Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,2,Mod(49,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.bv (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.98266508613\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.49 |
Dual form | 624.2.bv.b.433.1 |
$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 3.46410i | − | 1.54919i | −0.632456 | − | 0.774597i | \(-0.717953\pi\) | ||
0.632456 | − | 0.774597i | \(-0.282047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.50000 | + | 0.866025i | 0.566947 | + | 0.327327i | 0.755929 | − | 0.654654i | \(-0.227186\pi\) |
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | − | 1.73205i | 0.904534 | − | 0.522233i | 0.0258656 | − | 0.999665i | \(-0.491766\pi\) |
0.878668 | + | 0.477432i | \(0.158432\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.50000 | + | 0.866025i | 0.970725 | + | 0.240192i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.00000 | + | 1.73205i | −0.774597 | + | 0.447214i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | − | 1.73205i | −0.688247 | − | 0.397360i | 0.114708 | − | 0.993399i | \(-0.463407\pi\) |
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.73205i | − | 0.377964i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.00000 | −1.40000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | − | 5.19615i | −0.557086 | − | 0.964901i | −0.997738 | − | 0.0672232i | \(-0.978586\pi\) |
0.440652 | − | 0.897678i | \(-0.354747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.73205i | 0.311086i | 0.987829 | + | 0.155543i | \(0.0497126\pi\) | ||||
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.00000 | − | 1.73205i | −0.522233 | − | 0.301511i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.00000 | − | 5.19615i | 0.507093 | − | 0.878310i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | − | 3.46410i | −0.160128 | − | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | + | 3.46410i | −0.937043 | + | 0.541002i | −0.889032 | − | 0.457845i | \(-0.848621\pi\) |
−0.0480106 | + | 0.998847i | \(0.515288\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.500000 | + | 0.866025i | −0.0762493 | + | 0.132068i | −0.901629 | − | 0.432511i | \(-0.857628\pi\) |
0.825380 | + | 0.564578i | \(0.190961\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.00000 | + | 1.73205i | 0.447214 | + | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.46410i | 0.505291i | 0.967559 | + | 0.252646i | \(0.0813007\pi\) | ||||
−0.967559 | + | 0.252646i | \(0.918699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.00000 | − | 3.46410i | −0.285714 | − | 0.494872i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.0000 | 1.64833 | 0.824163 | − | 0.566352i | \(-0.191646\pi\) | ||||
0.824163 | + | 0.566352i | \(0.191646\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.00000 | − | 10.3923i | −0.809040 | − | 1.40130i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.46410i | 0.458831i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.00000 | + | 1.73205i | 0.390567 | + | 0.225494i | 0.682406 | − | 0.730974i | \(-0.260934\pi\) |
−0.291839 | + | 0.956467i | \(0.594267\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.500000 | + | 0.866025i | −0.0640184 | + | 0.110883i | −0.896258 | − | 0.443533i | \(-0.853725\pi\) |
0.832240 | + | 0.554416i | \(0.187058\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.50000 | + | 0.866025i | −0.188982 | + | 0.109109i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.00000 | − | 12.1244i | 0.372104 | − | 1.50384i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.50000 | + | 4.33013i | −0.916271 | + | 0.529009i | −0.882443 | − | 0.470418i | \(-0.844103\pi\) |
−0.0338274 | + | 0.999428i | \(0.510770\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.00000 | + | 5.19615i | −0.361158 | + | 0.625543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.00000 | + | 5.19615i | 1.06810 | + | 0.616670i | 0.927663 | − | 0.373419i | \(-0.121815\pi\) |
0.140441 | + | 0.990089i | \(0.455148\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.73205i | − | 0.202721i | −0.994850 | − | 0.101361i | \(-0.967680\pi\) | ||
0.994850 | − | 0.101361i | \(-0.0323196\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.50000 | + | 6.06218i | 0.404145 | + | 0.700000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.00000 | 0.683763 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.0000 | 1.23760 | 0.618798 | − | 0.785550i | \(-0.287620\pi\) | ||||
0.618798 | + | 0.785550i | \(0.287620\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 13.8564i | − | 1.52094i | −0.649374 | − | 0.760469i | \(-0.724969\pi\) | ||
0.649374 | − | 0.760469i | \(-0.275031\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.00000 | + | 5.19615i | −0.321634 | + | 0.557086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | − | 3.46410i | 0.635999 | − | 0.367194i | −0.147073 | − | 0.989126i | \(-0.546985\pi\) |
0.783072 | + | 0.621932i | \(0.213652\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.50000 | + | 4.33013i | 0.471728 | + | 0.453921i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.50000 | − | 0.866025i | 0.155543 | − | 0.0898027i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.00000 | + | 10.3923i | −0.615587 | + | 1.06623i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.50000 | − | 2.59808i | −0.456906 | − | 0.263795i | 0.253837 | − | 0.967247i | \(-0.418307\pi\) |
−0.710742 | + | 0.703452i | \(0.751641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.46410i | 0.348155i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.00000 | + | 15.5885i | 0.895533 | + | 1.55111i | 0.833143 | + | 0.553058i | \(0.186539\pi\) |
0.0623905 | + | 0.998052i | \(0.480128\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.00000 | 0.0985329 | 0.0492665 | − | 0.998786i | \(-0.484312\pi\) | ||||
0.0492665 | + | 0.998786i | \(0.484312\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.00000 | −0.585540 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.00000 | − | 5.19615i | −0.290021 | − | 0.502331i | 0.683793 | − | 0.729676i | \(-0.260329\pi\) |
−0.973814 | + | 0.227345i | \(0.926996\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.5885i | 1.49310i | 0.665327 | + | 0.746552i | \(0.268292\pi\) | ||||
−0.665327 | + | 0.746552i | \(0.731708\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | −18.0000 | + | 10.3923i | −1.67851 | + | 0.969087i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.50000 | + | 2.59808i | −0.231125 | + | 0.240192i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.00000 | + | 3.46410i | 0.541002 | + | 0.312348i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92820i | 0.619677i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.50000 | + | 11.2583i | 0.576782 | + | 0.999015i | 0.995846 | + | 0.0910585i | \(0.0290250\pi\) |
