Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(521,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.521");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.t (of order \(6\), degree \(2\), 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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{48})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1097.6 | ||
Root | \(0.130526 - 0.991445i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1097 |
Dual form | 1764.2.t.c.521.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.382683 | − | 0.662827i | 0.171141 | − | 0.296425i | −0.767678 | − | 0.640836i | \(-0.778588\pi\) |
0.938819 | + | 0.344411i | \(0.111921\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.73205 | − | 1.00000i | 0.522233 | − | 0.301511i | −0.215615 | − | 0.976478i | \(-0.569176\pi\) |
0.737848 | + | 0.674967i | \(0.235842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.317025i | 0.0879270i | 0.999033 | + | 0.0439635i | \(0.0139985\pi\) | ||||
−0.999033 | + | 0.0439635i | \(0.986001\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.77164 | + | 4.80062i | 0.672221 | + | 1.16432i | 0.977273 | + | 0.211985i | \(0.0679929\pi\) |
−0.305052 | + | 0.952336i | \(0.598674\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.20041 | + | 1.84776i | 0.734225 | + | 0.423905i | 0.819966 | − | 0.572412i | \(-0.193992\pi\) |
−0.0857408 | + | 0.996317i | \(0.527326\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.74666 | − | 1.58579i | −0.572719 | − | 0.330659i | 0.185516 | − | 0.982641i | \(-0.440604\pi\) |
−0.758234 | + | 0.651982i | \(0.773938\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.20711 | + | 3.82282i | 0.441421 | + | 0.764564i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.82843i | − | 1.26801i | −0.773330 | − | 0.634004i | \(-0.781410\pi\) | ||
0.773330 | − | 0.634004i | \(-0.218590\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.85172 | + | 3.37849i | −1.05100 | + | 0.606795i | −0.922929 | − | 0.384970i | \(-0.874212\pi\) |
−0.128071 | + | 0.991765i | \(0.540879\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.121320 | − | 0.210133i | 0.0199449 | − | 0.0345457i | −0.855881 | − | 0.517173i | \(-0.826984\pi\) |
0.875826 | + | 0.482628i | \(0.160318\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.74444 | 0.428610 | 0.214305 | − | 0.976767i | \(-0.431251\pi\) | ||||
0.214305 | + | 0.976767i | \(0.431251\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.82843 | 1.04133 | 0.520663 | − | 0.853762i | \(-0.325685\pi\) | ||||
0.520663 | + | 0.853762i | \(0.325685\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.99162 | − | 10.3778i | 0.873967 | − | 1.51376i | 0.0161088 | − | 0.999870i | \(-0.494872\pi\) |
0.857859 | − | 0.513886i | \(-0.171794\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.6024 | − | 6.12132i | 1.45636 | − | 0.840828i | 0.457527 | − | 0.889196i | \(-0.348735\pi\) |
0.998830 | + | 0.0483676i | \(0.0154019\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.53073i | − | 0.206404i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.62567 | + | 11.4760i | 0.862589 | + | 1.49405i | 0.869422 | + | 0.494071i | \(0.164492\pi\) |
−0.00683301 | + | 0.999977i | \(0.502175\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.08669 | + | 1.78210i | 0.395210 | + | 0.228175i | 0.684415 | − | 0.729093i | \(-0.260058\pi\) |
−0.289205 | + | 0.957267i | \(0.593391\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.210133 | + | 0.121320i | 0.0260638 | + | 0.0150479i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.24264 | + | 3.88437i | 0.273982 | + | 0.474551i | 0.969878 | − | 0.243592i | \(-0.0783257\pi\) |
−0.695896 | + | 0.718143i | \(0.744992\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.31371i | − | 1.10533i | −0.833402 | − | 0.552667i | \(-0.813610\pi\) | ||
0.833402 | − | 0.552667i | \(-0.186390\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.2641 | + | 5.92596i | −1.20132 | + | 0.693581i | −0.960848 | − | 0.277075i | \(-0.910635\pi\) |
−0.240470 | + | 0.970657i | \(0.577301\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.65685 | − | 9.79796i | 0.636446 | − | 1.10236i | −0.349761 | − | 0.936839i | \(-0.613737\pi\) |
0.986207 | − | 0.165518i | \(-0.0529295\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.32957 | −0.475232 | −0.237616 | − | 0.971359i | \(-0.576366\pi\) | ||||
−0.237616 | + | 0.971359i | \(0.576366\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.24264 | 0.460179 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.831025 | − | 1.43938i | 0.0880885 | − | 0.152574i | −0.818615 | − | 0.574343i | \(-0.805258\pi\) |
0.906703 | + | 0.421769i | \(0.138591\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.44949 | − | 1.41421i | 0.251312 | − | 0.145095i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.8519i | 1.20338i | 0.798730 | + | 0.601690i | \(0.205506\pi\) | ||||
−0.798730 | + | 0.601690i | \(0.794494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.92596 | + | 10.2641i | 0.589655 | + | 1.02131i | 0.994277 | + | 0.106829i | \(0.0340697\pi\) |
−0.404622 | + | 0.914484i | \(0.632597\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.72648 | + | 4.46088i | 0.761313 | + | 0.439544i | 0.829767 | − | 0.558110i | \(-0.188473\pi\) |
−0.0684542 | + | 0.997654i | \(0.521807\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.21076 | − | 3.58579i | −0.600417 | − | 0.346651i | 0.168788 | − | 0.985652i | \(-0.446015\pi\) |
