Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2592,2,Mod(863,2592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2592, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2592.863");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2592 = 2^{5} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2592.s (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: | \(20.6972242039\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 863.2 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2592.863 |
Dual form | 2592.2.s.e.1727.2 |
$q$-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 \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.44949 | − | 1.41421i | −1.09545 | − | 0.632456i | −0.160424 | − | 0.987048i | \(-0.551286\pi\) |
−0.935021 | + | 0.354593i | \(0.884620\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205 | − | 1.00000i | 0.654654 | − | 0.377964i | −0.135583 | − | 0.990766i | \(-0.543291\pi\) |
0.790237 | + | 0.612801i | \(0.209957\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.41421 | − | 2.44949i | −0.426401 | − | 0.738549i | 0.570149 | − | 0.821541i | \(-0.306886\pi\) |
−0.996550 | + | 0.0829925i | \(0.973552\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | − | 1.73205i | 0.277350 | − | 0.480384i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) |
0.970725 | + | 0.240192i | \(0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.00000i | − | 1.37649i | −0.725476 | − | 0.688247i | \(-0.758380\pi\) | ||
0.725476 | − | 0.688247i | \(-0.241620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.82843 | + | 4.89898i | −0.589768 | + | 1.02151i | 0.404495 | + | 0.914540i | \(0.367447\pi\) |
−0.994263 | + | 0.106967i | \(0.965886\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.50000 | + | 2.59808i | 0.300000 | + | 0.519615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.44949 | + | 1.41421i | −0.454859 | + | 0.262613i | −0.709880 | − | 0.704323i | \(-0.751251\pi\) |
0.255021 | + | 0.966935i | \(0.417918\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.73205 | − | 1.00000i | −0.311086 | − | 0.179605i | 0.336327 | − | 0.941745i | \(-0.390815\pi\) |
−0.647412 | + | 0.762140i | \(0.724149\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.65685 | −0.956183 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.89898 | − | 2.82843i | −0.765092 | − | 0.441726i | 0.0660290 | − | 0.997818i | \(-0.478967\pi\) |
−0.831121 | + | 0.556092i | \(0.812300\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.73205 | − | 1.00000i | 0.264135 | − | 0.152499i | −0.362084 | − | 0.932145i | \(-0.617935\pi\) |
0.626219 | + | 0.779647i | \(0.284601\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.65685 | + | 9.79796i | 0.825137 | + | 1.42918i | 0.901815 | + | 0.432123i | \(0.142235\pi\) |
−0.0766776 | + | 0.997056i | \(0.524431\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.50000 | + | 2.59808i | −0.214286 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 8.48528i | − | 1.16554i | −0.812636 | − | 0.582772i | \(-0.801968\pi\) | ||
0.812636 | − | 0.582772i | \(-0.198032\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.00000i | 1.07872i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.41421 | + | 2.44949i | −0.184115 | + | 0.318896i | −0.943278 | − | 0.332004i | \(-0.892275\pi\) |
0.759163 | + | 0.650901i | \(0.225609\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | + | 1.73205i | 0.128037 | + | 0.221766i | 0.922916 | − | 0.385002i | \(-0.125799\pi\) |
−0.794879 | + | 0.606768i | \(0.792466\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.89898 | + | 2.82843i | −0.607644 | + | 0.350823i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.73205 | − | 1.00000i | −0.211604 | − | 0.122169i | 0.390453 | − | 0.920623i | \(-0.372318\pi\) |
−0.602056 | + | 0.798454i | \(0.705652\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.65685 | −0.671345 | −0.335673 | − | 0.941979i | \(-0.608964\pi\) | ||||
−0.335673 | + | 0.941979i | \(0.608964\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.89898 | − | 2.82843i | −0.558291 | − | 0.322329i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.1244 | + | 7.00000i | −1.36410 | + | 0.787562i | −0.990166 | − | 0.139895i | \(-0.955323\pi\) |
−0.373930 | + | 0.927457i | \(0.621990\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.41421 | + | 2.44949i | 0.155230 | + | 0.268866i | 0.933143 | − | 0.359506i | \(-0.117055\pi\) |
−0.777913 | + | 0.628372i | \(0.783721\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 16.9706i | − | 1.79888i | −0.437048 | − | 0.899438i | \(-0.643976\pi\) | ||
0.437048 | − | 0.899438i | \(-0.356024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 4.00000i | − | 0.419314i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.48528 | + | 14.6969i | −0.870572 | + | 1.50787i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.00000 | − | 8.66025i | −0.507673 | − | 0.879316i | −0.999961 | − | 0.00888289i | \(-0.997172\pi\) |
0.492287 | − | 0.870433i | \(-0.336161\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.44949 | − | 1.41421i | 0.243733 | − | 0.140720i | −0.373158 | − | 0.927768i | \(-0.621725\pi\) |
0.616891 | + | 0.787048i | \(0.288392\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.1244 | + | 7.00000i | 1.19465 | + | 0.689730i | 0.959357 | − | 0.282194i | \(-0.0910623\pi\) |
