Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(361,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("1014.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.i (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: | \(8.09683076496\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.361 |
Dual form | 1014.2.i.e.823.1 |
$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | −0.974679 | − | 0.223607i | \(-0.928217\pi\) | ||
0.974679 | − | 0.223607i | \(-0.0717831\pi\) | |||||||
\(6\) | −0.866025 | − | 0.500000i | −0.353553 | − | 0.204124i | ||||
\(7\) | −1.73205 | − | 1.00000i | −0.654654 | − | 0.377964i | 0.135583 | − | 0.990766i | \(-0.456709\pi\) |
−0.790237 | + | 0.612801i | \(0.790043\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | −1.73205 | + | 1.00000i | −0.522233 | + | 0.301511i | −0.737848 | − | 0.674967i | \(-0.764158\pi\) |
0.215615 | + | 0.976478i | \(0.430824\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | 0.866025 | − | 0.500000i | 0.223607 | − | 0.129099i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.50000 | − | 4.33013i | 0.606339 | − | 1.05021i | −0.385499 | − | 0.922708i | \(-0.625971\pi\) |
0.991838 | − | 0.127502i | \(-0.0406959\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 1.73205 | + | 1.00000i | 0.397360 | + | 0.229416i | 0.685344 | − | 0.728219i | \(-0.259652\pi\) |
−0.287984 | + | 0.957635i | \(0.592985\pi\) | |||||||
\(20\) | −0.866025 | − | 0.500000i | −0.193649 | − | 0.111803i | ||||
\(21\) | − | 2.00000i | − | 0.436436i | ||||||
\(22\) | 1.00000 | − | 1.73205i | 0.213201 | − | 0.369274i | ||||
\(23\) | 3.00000 | + | 5.19615i | 0.625543 | + | 1.08347i | 0.988436 | + | 0.151642i | \(0.0484560\pi\) |
−0.362892 | + | 0.931831i | \(0.618211\pi\) | |||||||
\(24\) | −0.866025 | + | 0.500000i | −0.176777 | + | 0.102062i | ||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.73205 | + | 1.00000i | −0.327327 | + | 0.188982i | ||||
\(29\) | 4.50000 | + | 7.79423i | 0.835629 | + | 1.44735i | 0.893517 | + | 0.449029i | \(0.148230\pi\) |
−0.0578882 | + | 0.998323i | \(0.518437\pi\) | |||||||
\(30\) | −0.500000 | + | 0.866025i | −0.0912871 | + | 0.158114i | ||||
\(31\) | − | 4.00000i | − | 0.718421i | −0.933257 | − | 0.359211i | \(-0.883046\pi\) | ||
0.933257 | − | 0.359211i | \(-0.116954\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −1.73205 | − | 1.00000i | −0.301511 | − | 0.174078i | ||||
\(34\) | 5.00000i | 0.857493i | ||||||||
\(35\) | −1.00000 | + | 1.73205i | −0.169031 | + | 0.292770i | ||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | 9.52628 | − | 5.50000i | 1.56611 | − | 0.904194i | 0.569495 | − | 0.821995i | \(-0.307139\pi\) |
0.996616 | − | 0.0821995i | \(-0.0261945\pi\) | |||||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 4.33013 | − | 2.50000i | 0.676252 | − | 0.390434i | −0.122189 | − | 0.992507i | \(-0.538991\pi\) |
0.798441 | + | 0.602072i | \(0.205658\pi\) | |||||||
\(42\) | 1.00000 | + | 1.73205i | 0.154303 | + | 0.267261i | ||||
\(43\) | 5.00000 | − | 8.66025i | 0.762493 | − | 1.32068i | −0.179069 | − | 0.983836i | \(-0.557309\pi\) |
0.941562 | − | 0.336840i | \(-0.109358\pi\) | |||||||
\(44\) | 2.00000i | 0.301511i | ||||||||
\(45\) | 0.866025 | + | 0.500000i | 0.129099 | + | 0.0745356i | ||||
\(46\) | −5.19615 | − | 3.00000i | −0.766131 | − | 0.442326i | ||||
\(47\) | − | 2.00000i | − | 0.291730i | −0.989305 | − | 0.145865i | \(-0.953403\pi\) | ||
0.989305 | − | 0.145865i | \(-0.0465965\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | −1.50000 | − | 2.59808i | −0.214286 | − | 0.371154i | ||||
\(50\) | −3.46410 | + | 2.00000i | −0.489898 | + | 0.282843i | ||||
\(51\) | 5.00000 | 0.700140 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.00000 | −0.137361 | −0.0686803 | − | 0.997639i | \(-0.521879\pi\) | ||||
−0.0686803 | + | 0.997639i | \(0.521879\pi\) | |||||||
\(54\) | 0.866025 | − | 0.500000i | 0.117851 | − | 0.0680414i | ||||
\(55\) | 1.00000 | + | 1.73205i | 0.134840 | + | 0.233550i | ||||
\(56\) | 1.00000 | − | 1.73205i | 0.133631 | − | 0.231455i | ||||
\(57\) | 2.00000i | 0.264906i | ||||||||
\(58\) | −7.79423 | − | 4.50000i | −1.02343 | − | 0.590879i | ||||
\(59\) | −6.92820 | − | 4.00000i | −0.901975 | − | 0.520756i | −0.0241347 | − | 0.999709i | \(-0.507683\pi\) |
−0.877841 | + | 0.478953i | \(0.841016\pi\) | |||||||
\(60\) | − | 1.00000i | − | 0.129099i | ||||||
\(61\) | 5.50000 | − | 9.52628i | 0.704203 | − | 1.21972i | −0.262776 | − | 0.964857i | \(-0.584638\pi\) |
0.966978 | − | 0.254858i | \(-0.0820288\pi\) | |||||||
\(62\) | 2.00000 | + | 3.46410i | 0.254000 | + | 0.439941i | ||||
\(63\) | 1.73205 | − | 1.00000i | 0.218218 | − | 0.125988i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.00000 | 0.246183 | ||||||||
\(67\) | 1.73205 | − | 1.00000i | 0.211604 | − | 0.122169i | −0.390453 | − | 0.920623i | \(-0.627682\pi\) |
0.602056 | + | 0.798454i | \(0.294348\pi\) | |||||||
\(68\) | −2.50000 | − | 4.33013i | −0.303170 | − | 0.525105i | ||||
\(69\) | −3.00000 | + | 5.19615i | −0.361158 | + | 0.625543i | ||||
\(70\) | − | 2.00000i | − | 0.239046i | ||||||
\(71\) | 12.1244 | + | 7.00000i | 1.43890 | + | 0.830747i | 0.997773 | − | 0.0666994i | \(-0.0212469\pi\) |
0.441123 | + | 0.897447i | \(0.354580\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 13.0000i | 1.52153i | 0.649025 | + | 0.760767i | \(0.275177\pi\) | ||||
−0.649025 | + | 0.760767i | \(0.724823\pi\) | |||||||
\(74\) | −5.50000 | + | 9.52628i | −0.639362 | + | 1.10741i | ||||
\(75\) | 2.00000 | + | 3.46410i | 0.230940 | + | 0.400000i | ||||
\(76\) | 1.73205 | − | 1.00000i | 0.198680 | − | 0.114708i | ||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | −0.866025 | + | 0.500000i | −0.0968246 | + | 0.0559017i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.50000 | + | 4.33013i | −0.276079 | + | 0.478183i | ||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | −1.73205 | − | 1.00000i | −0.188982 | − | 0.109109i | ||||
\(85\) | −4.33013 | − | 2.50000i | −0.469668 | − | 0.271163i | ||||
\(86\) | 10.0000i | 1.07833i | ||||||||
\(87\) | −4.50000 | + | 7.79423i | −0.482451 | + | 0.835629i | ||||
\(88\) | −1.00000 | − | 1.73205i | −0.106600 | − | 0.184637i | ||||
\(89\) | −1.73205 | + | 1.00000i | −0.183597 | + | 0.106000i | −0.588982 | − | 0.808146i | \(-0.700471\pi\) |
0.405385 | + | 0.914146i | \(0.367138\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.00000 | 0.625543 | ||||||||
\(93\) | 3.46410 | − | 2.00000i | 0.359211 | − | 0.207390i | ||||
\(94\) | 1.00000 | + | 1.73205i | 0.103142 | + | 0.178647i | ||||
\(95\) | 1.00000 | − | 1.73205i | 0.102598 | − | 0.177705i | ||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 1.73205 | + | 1.00000i | 0.175863 | + | 0.101535i | 0.585348 | − | 0.810782i | \(-0.300958\pi\) |
−0.409484 | + | 0.912317i | \(0.634291\pi\) | |||||||
\(98\) | 2.59808 | + | 1.50000i | 0.262445 | + | 0.151523i | ||||
\(99\) | − | 2.00000i | − | 0.201008i | ||||||
\(100\) | 2.00000 | − | 3.46410i | 0.200000 | − | 0.346410i | ||||
\(101\) | −2.50000 | − | 4.33013i | −0.248759 | − | 0.430864i | 0.714423 | − | 0.699715i | \(-0.246689\pi\) |
−0.963182 | + | 0.268851i | \(0.913356\pi\) | |||||||
\(102\) | −4.33013 | + | 2.50000i | −0.428746 | + | 0.247537i | ||||
\(103\) | −10.0000 | −0.985329 | −0.492665 | − | 0.870219i | \(-0.663977\pi\) | ||||
−0.492665 | + | 0.870219i | \(0.663977\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00000 | −0.195180 | ||||||||
\(106\) | 0.866025 | − | 0.500000i | 0.0841158 | − | 0.0485643i | ||||
\(107\) | 9.00000 | + | 15.5885i | 0.870063 | + | 1.50699i | 0.861931 | + | 0.507026i | \(0.169255\pi\) |
0.00813215 | + | 0.999967i | \(0.497411\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | − | 2.00000i | − | 0.191565i | −0.995402 | − | 0.0957826i | \(-0.969465\pi\) | ||
0.995402 | − | 0.0957826i | \(-0.0305354\pi\) | |||||||
\(110\) | −1.73205 | − | 1.00000i | −0.165145 | − | 0.0953463i | ||||
\(111\) | 9.52628 | + | 5.50000i | 0.904194 | + | 0.522037i | ||||
\(112\) | 2.00000i | 0.188982i | ||||||||
\(113\) | 1.50000 | − | 2.59808i | 0.141108 | − | 0.244406i | −0.786806 | − | 0.617200i | \(-0.788267\pi\) |
0.927914 | + | 0.372794i | \(0.121600\pi\) | |||||||
\(114\) | −1.00000 | − | 1.73205i | −0.0936586 | − | 0.162221i | ||||
\(115\) | 5.19615 | − | 3.00000i | 0.484544 | − | 0.279751i | ||||
\(116\) | 9.00000 | 0.835629 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.00000 | 0.736460 | ||||||||
\(119\) | −8.66025 | + | 5.00000i | −0.793884 | + | 0.458349i | ||||
\(120\) | 0.500000 | + | 0.866025i | 0.0456435 | + | 0.0790569i | ||||
\(121\) | −3.50000 | + | 6.06218i | −0.318182 | + | 0.551107i | ||||
\(122\) | 11.0000i | 0.995893i | ||||||||
\(123\) | 4.33013 | + | 2.50000i | 0.390434 | + | 0.225417i | ||||
\(124\) | −3.46410 | − | 2.00000i | −0.311086 | − | 0.179605i | ||||
\(125\) | − | 9.00000i | − | 0.804984i | ||||||
