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: | \(30\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{9})\) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 97.4 | ||
Character | \(\chi\) | \(=\) | 432.97 |
Dual form | 432.2.u.f.49.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) |
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 | ||||||||
\(3\) | 0.968921 | − | 1.43569i | 0.559407 | − | 0.828893i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.72954 | − | 0.993471i | −1.22069 | − | 0.444294i | −0.350288 | − | 0.936642i | \(-0.613916\pi\) |
−0.870398 | + | 0.492348i | \(0.836139\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.186943 | − | 1.06021i | 0.0706577 | − | 0.400720i | −0.928882 | − | 0.370376i | \(-0.879229\pi\) |
0.999540 | − | 0.0303436i | \(-0.00966015\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.12238 | − | 2.78213i | −0.374128 | − | 0.927377i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.28397 | − | 1.19527i | 0.990153 | − | 0.360386i | 0.204373 | − | 0.978893i | \(-0.434484\pi\) |
0.785779 | + | 0.618507i | \(0.212262\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.77837 | + | 3.17043i | −1.04793 | + | 0.879319i | −0.992874 | − | 0.119165i | \(-0.961978\pi\) |
−0.0550565 | + | 0.998483i | \(0.517534\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.07102 | + | 2.95616i | −1.05113 | + | 0.763278i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.54041 | − | 6.13217i | −0.858675 | − | 1.48727i | −0.873193 | − | 0.487375i | \(-0.837955\pi\) |
0.0145173 | − | 0.999895i | \(-0.495379\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.08712 | + | 1.88294i | −0.249402 | + | 0.431976i | −0.963360 | − | 0.268212i | \(-0.913567\pi\) |
0.713958 | + | 0.700188i | \(0.246901\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.34099 | − | 1.29565i | −0.292628 | − | 0.282733i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.11177 | − | 6.30518i | −0.231821 | − | 1.31472i | −0.849206 | − | 0.528061i | \(-0.822919\pi\) |
0.617385 | − | 0.786661i | \(-0.288192\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.63317 | + | 2.20949i | 0.526634 | + | 0.441899i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.08177 | − | 1.08428i | −0.977986 | − | 0.208669i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.20769 | + | 1.85247i | 0.409958 | + | 0.343996i | 0.824328 | − | 0.566113i | \(-0.191553\pi\) |
−0.414370 | + | 0.910109i | \(0.635998\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.481312 | − | 2.72965i | −0.0864461 | − | 0.490260i | −0.997035 | − | 0.0769473i | \(-0.975483\pi\) |
0.910589 | − | 0.413313i | \(-0.135628\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.46588 | − | 5.87286i | 0.255177 | − | 1.02233i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.56355 | + | 2.70815i | −0.264288 | + | 0.457761i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.40997 | + | 7.63829i | 0.724995 | + | 1.25573i | 0.958976 | + | 0.283487i | \(0.0914911\pi\) |
−0.233982 | + | 0.972241i | \(0.575176\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.890795 | + | 8.49644i | 0.142641 | + | 1.36052i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.953592 | + | 0.800158i | −0.148926 | + | 0.124964i | −0.714207 | − | 0.699935i | \(-0.753212\pi\) |
0.565281 | + | 0.824899i | \(0.308768\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.05867 | − | 2.56915i | 1.07644 | − | 0.391791i | 0.257857 | − | 0.966183i | \(-0.416984\pi\) |
0.818580 | + | 0.574392i | \(0.194762\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.299623 | + | 8.70899i | 0.0446652 | + | 1.29826i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.575841 | − | 3.26576i | 0.0839951 | − | 0.476360i | −0.913574 | − | 0.406673i | \(-0.866689\pi\) |
0.997569 | − | 0.0696869i | \(-0.0222000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.48876 | + | 1.99775i | 0.784109 | + | 0.285392i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.2342 | − | 0.858675i | −1.71314 | − | 0.120239i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.88716 | −0.259222 | −0.129611 | − | 0.991565i | \(-0.541373\pi\) | ||||
−0.129611 | + | 0.991565i | \(0.541373\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.1512 | −1.36878 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.64998 | + | 3.38518i | 0.218545 | + | 0.448378i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.0776 | + | 4.75985i | 1.70256 | + | 0.619679i | 0.996112 | − | 0.0880908i | \(-0.0280766\pi\) |
0.706443 | + | 0.707770i | \(0.250299\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.65444 | − | 15.0541i | 0.339866 | − | 1.92748i | −0.0326905 | − | 0.999466i | \(-0.510408\pi\) |
0.372556 | − | 0.928010i | \(-0.378481\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.15945 | + | 0.669858i | −0.398053 | + | 0.0843941i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.4629 | − | 4.90011i | 1.66987 | − | 0.607783i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.47352 | − | 1.23643i | 0.180019 | − | 0.151054i | −0.548325 | − | 0.836265i | \(-0.684734\pi\) |
0.728345 | + | 0.685211i | \(0.240290\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.1295 | − | 4.51307i | −1.21945 | − | 0.543310i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.650072 | − | 1.12596i | −0.0771494 | − | 0.133627i | 0.824870 | − | 0.565323i | \(-0.191248\pi\) |
−0.902019 | + | 0.431696i | \(0.857915\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.86037 | − | 4.95431i | 0.334781 | − | 0.579858i | −0.648662 | − | 0.761077i | \(-0.724671\pi\) |
0.983443 | + | 0.181219i | \(0.0580043\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.72347 | − | 1.63958i | 0.660890 | − | 0.189323i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.653313 | − | 3.70512i | −0.0744519 | − | 0.422238i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.35069 | + | 6.16796i | 0.827017 | + | 0.693950i | 0.954604 | − | 0.297877i | \(-0.0962787\pi\) |
−0.127587 | + | 0.991827i | \(0.540723\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.48051 | + | 6.24524i | −0.720057 | + | 0.693915i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.95760 | − | 1.64262i | −0.214875 | − | 0.180301i | 0.528997 | − | 0.848624i | \(-0.322568\pi\) |
−0.743872 | + | 0.668322i | \(0.767013\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.57155 | + | 20.2553i | 0.387389 | + | 2.19699i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.79865 | − | 1.37465i | 0.514469 | − | 0.147378i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.77803 | − | 3.07963i | 0.188470 | − | 0.326440i | −0.756270 | − | 0.654259i | \(-0.772980\pi\) |
0.944740 | + | 0.327819i | \(0.106314\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.65497 | + | 4.59853i | 0.278316 | + | 0.482057i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.38528 | − | 1.95381i | −0.454732 | − | 0.202600i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.83797 | − | 4.05954i | 0.496365 | − | 0.416500i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.41676 | + | 2.33551i | −0.651523 | + | 0.237135i | −0.646572 | − | 0.762853i | \(-0.723798\pi\) |
−0.00495069 | + | 0.999988i | \(0.501576\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.01126 | − | 7.79488i | −0.704658 | − | 0.783415i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.761262 | + | 4.31733i | −0.0757484 | + | 0.429590i | 0.923224 | + | 0.384263i | \(0.125544\pi\) |
−0.998972 | + | 0.0453277i | \(0.985567\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.1304 | + | 4.41511i | 1.19525 | + | 0.435034i | 0.861563 | − | 0.507651i | \(-0.169486\pi\) |
0.333683 | + | 0.942685i | \(0.391708\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.37309 | + | 4.86875i | 0.231590 | + | 0.475141i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.84595 | −0.371803 | −0.185901 | − | 0.982568i | \(-0.559520\pi\) | ||||
−0.185901 | + | 0.982568i | \(0.559520\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.8768 | −1.04181 | −0.520906 | − | 0.853614i | \(-0.674406\pi\) | ||||