−0.419064 | + | 0.907957i | \(0.637642\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.00000 | 0.0880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | −0.524222 | −0.262111 | − | 0.965038i | \(-0.584419\pi\) | ||||
−0.262111 | + | 0.965038i | \(0.584419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.00000 | − | 5.19615i | −0.260133 | − | 0.450564i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 3.46410i | − | 0.298142i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.50000 | − | 4.33013i | 0.212047 | − | 0.367277i | −0.740308 | − | 0.672268i | \(-0.765320\pi\) |
0.952355 | + | 0.304991i | \(0.0986536\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | − | 1.73205i | 0.252646 | − | 0.145865i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.0000 | − | 3.46410i | 1.00349 | − | 0.289683i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.0000 | + | 10.3923i | −1.49482 | + | 0.863034i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.00000 | + | 3.46410i | −0.164957 | + | 0.285714i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | − | 3.46410i | −0.491539 | − | 0.283790i | 0.233674 | − | 0.972315i | \(-0.424925\pi\) |
−0.725213 | + | 0.688525i | \(0.758259\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.46410i | − | 0.281905i | −0.990016 | − | 0.140952i | \(-0.954984\pi\) | ||
0.990016 | − | 0.140952i | \(-0.0450164\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.00000 | 0.481932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0000 | 0.877896 | 0.438948 | − | 0.898513i | \(-0.355351\pi\) | ||||
0.438948 | + | 0.898513i | \(0.355351\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.00000 | − | 10.3923i | −0.475831 | − | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 10.3923i | − | 0.819028i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.5000 | + | 9.52628i | 1.29238 | + | 0.746156i | 0.979076 | − | 0.203497i | \(-0.0652307\pi\) |
0.313304 | + | 0.949653i | \(0.398564\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.00000 | + | 10.3923i | −0.467099 | + | 0.809040i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.00000 | − | 3.46410i | 0.464294 | − | 0.268060i | −0.249554 | − | 0.968361i | \(-0.580284\pi\) |
0.713848 | + | 0.700301i | \(0.246951\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5000 | + | 6.06218i | 0.884615 | + | 0.466321i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.00000 | − | 1.73205i | 0.229416 | − | 0.132453i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 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 | ||||||||
\(175\) | −10.5000 | − | 6.06218i | −0.793725 | − | 0.458258i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 3.46410i | − | 0.260378i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00000 | + | 10.3923i | 0.448461 | + | 0.776757i | 0.998286 | − | 0.0585225i | \(-0.0186389\pi\) |
−0.549825 | + | 0.835280i | \(0.685306\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.50000 | + | 0.866025i | 0.109109 | + | 0.0629941i | ||||
\(190\) | 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 | ||||||||
\(193\) | −13.5000 | + | 7.79423i | −0.971751 | + | 0.561041i | −0.899770 | − | 0.436365i | \(-0.856266\pi\) |
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12.0000 | + | 3.46410i | −0.859338 | + | 0.248069i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0000 | − | 6.92820i | 0.854965 | − | 0.493614i | −0.00735824 | − | 0.999973i | \(-0.502342\pi\) |
0.862323 | + | 0.506359i | \(0.169009\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.50000 | − | 6.06218i | 0.248108 | − | 0.429736i | −0.714893 | − | 0.699234i | \(-0.753524\pi\) |
0.963001 | + | 0.269498i | \(0.0868577\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.50000 | + | 4.33013i | 0.529009 | + | 0.305424i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 10.3923i | − | 0.729397i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.0000 | + | 20.7846i | 0.838116 | + | 1.45166i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.00000 | 0.417029 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.0000 | −0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.50000 | + | 11.2583i | 0.447478 | + | 0.775055i | 0.998221 | − | 0.0596196i | \(-0.0189888\pi\) |
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 10.3923i | − | 0.712069i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.00000 | + | 1.73205i | 0.204598 | + | 0.118125i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.50000 | + | 2.59808i | −0.101827 | + | 0.176369i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.50000 | + | 0.866025i | −0.101361 | + | 0.0585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.0000 | + | 8.66025i | −1.00447 | + | 0.579934i | −0.909569 | − | 0.415553i | \(-0.863588\pi\) |
−0.0949052 | + | 0.995486i | \(0.530255\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.50000 | − | 6.06218i | 0.233333 | − | 0.404145i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.0000 | − | 10.3923i | −1.19470 | − | 0.689761i | −0.235333 | − | 0.971915i | \(-0.575618\pi\) |
−0.959369 | + | 0.282153i | \(0.908951\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 27.7128i | − | 1.83131i | −0.401960 | − | 0.915657i | \(-0.631671\pi\) | ||
0.401960 | − | 0.915657i | \(-0.368329\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.00000 | − | 5.19615i | −0.197386 | − | 0.341882i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.0000 | 0.782794 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.50000 | − | 9.52628i | −0.357263 | − | 0.618798i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.0000 | + | 10.3923i | 1.15948 | + | 0.669427i | 0.951180 | − | 0.308637i | \(-0.0998729\pi\) |
0.208302 | + | 0.978065i | \(0.433206\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.0000 | + | 6.92820i | −0.766652 | + | 0.442627i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.00000 | − | 8.66025i | −0.572656 | − | 0.551039i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.0000 | + | 6.92820i | −0.760469 | + | 0.439057i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.00000 | − | 10.3923i | 0.378717 | − | 0.655956i | −0.612159 | − | 0.790735i | \(-0.709699\pi\) |
0.990876 | + | 0.134778i | \(0.0430322\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.0000 | − | 10.3923i | −1.13165 | − | 0.653359i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | 0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.00000 | + | 10.3923i | 0.369976 | + | 0.640817i | 0.989561 | − | 0.144112i | \(-0.0460326\pi\) |