0.235291 | + | 0.971925i | \(0.424396\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.48528 | −0.820303 | −0.410152 | − | 0.912017i | \(-0.634524\pi\) | ||||
−0.410152 | + | 0.912017i | \(0.634524\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.0000 | −1.72409 | −0.862044 | − | 0.506834i | \(-0.830816\pi\) | ||||
−0.862044 | + | 0.506834i | \(0.830816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.79796 | − | 5.65685i | −0.921714 | − | 0.532152i | −0.0375328 | − | 0.999295i | \(-0.511950\pi\) |
−0.884182 | + | 0.467143i | \(0.845283\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.8564 | − | 8.00000i | 1.29212 | − | 0.746004i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.50000 | − | 2.59808i | 0.136364 | − | 0.236189i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685i | 0.505964i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.0000i | 1.59724i | 0.601834 | + | 0.798621i | \(0.294437\pi\) | ||||
−0.601834 | + | 0.798621i | \(0.705563\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.89949 | + | 17.1464i | −0.864923 | + | 1.49809i | 0.00220084 | + | 0.999998i | \(0.499299\pi\) |
−0.867124 | + | 0.498093i | \(0.834034\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | − | 10.3923i | −0.520266 | − | 0.901127i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.89898 | − | 2.82843i | 0.418548 | − | 0.241649i | −0.275908 | − | 0.961184i | \(-0.588978\pi\) |
0.694456 | + | 0.719535i | \(0.255645\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.66025 | − | 5.00000i | −0.734553 | − | 0.424094i | 0.0855324 | − | 0.996335i | \(-0.472741\pi\) |
−0.820086 | + | 0.572241i | \(0.806074\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.65685 | −0.473050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.00000 | 0.664364 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.2474 | − | 7.07107i | −1.00335 | − | 0.579284i | −0.0941123 | − | 0.995562i | \(-0.530001\pi\) |
−0.909238 | + | 0.416277i | \(0.863335\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.1244 | + | 7.00000i | −0.986666 | + | 0.569652i | −0.904276 | − | 0.426948i | \(-0.859589\pi\) |
−0.0823900 | + | 0.996600i | \(0.526255\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.82843 | + | 4.89898i | 0.227185 | + | 0.393496i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.00000 | + | 12.1244i | −0.558661 | + | 0.967629i | 0.438948 | + | 0.898513i | \(0.355351\pi\) |
−0.997609 | + | 0.0691164i | \(0.977982\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.3137i | 0.891645i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 6.00000i | − | 0.469956i | −0.972001 | − | 0.234978i | \(-0.924498\pi\) | ||
0.972001 | − | 0.234978i | \(-0.0755019\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.82843 | − | 4.89898i | 0.218870 | − | 0.379094i | −0.735593 | − | 0.677424i | \(-0.763096\pi\) |
0.954463 | + | 0.298330i | \(0.0964295\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.2474 | + | 7.07107i | −0.931156 | + | 0.537603i | −0.887177 | − | 0.461429i | \(-0.847337\pi\) |
−0.0439792 | + | 0.999032i | \(0.514004\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.19615 | + | 3.00000i | 0.392792 | + | 0.226779i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.48528 | 0.634220 | 0.317110 | − | 0.948389i | \(-0.397288\pi\) | ||||
0.317110 | + | 0.948389i | \(0.397288\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.6969 | − | 8.48528i | −1.08054 | − | 0.623850i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.3137 | − | 19.5959i | −0.818631 | − | 1.41791i | −0.906691 | − | 0.421796i | \(-0.861400\pi\) |
0.0880597 | − | 0.996115i | \(-0.471933\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.00000 | − | 12.1244i | 0.503871 | − | 0.872730i | −0.496119 | − | 0.868255i | \(-0.665242\pi\) |
0.999990 | − | 0.00447566i | \(-0.00142465\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 19.7990i | − | 1.41062i | −0.708899 | − | 0.705310i | \(-0.750808\pi\) | ||
0.708899 | − | 0.705310i | \(-0.249192\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000i | 0.141776i | 0.997484 | + | 0.0708881i | \(0.0225833\pi\) | ||||
−0.997484 | + | 0.0708881i | \(0.977417\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.82843 | + | 4.89898i | −0.198517 | + | 0.343841i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.00000 | + | 13.8564i | 0.558744 | + | 0.967773i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.6969 | + | 8.48528i | −1.01661 | + | 0.586939i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.73205 | − | 1.00000i | −0.119239 | − | 0.0688428i | 0.439194 | − | 0.898392i | \(-0.355264\pi\) |
−0.558433 | + | 0.829549i | \(0.688597\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.65685 | −0.385794 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | −0.271538 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.73205 | − | 1.00000i | 0.115987 | − | 0.0669650i | −0.440884 | − | 0.897564i | \(-0.645335\pi\) |
0.556871 | + | 0.830599i | \(0.312002\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.07107 | + | 12.2474i | 0.469323 | + | 0.812892i | 0.999385 | − | 0.0350674i | \(-0.0111646\pi\) |
−0.530062 | + | 0.847959i | \(0.677831\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.00000 | − | 8.66025i | 0.330409 | − | 0.572286i | −0.652183 | − | 0.758062i | \(-0.726147\pi\) |