−0.520906 | + | 0.853614i | \(0.674406\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.2391 | + | 1.06957i | 1.44643 | + | 0.101519i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.82696 | − | 1.75687i | −0.454082 | − | 0.165272i | 0.104846 | − | 0.994488i | \(-0.466565\pi\) |
−0.558928 | + | 0.829216i | \(0.688787\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.22939 | + | 18.3148i | −0.301142 | + | 1.70786i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.0613 | + | 6.95348i | 1.20752 | + | 0.642850i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.16321 | + | 2.60720i | −0.656651 | + | 0.239001i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.929279 | − | 0.779758i | 0.0844799 | − | 0.0708871i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.224820 | + | 2.14435i | 0.0202714 | + | 0.193349i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.26951 | + | 3.93090i | 0.202991 | + | 0.351591i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.42554 | − | 5.93321i | 0.303968 | − | 0.526487i | −0.673063 | − | 0.739585i | \(-0.735022\pi\) |
0.977031 | + | 0.213098i | \(0.0683552\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.15081 | − | 12.6233i | 0.277413 | − | 1.11142i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.74217 | − | 21.2229i | −0.326955 | − | 1.85425i | −0.495565 | − | 0.868571i | \(-0.665039\pi\) |
0.168610 | − | 0.985683i | \(-0.446072\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.79307 | + | 1.50457i | 0.155479 | + | 0.130463i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 12.7937 | + | 8.00816i | 1.10110 | + | 0.689233i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.3829 | + | 13.7469i | 1.39969 | + | 1.17448i | 0.961239 | + | 0.275718i | \(0.0889155\pi\) |
0.438446 | + | 0.898757i | \(0.355529\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.43030 | + | 19.4542i | 0.290954 | + | 1.65008i | 0.683207 | + | 0.730225i | \(0.260585\pi\) |
−0.392253 | + | 0.919857i | \(0.628304\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.13066 | − | 3.99099i | −0.347864 | − | 0.336102i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.61853 | + | 14.9277i | −0.720718 | + | 1.24832i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.18560 | − | 7.24967i | −0.347595 | − | 0.602052i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.18631 | − | 5.94447i | 0.675195 | − | 0.490292i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.09436 | − | 1.75738i | 0.171577 | − | 0.143970i | −0.552956 | − | 0.833211i | \(-0.686500\pi\) |
0.724532 | + | 0.689241i | \(0.242056\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.2388 | − | 7.00235i | 1.56563 | − | 0.569843i | 0.593614 | − | 0.804750i | \(-0.297701\pi\) |
0.972018 | + | 0.234907i | \(0.0754784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.0868 | + | 16.7325i | −1.05801 | + | 1.35275i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.39807 | + | 7.92886i | −0.112296 | + | 0.636862i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.42835 | − | 1.61179i | −0.353421 | − | 0.128635i | 0.159208 | − | 0.987245i | \(-0.449106\pi\) |
−0.512629 | + | 0.858610i | \(0.671328\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.82851 | + | 2.70937i | −0.145011 | + | 0.214867i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.89263 | −0.543215 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24.9764 | −1.95630 | −0.978150 | − | 0.207899i | \(-0.933337\pi\) | ||||
−0.978150 | + | 0.207899i | \(0.933337\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.83568 | + | 14.5739i | −0.765707 | + | 1.13458i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.7375 | − | 5.36402i | −1.14042 | − | 0.415081i | −0.298358 | − | 0.954454i | \(-0.596439\pi\) |
−0.842067 | + | 0.539373i | \(0.818661\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.96703 | − | 11.1556i | 0.151310 | − | 0.858123i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.45875 | + | 0.911118i | 0.493913 | + | 0.0696749i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.6783 | + | 3.88659i | −0.811858 | + | 0.295492i | −0.714391 | − | 0.699747i | \(-0.753296\pi\) |
−0.0974666 | + | 0.995239i | \(0.531074\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.83477 | − | 2.37865i | 0.214288 | − | 0.179809i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 19.5048 | − | 14.1634i | 1.46607 | − | 1.06458i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.38452 | + | 12.7904i | 0.551945 | + | 0.955997i | 0.998134 | + | 0.0610585i | \(0.0194476\pi\) |
−0.446189 | + | 0.894939i | \(0.647219\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.65465 | − | 13.2582i | 0.568966 | − | 0.985478i | −0.427703 | − | 0.903919i | \(-0.640677\pi\) |
0.996669 | − | 0.0815582i | \(-0.0259896\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.0410 | − | 18.3971i | −1.40755 | − | 1.35996i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.44876 | − | 25.2302i | −0.327080 | − | 1.85496i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.9562 | − | 15.9061i | −1.38621 | − | 1.16317i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.09955 | + | 5.18502i | −0.152720 | + | 0.377154i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.62594 | − | 1.36432i | −0.117649 | − | 0.0987190i | 0.582065 | − | 0.813142i | \(-0.302245\pi\) |
−0.699714 | + | 0.714423i | \(0.746689\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.28004 | − | 7.25947i | −0.0921393 | − | 0.522548i | −0.995586 | − | 0.0938486i | \(-0.970083\pi\) |
0.903447 | − | 0.428699i | \(-0.141028\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.00951 | − | 24.0763i | 0.430350 | − | 1.72414i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.546844 | − | 0.947161i | 0.0389610 | − | 0.0674824i | −0.845887 | − | 0.533362i | \(-0.820929\pi\) |
0.884848 | + | 0.465879i | \(0.154262\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.44607 | − | 9.43287i | −0.386062 | − | 0.668678i | 0.605854 | − | 0.795576i | \(-0.292831\pi\) |
−0.991916 | + | 0.126897i | \(0.959498\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.347400 | − | 3.31352i | −0.0245037 | − | 0.233717i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.37671 | − | 1.99430i | 0.166813 | − | 0.139972i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.39780 | − | 1.23670i | 0.237313 | − | 0.0863747i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.2940 | + | 10.1699i | −1.13251 | + | 0.706860i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.31944 | + | 7.48290i | −0.0912674 | + | 0.517603i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0707 | − | 4.39337i | −0.830980 | − | 0.302452i | −0.108719 | − | 0.994073i | \(-0.534675\pi\) |
−0.722261 | + | 0.691620i | \(0.756897\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.24639 | − | 0.157665i | −0.153920 | − | 0.0108031i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −21.8193 | −1.48806 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.98397 | −0.202565 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.34135 | − | 8.90692i | −0.293361 | − | 0.601874i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 32.8186 | + | 11.9450i | 2.20762 | + | 0.803507i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.41853 | − | 8.04489i | 0.0949919 | − | 0.538726i | −0.899758 | − | 0.436389i | \(-0.856257\pi\) |
0.994750 | − | 0.102336i | \(-0.0326318\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.19167 | − | 9.80573i | 0.212778 | − | 0.653715i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.0494 | − | 4.38563i | 0.799749 | − | 0.291085i | 0.0903664 | − | 0.995909i | \(-0.471196\pi\) |
0.709382 | + | 0.704824i | \(0.248974\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.86465 | + | 7.43833i | −0.585793 | + | 0.491538i | −0.886844 | − | 0.462070i | \(-0.847107\pi\) |
0.301051 | + | 0.953608i | \(0.402663\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.95240 | − | 2.65202i | −0.391639 | − | 0.174490i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.64371 | + | 8.04314i | 0.304219 | + | 0.526923i | 0.977087 | − | 0.212839i | \(-0.0682711\pi\) |
