 | + | 3.97628i | −1.07890 | + | 0.628705i | ||||
\(41\) | −5.04156 | − | 2.91075i | −0.787359 | − | 0.454582i | 0.0516729 | − | 0.998664i | \(-0.483545\pi\) |
−0.839032 | + | 0.544082i | \(0.816878\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.69287 | − | 6.31788i | 0.258160 | − | 0.963468i | −0.708144 | − | 0.706068i | \(-0.750467\pi\) |
0.966305 | − | 0.257400i | \(-0.0828659\pi\) | |||||||
\(44\) | −7.82355 | − | 5.44689i | −1.17944 | − | 0.821150i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.535074 | + | 6.02288i | 0.0788924 | + | 0.888025i | ||||
\(47\) | −1.81739 | − | 3.14781i | −0.265093 | − | 0.459155i | 0.702495 | − | 0.711689i | \(-0.252069\pi\) |
−0.967588 | + | 0.252534i | \(0.918736\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.08016 | − | 3.60295i | 0.297166 | − | 0.514707i | ||||
\(50\) | 3.58653 | + | 1.66657i | 0.507212 | + | 0.235689i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.06826 | − | 0.260146i | −0.425491 | − | 0.0360758i | ||||
\(53\) | −0.762460 | − | 0.762460i | −0.104732 | − | 0.104732i | 0.652799 | − | 0.757531i | \(-0.273595\pi\) |
−0.757531 | + | 0.652799i | \(0.773595\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.3090i | 1.79458i | ||||||||
\(56\) | 6.65448 | − | 6.70824i | 0.889242 | − | 0.896427i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.542268 | + | 1.48367i | 0.0712033 | + | 0.194816i | ||||
\(59\) | 8.11476 | − | 2.17434i | 1.05645 | − | 0.283075i | 0.311536 | − | 0.950234i | \(-0.399156\pi\) |
0.744915 | + | 0.667159i | \(0.232490\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.74711 | + | 1.80788i | 0.863879 | + | 0.231476i | 0.663439 | − | 0.748230i | \(-0.269096\pi\) |
0.200440 | + | 0.979706i | \(0.435763\pi\) | |||||||
\(62\) | 5.34363 | − | 0.474729i | 0.678641 | − | 0.0602907i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.89579 | − | 4.05562i | 0.861974 | − | 0.506953i | ||||
\(65\) | 2.14950 | + | 3.72304i | 0.266612 | + | 0.461786i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.487339 | − | 1.81878i | −0.0595380 | − | 0.222199i | 0.929746 | − | 0.368201i | \(-0.120026\pi\) |
−0.989284 | + | 0.146002i | \(0.953359\pi\) | |||||||
\(68\) | −4.39799 | + | 12.1850i | −0.533335 | + | 1.47765i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −12.9944 | − | 2.27330i | −1.55313 | − | 0.271711i | ||||
\(71\) | − | 3.98472i | − | 0.472899i | −0.971644 | − | 0.236450i | \(-0.924016\pi\) | ||
0.971644 | − | 0.236450i | \(-0.0759838\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.45461i | 0.638414i | 0.947685 | + | 0.319207i | \(0.103417\pi\) | ||||
−0.947685 | + | 0.319207i | \(0.896583\pi\) | |||||||
\(74\) | 2.11838 | − | 12.1089i | 0.246257 | − | 1.40763i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.15092 | + | 2.45098i | 0.132020 | + | 0.281147i | ||||
\(77\) | −4.12126 | − | 15.3808i | −0.469662 | − | 1.75280i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.95225 | − | 5.11344i | −0.332154 | − | 0.575307i | 0.650780 | − | 0.759266i | \(-0.274442\pi\) |
−0.982934 | + | 0.183959i | \(0.941109\pi\) | |||||||
\(80\) | −10.1476 | − | 4.66580i | −1.13454 | − | 0.521652i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.728538 | − | 8.20053i | −0.0804535 | − | 0.905597i | ||||
\(83\) | 10.3428 | + | 2.77135i | 1.13527 | + | 0.304195i | 0.777048 | − | 0.629441i | \(-0.216716\pi\) |
0.358223 | + | 0.933636i | \(0.383383\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.4695 | − | 4.68093i | 1.89483 | − | 0.507718i | ||||
\(86\) | 8.68792 | − | 3.17535i | 0.936843 | − | 0.342407i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.0542436 | − | 13.4815i | −0.00578239 | − | 1.43713i | ||||
\(89\) | − | 2.24307i | − | 0.237765i | −0.992908 | − | 0.118883i | \(-0.962069\pi\) | ||
0.992908 | − | 0.118883i | \(-0.0379312\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.63698 | − | 3.63698i | −0.381259 | − | 0.381259i | ||||
\(92\) | −6.53582 | + | 5.51415i | −0.681407 | + | 0.574890i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.16615 | − | 4.66165i | 0.223422 | − | 0.480812i | ||||
\(95\) | 1.89016 | − | 3.27385i | 0.193926 | − | 0.335890i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.50191 | + | 11.2616i | 0.660169 | + | 1.14345i | 0.980571 | + | 0.196165i | \(0.0628488\pi\) |
−0.320402 | + | 0.947282i | \(0.603818\pi\) | |||||||
\(98\) | 5.86050 | − | 0.520649i | 0.592000 | − | 0.0525935i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.985980 | + | 5.50537i | 0.0985980 | + | 0.550537i | ||||
\(101\) | 2.36072 | − | 8.81034i | 0.234901 | − | 0.876662i | −0.743293 | − | 0.668966i | \(-0.766737\pi\) |
0.978194 | − | 0.207696i | \(-0.0665963\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.73262 | − | 2.15503i | −0.367786 | − | 0.212342i | 0.304705 | − | 0.952447i | \(-0.401442\pi\) |
−0.672491 | + | 0.740105i | \(0.734776\pi\) | |||||||
\(104\) | −2.19253 | − | 3.76252i | −0.214995 | − | 0.368946i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.262785 | − | 1.50211i | 0.0255239 | − | 0.145897i | ||||
\(107\) | −0.0516852 | − | 0.0516852i | −0.00499659 | − | 0.00499659i | 0.704604 | − | 0.709601i | \(-0.251125\pi\) |
−0.709601 | + | 0.704604i | \(0.751125\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.73510 | − | 5.73510i | 0.549323 | − | 0.549323i | −0.376922 | − | 0.926245i | \(-0.623018\pi\) |
0.926245 | + | 0.376922i | \(0.123018\pi\) | |||||||
\(110\) | −15.4034 | + | 10.8164i | −1.46866 | + | 1.03130i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 13.1721 | + | 2.24980i | 1.24464 | + | 0.212586i | ||||
\(113\) | −7.13575 | + | 12.3595i | −0.671275 | + | 1.16268i | 0.306268 | + | 0.951945i | \(0.400920\pi\) |
−0.977543 | + | 0.210737i | \(0.932414\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.5316 | + | 3.08988i | 1.07533 | + | 0.288133i | ||||
\(116\) | −1.27645 | + | 1.83340i | −0.118515 | + | 0.170227i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.11148 | + | 7.62464i | 0.838780 | + | 0.701905i | ||||
\(119\) | −18.7394 | + | 10.8192i | −1.71784 | + | 0.991794i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.1491 | − | 5.85956i | −0.922642 | − | 0.532688i | ||||
\(122\) | 3.39108 | + | 9.27818i | 0.307014 | + | 0.840007i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.89227 | + | 5.79872i | 0.439339 | + | 0.520740i | ||||
\(125\) | −4.35061 | + | 4.35061i | −0.389131 | + | 0.389131i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.2634 | −1.44315 | −0.721573 | − | 0.692338i | \(-0.756581\pi\) | ||||
−0.721573 | + | 0.692338i | \(0.756581\pi\) | |||||||
\(128\) | 10.2981 | + | 4.68491i | 0.910235 | + | 0.414091i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.56200 | + | 5.51351i | −0.224702 | + | 0.483567i | ||||
\(131\) | 4.58345 | + | 17.1057i | 0.400458 | + | 1.49453i | 0.812281 | + | 0.583267i | \(0.198226\pi\) |
−0.411822 | + | 0.911264i | \(0.635108\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.17061 | + | 4.36879i | −0.101505 | + | 0.378822i | ||||
\(134\) | 1.70892 | − | 2.04217i | 0.147629 | − | 0.176417i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −17.6768 | + | 4.81279i | −1.51577 | + | 0.412694i | ||||
\(137\) | 9.62551 | − | 5.55729i | 0.822363 | − | 0.474791i | −0.0288677 | − | 0.999583i | \(-0.509190\pi\) |
0.851231 | + | 0.524792i | \(0.175857\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.50347 | − | 1.74260i | 0.551617 | − | 0.147805i | 0.0277649 | − | 0.999614i | \(-0.491161\pi\) |
0.523852 | + | 0.851809i | \(0.324494\pi\) | |||||||
\(140\) | −7.92968 | − | 16.8868i | −0.670180 | − | 1.42720i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.61178 | − | 3.23843i | 0.387012 | − | 0.271763i | ||||
\(143\) | −7.33859 | −0.613684 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.11889 | 0.259009 | ||||||||
\(146\) | −6.31299 | + | 4.43303i | −0.522467 | + | 0.366880i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 15.7361 | − | 7.38930i | 1.29350 | − | 0.607396i | ||||
\(149\) | 10.7583 | − | 2.88268i | 0.881354 | − | 0.236158i | 0.210363 | − | 0.977623i | \(-0.432535\pi\) |
0.670991 | + | 0.741465i | \(0.265869\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.9045 | + | 10.9145i | −1.53842 | + | 0.888210i | −0.539493 | + | 0.841990i | \(0.681384\pi\) |
−0.998931 | + | 0.0462196i | \(0.985283\pi\) | |||||||
\(152\) | −1.90131 | + | 3.32398i | −0.154217 | + | 0.269611i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.4518 | − | 17.2700i | 1.16456 | − | 1.39165i | ||||
