Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,2,Mod(49,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("975.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.w (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: | \(7.78541419707\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 975.199 |
Dual form | 975.2.w.d.49.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(3\) | 0.866025 | + | 0.500000i | 0.500000 | + | 0.288675i | ||||
\(4\) | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.866025 | + | 1.50000i | 0.327327 | + | 0.566947i | 0.981981 | − | 0.188982i | \(-0.0605189\pi\) |
−0.654654 | + | 0.755929i | \(0.727186\pi\) | |||||||
\(8\) | 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 | \(-0.508234\pi\) |
−0.878668 | + | 0.477432i | \(0.841568\pi\) | |||||||
\(12\) | 2.00000i | 0.577350i | ||||||||
\(13\) | 0.866025 | + | 3.50000i | 0.240192 | + | 0.970725i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | + | 1.73205i | −0.688247 | + | 0.397360i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.73205i | 0.377964i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.19615 | + | 3.00000i | 1.08347 | + | 0.625543i | 0.931831 | − | 0.362892i | \(-0.118211\pi\) |
0.151642 | + | 0.988436i | \(0.451544\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −1.73205 | + | 3.00000i | −0.327327 | + | 0.566947i | ||||
\(29\) | 3.00000 | − | 5.19615i | 0.557086 | − | 0.964901i | −0.440652 | − | 0.897678i | \(-0.645253\pi\) |
0.997738 | − | 0.0672232i | \(-0.0214140\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.73205i | 0.311086i | 0.987829 | + | 0.155543i | \(0.0497126\pi\) | ||||
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.73205 | − | 3.00000i | −0.301511 | − | 0.522233i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | + | 1.73205i | −0.166667 | + | 0.288675i | ||||
\(37\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | + | 3.46410i | −0.160128 | + | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | − | 3.46410i | −0.937043 | − | 0.541002i | −0.0480106 | − | 0.998847i | \(-0.515288\pi\) |
−0.889032 | + | 0.457845i | \(0.848621\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.866025 | + | 0.500000i | −0.132068 | + | 0.0762493i | −0.564578 | − | 0.825380i | \(-0.690961\pi\) |
0.432511 | + | 0.901629i | \(0.357628\pi\) | |||||||
\(44\) | − | 6.92820i | − | 1.04447i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.46410 | 0.505291 | 0.252646 | − | 0.967559i | \(-0.418699\pi\) | ||||
0.252646 | + | 0.967559i | \(0.418699\pi\) | |||||||
\(48\) | −3.46410 | + | 2.00000i | −0.500000 | + | 0.288675i | ||||
\(49\) | 2.00000 | − | 3.46410i | 0.285714 | − | 0.494872i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.19615 | + | 5.00000i | −0.720577 | + | 0.693375i | ||||
\(53\) | 12.0000i | 1.64833i | 0.566352 | + | 0.824163i | \(0.308354\pi\) | ||||
−0.566352 | + | 0.824163i | \(0.691646\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.46410 | −0.458831 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.00000 | − | 1.73205i | 0.390567 | − | 0.225494i | −0.291839 | − | 0.956467i | \(-0.594267\pi\) |
0.682406 | + | 0.730974i | \(0.260934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.500000 | − | 0.866025i | −0.0640184 | − | 0.110883i | 0.832240 | − | 0.554416i | \(-0.187058\pi\) |
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.866025 | + | 1.50000i | −0.109109 | + | 0.188982i | ||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.33013 | − | 7.50000i | 0.529009 | − | 0.916271i | −0.470418 | − | 0.882443i | \(-0.655897\pi\) |
0.999428 | − | 0.0338274i | \(-0.0107696\pi\) | |||||||
\(68\) | 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 | \(-0.878185\pi\) |
−0.140441 | + | 0.990089i | \(0.544852\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.73205 | −0.202721 | −0.101361 | − | 0.994850i | \(-0.532320\pi\) | ||||
−0.101361 | + | 0.994850i | \(0.532320\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.00000 | − | 3.46410i | −0.688247 | − | 0.397360i | ||||
\(77\) | − | 6.00000i | − | 0.683763i | ||||||
\(78\) | 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 | ||||||||
\(83\) | 13.8564 | 1.52094 | 0.760469 | − | 0.649374i | \(-0.224969\pi\) | ||||
0.760469 | + | 0.649374i | \(0.224969\pi\) | |||||||
\(84\) | −3.00000 | + | 1.73205i | −0.327327 | + | 0.188982i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.19615 | − | 3.00000i | 0.557086 | − | 0.321634i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | − | 3.46410i | −0.635999 | − | 0.367194i | 0.147073 | − | 0.989126i | \(-0.453015\pi\) |
−0.783072 | + | 0.621932i | \(0.786348\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.50000 | + | 4.33013i | −0.471728 | + | 0.453921i | ||||
\(92\) | 12.0000i | 1.25109i | ||||||||
\(93\) | −0.866025 | + | 1.50000i | −0.0898027 | + | 0.155543i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.59808 | + | 4.50000i | 0.263795 | + | 0.456906i | 0.967247 | − | 0.253837i | \(-0.0816925\pi\) |
−0.703452 | + | 0.710742i | \(0.748359\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.46410i | − | 0.348155i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.00000 | − | 15.5885i | 0.895533 | − | 1.55111i | 0.0623905 | − | 0.998052i | \(-0.480128\pi\) |
0.833143 | − | 0.553058i | \(-0.186539\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.00000i | − | 0.0985329i | −0.998786 | − | 0.0492665i | \(-0.984312\pi\) | ||
0.998786 | − | 0.0492665i | \(-0.0156884\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.19615 | − | 3.00000i | −0.502331 | − | 0.290021i | 0.227345 | − | 0.973814i | \(-0.426996\pi\) |
−0.729676 | + | 0.683793i | \(0.760329\pi\) | |||||||
\(108\) | −1.73205 | + | 1.00000i | −0.166667 | + | 0.0962250i | ||||
\(109\) | 15.5885i | 1.49310i | 0.665327 | + | 0.746552i | \(0.268292\pi\) | ||||
−0.665327 | + | 0.746552i | \(0.731708\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.92820 | −0.654654 | ||||||||
\(113\) | 5.19615 | − | 3.00000i | 0.488813 | − | 0.282216i | −0.235269 | − | 0.971930i | \(-0.575597\pi\) |
0.724082 | + | 0.689714i | \(0.242264\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 12.0000 | 1.11417 | ||||||||