−0.769206 | + | 0.639001i | \(0.779348\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.53553 | + | 9.58783i | 0.530208 | + | 0.918347i | 0.999379 | + | 0.0352398i | \(0.0112195\pi\) |
−0.469171 | + | 0.883107i | \(0.655447\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 10.5858i | − | 0.995827i | −0.867227 | − | 0.497914i | \(-0.834100\pi\) | ||
0.867227 | − | 0.497914i | \(-0.165900\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.10220 | + | 1.21371i | −0.196032 | + | 0.113179i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.50000 | + | 6.06218i | −0.318182 | + | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.20533 | 0.644464 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.17157 | 0.103960 | 0.0519801 | − | 0.998648i | \(-0.483447\pi\) | ||||
0.0519801 | + | 0.998648i | \(0.483447\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.47343 | − | 14.6764i | 0.740327 | − | 1.28228i | −0.212020 | − | 0.977265i | \(-0.568004\pi\) |
0.952346 | − | 0.305018i | \(-0.0986626\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.37769 | − | 5.41421i | 0.801190 | − | 0.462567i | −0.0426968 | − | 0.999088i | \(-0.513595\pi\) |
0.843887 | + | 0.536521i | \(0.180262\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 15.6788i | − | 1.32985i | −0.746908 | − | 0.664927i | \(-0.768462\pi\) | ||
0.746908 | − | 0.664927i | \(-0.231538\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.317025 | + | 0.549104i | 0.0265110 | + | 0.0459184i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.52607 | − | 2.61313i | −0.375869 | − | 0.217008i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.12372 | + | 3.53553i | 0.501675 | + | 0.289642i | 0.729405 | − | 0.684082i | \(-0.239797\pi\) |
−0.227730 | + | 0.973724i | \(0.573130\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.07107 | − | 8.78335i | −0.412678 | − | 0.714779i | 0.582504 | − | 0.812828i | \(-0.302073\pi\) |
−0.995182 | + | 0.0980492i | \(0.968740\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.17157i | 0.415391i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.34972 | + | 3.08866i | −0.426954 | + | 0.246502i | −0.698048 | − | 0.716051i | \(-0.745948\pi\) |
0.271094 | + | 0.962553i | \(0.412615\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.41421 | + | 2.44949i | −0.110770 | + | 0.191859i | −0.916081 | − | 0.400994i | \(-0.868665\pi\) |
0.805311 | + | 0.592852i | \(0.201998\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.42742 | −0.187839 | −0.0939196 | − | 0.995580i | \(-0.529940\pi\) | ||||
−0.0939196 | + | 0.995580i | \(0.529940\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8995 | 0.992269 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.39731 | + | 16.2766i | −0.714464 | + | 1.23749i | 0.248702 | + | 0.968580i | \(0.419996\pi\) |
−0.963166 | + | 0.268908i | \(0.913337\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.06591 | + | 4.65685i | −0.602874 | + | 0.348070i | −0.770171 | − | 0.637837i | \(-0.779829\pi\) |
0.167297 | + | 0.985907i | \(0.446496\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.66205i | − | 0.123539i | −0.998090 | − | 0.0617696i | \(-0.980326\pi\) | ||
0.998090 | − | 0.0617696i | \(-0.0196744\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0928546 | − | 0.160829i | −0.00682680 | − | 0.0118244i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.60124 | + | 5.54328i | 0.702112 | + | 0.405365i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.9941 | − | 8.65685i | −1.08494 | − | 0.626388i | −0.152712 | − | 0.988271i | \(-0.548801\pi\) |
−0.932224 | + | 0.361883i | \(0.882134\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.82843 | + | 8.36308i | 0.347558 | + | 0.601988i | 0.985815 | − | 0.167835i | \(-0.0536777\pi\) |
−0.638257 | + | 0.769823i | \(0.720344\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.07107i | 0.218805i | 0.993998 | + | 0.109402i | \(0.0348937\pi\) | ||||
−0.993998 | + | 0.109402i | \(0.965106\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.40083 | − | 3.69552i | 0.453742 | − | 0.261968i | −0.255667 | − | 0.966765i | \(-0.582295\pi\) |
0.709409 | + | 0.704797i | \(0.248962\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.05025 | − | 1.81909i | 0.0733528 | − | 0.127051i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.39104 | 0.511249 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.6274 | −1.28236 | −0.641182 | − | 0.767389i | \(-0.721556\pi\) | ||||
−0.641182 | + | 0.767389i | \(0.721556\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.61313 | − | 4.52607i | 0.178214 | − | 0.308675i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.52192 | + | 0.878680i | −0.102375 | + | 0.0591064i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.8017i | 1.45995i | 0.683474 | + | 0.729975i | \(0.260468\pi\) | ||||
−0.683474 | + | 0.729975i | \(0.739532\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.37849 | − | 5.85172i | −0.224238 | − | 0.388392i | 0.731852 | − | 0.681463i | \(-0.238656\pi\) |
−0.956091 | + | 0.293071i | \(0.905323\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0136 | − | 8.09075i | −0.926044 | − | 0.534651i | −0.0404854 | − | 0.999180i | \(-0.512890\pi\) |
−0.885558 | + | 0.464529i | \(0.846224\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.1390 | + | 7.58579i | 0.860762 | + | 0.496961i | 0.864268 | − | 0.503032i | \(-0.167782\pi\) |
