Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(109,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.v (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(128\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 109.16 | ||
Character | \(\chi\) | \(=\) | 864.109 |
Dual form | 864.2.v.b.325.16 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.239074 | + | 1.39386i | −0.169051 | + | 0.985607i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.88569 | − | 0.666470i | −0.942844 | − | 0.333235i | ||||
\(5\) | 0.369546 | − | 0.153071i | 0.165266 | − | 0.0684554i | −0.298517 | − | 0.954404i | \(-0.596492\pi\) |
0.463783 | + | 0.885949i | \(0.346492\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.24156 | + | 1.24156i | −0.469265 | + | 0.469265i | −0.901676 | − | 0.432412i | \(-0.857663\pi\) |
0.432412 | + | 0.901676i | \(0.357663\pi\) | |||||||
\(8\) | 1.37978 | − | 2.46905i | 0.487827 | − | 0.872940i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.125011 | + | 0.551690i | 0.0395318 | + | 0.174460i | ||||
\(11\) | −0.490552 | − | 1.18430i | −0.147907 | − | 0.357079i | 0.832511 | − | 0.554009i | \(-0.186903\pi\) |
−0.980417 | + | 0.196930i | \(0.936903\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.60261 | + | 1.90646i | 1.27654 | + | 0.528758i | 0.914945 | − | 0.403579i | \(-0.132234\pi\) |
0.361590 | + | 0.932337i | \(0.382234\pi\) | |||||||
\(14\) | −1.43373 | − | 2.02738i | −0.383181 | − | 0.541840i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.11164 | + | 2.51351i | 0.777909 | + | 0.628377i | ||||
\(17\) | 4.73651i | 1.14877i | 0.818584 | + | 0.574387i | \(0.194759\pi\) | ||||
−0.818584 | + | 0.574387i | \(0.805241\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.25236 | + | 0.932959i | 0.516727 | + | 0.214035i | 0.625779 | − | 0.780001i | \(-0.284781\pi\) |
−0.109051 | + | 0.994036i | \(0.534781\pi\) | |||||||
\(20\) | −0.798865 | + | 0.0423528i | −0.178632 | + | 0.00947038i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.76802 | − | 0.400626i | 0.376943 | − | 0.0854137i | ||||
\(23\) | −4.41161 | − | 4.41161i | −0.919884 | − | 0.919884i | 0.0771364 | − | 0.997021i | \(-0.475422\pi\) |
−0.997021 | + | 0.0771364i | \(0.975422\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.42240 | + | 3.42240i | −0.684480 | + | 0.684480i | ||||
\(26\) | −3.75771 | + | 5.95961i | −0.736947 | + | 1.16878i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.16865 | − | 1.51373i | 0.598819 | − | 0.286068i | ||||
\(29\) | −3.72693 | + | 8.99760i | −0.692073 | + | 1.67081i | 0.0484889 | + | 0.998824i | \(0.484559\pi\) |
−0.740562 | + | 0.671988i | \(0.765441\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.82890 | 1.04690 | 0.523451 | − | 0.852056i | \(-0.324644\pi\) | ||||
0.523451 | + | 0.852056i | \(0.324644\pi\) | |||||||
\(32\) | −4.24739 | + | 3.73627i | −0.750839 | + | 0.660485i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.60203 | − | 1.13238i | −1.13224 | − | 0.194201i | ||||
\(35\) | −0.268766 | + | 0.648859i | −0.0454298 | + | 0.109677i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.91286 | + | 0.792332i | −0.314472 | + | 0.130259i | −0.534336 | − | 0.845272i | \(-0.679438\pi\) |
0.219865 | + | 0.975530i | \(0.429438\pi\) | |||||||
\(38\) | −1.83889 | + | 2.91643i | −0.298308 | + | 0.473108i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.131954 | − | 1.12363i | 0.0208637 | − | 0.177662i | ||||
\(41\) | −3.14074 | − | 3.14074i | −0.490501 | − | 0.490501i | 0.417963 | − | 0.908464i | \(-0.362744\pi\) |
−0.908464 | + | 0.417963i | \(0.862744\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.99088 | + | 4.80640i | 0.303606 | + | 0.732969i | 0.999885 | + | 0.0151975i | \(0.00483770\pi\) |
−0.696279 | + | 0.717771i | \(0.745162\pi\) | |||||||
\(44\) | 0.135729 | + | 2.56015i | 0.0204620 | + | 0.385957i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.20386 | − | 5.09446i | 1.06215 | − | 0.751138i | ||||
\(47\) | 3.99894i | 0.583305i | 0.956524 | + | 0.291652i | \(0.0942051\pi\) | ||||
−0.956524 | + | 0.291652i | \(0.905795\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.91707i | 0.559581i | ||||||||
\(50\) | −3.95214 | − | 5.58855i | −0.558917 | − | 0.790340i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.40849 | − | 6.66250i | −1.02737 | − | 0.923922i | ||||
\(53\) | 0.855802 | + | 2.06609i | 0.117553 | + | 0.283799i | 0.971694 | − | 0.236243i | \(-0.0759162\pi\) |
−0.854141 | + | 0.520042i | \(0.825916\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.362563 | − | 0.362563i | −0.0488879 | − | 0.0488879i | ||||
\(56\) | 1.35239 | + | 4.77854i | 0.180720 | + | 0.638560i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −11.6504 | − | 7.34590i | −1.52977 | − | 0.964564i | ||||
\(59\) | −1.65001 | + | 0.683456i | −0.214813 | + | 0.0889783i | −0.487495 | − | 0.873126i | \(-0.662089\pi\) |
0.272682 | + | 0.962104i | \(0.412089\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.408897 | − | 0.987165i | 0.0523539 | − | 0.126394i | −0.895539 | − | 0.444984i | \(-0.853209\pi\) |
0.947893 | + | 0.318590i | \(0.103209\pi\) | |||||||
\(62\) | −1.39354 | + | 8.12467i | −0.176979 | + | 1.03183i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.19240 | − | 6.81350i | −0.524050 | − | 0.851688i | ||||
\(65\) | 1.99270 | 0.247164 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.01800 | + | 9.70032i | −0.490877 | + | 1.18508i | 0.463397 | + | 0.886151i | \(0.346630\pi\) |
−0.954274 | + | 0.298932i | \(0.903370\pi\) | |||||||
\(68\) | 3.15674 | − | 8.93159i | 0.382811 | − | 1.08311i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.840163 | − | 0.529747i | −0.100419 | − | 0.0633169i | ||||
\(71\) | 2.17183 | − | 2.17183i | 0.257748 | − | 0.257748i | −0.566389 | − | 0.824138i | \(-0.691660\pi\) |
0.824138 | + | 0.566389i | \(0.191660\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.91821 | + | 7.91821i | 0.926757 | + | 0.926757i | 0.997495 | − | 0.0707380i | \(-0.0225354\pi\) |
−0.0707380 | + | 0.997495i | \(0.522535\pi\) | |||||||
\(74\) | −0.647085 | − | 2.85568i | −0.0752222 | − | 0.331966i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.62546 | − | 3.26040i | −0.415869 | − | 0.373994i | ||||
\(77\) | 2.07942 | + | 0.861324i | 0.236972 | + | 0.0981570i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 0.868785i | − | 0.0977460i | −0.998805 | − | 0.0488730i | \(-0.984437\pi\) | ||
0.998805 | − | 0.0488730i | \(-0.0155630\pi\) | |||||||
\(80\) | 1.53464 | + | 0.452555i | 0.171578 | + | 0.0505972i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.12862 | − | 3.62688i | 0.566361 | − | 0.400522i | ||||
\(83\) | −5.47101 | − | 2.26617i | −0.600521 | − | 0.248744i | 0.0616485 | − | 0.998098i | \(-0.480364\pi\) |
−0.662170 | + | 0.749354i | \(0.730364\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.725022 | + | 1.75036i | 0.0786397 | + | 0.189853i | ||||
\(86\) | −7.17541 | + | 1.62592i | −0.773744 | + | 0.175327i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.60094 | − | 0.422876i | −0.383861 | − | 0.0450788i | ||||
\(89\) | −4.82488 | + | 4.82488i | −0.511437 | + | 0.511437i | −0.914966 | − | 0.403530i | \(-0.867783\pi\) |
0.403530 | + | 0.914966i | \(0.367783\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.08139 | + | 3.34742i | −0.847160 | + | 0.350905i | ||||
\(92\) | 5.37871 | + | 11.2591i | 0.560770 | + | 1.17384i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.57396 | − | 0.956040i | −0.574910 | − | 0.0986080i | ||||
\(95\) | 0.975160 | 0.100049 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.97696 | 0.708403 | 0.354201 | − | 0.935169i | \(-0.384753\pi\) | ||||
0.354201 | + | 0.935169i | \(0.384753\pi\) | |||||||
\(98\) | −5.45985 | − | 0.936468i | −0.551528 | − | 0.0945975i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.73450 | − | 4.17265i | 0.873450 | − | 0.417265i | ||||
\(101\) | 9.37354 | − | 3.88265i | 0.932702 | − | 0.386338i | 0.135999 | − | 0.990709i | \(-0.456576\pi\) |
0.796703 | + | 0.604371i | \(0.206576\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.8340 | − | 11.8340i | 1.16604 | − | 1.16604i | 0.182906 | − | 0.983130i | \(-0.441450\pi\) |
0.983130 | − | 0.182906i | \(-0.0585504\pi\) | |||||||
\(104\) | 11.0578 | − | 8.73357i | 1.08430 | − | 0.856397i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.08444 | + | 0.698921i | −0.299587 | + | 0.0678852i | ||||
\(107\) | −5.36875 | − | 12.9613i | −0.519017 | − | 1.25302i | −0.938508 | − | 0.345258i | \(-0.887791\pi\) |
0.419491 | − | 0.907759i | \(-0.362209\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.3323 | − | 7.17926i | −1.66013 | − | 0.687649i | −0.662043 | − | 0.749466i | \(-0.730311\pi\) |
−0.998088 | + | 0.0618168i | \(0.980311\pi\) | |||||||
\(110\) | 0.592040 | − | 0.418682i | 0.0564488 | − | 0.0399198i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.98394 | + | 0.742611i | −0.659920 | + | 0.0701702i | ||||