−0.672868 | + | 0.739763i | \(0.734938\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.81622 | + | 8.34193i | −0.314175 | + | 0.544168i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.9775 | − | 4.57701i | 1.03785 | − | 0.297309i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.591690 | + | 3.35564i | 0.0382732 | + | 0.217058i | 0.997946 | − | 0.0640613i | \(-0.0204053\pi\) |
−0.959673 | + | 0.281120i | \(0.909294\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.24976 | + | 1.04867i | 0.0805039 | + | 0.0675508i | 0.682152 | − | 0.731211i | \(-0.261044\pi\) |
−0.601648 | + | 0.798762i | \(0.705489\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.68709 | + | 15.3551i | 0.172377 | + | 0.985031i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.9971 | − | 10.9058i | −0.830353 | − | 0.696749i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.86220 | − | 10.5611i | −0.118489 | − | 0.671984i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.25505 | + | 1.21893i | −0.269653 | + | 0.0772464i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.89990 | − | 6.75483i | 0.246160 | − | 0.426361i | −0.716297 | − | 0.697795i | \(-0.754165\pi\) |
0.962457 | + | 0.271434i | \(0.0874980\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.1874 | − | 19.3771i | −0.703346 | − | 1.21823i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 32.5408 | + | 14.4981i | 2.03778 | + | 0.907909i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.7171 | + | 17.3837i | −1.29229 | + | 1.08436i | −0.300872 | + | 0.953664i | \(0.597278\pi\) |
−0.991422 | + | 0.130699i | \(0.958278\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.92257 | − | 3.24755i | 0.554421 | − | 0.201793i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.67595 | − | 8.22127i | 0.165637 | − | 0.508884i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.01502 | + | 5.75649i | −0.0625891 | + | 0.354960i | 0.937389 | + | 0.348285i | \(0.113236\pi\) |
−0.999978 | + | 0.00667518i | \(0.997875\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.15109 | + | 1.87484i | 0.316429 | + | 0.115171i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.69861 | − | 5.53660i | −0.165152 | − | 0.338835i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.88970 | −0.420072 | −0.210036 | − | 0.977694i | \(-0.567358\pi\) | ||||
−0.210036 | + | 0.977694i | \(0.567358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.3560 | 0.811321 | 0.405660 | − | 0.914024i | \(-0.367042\pi\) | ||||
0.405660 | + | 0.914024i | \(0.367042\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.17450 | + | 0.643923i | 0.555266 | + | 0.0389720i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.2882 | + | 4.10856i | 0.680703 | + | 0.247756i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.57154 | − | 14.5839i | 0.154509 | − | 0.876265i | −0.804724 | − | 0.593649i | \(-0.797687\pi\) |
0.959233 | − | 0.282616i | \(-0.0912021\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.05404 | + | 4.40279i | −0.422314 | + | 0.263588i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.64712 | − | 2.41935i | 0.396534 | − | 0.144327i | −0.136054 | − | 0.990701i | \(-0.543442\pi\) |
0.532588 | + | 0.846375i | \(0.321220\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.918128 | − | 0.770401i | 0.0545771 | − | 0.0457956i | −0.615091 | − | 0.788456i | \(-0.710881\pi\) |
0.669668 | + | 0.742660i | \(0.266436\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.14061 | − | 10.8792i | −0.0675638 | − | 0.644427i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.670065 | + | 1.16059i | 0.0395527 | + | 0.0685073i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5690 | + | 28.6984i | −0.974647 | + | 1.68814i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.86428 | + | 11.4754i | −0.167907 | + | 0.672698i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.73358 | − | 15.5029i | −0.159697 | − | 0.905688i | −0.954365 | − | 0.298643i | \(-0.903466\pi\) |
0.794668 | − | 0.607045i | \(-0.207645\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −30.9670 | − | 25.9844i | −1.80297 | − | 1.51287i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −17.9843 | + | 2.51334i | −1.04356 | + | 0.145838i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 24.1908 | + | 20.2985i | 1.39899 | + | 1.17389i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.40425 | − | 7.96392i | −0.0809399 | − | 0.459033i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.46072 | + | 5.27608i | 0.313710 | + | 0.303103i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.2012 | + | 38.4535i | −1.27123 | + | 2.20184i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.13677 | − | 15.8253i | −0.521463 | − | 0.903200i | −0.999688 | − | 0.0249632i | \(-0.992053\pi\) |
0.478225 | − | 0.878237i | \(-0.341280\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.0921 | − | 13.1376i | 1.02923 | − | 0.747370i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.9485 | + | 15.0605i | −1.01776 | + | 0.854005i | −0.989345 | − | 0.145591i | \(-0.953492\pi\) |
−0.0284189 | + | 0.999596i | \(0.509047\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.8400 | + | 8.67707i | −1.34752 | + | 0.490457i | −0.912173 | − | 0.409806i | \(-0.865596\pi\) |
−0.435346 | + | 0.900263i | \(0.643374\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.28933 | + | 1.31042i | 0.523394 | + | 0.0738338i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.558276 | + | 3.16614i | −0.0313559 | + | 0.177828i | −0.996464 | − | 0.0840249i | \(-0.973222\pi\) |
0.965108 | + | 0.261853i | \(0.0843336\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.46418 | + | 3.44468i | 0.529892 | + | 0.192865i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.72643 | + | 5.52158i | −0.207989 | + | 0.308185i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.3953 | 0.856620 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.9541 | −0.940446 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.5388 | + | 15.6157i | −0.582796 | + | 0.863550i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.35472 | − | 1.22102i | −0.184952 | − | 0.0673170i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.21547 | + | 6.89327i | −0.0668083 | + | 0.378889i | 0.933010 | + | 0.359849i | \(0.117172\pi\) |
−0.999819 | + | 0.0190393i | \(0.993939\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.3011 | − | 20.8422i | 0.893292 | − | 1.14215i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.25039 | + | 1.91098i | −0.286859 | + | 0.104408i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.0519 | − | 13.4691i | 0.874402 | − | 0.733710i | −0.0906185 | − | 0.995886i | \(-0.528884\pi\) |
0.965020 | + | 0.262176i | \(0.0844399\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.19926 | + | 5.22773i | −0.391010 | + | 0.283931i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.84327 | − | 8.38879i | −0.262278 | − | 0.454279i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.91207 | − | 11.9720i | 0.373216 | − | 0.646430i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 23.1652 | + | 22.3819i | 1.24717 | + | 1.20500i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.04316 | + | 5.91606i | 0.0559999 | + | 0.317591i | 0.999921 | − | 0.0125804i | \(-0.00400457\pi\) |
−0.943921 | + | 0.330171i | \(0.892893\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.2988 | + | 17.0327i | 1.08657 | + | 0.911738i | 0.996449 | − | 0.0841926i | \(-0.0268311\pi\) |
0.0901181 | + | 0.995931i | \(0.471276\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.6384 | − | 12.0146i | 1.20835 | − | 0.641291i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.734318 | + | 0.616166i | 0.0390838 | + | 0.0327952i | 0.662120 | − | 0.749398i | \(-0.269657\pi\) |
−0.623037 | + | 0.782193i | \(0.714101\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.655790 | + | 3.71917i | 0.0348057 | + | 0.197393i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.19747 | + | 12.8103i | −0.169228 | + | 0.677992i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.88101 | − | 11.9183i | 0.363166 | − | 0.629022i | −0.625314 | − | 0.780373i | \(-0.715029\pi\) |