−0.00350513 | + | 0.999994i | \(0.501116\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.58579 | − | 7.94282i | −0.299144 | − | 0.518132i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.82843i | 0.571063i | 0.958369 | + | 0.285532i | \(0.0921702\pi\) | ||||
−0.958369 | + | 0.285532i | \(0.907830\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.1283 | − | 12.7758i | 1.42541 | − | 0.822962i | 0.428657 | − | 0.903467i | \(-0.358987\pi\) |
0.996754 | + | 0.0805055i | \(0.0256535\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.585786 | + | 1.01461i | −0.0372727 | + | 0.0645582i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.4972 | −1.60937 | −0.804685 | − | 0.593702i | \(-0.797666\pi\) | ||||
−0.804685 | + | 0.593702i | \(0.797666\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.34315 | −0.398790 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.2940 | + | 17.8297i | −0.642122 | + | 1.11219i | 0.342837 | + | 0.939395i | \(0.388612\pi\) |
−0.984958 | + | 0.172792i | \(0.944721\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.0233 | + | 9.82843i | −1.04970 | + | 0.606047i | −0.922566 | − | 0.385838i | \(-0.873912\pi\) |
−0.127137 | + | 0.991885i | \(0.540579\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 9.37011i | − | 0.575601i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.94897 | − | 15.5001i | −0.545628 | − | 0.945056i | −0.998567 | − | 0.0535141i | \(-0.982958\pi\) |
0.452939 | − | 0.891542i | \(-0.350376\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.75351 | + | 2.74444i | 0.288755 | + | 0.166713i | 0.637380 | − | 0.770549i | \(-0.280018\pi\) |
−0.348625 | + | 0.937262i | \(0.613351\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.64564 | + | 4.41421i | 0.461050 | + | 0.266187i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.48528 | − | 11.2328i | −0.389663 | − | 0.674916i | 0.602741 | − | 0.797937i | \(-0.294075\pi\) |
−0.992404 | + | 0.123021i | \(0.960742\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.4853i | 0.625499i | 0.949836 | + | 0.312750i | \(0.101250\pi\) | ||||
−0.949836 | + | 0.312750i | \(0.898750\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.52207 | + | 2.03347i | −0.209365 | + | 0.120877i | −0.601016 | − | 0.799237i | \(-0.705237\pi\) |
0.391651 | + | 0.920114i | \(0.371904\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.86396 | + | 11.8887i | −0.403762 | + | 0.699337i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.4441 | 0.960676 | 0.480338 | − | 0.877083i | \(-0.340514\pi\) | ||||
0.480338 | + | 0.877083i | \(0.340514\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.1421 | 0.590498 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.502734 | − | 0.870762i | 0.0290739 | − | 0.0503574i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.36245 | − | 1.36396i | 0.135273 | − | 0.0781002i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 27.1367i | − | 1.54877i | −0.632712 | − | 0.774387i | \(-0.718058\pi\) | ||
0.632712 | − | 0.774387i | \(-0.281942\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.3617 | − | 26.6073i | −0.871084 | − | 1.50876i | −0.860877 | − | 0.508814i | \(-0.830084\pi\) |
−0.0102070 | − | 0.999948i | \(-0.503249\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.0071 | − | 14.4379i | −1.41348 | − | 0.816076i | −0.417770 | − | 0.908553i | \(-0.637188\pi\) |
−0.995715 | + | 0.0924774i | \(0.970521\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.6463 | + | 7.87868i | 0.766451 | + | 0.442511i | 0.831607 | − | 0.555364i | \(-0.187421\pi\) |
−0.0651561 | + | 0.997875i | \(0.520755\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.82843 | − | 11.8272i | −0.382319 | − | 0.662195i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.4853i | 1.13983i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.21193 | + | 0.699709i | −0.0672258 | + | 0.0388129i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.6569 | − | 23.6544i | 0.750649 | − | 1.30016i | −0.196860 | − | 0.980432i | \(-0.563074\pi\) |
0.947509 | − | 0.319730i | \(-0.103592\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.43289 | 0.187559 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.0711 | −1.47466 | −0.737328 | − | 0.675535i | \(-0.763913\pi\) | ||||
−0.737328 | + | 0.675535i | \(0.763913\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.75699 | + | 11.7034i | −0.365911 | + | 0.633777i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.8067 | + | 14.8995i | −1.38538 | + | 0.799847i | −0.992790 | − | 0.119869i | \(-0.961753\pi\) |
−0.392586 | + | 0.919715i | \(0.628419\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.9372i | 1.70956i | 0.518993 | + | 0.854779i | \(0.326307\pi\) | ||||
−0.518993 | + | 0.854779i | \(0.673693\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.5726 | − | 18.3122i | −0.562720 | − | 0.974660i | −0.997258 | − | 0.0740064i | \(-0.976421\pi\) |
0.434537 | − | 0.900654i | \(-0.356912\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.17338 | − | 3.56420i | −0.327649 | − | 0.189168i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.8493 | − | 9.72792i | −0.889270 | − | 0.513420i | −0.0155661 | − | 0.999879i | \(-0.504955\pi\) |
