Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(361,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.h (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: | \(21.1284163748\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.361 |
Dual form | 2646.2.h.i.667.1 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | 0.904534 | 0.452267 | − | 0.891883i | \(-0.350615\pi\) | ||||
0.452267 | + | 0.891883i | \(0.350615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | − | 1.73205i | 0.277350 | − | 0.480384i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) |
0.970725 | + | 0.240192i | \(0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.50000 | − | 2.59808i | 0.363803 | − | 0.630126i | −0.624780 | − | 0.780801i | \(-0.714811\pi\) |
0.988583 | + | 0.150675i | \(0.0481447\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | − | 0.866025i | −0.114708 | − | 0.198680i | 0.802955 | − | 0.596040i | \(-0.203260\pi\) |
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.50000 | − | 2.59808i | 0.319801 | − | 0.553912i | ||||
\(23\) | 6.00000 | 1.25109 | 0.625543 | − | 0.780189i | \(-0.284877\pi\) | ||||
0.625543 | + | 0.780189i | \(0.284877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | −1.00000 | − | 1.73205i | −0.196116 | − | 0.339683i | ||||
\(27\) | 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 | ||||||||
\(31\) | −2.00000 | − | 3.46410i | −0.359211 | − | 0.622171i | 0.628619 | − | 0.777714i | \(-0.283621\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.50000 | − | 2.59808i | −0.257248 | − | 0.445566i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | + | 3.46410i | 0.328798 | + | 0.569495i | 0.982274 | − | 0.187453i | \(-0.0600231\pi\) |
−0.653476 | + | 0.756948i | \(0.726690\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.50000 | + | 7.79423i | −0.702782 | + | 1.21725i | 0.264704 | + | 0.964330i | \(0.414726\pi\) |
−0.967486 | + | 0.252924i | \(0.918608\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.500000 | + | 0.866025i | 0.0762493 | + | 0.132068i | 0.901629 | − | 0.432511i | \(-0.142372\pi\) |
−0.825380 | + | 0.564578i | \(0.809039\pi\) | |||||||
\(44\) | −1.50000 | − | 2.59808i | −0.226134 | − | 0.391675i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | − | 5.19615i | 0.442326 | − | 0.766131i | ||||
\(47\) | 3.00000 | − | 5.19615i | 0.437595 | − | 0.757937i | −0.559908 | − | 0.828554i | \(-0.689164\pi\) |
0.997503 | + | 0.0706177i | \(0.0224970\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.50000 | + | 4.33013i | −0.353553 | + | 0.612372i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.00000 | −0.277350 | ||||||||
\(53\) | 6.00000 | − | 10.3923i | 0.824163 | − | 1.42749i | −0.0783936 | − | 0.996922i | \(-0.524979\pi\) |
0.902557 | − | 0.430570i | \(-0.141688\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.00000 | 0.787839 | ||||||||
\(59\) | −1.50000 | − | 2.59808i | −0.195283 | − | 0.338241i | 0.751710 | − | 0.659494i | \(-0.229229\pi\) |
−0.946993 | + | 0.321253i | \(0.895896\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | − | 6.92820i | 0.512148 | − | 0.887066i | −0.487753 | − | 0.872982i | \(-0.662183\pi\) |
0.999901 | − | 0.0140840i | \(-0.00448323\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.50000 | − | 4.33013i | −0.305424 | − | 0.529009i | 0.671932 | − | 0.740613i | \(-0.265465\pi\) |
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | −3.00000 | −0.363803 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.50000 | − | 9.52628i | 0.643726 | − | 1.11497i | −0.340868 | − | 0.940111i | \(-0.610721\pi\) |
0.984594 | − | 0.174855i | \(-0.0559458\pi\) | |||||||
\(74\) | 4.00000 | 0.464991 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.500000 | + | 0.866025i | −0.0573539 | + | 0.0993399i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | − | 3.46410i | 0.225018 | − | 0.389742i | −0.731307 | − | 0.682048i | \(-0.761089\pi\) |
0.956325 | + | 0.292306i | \(0.0944227\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.50000 | + | 7.79423i | 0.496942 | + | 0.860729i | ||||
\(83\) | −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 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.00000 | 0.107833 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.00000 | −0.319801 | ||||||||
\(89\) | −3.00000 | − | 5.19615i | −0.317999 | − | 0.550791i | 0.662071 | − | 0.749441i | \(-0.269678\pi\) |
−0.980071 | + | 0.198650i | \(0.936344\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.00000 | − | 5.19615i | −0.312772 | − | 0.541736i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.00000 | − | 5.19615i | −0.309426 | − | 0.535942i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.50000 | + | 4.33013i | 0.253837 | + | 0.439658i | 0.964579 | − | 0.263795i | \(-0.0849741\pi\) |
−0.710742 | + | 0.703452i | \(0.751641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.50000 | + | 4.33013i | 0.250000 | + | 0.433013i | ||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.0000 | −1.37946 | −0.689730 | − | 0.724066i | \(-0.742271\pi\) | ||||
−0.689730 | + | 0.724066i | \(0.742271\pi\) | |||||||
\(104\) | −1.00000 | + | 1.73205i | −0.0980581 | + | 0.169842i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | − | 10.3923i | −0.582772 | − | 1.00939i | ||||
\(107\) | 1.50000 | + | 2.59808i | 0.145010 | + | 0.251166i | 0.929377 | − | 0.369132i | \(-0.120345\pi\) |
−0.784366 | + | 0.620298i | \(0.787012\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00000 | − | 13.8564i | 0.766261 | − | 1.32720i | −0.173316 | − | 0.984866i | \(-0.555448\pi\) |
0.939577 | − | 0.342337i | \(-0.111218\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.00000 | − | 5.19615i | 0.282216 | − | 0.488813i | −0.689714 | − | 0.724082i | \(-0.742264\pi\) |
0.971930 | + | 0.235269i | \(0.0755971\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.00000 | − | 5.19615i | 0.278543 | − | 0.482451i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.00000 | −0.276172 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | −4.00000 | − | 6.92820i | −0.362143 | − | 0.627250i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.00000 | + | 3.46410i | −0.179605 | + | 0.311086i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.00000 | −0.431934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.50000 | + | 2.59808i | −0.128624 | + | 0.222783i | ||||