\(155\) | 2.74141 | − | 10.2311i | 0.220195 | − | 0.821780i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.18429 | − | 8.15189i | −0.174326 | − | 0.650592i | −0.996666 | − | 0.0815954i | \(-0.973998\pi\) |
0.822340 | − | 0.568996i | \(-0.192668\pi\) | |||||||
\(158\) | 3.51880 | − | 7.57259i | 0.279941 | − | 0.602443i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.84705 | − | 15.5365i | −0.225079 | − | 1.22827i | ||||
\(161\) | −14.2835 | −1.12570 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.93193 | + | 6.93193i | −0.542950 | + | 0.542950i | −0.924393 | − | 0.381442i | \(-0.875428\pi\) |
0.381442 | + | 0.924393i | \(0.375428\pi\) | |||||||
\(164\) | 8.89893 | − | 7.50786i | 0.694890 | − | 0.586265i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.19827 | + | 14.2227i | 0.403464 | + | 1.10390i | ||||
\(167\) | −7.33544 | − | 4.23512i | −0.567633 | − | 0.327723i | 0.188570 | − | 0.982060i | \(-0.439615\pi\) |
−0.756204 | + | 0.654336i | \(0.772948\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.20544 | − | 5.31477i | 0.708111 | − | 0.408828i | ||||
\(170\) | 19.6152 | + | 16.4143i | 1.50442 | + | 1.25892i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.7358 | + | 7.47447i | 0.818599 | + | 0.569923i | ||||
\(173\) | 5.81815 | + | 1.55897i | 0.442346 | + | 0.118526i | 0.473116 | − | 0.881000i | \(-0.343129\pi\) |
−0.0307700 | + | 0.999526i | \(0.509796\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.67112 | + | 8.09061i | −0.353103 | + | 0.611593i | ||||
\(176\) | 15.5589 | − | 11.0193i | 1.17280 | − | 0.830614i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.59606 | − | 1.82297i | 0.194583 | − | 0.136638i | ||||
\(179\) | 8.34442 | − | 8.34442i | 0.623692 | − | 0.623692i | −0.322782 | − | 0.946473i | \(-0.604618\pi\) |
0.946473 | + | 0.322782i | \(0.104618\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.3444 | − | 13.3444i | −0.991880 | − | 0.991880i | 0.00808779 | − | 0.999967i | \(-0.497426\pi\) |
−0.999967 | + | 0.00808779i | \(0.997426\pi\) | |||||||
\(182\) | 1.25350 | − | 7.16513i | 0.0929156 | − | 0.531115i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −11.6936 | − | 3.08293i | −0.862066 | − | 0.227276i | ||||
\(185\) | −21.0192 | − | 12.1354i | −1.54536 | − | 0.892214i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.99059 | + | 29.8213i | −0.584330 | + | 2.18075i | ||||
\(188\) | 7.15570 | − | 1.28154i | 0.521883 | − | 0.0934661i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.32521 | − | 0.473093i | 0.386331 | − | 0.0343218i | ||||
\(191\) | 0.892527 | + | 1.54590i | 0.0645810 | + | 0.111858i | 0.896508 | − | 0.443027i | \(-0.146096\pi\) |
−0.831927 | + | 0.554885i | \(0.812762\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.20588 | + | 14.2130i | −0.590672 | + | 1.02307i | 0.403470 | + | 0.914993i | \(0.367804\pi\) |
−0.994142 | + | 0.108081i | \(0.965529\pi\) | |||||||
\(194\) | −7.74967 | + | 16.6776i | −0.556394 | + | 1.19738i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.36549 | + | 6.35962i | 0.383249 | + | 0.454258i | ||||
\(197\) | 3.44937 | + | 3.44937i | 0.245758 | + | 0.245758i | 0.819227 | − | 0.573469i | \(-0.194403\pi\) |
−0.573469 | + | 0.819227i | \(0.694403\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 15.0093i | − | 1.06398i | −0.846751 | − | 0.531990i | \(-0.821444\pi\) | ||
0.846751 | − | 0.531990i | \(-0.178556\pi\) | |||||||
\(200\) | −5.57042 | + | 5.61543i | −0.393888 | + | 0.397071i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.1154 | − | 4.42805i | 0.852436 | − | 0.311557i | ||||
\(203\) | −3.60439 | + | 0.965795i | −0.252979 | + | 0.0677855i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.7010 | − | 4.20707i | −1.09661 | − | 0.293835i | ||||
\(206\) | −0.539388 | − | 6.07144i | −0.0375809 | − | 0.423017i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.57273 | − | 5.59541i | 0.178386 | − | 0.387972i | ||||
\(209\) | 3.22660 | + | 5.58863i | 0.223189 | + | 0.386574i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.18415 | − | 11.8834i | −0.219206 | − | 0.818089i | −0.984643 | − | 0.174578i | \(-0.944144\pi\) |
0.765437 | − | 0.643511i | \(-0.222523\pi\) | |||||||
\(212\) | 1.95206 | − | 0.916642i | 0.134068 | − | 0.0629552i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.0178135 | − | 0.101824i | 0.00121771 | − | 0.00696054i | ||||
\(215\) | − | 18.2632i | − | 1.24554i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.6726i | 0.860274i | ||||||||
\(218\) | 11.2986 | + | 1.97663i | 0.765238 | + | 0.133874i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −25.0371 | − | 9.03676i | −1.68800 | − | 0.609258i | ||||
\(221\) | 2.58107 | + | 9.63269i | 0.173622 | + | 0.647965i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.258294 | + | 0.447379i | 0.0172967 | + | 0.0299587i | 0.874544 | − | 0.484946i | \(-0.161161\pi\) |
−0.857248 | + | 0.514905i | \(0.827827\pi\) | |||||||
\(224\) | 8.10127 | + | 17.0734i | 0.541289 | + | 1.14076i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −20.1038 | + | 1.78602i | −1.33728 | + | 0.118805i | ||||
\(227\) | −9.84745 | − | 2.63862i | −0.653598 | − | 0.175131i | −0.0832432 | − | 0.996529i | \(-0.526528\pi\) |
−0.570355 | + | 0.821398i | \(0.693194\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.6838 | + | 5.54222i | −1.36683 | + | 0.366240i | −0.866319 | − | 0.499491i | \(-0.833520\pi\) |
−0.500508 | + | 0.865732i | \(0.666854\pi\) | |||||||
\(230\) | 5.79575 | + | 15.8575i | 0.382160 | + | 1.04561i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.15931 | + | 0.0127117i | −0.207419 | + | 0.000834563i | ||||
\(233\) | 23.2468i | 1.52295i | 0.648194 | + | 0.761476i | \(0.275525\pi\) | ||||
−0.648194 | + | 0.761476i | \(0.724475\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.17649 | − | 7.17649i | −0.468142 | − | 0.468142i | ||||
\(236\) | −1.41949 | + | 16.7420i | −0.0924010 | + | 1.08981i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −27.7515 | − | 12.8955i | −1.79886 | − | 0.835889i | ||||
\(239\) | −0.219358 | + | 0.379939i | −0.0141891 | + | 0.0245762i | −0.873033 | − | 0.487662i | \(-0.837850\pi\) |
0.858844 | + | 0.512238i | \(0.171183\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.67406 | + | 13.2919i | 0.494330 | + | 0.856204i | 0.999979 | − | 0.00653501i | \(-0.00208017\pi\) |
−0.505649 | + | 0.862739i | \(0.668747\pi\) | |||||||
\(242\) | −1.46660 | − | 16.5083i | −0.0942769 | − | 1.06120i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.98228 | + | 11.4652i | −0.511013 | + | 0.733985i | ||||
\(245\) | 3.00658 | − | 11.2207i | 0.192083 | − | 0.716865i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.80521 | + | 1.04224i | 0.114863 | + | 0.0663159i | ||||
\(248\) | −2.73524 | + | 10.3748i | −0.173688 | + | 0.658803i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.57105 | − | 1.49946i | −0.542081 | − | 0.0948341i | ||||
\(251\) | −8.02147 | − | 8.02147i | −0.506310 | − | 0.506310i | 0.407081 | − | 0.913392i | \(-0.366547\pi\) |
−0.913392 | + | 0.407081i | \(0.866547\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.4104 | + | 14.4104i | −0.905977 | + | 0.905977i | ||||
\(254\) | −13.2175 | − | 18.8228i | −0.829339 | − | 1.18104i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.94727 | + | 15.7262i | 0.184204 | + | 0.982888i | ||||
\(257\) | −4.72936 | + | 8.19149i | −0.295009 | + | 0.510971i | −0.974987 | − | 0.222262i | \(-0.928656\pi\) |
0.679978 | + | 0.733233i | \(0.261989\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28.0490 | + | 7.51571i | 1.74288 | + | 0.467003i | ||||
\(260\) | −8.46332 | + | 1.51573i | −0.524873 | + | 0.0940016i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −16.0725 | + | 19.2067i | −0.992964 | + | 1.18660i | ||||
\(263\) | −16.2413 | + | 9.37694i | −1.00148 | + | 0.578207i | −0.908687 | − | 0.417478i | \(-0.862914\pi\) |
−0.0927966 | + | 0.995685i | \(0.529581\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.60743 | − | 1.50540i | −0.160173 | − | 0.0924759i | ||||
\(266\) | −6.00767 | + | 2.19574i | −0.368354 | + | 0.134630i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.75241 | + | 0.318153i | 0.229215 | + | 0.0194343i | ||||
\(269\) | 13.5606 | − | 13.5606i | 0.826805 | − | 0.826805i | −0.160269 | − | 0.987073i | \(-0.551236\pi\) |
0.987073 | + | 0.160269i | \(0.0512361\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.6233 | 1.86023 | 0.930115 | − | 0.367268i | \(-0.119707\pi\) | ||||
0.930115 | + | 0.367268i | \(0.119707\pi\) | |||||||
\(272\) | −19.9363 | − | 16.5471i | −1.20882 | − | 1.00332i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.2546 | + | 6.62377i | 0.861152 | + | 0.400156i | ||||