−0.873704 | + | 0.486459i | \(0.838288\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.67157 | − | 4.62730i | −0.140609 | − | 0.243542i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.07107i | 0.474801i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.2276 | − | 18.0292i | 1.63007 | − | 0.941119i | 0.645996 | − | 0.763341i | \(-0.276442\pi\) |
0.984071 | − | 0.177778i | \(-0.0568909\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.3137 | + | 26.5241i | −0.792914 | + | 1.37337i | 0.131242 | + | 0.991350i | \(0.458104\pi\) |
−0.924155 | + | 0.382017i | \(0.875230\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.16478 | 0.111492 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −36.2843 | −1.86380 | −0.931899 | − | 0.362718i | \(-0.881849\pi\) | ||||
−0.931899 | + | 0.362718i | \(0.881849\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.39104 | + | 12.8017i | −0.377664 | + | 0.654134i | −0.990722 | − | 0.135904i | \(-0.956606\pi\) |
0.613058 | + | 0.790038i | \(0.289939\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.01461 | + | 0.585786i | −0.0514429 | + | 0.0297006i | −0.525501 | − | 0.850793i | \(-0.676122\pi\) |
0.474058 | + | 0.880494i | \(0.342789\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 17.5809i | − | 0.889105i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.32957 | − | 7.49903i | −0.217844 | − | 0.377317i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.1388 | − | 7.00835i | −0.609230 | − | 0.351739i | 0.163434 | − | 0.986554i | \(-0.447743\pi\) |
−0.772664 | + | 0.634815i | \(0.781076\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.77589 | + | 2.75736i | 0.238496 | + | 0.137696i | 0.614485 | − | 0.788928i | \(-0.289364\pi\) |
−0.375989 | + | 0.926624i | \(0.622697\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.07107 | − | 1.85514i | −0.0533537 | − | 0.0924113i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.485281i | − | 0.0240545i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.984485 | + | 0.568393i | −0.0486796 | + | 0.0281052i | −0.524142 | − | 0.851631i | \(-0.675614\pi\) |
0.475463 | + | 0.879736i | \(0.342281\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.65685 | + | 2.86976i | −0.0813318 | + | 0.140871i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.6620 | −1.35138 | −0.675688 | − | 0.737187i | \(-0.736154\pi\) | ||||
−0.675688 | + | 0.737187i | \(0.736154\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.3137 | 0.746344 | 0.373172 | − | 0.927762i | \(-0.378270\pi\) | ||||
0.373172 | + | 0.927762i | \(0.378270\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.2346 | + | 21.1910i | −0.593465 | + | 1.02791i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.8505 | + | 16.6569i | −1.38968 | + | 0.802332i | −0.993279 | − | 0.115745i | \(-0.963075\pi\) |
−0.396402 | + | 0.918077i | \(0.629741\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.502734i | 0.0241599i | 0.999927 | + | 0.0120799i | \(0.00384526\pi\) | ||||
−0.999927 | + | 0.0120799i | \(0.996155\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.86030 | − | 10.1503i | −0.280336 | − | 0.485557i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.0251 | + | 6.94269i | 0.573927 | + | 0.331357i | 0.758716 | − | 0.651421i | \(-0.225827\pi\) |
−0.184789 | + | 0.982778i | \(0.559160\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.3864 | + | 14.6569i | 1.20615 | + | 0.696368i | 0.961915 | − | 0.273349i | \(-0.0881314\pi\) |
0.244230 | + | 0.969717i | \(0.421465\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.636039 | − | 1.10165i | −0.0301511 | − | 0.0522233i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.5563i | 0.545378i | 0.962102 | + | 0.272689i | \(0.0879130\pi\) | ||||
−0.962102 | + | 0.272689i | \(0.912087\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.75351 | − | 2.74444i | 0.223834 | − | 0.129231i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.0000 | − | 19.0526i | 0.514558 | − | 0.891241i | −0.485299 | − | 0.874348i | \(-0.661289\pi\) |
0.999857 | − | 0.0168929i | \(-0.00537742\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.17186 | −0.240877 | −0.120439 | − | 0.992721i | \(-0.538430\pi\) | ||||
−0.120439 | + | 0.992721i | \(0.538430\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.82843 | −0.131448 | −0.0657241 | − | 0.997838i | \(-0.520936\pi\) | ||||
−0.0657241 | + | 0.997838i | \(0.520936\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.11586 | − | 5.39683i | 0.144185 | − | 0.249735i | −0.784884 | − | 0.619643i | \(-0.787277\pi\) |
0.929069 | + | 0.369908i | \(0.120611\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.8272 | − | 6.82843i | 0.543814 | − | 0.313971i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.3128i | 0.748483i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.6662 | − | 20.2065i | −0.533043 | − | 0.923257i | −0.999255 | − | 0.0385845i | \(-0.987715\pi\) |
0.466213 | − | 0.884673i | \(-0.345618\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0666175 | + | 0.0384616i | 0.00303750 | + | 0.00175370i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.85578 | + | 4.53553i | 0.356712 | + | 0.205948i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.89949 | − | 17.1464i | −0.448589 | − | 0.776979i | 0.549706 | − | 0.835359i | \(-0.314740\pi\) |
−0.998294 | + | 0.0583797i | \(0.981407\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.4853i | 1.55630i | 0.628079 | + | 0.778149i | \(0.283841\pi\) | ||||
