Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,2,Mod(1217,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.1217");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.k (of order \(2\), degree \(1\), 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: | \(10.7318940317\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1217.1 | ||
Root | \(-1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.1217 |
Dual form | 1344.2.k.d.1217.2 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −1.22474 | − | 1.22474i | −0.707107 | − | 0.707107i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.44949 | −1.09545 | −0.547723 | − | 0.836660i | \(-0.684505\pi\) | ||||
−0.547723 | + | 0.836660i | \(0.684505\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | − | 2.44949i | 0.377964 | − | 0.925820i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 1.00000i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44949i | 0.679366i | 0.940540 | + | 0.339683i | \(0.110320\pi\) | ||||
−0.940540 | + | 0.339683i | \(0.889680\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.00000 | + | 3.00000i | 0.774597 | + | 0.774597i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.89898 | −1.18818 | −0.594089 | − | 0.804400i | \(-0.702487\pi\) | ||||
−0.594089 | + | 0.804400i | \(0.702487\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.44949i | 0.561951i | 0.959715 | + | 0.280976i | \(0.0906580\pi\) | ||||
−0.959715 | + | 0.280976i | \(0.909342\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.22474 | + | 1.77526i | −0.921915 | + | 0.387392i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.00000i | 1.25109i | 0.780189 | + | 0.625543i | \(0.215123\pi\) | ||||
−0.780189 | + | 0.625543i | \(0.784877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | − | 3.67423i | 0.707107 | − | 0.707107i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.00000i | − | 1.11417i | −0.830455 | − | 0.557086i | \(-0.811919\pi\) | ||
0.830455 | − | 0.557086i | \(-0.188081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.44949 | + | 6.00000i | −0.414039 | + | 1.01419i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.00000 | − | 3.00000i | 0.480384 | − | 0.480384i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.89898 | 0.765092 | 0.382546 | − | 0.923936i | \(-0.375047\pi\) | ||||
0.382546 | + | 0.923936i | \(0.375047\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 7.34847i | − | 1.09545i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.89898 | 0.714590 | 0.357295 | − | 0.933992i | \(-0.383699\pi\) | ||||
0.357295 | + | 0.933992i | \(0.383699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | − | 4.89898i | −0.714286 | − | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.00000 | + | 6.00000i | 0.840168 | + | 0.840168i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.00000 | − | 3.00000i | 0.397360 | − | 0.397360i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.2474 | 1.59448 | 0.797241 | − | 0.603661i | \(-0.206292\pi\) | ||||
0.797241 | + | 0.603661i | \(0.206292\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.2474i | 1.56813i | 0.620682 | + | 0.784063i | \(0.286856\pi\) | ||||
−0.620682 | + | 0.784063i | \(0.713144\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.34847 | + | 3.00000i | 0.925820 | + | 0.377964i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 6.00000i | − | 0.744208i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.34847 | − | 7.34847i | 0.884652 | − | 0.884652i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.79796i | 1.14676i | 0.819288 | + | 0.573382i | \(0.194369\pi\) | ||||
−0.819288 | + | 0.573382i | \(0.805631\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.22474 | − | 1.22474i | −0.141421 | − | 0.141421i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.0000 | 1.12509 | 0.562544 | − | 0.826767i | \(-0.309823\pi\) | ||||
0.562544 | + | 0.826767i | \(0.309823\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.44949 | −0.268866 | −0.134433 | − | 0.990923i | \(-0.542921\pi\) | ||||
−0.134433 | + | 0.990923i | \(0.542921\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0000 | 1.30158 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.34847 | + | 7.34847i | −0.787839 | + | 0.787839i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | + | 2.44949i | 0.628971 | + | 0.256776i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 6.00000i | − | 0.615587i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.89898i | 0.497416i | 0.968579 | + | 0.248708i | \(0.0800060\pi\) | ||||
−0.968579 | + | 0.248708i | \(0.919994\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.34847 | 0.731200 | 0.365600 | − | 0.930772i | \(-0.380864\pi\) | ||||
0.365600 | + | 0.930772i | \(0.380864\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.79796i | − | 0.965422i | −0.875780 | − | 0.482711i | \(-0.839652\pi\) | ||
0.875780 | − | 0.482711i | \(-0.160348\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.3485 | − | 4.34847i | 1.00991 | − | 0.424367i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0000i | 1.16008i | 0.814587 | + | 0.580042i | \(0.196964\pi\) | ||||
−0.814587 | + | 0.580042i | \(0.803036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.44949 | − | 2.44949i | −0.232495 | − | 0.232495i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.00000i | − | 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 14.6969i | − | 1.37050i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.34847 | −0.679366 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.89898 | + | 12.0000i | −0.449089 | + | 1.10004i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.00000 | − | 6.00000i | −0.541002 | − | 0.541002i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.79796 | 0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.89898 | − | 4.89898i | −0.431331 | − | 0.431331i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.34847 | −0.642039 | −0.321019 | − | 0.947073i | \(-0.604025\pi\) | ||||