\(117\) | −2.59808 | + | 2.50000i | −0.240192 | + | 0.231125i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.46410 | − | 6.00000i | −0.312348 | − | 0.541002i | ||||
\(124\) | −3.00000 | + | 1.73205i | −0.269408 | + | 0.155543i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.2583 | + | 6.50000i | 0.999015 | + | 0.576782i | 0.907957 | − | 0.419064i | \(-0.137642\pi\) |
0.0910585 | + | 0.995846i | \(0.470975\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.00000 | −0.0880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | 0.524222 | 0.262111 | − | 0.965038i | \(-0.415581\pi\) | ||||
0.262111 | + | 0.965038i | \(0.415581\pi\) | |||||||
\(132\) | 3.46410 | − | 6.00000i | 0.301511 | − | 0.522233i | ||||
\(133\) | −5.19615 | − | 3.00000i | −0.450564 | − | 0.260133i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.50000 | + | 4.33013i | 0.212047 | + | 0.367277i | 0.952355 | − | 0.304991i | \(-0.0986536\pi\) |
−0.740308 | + | 0.672268i | \(0.765320\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | + | 1.73205i | 0.252646 | + | 0.145865i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.46410 | − | 12.0000i | 0.289683 | − | 1.00349i | ||||
\(144\) | −4.00000 | −0.333333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.46410 | − | 2.00000i | 0.285714 | − | 0.164957i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.00000 | − | 3.46410i | 0.491539 | − | 0.283790i | −0.233674 | − | 0.972315i | \(-0.575075\pi\) |
0.725213 | + | 0.688525i | \(0.241741\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.00000 | + | 1.73205i | −0.560449 | + | 0.138675i | ||||
\(157\) | − | 11.0000i | − | 0.877896i | −0.898513 | − | 0.438948i | \(-0.855351\pi\) | ||
0.898513 | − | 0.438948i | \(-0.144649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.00000 | + | 10.3923i | −0.475831 | + | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.3923i | 0.819028i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.52628 | − | 16.5000i | −0.746156 | − | 1.29238i | −0.949653 | − | 0.313304i | \(-0.898564\pi\) |
0.203497 | − | 0.979076i | \(-0.434769\pi\) | |||||||
\(164\) | − | 13.8564i | − | 1.08200i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.46410 | + | 6.00000i | −0.268060 | + | 0.464294i | −0.968361 | − | 0.249554i | \(-0.919716\pi\) |
0.700301 | + | 0.713848i | \(0.253049\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5000 | + | 6.06218i | −0.884615 | + | 0.466321i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | − | 1.73205i | −0.229416 | − | 0.132453i | ||||
\(172\) | −1.73205 | − | 1.00000i | −0.132068 | − | 0.0762493i | ||||
\(173\) | −5.19615 | + | 3.00000i | −0.395056 | + | 0.228086i | −0.684349 | − | 0.729155i | \(-0.739913\pi\) |
0.289292 | + | 0.957241i | \(0.406580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12.0000 | − | 6.92820i | 0.904534 | − | 0.522233i | ||||
\(177\) | 3.46410 | 0.260378 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00000 | − | 10.3923i | 0.448461 | − | 0.776757i | −0.549825 | − | 0.835280i | \(-0.685306\pi\) |
0.998286 | + | 0.0585225i | \(0.0186389\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1.00000i | − | 0.0739221i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.46410 | + | 6.00000i | 0.252646 | + | 0.437595i | ||||
\(189\) | −1.50000 | + | 0.866025i | −0.109109 | + | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.00000 | + | 15.5885i | 0.651217 | + | 1.12794i | 0.982828 | + | 0.184525i | \(0.0590746\pi\) |
−0.331611 | + | 0.943416i | \(0.607592\pi\) | |||||||
\(192\) | −6.92820 | − | 4.00000i | −0.500000 | − | 0.288675i | ||||
\(193\) | 7.79423 | − | 13.5000i | 0.561041 | − | 0.971751i | −0.436365 | − | 0.899770i | \(-0.643734\pi\) |
0.997406 | − | 0.0719816i | \(-0.0229323\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.00000 | 0.571429 | ||||||||
\(197\) | 6.92820 | − | 12.0000i | 0.493614 | − | 0.854965i | −0.506359 | − | 0.862323i | \(-0.669009\pi\) |
0.999973 | + | 0.00735824i | \(0.00234222\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.50000 | + | 6.06218i | 0.248108 | + | 0.429736i | 0.963001 | − | 0.269498i | \(-0.0868577\pi\) |
−0.714893 | + | 0.699234i | \(0.753524\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.50000 | − | 4.33013i | 0.529009 | − | 0.305424i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.3923 | 0.729397 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.00000i | 0.417029i | ||||||||
\(208\) | −13.8564 | − | 4.00000i | −0.960769 | − | 0.277350i | ||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.50000 | + | 11.2583i | −0.447478 | + | 0.775055i | −0.998221 | − | 0.0596196i | \(-0.981011\pi\) |
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | −20.7846 | + | 12.0000i | −1.42749 | + | 0.824163i | ||||
\(213\) | −10.3923 | −0.712069 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.59808 | + | 1.50000i | −0.176369 | + | 0.101827i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.50000 | − | 0.866025i | −0.101361 | − | 0.0585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.66025 | + | 15.0000i | −0.579934 | + | 1.00447i | 0.415553 | + | 0.909569i | \(0.363588\pi\) |
−0.995486 | + | 0.0949052i | \(0.969745\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.3923 | − | 18.0000i | −0.689761 | − | 1.19470i | −0.971915 | − | 0.235333i | \(-0.924382\pi\) |
0.282153 | − | 0.959369i | \(-0.408951\pi\) | |||||||
\(228\) | −3.46410 | − | 6.00000i | −0.229416 | − | 0.397360i | ||||
\(229\) | − | 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 | ||||||||
\(233\) | − | 18.0000i | − | 1.17922i | −0.807688 | − | 0.589610i | \(-0.799282\pi\) | ||
0.807688 | − | 0.589610i | \(-0.200718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.00000 | + | 3.46410i | 0.390567 | + | 0.225494i | ||||
\(237\) | 9.52628 | + | 5.50000i | 0.618798 | + | 0.357263i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.0000 | − | 10.3923i | 1.15948 | − | 0.669427i | 0.208302 | − | 0.978065i | \(-0.433206\pi\) |
0.951180 | + | 0.308637i | \(0.0998729\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.866025 | + | 0.500000i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | 1.00000 | − | 1.73205i | 0.0640184 | − | 0.110883i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.66025 | − | 9.00000i | −0.551039 | − | 0.572656i | ||||
