Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(49,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.u (of order \(9\), degree \(6\), 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: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{9})\) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 97.1 | ||
Character | \(\chi\) | \(=\) | 432.97 |
Dual form | 432.2.u.e.49.1 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.73099 | − | 0.0606946i | −0.999386 | − | 0.0350420i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.00848388 | − | 0.00308788i | −0.00379411 | − | 0.00138094i | 0.340122 | − | 0.940381i | \(-0.389531\pi\) |
−0.343916 | + | 0.939000i | \(0.611754\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.356397 | − | 2.02123i | 0.134705 | − | 0.763952i | −0.840359 | − | 0.542030i | \(-0.817656\pi\) |
0.975064 | − | 0.221922i | \(-0.0712330\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.99263 | + | 0.210123i | 0.997544 | + | 0.0700410i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.47988 | + | 1.26657i | −1.04922 | + | 0.381886i | −0.808370 | − | 0.588675i | \(-0.799650\pi\) |
−0.240854 | + | 0.970561i | \(0.577427\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.25578 | + | 1.05372i | −0.348290 | + | 0.292250i | −0.800103 | − | 0.599863i | \(-0.795222\pi\) |
0.451813 | + | 0.892113i | \(0.350777\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0144981 | + | 0.00586000i | 0.00374338 | + | 0.00151305i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.38526 | − | 5.86344i | −0.821046 | − | 1.42209i | −0.904904 | − | 0.425615i | \(-0.860058\pi\) |
0.0838587 | − | 0.996478i | \(-0.473276\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.25280 | − | 2.16991i | 0.287412 | − | 0.497812i | −0.685779 | − | 0.727810i | \(-0.740538\pi\) |
0.973191 | + | 0.229997i | \(0.0738718\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.739596 | + | 3.47709i | −0.161393 | + | 0.758763i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.120050 | − | 0.680839i | −0.0250322 | − | 0.141965i | 0.969730 | − | 0.244179i | \(-0.0785184\pi\) |
−0.994762 | + | 0.102214i | \(0.967407\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.83016 | − | 3.21389i | −0.766032 | − | 0.642777i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.16745 | − | 0.545357i | −0.994477 | − | 0.104954i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.53937 | − | 2.13078i | −0.471549 | − | 0.395676i | 0.375810 | − | 0.926697i | \(-0.377364\pi\) |
−0.847359 | + | 0.531020i | \(0.821809\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.38196 | − | 7.83750i | −0.248208 | − | 1.40766i | −0.812923 | − | 0.582371i | \(-0.802125\pi\) |
0.564715 | − | 0.825286i | \(-0.308986\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.10050 | − | 1.98121i | 1.06196 | − | 0.344885i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.00926493 | + | 0.0160473i | −0.00156606 | + | 0.00271249i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.92995 | − | 5.07482i | −0.481680 | − | 0.834295i | 0.518099 | − | 0.855321i | \(-0.326640\pi\) |
−0.999779 | + | 0.0210263i | \(0.993307\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.23769 | − | 1.74776i | 0.358317 | − | 0.279866i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.22988 | + | 2.71019i | −0.504423 | + | 0.423261i | −0.859162 | − | 0.511704i | \(-0.829014\pi\) |
0.354739 | + | 0.934966i | \(0.384570\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.54298 | − | 2.38145i | 0.997795 | − | 0.363168i | 0.209061 | − | 0.977903i | \(-0.432959\pi\) |
0.788734 | + | 0.614735i | \(0.210737\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.0247403 | − | 0.0110235i | −0.00368806 | − | 0.00164329i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.67533 | + | 9.50130i | −0.244373 | + | 1.38591i | 0.577572 | + | 0.816340i | \(0.304000\pi\) |
−0.821945 | + | 0.569567i | \(0.807111\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.61951 | + | 0.953423i | 0.374215 | + | 0.136203i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.50396 | + | 10.3550i | 0.770708 | + | 1.44999i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.78317 | −0.931741 | −0.465870 | − | 0.884853i | \(-0.654259\pi\) | ||||
−0.465870 | + | 0.884853i | \(0.654259\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0334339 | 0.00450823 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.30028 | + | 3.68005i | −0.304680 | + | 0.487435i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.68702 | + | 0.977994i | 0.349820 | + | 0.127324i | 0.510953 | − | 0.859609i | \(-0.329293\pi\) |
−0.161133 | + | 0.986933i | \(0.551515\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.07092 | + | 11.7448i | −0.265154 | + | 1.50376i | 0.503443 | + | 0.864028i | \(0.332066\pi\) |
−0.768597 | + | 0.639733i | \(0.779045\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.49127 | − | 5.97390i | 0.187883 | − | 0.752641i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.0139076 | − | 0.00506196i | 0.00172503 | − | 0.000627859i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.998222 | − | 0.837608i | 0.121952 | − | 0.102330i | −0.579772 | − | 0.814779i | \(-0.696858\pi\) |
0.701724 | + | 0.712449i | \(0.252414\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.166482 | + | 1.18581i | 0.0200421 | + | 0.142755i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.11540 | + | 1.93193i | 0.132374 | + | 0.229278i | 0.924591 | − | 0.380961i | \(-0.124407\pi\) |
−0.792217 | + | 0.610239i | \(0.791073\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.05114 | − | 12.2129i | 0.825273 | − | 1.42942i | −0.0764371 | − | 0.997074i | \(-0.524354\pi\) |
0.901710 | − | 0.432341i | \(-0.142312\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.43489 | + | 5.79566i | 0.743037 | + | 0.669226i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.31981 | + | 7.48503i | 0.150407 | + | 0.852998i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.0110 | + | 9.23932i | 1.23883 | + | 1.03950i | 0.997614 | + | 0.0690334i | \(0.0219915\pi\) |
0.241219 | + | 0.970471i | \(0.422453\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.91170 | + | 1.25764i | 0.990189 | + | 0.139738i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.5731 | − | 9.71102i | −1.27032 | − | 1.06592i | −0.994503 | − | 0.104712i | \(-0.966608\pi\) |
−0.275815 | − | 0.961211i | \(-0.588948\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0106145 | + | 0.0601980i | 0.00115131 | + | 0.00652939i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.26629 | + | 3.84248i | 0.457394 | + | 0.411957i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.14879 | − | 3.72181i | 0.227771 | − | 0.394511i | −0.729376 | − | 0.684113i | \(-0.760190\pi\) |
0.957147 | + | 0.289602i | \(0.0935230\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.68226 | + | 2.91375i | 0.176348 | + | 0.305444i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.91647 | + | 13.6505i | 0.198728 | + | 1.41549i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.0173290 | + | 0.0145408i | −0.00177792 | + | 0.00149185i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.50133 | − | 2.36629i | 0.660110 | − | 0.240260i | 0.00982602 | − | 0.999952i | \(-0.496872\pi\) |
0.650284 | + | 0.759691i | \(0.274650\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.6801 | + | 3.05918i | −1.07339 | + | 0.307459i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.741769 | + | 4.20678i | −0.0738088 | + | 0.418590i | 0.925406 | + | 0.378977i | \(0.123724\pi\) |
−0.999215 | + | 0.0396139i | \(0.987387\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.1602 | − | 6.60979i | −1.78938 | − | 0.651282i | −0.999265 | − | 0.0383257i | \(-0.987798\pi\) |
−0.790117 | − | 0.612956i | \(-0.789980\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0170115 | − | 0.0272154i | 0.00166015 | − | 0.00265595i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.19236 | 0.695312 | 0.347656 | − | 0.937622i | \(-0.386978\pi\) | ||||
0.347656 | + | 0.937622i | \(0.386978\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.6780 | 1.50168 | 0.750838 | − | 0.660487i | \(-0.229650\pi\) | ||||