−0.321019 | + | 0.947073i | \(0.604025\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | + | 2.44949i | 0.520266 | + | 0.212398i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.00000 | + | 9.00000i | −0.774597 | + | 0.774597i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.0000i | 1.02523i | 0.858619 | + | 0.512615i | \(0.171323\pi\) | ||||
−0.858619 | + | 0.512615i | \(0.828677\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.44949i | 0.207763i | 0.994590 | + | 0.103882i | \(0.0331263\pi\) | ||||
−0.994590 | + | 0.103882i | \(0.966874\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | − | 6.00000i | −0.505291 | − | 0.505291i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.6969i | 1.22051i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.123724 | + | 12.1237i | 0.0102046 | + | 0.999948i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 6.00000i | − | 0.491539i | −0.969328 | − | 0.245770i | \(-0.920959\pi\) | ||
0.969328 | − | 0.245770i | \(-0.0790407\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 14.6969i | − | 1.18818i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.34847i | 0.586472i | 0.956040 | + | 0.293236i | \(0.0947321\pi\) | ||||
−0.956040 | + | 0.293236i | \(0.905268\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.34847 | − | 7.34847i | 0.582772 | − | 0.582772i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.6969 | + | 6.00000i | 1.15828 | + | 0.472866i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.0000 | −1.25322 | −0.626608 | − | 0.779334i | \(-0.715557\pi\) | ||||
−0.626608 | + | 0.779334i | \(0.715557\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.89898 | 0.379094 | 0.189547 | − | 0.981872i | \(-0.439298\pi\) | ||||
0.189547 | + | 0.981872i | \(0.439298\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.34847 | −0.561951 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.0454 | −1.67608 | −0.838041 | − | 0.545608i | \(-0.816299\pi\) | ||||
−0.838041 | + | 0.545608i | \(0.816299\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | − | 2.44949i | 0.0755929 | − | 0.185164i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.0000 | − | 15.0000i | −1.12747 | − | 1.12747i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 24.0000i | − | 1.79384i | −0.442189 | − | 0.896922i | \(-0.645798\pi\) | ||
0.442189 | − | 0.896922i | \(-0.354202\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 12.2474i | − | 0.910346i | −0.890403 | − | 0.455173i | \(-0.849577\pi\) | ||
0.890403 | − | 0.455173i | \(-0.150423\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.0000 | − | 15.0000i | 1.10883 | − | 1.10883i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.89898 | −0.360180 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.32577 | − | 12.6742i | −0.387392 | − | 0.921915i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.00000 | 0.287926 | 0.143963 | − | 0.989583i | \(-0.454015\pi\) | ||||
0.143963 | + | 0.989583i | \(0.454015\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.34847 | + | 7.34847i | −0.526235 | + | 0.526235i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000i | 1.28245i | 0.767354 | + | 0.641223i | \(0.221573\pi\) | ||||
−0.767354 | + | 0.641223i | \(0.778427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.79796i | 0.694559i | 0.937762 | + | 0.347279i | \(0.112894\pi\) | ||||
−0.937762 | + | 0.347279i | \(0.887106\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.79796 | − | 9.79796i | −0.691095 | − | 0.691095i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.6969 | − | 6.00000i | −1.03152 | − | 0.421117i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.0000 | −0.838116 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.0000 | −1.25109 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.79796 | −0.668215 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.0000 | − | 12.0000i | 0.810885 | − | 0.810885i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 12.0000i | − | 0.807207i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.6969i | 0.984180i | 0.870544 | + | 0.492090i | \(0.163767\pi\) | ||||
−0.870544 | + | 0.492090i | \(0.836233\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000i | 0.200000i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.34847 | 0.487735 | 0.243868 | − | 0.969809i | \(-0.421584\pi\) | ||||
0.243868 | + | 0.969809i | \(0.421584\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.0454i | 1.45680i | 0.685151 | + | 0.728401i | \(0.259736\pi\) | ||||
−0.685151 | + | 0.728401i | \(0.740264\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.0000i | 1.57229i | 0.618041 | + | 0.786146i | \(0.287927\pi\) | ||||
−0.618041 | + | 0.786146i | \(0.712073\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.0000 | −0.782794 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.2474 | − | 12.2474i | −0.795557 | − | 0.795557i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6.00000i | − | 0.388108i | −0.980991 | − | 0.194054i | \(-0.937836\pi\) | ||
0.980991 | − | 0.194054i | \(-0.0621637\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.4949i | 1.57786i | 0.614486 | + | 0.788928i | \(0.289363\pi\) | ||||
−0.614486 | + | 0.788928i | \(0.710637\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0227 | + | 11.0227i | 0.707107 | + | 0.707107i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.2474 | + | 12.0000i | 0.782461 | + | 0.766652i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.00000 | −0.381771 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.00000 | + | 3.00000i | 0.190117 | + | 0.190117i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.1464 | 1.08227 | 0.541136 | − | 0.840935i | \(-0.317994\pi\) | ||||