0.982592 | + | 0.185776i | \(0.0594799\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 5.65685i | − | 0.370593i | −0.982683 | − | 0.185296i | \(-0.940675\pi\) | ||
0.982683 | − | 0.185296i | \(-0.0593245\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 32.0000i | − | 2.08745i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.65685 | − | 9.79796i | 0.365911 | − | 0.633777i | −0.623011 | − | 0.782213i | \(-0.714091\pi\) |
0.988922 | + | 0.148436i | \(0.0474240\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | − | 1.73205i | −0.0644157 | − | 0.111571i | 0.832019 | − | 0.554747i | \(-0.187185\pi\) |
−0.896435 | + | 0.443176i | \(0.853852\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.34847 | − | 4.24264i | 0.469476 | − | 0.271052i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.3923 | − | 6.00000i | −0.661247 | − | 0.381771i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.48528 | −0.535586 | −0.267793 | − | 0.963476i | \(-0.586294\pi\) | ||||
−0.267793 | + | 0.963476i | \(0.586294\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0000 | 1.00591 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.5959 | + | 11.3137i | 1.22236 | + | 0.705730i | 0.965420 | − | 0.260698i | \(-0.0839526\pi\) |
0.256939 | + | 0.966428i | \(0.417286\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.3923 | − | 6.00000i | 0.645746 | − | 0.372822i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.82843 | + | 4.89898i | 0.174408 | + | 0.302084i | 0.939956 | − | 0.341295i | \(-0.110865\pi\) |
−0.765548 | + | 0.643379i | \(0.777532\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | + | 20.7846i | −0.737154 | + | 1.27679i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.48528i | 0.517357i | 0.965964 | + | 0.258678i | \(0.0832870\pi\) | ||||
−0.965964 | + | 0.258678i | \(0.916713\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.0000i | 1.09342i | 0.837321 | + | 0.546711i | \(0.184120\pi\) | ||||
−0.837321 | + | 0.546711i | \(0.815880\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.24264 | − | 7.34847i | 0.255841 | − | 0.443129i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.00000 | + | 8.66025i | 0.300421 | + | 0.520344i | 0.976231 | − | 0.216731i | \(-0.0695395\pi\) |
−0.675810 | + | 0.737075i | \(0.736206\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.89898 | − | 2.82843i | 0.292249 | − | 0.168730i | −0.346707 | − | 0.937974i | \(-0.612700\pi\) |
0.638955 | + | 0.769244i | \(0.279367\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.66025 | − | 5.00000i | −0.514799 | − | 0.297219i | 0.220005 | − | 0.975499i | \(-0.429393\pi\) |
−0.734804 | + | 0.678280i | \(0.762726\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.3137 | −0.667827 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.44949 | − | 1.41421i | −0.143101 | − | 0.0826192i | 0.426740 | − | 0.904374i | \(-0.359662\pi\) |
−0.569841 | + | 0.821755i | \(0.692995\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.92820 | − | 4.00000i | 0.403376 | − | 0.232889i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.65685 | + | 9.79796i | 0.327144 | + | 0.566631i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | − | 3.46410i | 0.115278 | − | 0.199667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 5.65685i | − | 0.323911i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 30.0000i | − | 1.71219i | −0.516818 | − | 0.856095i | \(-0.672884\pi\) | ||
0.516818 | − | 0.856095i | \(-0.327116\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.82843 | + | 4.89898i | −0.160385 | + | 0.277796i | −0.935007 | − | 0.354629i | \(-0.884607\pi\) |
0.774622 | + | 0.632425i | \(0.217940\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.00000 | − | 1.73205i | −0.0565233 | − | 0.0979013i | 0.836379 | − | 0.548151i | \(-0.184668\pi\) |
−0.892903 | + | 0.450250i | \(0.851335\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.44949 | + | 1.41421i | −0.137577 | + | 0.0794301i | −0.567209 | − | 0.823574i | \(-0.691977\pi\) |
0.429632 | + | 0.903004i | \(0.358643\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.92820 | + | 4.00000i | 0.387905 | + | 0.223957i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.00000 | 0.332820 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.5959 | + | 11.3137i | 1.08036 | + | 0.623745i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.66025 | − | 5.00000i | 0.476011 | − | 0.274825i | −0.242742 | − | 0.970091i | \(-0.578047\pi\) |
0.718752 | + | 0.695266i | \(0.244713\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.82843 | + | 4.89898i | 0.154533 | + | 0.267660i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0000 | − | 19.0526i | 0.599208 | − | 1.03786i | −0.393730 | − | 0.919226i | \(-0.628816\pi\) |
0.992938 | − | 0.118633i | \(-0.0378512\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.65685i | 0.306336i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.07107 | + | 12.2474i | −0.379595 | + | 0.657477i | −0.991003 | − | 0.133838i | \(-0.957270\pi\) |
0.611408 | + | 0.791315i | \(0.290603\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.00000 | − | 12.1244i | −0.374701 | − | 0.649002i | 0.615581 | − | 0.788074i | \(-0.288921\pi\) |
−0.990282 | + | 0.139072i | \(0.955588\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.5959 | − | 11.3137i | 1.04299 | − | 0.602168i | 0.122308 | − | 0.992492i | \(-0.460970\pi\) |