\(113\) | 4.58506i | 0.431327i | 0.976468 | + | 0.215663i | \(0.0691913\pi\) | ||||
−0.976468 | + | 0.215663i | \(0.930809\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.30558 | − | 0.955003i | −0.214997 | − | 0.0890545i | ||||
\(116\) | 13.0244 | − | 14.4828i | 1.20929 | − | 1.34469i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.558168 | − | 2.46328i | −0.0513835 | − | 0.226763i | ||||
\(119\) | −5.88065 | − | 5.88065i | −0.539079 | − | 0.539079i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.61626 | − | 6.61626i | 0.601478 | − | 0.601478i | ||||
\(122\) | 1.27821 | + | 0.805950i | 0.115724 | + | 0.0729673i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10.9915 | − | 3.88478i | −0.987064 | − | 0.348864i | ||||
\(125\) | −1.50622 | + | 3.63633i | −0.134720 | + | 0.325244i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.96737 | −0.263311 | −0.131656 | − | 0.991296i | \(-0.542029\pi\) | ||||
−0.131656 | + | 0.991296i | \(0.542029\pi\) | |||||||
\(128\) | 10.4994 | − | 4.21468i | 0.928021 | − | 0.372529i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.476402 | + | 2.77754i | −0.0417832 | + | 0.243607i | ||||
\(131\) | 4.48635 | − | 10.8310i | 0.391975 | − | 0.946311i | −0.597535 | − | 0.801843i | \(-0.703853\pi\) |
0.989510 | − | 0.144468i | \(-0.0461469\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.95476 | + | 1.63812i | −0.342921 | + | 0.142043i | ||||
\(134\) | −12.5603 | − | 7.91962i | −1.08504 | − | 0.684151i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.6947 | + | 6.53536i | 1.00281 | + | 0.560403i | ||||
\(137\) | 16.1892 | + | 16.1892i | 1.38314 | + | 1.38314i | 0.838991 | + | 0.544145i | \(0.183146\pi\) |
0.544145 | + | 0.838991i | \(0.316854\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.98923 | + | 7.21663i | 0.253543 | + | 0.612106i | 0.998485 | − | 0.0550224i | \(-0.0175230\pi\) |
−0.744942 | + | 0.667129i | \(0.767523\pi\) | |||||||
\(140\) | 0.939254 | − | 1.04442i | 0.0793814 | − | 0.0882696i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.50799 | + | 3.54645i | 0.210466 | + | 0.297611i | ||||
\(143\) | − | 6.38608i | − | 0.534031i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.89551i | 0.323504i | ||||||||
\(146\) | −12.9299 | + | 9.14384i | −1.07009 | + | 0.756750i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.13512 | − | 0.219228i | 0.339905 | − | 0.0180205i | ||||
\(149\) | −4.00080 | − | 9.65879i | −0.327759 | − | 0.791279i | −0.998758 | − | 0.0498215i | \(-0.984135\pi\) |
0.671000 | − | 0.741458i | \(-0.265865\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.96565 | + | 3.96565i | 0.322720 | + | 0.322720i | 0.849810 | − | 0.527090i | \(-0.176717\pi\) |
−0.527090 | + | 0.849810i | \(0.676717\pi\) | |||||||
\(152\) | 5.41129 | − | 4.27391i | 0.438914 | − | 0.346660i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.69770 | + | 2.69250i | −0.136804 | + | 0.216968i | ||||
\(155\) | 2.15405 | − | 0.892235i | 0.173017 | − | 0.0716660i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.375808 | + | 0.907280i | −0.0299927 | + | 0.0724088i | −0.938166 | − | 0.346185i | \(-0.887477\pi\) |
0.908174 | + | 0.418594i | \(0.137477\pi\) | |||||||
\(158\) | 1.21096 | + | 0.207704i | 0.0963391 | + | 0.0165240i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.997690 | + | 2.03087i | −0.0788743 | + | 0.160555i | ||||
\(161\) | 10.9545 | 0.863338 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.94673 | + | 11.9425i | −0.387458 | + | 0.935406i | 0.603019 | + | 0.797727i | \(0.293964\pi\) |
−0.990477 | + | 0.137679i | \(0.956036\pi\) | |||||||
\(164\) | 3.82925 | + | 8.01567i | 0.299014 | + | 0.625918i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.46669 | − | 7.08404i | 0.346682 | − | 0.549828i | ||||
\(167\) | 11.8590 | − | 11.8590i | 0.917677 | − | 0.917677i | −0.0791830 | − | 0.996860i | \(-0.525231\pi\) |
0.996860 | + | 0.0791830i | \(0.0252312\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.35705 | + | 8.35705i | 0.642850 | + | 0.642850i | ||||
\(170\) | −2.61309 | + | 0.592115i | −0.200415 | + | 0.0454131i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.550850 | − | 10.3902i | −0.0420019 | − | 0.792247i | ||||
\(173\) | 21.5118 | + | 8.91050i | 1.63552 | + | 0.677453i | 0.995834 | − | 0.0911875i | \(-0.0290663\pi\) |
0.639681 | + | 0.768640i | \(0.279066\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 8.49821i | − | 0.642405i | ||||||
\(176\) | 1.45032 | − | 4.91810i | 0.109322 | − | 0.370716i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.57171 | − | 7.87871i | −0.417617 | − | 0.590534i | ||||
\(179\) | 17.0995 | + | 7.08284i | 1.27808 | + | 0.529396i | 0.915410 | − | 0.402523i | \(-0.131867\pi\) |
0.362666 | + | 0.931919i | \(0.381867\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.33210 | − | 10.4586i | −0.322002 | − | 0.777383i | −0.999138 | − | 0.0415238i | \(-0.986779\pi\) |
0.677135 | − | 0.735859i | \(-0.263221\pi\) | |||||||
\(182\) | −2.73379 | − | 12.0646i | −0.202642 | − | 0.894288i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.9795 | + | 4.80541i | −1.25175 | + | 0.354260i | ||||
\(185\) | −0.585606 | + | 0.585606i | −0.0430546 | + | 0.0430546i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.60944 | − | 2.32350i | 0.410203 | − | 0.169911i | ||||
\(188\) | 2.66517 | − | 7.54075i | 0.194378 | − | 0.549966i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.233135 | + | 1.35924i | −0.0169134 | + | 0.0986093i | ||||
\(191\) | −25.8962 | −1.87378 | −0.936892 | − | 0.349619i | \(-0.886311\pi\) | ||||
−0.936892 | + | 0.349619i | \(0.886311\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.1836 | 1.23690 | 0.618452 | − | 0.785822i | \(-0.287760\pi\) | ||||
0.618452 | + | 0.785822i | \(0.287760\pi\) | |||||||
\(194\) | −1.66801 | + | 9.72490i | −0.119756 | + | 0.698207i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.61061 | − | 7.38637i | 0.186472 | − | 0.527598i | ||||
\(197\) | −11.0761 | + | 4.58787i | −0.789139 | + | 0.326872i | −0.740597 | − | 0.671949i | \(-0.765457\pi\) |
−0.0485417 | + | 0.998821i | \(0.515457\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.73738 | + | 1.73738i | −0.123159 | + | 0.123159i | −0.766000 | − | 0.642841i | \(-0.777756\pi\) |
0.642841 | + | 0.766000i | \(0.277756\pi\) | |||||||
\(200\) | 3.72790 | + | 13.1722i | 0.263602 | + | 0.931418i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.17090 | + | 13.9936i | 0.223104 | + | 0.984589i | ||||
\(203\) | −6.54384 | − | 15.7982i | −0.459288 | − | 1.10882i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.64140 | − | 0.679892i | −0.114641 | − | 0.0474857i | ||||
\(206\) | 13.6657 | + | 19.3241i | 0.952135 | + | 1.34637i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.52974 | + | 17.5009i | 0.660769 | + | 1.21347i | ||||
\(209\) | − | 3.12513i | − | 0.216170i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.05517 | − | 1.67971i | −0.279170 | − | 0.115636i | 0.238706 | − | 0.971092i | \(-0.423277\pi\) |
−0.517875 | + | 0.855456i | \(0.673277\pi\) | |||||||
\(212\) | −0.236790 | − | 4.46637i | −0.0162628 | − | 0.306751i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 19.3498 | − | 4.38458i | 1.32272 | − | 0.299724i | ||||
\(215\) | 1.47144 | + | 1.47144i | 0.100351 | + | 0.100351i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.23691 | + | 7.23691i | −0.491274 | + | 0.491274i | ||||
\(218\) | 14.1506 | − | 22.4424i | 0.958398 | − | 1.51999i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.442043 | + | 0.925317i | 0.0298025 | + | 0.0623848i | ||||
\(221\) | −9.03000 | + | 21.8003i | −0.607423 | + | 1.46645i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.31801 | 0.490050 | 0.245025 | − | 0.969517i | \(-0.421204\pi\) | ||||
0.245025 | + | 0.969517i | \(0.421204\pi\) | |||||||
\(224\) | 0.634579 | − | 9.91217i | 0.0423996 | − | 0.662285i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.39093 | − | 1.09617i | −0.425119 | − | 0.0729160i | ||||
\(227\) | −7.10939 | + | 17.1636i | −0.471867 | + | 1.13919i | 0.491470 | + | 0.870894i | \(0.336460\pi\) |
−0.963337 | + | 0.268293i | \(0.913540\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.35015 | − | 1.38768i | 0.221384 | − | 0.0917002i | −0.269235 | − | 0.963075i | \(-0.586771\pi\) |
0.490619 | + | 0.871374i | \(0.336771\pi\) | |||||||
\(230\) | 1.88234 | − | 2.98534i | 0.124118 | − | 0.196847i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 17.0732 | + | 21.6167i | 1.12091 | + | 1.41921i | ||||
\(233\) | −13.2085 | − | 13.2085i | −0.865315 | − | 0.865315i | 0.126634 | − | 0.991949i | \(-0.459583\pi\) |
−0.991949 | + | 0.126634i | \(0.959583\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.612121 | + | 1.47779i | 0.0399304 | + | 0.0964004i | ||||
