Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(25,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 10, 12]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.bq (of order \(9\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 25.4 | ||
Character | \(\chi\) | \(=\) | 756.25 |
Dual form | 756.2.bq.a.121.4 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −1.47274 | + | 0.911614i | −0.850286 | + | 0.526320i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.21812 | − | 1.17130i | −1.43919 | − | 0.523821i | −0.499638 | − | 0.866234i | \(-0.666534\pi\) |
−0.939549 | + | 0.342413i | \(0.888756\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.64556 | + | 0.0321766i | −0.999926 | + | 0.0121616i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.33792 | − | 2.68514i | 0.445974 | − | 0.895046i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.42330 | + | 1.97392i | −1.63519 | + | 0.595159i | −0.986188 | − | 0.165632i | \(-0.947034\pi\) |
−0.648997 | + | 0.760791i | \(0.724811\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.660511 | + | 3.74594i | 0.183193 | + | 1.03894i | 0.928255 | + | 0.371943i | \(0.121308\pi\) |
−0.745063 | + | 0.666994i | \(0.767581\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.80722 | − | 1.20866i | 1.49942 | − | 0.312076i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.51635 | 1.82298 | 0.911491 | − | 0.411320i | \(-0.134932\pi\) | ||||
0.911491 | + | 0.411320i | \(0.134932\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.16859 | 0.726924 | 0.363462 | − | 0.931609i | \(-0.381595\pi\) | ||||
0.363462 | + | 0.931609i | \(0.381595\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.86688 | − | 2.45911i | 0.843823 | − | 0.536622i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.59042 | − | 9.01972i | −0.331625 | − | 1.88074i | −0.458301 | − | 0.888797i | \(-0.651542\pi\) |
0.126676 | − | 0.991944i | \(-0.459569\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.15413 | + | 4.32483i | 1.03083 | + | 0.864966i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.477401 | + | 5.17418i | 0.0918758 | + | 0.995770i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.466529 | − | 2.64582i | 0.0866323 | − | 0.491316i | −0.910360 | − | 0.413817i | \(-0.864195\pi\) |
0.996992 | − | 0.0774991i | \(-0.0246935\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.32322 | − | 1.94941i | 0.417262 | − | 0.350124i | −0.409858 | − | 0.912149i | \(-0.634422\pi\) |
0.827120 | + | 0.562025i | \(0.189977\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.18765 | − | 7.85102i | 1.07713 | − | 1.36669i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.55140 | + | 2.99519i | 1.44545 | + | 0.506280i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.552756 | + | 0.957402i | −0.0908726 | + | 0.157396i | −0.907879 | − | 0.419233i | \(-0.862299\pi\) |
0.817006 | + | 0.576629i | \(0.195632\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.38761 | − | 4.91467i | −0.702580 | − | 0.786976i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.41205 | + | 8.00811i | 0.220524 | + | 1.25066i | 0.871059 | + | 0.491179i | \(0.163434\pi\) |
−0.650534 | + | 0.759477i | \(0.725455\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.468371 | + | 0.393010i | 0.0714259 | + | 0.0599335i | 0.677802 | − | 0.735245i | \(-0.262933\pi\) |
−0.606376 | + | 0.795178i | \(0.707377\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.45069 | + | 7.07399i | −1.11068 | + | 1.05453i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.75927 | − | 3.15440i | −0.548346 | − | 0.460117i | 0.326034 | − | 0.945358i | \(-0.394287\pi\) |
−0.874381 | + | 0.485241i | \(0.838732\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.99793 | − | 0.170250i | 0.999704 | − | 0.0243214i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.0696 | + | 6.85200i | −1.55006 | + | 0.959472i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.19430 | − | 3.80063i | 0.301410 | − | 0.522057i | −0.675046 | − | 0.737776i | \(-0.735876\pi\) |
0.976456 | + | 0.215719i | \(0.0692094\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.7649 | 2.66509 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.66651 | + | 2.88853i | −0.618094 | + | 0.382595i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.616398 | + | 3.49577i | 0.0802482 | + | 0.455110i | 0.998281 | + | 0.0586062i | \(0.0186656\pi\) |
−0.918033 | + | 0.396504i | \(0.870223\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.01209 | + | 6.72295i | 1.02584 | + | 0.860785i | 0.990351 | − | 0.138585i | \(-0.0442554\pi\) |
0.0354930 | + | 0.999370i | \(0.488700\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.45315 | + | 7.14673i | −0.435055 | + | 0.900404i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.26202 | − | 12.8286i | 0.280569 | − | 1.59119i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.76497 | + | 1.73431i | 0.582133 | + | 0.211879i | 0.616266 | − | 0.787538i | \(-0.288645\pi\) |
−0.0341327 | + | 0.999417i | \(0.510867\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.5648 | + | 11.8338i | 1.27185 | + | 1.42463i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.16171 | + | 2.01213i | 0.137869 | + | 0.238796i | 0.926690 | − | 0.375827i | \(-0.122641\pi\) |
−0.788821 | + | 0.614623i | \(0.789308\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.39063 | − | 5.87275i | −0.396844 | − | 0.687353i | 0.596491 | − | 0.802620i | \(-0.296561\pi\) |
−0.993335 | + | 0.115267i | \(0.963228\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.5333 | − | 1.67077i | −1.33175 | − | 0.192924i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.2841 | − | 5.39661i | 1.62783 | − | 0.615001i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.56596 | + | 2.38981i | −0.738728 | + | 0.268875i | −0.683855 | − | 0.729618i | \(-0.739698\pi\) |
−0.0548735 | + | 0.998493i | \(0.517476\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.41994 | − | 7.18500i | −0.602215 | − | 0.798334i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.804659 | − | 4.56345i | 0.0883228 | − | 0.500904i | −0.908267 | − | 0.418391i | \(-0.862594\pi\) |
0.996590 | − | 0.0825129i | \(-0.0262946\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.1885 | − | 8.80390i | −2.62361 | − | 0.954917i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.72489 | + | 4.32189i | 0.184927 | + | 0.463356i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.67020 | −0.601041 | −0.300520 | − | 0.953775i | \(-0.597160\pi\) | ||||
−0.300520 | + | 0.953775i | \(0.597160\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.86795 | − | 9.88885i | −0.195814 | − | 1.03663i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.64438 | + | 4.98885i | −0.170515 | + | 0.517320i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.1969 | − | 3.71137i | −1.04618 | − | 0.380779i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.52694 | − | 5.47675i | −0.662710 | − | 0.556080i | 0.248188 | − | 0.968712i | \(-0.420165\pi\) |
−0.910898 | + | 0.412632i | \(0.864609\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.95570 | + | 17.2032i | −0.196555 | + | 1.72899i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.21160 | − | 6.87134i | 0.120559 | − | 0.683724i | −0.863288 | − | 0.504712i | \(-0.831599\pi\) |
0.983847 | − | 0.179012i | \(-0.0572902\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.6175 | + | 6.04829i | 1.63737 | + | 0.595955i | 0.986577 | − | 0.163297i | \(-0.0522128\pi\) |
0.650797 | + | 0.759252i | \(0.274435\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −15.3244 | + | 3.38444i | −1.49551 | + | 0.330288i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.72120 | − | 6.44530i | −0.359742 | − | 0.623091i | 0.628176 | − | 0.778071i | \(-0.283802\pi\) |
−0.987918 | + | 0.154981i | \(0.950469\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.28310 | + | 3.95445i | −0.218682 | + | 0.378768i | −0.954405 | − | 0.298514i | \(-0.903509\pi\) |
0.735723 | + | 0.677282i | \(0.236842\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0587150 | − | 1.91390i | −0.00557298 | − | 0.181660i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.54391 | − | 5.49100i | 0.615600 | − | 0.516549i | −0.280817 | − | 0.959761i | \(-0.590606\pi\) |
