Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(181,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.181");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.k (of order \(2\), degree \(1\), 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: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 181.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 360.181 |
Dual form | 360.2.k.e.181.2 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.366025 | − | 1.36603i | −0.258819 | − | 0.965926i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.73205 | + | 1.00000i | −0.866025 | + | 0.500000i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.73205 | −1.03262 | −0.516309 | − | 0.856402i | \(-0.672694\pi\) | ||||
−0.516309 | + | 0.856402i | \(0.672694\pi\) | |||||||
\(8\) | 2.00000 | + | 2.00000i | 0.707107 | + | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.36603 | − | 0.366025i | 0.431975 | − | 0.115747i | ||||
\(11\) | 2.00000i | 0.603023i | 0.953463 | + | 0.301511i | \(0.0974911\pi\) | ||||
−0.953463 | + | 0.301511i | \(0.902509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.46410i | 0.960769i | 0.877058 | + | 0.480384i | \(0.159503\pi\) | ||||
−0.877058 | + | 0.480384i | \(0.840497\pi\) | |||||||
\(14\) | 1.00000 | + | 3.73205i | 0.267261 | + | 0.997433i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 3.46410 | 0.840168 | 0.420084 | − | 0.907485i | \(-0.362001\pi\) | ||||
0.420084 | + | 0.907485i | \(0.362001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.46410i | 1.71238i | 0.516659 | + | 0.856191i | \(0.327175\pi\) | ||||
−0.516659 | + | 0.856191i | \(0.672825\pi\) | |||||||
\(20\) | −1.00000 | − | 1.73205i | −0.223607 | − | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.73205 | − | 0.732051i | 0.582475 | − | 0.156074i | ||||
\(23\) | −4.19615 | −0.874958 | −0.437479 | − | 0.899229i | \(-0.644129\pi\) | ||||
−0.437479 | + | 0.899229i | \(0.644129\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 4.73205 | − | 1.26795i | 0.928032 | − | 0.248665i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.73205 | − | 2.73205i | 0.894274 | − | 0.516309i | ||||
\(29\) | 6.92820i | 1.28654i | 0.765641 | + | 0.643268i | \(0.222422\pi\) | ||||
−0.765641 | + | 0.643268i | \(0.777578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.46410 | 0.262960 | 0.131480 | − | 0.991319i | \(-0.458027\pi\) | ||||
0.131480 | + | 0.991319i | \(0.458027\pi\) | |||||||
\(32\) | −5.46410 | − | 1.46410i | −0.965926 | − | 0.258819i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.26795 | − | 4.73205i | −0.217451 | − | 0.811540i | ||||
\(35\) | − | 2.73205i | − | 0.461801i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.00000i | − | 0.328798i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) | ||
0.986394 | − | 0.164399i | \(-0.0525685\pi\) | |||||||
\(38\) | 10.1962 | − | 2.73205i | 1.65403 | − | 0.443197i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.00000 | + | 2.00000i | −0.316228 | + | 0.316228i | ||||
\(41\) | 5.46410 | 0.853349 | 0.426675 | − | 0.904405i | \(-0.359685\pi\) | ||||
0.426675 | + | 0.904405i | \(0.359685\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.73205i | − | 1.33163i | −0.746119 | − | 0.665813i | \(-0.768085\pi\) | ||
0.746119 | − | 0.665813i | \(-0.231915\pi\) | |||||||
\(44\) | −2.00000 | − | 3.46410i | −0.301511 | − | 0.522233i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.53590 | + | 5.73205i | 0.226456 | + | 0.845145i | ||||
\(47\) | −6.73205 | −0.981971 | −0.490985 | − | 0.871168i | \(-0.663363\pi\) | ||||
−0.490985 | + | 0.871168i | \(0.663363\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.464102 | 0.0663002 | ||||||||
\(50\) | 0.366025 | + | 1.36603i | 0.0517638 | + | 0.193185i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.46410 | − | 6.00000i | −0.480384 | − | 0.832050i | ||||
\(53\) | − | 4.53590i | − | 0.623054i | −0.950237 | − | 0.311527i | \(-0.899160\pi\) | ||
0.950237 | − | 0.311527i | \(-0.100840\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | −5.46410 | − | 5.46410i | −0.730171 | − | 0.730171i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.46410 | − | 2.53590i | 1.24270 | − | 0.332980i | ||||
\(59\) | 0.535898i | 0.0697680i | 0.999391 | + | 0.0348840i | \(0.0111062\pi\) | ||||
−0.999391 | + | 0.0348840i | \(0.988894\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.92820i | 0.630992i | 0.948927 | + | 0.315496i | \(0.102171\pi\) | ||||
−0.948927 | + | 0.315496i | \(0.897829\pi\) | |||||||
\(62\) | −0.535898 | − | 2.00000i | −0.0680592 | − | 0.254000i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | −3.46410 | −0.429669 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.26795i | 0.887921i | 0.896046 | + | 0.443961i | \(0.146427\pi\) | ||||
−0.896046 | + | 0.443961i | \(0.853573\pi\) | |||||||
\(68\) | −6.00000 | + | 3.46410i | −0.727607 | + | 0.420084i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.73205 | + | 1.00000i | −0.446065 | + | 0.119523i | ||||
\(71\) | 1.46410 | 0.173757 | 0.0868784 | − | 0.996219i | \(-0.472311\pi\) | ||||
0.0868784 | + | 0.996219i | \(0.472311\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.535898 | 0.0627222 | 0.0313611 | − | 0.999508i | \(-0.490016\pi\) | ||||
0.0313611 | + | 0.999508i | \(0.490016\pi\) | |||||||
\(74\) | −2.73205 | + | 0.732051i | −0.317594 | + | 0.0850992i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.46410 | − | 12.9282i | −0.856191 | − | 1.48297i | ||||
\(77\) | − | 5.46410i | − | 0.622692i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.9282 | −1.67955 | −0.839777 | − | 0.542931i | \(-0.817314\pi\) | ||||
−0.839777 | + | 0.542931i | \(0.817314\pi\) | |||||||
\(80\) | 3.46410 | + | 2.00000i | 0.387298 | + | 0.223607i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.00000 | − | 7.46410i | −0.220863 | − | 0.824272i | ||||
\(83\) | − | 4.73205i | − | 0.519410i | −0.965688 | − | 0.259705i | \(-0.916375\pi\) | ||
0.965688 | − | 0.259705i | \(-0.0836253\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.46410i | 0.375735i | ||||||||
\(86\) | −11.9282 | + | 3.19615i | −1.28625 | + | 0.344650i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.00000 | + | 4.00000i | −0.426401 | + | 0.426401i | ||||
\(89\) | 4.92820 | 0.522388 | 0.261194 | − | 0.965286i | \(-0.415884\pi\) | ||||
0.261194 | + | 0.965286i | \(0.415884\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 9.46410i | − | 0.992107i | ||||||
\(92\) | 7.26795 | − | 4.19615i | 0.757736 | − | 0.437479i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.46410 | + | 9.19615i | 0.254153 | + | 0.948511i | ||||
\(95\) | −7.46410 | −0.765801 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.39230 | 0.649040 | 0.324520 | − | 0.945879i | \(-0.394797\pi\) | ||||
0.324520 | + | 0.945879i | \(0.394797\pi\) | |||||||
\(98\) | −0.169873 | − | 0.633975i | −0.0171598 | − | 0.0640411i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.73205 | − | 1.00000i | 0.173205 | − | 0.100000i | ||||
\(101\) | 10.9282i | 1.08740i | 0.839281 | + | 0.543698i | \(0.182976\pi\) | ||||
−0.839281 | + | 0.543698i | \(0.817024\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.66025 | −0.163590 | −0.0817948 | − | 0.996649i | \(-0.526065\pi\) | ||||
−0.0817948 | + | 0.996649i | \(0.526065\pi\) | |||||||
\(104\) | −6.92820 | + | 6.92820i | −0.679366 | + | 0.679366i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.19615 | + | 1.66025i | −0.601824 | + | 0.161258i | ||||
\(107\) | 0.732051i | 0.0707700i | 0.999374 | + | 0.0353850i | \(0.0112658\pi\) | ||||
−0.999374 | + | 0.0353850i | \(0.988734\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.07180i | 0.294225i | 0.989120 | + | 0.147112i | \(0.0469979\pi\) | ||||
−0.989120 | + | 0.147112i | \(0.953002\pi\) | |||||||
\(110\) | 0.732051 | + | 2.73205i | 0.0697983 | + | 0.260491i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.46410 | + | 9.46410i | −0.516309 | + | 0.894274i | ||||