0.920677 | + | 0.390324i | \(0.127637\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.8564 | + | 8.00000i | 0.735422 | + | 0.424596i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.9706 | 0.895672 | 0.447836 | − | 0.894116i | \(-0.352195\pi\) | ||||
0.447836 | + | 0.894116i | \(0.352195\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.6969 | + | 8.48528i | 0.769273 | + | 0.444140i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.1244 | + | 7.00000i | −0.632886 | + | 0.365397i | −0.781869 | − | 0.623443i | \(-0.785733\pi\) |
0.148983 | + | 0.988840i | \(0.452400\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.48528 | − | 14.6969i | −0.440534 | − | 0.763027i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.0000 | − | 22.5167i | 0.673114 | − | 1.16587i | −0.303902 | − | 0.952703i | \(-0.598289\pi\) |
0.977016 | − | 0.213165i | \(-0.0683772\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.65685i | 0.291343i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.00000i | 0.102733i | 0.998680 | + | 0.0513665i | \(0.0163577\pi\) | ||||
−0.998680 | + | 0.0513665i | \(0.983642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.3137 | − | 19.5959i | 0.578103 | − | 1.00130i | −0.417593 | − | 0.908634i | \(-0.637126\pi\) |
0.995697 | − | 0.0926706i | \(-0.0295404\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.00000 | + | 13.8564i | 0.407718 | + | 0.706188i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.44949 | − | 1.41421i | 0.124194 | − | 0.0717035i | −0.436616 | − | 0.899648i | \(-0.643823\pi\) |
0.560810 | + | 0.827945i | \(0.310490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 39.5980 | 1.99239 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.0000 | −0.903394 | −0.451697 | − | 0.892171i | \(-0.649181\pi\) | ||||
−0.451697 | + | 0.892171i | \(0.649181\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.5959 | − | 11.3137i | −0.978573 | − | 0.564980i | −0.0767343 | − | 0.997052i | \(-0.524449\pi\) |
−0.901839 | + | 0.432072i | \(0.857783\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.46410 | + | 2.00000i | −0.172559 | + | 0.0996271i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.48528 | − | 14.6969i | −0.420600 | − | 0.728500i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.0000 | + | 22.5167i | −0.642809 | + | 1.11338i | 0.341994 | + | 0.939702i | \(0.388898\pi\) |
−0.984803 | + | 0.173675i | \(0.944436\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.65685i | 0.278356i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 8.00000i | − | 0.392705i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.3848 | − | 31.8434i | 0.898155 | − | 1.55565i | 0.0683046 | − | 0.997665i | \(-0.478241\pi\) |
0.829851 | − | 0.557986i | \(-0.188426\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.0000 | − | 19.0526i | −0.536107 | − | 0.928565i | −0.999109 | − | 0.0422075i | \(-0.986561\pi\) |
0.463002 | − | 0.886357i | \(-0.346772\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.46410 | + | 2.00000i | 0.167640 | + | 0.0967868i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.9411 | 1.63489 | 0.817443 | − | 0.576009i | \(-0.195391\pi\) | ||||
0.817443 | + | 0.576009i | \(0.195391\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.00000 | −0.288342 | −0.144171 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144171 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 29.3939 | + | 16.9706i | 1.40610 | + | 0.811812i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.1244 | + | 7.00000i | −0.578664 | + | 0.334092i | −0.760602 | − | 0.649218i | \(-0.775096\pi\) |
0.181938 | + | 0.983310i | \(0.441763\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.07107 | − | 12.2474i | −0.335957 | − | 0.581894i | 0.647712 | − | 0.761886i | \(-0.275726\pi\) |
−0.983668 | + | 0.179992i | \(0.942393\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.0000 | + | 41.5692i | −1.13771 | + | 1.97057i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.9411i | 1.60178i | 0.598811 | + | 0.800890i | \(0.295640\pi\) | ||||
−0.598811 | + | 0.800890i | \(0.704360\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.0000i | 0.753411i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.65685 | + | 9.79796i | −0.265197 | + | 0.459335i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.00000 | − | 8.66025i | −0.233890 | − | 0.405110i | 0.725059 | − | 0.688686i | \(-0.241812\pi\) |
−0.958950 | + | 0.283577i | \(0.908479\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.9444 | − | 15.5563i | 1.25493 | − | 0.724531i | 0.282842 | − | 0.959167i | \(-0.408723\pi\) |
0.972083 | + | 0.234635i | \(0.0753896\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.73205 | − | 1.00000i | −0.0804952 | − | 0.0464739i | 0.459212 | − | 0.888327i | \(-0.348132\pi\) |
−0.539707 | + | 0.841853i | \(0.681465\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.4558 | −1.17796 | −0.588978 | − | 0.808149i | \(-0.700470\pi\) | ||||
−0.588978 | + | 0.808149i | \(0.700470\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.00000 | −0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.89898 | − | 2.82843i | −0.225255 | − | 0.130051i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.5885 | − | 9.00000i | 0.715247 | − | 0.412948i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.3137 | + | 19.5959i | 0.516937 | + | 0.895360i | 0.999807 | + | 0.0196683i | \(0.00626102\pi\) |