0.896417 | + | 0.443212i | \(0.146161\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.44663 | + | 30.8894i | −0.507901 | + | 2.88045i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.9421 | + | 3.23821i | 1.01160 | + | 0.299373i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −19.8849 | + | 0.241850i | −1.82285 | + | 0.0221704i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.0893 | − | 14.3396i | 1.55357 | − | 1.30360i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.37988 | − | 10.5066i | −0.845755 | − | 0.947349i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.95931 | − | 5.12568i | −0.264689 | − | 0.458455i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.0473743 | − | 0.0820547i | 0.00420379 | − | 0.00728118i | −0.863916 | − | 0.503636i | \(-0.831995\pi\) |
0.868120 | + | 0.496355i | \(0.165329\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.04806 | − | 0.151828i | −0.0922767 | − | 0.0133677i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.03526 | + | 5.87122i | 0.0904507 | + | 0.512971i | 0.996047 | + | 0.0888302i | \(0.0283128\pi\) |
−0.905596 | + | 0.424141i | \(0.860576\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.38268 | + | 0.101954i | −0.726871 | + | 0.00884057i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.52418 | − | 17.2103i | 0.389379 | − | 1.48123i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.4972 | + | 8.80821i | 0.896837 | + | 0.752536i | 0.969570 | − | 0.244816i | \(-0.0787275\pi\) |
−0.0727324 | + | 0.997351i | \(0.523172\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.87962 | + | 3.23192i | 0.753160 | + | 0.274128i | 0.689935 | − | 0.723871i | \(-0.257639\pi\) |
0.0632251 | + | 0.997999i | \(0.479861\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.41202 | + | 1.21861i | 0.708420 | + | 0.102625i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.9763 | − | 19.0116i | −0.917887 | − | 1.58983i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.60039 | + | 7.96811i | −0.382042 | + | 0.661716i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.1509 | + | 6.63014i | −0.837234 | + | 0.546845i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.94544 | − | 5.82792i | 0.568993 | − | 0.477442i | −0.312319 | − | 0.949977i | \(-0.601106\pi\) |
0.881312 | + | 0.472536i | \(0.156661\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.99747 | − | 2.54687i | 0.569446 | − | 0.207261i | −0.0412195 | − | 0.999150i | \(-0.513124\pi\) |
0.610665 | + | 0.791889i | \(0.290902\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.0563 | − | 20.1824i | 0.813002 | − | 1.63165i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.75974 | + | 3.55225i | −0.783921 | + | 0.285324i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.53840 | − | 14.3960i | −0.202586 | − | 1.14892i | −0.901193 | − | 0.433418i | \(-0.857308\pi\) |
0.698607 | − | 0.715506i | \(-0.253804\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.233083 | + | 7.59769i | 0.0184847 | + | 0.602536i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.49777 | + | 23.8110i | 0.354474 | + | 1.87657i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.03106 | + | 5.24995i | 0.237411 | + | 0.411207i | 0.959971 | − | 0.280101i | \(-0.0903679\pi\) |
−0.722560 | + | 0.691308i | \(0.757035\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −29.1085 | + | 18.0179i | −2.26609 | + | 1.40269i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.8459 | + | 11.6181i | −1.07143 | + | 0.899035i | −0.995181 | − | 0.0980544i | \(-0.968738\pi\) |
−0.0762466 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.37981 | + | 0.502209i | −0.106139 | + | 0.0386314i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.23932 | − | 8.50810i | 0.324189 | − | 0.650631i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.57198 | − | 14.5864i | 0.195544 | − | 1.10898i | −0.716099 | − | 0.697999i | \(-0.754074\pi\) |
0.911642 | − | 0.410984i | \(-0.134815\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.7747 | − | 11.2757i | −1.04127 | − | 0.852366i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.09458 | − | 4.58644i | −0.307768 | − | 0.344738i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.5468 | 1.08728 | 0.543640 | − | 0.839318i | \(-0.317046\pi\) | ||||
0.543640 | + | 0.839318i | \(0.317046\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.81925 | − | 6.61513i | 0.283882 | − | 0.491699i | −0.688455 | − | 0.725279i | \(-0.741711\pi\) |
0.972338 | + | 0.233580i | \(0.0750441\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.9285 | − | 2.59721i | −1.32531 | − | 0.191991i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.90024 | − | 2.43359i | 0.213230 | − | 0.178921i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −40.7634 | + | 14.8367i | −2.98091 | + | 1.08496i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.42948 | − | 13.6732i | −0.103979 | − | 0.994579i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.38893 | + | 3.05332i | −0.607001 | + | 0.220930i | −0.627191 | − | 0.778866i | \(-0.715795\pi\) |
0.0201892 | + | 0.999796i | \(0.493573\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.04659 | + | 5.07369i | −0.435243 | + | 0.365212i | −0.833926 | − | 0.551877i | \(-0.813912\pi\) |
0.398683 | + | 0.917089i | \(0.369467\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.36332 | + | 20.9552i | 0.598910 | + | 1.50063i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.61207 | − | 16.6486i | 0.684832 | − | 1.18616i | −0.288658 | − | 0.957432i | \(-0.593209\pi\) |
0.973490 | − | 0.228731i | \(-0.0734576\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.58364 | 0.679366 | 0.339683 | − | 0.940540i | \(-0.389680\pi\) | ||||
0.339683 | + | 0.940540i | \(0.389680\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.59857 | + | 1.78963i | −0.606496 | + | 0.126231i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.14910 | + | 7.01467i | −0.0806507 | + | 0.492333i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.83576 | − | 27.4250i | 0.337744 | − | 1.91544i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −26.3470 | − | 7.79717i | −1.83125 | − | 0.541941i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.1842 | + | 6.25454i | −1.18866 | + | 0.432635i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.28493 | − | 6.95188i | 0.570358 | − | 0.478587i | −0.311407 | − | 0.950277i | \(-0.600800\pi\) |
0.881765 | + | 0.471689i | \(0.156356\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.54518 | − | 1.90432i | −0.242912 | − | 0.130482i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.04694 | − | 1.81336i | −0.0714009 | − | 0.123670i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.08347 | + | 5.23203i | −0.412973 | + | 0.355173i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.3472 | + | 5.55808i | 0.699199 | + | 0.375580i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.96463 | + | 28.1558i | 0.333957 | + | 1.89396i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.1785 | − | 7.70834i | 1.41822 | − | 0.516188i | 0.484686 | − | 0.874688i | \(-0.338934\pi\) |
0.933530 | + | 0.358500i | \(0.116712\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 18.5086 | − | 8.05328i | 1.23391 | − | 0.536885i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.62450 | − | 3.13906i | 0.572428 | − | 0.208347i | −0.0395553 | − | 0.999217i | \(-0.512594\pi\) |
0.611983 | + | 0.790871i | \(0.290372\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.2482 | + | 12.7947i | −1.00763 | + | 0.845500i | −0.988023 | − | 0.154308i | \(-0.950685\pi\) |
−0.0196049 | + | 0.999808i | \(0.506241\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.1171 | + | 20.9694i | −1.06043 | + | 1.37969i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.51577 | − | 2.62539i | 0.0993015 | − | 0.171995i | −0.812094 | − | 0.583526i | \(-0.801673\pi\) |