\(126\) | −1.00000 | + | 1.73205i | −0.0890871 | + | 0.154303i | ||||
\(127\) | −6.00000 | − | 10.3923i | −0.532414 | − | 0.922168i | −0.999284 | − | 0.0378419i | \(-0.987952\pi\) |
0.466870 | − | 0.884326i | \(-0.345382\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 10.0000 | 0.880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.00000 | −0.698963 | −0.349482 | − | 0.936943i | \(-0.613642\pi\) | ||||
−0.349482 | + | 0.936943i | \(0.613642\pi\) | |||||||
\(132\) | −1.73205 | + | 1.00000i | −0.150756 | + | 0.0870388i | ||||
\(133\) | −2.00000 | − | 3.46410i | −0.173422 | − | 0.300376i | ||||
\(134\) | −1.00000 | + | 1.73205i | −0.0863868 | + | 0.149626i | ||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | 4.33013 | + | 2.50000i | 0.371305 | + | 0.214373i | ||||
\(137\) | 14.7224 | + | 8.50000i | 1.25782 | + | 0.726204i | 0.972651 | − | 0.232273i | \(-0.0746161\pi\) |
0.285171 | + | 0.958477i | \(0.407949\pi\) | |||||||
\(138\) | − | 6.00000i | − | 0.510754i | ||||||
\(139\) | 6.00000 | − | 10.3923i | 0.508913 | − | 0.881464i | −0.491033 | − | 0.871141i | \(-0.663381\pi\) |
0.999947 | − | 0.0103230i | \(-0.00328598\pi\) | |||||||
\(140\) | 1.00000 | + | 1.73205i | 0.0845154 | + | 0.146385i | ||||
\(141\) | 1.73205 | − | 1.00000i | 0.145865 | − | 0.0842152i | ||||
\(142\) | −14.0000 | −1.17485 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 7.79423 | − | 4.50000i | 0.647275 | − | 0.373705i | ||||
\(146\) | −6.50000 | − | 11.2583i | −0.537944 | − | 0.931746i | ||||
\(147\) | 1.50000 | − | 2.59808i | 0.123718 | − | 0.214286i | ||||
\(148\) | − | 11.0000i | − | 0.904194i | ||||||
\(149\) | −2.59808 | − | 1.50000i | −0.212843 | − | 0.122885i | 0.389789 | − | 0.920904i | \(-0.372548\pi\) |
−0.602632 | + | 0.798019i | \(0.705881\pi\) | |||||||
\(150\) | −3.46410 | − | 2.00000i | −0.282843 | − | 0.163299i | ||||
\(151\) | 6.00000i | 0.488273i | 0.969741 | + | 0.244137i | \(0.0785045\pi\) | ||||
−0.969741 | + | 0.244137i | \(0.921495\pi\) | |||||||
\(152\) | −1.00000 | + | 1.73205i | −0.0811107 | + | 0.140488i | ||||
\(153\) | 2.50000 | + | 4.33013i | 0.202113 | + | 0.350070i | ||||
\(154\) | −3.46410 | + | 2.00000i | −0.279145 | + | 0.161165i | ||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.00000 | −0.558661 | −0.279330 | − | 0.960195i | \(-0.590112\pi\) | ||||
−0.279330 | + | 0.960195i | \(0.590112\pi\) | |||||||
\(158\) | 3.46410 | − | 2.00000i | 0.275589 | − | 0.159111i | ||||
\(159\) | −0.500000 | − | 0.866025i | −0.0396526 | − | 0.0686803i | ||||
\(160\) | 0.500000 | − | 0.866025i | 0.0395285 | − | 0.0684653i | ||||
\(161\) | − | 12.0000i | − | 0.945732i | ||||||
\(162\) | 0.866025 | + | 0.500000i | 0.0680414 | + | 0.0392837i | ||||
\(163\) | 17.3205 | + | 10.0000i | 1.35665 | + | 0.783260i | 0.989170 | − | 0.146772i | \(-0.0468885\pi\) |
0.367477 | + | 0.930033i | \(0.380222\pi\) | |||||||
\(164\) | − | 5.00000i | − | 0.390434i | ||||||
\(165\) | −1.00000 | + | 1.73205i | −0.0778499 | + | 0.134840i | ||||
\(166\) | −3.00000 | − | 5.19615i | −0.232845 | − | 0.403300i | ||||
\(167\) | −20.7846 | + | 12.0000i | −1.60836 | + | 0.928588i | −0.618624 | + | 0.785687i | \(0.712310\pi\) |
−0.989737 | + | 0.142901i | \(0.954357\pi\) | |||||||
\(168\) | 2.00000 | 0.154303 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 5.00000 | 0.383482 | ||||||||
\(171\) | −1.73205 | + | 1.00000i | −0.132453 | + | 0.0764719i | ||||
\(172\) | −5.00000 | − | 8.66025i | −0.381246 | − | 0.660338i | ||||
\(173\) | −11.0000 | + | 19.0526i | −0.836315 | + | 1.44854i | 0.0566411 | + | 0.998395i | \(0.481961\pi\) |
−0.892956 | + | 0.450145i | \(0.851372\pi\) | |||||||
\(174\) | − | 9.00000i | − | 0.682288i | ||||||
\(175\) | −6.92820 | − | 4.00000i | −0.523723 | − | 0.302372i | ||||
\(176\) | 1.73205 | + | 1.00000i | 0.130558 | + | 0.0753778i | ||||
\(177\) | − | 8.00000i | − | 0.601317i | ||||||
\(178\) | 1.00000 | − | 1.73205i | 0.0749532 | − | 0.129823i | ||||
\(179\) | −3.00000 | − | 5.19615i | −0.224231 | − | 0.388379i | 0.731858 | − | 0.681457i | \(-0.238654\pi\) |
−0.956088 | + | 0.293079i | \(0.905320\pi\) | |||||||
\(180\) | 0.866025 | − | 0.500000i | 0.0645497 | − | 0.0372678i | ||||
\(181\) | −5.00000 | −0.371647 | −0.185824 | − | 0.982583i | \(-0.559495\pi\) | ||||
−0.185824 | + | 0.982583i | \(0.559495\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.0000 | 0.813143 | ||||||||
\(184\) | −5.19615 | + | 3.00000i | −0.383065 | + | 0.221163i | ||||
\(185\) | −5.50000 | − | 9.52628i | −0.404368 | − | 0.700386i | ||||
\(186\) | −2.00000 | + | 3.46410i | −0.146647 | + | 0.254000i | ||||
\(187\) | 10.0000i | 0.731272i | ||||||||
\(188\) | −1.73205 | − | 1.00000i | −0.126323 | − | 0.0729325i | ||||
\(189\) | 1.73205 | + | 1.00000i | 0.125988 | + | 0.0727393i | ||||
\(190\) | 2.00000i | 0.145095i | ||||||||
\(191\) | −2.00000 | + | 3.46410i | −0.144715 | + | 0.250654i | −0.929267 | − | 0.369410i | \(-0.879560\pi\) |
0.784552 | + | 0.620063i | \(0.212893\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 14.7224 | − | 8.50000i | 1.05974 | − | 0.611843i | 0.134382 | − | 0.990930i | \(-0.457095\pi\) |
0.925361 | + | 0.379086i | \(0.123762\pi\) | |||||||
\(194\) | −2.00000 | −0.143592 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 5.19615 | − | 3.00000i | 0.370211 | − | 0.213741i | −0.303340 | − | 0.952882i | \(-0.598102\pi\) |
0.673550 | + | 0.739141i | \(0.264768\pi\) | |||||||
\(198\) | 1.00000 | + | 1.73205i | 0.0710669 | + | 0.123091i | ||||
\(199\) | 5.00000 | − | 8.66025i | 0.354441 | − | 0.613909i | −0.632581 | − | 0.774494i | \(-0.718005\pi\) |
0.987022 | + | 0.160585i | \(0.0513380\pi\) | |||||||
\(200\) | 4.00000i | 0.282843i | ||||||||
\(201\) | 1.73205 | + | 1.00000i | 0.122169 | + | 0.0705346i | ||||
\(202\) | 4.33013 | + | 2.50000i | 0.304667 | + | 0.175899i | ||||
\(203\) | − | 18.0000i | − | 1.26335i | ||||||
\(204\) | 2.50000 | − | 4.33013i | 0.175035 | − | 0.303170i | ||||
\(205\) | −2.50000 | − | 4.33013i | −0.174608 | − | 0.302429i | ||||
\(206\) | 8.66025 | − | 5.00000i | 0.603388 | − | 0.348367i | ||||
\(207\) | −6.00000 | −0.417029 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 1.73205 | − | 1.00000i | 0.119523 | − | 0.0690066i | ||||
\(211\) | −12.0000 | − | 20.7846i | −0.826114 | − | 1.43087i | −0.901065 | − | 0.433684i | \(-0.857213\pi\) |
0.0749508 | − | 0.997187i | \(-0.476120\pi\) | |||||||
\(212\) | −0.500000 | + | 0.866025i | −0.0343401 | + | 0.0594789i | ||||
\(213\) | 14.0000i | 0.959264i | ||||||||
\(214\) | −15.5885 | − | 9.00000i | −1.06561 | − | 0.615227i | ||||
\(215\) | −8.66025 | − | 5.00000i | −0.590624 | − | 0.340997i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −4.00000 | + | 6.92820i | −0.271538 | + | 0.470317i | ||||
\(218\) | 1.00000 | + | 1.73205i | 0.0677285 | + | 0.117309i | ||||
\(219\) | −11.2583 | + | 6.50000i | −0.760767 | + | 0.439229i | ||||
\(220\) | 2.00000 | 0.134840 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −11.0000 | −0.738272 | ||||||||
\(223\) | −13.8564 | + | 8.00000i | −0.927894 | + | 0.535720i | −0.886145 | − | 0.463409i | \(-0.846626\pi\) |
−0.0417488 | + | 0.999128i | \(0.513293\pi\) | |||||||
\(224\) | −1.00000 | − | 1.73205i | −0.0668153 | − | 0.115728i | ||||
\(225\) | −2.00000 | + | 3.46410i | −0.133333 | + | 0.230940i | ||||
\(226\) | 3.00000i | 0.199557i | ||||||||
\(227\) | −12.1244 | − | 7.00000i | −0.804722 | − | 0.464606i | 0.0403978 | − | 0.999184i | \(-0.487137\pi\) |
−0.845120 | + | 0.534577i | \(0.820471\pi\) | |||||||
\(228\) | 1.73205 | + | 1.00000i | 0.114708 | + | 0.0662266i | ||||
\(229\) | − | 10.0000i | − | 0.660819i | −0.943838 | − | 0.330409i | \(-0.892813\pi\) | ||
0.943838 | − | 0.330409i | \(-0.107187\pi\) | |||||||
\(230\) | −3.00000 | + | 5.19615i | −0.197814 | + | 0.342624i | ||||
\(231\) | 2.00000 | + | 3.46410i | 0.131590 | + | 0.227921i | ||||
\(232\) | −7.79423 | + | 4.50000i | −0.511716 | + | 0.295439i | ||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.00000 | −0.130466 | ||||||||
\(236\) | −6.92820 | + | 4.00000i | −0.450988 | + | 0.260378i | ||||
\(237\) | −2.00000 | − | 3.46410i | −0.129914 | − | 0.225018i | ||||
\(238\) | 5.00000 | − | 8.66025i | 0.324102 | − | 0.561361i | ||||
\(239\) | − | 6.00000i | − | 0.388108i | −0.980991 | − | 0.194054i | \(-0.937836\pi\) | ||
0.980991 | − | 0.194054i | \(-0.0621637\pi\) | |||||||
\(240\) | −0.866025 | − | 0.500000i | −0.0559017 | − | 0.0322749i | ||||
\(241\) | 6.06218 | + | 3.50000i | 0.390499 | + | 0.225455i | 0.682376 | − | 0.731001i | \(-0.260947\pi\) |
−0.291877 | + | 0.956456i | \(0.594280\pi\) | |||||||
\(242\) | − | 7.00000i | − | 0.449977i | ||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −5.50000 | − | 9.52628i | −0.352101 | − | 0.609858i | ||||
\(245\) | −2.59808 | + | 1.50000i | −0.165985 | + | 0.0958315i | ||||
\(246\) | −5.00000 | −0.318788 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | −5.19615 | + | 3.00000i | −0.329293 | + | 0.190117i | ||||