−0.482870 | + | 0.875692i | \(0.660406\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.00000 | − | 10.3923i | 0.273576 | − | 0.473848i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28.2843i | 1.28432i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.0000i | 0.815658i | 0.913058 | + | 0.407829i | \(0.133714\pi\) | ||||
−0.913058 | + | 0.407829i | \(0.866286\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.5563 | − | 26.9444i | 0.702048 | − | 1.21598i | −0.265698 | − | 0.964056i | \(-0.585602\pi\) |
0.967746 | − | 0.251927i | \(-0.0810642\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.79796 | + | 5.65685i | −0.439499 | + | 0.253745i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.4449 | − | 17.0000i | −1.31813 | − | 0.761025i | −0.334705 | − | 0.942323i | \(-0.608637\pi\) |
−0.983428 | + | 0.181298i | \(0.941970\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.65685 | 0.252227 | 0.126113 | − | 0.992016i | \(-0.459750\pi\) | ||||
0.126113 | + | 0.992016i | \(0.459750\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.00000 | −0.355995 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.44949 | + | 1.41421i | 0.108572 | + | 0.0626839i | 0.553303 | − | 0.832980i | \(-0.313367\pi\) |
−0.444731 | + | 0.895664i | \(0.646701\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.3923 | + | 6.00000i | −0.459728 | + | 0.265424i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.7990 | − | 34.2929i | −0.872448 | − | 1.51112i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.0000 | − | 27.7128i | 0.703679 | − | 1.21881i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.65685i | 0.247831i | 0.992293 | + | 0.123916i | \(0.0395452\pi\) | ||||
−0.992293 | + | 0.123916i | \(0.960455\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.0000i | 1.48672i | 0.668894 | + | 0.743358i | \(0.266768\pi\) | ||||
−0.668894 | + | 0.743358i | \(0.733232\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.50000 | − | 7.79423i | −0.195652 | − | 0.338880i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.79796 | + | 5.65685i | −0.424397 | + | 0.245026i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.7846 | + | 12.0000i | 0.898597 | + | 0.518805i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.48528 | 0.365487 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 44.0908 | + | 25.4558i | 1.88864 | + | 1.09041i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.9090 | + | 19.0000i | −1.40709 | + | 0.812381i | −0.995106 | − | 0.0988117i | \(-0.968496\pi\) |
−0.411980 | + | 0.911193i | \(0.635163\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.48528 | + | 14.6969i | 0.361485 | + | 0.626111i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.0000 | + | 24.2487i | −0.595341 | + | 1.03116i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.48528i | 0.359533i | 0.983709 | + | 0.179766i | \(0.0575342\pi\) | ||||
−0.983709 | + | 0.179766i | \(0.942466\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4.00000i | − | 0.169182i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.41421 | − | 2.44949i | 0.0596020 | − | 0.103234i | −0.834685 | − | 0.550728i | \(-0.814350\pi\) |
0.894287 | + | 0.447494i | \(0.147684\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.0000 | + | 27.7128i | 0.673125 | + | 1.16589i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.89898 | + | 2.82843i | −0.205376 | + | 0.118574i | −0.599161 | − | 0.800629i | \(-0.704499\pi\) |
0.393785 | + | 0.919203i | \(0.371166\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.0526 | + | 11.0000i | 0.797325 | + | 0.460336i | 0.842535 | − | 0.538642i | \(-0.181062\pi\) |
−0.0452101 | + | 0.998978i | \(0.514396\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.9706 | −0.707721 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.00000 | −0.249783 | −0.124892 | − | 0.992170i | \(-0.539858\pi\) | ||||
−0.124892 | + | 0.992170i | \(0.539858\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.89898 | + | 2.82843i | 0.203244 | + | 0.117343i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.7846 | + | 12.0000i | −0.860811 | + | 0.496989i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.07107 | − | 12.2474i | −0.291854 | − | 0.505506i | 0.682394 | − | 0.730985i | \(-0.260939\pi\) |
−0.974248 | + | 0.225478i | \(0.927606\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.00000 | + | 10.3923i | −0.247226 | + | 0.428207i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 33.9411i | − | 1.39379i | −0.717171 | − | 0.696897i | \(-0.754563\pi\) | ||
0.717171 | − | 0.696897i | \(-0.245437\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.7990 | − | 34.2929i | 0.808965 | − | 1.40117i | −0.104617 | − | 0.994513i | \(-0.533362\pi\) |
0.913582 | − | 0.406656i | \(-0.133305\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.00000 | − | 8.66025i | −0.203954 | − | 0.353259i | 0.745845 | − | 0.666120i | \(-0.232046\pi\) |
−0.949799 | + | 0.312861i | \(0.898713\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.34847 | + | 4.24264i | −0.298758 | + | 0.172488i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.1244 | + | 7.00000i | 0.492112 | + | 0.284121i | 0.725450 | − | 0.688274i | \(-0.241632\pi\) |
−0.233338 | + | 0.972396i | \(0.574965\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.6274 | 0.915407 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.00000 | 0.242338 | 0.121169 | − | 0.992632i | \(-0.461336\pi\) | ||||