−0.619586 | + | 0.784929i | \(0.712699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 41.5692i | − | 2.55358i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.00000 | − | 3.46410i | −0.367194 | − | 0.212000i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.50000 | − | 2.59808i | 0.273356 | − | 0.157822i | −0.357056 | − | 0.934083i | \(-0.616219\pi\) |
0.630412 | + | 0.776261i | \(0.282886\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.50000 | − | 6.06218i | 0.0907841 | − | 0.366900i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.0000 | + | 12.1244i | −1.26635 | + | 0.731126i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.00000 | − | 8.66025i | 0.300421 | − | 0.520344i | −0.675810 | − | 0.737075i | \(-0.736206\pi\) |
0.976231 | + | 0.216731i | \(0.0695395\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.50000 | − | 0.866025i | −0.0898027 | − | 0.0518476i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.2487i | 1.44656i | 0.690557 | + | 0.723278i | \(0.257366\pi\) | ||||
−0.690557 | + | 0.723278i | \(0.742634\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.50000 | − | 9.52628i | −0.326941 | − | 0.566279i | 0.654962 | − | 0.755662i | \(-0.272685\pi\) |
−0.981903 | + | 0.189383i | \(0.939351\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.0000 | 0.710819 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | −0.708338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.19615i | 0.304604i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.0000 | − | 8.66025i | −0.876309 | − | 0.505937i | −0.00686959 | − | 0.999976i | \(-0.502187\pi\) |
−0.869440 | + | 0.494039i | \(0.835520\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000 | − | 10.3923i | 0.349334 | − | 0.605063i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.00000 | − | 1.73205i | 0.174078 | − | 0.100504i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.00000 | − | 20.7846i | −0.346989 | − | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.50000 | + | 0.866025i | −0.0864586 | + | 0.0499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.00000 | − | 15.5885i | 0.517036 | − | 0.895533i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.00000 | + | 1.73205i | 0.171780 | + | 0.0991769i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.73205i | − | 0.0988534i | −0.998778 | − | 0.0494267i | \(-0.984261\pi\) | ||
0.998778 | − | 0.0494267i | \(-0.0157394\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.500000 | − | 0.866025i | −0.0284440 | − | 0.0492665i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.0000 | 1.36092 | 0.680458 | − | 0.732787i | \(-0.261781\pi\) | ||||
0.680458 | + | 0.732787i | \(0.261781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.0000 | 0.734803 | 0.367402 | − | 0.930062i | \(-0.380247\pi\) | ||||
0.367402 | + | 0.930062i | \(0.380247\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.00000 | + | 5.19615i | 0.169031 | + | 0.292770i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 6.92820i | − | 0.389127i | −0.980890 | − | 0.194563i | \(-0.937671\pi\) | ||
0.980890 | − | 0.194563i | \(-0.0623290\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.0000 | − | 10.3923i | −1.00781 | − | 0.581857i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.00000 | + | 5.19615i | −0.167444 | + | 0.290021i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.5000 | − | 6.06218i | −1.35902 | − | 0.336269i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.5000 | − | 7.79423i | 0.746552 | − | 0.431022i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.00000 | + | 5.19615i | −0.165395 | + | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.50000 | − | 2.59808i | −0.247342 | − | 0.142803i | 0.371204 | − | 0.928551i | \(-0.378945\pi\) |
−0.618547 | + | 0.785748i | \(0.712278\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.0000 | + | 25.9808i | 0.819538 | + | 1.41948i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.00000 | −0.272367 | −0.136184 | − | 0.990684i | \(-0.543484\pi\) | ||||
−0.136184 | + | 0.990684i | \(0.543484\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.00000 | + | 5.19615i | 0.162459 | + | 0.281387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.0526i | − | 1.02874i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.0000 | + | 10.3923i | 0.969087 | + | 0.559503i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.0000 | + | 20.7846i | −0.644194 | + | 1.11578i | 0.340293 | + | 0.940319i | \(0.389474\pi\) |
−0.984487 | + | 0.175457i | \(0.943860\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.5000 | + | 9.52628i | −0.883225 | + | 0.509930i | −0.871720 | − | 0.490004i | \(-0.836995\pi\) |
−0.0115044 | + | 0.999934i | \(0.503662\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.50000 | + | 0.866025i | 0.186816 | + | 0.0462250i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.00000 | − | 5.19615i | 0.479022 | − | 0.276563i | −0.240987 | − | 0.970528i | \(-0.577471\pi\) |
0.720009 | + | 0.693965i | \(0.244138\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.0000 | − | 31.1769i | 0.955341 | − | 1.65470i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.92820i | 0.365657i | 0.983145 | + | 0.182828i | \(0.0585252\pi\) | ||||
−0.983145 | + | 0.182828i | \(0.941475\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.50000 | − | 6.06218i | −0.184211 | − | 0.319062i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.50000 | + | 14.7224i | 0.443696 | + | 0.768505i | 0.997960 | − | 0.0638362i | \(-0.0203335\pi\) |
−0.554264 | + | 0.832341i | \(0.687000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 6.92820i | − | 0.360668i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.0000 | + | 10.3923i | 0.934513 | + | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.50000 | − | 9.52628i | 0.284779 | − | 0.493252i | −0.687776 | − | 0.725923i | \(-0.741413\pi\) |
0.972556 | + | 0.232671i | \(0.0747464\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.00000 | − | 3.46410i | 0.309839 | − | 0.178885i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.00000 | − | 20.7846i | −0.309016 | − | 1.07046i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.5000 | − | 11.2583i | 1.00165 | − | 0.578302i | 0.0929123 | − | 0.995674i | \(-0.470382\pi\) |
0.908735 | + | 0.417373i | \(0.137049\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.50000 | − | 11.2583i | 0.333005 | − | 0.576782i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.0000 | − | 13.8564i | −1.22634 | − | 0.708029i | −0.260080 | − | 0.965587i | \(-0.583749\pi\) |