0.988480 | + | 0.151351i | \(0.0483624\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.13636 | + | 12.3605i | 0.375598 | + | 0.650554i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.219088 | − | 2.08968i | −0.0114992 | − | 0.109680i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.7294 | + | 10.6813i | −0.666290 | + | 0.559083i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.3010 | − | 3.74925i | 0.537707 | − | 0.195709i | −0.0588694 | − | 0.998266i | \(-0.518750\pi\) |
0.596576 | + | 0.802556i | \(0.296527\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.29644 | + | 1.75493i | 0.171606 | + | 0.0913581i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.352792 | + | 2.00078i | −0.0183160 | + | 0.103875i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.7691 | + | 6.83140i | 0.971828 | + | 0.353716i | 0.778658 | − | 0.627449i | \(-0.215901\pi\) |
0.193170 | + | 0.981165i | \(0.438123\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.84251 | + | 0.550436i | 0.404986 | + | 0.0284244i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.2146 | −0.732089 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.8505 | 0.968285 | 0.484142 | − | 0.874989i | \(-0.339132\pi\) | ||||
0.484142 | + | 0.874989i | \(0.339132\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.19914 | − | 10.6668i | −0.266360 | − | 0.546477i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.3285 | + | 6.67102i | 0.936542 | + | 0.340873i | 0.764799 | − | 0.644269i | \(-0.222838\pi\) |
0.171742 | + | 0.985142i | \(0.445060\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.89769 | + | 10.7623i | −0.0967151 | + | 0.548499i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.0702 | − | 16.7546i | −0.766063 | − | 0.851683i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.4575 | + | 5.26210i | −0.733024 | + | 0.266799i | −0.681444 | − | 0.731870i | \(-0.738648\pi\) |
−0.0515798 | + | 0.998669i | \(0.516426\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −34.7283 | + | 29.1405i | −1.75629 | + | 1.47370i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −34.0953 | − | 15.1907i | −1.71988 | − | 0.766272i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.9363 | − | 24.1384i | −0.701211 | − | 1.21453i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.62904 | + | 13.2139i | −0.382891 | + | 0.663186i | −0.991474 | − | 0.130304i | \(-0.958405\pi\) |
0.608583 | + | 0.793490i | \(0.291738\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.89743 | − | 1.11648i | 0.195116 | − | 0.0558940i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.14588 | − | 12.1699i | −0.107160 | − | 0.607736i | −0.990335 | − | 0.138693i | \(-0.955710\pi\) |
0.883175 | − | 0.469043i | \(-0.155401\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.4727 | + | 8.78767i | 0.521684 | + | 0.437745i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 23.8933 | − | 10.6084i | 1.18727 | − | 0.527137i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.6120 | + | 19.8128i | 1.17040 | + | 0.982084i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.255472 | − | 1.44885i | −0.0126323 | − | 0.0716412i | 0.977840 | − | 0.209354i | \(-0.0671361\pi\) |
−0.990472 | + | 0.137713i | \(0.956025\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 35.6099 | − | 10.2010i | 1.75651 | − | 0.503180i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.49117 | − | 12.9751i | 0.368617 | − | 0.638463i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.71145 | + | 6.42842i | 0.182188 | + | 0.315559i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 31.2538 | + | 13.9247i | 1.53050 | + | 0.681898i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.6928 | + | 20.7198i | −1.20632 | + | 1.01223i | −0.206898 | + | 0.978363i | \(0.566337\pi\) |
−0.999426 | + | 0.0338638i | \(0.989219\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.6413 | − | 9.69665i | 1.29842 | − | 0.472586i | 0.401937 | − | 0.915667i | \(-0.368337\pi\) |
0.896481 | + | 0.443082i | \(0.146115\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.73208 | + | 2.06337i | −0.473190 | + | 0.100324i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.22648 | − | 23.9696i | 0.205015 | − | 1.16270i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.4642 | − | 5.62850i | −0.748363 | − | 0.272382i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.0808 | + | 26.8373i | 0.631549 | + | 1.29572i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.64545 | −0.223764 | −0.111882 | − | 0.993722i | \(-0.535688\pi\) | ||||
−0.111882 | + | 0.993722i | \(0.535688\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.4386 | 0.645818 | 0.322909 | − | 0.946430i | \(-0.395339\pi\) | ||||
0.322909 | + | 0.946430i | \(0.395339\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.4638 | − | 1.01516i | −0.693484 | − | 0.0486730i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.0809 | + | 4.76106i | 0.625745 | + | 0.227753i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.899835 | − | 5.10322i | 0.0429468 | − | 0.243563i | −0.955776 | − | 0.294097i | \(-0.904981\pi\) |
0.998722 | + | 0.0505338i | \(0.0160923\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.602505 | − | 17.5127i | −0.0286907 | − | 0.833938i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.7897 | − | 6.47493i | 0.845216 | − | 0.307633i | 0.117128 | − | 0.993117i | \(-0.462631\pi\) |
0.728088 | + | 0.685483i | \(0.240409\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.91271 | + | 6.63955i | −0.375098 | + | 0.314745i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.493770 | − | 4.70960i | −0.0233545 | − | 0.222756i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.37884 | + | 16.2446i | 0.442615 | + | 0.766631i | 0.997883 | − | 0.0650402i | \(-0.0207176\pi\) |
−0.555268 | + | 0.831672i | \(0.687384\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.17516 | + | 3.76749i | −0.102424 | + | 0.177404i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.58771 | − | 34.4056i | 0.403486 | − | 1.61652i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.67832 | − | 15.1895i | −0.125562 | − | 0.712095i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.2001 | + | 16.1108i | 0.898143 | + | 0.753631i | 0.969826 | − | 0.243796i | \(-0.0783928\pi\) |
−0.0716839 | + | 0.997427i | \(0.522837\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.3426 | + | 35.0010i | 0.529426 | + | 1.63371i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.41301 | + | 7.89845i | 0.438408 | + | 0.367868i | 0.835113 | − | 0.550078i | \(-0.185402\pi\) |
−0.396706 | + | 0.917946i | \(0.629847\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.99174 | − | 16.9670i | −0.139038 | − | 0.788525i | −0.971962 | − | 0.235137i | \(-0.924446\pi\) |
0.832924 | − | 0.553387i | \(-0.186665\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.0287 | + | 9.68963i | 0.465071 | + | 0.449346i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.84287 | + | 15.3163i | −0.409199 | + | 0.708754i | −0.994800 | − | 0.101846i | \(-0.967525\pi\) |
0.585601 | + | 0.810600i | \(0.300859\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.03541 | − | 1.79338i | −0.0478106 | − | 0.0828104i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.60474 | + | 4.79602i | −0.304330 | + | 0.220989i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.1096 | − | 16.8740i | 0.924641 | − | 0.775866i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.02291 | + | 2.55613i | −0.322233 | + | 0.117283i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.11812 | + | 5.25034i | 0.0969822 | + | 0.240397i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.80736 | − | 15.9213i | 0.128272 | − | 0.727464i | −0.851039 | − | 0.525102i | \(-0.824027\pi\) |
0.979311 | − | 0.202362i | \(-0.0648618\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −40.8792 | − | 14.8788i | −1.86393 | − | 0.678415i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.67841 | + | 9.89564i | −0.303878 | + | 0.450267i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.8350 | 0.900663 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.1628 | 1.27618 | 0.638088 | − | 0.769963i | \(-0.279725\pi\) | ||||
0.638088 | + | 0.769963i | \(0.279725\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.2001 | + | 35.8582i | −1.09437 | + | 1.62156i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.64776 | − | 1.32768i | −0.164621 | − | 0.0599172i | 0.258395 | − | 0.966039i | \(-0.416806\pi\) |