0.750838 | + | 0.660487i | \(0.229650\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.76368 | + | 8.96227i | 0.452149 | + | 0.850661i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3499 | + | 6.31485i | 1.63214 | + | 0.594051i | 0.985640 | − | 0.168861i | \(-0.0540089\pi\) |
0.646502 | + | 0.762912i | \(0.276231\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.00108386 | + | 0.00614686i | −0.000101070 | + | 0.000573198i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.97949 | + | 2.88954i | −0.367904 | + | 0.267138i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.0578 | + | 4.75266i | −1.19701 | + | 0.435676i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.07887 | − | 1.74438i | 0.188988 | − | 0.158580i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.75538 | − | 4.49527i | 0.518945 | − | 0.405325i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.0451414 | + | 0.0781872i | 0.00403757 | + | 0.00699328i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.11425 | + | 1.92993i | −0.0988735 | + | 0.171254i | −0.911219 | − | 0.411923i | \(-0.864857\pi\) |
0.812345 | + | 0.583177i | \(0.198191\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.4704 | + | 3.72514i | −1.00991 | + | 0.327980i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.72703 | − | 15.4658i | −0.238262 | − | 1.35125i | −0.835634 | − | 0.549287i | \(-0.814900\pi\) |
0.597372 | − | 0.801964i | \(-0.296212\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.93939 | − | 3.30554i | −0.341589 | − | 0.286627i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.0421561 | + | 0.0205832i | 0.00362822 | + | 0.00177152i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.607707 | + | 0.509926i | 0.0519199 | + | 0.0435660i | 0.668378 | − | 0.743821i | \(-0.266989\pi\) |
−0.616458 | + | 0.787387i | \(0.711433\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.0180715 | − | 0.102489i | −0.00153281 | − | 0.00869298i | 0.984032 | − | 0.177993i | \(-0.0569604\pi\) |
−0.985565 | + | 0.169300i | \(0.945849\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.47666 | − | 16.3449i | 0.292788 | − | 1.37649i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.03534 | − | 5.25736i | 0.253828 | − | 0.439643i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.0149641 | + | 0.0259186i | 0.00124270 | + | 0.00215242i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.47647 | − | 1.80935i | −0.369213 | − | 0.149233i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.0830 | + | 11.8171i | −1.15373 | + | 0.968092i | −0.999800 | − | 0.0199900i | \(-0.993637\pi\) |
−0.153927 | + | 0.988082i | \(0.549192\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.7155 | + | 7.90378i | −1.76718 | + | 0.643201i | −0.767181 | + | 0.641431i | \(0.778341\pi\) |
−0.999998 | + | 0.00176990i | \(0.999437\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.89879 | − | 18.2584i | −0.719424 | − | 1.47611i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.0124769 | + | 0.0707597i | −0.00100216 | + | 0.00568356i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.6177 | − | 4.95645i | −1.08681 | − | 0.395568i | −0.264374 | − | 0.964420i | \(-0.585165\pi\) |
−0.822440 | + | 0.568852i | \(0.807388\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.7416 | + | 0.411702i | 0.931168 | + | 0.0326501i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.41892 | −0.111826 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.90188 | 0.775575 | 0.387788 | − | 0.921749i | \(-0.373239\pi\) | ||||
0.387788 | + | 0.921749i | \(0.373239\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.0578736 | − | 0.00202926i | −0.00450546 | − | 0.000157977i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.3652 | + | 5.59247i | 1.18899 | + | 0.432759i | 0.859370 | − | 0.511354i | \(-0.170856\pi\) |
0.329624 | + | 0.944112i | \(0.393078\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.79078 | + | 10.1560i | −0.137752 | + | 0.781232i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.20512 | − | 6.23051i | 0.321573 | − | 0.476459i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.42271 | − | 1.60973i | 0.336252 | − | 0.122386i | −0.168375 | − | 0.985723i | \(-0.553852\pi\) |
0.504628 | + | 0.863337i | \(0.331630\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.86105 | + | 6.59620i | −0.594240 | + | 0.498626i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.59183 | − | 1.85598i | −0.345143 | − | 0.139504i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.40191 | − | 12.8205i | −0.553245 | − | 0.958248i | −0.998038 | − | 0.0626148i | \(-0.980056\pi\) |
0.444793 | − | 0.895633i | \(-0.353277\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.33215 | − | 14.4317i | 0.619324 | − | 1.07270i | −0.370285 | − | 0.928918i | \(-0.620740\pi\) |
0.989609 | − | 0.143782i | \(-0.0459266\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.29757 | − | 20.2043i | 0.317686 | − | 1.49355i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.00918689 | + | 0.0521014i | 0.000675433 | + | 0.00383057i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.2068 | + | 16.1164i | 1.40454 | + | 1.17855i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.94396 | + | 10.2502i | −0.214141 | + | 0.745595i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.43182 | + | 7.07514i | 0.610105 | + | 0.511939i | 0.894676 | − | 0.446716i | \(-0.147407\pi\) |
−0.284571 | + | 0.958655i | \(0.591851\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.07135 | + | 6.07593i | 0.0771175 | + | 0.437355i | 0.998781 | + | 0.0493644i | \(0.0157196\pi\) |
−0.921663 | + | 0.387991i | \(0.873169\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.0243812 | + | 0.00791807i | −0.00174597 | + | 0.000567025i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.58608 | − | 9.67538i | 0.397992 | − | 0.689342i | −0.595486 | − | 0.803366i | \(-0.703041\pi\) |
0.993478 | + | 0.114023i | \(0.0363739\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.36136 | − | 7.55409i | −0.309168 | − | 0.535495i | 0.669012 | − | 0.743251i | \(-0.266717\pi\) |
−0.978181 | + | 0.207756i | \(0.933384\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.77875 | + | 1.38930i | −0.125463 | + | 0.0979938i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.21182 | + | 4.37324i | −0.365798 | + | 0.306941i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0357707 | − | 0.0130195i | 0.00249833 | − | 0.000909319i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.216206 | − | 2.06273i | −0.0150274 | − | 0.143369i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.61124 | + | 9.13780i | −0.111452 | + | 0.632075i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.54967 | − | 0.564034i | −0.106684 | − | 0.0388297i | 0.288127 | − | 0.957592i | \(-0.406968\pi\) |
−0.394810 | + | 0.918763i | \(0.629190\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.81349 | − | 3.41185i | −0.124258 | − | 0.233776i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.0628635 | −0.00428725 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.3339 | −1.10882 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.9467 | + | 20.7125i | −0.874856 | + | 1.39962i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.4296 | + | 3.79605i | 0.701568 | + | 0.255350i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.10232 | − | 11.9229i | 0.140782 | − | 0.798414i | −0.829876 | − | 0.557948i | \(-0.811589\pi\) |
0.970658 | − | 0.240466i | \(-0.0773001\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.7869 | − | 10.4228i | −0.719130 | − | 0.694852i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.52456 | − | 1.28284i | 0.233933 | − | 0.0851448i | −0.222394 | − | 0.974957i | \(-0.571387\pi\) |
0.456327 | + | 0.889812i | \(0.349165\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.70736 | + | 5.62815i | −0.443235 | + | 0.371918i | −0.836918 | − | 0.547328i | \(-0.815645\pi\) |
0.393683 | + | 0.919246i | \(0.371201\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.83028 | − | 13.0366i | −0.120423 | − | 0.857745i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.0591 | − | 17.4229i | −0.658994 | − | 1.14141i | −0.980876 | − | 0.194631i | \(-0.937649\pi\) |