\(113\) | −0.928203 | −0.0873180 | −0.0436590 | − | 0.999046i | \(-0.513902\pi\) | ||||
−0.0436590 | + | 0.999046i | \(0.513902\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 4.19615i | − | 0.391293i | ||||||
\(116\) | −6.92820 | − | 12.0000i | −0.643268 | − | 1.11417i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.732051 | − | 0.196152i | 0.0673907 | − | 0.0180573i | ||||
\(119\) | −9.46410 | −0.867573 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 6.73205 | − | 1.80385i | 0.609491 | − | 0.163313i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.53590 | + | 1.46410i | −0.227730 | + | 0.131480i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.2679 | 1.17734 | 0.588670 | − | 0.808373i | \(-0.299652\pi\) | ||||
0.588670 | + | 0.808373i | \(0.299652\pi\) | |||||||
\(128\) | 10.9282 | − | 2.92820i | 0.965926 | − | 0.258819i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.26795 | + | 4.73205i | 0.111207 | + | 0.415028i | ||||
\(131\) | − | 7.85641i | − | 0.686417i | −0.939259 | − | 0.343209i | \(-0.888486\pi\) | ||
0.939259 | − | 0.343209i | \(-0.111514\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 20.3923i | − | 1.76824i | ||||||
\(134\) | 9.92820 | − | 2.66025i | 0.857666 | − | 0.229811i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.92820 | + | 6.92820i | 0.594089 | + | 0.594089i | ||||
\(137\) | 8.92820 | 0.762788 | 0.381394 | − | 0.924413i | \(-0.375444\pi\) | ||||
0.381394 | + | 0.924413i | \(0.375444\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 7.46410i | − | 0.633097i | −0.948576 | − | 0.316548i | \(-0.897476\pi\) | ||
0.948576 | − | 0.316548i | \(-0.102524\pi\) | |||||||
\(140\) | 2.73205 | + | 4.73205i | 0.230900 | + | 0.399931i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.535898 | − | 2.00000i | −0.0449716 | − | 0.167836i | ||||
\(143\) | −6.92820 | −0.579365 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.92820 | −0.575356 | ||||||||
\(146\) | −0.196152 | − | 0.732051i | −0.0162337 | − | 0.0605850i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.00000 | + | 3.46410i | 0.164399 | + | 0.284747i | ||||
\(149\) | − | 19.8564i | − | 1.62670i | −0.581775 | − | 0.813350i | \(-0.697641\pi\) | ||
0.581775 | − | 0.813350i | \(-0.302359\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.39230 | 0.682956 | 0.341478 | − | 0.939890i | \(-0.389073\pi\) | ||||
0.341478 | + | 0.939890i | \(0.389073\pi\) | |||||||
\(152\) | −14.9282 | + | 14.9282i | −1.21084 | + | 1.21084i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.46410 | + | 2.00000i | −0.601474 | + | 0.161165i | ||||
\(155\) | 1.46410i | 0.117599i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 16.9282i | − | 1.35102i | −0.737352 | − | 0.675509i | \(-0.763924\pi\) | ||
0.737352 | − | 0.675509i | \(-0.236076\pi\) | |||||||
\(158\) | 5.46410 | + | 20.3923i | 0.434701 | + | 1.62232i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.46410 | − | 5.46410i | 0.115747 | − | 0.431975i | ||||
\(161\) | 11.4641 | 0.903498 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.1962i | 0.798624i | 0.916815 | + | 0.399312i | \(0.130751\pi\) | ||||
−0.916815 | + | 0.399312i | \(0.869249\pi\) | |||||||
\(164\) | −9.46410 | + | 5.46410i | −0.739022 | + | 0.426675i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.46410 | + | 1.73205i | −0.501712 | + | 0.134433i | ||||
\(167\) | 20.1962 | 1.56283 | 0.781413 | − | 0.624015i | \(-0.214499\pi\) | ||||
0.781413 | + | 0.624015i | \(0.214499\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 4.73205 | − | 1.26795i | 0.362932 | − | 0.0972473i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.73205 | + | 15.1244i | 0.665813 | + | 1.15322i | ||||
\(173\) | − | 2.00000i | − | 0.152057i | −0.997106 | − | 0.0760286i | \(-0.975776\pi\) | ||
0.997106 | − | 0.0760286i | \(-0.0242240\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.73205 | 0.206524 | ||||||||
\(176\) | 6.92820 | + | 4.00000i | 0.522233 | + | 0.301511i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.80385 | − | 6.73205i | −0.135204 | − | 0.504589i | ||||
\(179\) | 15.4641i | 1.15584i | 0.816093 | + | 0.577921i | \(0.196136\pi\) | ||||
−0.816093 | + | 0.577921i | \(0.803864\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.0000i | 1.18927i | 0.803996 | + | 0.594635i | \(0.202704\pi\) | ||||
−0.803996 | + | 0.594635i | \(0.797296\pi\) | |||||||
\(182\) | −12.9282 | + | 3.46410i | −0.958302 | + | 0.256776i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.39230 | − | 8.39230i | −0.618689 | − | 0.618689i | ||||
\(185\) | 2.00000 | 0.147043 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.92820i | 0.506640i | ||||||||
\(188\) | 11.6603 | − | 6.73205i | 0.850411 | − | 0.490985i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.73205 | + | 10.1962i | 0.198204 | + | 0.739707i | ||||
\(191\) | 19.3205 | 1.39798 | 0.698991 | − | 0.715130i | \(-0.253633\pi\) | ||||
0.698991 | + | 0.715130i | \(0.253633\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.46410 | 0.537278 | 0.268639 | − | 0.963241i | \(-0.413426\pi\) | ||||
0.268639 | + | 0.963241i | \(0.413426\pi\) | |||||||
\(194\) | −2.33975 | − | 8.73205i | −0.167984 | − | 0.626925i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.803848 | + | 0.464102i | −0.0574177 | + | 0.0331501i | ||||
\(197\) | 12.5359i | 0.893146i | 0.894747 | + | 0.446573i | \(0.147356\pi\) | ||||
−0.894747 | + | 0.446573i | \(0.852644\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.8564 | 1.83291 | 0.916456 | − | 0.400135i | \(-0.131037\pi\) | ||||
0.916456 | + | 0.400135i | \(0.131037\pi\) | |||||||
\(200\) | −2.00000 | − | 2.00000i | −0.141421 | − | 0.141421i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.9282 | − | 4.00000i | 1.05034 | − | 0.281439i | ||||
\(203\) | − | 18.9282i | − | 1.32850i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.46410i | 0.381629i | ||||||||
\(206\) | 0.607695 | + | 2.26795i | 0.0423401 | + | 0.158016i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 12.0000 | + | 6.92820i | 0.832050 | + | 0.480384i | ||||
\(209\) | −14.9282 | −1.03261 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 14.7846i | − | 1.01781i | −0.860821 | − | 0.508907i | \(-0.830050\pi\) | ||
0.860821 | − | 0.508907i | \(-0.169950\pi\) | |||||||
\(212\) | 4.53590 | + | 7.85641i | 0.311527 | + | 0.539580i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.00000 | − | 0.267949i | 0.0683586 | − | 0.0183166i | ||||
\(215\) | 8.73205 | 0.595521 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | −0.271538 | ||||||||
\(218\) | 4.19615 | − | 1.12436i | 0.284199 | − | 0.0761510i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.46410 | − | 2.00000i | 0.233550 | − | 0.134840i | ||||
\(221\) | 12.0000i | 0.807207i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.1962 | −1.08457 | −0.542287 | − | 0.840193i | \(-0.682442\pi\) | ||||
−0.542287 | + | 0.840193i | \(0.682442\pi\) | |||||||
\(224\) | 14.9282 | + | 4.00000i | 0.997433 | + | 0.267261i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.339746 | + | 1.26795i | 0.0225996 | + | 0.0843427i | ||||
\(227\) | 28.0526i | 1.86191i | 0.365129 | + | 0.930957i | \(0.381025\pi\) | ||||
−0.365129 | + | 0.930957i | \(0.618975\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 4.00000i | − | 0.264327i | −0.991228 | − | 0.132164i | \(-0.957808\pi\) | ||
0.991228 | − | 0.132164i | \(-0.0421925\pi\) | |||||||
\(230\) | −5.73205 | + | 1.53590i | −0.377960 | + | 0.101274i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.8564 | + | 13.8564i | −0.909718 | + | 0.909718i | ||||
\(233\) | −29.3205 | −1.92085 | −0.960425 | − | 0.278538i | \(-0.910150\pi\) | ||||
−0.960425 | + | 0.278538i | \(0.910150\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 6.73205i | − | 0.439151i | ||||||