\(236\) | 3.56690 | − | 0.189104i | 0.232186 | − | 0.0123096i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.60271 | − | 6.79090i | 0.622451 | − | 0.440188i | ||||
\(239\) | − | 5.06396i | − | 0.327560i | −0.986497 | − | 0.163780i | \(-0.947631\pi\) | ||
0.986497 | − | 0.163780i | \(-0.0523687\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.2330i | 1.11008i | 0.831825 | + | 0.555038i | \(0.187296\pi\) | ||||
−0.831825 | + | 0.555038i | \(0.812704\pi\) | |||||||
\(242\) | 7.64036 | + | 10.8039i | 0.491141 | + | 0.694501i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.42897 | + | 1.58897i | −0.0914803 | + | 0.101723i | ||||
\(245\) | 0.599590 | + | 1.44754i | 0.0383064 | + | 0.0924798i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.58810 | + | 8.58810i | 0.546448 | + | 0.546448i | ||||
\(248\) | 8.04262 | − | 14.3918i | 0.510707 | − | 0.913882i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.70844 | − | 2.96881i | −0.297788 | − | 0.187764i | ||||
\(251\) | 13.4329 | − | 5.56408i | 0.847876 | − | 0.351202i | 0.0839221 | − | 0.996472i | \(-0.473255\pi\) |
0.763954 | + | 0.645270i | \(0.223255\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.06053 | + | 7.38877i | −0.192414 | + | 0.464528i | ||||
\(254\) | 0.709419 | − | 4.13610i | 0.0445129 | − | 0.259522i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.36456 | + | 15.6422i | 0.210285 | + | 0.977640i | ||||
\(257\) | 10.0676 | 0.628003 | 0.314001 | − | 0.949423i | \(-0.398330\pi\) | ||||
0.314001 | + | 0.949423i | \(0.398330\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.39120 | − | 3.35865i | 0.0864448 | − | 0.208696i | ||||
\(260\) | −3.75761 | − | 1.32807i | −0.233037 | − | 0.0823637i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.0243 | + | 8.84276i | 0.866427 | + | 0.546307i | ||||
\(263\) | 16.4698 | − | 16.4698i | 1.01557 | − | 1.01557i | 0.0156926 | − | 0.999877i | \(-0.495005\pi\) |
0.999877 | − | 0.0156926i | \(-0.00499531\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.632516 | + | 0.632516i | 0.0388552 | + | 0.0388552i | ||||
\(266\) | −1.33782 | − | 5.90401i | −0.0820272 | − | 0.361998i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.0417 | − | 15.6139i | 0.857731 | − | 0.953770i | ||||
\(269\) | −3.67390 | − | 1.52178i | −0.224002 | − | 0.0927845i | 0.267860 | − | 0.963458i | \(-0.413683\pi\) |
−0.491862 | + | 0.870673i | \(0.663683\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 19.6229i | − | 1.19201i | −0.802981 | − | 0.596005i | \(-0.796754\pi\) | ||
0.802981 | − | 0.596005i | \(-0.203246\pi\) | |||||||
\(272\) | −11.9053 | + | 14.7383i | −0.721863 | + | 0.893641i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −26.4359 | + | 18.6951i | −1.59705 | + | 1.12941i | ||||
\(275\) | 5.73200 | + | 2.37427i | 0.345653 | + | 0.143174i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.4955 | − | 27.7526i | −0.690699 | − | 1.66749i | −0.743368 | − | 0.668882i | \(-0.766773\pi\) |
0.0526694 | − | 0.998612i | \(-0.483227\pi\) | |||||||
\(278\) | −10.7736 | + | 2.44125i | −0.646158 | + | 0.146417i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.23122 | + | 1.55888i | 0.0735797 | + | 0.0931609i | ||||
\(281\) | −6.56486 | + | 6.56486i | −0.391627 | + | 0.391627i | −0.875267 | − | 0.483640i | \(-0.839314\pi\) |
0.483640 | + | 0.875267i | \(0.339314\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0853 | + | 5.42010i | −0.777839 | + | 0.322192i | −0.736043 | − | 0.676935i | \(-0.763308\pi\) |
−0.0417960 | + | 0.999126i | \(0.513308\pi\) | |||||||
\(284\) | −5.54284 | + | 2.64793i | −0.328907 | + | 0.157126i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.90129 | + | 1.52674i | 0.526344 | + | 0.0902781i | ||||
\(287\) | 7.79882 | 0.460350 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.43457 | −0.319680 | ||||||||
\(290\) | −5.42979 | − | 0.931313i | −0.318848 | − | 0.0546886i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.65403 | − | 20.2085i | −0.564959 | − | 1.18261i | ||||
\(293\) | 9.80395 | − | 4.06093i | 0.572753 | − | 0.237242i | −0.0774584 | − | 0.996996i | \(-0.524680\pi\) |
0.650211 | + | 0.759754i | \(0.274680\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.505136 | + | 0.505136i | −0.0294102 | + | 0.0294102i | ||||
\(296\) | −0.683024 | + | 5.81619i | −0.0397000 | + | 0.338059i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.4195 | − | 3.26740i | 0.835298 | − | 0.189275i | ||||
\(299\) | −11.8944 | − | 28.7155i | −0.687868 | − | 1.66066i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.43921 | − | 3.49563i | −0.486428 | − | 0.201485i | ||||
\(302\) | −6.47564 | + | 4.57948i | −0.372631 | + | 0.263519i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.66353 | + | 8.56436i | 0.267472 | + | 0.491200i | ||||
\(305\) | − | 0.427393i | − | 0.0244725i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.2604 | − | 9.63475i | −1.32754 | − | 0.549884i | −0.397586 | − | 0.917565i | \(-0.630152\pi\) |
−0.929952 | + | 0.367680i | \(0.880152\pi\) | |||||||
\(308\) | −3.34709 | − | 3.01006i | −0.190718 | − | 0.171514i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.728675 | + | 3.21575i | 0.0413859 | + | 0.182642i | ||||
\(311\) | 10.6265 | + | 10.6265i | 0.602574 | + | 0.602574i | 0.940995 | − | 0.338421i | \(-0.109893\pi\) |
−0.338421 | + | 0.940995i | \(0.609893\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.1006 | − | 17.1006i | 0.966586 | − | 0.966586i | −0.0328739 | − | 0.999460i | \(-0.510466\pi\) |
0.999460 | + | 0.0328739i | \(0.0104660\pi\) | |||||||
\(314\) | −1.17477 | − | 0.740729i | −0.0662964 | − | 0.0418018i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.579019 | + | 1.63826i | −0.0325724 | + | 0.0921592i | ||||
\(317\) | 1.32310 | − | 3.19425i | 0.0743128 | − | 0.179407i | −0.882358 | − | 0.470579i | \(-0.844045\pi\) |
0.956671 | + | 0.291172i | \(0.0940451\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.4841 | 0.698974 | ||||||||
\(320\) | −2.59223 | − | 1.87617i | −0.144910 | − | 0.104881i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.61894 | + | 15.2691i | −0.145948 | + | 0.850912i | ||||
\(323\) | −4.41897 | + | 10.6683i | −0.245878 | + | 0.593603i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.2767 | + | 9.22730i | −1.23569 | + | 0.511838i | ||||
\(326\) | −15.4635 | − | 9.75017i | −0.856443 | − | 0.540012i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −12.0882 | + | 3.42110i | −0.667458 | + | 0.188899i | ||||
\(329\) | −4.96491 | − | 4.96491i | −0.273724 | − | 0.273724i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.57155 | − | 15.8651i | −0.361205 | − | 0.872026i | −0.995124 | − | 0.0986269i | \(-0.968555\pi\) |
0.633920 | − | 0.773399i | \(-0.281445\pi\) | |||||||
\(332\) | 8.80628 | + | 7.91954i | 0.483308 | + | 0.434641i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.6946 | + | 19.3650i | 0.749336 | + | 1.05960i | ||||
\(335\) | 4.19975i | 0.229457i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 16.9321i | − | 0.922350i | −0.887309 | − | 0.461175i | \(-0.847428\pi\) | ||
0.887309 | − | 0.461175i | \(-0.152572\pi\) | |||||||
\(338\) | −13.6465 | + | 9.65060i | −0.742272 | + | 0.524924i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.200605 | − | 3.78384i | −0.0108793 | − | 0.205207i | ||||
\(341\) | −2.85938 | − | 6.90314i | −0.154844 | − | 0.373826i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.5542 | − | 13.5542i | −0.731856 | − | 0.731856i | ||||
\(344\) | 14.6142 | + | 1.71622i | 0.787945 | + | 0.0925324i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.5629 | + | 27.8542i | −0.944187 | + | 1.49745i | ||||
\(347\) | −25.5167 | + | 10.5694i | −1.36981 | + | 0.567393i | −0.941736 | − | 0.336352i | \(-0.890807\pi\) |
−0.428071 | + | 0.903745i | \(0.640807\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.7832 | − | 26.0329i | 0.577210 | − | 1.39351i | −0.318096 | − | 0.948058i | \(-0.603044\pi\) |
0.895307 | − | 0.445450i | \(-0.146956\pi\) | |||||||
\(350\) | 11.8453 | + | 2.03170i | 0.633159 | + | 0.108599i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.50841 | + | 3.19733i | 0.346900 | + | 0.170418i | ||||
\(353\) | 30.7053 | 1.63428 | 0.817140 | − | 0.576440i | \(-0.195558\pi\) | ||||
0.817140 | + | 0.576440i | \(0.195558\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.470146 | − | 1.13503i | 0.0249528 | − | 0.0602413i | ||||
\(356\) | 12.3139 | − | 5.88258i | 0.652633 | − | 0.311776i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.9605 | + | 22.1410i | −0.737836 | + | 1.17019i | ||||
\(359\) | 11.5340 | − | 11.5340i | 0.608740 | − | 0.608740i | −0.333877 | − | 0.942617i | \(-0.608357\pi\) |
0.942617 | + | 0.333877i | \(0.108357\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.23231 | − | 9.23231i | −0.485911 | − | 0.485911i | ||||
