Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3240,2,Mod(1081,3240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3240, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3240.1081");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3240.q (of order \(3\), 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: | \(25.8715302549\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1081.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3240.1081 |
Dual form | 3240.2.q.m.2161.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3240\mathbb{Z}\right)^\times\).
\(n\) | \(1297\) | \(1621\) | \(2431\) | \(3161\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | − | 3.46410i | −0.755929 | − | 1.30931i | −0.944911 | − | 0.327327i | \(-0.893852\pi\) |
0.188982 | − | 0.981981i | \(-0.439481\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | − | 5.19615i | 0.832050 | − | 1.44115i | −0.0643593 | − | 0.997927i | \(-0.520500\pi\) |
0.896410 | − | 0.443227i | \(-0.146166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | − | 6.92820i | 0.834058 | − | 1.44463i | −0.0607377 | − | 0.998154i | \(-0.519345\pi\) |
0.894795 | − | 0.446476i | \(-0.147321\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | + | 5.19615i | 0.557086 | + | 0.964901i | 0.997738 | + | 0.0672232i | \(0.0214140\pi\) |
−0.440652 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.00000 | −0.676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.00000 | + | 8.66025i | −0.780869 | + | 1.35250i | 0.150567 | + | 0.988600i | \(0.451890\pi\) |
−0.931436 | + | 0.363905i | \(0.881443\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | + | 3.46410i | 0.304997 | + | 0.528271i | 0.977261 | − | 0.212041i | \(-0.0680112\pi\) |
−0.672264 | + | 0.740312i | \(0.734678\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.00000 | − | 6.92820i | −0.583460 | − | 1.01058i | −0.995066 | − | 0.0992202i | \(-0.968365\pi\) |
0.411606 | − | 0.911362i | \(-0.364968\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.50000 | + | 7.79423i | −0.642857 | + | 1.11346i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.0000 | 1.37361 | 0.686803 | − | 0.726844i | \(-0.259014\pi\) | ||||
0.686803 | + | 0.726844i | \(0.259014\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | − | 5.19615i | −0.384111 | − | 0.665299i | 0.607535 | − | 0.794293i | \(-0.292159\pi\) |
−0.991645 | + | 0.128994i | \(0.958825\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.00000 | − | 5.19615i | −0.372104 | − | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | − | 3.46410i | 0.244339 | − | 0.423207i | −0.717607 | − | 0.696449i | \(-0.754762\pi\) |
0.961946 | + | 0.273241i | \(0.0880957\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.0000 | −1.63858 | −0.819288 | − | 0.573382i | \(-0.805631\pi\) | ||||
−0.819288 | + | 0.573382i | \(0.805631\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | − | 13.8564i | −0.900070 | − | 1.55897i | −0.827401 | − | 0.561611i | \(-0.810182\pi\) |
−0.0726692 | − | 0.997356i | \(-0.523152\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | − | 10.3923i | −0.658586 | − | 1.14070i | −0.980982 | − | 0.194099i | \(-0.937822\pi\) |
0.322396 | − | 0.946605i | \(-0.395512\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.00000 | + | 1.73205i | −0.108465 | + | 0.187867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −24.0000 | −2.51588 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | − | 3.46410i | 0.205196 | − | 0.355409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | − | 1.73205i | −0.101535 | − | 0.175863i | 0.810782 | − | 0.585348i | \(-0.199042\pi\) |
−0.912317 | + | 0.409484i | \(0.865709\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.00000 | + | 12.1244i | 0.696526 | + | 1.20642i | 0.969664 | + | 0.244443i | \(0.0786053\pi\) |
−0.273138 | + | 0.961975i | \(0.588061\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.00000 | + | 3.46410i | −0.197066 | + | 0.341328i | −0.947576 | − | 0.319531i | \(-0.896475\pi\) |
0.750510 | + | 0.660859i | \(0.229808\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.00000 | + | 5.19615i | −0.282216 | + | 0.488813i | −0.971930 | − | 0.235269i | \(-0.924403\pi\) |
0.689714 | + | 0.724082i | \(0.257736\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | − | 6.92820i | −0.373002 | − | 0.646058i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.00000 | + | 6.92820i | 0.366679 | + | 0.635107i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | − | 9.52628i | 0.500000 | − | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.00000 | + | 13.8564i | −0.698963 | + | 1.21064i | 0.269863 | + | 0.962899i | \(0.413022\pi\) |
