Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(35,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.v (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 35.6 | ||
Character | \(\chi\) | \(=\) | 432.35 |
Dual form | 432.2.v.a.395.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00831 | + | 0.991617i | −0.712985 | + | 0.701179i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.0333930 | − | 1.99972i | 0.0166965 | − | 0.999861i | ||||
\(5\) | −0.473330 | + | 1.76649i | −0.211679 | + | 0.789999i | 0.775630 | + | 0.631188i | \(0.217432\pi\) |
−0.987309 | + | 0.158810i | \(0.949234\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.40613 | − | 2.43549i | 0.531468 | − | 0.920530i | −0.467857 | − | 0.883804i | \(-0.654974\pi\) |
0.999325 | − | 0.0367260i | \(-0.0116929\pi\) | |||||||
\(8\) | 1.94929 | + | 2.04946i | 0.689177 | + | 0.724593i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.27442 | − | 2.25054i | −0.403006 | − | 0.711683i | ||||
\(11\) | −1.55262 | − | 5.79446i | −0.468133 | − | 1.74710i | −0.646288 | − | 0.763093i | \(-0.723680\pi\) |
0.178156 | − | 0.984002i | \(-0.442987\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.296913 | − | 1.10810i | 0.0823489 | − | 0.307330i | −0.912450 | − | 0.409188i | \(-0.865812\pi\) |
0.994799 | + | 0.101858i | \(0.0324787\pi\) | |||||||
\(14\) | 0.997253 | + | 3.85009i | 0.266527 | + | 1.02898i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.99777 | − | 0.133554i | −0.999442 | − | 0.0333884i | ||||
\(17\) | − | 0.699378i | − | 0.169624i | −0.996397 | − | 0.0848120i | \(-0.972971\pi\) | ||
0.996397 | − | 0.0848120i | \(-0.0270290\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.01481 | + | 2.01481i | −0.462228 | + | 0.462228i | −0.899385 | − | 0.437157i | \(-0.855985\pi\) |
0.437157 | + | 0.899385i | \(0.355985\pi\) | |||||||
\(20\) | 3.51668 | + | 1.00552i | 0.786354 | + | 0.224840i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.31141 | + | 4.30303i | 1.55880 | + | 0.917409i | ||||
\(23\) | 4.91498 | − | 2.83767i | 1.02485 | − | 0.591695i | 0.109341 | − | 0.994004i | \(-0.465126\pi\) |
0.915504 | + | 0.402310i | \(0.131792\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.43368 | + | 0.827735i | 0.286736 | + | 0.165547i | ||||
\(26\) | 0.799424 | + | 1.41173i | 0.156780 | + | 0.276863i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.82335 | − | 2.89320i | −0.911528 | − | 0.546764i | ||||
\(29\) | −1.45175 | − | 5.41802i | −0.269584 | − | 1.00610i | −0.959385 | − | 0.282101i | \(-0.908969\pi\) |
0.689801 | − | 0.723999i | \(-0.257698\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.15522 | − | 2.97637i | 0.925905 | − | 0.534572i | 0.0403909 | − | 0.999184i | \(-0.487140\pi\) |
0.885514 | + | 0.464612i | \(0.153806\pi\) | |||||||
\(32\) | 4.16344 | − | 3.82959i | 0.735999 | − | 0.676982i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.693515 | + | 0.705192i | 0.118937 | + | 0.120939i | ||||
\(35\) | 3.63671 | + | 3.63671i | 0.614717 | + | 0.614717i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.48490 | − | 3.48490i | 0.572913 | − | 0.572913i | −0.360028 | − | 0.932941i | \(-0.617233\pi\) |
0.932941 | + | 0.360028i | \(0.117233\pi\) | |||||||
\(38\) | 0.0336414 | − | 4.02947i | 0.00545736 | − | 0.653666i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.54301 | + | 2.47333i | −0.718312 | + | 0.391067i | ||||
\(41\) | 1.55998 | + | 2.70196i | 0.243628 | + | 0.421975i | 0.961745 | − | 0.273947i | \(-0.0883292\pi\) |
−0.718117 | + | 0.695922i | \(0.754996\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.09570 | − | 1.90129i | 1.08208 | − | 0.289944i | 0.326635 | − | 0.945151i | \(-0.394085\pi\) |
0.755450 | + | 0.655207i | \(0.227419\pi\) | |||||||
\(44\) | −11.6392 | + | 2.91131i | −1.75467 | + | 0.438897i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.14197 | + | 7.73504i | −0.315816 | + | 1.14047i | ||||
\(47\) | −2.83634 | + | 4.91269i | −0.413723 | + | 0.716589i | −0.995293 | − | 0.0969068i | \(-0.969105\pi\) |
0.581570 | + | 0.813496i | \(0.302438\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.454420 | − | 0.787079i | −0.0649172 | − | 0.112440i | ||||
\(50\) | −2.26639 | + | 0.587044i | −0.320517 | + | 0.0830205i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.20597 | − | 0.630746i | −0.305913 | − | 0.0874688i | ||||
\(53\) | −4.45605 | − | 4.45605i | −0.612086 | − | 0.612086i | 0.331403 | − | 0.943489i | \(-0.392478\pi\) |
−0.943489 | + | 0.331403i | \(0.892478\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.9708 | 1.47930 | ||||||||
\(56\) | 7.73240 | − | 1.86566i | 1.03329 | − | 0.249310i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.83642 | + | 4.02348i | 0.897666 | + | 0.528309i | ||||
\(59\) | 13.6570 | + | 3.65938i | 1.77799 | + | 0.476411i | 0.990215 | − | 0.139552i | \(-0.0445663\pi\) |
0.787775 | + | 0.615963i | \(0.211233\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.2354 | + | 3.54643i | −1.69463 | + | 0.454074i | −0.971577 | − | 0.236724i | \(-0.923926\pi\) |
−0.723048 | + | 0.690797i | \(0.757260\pi\) | |||||||
\(62\) | −2.24666 | + | 8.11312i | −0.285327 | + | 1.03037i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.400567 | + | 7.98997i | −0.0500709 | + | 0.998746i | ||||
\(65\) | 1.81690 | + | 1.04899i | 0.225359 | + | 0.130111i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.8958 | − | 3.45542i | −1.57547 | − | 0.422146i | −0.637952 | − | 0.770077i | \(-0.720218\pi\) |
−0.937520 | + | 0.347930i | \(0.886885\pi\) | |||||||
\(68\) | −1.39856 | − | 0.0233544i | −0.169600 | − | 0.00283213i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.27317 | − | 0.0607225i | −0.869310 | − | 0.00725773i | ||||
\(71\) | − | 7.21910i | − | 0.856749i | −0.903601 | − | 0.428375i | \(-0.859086\pi\) | ||
0.903601 | − | 0.428375i | \(-0.140914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.75535i | 0.439531i | 0.975553 | + | 0.219765i | \(0.0705292\pi\) | ||||
−0.975553 | + | 0.219765i | \(0.929471\pi\) | |||||||
\(74\) | −0.0581877 | + | 6.96955i | −0.00676418 | + | 0.810194i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.96177 | + | 4.09633i | 0.454446 | + | 0.469881i | ||||
\(77\) | −16.2956 | − | 4.36638i | −1.85705 | − | 0.497596i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.96345 | + | 1.71095i | 0.333415 | + | 0.192497i | 0.657356 | − | 0.753580i | \(-0.271675\pi\) |
−0.323942 | + | 0.946077i | \(0.605008\pi\) | |||||||
\(80\) | 2.12818 | − | 6.99881i | 0.237938 | − | 0.782490i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.25226 | − | 1.17752i | −0.469583 | − | 0.130036i | ||||
\(83\) | −1.15222 | + | 0.308735i | −0.126472 | + | 0.0338881i | −0.321500 | − | 0.946910i | \(-0.604187\pi\) |
0.195028 | + | 0.980798i | \(0.437520\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.23544 | + | 0.331036i | 0.134003 | + | 0.0359059i | ||||
\(86\) | −5.26935 | + | 8.95331i | −0.568208 | + | 0.965461i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.84901 | − | 14.4771i | 0.943308 | − | 1.54326i | ||||
\(89\) | 0.391835 | 0.0415344 | 0.0207672 | − | 0.999784i | \(-0.493389\pi\) | ||||
0.0207672 | + | 0.999784i | \(0.493389\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.28126 | − | 2.28126i | −0.239141 | − | 0.239141i | ||||
\(92\) | −5.51042 | − | 9.92336i | −0.574501 | − | 1.03458i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.01158 | − | 7.76609i | −0.207479 | − | 0.801011i | ||||
\(95\) | −2.60547 | − | 4.51280i | −0.267315 | − | 0.463004i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.875387 | + | 1.51622i | −0.0888821 | + | 0.153948i | −0.907039 | − | 0.421047i | \(-0.861663\pi\) |
0.818157 | + | 0.574995i | \(0.194996\pi\) | |||||||
\(98\) | 1.23868 | + | 0.343012i | 0.125125 | + | 0.0346494i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.70311 | − | 2.83932i | 0.170311 | − | 0.283932i | ||||
\(101\) | 0.816427 | − | 0.218761i | 0.0812375 | − | 0.0217675i | −0.217971 | − | 0.975955i | \(-0.569944\pi\) |
0.299209 | + | 0.954188i | \(0.403277\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.30341 | − | 9.18577i | −0.522560 | − | 0.905101i | −0.999655 | − | 0.0262492i | \(-0.991644\pi\) |
0.477095 | − | 0.878852i | \(-0.341690\pi\) | |||||||
\(104\) | 2.84976 | − | 1.55148i | 0.279442 | − | 0.152135i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.91180 | + | 0.0744032i | 0.865590 | + | 0.00722668i | ||||
\(107\) | −6.39894 | + | 6.39894i | −0.618609 | + | 0.618609i | −0.945174 | − | 0.326566i | \(-0.894109\pi\) |
0.326566 | + | 0.945174i | \(0.394109\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.52592 | + | 1.52592i | 0.146157 | + | 0.146157i | 0.776399 | − | 0.630242i | \(-0.217044\pi\) |
−0.630242 | + | 0.776399i | \(0.717044\pi\) | |||||||
\(110\) | −11.0620 | + | 10.8788i | −1.05472 | + | 1.03725i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.94666 | + | 9.54875i | −0.561907 | + | 0.902272i | ||||
\(113\) | −5.75213 | + | 3.32099i | −0.541115 | + | 0.312413i | −0.745531 | − | 0.666471i | \(-0.767804\pi\) |