0.541136 | + | 0.840935i | \(0.317994\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14.6969 | − | 14.6969i | −0.920358 | − | 0.920358i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −29.3939 | −1.83354 | −0.916770 | − | 0.399416i | \(-0.869213\pi\) | ||||
−0.916770 | + | 0.399416i | \(0.869213\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.00000 | − | 4.89898i | 0.124274 | − | 0.304408i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.0000 | 1.11417 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 24.0000i | − | 1.47990i | −0.672660 | − | 0.739952i | \(-0.734848\pi\) | ||
0.672660 | − | 0.739952i | \(-0.265152\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 14.6969i | − | 0.902826i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.2474 | −0.746740 | −0.373370 | − | 0.927682i | \(-0.621798\pi\) | ||||
−0.373370 | + | 0.927682i | \(0.621798\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.4949i | 1.48796i | 0.668202 | + | 0.743980i | \(0.267064\pi\) | ||||
−0.668202 | + | 0.743980i | \(0.732936\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.34847 | − | 10.3485i | −0.263181 | − | 0.626318i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.0000 | 1.32185 | 0.660926 | − | 0.750451i | \(-0.270164\pi\) | ||||
0.660926 | + | 0.750451i | \(0.270164\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.0454i | 1.31046i | 0.755428 | + | 0.655232i | \(0.227429\pi\) | ||||
−0.755428 | + | 0.655232i | \(0.772571\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.34847 | + | 7.34847i | −0.435286 | + | 0.435286i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.89898 | − | 12.0000i | 0.289178 | − | 0.708338i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.00000 | 0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00000 | − | 6.00000i | 0.351726 | − | 0.351726i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.44949 | 0.143101 | 0.0715504 | − | 0.997437i | \(-0.477205\pi\) | ||||
0.0715504 | + | 0.997437i | \(0.477205\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −30.0000 | −1.74667 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.6969 | −0.849946 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | − | 9.79796i | 0.230556 | − | 0.564745i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.00000 | − | 9.00000i | −0.517036 | − | 0.517036i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 30.0000i | − | 1.71780i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.34847i | − | 0.419399i | −0.977766 | − | 0.209700i | \(-0.932751\pi\) | ||
0.977766 | − | 0.209700i | \(-0.0672486\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.0000 | + | 12.0000i | −0.682656 | + | 0.682656i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.5959 | 1.11118 | 0.555591 | − | 0.831456i | \(-0.312492\pi\) | ||||
0.555591 | + | 0.831456i | \(0.312492\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 34.2929i | 1.93835i | 0.246380 | + | 0.969173i | \(0.420759\pi\) | ||||
−0.246380 | + | 0.969173i | \(0.579241\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −18.0000 | − | 7.34847i | −1.01419 | − | 0.414039i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.0000i | 1.01098i | 0.862832 | + | 0.505490i | \(0.168688\pi\) | ||||
−0.862832 | + | 0.505490i | \(0.831312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.6969 | − | 14.6969i | 0.820303 | − | 0.820303i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 12.0000i | − | 0.667698i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.44949i | 0.135873i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.2474 | + | 12.2474i | 0.677285 | + | 0.677285i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.89898 | − | 12.0000i | 0.270089 | − | 0.661581i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.00000i | 0.328798i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.5959 | −1.07064 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.0000 | −1.74315 | −0.871576 | − | 0.490261i | \(-0.836901\pi\) | ||||
−0.871576 | + | 0.490261i | \(0.836901\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.34847 | + | 7.34847i | −0.399114 | + | 0.399114i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −18.0000 | + | 18.0000i | −0.969087 | + | 0.969087i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.0000i | 0.644194i | 0.946707 | + | 0.322097i | \(0.104388\pi\) | ||||
−0.946707 | + | 0.322097i | \(0.895612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.44949i | − | 0.131118i | −0.997849 | − | 0.0655591i | \(-0.979117\pi\) | ||
0.997849 | − | 0.0655591i | \(-0.0208831\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.00000 | + | 9.00000i | 0.480384 | + | 0.480384i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.79796 | 0.521493 | 0.260746 | − | 0.965407i | \(-0.416031\pi\) | ||||
0.260746 | + | 0.965407i | \(0.416031\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 20.6969 | − | 8.69694i | 1.09540 | − | 0.460291i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6.00000i | − | 0.316668i | −0.987386 | − | 0.158334i | \(-0.949388\pi\) | ||
0.987386 | − | 0.158334i | \(-0.0506123\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.4722 | − | 13.4722i | −0.707107 | − | 0.707107i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 24.0000i | − | 1.25622i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4.89898i | − | 0.255725i | −0.991792 | − | 0.127862i | \(-0.959188\pi\) | ||
0.991792 | − | 0.127862i | \(-0.0408116\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.6969i | 0.765092i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.6969 | + | 6.00000i | 0.763027 | + | 0.311504i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.0000 | −0.724893 | −0.362446 | − | 0.932005i | \(-0.618058\pi\) | ||||
