Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,2,Mod(1549,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.1549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.d (of order \(2\), degree \(1\), 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: | \(14.3730723638\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1549.3 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.1549 |
Dual form | 1800.2.d.p.1549.4 |
$q$-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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36603 | − | 0.366025i | 0.965926 | − | 0.258819i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.73205 | − | 1.00000i | 0.866025 | − | 0.500000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.73205i | − | 1.03262i | −0.856402 | − | 0.516309i | \(-0.827306\pi\) | ||
0.856402 | − | 0.516309i | \(-0.172694\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.707107 | − | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000i | 0.603023i | 0.953463 | + | 0.301511i | \(0.0974911\pi\) | ||||
−0.953463 | + | 0.301511i | \(0.902509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.46410 | 0.960769 | 0.480384 | − | 0.877058i | \(-0.340497\pi\) | ||||
0.480384 | + | 0.877058i | \(0.340497\pi\) | |||||||
\(14\) | −1.00000 | − | 3.73205i | −0.267261 | − | 0.997433i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 3.46410i | 0.840168i | 0.907485 | + | 0.420084i | \(0.137999\pi\) | ||||
−0.907485 | + | 0.420084i | \(0.862001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.46410i | − | 1.71238i | −0.516659 | − | 0.856191i | \(-0.672825\pi\) | ||
0.516659 | − | 0.856191i | \(-0.327175\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.732051 | + | 2.73205i | 0.156074 | + | 0.582475i | ||||
\(23\) | 4.19615i | 0.874958i | 0.899229 | + | 0.437479i | \(0.144129\pi\) | ||||
−0.899229 | + | 0.437479i | \(0.855871\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.73205 | − | 1.26795i | 0.928032 | − | 0.248665i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.73205 | − | 4.73205i | −0.516309 | − | 0.894274i | ||||
\(29\) | − | 6.92820i | − | 1.28654i | −0.765641 | − | 0.643268i | \(-0.777578\pi\) | ||
0.765641 | − | 0.643268i | \(-0.222422\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.46410 | 0.262960 | 0.131480 | − | 0.991319i | \(-0.458027\pi\) | ||||
0.131480 | + | 0.991319i | \(0.458027\pi\) | |||||||
\(32\) | 1.46410 | − | 5.46410i | 0.258819 | − | 0.965926i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.26795 | + | 4.73205i | 0.217451 | + | 0.811540i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | −2.73205 | − | 10.1962i | −0.443197 | − | 1.65403i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.46410 | 0.853349 | 0.426675 | − | 0.904405i | \(-0.359685\pi\) | ||||
0.426675 | + | 0.904405i | \(0.359685\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.73205 | −1.33163 | −0.665813 | − | 0.746119i | \(-0.731915\pi\) | ||||
−0.665813 | + | 0.746119i | \(0.731915\pi\) | |||||||
\(44\) | 2.00000 | + | 3.46410i | 0.301511 | + | 0.522233i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.53590 | + | 5.73205i | 0.226456 | + | 0.845145i | ||||
\(47\) | − | 6.73205i | − | 0.981971i | −0.871168 | − | 0.490985i | \(-0.836637\pi\) | ||
0.871168 | − | 0.490985i | \(-0.163363\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.464102 | −0.0663002 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.00000 | − | 3.46410i | 0.832050 | − | 0.480384i | ||||
\(53\) | −4.53590 | −0.623054 | −0.311527 | − | 0.950237i | \(-0.600840\pi\) | ||||
−0.311527 | + | 0.950237i | \(0.600840\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.46410 | − | 5.46410i | −0.730171 | − | 0.730171i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.53590 | − | 9.46410i | −0.332980 | − | 1.24270i | ||||
\(59\) | − | 0.535898i | − | 0.0697680i | −0.999391 | − | 0.0348840i | \(-0.988894\pi\) | ||