0.121169 | + | 0.992632i | \(0.461336\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.4949 | + | 14.1421i | 0.986127 | + | 0.569341i | 0.904114 | − | 0.427290i | \(-0.140532\pi\) |
0.0820130 | + | 0.996631i | \(0.473865\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.66025 | − | 5.00000i | 0.348085 | − | 0.200967i | −0.315757 | − | 0.948840i | \(-0.602258\pi\) |
0.663842 | + | 0.747873i | \(0.268925\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.9706 | − | 29.3939i | −0.679911 | − | 1.17764i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5000 | − | 26.8468i | 0.620000 | − | 1.07387i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 30.0000i | − | 1.19428i | −0.802137 | − | 0.597141i | \(-0.796303\pi\) | ||
0.802137 | − | 0.597141i | \(-0.203697\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 25.4558 | − | 44.0908i | 1.01018 | − | 1.74969i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.00000 | + | 5.19615i | 0.118864 | + | 0.205879i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.79796 | − | 5.65685i | 0.386996 | − | 0.223432i | −0.293862 | − | 0.955848i | \(-0.594941\pi\) |
0.680858 | + | 0.732416i | \(0.261607\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.5167 | − | 13.0000i | −0.887970 | − | 0.512670i | −0.0146923 | − | 0.999892i | \(-0.504677\pi\) |
−0.873278 | + | 0.487222i | \(0.838010\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.9706 | 0.667182 | 0.333591 | − | 0.942718i | \(-0.391740\pi\) | ||||
0.333591 | + | 0.942718i | \(0.391740\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.00000 | 0.314027 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.2474 | + | 7.07107i | 0.479280 | + | 0.276712i | 0.720116 | − | 0.693853i | \(-0.244088\pi\) |
−0.240837 | + | 0.970566i | \(0.577422\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 48.4974 | − | 28.0000i | 1.89495 | − | 1.09405i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.07107 | + | 12.2474i | 0.275450 | + | 0.477093i | 0.970248 | − | 0.242111i | \(-0.0778399\pi\) |
−0.694799 | + | 0.719204i | \(0.744507\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.00000 | − | 8.66025i | 0.194477 | − | 0.336845i | −0.752252 | − | 0.658876i | \(-0.771032\pi\) |
0.946729 | + | 0.322031i | \(0.104366\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 33.9411i | 1.31618i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 16.0000i | − | 0.619522i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.82843 | − | 4.89898i | 0.109190 | − | 0.189123i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.00000 | − | 8.66025i | −0.192736 | − | 0.333828i | 0.753420 | − | 0.657539i | \(-0.228403\pi\) |
−0.946156 | + | 0.323711i | \(0.895069\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.44949 | − | 1.41421i | 0.0941415 | − | 0.0543526i | −0.452190 | − | 0.891922i | \(-0.649357\pi\) |
0.546332 | + | 0.837569i | \(0.316024\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.3205 | − | 10.0000i | −0.664700 | − | 0.383765i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −42.4264 | −1.62340 | −0.811701 | − | 0.584074i | \(-0.801458\pi\) | ||||
−0.811701 | + | 0.584074i | \(0.801458\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.0000 | −0.611329 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.6969 | − | 8.48528i | −0.559909 | − | 0.323263i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.5167 | − | 13.0000i | 0.856574 | − | 0.494543i | −0.00628943 | − | 0.999980i | \(-0.502002\pi\) |
0.862864 | + | 0.505437i | \(0.168669\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.1421 | + | 24.4949i | 0.536442 | + | 0.929144i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 25.4558i | − | 0.961454i | −0.876870 | − | 0.480727i | \(-0.840373\pi\) | ||
0.876870 | − | 0.480727i | \(-0.159627\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 36.0000i | − | 1.35777i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.82843 | − | 4.89898i | 0.106374 | − | 0.184245i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.0000 | − | 32.9090i | −0.713560 | − | 1.23592i | −0.963512 | − | 0.267664i | \(-0.913748\pi\) |
0.249952 | − | 0.968258i | \(-0.419585\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.79796 | − | 5.65685i | 0.366936 | − | 0.211851i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.8564 | + | 8.00000i | 0.518200 | + | 0.299183i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.9411 | 1.26579 | 0.632895 | − | 0.774237i | \(-0.281866\pi\) | ||||
0.632895 | + | 0.774237i | \(0.281866\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.0000 | 1.04277 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.34847 | − | 4.24264i | −0.272915 | − | 0.157568i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.4449 | − | 17.0000i | 1.09205 | − | 0.630495i | 0.157928 | − | 0.987451i | \(-0.449519\pi\) |
0.934121 | + | 0.356956i | \(0.116185\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.0000 | + | 39.8372i | −0.849524 | + | 1.47142i | 0.0321090 | + | 0.999484i | \(0.489778\pi\) |
−0.881633 | + | 0.471935i | \(0.843556\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.65685i | 0.208373i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.0000i | 1.25071i | 0.780340 | + | 0.625355i | \(0.215046\pi\) | ||||