\(137\) | 3.00000 | 0.256307 | 0.128154 | − | 0.991754i | \(-0.459095\pi\) | ||||
0.128154 | + | 0.991754i | \(0.459095\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.50000 | + | 16.4545i | −0.805779 | + | 1.39565i | 0.109984 | + | 0.993933i | \(0.464920\pi\) |
−0.915764 | + | 0.401718i | \(0.868413\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000 | − | 10.3923i | 0.503509 | − | 0.872103i | ||||
\(143\) | 3.00000 | − | 5.19615i | 0.250873 | − | 0.434524i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.50000 | − | 9.52628i | −0.455183 | − | 0.788400i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.00000 | − | 3.46410i | 0.164399 | − | 0.284747i | ||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.0000 | −0.813788 | −0.406894 | − | 0.913475i | \(-0.633388\pi\) | ||||
−0.406894 | + | 0.913475i | \(0.633388\pi\) | |||||||
\(152\) | 0.500000 | + | 0.866025i | 0.0405554 | + | 0.0702439i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | − | 3.46410i | −0.159617 | − | 0.276465i | 0.775113 | − | 0.631822i | \(-0.217693\pi\) |
−0.934731 | + | 0.355357i | \(0.884359\pi\) | |||||||
\(158\) | −2.00000 | − | 3.46410i | −0.159111 | − | 0.275589i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.00000 | + | 3.46410i | 0.156652 | + | 0.271329i | 0.933659 | − | 0.358162i | \(-0.116597\pi\) |
−0.777007 | + | 0.629492i | \(0.783263\pi\) | |||||||
\(164\) | 9.00000 | 0.702782 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.0000 | −0.931381 | ||||||||
\(167\) | 6.00000 | − | 10.3923i | 0.464294 | − | 0.804181i | −0.534875 | − | 0.844931i | \(-0.679641\pi\) |
0.999169 | + | 0.0407502i | \(0.0129748\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.500000 | − | 0.866025i | 0.0381246 | − | 0.0660338i | ||||
\(173\) | 3.00000 | − | 5.19615i | 0.228086 | − | 0.395056i | −0.729155 | − | 0.684349i | \(-0.760087\pi\) |
0.957241 | + | 0.289292i | \(0.0934200\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.50000 | + | 2.59808i | −0.113067 | + | 0.195837i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.00000 | −0.449719 | ||||||||
\(179\) | 6.00000 | − | 10.3923i | 0.448461 | − | 0.776757i | −0.549825 | − | 0.835280i | \(-0.685306\pi\) |
0.998286 | + | 0.0585225i | \(0.0186389\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.00000 | −0.442326 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.50000 | − | 7.79423i | 0.329073 | − | 0.569970i | ||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.00000 | + | 15.5885i | −0.651217 | + | 1.12794i | 0.331611 | + | 0.943416i | \(0.392408\pi\) |
−0.982828 | + | 0.184525i | \(0.940925\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.50000 | − | 4.33013i | −0.179954 | − | 0.311689i | 0.761911 | − | 0.647682i | \(-0.224262\pi\) |
−0.941865 | + | 0.335993i | \(0.890928\pi\) | |||||||
\(194\) | 5.00000 | 0.358979 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0000 | 0.854965 | 0.427482 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427482 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.00000 | + | 8.66025i | −0.354441 | + | 0.613909i | −0.987022 | − | 0.160585i | \(-0.948662\pi\) |
0.632581 | + | 0.774494i | \(0.281995\pi\) | |||||||
\(200\) | 5.00000 | 0.353553 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.00000 | + | 12.1244i | −0.487713 | + | 0.844744i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00000 | + | 1.73205i | 0.0693375 | + | 0.120096i | ||||
\(209\) | −1.50000 | − | 2.59808i | −0.103757 | − | 0.179713i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0000 | + | 17.3205i | −0.688428 | + | 1.19239i | 0.283918 | + | 0.958849i | \(0.408366\pi\) |
−0.972346 | + | 0.233544i | \(0.924968\pi\) | |||||||
\(212\) | −12.0000 | −0.824163 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.00000 | 0.205076 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −8.00000 | − | 13.8564i | −0.541828 | − | 0.938474i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | − | 5.19615i | −0.201802 | − | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.0000 | + | 22.5167i | 0.870544 | + | 1.50783i | 0.861435 | + | 0.507869i | \(0.169566\pi\) |
0.00910984 | + | 0.999959i | \(0.497100\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.00000 | − | 5.19615i | −0.199557 | − | 0.345643i | ||||
\(227\) | 21.0000 | 1.39382 | 0.696909 | − | 0.717159i | \(-0.254558\pi\) | ||||
0.696909 | + | 0.717159i | \(0.254558\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0000 | −0.925146 | −0.462573 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462573 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.00000 | − | 5.19615i | −0.196960 | − | 0.341144i | ||||
\(233\) | 1.50000 | + | 2.59808i | 0.0982683 | + | 0.170206i | 0.910968 | − | 0.412477i | \(-0.135336\pi\) |
−0.812700 | + | 0.582683i | \(0.802003\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.50000 | + | 2.59808i | −0.0976417 | + | 0.169120i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.00000 | − | 5.19615i | 0.194054 | − | 0.336111i | −0.752536 | − | 0.658551i | \(-0.771170\pi\) |
0.946590 | + | 0.322440i | \(0.104503\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.00000 | 0.450910 | 0.225455 | − | 0.974254i | \(-0.427613\pi\) | ||||
0.225455 | + | 0.974254i | \(0.427613\pi\) | |||||||
\(242\) | −1.00000 | + | 1.73205i | −0.0642824 | + | 0.111340i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.00000 | −0.512148 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.00000 | −0.127257 | ||||||||
\(248\) | 2.00000 | + | 3.46410i | 0.127000 | + | 0.219971i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.0000 | 1.32551 | 0.662754 | − | 0.748837i | \(-0.269387\pi\) | ||||
0.662754 | + | 0.748837i | \(0.269387\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | 1.13165 | ||||||||
\(254\) | 1.00000 | − | 1.73205i | 0.0627456 | − | 0.108679i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −21.0000 | −1.30994 | −0.654972 | − | 0.755653i | \(-0.727320\pi\) | ||||