\(236\) | −0.535898 | − | 0.928203i | −0.0348840 | − | 0.0604209i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.46410 | + | 12.9282i | 0.224544 | + | 0.838011i | ||||
\(239\) | 20.0000 | 1.29369 | 0.646846 | − | 0.762620i | \(-0.276088\pi\) | ||||
0.646846 | + | 0.762620i | \(0.276088\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.39230 | −0.282933 | −0.141467 | − | 0.989943i | \(-0.545182\pi\) | ||||
−0.141467 | + | 0.989943i | \(0.545182\pi\) | |||||||
\(242\) | −2.56218 | − | 9.56218i | −0.164703 | − | 0.614680i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.92820 | − | 8.53590i | −0.315496 | − | 0.546455i | ||||
\(245\) | 0.464102i | 0.0296504i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.8564 | −1.64520 | ||||||||
\(248\) | 2.92820 | + | 2.92820i | 0.185941 | + | 0.185941i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.36603 | + | 0.366025i | −0.0863950 | + | 0.0231495i | ||||
\(251\) | − | 11.0718i | − | 0.698846i | −0.936965 | − | 0.349423i | \(-0.886378\pi\) | ||
0.936965 | − | 0.349423i | \(-0.113622\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 8.39230i | − | 0.527620i | ||||||
\(254\) | −4.85641 | − | 18.1244i | −0.304718 | − | 1.13722i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 2.00000 | 0.124757 | 0.0623783 | − | 0.998053i | \(-0.480131\pi\) | ||||
0.0623783 | + | 0.998053i | \(0.480131\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.46410i | 0.339523i | ||||||||
\(260\) | 6.00000 | − | 3.46410i | 0.372104 | − | 0.214834i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.7321 | + | 2.87564i | −0.663028 | + | 0.177658i | ||||
\(263\) | −5.66025 | −0.349026 | −0.174513 | − | 0.984655i | \(-0.555835\pi\) | ||||
−0.174513 | + | 0.984655i | \(0.555835\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.53590 | 0.278638 | ||||||||
\(266\) | −27.8564 | + | 7.46410i | −1.70799 | + | 0.457653i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.26795 | − | 12.5885i | −0.443961 | − | 0.768962i | ||||
\(269\) | − | 4.92820i | − | 0.300478i | −0.988650 | − | 0.150239i | \(-0.951996\pi\) | ||
0.988650 | − | 0.150239i | \(-0.0480043\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.3205 | 0.930655 | 0.465327 | − | 0.885139i | \(-0.345937\pi\) | ||||
0.465327 | + | 0.885139i | \(0.345937\pi\) | |||||||
\(272\) | 6.92820 | − | 12.0000i | 0.420084 | − | 0.727607i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.26795 | − | 12.1962i | −0.197424 | − | 0.736797i | ||||
\(275\) | − | 2.00000i | − | 0.120605i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000i | 0.120168i | 0.998193 | + | 0.0600842i | \(0.0191369\pi\) | ||||
−0.998193 | + | 0.0600842i | \(0.980863\pi\) | |||||||
\(278\) | −10.1962 | + | 2.73205i | −0.611525 | + | 0.163858i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.46410 | − | 5.46410i | 0.326543 | − | 0.326543i | ||||
\(281\) | −17.4641 | −1.04182 | −0.520910 | − | 0.853611i | \(-0.674407\pi\) | ||||
−0.520910 | + | 0.853611i | \(0.674407\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.66025i | 0.455355i | 0.973737 | + | 0.227677i | \(0.0731132\pi\) | ||||
−0.973737 | + | 0.227677i | \(0.926887\pi\) | |||||||
\(284\) | −2.53590 | + | 1.46410i | −0.150478 | + | 0.0868784i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.53590 | + | 9.46410i | 0.149951 | + | 0.559624i | ||||
\(287\) | −14.9282 | −0.881184 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 2.53590 | + | 9.46410i | 0.148913 | + | 0.555751i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.928203 | + | 0.535898i | −0.0543190 | + | 0.0313611i | ||||
\(293\) | − | 11.8564i | − | 0.692659i | −0.938113 | − | 0.346329i | \(-0.887428\pi\) | ||
0.938113 | − | 0.346329i | \(-0.112572\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.535898 | −0.0312012 | ||||||||
\(296\) | 4.00000 | − | 4.00000i | 0.232495 | − | 0.232495i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −27.1244 | + | 7.26795i | −1.57127 | + | 0.421021i | ||||
\(299\) | − | 14.5359i | − | 0.840633i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.8564i | 1.37506i | ||||||||
\(302\) | −3.07180 | − | 11.4641i | −0.176762 | − | 0.659685i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 25.8564 | + | 14.9282i | 1.48297 | + | 0.856191i | ||||
\(305\) | −4.92820 | −0.282188 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.9808i | 1.53987i | 0.638120 | + | 0.769937i | \(0.279712\pi\) | ||||
−0.638120 | + | 0.769937i | \(0.720288\pi\) | |||||||
\(308\) | 5.46410 | + | 9.46410i | 0.311346 | + | 0.539267i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.00000 | − | 0.535898i | 0.113592 | − | 0.0304370i | ||||
\(311\) | 3.32051 | 0.188289 | 0.0941444 | − | 0.995559i | \(-0.469988\pi\) | ||||
0.0941444 | + | 0.995559i | \(0.469988\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.8564 | −1.80063 | −0.900315 | − | 0.435238i | \(-0.856664\pi\) | ||||
−0.900315 | + | 0.435238i | \(0.856664\pi\) | |||||||
\(314\) | −23.1244 | + | 6.19615i | −1.30498 | + | 0.349669i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 25.8564 | − | 14.9282i | 1.45454 | − | 0.839777i | ||||
\(317\) | − | 15.4641i | − | 0.868550i | −0.900780 | − | 0.434275i | \(-0.857005\pi\) | ||
0.900780 | − | 0.434275i | \(-0.142995\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.8564 | −0.775810 | ||||||||
\(320\) | −8.00000 | −0.447214 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.19615 | − | 15.6603i | −0.233842 | − | 0.872712i | ||||
\(323\) | 25.8564i | 1.43869i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 3.46410i | − | 0.192154i | ||||||
\(326\) | 13.9282 | − | 3.73205i | 0.771412 | − | 0.206699i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.9282 | + | 10.9282i | 0.603409 | + | 0.603409i | ||||
\(329\) | 18.3923 | 1.01400 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 14.0000i | − | 0.769510i | −0.923019 | − | 0.384755i | \(-0.874286\pi\) | ||
0.923019 | − | 0.384755i | \(-0.125714\pi\) | |||||||
\(332\) | 4.73205 | + | 8.19615i | 0.259705 | + | 0.449822i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.39230 | − | 27.5885i | −0.404489 | − | 1.50957i | ||||
\(335\) | −7.26795 | −0.397090 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.85641 | 0.427966 | 0.213983 | − | 0.976837i | \(-0.431356\pi\) | ||||
0.213983 | + | 0.976837i | \(0.431356\pi\) | |||||||
\(338\) | −0.366025 | − | 1.36603i | −0.0199092 | − | 0.0743020i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.46410 | − | 6.00000i | −0.187867 | − | 0.325396i | ||||
\(341\) | 2.92820i | 0.158571i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8564 | 0.964155 | ||||||||
\(344\) | 17.4641 | − | 17.4641i | 0.941601 | − | 0.941601i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.73205 | + | 0.732051i | −0.146876 | + | 0.0393553i | ||||
\(347\) | − | 15.6603i | − | 0.840686i | −0.907365 | − | 0.420343i | \(-0.861910\pi\) | ||
0.907365 | − | 0.420343i | \(-0.138090\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 28.0000i | − | 1.49881i | −0.662114 | − | 0.749403i | \(-0.730341\pi\) | ||
0.662114 | − | 0.749403i | \(-0.269659\pi\) | |||||||
\(350\) | −1.00000 | − | 3.73205i | −0.0534522 | − | 0.199487i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.92820 | − | 10.9282i | 0.156074 | − | 0.582475i | ||||
\(353\) | 0.928203 | 0.0494033 | 0.0247016 | − | 0.999695i | \(-0.492136\pi\) | ||||
0.0247016 | + | 0.999695i | \(0.492136\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.46410i | 0.0777064i | ||||||||
\(356\) | −8.53590 | + | 4.92820i | −0.452402 | + | 0.261194i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 21.1244 | − | 5.66025i | 1.11646 | − | 0.299154i | ||||
\(359\) | −5.07180 | −0.267679 | −0.133840 | − | 0.991003i | \(-0.542731\pi\) | ||||
−0.133840 | + | 0.991003i | \(0.542731\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −36.7128 | −1.93225 | ||||||||