−0.968826 | + | 0.247741i | \(0.920312\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | − | 13.8564i | −0.693688 | − | 1.20150i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.00000 | + | 15.5885i | 0.768922 | + | 1.33181i | 0.938148 | + | 0.346235i | \(0.112540\pi\) |
−0.169226 | + | 0.985577i | \(0.554127\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.00000 | − | 10.3923i | 0.508913 | − | 0.881464i | −0.491033 | − | 0.871141i | \(-0.663381\pi\) |
0.999947 | − | 0.0103230i | \(-0.00328598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.00000 | 0.498273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.00000 | + | 8.66025i | −0.399043 | + | 0.691164i | −0.993608 | − | 0.112884i | \(-0.963991\pi\) |
0.594565 | + | 0.804048i | \(0.297324\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −32.0000 | −2.52195 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.00000 | − | 6.92820i | 0.309529 | − | 0.536120i | −0.668730 | − | 0.743505i | \(-0.733162\pi\) |
0.978259 | + | 0.207385i | \(0.0664952\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5000 | − | 19.9186i | −0.884615 | − | 1.53220i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.00000 | − | 15.5885i | −0.684257 | − | 1.18517i | −0.973670 | − | 0.227964i | \(-0.926793\pi\) |
0.289412 | − | 0.957205i | \(-0.406540\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | + | 3.46410i | −0.151186 | + | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.00000 | 0.597948 | 0.298974 | − | 0.954261i | \(-0.403356\pi\) | ||||
0.298974 | + | 0.954261i | \(0.403356\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.00000 | + | 5.19615i | −0.220564 | + | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.00000 | − | 6.92820i | −0.289430 | − | 0.501307i | 0.684244 | − | 0.729253i | \(-0.260132\pi\) |
−0.973674 | + | 0.227946i | \(0.926799\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.00000 | − | 5.19615i | 0.215945 | − | 0.374027i | −0.737620 | − | 0.675216i | \(-0.764050\pi\) |
0.953564 | + | 0.301189i | \(0.0973836\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.0000 | 0.712470 | 0.356235 | − | 0.934396i | \(-0.384060\pi\) | ||||
0.356235 | + | 0.934396i | \(0.384060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.0000 | − | 20.7846i | 0.842235 | − | 1.45879i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.00000 | + | 8.66025i | 0.349215 | + | 0.604858i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.00000 | + | 10.3923i | −0.413057 | + | 0.715436i | −0.995222 | − | 0.0976347i | \(-0.968872\pi\) |
0.582165 | + | 0.813070i | \(0.302206\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.00000 | 0.272798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.00000 | + | 10.3923i | −0.403604 | + | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.00000 | − | 10.3923i | −0.401790 | − | 0.695920i | 0.592152 | − | 0.805826i | \(-0.298278\pi\) |
−0.993942 | + | 0.109906i | \(0.964945\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.00000 | + | 10.3923i | 0.398234 | + | 0.689761i | 0.993508 | − | 0.113761i | \(-0.0362899\pi\) |
−0.595274 | + | 0.803523i | \(0.702957\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.00000 | + | 5.19615i | −0.198246 | + | 0.343371i | −0.947960 | − | 0.318390i | \(-0.896858\pi\) |
0.749714 | + | 0.661762i | \(0.230191\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.0000 | −0.655122 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | −0.521862 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | − | 20.7846i | 0.776215 | − | 1.34444i | −0.157893 | − | 0.987456i | \(-0.550470\pi\) |
0.934109 | − | 0.356988i | \(-0.116196\pi\) | |||||||
\(240\) | 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 | ||||||||
\(245\) | 4.50000 | + | 7.79423i | 0.287494 | + | 0.497955i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000 | − | 20.7846i | 0.763542 | − | 1.32249i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.00000 | −0.504956 | −0.252478 | − | 0.967603i | \(-0.581245\pi\) | ||||
−0.252478 | + | 0.967603i | \(0.581245\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.00000 | + | 5.19615i | −0.187135 | + | 0.324127i | −0.944294 | − | 0.329104i | \(-0.893253\pi\) |
0.757159 | + | 0.653231i | \(0.226587\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.0000 | + | 20.7846i | 0.745644 | + | 1.29149i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.0000 | + | 20.7846i | 0.739952 | + | 1.28163i | 0.952517 | + | 0.304487i | \(0.0984850\pi\) |