−0.423016 | + | 0.906122i | \(0.639029\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.54355 | − | 20.0964i | 0.159593 | − | 0.905099i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.3935 | + | 28.2419i | 0.512100 | + | 1.26938i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.31527 | + | 0.478720i | −0.0589980 | + | 0.0214735i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.94018 | + | 3.30620i | −0.176387 | + | 0.148006i | −0.726707 | − | 0.686948i | \(-0.758950\pi\) |
0.550320 | + | 0.834954i | \(0.314506\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.9806 | + | 15.9611i | −0.982019 | + | 0.713091i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.4751 | − | 25.0716i | −0.645412 | − | 1.11789i | −0.984206 | − | 0.177026i | \(-0.943352\pi\) |
0.338794 | − | 0.940861i | \(-0.389981\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.36703 | − | 11.0280i | 0.283329 | − | 0.490741i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.1100 | − | 13.6329i | −0.626648 | − | 0.605460i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.18488 | + | 23.7337i | 0.185492 | + | 1.05198i | 0.925322 | + | 0.379182i | \(0.123795\pi\) |
−0.739830 | + | 0.672793i | \(0.765094\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.71786 | − | 3.95875i | −0.208706 | − | 0.175125i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.56610 | − | 8.38993i | 0.334051 | − | 0.370424i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −28.7242 | − | 24.1024i | −1.26574 | − | 1.06208i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.01241 | − | 11.4129i | −0.0885055 | − | 0.501940i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.76653 | + | 19.0965i | −0.209227 | + | 0.838243i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.53592 | + | 14.7846i | −0.373965 | + | 0.647727i | −0.990172 | − | 0.139858i | \(-0.955335\pi\) |
0.616206 | + | 0.787585i | \(0.288669\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.43922 | + | 16.3492i | 0.412748 | + | 0.714901i | 0.995189 | − | 0.0979723i | \(-0.0312356\pi\) |
−0.582441 | + | 0.812873i | \(0.697902\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.668330 | − | 6.37456i | −0.0291683 | − | 0.278209i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.0347 | + | 12.6156i | −0.654920 | + | 0.549543i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.9064 | + | 6.15342i | −0.735060 | + | 0.267540i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.43554 | − | 41.7259i | −0.0622969 | − | 1.81075i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.06618 | − | 6.04659i | 0.0461812 | − | 0.261907i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.4977 | + | 3.82084i | 0.453854 | + | 0.165189i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.5180 | + | 1.79101i | 1.10118 | + | 0.0772877i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.4127 | 0.879239 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.24128 | −0.354320 | −0.177160 | − | 0.984182i | \(-0.556691\pi\) | ||||
−0.177160 | + | 0.984182i | \(0.556691\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.6179 | − | 23.8359i | −0.498572 | − | 1.02289i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 29.6887 | + | 10.8058i | 1.27172 | + | 0.462870i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.61233 | − | 31.8291i | 0.239966 | − | 1.36091i | −0.591934 | − | 0.805987i | \(-0.701635\pi\) |
0.831899 | − | 0.554927i | \(-0.187254\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −44.8617 | + | 9.51144i | −1.91465 | + | 0.405938i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.88811 | + | 2.14310i | −0.250842 | + | 0.0912990i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.91346 | − | 6.64018i | 0.336515 | − | 0.282369i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −40.5331 | − | 18.0590i | −1.72053 | − | 0.766563i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.10631 | − | 7.11234i | −0.173990 | − | 0.301360i | 0.765821 | − | 0.643053i | \(-0.222333\pi\) |
−0.939811 | + | 0.341694i | \(0.888999\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.5250 | + | 32.0862i | −0.783523 | + | 1.35710i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −41.2032 | + | 11.8033i | −1.73960 | + | 0.498336i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.28986 | − | 7.31517i | −0.0543612 | − | 0.308298i | 0.945488 | − | 0.325657i | \(-0.105585\pi\) |
−0.999849 | + | 0.0173588i | \(0.994474\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.4300 | + | 9.59089i | 0.480863 | + | 0.403492i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.40975 | + | 8.03817i | 0.227188 | + | 0.337571i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.8325 | − | 15.8024i | −0.789500 | − | 0.662469i | 0.156121 | − | 0.987738i | \(-0.450101\pi\) |
−0.945622 | + | 0.325268i | \(0.894545\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.70985 | + | 43.7247i | 0.322647 | + | 1.82982i | 0.525719 | + | 0.850658i | \(0.323796\pi\) |
−0.203072 | + | 0.979164i | \(0.565093\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.53415 | + | 1.01241i | −0.147641 | + | 0.0422942i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.0038 | − | 19.0591i | 0.458889 | − | 0.794819i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.599153 | + | 1.03776i | 0.0249431 | + | 0.0432027i | 0.878227 | − | 0.478243i | \(-0.158726\pi\) |
−0.853284 | + | 0.521446i | \(0.825393\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.6626 | − | 5.19612i | −0.484680 | − | 0.215943i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.10748 | + | 1.76838i | −0.0874328 | + | 0.0733648i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.19738 | + | 2.25566i | −0.256669 | + | 0.0934200i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −28.7433 | − | 31.9558i | −1.18839 | − | 1.32121i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.33127 | + | 35.9064i | −0.261319 | + | 1.48202i | 0.517996 | + | 0.855383i | \(0.326678\pi\) |
−0.779315 | + | 0.626632i | \(0.784433\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.66302 | + | 2.06117i | 0.233340 | + | 0.0849290i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.829976 | − | 1.70282i | −0.0341407 | − | 0.0700446i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.8744 | 1.10360 | 0.551800 | − | 0.833977i | \(-0.313941\pi\) | ||||
0.551800 | + | 0.833977i | \(0.313941\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.1424 | 0.907751 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.8194 | − | 1.32086i | −0.770229 | − | 0.0540594i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.3665 | + | 4.13706i | 0.464422 | + | 0.169036i | 0.563624 | − | 0.826032i | \(-0.309407\pi\) |
−0.0992019 | + | 0.995067i | \(0.531629\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.30085 | + | 13.0487i | −0.0938535 | + | 0.532270i | 0.901239 | + | 0.433322i | \(0.142659\pi\) |
−0.995093 | + | 0.0989476i | \(0.968452\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.09377 | − | 2.71178i | −0.207434 | − | 0.110432i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.31117 | + | 1.20517i | −0.134618 | + | 0.0489970i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.4783 | − | 23.8961i | 1.15590 | − | 0.969914i | 0.156058 | − | 0.987748i | \(-0.450121\pi\) |
0.999841 | + | 0.0178336i | \(0.00567691\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.560338 | − | 5.34453i | −0.0227060 | − | 0.216571i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.17811 | + | 14.1649i | 0.330851 | + | 0.573051i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.12248 | + | 10.6044i | −0.247284 | + | 0.428309i | −0.962771 | − | 0.270317i | \(-0.912872\pi\) |
0.715487 | + | 0.698626i | \(0.246205\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.51669 | − | 6.07643i | 0.0611589 | − | 0.245025i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.56176 | − | 14.5284i | −0.103132 | − | 0.584893i | −0.991950 | − | 0.126631i | \(-0.959583\pi\) |
0.888817 | − | 0.458261i | \(-0.151528\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.0753697 | − | 0.0632427i | −0.00302936 | − | 0.00254194i | 0.641272 | − | 0.767314i | \(-0.278407\pi\) |