\(362\) | 21.8564 | − | 5.85641i | 1.14875 | − | 0.307806i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.46410 | + | 16.3923i | 0.496054 | + | 0.859190i | ||||
\(365\) | 0.535898i | 0.0280502i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.1244 | 1.41588 | 0.707940 | − | 0.706273i | \(-0.249625\pi\) | ||||
0.707940 | + | 0.706273i | \(0.249625\pi\) | |||||||
\(368\) | −8.39230 | + | 14.5359i | −0.437479 | + | 0.757736i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.732051 | − | 2.73205i | −0.0380575 | − | 0.142033i | ||||
\(371\) | 12.3923i | 0.643376i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.7128i | 1.53847i | 0.638965 | + | 0.769236i | \(0.279363\pi\) | ||||
−0.638965 | + | 0.769236i | \(0.720637\pi\) | |||||||
\(374\) | 9.46410 | − | 2.53590i | 0.489377 | − | 0.131128i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.4641 | − | 13.4641i | −0.694358 | − | 0.694358i | ||||
\(377\) | −24.0000 | −1.23606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.2487i | 0.629174i | 0.949229 | + | 0.314587i | \(0.101866\pi\) | ||||
−0.949229 | + | 0.314587i | \(0.898134\pi\) | |||||||
\(380\) | 12.9282 | − | 7.46410i | 0.663203 | − | 0.382900i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.07180 | − | 26.3923i | −0.361825 | − | 1.35035i | ||||
\(383\) | 3.12436 | 0.159647 | 0.0798236 | − | 0.996809i | \(-0.474564\pi\) | ||||
0.0798236 | + | 0.996809i | \(0.474564\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.46410 | 0.278476 | ||||||||
\(386\) | −2.73205 | − | 10.1962i | −0.139058 | − | 0.518970i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.0718 | + | 6.39230i | −0.562085 | + | 0.324520i | ||||
\(389\) | 34.7846i | 1.76365i | 0.471577 | + | 0.881825i | \(0.343685\pi\) | ||||
−0.471577 | + | 0.881825i | \(0.656315\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.5359 | −0.735112 | ||||||||
\(392\) | 0.928203 | + | 0.928203i | 0.0468813 | + | 0.0468813i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 17.1244 | − | 4.58846i | 0.862713 | − | 0.231163i | ||||
\(395\) | − | 14.9282i | − | 0.751119i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 16.2487i | − | 0.815499i | −0.913094 | − | 0.407750i | \(-0.866314\pi\) | ||
0.913094 | − | 0.407750i | \(-0.133686\pi\) | |||||||
\(398\) | −9.46410 | − | 35.3205i | −0.474393 | − | 1.77046i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | + | 3.46410i | −0.100000 | + | 0.173205i | ||||
\(401\) | −19.8564 | −0.991582 | −0.495791 | − | 0.868442i | \(-0.665122\pi\) | ||||
−0.495791 | + | 0.868442i | \(0.665122\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.07180i | 0.252644i | ||||||||
\(404\) | −10.9282 | − | 18.9282i | −0.543698 | − | 0.941713i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −25.8564 | + | 6.92820i | −1.28323 | + | 0.343841i | ||||
\(407\) | 4.00000 | 0.198273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.3205 | 1.15312 | 0.576562 | − | 0.817053i | \(-0.304394\pi\) | ||||
0.576562 | + | 0.817053i | \(0.304394\pi\) | |||||||
\(410\) | 7.46410 | − | 2.00000i | 0.368626 | − | 0.0987730i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.87564 | − | 1.66025i | 0.141673 | − | 0.0817948i | ||||
\(413\) | − | 1.46410i | − | 0.0720437i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.73205 | 0.232287 | ||||||||
\(416\) | 5.07180 | − | 18.9282i | 0.248665 | − | 0.928032i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.46410 | + | 20.3923i | 0.267258 | + | 0.997420i | ||||
\(419\) | 2.39230i | 0.116872i | 0.998291 | + | 0.0584359i | \(0.0186113\pi\) | ||||
−0.998291 | + | 0.0584359i | \(0.981389\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.8564i | 1.35764i | 0.734306 | + | 0.678819i | \(0.237508\pi\) | ||||
−0.734306 | + | 0.678819i | \(0.762492\pi\) | |||||||
\(422\) | −20.1962 | + | 5.41154i | −0.983133 | + | 0.263430i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.07180 | − | 9.07180i | 0.440565 | − | 0.440565i | ||||
\(425\) | −3.46410 | −0.168034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 13.4641i | − | 0.651574i | ||||||
\(428\) | −0.732051 | − | 1.26795i | −0.0353850 | − | 0.0612886i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.19615 | − | 11.9282i | −0.154132 | − | 0.575229i | ||||
\(431\) | 14.5359 | 0.700170 | 0.350085 | − | 0.936718i | \(-0.386153\pi\) | ||||
0.350085 | + | 0.936718i | \(0.386153\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.5359 | −0.602437 | −0.301218 | − | 0.953555i | \(-0.597393\pi\) | ||||
−0.301218 | + | 0.953555i | \(0.597393\pi\) | |||||||
\(434\) | 1.46410 | + | 5.46410i | 0.0702791 | + | 0.262285i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.07180 | − | 5.32051i | −0.147112 | − | 0.254806i | ||||
\(437\) | − | 31.3205i | − | 1.49826i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.784610 | −0.0374474 | −0.0187237 | − | 0.999825i | \(-0.505960\pi\) | ||||
−0.0187237 | + | 0.999825i | \(0.505960\pi\) | |||||||
\(440\) | −4.00000 | − | 4.00000i | −0.190693 | − | 0.190693i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.3923 | − | 4.39230i | 0.779702 | − | 0.208921i | ||||
\(443\) | 30.9808i | 1.47194i | 0.677014 | + | 0.735970i | \(0.263274\pi\) | ||||
−0.677014 | + | 0.735970i | \(0.736726\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.92820i | 0.233619i | ||||||||
\(446\) | 5.92820 | + | 22.1244i | 0.280709 | + | 1.04762i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 21.8564i | − | 1.03262i | ||||||
\(449\) | −11.3205 | −0.534248 | −0.267124 | − | 0.963662i | \(-0.586073\pi\) | ||||
−0.267124 | + | 0.963662i | \(0.586073\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.9282i | 0.514589i | ||||||||
\(452\) | 1.60770 | − | 0.928203i | 0.0756196 | − | 0.0436590i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 38.3205 | − | 10.2679i | 1.79847 | − | 0.481899i | ||||
\(455\) | 9.46410 | 0.443684 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.7846 | 0.691595 | 0.345797 | − | 0.938309i | \(-0.387608\pi\) | ||||
0.345797 | + | 0.938309i | \(0.387608\pi\) | |||||||
\(458\) | −5.46410 | + | 1.46410i | −0.255321 | + | 0.0684130i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.19615 | + | 7.26795i | 0.195647 | + | 0.338870i | ||||
\(461\) | − | 2.92820i | − | 0.136380i | −0.997672 | − | 0.0681900i | \(-0.978278\pi\) | ||
0.997672 | − | 0.0681900i | \(-0.0217224\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.7321 | −0.684656 | −0.342328 | − | 0.939580i | \(-0.611215\pi\) | ||||
−0.342328 | + | 0.939580i | \(0.611215\pi\) | |||||||
\(464\) | 24.0000 | + | 13.8564i | 1.11417 | + | 0.643268i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.7321 | + | 40.0526i | 0.497153 | + | 1.85540i | ||||
\(467\) | 8.33975i | 0.385917i | 0.981207 | + | 0.192959i | \(0.0618083\pi\) | ||||
−0.981207 | + | 0.192959i | \(0.938192\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 19.8564i | − | 0.916884i | ||||||
\(470\) | −9.19615 | + | 2.46410i | −0.424187 | + | 0.113661i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.07180 | + | 1.07180i | −0.0493334 | + | 0.0493334i | ||||
\(473\) | 17.4641 | 0.803000 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 7.46410i | − | 0.342476i | ||||||
\(476\) | 16.3923 | − | 9.46410i | 0.751340 | − | 0.433786i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.32051 | − | 27.3205i | −0.334832 | − | 1.24961i | ||||
\(479\) | 21.8564 | 0.998645 | 0.499322 | − | 0.866416i | \(-0.333582\pi\) | ||||
0.499322 | + | 0.866416i | \(0.333582\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.92820 | 0.315899 | ||||||||
\(482\) | 1.60770 | + | 6.00000i | 0.0732285 | + | 0.273293i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.1244 | + | 7.00000i | −0.551107 | + | 0.318182i | ||||
\(485\) | 6.39230i | 0.290260i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.5885 | −1.11421 | −0.557105 | − | 0.830442i | \(-0.688088\pi\) | ||||