−0.362446 | + | 0.932005i | \(0.618058\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.0000 | − | 12.0000i | −0.619677 | − | 0.619677i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.6969 | 0.756931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.79796 | + | 9.79796i | 0.501965 | + | 0.501965i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −34.2929 | −1.75228 | −0.876142 | − | 0.482054i | \(-0.839891\pi\) | ||||
−0.876142 | + | 0.482054i | \(0.839891\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.0000i | 0.609994i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 6.00000i | − | 0.304212i | −0.988364 | − | 0.152106i | \(-0.951394\pi\) | ||
0.988364 | − | 0.152106i | \(-0.0486055\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 29.3939i | − | 1.48651i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.00000 | + | 9.00000i | 0.453990 | + | 0.453990i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −24.4949 | −1.23247 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.34847i | 0.368809i | 0.982850 | + | 0.184405i | \(0.0590357\pi\) | ||||
−0.982850 | + | 0.184405i | \(0.940964\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.34847 | − | 10.3485i | −0.217696 | − | 0.518071i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 30.0000i | − | 1.49813i | −0.662497 | − | 0.749064i | \(-0.730503\pi\) | ||
0.662497 | − | 0.749064i | \(-0.269497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 22.0454 | 1.09545 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 34.2929i | − | 1.69567i | −0.530258 | − | 0.847836i | \(-0.677905\pi\) | ||
0.530258 | − | 0.847836i | \(-0.322095\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.6969 | − | 14.6969i | 0.724947 | − | 0.724947i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.2474 | − | 30.0000i | 0.602658 | − | 1.47620i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.00000 | − | 3.00000i | 0.146911 | − | 0.146911i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.2474 | −0.598327 | −0.299164 | − | 0.954202i | \(-0.596708\pi\) | ||||
−0.299164 | + | 0.954202i | \(0.596708\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.6969i | 0.714590i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.89898 | −0.237635 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 30.0000 | + | 12.2474i | 1.45180 | + | 0.592696i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.0000i | 1.44505i | 0.691345 | + | 0.722525i | \(0.257018\pi\) | ||||
−0.691345 | + | 0.722525i | \(0.742982\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 14.6969i | − | 0.706290i | −0.935569 | − | 0.353145i | \(-0.885112\pi\) | ||
0.935569 | − | 0.353145i | \(-0.114888\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 18.0000 | − | 18.0000i | 0.863034 | − | 0.863034i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.6969 | −0.703050 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 14.6969i | − | 0.701447i | −0.936479 | − | 0.350723i | \(-0.885936\pi\) | ||
0.936479 | − | 0.350723i | \(-0.114064\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.6969 | − | 15.0000i | 0.699854 | − | 0.714286i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 36.0000i | − | 1.71041i | −0.518289 | − | 0.855206i | \(-0.673431\pi\) | ||
0.518289 | − | 0.855206i | \(-0.326569\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.34847 | + | 7.34847i | −0.347571 | + | 0.347571i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.0000i | 1.69895i | 0.527633 | + | 0.849473i | \(0.323080\pi\) | ||||
−0.527633 | + | 0.849473i | \(0.676920\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.79796 | − | 9.79796i | −0.460348 | − | 0.460348i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.6969 | − | 6.00000i | −0.689003 | − | 0.281284i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.0000 | 1.30978 | 0.654892 | − | 0.755722i | \(-0.272714\pi\) | ||||
0.654892 | + | 0.755722i | \(0.272714\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18.0000 | + | 18.0000i | −0.840168 | + | 0.840168i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.8434 | 1.48309 | 0.741547 | − | 0.670901i | \(-0.234093\pi\) | ||||
0.741547 | + | 0.670901i | \(0.234093\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.0000 | −0.650635 | −0.325318 | − | 0.945605i | \(-0.605471\pi\) | ||||
−0.325318 | + | 0.945605i | \(0.605471\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.34847 | 0.340047 | 0.170023 | − | 0.985440i | \(-0.445616\pi\) | ||||
0.170023 | + | 0.985440i | \(0.445616\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.00000 | − | 19.5959i | 0.369406 | − | 0.904855i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.00000 | − | 9.00000i | 0.414698 | − | 0.414698i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.44949i | 0.112390i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18.0000 | −0.824163 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.4949 | 1.11920 | 0.559600 | − | 0.828763i | \(-0.310955\pi\) | ||||
0.559600 | + | 0.828763i | \(0.310955\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.89898i | 0.223374i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.6515 | − | 25.3485i | −0.484661 | − | 1.15340i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 12.0000i | − | 0.544892i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.0000 | 1.45006 | 0.725029 | − | 0.688718i | \(-0.241826\pi\) | ||||
0.725029 | + | 0.688718i | \(0.241826\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.5959 | + | 19.5959i | 0.886158 | + | 0.886158i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 29.3939i | 1.32383i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.0000 | −0.895323 | −0.447661 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447661 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | − | 6.00000i | −0.268060 | − | 0.268060i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.1918 | 1.74748 | 0.873739 | − | 0.486395i | \(-0.161689\pi\) | ||||