−0.966263 | + | 0.257558i | \(0.917082\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 20.7846i | − | 1.05928i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.500000 | − | 0.866025i | −0.0254164 | − | 0.0440225i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.0000 | 0.608424 | 0.304212 | − | 0.952604i | \(-0.401607\pi\) | ||||
0.304212 | + | 0.952604i | \(0.401607\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.00000 | + | 5.19615i | 0.151330 | + | 0.262111i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 38.1051i | − | 1.91728i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.5000 | + | 7.79423i | 0.677546 | + | 0.391181i | 0.798930 | − | 0.601424i | \(-0.205400\pi\) |
−0.121384 | + | 0.992606i | \(0.538733\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.00000 | + | 5.19615i | −0.150188 | + | 0.260133i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.50000 | + | 6.06218i | −0.0747203 | + | 0.301979i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.00000 | + | 1.73205i | −0.149071 | + | 0.0860663i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.50000 | + | 4.33013i | 0.370851 | + | 0.214111i | 0.673830 | − | 0.738886i | \(-0.264648\pi\) |
−0.302979 | + | 0.952997i | \(0.597981\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.00000 | + | 5.19615i | 0.147620 | + | 0.255686i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −48.0000 | −2.35623 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.00000 | −0.244851 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.00000 | − | 10.3923i | −0.293119 | − | 0.507697i | 0.681426 | − | 0.731887i | \(-0.261360\pi\) |
−0.974546 | + | 0.224189i | \(0.928027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.1244i | 0.590905i | 0.955357 | + | 0.295452i | \(0.0954704\pi\) | ||||
−0.955357 | + | 0.295452i | \(0.904530\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.00000 | − | 1.73205i | −0.145865 | − | 0.0842152i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.50000 | + | 0.866025i | −0.0725901 | + | 0.0419099i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.00000 | − | 8.66025i | −0.434524 | − | 0.418121i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.0000 | + | 10.3923i | −0.867029 | + | 0.500580i | −0.866360 | − | 0.499420i | \(-0.833546\pi\) |
−0.000669521 | 1.00000i | \(0.500213\pi\) | ||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.5000 | − | 19.9186i | 0.552655 | − | 0.957226i | −0.445427 | − | 0.895318i | \(-0.646948\pi\) |
0.998082 | − | 0.0619079i | \(-0.0197185\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 18.0000 | + | 10.3923i | 0.863034 | + | 0.498273i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.7846i | 0.994263i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.5000 | + | 30.3109i | 0.835229 | + | 1.44666i | 0.893843 | + | 0.448379i | \(0.147999\pi\) |
−0.0586141 | + | 0.998281i | \(0.518668\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.00000 | 0.190476 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.0000 | −1.14027 | −0.570137 | − | 0.821549i | \(-0.693110\pi\) | ||||
−0.570137 | + | 0.821549i | \(0.693110\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.0000 | − | 20.7846i | −0.568855 | − | 0.985285i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.92820i | 0.327693i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.0000 | + | 19.0526i | 1.55737 | + | 0.899146i | 0.997508 | + | 0.0705577i | \(0.0224779\pi\) |
0.559859 | + | 0.828588i | \(0.310855\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.0000 | + | 20.7846i | −0.565058 | + | 0.978709i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.00000 | + | 1.73205i | −0.140952 | + | 0.0813788i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.0000 | − | 15.5885i | 0.703211 | − | 0.730798i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.5000 | + | 18.1865i | −1.47351 | + | 0.850730i | −0.999555 | − | 0.0298202i | \(-0.990507\pi\) |
−0.473953 | + | 0.880550i | \(0.657173\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.0000 | − | 20.7846i | −1.67669 | − | 0.968036i | −0.963750 | − | 0.266808i | \(-0.914031\pi\) |
−0.712938 | − | 0.701228i | \(-0.752636\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 36.3731i | − | 1.69040i | −0.534450 | − | 0.845200i | \(-0.679481\pi\) | ||
0.534450 | − | 0.845200i | \(-0.320519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.00000 | − | 5.19615i | −0.139122 | − | 0.240966i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.00000 | −0.277647 | −0.138823 | − | 0.990317i | \(-0.544332\pi\) | ||||
−0.138823 | + | 0.990317i | \(0.544332\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.0000 | −0.692636 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.50000 | − | 9.52628i | −0.253427 | − | 0.438948i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.46410i | 0.159280i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.0000 | + | 12.1244i | 0.963546 | + | 0.556304i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | + | 10.3923i | −0.274721 | + | 0.475831i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.0000 | + | 17.3205i | −1.37073 | + | 0.791394i | −0.991021 | − | 0.133710i | \(-0.957311\pi\) |
−0.379714 | + | 0.925104i | \(0.623978\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.00000 | + | 5.19615i | −0.409514 | + | 0.236433i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.00000 | + | 15.5885i | −0.408669 | + | 0.707835i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.0000 | + | 12.1244i | 0.951601 | + | 0.549407i | 0.893578 | − | 0.448908i | \(-0.148187\pi\) |
0.0580230 | + | 0.998315i | \(0.481520\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 19.0526i | − | 0.861586i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.00000 | + | 5.19615i | 0.135388 | + | 0.234499i | 0.925746 | − | 0.378147i | \(-0.123439\pi\) |
−0.790358 | + | 0.612646i | \(0.790105\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.0000 | 0.539360 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.00000 | + | 15.5885i | 0.403705 | + | 0.699238i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.1769i | 1.39567i | 0.716258 | + | 0.697835i | \(0.245853\pi\) | ||||
−0.716258 | + | 0.697835i | \(0.754147\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | − | 3.46410i | −0.268060 | − | 0.154765i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.0000 | + | 25.9808i | −0.668817 | + | 1.15842i | 0.309418 | + | 0.950926i | \(0.399866\pi\) |