\(250\) | 4.50000 | + | 7.79423i | 0.284605 | + | 0.492950i | ||||
\(251\) | 2.00000 | − | 3.46410i | 0.126239 | − | 0.218652i | −0.795978 | − | 0.605326i | \(-0.793043\pi\) |
0.922217 | + | 0.386674i | \(0.126376\pi\) | |||||||
\(252\) | − | 2.00000i | − | 0.125988i | ||||||
\(253\) | −10.3923 | − | 6.00000i | −0.653359 | − | 0.377217i | ||||
\(254\) | 10.3923 | + | 6.00000i | 0.652071 | + | 0.376473i | ||||
\(255\) | − | 5.00000i | − | 0.313112i | ||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −1.50000 | − | 2.59808i | −0.0935674 | − | 0.162064i | 0.815442 | − | 0.578838i | \(-0.196494\pi\) |
−0.909010 | + | 0.416775i | \(0.863160\pi\) | |||||||
\(258\) | −8.66025 | + | 5.00000i | −0.539164 | + | 0.311286i | ||||
\(259\) | −22.0000 | −1.36701 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.00000 | −0.557086 | ||||||||
\(262\) | 6.92820 | − | 4.00000i | 0.428026 | − | 0.247121i | ||||
\(263\) | −7.00000 | − | 12.1244i | −0.431638 | − | 0.747620i | 0.565376 | − | 0.824833i | \(-0.308731\pi\) |
−0.997015 | + | 0.0772134i | \(0.975398\pi\) | |||||||
\(264\) | 1.00000 | − | 1.73205i | 0.0615457 | − | 0.106600i | ||||
\(265\) | 1.00000i | 0.0614295i | ||||||||
\(266\) | 3.46410 | + | 2.00000i | 0.212398 | + | 0.122628i | ||||
\(267\) | −1.73205 | − | 1.00000i | −0.106000 | − | 0.0611990i | ||||
\(268\) | − | 2.00000i | − | 0.122169i | ||||||
\(269\) | 7.00000 | − | 12.1244i | 0.426798 | − | 0.739235i | −0.569789 | − | 0.821791i | \(-0.692975\pi\) |
0.996586 | + | 0.0825561i | \(0.0263084\pi\) | |||||||
\(270\) | −0.500000 | − | 0.866025i | −0.0304290 | − | 0.0527046i | ||||
\(271\) | −6.92820 | + | 4.00000i | −0.420858 | + | 0.242983i | −0.695444 | − | 0.718580i | \(-0.744792\pi\) |
0.274586 | + | 0.961563i | \(0.411459\pi\) | |||||||
\(272\) | −5.00000 | −0.303170 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.0000 | −1.02701 | ||||||||
\(275\) | −6.92820 | + | 4.00000i | −0.417786 | + | 0.241209i | ||||
\(276\) | 3.00000 | + | 5.19615i | 0.180579 | + | 0.312772i | ||||
\(277\) | −5.50000 | + | 9.52628i | −0.330463 | + | 0.572379i | −0.982603 | − | 0.185720i | \(-0.940538\pi\) |
0.652140 | + | 0.758099i | \(0.273872\pi\) | |||||||
\(278\) | 12.0000i | 0.719712i | ||||||||
\(279\) | 3.46410 | + | 2.00000i | 0.207390 | + | 0.119737i | ||||
\(280\) | −1.73205 | − | 1.00000i | −0.103510 | − | 0.0597614i | ||||
\(281\) | − | 25.0000i | − | 1.49137i | −0.666296 | − | 0.745687i | \(-0.732121\pi\) | ||
0.666296 | − | 0.745687i | \(-0.267879\pi\) | |||||||
\(282\) | −1.00000 | + | 1.73205i | −0.0595491 | + | 0.103142i | ||||
\(283\) | 13.0000 | + | 22.5167i | 0.772770 | + | 1.33848i | 0.936039 | + | 0.351895i | \(0.114463\pi\) |
−0.163270 | + | 0.986581i | \(0.552204\pi\) | |||||||
\(284\) | 12.1244 | − | 7.00000i | 0.719448 | − | 0.415374i | ||||
\(285\) | 2.00000 | 0.118470 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.0000 | −0.590281 | ||||||||
\(288\) | −0.866025 | + | 0.500000i | −0.0510310 | + | 0.0294628i | ||||
\(289\) | −4.00000 | − | 6.92820i | −0.235294 | − | 0.407541i | ||||
\(290\) | −4.50000 | + | 7.79423i | −0.264249 | + | 0.457693i | ||||
\(291\) | 2.00000i | 0.117242i | ||||||||
\(292\) | 11.2583 | + | 6.50000i | 0.658844 | + | 0.380384i | ||||
\(293\) | −0.866025 | − | 0.500000i | −0.0505937 | − | 0.0292103i | 0.474490 | − | 0.880261i | \(-0.342633\pi\) |
−0.525084 | + | 0.851051i | \(0.675966\pi\) | |||||||
\(294\) | 3.00000i | 0.174964i | ||||||||
\(295\) | −4.00000 | + | 6.92820i | −0.232889 | + | 0.403376i | ||||
\(296\) | 5.50000 | + | 9.52628i | 0.319681 | + | 0.553704i | ||||
\(297\) | 1.73205 | − | 1.00000i | 0.100504 | − | 0.0580259i | ||||
\(298\) | 3.00000 | 0.173785 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.00000 | 0.230940 | ||||||||
\(301\) | −17.3205 | + | 10.0000i | −0.998337 | + | 0.576390i | ||||
\(302\) | −3.00000 | − | 5.19615i | −0.172631 | − | 0.299005i | ||||
\(303\) | 2.50000 | − | 4.33013i | 0.143621 | − | 0.248759i | ||||
\(304\) | − | 2.00000i | − | 0.114708i | ||||||
\(305\) | −9.52628 | − | 5.50000i | −0.545473 | − | 0.314929i | ||||
\(306\) | −4.33013 | − | 2.50000i | −0.247537 | − | 0.142915i | ||||
\(307\) | 14.0000i | 0.799022i | 0.916728 | + | 0.399511i | \(0.130820\pi\) | ||||
−0.916728 | + | 0.399511i | \(0.869180\pi\) | |||||||
\(308\) | 2.00000 | − | 3.46410i | 0.113961 | − | 0.197386i | ||||
\(309\) | −5.00000 | − | 8.66025i | −0.284440 | − | 0.492665i | ||||
\(310\) | 3.46410 | − | 2.00000i | 0.196748 | − | 0.113592i | ||||
\(311\) | −6.00000 | −0.340229 | −0.170114 | − | 0.985424i | \(-0.554414\pi\) | ||||
−0.170114 | + | 0.985424i | \(0.554414\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.00000 | 0.339140 | 0.169570 | − | 0.985518i | \(-0.445762\pi\) | ||||
0.169570 | + | 0.985518i | \(0.445762\pi\) | |||||||
\(314\) | 6.06218 | − | 3.50000i | 0.342108 | − | 0.197516i | ||||
\(315\) | −1.00000 | − | 1.73205i | −0.0563436 | − | 0.0975900i | ||||
\(316\) | −2.00000 | + | 3.46410i | −0.112509 | + | 0.194871i | ||||
\(317\) | − | 33.0000i | − | 1.85346i | −0.375722 | − | 0.926732i | \(-0.622605\pi\) | ||
0.375722 | − | 0.926732i | \(-0.377395\pi\) | |||||||
\(318\) | 0.866025 | + | 0.500000i | 0.0485643 | + | 0.0280386i | ||||
\(319\) | −15.5885 | − | 9.00000i | −0.872786 | − | 0.503903i | ||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −9.00000 | + | 15.5885i | −0.502331 | + | 0.870063i | ||||
\(322\) | 6.00000 | + | 10.3923i | 0.334367 | + | 0.579141i | ||||
\(323\) | 8.66025 | − | 5.00000i | 0.481869 | − | 0.278207i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −20.0000 | −1.10770 | ||||||||
\(327\) | 1.73205 | − | 1.00000i | 0.0957826 | − | 0.0553001i | ||||
\(328\) | 2.50000 | + | 4.33013i | 0.138039 | + | 0.239091i | ||||
\(329\) | −2.00000 | + | 3.46410i | −0.110264 | + | 0.190982i | ||||
\(330\) | − | 2.00000i | − | 0.110096i | ||||||
\(331\) | 24.2487 | + | 14.0000i | 1.33283 | + | 0.769510i | 0.985732 | − | 0.168320i | \(-0.0538340\pi\) |
0.347097 | + | 0.937829i | \(0.387167\pi\) | |||||||
\(332\) | 5.19615 | + | 3.00000i | 0.285176 | + | 0.164646i | ||||
\(333\) | 11.0000i | 0.602796i | ||||||||
\(334\) | 12.0000 | − | 20.7846i | 0.656611 | − | 1.13728i | ||||
\(335\) | −1.00000 | − | 1.73205i | −0.0546358 | − | 0.0946320i | ||||
\(336\) | −1.73205 | + | 1.00000i | −0.0944911 | + | 0.0545545i | ||||
\(337\) | 9.00000 | 0.490261 | 0.245131 | − | 0.969490i | \(-0.421169\pi\) | ||||
0.245131 | + | 0.969490i | \(0.421169\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.00000 | 0.162938 | ||||||||
\(340\) | −4.33013 | + | 2.50000i | −0.234834 | + | 0.135582i | ||||
\(341\) | 4.00000 | + | 6.92820i | 0.216612 | + | 0.375183i | ||||
\(342\) | 1.00000 | − | 1.73205i | 0.0540738 | − | 0.0936586i | ||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | 8.66025 | + | 5.00000i | 0.466930 | + | 0.269582i | ||||
\(345\) | 5.19615 | + | 3.00000i | 0.279751 | + | 0.161515i | ||||
\(346\) | − | 22.0000i | − | 1.18273i | ||||||
\(347\) | −3.00000 | + | 5.19615i | −0.161048 | + | 0.278944i | −0.935245 | − | 0.354001i | \(-0.884821\pi\) |
0.774197 | + | 0.632945i | \(0.218154\pi\) | |||||||
\(348\) | 4.50000 | + | 7.79423i | 0.241225 | + | 0.417815i | ||||
\(349\) | −5.19615 | + | 3.00000i | −0.278144 | + | 0.160586i | −0.632583 | − | 0.774493i | \(-0.718005\pi\) |
0.354439 | + | 0.935079i | \(0.384672\pi\) | |||||||
\(350\) | 8.00000 | 0.427618 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.00000 | −0.106600 | ||||||||
\(353\) | 14.7224 | − | 8.50000i | 0.783596 | − | 0.452409i | −0.0541072 | − | 0.998535i | \(-0.517231\pi\) |
0.837703 | + | 0.546126i | \(0.183898\pi\) | |||||||
\(354\) | 4.00000 | + | 6.92820i | 0.212598 | + | 0.368230i | ||||
\(355\) | 7.00000 | − | 12.1244i | 0.371521 | − | 0.643494i | ||||
\(356\) | 2.00000i | 0.106000i | ||||||||
\(357\) | −8.66025 | − | 5.00000i | −0.458349 | − | 0.264628i | ||||
\(358\) | 5.19615 | + | 3.00000i | 0.274625 | + | 0.158555i | ||||
\(359\) | 30.0000i | 1.58334i | 0.610949 | + | 0.791670i | \(0.290788\pi\) | ||||
−0.610949 | + | 0.791670i | \(0.709212\pi\) | |||||||
\(360\) | −0.500000 | + | 0.866025i | −0.0263523 | + | 0.0456435i | ||||
\(361\) | −7.50000 | − | 12.9904i | −0.394737 | − | 0.683704i | ||||
\(362\) | 4.33013 | − | 2.50000i | 0.227586 | − | 0.131397i | ||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.0000 | 0.680451 | ||||||||
\(366\) | −9.52628 | + | 5.50000i | −0.497947 | + | 0.287490i | ||||
\(367\) | 1.00000 | + | 1.73205i | 0.0521996 | + | 0.0904123i | 0.890945 | − | 0.454112i | \(-0.150043\pi\) |
−0.838745 | + | 0.544524i | \(0.816710\pi\) | |||||||
\(368\) | 3.00000 | − | 5.19615i | 0.156386 | − | 0.270868i | ||||
\(369\) | 5.00000i | 0.260290i | ||||||||
\(370\) | 9.52628 | + | 5.50000i | 0.495248 | + | 0.285931i | ||||
\(371\) | 1.73205 | + | 1.00000i | 0.0899236 | + | 0.0519174i | ||||