0.204416 | + | 0.978884i | \(0.434471\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.68630 | + | 10.0254i | 0.250499 | + | 0.934876i | ||||
\(116\) | −10.8830 | + | 2.72218i | −1.01046 | + | 0.252748i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −17.3992 | + | 9.85270i | −1.60173 | + | 0.907015i | ||||
\(119\) | −1.70333 | − | 0.983418i | −0.156144 | − | 0.0901498i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −21.6389 | + | 12.4932i | −1.96717 | + | 1.13575i | ||||
\(122\) | 9.82879 | − | 16.7004i | 0.889857 | − | 1.51198i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.77976 | − | 10.4084i | −0.519038 | − | 0.934701i | ||||
\(125\) | −8.60659 | + | 8.60659i | −0.769797 | + | 0.769797i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 13.8224i | − | 1.22654i | −0.789874 | − | 0.613270i | \(-0.789854\pi\) | ||
0.789874 | − | 0.613270i | \(-0.210146\pi\) | |||||||
\(128\) | −7.51908 | − | 8.45360i | −0.664599 | − | 0.747200i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.87220 | + | 0.743960i | −0.251909 | + | 0.0652496i | ||||
\(131\) | −2.40595 | + | 8.97914i | −0.210209 | + | 0.784511i | 0.777589 | + | 0.628773i | \(0.216442\pi\) |
−0.987798 | + | 0.155739i | \(0.950224\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.07396 | + | 7.74013i | 0.179835 | + | 0.671154i | ||||
\(134\) | 16.4295 | − | 9.30354i | 1.41929 | − | 0.803703i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.43335 | − | 1.36329i | 0.122908 | − | 0.116901i | ||||
\(137\) | 5.96603 | − | 10.3335i | 0.509712 | − | 0.882848i | −0.490224 | − | 0.871596i | \(-0.663085\pi\) |
0.999937 | − | 0.0112514i | \(-0.00358150\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.323448 | + | 1.20712i | −0.0274345 | + | 0.102387i | −0.978286 | − | 0.207262i | \(-0.933545\pi\) |
0.950851 | + | 0.309649i | \(0.100211\pi\) | |||||||
\(140\) | 7.39385 | − | 7.15097i | 0.624894 | − | 0.604367i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.15858 | + | 7.27912i | 0.600735 | + | 0.610850i | ||||
\(143\) | −6.88181 | −0.575486 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.2580 | 0.851884 | ||||||||
\(146\) | −3.72387 | − | 3.78657i | −0.308190 | − | 0.313379i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.85245 | − | 7.08519i | −0.563268 | − | 0.582399i | ||||
\(149\) | 0.930902 | − | 3.47417i | 0.0762625 | − | 0.284615i | −0.917254 | − | 0.398302i | \(-0.869599\pi\) |
0.993517 | + | 0.113687i | \(0.0362661\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.43126 | + | 9.40721i | −0.441989 | + | 0.765548i | −0.997837 | − | 0.0657361i | \(-0.979060\pi\) |
0.555848 | + | 0.831284i | \(0.312394\pi\) | |||||||
\(152\) | −8.05669 | − | 0.201830i | −0.653484 | − | 0.0163705i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 20.7608 | − | 11.7563i | 1.67295 | − | 0.947347i | ||||
\(155\) | 2.81761 | + | 10.5155i | 0.226316 | + | 0.844621i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.55352 | − | 9.52986i | 0.203793 | − | 0.760565i | −0.786021 | − | 0.618199i | \(-0.787862\pi\) |
0.989814 | − | 0.142366i | \(-0.0454709\pi\) | |||||||
\(158\) | −4.68470 | + | 1.21343i | −0.372695 | + | 0.0965357i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.79426 | + | 9.16734i | 0.379019 | + | 0.724742i | ||||
\(161\) | − | 15.9606i | − | 1.25787i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.66703 | + | 3.66703i | −0.287224 | + | 0.287224i | −0.835981 | − | 0.548758i | \(-0.815101\pi\) |
0.548758 | + | 0.835981i | \(0.315101\pi\) | |||||||
\(164\) | 5.45526 | − | 3.02929i | 0.425984 | − | 0.236548i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.855648 | − | 1.45386i | 0.0664112 | − | 0.112841i | ||||
\(167\) | 17.4253 | − | 10.0605i | 1.34841 | − | 0.778505i | 0.360385 | − | 0.932803i | \(-0.382645\pi\) |
0.988024 | + | 0.154299i | \(0.0493118\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.1186 | + | 5.84198i | 0.778355 | + | 0.449383i | ||||
\(170\) | −1.57398 | + | 0.891299i | −0.120719 | + | 0.0683595i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.56510 | − | 14.2529i | −0.271836 | − | 1.08677i | ||||
\(173\) | 2.70826 | + | 10.1074i | 0.205906 | + | 0.768450i | 0.989172 | + | 0.146763i | \(0.0468855\pi\) |
−0.783266 | + | 0.621687i | \(0.786448\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.03189 | − | 2.32781i | 0.304782 | − | 0.175966i | ||||
\(176\) | 5.43315 | + | 23.3723i | 0.409539 | + | 1.76175i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.395093 | + | 0.388550i | −0.0296135 | + | 0.0291231i | ||||
\(179\) | 12.4542 | + | 12.4542i | 0.930872 | + | 0.930872i | 0.997760 | − | 0.0668885i | \(-0.0213072\pi\) |
−0.0668885 | + | 0.997760i | \(0.521307\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.12083 | + | 9.12083i | −0.677946 | + | 0.677946i | −0.959535 | − | 0.281589i | \(-0.909139\pi\) |
0.281589 | + | 0.959535i | \(0.409139\pi\) | |||||||
\(182\) | 4.56236 | + | 0.0380904i | 0.338185 | + | 0.00282345i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 15.3964 | + | 4.54163i | 1.13504 | + | 0.334814i | ||||
\(185\) | 4.50653 | + | 7.80554i | 0.331327 | + | 0.573875i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.05252 | + | 1.08587i | −0.296349 | + | 0.0794066i | ||||
\(188\) | 9.72929 | + | 5.83594i | 0.709582 | + | 0.425630i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.10210 | + | 1.96670i | 0.515240 | + | 0.142679i | ||||
\(191\) | 1.76985 | − | 3.06547i | 0.128062 | − | 0.221810i | −0.794864 | − | 0.606788i | \(-0.792458\pi\) |
0.922926 | + | 0.384978i | \(0.125791\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.43004 | + | 12.8692i | 0.534826 | + | 0.926346i | 0.999172 | + | 0.0406916i | \(0.0129561\pi\) |
−0.464346 | + | 0.885654i | \(0.653711\pi\) | |||||||
\(194\) | −0.620839 | − | 2.39687i | −0.0445737 | − | 0.172085i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.58911 | + | 0.882431i | −0.113508 | + | 0.0630308i | ||||
\(197\) | 11.9105 | + | 11.9105i | 0.848589 | + | 0.848589i | 0.989957 | − | 0.141368i | \(-0.0451501\pi\) |
−0.141368 | + | 0.989957i | \(0.545150\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.5983 | 1.10574 | 0.552868 | − | 0.833269i | \(-0.313533\pi\) | ||||
0.552868 | + | 0.833269i | \(0.313533\pi\) | |||||||
\(200\) | 1.09824 | + | 4.55176i | 0.0776574 | + | 0.321858i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.606287 | + | 1.03016i | −0.0426582 | + | 0.0724819i | ||||
\(203\) | −15.2369 | − | 4.08272i | −1.06942 | − | 0.286551i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.51137 | + | 1.47677i | −0.384931 | + | 0.103142i | ||||
\(206\) | 14.4563 | + | 4.00319i | 1.00722 | + | 0.278916i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.33498 | + | 4.39026i | −0.0925643 | + | 0.304409i | ||||
\(209\) | 14.8029 | + | 8.54648i | 1.02394 | + | 0.591172i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.6018 | + | 4.18049i | 1.07407 | + | 0.287797i | 0.752165 | − | 0.658975i | \(-0.229010\pi\) |
0.321907 | + | 0.946771i | \(0.395676\pi\) | |||||||
\(212\) | −9.05967 | + | 8.76207i | −0.622221 | + | 0.601781i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.106844 | − | 12.7974i | 0.00730368 | − | 0.874814i | ||||
\(215\) | 13.4344i | 0.916220i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 16.7407i | − | 1.13643i | ||||||
\(218\) | −3.05174 | − | 0.0254785i | −0.206690 | − | 0.00172562i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.366347 | − | 21.9385i | 0.0246991 | − | 1.47909i | ||||
\(221\) | −0.774977 | − | 0.207655i | −0.0521306 | − | 0.0139684i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.9254 | − | 8.03982i | −0.932512 | − | 0.538386i | −0.0449068 | − | 0.998991i | \(-0.514299\pi\) |
−0.887605 | + | 0.460605i | \(0.847632\pi\) | |||||||
\(224\) | −3.47259 | − | 15.5249i | −0.232023 | − | 1.03730i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.50680 | − | 9.05251i | 0.166750 | − | 0.602164i | ||||
\(227\) | −10.6697 | + | 2.85895i | −0.708176 | + | 0.189755i | −0.594890 | − | 0.803807i | \(-0.702804\pi\) |
−0.113286 | + | 0.993562i | \(0.536138\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.390566 | − | 0.104652i | −0.0258093 | − | 0.00691559i | 0.245891 | − | 0.969297i | \(-0.420919\pi\) |
−0.271701 | + | 0.962382i | \(0.587586\pi\) | |||||||
\(230\) | −12.6500 | − | 7.44499i | −0.834117 | − | 0.490908i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.27413 | − | 13.5366i | 0.543223 | − | 0.888720i | ||||
\(233\) | 11.6252 | 0.761590 | 0.380795 | − | 0.924659i | \(-0.375650\pi\) | ||||
0.380795 | + | 0.924659i | \(0.375650\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.33569 | − | 7.33569i | −0.478528 | − | 0.478528i | ||||
\(236\) | 7.77379 | − | 27.1880i | 0.506031 | − | 1.76979i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.69267 | − | 0.697457i | 0.174540 | − | 0.0452094i | ||||
\(239\) | −1.55685 | − | 2.69654i | −0.100704 | − | 0.174425i | 0.811271 | − | 0.584671i | \(-0.198776\pi\) |