−0.654972 | + | 0.755653i | \(0.727320\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.0000 | −1.10993 | −0.554964 | − | 0.831875i | \(-0.687268\pi\) | ||||
−0.554964 | + | 0.831875i | \(0.687268\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.50000 | + | 4.33013i | −0.152712 | + | 0.264505i | ||||
\(269\) | 12.0000 | − | 20.7846i | 0.731653 | − | 1.26726i | −0.224523 | − | 0.974469i | \(-0.572083\pi\) |
0.956176 | − | 0.292791i | \(-0.0945841\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.0000 | + | 17.3205i | 0.607457 | + | 1.05215i | 0.991658 | + | 0.128897i | \(0.0411435\pi\) |
−0.384201 | + | 0.923249i | \(0.625523\pi\) | |||||||
\(272\) | 1.50000 | + | 2.59808i | 0.0909509 | + | 0.157532i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.50000 | − | 2.59808i | 0.0906183 | − | 0.156956i | ||||
\(275\) | −15.0000 | −0.904534 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.0000 | −0.600842 | −0.300421 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300421 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(278\) | 9.50000 | + | 16.4545i | 0.569772 | + | 0.986874i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.00000 | + | 5.19615i | 0.178965 | + | 0.309976i | 0.941526 | − | 0.336939i | \(-0.109392\pi\) |
−0.762561 | + | 0.646916i | \(0.776058\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.00000 | − | 3.46410i | −0.118888 | − | 0.205919i | 0.800439 | − | 0.599414i | \(-0.204600\pi\) |
−0.919327 | + | 0.393494i | \(0.871266\pi\) | |||||||
\(284\) | −6.00000 | − | 10.3923i | −0.356034 | − | 0.616670i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.00000 | − | 5.19615i | −0.177394 | − | 0.307255i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11.0000 | −0.643726 | ||||||||
\(293\) | −15.0000 | + | 25.9808i | −0.876309 | + | 1.51781i | −0.0209480 | + | 0.999781i | \(0.506668\pi\) |
−0.855361 | + | 0.518032i | \(0.826665\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.00000 | − | 3.46410i | −0.116248 | − | 0.201347i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00000 | − | 5.19615i | 0.173785 | − | 0.301005i | ||||
\(299\) | 6.00000 | − | 10.3923i | 0.346989 | − | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.00000 | + | 8.66025i | −0.287718 | + | 0.498342i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.00000 | 0.399511 | 0.199756 | − | 0.979846i | \(-0.435985\pi\) | ||||
0.199756 | + | 0.979846i | \(0.435985\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.00000 | + | 15.5885i | 0.510343 | + | 0.883940i | 0.999928 | + | 0.0119847i | \(0.00381495\pi\) |
−0.489585 | + | 0.871956i | \(0.662852\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.5000 | − | 25.1147i | 0.819588 | − | 1.41957i | −0.0863973 | − | 0.996261i | \(-0.527535\pi\) |
0.905986 | − | 0.423308i | \(-0.139131\pi\) | |||||||
\(314\) | −4.00000 | −0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.00000 | −0.225018 | ||||||||
\(317\) | −9.00000 | + | 15.5885i | −0.505490 | + | 0.875535i | 0.494489 | + | 0.869184i | \(0.335355\pi\) |
−0.999980 | + | 0.00635137i | \(0.997978\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.00000 | + | 15.5885i | 0.503903 | + | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.00000 | −0.166924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.00000 | + | 8.66025i | −0.277350 | + | 0.480384i | ||||
\(326\) | 4.00000 | 0.221540 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.50000 | − | 7.79423i | 0.248471 | − | 0.430364i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | − | 3.46410i | 0.109930 | − | 0.190404i | −0.805812 | − | 0.592172i | \(-0.798271\pi\) |
0.915742 | + | 0.401768i | \(0.131604\pi\) | |||||||
\(332\) | −6.00000 | + | 10.3923i | −0.329293 | + | 0.570352i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.00000 | − | 10.3923i | −0.328305 | − | 0.568642i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.500000 | − | 0.866025i | 0.0272367 | − | 0.0471754i | −0.852086 | − | 0.523402i | \(-0.824663\pi\) |
0.879322 | + | 0.476227i | \(0.157996\pi\) | |||||||
\(338\) | 9.00000 | 0.489535 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.00000 | − | 10.3923i | −0.324918 | − | 0.562775i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.500000 | − | 0.866025i | −0.0269582 | − | 0.0466930i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.00000 | − | 5.19615i | −0.161281 | − | 0.279347i | ||||
\(347\) | 16.5000 | + | 28.5788i | 0.885766 | + | 1.53419i | 0.844833 | + | 0.535031i | \(0.179700\pi\) |
0.0409337 | + | 0.999162i | \(0.486967\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.00000 | − | 13.8564i | −0.428230 | − | 0.741716i | 0.568486 | − | 0.822693i | \(-0.307529\pi\) |
−0.996716 | + | 0.0809766i | \(0.974196\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.50000 | + | 2.59808i | 0.0799503 | + | 0.138478i | ||||
\(353\) | −21.0000 | −1.11772 | −0.558859 | − | 0.829263i | \(-0.688761\pi\) | ||||
−0.558859 | + | 0.829263i | \(0.688761\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.00000 | + | 5.19615i | −0.159000 | + | 0.275396i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.00000 | − | 10.3923i | −0.317110 | − | 0.549250i | ||||
\(359\) | −9.00000 | − | 15.5885i | −0.475002 | − | 0.822727i | 0.524588 | − | 0.851356i | \(-0.324219\pi\) |
−0.999590 | + | 0.0286287i | \(0.990886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | − | 15.5885i | 0.473684 | − | 0.820445i | ||||
\(362\) | −7.00000 | + | 12.1244i | −0.367912 | + | 0.637242i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.0000 | 1.46159 | 0.730794 | − | 0.682598i | \(-0.239150\pi\) | ||||
0.730794 | + | 0.682598i | \(0.239150\pi\) | |||||||
\(368\) | −3.00000 | + | 5.19615i | −0.156386 | + | 0.270868i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −34.0000 | −1.76045 | −0.880227 | − | 0.474554i | \(-0.842610\pi\) | ||||
−0.880227 | + | 0.474554i | \(0.842610\pi\) | |||||||
\(374\) | −4.50000 | − | 7.79423i | −0.232689 | − | 0.403030i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00000 | + | 5.19615i | −0.154713 | + | 0.267971i | ||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.0000 | 1.18143 | 0.590715 | − | 0.806880i | \(-0.298846\pi\) | ||||