\(372\) | − | 4.00000i | − | 0.207390i | ||||||
\(373\) | −4.50000 | + | 7.79423i | −0.233001 | + | 0.403570i | −0.958690 | − | 0.284453i | \(-0.908188\pi\) |
0.725689 | + | 0.688023i | \(0.241521\pi\) | |||||||
\(374\) | −5.00000 | − | 8.66025i | −0.258544 | − | 0.447811i | ||||
\(375\) | 7.79423 | − | 4.50000i | 0.402492 | − | 0.232379i | ||||
\(376\) | 2.00000 | 0.103142 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.00000 | −0.102869 | ||||||||
\(379\) | 10.3923 | − | 6.00000i | 0.533817 | − | 0.308199i | −0.208752 | − | 0.977969i | \(-0.566940\pi\) |
0.742569 | + | 0.669769i | \(0.233607\pi\) | |||||||
\(380\) | −1.00000 | − | 1.73205i | −0.0512989 | − | 0.0888523i | ||||
\(381\) | 6.00000 | − | 10.3923i | 0.307389 | − | 0.532414i | ||||
\(382\) | − | 4.00000i | − | 0.204658i | ||||||
\(383\) | −20.7846 | − | 12.0000i | −1.06204 | − | 0.613171i | −0.136047 | − | 0.990702i | \(-0.543440\pi\) |
−0.925997 | + | 0.377531i | \(0.876773\pi\) | |||||||
\(384\) | 0.866025 | + | 0.500000i | 0.0441942 | + | 0.0255155i | ||||
\(385\) | − | 4.00000i | − | 0.203859i | ||||||
\(386\) | −8.50000 | + | 14.7224i | −0.432639 | + | 0.749352i | ||||
\(387\) | 5.00000 | + | 8.66025i | 0.254164 | + | 0.440225i | ||||
\(388\) | 1.73205 | − | 1.00000i | 0.0879316 | − | 0.0507673i | ||||
\(389\) | −19.0000 | −0.963338 | −0.481669 | − | 0.876353i | \(-0.659969\pi\) | ||||
−0.481669 | + | 0.876353i | \(0.659969\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.0000 | 1.51717 | ||||||||
\(392\) | 2.59808 | − | 1.50000i | 0.131223 | − | 0.0757614i | ||||
\(393\) | −4.00000 | − | 6.92820i | −0.201773 | − | 0.349482i | ||||
\(394\) | −3.00000 | + | 5.19615i | −0.151138 | + | 0.261778i | ||||
\(395\) | 4.00000i | 0.201262i | ||||||||
\(396\) | −1.73205 | − | 1.00000i | −0.0870388 | − | 0.0502519i | ||||
\(397\) | −15.5885 | − | 9.00000i | −0.782362 | − | 0.451697i | 0.0549046 | − | 0.998492i | \(-0.482515\pi\) |
−0.837267 | + | 0.546795i | \(0.815848\pi\) | |||||||
\(398\) | 10.0000i | 0.501255i | ||||||||
\(399\) | 2.00000 | − | 3.46410i | 0.100125 | − | 0.173422i | ||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | 23.3827 | − | 13.5000i | 1.16768 | − | 0.674158i | 0.214544 | − | 0.976714i | \(-0.431173\pi\) |
0.953131 | + | 0.302556i | \(0.0978401\pi\) | |||||||
\(402\) | −2.00000 | −0.0997509 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −5.00000 | −0.248759 | ||||||||
\(405\) | −0.866025 | + | 0.500000i | −0.0430331 | + | 0.0248452i | ||||
\(406\) | 9.00000 | + | 15.5885i | 0.446663 | + | 0.773642i | ||||
\(407\) | −11.0000 | + | 19.0526i | −0.545250 | + | 0.944400i | ||||
\(408\) | 5.00000i | 0.247537i | ||||||||
\(409\) | −19.9186 | − | 11.5000i | −0.984911 | − | 0.568638i | −0.0811615 | − | 0.996701i | \(-0.525863\pi\) |
−0.903749 | + | 0.428063i | \(0.859196\pi\) | |||||||
\(410\) | 4.33013 | + | 2.50000i | 0.213850 | + | 0.123466i | ||||
\(411\) | 17.0000i | 0.838548i | ||||||||
\(412\) | −5.00000 | + | 8.66025i | −0.246332 | + | 0.426660i | ||||
\(413\) | 8.00000 | + | 13.8564i | 0.393654 | + | 0.681829i | ||||
\(414\) | 5.19615 | − | 3.00000i | 0.255377 | − | 0.147442i | ||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.0000 | 0.587643 | ||||||||
\(418\) | 3.46410 | − | 2.00000i | 0.169435 | − | 0.0978232i | ||||
\(419\) | 16.0000 | + | 27.7128i | 0.781651 | + | 1.35386i | 0.930979 | + | 0.365072i | \(0.118956\pi\) |
−0.149328 | + | 0.988788i | \(0.547711\pi\) | |||||||
\(420\) | −1.00000 | + | 1.73205i | −0.0487950 | + | 0.0845154i | ||||
\(421\) | − | 23.0000i | − | 1.12095i | −0.828171 | − | 0.560476i | \(-0.810618\pi\) | ||
0.828171 | − | 0.560476i | \(-0.189382\pi\) | |||||||
\(422\) | 20.7846 | + | 12.0000i | 1.01178 | + | 0.584151i | ||||
\(423\) | 1.73205 | + | 1.00000i | 0.0842152 | + | 0.0486217i | ||||
\(424\) | − | 1.00000i | − | 0.0485643i | ||||||
\(425\) | 10.0000 | − | 17.3205i | 0.485071 | − | 0.840168i | ||||
\(426\) | −7.00000 | − | 12.1244i | −0.339151 | − | 0.587427i | ||||
\(427\) | −19.0526 | + | 11.0000i | −0.922018 | + | 0.532327i | ||||
\(428\) | 18.0000 | 0.870063 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.0000 | 0.482243 | ||||||||
\(431\) | −1.73205 | + | 1.00000i | −0.0834300 | + | 0.0481683i | −0.541135 | − | 0.840936i | \(-0.682005\pi\) |
0.457705 | + | 0.889104i | \(0.348672\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −10.5000 | + | 18.1865i | −0.504598 | + | 0.873989i | 0.495388 | + | 0.868672i | \(0.335026\pi\) |
−0.999986 | + | 0.00531724i | \(0.998307\pi\) | |||||||
\(434\) | − | 8.00000i | − | 0.384012i | ||||||
\(435\) | 7.79423 | + | 4.50000i | 0.373705 | + | 0.215758i | ||||
\(436\) | −1.73205 | − | 1.00000i | −0.0829502 | − | 0.0478913i | ||||
\(437\) | 12.0000i | 0.574038i | ||||||||
\(438\) | 6.50000 | − | 11.2583i | 0.310582 | − | 0.537944i | ||||
\(439\) | 5.00000 | + | 8.66025i | 0.238637 | + | 0.413331i | 0.960323 | − | 0.278889i | \(-0.0899661\pi\) |
−0.721686 | + | 0.692220i | \(0.756633\pi\) | |||||||
\(440\) | −1.73205 | + | 1.00000i | −0.0825723 | + | 0.0476731i | ||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.0000 | 0.950229 | 0.475114 | − | 0.879924i | \(-0.342407\pi\) | ||||
0.475114 | + | 0.879924i | \(0.342407\pi\) | |||||||
\(444\) | 9.52628 | − | 5.50000i | 0.452097 | − | 0.261018i | ||||
\(445\) | 1.00000 | + | 1.73205i | 0.0474045 | + | 0.0821071i | ||||
\(446\) | 8.00000 | − | 13.8564i | 0.378811 | − | 0.656120i | ||||
\(447\) | − | 3.00000i | − | 0.141895i | ||||||
\(448\) | 1.73205 | + | 1.00000i | 0.0818317 | + | 0.0472456i | ||||
\(449\) | −25.9808 | − | 15.0000i | −1.22611 | − | 0.707894i | −0.259895 | − | 0.965637i | \(-0.583688\pi\) |
−0.966213 | + | 0.257743i | \(0.917021\pi\) | |||||||
\(450\) | − | 4.00000i | − | 0.188562i | ||||||
\(451\) | −5.00000 | + | 8.66025i | −0.235441 | + | 0.407795i | ||||
\(452\) | −1.50000 | − | 2.59808i | −0.0705541 | − | 0.122203i | ||||
\(453\) | −5.19615 | + | 3.00000i | −0.244137 | + | 0.140952i | ||||
\(454\) | 14.0000 | 0.657053 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | 2.59808 | − | 1.50000i | 0.121533 | − | 0.0701670i | −0.438001 | − | 0.898974i | \(-0.644313\pi\) |
0.559534 | + | 0.828807i | \(0.310980\pi\) | |||||||
\(458\) | 5.00000 | + | 8.66025i | 0.233635 | + | 0.404667i | ||||
\(459\) | −2.50000 | + | 4.33013i | −0.116690 | + | 0.202113i | ||||
\(460\) | − | 6.00000i | − | 0.279751i | ||||||
\(461\) | −2.59808 | − | 1.50000i | −0.121004 | − | 0.0698620i | 0.438276 | − | 0.898840i | \(-0.355589\pi\) |
−0.559281 | + | 0.828978i | \(0.688923\pi\) | |||||||
\(462\) | −3.46410 | − | 2.00000i | −0.161165 | − | 0.0930484i | ||||
\(463\) | 14.0000i | 0.650635i | 0.945605 | + | 0.325318i | \(0.105471\pi\) | ||||
−0.945605 | + | 0.325318i | \(0.894529\pi\) | |||||||
\(464\) | 4.50000 | − | 7.79423i | 0.208907 | − | 0.361838i | ||||
\(465\) | −2.00000 | − | 3.46410i | −0.0927478 | − | 0.160644i | ||||
\(466\) | −5.19615 | + | 3.00000i | −0.240707 | + | 0.138972i | ||||
\(467\) | 22.0000 | 1.01804 | 0.509019 | − | 0.860755i | \(-0.330008\pi\) | ||||
0.509019 | + | 0.860755i | \(0.330008\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.00000 | −0.184703 | ||||||||
\(470\) | 1.73205 | − | 1.00000i | 0.0798935 | − | 0.0461266i | ||||
\(471\) | −3.50000 | − | 6.06218i | −0.161271 | − | 0.279330i | ||||
\(472\) | 4.00000 | − | 6.92820i | 0.184115 | − | 0.318896i | ||||
\(473\) | 20.0000i | 0.919601i | ||||||||
\(474\) | 3.46410 | + | 2.00000i | 0.159111 | + | 0.0918630i | ||||
\(475\) | 6.92820 | + | 4.00000i | 0.317888 | + | 0.183533i | ||||
\(476\) | 10.0000i | 0.458349i | ||||||||
\(477\) | 0.500000 | − | 0.866025i | 0.0228934 | − | 0.0396526i | ||||
\(478\) | 3.00000 | + | 5.19615i | 0.137217 | + | 0.237666i | ||||
\(479\) | −27.7128 | + | 16.0000i | −1.26623 | + | 0.731059i | −0.974273 | − | 0.225372i | \(-0.927640\pi\) |
−0.291958 | + | 0.956431i | \(0.594307\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −7.00000 | −0.318841 | ||||||||
\(483\) | 10.3923 | − | 6.00000i | 0.472866 | − | 0.273009i | ||||
\(484\) | 3.50000 | + | 6.06218i | 0.159091 | + | 0.275554i | ||||
\(485\) | 1.00000 | − | 1.73205i | 0.0454077 | − | 0.0786484i | ||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 22.5167 | + | 13.0000i | 1.02033 | + | 0.589086i | 0.914199 | − | 0.405266i | \(-0.132821\pi\) |
0.106129 | + | 0.994352i | \(0.466154\pi\) | |||||||
\(488\) | 9.52628 | + | 5.50000i | 0.431234 | + | 0.248973i | ||||
\(489\) | 20.0000i | 0.904431i | ||||||||
\(490\) | 1.50000 | − | 2.59808i | 0.0677631 | − | 0.117369i | ||||
\(491\) | −15.0000 | − | 25.9808i | −0.676941 | − | 1.17250i | −0.975898 | − | 0.218229i | \(-0.929972\pi\) |
0.298957 | − | 0.954267i | \(-0.403361\pi\) | |||||||
\(492\) | 4.33013 | − | 2.50000i | 0.195217 | − | 0.112709i | ||||
\(493\) | 45.0000 | 2.02670 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.00000 | −0.0898933 | ||||||||