−0.911975 | + | 0.410246i | \(0.865443\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.16669 | + | 12.4131i | −0.461647 | + | 0.799596i | −0.999043 | − | 0.0437337i | \(-0.986075\pi\) |
0.537396 | + | 0.843330i | \(0.319408\pi\) | |||||||
\(242\) | 9.43029 | − | 34.0545i | 0.606202 | − | 2.18911i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.64989 | + | 26.5856i | 0.425716 | + | 1.70197i | ||||
\(245\) | 1.60546 | − | 0.430181i | 0.102569 | − | 0.0274833i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.63437 | + | 2.83082i | 0.103993 | + | 0.180121i | ||||
\(248\) | 16.1489 | + | 4.76362i | 1.02546 | + | 0.302490i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.143705 | − | 17.2126i | 0.00908871 | − | 1.08862i | ||||
\(251\) | 3.06176 | − | 3.06176i | 0.193257 | − | 0.193257i | −0.603845 | − | 0.797102i | \(-0.706365\pi\) |
0.797102 | + | 0.603845i | \(0.206365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.0739 | − | 24.0739i | −1.51351 | − | 1.51351i | ||||
\(254\) | 13.7065 | + | 13.9373i | 0.860023 | + | 0.874505i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.9643 | + | 1.06783i | 0.997770 | + | 0.0667395i | ||||
\(257\) | −2.78074 | + | 1.60546i | −0.173458 | + | 0.100146i | −0.584215 | − | 0.811599i | \(-0.698598\pi\) |
0.410757 | + | 0.911745i | \(0.365264\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.58722 | − | 13.3877i | −0.222899 | − | 0.831870i | ||||
\(260\) | 2.15836 | − | 3.59827i | 0.133856 | − | 0.223155i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.47791 | − | 11.4396i | −0.400207 | − | 0.706739i | ||||
\(263\) | −2.63762 | − | 1.52283i | −0.162643 | − | 0.0939018i | 0.416469 | − | 0.909150i | \(-0.363267\pi\) |
−0.579112 | + | 0.815248i | \(0.696601\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.98076 | − | 5.76240i | 0.613113 | − | 0.353981i | ||||
\(266\) | −9.76645 | − | 5.74790i | −0.598819 | − | 0.352427i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.34050 | + | 25.6726i | −0.448393 | + | 1.56820i | ||||
\(269\) | −1.99648 | + | 1.99648i | −0.121727 | + | 0.121727i | −0.765346 | − | 0.643619i | \(-0.777432\pi\) |
0.643619 | + | 0.765346i | \(0.277432\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.9357i | 0.846534i | 0.906005 | + | 0.423267i | \(0.139117\pi\) | ||||
−0.906005 | + | 0.423267i | \(0.860883\pi\) | |||||||
\(272\) | −0.0934044 | + | 2.79595i | −0.00566347 | + | 0.169529i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.23121 | + | 16.3354i | 0.255617 | + | 0.986857i | ||||
\(275\) | 2.57032 | − | 9.59256i | 0.154996 | − | 0.578453i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.09885 | − | 30.2253i | −0.486613 | − | 1.81606i | −0.572686 | − | 0.819774i | \(-0.694099\pi\) |
0.0860738 | − | 0.996289i | \(-0.472568\pi\) | |||||||
\(278\) | −0.870867 | − | 1.53790i | −0.0522311 | − | 0.0922368i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.364301 | + | 14.5423i | −0.0217712 | + | 0.869068i | ||||
\(281\) | −11.3745 | + | 19.7012i | −0.678544 | + | 1.17527i | 0.296875 | + | 0.954916i | \(0.404056\pi\) |
−0.975419 | + | 0.220357i | \(0.929278\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.633463 | − | 2.36412i | 0.0376555 | − | 0.140532i | −0.944539 | − | 0.328399i | \(-0.893491\pi\) |
0.982194 | + | 0.187867i | \(0.0601575\pi\) | |||||||
\(284\) | −14.4362 | − | 0.241068i | −0.856630 | − | 0.0143047i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.93902 | − | 6.82411i | 0.410313 | − | 0.403518i | ||||
\(287\) | 8.77415 | 0.517921 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.5109 | 0.971228 | ||||||||
\(290\) | −10.3433 | + | 10.1720i | −0.607381 | + | 0.597323i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.50966 | + | 0.125403i | 0.439469 | + | 0.00733863i | ||||
\(293\) | −2.01774 | + | 7.53030i | −0.117877 | + | 0.439925i | −0.999486 | − | 0.0320565i | \(-0.989794\pi\) |
0.881609 | + | 0.471981i | \(0.156461\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.9285 | + | 22.3929i | −0.752728 | + | 1.30376i | ||||
\(296\) | 13.9352 | + | 0.349094i | 0.809968 | + | 0.0202907i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.50641 | + | 4.42616i | 0.145192 | + | 0.256400i | ||||
\(299\) | −1.68508 | − | 6.28881i | −0.0974508 | − | 0.363691i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.34693 | − | 19.9550i | 0.308192 | − | 1.15019i | ||||
\(302\) | −3.85194 | − | 14.8711i | −0.221654 | − | 0.855738i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.32381 | − | 7.78564i | 0.477403 | − | 0.446537i | ||||
\(305\) | − | 25.0589i | − | 1.43487i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.0831 | + | 24.0831i | −1.37450 | + | 1.37450i | −0.520843 | + | 0.853652i | \(0.674382\pi\) |
−0.853652 | + | 0.520843i | \(0.825618\pi\) | |||||||
\(308\) | −9.27571 | + | 32.4408i | −0.528532 | + | 1.84848i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −13.2683 | − | 7.80889i | −0.753590 | − | 0.443515i | ||||
\(311\) | −9.09165 | + | 5.24907i | −0.515540 | + | 0.297647i | −0.735108 | − | 0.677950i | \(-0.762869\pi\) |
0.219568 | + | 0.975597i | \(0.429535\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.1380 | + | 11.0493i | 1.08174 | + | 0.624544i | 0.931366 | − | 0.364085i | \(-0.118618\pi\) |
0.150376 | + | 0.988629i | \(0.451952\pi\) | |||||||
\(314\) | 6.87522 | + | 12.1412i | 0.387991 | + | 0.685167i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.52038 | − | 5.86895i | 0.198037 | − | 0.330154i | ||||
\(317\) | 5.71597 | + | 21.3323i | 0.321041 | + | 1.19814i | 0.918232 | + | 0.396042i | \(0.129617\pi\) |
−0.597192 | + | 0.802099i | \(0.703717\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −29.1405 | + | 16.8243i | −1.63155 | + | 0.941978i | ||||
\(320\) | −13.9246 | − | 4.48949i | −0.778409 | − | 0.250970i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 15.8267 | + | 16.0932i | 0.881990 | + | 0.896841i | ||||
\(323\) | 1.40911 | + | 1.40911i | 0.0784050 | + | 0.0784050i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.34289 | − | 1.34289i | 0.0744900 | − | 0.0744900i | ||||
\(326\) | 0.0612287 | − | 7.33380i | 0.00339114 | − | 0.406182i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.49672 | + | 8.46401i | −0.137858 | + | 0.467347i | ||||
\(329\) | 7.97655 | + | 13.8158i | 0.439761 | + | 0.761689i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.16734 | − | 0.848686i | 0.174093 | − | 0.0466480i | −0.170720 | − | 0.985320i | \(-0.554609\pi\) |
0.344812 | + | 0.938672i | \(0.387943\pi\) | |||||||
\(332\) | 0.578908 | + | 2.31442i | 0.0317717 | + | 0.127020i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.59401 | + | 27.4233i | −0.415525 | + | 1.50054i | ||||
\(335\) | 12.2079 | − | 21.1447i | 0.666990 | − | 1.15526i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.5710 | − | 20.0416i | −0.630315 | − | 1.09174i | −0.987487 | − | 0.157699i | \(-0.949593\pi\) |
0.357172 | − | 0.934038i | \(-0.383741\pi\) | |||||||
\(338\) | −15.9957 | + | 4.14323i | −0.870054 | + | 0.225362i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.703236 | − | 2.45949i | 0.0381383 | − | 0.133385i | ||||
\(341\) | −25.2506 | − | 25.2506i | −1.36739 | − | 1.36739i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.1300 | 0.924931 | ||||||||
\(344\) | 17.7282 | + | 10.8362i | 0.955839 | + | 0.584249i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.7534 | − | 7.50585i | −0.685628 | − | 0.403517i | ||||
\(347\) | −7.59002 | − | 2.03374i | −0.407454 | − | 0.109177i | 0.0492700 | − | 0.998785i | \(-0.484311\pi\) |
−0.456724 | + | 0.889609i | \(0.650977\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.9793 | − | 5.62138i | 1.12299 | − | 0.300905i | 0.350900 | − | 0.936413i | \(-0.385876\pi\) |
0.772095 | + | 0.635508i | \(0.219209\pi\) | |||||||
\(350\) | −1.75711 | + | 6.34525i | −0.0939216 | + | 0.339168i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −28.6547 | − | 18.1790i | −1.52730 | − | 0.968943i | ||||
\(353\) | 0.108858 | + | 0.0628489i | 0.00579390 | + | 0.00334511i | 0.502894 | − | 0.864348i | \(-0.332269\pi\) |
−0.497100 | + | 0.867693i | \(0.665602\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.7525 | + | 3.41701i | 0.676831 | + | 0.181356i | ||||
\(356\) | 0.0130846 | − | 0.783561i | 0.000693481 | − | 0.0415287i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −24.9076 | − | 0.207949i | −1.31641 | − | 0.0109905i | ||||
\(359\) | 4.07414i | 0.215025i | 0.994204 | + | 0.107512i | \(0.0342886\pi\) | ||||
−0.994204 | + | 0.107512i | \(0.965711\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.8811i | 0.572691i | ||||||||
\(362\) | 0.152291 | − | 18.2410i | 0.00800426 | − | 0.958727i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.63806 | + | 4.48571i | −0.243100 | + | 0.235115i | ||||
\(365\) | −6.63379 | − | 1.77752i | −0.347229 | − | 0.0930396i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.96310 | + | 2.86545i | 0.259072 | + | 0.149575i | 0.623911 | − | 0.781495i | \(-0.285543\pi\) |
−0.364839 | + | 0.931071i | \(0.618876\pi\) | |||||||
\(368\) | −20.0280 | + | 10.6879i | −1.04403 | + | 0.557147i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12.2841 | − | 3.40168i | −0.638620 | − | 0.176845i | ||||