\(248\) | 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 | \(-0.290301\pi\) |
−0.990876 | + | 0.134778i | \(0.956968\pi\) | |||||||
\(252\) | −3.46410 | −0.218218 | ||||||||
\(253\) | −10.3923 | − | 18.0000i | −0.653359 | − | 1.13165i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | 0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.3923 | − | 6.00000i | −0.640817 | − | 0.369976i | 0.144112 | − | 0.989561i | \(-0.453967\pi\) |
−0.784929 | + | 0.619586i | \(0.787301\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.46410 | − | 6.00000i | −0.212000 | − | 0.367194i | ||||
\(268\) | 17.3205 | 1.05802 | ||||||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.50000 | − | 2.59808i | −0.273356 | − | 0.157822i | 0.357056 | − | 0.934083i | \(-0.383781\pi\) |
−0.630412 | + | 0.776261i | \(0.717114\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.06218 | + | 1.50000i | −0.366900 | + | 0.0907841i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.00000 | + | 10.3923i | −0.361158 | + | 0.625543i | ||||
\(277\) | 8.66025 | − | 5.00000i | 0.520344 | − | 0.300421i | −0.216731 | − | 0.976231i | \(-0.569540\pi\) |
0.737075 | + | 0.675810i | \(0.236206\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.50000 | + | 0.866025i | −0.0898027 | + | 0.0518476i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 24.2487i | − | 1.44656i | −0.690557 | − | 0.723278i | \(-0.742634\pi\) | ||
0.690557 | − | 0.723278i | \(-0.257366\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.52628 | + | 5.50000i | 0.566279 | + | 0.326941i | 0.755662 | − | 0.654962i | \(-0.227315\pi\) |
−0.189383 | + | 0.981903i | \(0.560649\pi\) | |||||||
\(284\) | −18.0000 | − | 10.3923i | −1.06810 | − | 0.616670i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 12.0000i | − | 0.708338i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.50000 | + | 14.7224i | −0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.19615i | 0.304604i | ||||||||
\(292\) | −1.73205 | − | 3.00000i | −0.101361 | − | 0.175562i | ||||
\(293\) | −8.66025 | − | 15.0000i | −0.505937 | − | 0.876309i | −0.999976 | − | 0.00686959i | \(-0.997813\pi\) |
0.494039 | − | 0.869440i | \(-0.335520\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.73205 | − | 3.00000i | 0.100504 | − | 0.174078i | ||||
\(298\) | 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 | ||||||||
\(303\) | 15.5885 | − | 9.00000i | 0.895533 | − | 0.517036i | ||||
\(304\) | − | 13.8564i | − | 0.794719i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.73205 | −0.0988534 | −0.0494267 | − | 0.998778i | \(-0.515739\pi\) | ||||
−0.0494267 | + | 0.998778i | \(0.515739\pi\) | |||||||
\(308\) | 10.3923 | − | 6.00000i | 0.592157 | − | 0.341882i | ||||
\(309\) | 0.500000 | − | 0.866025i | 0.0284440 | − | 0.0492665i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.0000i | 0.734803i | 0.930062 | + | 0.367402i | \(0.119753\pi\) | ||||
−0.930062 | + | 0.367402i | \(0.880247\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.0000 | + | 19.0526i | 0.618798 | + | 1.07179i | ||||
\(317\) | 6.92820 | 0.389127 | 0.194563 | − | 0.980890i | \(-0.437671\pi\) | ||||
0.194563 | + | 0.980890i | \(0.437671\pi\) | |||||||
\(318\) | 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 | ||||||||
\(324\) | −2.00000 | −0.111111 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.79423 | + | 13.5000i | −0.431022 | + | 0.746552i | ||||
\(328\) | 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 | \(-0.621055\pi\) |
0.618547 | + | 0.785748i | \(0.287722\pi\) | |||||||
\(332\) | 13.8564 | + | 24.0000i | 0.760469 | + | 1.31717i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.00000 | − | 3.46410i | −0.327327 | − | 0.188982i | ||||
\(337\) | 5.00000i | 0.272367i | 0.990684 | + | 0.136184i | \(0.0434837\pi\) | ||||
−0.990684 | + | 0.136184i | \(0.956516\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.00000 | − | 5.19615i | 0.162459 | − | 0.281387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.0526 | 1.02874 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.7846 | − | 12.0000i | 1.11578 | − | 0.644194i | 0.175457 | − | 0.984487i | \(-0.443860\pi\) |
0.940319 | + | 0.340293i | \(0.110526\pi\) | |||||||
\(348\) | 10.3923 | + | 6.00000i | 0.557086 | + | 0.321634i | ||||
\(349\) | 16.5000 | + | 9.52628i | 0.883225 | + | 0.509930i | 0.871720 | − | 0.490004i | \(-0.163005\pi\) |
0.0115044 | + | 0.999934i | \(0.496338\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.50000 | + | 0.866025i | −0.186816 | + | 0.0462250i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.19615 | + | 9.00000i | −0.276563 | + | 0.479022i | −0.970528 | − | 0.240987i | \(-0.922529\pi\) |
0.693965 | + | 0.720009i | \(0.255862\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 13.8564i | − | 0.734388i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6.92820i | − | 0.365657i | −0.983145 | − | 0.182828i | \(-0.941475\pi\) | ||
0.983145 | − | 0.182828i | \(-0.0585252\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.50000 | + | 6.06218i | −0.184211 | + | 0.319062i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00000i | 0.0524864i | ||||||||
\(364\) | −12.0000 | − | 3.46410i | −0.628971 | − | 0.181568i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.7224 | + | 8.50000i | 0.768505 | + | 0.443696i | 0.832341 | − | 0.554264i | \(-0.187000\pi\) |
−0.0638362 | + | 0.997960i | \(0.520334\pi\) | |||||||
\(368\) | −20.7846 | + | 12.0000i | −1.08347 | + | 0.625543i | ||||
\(369\) | − | 6.92820i | − | 0.360668i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.0000 | + | 10.3923i | −0.934513 | + | 0.539542i | ||||
\(372\) | −3.46410 | −0.179605 | ||||||||
\(373\) | −9.52628 | + | 5.50000i | −0.493252 | + | 0.284779i | −0.725923 | − | 0.687776i | \(-0.758587\pi\) |
0.232671 | + | 0.972556i | \(0.425254\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.7846 | + | 6.00000i | 1.07046 | + | 0.309016i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.5000 | + | 11.2583i | 1.00165 | + | 0.578302i | 0.908735 | − | 0.417373i | \(-0.137049\pi\) |