\(496\) | −3.46410 | + | 2.00000i | −0.155543 | + | 0.0898027i | ||||
\(497\) | −14.0000 | − | 24.2487i | −0.627986 | − | 1.08770i | ||||
\(498\) | 3.00000 | − | 5.19615i | 0.134433 | − | 0.232845i | ||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | −7.79423 | − | 4.50000i | −0.348569 | − | 0.201246i | ||||
\(501\) | −20.7846 | − | 12.0000i | −0.928588 | − | 0.536120i | ||||
\(502\) | 4.00000i | 0.178529i | ||||||||
\(503\) | 7.00000 | − | 12.1244i | 0.312115 | − | 0.540598i | −0.666705 | − | 0.745321i | \(-0.732296\pi\) |
0.978820 | + | 0.204723i | \(0.0656294\pi\) | |||||||
\(504\) | 1.00000 | + | 1.73205i | 0.0445435 | + | 0.0771517i | ||||
\(505\) | −4.33013 | + | 2.50000i | −0.192688 | + | 0.111249i | ||||
\(506\) | 12.0000 | 0.533465 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.0000 | −0.532414 | ||||||||
\(509\) | 12.9904 | − | 7.50000i | 0.575789 | − | 0.332432i | −0.183669 | − | 0.982988i | \(-0.558798\pi\) |
0.759458 | + | 0.650556i | \(0.225464\pi\) | |||||||
\(510\) | 2.50000 | + | 4.33013i | 0.110702 | + | 0.191741i | ||||
\(511\) | 13.0000 | − | 22.5167i | 0.575086 | − | 0.996078i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −1.73205 | − | 1.00000i | −0.0764719 | − | 0.0441511i | ||||
\(514\) | 2.59808 | + | 1.50000i | 0.114596 | + | 0.0661622i | ||||
\(515\) | 10.0000i | 0.440653i | ||||||||
\(516\) | 5.00000 | − | 8.66025i | 0.220113 | − | 0.381246i | ||||
\(517\) | 2.00000 | + | 3.46410i | 0.0879599 | + | 0.152351i | ||||
\(518\) | 19.0526 | − | 11.0000i | 0.837121 | − | 0.483312i | ||||
\(519\) | −22.0000 | −0.965693 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.0000 | 1.09527 | 0.547635 | − | 0.836717i | \(-0.315528\pi\) | ||||
0.547635 | + | 0.836717i | \(0.315528\pi\) | |||||||
\(522\) | 7.79423 | − | 4.50000i | 0.341144 | − | 0.196960i | ||||
\(523\) | 19.0000 | + | 32.9090i | 0.830812 | + | 1.43901i | 0.897395 | + | 0.441228i | \(0.145457\pi\) |
−0.0665832 | + | 0.997781i | \(0.521210\pi\) | |||||||
\(524\) | −4.00000 | + | 6.92820i | −0.174741 | + | 0.302660i | ||||
\(525\) | − | 8.00000i | − | 0.349149i | ||||||
\(526\) | 12.1244 | + | 7.00000i | 0.528647 | + | 0.305215i | ||||
\(527\) | −17.3205 | − | 10.0000i | −0.754493 | − | 0.435607i | ||||
\(528\) | 2.00000i | 0.0870388i | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | −0.500000 | − | 0.866025i | −0.0217186 | − | 0.0376177i | ||||
\(531\) | 6.92820 | − | 4.00000i | 0.300658 | − | 0.173585i | ||||
\(532\) | −4.00000 | −0.173422 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 2.00000 | 0.0865485 | ||||||||
\(535\) | 15.5885 | − | 9.00000i | 0.673948 | − | 0.389104i | ||||
\(536\) | 1.00000 | + | 1.73205i | 0.0431934 | + | 0.0748132i | ||||
\(537\) | 3.00000 | − | 5.19615i | 0.129460 | − | 0.224231i | ||||
\(538\) | 14.0000i | 0.603583i | ||||||||
\(539\) | 5.19615 | + | 3.00000i | 0.223814 | + | 0.129219i | ||||
\(540\) | 0.866025 | + | 0.500000i | 0.0372678 | + | 0.0215166i | ||||
\(541\) | 7.00000i | 0.300954i | 0.988614 | + | 0.150477i | \(0.0480809\pi\) | ||||
−0.988614 | + | 0.150477i | \(0.951919\pi\) | |||||||
\(542\) | 4.00000 | − | 6.92820i | 0.171815 | − | 0.297592i | ||||
\(543\) | −2.50000 | − | 4.33013i | −0.107285 | − | 0.185824i | ||||
\(544\) | 4.33013 | − | 2.50000i | 0.185653 | − | 0.107187i | ||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.00000 | 0.0855138 | 0.0427569 | − | 0.999086i | \(-0.486386\pi\) | ||||
0.0427569 | + | 0.999086i | \(0.486386\pi\) | |||||||
\(548\) | 14.7224 | − | 8.50000i | 0.628911 | − | 0.363102i | ||||
\(549\) | 5.50000 | + | 9.52628i | 0.234734 | + | 0.406572i | ||||
\(550\) | 4.00000 | − | 6.92820i | 0.170561 | − | 0.295420i | ||||
\(551\) | 18.0000i | 0.766826i | ||||||||
\(552\) | −5.19615 | − | 3.00000i | −0.221163 | − | 0.127688i | ||||
\(553\) | 6.92820 | + | 4.00000i | 0.294617 | + | 0.170097i | ||||
\(554\) | − | 11.0000i | − | 0.467345i | ||||||
\(555\) | 5.50000 | − | 9.52628i | 0.233462 | − | 0.404368i | ||||
\(556\) | −6.00000 | − | 10.3923i | −0.254457 | − | 0.440732i | ||||
\(557\) | 7.79423 | − | 4.50000i | 0.330252 | − | 0.190671i | −0.325701 | − | 0.945473i | \(-0.605600\pi\) |
0.655953 | + | 0.754802i | \(0.272267\pi\) | |||||||
\(558\) | −4.00000 | −0.169334 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.00000 | 0.0845154 | ||||||||
\(561\) | −8.66025 | + | 5.00000i | −0.365636 | + | 0.211100i | ||||
\(562\) | 12.5000 | + | 21.6506i | 0.527281 | + | 0.913277i | ||||
\(563\) | 20.0000 | − | 34.6410i | 0.842900 | − | 1.45994i | −0.0445334 | − | 0.999008i | \(-0.514180\pi\) |
0.887433 | − | 0.460937i | \(-0.152487\pi\) | |||||||
\(564\) | − | 2.00000i | − | 0.0842152i | ||||||
\(565\) | −2.59808 | − | 1.50000i | −0.109302 | − | 0.0631055i | ||||
\(566\) | −22.5167 | − | 13.0000i | −0.946446 | − | 0.546431i | ||||
\(567\) | 2.00000i | 0.0839921i | ||||||||
\(568\) | −7.00000 | + | 12.1244i | −0.293713 | + | 0.508727i | ||||
\(569\) | 3.00000 | + | 5.19615i | 0.125767 | + | 0.217834i | 0.922032 | − | 0.387113i | \(-0.126528\pi\) |
−0.796266 | + | 0.604947i | \(0.793194\pi\) | |||||||
\(570\) | −1.73205 | + | 1.00000i | −0.0725476 | + | 0.0418854i | ||||
\(571\) | 2.00000 | 0.0836974 | 0.0418487 | − | 0.999124i | \(-0.486675\pi\) | ||||
0.0418487 | + | 0.999124i | \(0.486675\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.00000 | −0.167102 | ||||||||
\(574\) | 8.66025 | − | 5.00000i | 0.361472 | − | 0.208696i | ||||
\(575\) | 12.0000 | + | 20.7846i | 0.500435 | + | 0.866778i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 27.0000i | 1.12402i | 0.827129 | + | 0.562012i | \(0.189973\pi\) | ||||
−0.827129 | + | 0.562012i | \(0.810027\pi\) | |||||||
\(578\) | 6.92820 | + | 4.00000i | 0.288175 | + | 0.166378i | ||||
\(579\) | 14.7224 | + | 8.50000i | 0.611843 | + | 0.353248i | ||||
\(580\) | − | 9.00000i | − | 0.373705i | ||||||
\(581\) | 6.00000 | − | 10.3923i | 0.248922 | − | 0.431145i | ||||
\(582\) | −1.00000 | − | 1.73205i | −0.0414513 | − | 0.0717958i | ||||
\(583\) | 1.73205 | − | 1.00000i | 0.0717342 | − | 0.0414158i | ||||
\(584\) | −13.0000 | −0.537944 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.00000 | 0.0413096 | ||||||||
\(587\) | −27.7128 | + | 16.0000i | −1.14383 | + | 0.660391i | −0.947376 | − | 0.320122i | \(-0.896276\pi\) |
−0.196454 | + | 0.980513i | \(0.562943\pi\) | |||||||
\(588\) | −1.50000 | − | 2.59808i | −0.0618590 | − | 0.107143i | ||||
\(589\) | 4.00000 | − | 6.92820i | 0.164817 | − | 0.285472i | ||||
\(590\) | − | 8.00000i | − | 0.329355i | ||||||
\(591\) | 5.19615 | + | 3.00000i | 0.213741 | + | 0.123404i | ||||
\(592\) | −9.52628 | − | 5.50000i | −0.391528 | − | 0.226049i | ||||
\(593\) | 39.0000i | 1.60154i | 0.598973 | + | 0.800769i | \(0.295576\pi\) | ||||
−0.598973 | + | 0.800769i | \(0.704424\pi\) | |||||||
\(594\) | −1.00000 | + | 1.73205i | −0.0410305 | + | 0.0710669i | ||||
\(595\) | 5.00000 | + | 8.66025i | 0.204980 | + | 0.355036i | ||||
\(596\) | −2.59808 | + | 1.50000i | −0.106421 | + | 0.0614424i | ||||
\(597\) | 10.0000 | 0.409273 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | −3.46410 | + | 2.00000i | −0.141421 | + | 0.0816497i | ||||
\(601\) | −5.50000 | − | 9.52628i | −0.224350 | − | 0.388585i | 0.731774 | − | 0.681547i | \(-0.238692\pi\) |
−0.956124 | + | 0.292962i | \(0.905359\pi\) | |||||||
\(602\) | 10.0000 | − | 17.3205i | 0.407570 | − | 0.705931i | ||||
\(603\) | 2.00000i | 0.0814463i | ||||||||
\(604\) | 5.19615 | + | 3.00000i | 0.211428 | + | 0.122068i | ||||
\(605\) | 6.06218 | + | 3.50000i | 0.246463 | + | 0.142295i | ||||
\(606\) | 5.00000i | 0.203111i | ||||||||
\(607\) | −16.0000 | + | 27.7128i | −0.649420 | + | 1.12483i | 0.333842 | + | 0.942629i | \(0.391655\pi\) |
−0.983262 | + | 0.182199i | \(0.941678\pi\) | |||||||
\(608\) | 1.00000 | + | 1.73205i | 0.0405554 | + | 0.0702439i | ||||
\(609\) | 15.5885 | − | 9.00000i | 0.631676 | − | 0.364698i | ||||
\(610\) | 11.0000 | 0.445377 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 5.00000 | 0.202113 | ||||||||
\(613\) | 11.2583 | − | 6.50000i | 0.454720 | − | 0.262533i | −0.255102 | − | 0.966914i | \(-0.582109\pi\) |
0.709821 | + | 0.704382i | \(0.248776\pi\) | |||||||
\(614\) | −7.00000 | − | 12.1244i | −0.282497 | − | 0.489299i | ||||
\(615\) | 2.50000 | − | 4.33013i | 0.100810 | − | 0.174608i | ||||
\(616\) | 4.00000i | 0.161165i | ||||||||
\(617\) | 12.9904 | + | 7.50000i | 0.522973 | + | 0.301939i | 0.738150 | − | 0.674636i | \(-0.235700\pi\) |
−0.215177 | + | 0.976575i | \(0.569033\pi\) | |||||||
\(618\) | 8.66025 | + | 5.00000i | 0.348367 | + | 0.201129i | ||||
\(619\) | − | 32.0000i | − | 1.28619i | −0.765787 | − | 0.643094i | \(-0.777650\pi\) | ||
0.765787 | − | 0.643094i | \(-0.222350\pi\) | |||||||
\(620\) | −2.00000 | + | 3.46410i | −0.0803219 | + | 0.139122i | ||||
\(621\) | −3.00000 | − | 5.19615i | −0.120386 | − | 0.208514i | ||||