\(362\) | 15.6135 | − | 3.53796i | 0.820629 | − | 0.185951i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 17.4699 | − | 0.926190i | 0.915674 | − | 0.0485455i | ||||
\(365\) | 4.13819 | + | 1.71410i | 0.216603 | + | 0.0897198i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.72042i | − | 0.142005i | −0.997476 | − | 0.0710024i | \(-0.977380\pi\) | ||
0.997476 | − | 0.0710024i | \(-0.0226198\pi\) | |||||||
\(368\) | −2.63871 | − | 24.8159i | −0.137552 | − | 1.29362i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.676249 | − | 0.956255i | −0.0351565 | − | 0.0497133i | ||||
\(371\) | −3.62770 | − | 1.50264i | −0.188341 | − | 0.0780132i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.956551 | + | 2.30932i | 0.0495283 | + | 0.119572i | 0.946707 | − | 0.322095i | \(-0.104387\pi\) |
−0.897179 | + | 0.441667i | \(0.854387\pi\) | |||||||
\(374\) | 1.89757 | + | 8.37425i | 0.0981210 | + | 0.433022i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.87357 | + | 5.51767i | 0.509190 | + | 0.284552i | ||||
\(377\) | −34.3072 | + | 34.3072i | −1.76691 | + | 1.76691i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.2748 | + | 8.81229i | −1.09281 | + | 0.452657i | −0.854986 | − | 0.518651i | \(-0.826434\pi\) |
−0.237825 | + | 0.971308i | \(0.576434\pi\) | |||||||
\(380\) | −1.83885 | − | 0.649915i | −0.0943309 | − | 0.0333399i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.19110 | − | 36.0957i | 0.316764 | − | 1.84681i | ||||
\(383\) | −27.4698 | −1.40364 | −0.701821 | − | 0.712354i | \(-0.747629\pi\) | ||||
−0.701821 | + | 0.712354i | \(0.747629\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.900285 | 0.0458827 | ||||||||
\(386\) | −4.10815 | + | 23.9516i | −0.209099 | + | 1.21910i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.1564 | − | 4.64993i | −0.667913 | − | 0.236065i | ||||
\(389\) | 1.59053 | − | 0.658819i | 0.0806430 | − | 0.0334034i | −0.341997 | − | 0.939701i | \(-0.611103\pi\) |
0.422640 | + | 0.906298i | \(0.361103\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.8956 | − | 20.8956i | 1.05674 | − | 1.05674i | ||||
\(392\) | 9.67144 | + | 5.40471i | 0.488481 | + | 0.272979i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.74684 | − | 16.5354i | −0.188763 | − | 0.833039i | ||||
\(395\) | −0.132986 | − | 0.321056i | −0.00669124 | − | 0.0161541i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.440821 | − | 0.182594i | −0.0221242 | − | 0.00916414i | 0.371594 | − | 0.928395i | \(-0.378811\pi\) |
−0.393718 | + | 0.919231i | \(0.628811\pi\) | |||||||
\(398\) | −2.00630 | − | 2.83702i | −0.100567 | − | 0.142207i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −19.2515 | + | 2.04704i | −0.962575 | + | 0.102352i | ||||
\(401\) | 13.7833i | 0.688307i | 0.938913 | + | 0.344154i | \(0.111834\pi\) | ||||
−0.938913 | + | 0.344154i | \(0.888166\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.8282 | + | 11.1126i | 1.33641 | + | 0.553558i | ||||
\(404\) | −20.2632 | + | 1.07428i | −1.00813 | + | 0.0534474i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 23.5850 | − | 5.34426i | 1.17050 | − | 0.265231i | ||||
\(407\) | 1.87671 | + | 1.87671i | 0.0930251 | + | 0.0930251i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.34078 | + | 5.34078i | −0.264085 | + | 0.264085i | −0.826711 | − | 0.562627i | \(-0.809791\pi\) |
0.562627 | + | 0.826711i | \(0.309791\pi\) | |||||||
\(410\) | 1.34009 | − | 2.12534i | 0.0661823 | − | 0.104963i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −30.2022 | + | 14.4282i | −1.48795 | + | 0.710826i | ||||
\(413\) | 1.20003 | − | 2.89713i | 0.0590496 | − | 0.142558i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.36867 | −0.116274 | ||||||||
\(416\) | −26.6721 | + | 9.09911i | −1.30771 | + | 0.446121i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.35599 | + | 0.747136i | 0.213058 | + | 0.0365436i | ||||
\(419\) | 4.20919 | − | 10.1619i | 0.205632 | − | 0.496440i | −0.787094 | − | 0.616833i | \(-0.788415\pi\) |
0.992726 | + | 0.120393i | \(0.0384154\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.39263 | + | 3.47634i | −0.409032 | + | 0.169427i | −0.577705 | − | 0.816245i | \(-0.696052\pi\) |
0.168673 | + | 0.985672i | \(0.446052\pi\) | |||||||
\(422\) | 3.31076 | − | 5.25077i | 0.161165 | − | 0.255603i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.28210 | + | 0.737738i | 0.305086 | + | 0.0358277i | ||||
\(425\) | −16.2102 | − | 16.2102i | −0.786313 | − | 0.786313i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.717953 | + | 1.73329i | 0.0347442 | + | 0.0838798i | ||||
\(428\) | 1.48547 | + | 28.0191i | 0.0718027 | + | 1.35435i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.40276 | + | 1.69920i | −0.115871 | + | 0.0819426i | ||||
\(431\) | 36.2680i | 1.74697i | 0.486852 | + | 0.873485i | \(0.338145\pi\) | ||||
−0.486852 | + | 0.873485i | \(0.661855\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.42391i | − | 0.0684286i | −0.999415 | − | 0.0342143i | \(-0.989107\pi\) | ||
0.999415 | − | 0.0342143i | \(-0.0108929\pi\) | |||||||
\(434\) | −8.35708 | − | 11.8174i | −0.401153 | − | 0.567253i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 27.8985 | + | 25.0893i | 1.33610 | + | 1.20156i | ||||
\(437\) | −5.82069 | − | 14.0524i | −0.278441 | − | 0.672217i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.2959 | − | 28.2959i | −1.35049 | − | 1.35049i | −0.885111 | − | 0.465381i | \(-0.845917\pi\) |
−0.465381 | − | 0.885111i | \(-0.654083\pi\) | |||||||
\(440\) | −1.39544 | + | 0.394927i | −0.0665251 | + | 0.0188274i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −28.2278 | − | 17.7984i | −1.34266 | − | 0.846585i | ||||
\(443\) | −33.4735 | + | 13.8652i | −1.59037 | + | 0.658755i | −0.990013 | − | 0.140975i | \(-0.954976\pi\) |
−0.600361 | + | 0.799729i | \(0.704976\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.04447 | + | 2.52156i | −0.0495124 | + | 0.119534i | ||||
\(446\) | −1.74954 | + | 10.2003i | −0.0828432 | + | 0.482997i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 13.6645 | + | 3.25425i | 0.645585 | + | 0.153749i | ||||
\(449\) | 15.1120 | 0.713182 | 0.356591 | − | 0.934261i | \(-0.383939\pi\) | ||||
0.356591 | + | 0.934261i | \(0.383939\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.17887 | + | 5.26026i | −0.102599 | + | 0.247696i | ||||
\(452\) | 3.05581 | − | 8.64600i | 0.143733 | − | 0.406674i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −22.2240 | − | 14.0129i | −1.04302 | − | 0.657656i | ||||
\(455\) | −2.47405 | + | 2.47405i | −0.115985 | + | 0.115985i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.8696 | + | 22.8696i | 1.06979 | + | 1.06979i | 0.997374 | + | 0.0724182i | \(0.0230716\pi\) |
0.0724182 | + | 0.997374i | \(0.476928\pi\) | |||||||
\(458\) | 1.13329 | + | 5.00139i | 0.0529554 | + | 0.233700i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.71113 | + | 3.33744i | 0.173032 | + | 0.155609i | ||||
\(461\) | 1.28205 | + | 0.531041i | 0.0597108 | + | 0.0247330i | 0.412339 | − | 0.911030i | \(-0.364712\pi\) |
−0.352628 | + | 0.935764i | \(0.614712\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 25.7372i | − | 1.19611i | −0.801455 | − | 0.598055i | \(-0.795940\pi\) | ||
0.801455 | − | 0.598055i | \(-0.204060\pi\) | |||||||
\(464\) | −34.2124 | + | 18.6296i | −1.58827 | + | 0.864857i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21.5685 | − | 15.2529i | 0.999143 | − | 0.706579i | ||||
\(467\) | 20.9980 | + | 8.69764i | 0.971670 | + | 0.402479i | 0.811333 | − | 0.584584i | \(-0.198742\pi\) |
0.160336 | + | 0.987062i | \(0.448742\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.05492 | − | 17.0321i | −0.325766 | − | 0.786469i | ||||
\(470\) | −2.20617 | + | 0.499910i | −0.101763 | + | 0.0230591i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.589168 | + | 5.01697i | −0.0271187 | + | 0.230925i | ||||
\(473\) | 4.71557 | − | 4.71557i | 0.216822 | − | 0.216822i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.9014 | + | 4.51553i | −0.500193 | + | 0.207187i | ||||
\(476\) | 7.16980 | + | 15.0084i | 0.328627 | + | 0.687907i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.05844 | + | 1.21066i | 0.322846 | + | 0.0553742i | ||||
\(479\) | −26.0170 | −1.18875 | −0.594373 | − | 0.804190i | \(-0.702600\pi\) | ||||
−0.594373 | + | 0.804190i | \(0.702600\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.3147 | −0.470310 | ||||||||
\(482\) | −24.0204 | − | 4.11996i | −1.09410 | − | 0.187659i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16.8857 | + | 8.06666i | −0.767533 | + | 0.366666i | ||||
\(485\) | 2.57831 | − | 1.06797i | 0.117075 | − | 0.0484940i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.6649 | − | 17.6649i | 0.800474 | − | 0.800474i | −0.182695 | − | 0.983170i | \(-0.558482\pi\) |
0.983170 | + | 0.182695i | \(0.0584822\pi\) | |||||||