\(275\) | 3.44988 | + | 12.8751i | 0.208036 | + | 0.776400i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.40521 | − | 20.1725i | 0.324767 | − | 1.21205i | −0.589778 | − | 0.807565i | \(-0.700785\pi\) |
0.914545 | − | 0.404483i | \(-0.132549\pi\) | |||||||
\(278\) | 7.30228 | + | 6.11067i | 0.437962 | + | 0.366494i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 13.0997 | − | 22.9017i | 0.782858 | − | 1.36864i | ||||
\(281\) | −10.6538 | + | 6.15097i | −0.635552 | + | 0.366936i | −0.782899 | − | 0.622149i | \(-0.786260\pi\) |
0.147347 | + | 0.989085i | \(0.452927\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.8013 | − | 3.43009i | 0.760957 | − | 0.203898i | 0.142584 | − | 0.989783i | \(-0.454459\pi\) |
0.618373 | + | 0.785885i | \(0.287792\pi\) | |||||||
\(284\) | 7.49611 | + | 2.70561i | 0.444812 | + | 0.160548i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.96417 | − | 8.49345i | −0.352669 | − | 0.502228i | ||||
\(287\) | 19.4479 | 1.14797 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.9540 | 1.46788 | ||||||||
\(290\) | 2.53476 | + | 3.60970i | 0.148846 | + | 0.211969i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.2613 | − | 3.70366i | −0.600497 | − | 0.216741i | ||||
\(293\) | −21.3351 | + | 5.71672i | −1.24641 | + | 0.333974i | −0.820948 | − | 0.571003i | \(-0.806554\pi\) |
−0.425460 | + | 0.904977i | \(0.639888\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.3148 | − | 11.7287i | 1.18277 | − | 0.682874i | ||||
\(296\) | 21.3410 | + | 12.2070i | 1.24042 | + | 0.709518i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.0797 | + | 10.1085i | 0.699759 | + | 0.585570i | ||||
\(299\) | −1.70377 | + | 6.35854i | −0.0985313 | + | 0.367724i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.65539 | + | 21.1062i | 0.325971 | + | 1.21654i | ||||
\(302\) | −27.9960 | − | 13.0091i | −1.61099 | − | 0.748587i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.39229 | + | 0.500928i | −0.309269 | + | 0.0287302i | ||||
\(305\) | 19.5040 | 1.11680 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.59225 | + | 3.59225i | −0.205021 | + | 0.205021i | −0.802147 | − | 0.597126i | \(-0.796309\pi\) |
0.597126 | + | 0.802147i | \(0.296309\pi\) | |||||||
\(308\) | 31.7328 | + | 2.69051i | 1.80815 | + | 0.153306i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14.0691 | − | 5.14211i | 0.799071 | − | 0.292052i | ||||
\(311\) | 8.62665 | + | 4.98060i | 0.489173 | + | 0.282424i | 0.724231 | − | 0.689557i | \(-0.242195\pi\) |
−0.235058 | + | 0.971981i | \(0.575528\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.1588 | + | 12.7934i | −1.25249 | + | 0.723124i | −0.971603 | − | 0.236617i | \(-0.923961\pi\) |
−0.280885 | + | 0.959741i | \(0.590628\pi\) | |||||||
\(314\) | 7.65953 | − | 9.15317i | 0.432252 | − | 0.516543i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.6240 | − | 2.08180i | 0.653903 | − | 0.117110i | ||||
\(317\) | −17.8781 | − | 4.79041i | −1.00413 | − | 0.269056i | −0.280957 | − | 0.959720i | \(-0.590652\pi\) |
−0.723176 | + | 0.690664i | \(0.757318\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.66205 | + | 4.61080i | −0.149046 | + | 0.258155i | ||||
\(320\) | 15.6676 | − | 15.9218i | 0.875843 | − | 0.890054i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11.6084 | − | 16.5313i | −0.646910 | − | 0.921251i | ||||
\(323\) | 6.20084 | − | 6.20084i | 0.345024 | − | 0.345024i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.04449 | + | 3.04449i | 0.168878 | + | 0.168878i | ||||
\(326\) | −13.6564 | − | 2.38912i | −0.756361 | − | 0.132321i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 15.9216 | + | 4.19760i | 0.879125 | + | 0.231774i | ||||
\(329\) | 10.5159 | + | 6.07136i | 0.579760 | + | 0.334725i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.10146 | − | 19.0389i | 0.280402 | − | 1.04647i | −0.671733 | − | 0.740794i | \(-0.734450\pi\) |
0.952134 | − | 0.305680i | \(-0.0988836\pi\) | |||||||
\(332\) | −12.2362 | + | 17.5753i | −0.671550 | + | 0.964570i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.06002 | − | 11.9317i | −0.0580016 | − | 0.652875i | ||||
\(335\) | −2.62878 | − | 4.55319i | −0.143626 | − | 0.248767i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.29609 | − | 5.70899i | 0.179549 | − | 0.310988i | −0.762177 | − | 0.647369i | \(-0.775869\pi\) |
0.941726 | + | 0.336380i | \(0.109203\pi\) | |||||||
\(338\) | 13.6325 | + | 6.33470i | 0.741511 | + | 0.344562i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.05588 | + | 36.0421i | −0.165729 | + | 1.95466i | ||||
\(341\) | 12.7852 | + | 12.7852i | 0.692360 | + | 0.692360i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 9.48653i | − | 0.512224i | ||||||
\(344\) | 0.0744356 | + | 18.4999i | 0.00401330 | + | 0.997447i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.92418 | + | 8.00073i | 0.157205 | + | 0.430122i | ||||
\(347\) | 3.20074 | − | 0.857635i | 0.171825 | − | 0.0460403i | −0.171881 | − | 0.985118i | \(-0.554984\pi\) |
0.343706 | + | 0.939077i | \(0.388318\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.0000 | − | 5.89488i | −1.17763 | − | 0.315546i | −0.383645 | − | 0.923480i | \(-0.625331\pi\) |
−0.793987 | + | 0.607935i | \(0.791998\pi\) | |||||||
\(350\) | −13.1601 | + | 1.16915i | −0.703436 | + | 0.0624935i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 25.3984 | + | 9.05183i | 1.35374 | + | 0.482464i | ||||
\(353\) | −14.2071 | − | 24.6074i | −0.756167 | − | 1.30972i | −0.944792 | − | 0.327670i | \(-0.893737\pi\) |
0.188626 | − | 0.982049i | \(-0.439597\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.87967 | − | 10.7471i | −0.152837 | − | 0.570396i | ||||
\(356\) | 4.21970 | + | 1.52304i | 0.223644 | + | 0.0807209i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.4392 | + | 2.87594i | 0.868838 | + | 0.151998i | ||||
\(359\) | 7.35521i | 0.388193i | 0.980982 | + | 0.194097i | \(0.0621775\pi\) | ||||
−0.980982 | + | 0.194097i | \(0.937823\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.1670i | 0.903527i | ||||||||
\(362\) | 4.59920 | − | 26.2895i | 0.241728 | − | 1.38174i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.31142 | − | 4.37243i | 0.488051 | − | 0.229178i | ||||
\(365\) | 3.94194 | + | 14.7115i | 0.206330 | + | 0.770035i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.0496 | − | 29.5308i | −0.889984 | − | 1.54150i | −0.839893 | − | 0.542752i | \(-0.817382\pi\) |
−0.0500906 | − | 0.998745i | \(-0.515951\pi\) | |||||||
\(368\) | −5.93549 | − | 16.0394i | −0.309409 | − | 0.836110i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.03740 | − | 34.1895i | −0.157907 | − | 1.77743i | ||||
\(371\) | 3.47948 | + | 0.932323i | 0.180646 | + | 0.0484038i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.8179 | − | 6.38198i | 1.23324 | − | 0.330447i | 0.417402 | − | 0.908722i | \(-0.362941\pi\) |
0.815842 | + | 0.578275i | \(0.196274\pi\) | |||||||
\(374\) | −41.0082 | + | 14.9881i | −2.12048 | + | 0.775015i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.29874 | + | 7.24024i | 0.376404 | + | 0.373387i | ||||
\(377\) | 1.71976i | 0.0885720i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.66916 | − | 2.66916i | −0.137106 | − | 0.137106i | 0.635223 | − | 0.772329i | \(-0.280908\pi\) |
−0.772329 | + | 0.635223i | \(0.780908\pi\) | |||||||
\(380\) | 4.87540 | + | 5.77873i | 0.250103 | + | 0.296443i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.06381 | + | 2.28936i | −0.0544292 | + | 0.117134i | ||||
\(383\) | 3.14570 | − | 5.44851i | 0.160738 | − | 0.278406i | −0.774396 | − | 0.632701i | \(-0.781946\pi\) |
0.935133 | + | 0.354296i | \(0.115279\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −22.2307 | − | 38.5047i | −1.13298 | − | 1.96238i | ||||
\(386\) | −23.1187 | + | 2.05387i | −1.17671 | + | 0.104539i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −25.6003 | + | 4.58487i | −1.29966 | + | 0.232761i | ||||
\(389\) | 0.724164 | − | 2.70262i | 0.0367166 | − | 0.137028i | −0.945135 | − | 0.326681i | \(-0.894070\pi\) |
0.981851 | + | 0.189653i | \(0.0607363\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.9836 | + | 13.8469i | 1.21290 | + | 0.700269i | ||||
\(392\) | −2.99981 | + | 11.3784i | −0.151513 | + | 0.574695i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.18884 | + | 6.79554i | −0.0598930 | + | 0.342354i | ||||
\(395\) | −11.6578 | − | 11.6578i | −0.586568 | − | 0.586568i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.29700 | + | 4.29700i | −0.215660 | + | 0.215660i | −0.806667 | − | 0.591007i | \(-0.798731\pi\) |
0.591007 | + | 0.806667i | \(0.298731\pi\) | |||||||