0.0929123 | + | 0.995674i | \(0.470382\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.50000 | + | 11.2583i | 0.333005 | + | 0.576782i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.8564 | + | 24.0000i | 0.708029 | + | 1.22634i | 0.965587 | + | 0.260080i | \(0.0837489\pi\) |
−0.257558 | + | 0.966263i | \(0.582918\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.866025 | − | 0.500000i | −0.0440225 | − | 0.0254164i | ||||
\(388\) | −5.19615 | + | 9.00000i | −0.263795 | + | 0.456906i | ||||
\(389\) | −12.0000 | −0.608424 | −0.304212 | − | 0.952604i | \(-0.598393\pi\) | ||||
−0.304212 | + | 0.952604i | \(0.598393\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.19615 | + | 3.00000i | 0.262111 | + | 0.151330i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.00000 | − | 3.46410i | 0.301511 | − | 0.174078i | ||||
\(397\) | −7.79423 | − | 13.5000i | −0.391181 | − | 0.677546i | 0.601424 | − | 0.798930i | \(-0.294600\pi\) |
−0.992606 | + | 0.121384i | \(0.961267\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.00000 | − | 5.19615i | −0.150188 | − | 0.260133i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.06218 | + | 1.50000i | −0.301979 | + | 0.0747203i | ||||
\(404\) | 36.0000 | 1.79107 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.50000 | + | 4.33013i | −0.370851 | + | 0.214111i | −0.673830 | − | 0.738886i | \(-0.735352\pi\) |
0.302979 | + | 0.952997i | \(0.402019\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.73205 | − | 1.00000i | 0.0853320 | − | 0.0492665i | ||||
\(413\) | 5.19615 | + | 3.00000i | 0.255686 | + | 0.147620i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.00000i | 0.244851i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.00000 | + | 10.3923i | −0.293119 | + | 0.507697i | −0.974546 | − | 0.224189i | \(-0.928027\pi\) |
0.681426 | + | 0.731887i | \(0.261360\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 12.1244i | − | 0.590905i | −0.955357 | − | 0.295452i | \(-0.904530\pi\) | ||
0.955357 | − | 0.295452i | \(-0.0954704\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.73205 | + | 3.00000i | 0.0842152 | + | 0.145865i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.866025 | − | 1.50000i | 0.0419099 | − | 0.0725901i | ||||
\(428\) | − | 12.0000i | − | 0.580042i | ||||||
\(429\) | 9.00000 | − | 8.66025i | 0.434524 | − | 0.418121i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.0000 | + | 10.3923i | 0.867029 | + | 0.500580i | 0.866360 | − | 0.499420i | \(-0.166454\pi\) |
0.000669521 | 1.00000i | \(0.499787\pi\) | ||||||||
\(432\) | −3.46410 | − | 2.00000i | −0.166667 | − | 0.0962250i | ||||
\(433\) | −19.9186 | + | 11.5000i | −0.957226 | + | 0.552655i | −0.895318 | − | 0.445427i | \(-0.853052\pi\) |
−0.0619079 | + | 0.998082i | \(0.519718\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −27.0000 | + | 15.5885i | −1.29307 | + | 0.746552i | ||||
\(437\) | −20.7846 | −0.994263 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.5000 | − | 30.3109i | 0.835229 | − | 1.44666i | −0.0586141 | − | 0.998281i | \(-0.518668\pi\) |
0.893843 | − | 0.448379i | \(-0.147999\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.00000 | 0.190476 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.0000i | 1.14027i | 0.821549 | + | 0.570137i | \(0.193110\pi\) | ||||
−0.821549 | + | 0.570137i | \(0.806890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.92820 | 0.327693 | ||||||||
\(448\) | −6.92820 | − | 12.0000i | −0.327327 | − | 0.566947i | ||||
\(449\) | −33.0000 | + | 19.0526i | −1.55737 | + | 0.899146i | −0.559859 | + | 0.828588i | \(0.689145\pi\) |
−0.997508 | + | 0.0705577i | \(0.977522\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | + | 20.7846i | 0.565058 | + | 0.978709i | ||||
\(452\) | 10.3923 | + | 6.00000i | 0.488813 | + | 0.282216i | ||||
\(453\) | 1.73205 | − | 3.00000i | 0.0813788 | − | 0.140952i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.1865 | + | 31.5000i | −0.850730 | + | 1.47351i | 0.0298202 | + | 0.999555i | \(0.490507\pi\) |
−0.880550 | + | 0.473953i | \(0.842827\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.0000 | + | 20.7846i | −1.67669 | + | 0.968036i | −0.712938 | + | 0.701228i | \(0.752636\pi\) |
−0.963750 | + | 0.266808i | \(0.914031\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.3731 | 1.69040 | 0.845200 | − | 0.534450i | \(-0.179481\pi\) | ||||
0.845200 | + | 0.534450i | \(0.179481\pi\) | |||||||
\(464\) | 12.0000 | + | 20.7846i | 0.557086 | + | 0.964901i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 6.00000i | − | 0.277647i | −0.990317 | − | 0.138823i | \(-0.955668\pi\) | ||
0.990317 | − | 0.138823i | \(-0.0443321\pi\) | |||||||
\(468\) | −6.92820 | − | 2.00000i | −0.320256 | − | 0.0924500i | ||||
\(469\) | 15.0000 | 0.692636 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.50000 | − | 9.52628i | 0.253427 | − | 0.438948i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.46410 | 0.159280 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.3923 | + | 6.00000i | −0.475831 | + | 0.274721i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.0000 | − | 17.3205i | −1.37073 | − | 0.791394i | −0.379714 | − | 0.925104i | \(-0.623978\pi\) |
−0.991021 | + | 0.133710i | \(0.957311\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.19615 | + | 9.00000i | −0.236433 | + | 0.409514i | ||||
\(484\) | −1.00000 | + | 1.73205i | −0.0454545 | + | 0.0787296i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.1244 | + | 21.0000i | 0.549407 | + | 0.951601i | 0.998315 | + | 0.0580230i | \(0.0184797\pi\) |
−0.448908 | + | 0.893578i | \(0.648187\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 19.0526i | − | 0.861586i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.00000 | + | 5.19615i | −0.135388 | + | 0.234499i | −0.925746 | − | 0.378147i | \(-0.876561\pi\) |
0.790358 | + | 0.612646i | \(0.209895\pi\) | |||||||
\(492\) | 6.92820 | − | 12.0000i | 0.312348 | − | 0.541002i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.00000 | − | 3.46410i | −0.269408 | − | 0.155543i | ||||
\(497\) | −15.5885 | − | 9.00000i | −0.699238 | − | 0.403705i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 31.1769i | − | 1.39567i | −0.716258 | − | 0.697835i | \(-0.754147\pi\) | ||