\(371\) | −17.1185 | + | 4.58689i | −0.888748 | + | 0.238139i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.7409 | + | 5.28955i | 1.02214 | + | 0.273882i | 0.730695 | − | 0.682704i | \(-0.239196\pi\) |
0.291448 | + | 0.956587i | \(0.405863\pi\) | |||||||
\(374\) | 3.00944 | − | 5.11344i | 0.155615 | − | 0.264410i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −15.5972 | + | 3.76327i | −0.804364 | + | 0.194076i | ||||
\(377\) | −6.43473 | −0.331405 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.85273 | − | 2.85273i | −0.146535 | − | 0.146535i | 0.630033 | − | 0.776568i | \(-0.283041\pi\) |
−0.776568 | + | 0.630033i | \(0.783041\pi\) | |||||||
\(380\) | −9.11135 | + | 5.05951i | −0.467402 | + | 0.259547i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.25521 | + | 4.84597i | 0.0642220 | + | 0.247941i | ||||
\(383\) | −7.78731 | − | 13.4880i | −0.397913 | − | 0.689206i | 0.595555 | − | 0.803314i | \(-0.296932\pi\) |
−0.993468 | + | 0.114109i | \(0.963599\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.4263 | − | 26.7192i | 0.786200 | − | 1.36174i | ||||
\(386\) | −20.2531 | − | 5.60845i | −1.03086 | − | 0.285462i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.00278 | + | 1.80116i | 0.152443 | + | 0.0914401i | ||||
\(389\) | 26.9587 | − | 7.22357i | 1.36686 | − | 0.366250i | 0.500531 | − | 0.865719i | \(-0.333138\pi\) |
0.866332 | + | 0.499469i | \(0.166471\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.98460 | − | 3.43743i | −0.100366 | − | 0.173838i | ||||
\(392\) | 0.727291 | − | 2.46556i | 0.0367337 | − | 0.124529i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −23.8202 | − | 0.198871i | −1.20004 | − | 0.0100190i | ||||
\(395\) | −4.42507 | + | 4.42507i | −0.222649 | + | 0.222649i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.4204 | + | 27.4204i | 1.37619 | + | 1.37619i | 0.850961 | + | 0.525230i | \(0.176021\pi\) |
0.525230 | + | 0.850961i | \(0.323979\pi\) | |||||||
\(398\) | −15.7280 | + | 15.4676i | −0.788374 | + | 0.775319i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.62097 | − | 3.50057i | −0.281049 | − | 0.175028i | ||||
\(401\) | 14.6316 | − | 8.44757i | 0.730669 | − | 0.421852i | −0.0879981 | − | 0.996121i | \(-0.528047\pi\) |
0.818667 | + | 0.574269i | \(0.194714\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.76745 | − | 6.59620i | −0.0880428 | − | 0.328580i | ||||
\(404\) | −0.410198 | − | 1.63993i | −0.0204081 | − | 0.0815896i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 19.4121 | − | 10.9925i | 0.963405 | − | 0.545549i | ||||
\(407\) | −25.6038 | − | 14.7824i | −1.26913 | − | 0.732735i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.9737 | + | 8.64508i | −0.740402 | + | 0.427471i | −0.822216 | − | 0.569176i | \(-0.807262\pi\) |
0.0818133 | + | 0.996648i | \(0.473929\pi\) | |||||||
\(410\) | 4.09280 | − | 6.95421i | 0.202129 | − | 0.343444i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −18.5461 | + | 10.2986i | −0.913700 | + | 0.507375i | ||||
\(413\) | 28.1160 | − | 28.1160i | 1.38350 | − | 1.38350i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2.18151i | − | 0.107086i | ||||||
\(416\) | −3.00737 | − | 5.75054i | −0.147449 | − | 0.281944i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −23.4008 | + | 6.06131i | −1.14457 | + | 0.296468i | ||||
\(419\) | −0.788205 | + | 2.94162i | −0.0385063 | + | 0.143708i | −0.982503 | − | 0.186248i | \(-0.940367\pi\) |
0.943996 | + | 0.329956i | \(0.107034\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.38357 | − | 8.89561i | −0.116168 | − | 0.433546i | 0.883203 | − | 0.468990i | \(-0.155382\pi\) |
−0.999372 | + | 0.0354445i | \(0.988715\pi\) | |||||||
\(422\) | −19.8769 | + | 11.2558i | −0.967595 | + | 0.547922i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.446378 | − | 17.8186i | 0.0216780 | − | 0.865349i | ||||
\(425\) | 0.578900 | − | 1.00268i | 0.0280808 | − | 0.0486373i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.97350 | + | 37.2216i | −0.482651 | + | 1.80128i | ||||
\(428\) | 12.5824 | + | 13.0098i | 0.608194 | + | 0.628851i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −13.3218 | − | 13.5461i | −0.642434 | − | 0.653252i | ||||
\(431\) | −7.28002 | −0.350666 | −0.175333 | − | 0.984509i | \(-0.556100\pi\) | ||||
−0.175333 | + | 0.984509i | \(0.556100\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.9763 | −0.960002 | −0.480001 | − | 0.877268i | \(-0.659364\pi\) | ||||
−0.480001 | + | 0.877268i | \(0.659364\pi\) | |||||||
\(434\) | 16.6003 | + | 16.8799i | 0.796842 | + | 0.810259i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.10237 | − | 3.00046i | 0.148577 | − | 0.143696i | ||||
\(437\) | −4.18539 | + | 15.6201i | −0.200214 | + | 0.747210i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.3133 | − | 26.5235i | 0.730866 | − | 1.26590i | −0.225647 | − | 0.974209i | \(-0.572450\pi\) |
0.956513 | − | 0.291688i | \(-0.0942170\pi\) | |||||||
\(440\) | 21.3852 | + | 22.4841i | 1.01950 | + | 1.07189i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.987334 | − | 0.559099i | 0.0469627 | − | 0.0265937i | ||||
\(443\) | −7.70884 | − | 28.7698i | −0.366258 | − | 1.36689i | −0.865708 | − | 0.500550i | \(-0.833131\pi\) |
0.499450 | − | 0.866343i | \(-0.333536\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.185467 | + | 0.692173i | −0.00879199 | + | 0.0328121i | ||||
\(446\) | 22.0136 | − | 5.70197i | 1.04237 | − | 0.269996i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 18.8963 | + | 12.2105i | 0.892764 | + | 0.576893i | ||||
\(449\) | 26.8028i | 1.26490i | 0.774599 | + | 0.632452i | \(0.217952\pi\) | ||||
−0.774599 | + | 0.632452i | \(0.782048\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.2344 | − | 13.2344i | 0.623181 | − | 0.623181i | ||||
\(452\) | 6.44898 | + | 11.6136i | 0.303335 | + | 0.546256i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.92347 | − | 13.4630i | 0.371867 | − | 0.631851i | ||||
\(455\) | 5.10961 | − | 2.95004i | 0.239542 | − | 0.138300i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.25342 | − | 1.87837i | −0.152189 | − | 0.0878662i | 0.421972 | − | 0.906609i | \(-0.361338\pi\) |
−0.574161 | + | 0.818743i | \(0.694671\pi\) | |||||||
\(458\) | 0.497588 | − | 0.281770i | 0.0232507 | − | 0.0131662i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 20.1378 | − | 5.03708i | 0.938928 | − | 0.234855i | ||||
\(461\) | −1.05208 | − | 3.92641i | −0.0490002 | − | 0.182871i | 0.937088 | − | 0.349092i | \(-0.113510\pi\) |
−0.986088 | + | 0.166221i | \(0.946843\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.2888 | − | 11.7137i | 0.942899 | − | 0.544383i | 0.0520310 | − | 0.998645i | \(-0.483431\pi\) |
0.890868 | + | 0.454263i | \(0.150097\pi\) | |||||||
\(464\) | 5.08018 | + | 21.8539i | 0.235842 | + | 1.01454i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.7218 | + | 11.5277i | −0.543003 | + | 0.534011i | ||||
\(467\) | −13.2570 | − | 13.2570i | −0.613463 | − | 0.613463i | 0.330384 | − | 0.943847i | \(-0.392822\pi\) |
−0.943847 | + | 0.330384i | \(0.892822\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.5489 | + | 26.5489i | −1.22591 | + | 1.22591i | ||||
\(470\) | 14.6709 | + | 0.122485i | 0.676717 | + | 0.00564980i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 19.1216 | + | 35.1226i | 0.880145 | + | 1.61665i | ||||
\(473\) | −22.0339 | − | 38.1638i | −1.01312 | − | 1.75477i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.55631 | + | 1.22086i | −0.209058 | + | 0.0560169i | ||||
\(476\) | −2.02344 | + | 3.37335i | −0.0927443 | + | 0.154617i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.24372 | + | 1.17516i | 0.194103 | + | 0.0537506i | ||||
\(479\) | −17.6429 | + | 30.5584i | −0.806124 | + | 1.39625i | 0.109405 | + | 0.993997i | \(0.465105\pi\) |
−0.915529 | + | 0.402251i | \(0.868228\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.82689 | − | 4.89631i | −0.128895 | − | 0.223252i | ||||
\(482\) | −5.08274 | − | 19.6229i | −0.231512 | − | 0.893798i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 24.2603 | + | 43.6889i | 1.10274 | + | 1.98586i | ||||
\(485\) | −2.26403 | − | 2.26403i | −0.102804 | − | 0.102804i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.1433 | −0.550266 | −0.275133 | − | 0.961406i | \(-0.588722\pi\) | ||||
−0.275133 | + | 0.961406i | \(0.588722\pi\) | |||||||
\(488\) | −33.0679 | − | 20.2125i | −1.49692 | − | 0.914977i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.19223 | + | 2.02576i | −0.0538595 | + | 0.0915143i | ||||
\(491\) | 0.746514 | + | 0.200028i | 0.0336897 | + | 0.00902713i | 0.275625 | − | 0.961265i | \(-0.411115\pi\) |
−0.241935 | + | 0.970293i | \(0.577782\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.78924 | + | 1.01532i | −0.170659 | + | 0.0457279i | ||||
\(494\) | −4.45505 | − | 1.23368i | −0.200442 | − | 0.0555059i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21.0069 | + | 11.2103i | −0.943237 | + | 0.503359i | ||||