\(398\) | 17.3712 | − | 12.1982i | 0.870742 | − | 0.611442i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11.0263 | − | 1.88329i | −0.551313 | − | 0.0941646i | ||||
\(401\) | 6.63116 | − | 11.4855i | 0.331145 | − | 0.573559i | −0.651592 | − | 0.758570i | \(-0.725899\pi\) |
0.982737 | + | 0.185010i | \(0.0592319\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.64143 | + | 1.51162i | 0.281020 | + | 0.0752990i | ||||
\(404\) | 14.9712 | + | 10.4232i | 0.744846 | + | 0.518575i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.04712 | − | 3.38669i | −0.200855 | − | 0.168079i | ||||
\(407\) | 35.8808 | − | 20.7158i | 1.77854 | − | 1.02684i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.6538 | − | 6.15100i | −0.526799 | − | 0.304147i | 0.212913 | − | 0.977071i | \(-0.431705\pi\) |
−0.739712 | + | 0.672924i | \(0.765038\pi\) | |||||||
\(410\) | −7.89128 | − | 21.5910i | −0.389722 | − | 1.06630i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.58851 | − | 5.55860i | 0.324593 | − | 0.273853i | ||||
\(413\) | −19.8452 | + | 19.8452i | −0.976518 | + | 0.976518i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29.8981 | 1.46764 | ||||||||
\(416\) | 8.56683 | − | 1.56987i | 0.420023 | − | 0.0769691i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.84580 | + | 8.27631i | −0.188104 | + | 0.404808i | ||||
\(419\) | −7.82317 | − | 29.1965i | −0.382187 | − | 1.42634i | −0.842554 | − | 0.538612i | \(-0.818949\pi\) |
0.460367 | − | 0.887729i | \(-0.347718\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.75964 | + | 21.4953i | −0.280708 | + | 1.04762i | 0.671211 | + | 0.741266i | \(0.265774\pi\) |
−0.951919 | + | 0.306350i | \(0.900892\pi\) | |||||||
\(422\) | 11.1657 | − | 13.3430i | 0.543537 | − | 0.649529i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.64735 | + | 1.51428i | 0.128567 | + | 0.0735399i | ||||
\(425\) | 15.6866 | − | 9.05668i | 0.760913 | − | 0.439314i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.5401 | + | 6.03961i | −1.09079 | + | 0.292277i | ||||
\(428\) | 0.132325 | − | 0.0621368i | 0.00639616 | − | 0.00300349i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21.1372 | − | 14.8427i | 1.01933 | − | 0.715780i | ||||
\(431\) | −15.3940 | −0.741505 | −0.370752 | − | 0.928732i | \(-0.620900\pi\) | ||||
−0.370752 | + | 0.928732i | \(0.620900\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.2454 | −0.828763 | −0.414382 | − | 0.910103i | \(-0.636002\pi\) | ||||
−0.414382 | + | 0.910103i | \(0.636002\pi\) | |||||||
\(434\) | −14.6669 | + | 10.2992i | −0.704033 | + | 0.494378i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.89483 | + | 14.6831i | 0.330203 | + | 0.703191i | ||||
\(437\) | 5.59138 | − | 1.49821i | 0.267472 | − | 0.0716690i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.55070 | + | 2.62735i | −0.217193 | + | 0.125397i | −0.604650 | − | 0.796491i | \(-0.706687\pi\) |
0.387457 | + | 0.921888i | \(0.373354\pi\) | |||||||
\(440\) | −9.88908 | − | 36.3214i | −0.471443 | − | 1.73155i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.05089 | + | 10.8159i | −0.430507 | + | 0.514458i | ||||
\(443\) | −3.35032 | + | 12.5036i | −0.159179 | + | 0.594062i | 0.839533 | + | 0.543309i | \(0.182829\pi\) |
−0.998711 | + | 0.0507532i | \(0.983838\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.62102 | − | 6.04974i | −0.0768438 | − | 0.286785i | ||||
\(446\) | −0.307863 | + | 0.662532i | −0.0145777 | + | 0.0313718i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −13.1761 | + | 23.2519i | −0.622514 | + | 1.09855i | ||||
\(449\) | −27.9740 | −1.32018 | −0.660088 | − | 0.751189i | \(-0.729481\pi\) | ||||
−0.660088 | + | 0.751189i | \(0.729481\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.6207 | − | 19.6207i | 0.923904 | − | 0.923904i | ||||
\(452\) | −18.4057 | − | 21.8159i | −0.865730 | − | 1.02613i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.94930 | − | 13.5416i | −0.232282 | − | 0.635537i | ||||
\(455\) | −12.4376 | − | 7.18083i | −0.583082 | − | 0.336643i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.2732 | − | 20.3650i | 1.65001 | − | 0.952635i | 0.672947 | − | 0.739690i | \(-0.265028\pi\) |
0.977064 | − | 0.212944i | \(-0.0683053\pi\) | |||||||
\(458\) | −23.2244 | − | 19.4346i | −1.08521 | − | 0.908118i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −13.6426 | + | 19.5954i | −0.636092 | + | 0.913639i | ||||
\(461\) | 36.8721 | + | 9.87984i | 1.71730 | + | 0.460150i | 0.977196 | − | 0.212339i | \(-0.0681082\pi\) |
0.740107 | + | 0.672489i | \(0.234775\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.7637 | + | 30.7676i | −0.825549 | + | 1.42989i | 0.0759497 | + | 0.997112i | \(0.475801\pi\) |
−0.901499 | + | 0.432781i | \(0.857532\pi\) | |||||||
\(464\) | −2.58232 | − | 3.64614i | −0.119881 | − | 0.169268i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −26.9051 | + | 18.8930i | −1.24636 | + | 0.875201i | ||||
\(467\) | 17.1010 | − | 17.1010i | 0.791341 | − | 0.791341i | −0.190371 | − | 0.981712i | \(-0.560969\pi\) |
0.981712 | + | 0.190371i | \(0.0609692\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.44794 | + | 4.44794i | 0.205387 | + | 0.205387i | ||||
\(470\) | 2.47341 | − | 14.1383i | 0.114090 | − | 0.652149i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −20.5302 | + | 11.9635i | −0.944981 | + | 0.550666i | ||||
\(473\) | 26.9994 | + | 15.5881i | 1.24143 | + | 0.716742i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.979914 | − | 3.65709i | 0.0449615 | − | 0.167799i | ||||
\(476\) | −7.62923 | − | 42.5990i | −0.349685 | − | 1.95252i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.618004 | + | 0.0549036i | −0.0282668 | + | 0.00251123i | ||||
\(479\) | 6.76619 | + | 11.7194i | 0.309155 | + | 0.535473i | 0.978178 | − | 0.207769i | \(-0.0666204\pi\) |
−0.669023 | + | 0.743242i | \(0.733287\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.69148 | − | 11.5900i | 0.305105 | − | 0.528458i | ||||
\(482\) | −9.14676 | + | 19.6842i | −0.416624 | + | 0.896590i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 17.9143 | − | 15.1139i | 0.814285 | − | 0.686997i | ||||
\(485\) | 25.6747 | + | 25.6747i | 1.16583 | + | 1.16583i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.1436i | 0.731536i | 0.930706 | + | 0.365768i | \(0.119194\pi\) | ||||
−0.930706 | + | 0.365768i | \(0.880806\pi\) | |||||||
\(488\) | −19.7568 | + | 0.0794927i | −0.894347 | + | 0.00359847i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 15.4300 | − | 5.63950i | 0.697055 | − | 0.254766i | ||||
\(491\) | 34.9555 | − | 9.36630i | 1.57752 | − | 0.422695i | 0.639363 | − | 0.768905i | \(-0.279198\pi\) |
0.938157 | + | 0.346209i | \(0.112531\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.98844 | + | 1.87255i | 0.314744 | + | 0.0843353i | ||||
\(494\) | 0.260864 | + | 2.93633i | 0.0117368 | + | 0.132112i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.2305 | + | 5.26609i | −0.638967 | + | 0.236454i | ||||
\(497\) | 6.65589 | + | 11.5283i | 0.298557 | + | 0.517117i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.70347 | − | 6.35742i | −0.0762576 | − | 0.284597i | 0.917258 | − | 0.398294i | \(-0.130398\pi\) |
−0.993516 | + | 0.113696i | \(0.963731\pi\) | |||||||
\(500\) | −5.23038 | − | 11.1385i | −0.233910 | − | 0.498128i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.76463 | − | 15.8029i | 0.123392 | − | 0.705319i | ||||
\(503\) | 8.67964i | 0.387006i | 0.981100 | + | 0.193503i | \(0.0619849\pi\) | ||||
−0.981100 | + | 0.193503i | \(0.938015\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 25.4682i | − | 1.13332i | ||||||
\(506\) | −28.3897 | − | 4.96662i | −1.26208 | − | 0.220793i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.0428 | − | 30.5950i | 0.489946 | − | 1.35743i | ||||
\(509\) | −0.894794 | − | 3.33942i | −0.0396611 | − | 0.148017i | 0.943256 | − | 0.332067i | \(-0.107746\pi\) |
−0.982917 | + | 0.184050i | \(0.941079\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.11113 | − | 15.7809i | −0.403053 | − | 0.698108i | ||||
\(512\) | −15.8057 | + | 16.1920i | −0.698520 | + | 0.715590i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.3242 | + | 1.18372i | −0.587704 | + | 0.0522118i | ||||
\(515\) | −11.6246 | − | 3.11479i | −0.512240 | − | 0.137254i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.7347 | − | 4.48404i | 0.735990 | − | 0.197208i | ||||
\(518\) | 14.0973 | + | 38.5711i | 0.619402 | + | 1.69472i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.63251 | − | 8.56332i | −0.378560 | − | 0.375526i | ||||
\(521\) | − | 15.7843i | − | 0.691524i | −0.938322 | − | 0.345762i | \(-0.887620\pi\) | ||