−0.212565 | + | 0.977147i | \(0.568182\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.00000 | − | 8.66025i | 0.307148 | − | 0.531995i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.00000 | −0.365826 | −0.182913 | − | 0.983129i | \(-0.558553\pi\) | ||||
−0.182913 | + | 0.983129i | \(0.558553\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.00000 | − | 8.66025i | −0.300421 | − | 0.520344i | 0.675810 | − | 0.737075i | \(-0.263794\pi\) |
−0.976231 | + | 0.216731i | \(0.930460\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.00000 | − | 1.73205i | −0.0596550 | − | 0.103325i | 0.834656 | − | 0.550772i | \(-0.185667\pi\) |
−0.894311 | + | 0.447447i | \(0.852333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.00000 | + | 3.46410i | −0.118888 | + | 0.205919i | −0.919327 | − | 0.393494i | \(-0.871266\pi\) |
0.800439 | + | 0.599414i | \(0.204600\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 40.0000 | 2.36113 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.00000 | + | 8.66025i | −0.292103 | + | 0.505937i | −0.974307 | − | 0.225225i | \(-0.927688\pi\) |
0.682204 | + | 0.731162i | \(0.261022\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.0000 | − | 41.5692i | −1.38796 | − | 2.40401i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | − | 13.8564i | 0.461112 | − | 0.798670i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.00000 | −0.343559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00000 | 0.228292 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.00000 | + | 13.8564i | −0.453638 | + | 0.785725i | −0.998609 | − | 0.0527306i | \(-0.983208\pi\) |
0.544970 | + | 0.838455i | \(0.316541\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.00000 | + | 12.1244i | 0.395663 | + | 0.685309i | 0.993186 | − | 0.116543i | \(-0.0371814\pi\) |
−0.597522 | + | 0.801852i | \(0.703848\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.00000 | − | 1.73205i | −0.0561656 | − | 0.0972817i | 0.836576 | − | 0.547852i | \(-0.184554\pi\) |
−0.892741 | + | 0.450570i | \(0.851221\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.00000 | −0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.00000 | −0.332820 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.0000 | + | 27.7128i | −0.882109 | + | 1.52786i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.0000 | − | 24.2487i | −0.769510 | − | 1.33283i | −0.937829 | − | 0.347097i | \(-0.887167\pi\) |
0.168320 | − | 0.985732i | \(-0.446166\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.00000 | − | 3.46410i | −0.109272 | − | 0.189264i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.00000 | + | 8.66025i | −0.272367 | + | 0.471754i | −0.969468 | − | 0.245220i | \(-0.921140\pi\) |
0.697100 | + | 0.716974i | \(0.254473\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.00000 | 0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.0000 | − | 31.1769i | 0.966291 | − | 1.67366i | 0.260184 | − | 0.965559i | \(-0.416217\pi\) |
0.706107 | − | 0.708105i | \(-0.250450\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.0000 | + | 22.5167i | 0.695874 | + | 1.20529i | 0.969885 | + | 0.243563i | \(0.0783162\pi\) |
−0.274011 | + | 0.961727i | \(0.588351\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.00000 | + | 15.5885i | 0.479022 | + | 0.829690i | 0.999711 | − | 0.0240566i | \(-0.00765819\pi\) |
−0.520689 | + | 0.853746i | \(0.674325\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.00000 | 0.422224 | 0.211112 | − | 0.977462i | \(-0.432292\pi\) | ||||
0.211112 | + | 0.977462i | \(0.432292\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.00000 | + | 12.1244i | −0.366397 | + | 0.634618i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.0000 | − | 24.2487i | −0.730794 | − | 1.26577i | −0.956544 | − | 0.291587i | \(-0.905817\pi\) |
0.225750 | − | 0.974185i | \(-0.427517\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.0000 | − | 34.6410i | −1.03835 | − | 1.79847i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.00000 | + | 1.73205i | −0.0517780 | + | 0.0896822i | −0.890753 | − | 0.454488i | \(-0.849822\pi\) |
0.838975 | + | 0.544170i | \(0.183156\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 36.0000 | 1.85409 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.00000 | 0.205466 | 0.102733 | − | 0.994709i | \(-0.467241\pi\) | ||||
0.102733 | + | 0.994709i | \(0.467241\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.00000 | + | 6.92820i | −0.204390 | + | 0.354015i | −0.949938 | − | 0.312437i | \(-0.898855\pi\) |
0.745548 | + | 0.666452i | \(0.232188\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.00000 | + | 5.19615i | 0.152106 | + | 0.263455i | 0.932002 | − | 0.362454i | \(-0.118061\pi\) |