\(622\) | 5.19615 | − | 3.00000i | 0.208347 | − | 0.120289i | ||||
\(623\) | 4.00000 | 0.160257 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | −5.19615 | + | 3.00000i | −0.207680 | + | 0.119904i | ||||
\(627\) | −2.00000 | − | 3.46410i | −0.0798723 | − | 0.138343i | ||||
\(628\) | −3.50000 | + | 6.06218i | −0.139665 | + | 0.241907i | ||||
\(629\) | − | 55.0000i | − | 2.19299i | ||||||
\(630\) | 1.73205 | + | 1.00000i | 0.0690066 | + | 0.0398410i | ||||
\(631\) | 10.3923 | + | 6.00000i | 0.413711 | + | 0.238856i | 0.692383 | − | 0.721530i | \(-0.256561\pi\) |
−0.278672 | + | 0.960386i | \(0.589894\pi\) | |||||||
\(632\) | − | 4.00000i | − | 0.159111i | ||||||
\(633\) | 12.0000 | − | 20.7846i | 0.476957 | − | 0.826114i | ||||
\(634\) | 16.5000 | + | 28.5788i | 0.655299 | + | 1.13501i | ||||
\(635\) | −10.3923 | + | 6.00000i | −0.412406 | + | 0.238103i | ||||
\(636\) | −1.00000 | −0.0396526 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 18.0000 | 0.712627 | ||||||||
\(639\) | −12.1244 | + | 7.00000i | −0.479632 | + | 0.276916i | ||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | 2.50000 | − | 4.33013i | 0.0987441 | − | 0.171030i | −0.812421 | − | 0.583071i | \(-0.801851\pi\) |
0.911165 | + | 0.412042i | \(0.135184\pi\) | |||||||
\(642\) | − | 18.0000i | − | 0.710403i | ||||||
\(643\) | −6.92820 | − | 4.00000i | −0.273222 | − | 0.157745i | 0.357129 | − | 0.934055i | \(-0.383756\pi\) |
−0.630351 | + | 0.776310i | \(0.717089\pi\) | |||||||
\(644\) | −10.3923 | − | 6.00000i | −0.409514 | − | 0.236433i | ||||
\(645\) | − | 10.0000i | − | 0.393750i | ||||||
\(646\) | −5.00000 | + | 8.66025i | −0.196722 | + | 0.340733i | ||||
\(647\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | 16.0000 | 0.628055 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.00000 | −0.313545 | ||||||||
\(652\) | 17.3205 | − | 10.0000i | 0.678323 | − | 0.391630i | ||||
\(653\) | 11.0000 | + | 19.0526i | 0.430463 | + | 0.745584i | 0.996913 | − | 0.0785119i | \(-0.0250169\pi\) |
−0.566450 | + | 0.824096i | \(0.691684\pi\) | |||||||
\(654\) | −1.00000 | + | 1.73205i | −0.0391031 | + | 0.0677285i | ||||
\(655\) | 8.00000i | 0.312586i | ||||||||
\(656\) | −4.33013 | − | 2.50000i | −0.169063 | − | 0.0976086i | ||||
\(657\) | −11.2583 | − | 6.50000i | −0.439229 | − | 0.253589i | ||||
\(658\) | − | 4.00000i | − | 0.155936i | ||||||
\(659\) | −12.0000 | + | 20.7846i | −0.467454 | + | 0.809653i | −0.999309 | − | 0.0371821i | \(-0.988162\pi\) |
0.531855 | + | 0.846836i | \(0.321495\pi\) | |||||||
\(660\) | 1.00000 | + | 1.73205i | 0.0389249 | + | 0.0674200i | ||||
\(661\) | −21.6506 | + | 12.5000i | −0.842112 | + | 0.486194i | −0.857982 | − | 0.513680i | \(-0.828282\pi\) |
0.0158695 | + | 0.999874i | \(0.494948\pi\) | |||||||
\(662\) | −28.0000 | −1.08825 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | −3.46410 | + | 2.00000i | −0.134332 | + | 0.0775567i | ||||
\(666\) | −5.50000 | − | 9.52628i | −0.213121 | − | 0.369136i | ||||
\(667\) | −27.0000 | + | 46.7654i | −1.04544 | + | 1.81076i | ||||
\(668\) | 24.0000i | 0.928588i | ||||||||
\(669\) | −13.8564 | − | 8.00000i | −0.535720 | − | 0.309298i | ||||
\(670\) | 1.73205 | + | 1.00000i | 0.0669150 | + | 0.0386334i | ||||
\(671\) | 22.0000i | 0.849301i | ||||||||
\(672\) | 1.00000 | − | 1.73205i | 0.0385758 | − | 0.0668153i | ||||
\(673\) | 21.5000 | + | 37.2391i | 0.828764 | + | 1.43546i | 0.899008 | + | 0.437932i | \(0.144289\pi\) |
−0.0702442 | + | 0.997530i | \(0.522378\pi\) | |||||||
\(674\) | −7.79423 | + | 4.50000i | −0.300222 | + | 0.173334i | ||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −46.0000 | −1.76792 | −0.883962 | − | 0.467559i | \(-0.845134\pi\) | ||||
−0.883962 | + | 0.467559i | \(0.845134\pi\) | |||||||
\(678\) | −2.59808 | + | 1.50000i | −0.0997785 | + | 0.0576072i | ||||
\(679\) | −2.00000 | − | 3.46410i | −0.0767530 | − | 0.132940i | ||||
\(680\) | 2.50000 | − | 4.33013i | 0.0958706 | − | 0.166053i | ||||
\(681\) | − | 14.0000i | − | 0.536481i | ||||||
\(682\) | −6.92820 | − | 4.00000i | −0.265295 | − | 0.153168i | ||||
\(683\) | −34.6410 | − | 20.0000i | −1.32550 | − | 0.765279i | −0.340901 | − | 0.940099i | \(-0.610732\pi\) |
−0.984600 | + | 0.174820i | \(0.944066\pi\) | |||||||
\(684\) | 2.00000i | 0.0764719i | ||||||||
\(685\) | 8.50000 | − | 14.7224i | 0.324768 | − | 0.562515i | ||||
\(686\) | −10.0000 | − | 17.3205i | −0.381802 | − | 0.661300i | ||||
\(687\) | 8.66025 | − | 5.00000i | 0.330409 | − | 0.190762i | ||||
\(688\) | −10.0000 | −0.381246 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −6.00000 | −0.228416 | ||||||||
\(691\) | −1.73205 | + | 1.00000i | −0.0658903 | + | 0.0380418i | −0.532583 | − | 0.846378i | \(-0.678779\pi\) |
0.466693 | + | 0.884419i | \(0.345445\pi\) | |||||||
\(692\) | 11.0000 | + | 19.0526i | 0.418157 | + | 0.724270i | ||||
\(693\) | −2.00000 | + | 3.46410i | −0.0759737 | + | 0.131590i | ||||
\(694\) | − | 6.00000i | − | 0.227757i | ||||||
\(695\) | −10.3923 | − | 6.00000i | −0.394203 | − | 0.227593i | ||||
\(696\) | −7.79423 | − | 4.50000i | −0.295439 | − | 0.170572i | ||||
\(697\) | − | 25.0000i | − | 0.946943i | ||||||
\(698\) | 3.00000 | − | 5.19615i | 0.113552 | − | 0.196677i | ||||
\(699\) | 3.00000 | + | 5.19615i | 0.113470 | + | 0.196537i | ||||
\(700\) | −6.92820 | + | 4.00000i | −0.261861 | + | 0.151186i | ||||
\(701\) | −34.0000 | −1.28416 | −0.642081 | − | 0.766637i | \(-0.721929\pi\) | ||||
−0.642081 | + | 0.766637i | \(0.721929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.0000 | 0.829746 | ||||||||
\(704\) | 1.73205 | − | 1.00000i | 0.0652791 | − | 0.0376889i | ||||
\(705\) | −1.00000 | − | 1.73205i | −0.0376622 | − | 0.0652328i | ||||
\(706\) | −8.50000 | + | 14.7224i | −0.319902 | + | 0.554086i | ||||
\(707\) | 10.0000i | 0.376089i | ||||||||
\(708\) | −6.92820 | − | 4.00000i | −0.260378 | − | 0.150329i | ||||
\(709\) | −12.9904 | − | 7.50000i | −0.487864 | − | 0.281668i | 0.235824 | − | 0.971796i | \(-0.424221\pi\) |
−0.723688 | + | 0.690127i | \(0.757554\pi\) | |||||||
\(710\) | 14.0000i | 0.525411i | ||||||||
\(711\) | 2.00000 | − | 3.46410i | 0.0750059 | − | 0.129914i | ||||
\(712\) | −1.00000 | − | 1.73205i | −0.0374766 | − | 0.0649113i | ||||
\(713\) | 20.7846 | − | 12.0000i | 0.778390 | − | 0.449404i | ||||
\(714\) | 10.0000 | 0.374241 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.00000 | −0.224231 | ||||||||
\(717\) | 5.19615 | − | 3.00000i | 0.194054 | − | 0.112037i | ||||
\(718\) | −15.0000 | − | 25.9808i | −0.559795 | − | 0.969593i | ||||
\(719\) | 12.0000 | − | 20.7846i | 0.447524 | − | 0.775135i | −0.550700 | − | 0.834703i | \(-0.685639\pi\) |
0.998224 | + | 0.0595683i | \(0.0189724\pi\) | |||||||
\(720\) | − | 1.00000i | − | 0.0372678i | ||||||
\(721\) | 17.3205 | + | 10.0000i | 0.645049 | + | 0.372419i | ||||
\(722\) | 12.9904 | + | 7.50000i | 0.483452 | + | 0.279121i | ||||
\(723\) | 7.00000i | 0.260333i | ||||||||
\(724\) | −2.50000 | + | 4.33013i | −0.0929118 | + | 0.160928i | ||||
\(725\) | 18.0000 | + | 31.1769i | 0.668503 | + | 1.15788i | ||||
\(726\) | 6.06218 | − | 3.50000i | 0.224989 | − | 0.129897i | ||||
\(727\) | −2.00000 | −0.0741759 | −0.0370879 | − | 0.999312i | \(-0.511808\pi\) | ||||
−0.0370879 | + | 0.999312i | \(0.511808\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −11.2583 | + | 6.50000i | −0.416689 | + | 0.240576i | ||||
\(731\) | −25.0000 | − | 43.3013i | −0.924658 | − | 1.60156i | ||||
\(732\) | 5.50000 | − | 9.52628i | 0.203286 | − | 0.352101i | ||||
\(733\) | 13.0000i | 0.480166i | 0.970752 | + | 0.240083i | \(0.0771747\pi\) | ||||
−0.970752 | + | 0.240083i | \(0.922825\pi\) | |||||||
\(734\) | −1.73205 | − | 1.00000i | −0.0639312 | − | 0.0369107i | ||||
\(735\) | −2.59808 | − | 1.50000i | −0.0958315 | − | 0.0553283i | ||||
\(736\) | 6.00000i | 0.221163i | ||||||||
\(737\) | −2.00000 | + | 3.46410i | −0.0736709 | + | 0.127602i | ||||
\(738\) | −2.50000 | − | 4.33013i | −0.0920263 | − | 0.159394i | ||||
\(739\) | −13.8564 | + | 8.00000i | −0.509716 | + | 0.294285i | −0.732717 | − | 0.680534i | \(-0.761748\pi\) |
0.223001 | + | 0.974818i | \(0.428415\pi\) | |||||||
\(740\) | −11.0000 | −0.404368 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.00000 | −0.0734223 | ||||||||
\(743\) | −10.3923 | + | 6.00000i | −0.381257 | + | 0.220119i | −0.678365 | − | 0.734725i | \(-0.737311\pi\) |
0.297108 | + | 0.954844i | \(0.403978\pi\) | |||||||
\(744\) | 2.00000 | + | 3.46410i | 0.0733236 | + | 0.127000i | ||||
\(745\) | −1.50000 | + | 2.59808i | −0.0549557 | + | 0.0951861i | ||||
\(746\) | − | 9.00000i | − | 0.329513i | ||||||
\(747\) | −5.19615 | − | 3.00000i | −0.190117 | − | 0.109764i | ||||
\(748\) | 8.66025 | + | 5.00000i | 0.316650 | + | 0.182818i | ||||
\(749\) | − | 36.0000i | − | 1.31541i | ||||||
\(750\) | −4.50000 | + | 7.79423i | −0.164317 | + | 0.284605i | ||||