−0.978235 | + | 0.207499i | \(0.933468\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 54.0000 | − | 31.1769i | 2.40297 | − | 1.38735i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.500000 | − | 12.9904i | −0.0222058 | − | 0.576923i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.0000 | + | 8.66025i | −0.664863 | + | 0.383859i | −0.794128 | − | 0.607751i | \(-0.792072\pi\) |
0.129264 | + | 0.991610i | \(0.458738\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.50000 | − | 2.59808i | 0.0663561 | − | 0.114932i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.00000 | − | 1.73205i | −0.132453 | − | 0.0764719i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 3.46410i | − | 0.152647i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.00000 | + | 10.3923i | 0.263880 | + | 0.457053i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.0000 | −1.05146 | −0.525730 | − | 0.850652i | \(-0.676208\pi\) | ||||
−0.525730 | + | 0.850652i | \(0.676208\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.0000 | − | 24.2487i | −0.612177 | − | 1.06032i | −0.990873 | − | 0.134801i | \(-0.956961\pi\) |
0.378695 | − | 0.925521i | \(-0.376373\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.1244i | 0.529150i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.00000 | + | 1.73205i | −0.130189 | + | 0.0751646i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.0000 | + | 6.92820i | −1.03956 | + | 0.300094i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.0000 | + | 10.3923i | −0.778208 | + | 0.449299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.00000 | − | 10.3923i | 0.258919 | − | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.0000 | − | 6.92820i | −0.516877 | − | 0.298419i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.4449i | 1.26593i | 0.774179 | + | 0.632967i | \(0.218163\pi\) | ||||
−0.774179 | + | 0.632967i | \(0.781837\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.00000 | − | 12.1244i | −0.300399 | − | 0.520306i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 54.0000 | 2.31311 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.0000 | 0.812381 | 0.406191 | − | 0.913788i | \(-0.366857\pi\) | ||||
0.406191 | + | 0.913788i | \(0.366857\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.500000 | − | 0.866025i | −0.0213395 | − | 0.0369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.7846i | 0.885454i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.5000 | + | 9.52628i | 0.701651 | + | 0.405099i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.0000 | + | 13.8564i | −1.01691 | + | 0.587115i | −0.913208 | − | 0.407493i | \(-0.866403\pi\) |
−0.103704 | + | 0.994608i | \(0.533070\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.50000 | + | 2.59808i | −0.105739 | + | 0.109887i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.0000 | + | 36.3731i | −0.885044 | + | 1.53294i | −0.0393818 | + | 0.999224i | \(0.512539\pi\) |
−0.845663 | + | 0.533718i | \(0.820794\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.0000 | + | 10.3923i | 0.757266 | + | 0.437208i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1.73205i | − | 0.0727393i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.00000 | + | 5.19615i | 0.125767 | + | 0.217834i | 0.922032 | − | 0.387113i | \(-0.126528\pi\) |
−0.796266 | + | 0.604947i | \(0.793194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.0000 | 1.84134 | 0.920671 | − | 0.390339i | \(-0.127642\pi\) | ||||
0.920671 | + | 0.390339i | \(0.127642\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.0000 | 0.751961 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.0000 | + | 36.3731i | 0.875761 | + | 1.51686i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.6410i | 1.44212i | 0.692870 | + | 0.721062i | \(0.256346\pi\) | ||||
−0.692870 | + | 0.721062i | \(0.743654\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.5000 | + | 7.79423i | 0.561041 | + | 0.323917i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000 | − | 20.7846i | 0.497844 | − | 0.862291i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 36.0000 | − | 20.7846i | 1.49097 | − | 0.860811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.00000 | + | 8.66025i | 0.372104 | + | 0.358057i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.0000 | − | 15.5885i | 1.11441 | − | 0.643404i | 0.174441 | − | 0.984668i | \(-0.444188\pi\) |
0.939968 | + | 0.341263i | \(0.110855\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.00000 | − | 5.19615i | 0.123613 | − | 0.214104i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.0000 | − | 6.92820i | −0.493614 | − | 0.284988i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 3.46410i | − | 0.142254i | −0.997467 | − | 0.0711268i | \(-0.977341\pi\) | ||
0.997467 | − | 0.0711268i | \(-0.0226595\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.00000 | −0.286491 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.0000 | 1.22577 | 0.612883 | − | 0.790173i | \(-0.290010\pi\) | ||||
0.612883 | + | 0.790173i | \(0.290010\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.0000 | + | 22.5167i | 0.530281 | + | 0.918474i | 0.999376 | + | 0.0353259i | \(0.0112469\pi\) |
−0.469095 | + | 0.883148i | \(0.655420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 8.66025i | − | 0.352673i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.00000 | − | 1.73205i | −0.121967 | − | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.00000 | − | 6.92820i | 0.162355 | − | 0.281207i | −0.773358 | − | 0.633970i | \(-0.781424\pi\) |
0.935713 | + | 0.352763i | \(0.114758\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.00000 | + | 5.19615i | −0.364698 | + | 0.210559i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.00000 | + | 12.1244i | −0.121367 | + | 0.490499i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.50000 | − | 4.33013i | 0.302922 | − | 0.174892i | −0.340833 | − | 0.940124i | \(-0.610709\pi\) |
0.643755 | + | 0.765232i | \(0.277376\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.0000 | − | 20.7846i | 0.483887 | − | 0.838116i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.00000 | − | 5.19615i | −0.362326 | − | 0.209189i | 0.307774 | − | 0.951459i | \(-0.400416\pi\) |
−0.670101 | + | 0.742270i | \(0.733749\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.9808i | 1.04425i | 0.852867 | + | 0.522127i | \(0.174861\pi\) | ||||
−0.852867 | + | 0.522127i | \(0.825139\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.00000 | − | 5.19615i | −0.120386 | − | 0.208514i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.0000 | 0.480770 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.00000 | + | 10.3923i | 0.239617 | + | 0.415029i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.50000 | − | 0.866025i | −0.0597141 | − | 0.0344759i | 0.469846 | − | 0.882749i | \(-0.344310\pi\) |