−0.779895 | + | 0.625910i | \(0.784728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.00000 | + | 13.8564i | −0.404577 | + | 0.700749i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.0000 | −0.805047 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.00000 | − | 5.19615i | 0.149813 | − | 0.259483i | −0.781345 | − | 0.624099i | \(-0.785466\pi\) |
0.931158 | + | 0.364615i | \(0.118800\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.0000 | − | 32.9090i | 0.939490 | − | 1.62724i | 0.173064 | − | 0.984911i | \(-0.444633\pi\) |
0.766426 | − | 0.642333i | \(-0.222033\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | −0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.00000 | − | 13.8564i | 0.390826 | − | 0.676930i | −0.601733 | − | 0.798697i | \(-0.705523\pi\) |
0.992559 | + | 0.121768i | \(0.0388562\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.00000 | − | 5.19615i | −0.146211 | − | 0.253245i | 0.783613 | − | 0.621249i | \(-0.213375\pi\) |
−0.929824 | + | 0.368004i | \(0.880041\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.00000 | + | 1.73205i | 0.0485071 | + | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.0000 | + | 20.7846i | −0.580721 | + | 1.00584i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.0000 | −1.54139 | −0.770693 | − | 0.637207i | \(-0.780090\pi\) | ||||
−0.770693 | + | 0.637207i | \(0.780090\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.0000 | 0.480569 | 0.240285 | − | 0.970702i | \(-0.422759\pi\) | ||||
0.240285 | + | 0.970702i | \(0.422759\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.0000 | − | 27.7128i | 0.765384 | − | 1.32568i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0000 | + | 27.7128i | 0.763638 | + | 1.32266i | 0.940963 | + | 0.338508i | \(0.109922\pi\) |
−0.177325 | + | 0.984152i | \(0.556744\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.00000 | − | 10.3923i | −0.285069 | − | 0.493753i | 0.687557 | − | 0.726130i | \(-0.258683\pi\) |
−0.972626 | + | 0.232377i | \(0.925350\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.00000 | − | 1.73205i | 0.0474045 | − | 0.0821071i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.0000 | 1.22702 | 0.613508 | − | 0.789689i | \(-0.289758\pi\) | ||||
0.613508 | + | 0.789689i | \(0.289758\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.0000 | + | 20.7846i | −0.562569 | + | 0.974398i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.0000 | + | 32.9090i | 0.888783 | + | 1.53942i | 0.841316 | + | 0.540544i | \(0.181781\pi\) |
0.0474665 | + | 0.998873i | \(0.484885\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.00000 | − | 1.73205i | −0.0465746 | − | 0.0806696i | 0.841798 | − | 0.539792i | \(-0.181497\pi\) |
−0.888373 | + | 0.459123i | \(0.848164\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.00000 | + | 3.46410i | −0.0929479 | + | 0.160990i | −0.908750 | − | 0.417340i | \(-0.862962\pi\) |
0.815802 | + | 0.578331i | \(0.196296\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.0000 | −0.925490 | −0.462745 | − | 0.886492i | \(-0.653135\pi\) | ||||
−0.462745 | + | 0.886492i | \(0.653135\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.00000 | − | 3.46410i | −0.0917663 | − | 0.158944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.0000 | + | 20.7846i | 0.548294 | + | 0.949673i | 0.998392 | + | 0.0566937i | \(0.0180558\pi\) |
−0.450098 | + | 0.892979i | \(0.648611\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.0000 | + | 31.1769i | −0.820729 | + | 1.42154i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.00000 | −0.0908153 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.0000 | −1.63132 | −0.815658 | − | 0.578535i | \(-0.803625\pi\) | ||||
−0.815658 | + | 0.578535i | \(0.803625\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.0000 | − | 34.6410i | 0.902587 | − | 1.56333i | 0.0784639 | − | 0.996917i | \(-0.474998\pi\) |
0.824123 | − | 0.566410i | \(-0.191668\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.00000 | − | 10.3923i | −0.270226 | − | 0.468046i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.0000 | + | 17.3205i | −0.447661 | + | 0.775372i | −0.998233 | − | 0.0594153i | \(-0.981076\pi\) |
0.550572 | + | 0.834788i | \(0.314410\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.0000 | 0.622992 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.00000 | − | 5.19615i | 0.132973 | − | 0.230315i | −0.791849 | − | 0.610718i | \(-0.790881\pi\) |