0.590715 | + | 0.806880i | \(0.298846\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.00000 | + | 15.5885i | 0.460480 | + | 0.797575i | ||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.00000 | −0.254493 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.50000 | − | 4.33013i | 0.126918 | − | 0.219829i | ||||
\(389\) | −18.0000 | −0.912636 | −0.456318 | − | 0.889817i | \(-0.650832\pi\) | ||||
−0.456318 | + | 0.889817i | \(0.650832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.00000 | − | 15.5885i | 0.455150 | − | 0.788342i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.00000 | − | 10.3923i | 0.302276 | − | 0.523557i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0000 | + | 17.3205i | 0.501886 | + | 0.869291i | 0.999998 | + | 0.00217869i | \(0.000693499\pi\) |
−0.498112 | + | 0.867113i | \(0.665973\pi\) | |||||||
\(398\) | 5.00000 | + | 8.66025i | 0.250627 | + | 0.434099i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.50000 | − | 4.33013i | 0.125000 | − | 0.216506i | ||||
\(401\) | 27.0000 | 1.34832 | 0.674158 | − | 0.738587i | \(-0.264507\pi\) | ||||
0.674158 | + | 0.738587i | \(0.264507\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.00000 | −0.398508 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.00000 | + | 10.3923i | 0.297409 | + | 0.515127i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.50000 | + | 14.7224i | 0.420298 | + | 0.727977i | 0.995968 | − | 0.0897044i | \(-0.0285922\pi\) |
−0.575670 | + | 0.817682i | \(0.695259\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.00000 | + | 12.1244i | 0.344865 | + | 0.597324i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.00000 | −0.146735 | ||||||||
\(419\) | 6.00000 | − | 10.3923i | 0.293119 | − | 0.507697i | −0.681426 | − | 0.731887i | \(-0.738640\pi\) |
0.974546 | + | 0.224189i | \(0.0719734\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | − | 17.3205i | −0.487370 | − | 0.844150i | 0.512524 | − | 0.858673i | \(-0.328710\pi\) |
−0.999895 | + | 0.0145228i | \(0.995377\pi\) | |||||||
\(422\) | 10.0000 | + | 17.3205i | 0.486792 | + | 0.843149i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | + | 10.3923i | −0.291386 | + | 0.504695i | ||||
\(425\) | −7.50000 | + | 12.9904i | −0.363803 | + | 0.630126i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.50000 | − | 2.59808i | 0.0725052 | − | 0.125583i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.0000 | + | 25.9808i | −0.722525 | + | 1.25145i | 0.237460 | + | 0.971397i | \(0.423685\pi\) |
−0.959985 | + | 0.280052i | \(0.909648\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.00000 | 0.336399 | 0.168199 | − | 0.985753i | \(-0.446205\pi\) | ||||
0.168199 | + | 0.985753i | \(0.446205\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.0000 | −0.766261 | ||||||||
\(437\) | −3.00000 | − | 5.19615i | −0.143509 | − | 0.248566i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.00000 | − | 6.92820i | 0.190910 | − | 0.330665i | −0.754642 | − | 0.656136i | \(-0.772190\pi\) |
0.945552 | + | 0.325471i | \(0.105523\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.00000 | −0.285391 | ||||||||
\(443\) | 1.50000 | − | 2.59808i | 0.0712672 | − | 0.123438i | −0.828190 | − | 0.560448i | \(-0.810629\pi\) |
0.899457 | + | 0.437009i | \(0.143962\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 26.0000 | 1.23114 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.00000 | −0.424736 | −0.212368 | − | 0.977190i | \(-0.568118\pi\) | ||||
−0.212368 | + | 0.977190i | \(0.568118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.5000 | + | 23.3827i | −0.635690 | + | 1.10105i | ||||
\(452\) | −6.00000 | −0.282216 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.5000 | − | 18.1865i | 0.492789 | − | 0.853536i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.50000 | + | 14.7224i | −0.397613 | + | 0.688686i | −0.993431 | − | 0.114433i | \(-0.963495\pi\) |
0.595818 | + | 0.803120i | \(0.296828\pi\) | |||||||
\(458\) | −7.00000 | + | 12.1244i | −0.327089 | + | 0.566534i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.0000 | + | 25.9808i | 0.698620 | + | 1.21004i | 0.968945 | + | 0.247276i | \(0.0795353\pi\) |
−0.270326 | + | 0.962769i | \(0.587131\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.0000 | + | 17.3205i | −0.464739 | + | 0.804952i | −0.999190 | − | 0.0402476i | \(-0.987185\pi\) |
0.534450 | + | 0.845200i | \(0.320519\pi\) | |||||||
\(464\) | −6.00000 | −0.278543 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.00000 | 0.138972 | ||||||||
\(467\) | 7.50000 | + | 12.9904i | 0.347059 | + | 0.601123i | 0.985726 | − | 0.168360i | \(-0.0538472\pi\) |
−0.638667 | + | 0.769483i | \(0.720514\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.50000 | + | 2.59808i | 0.0690431 | + | 0.119586i | ||||
\(473\) | 1.50000 | + | 2.59808i | 0.0689701 | + | 0.119460i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.50000 | + | 4.33013i | 0.114708 | + | 0.198680i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.00000 | − | 5.19615i | −0.137217 | − | 0.237666i | ||||
\(479\) | −42.0000 | −1.91903 | −0.959514 | − | 0.281659i | \(-0.909115\pi\) | ||||
−0.959514 | + | 0.281659i | \(0.909115\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.00000 | 0.364769 | ||||||||
\(482\) | 3.50000 | − | 6.06218i | 0.159421 | − | 0.276125i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.0000 | + | 22.5167i | −0.589086 | + | 1.02033i | 0.405266 | + | 0.914199i | \(0.367179\pi\) |
−0.994352 | + | 0.106129i | \(0.966154\pi\) | |||||||
\(488\) | −4.00000 | + | 6.92820i | −0.181071 | + | 0.313625i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.50000 | + | 12.9904i | −0.338470 | + | 0.586248i | −0.984145 | − | 0.177365i | \(-0.943243\pi\) |
0.645675 | + | 0.763612i | \(0.276576\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.0000 | 0.810679 | ||||||||
\(494\) | −1.00000 | + | 1.73205i | −0.0449921 | + | 0.0779287i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.00000 | 0.179605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.0000 | −0.581960 | −0.290980 | − | 0.956729i | \(-0.593981\pi\) | ||||