−0.644301 | + | 0.764772i | \(0.722852\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.18678 | + | 33.2469i | −0.0476240 | + | 1.33415i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.93265 | − | 2.46079i | −0.117494 | − | 0.0985893i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.27393 | − | 29.9099i | −0.210957 | − | 1.19640i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.46466 | + | 9.14464i | 0.377982 | + | 0.365202i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.2262 | − | 54.0854i | 1.24507 | − | 2.15652i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.793583 | − | 1.37453i | −0.0315921 | − | 0.0547190i | 0.849797 | − | 0.527110i | \(-0.176724\pi\) |
−0.881389 | + | 0.472391i | \(0.843391\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.0030 | + | 13.0729i | −0.715557 | + | 0.519600i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.2446 | + | 12.7918i | −0.604964 | + | 0.507625i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27.0723 | + | 9.85350i | −1.07264 | + | 0.390410i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.40293 | + | 3.07234i | −0.0950585 | + | 0.121540i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.33921 | + | 7.59503i | −0.0528956 | + | 0.299986i | −0.999766 | − | 0.0216294i | \(-0.993115\pi\) |
0.946870 | + | 0.321615i | \(0.104226\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.0605107 | + | 0.0220241i | 0.00238631 | + | 0.000868545i | 0.343213 | − | 0.939258i | \(-0.388485\pi\) |
−0.340827 | + | 0.940126i | \(0.610707\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −21.1412 | + | 31.3256i | −0.832432 | + | 1.23344i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.2653 | 1.30780 | 0.653898 | − | 0.756583i | \(-0.273133\pi\) | ||||
0.653898 | + | 0.756583i | \(0.273133\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 48.6356 | 1.90911 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.89123 | + | 4.28404i | −0.113316 | + | 0.167905i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.98055 | − | 0.720861i | −0.0775049 | − | 0.0282095i | 0.302977 | − | 0.952998i | \(-0.402020\pi\) |
−0.380482 | + | 0.924788i | \(0.624242\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.8699 | + | 61.6465i | −0.424724 | + | 2.40873i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.9940 | − | 2.39729i | −0.662998 | − | 0.0935273i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.24248 | − | 3.00002i | 0.321081 | − | 0.116864i | −0.176451 | − | 0.984309i | \(-0.556462\pi\) |
0.497533 | + | 0.867445i | \(0.334240\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.5416 | − | 21.4319i | 0.993453 | − | 0.833606i | 0.00738903 | − | 0.999973i | \(-0.497648\pi\) |
0.986064 | + | 0.166367i | \(0.0532035\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 48.9478 | − | 35.5434i | 1.90098 | − | 1.38039i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.39952 | − | 5.88814i | −0.131828 | − | 0.228332i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.22573 | − | 15.9794i | 0.357222 | − | 0.618726i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.1755 | − | 9.83143i | −0.393407 | − | 0.380105i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.27652 | − | 52.6098i | −0.358116 | − | 2.03098i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.2710 | − | 26.2395i | −1.20541 | − | 1.01146i | −0.999459 | − | 0.0328940i | \(-0.989528\pi\) |
−0.205948 | − | 0.978563i | \(-0.566028\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.9855 | − | 14.0832i | −0.422831 | − | 0.542063i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.8176 | − | 30.8936i | −1.41501 | − | 1.18734i | −0.953948 | − | 0.299972i | \(-0.903023\pi\) |
−0.461066 | − | 0.887366i | \(-0.652533\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.27655 | + | 7.23968i | 0.0489896 | + | 0.277834i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.37856 | − | 21.5485i | 0.206107 | − | 0.825741i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.0527 | − | 26.0720i | 0.575975 | − | 0.997619i | −0.419960 | − | 0.907543i | \(-0.637956\pi\) |
0.995935 | − | 0.0900758i | \(-0.0287109\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.0606 | − | 53.7986i | −1.18676 | − | 2.05554i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.08995 | + | 19.9340i | 0.0797364 | + | 0.760530i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.13040 | − | 5.98312i | 0.271647 | − | 0.227939i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.0660 | + | 9.85122i | −1.02964 | + | 0.374758i | −0.800944 | − | 0.598740i | \(-0.795668\pi\) |
−0.228696 | + | 0.973498i | \(0.573446\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.57487 | + | 5.97617i | −0.363719 | + | 0.227016i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.96403 | − | 56.5088i | 0.377957 | − | 2.14350i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.28281 | + | 3.01470i | 0.313734 | + | 0.114190i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.0468 | + | 1.12626i | 0.606946 | + | 0.0425992i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.0584 | 0.379902 | 0.189951 | − | 0.981794i | \(-0.439167\pi\) | ||||
0.189951 | + | 0.981794i | \(0.439167\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.1766 | −0.723259 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.30985 | + | 14.9972i | 0.275305 | + | 0.564829i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.43494 | + | 1.61419i | 0.166793 | + | 0.0607078i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.65867 | + | 37.7632i | −0.250071 | + | 1.41823i | 0.558342 | + | 0.829611i | \(0.311438\pi\) |
−0.808414 | + | 0.588615i | \(0.799673\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.90978 | − | 27.3734i | 0.334143 | − | 1.02658i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.6759 | + | 6.06952i | −0.624516 | + | 0.227305i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 38.3549 | − | 32.1836i | 1.43439 | − | 1.20360i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.39094 | + | 2.40187i | 0.201328 | + | 0.0896995i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.63910 | + | 8.03516i | 0.173009 | + | 0.299661i | 0.939471 | − | 0.342630i | \(-0.111318\pi\) |
−0.766461 | + | 0.642290i | \(0.777984\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.94862 | − | 12.0354i | 0.258780 | − | 0.448220i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.71648 | − | 0.778178i | 0.101027 | − | 0.0289407i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.72020 | + | 9.75576i | 0.0638868 | + | 0.362320i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.1660 | + | 17.7604i | 0.785004 | + | 0.658696i | 0.944503 | − | 0.328502i | \(-0.106544\pi\) |
−0.159500 | + | 0.987198i | \(0.550988\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.6487 | + | 11.0201i | 0.912914 | + | 0.408151i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −40.7450 | − | 34.1891i | −1.50701 | − | 1.26453i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.68032 | + | 43.5573i | 0.283679 | + | 1.60882i | 0.709966 | + | 0.704236i | \(0.248710\pi\) |
−0.426286 | + | 0.904588i | \(0.640178\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −28.2505 | + | 8.09281i | −1.04204 | + | 0.298508i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.36113 | − | 5.82164i | 0.123809 | − | 0.214443i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.02889 | − | 1.78209i | −0.0378484 | − | 0.0655553i | 0.846481 | − | 0.532419i | \(-0.178717\pi\) |
−0.884329 | + | 0.466864i | \(0.845384\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.9667 | − | 7.55931i | −0.623287 | − | 0.277698i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.2183 | + | 18.6434i | −0.815111 | + | 0.683959i | −0.951822 | − | 0.306652i | \(-0.900791\pi\) |
0.136711 | + | 0.990611i | \(0.456347\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.46254 | + | 2.71614i | −0.273406 | + | 0.0995117i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.37281 | + | 7.28995i | −0.0868166 | + | 0.266725i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.718973 | + | 4.07750i | −0.0262707 | + | 0.148989i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.44493 | − | 0.889882i | −0.0892168 | − | 0.0324723i | 0.297026 | − | 0.954869i | \(-0.404005\pi\) |