0.321883 | − | 0.946780i | \(-0.395684\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.0435522 | − | 0.0754346i | 0.00284103 | − | 0.00492081i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −18.4991 | − | 16.6614i | −1.20165 | − | 1.08228i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.74909 | + | 9.91957i | 0.113139 | + | 0.641644i | 0.987655 | + | 0.156646i | \(0.0500683\pi\) |
−0.874516 | + | 0.484997i | \(0.838821\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.32726 | − | 1.11370i | −0.0854963 | − | 0.0717399i | 0.599038 | − | 0.800721i | \(-0.295550\pi\) |
−0.684534 | + | 0.728981i | \(0.739994\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.3497 | − | 2.71785i | −0.984684 | − | 0.174350i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.0192795 | − | 0.0161774i | −0.00123172 | − | 0.00103354i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.713248 | + | 4.04503i | 0.0453829 | + | 0.257379i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.4435 | + | 17.5121i | 1.23218 | + | 1.10978i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.7741 | − | 20.3934i | 0.743177 | − | 1.28722i | −0.207864 | − | 0.978158i | \(-0.566651\pi\) |
0.951042 | − | 0.309063i | \(-0.100015\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.28009 | + | 2.21719i | 0.0804788 | + | 0.139393i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.0147199 | − | 0.104846i | −0.000921797 | − | 0.00656572i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.3397 | − | 12.8716i | 0.956867 | − | 0.802906i | −0.0235740 | − | 0.999722i | \(-0.507505\pi\) |
0.980440 | + | 0.196816i | \(0.0630601\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.3016 | + | 4.11344i | −0.702246 | + | 0.255597i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.15167 | − | 6.91023i | −0.442677 | − | 0.427732i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.36755 | − | 7.75576i | 0.0843267 | − | 0.478240i | −0.913173 | − | 0.407572i | \(-0.866376\pi\) |
0.997500 | − | 0.0706686i | \(-0.0225133\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.0575476 | + | 0.0209456i | 0.00353512 | + | 0.00128668i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.94541 | + | 6.31198i | −0.241455 | + | 0.386287i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.2541 | 1.11297 | 0.556485 | − | 0.830858i | \(-0.312150\pi\) | ||||
0.556485 | + | 0.830858i | \(0.312150\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.59097 | −0.278881 | −0.139441 | − | 0.990230i | \(-0.544530\pi\) | ||||
−0.139441 | + | 0.990230i | \(0.544530\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.73512 | − | 5.14578i | −0.165537 | − | 0.311436i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.3991 | + | 6.33276i | 1.04921 | + | 0.381880i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.05675 | + | 23.0070i | −0.243746 | + | 1.38235i | 0.579640 | + | 0.814873i | \(0.303193\pi\) |
−0.823386 | + | 0.567482i | \(0.807918\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.48887 | − | 23.7451i | −0.149005 | − | 1.42158i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.1961 | + | 10.6265i | −1.74170 | + | 0.633926i | −0.999349 | − | 0.0360893i | \(-0.988510\pi\) |
−0.742348 | + | 0.670015i | \(0.766288\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.89410 | + | 2.42844i | −0.172036 | + | 0.144356i | −0.724741 | − | 0.689022i | \(-0.758040\pi\) |
0.552704 | + | 0.833378i | \(0.313596\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.0308789 | − | 0.0241181i | 0.00182911 | − | 0.00142863i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.32680 | + | 7.49423i | 0.255403 | + | 0.442371i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.4199 | + | 24.9761i | −0.848232 | + | 1.46918i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.3973 | + | 3.70142i | −0.668124 | + | 0.216981i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.93174 | − | 27.9693i | −0.288116 | − | 1.63398i | −0.693939 | − | 0.720033i | \(-0.744126\pi\) |
0.405824 | − | 0.913951i | \(-0.366985\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.0197764 | − | 0.0165944i | −0.00115143 | − | 0.000966161i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.6729 | − | 4.64718i | 1.08351 | − | 0.269657i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.868172 | + | 0.728483i | 0.0502077 | + | 0.0421293i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.48155 | − | 14.0736i | −0.143034 | − | 0.811188i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.53932 | − | 7.23686i | 0.0884317 | − | 0.415747i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.0538358 | − | 0.0932463i | 0.00308263 | − | 0.00533927i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.13689 | + | 1.96916i | 0.0648860 | + | 0.112386i | 0.896643 | − | 0.442753i | \(-0.145998\pi\) |
−0.831757 | + | 0.555139i | \(0.812665\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 31.0340 | + | 12.5437i | 1.76546 | + | 0.713585i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.15664 | + | 3.48783i | −0.235701 | + | 0.197777i | −0.752986 | − | 0.658037i | \(-0.771387\pi\) |
0.517285 | + | 0.855813i | \(0.326943\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.2769 | − | 4.10446i | 0.637409 | − | 0.231998i | −0.00304407 | − | 0.999995i | \(-0.500969\pi\) |
0.640453 | + | 0.767998i | \(0.278747\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0310985 | + | 0.0460770i | −0.00175220 | + | 0.00259614i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.94756 | − | 28.0590i | 0.277883 | − | 1.57595i | −0.451771 | − | 0.892134i | \(-0.649208\pi\) |
0.729654 | − | 0.683817i | \(-0.239681\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.5355 | + | 4.19857i | 0.645863 | + | 0.235075i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.4499 | − | 0.436537i | −0.694885 | − | 0.0243651i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.9642 | −0.943914 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.19637 | 0.454653 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −27.1383 | − | 0.951567i | −1.50075 | − | 0.0526218i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.6072 | + | 6.77247i | 1.02585 | + | 0.373378i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.721397 | − | 4.09124i | 0.0396516 | − | 0.224875i | −0.958542 | − | 0.284950i | \(-0.908023\pi\) |
0.998194 | + | 0.0600751i | \(0.0191340\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.70192 | − | 15.8027i | −0.422062 | − | 0.865983i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.0110552 | + | 0.00402377i | −0.000604012 | + | 0.000219842i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.8871 | + | 11.6527i | −0.756481 | + | 0.634763i | −0.937208 | − | 0.348770i | \(-0.886599\pi\) |
0.180727 | + | 0.983533i | \(0.442155\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −29.6492 | − | 11.9840i | −1.61032 | − | 0.650880i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.7358 | + | 25.5232i | 0.797990 | + | 1.38216i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0441 | − | 17.3969i | 0.542330 | − | 0.939343i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.00224922 | − | 0.0105743i | 0.000121094 | − | 0.000569304i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.453011 | + | 2.56915i | 0.0243189 | + | 0.137919i | 0.994550 | − | 0.104262i | \(-0.0332481\pi\) |
−0.970231 | + | 0.242182i | \(0.922137\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.4687 | + | 9.62341i | 0.613907 | + | 0.515129i | 0.895882 | − | 0.444293i | \(-0.146545\pi\) |
−0.281975 | + | 0.959422i | \(0.590989\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.06383 | − | 4.76021i | 0.377039 | − | 0.254081i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.61951 | + | 2.19803i | 0.139422 | + | 0.116989i | 0.709832 | − | 0.704371i | \(-0.248771\pi\) |
−0.570409 | + | 0.821361i | \(0.693215\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.00349736 | − | 0.0198345i | −0.000185620 | − | 0.00105271i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 22.8914 | − | 7.43426i | 1.21154 | − | 0.393463i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.89460 | + | 17.1380i | −0.522217 | + | 0.904507i | 0.477449 | + | 0.878660i | \(0.341562\pi\) |