−0.557105 | + | 0.830442i | \(0.688088\pi\) | |||||||
\(488\) | −9.85641 | + | 9.85641i | −0.446179 | + | 0.446179i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.633975 | − | 0.169873i | 0.0286401 | − | 0.00767408i | ||||
\(491\) | 3.07180i | 0.138628i | 0.997595 | + | 0.0693141i | \(0.0220811\pi\) | ||||
−0.997595 | + | 0.0693141i | \(0.977919\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.0000i | 1.08091i | ||||||||
\(494\) | 9.46410 | + | 35.3205i | 0.425810 | + | 1.58914i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.92820 | − | 5.07180i | 0.131480 | − | 0.227730i | ||||
\(497\) | −4.00000 | −0.179425 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.5359i | 1.09838i | 0.835698 | + | 0.549189i | \(0.185063\pi\) | ||||
−0.835698 | + | 0.549189i | \(0.814937\pi\) | |||||||
\(500\) | 1.00000 | + | 1.73205i | 0.0447214 | + | 0.0774597i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15.1244 | + | 4.05256i | −0.675033 | + | 0.180875i | ||||
\(503\) | 17.6603 | 0.787432 | 0.393716 | − | 0.919232i | \(-0.371189\pi\) | ||||
0.393716 | + | 0.919232i | \(0.371189\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.9282 | −0.486299 | ||||||||
\(506\) | −11.4641 | + | 3.07180i | −0.509641 | + | 0.136558i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −22.9808 | + | 13.2679i | −1.01961 | + | 0.588670i | ||||
\(509\) | − | 25.8564i | − | 1.14607i | −0.819533 | − | 0.573033i | \(-0.805767\pi\) | ||
0.819533 | − | 0.573033i | \(-0.194233\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.46410 | −0.0647680 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.707107 | + | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.732051 | − | 2.73205i | −0.0322894 | − | 0.120506i | ||||
\(515\) | − | 1.66025i | − | 0.0731595i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 13.4641i | − | 0.592151i | ||||||
\(518\) | 7.46410 | − | 2.00000i | 0.327954 | − | 0.0878750i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.92820 | − | 6.92820i | −0.303822 | − | 0.303822i | ||||
\(521\) | 16.1436 | 0.707264 | 0.353632 | − | 0.935385i | \(-0.384947\pi\) | ||||
0.353632 | + | 0.935385i | \(0.384947\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 22.1962i | − | 0.970570i | −0.874356 | − | 0.485285i | \(-0.838716\pi\) | ||
0.874356 | − | 0.485285i | \(-0.161284\pi\) | |||||||
\(524\) | 7.85641 | + | 13.6077i | 0.343209 | + | 0.594455i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.07180 | + | 7.73205i | 0.0903346 | + | 0.337133i | ||||
\(527\) | 5.07180 | 0.220931 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.39230 | −0.234448 | ||||||||
\(530\) | −1.66025 | − | 6.19615i | −0.0721168 | − | 0.269144i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 20.3923 | + | 35.3205i | 0.884119 | + | 1.53134i | ||||
\(533\) | 18.9282i | 0.819871i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.732051 | −0.0316493 | ||||||||
\(536\) | −14.5359 | + | 14.5359i | −0.627855 | + | 0.627855i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.73205 | + | 1.80385i | −0.290239 | + | 0.0777694i | ||||
\(539\) | 0.928203i | 0.0399805i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 13.0718i | − | 0.562000i | −0.959708 | − | 0.281000i | \(-0.909334\pi\) | ||
0.959708 | − | 0.281000i | \(-0.0906662\pi\) | |||||||
\(542\) | −5.60770 | − | 20.9282i | −0.240871 | − | 0.898943i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −18.9282 | − | 5.07180i | −0.811540 | − | 0.217451i | ||||
\(545\) | −3.07180 | −0.131581 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.7321i | 1.57055i | 0.619148 | + | 0.785275i | \(0.287478\pi\) | ||||
−0.619148 | + | 0.785275i | \(0.712522\pi\) | |||||||
\(548\) | −15.4641 | + | 8.92820i | −0.660594 | + | 0.381394i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.73205 | + | 0.732051i | −0.116495 | + | 0.0312148i | ||||
\(551\) | −51.7128 | −2.20304 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 40.7846 | 1.73434 | ||||||||
\(554\) | 2.73205 | − | 0.732051i | 0.116074 | − | 0.0311019i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.46410 | + | 12.9282i | 0.316548 | + | 0.548278i | ||||
\(557\) | 26.7846i | 1.13490i | 0.823408 | + | 0.567450i | \(0.192070\pi\) | ||||
−0.823408 | + | 0.567450i | \(0.807930\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.2487 | 1.27938 | ||||||||
\(560\) | −9.46410 | − | 5.46410i | −0.399931 | − | 0.230900i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.39230 | + | 23.8564i | 0.269643 | + | 1.00632i | ||||
\(563\) | − | 16.0526i | − | 0.676535i | −0.941050 | − | 0.338267i | \(-0.890159\pi\) | ||
0.941050 | − | 0.338267i | \(-0.109841\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 0.928203i | − | 0.0390498i | ||||||
\(566\) | 10.4641 | − | 2.80385i | 0.439839 | − | 0.117855i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.92820 | + | 2.92820i | 0.122865 | + | 0.122865i | ||||
\(569\) | 6.53590 | 0.273999 | 0.137000 | − | 0.990571i | \(-0.456254\pi\) | ||||
0.137000 | + | 0.990571i | \(0.456254\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 34.7846i | − | 1.45569i | −0.685741 | − | 0.727845i | \(-0.740522\pi\) | ||
0.685741 | − | 0.727845i | \(-0.259478\pi\) | |||||||
\(572\) | 12.0000 | − | 6.92820i | 0.501745 | − | 0.289683i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.46410 | + | 20.3923i | 0.228067 | + | 0.851158i | ||||
\(575\) | 4.19615 | 0.174992 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −43.5692 | −1.81381 | −0.906905 | − | 0.421335i | \(-0.861562\pi\) | ||||
−0.906905 | + | 0.421335i | \(0.861562\pi\) | |||||||
\(578\) | 1.83013 | + | 6.83013i | 0.0761232 | + | 0.284096i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12.0000 | − | 6.92820i | 0.498273 | − | 0.287678i | ||||
\(581\) | 12.9282i | 0.536352i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.07180 | 0.375715 | ||||||||
\(584\) | 1.07180 | + | 1.07180i | 0.0443513 | + | 0.0443513i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.1962 | + | 4.33975i | −0.669057 | + | 0.179273i | ||||
\(587\) | 14.1962i | 0.585938i | 0.956122 | + | 0.292969i | \(0.0946433\pi\) | ||||
−0.956122 | + | 0.292969i | \(0.905357\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.9282i | 0.450289i | ||||||||
\(590\) | 0.196152 | + | 0.732051i | 0.00807547 | + | 0.0301381i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.92820 | − | 4.00000i | −0.284747 | − | 0.164399i | ||||
\(593\) | 36.6410 | 1.50467 | 0.752333 | − | 0.658783i | \(-0.228928\pi\) | ||||
0.752333 | + | 0.658783i | \(0.228928\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 9.46410i | − | 0.387990i | ||||||
\(596\) | 19.8564 | + | 34.3923i | 0.813350 | + | 1.40876i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −19.8564 | + | 5.32051i | −0.811989 | + | 0.217572i | ||||
\(599\) | −34.6410 | −1.41539 | −0.707697 | − | 0.706516i | \(-0.750266\pi\) | ||||
−0.707697 | + | 0.706516i | \(0.750266\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.4641 | 1.03870 | 0.519351 | − | 0.854561i | \(-0.326174\pi\) | ||||
0.519351 | + | 0.854561i | \(0.326174\pi\) | |||||||
\(602\) | 32.5885 | − | 8.73205i | 1.32821 | − | 0.355892i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.5359 | + | 8.39230i | −0.591457 | + | 0.341478i | ||||
\(605\) | 7.00000i | 0.284590i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.9808 | −0.851583 | −0.425791 | − | 0.904821i | \(-0.640004\pi\) | ||||
−0.425791 | + | 0.904821i | \(0.640004\pi\) | |||||||
\(608\) | 10.9282 | − | 40.7846i | 0.443197 | − | 1.65403i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.80385 | + | 6.73205i | 0.0730357 | + | 0.272573i | ||||
\(611\) | − | 23.3205i | − | 0.943447i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.60770i | 0.226493i | 0.993567 | + | 0.113246i | \(0.0361249\pi\) | ||||
−0.993567 | + | 0.113246i | \(0.963875\pi\) | |||||||