\(497\) | −17.5821 | − | 10.1510i | −0.788664 | − | 0.455335i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.785369 | + | 0.210439i | 0.0351579 | + | 0.00942054i | 0.276355 | − | 0.961056i | \(-0.410873\pi\) |
−0.241197 | + | 0.970476i | \(0.577540\pi\) | |||||||
\(500\) | 16.9234 | + | 17.4982i | 0.756837 | + | 0.782543i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.0511225 | + | 6.12331i | −0.00228171 | + | 0.273297i | ||||
\(503\) | 5.40486i | 0.240991i | 0.992714 | + | 0.120495i | \(0.0384483\pi\) | ||||
−0.992714 | + | 0.120495i | \(0.961552\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.54576i | 0.0687852i | ||||||||
\(506\) | 48.1460 | + | 0.401964i | 2.14035 | + | 0.0178695i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −27.6409 | − | 0.461572i | −1.22637 | − | 0.0204789i | ||||
\(509\) | 27.7030 | + | 7.42301i | 1.22792 | + | 0.329019i | 0.813768 | − | 0.581191i | \(-0.197413\pi\) |
0.414148 | + | 0.910210i | \(0.364080\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.14614 | + | 5.28052i | 0.404601 | + | 0.233597i | ||||
\(512\) | −17.1559 | + | 14.7538i | −0.758192 | + | 0.652031i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.21186 | − | 4.37624i | 0.0534528 | − | 0.193028i | ||||
\(515\) | 18.7368 | − | 5.02052i | 0.825644 | − | 0.221231i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32.8701 | + | 8.80753i | 1.44563 | + | 0.387355i | ||||
\(518\) | 16.8925 | + | 9.94183i | 0.742213 | + | 0.436819i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.39180 | + | 5.76845i | 0.0610345 | + | 0.252963i | ||||
\(521\) | 12.8208 | 0.561689 | 0.280845 | − | 0.959753i | \(-0.409385\pi\) | ||||
0.280845 | + | 0.959753i | \(0.409385\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.08204 | − | 2.08204i | −0.0910411 | − | 0.0910411i | 0.660120 | − | 0.751161i | \(-0.270506\pi\) |
−0.751161 | + | 0.660120i | \(0.770506\pi\) | |||||||
\(524\) | 17.8754 | + | 5.11108i | 0.780892 | + | 0.223278i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.16962 | − | 1.08002i | 0.181804 | − | 0.0470910i | ||||
\(527\) | −2.08161 | − | 3.60545i | −0.0906762 | − | 0.157056i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.60471 | − | 7.97560i | 0.200205 | − | 0.346765i | ||||
\(530\) | −4.34965 | + | 15.7074i | −0.188937 | + | 0.682285i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 15.5474 | − | 3.88888i | 0.674063 | − | 0.168604i | ||||
\(533\) | 3.45721 | − | 0.926356i | 0.149748 | − | 0.0401249i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.27485 | − | 14.3325i | −0.357753 | − | 0.619647i | ||||
\(536\) | −18.0559 | − | 33.1650i | −0.779894 | − | 1.43251i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.0333354 | − | 3.99281i | 0.00143719 | − | 0.172142i | ||||
\(539\) | −3.85515 | + | 3.85515i | −0.166053 | + | 0.166053i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.7002 | + | 22.7002i | 0.975956 | + | 0.975956i | 0.999718 | − | 0.0237613i | \(-0.00756417\pi\) |
−0.0237613 | + | 0.999718i | \(0.507564\pi\) | |||||||
\(542\) | −13.8189 | − | 14.0516i | −0.593572 | − | 0.603566i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.67833 | − | 2.91182i | −0.114833 | − | 0.124843i | ||||
\(545\) | −3.41779 | + | 1.97326i | −0.146402 | + | 0.0845253i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.33444 | − | 19.9084i | −0.228084 | − | 0.851222i | −0.981145 | − | 0.193271i | \(-0.938090\pi\) |
0.753061 | − | 0.657951i | \(-0.228576\pi\) | |||||||
\(548\) | −20.4648 | − | 12.2755i | −0.874214 | − | 0.524382i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.92045 | + | 12.2211i | 0.295089 | + | 0.521109i | ||||
\(551\) | 13.8413 | + | 7.99125i | 0.589657 | + | 0.340439i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.33402 | − | 4.81165i | 0.354399 | − | 0.204612i | ||||
\(554\) | 38.1381 | + | 22.4456i | 1.62033 | + | 0.953624i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.40311 | + | 0.687115i | 0.101915 | + | 0.0291402i | ||||
\(557\) | 10.7551 | − | 10.7551i | 0.455708 | − | 0.455708i | −0.441535 | − | 0.897244i | \(-0.645566\pi\) |
0.897244 | + | 0.441535i | \(0.145566\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.42723i | − | 0.356434i | ||||||
\(560\) | −14.0530 | − | 15.0244i | −0.593849 | − | 0.634898i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.06697 | − | 31.1441i | −0.340285 | − | 1.31373i | ||||
\(563\) | 5.56420 | − | 20.7659i | 0.234503 | − | 0.875177i | −0.743869 | − | 0.668325i | \(-0.767012\pi\) |
0.978372 | − | 0.206852i | \(-0.0663218\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.14385 | − | 11.7330i | −0.132263 | − | 0.493611i | ||||
\(566\) | 1.70557 | + | 3.01192i | 0.0716904 | + | 0.126601i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.7953 | − | 14.0721i | 0.620795 | − | 0.590452i | ||||
\(569\) | −1.88272 | + | 3.26097i | −0.0789277 | + | 0.136707i | −0.902788 | − | 0.430087i | \(-0.858483\pi\) |
0.823860 | + | 0.566794i | \(0.191816\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.37466 | + | 16.3264i | −0.183074 | + | 0.683241i | 0.811961 | + | 0.583712i | \(0.198400\pi\) |
−0.995035 | + | 0.0995287i | \(0.968266\pi\) | |||||||
\(572\) | −0.229804 | + | 13.7617i | −0.00960861 | + | 0.575405i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.84709 | + | 8.70059i | −0.369270 | + | 0.363156i | ||||
\(575\) | 9.39535 | 0.391813 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.76787 | −0.406642 | −0.203321 | − | 0.979112i | \(-0.565173\pi\) | ||||
−0.203321 | + | 0.979112i | \(0.565173\pi\) | |||||||
\(578\) | −16.6481 | + | 16.3725i | −0.692471 | + | 0.681004i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.342547 | − | 20.5132i | 0.0142235 | − | 0.851765i | ||||
\(581\) | −0.868246 | + | 3.24034i | −0.0360209 | + | 0.134432i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.9019 | + | 32.7390i | −0.782835 | + | 1.35591i | ||||
\(584\) | −7.69644 | + | 7.32026i | −0.318481 | + | 0.302914i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.43266 | − | 9.59372i | −0.224421 | − | 0.396313i | ||||
\(587\) | 5.94132 | + | 22.1733i | 0.245224 | + | 0.915190i | 0.973271 | + | 0.229662i | \(0.0737620\pi\) |
−0.728046 | + | 0.685528i | \(0.759571\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.38996 | + | 16.3836i | −0.180885 | + | 0.675073i | ||||
\(590\) | −9.16912 | − | 35.3992i | −0.377487 | − | 1.45736i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −14.3972 | + | 13.4664i | −0.591723 | + | 0.553465i | ||||
\(593\) | 1.37926i | 0.0566394i | 0.999599 | + | 0.0283197i | \(0.00901564\pi\) | ||||
−0.999599 | + | 0.0283197i | \(0.990984\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.54344 | − | 2.54344i | 0.104271 | − | 0.104271i | ||||
\(596\) | −6.91629 | − | 1.97756i | −0.283302 | − | 0.0810039i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.93518 | + | 4.67014i | 0.324494 | + | 0.190976i | ||||
\(599\) | −26.6820 | + | 15.4049i | −1.09020 | + | 0.629425i | −0.933629 | − | 0.358242i | \(-0.883376\pi\) |
−0.156568 | + | 0.987667i | \(0.550043\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.43951 | + | 1.40845i | 0.0995098 | + | 0.0574520i | 0.548929 | − | 0.835869i | \(-0.315036\pi\) |
−0.449419 | + | 0.893321i | \(0.648369\pi\) | |||||||
\(602\) | 14.3963 | + | 25.4230i | 0.586751 | + | 1.03616i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 18.6304 | + | 11.1751i | 0.758062 | + | 0.454710i | ||||
\(605\) | −11.8268 | − | 44.1382i | −0.480828 | − | 1.79447i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.2297 | − | 15.1437i | 1.06463 | − | 0.614666i | 0.137922 | − | 0.990443i | \(-0.455958\pi\) |
0.926710 | + | 0.375777i | \(0.122624\pi\) | |||||||
\(608\) | −0.672641 | + | 16.1044i | −0.0272792 | + | 0.653120i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 24.8488 | + | 25.2673i | 1.00610 | + | 1.02304i | ||||
\(611\) | 4.60158 | + | 4.60158i | 0.186160 | + | 0.186160i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.66344 | − | 3.66344i | 0.147965 | − | 0.147965i | −0.629243 | − | 0.777208i | \(-0.716635\pi\) |
0.777208 | + | 0.629243i | \(0.216635\pi\) | |||||||
\(614\) | 0.402118 | − | 48.1645i | 0.0162282 | − | 1.94376i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.8160 | − | 41.9084i | −0.919282 | − | 1.68854i | ||||
\(617\) | 13.2053 | + | 22.8722i | 0.531624 | + | 0.920799i | 0.999319 | + | 0.0369091i | \(0.0117512\pi\) |
−0.467695 | + | 0.883890i | \(0.654915\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.2262 | − | 12.6542i | 1.89818 | − | 0.508617i | 0.900981 | − | 0.433858i | \(-0.142848\pi\) |
0.997202 | − | 0.0747583i | \(-0.0238185\pi\) | |||||||
\(620\) | 21.1221 | − | 5.28329i | 0.848282 | − | 0.212182i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.96218 | − | 14.3081i | 0.158869 | − | 0.573704i | ||||
\(623\) | 0.550972 | − | 0.954312i | 0.0220742 | − | 0.0382337i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.99103 | − | 12.1088i | −0.279641 | − | 0.484353i | ||||
\(626\) | −30.2538 | + | 7.83636i | −1.20918 | + | 0.313204i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −18.9718 | − | 5.42455i | −0.757057 | − | 0.216463i | ||||