−0.999666 | + | 0.0258470i | \(0.991772\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.36098 | + | 11.0175i | 0.334789 | + | 0.579871i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.70437 | + | 2.89332i | −0.194429 | + | 0.151860i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.0975330 | + | 0.0818399i | −0.00510511 | + | 0.00428370i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.4071 | + | 6.33566i | −0.908643 | + | 0.330719i | −0.753711 | − | 0.657206i | \(-0.771738\pi\) |
−0.154932 | + | 0.987925i | \(0.549516\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.2353 | + | 7.43194i | −0.532830 | + | 0.386891i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.41750 | + | 13.7103i | −0.125510 | + | 0.711805i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.60952 | − | 3.49758i | −0.497562 | − | 0.181098i | 0.0810349 | − | 0.996711i | \(-0.474177\pi\) |
−0.578597 | + | 0.815613i | \(0.696400\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.0733936 | − | 0.138081i | −0.00379003 | − | 0.00713047i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.43413 | 0.279872 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0913 | 0.518353 | 0.259177 | − | 0.965830i | \(-0.416549\pi\) | ||||
0.259177 | + | 0.965830i | \(0.416549\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.04589 | − | 3.27306i | 0.104814 | − | 0.167684i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.9473 | + | 10.5359i | 1.47914 | + | 0.538362i | 0.950565 | − | 0.310526i | \(-0.100505\pi\) |
0.528572 | + | 0.848888i | \(0.322728\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0119157 | − | 0.0675775i | 0.000607282 | − | 0.00344407i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.0811 | − | 5.75197i | 1.02078 | − | 0.292389i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.30592 | − | 0.475315i | 0.0662126 | − | 0.0240994i | −0.308702 | − | 0.951159i | \(-0.599894\pi\) |
0.374914 | + | 0.927060i | \(0.377672\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.58566 | + | 3.00872i | −0.181335 | + | 0.152158i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.78177 | + | 26.9366i | 0.190765 | + | 1.35877i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.0648860 | − | 0.112386i | −0.00326477 | − | 0.00565474i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.1396 | + | 21.0264i | −0.609269 | + | 1.05528i | 0.382092 | + | 0.924124i | \(0.375204\pi\) |
−0.991361 | + | 0.131160i | \(0.958130\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.61841 | + | 5.96095i | 0.331335 | + | 0.298421i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.96102 | − | 11.1215i | −0.0979284 | − | 0.555380i | −0.993811 | − | 0.111088i | \(-0.964566\pi\) |
0.895882 | − | 0.444292i | \(-0.146545\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.99399 | + | 8.38595i | 0.497836 | + | 0.417734i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.0717223 | − | 0.0381879i | −0.00356391 | − | 0.00189757i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.6235 | + | 13.9488i | 0.823995 | + | 0.691414i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.600991 | + | 3.40839i | 0.0297171 | + | 0.168534i | 0.996054 | − | 0.0887443i | \(-0.0282854\pi\) |
−0.966337 | + | 0.257278i | \(0.917174\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.02098 | − | 0.919561i | −0.0503614 | − | 0.0453586i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.93439 | − | 5.08252i | 0.144392 | − | 0.250094i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.0681987 | + | 0.118124i | 0.00334774 | + | 0.00579846i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.0250611 | + | 0.178504i | 0.00122725 | + | 0.00874135i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.0677 | + | 9.28692i | −0.540694 | + | 0.453696i | −0.871775 | − | 0.489906i | \(-0.837031\pi\) |
0.331081 | + | 0.943602i | \(0.392587\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.3041 | − | 8.11803i | 1.08704 | − | 0.395649i | 0.264514 | − | 0.964382i | \(-0.414789\pi\) |
0.822522 | + | 0.568733i | \(0.192566\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.01010 | + | 28.0819i | −0.340843 | + | 1.36539i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.87834 | + | 33.3377i | −0.285141 | + | 1.61712i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.0007 | + | 8.37159i | 1.11308 | + | 0.405129i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.57322 | + | 8.91619i | −0.269078 | + | 0.430478i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.4234 | 0.887422 | 0.443711 | − | 0.896170i | \(-0.353662\pi\) | ||||
0.443711 | + | 0.896170i | \(0.353662\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.6349 | −0.751364 | −0.375682 | − | 0.926749i | \(-0.622592\pi\) | ||||
−0.375682 | + | 0.926749i | \(0.622592\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.0243295 | − | 0.0457729i | −0.00116651 | − | 0.00219464i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.62776 | − | 0.592457i | −0.0778664 | − | 0.0283410i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.20585 | + | 6.83869i | −0.0575519 | + | 0.326393i | −0.999968 | − | 0.00805081i | \(-0.997437\pi\) |
0.942416 | + | 0.334444i | \(0.108548\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.63889 | + | 3.40366i | 0.363757 | + | 0.162079i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.3559 | − | 8.86481i | 1.15718 | − | 0.421180i | 0.309092 | − | 0.951032i | \(-0.399975\pi\) |
0.848090 | + | 0.529852i | \(0.177753\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.0297225 | + | 0.0249402i | −0.00140898 | + | 0.00118228i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 25.0948 | − | 19.6004i | 1.18694 | − | 0.927069i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.72425 | − | 6.45058i | −0.175758 | − | 0.304422i | 0.764665 | − | 0.644428i | \(-0.222904\pi\) |
−0.940423 | + | 0.340006i | \(0.889571\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.80695 | − | 13.5220i | 0.367615 | − | 0.636728i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 38.0689 | − | 12.3633i | 1.78863 | − | 0.580880i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.00527474 | − | 0.0299145i | −0.000247284 | − | 0.00140242i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.1948 | − | 17.7845i | −0.991451 | − | 0.831926i | −0.00567382 | − | 0.999984i | \(-0.501806\pi\) |
−0.985777 | + | 0.168058i | \(0.946250\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.2955 | + | 32.1452i | 0.667257 | + | 1.50041i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.09589 | − | 5.11506i | −0.283914 | − | 0.238232i | 0.489697 | − | 0.871892i | \(-0.337107\pi\) |
−0.773611 | + | 0.633660i | \(0.781552\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.91081 | + | 16.5080i | 0.135277 | + | 0.767193i | 0.974667 | + | 0.223663i | \(0.0718015\pi\) |
−0.839390 | + | 0.543530i | \(0.817087\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.0258920 | − | 0.121727i | 0.00120071 | − | 0.00564495i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.868873 | + | 1.50493i | −0.0402067 | + | 0.0696400i | −0.885428 | − | 0.464776i | \(-0.846135\pi\) |
0.845222 | + | 0.534416i | \(0.179468\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.33723 | − | 2.31615i | −0.0617477 | − | 0.106950i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.2713 | + | 9.40607i | 1.07228 | + | 0.433409i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.7525 | + | 16.5743i | −0.908221 | + | 0.762088i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.7723 | + | 4.28476i | −0.540149 | + | 0.196598i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.2995 | − | 1.42530i | −0.929452 | − | 0.0652601i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.53147 | − | 31.3706i | 0.252740 | − | 1.43336i | −0.549069 | − | 0.835777i | \(-0.685018\pi\) |
0.801809 | − | 0.597580i | \(-0.203871\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.02681 | + | 3.28549i | 0.411587 | + | 0.149805i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.45613 | + | 0.0861206i | 0.111758 | + | 0.00391862i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.0624633 | −0.00283631 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.12802 | −0.232373 | −0.116186 | − | 0.993227i | \(-0.537067\pi\) | ||||
−0.116186 | + | 0.993227i | \(0.537067\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.1400 | − | 0.600991i | −0.775099 | − | 0.0271777i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.30464 | − | 1.56676i | −0.194266 | − | 0.0707069i | 0.243055 | − | 0.970012i | \(-0.421850\pi\) |