0.716258 | − | 0.697835i | \(-0.245853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | + | 3.46410i | −0.268060 | + | 0.154765i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.9808 | + | 15.0000i | −1.15842 | + | 0.668817i | −0.950926 | − | 0.309418i | \(-0.899866\pi\) |
−0.207499 | + | 0.978235i | \(0.566532\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.9904 | − | 0.500000i | −0.576923 | − | 0.0222058i | ||||
\(508\) | 26.0000i | 1.15356i | ||||||||
\(509\) | 15.0000 | + | 8.66025i | 0.664863 | + | 0.383859i | 0.794128 | − | 0.607751i | \(-0.207928\pi\) |
−0.129264 | + | 0.991610i | \(0.541262\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.50000 | − | 2.59808i | −0.0663561 | − | 0.114932i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.73205 | − | 3.00000i | −0.0764719 | − | 0.132453i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.00000 | − | 1.73205i | −0.0440225 | − | 0.0762493i | ||||
\(517\) | −10.3923 | − | 6.00000i | −0.457053 | − | 0.263880i | ||||
\(518\) | 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 | ||||||||
\(523\) | 24.2487 | + | 14.0000i | 1.06032 | + | 0.612177i | 0.925521 | − | 0.378695i | \(-0.123627\pi\) |
0.134801 | + | 0.990873i | \(0.456961\pi\) | |||||||
\(524\) | 6.00000 | + | 10.3923i | 0.262111 | + | 0.453990i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 13.8564 | 0.603023 | ||||||||
\(529\) | 6.50000 | + | 11.2583i | 0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.00000 | + | 1.73205i | 0.130189 | + | 0.0751646i | ||||
\(532\) | − | 12.0000i | − | 0.520266i | ||||||
\(533\) | 6.92820 | − | 24.0000i | 0.300094 | − | 1.03956i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.3923 | − | 6.00000i | 0.448461 | − | 0.258919i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.0000 | + | 6.92820i | −0.516877 | + | 0.298419i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 29.4449i | − | 1.26593i | −0.774179 | − | 0.632967i | \(-0.781837\pi\) | ||
0.774179 | − | 0.632967i | \(-0.218163\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.1244 | + | 7.00000i | 0.520306 | + | 0.300399i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.0000i | 0.812381i | 0.913788 | + | 0.406191i | \(0.133143\pi\) | ||||
−0.913788 | + | 0.406191i | \(0.866857\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.500000 | − | 0.866025i | 0.0213395 | − | 0.0369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.7846i | 0.885454i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.52628 | + | 16.5000i | 0.405099 | + | 0.701651i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.00000 | + | 8.66025i | −0.212047 | + | 0.367277i | ||||
\(557\) | −13.8564 | + | 24.0000i | −0.587115 | + | 1.01691i | 0.407493 | + | 0.913208i | \(0.366403\pi\) |
−0.994608 | + | 0.103704i | \(0.966930\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.50000 | − | 2.59808i | −0.105739 | − | 0.109887i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.3731 | + | 21.0000i | −1.53294 | + | 0.885044i | −0.533718 | + | 0.845663i | \(0.679206\pi\) |
−0.999224 | + | 0.0393818i | \(0.987461\pi\) | |||||||
\(564\) | 6.92820i | 0.291730i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.73205 | −0.0727393 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.00000 | + | 5.19615i | −0.125767 | + | 0.217834i | −0.922032 | − | 0.387113i | \(-0.873472\pi\) |
0.796266 | + | 0.604947i | \(0.206806\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.0000 | −1.84134 | −0.920671 | − | 0.390339i | \(-0.872358\pi\) | ||||
−0.920671 | + | 0.390339i | \(0.872358\pi\) | |||||||
\(572\) | 24.2487 | − | 6.00000i | 1.01389 | − | 0.250873i | ||||
\(573\) | 18.0000i | 0.751961i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.00000 | − | 6.92820i | −0.166667 | − | 0.288675i | ||||
\(577\) | −34.6410 | −1.44212 | −0.721062 | − | 0.692870i | \(-0.756346\pi\) | ||||
−0.721062 | + | 0.692870i | \(0.756346\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | 20.7846 | − | 36.0000i | 0.860811 | − | 1.49097i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.5885 | + | 27.0000i | −0.643404 | + | 1.11441i | 0.341263 | + | 0.939968i | \(0.389145\pi\) |
−0.984668 | + | 0.174441i | \(0.944188\pi\) | |||||||
\(588\) | 6.92820 | + | 4.00000i | 0.285714 | + | 0.164957i | ||||
\(589\) | −3.00000 | − | 5.19615i | −0.123613 | − | 0.214104i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.0000 | − | 6.92820i | 0.493614 | − | 0.284988i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.46410 | −0.142254 | −0.0711268 | − | 0.997467i | \(-0.522659\pi\) | ||||
−0.0711268 | + | 0.997467i | \(0.522659\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.0000 | + | 6.92820i | 0.491539 | + | 0.283790i | ||||
\(597\) | 7.00000i | 0.286491i | ||||||||
\(598\) | 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 | −0.469095 | − | 0.883148i | \(-0.655420\pi\) |
0.999376 | − | 0.0353259i | \(-0.0112469\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.66025 | 0.352673 | ||||||||
\(604\) | 6.00000 | − | 3.46410i | 0.244137 | − | 0.140952i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.92820 | + | 4.00000i | −0.281207 | + | 0.162355i | −0.633970 | − | 0.773358i | \(-0.718576\pi\) |
0.352763 | + | 0.935713i | \(0.385242\pi\) | |||||||
\(608\) | 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 | ||||||||
\(613\) | −4.33013 | + | 7.50000i | −0.174892 | + | 0.302922i | −0.940124 | − | 0.340833i | \(-0.889291\pi\) |
0.765232 | + | 0.643755i | \(0.222624\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.19615 | + | 9.00000i | 0.209189 | + | 0.362326i | 0.951459 | − | 0.307774i | \(-0.0995842\pi\) |
−0.742270 | + | 0.670101i | \(0.766251\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 25.9808i | − | 1.04425i | −0.852867 | − | 0.522127i | \(-0.825139\pi\) | ||
0.852867 | − | 0.522127i | \(-0.174861\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.00000 | + | 5.19615i | −0.120386 | + | 0.208514i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 12.0000i | − | 0.480770i | ||||||
\(624\) | −10.0000 | − | 10.3923i | −0.400320 | − | 0.416025i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.3923 | + | 6.00000i | 0.415029 | + | 0.239617i | ||||