0.938322 | − | 0.345762i | \(-0.112380\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.62449 | + | 6.62449i | 0.289669 | + | 0.289669i | 0.836949 | − | 0.547280i | \(-0.184337\pi\) |
−0.547280 | + | 0.836949i | \(0.684337\pi\) | |||||||
\(524\) | −35.2916 | − | 2.99225i | −1.54172 | − | 0.130717i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.0521 | − | 11.1764i | −1.04872 | − | 0.487315i | ||||
\(527\) | 12.2853 | − | 21.2787i | 0.535155 | − | 0.926916i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.35965 | − | 4.08703i | −0.102593 | − | 0.177697i | ||||
\(530\) | −0.376790 | − | 4.24120i | −0.0163667 | − | 0.184226i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.42379 | − | 5.16857i | −0.321862 | − | 0.224086i | ||||
\(533\) | 2.31978 | − | 8.65755i | 0.100481 | − | 0.375000i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.176751 | − | 0.102047i | −0.00764160 | − | 0.00441188i | ||||
\(536\) | 2.68141 | + | 4.60148i | 0.115819 | + | 0.198754i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 26.7155 | + | 4.67372i | 1.15179 | + | 0.201498i | ||||
\(539\) | 14.0219 | + | 14.0219i | 0.603967 | + | 0.603967i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.2832 | − | 32.2832i | 1.38796 | − | 1.38796i | 0.558377 | − | 0.829587i | \(-0.311424\pi\) |
0.829587 | − | 0.558377i | \(-0.188576\pi\) | |||||||
\(542\) | 24.8879 | + | 35.4423i | 1.06903 | + | 1.52238i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.94859 | − | 36.5217i | 0.126420 | − | 1.56585i | ||||
\(545\) | 11.3234 | − | 19.6126i | 0.485040 | − | 0.840113i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.43060 | − | 1.99102i | −0.317710 | − | 0.0851300i | 0.0964402 | − | 0.995339i | \(-0.469254\pi\) |
−0.414150 | + | 0.910209i | \(0.635921\pi\) | |||||||
\(548\) | 3.91876 | + | 21.8810i | 0.167401 | + | 0.934711i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −12.0975 | + | 14.4566i | −0.515839 | + | 0.616430i | ||||
\(551\) | 1.30966 | − | 0.756135i | 0.0557936 | − | 0.0322124i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.0825 | + | 9.86259i | 0.726422 | + | 0.419400i | ||||
\(554\) | 27.7399 | − | 10.1386i | 1.17855 | − | 0.430750i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.13763 | + | 13.4176i | −0.0482464 | + | 0.569035i | ||||
\(557\) | −24.4143 | + | 24.4143i | −1.03447 | + | 1.03447i | −0.0350828 | + | 0.999384i | \(0.511170\pi\) |
−0.999384 | + | 0.0350828i | \(0.988830\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.0704 | 0.425931 | ||||||||
\(560\) | 37.1520 | − | 3.45131i | 1.56996 | − | 0.145844i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.7774 | − | 7.33138i | −0.665530 | − | 0.309256i | ||||
\(563\) | −3.30278 | − | 12.3261i | −0.139196 | − | 0.519485i | −0.999945 | − | 0.0104567i | \(-0.996671\pi\) |
0.860750 | − | 0.509028i | \(-0.169995\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.3137 | + | 38.4913i | −0.433901 | + | 1.61934i | ||||
\(566\) | 14.3736 | + | 12.0281i | 0.604169 | + | 0.505578i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.96079 | + | 10.8746i | 0.124232 | + | 0.456289i | ||||
\(569\) | −22.2747 | + | 12.8603i | −0.933803 | + | 0.539132i | −0.888012 | − | 0.459819i | \(-0.847914\pi\) |
−0.0457910 | + | 0.998951i | \(0.514581\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.6207 | − | 9.00865i | 1.40698 | − | 0.377000i | 0.526136 | − | 0.850400i | \(-0.323640\pi\) |
0.880848 | + | 0.473400i | \(0.156973\pi\) | |||||||
\(572\) | 4.98288 | − | 13.8055i | 0.208345 | − | 0.577235i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 15.8055 | + | 22.5084i | 0.659711 | + | 0.939480i | ||||
\(575\) | 11.9566 | 0.498626 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.7695 | −1.11443 | −0.557215 | − | 0.830369i | \(-0.688130\pi\) | ||||
−0.557215 | + | 0.830369i | \(0.688130\pi\) | |||||||
\(578\) | 20.2804 | + | 28.8809i | 0.843554 | + | 1.20129i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.11771 | + | 5.86729i | −0.0879333 | + | 0.243626i | ||||
\(581\) | −34.5523 | + | 9.25826i | −1.43347 | + | 0.384097i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.45101 | − | 2.56979i | 0.184342 | − | 0.106430i | ||||
\(584\) | −4.05298 | − | 14.8861i | −0.167714 | − | 0.615991i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.9556 | − | 20.0465i | −0.989598 | − | 0.828112i | ||||
\(587\) | −9.79668 | + | 36.5617i | −0.404352 | + | 1.50906i | 0.400895 | + | 0.916124i | \(0.368699\pi\) |
−0.805247 | + | 0.592939i | \(0.797967\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.32924 | − | 4.96080i | −0.0547704 | − | 0.204406i | ||||
\(590\) | 30.0845 | + | 13.9796i | 1.23856 | + | 0.575529i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.21611 | + | 34.6202i | 0.132181 | + | 1.42288i | ||||
\(593\) | 7.98596 | 0.327944 | 0.163972 | − | 0.986465i | \(-0.447569\pi\) | ||||
0.163972 | + | 0.986465i | \(0.447569\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −42.7228 | + | 42.7228i | −1.75146 | + | 1.75146i | ||||
\(596\) | −1.88192 | + | 22.1960i | −0.0770863 | + | 0.909183i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.74383 | + | 3.19578i | −0.357562 | + | 0.130685i | ||||
\(599\) | −1.64879 | − | 0.951932i | −0.0673679 | − | 0.0388949i | 0.465938 | − | 0.884818i | \(-0.345717\pi\) |
−0.533306 | + | 0.845923i | \(0.679050\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.7530 | + | 6.78561i | −0.479416 | + | 0.276791i | −0.720173 | − | 0.693794i | \(-0.755938\pi\) |
0.240757 | + | 0.970585i | \(0.422604\pi\) | |||||||
\(602\) | −19.8314 | + | 23.6986i | −0.808268 | + | 0.965884i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.69643 | − | 42.9743i | −0.313163 | − | 1.74860i | ||||
\(605\) | −31.6074 | − | 8.46917i | −1.28502 | − | 0.344321i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.16527 | + | 5.48241i | −0.128474 | + | 0.222524i | −0.923086 | − | 0.384594i | \(-0.874341\pi\) |
0.794611 | + | 0.607119i | \(0.207675\pi\) | |||||||
\(608\) | −4.96214 | − | 5.83375i | −0.201241 | − | 0.236590i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.8511 | + | 22.5733i | 0.641794 | + | 0.913966i | ||||
\(611\) | 3.95712 | − | 3.95712i | 0.160088 | − | 0.160088i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.83081 | − | 1.83081i | −0.0739458 | − | 0.0739458i | 0.669167 | − | 0.743112i | \(-0.266651\pi\) |
−0.743112 | + | 0.669167i | \(0.766651\pi\) | |||||||
\(614\) | −7.07703 | − | 1.23809i | −0.285606 | − | 0.0499651i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 22.6758 | + | 38.9131i | 0.913632 | + | 1.56786i | ||||
\(617\) | −3.82758 | − | 2.20985i | −0.154092 | − | 0.0889653i | 0.420971 | − | 0.907074i | \(-0.361689\pi\) |
−0.575064 | + | 0.818109i | \(0.695023\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.75899 | − | 14.0287i | 0.151087 | − | 0.563863i | −0.848322 | − | 0.529480i | \(-0.822387\pi\) |
0.999409 | − | 0.0343824i | \(-0.0109464\pi\) | |||||||
\(620\) | 17.3854 | + | 12.1040i | 0.698216 | + | 0.486110i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.24661 | + | 14.0320i | 0.0499844 | + | 0.562632i | ||||
\(623\) | 3.74672 | + | 6.48952i | 0.150109 | + | 0.259997i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.5810 | + | 26.9872i | −0.623242 | + | 1.07949i | ||||
\(626\) | −32.8154 | − | 15.2485i | −1.31157 | − | 0.609453i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.8186 | + | 1.42599i | 0.671134 | + | 0.0569031i | ||||
\(629\) | −39.8114 | − | 39.8114i | −1.58738 | − | 1.58738i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 33.6255i | − | 1.33861i | −0.742987 | − | 0.669305i | \(-0.766592\pi\) | ||
0.742987 | − | 0.669305i | \(-0.233408\pi\) | |||||||
\(632\) | 11.8564 | + | 11.7614i | 0.471622 | + | 0.467842i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.98546 | − | 24.5847i | −0.356858 | − | 0.976384i | ||||
\(635\) | −43.8637 | + | 11.7532i | −1.74068 | + | 0.466413i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.18711 | + | 1.65783i | 0.245142 | + | 0.0656857i | ||||
\(638\) | −7.49987 | + | 0.666291i | −0.296923 | + | 0.0263787i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 31.1605 | + | 5.19330i | 1.23173 | + | 0.205283i | ||||
\(641\) | 22.9601 | + | 39.7681i | 0.906871 | + | 1.57075i | 0.818386 | + | 0.574668i | \(0.194869\pi\) |
0.0884843 | + | 0.996078i | \(0.471798\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.92565 | + | 25.8469i | 0.273121 | + | 1.01930i | 0.957090 | + | 0.289790i | \(0.0935855\pi\) |
−0.683969 | + | 0.729511i | \(0.739748\pi\) | |||||||
\(644\) | 9.69845 | − | 26.8703i | 0.382173 | − | 1.05884i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.2162 | + | 2.13715i | 0.480638 | + | 0.0840850i | ||||