0.873739 | + | 0.486395i | \(0.161689\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.0000 | −0.800989 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.57321 | − | 8.57321i | −0.380750 | − | 0.380750i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.2474 | −0.542859 | −0.271429 | − | 0.962458i | \(-0.587496\pi\) | ||||
−0.271429 | + | 0.962458i | \(0.587496\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.0000 | + | 9.79796i | 1.06170 | + | 0.433436i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.00000 | + | 9.00000i | 0.397360 | + | 0.397360i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.0000i | 1.05757i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.0000 | + | 27.0000i | 1.18517 | + | 1.18517i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.89898 | 0.214628 | 0.107314 | − | 0.994225i | \(-0.465775\pi\) | ||||
0.107314 | + | 0.994225i | \(0.465775\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.44949i | − | 0.107109i | −0.998565 | − | 0.0535544i | \(-0.982945\pi\) | ||
0.998565 | − | 0.0535544i | \(-0.0170550\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.22474 | + | 1.77526i | −0.184383 | + | 0.0774785i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 36.7423i | 1.59448i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000i | 0.519778i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 29.3939i | − | 1.27081i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −29.3939 | + | 29.3939i | −1.26844 | + | 1.26844i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.0000 | + | 15.0000i | −0.643712 | + | 0.643712i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.4949 | 1.04925 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −36.7423 | −1.56813 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.6969 | 0.626111 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.0000 | − | 24.4949i | 0.425243 | − | 1.04163i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.00000 | + | 6.00000i | 0.254686 | + | 0.254686i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.0000i | 0.762684i | 0.924434 | + | 0.381342i | \(0.124538\pi\) | ||||
−0.924434 | + | 0.381342i | \(0.875462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.79796i | 0.414410i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.0454 | 0.929103 | 0.464552 | − | 0.885546i | \(-0.346216\pi\) | ||||
0.464552 | + | 0.885546i | \(0.346216\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.6969i | 0.618305i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.00000 | + | 22.0454i | −0.377964 | + | 0.925820i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.00000i | 0.251533i | 0.992060 | + | 0.125767i | \(0.0401390\pi\) | ||||
−0.992060 | + | 0.125767i | \(0.959861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.0000 | 1.33916 | 0.669579 | − | 0.742741i | \(-0.266474\pi\) | ||||
0.669579 | + | 0.742741i | \(0.266474\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.00000i | 0.250217i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 19.5959i | − | 0.815789i | −0.913029 | − | 0.407894i | \(-0.866263\pi\) | ||
0.913029 | − | 0.407894i | \(-0.133737\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.89898 | − | 4.89898i | −0.203595 | − | 0.203595i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.44949 | + | 6.00000i | −0.101622 | + | 0.248922i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.0000 | 0.744208 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.34847 | 0.303304 | 0.151652 | − | 0.988434i | \(-0.451541\pi\) | ||||
0.151652 | + | 0.988434i | \(0.451541\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.0454 | − | 22.0454i | 0.906827 | − | 0.906827i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −39.1918 | −1.60942 | −0.804708 | − | 0.593671i | \(-0.797678\pi\) | ||||
−0.804708 | + | 0.593671i | \(0.797678\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.0000 | − | 29.3939i | 0.491952 | − | 1.20503i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.0000 | − | 12.0000i | 0.491127 | − | 0.491127i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0000i | 0.980613i | 0.871550 | + | 0.490307i | \(0.163115\pi\) | ||||
−0.871550 | + | 0.490307i | \(0.836885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.0000i | 0.977356i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −26.9444 | −1.09545 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 4.89898i | − | 0.198843i | −0.995045 | − | 0.0994217i | \(-0.968301\pi\) | ||
0.995045 | − | 0.0994217i | \(-0.0316993\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.6515 | + | 25.3485i | 0.431622 | + | 1.02717i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.0000i | 0.485468i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.0000 | −0.565455 | −0.282727 | − | 0.959200i | \(-0.591239\pi\) | ||||
−0.282727 | + | 0.959200i | \(0.591239\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14.6969 | + | 14.6969i | 0.592638 | + | 0.592638i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 18.0000i | − | 0.724653i | −0.932051 | − | 0.362326i | \(-0.881983\pi\) | ||
0.932051 | − | 0.362326i | \(-0.118017\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.9444i | 1.08299i | 0.840705 | + | 0.541493i | \(0.182141\pi\) | ||||
−0.840705 | + | 0.541493i | \(0.817859\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.0454 | + | 22.0454i | 0.884652 | + | 0.884652i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.79796 | −0.390670 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.00000 | −0.0796187 | −0.0398094 | − | 0.999207i | \(-0.512675\pi\) | ||||