\(628\) | 19.0526 | − | 11.0000i | 0.760280 | − | 0.438948i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.50000 | − | 0.866025i | 0.0597141 | − | 0.0344759i | −0.469846 | − | 0.882749i | \(-0.655690\pi\) |
0.529560 | + | 0.848273i | \(0.322357\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.2583 | + | 6.50000i | −0.447478 | + | 0.258352i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −24.0000 | −0.951662 | ||||||||
\(637\) | 13.8564 | + | 4.00000i | 0.549011 | + | 0.158486i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.00000 | − | 5.19615i | −0.356034 | − | 0.205557i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.00000 | − | 15.5885i | −0.355479 | − | 0.615707i | 0.631721 | − | 0.775196i | \(-0.282349\pi\) |
−0.987200 | + | 0.159489i | \(0.949015\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.52628 | + | 16.5000i | 0.375680 | + | 0.650696i | 0.990429 | − | 0.138027i | \(-0.0440759\pi\) |
−0.614749 | + | 0.788723i | \(0.710743\pi\) | |||||||
\(644\) | −18.0000 | + | 10.3923i | −0.709299 | + | 0.409514i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.5885 | − | 9.00000i | −0.612845 | − | 0.353827i | 0.161233 | − | 0.986916i | \(-0.448453\pi\) |
−0.774078 | + | 0.633090i | \(0.781786\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.0000 | −0.471041 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.00000 | −0.117579 | ||||||||
\(652\) | 19.0526 | − | 33.0000i | 0.746156 | − | 1.29238i | ||||
\(653\) | −31.1769 | − | 18.0000i | −1.22005 | − | 0.704394i | −0.255119 | − | 0.966910i | \(-0.582115\pi\) |
−0.964928 | + | 0.262515i | \(0.915448\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 24.0000 | − | 13.8564i | 0.937043 | − | 0.541002i | ||||
\(657\) | −0.866025 | − | 1.50000i | −0.0337869 | − | 0.0585206i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.0000 | + | 41.5692i | 0.934907 | + | 1.61931i | 0.774799 | + | 0.632207i | \(0.217851\pi\) |
0.160108 | + | 0.987099i | \(0.448816\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.5000 | − | 12.9904i | −0.875149 | − | 0.505267i | −0.00609283 | − | 0.999981i | \(-0.501939\pi\) |
−0.869056 | + | 0.494714i | \(0.835273\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.1769 | − | 18.0000i | 1.20717 | − | 0.696963i | ||||
\(668\) | −13.8564 | −0.536120 | ||||||||
\(669\) | −15.0000 | + | 8.66025i | −0.579934 | + | 0.334825i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.46410i | 0.133730i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.866025 | + | 0.500000i | 0.0333828 | + | 0.0192736i | 0.516599 | − | 0.856228i | \(-0.327198\pi\) |
−0.483216 | + | 0.875501i | \(0.660531\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.0000 | − | 13.8564i | −0.846154 | − | 0.532939i | ||||
\(677\) | − | 48.0000i | − | 1.84479i | −0.386248 | − | 0.922395i | \(-0.626229\pi\) | ||
0.386248 | − | 0.922395i | \(-0.373771\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.50000 | + | 7.79423i | −0.172694 | + | 0.299115i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 20.7846i | − | 0.796468i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.1244 | + | 21.0000i | 0.463926 | + | 0.803543i | 0.999152 | − | 0.0411658i | \(-0.0131072\pi\) |
−0.535227 | + | 0.844708i | \(0.679774\pi\) | |||||||
\(684\) | − | 6.92820i | − | 0.264906i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.8564 | − | 24.0000i | 0.528655 | − | 0.915657i | ||||
\(688\) | − | 4.00000i | − | 0.152499i | ||||||
\(689\) | −42.0000 | + | 10.3923i | −1.60007 | + | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.5000 | + | 21.6506i | 1.42657 | + | 0.823629i | 0.996848 | − | 0.0793336i | \(-0.0252792\pi\) |
0.429719 | + | 0.902963i | \(0.358613\pi\) | |||||||
\(692\) | −10.3923 | − | 6.00000i | −0.395056 | − | 0.228086i | ||||
\(693\) | 5.19615 | − | 3.00000i | 0.197386 | − | 0.113961i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 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 | ||||||||
\(704\) | 24.0000 | + | 13.8564i | 0.904534 | + | 0.522233i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.1769 | 1.17253 | ||||||||
\(708\) | 3.46410 | + | 6.00000i | 0.130189 | + | 0.225494i | ||||
\(709\) | 16.5000 | − | 9.52628i | 0.619671 | − | 0.357767i | −0.157070 | − | 0.987587i | \(-0.550205\pi\) |
0.776741 | + | 0.629821i | \(0.216872\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.50000 | + | 9.52628i | 0.206266 | + | 0.357263i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.19615 | + | 9.00000i | −0.194597 | + | 0.337053i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.0000 | 0.896922 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.00000 | − | 5.19615i | −0.111881 | − | 0.193784i | 0.804648 | − | 0.593753i | \(-0.202354\pi\) |
−0.916529 | + | 0.399969i | \(0.869021\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.50000 | − | 0.866025i | 0.0558629 | − | 0.0322525i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.7846 | 0.772988 | ||||||||
\(724\) | 14.0000 | + | 24.2487i | 0.520306 | + | 0.901196i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.0000i | 1.29808i | 0.760755 | + | 0.649039i | \(0.224829\pi\) | ||||
−0.760755 | + | 0.649039i | \(0.775171\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1.73205 | − | 1.00000i | 0.0640184 | − | 0.0369611i | ||||
\(733\) | −39.8372 | −1.47142 | −0.735710 | − | 0.677297i | \(-0.763151\pi\) | ||||
−0.735710 | + | 0.677297i | \(0.763151\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.9808 | + | 15.0000i | −0.957014 | + | 0.552532i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.0000 | − | 22.5167i | −1.43464 | − | 0.828289i | −0.437168 | − | 0.899380i | \(-0.644019\pi\) |
−0.997470 | + | 0.0710909i | \(0.977352\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.00000 | − | 12.1244i | −0.110208 | − | 0.445399i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.19615 | − | 9.00000i | 0.190628 | − | 0.330178i | −0.754830 | − | 0.655920i | \(-0.772281\pi\) |
0.945459 | + | 0.325742i | \(0.105614\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.92820 | + | 12.0000i | 0.253490 | + | 0.439057i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 10.3923i | − | 0.379727i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.00000 | + | 6.92820i | −0.145962 | + | 0.252814i | −0.929731 | − | 0.368238i | \(-0.879961\pi\) |