\(488\) | −1.87317 | − | 2.37166i | −0.0847944 | − | 0.107360i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.16101 | + | 0.489676i | −0.0976244 | + | 0.0221213i | ||||
\(491\) | 15.0583 | + | 36.3539i | 0.679571 | + | 1.64063i | 0.764799 | + | 0.644269i | \(0.222838\pi\) |
−0.0852275 | + | 0.996362i | \(0.527162\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −42.6172 | − | 17.6526i | −1.91938 | − | 0.795035i | ||||
\(494\) | −14.0238 | + | 9.91741i | −0.630960 | + | 0.446206i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.1374 | + | 14.6510i | 0.814394 | + | 0.657848i | ||||
\(497\) | 5.39290i | 0.241904i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.96691 | − | 2.88579i | −0.311882 | − | 0.129186i | 0.221252 | − | 0.975217i | \(-0.428986\pi\) |
−0.533134 | + | 0.846031i | \(0.678986\pi\) | |||||||
\(500\) | 5.26376 | − | 5.85314i | 0.235403 | − | 0.261760i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.54410 | + | 20.0538i | 0.202813 | + | 0.895044i | ||||
\(503\) | −10.7377 | − | 10.7377i | −0.478769 | − | 0.478769i | 0.425969 | − | 0.904738i | \(-0.359933\pi\) |
−0.904738 | + | 0.425969i | \(0.859933\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.86963 | − | 2.86963i | 0.127697 | − | 0.127697i | ||||
\(506\) | −9.56722 | − | 6.03241i | −0.425315 | − | 0.268173i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.59553 | + | 1.97766i | 0.248262 | + | 0.0877445i | ||||
\(509\) | −13.1996 | + | 31.8667i | −0.585062 | + | 1.41247i | 0.303111 | + | 0.952955i | \(0.401975\pi\) |
−0.888173 | + | 0.459510i | \(0.848025\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.6618 | −0.869788 | ||||||||
\(512\) | −22.6075 | + | 0.950078i | −0.999118 | + | 0.0419879i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.40691 | + | 14.0329i | −0.106164 | + | 0.618964i | ||||
\(515\) | 2.56176 | − | 6.18463i | 0.112885 | − | 0.272528i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.73593 | − | 1.96169i | 0.208286 | − | 0.0862748i | ||||
\(518\) | 4.34889 | + | 2.74210i | 0.191079 | + | 0.120481i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.74949 | − | 4.92007i | 0.120573 | − | 0.215760i | ||||
\(521\) | −24.7770 | − | 24.7770i | −1.08550 | − | 1.08550i | −0.995985 | − | 0.0895150i | \(-0.971468\pi\) |
−0.0895150 | − | 0.995985i | \(-0.528532\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.84025 | + | 21.3423i | 0.386557 | + | 0.933232i | 0.990664 | + | 0.136328i | \(0.0435302\pi\) |
−0.604106 | + | 0.796904i | \(0.706470\pi\) | |||||||
\(524\) | −15.6784 | + | 17.4339i | −0.684915 | + | 0.761603i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.0191 | + | 26.8940i | 0.829270 | + | 1.17264i | ||||
\(527\) | 27.6087i | 1.20265i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.9246i | 0.692374i | ||||||||
\(530\) | −1.03286 | + | 0.730421i | −0.0448644 | + | 0.0317275i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.54920 | − | 0.453246i | 0.370655 | − | 0.0196507i | ||||
\(533\) | −8.46790 | − | 20.4433i | −0.366786 | − | 0.885499i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.96800 | − | 3.96800i | −0.171552 | − | 0.171552i | ||||
\(536\) | 18.4066 | + | 23.3050i | 0.795043 | + | 1.00662i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.99948 | − | 4.75708i | 0.129317 | − | 0.205092i | ||||
\(539\) | 4.63897 | − | 1.92152i | 0.199815 | − | 0.0827659i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.50552 | − | 20.5341i | 0.365681 | − | 0.882832i | −0.628766 | − | 0.777594i | \(-0.716440\pi\) |
0.994447 | − | 0.105237i | \(-0.0335602\pi\) | |||||||
\(542\) | 27.3516 | + | 4.69133i | 1.17485 | + | 0.201510i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −17.6969 | − | 20.1178i | −0.758748 | − | 0.862544i | ||||
\(545\) | −7.50401 | −0.321436 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.76171 | + | 4.25314i | −0.0753252 | + | 0.181851i | −0.957057 | − | 0.289900i | \(-0.906378\pi\) |
0.881732 | + | 0.471751i | \(0.156378\pi\) | |||||||
\(548\) | −19.7382 | − | 41.3174i | −0.843172 | − | 1.76499i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.67977 | + | 7.42198i | −0.199546 | + | 0.316474i | ||||
\(551\) | −16.7888 | + | 16.7888i | −0.715226 | + | 0.715226i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.07865 | + | 1.07865i | 0.0458687 | + | 0.0458687i | ||||
\(554\) | 41.4315 | − | 9.38822i | 1.76026 | − | 0.398867i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.827081 | − | 15.6005i | −0.0350761 | − | 0.661610i | ||||
\(557\) | −39.6505 | − | 16.4238i | −1.68004 | − | 0.695897i | −0.680716 | − | 0.732548i | \(-0.738331\pi\) |
−0.999328 | + | 0.0366506i | \(0.988331\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.9175i | 1.09619i | ||||||||
\(560\) | −2.46721 | + | 1.34347i | −0.104259 | + | 0.0567718i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.58100 | − | 10.7200i | −0.319785 | − | 0.452195i | ||||
\(563\) | 39.2925 | + | 16.2755i | 1.65598 | + | 0.685930i | 0.997760 | − | 0.0668949i | \(-0.0213092\pi\) |
0.658221 | + | 0.752825i | \(0.271309\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.701840 | + | 1.69439i | 0.0295266 | + | 0.0712836i | ||||
\(566\) | −4.42651 | − | 19.5348i | −0.186060 | − | 0.821111i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.36570 | − | 8.35899i | −0.0992624 | − | 0.350736i | ||||
\(569\) | 12.7803 | − | 12.7803i | 0.535780 | − | 0.535780i | −0.386507 | − | 0.922287i | \(-0.626318\pi\) |
0.922287 | + | 0.386507i | \(0.126318\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.3723 | + | 11.3380i | −1.14550 | + | 0.474480i | −0.873021 | − | 0.487683i | \(-0.837842\pi\) |
−0.272475 | + | 0.962163i | \(0.587842\pi\) | |||||||
\(572\) | −4.25613 | + | 12.0421i | −0.177958 | + | 0.503507i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.86449 | + | 10.8705i | −0.0778224 | + | 0.453724i | ||||
\(575\) | 30.1966 | 1.25928 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.5299 | 0.771412 | 0.385706 | − | 0.922622i | \(-0.373958\pi\) | ||||
0.385706 | + | 0.922622i | \(0.373958\pi\) | |||||||
\(578\) | 1.29926 | − | 7.57502i | 0.0540421 | − | 0.315079i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.59624 | − | 7.34571i | 0.107803 | − | 0.305014i | ||||
\(581\) | 9.60615 | − | 3.97900i | 0.398530 | − | 0.165077i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.02705 | − | 2.02705i | 0.0839517 | − | 0.0839517i | ||||
\(584\) | 30.4759 | − | 8.62504i | 1.26110 | − | 0.356907i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.31650 | + | 14.6362i | 0.137003 | + | 0.604615i | ||||
\(587\) | −1.97372 | − | 4.76497i | −0.0814640 | − | 0.196671i | 0.877899 | − | 0.478845i | \(-0.158945\pi\) |
−0.959363 | + | 0.282174i | \(0.908945\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.1288 | + | 5.43812i | 0.540962 | + | 0.224074i | ||||
\(590\) | −0.583324 | − | 0.824854i | −0.0240151 | − | 0.0339587i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.94365 | − | 2.34254i | −0.326482 | − | 0.0962776i | ||||
\(593\) | − | 37.8468i | − | 1.55418i | −0.629387 | − | 0.777092i | \(-0.716694\pi\) | ||
0.629387 | − | 0.777092i | \(-0.283306\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.07333 | − | 1.27301i | −0.125994 | − | 0.0521885i | ||||
\(596\) | 1.10697 | + | 20.8799i | 0.0453434 | + | 0.855273i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 42.8690 | − | 9.71394i | 1.75304 | − | 0.397232i | ||||
\(599\) | 13.1026 | + | 13.1026i | 0.535358 | + | 0.535358i | 0.922162 | − | 0.386804i | \(-0.126421\pi\) |
−0.386804 | + | 0.922162i | \(0.626421\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.6421 | + | 23.6421i | −0.964383 | + | 0.964383i | −0.999387 | − | 0.0350039i | \(-0.988856\pi\) |
0.0350039 | + | 0.999387i | \(0.488856\pi\) | |||||||
\(602\) | 6.89001 | − | 10.9274i | 0.280816 | − | 0.445366i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.83499 | − | 10.1210i | −0.196733 | − | 0.411816i | ||||
\(605\) | 1.43225 | − | 3.45777i | 0.0582294 | − | 0.140578i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.7663 | 1.65465 | 0.827327 | − | 0.561721i | \(-0.189860\pi\) | ||||
0.827327 | + | 0.561721i | \(0.189860\pi\) | |||||||
\(608\) | −13.0524 | + | 4.45280i | −0.529346 | + | 0.180585i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.595726 | + | 0.102178i | 0.0241202 | + | 0.00413708i | ||||
\(611\) | −7.62383 | + | 18.4056i | −0.308427 | + | 0.744609i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.6836 | − | 11.0527i | 1.07774 | − | 0.446414i | 0.228024 | − | 0.973656i | \(-0.426774\pi\) |
0.849716 | + | 0.527241i | \(0.176774\pi\) | |||||||
\(614\) | 18.9904 | − | 30.1182i | 0.766391 | − | 1.21547i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.99580 | − | 3.94575i | 0.201286 | − | 0.158979i | ||||