−0.437321 | + | 0.899306i | \(0.644073\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.89730 | + | 22.1027i | −0.175525 | + | 0.995454i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.100055 | + | 0.00702523i | 0.00449715 | + | 0.000315761i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.30240 | − | 1.56595i | 0.192989 | − | 0.0702422i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.12857 | − | 7.65978i | 0.408651 | − | 0.342899i | −0.415175 | − | 0.909741i | \(-0.636280\pi\) |
0.823826 | + | 0.566843i | \(0.191835\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −26.2575 | − | 10.6131i | −1.17310 | − | 0.474158i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.7483 | − | 25.5448i | −0.657593 | − | 1.13898i | −0.981237 | − | 0.192806i | \(-0.938241\pi\) |
0.323644 | − | 0.946179i | \(-0.395092\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.0192831 | − | 0.0333993i | 0.000858087 | − | 0.00148625i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.71623 | − | 17.4712i | 0.165044 | − | 0.775925i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.48842 | − | 25.4551i | −0.198946 | − | 1.12828i | −0.906686 | − | 0.421805i | \(-0.861397\pi\) |
0.707741 | − | 0.706472i | \(-0.249715\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.1721 | − | 18.6046i | −0.980836 | − | 0.823019i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.65716 | + | 10.5297i | −0.338072 | + | 0.464898i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.133659 | + | 0.112153i | 0.00588972 | + | 0.00494206i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.20412 | − | 35.1853i | −0.272857 | − | 1.54745i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.75335 | + | 2.51799i | −0.340334 | + | 0.110528i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.14931 | + | 7.18682i | −0.181785 | + | 0.314860i | −0.942488 | − | 0.334239i | \(-0.891521\pi\) |
0.760704 | + | 0.649099i | \(0.224854\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.68608 | − | 2.92038i | −0.0737273 | − | 0.127699i | 0.826805 | − | 0.562489i | \(-0.190156\pi\) |
−0.900532 | + | 0.434790i | \(0.856823\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 14.0077 | − | 10.9408i | 0.611347 | − | 0.477497i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −41.2764 | + | 34.6350i | −1.79803 | + | 1.50873i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.1638 | − | 7.70299i | 0.920165 | − | 0.334913i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.83576 | + | 3.49138i | 0.340043 | + | 0.151513i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.20022 | − | 6.80680i | 0.0519874 | − | 0.294835i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.0610191 | − | 0.0222091i | −0.00263809 | − | 0.000960185i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.0345 | + | 22.6414i | 0.519326 | + | 0.977047i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.3232 | −0.444650 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.7788 | 1.02233 | 0.511166 | − | 0.859482i | \(-0.329214\pi\) | ||||
0.511166 | + | 0.859482i | \(0.329214\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.2988 | + | 24.4754i | −0.656533 | + | 1.05034i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.133010 | − | 0.0484116i | −0.00569752 | − | 0.00207373i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.15310 | − | 6.53956i | 0.0493030 | − | 0.279611i | −0.950182 | − | 0.311695i | \(-0.899103\pi\) |
0.999485 | + | 0.0320838i | \(0.0102143\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.66533 | + | 34.7126i | −0.369827 | + | 1.48150i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.80493 | + | 2.84076i | −0.332501 | + | 0.121021i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.5990 | − | 18.9628i | 0.961009 | − | 0.806382i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.0127401 | − | 0.0907445i | −0.000540788 | − | 0.00385189i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.9195 | + | 25.8413i | 0.632160 | + | 1.09493i | 0.987109 | + | 0.160047i | \(0.0511647\pi\) |
−0.354950 | + | 0.934885i | \(0.615502\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.70714 | + | 9.88506i | −0.241386 | + | 0.418093i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −32.2685 | − | 29.0630i | −1.36238 | − | 1.22704i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.19846 | − | 29.4819i | −0.219089 | − | 1.24252i | −0.873668 | − | 0.486522i | \(-0.838265\pi\) |
0.654579 | − | 0.755993i | \(-0.272846\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.127695 | − | 0.107149i | −0.00537217 | − | 0.00450778i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.71808 | − | 17.5643i | 0.240137 | − | 0.737633i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.98163 | + | 1.66278i | 0.0830742 | + | 0.0697075i | 0.683379 | − | 0.730064i | \(-0.260510\pi\) |
−0.600305 | + | 0.799771i | \(0.704954\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.14782 | + | 12.1809i | 0.0898836 | + | 0.509755i | 0.996196 | + | 0.0871460i | \(0.0277747\pi\) |
−0.906312 | + | 0.422609i | \(0.861114\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.1659 | − | 12.7587i | −0.591791 | − | 0.533004i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.72833 | + | 2.99355i | −0.0720763 | + | 0.124840i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.91640 | − | 3.31931i | −0.0797808 | − | 0.138184i | 0.823374 | − | 0.567498i | \(-0.192089\pi\) |
−0.903155 | + | 0.429314i | \(0.858755\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.48572 | − | 10.5824i | −0.0617443 | − | 0.439789i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.7528 | + | 19.9310i | −0.985432 | + | 0.826876i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.6046 | − | 8.59138i | 0.977604 | − | 0.355819i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.0426841 | − | 0.0122263i | 0.00176477 | − | 0.000505494i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.63559 | − | 14.9472i | 0.108783 | − | 0.616937i | −0.880859 | − | 0.473378i | \(-0.843034\pi\) |
0.989642 | − | 0.143559i | \(-0.0458545\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.7380 | − | 6.82008i | −0.772087 | − | 0.281017i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.2567 | + | 16.4089i | −0.421903 | + | 0.674972i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.889100 | −0.0365110 | −0.0182555 | − | 0.999833i | \(-0.505811\pi\) | ||||
−0.0182555 | + | 0.999833i | \(0.505811\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.125457 | 0.00514322 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.09096 | + | 13.3407i | 0.290214 | + | 0.546000i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.6477 | − | 11.1548i | −1.25223 | − | 0.455774i | −0.371075 | − | 0.928603i | \(-0.621011\pi\) |
−0.881155 | + | 0.472828i | \(0.843233\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.96466 | − | 45.1698i | 0.324885 | − | 1.84252i | −0.185594 | − | 0.982626i | \(-0.559421\pi\) |
0.510480 | − | 0.859890i | \(-0.329468\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.16331 | − | 2.29690i | 0.128820 | − | 0.0935371i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.0230233 | + | 0.00837979i | −0.000936030 | + | 0.000340687i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.59603 | − | 3.01742i | 0.145958 | − | 0.122473i | −0.566885 | − | 0.823797i | \(-0.691852\pi\) |
0.712843 | + | 0.701324i | \(0.247407\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.28702 | − | 7.25368i | 0.376329 | − | 0.293934i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.90788 | − | 13.6968i | −0.319919 | − | 0.554115i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.0007 | − | 36.3743i | 0.848210 | − | 1.46914i | −0.0345948 | − | 0.999401i | \(-0.511014\pi\) |
0.882804 | − | 0.469741i | \(-0.155653\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.0627088 | + | 0.0203654i | −0.00252866 | + | 0.000821214i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.28309 | − | 24.2906i | −0.172431 | − | 0.977902i | −0.941068 | − | 0.338218i | \(-0.890176\pi\) |
0.768637 | − | 0.639685i | \(-0.220935\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.6288 | − | 17.3096i | −0.829140 | − | 0.695731i | 0.125953 | − | 0.992036i | \(-0.459801\pi\) |