0.911396 | + | 0.411531i | \(0.135006\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.40304 | + | 14.5545i | 0.548154 | + | 0.949430i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.49136 | − | 9.50519i | 0.486616 | − | 0.617429i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.36486 | + | 2.68059i | 0.476393 | + | 0.173393i | 0.569046 | − | 0.822306i | \(-0.307313\pi\) |
−0.0926532 | + | 0.995698i | \(0.529535\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.2956 | + | 10.3173i | 0.792032 | + | 0.664594i | 0.946248 | − | 0.323443i | \(-0.104840\pi\) |
−0.154215 | + | 0.988037i | \(0.549285\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.5321 | + | 5.64075i | 0.932235 | + | 0.361854i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −22.7196 | − | 7.64879i | −1.45150 | − | 0.488663i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.09289 | + | 11.8694i | 0.133167 | + | 0.755229i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.97505 | + | 7.45431i | 0.188536 | + | 0.472398i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.17868 | − | 12.4338i | 0.453114 | − | 0.784817i | −0.545463 | − | 0.838135i | \(-0.683646\pi\) |
0.998578 | + | 0.0533178i | \(0.0169796\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.4295 | + | 45.7772i | 1.66161 | + | 2.87799i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 43.6491 | − | 9.08473i | 2.73341 | − | 0.568908i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.9282 | + | 17.5609i | −1.30547 | + | 1.09542i | −0.316294 | + | 0.948661i | \(0.602439\pi\) |
−0.989173 | + | 0.146756i | \(0.953117\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.43154 | − | 2.55065i | 0.0889517 | − | 0.158489i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.48021 | − | 4.79259i | −0.401115 | − | 0.296654i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.523469 | + | 2.96874i | −0.0322785 | + | 0.183061i | −0.996684 | − | 0.0813663i | \(-0.974072\pi\) |
0.964406 | + | 0.264427i | \(0.0851828\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.5132 | + | 9.66072i | −0.707250 | + | 0.593453i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.35073 | − | 5.16904i | 0.511057 | − | 0.316340i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.19714 | + | 15.9299i | −0.560760 | + | 0.971264i | 0.436671 | + | 0.899621i | \(0.356157\pi\) |
−0.997430 | + | 0.0716428i | \(0.977176\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.75087 | − | 15.1569i | −0.531577 | − | 0.920719i | −0.999321 | − | 0.0368545i | \(-0.988266\pi\) |
0.467743 | − | 0.883864i | \(-0.345067\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.7658 | + | 12.8608i | 0.712099 | + | 0.778374i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −36.4892 | − | 13.2810i | −2.20038 | − | 0.800874i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.36810 | − | 13.4302i | 0.142285 | − | 0.806940i | −0.827222 | − | 0.561876i | \(-0.810080\pi\) |
0.969507 | − | 0.245064i | \(-0.0788090\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.12616 | − | 8.84632i | −0.127290 | − | 0.529615i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.84240 | + | 6.58056i | 0.467839 | + | 0.392563i | 0.846005 | − | 0.533174i | \(-0.179001\pi\) |
−0.378167 | + | 0.925737i | \(0.623445\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.4426 | − | 3.80079i | −0.620748 | − | 0.225934i | 0.0124515 | − | 0.999922i | \(-0.496036\pi\) |
−0.633199 | + | 0.773989i | \(0.718259\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 18.4007 | − | 3.82976i | 1.08996 | − | 0.226855i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.99332 | − | 21.1405i | −0.235718 | − | 1.24788i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 39.4955 | 2.32326 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.6052 | + | 2.11578i | 0.856170 | + | 0.124029i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.0729 | − | 4.03021i | −0.646886 | − | 0.235447i | −0.00232167 | − | 0.999997i | \(-0.500739\pi\) |
−0.644564 | + | 0.764550i | \(0.722961\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.11095 | − | 11.9718i | 0.122904 | − | 0.697025i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.8025 | − | 27.1187i | −0.742875 | − | 1.57359i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 32.7369 | − | 11.9152i | 1.89322 | − | 0.689076i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.25175 | − | 1.02466i | −0.0721495 | − | 0.0590604i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.47964 | + | 11.2242i | 0.257348 | + | 0.644814i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.9093 | − | 31.0198i | −1.02548 | − | 1.77619i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.88732 | − | 5.00098i | −0.164788 | − | 0.285421i | 0.771792 | − | 0.635875i | \(-0.219361\pi\) |
−0.936580 | + | 0.350454i | \(0.886027\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −29.9870 | + | 6.24122i | −1.70590 | + | 0.355051i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.0607 | + | 5.84563i | 0.910721 | + | 0.331475i | 0.754541 | − | 0.656253i | \(-0.227860\pi\) |
0.156180 | + | 0.987729i | \(0.450082\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.567255 | − | 3.21706i | 0.0320631 | − | 0.181839i | −0.964570 | − | 0.263826i | \(-0.915015\pi\) |
0.996633 | + | 0.0819870i | \(0.0261266\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 19.4836 | − | 18.9544i | 1.09778 | − | 1.06796i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.14221 | − | 4.31482i | −0.288815 | − | 0.242345i | 0.486856 | − | 0.873482i | \(-0.338144\pi\) |
−0.775671 | + | 0.631138i | \(0.782588\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.69250 | + | 15.2699i | 0.150751 | + | 0.854953i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.3560 | + | 6.09995i | 0.633829 | + | 0.340466i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.8162 | 1.32517 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.7962 | + | 22.1637i | −0.709806 | + | 1.22942i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.242516 | − | 7.90518i | −0.0134112 | − | 0.437158i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.0469 | + | 8.22419i | 0.553901 | + | 0.453414i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.09302 | + | 0.917149i | 0.0600776 | + | 0.0504111i | 0.672332 | − | 0.740250i | \(-0.265293\pi\) |
−0.612254 | + | 0.790661i | \(0.709737\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.83121 | + | 2.76516i | 0.100350 | + | 0.151530i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.3028 | − | 11.1624i | −0.726812 | − | 0.609868i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.86833 | − | 16.2671i | −0.156248 | − | 0.886127i | −0.957636 | − | 0.287982i | \(-0.907016\pi\) |
0.801388 | − | 0.598145i | \(-0.204095\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.63181 | + | 14.0523i | −0.251565 | + | 0.763218i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.75152 | + | 15.1581i | −0.473921 | + | 0.820855i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5079 | + | 0.675575i | −0.999334 | + | 0.0364776i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −20.1377 | − | 50.4572i | −1.08418 | − | 2.71653i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.54372 | + | 6.32993i | −0.404968 | + | 0.339808i | −0.822410 | − | 0.568895i | \(-0.807371\pi\) |
0.417442 | + | 0.908703i | \(0.362927\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.99392 | + | 16.9794i | −0.160261 | + | 0.908885i | 0.793556 | + | 0.608497i | \(0.208227\pi\) |
−0.953817 | + | 0.300388i | \(0.902884\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.0668 | + | 5.20591i | −1.01771 | + | 0.277871i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.43269 | + | 3.71947i | 0.235928 | + | 0.197967i | 0.753085 | − | 0.657924i | \(-0.228565\pi\) |
−0.517156 | + | 0.855891i | \(0.673009\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.38170 | − | 7.83600i | −0.0733329 | − | 0.415892i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 29.0648 | − | 18.4835i | 1.53827 | − | 0.978253i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.7530 | 1.35919 | 0.679596 | − | 0.733587i | \(-0.262155\pi\) | ||||