\(617\) | −9.58241 | − | 9.58241i | −0.385773 | − | 0.385773i | 0.487404 | − | 0.873177i | \(-0.337944\pi\) |
−0.873177 | + | 0.487404i | \(0.837944\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.72395 | + | 18.6473i | 0.310452 | + | 0.749496i | 0.999688 | + | 0.0249603i | \(0.00794594\pi\) |
−0.689237 | + | 0.724536i | \(0.742054\pi\) | |||||||
\(620\) | −4.65650 | + | 0.246870i | −0.187010 | + | 0.00991455i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17.3524 | + | 12.2714i | −0.695767 | + | 0.492036i | ||||
\(623\) | − | 11.9807i | − | 0.479998i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 22.6257i | − | 0.905027i | ||||||
\(626\) | 19.7476 | + | 27.9242i | 0.789272 | + | 1.11608i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.31333 | − | 1.46038i | 0.0524076 | − | 0.0582756i | ||||
\(629\) | −3.75289 | − | 9.06028i | −0.149638 | − | 0.361257i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.5702 | + | 12.5702i | 0.500413 | + | 0.500413i | 0.911566 | − | 0.411153i | \(-0.134874\pi\) |
−0.411153 | + | 0.911566i | \(0.634874\pi\) | |||||||
\(632\) | −2.14507 | − | 1.19874i | −0.0853264 | − | 0.0476831i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.13602 | + | 2.60788i | 0.164262 | + | 0.103572i | ||||
\(635\) | −1.09658 | + | 0.454218i | −0.0435164 | + | 0.0180251i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.46776 | + | 18.0288i | −0.295883 | + | 0.714325i | ||||
\(638\) | −2.98461 | + | 17.4010i | −0.118162 | + | 0.688914i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.23485 | − | 3.16466i | 0.127869 | − | 0.125094i | ||||
\(641\) | 33.2881 | 1.31480 | 0.657401 | − | 0.753541i | \(-0.271656\pi\) | ||||
0.657401 | + | 0.753541i | \(0.271656\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.1295 | + | 41.3543i | −0.675521 | + | 1.63085i | 0.0965583 | + | 0.995327i | \(0.469217\pi\) |
−0.772080 | + | 0.635526i | \(0.780783\pi\) | |||||||
\(644\) | −20.6568 | − | 7.30086i | −0.813993 | − | 0.287694i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.8137 | − | 8.70995i | −0.543493 | − | 0.342688i | ||||
\(647\) | 17.7157 | − | 17.7157i | 0.696477 | − | 0.696477i | −0.267171 | − | 0.963649i | \(-0.586089\pi\) |
0.963649 | + | 0.267171i | \(0.0860890\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.61883 | + | 1.61883i | 0.0635446 | + | 0.0635446i | ||||
\(650\) | −7.53579 | − | 33.2565i | −0.295578 | − | 1.30443i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.2873 | − | 19.2229i | 0.677022 | − | 0.752827i | ||||
\(653\) | 15.9543 | + | 6.60849i | 0.624340 | + | 0.258610i | 0.672346 | − | 0.740237i | \(-0.265287\pi\) |
−0.0480060 | + | 0.998847i | \(0.515287\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 4.68929i | − | 0.183226i | ||||||
\(656\) | −1.87857 | − | 17.6671i | −0.0733458 | − | 0.689785i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.10737 | − | 5.73341i | 0.316058 | − | 0.223512i | ||||
\(659\) | 23.0850 | + | 9.56212i | 0.899264 | + | 0.372487i | 0.783937 | − | 0.620840i | \(-0.213208\pi\) |
0.115327 | + | 0.993328i | \(0.463208\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.95887 | + | 16.8002i | 0.270669 | + | 0.653452i | 0.999512 | − | 0.0312280i | \(-0.00994181\pi\) |
−0.728843 | + | 0.684680i | \(0.759942\pi\) | |||||||
\(662\) | 23.6848 | − | 5.36688i | 0.920537 | − | 0.208590i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.1441 | + | 10.3814i | −0.510089 | + | 0.402875i | ||||
\(665\) | −1.21072 | + | 1.21072i | −0.0469496 | + | 0.0469496i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 56.1356 | − | 23.2521i | 2.17358 | − | 0.900326i | ||||
\(668\) | −30.2660 | + | 14.4587i | −1.17103 | + | 0.559424i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.85386 | − | 1.00405i | −0.226154 | − | 0.0387898i | ||||
\(671\) | −1.36968 | −0.0528759 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.1001 | 1.43010 | 0.715052 | − | 0.699072i | \(-0.246403\pi\) | ||||
0.715052 | + | 0.699072i | \(0.246403\pi\) | |||||||
\(674\) | 23.6009 | + | 4.04801i | 0.909075 | + | 0.155924i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.1891 | − | 21.3285i | −0.391887 | − | 0.820327i | ||||
\(677\) | 21.1103 | − | 8.74417i | 0.811335 | − | 0.336066i | 0.0618482 | − | 0.998086i | \(-0.480301\pi\) |
0.749486 | + | 0.662020i | \(0.230301\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.66230 | + | 8.66230i | −0.332428 | + | 0.332428i | ||||
\(680\) | 5.32209 | + | 0.625000i | 0.204093 | + | 0.0239677i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.3056 | − | 2.33521i | 0.394622 | − | 0.0894198i | ||||
\(683\) | −14.5245 | − | 35.0654i | −0.555766 | − | 1.34174i | −0.913090 | − | 0.407758i | \(-0.866311\pi\) |
0.357324 | − | 0.933981i | \(-0.383689\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.46074 | + | 3.50455i | 0.323268 | + | 0.133902i | ||||
\(686\) | 22.1330 | − | 15.6522i | 0.845044 | − | 0.597602i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.88604 | + | 19.9598i | −0.224403 | + | 0.760962i | ||||
\(689\) | 11.1410i | 0.424437i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.6524 | − | 5.24080i | −0.481320 | − | 0.199369i | 0.128812 | − | 0.991669i | \(-0.458884\pi\) |
−0.610132 | + | 0.792300i | \(0.708884\pi\) | |||||||
\(692\) | −34.6260 | − | 31.1394i | −1.31628 | − | 1.18374i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.63183 | − | 38.0935i | −0.327660 | − | 1.44601i | ||||
\(695\) | 2.20931 | + | 2.20931i | 0.0838040 | + | 0.0838040i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.8762 | − | 14.8762i | 0.563475 | − | 0.563475i | ||||
\(698\) | 33.7082 | + | 21.2540i | 1.27587 | + | 0.804476i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.66380 | + | 16.0250i | −0.214072 | + | 0.605687i | ||||
\(701\) | −9.65633 | + | 23.3124i | −0.364714 | + | 0.880498i | 0.629883 | + | 0.776690i | \(0.283103\pi\) |
−0.994597 | + | 0.103808i | \(0.966897\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.04766 | −0.190376 | ||||||||
\(704\) | −6.01262 | + | 8.30741i | −0.226609 | + | 0.313097i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.34083 | + | 42.7989i | −0.276276 | + | 1.61076i | ||||
\(707\) | −6.81726 | + | 16.4583i | −0.256389 | + | 0.618979i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.738551 | + | 0.305918i | −0.0277369 | + | 0.0114890i | −0.396509 | − | 0.918031i | \(-0.629778\pi\) |
0.368772 | + | 0.929520i | \(0.379778\pi\) | |||||||
\(710\) | 1.46968 | + | 0.926674i | 0.0551560 | + | 0.0347775i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.25558 | + | 18.5702i | 0.196961 | + | 0.695946i | ||||
\(713\) | −25.7148 | − | 25.7148i | −0.963028 | − | 0.963028i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.977522 | − | 2.35995i | −0.0365573 | − | 0.0882570i | ||||
\(716\) | −27.5238 | − | 24.7523i | −1.02861 | − | 0.925038i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.3193 | + | 18.8342i | 0.497071 | + | 0.702886i | ||||
\(719\) | 36.8730i | 1.37513i | 0.726122 | + | 0.687566i | \(0.241321\pi\) | ||||
−0.726122 | + | 0.687566i | \(0.758679\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.3851i | 1.09436i | ||||||||
\(722\) | 15.0757 | − | 10.6613i | 0.561061 | − | 0.396774i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.19864 | + | 22.6089i | 0.0445470 | + | 0.840253i | ||||
\(725\) | −18.0383 | − | 43.5484i | −0.669927 | − | 1.61735i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.3080 | + | 32.3080i | 1.19824 | + | 1.19824i | 0.974694 | + | 0.223544i | \(0.0717626\pi\) |
0.223544 | + | 0.974694i | \(0.428237\pi\) | |||||||
\(728\) | −2.88562 | + | 24.5721i | −0.106948 | + | 0.910701i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.37854 | + | 5.35826i | −0.125045 | + | 0.198318i | ||||
\(731\) | −22.7656 | + | 9.42981i | −0.842015 | + | 0.348774i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.2720 | + | 27.2131i | −0.416343 | + | 1.00514i | 0.567056 | + | 0.823679i | \(0.308082\pi\) |
−0.983398 | + | 0.181460i | \(0.941918\pi\) | |||||||
\(734\) | 3.79188 | + | 0.650381i | 0.139961 | + | 0.0240060i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 35.2208 | + | 2.25484i | 1.29825 | + | 0.0831146i | ||||
\(737\) | 13.4591 | 0.495772 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.5065 | − | 32.6075i | 0.496843 | − | 1.19948i | −0.454332 | − | 0.890832i | \(-0.650122\pi\) |
0.951175 | − | 0.308652i | \(-0.0998780\pi\) | |||||||
\(740\) | 1.49456 | − | 0.713981i | 0.0549411 | − | 0.0262465i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.96176 | − | 4.69726i | 0.108729 | − | 0.172442i | ||||
\(743\) | 30.1102 | − | 30.1102i | 1.10464 | − | 1.10464i | 0.110792 | − | 0.993844i | \(-0.464661\pi\) |
0.993844 | − | 0.110792i | \(-0.0353387\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.95696 | − | 2.95696i | −0.108335 | − | 0.108335i | ||||