−0.628079 | + | 0.778149i | \(0.716159\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.7807 | − | 18.9259i | 1.47637 | − | 0.852381i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.0711 | + | 22.6398i | −0.585141 | + | 1.01349i | 0.409716 | + | 0.912213i | \(0.365628\pi\) |
−0.994858 | + | 0.101282i | \(0.967706\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.5641 | 1.31820 | 0.659100 | − | 0.752055i | \(-0.270937\pi\) | ||||
0.659100 | + | 0.752055i | \(0.270937\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.07107 | 0.403657 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.46716 | + | 11.2014i | −0.286652 | + | 0.496495i | −0.973008 | − | 0.230770i | \(-0.925876\pi\) |
0.686357 | + | 0.727265i | \(0.259209\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.91359 | − | 3.41421i | 0.260584 | − | 0.150448i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 23.9665i | − | 1.05404i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.01673 | + | 1.76104i | 0.0445439 | + | 0.0771523i | 0.887438 | − | 0.460928i | \(-0.152483\pi\) |
−0.842894 | + | 0.538080i | \(0.819150\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.7746 | − | 9.10748i | −0.689776 | − | 0.398242i | 0.113752 | − | 0.993509i | \(-0.463713\pi\) |
−0.803528 | + | 0.595267i | \(0.797046\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −32.4377 | − | 18.7279i | −1.41301 | − | 0.815801i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.47056 | − | 11.2073i | −0.281329 | − | 0.487276i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.870058i | 0.0376864i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.75351 | + | 2.74444i | −0.205512 | + | 0.118653i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.17157 | + | 7.22538i | −0.179350 | + | 0.310643i | −0.941658 | − | 0.336571i | \(-0.890733\pi\) |
0.762308 | + | 0.647214i | \(0.224066\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.47343 | 0.362962 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.0000 | 0.684111 | 0.342055 | − | 0.939680i | \(-0.388877\pi\) | ||||
0.342055 | + | 0.939680i | \(0.388877\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.6173 | − | 21.8538i | 0.537515 | − | 0.931003i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.4868 | + | 8.36396i | −0.613826 | + | 0.354392i | −0.774461 | − | 0.632621i | \(-0.781979\pi\) |
0.160636 | + | 0.987014i | \(0.448646\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.16478i | 0.0915606i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.0322 | + | 19.1083i | 0.464950 | + | 0.805317i | 0.999199 | − | 0.0400098i | \(-0.0127389\pi\) |
−0.534249 | + | 0.845327i | \(0.679406\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.01655 | − | 4.05101i | −0.295188 | − | 0.170427i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.420266 | + | 0.242641i | 0.0176185 | + | 0.0101720i | 0.508783 | − | 0.860895i | \(-0.330095\pi\) |
−0.491165 | + | 0.871067i | \(0.663429\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.31371 | + | 2.27541i | 0.0549770 | + | 0.0952229i | 0.892204 | − | 0.451632i | \(-0.149158\pi\) |
−0.837227 | + | 0.546855i | \(0.815825\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 14.0000i | − | 0.583840i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.2140 | + | 9.93850i | −0.716628 | + | 0.413745i | −0.813510 | − | 0.581551i | \(-0.802446\pi\) |
0.0968824 | + | 0.995296i | \(0.469113\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.2426 | − | 21.2049i | 0.507038 | − | 0.878216i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.0334 | −1.15706 | −0.578531 | − | 0.815660i | \(-0.696374\pi\) | ||||
−0.578531 | + | 0.815660i | \(0.696374\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.9706 | −1.02889 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.3889 | + | 26.6544i | −0.631947 | + | 1.09457i | 0.355206 | + | 0.934788i | \(0.384411\pi\) |
−0.987153 | + | 0.159777i | \(0.948922\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.06591 | − | 4.65685i | 0.329564 | − | 0.190274i | −0.326083 | − | 0.945341i | \(-0.605729\pi\) |
0.655648 | + | 0.755067i | \(0.272396\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.9121i | 0.975394i | 0.873013 | + | 0.487697i | \(0.162163\pi\) | ||||
−0.873013 | + | 0.487697i | \(0.837837\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.67878 | + | 4.63979i | 0.108908 | + | 0.188634i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.9269 | + | 6.30864i | 0.443509 | + | 0.256060i | 0.705085 | − | 0.709123i | \(-0.250909\pi\) |
−0.261576 | + | 0.965183i | \(0.584242\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.29002 | + | 1.89949i | 0.133100 | + | 0.0768453i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.6066 | + | 39.1558i | 0.913072 | + | 1.58149i | 0.809700 | + | 0.586844i | \(0.199630\pi\) |
0.103372 | + | 0.994643i | \(0.467037\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 17.4558i | − | 0.702746i | −0.936236 | − | 0.351373i | \(-0.885715\pi\) | ||
0.936236 | − | 0.351373i | \(-0.114285\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.55310 | + | 0.896683i | −0.0624244 | + | 0.0360407i | −0.530887 | − | 0.847442i | \(-0.678141\pi\) |
0.468463 | + | 0.883483i | \(0.344808\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.27817 | + | 14.3382i | −0.331127 | + | 0.573529i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.34502 | 0.0536296 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.4853 | −0.497031 | −0.248516 | − | 0.968628i | \(-0.579943\pi\) | ||||