0.999391 | − | 0.0348840i | \(-0.0111062\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.92820i | 0.630992i | 0.948927 | + | 0.315496i | \(0.102171\pi\) | ||||
−0.948927 | + | 0.315496i | \(0.897829\pi\) | |||||||
\(62\) | 2.00000 | − | 0.535898i | 0.254000 | − | 0.0680592i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.26795 | −0.887921 | −0.443961 | − | 0.896046i | \(-0.646427\pi\) | ||||
−0.443961 | + | 0.896046i | \(0.646427\pi\) | |||||||
\(68\) | 3.46410 | + | 6.00000i | 0.420084 | + | 0.727607i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.46410 | 0.173757 | 0.0868784 | − | 0.996219i | \(-0.472311\pi\) | ||||
0.0868784 | + | 0.996219i | \(0.472311\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.535898i | − | 0.0627222i | −0.999508 | − | 0.0313611i | \(-0.990016\pi\) | ||
0.999508 | − | 0.0313611i | \(-0.00998418\pi\) | |||||||
\(74\) | 2.73205 | − | 0.732051i | 0.317594 | − | 0.0850992i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.46410 | − | 12.9282i | −0.856191 | − | 1.48297i | ||||
\(77\) | 5.46410 | 0.622692 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.9282 | 1.67955 | 0.839777 | − | 0.542931i | \(-0.182686\pi\) | ||||
0.839777 | + | 0.542931i | \(0.182686\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.46410 | − | 2.00000i | 0.824272 | − | 0.220863i | ||||
\(83\) | −4.73205 | −0.519410 | −0.259705 | − | 0.965688i | \(-0.583625\pi\) | ||||
−0.259705 | + | 0.965688i | \(0.583625\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −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 | \(-0.584116\pi\) | ||||
−0.261194 | + | 0.965286i | \(0.584116\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 9.46410i | − | 0.992107i | ||||||
\(92\) | 4.19615 | + | 7.26795i | 0.437479 | + | 0.757736i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.46410 | − | 9.19615i | −0.254153 | − | 0.948511i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.39230i | 0.649040i | 0.945879 | + | 0.324520i | \(0.105203\pi\) | ||||
−0.945879 | + | 0.324520i | \(0.894797\pi\) | |||||||
\(98\) | −0.633975 | + | 0.169873i | −0.0640411 | + | 0.0171598i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.9282i | 1.08740i | 0.839281 | + | 0.543698i | \(0.182976\pi\) | ||||
−0.839281 | + | 0.543698i | \(0.817024\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.66025i | 0.163590i | 0.996649 | + | 0.0817948i | \(0.0260652\pi\) | ||||
−0.996649 | + | 0.0817948i | \(0.973935\pi\) | |||||||
\(104\) | 6.92820 | − | 6.92820i | 0.679366 | − | 0.679366i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.19615 | + | 1.66025i | −0.601824 | + | 0.161258i | ||||
\(107\) | −0.732051 | −0.0707700 | −0.0353850 | − | 0.999374i | \(-0.511266\pi\) | ||||
−0.0353850 | + | 0.999374i | \(0.511266\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.07180i | − | 0.294225i | −0.989120 | − | 0.147112i | \(-0.953002\pi\) | ||
0.989120 | − | 0.147112i | \(-0.0469979\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.46410 | − | 5.46410i | −0.894274 | − | 0.516309i | ||||
\(113\) | 0.928203i | 0.0873180i | 0.999046 | + | 0.0436590i | \(0.0139015\pi\) | ||||
−0.999046 | + | 0.0436590i | \(0.986098\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.92820 | − | 12.0000i | −0.643268 | − | 1.11417i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.196152 | − | 0.732051i | −0.0180573 | − | 0.0673907i | ||||
\(119\) | 9.46410 | 0.867573 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 1.80385 | + | 6.73205i | 0.163313 | + | 0.609491i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.53590 | − | 1.46410i | 0.227730 | − | 0.131480i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.2679i | 1.17734i | 0.808373 | + | 0.588670i | \(0.200348\pi\) | ||||
−0.808373 | + | 0.588670i | \(0.799652\pi\) | |||||||
\(128\) | −2.92820 | − | 10.9282i | −0.258819 | − | 0.965926i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 7.85641i | − | 0.686417i | −0.939259 | − | 0.343209i | \(-0.888486\pi\) | ||