\(614\) | 36.8564 | − | 9.87564i | 1.48740 | − | 0.398549i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.9282 | − | 10.9282i | 0.440310 | − | 0.440310i | ||||
\(617\) | 27.4641 | 1.10566 | 0.552832 | − | 0.833293i | \(-0.313547\pi\) | ||||
0.552832 | + | 0.833293i | \(0.313547\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 33.3205i | − | 1.33926i | −0.742693 | − | 0.669632i | \(-0.766452\pi\) | ||
0.742693 | − | 0.669632i | \(-0.233548\pi\) | |||||||
\(620\) | −1.46410 | − | 2.53590i | −0.0587997 | − | 0.101844i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.21539 | − | 4.53590i | −0.0487327 | − | 0.181873i | ||||
\(623\) | −13.4641 | −0.539428 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 11.6603 | + | 43.5167i | 0.466037 | + | 1.73928i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.9282 | + | 29.3205i | 0.675509 | + | 1.17002i | ||||
\(629\) | − | 6.92820i | − | 0.276246i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.3205 | 0.450662 | 0.225331 | − | 0.974282i | \(-0.427654\pi\) | ||||
0.225331 | + | 0.974282i | \(0.427654\pi\) | |||||||
\(632\) | −29.8564 | − | 29.8564i | −1.18762 | − | 1.18762i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −21.1244 | + | 5.66025i | −0.838955 | + | 0.224797i | ||||
\(635\) | 13.2679i | 0.526523i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.60770i | 0.0636992i | ||||||||
\(638\) | 5.07180 | + | 18.9282i | 0.200794 | + | 0.749375i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.92820 | + | 10.9282i | 0.115747 | + | 0.431975i | ||||
\(641\) | 20.3923 | 0.805448 | 0.402724 | − | 0.915322i | \(-0.368064\pi\) | ||||
0.402724 | + | 0.915322i | \(0.368064\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.8756i | 0.586638i | 0.956015 | + | 0.293319i | \(0.0947598\pi\) | ||||
−0.956015 | + | 0.293319i | \(0.905240\pi\) | |||||||
\(644\) | −19.8564 | + | 11.4641i | −0.782452 | + | 0.451749i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 35.3205 | − | 9.46410i | 1.38967 | − | 0.372360i | ||||
\(647\) | −13.2679 | −0.521617 | −0.260808 | − | 0.965391i | \(-0.583989\pi\) | ||||
−0.260808 | + | 0.965391i | \(0.583989\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.07180 | −0.0420717 | ||||||||
\(650\) | −4.73205 | + | 1.26795i | −0.185606 | + | 0.0497331i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.1962 | − | 17.6603i | −0.399312 | − | 0.691629i | ||||
\(653\) | 36.2487i | 1.41852i | 0.704946 | + | 0.709261i | \(0.250971\pi\) | ||||
−0.704946 | + | 0.709261i | \(0.749029\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.85641 | 0.306975 | ||||||||
\(656\) | 10.9282 | − | 18.9282i | 0.426675 | − | 0.739022i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.73205 | − | 25.1244i | −0.262443 | − | 0.979449i | ||||
\(659\) | − | 17.3205i | − | 0.674711i | −0.941377 | − | 0.337356i | \(-0.890468\pi\) | ||
0.941377 | − | 0.337356i | \(-0.109532\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 35.8564i | − | 1.39465i | −0.716754 | − | 0.697326i | \(-0.754373\pi\) | ||
0.716754 | − | 0.697326i | \(-0.245627\pi\) | |||||||
\(662\) | −19.1244 | + | 5.12436i | −0.743289 | + | 0.199164i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.46410 | − | 9.46410i | 0.367278 | − | 0.367278i | ||||
\(665\) | 20.3923 | 0.790780 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 29.0718i | − | 1.12566i | ||||||
\(668\) | −34.9808 | + | 20.1962i | −1.35345 | + | 0.781413i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.66025 | + | 9.92820i | 0.102775 | + | 0.383560i | ||||
\(671\) | −9.85641 | −0.380502 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.4641 | 0.750286 | 0.375143 | − | 0.926967i | \(-0.377594\pi\) | ||||
0.375143 | + | 0.926967i | \(0.377594\pi\) | |||||||
\(674\) | −2.87564 | − | 10.7321i | −0.110766 | − | 0.413383i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.73205 | + | 1.00000i | −0.0666173 | + | 0.0384615i | ||||
\(677\) | − | 38.3923i | − | 1.47554i | −0.675054 | − | 0.737768i | \(-0.735880\pi\) | ||
0.675054 | − | 0.737768i | \(-0.264120\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.4641 | −0.670211 | ||||||||
\(680\) | −6.92820 | + | 6.92820i | −0.265684 | + | 0.265684i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.00000 | − | 1.07180i | 0.153168 | − | 0.0410412i | ||||
\(683\) | − | 34.9808i | − | 1.33850i | −0.743037 | − | 0.669251i | \(-0.766615\pi\) | ||
0.743037 | − | 0.669251i | \(-0.233385\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.92820i | 0.341129i | ||||||||
\(686\) | −6.53590 | − | 24.3923i | −0.249542 | − | 0.931303i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −30.2487 | − | 17.4641i | −1.15322 | − | 0.665813i | ||||
\(689\) | 15.7128 | 0.598610 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.0000i | 0.684752i | 0.939563 | + | 0.342376i | \(0.111232\pi\) | ||||
−0.939563 | + | 0.342376i | \(0.888768\pi\) | |||||||
\(692\) | 2.00000 | + | 3.46410i | 0.0760286 | + | 0.131685i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.3923 | + | 5.73205i | −0.812041 | + | 0.217586i | ||||
\(695\) | 7.46410 | 0.283130 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.9282 | 0.716957 | ||||||||
\(698\) | −38.2487 | + | 10.2487i | −1.44774 | + | 0.387919i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.73205 | + | 2.73205i | −0.178855 | + | 0.103262i | ||||
\(701\) | − | 32.9282i | − | 1.24368i | −0.783144 | − | 0.621841i | \(-0.786385\pi\) | ||
0.783144 | − | 0.621841i | \(-0.213615\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.9282 | 0.563028 | ||||||||
\(704\) | −16.0000 | −0.603023 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.339746 | − | 1.26795i | −0.0127865 | − | 0.0477199i | ||||
\(707\) | − | 29.8564i | − | 1.12287i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.7846i | 1.08103i | 0.841335 | + | 0.540514i | \(0.181770\pi\) | ||||
−0.841335 | + | 0.540514i | \(0.818230\pi\) | |||||||
\(710\) | 2.00000 | − | 0.535898i | 0.0750587 | − | 0.0201119i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.85641 | + | 9.85641i | 0.369384 | + | 0.369384i | ||||
\(713\) | −6.14359 | −0.230079 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 6.92820i | − | 0.259100i | ||||||
\(716\) | −15.4641 | − | 26.7846i | −0.577921 | − | 1.00099i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.85641 | + | 6.92820i | 0.0692805 | + | 0.258558i | ||||
\(719\) | −25.8564 | −0.964281 | −0.482141 | − | 0.876094i | \(-0.660141\pi\) | ||||
−0.482141 | + | 0.876094i | \(0.660141\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.53590 | 0.168926 | ||||||||
\(722\) | 13.4378 | + | 50.1506i | 0.500104 | + | 1.86641i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16.0000 | − | 27.7128i | −0.594635 | − | 1.02994i | ||||
\(725\) | − | 6.92820i | − | 0.257307i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0526 | 0.521181 | 0.260590 | − | 0.965449i | \(-0.416083\pi\) | ||||
0.260590 | + | 0.965449i | \(0.416083\pi\) | |||||||
\(728\) | 18.9282 | − | 18.9282i | 0.701526 | − | 0.701526i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.732051 | − | 0.196152i | 0.0270944 | − | 0.00725993i | ||||
\(731\) | − | 30.2487i | − | 1.11879i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 48.9282i | − | 1.80720i | −0.428373 | − | 0.903602i | \(-0.640913\pi\) | ||
0.428373 | − | 0.903602i | \(-0.359087\pi\) | |||||||
\(734\) | −9.92820 | − | 37.0526i | −0.366457 | − | 1.36763i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.9282 | + | 6.14359i | 0.845145 | + | 0.226456i | ||||
\(737\) | −14.5359 | −0.535437 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 5.32051i | − | 0.195718i | −0.995200 | − | 0.0978590i | \(-0.968801\pi\) | ||
0.995200 | − | 0.0978590i | \(-0.0311994\pi\) | |||||||
\(740\) | −3.46410 | + | 2.00000i | −0.127343 | + | 0.0735215i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 16.9282 | − | 4.53590i | 0.621454 | − | 0.166518i | ||||