0.783769 | + | 0.621052i | \(0.213294\pi\) | |||||||
\(752\) | −6.92820 | + | 12.0000i | −0.252646 | + | 0.437595i | ||||
\(753\) | − | 12.0000i | − | 0.437304i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.00000 | − | 1.73205i | −0.109109 | − | 0.0629941i | ||||
\(757\) | 29.4449 | + | 17.0000i | 1.07019 | + | 0.617876i | 0.928234 | − | 0.371997i | \(-0.121327\pi\) |
0.141958 | + | 0.989873i | \(0.454660\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 20.7846i | − | 0.754434i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.0000 | + | 10.3923i | −0.652499 | + | 0.376721i | −0.789413 | − | 0.613862i | \(-0.789615\pi\) |
0.136914 | + | 0.990583i | \(0.456282\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.3827 | + | 13.5000i | −0.846510 | + | 0.488733i | ||||
\(764\) | −18.0000 | + | 31.1769i | −0.651217 | + | 1.12794i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.66025 | + | 9.00000i | 0.312704 | + | 0.324971i | ||||
\(768\) | − | 16.0000i | − | 0.577350i | ||||||
\(769\) | 6.00000 | + | 3.46410i | 0.216366 | + | 0.124919i | 0.604266 | − | 0.796782i | \(-0.293466\pi\) |
−0.387901 | + | 0.921701i | \(0.626800\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 31.1769 | 1.12208 | ||||||||
\(773\) | −25.9808 | − | 45.0000i | −0.934463 | − | 1.61854i | −0.775589 | − | 0.631239i | \(-0.782547\pi\) |
−0.158874 | − | 0.987299i | \(-0.550787\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.0000 | 0.859889 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0000 | 1.28818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.19615 | + | 3.00000i | 0.185695 | + | 0.107211i | ||||
\(784\) | 8.00000 | + | 13.8564i | 0.285714 | + | 0.494872i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.4545 | − | 28.5000i | −0.586539 | − | 1.01592i | −0.994682 | − | 0.102997i | \(-0.967157\pi\) |
0.408143 | − | 0.912918i | \(-0.366177\pi\) | |||||||
\(788\) | 27.7128 | 0.987228 | ||||||||
\(789\) | −6.00000 | − | 10.3923i | −0.213606 | − | 0.369976i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.00000 | + | 5.19615i | 0.320003 | + | 0.184754i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.59808 | − | 2.50000i | 0.0922604 | − | 0.0887776i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.00000 | + | 12.1244i | −0.248108 | + | 0.429736i | ||||
\(797\) | −10.3923 | + | 6.00000i | −0.368114 | + | 0.212531i | −0.672634 | − | 0.739975i | \(-0.734837\pi\) |
0.304520 | + | 0.952506i | \(0.401504\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 6.92820i | − | 0.244796i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.19615 | + | 3.00000i | 0.183368 | + | 0.105868i | ||||
\(804\) | 15.0000 | + | 8.66025i | 0.529009 | + | 0.305424i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.00000 | − | 10.3923i | 0.210949 | − | 0.365374i | −0.741063 | − | 0.671436i | \(-0.765678\pi\) |
0.952012 | + | 0.306062i | \(0.0990113\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 25.9808i | − | 0.912308i | −0.889901 | − | 0.456154i | \(-0.849227\pi\) | ||
0.889901 | − | 0.456154i | \(-0.150773\pi\) | |||||||
\(812\) | 10.3923 | + | 18.0000i | 0.364698 | + | 0.631676i | ||||
\(813\) | −2.59808 | − | 4.50000i | −0.0911185 | − | 0.157822i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.73205 | − | 3.00000i | 0.0605968 | − | 0.104957i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.00000 | − | 1.73205i | −0.209657 | − | 0.0605228i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.0000 | + | 12.1244i | 0.732905 | + | 0.423143i | 0.819484 | − | 0.573102i | \(-0.194260\pi\) |
−0.0865789 | + | 0.996245i | \(0.527593\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.7128 | − | 16.0000i | 0.966008 | − | 0.557725i | 0.0679910 | − | 0.997686i | \(-0.478341\pi\) |
0.898017 | + | 0.439961i | \(0.145008\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.4974 | 1.68642 | 0.843210 | − | 0.537584i | \(-0.180663\pi\) | ||||
0.843210 | + | 0.537584i | \(0.180663\pi\) | |||||||
\(828\) | −10.3923 | + | 6.00000i | −0.361158 | + | 0.208514i | ||||
\(829\) | 15.5000 | − | 26.8468i | 0.538337 | − | 0.932427i | −0.460657 | − | 0.887578i | \(-0.652386\pi\) |
0.998994 | − | 0.0448490i | \(-0.0142807\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.0000 | 0.346896 | ||||||||
\(832\) | −6.92820 | − | 28.0000i | −0.240192 | − | 0.970725i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.0000 | + | 20.7846i | 0.415029 | + | 0.718851i | ||||
\(837\) | −1.73205 | −0.0598684 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.0000 | + | 15.5885i | −0.932144 | + | 0.538173i | −0.887489 | − | 0.460829i | \(-0.847552\pi\) |
−0.0446547 | + | 0.999002i | \(0.514219\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | − | 6.06218i | −0.120690 | − | 0.209041i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.1244 | − | 21.0000i | 0.417585 | − | 0.723278i | ||||
\(844\) | −26.0000 | −0.894957 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.866025 | + | 1.50000i | −0.0297570 | + | 0.0515406i | ||||
\(848\) | −41.5692 | − | 24.0000i | −1.42749 | − | 0.824163i | ||||
\(849\) | 5.50000 | + | 9.52628i | 0.188760 | + | 0.326941i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −10.3923 | − | 18.0000i | −0.356034 | − | 0.616670i | ||||
\(853\) | 25.9808 | 0.889564 | 0.444782 | − | 0.895639i | \(-0.353281\pi\) | ||||
0.444782 | + | 0.895639i | \(0.353281\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 18.0000i | − | 0.614868i | −0.951569 | − | 0.307434i | \(-0.900530\pi\) | ||
0.951569 | − | 0.307434i | \(-0.0994704\pi\) | |||||||
\(858\) | 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 | ||||||||
\(863\) | 17.3205 | 0.589597 | 0.294798 | − | 0.955559i | \(-0.404747\pi\) | ||||
0.294798 | + | 0.955559i | \(0.404747\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.7224 | + | 8.50000i | −0.500000 | + | 0.288675i | ||||
\(868\) | −5.19615 | − | 3.00000i | −0.176369 | − | 0.101827i | ||||
\(869\) | −33.0000 | − | 19.0526i | −1.11945 | − | 0.646314i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.0000 | + | 8.66025i | 1.01651 | + | 0.293442i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.59808 | + | 4.50000i | −0.0879316 | + | 0.152302i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 3.46410i | − | 0.117041i | ||||||