0.939259 | − | 0.343209i | \(-0.111514\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.3923 | −1.76824 | ||||||||
\(134\) | −9.92820 | + | 2.66025i | −0.857666 | + | 0.229811i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.92820 | + | 6.92820i | 0.594089 | + | 0.594089i | ||||
\(137\) | 8.92820i | 0.762788i | 0.924413 | + | 0.381394i | \(0.124556\pi\) | ||||
−0.924413 | + | 0.381394i | \(0.875444\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.46410i | 0.633097i | 0.948576 | + | 0.316548i | \(0.102524\pi\) | ||||
−0.948576 | + | 0.316548i | \(0.897476\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.00000 | − | 0.535898i | 0.167836 | − | 0.0449716i | ||||
\(143\) | 6.92820i | 0.579365i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.196152 | − | 0.732051i | −0.0162337 | − | 0.0605850i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.46410 | − | 2.00000i | 0.284747 | − | 0.164399i | ||||
\(149\) | 19.8564i | 1.62670i | 0.581775 | + | 0.813350i | \(0.302359\pi\) | ||||
−0.581775 | + | 0.813350i | \(0.697641\pi\) | |||||||
\(150\) | 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 | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.9282 | 1.35102 | 0.675509 | − | 0.737352i | \(-0.263924\pi\) | ||||
0.675509 | + | 0.737352i | \(0.263924\pi\) | |||||||
\(158\) | 20.3923 | − | 5.46410i | 1.62232 | − | 0.434701i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.4641 | 0.903498 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.1962 | 0.798624 | 0.399312 | − | 0.916815i | \(-0.369249\pi\) | ||||
0.399312 | + | 0.916815i | \(0.369249\pi\) | |||||||
\(164\) | 9.46410 | − | 5.46410i | 0.739022 | − | 0.426675i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.46410 | + | 1.73205i | −0.501712 | + | 0.134433i | ||||
\(167\) | 20.1962i | 1.56283i | 0.624015 | + | 0.781413i | \(0.285501\pi\) | ||||
−0.624015 | + | 0.781413i | \(0.714499\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −15.1244 | + | 8.73205i | −1.15322 | + | 0.665813i | ||||
\(173\) | −2.00000 | −0.152057 | −0.0760286 | − | 0.997106i | \(-0.524224\pi\) | ||||
−0.0760286 | + | 0.997106i | \(0.524224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.92820 | + | 4.00000i | 0.522233 | + | 0.301511i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.73205 | + | 1.80385i | −0.504589 | + | 0.135204i | ||||
\(179\) | − | 15.4641i | − | 1.15584i | −0.816093 | − | 0.577921i | \(-0.803864\pi\) | ||
0.816093 | − | 0.577921i | \(-0.196136\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.0000i | 1.18927i | 0.803996 | + | 0.594635i | \(0.202704\pi\) | ||||
−0.803996 | + | 0.594635i | \(0.797296\pi\) | |||||||
\(182\) | −3.46410 | − | 12.9282i | −0.256776 | − | 0.958302i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.39230 | + | 8.39230i | 0.618689 | + | 0.618689i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.92820 | −0.506640 | ||||||||
\(188\) | −6.73205 | − | 11.6603i | −0.490985 | − | 0.850411i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.3205 | 1.39798 | 0.698991 | − | 0.715130i | \(-0.253633\pi\) | ||||
0.698991 | + | 0.715130i | \(0.253633\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 7.46410i | − | 0.537278i | −0.963241 | − | 0.268639i | \(-0.913426\pi\) | ||
0.963241 | − | 0.268639i | \(-0.0865738\pi\) | |||||||
\(194\) | 2.33975 | + | 8.73205i | 0.167984 | + | 0.626925i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.803848 | + | 0.464102i | −0.0574177 | + | 0.0331501i | ||||
\(197\) | −12.5359 | −0.893146 | −0.446573 | − | 0.894747i | \(-0.647356\pi\) | ||||
−0.446573 | + | 0.894747i | \(0.647356\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.8564 | −1.83291 | −0.916456 | − | 0.400135i | \(-0.868963\pi\) | ||||
−0.916456 | + | 0.400135i | \(0.868963\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.00000 | + | 14.9282i | 0.281439 | + | 1.05034i | ||||