\(629\) | −2.43726 | − | 2.43726i | −0.0971799 | − | 0.0971799i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.5500 | −1.45503 | −0.727516 | − | 0.686090i | \(-0.759325\pi\) | ||||
−0.727516 | + | 0.686090i | \(0.759325\pi\) | |||||||
\(632\) | 2.27009 | + | 9.40861i | 0.0902995 | + | 0.374254i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −26.9169 | − | 15.8416i | −1.06901 | − | 0.629150i | ||||
\(635\) | 24.4171 | + | 6.54255i | 0.968964 | + | 0.259633i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00708 | + | 0.269847i | −0.0399020 | + | 0.0106917i | ||||
\(638\) | 12.6995 | − | 45.8603i | 0.502779 | − | 1.81563i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 18.4922 | − | 9.28105i | 0.730969 | − | 0.366866i | ||||
\(641\) | 5.95425 | + | 3.43769i | 0.235179 | + | 0.135780i | 0.612959 | − | 0.790115i | \(-0.289979\pi\) |
−0.377780 | + | 0.925895i | \(0.623312\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.3564 | + | 7.59808i | 1.11827 | + | 0.299639i | 0.770183 | − | 0.637823i | \(-0.220165\pi\) |
0.348086 | + | 0.937463i | \(0.386832\pi\) | |||||||
\(644\) | −31.9167 | − | 0.532971i | −1.25769 | − | 0.0210020i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.81812 | − | 0.0235281i | −0.110878 | − | 0.000925699i | ||||
\(647\) | − | 1.90726i | − | 0.0749821i | −0.999297 | − | 0.0374911i | \(-0.988063\pi\) | ||
0.999297 | − | 0.0374911i | \(-0.0119366\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 84.8166i | − | 3.32934i | ||||||
\(650\) | −0.0224223 | + | 2.68568i | −0.000879476 | + | 0.105341i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.21058 | + | 7.45548i | 0.282388 | + | 0.291979i | ||||
\(653\) | 22.1710 | + | 5.94070i | 0.867618 | + | 0.232478i | 0.665057 | − | 0.746792i | \(-0.268407\pi\) |
0.202560 | + | 0.979270i | \(0.435074\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.7228 | − | 8.50019i | −0.575266 | − | 0.332130i | ||||
\(656\) | −5.87558 | − | 11.0102i | −0.229403 | − | 0.429874i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −21.7428 | − | 6.02097i | −0.847624 | − | 0.234722i | ||||
\(659\) | 14.4059 | − | 3.86006i | 0.561175 | − | 0.150366i | 0.0329291 | − | 0.999458i | \(-0.489516\pi\) |
0.528246 | + | 0.849091i | \(0.322850\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.4336 | − | 9.76236i | −1.41710 | − | 0.379712i | −0.532648 | − | 0.846337i | \(-0.678803\pi\) |
−0.884455 | + | 0.466625i | \(0.845470\pi\) | |||||||
\(662\) | −2.35210 | + | 3.99653i | −0.0914170 | + | 0.155329i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.87874 | − | 1.75961i | −0.111717 | − | 0.0682860i | ||||
\(665\) | −14.6545 | −0.568278 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.5099 | − | 22.5099i | −0.871586 | − | 0.871586i | ||||
\(668\) | −19.5363 | − | 35.1817i | −0.755882 | − | 1.36122i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.65806 | + | 33.4261i | 0.334490 | + | 1.29136i | ||||
\(671\) | 41.0993 | + | 71.1860i | 1.58662 | + | 2.74811i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.2966 | + | 19.5664i | −0.435454 | + | 0.754228i | −0.997333 | − | 0.0729916i | \(-0.976745\pi\) |
0.561879 | + | 0.827220i | \(0.310079\pi\) | |||||||
\(674\) | 31.5409 | + | 8.73421i | 1.21491 | + | 0.336429i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.0202 | − | 20.0393i | 0.462317 | − | 0.770743i | ||||
\(677\) | −30.3860 | + | 8.14191i | −1.16783 | + | 0.312919i | −0.790089 | − | 0.612992i | \(-0.789966\pi\) |
−0.377741 | + | 0.925911i | \(0.623299\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.46182 | + | 4.26400i | 0.0944760 | + | 0.163637i | ||||
\(680\) | 1.72979 | + | 3.17728i | 0.0663344 | + | 0.121843i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 50.4993 | + | 0.421611i | 1.93372 | + | 0.0161443i | ||||
\(683\) | 24.1502 | − | 24.1502i | 0.924081 | − | 0.924081i | −0.0732336 | − | 0.997315i | \(-0.523332\pi\) |
0.997315 | + | 0.0732336i | \(0.0233319\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.4301 | + | 15.4301i | 0.589553 | + | 0.589553i | ||||
\(686\) | −17.2724 | + | 16.9864i | −0.659462 | + | 0.648542i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −28.6209 | + | 6.65326i | −1.09116 | + | 0.253653i | ||||
\(689\) | −6.26079 | + | 3.61467i | −0.238517 | + | 0.137708i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.7138 | − | 39.9843i | −0.407571 | − | 1.52108i | −0.799264 | − | 0.600980i | \(-0.794777\pi\) |
0.391693 | − | 0.920096i | \(-0.371889\pi\) | |||||||
\(692\) | 20.3024 | − | 5.07826i | 0.771781 | − | 0.193046i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.66981 | − | 5.47574i | 0.367061 | − | 0.207856i | ||||
\(695\) | −1.97928 | − | 1.14273i | −0.0750782 | − | 0.0433464i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.88969 | − | 1.09101i | 0.0715772 | − | 0.0413251i | ||||
\(698\) | −15.5794 | + | 26.4715i | −0.589690 | + | 1.00196i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.52034 | − | 8.14039i | −0.170853 | − | 0.307678i | ||||
\(701\) | −21.1814 | + | 21.1814i | −0.800009 | + | 0.800009i | −0.983097 | − | 0.183088i | \(-0.941391\pi\) |
0.183088 | + | 0.983097i | \(0.441391\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.0428i | 0.529633i | ||||||||
\(704\) | 46.9195 | − | 10.0843i | 1.76834 | − | 0.380067i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.172085 | + | 0.0445735i | −0.00647649 | + | 0.00167755i | ||||
\(707\) | 0.615214 | − | 2.29601i | 0.0231375 | − | 0.0863503i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.24787 | + | 15.8532i | 0.159532 | + | 0.595381i | 0.998675 | + | 0.0514698i | \(0.0163906\pi\) |
−0.839143 | + | 0.543911i | \(0.816943\pi\) | |||||||
\(710\) | −16.2469 | + | 9.20014i | −0.609734 | + | 0.345275i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.763799 | + | 0.803050i | 0.0286246 | + | 0.0300956i | ||||
\(713\) | 16.8919 | − | 29.2576i | 0.632606 | − | 1.09571i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.25736 | − | 12.1566i | 0.121819 | − | 0.454633i | ||||
\(716\) | 25.3208 | − | 24.4891i | 0.946284 | − | 0.915200i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.03999 | − | 4.10801i | −0.150771 | − | 0.153310i | ||||
\(719\) | −23.3461 | −0.870664 | −0.435332 | − | 0.900270i | \(-0.643369\pi\) | ||||
−0.435332 | + | 0.900270i | \(0.643369\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.8292 | −1.11090 | ||||||||
\(722\) | −10.7899 | − | 10.9716i | −0.401558 | − | 0.408320i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 17.9345 | + | 18.5437i | 0.666532 | + | 0.689171i | ||||
\(725\) | 2.40334 | − | 8.96937i | 0.0892576 | − | 0.333114i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.90255 | + | 5.02736i | −0.107650 | + | 0.186454i | −0.914818 | − | 0.403867i | \(-0.867666\pi\) |
0.807168 | + | 0.590322i | \(0.200999\pi\) | |||||||
\(728\) | 0.228521 | − | 9.12218i | 0.00846956 | − | 0.338090i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.45156 | − | 4.78588i | 0.312806 | − | 0.177133i | ||||
\(731\) | −1.32972 | − | 4.96258i | −0.0491814 | − | 0.183548i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.240792 | + | 0.898647i | −0.00889384 | + | 0.0331923i | −0.970230 | − | 0.242185i | \(-0.922136\pi\) |
0.961336 | + | 0.275377i | \(0.0888027\pi\) | |||||||
\(734\) | −7.84579 | + | 2.03222i | −0.289593 | + | 0.0750107i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.59614 | − | 30.6368i | 0.353718 | − | 1.12929i | ||||
\(737\) | 80.0891i | 2.95012i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.91328 | − | 5.91328i | 0.217523 | − | 0.217523i | −0.589931 | − | 0.807454i | \(-0.700845\pi\) |
0.807454 | + | 0.589931i | \(0.200845\pi\) | |||||||
\(740\) | 15.7594 | − | 8.75116i | 0.579327 | − | 0.321699i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.7124 | − | 21.6000i | 0.466686 | − | 0.792961i | ||||
\(743\) | −20.3899 | + | 11.7721i | −0.748032 | + | 0.431876i | −0.824982 | − | 0.565158i | \(-0.808815\pi\) |
0.0769504 | + | 0.997035i | \(0.475482\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.69647 | + | 3.28886i | 0.208703 | + | 0.120494i | ||||
\(746\) | −25.1502 | + | 14.2418i | −0.920814 | + | 0.521431i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.03611 | + | 8.14017i | 0.0744475 | + | 0.297634i | ||||
\(749\) | 6.58682 | + | 24.5823i | 0.240677 | + | 0.898219i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.0649 | + | 7.54301i | −0.476744 | + | 0.275248i | −0.719059 | − | 0.694949i | \(-0.755427\pi\) |
0.242315 | + | 0.970198i | \(0.422093\pi\) | |||||||
\(752\) | 11.9951 | − | 19.2610i | 0.437418 | − | 0.702376i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.48822 | − | 6.38078i | 0.236287 | − | 0.232374i | ||||
\(755\) | −14.0470 | − | 14.0470i | −0.511222 | − | 0.511222i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.48920 | − | 4.48920i | 0.163163 | − | 0.163163i | −0.620803 | − | 0.783966i | \(-0.713193\pi\) |
0.783966 | + | 0.620803i | \(0.213193\pi\) | |||||||