−0.290980 | + | 0.956729i | \(0.593981\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.5000 | − | 18.1865i | 0.468638 | − | 0.811705i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.00000 | − | 15.5885i | 0.400099 | − | 0.692991i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.00000 | − | 1.73205i | −0.0443678 | − | 0.0768473i | ||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.5000 | + | 18.1865i | −0.463135 | + | 0.802174i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.00000 | − | 15.5885i | 0.395820 | − | 0.685580i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.50000 | − | 2.59808i | 0.0657162 | − | 0.113824i | −0.831295 | − | 0.555831i | \(-0.812400\pi\) |
0.897011 | + | 0.442007i | \(0.145733\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.0000 | + | 17.3205i | 0.437269 | + | 0.757373i | 0.997478 | − | 0.0709788i | \(-0.0226123\pi\) |
−0.560208 | + | 0.828352i | \(0.689279\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.00000 | + | 15.5885i | −0.392419 | + | 0.679689i | ||||
\(527\) | −12.0000 | −0.522728 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.00000 | + | 15.5885i | 0.389833 | + | 0.675211i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.50000 | + | 4.33013i | 0.107984 | + | 0.187033i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12.0000 | − | 20.7846i | −0.517357 | − | 0.896088i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | + | 3.46410i | 0.0859867 | + | 0.148933i | 0.905811 | − | 0.423681i | \(-0.139262\pi\) |
−0.819825 | + | 0.572615i | \(0.805929\pi\) | |||||||
\(542\) | 20.0000 | 0.859074 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.00000 | 0.128624 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.500000 | + | 0.866025i | 0.0213785 | + | 0.0370286i | 0.876517 | − | 0.481371i | \(-0.159861\pi\) |
−0.855138 | + | 0.518400i | \(0.826528\pi\) | |||||||
\(548\) | −1.50000 | − | 2.59808i | −0.0640768 | − | 0.110984i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.50000 | + | 12.9904i | −0.319801 | + | 0.553912i | ||||
\(551\) | 3.00000 | − | 5.19615i | 0.127804 | − | 0.221364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5.00000 | + | 8.66025i | −0.212430 | + | 0.367939i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.0000 | 0.805779 | ||||||||
\(557\) | −15.0000 | + | 25.9808i | −0.635570 | + | 1.10084i | 0.350824 | + | 0.936442i | \(0.385902\pi\) |
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.00000 | 0.0845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.00000 | 0.253095 | ||||||||
\(563\) | 19.5000 | + | 33.7750i | 0.821827 | + | 1.42345i | 0.904320 | + | 0.426855i | \(0.140378\pi\) |
−0.0824933 | + | 0.996592i | \(0.526288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.0000 | −0.503509 | ||||||||
\(569\) | 22.5000 | − | 38.9711i | 0.943249 | − | 1.63376i | 0.184030 | − | 0.982921i | \(-0.441086\pi\) |
0.759220 | − | 0.650835i | \(-0.225581\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.5000 | + | 32.0429i | 0.774201 | + | 1.34096i | 0.935243 | + | 0.354008i | \(0.115181\pi\) |
−0.161042 | + | 0.986948i | \(0.551485\pi\) | |||||||
\(572\) | −6.00000 | −0.250873 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.0000 | −1.25109 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.50000 | − | 9.52628i | 0.228968 | − | 0.396584i | −0.728535 | − | 0.685009i | \(-0.759798\pi\) |
0.957503 | + | 0.288425i | \(0.0931316\pi\) | |||||||
\(578\) | 8.00000 | 0.332756 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.0000 | − | 31.1769i | 0.745484 | − | 1.29122i | ||||
\(584\) | −5.50000 | + | 9.52628i | −0.227592 | + | 0.394200i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.0000 | + | 25.9808i | 0.619644 | + | 1.07326i | ||||
\(587\) | 4.50000 | + | 7.79423i | 0.185735 | + | 0.321702i | 0.943824 | − | 0.330449i | \(-0.107200\pi\) |
−0.758089 | + | 0.652151i | \(0.773867\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | + | 3.46410i | −0.0824086 | + | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.00000 | −0.164399 | ||||||||
\(593\) | −3.00000 | − | 5.19615i | −0.123195 | − | 0.213380i | 0.797831 | − | 0.602881i | \(-0.205981\pi\) |
−0.921026 | + | 0.389501i | \(0.872647\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.00000 | − | 5.19615i | −0.122885 | − | 0.212843i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.00000 | − | 10.3923i | −0.245358 | − | 0.424973i | ||||
\(599\) | 6.00000 | + | 10.3923i | 0.245153 | + | 0.424618i | 0.962175 | − | 0.272433i | \(-0.0878284\pi\) |
−0.717021 | + | 0.697051i | \(0.754495\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.5000 | − | 32.0429i | −0.754631 | − | 1.30706i | −0.945558 | − | 0.325455i | \(-0.894483\pi\) |
0.190927 | − | 0.981604i | \(-0.438851\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.00000 | + | 8.66025i | 0.203447 | + | 0.352381i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.0000 | 1.13648 | 0.568242 | − | 0.822861i | \(-0.307624\pi\) | ||||
0.568242 | + | 0.822861i | \(0.307624\pi\) | |||||||
\(608\) | 0.500000 | − | 0.866025i | 0.0202777 | − | 0.0351220i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.00000 | − | 10.3923i | −0.242734 | − | 0.420428i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.00000 | − | 13.8564i | 0.323117 | − | 0.559655i | −0.658012 | − | 0.753007i | \(-0.728603\pi\) |
0.981129 | + | 0.193352i | \(0.0619359\pi\) | |||||||
\(614\) | 3.50000 | − | 6.06218i | 0.141249 | − | 0.244650i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.5000 | − | 23.3827i | 0.543490 | − | 0.941351i | −0.455211 | − | 0.890384i | \(-0.650436\pi\) |
0.998700 | − | 0.0509678i | \(-0.0162306\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.0000 | −1.40677 | −0.703384 | − | 0.710810i | \(-0.748329\pi\) | ||||
−0.703384 | + | 0.710810i | \(0.748329\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 18.0000 | 0.721734 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | −14.5000 | − | 25.1147i | −0.579537 | − | 1.00379i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.00000 | + | 3.46410i | −0.0798087 | + | 0.138233i | ||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.0000 | −1.59237 | −0.796187 | − | 0.605050i | \(-0.793153\pi\) | ||||