0.679596 | + | 0.733587i | \(0.262155\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.96004 | −0.471581 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.0959 | + | 36.6973i | −0.634869 | + | 1.92611i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.03271 | + | 22.8707i | 0.211082 | + | 1.19710i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.0269 | − | 9.83697i | 1.41079 | − | 0.513486i | 0.479429 | − | 0.877581i | \(-0.340844\pi\) |
0.931362 | + | 0.364095i | \(0.118622\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 23.3921 | + | 6.92268i | 1.21774 | + | 0.360380i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.68284 | + | 10.1254i | −0.295039 | + | 0.525684i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.3460 | − | 12.1370i | −1.72659 | − | 0.628428i | −0.728212 | − | 0.685352i | \(-0.759648\pi\) |
−0.998378 | + | 0.0569244i | \(0.981871\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.03094 | + | 4.85104i | 0.466356 | + | 0.250507i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.2192 | 0.526317 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.3221 | 1.66028 | 0.830138 | − | 0.557557i | \(-0.188261\pi\) | ||||
0.830138 | + | 0.557557i | \(0.188261\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.00503220 | + | 0.164032i | 0.000257808 | + | 0.00840363i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.5447 | + | 11.4813i | 1.61186 | + | 0.586668i | 0.981806 | − | 0.189885i | \(-0.0608115\pi\) |
0.630052 | + | 0.776553i | \(0.283034\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −52.2891 | + | 0.635966i | −2.66490 | + | 0.0324118i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.68193 | − | 0.731825i | 0.0854973 | − | 0.0372008i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.3023 | − | 10.6652i | 1.48568 | − | 0.540745i | 0.533374 | − | 0.845879i | \(-0.320924\pi\) |
0.952309 | + | 0.305135i | \(0.0987015\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.9541 | − | 67.7953i | −0.604547 | − | 3.42856i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.87695 | − | 7.70303i | −0.346896 | − | 0.388566i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 23.9292 | 1.20401 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.66082 | −0.233920 | −0.116960 | − | 0.993137i | \(-0.537315\pi\) | ||||
−0.116960 | + | 0.993137i | \(0.537315\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.2526 | − | 7.79192i | 0.613395 | − | 0.390084i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.0943919 | + | 0.535323i | 0.00471371 | + | 0.0267328i | 0.987074 | − | 0.160266i | \(-0.0512351\pi\) |
−0.982360 | + | 0.186999i | \(0.940124\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.83689 | + | 7.41503i | 0.440197 | + | 0.369369i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.02621 | + | 29.4706i | 0.448516 | + | 1.46440i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.10793 | − | 6.28337i | 0.0549179 | − | 0.311455i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.4687 | − | 20.5317i | 1.20990 | − | 1.01523i | 0.210609 | − | 0.977570i | \(-0.432455\pi\) |
0.999291 | − | 0.0376559i | \(-0.0119891\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.4893 | − | 3.40279i | −1.15864 | − | 0.167847i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.74320 | − | 9.22842i | −0.0857772 | − | 0.454101i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.93466 | + | 13.7432i | −0.389497 | + | 0.674629i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.0236 | + | 3.33501i | −0.784681 | + | 0.163316i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.45228 | + | 19.5788i | 0.168655 | + | 0.956489i | 0.945216 | + | 0.326447i | \(0.105851\pi\) |
−0.776561 | + | 0.630042i | \(0.783037\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.70095 | + | 5.62276i | 0.326584 | + | 0.274037i | 0.791306 | − | 0.611420i | \(-0.209401\pi\) |
−0.464722 | + | 0.885457i | \(0.653846\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.4996 | + | 5.87382i | −0.656374 | + | 0.285595i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 38.7402 | + | 32.5069i | 1.87918 | + | 1.57682i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.4128 | − | 17.5281i | −1.03624 | − | 0.848245i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 33.4965 | + | 17.9929i | 1.61722 | + | 0.868705i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.761083 | − | 1.31823i | 0.0366601 | − | 0.0634971i | −0.847113 | − | 0.531412i | \(-0.821661\pi\) |
0.883773 | + | 0.467915i | \(0.154995\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.5151 | 0.553382 | 0.276691 | − | 0.960959i | \(-0.410762\pi\) | ||||
0.276691 | + | 0.960959i | \(0.410762\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.488664 | − | 15.9287i | −0.0234296 | − | 0.763724i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.03939 | − | 28.5798i | −0.241067 | − | 1.36716i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.0913 | − | 8.46762i | −0.481632 | − | 0.404137i | 0.369384 | − | 0.929277i | \(-0.379569\pi\) |
−0.851016 | + | 0.525139i | \(0.824013\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.90553 | − | 19.0182i | 0.424073 | − | 0.905628i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.05176 | + | 22.9787i | −0.192505 | + | 1.09175i | 0.723422 | + | 0.690406i | \(0.242568\pi\) |
−0.915927 | + | 0.401344i | \(0.868543\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.2474 | + | 6.64151i | 0.865010 | + | 0.314838i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.91602 | + | 14.9146i | −0.232520 | + | 0.705435i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.6509 | + | 28.8402i | 0.785803 | + | 1.36105i | 0.928518 | + | 0.371287i | \(0.121083\pi\) |
−0.142715 | + | 0.989764i | \(0.545583\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.4653 | − | 40.6431i | −1.10494 | − | 1.91381i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.98368 | + | 10.1299i | −0.375106 | + | 0.475942i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.57152 | + | 34.0114i | −0.261197 | + | 1.59448i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.09268 | + | 0.397705i | −0.0511136 | + | 0.0186038i | −0.367450 | − | 0.930043i | \(-0.619769\pi\) |
0.316337 | + | 0.948647i | \(0.397547\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.58831 | + | 38.8909i | 0.167488 | + | 1.81527i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.29091 | + | 24.3350i | −0.199848 | + | 1.13339i | 0.705496 | + | 0.708714i | \(0.250724\pi\) |
−0.905344 | + | 0.424679i | \(0.860387\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −37.5340 | − | 13.6613i | −1.74435 | − | 0.634893i | −0.744875 | − | 0.667204i | \(-0.767491\pi\) |
−0.999478 | + | 0.0323113i | \(0.989713\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.1353 | − | 14.1287i | 0.516385 | − | 0.655201i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.7646 | −1.37734 | −0.688670 | − | 0.725074i | \(-0.741805\pi\) | ||||
−0.688670 | + | 0.725074i | \(0.741805\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.6618 | − | 4.43488i | −0.584667 | − | 0.204784i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.8620 | + | 18.8875i | 0.776958 | + | 0.870288i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.31588 | − | 1.20688i | −0.152465 | − | 0.0554926i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.3313 | + | 13.7036i | 0.749333 | + | 0.628765i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.26943 | − | 10.9769i | −0.332844 | − | 0.502599i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.81299 | − | 15.9533i | 0.128529 | − | 0.728924i | −0.850620 | − | 0.525781i | \(-0.823773\pi\) |
0.979149 | − | 0.203143i | \(-0.0651157\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.95147 | − | 1.43822i | −0.180172 | − | 0.0655771i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −28.3305 | − | 30.9671i | −1.28908 | − | 1.40905i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.5896 | + | 25.2698i | 0.662477 | + | 1.14744i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.5298 | − | 26.8984i | 0.703721 | − | 1.21888i | −0.263429 | − | 0.964679i | \(-0.584854\pi\) |
0.967151 | − | 0.254203i | \(-0.0818130\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.24988 | − | 4.96865i | −0.418294 | − | 0.224690i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.0069 | + | 15.1096i | −0.812640 | + | 0.681886i | −0.951236 | − | 0.308463i | \(-0.900185\pi\) |