0.924821 | + | 0.380402i | \(0.124214\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.0000 | + | 48.4974i | 1.23865 | + | 2.14540i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.00000 | + | 3.46410i | 0.0881305 | + | 0.152647i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.0000 | −0.613351 | −0.306676 | − | 0.951814i | \(-0.599217\pi\) | ||||
−0.306676 | + | 0.951814i | \(0.599217\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.0000 | 1.57417 | 0.787085 | − | 0.616844i | \(-0.211589\pi\) | ||||
0.787085 | + | 0.616844i | \(0.211589\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5000 | − | 35.5070i | −0.891304 | − | 1.54378i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.0000 | + | 51.9615i | 1.29944 | + | 2.25070i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.00000 | − | 3.46410i | 0.0864675 | − | 0.149766i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0000 | −0.429934 | −0.214967 | − | 0.976621i | \(-0.568964\pi\) | ||||
−0.214967 | + | 0.976621i | \(0.568964\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.00000 | + | 8.66025i | −0.214176 | + | 0.370965i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.00000 | − | 3.46410i | −0.0855138 | − | 0.148114i | 0.820096 | − | 0.572226i | \(-0.193920\pi\) |
−0.905610 | + | 0.424111i | \(0.860587\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.0000 | + | 20.7846i | 0.511217 | + | 0.885454i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −32.0000 | + | 55.4256i | −1.36078 | + | 2.35694i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.0000 | −0.593199 | −0.296600 | − | 0.955002i | \(-0.595853\pi\) | ||||
−0.296600 | + | 0.955002i | \(0.595853\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.0000 | 1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.0000 | + | 31.1769i | −0.758610 | + | 1.31395i | 0.184950 | + | 0.982748i | \(0.440788\pi\) |
−0.943560 | + | 0.331202i | \(0.892546\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.00000 | + | 5.19615i | 0.126211 | + | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.00000 | + | 12.1244i | 0.293455 | + | 0.508279i | 0.974624 | − | 0.223847i | \(-0.0718615\pi\) |
−0.681169 | + | 0.732126i | \(0.738528\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.0000 | − | 17.3205i | 0.418487 | − | 0.724841i | −0.577301 | − | 0.816532i | \(-0.695894\pi\) |
0.995788 | + | 0.0916910i | \(0.0292272\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.00000 | −0.333623 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.0000 | 1.41544 | 0.707719 | − | 0.706494i | \(-0.249724\pi\) | ||||
0.707719 | + | 0.706494i | \(0.249724\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.0000 | + | 41.5692i | −0.995688 | + | 1.72458i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.0000 | − | 31.1769i | −0.742940 | − | 1.28681i | −0.951151 | − | 0.308725i | \(-0.900098\pi\) |
0.208212 | − | 0.978084i | \(-0.433236\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.0000 | 0.903432 | 0.451716 | − | 0.892162i | \(-0.350812\pi\) | ||||
0.451716 | + | 0.892162i | \(0.350812\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.00000 | 0.327968 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.00000 | + | 6.92820i | −0.163436 | + | 0.283079i | −0.936099 | − | 0.351738i | \(-0.885591\pi\) |
0.772663 | + | 0.634816i | \(0.218924\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.0000 | + | 19.0526i | 0.448699 | + | 0.777170i | 0.998302 | − | 0.0582563i | \(-0.0185541\pi\) |
−0.549602 | + | 0.835426i | \(0.685221\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.50000 | − | 9.52628i | −0.223607 | − | 0.387298i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.00000 | − | 10.3923i | 0.243532 | − | 0.421811i | −0.718186 | − | 0.695852i | \(-0.755027\pi\) |
0.961718 | + | 0.274041i | \(0.0883604\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −48.0000 | −1.94187 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.0000 | 1.05013 | 0.525065 | − | 0.851062i | \(-0.324041\pi\) | ||||
0.525065 | + | 0.851062i | \(0.324041\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.0000 | − | 22.5167i | 0.523360 | − | 0.906487i | −0.476270 | − | 0.879299i | \(-0.658012\pi\) |
0.999630 | − | 0.0271876i | \(-0.00865514\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.0000 | + | 24.2487i | 0.562708 | + | 0.974638i | 0.997259 | + | 0.0739910i | \(0.0235736\pi\) |
−0.434551 | + | 0.900647i | \(0.643093\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.00000 | − | 6.92820i | −0.160257 | − | 0.277573i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.0000 | 1.59237 | 0.796187 | − | 0.605050i | \(-0.206847\pi\) | ||||