−0.796187 | + | 0.605050i | \(0.793153\pi\) | |||||||
\(632\) | −2.00000 | + | 3.46410i | −0.0795557 | + | 0.137795i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.00000 | + | 15.5885i | 0.357436 | + | 0.619097i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 18.0000 | 0.712627 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.00000 | 0.118493 | 0.0592464 | − | 0.998243i | \(-0.481130\pi\) | ||||
0.0592464 | + | 0.998243i | \(0.481130\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.5000 | − | 19.9186i | 0.453516 | − | 0.785512i | −0.545086 | − | 0.838380i | \(-0.683503\pi\) |
0.998602 | + | 0.0528680i | \(0.0168363\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.50000 | + | 2.59808i | −0.0590167 | + | 0.102220i | ||||
\(647\) | −9.00000 | + | 15.5885i | −0.353827 | + | 0.612845i | −0.986916 | − | 0.161233i | \(-0.948453\pi\) |
0.633090 | + | 0.774078i | \(0.281786\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.50000 | − | 7.79423i | −0.176640 | − | 0.305950i | ||||
\(650\) | 5.00000 | + | 8.66025i | 0.196116 | + | 0.339683i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.00000 | − | 3.46410i | 0.0783260 | − | 0.135665i | ||||
\(653\) | 6.00000 | 0.234798 | 0.117399 | − | 0.993085i | \(-0.462544\pi\) | ||||
0.117399 | + | 0.993085i | \(0.462544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.50000 | − | 7.79423i | −0.175695 | − | 0.304314i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.0000 | − | 31.1769i | −0.701180 | − | 1.21448i | −0.968052 | − | 0.250748i | \(-0.919323\pi\) |
0.266872 | − | 0.963732i | \(-0.414010\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.00000 | − | 3.46410i | −0.0777910 | − | 0.134738i | 0.824506 | − | 0.565854i | \(-0.191453\pi\) |
−0.902297 | + | 0.431116i | \(0.858120\pi\) | |||||||
\(662\) | −2.00000 | − | 3.46410i | −0.0777322 | − | 0.134636i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | + | 10.3923i | 0.232845 | + | 0.403300i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.0000 | + | 31.1769i | 0.696963 | + | 1.20717i | ||||
\(668\) | −12.0000 | −0.464294 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0000 | − | 20.7846i | 0.463255 | − | 0.802381i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.0000 | + | 19.0526i | 0.424019 | + | 0.734422i | 0.996328 | − | 0.0856156i | \(-0.0272857\pi\) |
−0.572309 | + | 0.820038i | \(0.693952\pi\) | |||||||
\(674\) | −0.500000 | − | 0.866025i | −0.0192593 | − | 0.0333581i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.50000 | − | 7.79423i | 0.173077 | − | 0.299778i | ||||
\(677\) | −18.0000 | + | 31.1769i | −0.691796 | + | 1.19823i | 0.279453 | + | 0.960159i | \(0.409847\pi\) |
−0.971249 | + | 0.238067i | \(0.923486\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.0000 | −0.459504 | ||||||||
\(683\) | −4.50000 | + | 7.79423i | −0.172188 | + | 0.298238i | −0.939184 | − | 0.343413i | \(-0.888417\pi\) |
0.766997 | + | 0.641651i | \(0.221750\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.00000 | −0.0381246 | ||||||||
\(689\) | −12.0000 | − | 20.7846i | −0.457164 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.00000 | − | 6.92820i | 0.152167 | − | 0.263561i | −0.779857 | − | 0.625958i | \(-0.784708\pi\) |
0.932024 | + | 0.362397i | \(0.118041\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 33.0000 | 1.25266 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.5000 | + | 23.3827i | 0.511349 | + | 0.885682i | ||||
\(698\) | −16.0000 | −0.605609 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.0000 | −1.13308 | −0.566542 | − | 0.824033i | \(-0.691719\pi\) | ||||
−0.566542 | + | 0.824033i | \(0.691719\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.00000 | − | 3.46410i | 0.0754314 | − | 0.130651i | ||||
\(704\) | 3.00000 | 0.113067 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.5000 | + | 18.1865i | −0.395173 | + | 0.684459i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.00000 | − | 3.46410i | 0.0751116 | − | 0.130097i | −0.826023 | − | 0.563636i | \(-0.809402\pi\) |
0.901135 | + | 0.433539i | \(0.142735\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.00000 | + | 5.19615i | 0.112430 | + | 0.194734i | ||||
\(713\) | −12.0000 | − | 20.7846i | −0.449404 | − | 0.778390i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18.0000 | −0.671754 | ||||||||
\(719\) | 18.0000 | + | 31.1769i | 0.671287 | + | 1.16270i | 0.977539 | + | 0.210752i | \(0.0675914\pi\) |
−0.306253 | + | 0.951950i | \(0.599075\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −9.00000 | − | 15.5885i | −0.334945 | − | 0.580142i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.00000 | + | 12.1244i | 0.260153 | + | 0.450598i | ||||
\(725\) | −15.0000 | − | 25.9808i | −0.557086 | − | 0.964901i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.0000 | + | 22.5167i | 0.482143 | + | 0.835097i | 0.999790 | − | 0.0204978i | \(-0.00652512\pi\) |
−0.517647 | + | 0.855595i | \(0.673192\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.00000 | 0.110959 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.0000 | −0.517102 | −0.258551 | − | 0.965998i | \(-0.583245\pi\) | ||||
−0.258551 | + | 0.965998i | \(0.583245\pi\) | |||||||
\(734\) | 14.0000 | − | 24.2487i | 0.516749 | − | 0.895036i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | + | 5.19615i | 0.110581 | + | 0.191533i | ||||
\(737\) | −7.50000 | − | 12.9904i | −0.276266 | − | 0.478507i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.5000 | + | 40.7032i | −0.864461 | + | 1.49729i | 0.00311943 | + | 0.999995i | \(0.499007\pi\) |
−0.867581 | + | 0.497296i | \(0.834326\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.00000 | − | 5.19615i | 0.110059 | − | 0.190628i | −0.805735 | − | 0.592277i | \(-0.798229\pi\) |
0.915794 | + | 0.401648i | \(0.131563\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −17.0000 | + | 29.4449i | −0.622414 | + | 1.07805i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.00000 | −0.329073 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | 0.291924 | 0.145962 | − | 0.989290i | \(-0.453372\pi\) | ||||