−0.529560 | + | 0.848273i | \(0.677643\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.50000 | − | 11.2583i | 0.258352 | − | 0.447478i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 39.0000 | − | 22.5167i | 1.54767 | − | 0.893546i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.00000 | − | 13.8564i | −0.158486 | − | 0.549011i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.00000 | + | 5.19615i | −0.356034 | + | 0.205557i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.00000 | + | 15.5885i | −0.355479 | + | 0.615707i | −0.987200 | − | 0.159489i | \(-0.949015\pi\) |
0.631721 | + | 0.775196i | \(0.282349\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.5000 | − | 9.52628i | −0.650696 | − | 0.375680i | 0.138027 | − | 0.990429i | \(-0.455924\pi\) |
−0.788723 | + | 0.614749i | \(0.789257\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 3.46410i | − | 0.136399i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.00000 | − | 15.5885i | −0.353827 | − | 0.612845i | 0.633090 | − | 0.774078i | \(-0.281786\pi\) |
−0.986916 | + | 0.161233i | \(0.948453\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.0000 | 0.471041 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.00000 | 0.117579 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.0000 | − | 31.1769i | −0.704394 | − | 1.22005i | −0.966910 | − | 0.255119i | \(-0.917885\pi\) |
0.262515 | − | 0.964928i | \(-0.415448\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.7846i | 0.812122i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.50000 | + | 0.866025i | 0.0585206 | + | 0.0337869i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.0000 | − | 41.5692i | 0.934907 | − | 1.61931i | 0.160108 | − | 0.987099i | \(-0.448816\pi\) |
0.774799 | − | 0.632207i | \(-0.217851\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.5000 | + | 12.9904i | −0.875149 | + | 0.505267i | −0.869056 | − | 0.494714i | \(-0.835273\pi\) |
−0.00609283 | + | 0.999981i | \(0.501939\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18.0000 | + | 10.3923i | −0.698010 | + | 0.402996i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.0000 | + | 31.1769i | −0.696963 | + | 1.20717i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.0000 | + | 8.66025i | 0.579934 | + | 0.334825i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.46410i | 0.133730i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.500000 | + | 0.866025i | 0.0192736 | + | 0.0333828i | 0.875501 | − | 0.483216i | \(-0.160531\pi\) |
−0.856228 | + | 0.516599i | \(0.827198\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.00000 | −0.269430 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 48.0000 | 1.84479 | 0.922395 | − | 0.386248i | \(-0.126229\pi\) | ||||
0.922395 | + | 0.386248i | \(0.126229\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.50000 | − | 7.79423i | −0.172694 | − | 0.299115i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.7846i | 0.796468i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.0000 | − | 12.1244i | −0.803543 | − | 0.463926i | 0.0411658 | − | 0.999152i | \(-0.486893\pi\) |
−0.844708 | + | 0.535227i | \(0.820226\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.0000 | + | 13.8564i | −0.915657 | + | 0.528655i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 42.0000 | + | 10.3923i | 1.60007 | + | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.5000 | + | 21.6506i | −1.42657 | + | 0.823629i | −0.996848 | − | 0.0793336i | \(-0.974721\pi\) |
−0.429719 | + | 0.902963i | \(0.641387\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.00000 | + | 5.19615i | −0.113961 | + | 0.197386i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.0000 | − | 8.66025i | −0.568982 | − | 0.328502i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.00000 | + | 15.5885i | 0.340411 | + | 0.589610i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.0000 | −0.453234 | −0.226617 | − | 0.973984i | \(-0.572767\pi\) | ||||
−0.226617 | + | 0.973984i | \(0.572767\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.00000 | − | 10.3923i | −0.225973 | − | 0.391397i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.1769i | 1.17253i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.5000 | − | 9.52628i | −0.619671 | − | 0.357767i | 0.157070 | − | 0.987587i | \(-0.449795\pi\) |
−0.776741 | + | 0.629821i | \(0.783128\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.50000 | + | 9.52628i | −0.206266 | + | 0.357263i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.00000 | − | 5.19615i | 0.337053 | − | 0.194597i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0000 | − | 41.5692i | −0.448775 | − | 1.55460i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.00000 | + | 5.19615i | −0.111881 | + | 0.193784i | −0.916529 | − | 0.399969i | \(-0.869021\pi\) |
0.804648 | + | 0.593753i | \(0.202354\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.50000 | + | 0.866025i | 0.0558629 | + | 0.0322525i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 20.7846i | − | 0.772988i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.0000 | + | 36.3731i | 0.779920 | + | 1.35086i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.0000 | 1.29808 | 0.649039 | − | 0.760755i | \(-0.275171\pi\) | ||||
0.649039 | + | 0.760755i | \(0.275171\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 39.8372i | − | 1.47142i | −0.677297 | − | 0.735710i | \(-0.736849\pi\) | ||
0.677297 | − | 0.735710i | \(-0.263151\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.0000 | + | 6.92820i | 0.442627 | + | 0.255551i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.0000 | + | 25.9808i | −0.552532 | + | 0.957014i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.0000 | + | 22.5167i | −1.43464 | + | 0.828289i | −0.997470 | − | 0.0710909i | \(-0.977352\pi\) |
−0.437168 | + | 0.899380i | \(0.644019\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.00000 | + | 12.1244i | −0.110208 | + | 0.445399i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.00000 | − | 5.19615i | 0.330178 | − | 0.190628i | −0.325742 | − | 0.945459i | \(-0.605614\pi\) |
0.655920 | + | 0.754830i | \(0.272281\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.0000 | + | 20.7846i | −0.439646 | + | 0.761489i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.0000 | + | 6.92820i | 0.439057 | + | 0.253490i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 10.3923i | − | 0.379727i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.00000 | + | 6.92820i | 0.145962 | + | 0.252814i | 0.929731 | − | 0.368238i | \(-0.120039\pi\) |