\(203\) | −18.9282 | −1.32850 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.607695 | + | 2.26795i | 0.0423401 | + | 0.158016i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.92820 | − | 12.0000i | 0.480384 | − | 0.832050i | ||||
\(209\) | 14.9282 | 1.03261 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 14.7846i | − | 1.01781i | −0.860821 | − | 0.508907i | \(-0.830050\pi\) | ||
0.860821 | − | 0.508907i | \(-0.169950\pi\) | |||||||
\(212\) | −7.85641 | + | 4.53590i | −0.539580 | + | 0.311527i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.00000 | + | 0.267949i | −0.0683586 | + | 0.0183166i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 4.00000i | − | 0.271538i | ||||||
\(218\) | −1.12436 | − | 4.19615i | −0.0761510 | − | 0.284199i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000i | 0.807207i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.1962i | 1.08457i | 0.840193 | + | 0.542287i | \(0.182442\pi\) | ||||
−0.840193 | + | 0.542287i | \(0.817558\pi\) | |||||||
\(224\) | −14.9282 | − | 4.00000i | −0.997433 | − | 0.267261i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.339746 | + | 1.26795i | 0.0225996 | + | 0.0843427i | ||||
\(227\) | −28.0526 | −1.86191 | −0.930957 | − | 0.365129i | \(-0.881025\pi\) | ||||
−0.930957 | + | 0.365129i | \(0.881025\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.00000i | 0.264327i | 0.991228 | + | 0.132164i | \(0.0421925\pi\) | ||||
−0.991228 | + | 0.132164i | \(0.957808\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.8564 | − | 13.8564i | −0.909718 | − | 0.909718i | ||||
\(233\) | 29.3205i | 1.92085i | 0.278538 | + | 0.960425i | \(0.410150\pi\) | ||||
−0.278538 | + | 0.960425i | \(0.589850\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.535898 | − | 0.928203i | −0.0348840 | − | 0.0604209i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 12.9282 | − | 3.46410i | 0.838011 | − | 0.224544i | ||||
\(239\) | −20.0000 | −1.29369 | −0.646846 | − | 0.762620i | \(-0.723912\pi\) | ||||
−0.646846 | + | 0.762620i | \(0.723912\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.39230 | −0.282933 | −0.141467 | − | 0.989943i | \(-0.545182\pi\) | ||||
−0.141467 | + | 0.989943i | \(0.545182\pi\) | |||||||
\(242\) | 9.56218 | − | 2.56218i | 0.614680 | − | 0.164703i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.92820 | + | 8.53590i | 0.315496 | + | 0.546455i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 25.8564i | − | 1.64520i | ||||||
\(248\) | 2.92820 | − | 2.92820i | 0.185941 | − | 0.185941i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 11.0718i | − | 0.698846i | −0.936965 | − | 0.349423i | \(-0.886378\pi\) | ||
0.936965 | − | 0.349423i | \(-0.113622\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.39230 | −0.527620 | ||||||||
\(254\) | 4.85641 | + | 18.1244i | 0.304718 | + | 1.13722i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 2.00000i | 0.124757i | 0.998053 | + | 0.0623783i | \(0.0198685\pi\) | ||||
−0.998053 | + | 0.0623783i | \(0.980131\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 5.46410i | − | 0.339523i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.87564 | − | 10.7321i | −0.177658 | − | 0.663028i | ||||
\(263\) | 5.66025i | 0.349026i | 0.984655 | + | 0.174513i | \(0.0558351\pi\) | ||||
−0.984655 | + | 0.174513i | \(0.944165\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −27.8564 | + | 7.46410i | −1.70799 | + | 0.457653i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.5885 | + | 7.26795i | −0.768962 | + | 0.443961i | ||||
\(269\) | 4.92820i | 0.300478i | 0.988650 | + | 0.150239i | \(0.0480043\pi\) | ||||
−0.988650 | + | 0.150239i | \(0.951996\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.3205 | 0.930655 | 0.465327 | − | 0.885139i | \(-0.345937\pi\) | ||||
0.465327 | + | 0.885139i | \(0.345937\pi\) | |||||||