\(647\) | 11.4351i | 0.449559i | 0.974410 | + | 0.224780i | \(0.0721662\pi\) | ||||
−0.974410 | + | 0.224780i | \(0.927834\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.0431i | 1.57183i | ||||||||
\(650\) | −1.04930 | + | 5.99789i | −0.0411568 | + | 0.235256i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.33368 | − | 17.7472i | −0.326372 | − | 0.695034i | ||||
\(653\) | −5.73613 | − | 21.4075i | −0.224472 | − | 0.837741i | −0.982615 | − | 0.185653i | \(-0.940560\pi\) |
0.758143 | − | 0.652088i | \(-0.226107\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.7239 | + | 42.8230i | 0.966041 | + | 1.67323i | ||||
\(656\) | 8.08154 | + | 21.8386i | 0.315531 | + | 0.852654i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.51962 | + | 17.1050i | 0.0592408 | + | 0.666823i | ||||
\(659\) | −26.7345 | − | 7.16348i | −1.04143 | − | 0.279050i | −0.302723 | − | 0.953079i | \(-0.597896\pi\) |
−0.738705 | + | 0.674029i | \(0.764562\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.68293 | − | 2.59453i | 0.376622 | − | 0.100916i | −0.0655417 | − | 0.997850i | \(-0.520878\pi\) |
0.442164 | + | 0.896934i | \(0.354211\pi\) | |||||||
\(662\) | 26.1810 | − | 9.56890i | 1.01755 | − | 0.371906i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −30.2856 | + | 0.121856i | −1.17531 | + | 0.00472894i | ||||
\(665\) | 12.6289i | 0.489729i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.37700 | + | 3.37700i | 0.130758 | + | 0.130758i | ||||
\(668\) | 12.9479 | − | 10.9239i | 0.500969 | − | 0.422658i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.13326 | − | 6.74290i | 0.121048 | − | 0.260501i | ||||
\(671\) | −16.6472 | + | 28.8337i | −0.642656 | + | 1.11311i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.7789 | − | 29.0620i | −0.646781 | − | 1.12026i | −0.983887 | − | 0.178791i | \(-0.942782\pi\) |
0.337106 | − | 0.941467i | \(-0.390552\pi\) | |||||||
\(674\) | 9.28616 | − | 0.824985i | 0.357690 | − | 0.0317773i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.74774 | + | 20.9261i | 0.144144 | + | 0.804850i | ||||
\(677\) | −6.92612 | + | 25.8486i | −0.266192 | + | 0.993443i | 0.695324 | + | 0.718696i | \(0.255261\pi\) |
−0.961517 | + | 0.274747i | \(0.911406\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −37.6218 | − | 21.7210i | −1.44379 | − | 0.833575i | ||||
\(680\) | −44.1975 | + | 25.7551i | −1.69490 | + | 0.987664i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.40649 | + | 25.1880i | −0.168733 | + | 0.964497i | ||||
\(683\) | 9.62993 | + | 9.62993i | 0.368479 | + | 0.368479i | 0.866922 | − | 0.498443i | \(-0.166095\pi\) |
−0.498443 | + | 0.866922i | \(0.666095\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.9446 | − | 21.9446i | 0.838460 | − | 0.838460i | ||||
\(686\) | 10.9794 | − | 7.70982i | 0.419195 | − | 0.294362i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −21.3507 | + | 15.1212i | −0.813987 | + | 0.576492i | ||||
\(689\) | 0.830078 | − | 1.43774i | 0.0316235 | − | 0.0547734i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.8896 | − | 9.88454i | −1.40335 | − | 0.376025i | −0.523801 | − | 0.851841i | \(-0.675486\pi\) |
−0.879545 | + | 0.475815i | \(0.842153\pi\) | |||||||
\(692\) | −6.88325 | + | 9.88664i | −0.261662 | + | 0.375834i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.59388 | + | 3.00742i | 0.136422 | + | 0.114160i | ||||
\(695\) | 16.2810 | − | 9.39985i | 0.617574 | − | 0.356557i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.6551 | − | 18.8534i | −1.23690 | − | 0.714125i | ||||
\(698\) | −11.0571 | − | 30.2529i | −0.418518 | − | 1.14509i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −12.0485 | − | 14.2809i | −0.455390 | − | 0.539766i | ||||
\(701\) | 24.7308 | − | 24.7308i | 0.934070 | − | 0.934070i | −0.0638873 | − | 0.997957i | \(-0.520350\pi\) |
0.997957 | + | 0.0638873i | \(0.0203498\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.7683 | −0.443851 | ||||||||
\(704\) | 10.1653 | + | 36.7518i | 0.383118 | + | 1.38513i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.9335 | − | 36.4415i | 0.637301 | − | 1.37150i | ||||
\(707\) | 7.88649 | + | 29.4328i | 0.296602 | + | 1.10693i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.27509 | + | 27.1510i | −0.273222 | + | 1.01968i | 0.683802 | + | 0.729668i | \(0.260325\pi\) |
−0.957024 | + | 0.290010i | \(0.906341\pi\) | |||||||
\(710\) | 10.0980 | − | 12.0671i | 0.378970 | − | 0.452871i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.66669 | + | 6.12153i | 0.0624617 | + | 0.229414i | ||||
\(713\) | 14.0461 | − | 8.10951i | 0.526030 | − | 0.303704i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.7927 | + | 5.30345i | −0.740207 | + | 0.198338i | ||||
\(716\) | 10.0318 | + | 21.3635i | 0.374906 | + | 0.798391i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.51267 | + | 5.97767i | −0.317690 | + | 0.223085i | ||||
\(719\) | −12.7928 | −0.477091 | −0.238546 | − | 0.971131i | \(-0.576671\pi\) | ||||
−0.238546 | + | 0.971131i | \(0.576671\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.3987 | 0.536234 | ||||||||
\(722\) | −19.8685 | + | 13.9519i | −0.739430 | + | 0.519234i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 34.1644 | − | 16.0428i | 1.26971 | − | 0.596227i | ||||
\(725\) | 3.01722 | − | 0.808460i | 0.112057 | − | 0.0300255i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.44828 | − | 1.99086i | 0.127890 | − | 0.0738371i | −0.434690 | − | 0.900580i | \(-0.643142\pi\) |
0.562580 | + | 0.826743i | \(0.309809\pi\) | |||||||
\(728\) | 12.6280 | + | 7.22320i | 0.468026 | + | 0.267710i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −13.8230 | + | 16.5185i | −0.511610 | + | 0.611377i | ||||
\(731\) | 10.9650 | − | 40.9221i | 0.405557 | − | 1.51356i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.71206 | + | 36.2459i | 0.358723 | + | 1.33877i | 0.875734 | + | 0.482794i | \(0.160378\pi\) |
−0.517011 | + | 0.855979i | \(0.672955\pi\) | |||||||
\(734\) | 20.3216 | − | 43.7328i | 0.750082 | − | 1.61421i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.7396 | − | 19.9049i | 0.506448 | − | 0.733705i | ||||
\(737\) | 8.97493 | 0.330596 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.06425 | − | 3.06425i | 0.112720 | − | 0.112720i | −0.648497 | − | 0.761217i | \(-0.724602\pi\) |
0.761217 | + | 0.648497i | \(0.224602\pi\) | |||||||
\(740\) | 37.1012 | − | 31.3016i | 1.36387 | − | 1.15067i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.74878 | + | 4.78474i | 0.0641996 | + | 0.175653i | ||||
\(743\) | 30.1059 | + | 17.3817i | 1.10448 | + | 0.637671i | 0.937394 | − | 0.348272i | \(-0.113231\pi\) |
0.167085 | + | 0.985943i | \(0.446565\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26.9327 | − | 15.5496i | 0.986738 | − | 0.569693i | ||||
\(746\) | 26.7434 | + | 22.3793i | 0.979145 | + | 0.819365i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −50.6746 | − | 35.2805i | −1.85285 | − | 1.28998i | ||||
\(749\) | 0.235865 | + | 0.0631998i | 0.00861831 | + | 0.00230927i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.10890 | + | 12.3130i | −0.259407 | + | 0.449307i | −0.966083 | − | 0.258231i | \(-0.916861\pi\) |
0.706676 | + | 0.707537i | \(0.250194\pi\) | |||||||
\(752\) | −2.44784 | + | 14.3316i | −0.0892635 | + | 0.522618i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.99039 | + | 1.39767i | −0.0724858 | + | 0.0509001i | ||||
\(755\) | −43.0991 | + | 43.0991i | −1.56854 | + | 1.56854i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.11199 | + | 2.11199i | 0.0767615 | + | 0.0767615i | 0.744445 | − | 0.667684i | \(-0.232714\pi\) |
−0.667684 | + | 0.744445i | \(0.732714\pi\) | |||||||
\(758\) | 0.919938 | − | 5.25846i | 0.0334137 | − | 0.190996i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.72581 | + | 10.3391i | −0.0988755 | + | 0.375038i | ||||
\(761\) | 16.3519 | + | 9.44076i | 0.592755 | + | 0.342227i | 0.766186 | − | 0.642619i | \(-0.222152\pi\) |
−0.173431 | + | 0.984846i | \(0.555485\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.01279 | + | 26.1721i | −0.253880 | + | 0.947493i | ||||
\(764\) | −3.51419 | + | 0.629371i | −0.127139 | + | 0.0227699i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.86247 | − | 0.787345i | 0.320214 | − | 0.0284479i | ||||
\(767\) | 6.46724 | + | 11.2016i | 0.233519 | + | 0.404466i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.50579 | − | 6.07221i | 0.126422 | − | 0.218970i | −0.795866 | − | 0.605473i | \(-0.792984\pi\) |
0.922288 | + | 0.386503i | \(0.126317\pi\) | |||||||