−0.386243 | + | 0.922397i | \(0.626227\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.91911 | − | 12.1439i | −0.215704 | − | 0.442549i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −59.4697 | −2.16432 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.54321 | 0.0560890 | 0.0280445 | − | 0.999607i | \(-0.491072\pi\) | ||||
0.0280445 | + | 0.999607i | \(0.491072\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −38.6592 | − | 2.71334i | −1.40324 | − | 0.0984880i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.2016 | − | 8.44468i | −0.841057 | − | 0.306120i | −0.114668 | − | 0.993404i | \(-0.536580\pi\) |
−0.726388 | + | 0.687284i | \(0.758803\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.03334 | + | 11.5317i | −0.0736120 | + | 0.417474i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 52.3442 | − | 32.6707i | 1.89251 | − | 1.18121i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −64.5027 | + | 23.4770i | −2.32906 | + | 0.847707i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.9729 | + | 10.8856i | −0.467815 | + | 0.392544i | −0.845997 | − | 0.533188i | \(-0.820994\pi\) |
0.378182 | + | 0.925731i | \(0.376550\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.88429 | + | 46.5866i | 0.175903 | + | 1.67777i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.52442 | − | 7.83653i | −0.162732 | − | 0.281860i | 0.773116 | − | 0.634265i | \(-0.218697\pi\) |
−0.935848 | + | 0.352405i | \(0.885364\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.76378 | − | 8.25110i | 0.171120 | − | 0.296388i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.98281 | − | 15.9566i | 0.142882 | − | 0.572441i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.469986 | − | 2.66542i | −0.0168390 | − | 0.0954986i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.48063 | − | 2.92060i | −0.124547 | − | 0.104507i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.21038 | − | 11.8076i | −0.329152 | − | 0.421968i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.4861 | + | 8.79887i | 0.374264 | + | 0.314045i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.79697 | − | 21.5337i | −0.135347 | − | 0.767592i | −0.974617 | − | 0.223878i | \(-0.928128\pi\) |
0.839270 | − | 0.543715i | \(-0.182983\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.28103 | + | 7.03484i | 0.259211 | + | 0.250447i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.76501 | + | 4.78914i | −0.0983124 | + | 0.170282i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 37.6984 | + | 65.2955i | 1.33871 | + | 2.31871i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.68268 | − | 5.57876i | 0.272477 | − | 0.197858i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.1313 | + | 17.7312i | −0.748507 | + | 0.628072i | −0.935108 | − | 0.354364i | \(-0.884697\pi\) |
0.186600 | + | 0.982436i | \(0.440253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.0649 | + | 8.03097i | −0.780600 | + | 0.284115i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.5636 | − | 1.49017i | −0.373245 | − | 0.0526527i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.47164 | − | 19.6887i | 0.122512 | − | 0.694798i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.8137 | + | 6.84762i | 0.663095 | + | 0.241347i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.67557 | + | 9.89144i | −0.234991 | + | 0.348195i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.52715 | 0.194324 | 0.0971621 | − | 0.995269i | \(-0.469023\pi\) | ||||
0.0971621 | + | 0.995269i | \(0.469023\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.7570 | 1.04491 | 0.522454 | − | 0.852667i | \(-0.325017\pi\) | ||||
0.522454 | + | 0.852667i | \(0.325017\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.9409 | − | 19.1750i | 0.453858 | − | 0.672498i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 68.1740 | + | 24.8133i | 2.38803 | + | 0.869172i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.83605 | + | 16.0840i | −0.0992207 | + | 0.562708i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.81384 | − | 12.5478i | 0.342923 | − | 0.438455i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.1564 | − | 13.1599i | 1.26187 | − | 0.459282i | 0.377472 | − | 0.926021i | \(-0.376793\pi\) |
0.884395 | + | 0.466739i | \(0.154571\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.0223 | + | 19.3180i | −0.802507 | + | 0.673383i | −0.948807 | − | 0.315857i | \(-0.897708\pi\) |
0.146300 | + | 0.989240i | \(0.453264\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 16.8360 | − | 12.2254i | 0.586153 | − | 0.425634i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.21104 | + | 9.02579i | 0.181206 | + | 0.313857i | 0.942291 | − | 0.334794i | \(-0.108667\pi\) |
−0.761086 | + | 0.648651i | \(0.775333\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.86269 | + | 10.1545i | −0.203620 | + | 0.352679i | −0.949692 | − | 0.313185i | \(-0.898604\pi\) |
0.746072 | + | 0.665865i | \(0.231937\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.4463 | − | 17.8226i | −0.639896 | − | 0.618260i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.18195 | − | 40.7309i | −0.248840 | − | 1.41124i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 34.8977 | + | 29.2826i | 1.20768 | + | 1.01337i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.513785 | + | 14.3933i | −0.0177590 | + | 0.497506i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.16305 | + | 0.975911i | 0.0401528 | + | 0.0336922i | 0.662643 | − | 0.748935i | \(-0.269435\pi\) |
−0.622490 | + | 0.782627i | \(0.713879\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.59355 | − | 20.3800i | −0.123916 | − | 0.702760i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.96710 | − | 11.8873i | 0.102193 | − | 0.409422i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.4518 | + | 28.4954i | −0.565961 | + | 0.980273i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.652981 | − | 1.13100i | −0.0224367 | − | 0.0388615i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.216460 | − | 2.06460i | −0.00742887 | − | 0.0708569i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 43.2580 | − | 36.2977i | 1.48286 | − | 1.24427i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.0903 | − | 6.58434i | 0.619401 | − | 0.225444i | −0.0132104 | − | 0.999913i | \(-0.504205\pi\) |
0.632612 | + | 0.774469i | \(0.281983\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.7242 | − | 8.90351i | −0.571957 | − | 0.304494i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.47302 | − | 31.0390i | 0.186955 | − | 1.06027i | −0.736463 | − | 0.676478i | \(-0.763506\pi\) |
0.923418 | − | 0.383796i | \(-0.125383\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.4260 | − | 4.88666i | −0.458089 | − | 0.166731i | 0.102660 | − | 0.994716i | \(-0.467265\pi\) |
−0.560749 | + | 0.827986i | \(0.689487\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.31548 | + | 0.162515i | 0.0789113 | + | 0.00553848i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.2533 | 0.893672 | 0.446836 | − | 0.894616i | \(-0.352551\pi\) | ||||
0.446836 | + | 0.894616i | \(0.352551\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.0081 | 1.12231 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25.1477 | + | 51.5943i | 0.854062 | + | 1.75223i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31.5118 | + | 11.4693i | 1.06896 | + | 0.389071i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.64749 | + | 9.34338i | −0.0558231 | + | 0.316588i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.6998 | + | 15.2309i | 0.463666 | + | 0.515489i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.59183 | − | 1.67129i | 0.155232 | − | 0.0564999i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.52599 | + | 4.63686i | −0.186599 | + | 0.156576i | −0.731302 | − | 0.682054i | \(-0.761087\pi\) |
0.544703 | + | 0.838629i | \(0.316643\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.9059 | − | 11.0965i | −0.840054 | − | 0.374276i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.5633 | + | 44.2769i | 0.861249 | + | 1.49173i | 0.870724 | + | 0.491773i | \(0.163651\pi\) |