\(272\) | 12.0000 | + | 6.92820i | 0.727607 | + | 0.420084i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.26795 | + | 12.1962i | 0.197424 | + | 0.736797i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00000 | −0.120168 | −0.0600842 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600842 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(278\) | 2.73205 | + | 10.1962i | 0.163858 | + | 0.611525i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.4641 | −1.04182 | −0.520910 | − | 0.853611i | \(-0.674407\pi\) | ||||
−0.520910 | + | 0.853611i | \(0.674407\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.66025 | 0.455355 | 0.227677 | − | 0.973737i | \(-0.426887\pi\) | ||||
0.227677 | + | 0.973737i | \(0.426887\pi\) | |||||||
\(284\) | 2.53590 | − | 1.46410i | 0.150478 | − | 0.0868784i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.53590 | + | 9.46410i | 0.149951 | + | 0.559624i | ||||
\(287\) | − | 14.9282i | − | 0.881184i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.00000 | 0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.535898 | − | 0.928203i | −0.0313611 | − | 0.0543190i | ||||
\(293\) | −11.8564 | −0.692659 | −0.346329 | − | 0.938113i | \(-0.612572\pi\) | ||||
−0.346329 | + | 0.938113i | \(0.612572\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.00000 | − | 4.00000i | 0.232495 | − | 0.232495i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.26795 | + | 27.1244i | 0.421021 | + | 1.57127i | ||||
\(299\) | 14.5359i | 0.840633i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.8564i | 1.37506i | ||||||||
\(302\) | 11.4641 | − | 3.07180i | 0.659685 | − | 0.176762i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −25.8564 | − | 14.9282i | −1.48297 | − | 0.856191i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.9808 | −1.53987 | −0.769937 | − | 0.638120i | \(-0.779712\pi\) | ||||
−0.769937 | + | 0.638120i | \(0.779712\pi\) | |||||||
\(308\) | 9.46410 | − | 5.46410i | 0.539267 | − | 0.311346i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.32051 | 0.188289 | 0.0941444 | − | 0.995559i | \(-0.469988\pi\) | ||||
0.0941444 | + | 0.995559i | \(0.469988\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.8564i | 1.80063i | 0.435238 | + | 0.900315i | \(0.356664\pi\) | ||||
−0.435238 | + | 0.900315i | \(0.643336\pi\) | |||||||
\(314\) | 23.1244 | − | 6.19615i | 1.30498 | − | 0.349669i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 25.8564 | − | 14.9282i | 1.45454 | − | 0.839777i | ||||
\(317\) | 15.4641 | 0.868550 | 0.434275 | − | 0.900780i | \(-0.357005\pi\) | ||||
0.434275 | + | 0.900780i | \(0.357005\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.8564 | 0.775810 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 15.6603 | − | 4.19615i | 0.872712 | − | 0.233842i | ||||
\(323\) | 25.8564 | 1.43869 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 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 | \(-0.125714\pi\) | |||||||
\(332\) | −8.19615 | + | 4.73205i | −0.449822 | + | 0.259705i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.39230 | + | 27.5885i | 0.404489 | + | 1.50957i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.85641i | 0.427966i | 0.976837 | + | 0.213983i | \(0.0686437\pi\) | ||||
−0.976837 | + | 0.213983i | \(0.931356\pi\) | |||||||
\(338\) | −1.36603 | + | 0.366025i | −0.0743020 | + | 0.0199092i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.92820i | 0.158571i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.8564i | − | 0.964155i | ||||||
\(344\) | −17.4641 | + | 17.4641i | −0.941601 | + | 0.941601i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.73205 | + | 0.732051i | −0.146876 | + | 0.0393553i | ||||
\(347\) | 15.6603 | 0.840686 | 0.420343 | − | 0.907365i | \(-0.361910\pi\) | ||||
0.420343 | + | 0.907365i | \(0.361910\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.0000i | 1.49881i | 0.662114 | + | 0.749403i | \(0.269659\pi\) | ||||
−0.662114 | + | 0.749403i | \(0.730341\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.9282 | + | 2.92820i | 0.582475 | + | 0.156074i | ||||