−0.780340 | + | 0.625355i | \(0.784954\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.82843 | − | 4.89898i | 0.103765 | − | 0.179726i | −0.809468 | − | 0.587164i | \(-0.800244\pi\) |
0.913233 | + | 0.407438i | \(0.133578\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.0000 | + | 34.6410i | 0.732743 | + | 1.26915i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.6969 | + | 8.48528i | −0.537014 | + | 0.310045i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.4449 | − | 17.0000i | −1.07446 | − | 0.620339i | −0.145062 | − | 0.989423i | \(-0.546338\pi\) |
−0.929396 | + | 0.369084i | \(0.879672\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.5980 | 1.44112 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.0000 | 1.38113 | 0.690567 | − | 0.723269i | \(-0.257361\pi\) | ||||
0.690567 | + | 0.723269i | \(0.257361\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.4949 | + | 14.1421i | 0.887939 | + | 0.512652i | 0.873268 | − | 0.487240i | \(-0.161996\pi\) |
0.0146714 | + | 0.999892i | \(0.495330\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −31.1769 | + | 18.0000i | −1.12868 | + | 0.651644i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.82843 | + | 4.89898i | 0.102129 | + | 0.176892i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.0000 | − | 39.8372i | 0.829401 | − | 1.43657i | −0.0691074 | − | 0.997609i | \(-0.522015\pi\) |
0.898509 | − | 0.438956i | \(-0.144652\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.4558i | 0.915583i | 0.889060 | + | 0.457792i | \(0.151359\pi\) | ||||
−0.889060 | + | 0.457792i | \(0.848641\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 6.00000i | − | 0.215526i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.9706 | + | 29.3939i | −0.608034 | + | 1.05314i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | + | 13.8564i | 0.286263 | + | 0.495821i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 34.2929 | − | 19.7990i | 1.22396 | − | 0.706656i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.9090 | + | 19.0000i | 1.17308 | + | 0.677277i | 0.954403 | − | 0.298521i | \(-0.0964933\pi\) |
0.218675 | + | 0.975798i | \(0.429827\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.6274 | −0.804538 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.00000 | 0.142044 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.44949 | + | 1.41421i | 0.0867654 | + | 0.0500940i | 0.542755 | − | 0.839891i | \(-0.317381\pi\) |
−0.455990 | + | 0.889985i | \(0.650715\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.48528 | + | 14.6969i | 0.299439 | + | 0.518644i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.0000 | − | 27.7128i | 0.563926 | − | 0.976748i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 50.9117i | 1.78996i | 0.446107 | + | 0.894980i | \(0.352810\pi\) | ||||
−0.446107 | + | 0.894980i | \(0.647190\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 30.0000i | − | 1.05344i | −0.850038 | − | 0.526721i | \(-0.823421\pi\) | ||
0.850038 | − | 0.526721i | \(-0.176579\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.48528 | + | 14.6969i | −0.297226 | + | 0.514811i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.00000 | − | 10.3923i | −0.209913 | − | 0.363581i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.2474 | − | 7.07107i | 0.427439 | − | 0.246782i | −0.270816 | − | 0.962631i | \(-0.587294\pi\) |
0.698255 | + | 0.715849i | \(0.253960\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.73205 | − | 1.00000i | −0.0603755 | − | 0.0348578i | 0.469508 | − | 0.882928i | \(-0.344431\pi\) |
−0.529884 | + | 0.848070i | \(0.677765\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.4558 | 0.885186 | 0.442593 | − | 0.896723i | \(-0.354059\pi\) | ||||
0.442593 | + | 0.896723i | \(0.354059\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.0000 | −0.625166 | −0.312583 | − | 0.949890i | \(-0.601194\pi\) | ||||
−0.312583 | + | 0.949890i | \(0.601194\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.8564 | + | 8.00000i | −0.479521 | + | 0.276851i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.7990 | − | 34.2929i | −0.683537 | − | 1.18392i | −0.973894 | − | 0.227003i | \(-0.927107\pi\) |
0.290357 | − | 0.956918i | \(-0.406226\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.5000 | + | 18.1865i | −0.362069 | + | 0.627122i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 25.4558i | − | 0.875708i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 6.00000i | − | 0.206162i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.9706 | + | 29.3939i | −0.581743 | + | 1.00761i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.0000 | + | 22.5167i | 0.445112 | + | 0.770956i | 0.998060 | − | 0.0622597i | \(-0.0198307\pi\) |
−0.552948 | + | 0.833215i | \(0.686497\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.4949 | + | 14.1421i | −0.836730 | + | 0.483086i | −0.856151 | − | 0.516725i | \(-0.827151\pi\) |
0.0194215 | + | 0.999811i | \(0.493818\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.73205 | − | 1.00000i | −0.0590968 | − | 0.0341196i | 0.470160 | − | 0.882581i | \(-0.344196\pi\) |
−0.529257 | + | 0.848461i | \(0.677529\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40.0000 | 1.36004 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34.2929 | + | 19.7990i | 1.16331 | + | 0.671635i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.46410 | + | 2.00000i | −0.117377 | + | 0.0677674i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.65685 | + | 9.79796i | 0.191237 | + | 0.331231i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.00000 | − | 1.73205i | 0.0337676 | − | 0.0584872i | −0.848648 | − | 0.528958i | \(-0.822583\pi\) |