0.796187 | + | 0.605050i | \(0.206847\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.00000 | + | 3.46410i | −0.0793676 | + | 0.137469i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.0000 | + | 46.7654i | 1.06978 | + | 1.85291i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.00000 | − | 15.5885i | −0.355479 | − | 0.615707i | 0.631721 | − | 0.775196i | \(-0.282349\pi\) |
−0.987200 | + | 0.159489i | \(0.949015\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.0000 | − | 31.1769i | 0.709851 | − | 1.22950i | −0.255062 | − | 0.966925i | \(-0.582096\pi\) |
0.964912 | − | 0.262573i | \(-0.0845709\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 48.0000 | 1.88707 | 0.943537 | − | 0.331266i | \(-0.107476\pi\) | ||||
0.943537 | + | 0.331266i | \(0.107476\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.00000 | + | 15.5885i | −0.352197 | + | 0.610023i | −0.986634 | − | 0.162951i | \(-0.947899\pi\) |
0.634437 | + | 0.772975i | \(0.281232\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.00000 | + | 13.8564i | 0.312586 | + | 0.541415i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.00000 | + | 13.8564i | 0.311636 | + | 0.539769i | 0.978717 | − | 0.205216i | \(-0.0657898\pi\) |
−0.667081 | + | 0.744985i | \(0.732456\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.00000 | − | 1.73205i | 0.0388955 | − | 0.0673690i | −0.845922 | − | 0.533306i | \(-0.820949\pi\) |
0.884818 | + | 0.465937i | \(0.154283\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.0000 | −0.620453 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.0000 | 1.85857 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.0000 | + | 19.0526i | 0.424019 | + | 0.734422i | 0.996328 | − | 0.0856156i | \(-0.0272857\pi\) |
−0.572309 | + | 0.820038i | \(0.693952\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.00000 | + | 5.19615i | 0.115299 | + | 0.199704i | 0.917899 | − | 0.396813i | \(-0.129884\pi\) |
−0.802600 | + | 0.596518i | \(0.796551\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.00000 | + | 6.92820i | −0.153506 | + | 0.265880i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.0000 | 1.37750 | 0.688751 | − | 0.724998i | \(-0.258159\pi\) | ||||
0.688751 | + | 0.724998i | \(0.258159\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.0000 | 0.687745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 30.0000 | − | 51.9615i | 1.14291 | − | 1.97958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.00000 | − | 3.46410i | −0.0760836 | − | 0.131781i | 0.825473 | − | 0.564441i | \(-0.190908\pi\) |
−0.901557 | + | 0.432660i | \(0.857575\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.00000 | − | 10.3923i | −0.227593 | − | 0.394203i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.0000 | − | 17.3205i | 0.378777 | − | 0.656061i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.0000 | −1.43524 | −0.717620 | − | 0.696435i | \(-0.754769\pi\) | ||||
−0.717620 | + | 0.696435i | \(0.754769\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.0000 | −0.905177 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.0000 | − | 48.4974i | 1.05305 | − | 1.82393i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.0000 | − | 19.0526i | −0.413114 | − | 0.715534i | 0.582115 | − | 0.813107i | \(-0.302225\pi\) |
−0.995228 | + | 0.0975728i | \(0.968892\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 48.0000 | 1.79010 | 0.895049 | − | 0.445968i | \(-0.147140\pi\) | ||||
0.895049 | + | 0.445968i | \(0.147140\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | 0.595871 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.00000 | − | 5.19615i | 0.111417 | − | 0.192980i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.00000 | + | 3.46410i | 0.0741759 | + | 0.128476i | 0.900728 | − | 0.434384i | \(-0.143034\pi\) |
−0.826552 | + | 0.562861i | \(0.809701\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.00000 | − | 6.92820i | −0.147945 | − | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.0000 | − | 39.8372i | 0.849524 | − | 1.47142i | −0.0321090 | − | 0.999484i | \(-0.510222\pi\) |
0.881633 | − | 0.471935i | \(-0.156444\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.00000 | 0.147142 | 0.0735712 | − | 0.997290i | \(-0.476560\pi\) | ||||
0.0735712 | + | 0.997290i | \(0.476560\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.00000 | − | 5.19615i | −0.109911 | − | 0.190372i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.00000 | − | 13.8564i | −0.292314 | − | 0.506302i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.0000 | − | 41.5692i | 0.875772 | − | 1.51688i | 0.0198348 | − | 0.999803i | \(-0.493686\pi\) |