−0.248516 | + | 0.968628i | \(0.579943\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.448342 | − | 0.776550i | 0.0177919 | − | 0.0308165i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.3134 | + | 11.7279i | −0.802329 | + | 0.463225i | −0.844285 | − | 0.535894i | \(-0.819975\pi\) |
0.0419557 | + | 0.999119i | \(0.486641\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 32.5168i | − | 1.28234i | −0.767400 | − | 0.641169i | \(-0.778450\pi\) | ||
0.767400 | − | 0.641169i | \(-0.221550\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.19278 | − | 5.53006i | −0.125521 | − | 0.217409i | 0.796415 | − | 0.604750i | \(-0.206727\pi\) |
−0.921937 | + | 0.387341i | \(0.873394\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.9520 | + | 13.2513i | 0.900944 | + | 0.520161i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.07306 | + | 2.92893i | 0.198524 | + | 0.114618i | 0.595967 | − | 0.803009i | \(-0.296769\pi\) |
−0.397443 | + | 0.917627i | \(0.630102\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.48528 | − | 11.2328i | −0.253401 | − | 0.438903i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 2.97056i | − | 0.115717i | −0.998325 | − | 0.0578583i | \(-0.981573\pi\) | ||
0.998325 | − | 0.0578583i | \(-0.0184272\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.2536 | + | 11.6934i | −0.787773 | + | 0.454821i | −0.839178 | − | 0.543857i | \(-0.816963\pi\) |
0.0514050 | + | 0.998678i | \(0.483630\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.8284 | + | 18.7554i | −0.419278 | + | 0.726211i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.12840 | 0.275189 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0416 | 0.772548 | 0.386274 | − | 0.922384i | \(-0.373762\pi\) | ||||
0.386274 | + | 0.922384i | \(0.373762\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.9895 | − | 24.2305i | 0.537661 | − | 0.931255i | −0.461369 | − | 0.887208i | \(-0.652642\pi\) |
0.999029 | − | 0.0440470i | \(-0.0140251\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 40.6777 | − | 23.4853i | 1.55649 | − | 0.898639i | 0.558900 | − | 0.829235i | \(-0.311223\pi\) |
0.997589 | − | 0.0694045i | \(-0.0221099\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 8.28772i | − | 0.316657i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.94061 | + | 3.36124i | 0.0739315 | + | 0.128053i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.1754 | + | 12.8030i | 0.843594 | + | 0.487049i | 0.858484 | − | 0.512840i | \(-0.171407\pi\) |
−0.0148906 | + | 0.999889i | \(0.504740\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.3923 | − | 6.00000i | −0.394203 | − | 0.227593i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.60660 | + | 13.1750i | 0.288121 | + | 0.499039i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 15.4558i | − | 0.583759i | −0.956455 | − | 0.291880i | \(-0.905719\pi\) | ||
0.956455 | − | 0.291880i | \(-0.0942807\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.776550 | − | 0.448342i | 0.0292881 | − | 0.0169095i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.4350 | − | 26.7343i | 0.579675 | − | 1.00403i | −0.415842 | − | 0.909437i | \(-0.636513\pi\) |
0.995516 | − | 0.0945890i | \(-0.0301537\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.4303 | 0.802570 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.485281 | 0.0181485 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.81845 | − | 17.0061i | 0.366167 | − | 0.634219i | −0.622796 | − | 0.782384i | \(-0.714003\pi\) |
0.988963 | + | 0.148165i | \(0.0473367\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 26.1039 | − | 15.0711i | 0.969473 | − | 0.559725i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 53.7933i | 1.99508i | 0.0700903 | + | 0.997541i | \(0.477671\pi\) | ||||
−0.0700903 | + | 0.997541i | \(0.522329\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.9259 | + | 32.7807i | 0.700001 | + | 1.21244i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.3162 | − | 11.1522i | −0.713460 | − | 0.411916i | 0.0988808 | − | 0.995099i | \(-0.468474\pi\) |
−0.812341 | + | 0.583183i | \(0.801807\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.76874 | + | 4.48528i | 0.286165 | + | 0.165217i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.27208 | − | 2.20330i | −0.0467941 | − | 0.0810498i | 0.841680 | − | 0.539977i | \(-0.181567\pi\) |
−0.888474 | + | 0.458927i | \(0.848234\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 43.6569i | − | 1.60161i | −0.598922 | − | 0.800807i | \(-0.704404\pi\) | ||
0.598922 | − | 0.800807i | \(-0.295596\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.68690 | − | 2.70598i | 0.171715 | − | 0.0991395i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.1421 | − | 31.4231i | 0.662016 | − | 1.14665i | −0.318069 | − | 0.948067i | \(-0.603034\pi\) |
0.980085 | − | 0.198578i | \(-0.0636322\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.76245 | −0.282505 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.1005 | 0.657874 | 0.328937 | − | 0.944352i | \(-0.393310\pi\) | ||||
0.328937 | + | 0.944352i | \(0.393310\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.8310 | − | 46.4726i | 0.972622 | − | 1.68463i | 0.285052 | − | 0.958512i | \(-0.407989\pi\) |
0.687570 | − | 0.726118i | \(-0.258678\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.63818 | + | 2.10051i | −0.131367 | + | 0.0758448i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 14.2793i | − | 0.514926i | −0.966288 | − | 0.257463i | \(-0.917113\pi\) | ||