0.145962 | + | 0.989290i | \(0.453372\pi\) | |||||||
\(752\) | 3.00000 | + | 5.19615i | 0.109399 | + | 0.189484i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.00000 | − | 10.3923i | 0.218507 | − | 0.378465i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | 11.5000 | − | 19.9186i | 0.417699 | − | 0.723476i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.0000 | 1.52250 | 0.761249 | − | 0.648459i | \(-0.224586\pi\) | ||||
0.761249 | + | 0.648459i | \(0.224586\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 18.0000 | 0.651217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.00000 | −0.216647 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.00000 | − | 1.73205i | 0.0360609 | − | 0.0624593i | −0.847432 | − | 0.530904i | \(-0.821852\pi\) |
0.883493 | + | 0.468445i | \(0.155186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.50000 | + | 4.33013i | −0.0899770 | + | 0.155845i | ||||
\(773\) | −9.00000 | + | 15.5885i | −0.323708 | + | 0.560678i | −0.981250 | − | 0.192740i | \(-0.938263\pi\) |
0.657542 | + | 0.753418i | \(0.271596\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.0000 | + | 17.3205i | 0.359211 | + | 0.622171i | ||||
\(776\) | −2.50000 | − | 4.33013i | −0.0897448 | − | 0.155443i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.00000 | + | 15.5885i | −0.322666 | + | 0.558873i | ||||
\(779\) | 9.00000 | 0.322458 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0000 | 1.28818 | ||||||||
\(782\) | −9.00000 | − | 15.5885i | −0.321839 | − | 0.557442i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.00000 | − | 3.46410i | −0.0712923 | − | 0.123482i | 0.828176 | − | 0.560469i | \(-0.189379\pi\) |
−0.899468 | + | 0.436987i | \(0.856046\pi\) | |||||||
\(788\) | −6.00000 | − | 10.3923i | −0.213741 | − | 0.370211i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.00000 | − | 13.8564i | −0.284088 | − | 0.492055i | ||||
\(794\) | 20.0000 | 0.709773 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.0000 | 0.354441 | ||||||||
\(797\) | 6.00000 | − | 10.3923i | 0.212531 | − | 0.368114i | −0.739975 | − | 0.672634i | \(-0.765163\pi\) |
0.952506 | + | 0.304520i | \(0.0984960\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.00000 | − | 15.5885i | −0.318397 | − | 0.551480i | ||||
\(800\) | −2.50000 | − | 4.33013i | −0.0883883 | − | 0.153093i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 13.5000 | − | 23.3827i | 0.476702 | − | 0.825671i | ||||
\(803\) | 16.5000 | − | 28.5788i | 0.582272 | − | 1.00853i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.00000 | + | 6.92820i | −0.140894 | + | 0.244036i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.5000 | − | 28.5788i | 0.580109 | − | 1.00478i | −0.415357 | − | 0.909659i | \(-0.636343\pi\) |
0.995466 | − | 0.0951198i | \(-0.0303234\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.00000 | 0.245803 | 0.122902 | − | 0.992419i | \(-0.460780\pi\) | ||||
0.122902 | + | 0.992419i | \(0.460780\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.0000 | 0.420600 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.500000 | − | 0.866025i | 0.0174928 | − | 0.0302984i | ||||
\(818\) | 17.0000 | 0.594391 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.00000 | + | 15.5885i | −0.314102 | + | 0.544041i | −0.979246 | − | 0.202674i | \(-0.935037\pi\) |
0.665144 | + | 0.746715i | \(0.268370\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.00000 | + | 13.8564i | 0.278862 | + | 0.483004i | 0.971102 | − | 0.238664i | \(-0.0767093\pi\) |
−0.692240 | + | 0.721668i | \(0.743376\pi\) | |||||||
\(824\) | 14.0000 | 0.487713 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.00000 | + | 8.66025i | −0.173657 | + | 0.300783i | −0.939696 | − | 0.342012i | \(-0.888892\pi\) |
0.766039 | + | 0.642795i | \(0.222225\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.00000 | − | 1.73205i | 0.0346688 | − | 0.0600481i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.50000 | + | 2.59808i | −0.0518786 | + | 0.0898563i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.00000 | − | 10.3923i | −0.207267 | − | 0.358996i | ||||
\(839\) | −6.00000 | − | 10.3923i | −0.207143 | − | 0.358782i | 0.743670 | − | 0.668546i | \(-0.233083\pi\) |
−0.950813 | + | 0.309764i | \(0.899750\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | −20.0000 | −0.689246 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20.0000 | 0.688428 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.00000 | + | 10.3923i | 0.206041 | + | 0.356873i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7.50000 | + | 12.9904i | 0.257248 | + | 0.445566i | ||||
\(851\) | 12.0000 | + | 20.7846i | 0.411355 | + | 0.712487i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.0000 | + | 22.5167i | 0.445112 | + | 0.770956i | 0.998060 | − | 0.0622597i | \(-0.0198307\pi\) |
−0.552948 | + | 0.833215i | \(0.686497\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.50000 | − | 2.59808i | −0.0512689 | − | 0.0888004i | ||||
\(857\) | −42.0000 | −1.43469 | −0.717346 | − | 0.696717i | \(-0.754643\pi\) | ||||
−0.717346 | + | 0.696717i | \(0.754643\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.0000 | −1.19418 | −0.597092 | − | 0.802173i | \(-0.703677\pi\) | ||||
−0.597092 | + | 0.802173i | \(0.703677\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.0000 | + | 25.9808i | 0.510902 | + | 0.884908i | ||||
\(863\) | 12.0000 | + | 20.7846i | 0.408485 | + | 0.707516i | 0.994720 | − | 0.102624i | \(-0.0327240\pi\) |
−0.586235 | + | 0.810141i | \(0.699391\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.50000 | − | 6.06218i | 0.118935 | − | 0.206001i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.00000 | − | 10.3923i | 0.203536 | − | 0.352535i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.0000 | −0.338837 | ||||||||
\(872\) | −8.00000 | + | 13.8564i | −0.270914 | + | 0.469237i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.00000 | −0.202953 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.00000 | 0.270141 | 0.135070 | − | 0.990836i | \(-0.456874\pi\) | ||||