\(353\) | − | 0.928203i | − | 0.0494033i | −0.999695 | − | 0.0247016i | \(-0.992136\pi\) | ||
0.999695 | − | 0.0247016i | \(-0.00786357\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8.53590 | + | 4.92820i | −0.452402 | + | 0.261194i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.66025 | − | 21.1244i | −0.299154 | − | 1.11646i | ||||
\(359\) | 5.07180 | 0.267679 | 0.133840 | − | 0.991003i | \(-0.457269\pi\) | ||||
0.133840 | + | 0.991003i | \(0.457269\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −36.7128 | −1.93225 | ||||||||
\(362\) | 5.85641 | + | 21.8564i | 0.307806 | + | 1.14875i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.46410 | − | 16.3923i | −0.496054 | − | 0.859190i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.1244i | 1.41588i | 0.706273 | + | 0.707940i | \(0.250375\pi\) | ||||
−0.706273 | + | 0.707940i | \(0.749625\pi\) | |||||||
\(368\) | 14.5359 | + | 8.39230i | 0.757736 | + | 0.437479i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.3923i | 0.643376i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.7128 | 1.53847 | 0.769236 | − | 0.638965i | \(-0.220637\pi\) | ||||
0.769236 | + | 0.638965i | \(0.220637\pi\) | |||||||
\(374\) | −9.46410 | + | 2.53590i | −0.489377 | + | 0.131128i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.4641 | − | 13.4641i | −0.694358 | − | 0.694358i | ||||
\(377\) | − | 24.0000i | − | 1.23606i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 12.2487i | − | 0.629174i | −0.949229 | − | 0.314587i | \(-0.898134\pi\) | ||
0.949229 | − | 0.314587i | \(-0.101866\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 26.3923 | − | 7.07180i | 1.35035 | − | 0.361825i | ||||
\(383\) | − | 3.12436i | − | 0.159647i | −0.996809 | − | 0.0798236i | \(-0.974564\pi\) | ||
0.996809 | − | 0.0798236i | \(-0.0254357\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.73205 | − | 10.1962i | −0.139058 | − | 0.518970i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.39230 | + | 11.0718i | 0.324520 | + | 0.562085i | ||||
\(389\) | − | 34.7846i | − | 1.76365i | −0.471577 | − | 0.881825i | \(-0.656315\pi\) | ||
0.471577 | − | 0.881825i | \(-0.343685\pi\) | |||||||
\(390\) | 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 | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.2487 | 0.815499 | 0.407750 | − | 0.913094i | \(-0.366314\pi\) | ||||
0.407750 | + | 0.913094i | \(0.366314\pi\) | |||||||
\(398\) | −35.3205 | + | 9.46410i | −1.77046 | + | 0.474393i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.8564 | −0.991582 | −0.495791 | − | 0.868442i | \(-0.665122\pi\) | ||||
−0.495791 | + | 0.868442i | \(0.665122\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.07180 | 0.252644 | ||||||||
\(404\) | 10.9282 | + | 18.9282i | 0.543698 | + | 0.941713i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −25.8564 | + | 6.92820i | −1.28323 | + | 0.343841i | ||||
\(407\) | 4.00000i | 0.198273i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.3205 | −1.15312 | −0.576562 | − | 0.817053i | \(-0.695606\pi\) | ||||
−0.576562 | + | 0.817053i | \(0.695606\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.66025 | + | 2.87564i | 0.0817948 | + | 0.141673i | ||||
\(413\) | −1.46410 | −0.0720437 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.07180 | − | 18.9282i | 0.248665 | − | 0.928032i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 20.3923 | − | 5.46410i | 0.997420 | − | 0.267258i | ||||
\(419\) | − | 2.39230i | − | 0.116872i | −0.998291 | − | 0.0584359i | \(-0.981389\pi\) | ||
0.998291 | − | 0.0584359i | \(-0.0186113\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.8564i | 1.35764i | 0.734306 | + | 0.678819i | \(0.237508\pi\) | ||||
−0.734306 | + | 0.678819i | \(0.762492\pi\) | |||||||
\(422\) | −5.41154 | − | 20.1962i | −0.263430 | − | 0.983133i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.07180 | + | 9.07180i | −0.440565 | + | 0.440565i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.4641 | 0.651574 | ||||||||