\(746\) | −3.44755 | + | 0.781201i | −0.126224 | + | 0.0286018i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12.1262 | + | 0.642885i | −0.443377 | + | 0.0235062i | ||||
\(749\) | 22.7578 | + | 9.42660i | 0.831553 | + | 0.344440i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 3.38793i | − | 0.123627i | −0.998088 | − | 0.0618137i | \(-0.980312\pi\) | ||
0.998088 | − | 0.0618137i | \(-0.0196885\pi\) | |||||||
\(752\) | −10.0514 | + | 12.4432i | −0.366535 | + | 0.453758i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −39.6175 | − | 56.0214i | −1.44278 | − | 2.04018i | ||||
\(755\) | 2.07252 | + | 0.858464i | 0.0754266 | + | 0.0312427i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.1514 | + | 26.9218i | 0.405304 | + | 0.978491i | 0.986356 | + | 0.164624i | \(0.0526412\pi\) |
−0.581052 | + | 0.813866i | \(0.697359\pi\) | |||||||
\(758\) | −7.19686 | − | 31.7608i | −0.261402 | − | 1.15360i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.34551 | − | 2.40772i | 0.0488068 | − | 0.0873371i | ||||
\(761\) | −8.70271 | + | 8.70271i | −0.315473 | + | 0.315473i | −0.847025 | − | 0.531553i | \(-0.821609\pi\) |
0.531553 | + | 0.847025i | \(0.321609\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.4325 | − | 12.6055i | 1.10173 | − | 0.456351i | ||||
\(764\) | 48.8322 | + | 17.2590i | 1.76669 | + | 0.624410i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.56730 | − | 38.2890i | 0.237286 | − | 1.38344i | ||||
\(767\) | −8.89733 | −0.321264 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.2614 | −1.74035 | −0.870175 | − | 0.492743i | \(-0.835994\pi\) | ||||
−0.870175 | + | 0.492743i | \(0.835994\pi\) | |||||||
\(770\) | −0.215234 | + | 1.25487i | −0.00775650 | + | 0.0452224i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −32.4029 | − | 11.4524i | −1.16621 | − | 0.412180i | ||||
\(773\) | 13.9602 | − | 5.78251i | 0.502114 | − | 0.207983i | −0.117226 | − | 0.993105i | \(-0.537400\pi\) |
0.619340 | + | 0.785123i | \(0.287400\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.9488 | + | 19.9488i | −0.716583 | + | 0.716583i | ||||
\(776\) | 9.62669 | − | 17.2265i | 0.345578 | − | 0.618394i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.538047 | + | 2.37448i | 0.0192899 | + | 0.0851292i | ||||
\(779\) | −4.14390 | − | 10.0043i | −0.148471 | − | 0.358440i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.63748 | − | 1.50669i | −0.130159 | − | 0.0539137i | ||||
\(782\) | 24.1300 | + | 34.1212i | 0.862887 | + | 1.22017i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.84559 | + | 12.1885i | −0.351628 | + | 0.435304i | ||||
\(785\) | 0.392807i | 0.0140199i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.99927 | − | 3.72762i | −0.320789 | − | 0.132875i | 0.216477 | − | 0.976288i | \(-0.430543\pi\) |
−0.537267 | + | 0.843412i | \(0.680543\pi\) | |||||||
\(788\) | 23.9437 | − | 1.26941i | 0.852960 | − | 0.0452207i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.479300 | − | 0.108607i | 0.0170527 | − | 0.00386408i | ||||
\(791\) | −5.69262 | − | 5.69262i | −0.202406 | − | 0.202406i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.76399 | − | 3.76399i | 0.133663 | − | 0.133663i | ||||
\(794\) | 0.359899 | − | 0.570789i | 0.0127723 | − | 0.0202566i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.43405 | − | 2.11824i | 0.157161 | − | 0.0750790i | ||||
\(797\) | 2.18185 | − | 5.26744i | 0.0772849 | − | 0.186582i | −0.880515 | − | 0.474019i | \(-0.842803\pi\) |
0.957800 | + | 0.287436i | \(0.0928029\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.9410 | −0.670085 | ||||||||
\(800\) | 1.74924 | − | 27.3233i | 0.0618450 | − | 0.966023i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.2120 | − | 3.29523i | −0.678401 | − | 0.116359i | ||||
\(803\) | 5.49322 | − | 13.2618i | 0.193851 | − | 0.467999i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.04820 | − | 1.67682i | 0.142680 | − | 0.0591001i | ||||
\(806\) | −21.9033 | + | 34.7380i | −0.771511 | + | 1.22359i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.34701 | − | 28.5009i | 0.117747 | − | 1.00266i | ||||
\(809\) | 10.2116 | + | 10.2116i | 0.359021 | + | 0.359021i | 0.863452 | − | 0.504431i | \(-0.168298\pi\) |
−0.504431 | + | 0.863452i | \(0.668298\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.5071 | − | 32.6089i | −0.474297 | − | 1.14505i | −0.962246 | − | 0.272182i | \(-0.912255\pi\) |
0.487949 | − | 0.872872i | \(-0.337745\pi\) | |||||||
\(812\) | 1.81060 | + | 34.1518i | 0.0635396 | + | 1.19849i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.06454 | + | 2.16720i | −0.107412 | + | 0.0759603i | ||||
\(815\) | 5.17049i | 0.181114i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.6832i | 0.443727i | ||||||||
\(818\) | −6.16746 | − | 8.72114i | −0.215640 | − | 0.304927i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.64205 | + | 2.37601i | 0.0922643 | + | 0.0829739i | ||||
\(821\) | −15.3137 | − | 36.9705i | −0.534451 | − | 1.29028i | −0.928549 | − | 0.371210i | \(-0.878943\pi\) |
0.394098 | − | 0.919068i | \(-0.371057\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.234300 | − | 0.234300i | −0.00816720 | − | 0.00816720i | 0.703011 | − | 0.711179i | \(-0.251838\pi\) |
−0.711179 | + | 0.703011i | \(0.751838\pi\) | |||||||
\(824\) | −12.8903 | − | 45.5470i | −0.449056 | − | 1.58670i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.75129 | + | 2.36530i | 0.130524 | + | 0.0822993i | ||||
\(827\) | 44.4802 | − | 18.4243i | 1.54673 | − | 0.640675i | 0.564007 | − | 0.825770i | \(-0.309259\pi\) |
0.982721 | + | 0.185095i | \(0.0592592\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.62628 | − | 3.92618i | 0.0564829 | − | 0.136362i | −0.893119 | − | 0.449821i | \(-0.851488\pi\) |
0.949602 | + | 0.313459i | \(0.101488\pi\) | |||||||
\(830\) | 0.566287 | − | 3.30160i | 0.0196561 | − | 0.114600i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.30628 | − | 39.3526i | −0.218631 | − | 1.36430i | ||||
\(833\) | −18.5533 | −0.642832 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.56718 | − | 6.19771i | 0.0888408 | − | 0.214481i | ||||
\(836\) | −2.08280 | + | 5.89302i | −0.0720353 | + | 0.203814i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.1579 | + | 8.29645i | 0.454533 | + | 0.286596i | ||||
\(839\) | 1.45311 | − | 1.45311i | 0.0501669 | − | 0.0501669i | −0.681578 | − | 0.731745i | \(-0.738706\pi\) |
0.731745 | + | 0.681578i | \(0.238706\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −46.5607 | − | 46.5607i | −1.60554 | − | 1.60554i | ||||
\(842\) | −2.83908 | − | 12.5293i | −0.0978410 | − | 0.431786i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.52732 | + | 5.87005i | 0.224679 | + | 0.202056i | ||||
\(845\) | 4.36753 | + | 1.80909i | 0.150248 | + | 0.0622347i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.4289i | 0.564505i | ||||||||
\(848\) | −2.53019 | + | 8.57998i | −0.0868869 | + | 0.294638i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 26.4702 | − | 18.7194i | 0.907922 | − | 0.642069i | ||||
\(851\) | 11.9342 | + | 4.94333i | 0.409101 | + | 0.169455i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.33038 | − | 20.1113i | −0.285227 | − | 0.688598i | 0.714715 | − | 0.699416i | \(-0.246556\pi\) |
−0.999941 | + | 0.0108179i | \(0.996556\pi\) | |||||||
\(854\) | −2.58761 | + | 0.586341i | −0.0885461 | + | 0.0200642i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −39.4098 | − | 4.62809i | −1.34700 | − | 0.158185i | ||||
\(857\) | 4.03789 | − | 4.03789i | 0.137932 | − | 0.137932i | −0.634770 | − | 0.772701i | \(-0.718905\pi\) |
0.772701 | + | 0.634770i | \(0.218905\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.6309 | + | 10.6167i | −0.874516 | + | 0.362236i | −0.774367 | − | 0.632736i | \(-0.781932\pi\) |
−0.100148 | + | 0.994973i | \(0.531932\pi\) | |||||||
\(860\) | −1.79401 | − | 3.75535i | −0.0611751 | − | 0.128056i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −50.5525 | − | 8.67072i | −1.72183 | − | 0.295326i | ||||
\(863\) | −12.2309 | −0.416345 | −0.208173 | − | 0.978092i | \(-0.566752\pi\) | ||||
−0.208173 | + | 0.978092i | \(0.566752\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.31355 | 0.316670 | ||||||||
\(866\) | 1.98473 | + | 0.340418i | 0.0674437 | + | 0.0115679i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 18.4697 | − | 8.82337i | 0.626904 | − | 0.299485i | ||||
\(869\) | −1.02890 | + | 0.426184i | −0.0349030 | + | 0.0144573i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −36.9866 | + | 36.9866i | −1.25324 | + | 1.25324i | ||||
\(872\) | −41.6407 | + | 32.8884i | −1.41013 | + | 1.11374i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 20.9786 | − | 4.75367i | 0.709613 | − | 0.160795i | ||||
\(875\) | −2.64466 | − | 6.38477i | −0.0894058 | − | 0.215845i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.4465 | + | 17.9961i | 1.46709 | + | 0.607687i | 0.966192 | − | 0.257822i | \(-0.0830049\pi\) |