−0.0398094 | + | 0.999207i | \(0.512675\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.79796 | + | 9.79796i | 0.389434 | + | 0.389434i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.5959 | 0.777640 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.0000 | − | 12.2474i | 0.475457 | − | 0.485262i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.0000i | 1.18493i | 0.805597 | + | 0.592464i | \(0.201845\pi\) | ||||
−0.805597 | + | 0.592464i | \(0.798155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.0454i | 0.869386i | 0.900579 | + | 0.434693i | \(0.143143\pi\) | ||||
−0.900579 | + | 0.434693i | \(0.856857\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.0000 | + | 12.0000i | 0.472500 | + | 0.472500i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −44.0908 | −1.73339 | −0.866694 | − | 0.498839i | \(-0.833760\pi\) | ||||
−0.866694 | + | 0.498839i | \(0.833760\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.00000i | 0.234798i | 0.993085 | + | 0.117399i | \(0.0374557\pi\) | ||||
−0.993085 | + | 0.117399i | \(0.962544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.0000 | 0.703318 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −29.3939 | −1.14676 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.0000i | 1.40236i | 0.712984 | + | 0.701180i | \(0.247343\pi\) | ||||
−0.712984 | + | 0.701180i | \(0.752657\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 12.2474i | − | 0.476371i | −0.971220 | − | 0.238185i | \(-0.923447\pi\) | ||
0.971220 | − | 0.238185i | \(-0.0765525\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.6969 | + | 14.6969i | −0.570782 | + | 0.570782i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.6969 | − | 6.00000i | −0.569923 | − | 0.232670i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.0000 | 1.39393 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.0000 | − | 18.0000i | 0.695920 | − | 0.695920i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.0000 | 1.31060 | 0.655302 | − | 0.755367i | \(-0.272541\pi\) | ||||
0.655302 | + | 0.755367i | \(0.272541\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.67423 | − | 3.67423i | 0.141421 | − | 0.141421i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.34847 | −0.282425 | −0.141212 | − | 0.989979i | \(-0.545100\pi\) | ||||
−0.141212 | + | 0.989979i | \(0.545100\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0000 | + | 4.89898i | 0.460518 | + | 0.188006i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.00000 | − | 9.00000i | −0.344881 | − | 0.344881i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.0000i | 0.918334i | 0.888350 | + | 0.459167i | \(0.151852\pi\) | ||||
−0.888350 | + | 0.459167i | \(0.848148\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 29.3939i | − | 1.12308i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.0000 | − | 27.0000i | 1.03011 | − | 1.03011i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.6969 | −0.559909 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 36.7423i | − | 1.39774i | −0.715246 | − | 0.698872i | \(-0.753686\pi\) | ||
0.715246 | − | 0.698872i | \(-0.246314\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 6.00000i | − | 0.227593i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.0000 | −0.909065 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.3939 | − | 29.3939i | 1.11178 | − | 1.11178i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000i | 1.13308i | 0.824033 | + | 0.566542i | \(0.191719\pi\) | ||||
−0.824033 | + | 0.566542i | \(0.808281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.89898i | 0.184769i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.6969 | + | 14.6969i | 0.553519 | + | 0.553519i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.34847 | − | 18.0000i | 0.276368 | − | 0.676960i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.0000 | −0.375558 | −0.187779 | − | 0.982211i | \(-0.560129\pi\) | ||||
−0.187779 | + | 0.982211i | \(0.560129\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 30.0000i | 1.12509i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.34847 | + | 7.34847i | −0.274434 | + | 0.274434i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.4949 | 0.913506 | 0.456753 | − | 0.889594i | \(-0.349012\pi\) | ||||
0.456753 | + | 0.889594i | \(0.349012\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0000 | − | 9.79796i | −0.893807 | − | 0.364895i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 30.0000 | − | 30.0000i | 1.11571 | − | 1.11571i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 6.00000i | − | 0.222834i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 29.3939i | − | 1.09016i | −0.838385 | − | 0.545079i | \(-0.816500\pi\) | ||
0.838385 | − | 0.545079i | \(-0.183500\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.5959 | −0.724781 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 22.0454i | − | 0.814266i | −0.913369 | − | 0.407133i | \(-0.866529\pi\) | ||
0.913369 | − | 0.407133i | \(-0.133471\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.303062 | − | 29.6969i | −0.0111786 | − | 1.09539i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.34847 | + | 7.34847i | 0.269953 | + | 0.269953i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.00000i | 0.220119i | 0.993925 | + | 0.110059i | \(0.0351041\pi\) | ||||
−0.993925 | + | 0.110059i | \(0.964896\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.6969i | 0.538454i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 7.34847i | − | 0.268866i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.3939 | + | 12.0000i | 1.07403 | + | 0.438470i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | 0.291924 | 0.145962 | − | 0.989290i | \(-0.453372\pi\) | ||||
0.145962 | + | 0.989290i | \(0.453372\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.0000 | − | 21.0000i | −0.765283 | − | 0.765283i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.5959 | −0.713168 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.89898 | 0.177588 | 0.0887939 | − | 0.996050i | \(-0.471699\pi\) | ||||