0.138596 | + | 0.990349i | \(0.455741\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.50659 | − | 19.8869i | 0.157929 | − | 0.895660i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 26.4438 | − | 53.0714i | 1.18856 | − | 2.38538i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.13810 | − | 5.28584i | −0.140763 | − | 0.237102i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.37489 | − | 2.83187i | 0.151081 | − | 0.126772i | −0.564114 | − | 0.825697i | \(-0.690782\pi\) |
0.715195 | + | 0.698925i | \(0.246338\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.80019 | − | 29.7325i | 0.437840 | − | 1.32835i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.8654 | + | 29.2118i | 0.751992 | + | 1.30249i | 0.946856 | + | 0.321658i | \(0.104240\pi\) |
−0.194864 | + | 0.980830i | \(0.562427\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.9475 | + | 20.6937i | −0.531656 | + | 0.920856i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.57428 | − | 1.99747i | 0.0699160 | − | 0.0887109i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.66843 | + | 32.1473i | 0.251249 | + | 1.42490i | 0.805521 | + | 0.592567i | \(0.201885\pi\) |
−0.554273 | + | 0.832335i | \(0.687003\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.15907 | + | 15.4276i | 0.405173 | + | 0.682476i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.51269 | + | 16.3948i | 0.0667868 | + | 0.723850i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −46.3928 | − | 38.9282i | −2.04431 | − | 1.71538i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.6142 | + | 9.68677i | 1.17049 | + | 0.426024i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.50931 | + | 23.8266i | 0.417412 | + | 1.04587i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.0876612 | + | 0.151834i | 0.00384051 | + | 0.00665195i | 0.867939 | − | 0.496670i | \(-0.165444\pi\) |
−0.864099 | + | 0.503322i | \(0.832111\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.5065 | − | 35.5183i | 0.896686 | − | 1.55311i | 0.0649821 | − | 0.997886i | \(-0.479301\pi\) |
0.831704 | − | 0.555219i | \(-0.187366\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 30.5657 | + | 4.04901i | 1.33399 | + | 0.176713i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.4621 | − | 14.6524i | 0.760661 | − | 0.638271i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −57.2129 | + | 20.8238i | −2.48752 | + | 0.905383i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.2113 | + | 3.02195i | 0.443133 | + | 0.131141i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29.0652 | + | 10.5789i | −1.25896 | + | 0.458222i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.42588 | + | 25.1004i | 0.191347 | + | 1.08518i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.4237 | + | 13.2611i | −0.924500 | + | 0.572258i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −37.6158 | + | 14.7367i | −1.62023 | + | 0.634753i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.4531 | − | 26.7655i | −0.664380 | − | 1.15074i | −0.979453 | − | 0.201672i | \(-0.935362\pi\) |
0.315073 | − | 0.949067i | \(-0.397971\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.405689 | + | 13.2240i | 0.0174098 | + | 0.567498i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.9792 | − | 10.0517i | 0.513131 | − | 0.430568i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.9716 | + | 15.2764i | −1.79457 | + | 0.653172i | −0.795702 | + | 0.605688i | \(0.792898\pi\) |
−0.998872 | + | 0.0474837i | \(0.984880\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 28.7716 | − | 12.5188i | 1.22794 | − | 0.534290i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.47824 | − | 8.38351i | 0.0629751 | − | 0.357150i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.2937 | − | 6.53366i | 0.735404 | − | 0.277839i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.05280 | + | 6.22795i | −0.0871367 | + | 0.264362i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.41393 | 0.271767 | 0.135883 | − | 0.990725i | \(-0.456613\pi\) | ||||
0.135883 | + | 0.990725i | \(0.456613\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.16283 | + | 2.01408i | −0.0491824 | + | 0.0851865i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 46.5085 | − | 59.0110i | 1.96359 | − | 2.49144i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.3430 | − | 9.51791i | 0.478051 | − | 0.401132i | −0.371670 | − | 0.928365i | \(-0.621215\pi\) |
0.849721 | + | 0.527233i | \(0.176770\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.4907 | + | 10.0058i | −1.15654 | + | 0.420947i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.5699 | + | 18.8339i | 0.611880 | + | 0.790951i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.58688 | − | 3.48934i | 0.401903 | − | 0.146281i | −0.133157 | − | 0.991095i | \(-0.542511\pi\) |
0.535060 | + | 0.844814i | \(0.320289\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.2614 | + | 23.7141i | −1.18270 | + | 0.992404i | −0.182744 | + | 0.983160i | \(0.558498\pi\) |
−0.999957 | + | 0.00924397i | \(0.997058\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.57125 | − | 12.1442i | 0.399845 | − | 0.507331i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.8115 | − | 53.3671i | 1.28493 | − | 2.22556i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.8368 | 0.909078 | 0.454539 | − | 0.890727i | \(-0.349804\pi\) | ||||
0.454539 | + | 0.890727i | \(0.349804\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.27980 | − | 12.9844i | 0.177862 | − | 0.539612i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.98193 | + | 12.0987i | −0.0822245 | + | 0.501941i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.39818 | + | 24.9433i | −0.182154 | + | 1.03305i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −31.4200 | − | 23.2374i | −1.29906 | − | 0.960749i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.574415 | + | 0.209070i | −0.0237087 | + | 0.00862925i | −0.353847 | − | 0.935303i | \(-0.615127\pi\) |
0.330139 | + | 0.943932i | \(0.392905\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.36132 | − | 6.17688i | 0.303318 | − | 0.254514i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.02102 | + | 33.2815i | 0.0419990 | + | 1.36902i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.6799 | + | 32.3545i | 0.767091 | + | 1.32864i | 0.939134 | + | 0.343552i | \(0.111630\pi\) |
−0.172043 | + | 0.985090i | \(0.555037\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 64.2753 | + | 22.5129i | 2.63503 | + | 0.922939i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.1142 | + | 8.73658i | −0.577656 | + | 0.357564i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.34928 | − | 18.9947i | −0.136848 | − | 0.776102i | −0.973555 | − | 0.228452i | \(-0.926634\pi\) |
0.836707 | − | 0.547650i | \(-0.184478\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.97144 | + | 2.53740i | −0.284371 | + | 0.103503i | −0.480268 | − | 0.877122i | \(-0.659460\pi\) |
0.195897 | + | 0.980625i | \(0.437238\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.0320 | − | 10.4742i | 0.449258 | − | 0.426544i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −71.7914 | + | 26.1299i | −2.91873 | + | 1.06233i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.72921 | + | 8.16378i | −0.394897 | + | 0.331358i | −0.818517 | − | 0.574482i | \(-0.805203\pi\) |
0.423620 | + | 0.905840i | \(0.360759\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.70235 | − | 11.3783i | −0.190549 | − | 0.461072i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.33318 | − | 16.1655i | 0.377580 | − | 0.653987i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.515883 | + | 0.893535i | 0.0208363 | + | 0.0360895i | 0.876256 | − | 0.481847i | \(-0.160034\pi\) |
−0.855419 | + | 0.517936i | \(0.826700\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 17.8792 | + | 44.7982i | 0.720958 | + | 1.80644i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.43837 | + | 1.97941i | 0.218941 | + | 0.0796879i | 0.449162 | − | 0.893450i | \(-0.351723\pi\) |