0.500893 | + | 0.865509i | \(0.333005\pi\) | |||||||
\(878\) | 46.2054 | − | 32.6757i | 1.55936 | − | 1.10275i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.216859 | − | 2.03947i | −0.00731032 | − | 0.0687504i | ||||
\(881\) | − | 23.7025i | − | 0.798558i | −0.916829 | − | 0.399279i | \(-0.869260\pi\) | ||
0.916829 | − | 0.399279i | \(-0.130740\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.2088 | + | 21.6256i | 1.75697 | + | 0.727759i | 0.996966 | + | 0.0778345i | \(0.0248006\pi\) |
0.759999 | + | 0.649924i | \(0.225199\pi\) | |||||||
\(884\) | 31.5570 | − | 35.0904i | 1.06138 | − | 1.18022i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.3235 | − | 49.9722i | −0.380420 | − | 1.67885i | ||||
\(887\) | 36.1569 | + | 36.1569i | 1.21403 | + | 1.21403i | 0.969689 | + | 0.244341i | \(0.0785717\pi\) |
0.244341 | + | 0.969689i | \(0.421428\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.68416 | − | 3.68416i | 0.123563 | − | 0.123563i | ||||
\(890\) | −3.26500 | − | 2.05868i | −0.109443 | − | 0.0690071i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.7995 | − | 4.87723i | −0.462041 | − | 0.163302i | ||||
\(893\) | −3.73085 | + | 9.00706i | −0.124848 | + | 0.301410i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.40322 | 0.247462 | ||||||||
\(896\) | −7.80278 | + | 18.2683i | −0.260673 | + | 0.610302i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.61289 | + | 21.0641i | −0.120564 | + | 0.702917i | ||||
\(899\) | −21.7239 | + | 52.4461i | −0.724532 | + | 1.74917i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.78606 | + | 4.05352i | −0.326021 | + | 0.135042i | ||||
\(902\) | −6.81116 | − | 4.29463i | −0.226787 | − | 0.142996i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.3207 | + | 6.32639i | 0.376522 | + | 0.210413i | ||||
\(905\) | −3.20182 | − | 3.20182i | −0.106432 | − | 0.106432i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.370321 | − | 0.894034i | −0.0122963 | − | 0.0296859i | 0.917612 | − | 0.397477i | \(-0.130114\pi\) |
−0.929908 | + | 0.367791i | \(0.880114\pi\) | |||||||
\(908\) | 24.8451 | − | 27.6270i | 0.824514 | − | 0.916834i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.85700 | − | 4.03996i | −0.0947086 | − | 0.133923i | ||||
\(911\) | 17.0794i | 0.565867i | 0.959140 | + | 0.282933i | \(0.0913075\pi\) | ||||
−0.959140 | + | 0.282933i | \(0.908692\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.59097i | 0.251224i | ||||||||
\(914\) | −37.3444 | + | 26.4094i | −1.23524 | + | 0.873546i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.24218 | + | 0.383953i | −0.239288 | + | 0.0126862i | ||||
\(917\) | 7.87726 | + | 19.0174i | 0.260130 | + | 0.628010i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.09765 | + | 7.09765i | 0.234130 | + | 0.234130i | 0.814414 | − | 0.580284i | \(-0.197059\pi\) |
−0.580284 | + | 0.814414i | \(0.697059\pi\) | |||||||
\(920\) | −5.53915 | + | 4.37489i | −0.182620 | + | 0.144236i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.04670 | + | 1.66003i | −0.0344712 | + | 0.0546703i | ||||
\(923\) | 14.1366 | − | 5.85557i | 0.465311 | − | 0.192738i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.83489 | − | 9.25824i | 0.126090 | − | 0.304409i | ||||
\(926\) | 35.8741 | + | 6.15309i | 1.17889 | + | 0.202203i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −17.7878 | − | 52.1411i | −0.583912 | − | 1.71161i | ||||
\(929\) | 5.65079 | 0.185396 | 0.0926982 | − | 0.995694i | \(-0.470451\pi\) | ||||
0.0926982 | + | 0.995694i | \(0.470451\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.65447 | + | 8.82266i | −0.119770 | + | 0.289151i | ||||
\(932\) | 16.1040 | + | 33.7101i | 0.527504 | + | 1.10421i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17.1433 | + | 27.1888i | −0.560947 | + | 0.889646i | ||||
\(935\) | 1.71728 | − | 1.71728i | 0.0561612 | − | 0.0561612i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.4460 | + | 36.4460i | 1.19064 | + | 1.19064i | 0.976889 | + | 0.213749i | \(0.0685675\pi\) |
0.213749 | + | 0.976889i | \(0.431432\pi\) | |||||||
\(938\) | 25.4270 | − | 5.76165i | 0.830220 | − | 0.188124i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.169366 | − | 3.19461i | −0.00552412 | − | 0.104197i | ||||
\(941\) | −0.420815 | − | 0.174307i | −0.0137182 | − | 0.00568225i | 0.375814 | − | 0.926695i | \(-0.377363\pi\) |
−0.389532 | + | 0.921013i | \(0.627363\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.7114i | 0.902409i | ||||||||
\(944\) | −6.85210 | − | 2.02064i | −0.223017 | − | 0.0657663i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.44548 | + | 7.70021i | 0.177048 | + | 0.250356i | ||||
\(947\) | 19.0759 | + | 7.90148i | 0.619882 | + | 0.256764i | 0.670447 | − | 0.741957i | \(-0.266102\pi\) |
−0.0505652 | + | 0.998721i | \(0.516102\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.3487 | + | 51.5403i | 0.693007 | + | 1.67307i | ||||
\(950\) | −3.68776 | − | 16.2746i | −0.119647 | − | 0.528019i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −22.6336 | + | 6.40559i | −0.733561 | + | 0.207606i | ||||
\(953\) | −18.8477 | + | 18.8477i | −0.610537 | + | 0.610537i | −0.943086 | − | 0.332549i | \(-0.892091\pi\) |
0.332549 | + | 0.943086i | \(0.392091\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.56984 | + | 3.96396i | −0.309673 | + | 0.128271i | ||||
\(956\) | −3.37497 | + | 9.54904i | −0.109154 | + | 0.308838i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.21997 | − | 36.2640i | 0.200958 | − | 1.17164i | ||||
\(959\) | −40.1996 | −1.29811 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.97606 | 0.0960020 | ||||||||
\(962\) | 2.46597 | − | 14.3772i | 0.0795061 | − | 0.463541i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.4853 | − | 32.4961i | 0.369916 | − | 1.04663i | ||||
\(965\) | 6.35014 | − | 2.63031i | 0.204418 | − | 0.0846728i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.9198 | − | 13.9198i | 0.447631 | − | 0.447631i | −0.446935 | − | 0.894566i | \(-0.647485\pi\) |
0.894566 | + | 0.446935i | \(0.147485\pi\) | |||||||
\(968\) | −7.20686 | − | 25.4649i | −0.231637 | − | 0.818472i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.872195 | + | 3.84912i | 0.0280045 | + | 0.123588i | ||||
\(971\) | 1.40929 | + | 3.40232i | 0.0452262 | + | 0.109186i | 0.944878 | − | 0.327422i | \(-0.106180\pi\) |
−0.899652 | + | 0.436608i | \(0.856180\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.6712 | − | 5.24856i | −0.406219 | − | 0.168261i | ||||
\(974\) | 20.3992 | + | 28.8456i | 0.653633 | + | 0.924274i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.75359 | − | 2.04393i | 0.120149 | − | 0.0654247i | ||||
\(977\) | − | 40.1892i | − | 1.28577i | −0.765964 | − | 0.642883i | \(-0.777738\pi\) | ||
0.765964 | − | 0.642883i | \(-0.222262\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.08094 | + | 3.34724i | 0.258268 | + | 0.106978i | ||||
\(980\) | −0.165899 | − | 3.12921i | −0.00529945 | − | 0.0999590i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −54.2723 | + | 12.2979i | −1.73190 | + | 0.392441i | ||||
\(983\) | 16.1343 | + | 16.1343i | 0.514603 | + | 0.514603i | 0.915933 | − | 0.401331i | \(-0.131452\pi\) |
−0.401331 | + | 0.915933i | \(0.631452\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.39086 | + | 3.39086i | −0.108042 | + | 0.108042i | ||||
\(986\) | 34.7940 | − | 55.1822i | 1.10807 | − | 1.75736i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.4708 | − | 21.9182i | −0.333119 | − | 0.697310i | ||||
\(989\) | 12.4210 | − | 29.9869i | 0.394964 | − | 0.953528i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.74370 | 0.118923 | 0.0594614 | − | 0.998231i | \(-0.481062\pi\) | ||||
0.0594614 | + | 0.998231i | \(0.481062\pi\) | |||||||
\(992\) | −24.7576 | + | 21.7783i | −0.786054 | + | 0.691463i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.51694 | − | 1.28930i | −0.238423 | − | 0.0408941i | ||||
\(995\) | −0.376098 | + | 0.907981i | −0.0119231 | + | 0.0287849i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.64519 | − | 0.681459i | 0.0521036 | − | 0.0215820i | −0.356479 | − | 0.934303i | \(-0.616023\pi\) |
0.408583 | + | 0.912721i | \(0.366023\pi\) | |||||||
\(998\) | 5.68799 | − | 9.02097i | 0.180050 | − | 0.285554i | ||||
\(999\) | 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 | 864.2.v.b.109.16 | ✓ | 128 | |
3.2 | odd | 2 | inner | 864.2.v.b.109.17 | yes | 128 | |
32.5 | even | 8 | inner | 864.2.v.b.325.16 | yes | 128 | |
96.5 | odd | 8 | inner | 864.2.v.b.325.17 | yes | 128 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.2.v.b.109.16 | ✓ | 128 | 1.1 | even | 1 | trivial | |
864.2.v.b.109.17 | yes | 128 | 3.2 | odd | 2 | inner | |
864.2.v.b.325.16 | yes | 128 | 32.5 | even | 8 | inner | |
864.2.v.b.325.17 | yes | 128 | 96.5 | odd | 8 | inner |