\(743\) | 40.9808 | 1.50344 | 0.751719 | − | 0.659483i | \(-0.229225\pi\) | ||||
0.751719 | + | 0.659483i | \(0.229225\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.8564 | 0.727482 | ||||||||
\(746\) | 40.5885 | − | 10.8756i | 1.48605 | − | 0.398186i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.92820 | − | 12.0000i | −0.253320 | − | 0.438763i | ||||
\(749\) | − | 2.00000i | − | 0.0730784i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.2487 | −0.811867 | −0.405934 | − | 0.913903i | \(-0.633054\pi\) | ||||
−0.405934 | + | 0.913903i | \(0.633054\pi\) | |||||||
\(752\) | −13.4641 | + | 23.3205i | −0.490985 | + | 0.850411i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.78461 | + | 32.7846i | 0.319917 | + | 1.19395i | ||||
\(755\) | 8.39230i | 0.305427i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 32.9282i | − | 1.19680i | −0.801199 | − | 0.598398i | \(-0.795804\pi\) | ||
0.801199 | − | 0.598398i | \(-0.204196\pi\) | |||||||
\(758\) | 16.7321 | − | 4.48334i | 0.607735 | − | 0.162842i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −14.9282 | − | 14.9282i | −0.541503 | − | 0.541503i | ||||
\(761\) | −49.7128 | −1.80209 | −0.901044 | − | 0.433728i | \(-0.857198\pi\) | ||||
−0.901044 | + | 0.433728i | \(0.857198\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 8.39230i | − | 0.303822i | ||||||
\(764\) | −33.4641 | + | 19.3205i | −1.21069 | + | 0.698991i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.14359 | − | 4.26795i | −0.0413197 | − | 0.154207i | ||||
\(767\) | −1.85641 | −0.0670310 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.928203 | −0.0334719 | −0.0167359 | − | 0.999860i | \(-0.505327\pi\) | ||||
−0.0167359 | + | 0.999860i | \(0.505327\pi\) | |||||||
\(770\) | −2.00000 | − | 7.46410i | −0.0720750 | − | 0.268988i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.9282 | + | 7.46410i | −0.465296 | + | 0.268639i | ||||
\(773\) | 1.60770i | 0.0578248i | 0.999582 | + | 0.0289124i | \(0.00920438\pi\) | ||||
−0.999582 | + | 0.0289124i | \(0.990796\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.46410 | −0.0525921 | ||||||||
\(776\) | 12.7846 | + | 12.7846i | 0.458941 | + | 0.458941i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 47.5167 | − | 12.7321i | 1.70355 | − | 0.456466i | ||||
\(779\) | 40.7846i | 1.46126i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.92820i | 0.104779i | ||||||||
\(782\) | 5.32051 | + | 19.8564i | 0.190261 | + | 0.710064i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.928203 | − | 1.60770i | 0.0331501 | − | 0.0574177i | ||||
\(785\) | 16.9282 | 0.604193 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 14.5885i | − | 0.520022i | −0.965606 | − | 0.260011i | \(-0.916274\pi\) | ||
0.965606 | − | 0.260011i | \(-0.0837262\pi\) | |||||||
\(788\) | −12.5359 | − | 21.7128i | −0.446573 | − | 0.773487i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −20.3923 | + | 5.46410i | −0.725526 | + | 0.194404i | ||||
\(791\) | 2.53590 | 0.0901662 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.0718 | −0.606237 | ||||||||
\(794\) | −22.1962 | + | 5.94744i | −0.787712 | + | 0.211067i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −44.7846 | + | 25.8564i | −1.58735 | + | 0.916456i | ||||
\(797\) | 26.1051i | 0.924691i | 0.886700 | + | 0.462345i | \(0.152992\pi\) | ||||
−0.886700 | + | 0.462345i | \(0.847008\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.3205 | −0.825020 | ||||||||
\(800\) | 5.46410 | + | 1.46410i | 0.193185 | + | 0.0517638i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.26795 | + | 27.1244i | 0.256640 | + | 0.957794i | ||||
\(803\) | 1.07180i | 0.0378229i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.4641i | 0.404056i | ||||||||
\(806\) | 6.92820 | − | 1.85641i | 0.244036 | − | 0.0653891i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −21.8564 | + | 21.8564i | −0.768906 | + | 0.768906i | ||||
\(809\) | 3.85641 | 0.135584 | 0.0677920 | − | 0.997699i | \(-0.478405\pi\) | ||||
0.0677920 | + | 0.997699i | \(0.478405\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 15.0718i | − | 0.529242i | −0.964352 | − | 0.264621i | \(-0.914753\pi\) | ||
0.964352 | − | 0.264621i | \(-0.0852469\pi\) | |||||||
\(812\) | 18.9282 | + | 32.7846i | 0.664250 | + | 1.15051i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.46410 | − | 5.46410i | −0.0513167 | − | 0.191517i | ||||
\(815\) | −10.1962 | −0.357156 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 65.1769 | 2.28025 | ||||||||
\(818\) | −8.53590 | − | 31.8564i | −0.298451 | − | 1.11383i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.46410 | − | 9.46410i | −0.190815 | − | 0.330501i | ||||
\(821\) | 6.78461i | 0.236785i | 0.992967 | + | 0.118392i | \(0.0377740\pi\) | ||||
−0.992967 | + | 0.118392i | \(0.962226\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.1244 | 0.527202 | 0.263601 | − | 0.964632i | \(-0.415090\pi\) | ||||
0.263601 | + | 0.964632i | \(0.415090\pi\) | |||||||
\(824\) | −3.32051 | − | 3.32051i | −0.115675 | − | 0.115675i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.00000 | + | 0.535898i | −0.0695889 | + | 0.0186463i | ||||
\(827\) | 1.12436i | 0.0390977i | 0.999809 | + | 0.0195488i | \(0.00622298\pi\) | ||||
−0.999809 | + | 0.0195488i | \(0.993777\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.0718i | 0.523465i | 0.965140 | + | 0.261733i | \(0.0842938\pi\) | ||||
−0.965140 | + | 0.261733i | \(0.915706\pi\) | |||||||
\(830\) | −1.73205 | − | 6.46410i | −0.0601204 | − | 0.224372i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −27.7128 | −0.960769 | ||||||||
\(833\) | 1.60770 | 0.0557033 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.1962i | 0.698917i | ||||||||
\(836\) | 25.8564 | − | 14.9282i | 0.894263 | − | 0.516303i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.26795 | − | 0.875644i | 0.112889 | − | 0.0302486i | ||||
\(839\) | 16.7846 | 0.579469 | 0.289735 | − | 0.957107i | \(-0.406433\pi\) | ||||
0.289735 | + | 0.957107i | \(0.406433\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.0000 | −0.655172 | ||||||||
\(842\) | 38.0526 | − | 10.1962i | 1.31138 | − | 0.351383i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.7846 | + | 25.6077i | 0.508907 | + | 0.881453i | ||||
\(845\) | 1.00000i | 0.0344010i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.1244 | −0.657121 | ||||||||
\(848\) | −15.7128 | − | 9.07180i | −0.539580 | − | 0.311527i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.26795 | + | 4.73205i | 0.0434903 | + | 0.162308i | ||||
\(851\) | 8.39230i | 0.287685i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 42.3923i | − | 1.45148i | −0.687967 | − | 0.725742i | \(-0.741496\pi\) | ||
0.687967 | − | 0.725742i | \(-0.258504\pi\) | |||||||
\(854\) | −18.3923 | + | 4.92820i | −0.629372 | + | 0.168640i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.46410 | + | 1.46410i | −0.0500420 | + | 0.0500420i | ||||
\(857\) | −7.85641 | −0.268370 | −0.134185 | − | 0.990956i | \(-0.542842\pi\) | ||||
−0.134185 | + | 0.990956i | \(0.542842\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 20.2487i | − | 0.690877i | −0.938441 | − | 0.345439i | \(-0.887730\pi\) | ||
0.938441 | − | 0.345439i | \(-0.112270\pi\) | |||||||
\(860\) | −15.1244 | + | 8.73205i | −0.515736 | + | 0.297760i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.32051 | − | 19.8564i | −0.181217 | − | 0.676312i | ||||
\(863\) | −30.3397 | −1.03278 | −0.516388 | − | 0.856354i | \(-0.672724\pi\) | ||||
−0.516388 | + | 0.856354i | \(0.672724\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.00000 | 0.0680020 | ||||||||
\(866\) | 4.58846 | + | 17.1244i | 0.155922 | + | 0.581909i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.92820 | − | 4.00000i | 0.235159 | − | 0.135769i | ||||