−0.955093 | + | 0.296305i | \(0.904246\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.249054 | + | 3.58368i | 0.00999420 | + | 0.143808i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.75679 | − | 5.66962i | −0.270705 | − | 0.227149i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.34099 | + | 24.6190i | 0.173640 | + | 0.984760i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.34365 | − | 15.7196i | 0.133533 | − | 0.627781i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.8372 | + | 34.3591i | −0.790963 | + | 1.36999i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.07564 | − | 1.86306i | −0.0428204 | − | 0.0741671i | 0.843821 | − | 0.536625i | \(-0.180301\pi\) |
−0.886641 | + | 0.462458i | \(0.846968\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.64822 | + | 1.07039i | 0.105257 | + | 0.0425442i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.0154125 | − | 0.0129327i | 0.000611628 | − | 0.000513217i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.29416 | + | 1.56295i | −0.170141 | + | 0.0619262i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.93204 | + | 6.01593i | 0.115990 | + | 0.237987i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.105240 | − | 0.596848i | 0.00415675 | − | 0.0235741i | −0.982659 | − | 0.185423i | \(-0.940635\pi\) |
0.986816 | + | 0.161849i | \(0.0517457\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.5046 | − | 12.9226i | −1.40017 | − | 0.509618i | −0.471938 | − | 0.881632i | \(-0.656445\pi\) |
−0.928227 | + | 0.372013i | \(0.878668\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.108816 | + | 0.00381547i | 0.00428462 | + | 0.000150234i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.1063 | −1.02634 | −0.513172 | − | 0.858286i | \(-0.671530\pi\) | ||||
−0.513172 | + | 0.858286i | \(0.671530\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.5892 | −0.415662 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 28.2738 | + | 0.991379i | 1.10814 | + | 0.0388552i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.7315 | − | 5.36184i | −0.576490 | − | 0.209825i | 0.0372873 | − | 0.999305i | \(-0.488128\pi\) |
−0.613777 | + | 0.789480i | \(0.710351\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.0246206 | + | 0.139630i | −0.000962007 | + | 0.00545581i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.6677 | − | 35.0672i | 0.923364 | − | 1.36810i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.2589 | − | 4.46189i | 0.477541 | − | 0.173811i | −0.0920245 | − | 0.995757i | \(-0.529334\pi\) |
0.569565 | + | 0.821946i | \(0.307112\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.3640 | − | 19.6047i | 0.908752 | − | 0.762534i | −0.0631288 | − | 0.998005i | \(-0.520108\pi\) |
0.971881 | + | 0.235472i | \(0.0756634\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.8230 | − | 7.20393i | −0.692190 | − | 0.279778i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.0232142 | + | 0.0402082i | 0.000900209 | + | 0.00155921i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.14587 | + | 1.98470i | −0.0443682 | + | 0.0768480i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.36275 | + | 20.5107i | −0.168673 | + | 0.792990i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.66904 | − | 43.4933i | −0.296060 | − | 1.67904i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.49892 | − | 5.45324i | −0.250515 | − | 0.210207i | 0.508879 | − | 0.860838i | \(-0.330060\pi\) |
−0.759394 | + | 0.650631i | \(0.774504\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.0395 | + | 18.6964i | 0.694339 | + | 0.719625i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.222584 | − | 0.186770i | −0.00855461 | − | 0.00717817i | 0.638500 | − | 0.769622i | \(-0.279555\pi\) |
−0.647055 | + | 0.762443i | \(0.724000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.46576 | − | 13.9840i | −0.0946270 | − | 0.536657i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.17883 | + | 2.00665i | −0.236773 | + | 0.0768950i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.6164 | + | 32.2446i | −0.712339 | + | 1.23381i | 0.251638 | + | 0.967821i | \(0.419031\pi\) |
−0.963977 | + | 0.265985i | \(0.914303\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.00358112 | − | 0.00620268i | −0.000136827 | − | 0.000236992i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.9520 | − | 9.33515i | 0.455996 | − | 0.356158i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.51816 | − | 7.14758i | 0.324516 | − | 0.272301i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.9897 | + | 8.00361i | −0.836529 | + | 0.304472i | −0.724536 | − | 0.689237i | \(-0.757946\pi\) |
−0.111993 | + | 0.993709i | \(0.535724\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.37694 | + | 22.6773i | 0.0902924 | + | 0.861438i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.000163156 | 0 | 0.000925305i | −6.18887e−6 | 0 | 3.50988e-5i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.8250 | + | 9.76352i | 1.01607 | + | 0.369820i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.3547 | + | 30.7693i | 0.618592 | + | 1.16380i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.89418 | 0.184851 | 0.0924253 | − | 0.995720i | \(-0.470538\pi\) | ||||
0.0924253 | + | 0.995720i | \(0.470538\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.6825 | −0.553763 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.0799667 | + | 0.127933i | −0.00301172 | + | 0.00481823i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.23850 | + | 2.99857i | 0.309841 | + | 0.112773i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.22367 | − | 35.2962i | 0.233735 | − | 1.32558i | −0.611527 | − | 0.791224i | \(-0.709444\pi\) |
0.845262 | − | 0.534353i | \(-0.179445\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.0104 | + | 29.9635i | 1.16298 | + | 1.12372i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.17018 | + | 1.88179i | −0.193625 | + | 0.0704736i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0419855 | + | 0.0352300i | −0.00157017 | + | 0.00131753i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.42558 | − | 17.2768i | −0.0905851 | − | 0.645214i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.7374 | + | 34.1863i | 0.736083 | + | 1.27493i | 0.954247 | + | 0.299020i | \(0.0966598\pi\) |
−0.218164 | + | 0.975912i | \(0.570007\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.8321 | + | 34.3503i | −0.738588 | + | 1.27927i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.22987 | + | 2.00836i | 0.0829298 | + | 0.0746918i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.87809 | + | 16.3225i | 0.106890 | + | 0.606202i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.53124 | − | 2.12397i | −0.0938786 | − | 0.0787735i | 0.594640 | − | 0.803992i | \(-0.297294\pi\) |
−0.688519 | + | 0.725218i | \(0.741739\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.4052 | + | 5.63621i | 0.977969 | + | 0.208749i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −36.1132 | − | 30.3025i | −1.33569 | − | 1.12078i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.01650 | + | 22.7787i | 0.148353 | + | 0.841350i | 0.964614 | + | 0.263667i | \(0.0849320\pi\) |
−0.816261 | + | 0.577683i | \(0.803957\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.0323907 | + | 0.0291731i | 0.00119475 | + | 0.00107607i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.41280 | + | 4.17910i | −0.0888767 | + | 0.153939i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.15368 | − | 1.99824i | −0.0424390 | − | 0.0735064i | 0.844026 | − | 0.536303i | \(-0.180179\pi\) |
−0.886465 | + | 0.462796i | \(0.846846\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.989112 | − | 7.04519i | −0.0363359 | − | 0.258811i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.70414 | − | 8.14274i | 0.356010 | − | 0.298728i | −0.447188 | − | 0.894440i | \(-0.647574\pi\) |
0.803198 | + | 0.595712i | \(0.203130\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.155968 | − | 0.0567679i | 0.00571424 | − | 0.00207981i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −32.5936 | − | 31.4933i | −1.19254 | − | 1.15228i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.56334 | − | 14.5374i | 0.0936622 | − | 0.531185i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.9861 | + | 10.9140i | 1.09421 | + | 0.398259i | 0.825178 | − | 0.564873i | \(-0.191075\pi\) |