−0.230221 | + | 0.973138i | \(0.573945\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.99908 | + | 7.55112i | 0.361703 | + | 0.303505i | 0.805469 | − | 0.592638i | \(-0.201913\pi\) |
−0.443766 | + | 0.896143i | \(0.646358\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 45.9103 | − | 12.5351i | 1.84232 | − | 0.503017i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.0008 | − | 0.182448i | 0.600996 | − | 0.00730962i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.32202 | − | 13.1688i | −0.0928807 | − | 0.526753i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19.6061 | − | 24.8767i | 0.782993 | − | 0.993478i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.15471 | + | 7.19616i | −0.165659 | + | 0.286930i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.87426 | + | 4.97837i | 0.114423 | + | 0.198186i | 0.917549 | − | 0.397623i | \(-0.130165\pi\) |
−0.803126 | + | 0.595809i | \(0.796832\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.86411 | + | 17.7910i | −0.233077 | + | 0.707128i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.248567 | + | 0.208572i | −0.00986408 | + | 0.00827694i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.25995 | + | 26.1014i | 0.208407 | + | 1.03417i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.95713 | − | 0.427266i | 0.275220 | − | 0.0169024i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.11163 | − | 40.3320i | 0.280892 | − | 1.59302i | −0.438707 | − | 0.898630i | \(-0.644563\pi\) |
0.719599 | − | 0.694389i | \(-0.244325\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.2014 | − | 12.7555i | 0.599486 | − | 0.503028i | −0.291795 | − | 0.956481i | \(-0.594252\pi\) |
0.891280 | + | 0.453453i | \(0.149808\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.19495 | + | 1.71619i | 0.125801 | + | 0.0675751i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.9573 | + | 29.3710i | −0.666662 | + | 1.15469i | 0.312170 | + | 0.950026i | \(0.398944\pi\) |
−0.978832 | + | 0.204666i | \(0.934389\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.2433 | − | 17.7419i | −0.402084 | − | 0.696429i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.18978 | − | 13.2512i | 0.164211 | − | 0.519355i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.58749 | + | 0.941769i | 0.101256 | + | 0.0368543i | 0.392152 | − | 0.919901i | \(-0.371731\pi\) |
−0.290895 | + | 0.956755i | \(0.593953\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.54539 | − | 20.1069i | 0.138530 | − | 0.785642i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.3055 | + | 1.24705i | −0.792194 | + | 0.0486519i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.71271 | − | 2.27623i | −0.105672 | − | 0.0886695i | 0.588421 | − | 0.808555i | \(-0.299750\pi\) |
−0.694093 | + | 0.719885i | \(0.744194\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.5490 | − | 10.7550i | −1.14932 | − | 0.418319i | −0.304051 | − | 0.952656i | \(-0.598339\pi\) |
−0.845272 | + | 0.534337i | \(0.820562\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −32.9788 | − | 36.9403i | −1.28079 | − | 1.43464i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 27.0959 | + | 9.49053i | 1.05073 | + | 0.368027i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.6065 | −0.952768 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.1633 | + | 30.6590i | −0.934209 | + | 1.18534i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −56.7225 | − | 20.6453i | −2.18975 | − | 0.797003i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.446620 | − | 2.53291i | 0.0172159 | − | 0.0976363i | −0.974989 | − | 0.222253i | \(-0.928659\pi\) |
0.992205 | + | 0.124617i | \(0.0397701\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19.9168 | + | 28.7331i | −0.766600 | + | 1.10594i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.76256 | − | 3.55328i | 0.375206 | − | 0.136564i | −0.147532 | − | 0.989057i | \(-0.547133\pi\) |
0.522738 | + | 0.852494i | \(0.324911\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.4436 | + | 14.2790i | 0.669424 | + | 0.547979i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.84003 | + | 12.4852i | −0.377071 | + | 0.478435i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.33259 | + | 12.7004i | 0.280574 | + | 0.485968i | 0.971526 | − | 0.236932i | \(-0.0761419\pi\) |
−0.690952 | + | 0.722900i | \(0.742809\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23.4642 | − | 40.6412i | −0.896522 | − | 1.55282i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.7927 | − | 32.7438i | 0.411768 | − | 1.24925i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.6863 | + | 5.70935i | 0.597601 | + | 0.217509i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.640328 | + | 3.63148i | −0.0243592 | + | 0.138148i | −0.994562 | − | 0.104146i | \(-0.966789\pi\) |
0.970203 | + | 0.242295i | \(0.0779000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.62036 | − | 45.5751i | 0.175513 | − | 1.73125i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −24.7902 | − | 20.8014i | −0.940344 | − | 0.789042i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.6134 | + | 60.1917i | 0.402012 | + | 2.27992i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.161009 | + | 5.24832i | 0.00608991 | + | 0.198510i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.4154 | −1.67755 | −0.838774 | − | 0.544480i | \(-0.816727\pi\) | ||||
−0.838774 | + | 0.544480i | \(0.816727\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.75146 | + | 3.03361i | −0.0660575 | + | 0.114415i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −25.6435 | − | 13.7746i | −0.965792 | − | 0.518783i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.98427 | + | 18.2175i | −0.112235 | + | 0.685140i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.5183 | + | 12.1823i | 0.545246 | + | 0.457516i | 0.873327 | − | 0.487134i | \(-0.161958\pi\) |
−0.328081 | + | 0.944649i | \(0.606402\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.36775 | + | 20.8279i | −0.0887977 | + | 0.781107i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.2780 | − | 17.8544i | −0.796868 | − | 0.668652i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.0549 | + | 74.0381i | 0.488226 | + | 2.76887i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.2902 | + | 2.76610i | −0.496331 | + | 0.103302i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.55541 | + | 13.0864i | −0.281769 | + | 0.488039i | −0.971821 | − | 0.235722i | \(-0.924255\pi\) |
0.690051 | + | 0.723760i | \(0.257588\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −44.1572 | − | 15.4664i | −1.64450 | − | 0.575998i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −27.5137 | − | 3.98577i | −1.02324 | − | 0.148232i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.8473 | − | 11.6192i | 0.514275 | − | 0.431528i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.83299 | − | 27.4092i | 0.179246 | − | 1.01655i | −0.753883 | − | 0.657009i | \(-0.771821\pi\) |
0.933128 | − | 0.359543i | \(-0.117067\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.5442 | + | 4.94031i | −0.983118 | + | 0.182974i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.52044 | + | 2.95400i | 0.130208 | + | 0.109258i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.68148 | − | 20.8787i | −0.135979 | − | 0.771173i | −0.974173 | − | 0.225802i | \(-0.927500\pi\) |
0.838195 | − | 0.545371i | \(-0.183611\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 40.4328 | − | 9.44682i | 1.49139 | − | 0.348451i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.2652 | −1.07800 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.0470 | −0.994940 | −0.497470 | − | 0.867481i | \(-0.665738\pi\) | ||||
−0.497470 | + | 0.867481i | \(0.665738\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.9025 | − | 15.5726i | −0.510723 | − | 0.572072i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.65459 | − | 20.7262i | −0.134074 | − | 0.760371i | −0.975500 | − | 0.219999i | \(-0.929395\pi\) |