\(758\) | 5.70527 | + | 0.0476324i | 0.207225 | + | 0.00173009i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.17000 | − | 14.1365i | 0.151262 | − | 0.512786i | ||||
\(761\) | −19.0628 | − | 33.0177i | −0.691025 | − | 1.19689i | −0.971502 | − | 0.237030i | \(-0.923826\pi\) |
0.280477 | − | 0.959861i | \(-0.409507\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.86202 | − | 1.57072i | 0.212219 | − | 0.0568640i | ||||
\(764\) | −6.07099 | − | 3.64157i | −0.219641 | − | 0.131747i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.2270 | + | 5.87813i | 0.766963 | + | 0.212385i | ||||
\(767\) | 8.10989 | − | 14.0467i | 0.292831 | − | 0.507198i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.5683 | + | 30.4291i | 0.633528 | + | 1.09730i | 0.986825 | + | 0.161791i | \(0.0517271\pi\) |
−0.353297 | + | 0.935511i | \(0.614940\pi\) | |||||||
\(770\) | 10.9406 | + | 42.2384i | 0.394273 | + | 1.52217i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 25.9829 | − | 14.4283i | 0.935146 | − | 0.519285i | ||||
\(773\) | 23.4773 | + | 23.4773i | 0.844420 | + | 0.844420i | 0.989430 | − | 0.145010i | \(-0.0463216\pi\) |
−0.145010 | + | 0.989430i | \(0.546322\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.85458 | 0.353987 | ||||||||
\(776\) | −4.81380 | + | 1.16147i | −0.172805 | + | 0.0416942i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.0199 | + | 34.0164i | −0.717747 | + | 1.21955i | ||||
\(779\) | −8.58698 | − | 2.30087i | −0.307660 | − | 0.0824374i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −41.8308 | + | 11.2085i | −1.49682 | + | 0.401073i | ||||
\(782\) | 5.40972 | + | 1.49805i | 0.193451 | + | 0.0535700i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.71155 | + | 3.20725i | 0.0611268 | + | 0.114545i | ||||
\(785\) | 15.6257 | + | 9.02153i | 0.557707 | + | 0.321992i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.208763 | − | 0.0559379i | −0.00744160 | − | 0.00199397i | 0.255096 | − | 0.966916i | \(-0.417893\pi\) |
−0.262538 | + | 0.964922i | \(0.584559\pi\) | |||||||
\(788\) | 24.2154 | − | 23.4200i | 0.862639 | − | 0.834302i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.0738858 | − | 8.84983i | 0.00262874 | − | 0.314863i | ||||
\(791\) | 18.6790i | 0.664150i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.7191i | 0.558202i | ||||||||
\(794\) | −54.8389 | − | 0.457841i | −1.94616 | − | 0.0162482i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.520876 | − | 31.1923i | 0.0184619 | − | 1.10558i | ||||
\(797\) | 2.95273 | + | 0.791183i | 0.104591 | + | 0.0280251i | 0.310735 | − | 0.950497i | \(-0.399425\pi\) |
−0.206144 | + | 0.978522i | \(0.566091\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.43583 | + | 1.98367i | 0.121551 | + | 0.0701774i | ||||
\(800\) | 9.13893 | − | 2.04418i | 0.323110 | − | 0.0722727i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.37652 | + | 23.0268i | −0.225163 | + | 0.813103i | ||||
\(803\) | 21.7602 | − | 5.83064i | 0.767902 | − | 0.205759i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28.1942 | + | 7.55460i | 0.993714 | + | 0.266265i | ||||
\(806\) | 8.32304 | + | 4.89841i | 0.293167 | + | 0.172539i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.03979 | + | 1.24681i | 0.0717596 | + | 0.0438625i | ||||
\(809\) | −42.5506 | −1.49600 | −0.748000 | − | 0.663699i | \(-0.768986\pi\) | ||||
−0.748000 | + | 0.663699i | \(0.768986\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.1448 | + | 15.1448i | 0.531806 | + | 0.531806i | 0.921109 | − | 0.389304i | \(-0.127284\pi\) |
−0.389304 | + | 0.921109i | \(0.627284\pi\) | |||||||
\(812\) | −8.67310 | + | 30.3332i | −0.304366 | + | 1.06449i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 40.4751 | − | 10.4839i | 1.41865 | − | 0.367461i | ||||
\(815\) | −4.74206 | − | 8.21348i | −0.166107 | − | 0.287706i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.4657 | + | 18.1272i | −0.366150 | + | 0.634190i | ||||
\(818\) | 6.52560 | − | 23.5651i | 0.228162 | − | 0.823935i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.76908 | + | 11.0705i | 0.0967006 | + | 0.386599i | ||||
\(821\) | −26.6973 | + | 7.15352i | −0.931742 | + | 0.249660i | −0.692598 | − | 0.721324i | \(-0.743534\pi\) |
−0.239145 | + | 0.970984i | \(0.576867\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.1921 | − | 17.6532i | −0.355273 | − | 0.615350i | 0.631892 | − | 0.775057i | \(-0.282279\pi\) |
−0.987165 | + | 0.159706i | \(0.948945\pi\) | |||||||
\(824\) | 8.48801 | − | 28.7748i | 0.295694 | − | 1.00242i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.469455 | + | 56.2300i | −0.0163344 | + | 1.95649i | ||||
\(827\) | −8.34698 | + | 8.34698i | −0.290253 | + | 0.290253i | −0.837180 | − | 0.546927i | \(-0.815797\pi\) |
0.546927 | + | 0.837180i | \(0.315797\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.48126 | − | 2.48126i | −0.0861778 | − | 0.0861778i | 0.662704 | − | 0.748882i | \(-0.269409\pi\) |
−0.748882 | + | 0.662704i | \(0.769409\pi\) | |||||||
\(830\) | 2.16322 | + | 2.19965i | 0.0750866 | + | 0.0763509i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.73471 | + | 2.81619i | 0.302822 | + | 0.0976339i | ||||
\(833\) | −0.550465 | + | 0.317811i | −0.0190725 | + | 0.0110115i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.52386 | + | 35.5435i | 0.329587 | + | 1.23004i | ||||
\(836\) | 17.5849 | − | 29.3164i | 0.608186 | − | 1.01393i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.12220 | − | 3.74767i | −0.0733103 | − | 0.129461i | ||||
\(839\) | 17.7430 | + | 10.2439i | 0.612558 | + | 0.353660i | 0.773966 | − | 0.633227i | \(-0.218270\pi\) |
−0.161408 | + | 0.986888i | \(0.551604\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.13260 | + | 1.23126i | −0.0735380 | + | 0.0424572i | ||||
\(842\) | 11.2244 | + | 6.60598i | 0.386819 | + | 0.227657i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.88080 | − | 31.0596i | 0.305690 | − | 1.06912i | ||||
\(845\) | −15.1092 | + | 15.1092i | −0.519774 | + | 0.519774i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 70.2684i | 2.41445i | ||||||||
\(848\) | 17.2192 | + | 18.4094i | 0.591308 | + | 0.632182i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.410565 | + | 1.58507i | 0.0140823 | + | 0.0543673i | ||||
\(851\) | 7.23923 | − | 27.0172i | 0.248158 | − | 0.926137i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.06296 | + | 15.1632i | 0.139113 | + | 0.519177i | 0.999947 | + | 0.0102909i | \(0.00327574\pi\) |
−0.860834 | + | 0.508886i | \(0.830058\pi\) | |||||||
\(854\) | −26.8531 | − | 47.4209i | −0.918896 | − | 1.62271i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25.5877 | − | 0.641003i | −0.874570 | − | 0.0219090i | ||||
\(857\) | −0.102894 | + | 0.178217i | −0.00351478 | + | 0.00608778i | −0.867777 | − | 0.496953i | \(-0.834452\pi\) |
0.864263 | + | 0.503041i | \(0.167785\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.733242 | + | 2.73650i | −0.0250179 | + | 0.0933681i | −0.977306 | − | 0.211833i | \(-0.932057\pi\) |
0.952288 | + | 0.305201i | \(0.0987235\pi\) | |||||||
\(860\) | 26.8651 | + | 0.448616i | 0.916093 | + | 0.0152977i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.34054 | − | 7.21898i | 0.250020 | − | 0.245880i | ||||
\(863\) | 26.9928 | 0.918846 | 0.459423 | − | 0.888218i | \(-0.348056\pi\) | ||||
0.459423 | + | 0.888218i | \(0.348056\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.1365 | −0.650660 | ||||||||
\(866\) | 20.1424 | − | 19.8089i | 0.684467 | − | 0.673133i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −33.4767 | − | 0.559022i | −1.13627 | − | 0.0189744i | ||||
\(869\) | 5.31292 | − | 19.8281i | 0.180228 | − | 0.672621i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.65786 | + | 13.2638i | −0.259477 | + | 0.449427i | ||||
\(872\) | −0.152857 | + | 6.10177i | −0.00517638 | + | 0.206632i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.2689 | − | 19.9002i | −0.381178 | − | 0.673136i | ||||
\(875\) | 8.85929 | + | 33.0633i | 0.299499 | + | 1.11774i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.9344 | + | 52.0038i | −0.470531 | + | 1.75604i | 0.167338 | + | 0.985900i | \(0.446483\pi\) |
−0.637869 | + | 0.770145i | \(0.720184\pi\) | |||||||
\(878\) | 10.8605 | + | 41.9290i | 0.366524 | + | 1.41503i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −43.8586 | − | 1.46518i | −1.47847 | − | 0.0493913i | ||||
\(881\) | − | 27.9049i | − | 0.940139i | −0.882629 | − | 0.470069i | \(-0.844229\pi\) | ||
0.882629 | − | 0.470069i | \(-0.155771\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.83601 | − | 3.83601i | 0.129092 | − | 0.129092i | −0.639609 | − | 0.768701i | \(-0.720904\pi\) |
0.768701 | + | 0.639609i | \(0.220904\pi\) | |||||||
\(884\) | −0.441130 | + | 1.54280i | −0.0148368 | + | 0.0518901i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36.3015 | + | 21.3647i | 1.21957 | + | 0.717763i | ||||
\(887\) | 44.3036 | − | 25.5787i | 1.48757 | − | 0.858849i | 0.487671 | − | 0.873028i | \(-0.337847\pi\) |
0.999899 | + | 0.0141788i | \(0.00451340\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −33.6644 | − | 19.4361i | −1.12907 | − | 0.651867i | ||||