0.135070 | + | 0.990836i | \(0.456874\pi\) | |||||||
\(878\) | −4.00000 | − | 6.92820i | −0.134993 | − | 0.233816i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.0000 | −1.41502 | −0.707508 | − | 0.706705i | \(-0.750181\pi\) | ||||
−0.707508 | + | 0.706705i | \(0.750181\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.0000 | −0.639401 | −0.319700 | − | 0.947519i | \(-0.603582\pi\) | ||||
−0.319700 | + | 0.947519i | \(0.603582\pi\) | |||||||
\(884\) | −3.00000 | + | 5.19615i | −0.100901 | + | 0.174766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.50000 | − | 2.59808i | −0.0503935 | − | 0.0872841i | ||||
\(887\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.0000 | − | 22.5167i | 0.435272 | − | 0.753914i | ||||
\(893\) | −6.00000 | −0.200782 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.50000 | + | 7.79423i | −0.150167 | + | 0.260097i | ||||
\(899\) | 12.0000 | − | 20.7846i | 0.400222 | − | 0.693206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.0000 | − | 31.1769i | −0.599667 | − | 1.03865i | ||||
\(902\) | 13.5000 | + | 23.3827i | 0.449501 | + | 0.778558i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.00000 | + | 5.19615i | −0.0997785 | + | 0.172821i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.0000 | −1.02934 | −0.514669 | − | 0.857389i | \(-0.672085\pi\) | ||||
−0.514669 | + | 0.857389i | \(0.672085\pi\) | |||||||
\(908\) | −10.5000 | − | 18.1865i | −0.348455 | − | 0.603541i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.0000 | + | 41.5692i | 0.795155 | + | 1.37725i | 0.922740 | + | 0.385422i | \(0.125944\pi\) |
−0.127585 | + | 0.991828i | \(0.540723\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.0000 | − | 31.1769i | −0.595713 | − | 1.03181i | ||||
\(914\) | 8.50000 | + | 14.7224i | 0.281155 | + | 0.486975i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.00000 | + | 12.1244i | 0.231287 | + | 0.400600i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.0000 | − | 32.9090i | −0.626752 | − | 1.08557i | −0.988199 | − | 0.153174i | \(-0.951051\pi\) |
0.361447 | − | 0.932393i | \(-0.382283\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 30.0000 | 0.987997 | ||||||||
\(923\) | 12.0000 | − | 20.7846i | 0.394985 | − | 0.684134i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0000 | − | 17.3205i | −0.328798 | − | 0.569495i | ||||
\(926\) | 10.0000 | + | 17.3205i | 0.328620 | + | 0.569187i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.00000 | + | 5.19615i | −0.0984798 | + | 0.170572i | ||||
\(929\) | 3.00000 | − | 5.19615i | 0.0984268 | − | 0.170480i | −0.812607 | − | 0.582812i | \(-0.801952\pi\) |
0.911034 | + | 0.412332i | \(0.135286\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.50000 | − | 2.59808i | 0.0491341 | − | 0.0851028i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 15.0000 | 0.490815 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.0000 | −0.457360 | −0.228680 | − | 0.973502i | \(-0.573441\pi\) | ||||
−0.228680 | + | 0.973502i | \(0.573441\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.0000 | + | 51.9615i | 0.977972 | + | 1.69390i | 0.669757 | + | 0.742581i | \(0.266398\pi\) |
0.308215 | + | 0.951317i | \(0.400268\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.0000 | + | 46.7654i | −0.879241 | + | 1.52289i | ||||
\(944\) | 3.00000 | 0.0976417 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.00000 | 0.0975384 | ||||||||
\(947\) | 1.50000 | − | 2.59808i | 0.0487435 | − | 0.0844261i | −0.840624 | − | 0.541619i | \(-0.817812\pi\) |
0.889368 | + | 0.457193i | \(0.151145\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.0000 | − | 19.0526i | −0.357075 | − | 0.618472i | ||||
\(950\) | 5.00000 | 0.162221 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.00000 | −0.291539 | −0.145769 | − | 0.989319i | \(-0.546566\pi\) | ||||
−0.145769 | + | 0.989319i | \(0.546566\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.00000 | −0.194054 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.0000 | + | 36.3731i | −0.678479 | + | 1.17516i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | 4.00000 | − | 6.92820i | 0.128965 | − | 0.223374i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.50000 | − | 6.06218i | −0.112727 | − | 0.195250i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.0000 | − | 19.0526i | 0.353736 | − | 0.612689i | −0.633165 | − | 0.774017i | \(-0.718244\pi\) |
0.986901 | + | 0.161328i | \(0.0515777\pi\) | |||||||
\(968\) | 2.00000 | 0.0642824 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.0000 | + | 31.1769i | 0.577647 | + | 1.00051i | 0.995748 | + | 0.0921142i | \(0.0293625\pi\) |
−0.418101 | + | 0.908401i | \(0.637304\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 13.0000 | + | 22.5167i | 0.416547 | + | 0.721480i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.00000 | + | 6.92820i | 0.128037 | + | 0.221766i | ||||
\(977\) | −25.5000 | − | 44.1673i | −0.815817 | − | 1.41304i | −0.908740 | − | 0.417364i | \(-0.862954\pi\) |
0.0929223 | − | 0.995673i | \(-0.470379\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.00000 | − | 15.5885i | −0.287641 | − | 0.498209i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.50000 | + | 12.9904i | 0.239335 | + | 0.414540i | ||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.00000 | − | 15.5885i | 0.286618 | − | 0.496438i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.00000 | + | 1.73205i | 0.0318142 | + | 0.0551039i | ||||
\(989\) | 3.00000 | + | 5.19615i | 0.0953945 | + | 0.165228i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | − | 13.8564i | 0.254128 | − | 0.440163i | −0.710530 | − | 0.703667i | \(-0.751545\pi\) |
0.964658 | + | 0.263504i | \(0.0848781\pi\) | |||||||
\(992\) | 2.00000 | − | 3.46410i | 0.0635001 | − | 0.109985i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.0000 | 0.886769 | 0.443384 | − | 0.896332i | \(-0.353778\pi\) | ||||
0.443384 | + | 0.896332i | \(0.353778\pi\) | |||||||
\(998\) | −6.50000 | + | 11.2583i | −0.205754 | + | 0.356376i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))