\(770\) | 26.4969 | − | 57.0224i | 0.954883 | − | 2.05494i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21.1659 | − | 25.0876i | −0.761778 | − | 0.902922i | ||||
\(773\) | −8.54407 | − | 8.54407i | −0.307309 | − | 0.307309i | 0.536556 | − | 0.843865i | \(-0.319725\pi\) |
−0.843865 | + | 0.536556i | \(0.819725\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 10.6082i | − | 0.381057i | ||||||
\(776\) | −26.1121 | − | 25.9028i | −0.937369 | − | 0.929856i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.71646 | − | 1.35833i | 0.133241 | − | 0.0486984i | ||||
\(779\) | −7.61302 | + | 2.03990i | −0.272765 | + | 0.0730871i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.3458 | + | 4.91575i | 0.656465 | + | 0.175899i | ||||
\(782\) | 3.46578 | + | 39.0113i | 0.123936 | + | 1.39504i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −15.6069 | + | 5.77547i | −0.557391 | + | 0.206267i | ||||
\(785\) | −11.7824 | − | 20.4077i | −0.420532 | − | 0.728383i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.16205 | − | 22.9971i | −0.219653 | − | 0.819758i | −0.984476 | − | 0.175517i | \(-0.943840\pi\) |
0.764823 | − | 0.644241i | \(-0.222826\pi\) | |||||||
\(788\) | −8.83112 | + | 4.14689i | −0.314596 | + | 0.147727i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.01792 | − | 22.9668i | 0.142951 | − | 0.817122i | ||||
\(791\) | − | 47.6769i | − | 1.69519i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.7545i | 0.381904i | ||||||||
\(794\) | −8.46542 | − | 1.48098i | −0.300427 | − | 0.0525580i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 28.2357 | + | 10.1912i | 1.00079 | + | 0.361219i | ||||
\(797\) | −1.78931 | − | 6.67778i | −0.0633804 | − | 0.236539i | 0.926968 | − | 0.375141i | \(-0.122406\pi\) |
−0.990348 | + | 0.138602i | \(0.955739\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.7716 | − | 20.3889i | −0.416448 | − | 0.721309i | ||||
\(800\) | −6.78152 | − | 14.2920i | −0.239763 | − | 0.505299i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.6822 | − | 1.65973i | 0.659691 | − | 0.0586071i | ||||
\(803\) | −25.1133 | − | 6.72909i | −0.886229 | − | 0.237464i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −38.5237 | + | 10.3224i | −1.35778 | + | 0.363817i | ||||
\(806\) | 2.83537 | + | 7.75772i | 0.0998715 | + | 0.273254i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.103801 | + | 25.7983i | 0.00365171 | + | 0.907580i | ||||
\(809\) | − | 39.0505i | − | 1.37294i | −0.727157 | − | 0.686471i | \(-0.759159\pi\) | ||
0.727157 | − | 0.686471i | \(-0.240841\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.40853 | − | 2.40853i | −0.0845748 | − | 0.0845748i | 0.663554 | − | 0.748129i | \(-0.269047\pi\) |
−0.748129 | + | 0.663554i | \(0.769047\pi\) | |||||||
\(812\) | 0.630506 | − | 7.43641i | 0.0221264 | − | 0.260967i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 53.1365 | + | 24.6912i | 1.86243 | + | 0.865428i | ||||
\(815\) | −13.6864 | + | 23.7055i | −0.479413 | + | 0.830367i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.42769 | − | 7.66898i | −0.154905 | − | 0.268304i | ||||
\(818\) | −1.53955 | − | 17.3294i | −0.0538291 | − | 0.605908i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 18.5753 | − | 26.6803i | 0.648678 | − | 0.931718i | ||||
\(821\) | −7.66611 | + | 28.6103i | −0.267549 | + | 0.998506i | 0.693123 | + | 0.720820i | \(0.256234\pi\) |
−0.960672 | + | 0.277687i | \(0.910432\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.1086 | + | 12.7644i | 0.770659 | + | 0.444940i | 0.833110 | − | 0.553108i | \(-0.186558\pi\) |
−0.0624509 | + | 0.998048i | \(0.519892\pi\) | |||||||
\(824\) | 11.7879 | + | 3.10778i | 0.410651 | + | 0.108265i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −39.0966 | − | 6.83973i | −1.36034 | − | 0.237985i | ||||
\(827\) | −5.10050 | − | 5.10050i | −0.177362 | − | 0.177362i | 0.612843 | − | 0.790205i | \(-0.290026\pi\) |
−0.790205 | + | 0.612843i | \(0.790026\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.30033 | − | 1.30033i | 0.0451624 | − | 0.0451624i | −0.684165 | − | 0.729327i | \(-0.739833\pi\) |
0.729327 | + | 0.684165i | \(0.239833\pi\) | |||||||
\(830\) | 24.2986 | + | 34.6031i | 0.843416 | + | 1.20109i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.77928 | + | 8.63911i | 0.304367 | + | 0.299507i | ||||
\(833\) | 13.4736 | − | 23.3370i | 0.466833 | − | 0.808578i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.8449 | − | 6.12126i | −0.790579 | − | 0.211835i | ||||
\(836\) | −12.7043 | + | 2.27526i | −0.439386 | + | 0.0786914i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 27.4330 | − | 32.7826i | 0.947658 | − | 1.13246i | ||||
\(839\) | 28.6072 | − | 16.5164i | 0.987631 | − | 0.570209i | 0.0830657 | − | 0.996544i | \(-0.473529\pi\) |
0.904565 | + | 0.426335i | \(0.140196\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.0342 | − | 13.8762i | −0.828766 | − | 0.478488i | ||||
\(842\) | −29.5589 | + | 10.8035i | −1.01867 | + | 0.372312i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 24.5173 | + | 2.07873i | 0.843920 | + | 0.0715529i | ||||
\(845\) | 20.9869 | − | 20.9869i | 0.721972 | − | 0.721972i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 39.1502 | 1.34522 | ||||||||
\(848\) | 0.398959 | + | 4.29463i | 0.0137003 | + | 0.147478i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 23.2306 | + | 10.7947i | 0.796804 | + | 0.370256i | ||||
\(851\) | −9.61896 | − | 35.8984i | −0.329734 | − | 1.23058i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.12451 | + | 15.3929i | −0.141221 | + | 0.527043i | 0.858674 | + | 0.512522i | \(0.171289\pi\) |
−0.999895 | + | 0.0145204i | \(0.995378\pi\) | |||||||
\(854\) | −25.3087 | − | 21.1787i | −0.866046 | − | 0.724721i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.179457 | + | 0.102649i | 0.00613372 | + | 0.00350847i | ||||
\(857\) | 13.6603 | − | 7.88675i | 0.466625 | − | 0.269406i | −0.248201 | − | 0.968709i | \(-0.579839\pi\) |
0.714826 | + | 0.699302i | \(0.246506\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.9956 | + | 8.57320i | −1.09168 | + | 0.292514i | −0.759371 | − | 0.650658i | \(-0.774493\pi\) |
−0.332306 | + | 0.943172i | \(0.607827\pi\) | |||||||
\(860\) | 34.3570 | + | 12.4007i | 1.17156 | + | 0.422859i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.5109 | − | 17.8166i | −0.426124 | − | 0.606834i | ||||
\(863\) | −37.4407 | −1.27449 | −0.637247 | − | 0.770659i | \(-0.719927\pi\) | ||||
−0.637247 | + | 0.770659i | \(0.719927\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.8186 | 0.571850 | ||||||||
\(866\) | −14.0156 | − | 19.9593i | −0.476269 | − | 0.678245i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −23.8399 | − | 8.60467i | −0.809180 | − | 0.292062i | ||||
\(869\) | 27.1845 | − | 7.28408i | 0.922173 | − | 0.247095i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.51063 | − | 1.44951i | 0.0850695 | − | 0.0491149i | ||||
\(872\) | −11.3902 | + | 19.9130i | −0.385720 | + | 0.674338i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.27816 | + | 5.25367i | 0.212362 | + | 0.177708i | ||||
\(875\) | 5.31986 | − | 19.8540i | 0.179844 | − | 0.671187i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.55790 | + | 28.2065i | 0.255212 | + | 0.952465i | 0.967972 | + | 0.251057i | \(0.0807781\pi\) |
−0.712760 | + | 0.701408i | \(0.752555\pi\) | |||||||
\(878\) | −6.73922 | − | 3.13155i | −0.227438 | − | 0.105685i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 34.0002 | − | 40.9641i | 1.14614 | − | 1.38090i | ||||
\(881\) | 11.5567 | 0.389355 | 0.194678 | − | 0.980867i | \(-0.437634\pi\) | ||||
0.194678 | + | 0.980867i | \(0.437634\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.2632 | + | 19.2632i | −0.648260 | + | 0.648260i | −0.952572 | − | 0.304313i | \(-0.901573\pi\) |
0.304313 | + | 0.952572i | \(0.401573\pi\) | |||||||
\(884\) | −19.8737 | − | 1.68502i | −0.668424 | − | 0.0566733i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.1941 | + | 6.28426i | −0.577646 | + | 0.211124i | ||||
\(887\) | 19.8424 | + | 11.4560i | 0.666243 | + | 0.384656i | 0.794652 | − | 0.607066i | \(-0.207653\pi\) |
−0.128408 | + | 0.991721i | \(0.540987\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 47.0523 | − | 27.1657i | 1.57808 | − | 0.911107i | ||||
\(890\) | 5.68434 | − | 6.79281i | 0.190540 | − | 0.227696i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.01700 | + | 0.182138i | −0.0340515 | + | 0.00609843i | ||||
\(893\) | −4.75336 | − | 1.27366i | −0.159065 | − | 0.0426214i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.4752 | − | 28.5359i | 0.550705 | − | 0.953850i | ||||