\(869\) | − | 29.8564i | − | 1.01281i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.1769 | −0.853087 | ||||||||
\(872\) | −6.14359 | + | 6.14359i | −0.208048 | + | 0.208048i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −42.7846 | + | 11.4641i | −1.44721 | + | 0.387779i | ||||
\(875\) | 2.73205i | 0.0923602i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 53.7128i | 1.81375i | 0.421397 | + | 0.906876i | \(0.361540\pi\) | ||||
−0.421397 | + | 0.906876i | \(0.638460\pi\) | |||||||
\(878\) | 0.287187 | + | 1.07180i | 0.00969209 | + | 0.0361714i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.00000 | + | 6.92820i | −0.134840 | + | 0.233550i | ||||
\(881\) | −2.53590 | −0.0854366 | −0.0427183 | − | 0.999087i | \(-0.513602\pi\) | ||||
−0.0427183 | + | 0.999087i | \(0.513602\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.9090i | 1.27574i | 0.770145 | + | 0.637869i | \(0.220184\pi\) | ||||
−0.770145 | + | 0.637869i | \(0.779816\pi\) | |||||||
\(884\) | −12.0000 | − | 20.7846i | −0.403604 | − | 0.699062i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 42.3205 | − | 11.3397i | 1.42179 | − | 0.380966i | ||||
\(887\) | −51.9090 | −1.74293 | −0.871466 | − | 0.490455i | \(-0.836830\pi\) | ||||
−0.871466 | + | 0.490455i | \(0.836830\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.2487 | −1.21574 | ||||||||
\(890\) | 6.73205 | − | 1.80385i | 0.225659 | − | 0.0604651i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 28.0526 | − | 16.1962i | 0.939269 | − | 0.542287i | ||||
\(893\) | − | 50.2487i | − | 1.68151i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.4641 | −0.516908 | ||||||||
\(896\) | −29.8564 | + | 8.00000i | −0.997433 | + | 0.267261i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.14359 | + | 15.4641i | 0.138274 | + | 0.516044i | ||||
\(899\) | 10.1436i | 0.338308i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 15.7128i | − | 0.523470i | ||||||
\(902\) | 14.9282 | − | 4.00000i | 0.497055 | − | 0.133185i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.85641 | − | 1.85641i | −0.0617432 | − | 0.0617432i | ||||
\(905\) | −16.0000 | −0.531858 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.1244i | 0.967058i | 0.875328 | + | 0.483529i | \(0.160645\pi\) | ||||
−0.875328 | + | 0.483529i | \(0.839355\pi\) | |||||||
\(908\) | −28.0526 | − | 48.5885i | −0.930957 | − | 1.61246i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.46410 | − | 12.9282i | −0.114834 | − | 0.428566i | ||||
\(911\) | −13.1769 | −0.436571 | −0.218285 | − | 0.975885i | \(-0.570046\pi\) | ||||
−0.218285 | + | 0.975885i | \(0.570046\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.46410 | 0.313216 | ||||||||
\(914\) | −5.41154 | − | 20.1962i | −0.178998 | − | 0.668029i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.00000 | + | 6.92820i | 0.132164 | + | 0.228914i | ||||
\(917\) | 21.4641i | 0.708807i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.0718 | −0.827042 | −0.413521 | − | 0.910495i | \(-0.635701\pi\) | ||||
−0.413521 | + | 0.910495i | \(0.635701\pi\) | |||||||
\(920\) | 8.39230 | − | 8.39230i | 0.276686 | − | 0.276686i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.00000 | + | 1.07180i | −0.131733 | + | 0.0352977i | ||||
\(923\) | 5.07180i | 0.166940i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000i | 0.0657596i | ||||||||
\(926\) | 5.39230 | + | 20.1244i | 0.177202 | + | 0.661327i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10.1436 | − | 37.8564i | 0.332980 | − | 1.24270i | ||||
\(929\) | 10.5359 | 0.345672 | 0.172836 | − | 0.984951i | \(-0.444707\pi\) | ||||
0.172836 | + | 0.984951i | \(0.444707\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.46410i | 0.113531i | ||||||||
\(932\) | 50.7846 | − | 29.3205i | 1.66351 | − | 0.960425i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.3923 | − | 3.05256i | 0.372768 | − | 0.0998828i | ||||
\(935\) | −6.92820 | −0.226576 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.2487 | −1.44554 | −0.722771 | − | 0.691087i | \(-0.757132\pi\) | ||||
−0.722771 | + | 0.691087i | \(0.757132\pi\) | |||||||
\(938\) | −27.1244 | + | 7.26795i | −0.885642 | + | 0.237307i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.73205 | + | 11.6603i | 0.219575 | + | 0.380316i | ||||
\(941\) | 32.0000i | 1.04317i | 0.853199 | + | 0.521585i | \(0.174659\pi\) | ||||
−0.853199 | + | 0.521585i | \(0.825341\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.9282 | −0.746645 | ||||||||
\(944\) | 1.85641 | + | 1.07180i | 0.0604209 | + | 0.0348840i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.39230 | − | 23.8564i | −0.207832 | − | 0.775639i | ||||
\(947\) | − | 21.1244i | − | 0.686449i | −0.939253 | − | 0.343225i | \(-0.888481\pi\) | ||
0.939253 | − | 0.343225i | \(-0.111519\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.85641i | 0.0602615i | ||||||||
\(950\) | −10.1962 | + | 2.73205i | −0.330807 | + | 0.0886394i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −18.9282 | − | 18.9282i | −0.613467 | − | 0.613467i | ||||
\(953\) | 58.7846 | 1.90422 | 0.952110 | − | 0.305755i | \(-0.0989089\pi\) | ||||
0.952110 | + | 0.305755i | \(0.0989089\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.3205i | 0.625197i | ||||||||
\(956\) | −34.6410 | + | 20.0000i | −1.12037 | + | 0.646846i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.00000 | − | 29.8564i | −0.258468 | − | 0.964617i | ||||
\(959\) | −24.3923 | −0.787669 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.8564 | −0.930852 | ||||||||
\(962\) | −2.53590 | − | 9.46410i | −0.0817606 | − | 0.305135i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.60770 | − | 4.39230i | 0.245027 | − | 0.141467i | ||||
\(965\) | 7.46410i | 0.240278i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.6603 | 1.08244 | 0.541220 | − | 0.840881i | \(-0.317962\pi\) | ||||
0.541220 | + | 0.840881i | \(0.317962\pi\) | |||||||
\(968\) | 14.0000 | + | 14.0000i | 0.449977 | + | 0.449977i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.73205 | − | 2.33975i | 0.280369 | − | 0.0751247i | ||||
\(971\) | − | 23.0718i | − | 0.740409i | −0.928950 | − | 0.370205i | \(-0.879288\pi\) | ||
0.928950 | − | 0.370205i | \(-0.120712\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.3923i | 0.653747i | ||||||||
\(974\) | 9.00000 | + | 33.5885i | 0.288379 | + | 1.07624i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 17.0718 | + | 9.85641i | 0.546455 | + | 0.315496i | ||||
\(977\) | 31.4641 | 1.00663 | 0.503313 | − | 0.864104i | \(-0.332114\pi\) | ||||
0.503313 | + | 0.864104i | \(0.332114\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.85641i | 0.315012i | ||||||||
\(980\) | −0.464102 | − | 0.803848i | −0.0148252 | − | 0.0256780i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.19615 | − | 1.12436i | 0.133905 | − | 0.0358796i | ||||
\(983\) | 45.2679 | 1.44382 | 0.721912 | − | 0.691985i | \(-0.243264\pi\) | ||||
0.721912 | + | 0.691985i | \(0.243264\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.5359 | −0.399427 | ||||||||
\(986\) | 32.7846 | − | 8.78461i | 1.04407 | − | 0.279759i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 44.7846 | − | 25.8564i | 1.42479 | − | 0.822602i | ||||
\(989\) | 36.6410i | 1.16512i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.5359 | 1.09707 | 0.548534 | − | 0.836128i | \(-0.315186\pi\) | ||||
0.548534 | + | 0.836128i | \(0.315186\pi\) | |||||||
\(992\) | −8.00000 | − | 2.14359i | −0.254000 | − | 0.0680592i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.46410 | + | 5.46410i | 0.0464385 | + | 0.173311i | ||||
\(995\) | 25.8564i | 0.819703i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.1769i | 1.62079i | 0.585884 | + | 0.810395i | \(0.300747\pi\) | ||||
−0.585884 | + | 0.810395i | \(0.699253\pi\) | |||||||
\(998\) | 33.5167 | − | 8.98076i | 1.06095 | − | 0.284281i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))