\(877\) | −20.7846 | − | 36.0000i | −0.701846 | − | 1.21563i | −0.967818 | − | 0.251653i | \(-0.919026\pi\) |
0.265971 | − | 0.963981i | \(-0.414307\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 17.3205i | − | 0.584206i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.00000 | − | 10.3923i | 0.202145 | − | 0.350126i | −0.747074 | − | 0.664741i | \(-0.768542\pi\) |
0.949219 | + | 0.314615i | \(0.101875\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 5.00000i | − | 0.168263i | −0.996455 | − | 0.0841317i | \(-0.973188\pi\) | ||
0.996455 | − | 0.0841317i | \(-0.0268116\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.3731 | − | 21.0000i | −1.22129 | − | 0.705111i | −0.256096 | − | 0.966651i | \(-0.582436\pi\) |
−0.965193 | + | 0.261540i | \(0.915770\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.5167i | 0.755185i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.00000 | − | 1.73205i | 0.100504 | − | 0.0580259i | ||||
\(892\) | −34.6410 | −1.15987 | ||||||||
\(893\) | −10.3923 | + | 6.00000i | −0.347765 | + | 0.200782i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15.5885 | + | 15.0000i | −0.520483 | + | 0.500835i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.00000 | + | 5.19615i | 0.300167 | + | 0.173301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.866025 | − | 1.50000i | −0.0288195 | − | 0.0499169i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.1051 | − | 22.0000i | −1.26526 | − | 0.730498i | −0.291172 | − | 0.956671i | \(-0.594045\pi\) |
−0.974087 | + | 0.226173i | \(0.927379\pi\) | |||||||
\(908\) | 20.7846 | − | 36.0000i | 0.689761 | − | 1.19470i | ||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | 6.92820 | − | 12.0000i | 0.229416 | − | 0.397360i | ||||
\(913\) | −41.5692 | − | 24.0000i | −1.37574 | − | 0.794284i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 48.0000 | − | 27.7128i | 1.58596 | − | 0.915657i | ||||
\(917\) | 5.19615 | + | 9.00000i | 0.171592 | + | 0.297206i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.0000 | − | 27.7128i | −0.527791 | − | 0.914161i | −0.999475 | − | 0.0323936i | \(-0.989687\pi\) |
0.471684 | − | 0.881768i | \(-0.343646\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.50000 | − | 0.866025i | −0.0494267 | − | 0.0285365i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25.9808 | − | 27.0000i | −0.855167 | − | 0.888716i | ||||
\(924\) | 12.0000 | 0.394771 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.866025 | − | 0.500000i | 0.0284440 | − | 0.0164222i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.0000 | − | 10.3923i | 0.590561 | − | 0.340960i | −0.174758 | − | 0.984611i | \(-0.555914\pi\) |
0.765319 | + | 0.643651i | \(0.222581\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.8564i | 0.454125i | ||||||||
\(932\) | 31.1769 | − | 18.0000i | 1.02123 | − | 0.589610i | ||||
\(933\) | −20.7846 | − | 12.0000i | −0.680458 | − | 0.392862i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.0000i | 0.457360i | 0.973502 | + | 0.228680i | \(0.0734410\pi\) | ||||
−0.973502 | + | 0.228680i | \(0.926559\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.50000 | + | 11.2583i | −0.212119 | + | 0.367402i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 10.3923i | − | 0.338779i | −0.985549 | − | 0.169390i | \(-0.945820\pi\) | ||
0.985549 | − | 0.169390i | \(-0.0541797\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.7846 | − | 36.0000i | −0.676840 | − | 1.17232i | ||||
\(944\) | 13.8564i | 0.450988i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.2487 | + | 42.0000i | −0.787977 | + | 1.36482i | 0.139227 | + | 0.990260i | \(0.455538\pi\) |
−0.927204 | + | 0.374556i | \(0.877795\pi\) | |||||||
\(948\) | 22.0000i | 0.714527i | ||||||||
\(949\) | −1.50000 | − | 6.06218i | −0.0486921 | − | 0.196787i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.00000 | + | 3.46410i | 0.194563 | + | 0.112331i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.19615 | − | 3.00000i | 0.168320 | − | 0.0971795i | −0.413473 | − | 0.910516i | \(-0.635685\pi\) |
0.581793 | + | 0.813337i | \(0.302351\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20.7846 | −0.671871 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.0000 | 0.903226 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 6.00000i | − | 0.193347i | ||||||
\(964\) | 36.0000 | + | 20.7846i | 1.15948 | + | 0.669427i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.2487 | −0.779786 | −0.389893 | − | 0.920860i | \(-0.627488\pi\) | ||||
−0.389893 | + | 0.920860i | \(0.627488\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.0000 | − | 31.1769i | −0.577647 | − | 1.00051i | −0.995748 | − | 0.0921142i | \(-0.970638\pi\) |
0.418101 | − | 0.908401i | \(-0.362696\pi\) | |||||||
\(972\) | −1.73205 | − | 1.00000i | −0.0555556 | − | 0.0320750i | ||||
\(973\) | −4.33013 | + | 7.50000i | −0.138817 | + | 0.240439i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.00000 | 0.128037 | ||||||||
\(977\) | −13.8564 | + | 24.0000i | −0.443306 | + | 0.767828i | −0.997932 | − | 0.0642712i | \(-0.979528\pi\) |
0.554627 | + | 0.832099i | \(0.312861\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | 10.3923 | 0.331463 | 0.165732 | − | 0.986171i | \(-0.447001\pi\) | ||||
0.165732 | + | 0.986171i | \(0.447001\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.00000i | 0.190982i | ||||||||
\(988\) | 6.92820 | − | 24.0000i | 0.220416 | − | 0.763542i | ||||
\(989\) | −6.00000 | −0.190789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | − | 13.8564i | 0.254128 | − | 0.440163i | −0.710530 | − | 0.703667i | \(-0.751545\pi\) |
0.964658 | + | 0.263504i | \(0.0848781\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.19615 | 0.164895 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 27.7128i | 0.878114i | ||||||||
\(997\) | −30.3109 | + | 17.5000i | −0.959955 | + | 0.554231i | −0.896159 | − | 0.443732i | \(-0.853654\pi\) |
−0.0637961 | + | 0.997963i | \(0.520321\pi\) | |||||||
\(998\) | 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 \(a_p\))