−0.00947431 | + | 0.999955i | \(0.503016\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.77384 | − | 3.07239i | 0.0596946 | − | 0.103394i | −0.834634 | − | 0.550805i | \(-0.814321\pi\) |
0.894328 | + | 0.447411i | \(0.147654\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −67.3099 | + | 19.2820i | −2.26260 | + | 0.648158i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.39045 | + | 36.2420i | 0.214570 | + | 1.21689i | 0.881651 | + | 0.471903i | \(0.156433\pi\) |
−0.667080 | + | 0.744986i | \(0.732456\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.65004 | − | 4.74095i | −0.189496 | − | 0.159006i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.8170 | + | 28.2551i | −0.462889 | + | 0.946581i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.52322 | + | 4.63453i | 0.184828 | + | 0.155089i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.44948 | − | 42.2481i | −0.249009 | − | 1.41220i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 52.5813 | − | 15.0628i | 1.75564 | − | 0.502931i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.99402 | − | 6.91785i | 0.133208 | − | 0.230723i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.68133 | + | 11.5724i | 0.222588 | + | 0.385533i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.7943 | − | 5.70034i | −0.425768 | − | 0.189696i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −34.0653 | + | 28.5842i | −1.13237 | + | 0.950171i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.8043 | + | 6.11628i | −0.557979 | + | 0.203088i | −0.605588 | − | 0.795778i | \(-0.707062\pi\) |
0.0476090 | + | 0.998866i | \(0.484840\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.8658 | − | 2.72777i | 0.426732 | − | 0.0904744i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.42880 | + | 42.1308i | −0.246127 | + | 1.39586i | 0.571733 | + | 0.820440i | \(0.306271\pi\) |
−0.817860 | + | 0.575417i | \(0.804840\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.39206 | − | 3.05446i | −0.277737 | − | 0.101088i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 33.6960 | + | 69.1323i | 1.11396 | + | 2.28544i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23.2002 | −0.766138 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.89290 | −0.194389 | −0.0971944 | − | 0.995265i | \(-0.530987\pi\) | ||||
−0.0971944 | + | 0.995265i | \(0.530987\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.5730 | − | 2.21599i | −1.04037 | − | 0.0730194i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.02598 | + | 2.19328i | 0.198348 | + | 0.0721926i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.26455 | + | 29.8567i | −0.173097 | + | 0.981684i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.33157 | − | 38.7039i | −0.0437343 | − | 1.27120i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.0428 | − | 12.7546i | 1.14972 | − | 0.418463i | 0.304304 | − | 0.952575i | \(-0.401576\pi\) |
0.845414 | + | 0.534112i | \(0.179354\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.72856 | + | 8.16323i | −0.318841 | + | 0.267539i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.23156 | + | 40.3608i | 0.138535 | + | 1.32135i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 35.9393 | + | 62.2487i | 1.17534 | + | 2.03575i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.42858 | − | 16.3308i | 0.308018 | − | 0.533503i | −0.669910 | − | 0.742442i | \(-0.733668\pi\) |
0.977929 | + | 0.208938i | \(0.0670008\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.6416 | + | 42.6342i | −0.347275 | + | 1.39131i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.26953 | + | 41.2276i | 0.236980 | + | 1.34398i | 0.838404 | + | 0.545050i | \(0.183489\pi\) |
−0.601424 | + | 0.798930i | \(0.705400\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.10533 | + | 5.12298i | 0.198817 | + | 0.166827i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.8820 | − | 12.0669i | 0.353991 | − | 0.392535i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.5259 | − | 21.4188i | −0.829481 | − | 0.696017i | 0.125691 | − | 0.992069i | \(-0.459885\pi\) |
−0.955172 | + | 0.296053i | \(0.904330\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.89974 | + | 27.7878i | 0.159052 | + | 0.902030i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.00465 | + | 3.86925i | 0.129860 | + | 0.125469i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.4362 | − | 38.8607i | 0.726781 | − | 1.25882i | −0.231456 | − | 0.972845i | \(-0.574349\pi\) |
0.958237 | − | 0.285976i | \(-0.0923177\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.08264 | + | 5.33930i | 0.0997520 | + | 0.172776i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.1155 | − | 10.2500i | 0.456290 | − | 0.331334i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.6372 | − | 14.7993i | 0.569534 | − | 0.477896i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.9111 | − | 7.97500i | 0.706810 | − | 0.257258i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.31664 | + | 10.7000i | 0.139102 | + | 0.344801i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.71815 | + | 21.0867i | −0.119691 | + | 0.678804i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.03992 | − | 2.56232i | −0.226389 | − | 0.0823987i | 0.226335 | − | 0.974049i | \(-0.427325\pi\) |
−0.452724 | + | 0.891651i | \(0.649548\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.9169 | − | 22.1029i | 0.479199 | − | 0.710046i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.9164 | 0.831698 | 0.415849 | − | 0.909434i | \(-0.363485\pi\) | ||||
0.415849 | + | 0.909434i | \(0.363485\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.2667 | 0.681779 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.4272 | + | 24.3408i | −0.526092 | + | 0.779530i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.1356 | − | 6.60080i | −0.580208 | − | 0.211178i | 0.0352094 | − | 0.999380i | \(-0.488790\pi\) |
−0.615417 | + | 0.788202i | \(0.711012\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.15800 | − | 12.2386i | 0.0689699 | − | 0.391148i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.2080 | + | 30.2608i | 0.389771 | + | 0.966152i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.0238 | − | 16.3873i | 1.43604 | − | 0.522675i | 0.497382 | − | 0.867532i | \(-0.334295\pi\) |
0.938655 | + | 0.344857i | \(0.112073\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.43361 | + | 2.04204i | −0.0775412 | + | 0.0650648i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.00346 | + | 3.63326i | −0.159262 | + | 0.115648i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.0466 | − | 41.6499i | −0.764637 | − | 1.32439i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.09981 | − | 15.7613i | 0.289065 | − | 0.500675i | −0.684522 | − | 0.728992i | \(-0.739989\pi\) |
0.973587 | + | 0.228317i | \(0.0733223\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.71887 | + | 8.42407i | 0.276685 | + | 0.267330i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.49398 | + | 31.1579i | 0.174171 | + | 0.987771i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.7385 | − | 14.8844i | −0.561785 | − | 0.471394i | 0.317123 | − | 0.948384i | \(-0.397283\pi\) |
−0.878908 | + | 0.476990i | \(0.841728\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.1284 | − | 43.5976i | −0.447003 | − | 1.37937i |
(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.f.97.4 | 30 | ||
4.3 | odd | 2 | 216.2.q.b.97.2 | yes | 30 | ||
12.11 | even | 2 | 648.2.q.b.289.4 | 30 | |||
27.22 | even | 9 | inner | 432.2.u.f.49.4 | 30 | ||
108.7 | odd | 18 | 5832.2.a.k.1.13 | 15 | |||
108.47 | even | 18 | 5832.2.a.l.1.3 | 15 | |||
108.59 | even | 18 | 648.2.q.b.361.4 | 30 | |||
108.103 | odd | 18 | 216.2.q.b.49.2 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.q.b.49.2 | ✓ | 30 | 108.103 | odd | 18 | ||
216.2.q.b.97.2 | yes | 30 | 4.3 | odd | 2 | ||
432.2.u.f.49.4 | 30 | 27.22 | even | 9 | inner | ||
432.2.u.f.97.4 | 30 | 1.1 | even | 1 | trivial | ||
648.2.q.b.289.4 | 30 | 12.11 | even | 2 | |||
648.2.q.b.361.4 | 30 | 108.59 | even | 18 | |||
5832.2.a.k.1.13 | 15 | 108.7 | odd | 18 | |||
5832.2.a.l.1.3 | 15 | 108.47 | even | 18 |