0.966288 | − | 0.257463i | \(-0.0828866\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.7883 | + | 29.0783i | 0.603835 | + | 1.04587i | 0.992234 | + | 0.124381i | \(0.0396947\pi\) |
−0.388400 | + | 0.921491i | \(0.626972\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25.8307 | − | 14.9134i | −0.927868 | − | 0.535705i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.78335 | + | 5.07107i | 0.314696 | + | 0.181690i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.31371 | − | 16.1318i | −0.333271 | − | 0.577242i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.72792i | 0.168747i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.7076 | + | 25.2346i | −1.55801 | + | 0.899515i | −0.560559 | + | 0.828115i | \(0.689414\pi\) |
−0.997448 | + | 0.0714009i | \(0.977253\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.564971 | + | 0.978559i | −0.0200627 | + | 0.0347496i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.3714 | −0.934122 | −0.467061 | − | 0.884225i | \(-0.654687\pi\) | ||||
−0.467061 | + | 0.884225i | \(0.654687\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 66.4264 | 2.35000 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.8519 | + | 20.5281i | −0.418245 | + | 0.724422i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.3712 | − | 10.6066i | 0.645896 | − | 0.372908i | −0.140986 | − | 0.990012i | \(-0.545027\pi\) |
0.786882 | + | 0.617103i | \(0.211694\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 42.1814i | − | 1.48119i | −0.671951 | − | 0.740595i | \(-0.734544\pi\) | ||
0.671951 | − | 0.740595i | \(-0.265456\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.08239 | + | 1.87476i | 0.0379145 | + | 0.0656699i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.8538 | + | 12.6173i | 0.764567 | + | 0.441423i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.2288 | − | 25.5355i | −1.54360 | − | 0.891196i | −0.998608 | − | 0.0527535i | \(-0.983200\pi\) |
−0.544990 | − | 0.838443i | \(-0.683466\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.1421 | + | 34.8872i | 0.702111 | + | 1.21609i | 0.967724 | + | 0.252012i | \(0.0810922\pi\) |
−0.265613 | + | 0.964080i | \(0.585574\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.4853i | 0.642796i | 0.946944 | + | 0.321398i | \(0.104153\pi\) | ||||
−0.946944 | + | 0.321398i | \(0.895847\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.6314 | + | 17.6850i | −1.06387 | + | 0.614226i | −0.926501 | − | 0.376293i | \(-0.877198\pi\) |
−0.137371 | + | 0.990520i | \(0.543865\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.928932 | + | 1.60896i | −0.0321470 | + | 0.0556803i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.8882 | 1.13543 | 0.567714 | − | 0.823226i | \(-0.307828\pi\) | ||||
0.567714 | + | 0.823226i | \(0.307828\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.6274 | −0.607842 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.93642 | − | 8.55014i | 0.169818 | − | 0.294134i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.666452 | + | 0.384776i | −0.0228457 | + | 0.0131900i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 57.2805i | 1.96125i | 0.195899 | + | 0.980624i | \(0.437237\pi\) | ||||
−0.195899 | + | 0.980624i | \(0.562763\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.8114 | + | 34.3143i | 0.676743 | + | 1.17215i | 0.975956 | + | 0.217967i | \(0.0699424\pi\) |
−0.299213 | + | 0.954186i | \(0.596724\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.9309 | + | 6.88830i | 0.407077 | + | 0.235026i | 0.689533 | − | 0.724254i | \(-0.257816\pi\) |
−0.282456 | + | 0.959280i | \(0.591149\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.7482 | + | 12.5563i | 0.740319 | + | 0.427423i | 0.822185 | − | 0.569220i | \(-0.192755\pi\) |
−0.0818666 | + | 0.996643i | \(0.526088\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.19239 | + | 12.4576i | 0.244549 | + | 0.423570i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 22.6274i | − | 0.767583i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.23144 | + | 0.710974i | −0.0417259 | + | 0.0240904i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.464466 | + | 0.804479i | −0.0156839 | + | 0.0271653i | −0.873761 | − | 0.486356i | \(-0.838326\pi\) |
0.858077 | + | 0.513521i | \(0.171659\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.1187 | −0.745198 | −0.372599 | − | 0.927992i | \(-0.621533\pi\) | ||||
−0.372599 | + | 0.927992i | \(0.621533\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.8579 | −0.735576 | −0.367788 | − | 0.929910i | \(-0.619885\pi\) | ||||
−0.367788 | + | 0.929910i | \(0.619885\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.94977 | − | 17.2335i | 0.334081 | − | 0.578644i | −0.649227 | − | 0.760595i | \(-0.724908\pi\) |
0.983308 | + | 0.181950i | \(0.0582409\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 38.3513 | − | 22.1421i | 1.28338 | − | 0.740958i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.12840i | 0.238276i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23.0698 | + | 39.9581i | 0.769421 | + | 1.33268i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58.7723 | + | 33.9322i | 1.95799 | + | 1.13044i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.10165 | − | 0.636039i | −0.0366201 | − | 0.0211427i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.2426 | + | 28.1331i | 0.539328 | + | 0.934144i | 0.998940 | + | 0.0460239i | \(0.0146550\pi\) |