\(751\) | 13.0000 | + | 22.5167i | 0.474377 | + | 0.821645i | 0.999570 | − | 0.0293387i | \(-0.00934013\pi\) |
−0.525193 | + | 0.850983i | \(0.676007\pi\) | |||||||
\(752\) | −1.73205 | + | 1.00000i | −0.0631614 | + | 0.0364662i | ||||
\(753\) | 4.00000 | 0.145768 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.00000 | 0.218362 | ||||||||
\(756\) | 1.73205 | − | 1.00000i | 0.0629941 | − | 0.0363696i | ||||
\(757\) | 9.00000 | + | 15.5885i | 0.327111 | + | 0.566572i | 0.981937 | − | 0.189207i | \(-0.0605917\pi\) |
−0.654827 | + | 0.755779i | \(0.727258\pi\) | |||||||
\(758\) | −6.00000 | + | 10.3923i | −0.217930 | + | 0.377466i | ||||
\(759\) | − | 12.0000i | − | 0.435572i | ||||||
\(760\) | 1.73205 | + | 1.00000i | 0.0628281 | + | 0.0362738i | ||||
\(761\) | 29.4449 | + | 17.0000i | 1.06738 | + | 0.616250i | 0.927463 | − | 0.373914i | \(-0.121985\pi\) |
0.139912 | + | 0.990164i | \(0.455318\pi\) | |||||||
\(762\) | 12.0000i | 0.434714i | ||||||||
\(763\) | −2.00000 | + | 3.46410i | −0.0724049 | + | 0.125409i | ||||
\(764\) | 2.00000 | + | 3.46410i | 0.0723575 | + | 0.125327i | ||||
\(765\) | 4.33013 | − | 2.50000i | 0.156556 | − | 0.0903877i | ||||
\(766\) | 24.0000 | 0.867155 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −29.4449 | + | 17.0000i | −1.06181 | + | 0.613036i | −0.925932 | − | 0.377690i | \(-0.876718\pi\) |
−0.135877 | + | 0.990726i | \(0.543385\pi\) | |||||||
\(770\) | 2.00000 | + | 3.46410i | 0.0720750 | + | 0.124838i | ||||
\(771\) | 1.50000 | − | 2.59808i | 0.0540212 | − | 0.0935674i | ||||
\(772\) | − | 17.0000i | − | 0.611843i | ||||||
\(773\) | −15.5885 | − | 9.00000i | −0.560678 | − | 0.323708i | 0.192740 | − | 0.981250i | \(-0.438263\pi\) |
−0.753418 | + | 0.657542i | \(0.771596\pi\) | |||||||
\(774\) | −8.66025 | − | 5.00000i | −0.311286 | − | 0.179721i | ||||
\(775\) | − | 16.0000i | − | 0.574737i | ||||||
\(776\) | −1.00000 | + | 1.73205i | −0.0358979 | + | 0.0621770i | ||||
\(777\) | −11.0000 | − | 19.0526i | −0.394623 | − | 0.683507i | ||||
\(778\) | 16.4545 | − | 9.50000i | 0.589922 | − | 0.340592i | ||||
\(779\) | 10.0000 | 0.358287 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.0000 | −1.00192 | ||||||||
\(782\) | −25.9808 | + | 15.0000i | −0.929070 | + | 0.536399i | ||||
\(783\) | −4.50000 | − | 7.79423i | −0.160817 | − | 0.278543i | ||||
\(784\) | −1.50000 | + | 2.59808i | −0.0535714 | + | 0.0927884i | ||||
\(785\) | 7.00000i | 0.249841i | ||||||||
\(786\) | 6.92820 | + | 4.00000i | 0.247121 | + | 0.142675i | ||||
\(787\) | 3.46410 | + | 2.00000i | 0.123482 | + | 0.0712923i | 0.560469 | − | 0.828176i | \(-0.310621\pi\) |
−0.436987 | + | 0.899468i | \(0.643954\pi\) | |||||||
\(788\) | − | 6.00000i | − | 0.213741i | ||||||
\(789\) | 7.00000 | − | 12.1244i | 0.249207 | − | 0.431638i | ||||
\(790\) | −2.00000 | − | 3.46410i | −0.0711568 | − | 0.123247i | ||||
\(791\) | −5.19615 | + | 3.00000i | −0.184754 | + | 0.106668i | ||||
\(792\) | 2.00000 | 0.0710669 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 18.0000 | 0.638796 | ||||||||
\(795\) | −0.866025 | + | 0.500000i | −0.0307148 | + | 0.0177332i | ||||
\(796\) | −5.00000 | − | 8.66025i | −0.177220 | − | 0.306955i | ||||
\(797\) | −1.00000 | + | 1.73205i | −0.0354218 | + | 0.0613524i | −0.883193 | − | 0.469010i | \(-0.844611\pi\) |
0.847771 | + | 0.530362i | \(0.177944\pi\) | |||||||
\(798\) | 4.00000i | 0.141598i | ||||||||
\(799\) | −8.66025 | − | 5.00000i | −0.306378 | − | 0.176887i | ||||
\(800\) | 3.46410 | + | 2.00000i | 0.122474 | + | 0.0707107i | ||||
\(801\) | − | 2.00000i | − | 0.0706665i | ||||||
\(802\) | −13.5000 | + | 23.3827i | −0.476702 | + | 0.825671i | ||||
\(803\) | −13.0000 | − | 22.5167i | −0.458760 | − | 0.794596i | ||||
\(804\) | 1.73205 | − | 1.00000i | 0.0610847 | − | 0.0352673i | ||||
\(805\) | −12.0000 | −0.422944 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.0000 | 0.492823 | ||||||||
\(808\) | 4.33013 | − | 2.50000i | 0.152333 | − | 0.0879497i | ||||
\(809\) | −2.50000 | − | 4.33013i | −0.0878953 | − | 0.152239i | 0.818726 | − | 0.574184i | \(-0.194681\pi\) |
−0.906621 | + | 0.421945i | \(0.861347\pi\) | |||||||
\(810\) | 0.500000 | − | 0.866025i | 0.0175682 | − | 0.0304290i | ||||
\(811\) | − | 36.0000i | − | 1.26413i | −0.774915 | − | 0.632065i | \(-0.782207\pi\) | ||
0.774915 | − | 0.632065i | \(-0.217793\pi\) | |||||||
\(812\) | −15.5885 | − | 9.00000i | −0.547048 | − | 0.315838i | ||||
\(813\) | −6.92820 | − | 4.00000i | −0.242983 | − | 0.140286i | ||||
\(814\) | − | 22.0000i | − | 0.771100i | ||||||
\(815\) | 10.0000 | − | 17.3205i | 0.350285 | − | 0.606711i | ||||
\(816\) | −2.50000 | − | 4.33013i | −0.0875175 | − | 0.151585i | ||||
\(817\) | 17.3205 | − | 10.0000i | 0.605968 | − | 0.349856i | ||||
\(818\) | 23.0000 | 0.804176 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.00000 | −0.174608 | ||||||||
\(821\) | −25.9808 | + | 15.0000i | −0.906735 | + | 0.523504i | −0.879379 | − | 0.476122i | \(-0.842042\pi\) |
−0.0273557 | + | 0.999626i | \(0.508709\pi\) | |||||||
\(822\) | −8.50000 | − | 14.7224i | −0.296472 | − | 0.513504i | ||||
\(823\) | −8.00000 | + | 13.8564i | −0.278862 | + | 0.483004i | −0.971102 | − | 0.238664i | \(-0.923291\pi\) |
0.692240 | + | 0.721668i | \(0.256624\pi\) | |||||||
\(824\) | − | 10.0000i | − | 0.348367i | ||||||
\(825\) | −6.92820 | − | 4.00000i | −0.241209 | − | 0.139262i | ||||
\(826\) | −13.8564 | − | 8.00000i | −0.482126 | − | 0.278356i | ||||
\(827\) | 8.00000i | 0.278187i | 0.990279 | + | 0.139094i | \(0.0444189\pi\) | ||||
−0.990279 | + | 0.139094i | \(0.955581\pi\) | |||||||
\(828\) | −3.00000 | + | 5.19615i | −0.104257 | + | 0.180579i | ||||
\(829\) | −17.5000 | − | 30.3109i | −0.607800 | − | 1.05274i | −0.991602 | − | 0.129325i | \(-0.958719\pi\) |
0.383802 | − | 0.923415i | \(-0.374614\pi\) | |||||||
\(830\) | −5.19615 | + | 3.00000i | −0.180361 | + | 0.104132i | ||||
\(831\) | −11.0000 | −0.381586 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.0000 | −0.519719 | ||||||||
\(834\) | −10.3923 | + | 6.00000i | −0.359856 | + | 0.207763i | ||||
\(835\) | 12.0000 | + | 20.7846i | 0.415277 | + | 0.719281i | ||||
\(836\) | −2.00000 | + | 3.46410i | −0.0691714 | + | 0.119808i | ||||
\(837\) | 4.00000i | 0.138260i | ||||||||
\(838\) | −27.7128 | − | 16.0000i | −0.957323 | − | 0.552711i | ||||
\(839\) | 38.1051 | + | 22.0000i | 1.31553 | + | 0.759524i | 0.983007 | − | 0.183569i | \(-0.0587651\pi\) |
0.332528 | + | 0.943093i | \(0.392098\pi\) | |||||||
\(840\) | − | 2.00000i | − | 0.0690066i | ||||||
\(841\) | −26.0000 | + | 45.0333i | −0.896552 | + | 1.55287i | ||||
\(842\) | 11.5000 | + | 19.9186i | 0.396316 | + | 0.686440i | ||||
\(843\) | 21.6506 | − | 12.5000i | 0.745687 | − | 0.430523i | ||||
\(844\) | −24.0000 | −0.826114 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.00000 | −0.0687614 | ||||||||
\(847\) | 12.1244 | − | 7.00000i | 0.416598 | − | 0.240523i | ||||
\(848\) | 0.500000 | + | 0.866025i | 0.0171701 | + | 0.0297394i | ||||
\(849\) | −13.0000 | + | 22.5167i | −0.446159 | + | 0.772770i | ||||
\(850\) | 20.0000i | 0.685994i | ||||||||
\(851\) | 57.1577 | + | 33.0000i | 1.95934 | + | 1.13123i | ||||
\(852\) | 12.1244 | + | 7.00000i | 0.415374 | + | 0.239816i | ||||
\(853\) | − | 49.0000i | − | 1.67773i | −0.544341 | − | 0.838864i | \(-0.683220\pi\) | ||
0.544341 | − | 0.838864i | \(-0.316780\pi\) | |||||||
\(854\) | 11.0000 | − | 19.0526i | 0.376412 | − | 0.651965i | ||||
\(855\) | 1.00000 | + | 1.73205i | 0.0341993 | + | 0.0592349i | ||||
\(856\) | −15.5885 | + | 9.00000i | −0.532803 | + | 0.307614i | ||||
\(857\) | −45.0000 | −1.53717 | −0.768585 | − | 0.639747i | \(-0.779039\pi\) | ||||
−0.768585 | + | 0.639747i | \(0.779039\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −50.0000 | −1.70598 | −0.852989 | − | 0.521929i | \(-0.825213\pi\) | ||||
−0.852989 | + | 0.521929i | \(0.825213\pi\) | |||||||
\(860\) | −8.66025 | + | 5.00000i | −0.295312 | + | 0.170499i | ||||
\(861\) | −5.00000 | − | 8.66025i | −0.170400 | − | 0.295141i | ||||
\(862\) | 1.00000 | − | 1.73205i | 0.0340601 | − | 0.0589939i | ||||
\(863\) | 46.0000i | 1.56586i | 0.622111 | + | 0.782929i | \(0.286275\pi\) | ||||
−0.622111 | + | 0.782929i | \(0.713725\pi\) | |||||||
\(864\) | −0.866025 | − | 0.500000i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 19.0526 | + | 11.0000i | 0.647806 | + | 0.374011i | ||||
\(866\) | − | 21.0000i | − | 0.713609i | ||||||
\(867\) | 4.00000 | − | 6.92820i | 0.135847 | − | 0.235294i | ||||
\(868\) | 4.00000 | + | 6.92820i | 0.135769 | + | 0.235159i | ||||
\(869\) | 6.92820 | − | 4.00000i | 0.235023 | − | 0.135691i | ||||
\(870\) | −9.00000 | −0.305129 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 2.00000 | 0.0677285 | ||||||||
\(873\) | −1.73205 | + | 1.00000i | −0.0586210 | + | 0.0338449i | ||||
\(874\) | −6.00000 | − | 10.3923i | −0.202953 | − | 0.351525i | ||||
\(875\) | −9.00000 | + | 15.5885i | −0.304256 | + | 0.526986i | ||||