0.841426 | − | 0.540372i | \(-0.181717\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29.1775 | + | 10.6197i | −1.06898 | + | 0.389077i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.1769 | − | 8.26615i | −0.408942 | − | 0.302443i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.0520 | + | 16.9317i | 0.367293 | + | 0.618670i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.85761 | + | 1.40406i | 0.140766 | + | 0.0512348i | 0.411443 | − | 0.911436i | \(-0.365025\pi\) |
−0.270676 | + | 0.962670i | \(0.587247\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.762535 | + | 24.8560i | 0.0277883 | + | 0.905802i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.5018 | −0.928107 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.6566 | −0.532703 | −0.266352 | − | 0.963876i | \(-0.585818\pi\) | ||||
−0.266352 | + | 0.963876i | \(0.585818\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −80.6549 | − | 43.3244i | −2.92759 | − | 1.57258i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46.6259 | − | 16.9705i | −1.69019 | − | 0.615178i | −0.695539 | − | 0.718488i | \(-0.744835\pi\) |
−0.994649 | + | 0.103309i | \(0.967057\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.91284 | − | 10.5352i | 0.214059 | − | 0.381399i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −56.0020 | + | 53.1706i | −2.02476 | + | 1.92239i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.6878 | + | 4.61799i | −0.458130 | + | 0.166746i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.64912 | + | 20.6952i | 0.131590 | + | 0.746287i | 0.977174 | + | 0.212443i | \(0.0681419\pi\) |
−0.845583 | + | 0.533844i | \(0.820747\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.8131 | − | 44.9410i | 0.533480 | − | 1.61851i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.3099 | −0.442758 | −0.221379 | − | 0.975188i | \(-0.571056\pi\) | ||||
−0.221379 | + | 0.975188i | \(0.571056\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.4050 | 0.732971 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.216917 | + | 5.06145i | 0.00778184 | + | 0.181578i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.47419 | + | 25.3744i | 0.160305 | + | 0.909133i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.2721 | − | 8.61929i | −0.367563 | − | 0.308422i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13.9126 | + | 1.15079i | 0.497197 | + | 0.0411258i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.69313 | + | 49.3012i | −0.310271 | + | 1.75963i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.3207 | − | 15.3729i | 0.653064 | − | 0.547985i | −0.254935 | − | 0.966958i | \(-0.582054\pi\) |
0.907999 | + | 0.418973i | \(0.137610\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.93541 | − | 4.84939i | −0.0689025 | − | 0.172643i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.1356 | + | 14.7373i | −0.609272 | + | 0.523998i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.8917 | + | 34.4534i | −0.706375 | + | 1.22348i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.14909 | − | 24.7233i | 0.289018 | − | 0.876845i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.83496 | − | 33.0917i | −0.206685 | − | 1.17217i | −0.894766 | − | 0.446535i | \(-0.852658\pi\) |
0.688081 | − | 0.725634i | \(-0.258453\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.2560 | − | 23.7096i | −0.999625 | − | 0.838785i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.58629 | + | 15.2253i | −0.268048 | + | 0.537959i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29.9807 | + | 25.1568i | 1.05800 | + | 0.887765i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.4155 | − | 81.8949i | 0.472833 | − | 2.88641i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.976941 | − | 31.8449i | −0.0343899 | − | 1.12099i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.8893 | − | 18.8608i | 0.382846 | − | 0.663110i | −0.608621 | − | 0.793461i | \(-0.708277\pi\) |
0.991468 | + | 0.130351i | \(0.0416105\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.09426 | −0.178884 | −0.0894418 | − | 0.995992i | \(-0.528508\pi\) | ||||
−0.0894418 | + | 0.995992i | \(0.528508\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.7050 | + | 14.3448i | 0.936586 | + | 0.503095i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.60505 | − | 20.4452i | −0.126279 | − | 0.716165i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.48408 | + | 1.24529i | 0.0519213 | + | 0.0435671i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −29.0521 | − | 8.21479i | −1.01516 | − | 0.287048i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.32362 | − | 13.1779i | 0.0810947 | − | 0.459911i | −0.917036 | − | 0.398803i | \(-0.869426\pi\) |
0.998131 | − | 0.0611077i | \(-0.0194633\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.6365 | + | 15.1545i | 1.45136 | + | 0.528251i | 0.942970 | − | 0.332877i | \(-0.108019\pi\) |
0.508388 | + | 0.861128i | \(0.330242\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 65.8463 | − | 13.7046i | 2.29247 | − | 0.477135i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.5944 | − | 40.8667i | −0.820457 | − | 1.42107i | −0.905343 | − | 0.424682i | \(-0.860386\pi\) |
0.0848859 | − | 0.996391i | \(-0.472947\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.6222 | + | 28.7904i | 0.577312 | + | 0.999933i | 0.995786 | + | 0.0917045i | \(0.0292315\pi\) |
−0.418475 | + | 0.908228i | \(0.637435\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.75552 | + | 21.9379i | 0.303726 | + | 0.761017i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 52.5989 | − | 1.27966i | 1.82244 | − | 0.0443375i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 58.1660 | − | 21.1707i | 2.01292 | − | 0.732642i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.1957 | + | 11.0901i | 0.386980 | + | 0.383329i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.31042 | − | 30.1169i | 0.183336 | − | 1.03975i | −0.744738 | − | 0.667357i | \(-0.767426\pi\) |
0.928075 | − | 0.372395i | \(-0.121463\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.4684 | + | 7.44988i | 0.705806 | + | 0.256893i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.5487 | − | 2.54220i | −0.604411 | − | 0.0875581i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.02862 | 0.172990 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −44.7493 | + | 38.4861i | −1.53760 | + | 1.32240i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.8441 | − | 3.92204i | 0.646727 | − | 0.134604i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.51461 | + | 3.46303i | 0.326157 | + | 0.118711i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.7735 | − | 18.2701i | −0.745510 | − | 0.625557i | 0.188801 | − | 0.982015i | \(-0.439540\pi\) |
−0.934311 | + | 0.356458i | \(0.883984\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −23.6082 | + | 22.4146i | −0.807383 | + | 0.766562i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.10089 | + | 34.5998i | −0.208402 | + | 1.18191i | 0.683593 | + | 0.729863i | \(0.260416\pi\) |
−0.891995 | + | 0.452045i | \(0.850695\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.5318 | − | 10.7487i | −1.00761 | − | 0.366741i | −0.215097 | − | 0.976593i | \(-0.569007\pi\) |
−0.792516 | + | 0.609852i | \(0.791229\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 25.1530 | + | 27.4940i | 0.857214 | + | 0.936994i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.33016 | + | 16.1603i | 0.317602 | + | 0.550104i | 0.979987 | − | 0.199060i | \(-0.0637889\pi\) |
−0.662385 | + | 0.749164i | \(0.730456\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25.3620 | + | 43.9282i | −0.862333 | + | 1.49360i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −58.1665 | + | 36.0046i | −1.97544 | + | 1.22278i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30.8918 | − | 25.9213i | 1.04793 | − | 0.879321i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.34930 | + | 18.9948i | −0.113487 | + | 0.643615i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −23.4384 | + | 10.1983i | −0.793268 | + | 0.345159i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.99396 | + | 13.4651i | 0.270245 | + | 0.455202i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.7131 | − | 19.0585i | 0.766967 | − | 0.643561i | −0.172963 | − | 0.984928i | \(-0.555334\pi\) |