\(896\) | −37.6194 | + | 3.64746i | −1.25678 | + | 0.121853i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.7348 | − | 32.3762i | −0.758671 | − | 1.08041i | ||||
\(899\) | 2.99615 | − | 2.99615i | 0.0999272 | − | 0.0999272i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.93860 | − | 4.93860i | −0.164529 | − | 0.164529i | ||||
\(902\) | 38.6544 | + | 6.76237i | 1.28705 | + | 0.225162i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.2905 | − | 39.0322i | 0.342257 | − | 1.29819i | ||||
\(905\) | −45.6345 | − | 26.3471i | −1.51694 | − | 0.875807i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.7169 | + | 47.4603i | −0.422259 | + | 1.57589i | 0.347577 | + | 0.937651i | \(0.387005\pi\) |
−0.769836 | + | 0.638242i | \(0.779662\pi\) | |||||||
\(908\) | 11.6502 | − | 16.7335i | 0.386625 | − | 0.555322i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.79731 | − | 20.2308i | −0.0595802 | − | 0.670644i | ||||
\(911\) | −6.47683 | − | 11.2182i | −0.214587 | − | 0.371675i | 0.738558 | − | 0.674190i | \(-0.235507\pi\) |
−0.953145 | + | 0.302515i | \(0.902174\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.5188 | + | 44.1999i | −0.844550 | + | 1.46280i | ||||
\(914\) | 52.2368 | + | 24.2732i | 1.72784 | + | 0.802885i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.61816 | − | 42.6739i | 0.119548 | − | 1.40998i | ||||
\(917\) | −41.8331 | − | 41.8331i | −1.38145 | − | 1.38145i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 5.55214i | − | 0.183148i | −0.995798 | − | 0.0915740i | \(-0.970810\pi\) | ||
0.995798 | − | 0.0915740i | \(-0.0291898\pi\) | |||||||
\(920\) | −33.7666 | + | 0.135862i | −1.11325 | + | 0.00447925i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.5318 | + | 50.7040i | 0.610312 | + | 1.66985i | ||||
\(923\) | 5.92596 | − | 1.58786i | 0.195055 | − | 0.0522649i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.4796 | − | 6.29135i | −0.772006 | − | 0.206858i | ||||
\(926\) | −50.0462 | + | 4.44612i | −1.64462 | + | 0.146109i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.12124 | − | 5.95196i | 0.0696333 | − | 0.195383i | ||||
\(929\) | −28.8356 | − | 49.9447i | −0.946066 | − | 1.63863i | −0.753603 | − | 0.657330i | \(-0.771686\pi\) |
−0.192462 | − | 0.981304i | \(-0.561647\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.45782 | − | 5.44064i | −0.0477780 | − | 0.178310i | ||||
\(932\) | −43.7323 | − | 15.7845i | −1.43250 | − | 0.517039i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 33.6904 | + | 5.89394i | 1.10238 | + | 0.192856i | ||||
\(935\) | 86.2049i | 2.81920i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 44.7899i | − | 1.46322i | −0.681722 | − | 0.731612i | \(-0.738768\pi\) | ||
0.681722 | − | 0.731612i | \(-0.261232\pi\) | |||||||
\(938\) | −1.53300 | + | 8.76279i | −0.0500543 | + | 0.286115i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 18.3733 | − | 8.62769i | 0.599271 | − | 0.281404i | ||||
\(941\) | 9.72682 | + | 36.3010i | 0.317085 | + | 1.18338i | 0.922032 | + | 0.387113i | \(0.126528\pi\) |
−0.604947 | + | 0.796266i | \(0.706806\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.4452 | − | 21.5557i | −0.405270 | − | 0.701949i | ||||
\(944\) | −30.5314 | − | 14.0381i | −0.993712 | − | 0.456901i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.90159 | + | 43.9169i | 0.126852 | + | 1.42786i | ||||
\(947\) | 54.8652 | + | 14.7011i | 1.78288 | + | 0.477721i | 0.991104 | − | 0.133093i | \(-0.0424908\pi\) |
0.791775 | + | 0.610813i | \(0.209157\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.11194 | + | 2.17359i | −0.263325 | + | 0.0705577i | ||||
\(950\) | 5.02898 | − | 1.83804i | 0.163162 | − | 0.0596339i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 43.1023 | − | 43.4506i | 1.39695 | − | 1.40824i | ||||
\(953\) | − | 7.26359i | − | 0.235291i | −0.993056 | − | 0.117645i | \(-0.962465\pi\) | ||
0.993056 | − | 0.117645i | \(-0.0375346\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.52440 | + | 3.52440i | 0.114047 | + | 0.114047i | ||||
\(956\) | −0.565803 | − | 0.670636i | −0.0182994 | − | 0.0216899i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.06467 | + | 17.3555i | −0.260558 | + | 0.560730i | ||||
\(959\) | −18.5653 | + | 32.1560i | −0.599504 | + | 1.03837i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.30507 | + | 14.3848i | 0.267905 | + | 0.464026i | ||||
\(962\) | 18.8521 | − | 1.67483i | 0.607817 | − | 0.0539986i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −30.2155 | + | 5.41142i | −0.973176 | + | 0.174290i | ||||
\(965\) | −11.8604 | + | 44.2638i | −0.381801 | + | 1.42490i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.17378 | + | 2.40973i | 0.134220 | + | 0.0774917i | 0.565606 | − | 0.824675i | \(-0.308642\pi\) |
−0.431387 | + | 0.902167i | \(0.641976\pi\) | |||||||
\(968\) | 32.0515 | + | 8.45010i | 1.03017 | + | 0.271597i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.84890 | + | 50.5812i | −0.284121 | + | 1.62407i | ||||
\(971\) | −2.69916 | − | 2.69916i | −0.0866202 | − | 0.0866202i | 0.662469 | − | 0.749089i | \(-0.269509\pi\) |
−0.749089 | + | 0.662469i | \(0.769509\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.9047 | + | 15.9047i | −0.509881 | + | 0.509881i | ||||
\(974\) | −18.6841 | + | 13.1201i | −0.598676 | + | 0.420395i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.1486 | − | 22.8012i | −0.516903 | − | 0.729849i | ||||
\(977\) | 6.16168 | − | 10.6724i | 0.197130 | − | 0.341439i | −0.750467 | − | 0.660908i | \(-0.770171\pi\) |
0.947597 | + | 0.319469i | \(0.103505\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.3272 | + | 2.76717i | 0.330059 | + | 0.0884390i | ||||
\(980\) | 19.0671 | + | 13.2748i | 0.609076 | + | 0.424049i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 39.2490 | + | 32.8443i | 1.25249 | + | 1.04810i | ||||
\(983\) | −42.5445 | + | 24.5631i | −1.35696 | + | 0.783441i | −0.989213 | − | 0.146485i | \(-0.953204\pi\) |
−0.367747 | + | 0.929926i | \(0.619871\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.7960 | + | 6.81043i | 0.375852 | + | 0.216998i | ||||
\(986\) | 3.51237 | + | 9.61004i | 0.111857 | + | 0.306046i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.18640 | + | 2.68830i | −0.101373 | + | 0.0855263i | ||||
\(989\) | 19.7747 | − | 19.7747i | 0.628798 | − | 0.628798i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.4968 | −1.28642 | −0.643212 | − | 0.765688i | \(-0.722399\pi\) | ||||
−0.643212 | + | 0.765688i | \(0.722399\pi\) | |||||||
\(992\) | −17.6601 | − | 12.1901i | −0.560708 | − | 0.387035i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.93319 | + | 17.0725i | −0.251626 | + | 0.541508i | ||||
\(995\) | −10.8469 | − | 40.4812i | −0.343870 | − | 1.28334i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.26425 | − | 23.3785i | 0.198391 | − | 0.740404i | −0.792972 | − | 0.609258i | \(-0.791467\pi\) |
0.991363 | − | 0.131147i | \(-0.0418659\pi\) | |||||||
\(998\) | 5.97344 | − | 7.13829i | 0.189086 | − | 0.225959i | ||||
\(999\) | 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 | 432.2.y.e.37.13 | 72 | ||
3.2 | odd | 2 | 144.2.x.e.85.6 | yes | 72 | ||
4.3 | odd | 2 | 1728.2.bc.e.1009.17 | 72 | |||
9.2 | odd | 6 | 144.2.x.e.133.6 | yes | 72 | ||
9.7 | even | 3 | inner | 432.2.y.e.181.13 | 72 | ||
12.11 | even | 2 | 576.2.bb.e.49.11 | 72 | |||
16.3 | odd | 4 | 1728.2.bc.e.145.2 | 72 | |||
16.13 | even | 4 | inner | 432.2.y.e.253.13 | 72 | ||
36.7 | odd | 6 | 1728.2.bc.e.1585.2 | 72 | |||
36.11 | even | 6 | 576.2.bb.e.241.3 | 72 | |||
48.29 | odd | 4 | 144.2.x.e.13.6 | ✓ | 72 | ||
48.35 | even | 4 | 576.2.bb.e.337.3 | 72 | |||
144.29 | odd | 12 | 144.2.x.e.61.6 | yes | 72 | ||
144.61 | even | 12 | inner | 432.2.y.e.397.13 | 72 | ||
144.83 | even | 12 | 576.2.bb.e.529.11 | 72 | |||
144.115 | odd | 12 | 1728.2.bc.e.721.17 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.e.13.6 | ✓ | 72 | 48.29 | odd | 4 | ||
144.2.x.e.61.6 | yes | 72 | 144.29 | odd | 12 | ||
144.2.x.e.85.6 | yes | 72 | 3.2 | odd | 2 | ||
144.2.x.e.133.6 | yes | 72 | 9.2 | odd | 6 | ||
432.2.y.e.37.13 | 72 | 1.1 | even | 1 | trivial | ||
432.2.y.e.181.13 | 72 | 9.7 | even | 3 | inner | ||
432.2.y.e.253.13 | 72 | 16.13 | even | 4 | inner | ||
432.2.y.e.397.13 | 72 | 144.61 | even | 12 | inner | ||
576.2.bb.e.49.11 | 72 | 12.11 | even | 2 | |||
576.2.bb.e.241.3 | 72 | 36.11 | even | 6 | |||
576.2.bb.e.337.3 | 72 | 48.35 | even | 4 | |||
576.2.bb.e.529.11 | 72 | 144.83 | even | 12 | |||
1728.2.bc.e.145.2 | 72 | 16.3 | odd | 4 | |||
1728.2.bc.e.721.17 | 72 | 144.115 | odd | 12 | |||
1728.2.bc.e.1009.17 | 72 | 4.3 | odd | 2 | |||
1728.2.bc.e.1585.2 | 72 | 36.7 | odd | 6 |