\(428\) | −1.26795 | + | 0.732051i | −0.0612886 | + | 0.0353850i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.5359 | 0.700170 | 0.350085 | − | 0.936718i | \(-0.386153\pi\) | ||||
0.350085 | + | 0.936718i | \(0.386153\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.5359i | 0.602437i | 0.953555 | + | 0.301218i | \(0.0973933\pi\) | ||||
−0.953555 | + | 0.301218i | \(0.902607\pi\) | |||||||
\(434\) | −1.46410 | − | 5.46410i | −0.0702791 | − | 0.262285i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.07180 | − | 5.32051i | −0.147112 | − | 0.254806i | ||||
\(437\) | 31.3205 | 1.49826 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.784610 | 0.0374474 | 0.0187237 | − | 0.999825i | \(-0.494040\pi\) | ||||
0.0187237 | + | 0.999825i | \(0.494040\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.39230 | + | 16.3923i | 0.208921 | + | 0.779702i | ||||
\(443\) | 30.9808 | 1.47194 | 0.735970 | − | 0.677014i | \(-0.236726\pi\) | ||||
0.735970 | + | 0.677014i | \(0.236726\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.92820 | + | 22.1244i | 0.280709 | + | 1.04762i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −21.8564 | −1.03262 | ||||||||
\(449\) | 11.3205 | 0.534248 | 0.267124 | − | 0.963662i | \(-0.413927\pi\) | ||||
0.267124 | + | 0.963662i | \(0.413927\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.9282i | 0.514589i | ||||||||
\(452\) | 0.928203 | + | 1.60770i | 0.0436590 | + | 0.0756196i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −38.3205 | + | 10.2679i | −1.79847 | + | 0.481899i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.7846i | 0.691595i | 0.938309 | + | 0.345797i | \(0.112392\pi\) | ||||
−0.938309 | + | 0.345797i | \(0.887608\pi\) | |||||||
\(458\) | 1.46410 | + | 5.46410i | 0.0684130 | + | 0.255321i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.92820i | − | 0.136380i | −0.997672 | − | 0.0681900i | \(-0.978278\pi\) | ||
0.997672 | − | 0.0681900i | \(-0.0217224\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.7321i | 0.684656i | 0.939580 | + | 0.342328i | \(0.111215\pi\) | ||||
−0.939580 | + | 0.342328i | \(0.888785\pi\) | |||||||
\(464\) | −24.0000 | − | 13.8564i | −1.11417 | − | 0.643268i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.7321 | + | 40.0526i | 0.497153 | + | 1.85540i | ||||
\(467\) | −8.33975 | −0.385917 | −0.192959 | − | 0.981207i | \(-0.561808\pi\) | ||||
−0.192959 | + | 0.981207i | \(0.561808\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.8564i | 0.916884i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.07180 | − | 1.07180i | −0.0493334 | − | 0.0493334i | ||||
\(473\) | − | 17.4641i | − | 0.803000i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 16.3923 | − | 9.46410i | 0.751340 | − | 0.433786i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −27.3205 | + | 7.32051i | −1.24961 | + | 0.334832i | ||||
\(479\) | −21.8564 | −0.998645 | −0.499322 | − | 0.866416i | \(-0.666418\pi\) | ||||
−0.499322 | + | 0.866416i | \(0.666418\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.92820 | 0.315899 | ||||||||
\(482\) | −6.00000 | + | 1.60770i | −0.273293 | + | 0.0732285i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.1244 | − | 7.00000i | 0.551107 | − | 0.318182i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 24.5885i | − | 1.11421i | −0.830442 | − | 0.557105i | \(-0.811912\pi\) | ||
0.830442 | − | 0.557105i | \(-0.188088\pi\) | |||||||
\(488\) | 9.85641 | + | 9.85641i | 0.446179 | + | 0.446179i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.07180i | 0.138628i | 0.997595 | + | 0.0693141i | \(0.0220811\pi\) | ||||
−0.997595 | + | 0.0693141i | \(0.977919\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.0000 | 1.08091 | ||||||||
\(494\) | −9.46410 | − | 35.3205i | −0.425810 | − | 1.58914i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.92820 | − | 5.07180i | 0.131480 | − | 0.227730i | ||||