\(876\) | 13.0000i | 0.439229i | ||||||||
\(877\) | −32.0429 | − | 18.5000i | −1.08201 | − | 0.624701i | −0.150574 | − | 0.988599i | \(-0.548112\pi\) |
−0.931439 | + | 0.363898i | \(0.881446\pi\) | |||||||
\(878\) | −8.66025 | − | 5.00000i | −0.292269 | − | 0.168742i | ||||
\(879\) | − | 1.00000i | − | 0.0337292i | ||||||
\(880\) | 1.00000 | − | 1.73205i | 0.0337100 | − | 0.0583874i | ||||
\(881\) | 8.50000 | + | 14.7224i | 0.286372 | + | 0.496011i | 0.972941 | − | 0.231054i | \(-0.0742173\pi\) |
−0.686569 | + | 0.727065i | \(0.740884\pi\) | |||||||
\(882\) | −2.59808 | + | 1.50000i | −0.0874818 | + | 0.0505076i | ||||
\(883\) | 8.00000 | 0.269221 | 0.134611 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134611 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.00000 | −0.268917 | ||||||||
\(886\) | −17.3205 | + | 10.0000i | −0.581894 | + | 0.335957i | ||||
\(887\) | −12.0000 | − | 20.7846i | −0.402921 | − | 0.697879i | 0.591156 | − | 0.806557i | \(-0.298672\pi\) |
−0.994077 | + | 0.108678i | \(0.965338\pi\) | |||||||
\(888\) | −5.50000 | + | 9.52628i | −0.184568 | + | 0.319681i | ||||
\(889\) | 24.0000i | 0.804934i | ||||||||
\(890\) | −1.73205 | − | 1.00000i | −0.0580585 | − | 0.0335201i | ||||
\(891\) | 1.73205 | + | 1.00000i | 0.0580259 | + | 0.0335013i | ||||
\(892\) | 16.0000i | 0.535720i | ||||||||
\(893\) | 2.00000 | − | 3.46410i | 0.0669274 | − | 0.115922i | ||||
\(894\) | 1.50000 | + | 2.59808i | 0.0501675 | + | 0.0868927i | ||||
\(895\) | −5.19615 | + | 3.00000i | −0.173688 | + | 0.100279i | ||||
\(896\) | −2.00000 | −0.0668153 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 30.0000 | 1.00111 | ||||||||
\(899\) | 31.1769 | − | 18.0000i | 1.03981 | − | 0.600334i | ||||
\(900\) | 2.00000 | + | 3.46410i | 0.0666667 | + | 0.115470i | ||||
\(901\) | −2.50000 | + | 4.33013i | −0.0832871 | + | 0.144257i | ||||
\(902\) | − | 10.0000i | − | 0.332964i | ||||||
\(903\) | −17.3205 | − | 10.0000i | −0.576390 | − | 0.332779i | ||||
\(904\) | 2.59808 | + | 1.50000i | 0.0864107 | + | 0.0498893i | ||||
\(905\) | 5.00000i | 0.166206i | ||||||||
\(906\) | 3.00000 | − | 5.19615i | 0.0996683 | − | 0.172631i | ||||
\(907\) | −22.0000 | − | 38.1051i | −0.730498 | − | 1.26526i | −0.956671 | − | 0.291172i | \(-0.905955\pi\) |
0.226173 | − | 0.974087i | \(-0.427379\pi\) | |||||||
\(908\) | −12.1244 | + | 7.00000i | −0.402361 | + | 0.232303i | ||||
\(909\) | 5.00000 | 0.165840 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.0000 | −1.06021 | −0.530104 | − | 0.847933i | \(-0.677847\pi\) | ||||
−0.530104 | + | 0.847933i | \(0.677847\pi\) | |||||||
\(912\) | 1.73205 | − | 1.00000i | 0.0573539 | − | 0.0331133i | ||||
\(913\) | −6.00000 | − | 10.3923i | −0.198571 | − | 0.343935i | ||||
\(914\) | −1.50000 | + | 2.59808i | −0.0496156 | + | 0.0859367i | ||||
\(915\) | − | 11.0000i | − | 0.363649i | ||||||
\(916\) | −8.66025 | − | 5.00000i | −0.286143 | − | 0.165205i | ||||
\(917\) | 13.8564 | + | 8.00000i | 0.457579 | + | 0.264183i | ||||
\(918\) | − | 5.00000i | − | 0.165025i | ||||||
\(919\) | 8.00000 | − | 13.8564i | 0.263896 | − | 0.457081i | −0.703378 | − | 0.710816i | \(-0.748326\pi\) |
0.967274 | + | 0.253735i | \(0.0816592\pi\) | |||||||
\(920\) | 3.00000 | + | 5.19615i | 0.0989071 | + | 0.171312i | ||||
\(921\) | −12.1244 | + | 7.00000i | −0.399511 | + | 0.230658i | ||||
\(922\) | 3.00000 | 0.0987997 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 4.00000 | 0.131590 | ||||||||
\(925\) | 38.1051 | − | 22.0000i | 1.25289 | − | 0.723356i | ||||
\(926\) | −7.00000 | − | 12.1244i | −0.230034 | − | 0.398431i | ||||
\(927\) | 5.00000 | − | 8.66025i | 0.164222 | − | 0.284440i | ||||
\(928\) | 9.00000i | 0.295439i | ||||||||
\(929\) | 19.9186 | + | 11.5000i | 0.653508 | + | 0.377303i | 0.789799 | − | 0.613366i | \(-0.210185\pi\) |
−0.136291 | + | 0.990669i | \(0.543518\pi\) | |||||||
\(930\) | 3.46410 | + | 2.00000i | 0.113592 | + | 0.0655826i | ||||
\(931\) | − | 6.00000i | − | 0.196642i | ||||||
\(932\) | 3.00000 | − | 5.19615i | 0.0982683 | − | 0.170206i | ||||
\(933\) | −3.00000 | − | 5.19615i | −0.0982156 | − | 0.170114i | ||||
\(934\) | −19.0526 | + | 11.0000i | −0.623419 | + | 0.359931i | ||||
\(935\) | 10.0000 | 0.327035 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.00000 | −0.0326686 | −0.0163343 | − | 0.999867i | \(-0.505200\pi\) | ||||
−0.0163343 | + | 0.999867i | \(0.505200\pi\) | |||||||
\(938\) | 3.46410 | − | 2.00000i | 0.113107 | − | 0.0653023i | ||||
\(939\) | 3.00000 | + | 5.19615i | 0.0979013 | + | 0.169570i | ||||
\(940\) | −1.00000 | + | 1.73205i | −0.0326164 | + | 0.0564933i | ||||
\(941\) | − | 22.0000i | − | 0.717180i | −0.933495 | − | 0.358590i | \(-0.883258\pi\) | ||
0.933495 | − | 0.358590i | \(-0.116742\pi\) | |||||||
\(942\) | 6.06218 | + | 3.50000i | 0.197516 | + | 0.114036i | ||||
\(943\) | 25.9808 | + | 15.0000i | 0.846050 | + | 0.488467i | ||||
\(944\) | 8.00000i | 0.260378i | ||||||||
\(945\) | 1.00000 | − | 1.73205i | 0.0325300 | − | 0.0563436i | ||||
\(946\) | −10.0000 | − | 17.3205i | −0.325128 | − | 0.563138i | ||||
\(947\) | −6.92820 | + | 4.00000i | −0.225136 | + | 0.129983i | −0.608326 | − | 0.793687i | \(-0.708159\pi\) |
0.383190 | + | 0.923670i | \(0.374825\pi\) | |||||||
\(948\) | −4.00000 | −0.129914 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −8.00000 | −0.259554 | ||||||||
\(951\) | 28.5788 | − | 16.5000i | 0.926732 | − | 0.535049i | ||||
\(952\) | −5.00000 | − | 8.66025i | −0.162051 | − | 0.280680i | ||||
\(953\) | 27.0000 | − | 46.7654i | 0.874616 | − | 1.51488i | 0.0174443 | − | 0.999848i | \(-0.494447\pi\) |
0.857171 | − | 0.515031i | \(-0.172220\pi\) | |||||||
\(954\) | 1.00000i | 0.0323762i | ||||||||
\(955\) | 3.46410 | + | 2.00000i | 0.112096 | + | 0.0647185i | ||||
\(956\) | −5.19615 | − | 3.00000i | −0.168056 | − | 0.0970269i | ||||
\(957\) | − | 18.0000i | − | 0.581857i | ||||||
\(958\) | 16.0000 | − | 27.7128i | 0.516937 | − | 0.895360i | ||||
\(959\) | −17.0000 | − | 29.4449i | −0.548959 | − | 0.950824i | ||||
\(960\) | −0.866025 | + | 0.500000i | −0.0279508 | + | 0.0161374i | ||||
\(961\) | 15.0000 | 0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.0000 | −0.580042 | ||||||||
\(964\) | 6.06218 | − | 3.50000i | 0.195250 | − | 0.112727i | ||||
\(965\) | −8.50000 | − | 14.7224i | −0.273625 | − | 0.473932i | ||||
\(966\) | −6.00000 | + | 10.3923i | −0.193047 | + | 0.334367i | ||||
\(967\) | − | 50.0000i | − | 1.60789i | −0.594703 | − | 0.803946i | \(-0.702730\pi\) | ||
0.594703 | − | 0.803946i | \(-0.297270\pi\) | |||||||
\(968\) | −6.06218 | − | 3.50000i | −0.194846 | − | 0.112494i | ||||
\(969\) | 8.66025 | + | 5.00000i | 0.278207 | + | 0.160623i | ||||
\(970\) | 2.00000i | 0.0642161i | ||||||||
\(971\) | −10.0000 | + | 17.3205i | −0.320915 | + | 0.555842i | −0.980677 | − | 0.195633i | \(-0.937324\pi\) |
0.659762 | + | 0.751475i | \(0.270657\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | −20.7846 | + | 12.0000i | −0.666324 | + | 0.384702i | ||||
\(974\) | −26.0000 | −0.833094 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.0000 | −0.352101 | ||||||||
\(977\) | 18.1865 | − | 10.5000i | 0.581839 | − | 0.335925i | −0.180025 | − | 0.983662i | \(-0.557618\pi\) |
0.761864 | + | 0.647737i | \(0.224285\pi\) | |||||||
\(978\) | −10.0000 | − | 17.3205i | −0.319765 | − | 0.553849i | ||||
\(979\) | 2.00000 | − | 3.46410i | 0.0639203 | − | 0.110713i | ||||
\(980\) | 3.00000i | 0.0958315i | ||||||||
\(981\) | 1.73205 | + | 1.00000i | 0.0553001 | + | 0.0319275i | ||||
\(982\) | 25.9808 | + | 15.0000i | 0.829079 | + | 0.478669i | ||||
\(983\) | − | 60.0000i | − | 1.91370i | −0.290578 | − | 0.956851i | \(-0.593847\pi\) | ||
0.290578 | − | 0.956851i | \(-0.406153\pi\) | |||||||
\(984\) | −2.50000 | + | 4.33013i | −0.0796971 | + | 0.138039i | ||||
\(985\) | −3.00000 | − | 5.19615i | −0.0955879 | − | 0.165563i | ||||
\(986\) | −38.9711 | + | 22.5000i | −1.24109 | + | 0.716546i | ||||
\(987\) | −4.00000 | −0.127321 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 60.0000 | 1.90789 | ||||||||
\(990\) | 1.73205 | − | 1.00000i | 0.0550482 | − | 0.0317821i | ||||
\(991\) | −9.00000 | − | 15.5885i | −0.285894 | − | 0.495184i | 0.686931 | − | 0.726722i | \(-0.258957\pi\) |
−0.972826 | + | 0.231539i | \(0.925624\pi\) | |||||||
\(992\) | 2.00000 | − | 3.46410i | 0.0635001 | − | 0.109985i | ||||
\(993\) | 28.0000i | 0.888553i | ||||||||
\(994\) | 24.2487 | + | 14.0000i | 0.769122 | + | 0.444053i | ||||
\(995\) | −8.66025 | − | 5.00000i | −0.274549 | − | 0.158511i | ||||
\(996\) | 6.00000i | 0.190117i | ||||||||
\(997\) | 11.5000 | − | 19.9186i | 0.364209 | − | 0.630828i | −0.624440 | − | 0.781073i | \(-0.714673\pi\) |
0.988649 | + | 0.150245i | \(0.0480062\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.52628 | + | 5.50000i | −0.301398 | + | 0.174012i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))