0.939930 | + | 0.341367i | \(0.110890\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.9815 | − | 4.15877i | 0.673959 | − | 0.140272i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.686405 | − | 1.18889i | −0.0231256 | − | 0.0400547i | 0.854231 | − | 0.519894i | \(-0.174028\pi\) |
−0.877357 | + | 0.479839i | \(0.840695\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.5910 | − | 30.4685i | 0.591984 | − | 1.02535i | −0.401981 | − | 0.915648i | \(-0.631678\pi\) |
0.993965 | − | 0.109698i | \(-0.0349884\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.80477 | + | 19.5557i | 0.262355 | + | 0.657358i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.33083 | + | 18.8901i | 0.111838 | + | 0.634266i | 0.988267 | + | 0.152735i | \(0.0488081\pi\) |
−0.876429 | + | 0.481531i | \(0.840081\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.122691 | + | 0.218605i | −0.00411493 | + | 0.00733176i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 43.5765 | + | 28.2679i | 1.45987 | + | 0.947010i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.9116 | − | 9.99501i | −0.398606 | − | 0.334470i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −46.8134 | − | 17.0387i | −1.56480 | − | 0.569541i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −37.3507 | + | 47.3914i | −1.24711 | + | 1.58235i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.07394 | − | 7.05627i | −0.135873 | − | 0.235340i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.4931 | − | 28.5669i | 0.549465 | − | 0.951701i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.77759 | + | 0.367946i | 0.0924324 | + | 0.0122445i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.0391 | + | 16.8148i | −0.666122 | + | 0.558943i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.5844 | − | 15.4994i | 1.41399 | − | 0.514651i | 0.481693 | − | 0.876340i | \(-0.340022\pi\) |
0.932299 | + | 0.361690i | \(0.117800\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.8295 | − | 12.4466i | −0.558199 | − | 0.412829i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.9489 | + | 6.53288i | −0.594675 | + | 0.216444i | −0.621784 | − | 0.783188i | \(-0.713592\pi\) |
0.0271093 | + | 0.999632i | \(0.491370\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.64397 | + | 26.3373i | 0.153693 | + | 0.871636i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 54.6538 | + | 29.3577i | 1.80680 | + | 0.970537i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.92774 | − | 15.4993i | −0.0966825 | − | 0.511833i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.4129 | − | 18.0356i | −0.343489 | − | 0.594941i | 0.641589 | − | 0.767049i | \(-0.278276\pi\) |
−0.985078 | + | 0.172108i | \(0.944942\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.81123 | + | 4.73302i | 0.290340 | + | 0.155958i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.77002 | + | 5.68072i | −0.222838 | + | 0.186983i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.98958 | + | 2.54400i | −0.229816 | + | 0.0836462i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 38.4734 | − | 36.5282i | 1.26363 | − | 1.19974i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.23922 | + | 24.0418i | −0.139084 | + | 0.788786i | 0.832844 | + | 0.553508i | \(0.186711\pi\) |
−0.971928 | + | 0.235278i | \(0.924400\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.1736 | − | 0.539452i | 0.726709 | − | 0.0176798i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28.9822 | + | 6.03210i | −0.948836 | + | 0.197482i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 148.560 | 4.85842 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.331776 | − | 0.574653i | 0.0108387 | − | 0.0187731i | −0.860555 | − | 0.509357i | \(-0.829883\pi\) |
0.871394 | + | 0.490584i | \(0.163217\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.09730 | + | 5.25501i | 0.0684428 | + | 0.171491i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.3068 | − | 28.7868i | 1.11837 | − | 0.938423i | 0.119848 | − | 0.992792i | \(-0.461759\pi\) |
0.998521 | + | 0.0543689i | \(0.0173147\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 69.9851 | − | 25.4725i | 2.27903 | − | 0.829499i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11.4152 | + | 45.6764i | −0.371336 | + | 1.48585i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.36627 | − | 3.40904i | 0.304363 | − | 0.110779i | −0.185324 | − | 0.982678i | \(-0.559333\pi\) |
0.489687 | + | 0.871898i | \(0.337111\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.7594 | − | 16.5801i | 0.641418 | − | 0.538214i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.5066 | + | 1.66690i | 0.373126 | + | 0.0540530i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.4619 | − | 18.1205i | 0.338894 | − | 0.586981i | −0.645331 | − | 0.763903i | \(-0.723281\pi\) |
0.984225 | + | 0.176922i | \(0.0566139\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.5729 | 0.989317 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −17.8856 | − | 20.0341i | −0.578161 | − | 0.647611i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.0544 | − | 22.9648i | −0.905923 | − | 0.741573i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.78596 | + | 21.4712i | −0.122128 | + | 0.692620i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.2852 | + | 1.36862i | −0.718130 | + | 0.0441033i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.4015 | − | 9.24537i | 0.817702 | − | 0.297619i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.5314 | − | 23.1016i | 0.885351 | − | 0.742897i | −0.0819215 | − | 0.996639i | \(-0.526106\pi\) |
0.967272 | + | 0.253741i | \(0.0816612\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −35.0751 | + | 21.7112i | −1.12677 | + | 0.697464i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.0313675 | − | 0.0543300i | −0.00100663 | − | 0.00174353i | 0.865522 | − | 0.500872i | \(-0.166987\pi\) |
−0.866528 | + | 0.499128i | \(0.833654\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.5955 | − | 8.26451i | −0.756438 | − | 0.264948i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.35924 | − | 44.3065i | −0.0435306 | − | 1.41894i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.78539 | − | 38.4819i | −0.217084 | − | 1.23114i | −0.877253 | − | 0.480027i | \(-0.840627\pi\) |
0.660170 | − | 0.751117i | \(-0.270484\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.7512 | − | 11.1925i | 0.982812 | − | 0.357714i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.56364 | + | 11.4212i | 0.241488 | + | 0.364651i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.5526 | − | 5.66068i | 0.496051 | − | 0.180548i | −0.0818663 | − | 0.996643i | \(-0.526088\pi\) |
0.577917 | + | 0.816096i | \(0.303866\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −50.4333 | + | 42.3186i | −1.60694 | + | 1.34838i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.2937 | − | 2.95323i | −0.709616 | − | 0.0940023i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.79993 | − | 4.84963i | 0.0890327 | − | 0.154209i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.21944 | + | 7.30828i | 0.134035 | + | 0.232155i | 0.925228 | − | 0.379411i | \(-0.123873\pi\) |
−0.791193 | + | 0.611566i | \(0.790540\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.44581 | − | 0.354313i | −0.0776155 | − | 0.0112438i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.8413 | − | 11.2253i | −0.977735 | − | 0.355866i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.1535 | − | 16.9108i | −0.638269 | − | 0.535571i | 0.265217 | − | 0.964189i | \(-0.414556\pi\) |
−0.903486 | + | 0.428618i | \(0.859001\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.21765 | − | 2.40299i | −0.165079 | − | 0.0760274i |
(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 | 756.2.bq.a.25.4 | yes | 144 | |
7.2 | even | 3 | 756.2.bp.a.457.13 | yes | 144 | ||
27.13 | even | 9 | 756.2.bp.a.445.13 | ✓ | 144 | ||
189.121 | even | 9 | inner | 756.2.bq.a.121.4 | yes | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.bp.a.445.13 | ✓ | 144 | 27.13 | even | 9 | ||
756.2.bp.a.457.13 | yes | 144 | 7.2 | even | 3 | ||
756.2.bq.a.25.4 | yes | 144 | 1.1 | even | 1 | trivial | |
756.2.bq.a.121.4 | yes | 144 | 189.121 | even | 9 | inner |