0.0887939 | + | 0.996050i | \(0.471699\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.0000 | + | 24.4949i | −0.362024 | + | 0.886775i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 36.0000i | 1.30158i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 30.0000i | 1.08324i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 34.2929i | − | 1.23663i | −0.785930 | − | 0.618316i | \(-0.787815\pi\) | ||
0.785930 | − | 0.618316i | \(-0.212185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.0000 | + | 36.0000i | 1.29651 | + | 1.29651i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.9444 | 0.969122 | 0.484561 | − | 0.874757i | \(-0.338979\pi\) | ||||
0.484561 | + | 0.874757i | \(0.338979\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.44949 | + | 3.55051i | −0.303124 | + | 0.127374i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.0000i | 0.429945i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22.0454 | − | 22.0454i | −0.787839 | − | 0.787839i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 18.0000i | − | 0.642448i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 31.8434i | − | 1.13509i | −0.823341 | − | 0.567547i | \(-0.807893\pi\) | ||
0.823341 | − | 0.567547i | \(-0.192107\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −29.3939 | + | 29.3939i | −1.04645 | + | 1.04645i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.6969 | − | 6.00000i | −0.522563 | − | 0.213335i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.0000 | −1.06533 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18.0000 | + | 18.0000i | −0.638394 | + | 0.638394i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.34847 | −0.260296 | −0.130148 | − | 0.991495i | \(-0.541545\pi\) | ||||
−0.130148 | + | 0.991495i | \(0.541545\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −36.0000 | − | 14.6969i | −1.26883 | − | 0.517999i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.0000 | + | 15.0000i | 0.528025 | + | 0.528025i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.00000i | 0.210949i | 0.994422 | + | 0.105474i | \(0.0336361\pi\) | ||||
−0.994422 | + | 0.105474i | \(0.966364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 36.7423i | − | 1.29020i | −0.764099 | − | 0.645099i | \(-0.776816\pi\) | ||
0.764099 | − | 0.645099i | \(-0.223184\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.0000 | − | 30.0000i | 1.05215 | − | 1.05215i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 39.1918 | 1.37283 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.79796i | 0.342787i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.34847 | + | 18.0000i | −0.256776 | + | 0.628971i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 30.0000i | − | 1.04701i | −0.852023 | − | 0.523504i | \(-0.824625\pi\) | ||
0.852023 | − | 0.523504i | \(-0.175375\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.0000 | −0.488009 | −0.244005 | − | 0.969774i | \(-0.578461\pi\) | ||||
−0.244005 | + | 0.969774i | \(0.578461\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.0000i | 0.417281i | 0.977992 | + | 0.208640i | \(0.0669038\pi\) | ||||
−0.977992 | + | 0.208640i | \(0.933096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 26.9444i | − | 0.935817i | −0.883777 | − | 0.467909i | \(-0.845008\pi\) | ||
0.883777 | − | 0.467909i | \(-0.154992\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.9444 | − | 26.9444i | −0.934690 | − | 0.934690i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.4949 | + | 24.0000i | 0.848698 | + | 0.831551i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.0000 | −0.415277 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.4949 | −0.845658 | −0.422829 | − | 0.906210i | \(-0.638963\pi\) | ||||
−0.422829 | + | 0.906210i | \(0.638963\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.1464 | −0.589855 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.0000 | − | 26.9444i | 0.377964 | − | 0.925820i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27.0000 | − | 27.0000i | 0.926638 | − | 0.926638i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.0000i | 0.411355i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.44949i | 0.0838689i | 0.999120 | + | 0.0419345i | \(0.0133521\pi\) | ||||
−0.999120 | + | 0.0419345i | \(0.986648\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.0000 | 0.615587 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.89898 | −0.167346 | −0.0836730 | − | 0.996493i | \(-0.526665\pi\) | ||||
−0.0836730 | + | 0.996493i | \(0.526665\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.9444i | 0.919331i | 0.888092 | + | 0.459665i | \(0.152031\pi\) | ||||
−0.888092 | + | 0.459665i | \(0.847969\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20.6969 | + | 8.69694i | −0.705350 | + | 0.296391i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 24.0000i | − | 0.816970i | −0.912765 | − | 0.408485i | \(-0.866057\pi\) | ||
0.912765 | − | 0.408485i | \(-0.133943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 54.0000 | 1.83606 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.57321 | − | 8.57321i | −0.291162 | − | 0.291162i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.5959i | 0.663982i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.6969 | −0.497416 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.79796 | − | 24.0000i | 0.331231 | − | 0.811348i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.0000 | 0.742887 | 0.371444 | − | 0.928456i | \(-0.378863\pi\) | ||||
0.371444 | + | 0.928456i | \(0.378863\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.00000 | − | 3.00000i | −0.101187 | − | 0.101187i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.3939 | 0.990305 | 0.495152 | − | 0.868806i | \(-0.335112\pi\) | ||||