0.855938 | − | 0.517079i | \(-0.172981\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.0000 | 1.52652 | 0.763258 | − | 0.646094i | \(-0.223599\pi\) | ||||
0.763258 | + | 0.646094i | \(0.223599\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.0000 | + | 43.3013i | −0.906249 | + | 1.56967i | −0.0870179 | + | 0.996207i | \(0.527734\pi\) |
−0.819231 | + | 0.573463i | \(0.805600\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.0000 | + | 34.6410i | 0.724049 | + | 1.25409i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.0000 | − | 25.9808i | 0.540914 | − | 0.936890i | −0.457938 | − | 0.888984i | \(-0.651412\pi\) |
0.998852 | − | 0.0479061i | \(-0.0152548\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38.0000 | −1.36677 | −0.683383 | − | 0.730061i | \(-0.739492\pi\) | ||||
−0.683383 | + | 0.730061i | \(0.739492\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.0000 | + | 34.6410i | −0.716574 | + | 1.24114i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.00000 | + | 8.66025i | 0.178458 | + | 0.309098i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.00000 | + | 10.3923i | −0.213877 | + | 0.370446i | −0.952925 | − | 0.303207i | \(-0.901942\pi\) |
0.739048 | + | 0.673653i | \(0.235276\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.0000 | 0.853342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.0000 | −1.27840 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.0000 | + | 29.4449i | −0.602171 | + | 1.04299i | 0.390321 | + | 0.920679i | \(0.372364\pi\) |
−0.992492 | + | 0.122312i | \(0.960969\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000 | + | 13.8564i | 0.283020 | + | 0.490204i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.0000 | + | 27.7128i | −0.563926 | + | 0.976748i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.00000 | −0.210949 | −0.105474 | − | 0.994422i | \(-0.533636\pi\) | ||||
−0.105474 | + | 0.994422i | \(0.533636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.0000 | −0.421377 | −0.210688 | − | 0.977553i | \(-0.567571\pi\) | ||||
−0.210688 | + | 0.977553i | \(0.567571\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.00000 | + | 3.46410i | −0.0700569 | + | 0.121342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.00000 | + | 13.8564i | 0.279885 | + | 0.484774i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.0000 | − | 43.3013i | −0.872506 | − | 1.51122i | −0.859396 | − | 0.511311i | \(-0.829160\pi\) |
−0.0131101 | − | 0.999914i | \(-0.504173\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.00000 | − | 3.46410i | 0.0697156 | − | 0.120751i | −0.829060 | − | 0.559159i | \(-0.811124\pi\) |
0.898776 | + | 0.438408i | \(0.144457\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.0000 | −0.695468 | −0.347734 | − | 0.937593i | \(-0.613049\pi\) | ||||
−0.347734 | + | 0.937593i | \(0.613049\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.0000 | 1.31979 | 0.659897 | − | 0.751356i | \(-0.270600\pi\) | ||||
0.659897 | + | 0.751356i | \(0.270600\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.00000 | − | 15.5885i | 0.311832 | − | 0.540108i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.00000 | − | 6.92820i | −0.138426 | − | 0.239760i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.0000 | + | 34.6410i | 0.690477 | + | 1.19594i | 0.971682 | + | 0.236293i | \(0.0759325\pi\) |
−0.281205 | + | 0.959648i | \(0.590734\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23.0000 | −0.791224 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −44.0000 | −1.51186 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.0000 | + | 41.5692i | −0.822709 | + | 1.42497i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.00000 | − | 8.66025i | −0.171197 | − | 0.296521i | 0.767642 | − | 0.640879i | \(-0.221430\pi\) |
−0.938839 | + | 0.344358i | \(0.888097\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.0000 | − | 32.9090i | −0.649028 | − | 1.12415i | −0.983355 | − | 0.181692i | \(-0.941843\pi\) |
0.334328 | − | 0.942457i | \(-0.391491\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.0000 | + | 31.1769i | −0.614152 | + | 1.06374i | 0.376381 | + | 0.926465i | \(0.377169\pi\) |
−0.990533 | + | 0.137277i | \(0.956165\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.0000 | 0.544646 | 0.272323 | − | 0.962206i | \(-0.412208\pi\) | ||||
0.272323 | + | 0.962206i | \(0.412208\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.0000 | −0.612018 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0000 | − | 20.7846i | −0.406604 | − | 0.704260i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.00000 | + | 3.46410i | 0.0676123 | + | 0.117108i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.00000 | + | 8.66025i | −0.168838 | + | 0.292436i | −0.938012 | − | 0.346604i | \(-0.887335\pi\) |