0.882415 | + | 0.470471i | \(0.155916\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 33.9411i | − | 1.14351i | −0.820426 | − | 0.571753i | \(-0.806264\pi\) | ||
0.820426 | − | 0.571753i | \(-0.193736\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 6.00000i | − | 0.201916i | −0.994891 | − | 0.100958i | \(-0.967809\pi\) | ||
0.994891 | − | 0.100958i | \(-0.0321908\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.82843 | + | 4.89898i | −0.0949693 | + | 0.164492i | −0.909596 | − | 0.415494i | \(-0.863609\pi\) |
0.814627 | + | 0.579986i | \(0.196942\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0000 | + | 31.1769i | 0.603701 | + | 1.04564i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 58.7878 | − | 33.9411i | 1.96726 | − | 1.13580i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.7846 | − | 12.0000i | −0.694753 | − | 0.401116i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.65685 | 0.188667 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.6969 | − | 8.48528i | −0.488543 | − | 0.282060i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.73205 | − | 1.00000i | 0.0575118 | − | 0.0332045i | −0.470968 | − | 0.882150i | \(-0.656095\pi\) |
0.528480 | + | 0.848946i | \(0.322762\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.65685 | − | 9.79796i | −0.187420 | − | 0.324621i | 0.756969 | − | 0.653450i | \(-0.226679\pi\) |
−0.944389 | + | 0.328830i | \(0.893346\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.00000 | − | 6.92820i | 0.132381 | − | 0.229290i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 39.5980i | 1.30764i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 30.0000i | − | 0.989609i | −0.869004 | − | 0.494804i | \(-0.835240\pi\) | ||
0.869004 | − | 0.494804i | \(-0.164760\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.65685 | + | 9.79796i | −0.186198 | + | 0.322504i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.00000 | + | 15.5885i | 0.295918 | + | 0.512545i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.79796 | + | 5.65685i | −0.321461 | + | 0.185595i | −0.652043 | − | 0.758182i | \(-0.726088\pi\) |
0.330583 | + | 0.943777i | \(0.392755\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.5885 | + | 9.00000i | 0.510891 | + | 0.294963i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.0000 | −0.980057 | −0.490029 | − | 0.871706i | \(-0.663014\pi\) | ||||
−0.490029 | + | 0.871706i | \(0.663014\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46.5403 | − | 26.8701i | −1.51717 | − | 0.875939i | −0.999796 | − | 0.0201796i | \(-0.993576\pi\) |
−0.517374 | − | 0.855759i | \(-0.673090\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.7128 | − | 16.0000i | 0.902453 | − | 0.521032i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.07107 | + | 12.2474i | 0.229779 | + | 0.397989i | 0.957742 | − | 0.287627i | \(-0.0928664\pi\) |
−0.727964 | + | 0.685616i | \(0.759533\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.00000 | + | 10.3923i | −0.194768 | + | 0.337348i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 50.9117i | − | 1.64919i | −0.565723 | − | 0.824596i | \(-0.691403\pi\) | ||
0.565723 | − | 0.824596i | \(-0.308597\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 64.0000i | 2.07099i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.65685 | − | 9.79796i | 0.182669 | − | 0.316393i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.5000 | − | 23.3827i | −0.435484 | − | 0.754280i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −34.2929 | + | 19.7990i | −1.10393 | + | 0.637352i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.3013 | − | 25.0000i | −1.39247 | − | 0.803946i | −0.398886 | − | 0.917000i | \(-0.630603\pi\) |
−0.993589 | + | 0.113055i | \(0.963936\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.7990 | −0.635380 | −0.317690 | − | 0.948195i | \(-0.602907\pi\) | ||||
−0.317690 | + | 0.948195i | \(0.602907\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.0000 | −0.641171 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −39.1918 | − | 22.6274i | −1.25386 | − | 0.723915i | −0.281984 | − | 0.959419i | \(-0.590993\pi\) |
−0.971873 | + | 0.235504i | \(0.924326\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −41.5692 | + | 24.0000i | −1.32856 | + | 0.767043i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.1421 | − | 24.4949i | −0.451064 | − | 0.781266i | 0.547388 | − | 0.836879i | \(-0.315622\pi\) |
−0.998452 | + | 0.0556128i | \(0.982289\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.0000 | + | 48.4974i | −0.892154 | + | 1.54526i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.3137i | 0.359755i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.0000i | 0.571789i | 0.958261 | + | 0.285894i | \(0.0922907\pi\) | ||||
−0.958261 | + | 0.285894i | \(0.907709\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.82843 | − | 4.89898i | 0.0896672 | − | 0.155308i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.0000 | − | 32.9090i | −0.601736 | − | 1.04224i | −0.992558 | − | 0.121771i | \(-0.961143\pi\) |
0.390822 | − | 0.920466i | \(-0.372191\pi\) | |||||||
\(998\) | 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 \(a_p\))