0.495152 | + | 0.868806i | \(0.335112\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −56.0000 | −1.88455 | −0.942275 | − | 0.334840i | \(-0.891318\pi\) | ||||
−0.942275 | + | 0.334840i | \(0.891318\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 36.7423 | + | 36.7423i | 1.23508 | + | 1.23508i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.89898 | 0.164492 | 0.0822458 | − | 0.996612i | \(-0.473791\pi\) | ||||
0.0822458 | + | 0.996612i | \(0.473791\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.00000 | + | 19.5959i | −0.268311 | + | 0.657226i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.0000i | 0.401565i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 58.7878i | 1.96506i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.0000 | + | 18.0000i | 0.601003 | + | 0.601003i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 29.3939i | − | 0.979252i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.8990 | + | 7.10102i | −0.562363 | + | 0.236307i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30.0000i | 0.997234i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.0000 | 0.929725 | 0.464862 | − | 0.885383i | \(-0.346104\pi\) | ||||
0.464862 | + | 0.885383i | \(0.346104\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22.0454i | 0.731200i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0000i | 0.993944i | 0.867766 | + | 0.496972i | \(0.165555\pi\) | ||||
−0.867766 | + | 0.496972i | \(0.834445\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −36.7423 | + | 36.7423i | −1.21466 | + | 1.21466i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.34847 | + | 18.0000i | −0.242668 | + | 0.594412i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.0000 | −0.329870 | −0.164935 | − | 0.986304i | \(-0.552741\pi\) | ||||
−0.164935 | + | 0.986304i | \(0.552741\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.00000 | + | 9.00000i | −0.296560 | + | 0.296560i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000 | 0.0657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 29.3939 | 0.965422 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.4949 | 0.803652 | 0.401826 | − | 0.915716i | \(-0.368376\pi\) | ||||
0.401826 | + | 0.915716i | \(0.368376\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.0000 | − | 12.2474i | 0.393284 | − | 0.401394i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.0000 | − | 24.0000i | −0.785725 | − | 0.785725i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19.5959i | − | 0.640171i | −0.947389 | − | 0.320085i | \(-0.896288\pi\) | ||
0.947389 | − | 0.320085i | \(-0.103712\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 42.0000 | − | 42.0000i | 1.37062 | − | 1.37062i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.8434 | 1.03806 | 0.519032 | − | 0.854755i | \(-0.326293\pi\) | ||||
0.519032 | + | 0.854755i | \(0.326293\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.3939i | 0.957196i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.0454 | + | 31.0454i | 0.424367 | + | 1.00991i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.0000i | 0.389948i | 0.980808 | + | 0.194974i | \(0.0624622\pi\) | ||||
−0.980808 | + | 0.194974i | \(0.937538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.0000 | −0.779073 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.0454 | − | 22.0454i | 0.714871 | − | 0.714871i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 36.0000i | − | 1.16615i | −0.812417 | − | 0.583077i | \(-0.801849\pi\) | ||
0.812417 | − | 0.583077i | \(-0.198151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29.3939 | + | 12.0000i | 0.949178 | + | 0.387500i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −36.0000 | −1.16008 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.79796 | −0.315407 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.00000 | −0.257263 | −0.128631 | − | 0.991692i | \(-0.541058\pi\) | ||||
−0.128631 | + | 0.991692i | \(0.541058\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.6969 | + | 14.6969i | −0.472134 | + | 0.472134i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.6413 | 1.33633 | 0.668167 | − | 0.744011i | \(-0.267079\pi\) | ||||
0.668167 | + | 0.744011i | \(0.267079\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.00000 | + | 2.44949i | 0.192351 | + | 0.0785270i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.00000 | − | 3.00000i | 0.0960769 | − | 0.0960769i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.0000i | 0.383914i | 0.981403 | + | 0.191957i | \(0.0614834\pi\) | ||||
−0.981403 | + | 0.191957i | \(0.938517\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 30.0000i | − | 0.957826i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34.2929 | −1.09377 | −0.546886 | − | 0.837207i | \(-0.684187\pi\) | ||||
−0.546886 | + | 0.837207i | \(0.684187\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 44.0908i | − | 1.40485i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −20.6969 | + | 8.69694i | −0.658791 | + | 0.276827i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.0000i | 0.763156i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.0000 | 1.20711 | 0.603555 | − | 0.797321i | \(-0.293750\pi\) | ||||
0.603555 | + | 0.797321i | \(0.293750\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.79796 | + | 9.79796i | 0.310929 | + | 0.310929i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 24.0000i | − | 0.760851i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.34847i | 0.232728i | 0.993207 | + | 0.116364i | \(0.0371240\pi\) | ||||
−0.993207 | + | 0.116364i | \(0.962876\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.34847 | − | 7.34847i | 0.232495 | − | 0.232495i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))