−0.783769 | + | 0.621052i | \(0.786706\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.0000 | −0.437304 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.0000 | −0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.0000 | − | 29.4449i | −0.617876 | − | 1.07019i | −0.989873 | − | 0.141958i | \(-0.954660\pi\) |
0.371997 | − | 0.928234i | \(-0.378673\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.7846i | 0.754434i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.0000 | − | 10.3923i | −0.652499 | − | 0.376721i | 0.136914 | − | 0.990583i | \(-0.456282\pi\) |
−0.789413 | + | 0.613862i | \(0.789615\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.5000 | + | 23.3827i | −0.488733 | + | 0.846510i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.00000 | + | 8.66025i | 0.324971 | + | 0.312704i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.00000 | + | 3.46410i | −0.216366 | + | 0.124919i | −0.604266 | − | 0.796782i | \(-0.706534\pi\) |
0.387901 | + | 0.921701i | \(0.373200\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −45.0000 | − | 25.9808i | −1.61854 | − | 0.934463i | −0.987299 | − | 0.158874i | \(-0.949213\pi\) |
−0.631239 | − | 0.775589i | \(-0.717453\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 12.1244i | − | 0.435520i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.0000 | 0.859889 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0000 | 1.28818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.00000 | − | 5.19615i | −0.107211 | − | 0.185695i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 38.1051i | − | 1.36003i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.5000 | − | 16.4545i | −1.01592 | − | 0.586539i | −0.102997 | − | 0.994682i | \(-0.532843\pi\) |
−0.912918 | + | 0.408143i | \(0.866177\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.00000 | − | 10.3923i | 0.213606 | − | 0.369976i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.00000 | + | 5.19615i | −0.320003 | + | 0.184754i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.50000 | + | 2.59808i | −0.0887776 | + | 0.0922604i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −36.0000 | + | 20.7846i | −1.27679 | + | 0.737154i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.00000 | + | 10.3923i | −0.212531 | + | 0.368114i | −0.952506 | − | 0.304520i | \(-0.901504\pi\) |
0.739975 | + | 0.672634i | \(0.234837\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.92820i | 0.244796i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.00000 | − | 5.19615i | −0.105868 | − | 0.183368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −36.0000 | −1.26883 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.00000 | − | 10.3923i | −0.210949 | − | 0.365374i | 0.741063 | − | 0.671436i | \(-0.234322\pi\) |
−0.952012 | + | 0.306062i | \(0.900989\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 25.9808i | − | 0.912308i | −0.889901 | − | 0.456154i | \(-0.849227\pi\) | ||
0.889901 | − | 0.456154i | \(-0.150773\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.50000 | − | 2.59808i | −0.157822 | − | 0.0911185i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 33.0000 | − | 57.1577i | 1.15594 | − | 2.00215i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.00000 | − | 1.73205i | 0.104957 | − | 0.0605968i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.00000 | + | 1.73205i | −0.209657 | + | 0.0605228i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.0000 | − | 12.1244i | 0.732905 | − | 0.423143i | −0.0865789 | − | 0.996245i | \(-0.527593\pi\) |
0.819484 | + | 0.573102i | \(0.194260\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.0000 | − | 27.7128i | 0.557725 | − | 0.966008i | −0.439961 | − | 0.898017i | \(-0.645008\pi\) |
0.997686 | − | 0.0679910i | \(-0.0216589\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21.0000 | + | 12.1244i | 0.731126 | + | 0.422116i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.4974i | 1.68642i | 0.537584 | + | 0.843210i | \(0.319337\pi\) | ||||
−0.537584 | + | 0.843210i | \(0.680663\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.5000 | − | 26.8468i | −0.538337 | − | 0.932427i | −0.998994 | − | 0.0448490i | \(-0.985719\pi\) |
0.460657 | − | 0.887578i | \(-0.347614\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.0000 | −0.346896 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.0000 | − | 20.7846i | −0.415277 | − | 0.719281i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.73205i | 0.0598684i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.0000 | − | 15.5885i | −0.932144 | − | 0.538173i | −0.0446547 | − | 0.999002i | \(-0.514219\pi\) |
−0.887489 | + | 0.460829i | \(0.847552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.0000 | − | 12.1244i | 0.723278 | − | 0.417585i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.0000 | − | 39.8372i | 0.722422 | − | 1.37044i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.50000 | − | 0.866025i | 0.0515406 | − | 0.0297570i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.50000 | + | 9.52628i | −0.188760 | + | 0.326941i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.9808i | 0.889564i | 0.895639 | + | 0.444782i | \(0.146719\pi\) | ||||
−0.895639 | + | 0.444782i | \(0.853281\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.00000 | − | 10.3923i | −0.205196 | − | 0.355409i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.0000 | 0.614868 | 0.307434 | − | 0.951569i | \(-0.400530\pi\) | ||||
0.307434 | + | 0.951569i | \(0.400530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.0000 | −0.443554 | −0.221777 | − | 0.975097i | \(-0.571186\pi\) | ||||
−0.221777 | + | 0.975097i | \(0.571186\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.00000 | + | 10.3923i | 0.204479 | + | 0.354169i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 17.3205i | − | 0.589597i | −0.955559 | − | 0.294798i | \(-0.904747\pi\) | ||
0.955559 | − | 0.294798i | \(-0.0952525\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.0000 | − | 10.3923i | −0.612018 | − | 0.353349i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.50000 | − | 14.7224i | 0.288675 | − | 0.500000i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.0000 | − | 19.0526i | 1.11945 | − | 0.646314i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.0000 | + | 8.66025i | −1.01651 | + | 0.293442i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.50000 | − | 2.59808i | 0.152302 | − | 0.0879316i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.00000 | + | 10.3923i | −0.202837 | + | 0.351324i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.0000 | + | 20.7846i | 1.21563 | + | 0.701846i | 0.963981 | − | 0.265971i | \(-0.0856926\pi\) |