0.269030 | + | 0.963132i | \(0.413297\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.6187 | + | 34.5861i | −0.787828 | + | 1.26039i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.208637 | 0.00759309 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.2146 | −1.20721 | −0.603603 | − | 0.797285i | \(-0.706269\pi\) | ||||
−0.603603 | + | 0.797285i | \(0.706269\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.08125 | − | 3.91562i | −0.0755447 | − | 0.142128i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.4090 | + | 10.3400i | 1.02982 | + | 0.374825i | 0.801014 | − | 0.598646i | \(-0.204294\pi\) |
0.228810 | + | 0.973471i | \(0.426516\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.58757 | − | 31.6887i | 0.202284 | − | 1.14721i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.0191164 | + | 0.182381i | 0.000691154 | + | 0.00659399i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.40483 | + | 1.60323i | −0.159049 | + | 0.0578892i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.7530 | − | 13.2183i | 0.568068 | − | 0.476666i | −0.312936 | − | 0.949774i | \(-0.601313\pi\) |
0.881004 | + | 0.473109i | \(0.156868\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.3341 | + | 21.3495i | −0.984414 | + | 0.768883i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.11051 | + | 1.92346i | 0.0399424 | + | 0.0691822i | 0.885305 | − | 0.465010i | \(-0.153949\pi\) |
−0.845363 | + | 0.534192i | \(0.820616\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.8957 | + | 34.4604i | −0.714675 | + | 1.23785i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.8125 | − | 6.43436i | 0.710771 | − | 0.230832i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.83449 | + | 10.4039i | 0.0657274 | + | 0.372758i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.32840 | − | 5.31015i | −0.226448 | − | 0.190012i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.9600 | + | 12.3956i | 0.427417 | + | 0.442982i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.100226 | + | 0.0840998i | 0.00357723 | + | 0.00300165i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.984197 | − | 5.58166i | −0.0350828 | − | 0.198965i | 0.962229 | − | 0.272242i | \(-0.0877652\pi\) |
−0.997312 | + | 0.0732776i | \(0.976654\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.83794 | + | 13.3421i | −0.101033 | + | 0.474992i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.9472 | − | 32.8175i | 0.673685 | − | 1.16686i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.77510 | − | 16.9310i | −0.347124 | − | 0.601236i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.0983429 | − | 0.0397494i | −0.00348786 | − | 0.00140977i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.8828 | + | 25.0746i | −1.05850 | + | 0.888189i | −0.993962 | − | 0.109726i | \(-0.965003\pi\) |
−0.0645410 | + | 0.997915i | \(0.520558\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 61.3817 | − | 22.3411i | 2.17153 | − | 0.790372i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.21256 | − | 10.6865i | 0.254843 | − | 0.377588i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.06855 | + | 51.4303i | −0.320022 | + | 1.81494i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0120379 | + | 0.00438144i | 0.000424281 | + | 0.000154426i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −31.5976 | − | 1.10792i | −1.11229 | − | 0.0390007i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −40.9853 | −1.44097 | −0.720484 | − | 0.693472i | \(-0.756080\pi\) | ||||
−0.720484 | + | 0.693472i | \(0.756080\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.2369 | −0.851072 | −0.425536 | − | 0.904942i | \(-0.639914\pi\) | ||||
−0.425536 | + | 0.904942i | \(0.639914\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.94691 | + | 0.278647i | 0.278710 | + | 0.00977258i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.0840063 | − | 0.0305758i | −0.00294261 | − | 0.00107102i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.02951 | − | 17.1812i | 0.105989 | − | 0.601094i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.42213 | + | 9.07328i | 0.154522 | + | 0.317046i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.8003 | − | 8.66260i | 0.830636 | − | 0.302327i | 0.108516 | − | 0.994095i | \(-0.465390\pi\) |
0.722120 | + | 0.691768i | \(0.243168\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.9722 | − | 29.3452i | 1.21906 | − | 1.02291i | 0.220182 | − | 0.975459i | \(-0.429335\pi\) |
0.998874 | − | 0.0474499i | \(-0.0151094\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −29.7333 | − | 12.0180i | −1.03518 | − | 0.418412i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.1400 | + | 47.0079i | 0.943752 | + | 1.63463i | 0.758232 | + | 0.651985i | \(0.226064\pi\) |
0.185520 | + | 0.982640i | \(0.440603\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.2155 | − | 19.4259i | 0.389531 | − | 0.674688i | −0.602855 | − | 0.797851i | \(-0.705970\pi\) |
0.992387 | + | 0.123163i | \(0.0393037\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.41858 | − | 39.5785i | 0.292037 | − | 1.37296i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.27737 | − | 18.5869i | −0.113554 | − | 0.643998i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.113088 | − | 0.0948917i | −0.00391356 | − | 0.00328386i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.86699 | + | 41.2536i | 0.0990978 | + | 1.42593i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.8322 | + | 17.4803i | 0.719206 | + | 0.603486i | 0.927166 | − | 0.374652i | \(-0.122238\pi\) |
−0.207959 | + | 0.978137i | \(0.566682\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.12764 | − | 17.7377i | −0.107850 | − | 0.611646i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 51.1831 | − | 16.6223i | 1.76284 | − | 0.572504i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.0465533 | − | 0.0806327i | 0.00160148 | − | 0.00277385i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.78488 | − | 4.82356i | −0.0956897 | − | 0.165739i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.15704 | − | 4.02794i | 0.176989 | − | 0.138238i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.10339 | + | 2.60406i | −0.106383 | + | 0.0892659i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.2708 | + | 15.3853i | −1.44733 | + | 0.526784i | −0.941843 | − | 0.336053i | \(-0.890908\pi\) |
−0.505483 | + | 0.862837i | \(0.668686\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.0549148 | + | 0.0398740i | −0.00187805 | + | 0.00136366i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.11847 | − | 12.0145i | 0.0723656 | − | 0.410406i | −0.927009 | − | 0.375040i | \(-0.877629\pi\) |
0.999374 | − | 0.0353663i | \(-0.0112598\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.6476 | + | 15.5224i | 1.45512 | + | 0.529619i | 0.944015 | − | 0.329902i | \(-0.107016\pi\) |
0.511101 | + | 0.859521i | \(0.329238\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.03477 | − | 13.2350i | −0.239744 | − | 0.451049i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.90855 | −0.235170 | −0.117585 | − | 0.993063i | \(-0.537515\pi\) | ||||
−0.117585 | + | 0.993063i | \(0.537515\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.0424924 | −0.00144478 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.4766 | − | 42.3580i | 0.899194 | − | 1.43855i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −50.0192 | − | 18.2055i | −1.69678 | − | 0.617579i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.370939 | + | 2.10370i | −0.0125688 | + | 0.0712811i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 19.9533 | − | 5.71536i | 0.675317 | − | 0.193435i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.174122 | − | 0.0633754i | 0.00588641 | − | 0.00214248i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.5767 | + | 26.4960i | −1.06627 | + | 0.894708i | −0.994709 | − | 0.102729i | \(-0.967243\pi\) |
−0.0715616 | + | 0.997436i | \(0.522798\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.83920 | + | 48.7138i | 0.230680 | + | 1.64308i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.7930 | − | 32.5505i | −0.633153 | − | 1.09665i | −0.986903 | − | 0.161313i | \(-0.948427\pi\) |