0.769174 | + | 0.639040i | \(0.220668\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.0000 | 0.875962 | 0.437981 | − | 0.898984i | \(-0.355694\pi\) | ||||
0.437981 | + | 0.898984i | \(0.355694\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.0000 | 0.942275 | 0.471138 | − | 0.882060i | \(-0.343844\pi\) | ||||
0.471138 | + | 0.882060i | \(0.343844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.0000 | + | 20.7846i | −0.402921 | + | 0.697879i | −0.994077 | − | 0.108678i | \(-0.965338\pi\) |
0.591156 | + | 0.806557i | \(0.298672\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.00000 | + | 13.8564i | 0.268311 | + | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.0000 | − | 27.7128i | −0.535420 | − | 0.927374i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.00000 | − | 6.92820i | 0.133705 | − | 0.231584i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.0000 | −0.666297 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.00000 | − | 12.1244i | 0.232688 | − | 0.403027i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.0000 | − | 24.2487i | −0.464862 | − | 0.805165i | 0.534333 | − | 0.845274i | \(-0.320563\pi\) |
−0.999195 | + | 0.0401089i | \(0.987230\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.0000 | + | 27.7128i | 0.530104 | + | 0.918166i | 0.999383 | + | 0.0351168i | \(0.0111803\pi\) |
−0.469280 | + | 0.883050i | \(0.655486\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 64.0000 | 2.11347 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.0000 | 1.31948 | 0.659739 | − | 0.751495i | \(-0.270667\pi\) | ||||
0.659739 | + | 0.751495i | \(0.270667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.00000 | + | 5.19615i | 0.0986394 | + | 0.170848i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.00000 | + | 5.19615i | 0.0984268 | + | 0.170480i | 0.911034 | − | 0.412332i | \(-0.135286\pi\) |
−0.812607 | + | 0.582812i | \(0.801952\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.0000 | + | 31.1769i | −0.589926 | + | 1.02178i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0000 | 0.849383 | 0.424691 | − | 0.905338i | \(-0.360383\pi\) | ||||
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.00000 | − | 12.1244i | 0.228193 | − | 0.395243i | −0.729079 | − | 0.684429i | \(-0.760051\pi\) |
0.957273 | + | 0.289187i | \(0.0933848\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40.0000 | + | 69.2820i | 1.30258 | + | 2.25613i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.0000 | + | 38.1051i | 0.714904 | + | 1.23825i | 0.962997 | + | 0.269514i | \(0.0868629\pi\) |
−0.248093 | + | 0.968736i | \(0.579804\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.0000 | + | 72.7461i | −1.36338 | + | 2.36144i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.0000 | −0.583077 | −0.291539 | − | 0.956559i | \(-0.594167\pi\) | ||||
−0.291539 | + | 0.956559i | \(0.594167\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.00000 | −0.258874 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 36.0000 | − | 62.3538i | 1.16250 | − | 2.01351i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5000 | + | 26.8468i | 0.500000 | + | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.00000 | − | 5.19615i | −0.0965734 | − | 0.167270i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.0000 | + | 17.3205i | −0.321578 | + | 0.556990i | −0.980814 | − | 0.194946i | \(-0.937547\pi\) |
0.659236 | + | 0.751936i | \(0.270880\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −56.0000 | −1.79713 | −0.898563 | − | 0.438845i | \(-0.855388\pi\) | ||||
−0.898563 | + | 0.438845i | \(0.855388\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −48.0000 | −1.53881 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.0000 | − | 43.3013i | 0.799821 | − | 1.38533i | −0.119912 | − | 0.992785i | \(-0.538261\pi\) |
0.919732 | − | 0.392546i | \(-0.128406\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.00000 | − | 8.66025i | 0.159313 | − | 0.275939i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.0000 | 1.01754 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 56.0000 | 1.77890 | 0.889449 | − | 0.457034i | \(-0.151088\pi\) | ||||
0.889449 | + | 0.457034i | \(0.151088\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.0000 | + | 25.9808i | 0.475055 | + | 0.822819i | 0.999592 | − | 0.0285686i | \(-0.00909491\pi\) |
−0.524537 | + | 0.851388i | \(0.675762\pi\) | |||||||
\(998\) | 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 \(a_p\))