0.251653 | + | 0.967818i | \(0.419026\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17.3205i | 0.584206i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.00000 | + | 10.3923i | 0.202145 | + | 0.350126i | 0.949219 | − | 0.314615i | \(-0.101875\pi\) |
−0.747074 | + | 0.664741i | \(0.768542\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.00000 | 0.168263 | 0.0841317 | − | 0.996455i | \(-0.473188\pi\) | ||||
0.0841317 | + | 0.996455i | \(0.473188\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.0000 | −0.403376 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.0000 | − | 36.3731i | −0.705111 | − | 1.22129i | −0.966651 | − | 0.256096i | \(-0.917564\pi\) |
0.261540 | − | 0.965193i | \(-0.415770\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.5167i | 0.755185i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.00000 | − | 1.73205i | −0.100504 | − | 0.0580259i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.00000 | − | 10.3923i | 0.200782 | − | 0.347765i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.0000 | − | 20.7846i | 1.20335 | − | 0.694753i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15.0000 | + | 15.5885i | −0.500835 | + | 0.520483i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.00000 | − | 5.19615i | 0.300167 | − | 0.173301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.50000 | + | 0.866025i | 0.0499169 | + | 0.0288195i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 48.4974i | − | 1.61211i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.0000 | − | 38.1051i | −0.730498 | − | 1.26526i | −0.956671 | − | 0.291172i | \(-0.905955\pi\) |
0.226173 | − | 0.974087i | \(-0.427379\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.0000 | −0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.0000 | − | 41.5692i | −0.794284 | − | 1.37574i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 3.46410i | − | 0.114520i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.00000 | − | 5.19615i | −0.297206 | − | 0.171592i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.0000 | + | 27.7128i | −0.527791 | + | 0.914161i | 0.471684 | + | 0.881768i | \(0.343646\pi\) |
−0.999475 | + | 0.0323936i | \(0.989687\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.50000 | + | 0.866025i | −0.0494267 | + | 0.0285365i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.0000 | + | 25.9808i | 0.888716 | + | 0.855167i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.500000 | + | 0.866025i | −0.0164222 | + | 0.0284440i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.0000 | − | 10.3923i | −0.590561 | − | 0.340960i | 0.174758 | − | 0.984611i | \(-0.444086\pi\) |
−0.765319 | + | 0.643651i | \(0.777419\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.8564i | 0.454125i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.0000 | − | 20.7846i | −0.392862 | − | 0.680458i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 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 | ||||||||
\(939\) | −6.50000 | − | 11.2583i | −0.212119 | − | 0.367402i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.3923i | 0.338779i | 0.985549 | + | 0.169390i | \(0.0541797\pi\) | ||||
−0.985549 | + | 0.169390i | \(0.945820\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.0000 | + | 20.7846i | 1.17232 | + | 0.676840i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.00000 | − | 5.19615i | 0.0975900 | − | 0.169031i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 42.0000 | − | 24.2487i | 1.36482 | − | 0.787977i | 0.374556 | − | 0.927204i | \(-0.377795\pi\) |
0.990260 | + | 0.139227i | \(0.0444618\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.50000 | − | 6.06218i | 0.0486921 | − | 0.196787i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.00000 | + | 3.46410i | −0.194563 | + | 0.112331i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.00000 | + | 5.19615i | −0.0971795 | + | 0.168320i | −0.910516 | − | 0.413473i | \(-0.864315\pi\) |
0.813337 | + | 0.581793i | \(0.197649\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 54.0000 | + | 31.1769i | 1.74740 | + | 1.00886i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.7846i | 0.671871i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.0000 | 0.903226 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.00000 | 0.193347 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27.0000 | + | 46.7654i | 0.869161 | + | 1.50543i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 24.2487i | − | 0.779786i | −0.920860 | − | 0.389893i | \(-0.872512\pi\) | ||
0.920860 | − | 0.389893i | \(-0.127488\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.0000 | − | 31.1769i | 0.577647 | − | 1.00051i | −0.418101 | − | 0.908401i | \(-0.637304\pi\) |
0.995748 | − | 0.0921142i | \(-0.0293625\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.50000 | − | 4.33013i | 0.240439 | − | 0.138817i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.00000 | + | 24.2487i | 0.224179 | + | 0.776580i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.0000 | + | 13.8564i | −0.767828 | + | 0.443306i | −0.832099 | − | 0.554627i | \(-0.812861\pi\) |
0.0642712 | + | 0.997932i | \(0.479528\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0000 | − | 20.7846i | 0.383522 | − | 0.664279i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.5000 | − | 7.79423i | −0.431022 | − | 0.248851i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 10.3923i | − | 0.331463i | −0.986171 | − | 0.165732i | \(-0.947001\pi\) | ||
0.986171 | − | 0.165732i | \(-0.0529985\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.0000 | − | 41.5692i | −0.764704 | − | 1.32451i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.00000 | 0.190982 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.00000 | 0.190789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.00000 | − | 13.8564i | −0.254128 | − | 0.440163i | 0.710530 | − | 0.703667i | \(-0.248455\pi\) |
−0.964658 | + | 0.263504i | \(0.915122\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.19615i | 0.164895i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.0000 | − | 12.1244i | −0.665745 | − | 0.384368i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.5000 | + | 30.3109i | −0.554231 | + | 0.959955i | 0.443732 | + | 0.896159i | \(0.353654\pi\) |
−0.997963 | + | 0.0637961i | \(0.979679\pi\) | |||||||
\(998\) | 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 \(a_p\))