\(890\) | −0.499361 | − | 0.881840i | −0.0167386 | − | 0.0295593i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16.5424 | + | 27.5784i | −0.553881 | + | 0.923393i | ||||
\(893\) | −4.18343 | − | 15.6128i | −0.139993 | − | 0.522462i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.8952 | + | 16.1053i | −0.932434 | + | 0.538341i | ||||
\(896\) | −31.1615 | + | 6.42580i | −1.04103 | + | 0.214671i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −26.5781 | − | 27.0257i | −0.886924 | − | 0.901858i | ||||
\(899\) | −23.6101 | − | 23.6101i | −0.787442 | − | 0.787442i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.11647 | + | 3.11647i | −0.103825 | + | 0.103825i | ||||
\(902\) | −0.220975 | + | 26.4678i | −0.00735767 | + | 0.881281i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18.0188 | − | 5.31519i | −0.599296 | − | 0.176781i | ||||
\(905\) | −11.7947 | − | 20.4290i | −0.392069 | − | 0.679084i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.99802 | + | 2.67896i | −0.331979 | + | 0.0889535i | −0.420958 | − | 0.907080i | \(-0.638306\pi\) |
0.0889794 | + | 0.996033i | \(0.471639\pi\) | |||||||
\(908\) | 5.36081 | + | 21.4320i | 0.177905 | + | 0.711246i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.22679 | + | 8.04134i | −0.0738173 | + | 0.266568i | ||||
\(911\) | 5.69107 | − | 9.85722i | 0.188553 | − | 0.326584i | −0.756215 | − | 0.654324i | \(-0.772953\pi\) |
0.944768 | + | 0.327739i | \(0.106287\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.57791 | + | 6.19712i | 0.118411 | + | 0.205095i | ||||
\(914\) | 5.14309 | − | 1.33217i | 0.170118 | − | 0.0440642i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.222317 | + | 0.777528i | −0.00734555 | + | 0.0256903i | ||||
\(917\) | 18.4856 | + | 18.4856i | 0.610447 | + | 0.610447i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.8316 | 0.390288 | 0.195144 | − | 0.980775i | \(-0.437483\pi\) | ||||
0.195144 | + | 0.980775i | \(0.437483\pi\) | |||||||
\(920\) | −15.3103 | + | 25.0479i | −0.504766 | + | 0.825805i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.95432 | + | 2.91579i | 0.163162 | + | 0.0960266i | ||||
\(923\) | −7.99945 | − | 2.14345i | −0.263305 | − | 0.0705524i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.88080 | − | 2.11165i | 0.259119 | − | 0.0694307i | ||||
\(926\) | −8.84192 | + | 31.9298i | −0.290563 | + | 1.04928i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −26.7931 | − | 16.9980i | −0.879526 | − | 0.557986i | ||||
\(929\) | −35.7139 | − | 20.6194i | −1.17174 | − | 0.676502i | −0.217647 | − | 0.976027i | \(-0.569838\pi\) |
−0.954088 | + | 0.299525i | \(0.903172\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.50138 | + | 0.670242i | 0.0819794 | + | 0.0219663i | ||||
\(932\) | 0.388200 | − | 23.2471i | 0.0127159 | − | 0.761484i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 26.5132 | + | 0.221354i | 0.867537 | + | 0.00724293i | ||||
\(935\) | − | 7.67271i | − | 0.250924i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 15.6750i | − | 0.512081i | −0.966666 | − | 0.256041i | \(-0.917582\pi\) | ||
0.966666 | − | 0.256041i | \(-0.0824181\pi\) | |||||||
\(938\) | 0.443289 | − | 53.0959i | 0.0144739 | − | 1.73364i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −14.9143 | + | 14.4244i | −0.486451 | + | 0.470471i | ||||
\(941\) | −9.63753 | − | 2.58237i | −0.314174 | − | 0.0841828i | 0.0982863 | − | 0.995158i | \(-0.468664\pi\) |
−0.412461 | + | 0.910975i | \(0.635331\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.3345 | + | 8.85340i | 0.499361 | + | 0.288306i | ||||
\(944\) | −54.1088 | − | 16.4533i | −1.76109 | − | 0.535509i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 60.0609 | + | 16.6319i | 1.95275 | + | 0.540750i | ||||
\(947\) | 2.28712 | − | 0.612832i | 0.0743214 | − | 0.0199144i | −0.221467 | − | 0.975168i | \(-0.571084\pi\) |
0.295788 | + | 0.955254i | \(0.404418\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.16129 | + | 1.11501i | 0.135081 | + | 0.0361949i | ||||
\(950\) | 3.38357 | − | 5.74912i | 0.109777 | − | 0.186526i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.30480 | − | 5.40787i | −0.0422889 | − | 0.175270i | ||||
\(953\) | −43.1152 | −1.39664 | −0.698320 | − | 0.715786i | \(-0.746069\pi\) | ||||
−0.698320 | + | 0.715786i | \(0.746069\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.57740 | + | 4.57740i | 0.148121 | + | 0.148121i | ||||
\(956\) | −5.44432 | + | 3.02322i | −0.176082 | + | 0.0977778i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.5126 | − | 48.3074i | −0.404265 | − | 1.56074i | ||||
\(959\) | −16.7781 | − | 29.0605i | −0.541792 | − | 0.938411i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.21754 | − | 3.84089i | 0.0715334 | − | 0.123900i | ||||
\(962\) | 7.70565 | + | 2.13383i | 0.248440 | + | 0.0687974i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 24.5834 | + | 14.7459i | 0.791777 | + | 0.474933i | ||||
\(965\) | −26.2502 | + | 7.03372i | −0.845023 | + | 0.226423i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.1271 | − | 36.5932i | −0.679401 | − | 1.17676i | −0.975162 | − | 0.221495i | \(-0.928906\pi\) |
0.295761 | − | 0.955262i | \(-0.404427\pi\) | |||||||
\(968\) | −67.7846 | − | 19.9951i | −2.17868 | − | 0.642668i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.52791 | + | 0.0378028i | 0.145382 | + | 0.00121377i | ||||
\(971\) | −11.0093 | + | 11.0093i | −0.353305 | + | 0.353305i | −0.861338 | − | 0.508033i | \(-0.830373\pi\) |
0.508033 | + | 0.861338i | \(0.330373\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.48513 | + | 2.48513i | 0.0796697 | + | 0.0796697i | ||||
\(974\) | 12.2443 | − | 12.0415i | 0.392331 | − | 0.385835i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 53.3859 | − | 12.4102i | 1.70884 | − | 0.397240i | ||||
\(977\) | −30.5197 | + | 17.6206i | −0.976413 | + | 0.563732i | −0.901185 | − | 0.433434i | \(-0.857302\pi\) |
−0.0752275 | + | 0.997166i | \(0.523968\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.608371 | − | 2.27047i | −0.0194436 | − | 0.0725646i | ||||
\(980\) | −0.806631 | − | 3.22483i | −0.0257669 | − | 0.103013i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.951071 | + | 0.538565i | −0.0303499 | + | 0.0171863i | ||||
\(983\) | 33.9109 | + | 19.5785i | 1.08159 | + | 0.624456i | 0.931325 | − | 0.364190i | \(-0.118654\pi\) |
0.150264 | + | 0.988646i | \(0.451987\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26.6774 | + | 15.4022i | −0.850013 | + | 0.490755i | ||||
\(986\) | 2.81393 | − | 4.78124i | 0.0896139 | − | 0.152266i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.71542 | − | 3.17376i | 0.181832 | − | 0.100971i | ||||
\(989\) | 29.4801 | − | 29.4801i | 0.937411 | − | 0.937411i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 15.1164i | − | 0.480188i | −0.970750 | − | 0.240094i | \(-0.922822\pi\) | ||
0.970750 | − | 0.240094i | \(-0.0771783\pi\) | |||||||
\(992\) | 10.0652 | − | 32.1343i | 0.319570 | − | 1.02027i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 27.7942 | − | 7.19927i | 0.881577 | − | 0.228347i | ||||
\(995\) | −7.38315 | + | 27.5543i | −0.234062 | + | 0.873530i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.3875 | − | 38.7668i | −0.328976 | − | 1.22776i | −0.910254 | − | 0.414051i | \(-0.864113\pi\) |
0.581277 | − | 0.813706i | \(-0.302553\pi\) | |||||||
\(998\) | −1.00057 | + | 0.566596i | −0.0316726 | + | 0.0179353i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 432.2.v.a.35.6 | 88 | ||
3.2 | odd | 2 | 144.2.u.a.83.17 | yes | 88 | ||
4.3 | odd | 2 | 1728.2.z.a.1007.6 | 88 | |||
9.4 | even | 3 | 144.2.u.a.131.10 | yes | 88 | ||
9.5 | odd | 6 | inner | 432.2.v.a.179.13 | 88 | ||
12.11 | even | 2 | 576.2.y.a.47.18 | 88 | |||
16.5 | even | 4 | 1728.2.z.a.143.6 | 88 | |||
16.11 | odd | 4 | inner | 432.2.v.a.251.13 | 88 | ||
36.23 | even | 6 | 1728.2.z.a.1583.6 | 88 | |||
36.31 | odd | 6 | 576.2.y.a.239.16 | 88 | |||
48.5 | odd | 4 | 576.2.y.a.335.16 | 88 | |||
48.11 | even | 4 | 144.2.u.a.11.10 | ✓ | 88 | ||
144.5 | odd | 12 | 1728.2.z.a.719.6 | 88 | |||
144.59 | even | 12 | inner | 432.2.v.a.395.6 | 88 | ||
144.85 | even | 12 | 576.2.y.a.527.18 | 88 | |||
144.139 | odd | 12 | 144.2.u.a.59.17 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.u.a.11.10 | ✓ | 88 | 48.11 | even | 4 | ||
144.2.u.a.59.17 | yes | 88 | 144.139 | odd | 12 | ||
144.2.u.a.83.17 | yes | 88 | 3.2 | odd | 2 | ||
144.2.u.a.131.10 | yes | 88 | 9.4 | even | 3 | ||
432.2.v.a.35.6 | 88 | 1.1 | even | 1 | trivial | ||
432.2.v.a.179.13 | 88 | 9.5 | odd | 6 | inner | ||
432.2.v.a.251.13 | 88 | 16.11 | odd | 4 | inner | ||
432.2.v.a.395.6 | 88 | 144.59 | even | 12 | inner | ||
576.2.y.a.47.18 | 88 | 12.11 | even | 2 | |||
576.2.y.a.239.16 | 88 | 36.31 | odd | 6 | |||
576.2.y.a.335.16 | 88 | 48.5 | odd | 4 | |||
576.2.y.a.527.18 | 88 | 144.85 | even | 12 | |||
1728.2.z.a.143.6 | 88 | 16.5 | even | 4 | |||
1728.2.z.a.719.6 | 88 | 144.5 | odd | 12 | |||
1728.2.z.a.1007.6 | 88 | 4.3 | odd | 2 | |||
1728.2.z.a.1583.6 | 88 | 36.23 | even | 6 |