−0.459612 | + | 0.888120i | \(0.652012\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 42.2843i | − | 1.40094i | −0.713682 | − | 0.700470i | \(-0.752974\pi\) | ||
0.713682 | − | 0.700470i | \(-0.247026\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.49903 | + | 4.32957i | −0.248182 | + | 0.143288i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.75736 | − | 13.4361i | 0.255892 | − | 0.443217i | −0.709246 | − | 0.704961i | \(-0.750964\pi\) |
0.965137 | + | 0.261744i | \(0.0842976\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.95268 | 0.0971887 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.07107 | 0.0352165 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.1522 | − | 19.3162i | 0.365892 | − | 0.633744i | −0.623027 | − | 0.782201i | \(-0.714097\pi\) |
0.988919 | + | 0.148457i | \(0.0474305\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.34847 | − | 4.24264i | 0.240321 | − | 0.138749i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 16.5210i | − | 0.539719i | −0.962900 | − | 0.269860i | \(-0.913023\pi\) | ||
0.962900 | − | 0.269860i | \(-0.0869773\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.18651 | − | 2.05510i | −0.0386792 | − | 0.0669943i | 0.846038 | − | 0.533123i | \(-0.178982\pi\) |
−0.884717 | + | 0.466129i | \(0.845648\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.53806 | − | 4.35210i | −0.245473 | − | 0.141724i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.64564 | − | 4.41421i | −0.248450 | − | 0.143443i | 0.370604 | − | 0.928791i | \(-0.379151\pi\) |
−0.619054 | + | 0.785348i | \(0.712484\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.87868 | − | 3.25397i | −0.0609845 | − | 0.105628i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 58.8701i | − | 1.90699i | −0.301412 | − | 0.953494i | \(-0.597458\pi\) | ||
0.301412 | − | 0.953494i | \(-0.402542\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.4760 | + | 6.62567i | −0.371355 | + | 0.214402i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.32843 | − | 12.6932i | 0.236401 | − | 0.409458i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.39104 | 0.237926 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.5147 | 0.498920 | 0.249460 | − | 0.968385i | \(-0.419747\pi\) | ||||
0.249460 | + | 0.968385i | \(0.419747\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.6173 | − | 21.8538i | 0.404908 | − | 0.701321i | −0.589403 | − | 0.807839i | \(-0.700637\pi\) |
0.994311 | + | 0.106518i | \(0.0339702\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.420266 | + | 0.242641i | −0.0134455 | + | 0.00776276i | −0.506708 | − | 0.862118i | \(-0.669138\pi\) |
0.493262 | + | 0.869881i | \(0.335804\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3.32410i | − | 0.106239i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.50981 | + | 6.07917i | 0.111946 | + | 0.193895i | 0.916555 | − | 0.399910i | \(-0.130958\pi\) |
−0.804609 | + | 0.593805i | \(0.797625\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.03559 | + | 1.17525i | 0.0648592 | + | 0.0374465i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.7554 | − | 10.8284i | −0.596387 | − | 0.344324i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.92893 | + | 8.53716i | 0.156573 | + | 0.271192i | 0.933631 | − | 0.358237i | \(-0.116622\pi\) |
−0.777058 | + | 0.629429i | \(0.783289\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 5.65685i | − | 0.179334i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.3979 | − | 7.73526i | 0.424314 | − | 0.244978i | −0.272607 | − | 0.962125i | \(-0.587886\pi\) |
0.696922 | + | 0.717147i | \(0.254553\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1764.2.t.c.1097.6 | 16 | ||
3.2 | odd | 2 | inner | 1764.2.t.c.1097.3 | 16 | ||
7.2 | even | 3 | 1764.2.f.b.881.4 | yes | 8 | ||
7.3 | odd | 6 | inner | 1764.2.t.c.521.3 | 16 | ||
7.4 | even | 3 | inner | 1764.2.t.c.521.5 | 16 | ||
7.5 | odd | 6 | 1764.2.f.b.881.6 | yes | 8 | ||
7.6 | odd | 2 | inner | 1764.2.t.c.1097.4 | 16 | ||
21.2 | odd | 6 | 1764.2.f.b.881.5 | yes | 8 | ||
21.5 | even | 6 | 1764.2.f.b.881.3 | ✓ | 8 | ||
21.11 | odd | 6 | inner | 1764.2.t.c.521.4 | 16 | ||
21.17 | even | 6 | inner | 1764.2.t.c.521.6 | 16 | ||
21.20 | even | 2 | inner | 1764.2.t.c.1097.5 | 16 | ||
28.19 | even | 6 | 7056.2.k.e.881.5 | 8 | |||
28.23 | odd | 6 | 7056.2.k.e.881.3 | 8 | |||
84.23 | even | 6 | 7056.2.k.e.881.6 | 8 | |||
84.47 | odd | 6 | 7056.2.k.e.881.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.2.f.b.881.3 | ✓ | 8 | 21.5 | even | 6 | ||
1764.2.f.b.881.4 | yes | 8 | 7.2 | even | 3 | ||
1764.2.f.b.881.5 | yes | 8 | 21.2 | odd | 6 | ||
1764.2.f.b.881.6 | yes | 8 | 7.5 | odd | 6 | ||
1764.2.t.c.521.3 | 16 | 7.3 | odd | 6 | inner | ||
1764.2.t.c.521.4 | 16 | 21.11 | odd | 6 | inner | ||
1764.2.t.c.521.5 | 16 | 7.4 | even | 3 | inner | ||
1764.2.t.c.521.6 | 16 | 21.17 | even | 6 | inner | ||
1764.2.t.c.1097.3 | 16 | 3.2 | odd | 2 | inner | ||
1764.2.t.c.1097.4 | 16 | 7.6 | odd | 2 | inner | ||
1764.2.t.c.1097.5 | 16 | 21.20 | even | 2 | inner | ||
1764.2.t.c.1097.6 | 16 | 1.1 | even | 1 | trivial | ||
7056.2.k.e.881.3 | 8 | 28.23 | odd | 6 | |||
7056.2.k.e.881.4 | 8 | 84.47 | odd | 6 | |||
7056.2.k.e.881.5 | 8 | 28.19 | even | 6 | |||
7056.2.k.e.881.6 | 8 | 84.23 | even | 6 |