0.353751 | − | 0.935340i | \(-0.384906\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.6493 | + | 27.1054i | −0.526642 | + | 0.912171i | 0.472876 | + | 0.881129i | \(0.343216\pi\) |
−0.999518 | + | 0.0310417i | \(0.990118\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.0332255 | + | 0.0299250i | 0.00111686 | + | 0.00100592i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.95465 | − | 33.7705i | −0.199938 | − | 1.13390i | −0.905210 | − | 0.424966i | \(-0.860286\pi\) |
0.705272 | − | 0.708937i | \(-0.250825\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.50372 | + | 2.93997i | 0.117511 | + | 0.0986034i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −32.6045 | + | 6.91087i | −1.09229 | + | 0.231523i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.5181 | + | 15.5386i | 0.619686 | + | 0.519978i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.0232088 | + | 0.131624i | 0.000775785 | + | 0.00439969i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.45858 | − | 1.31369i | −0.0487006 | − | 0.0438628i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.1907 | + | 22.8470i | −0.439935 | + | 0.761989i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.9628 | + | 39.7727i | 0.765002 | + | 1.32502i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.44135 | + | 24.5118i | 0.114521 | + | 0.815703i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.115252 | + | 0.0967082i | −0.00383112 | + | 0.00321469i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.3753 | − | 7.41602i | 0.676552 | − | 0.246245i | 0.0191857 | − | 0.999816i | \(-0.493893\pi\) |
0.657366 | + | 0.753571i | \(0.271670\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.10378 | + | 12.4335i | −0.102946 | + | 0.412393i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.81687 | − | 27.3178i | 0.159590 | − | 0.905080i | −0.794879 | − | 0.606768i | \(-0.792466\pi\) |
0.954469 | − | 0.298311i | \(-0.0964234\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 52.5728 | + | 19.1350i | 1.73991 | + | 0.633274i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.0988486 | + | 0.158141i | −0.00326783 | + | 0.00522797i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −32.2317 | −1.06439 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.2970 | 1.13135 | 0.565676 | − | 0.824628i | \(-0.308615\pi\) | ||||
0.565676 | + | 0.824628i | \(0.308615\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.84843 | − | 3.47759i | −0.0609079 | − | 0.114591i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.43642 | − | 1.25075i | −0.113111 | − | 0.0411690i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.08771 | + | 28.8539i | −0.167283 | + | 0.948709i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −52.9581 | − | 23.5966i | −1.73937 | − | 0.775013i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33.7239 | − | 12.2745i | 1.10645 | − | 0.402714i | 0.276758 | − | 0.960940i | \(-0.410740\pi\) |
0.829689 | + | 0.558226i | \(0.188518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.35056 | − | 4.48966i | 0.175358 | − | 0.147143i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.40678 | − | 5.78511i | 0.242487 | − | 0.189396i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.113182 | − | 0.196038i | −0.00370146 | − | 0.00641111i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.97725 | + | 17.2811i | −0.325943 | + | 0.564549i | −0.981703 | − | 0.190420i | \(-0.939015\pi\) |
0.655760 | + | 0.754969i | \(0.272348\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.7693 | + | 6.42032i | −0.645147 | + | 0.209519i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.559581 | − | 3.17354i | −0.0182418 | − | 0.103454i | 0.974327 | − | 0.225136i | \(-0.0722825\pi\) |
−0.992569 | + | 0.121681i | \(0.961171\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.23296 | + | 1.87367i | 0.0727150 | + | 0.0610152i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.0566276 | − | 0.0778712i | 0.00184210 | − | 0.00253315i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.3769 | + | 19.6156i | 0.759648 | + | 0.637420i | 0.938035 | − | 0.346540i | \(-0.112644\pi\) |
−0.178387 | + | 0.983960i | \(0.557088\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.01438 | + | 22.7667i | 0.130312 | + | 0.739037i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.2672 | + | 48.2695i | −0.332937 | + | 1.56525i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.91496 | − | 17.1732i | 0.321177 | − | 0.556295i | −0.659554 | − | 0.751657i | \(-0.729255\pi\) |
0.980731 | + | 0.195362i | \(0.0625883\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.0496874 | − | 0.0860610i | −0.00160785 | − | 0.00278487i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.7129 | − | 7.96782i | −0.637229 | − | 0.257563i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.24726 | − | 1.04658i | 0.0402762 | − | 0.0337957i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3861 | + | 11.0597i | −0.980198 | + | 0.356763i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21.5241 | + | 1.51128i | 0.693604 | + | 0.0487004i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.00967253 | − | 0.0548556i | 0.000311370 | − | 0.00176587i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.9594 | − | 5.80873i | −0.513218 | − | 0.186796i | 0.0724115 | − | 0.997375i | \(-0.476931\pi\) |
−0.585630 | + | 0.810579i | \(0.699153\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 29.3648 | + | 1.02964i | 0.943334 | + | 0.0330767i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.8069 | 1.18119 | 0.590595 | − | 0.806968i | \(-0.298893\pi\) | ||||
0.590595 | + | 0.806968i | \(0.298893\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.213594 | −0.00684750 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.1878 | − | 0.497475i | −0.454374 | − | 0.0159320i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.1112 | + | 15.6912i | 1.37925 | + | 0.502006i | 0.921951 | − | 0.387307i | \(-0.126595\pi\) |
0.457299 | + | 0.889313i | \(0.348817\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.76358 | + | 15.6730i | −0.0883243 | + | 0.500912i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 46.9184 | + | 3.29430i | 1.49799 | + | 0.105179i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.30989 | + | 2.66058i | −0.233149 | + | 0.0848594i | −0.455953 | − | 0.890004i | \(-0.650701\pi\) |
0.222803 | + | 0.974863i | \(0.428479\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.0772680 | + | 0.0648356i | −0.00246196 | + | 0.00206583i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −31.7978 | − | 12.8524i | −1.01213 | − | 0.409097i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.40687 | − | 4.16883i | −0.0765341 | − | 0.132561i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.87090 | − | 6.70460i | 0.122963 | − | 0.212979i | −0.797972 | − | 0.602695i | \(-0.794094\pi\) |
0.920935 | + | 0.389716i | \(0.127427\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.49704 | + | 7.03811i | −0.0475073 | + | 0.223348i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.0136751 | + | 0.0775553i | 0.000433530 | + | 0.00245867i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.97977 | + | 6.69582i | 0.252722 | + | 0.212059i | 0.760343 | − | 0.649521i | \(-0.225031\pi\) |
−0.507622 | + | 0.861580i | \(0.669475\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.3728 | + | 27.8217i | 0.391457 | + | 0.880241i |
(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.u.e.97.1 | 24 | ||
4.3 | odd | 2 | 216.2.q.a.97.4 | yes | 24 | ||
12.11 | even | 2 | 648.2.q.a.289.3 | 24 | |||
27.22 | even | 9 | inner | 432.2.u.e.49.1 | 24 | ||
108.7 | odd | 18 | 5832.2.a.h.1.7 | 12 | |||
108.47 | even | 18 | 5832.2.a.i.1.6 | 12 | |||
108.59 | even | 18 | 648.2.q.a.361.3 | 24 | |||
108.103 | odd | 18 | 216.2.q.a.49.4 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.q.a.49.4 | ✓ | 24 | 108.103 | odd | 18 | ||
216.2.q.a.97.4 | yes | 24 | 4.3 | odd | 2 | ||
432.2.u.e.49.1 | 24 | 27.22 | even | 9 | inner | ||
432.2.u.e.97.1 | 24 | 1.1 | even | 1 | trivial | ||
648.2.q.a.289.3 | 24 | 12.11 | even | 2 | |||
648.2.q.a.361.3 | 24 | 108.59 | even | 18 | |||
5832.2.a.h.1.7 | 12 | 108.7 | odd | 18 | |||
5832.2.a.i.1.6 | 12 | 108.47 | even | 18 |