\(497\) | − | 4.00000i | − | 0.179425i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 24.5359i | − | 1.09838i | −0.835698 | − | 0.549189i | \(-0.814937\pi\) | ||
0.835698 | − | 0.549189i | \(-0.185063\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.05256 | − | 15.1244i | −0.180875 | − | 0.675033i | ||||
\(503\) | − | 17.6603i | − | 0.787432i | −0.919232 | − | 0.393716i | \(-0.871189\pi\) | ||
0.919232 | − | 0.393716i | \(-0.128811\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −11.4641 | + | 3.07180i | −0.509641 | + | 0.136558i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.2679 | + | 22.9808i | 0.588670 | + | 1.01961i | ||||
\(509\) | 25.8564i | 1.14607i | 0.819533 | + | 0.573033i | \(0.194233\pi\) | ||||
−0.819533 | + | 0.573033i | \(0.805767\pi\) | |||||||
\(510\) | 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 | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.4641 | 0.592151 | ||||||||
\(518\) | −2.00000 | − | 7.46410i | −0.0878750 | − | 0.327954i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.1436 | 0.707264 | 0.353632 | − | 0.935385i | \(-0.384947\pi\) | ||||
0.353632 | + | 0.935385i | \(0.384947\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.1962 | −0.970570 | −0.485285 | − | 0.874356i | \(-0.661284\pi\) | ||||
−0.485285 | + | 0.874356i | \(0.661284\pi\) | |||||||
\(524\) | −7.85641 | − | 13.6077i | −0.343209 | − | 0.594455i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.07180 | + | 7.73205i | 0.0903346 | + | 0.337133i | ||||
\(527\) | 5.07180i | 0.220931i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.39230 | 0.234448 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −35.3205 | + | 20.3923i | −1.53134 | + | 0.884119i | ||||
\(533\) | 18.9282 | 0.819871 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14.5359 | + | 14.5359i | −0.627855 | + | 0.627855i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.80385 | + | 6.73205i | 0.0777694 | + | 0.290239i | ||||
\(539\) | − | 0.928203i | − | 0.0399805i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 13.0718i | − | 0.562000i | −0.959708 | − | 0.281000i | \(-0.909334\pi\) | ||
0.959708 | − | 0.281000i | \(-0.0906662\pi\) | |||||||
\(542\) | 20.9282 | − | 5.60770i | 0.898943 | − | 0.240871i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.9282 | + | 5.07180i | 0.811540 | + | 0.217451i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.7321 | −1.57055 | −0.785275 | − | 0.619148i | \(-0.787478\pi\) | ||||
−0.785275 | + | 0.619148i | \(0.787478\pi\) | |||||||
\(548\) | 8.92820 | + | 15.4641i | 0.381394 | + | 0.660594i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −51.7128 | −2.20304 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 40.7846i | − | 1.73434i | ||||||
\(554\) | −2.73205 | + | 0.732051i | −0.116074 | + | 0.0311019i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.46410 | + | 12.9282i | 0.316548 | + | 0.548278i | ||||
\(557\) | −26.7846 | −1.13490 | −0.567450 | − | 0.823408i | \(-0.692070\pi\) | ||||
−0.567450 | + | 0.823408i | \(0.692070\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −30.2487 | −1.27938 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23.8564 | + | 6.39230i | −1.00632 | + | 0.269643i | ||||
\(563\) | −16.0526 | −0.676535 | −0.338267 | − | 0.941050i | \(-0.609841\pi\) | ||||
−0.338267 | + | 0.941050i | \(0.609841\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 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 | \(-0.543746\pi\) | ||||
−0.137000 | + | 0.990571i | \(0.543746\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 34.7846i | − | 1.45569i | −0.685741 | − | 0.727845i | \(-0.740522\pi\) | ||
0.685741 | − | 0.727845i | \(-0.259478\pi\) | |||||||
\(572\) | 6.92820 | + | 12.0000i | 0.289683 | + | 0.501745i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.46410 | − | 20.3923i | −0.228067 | − | 0.851158i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 43.5692i | − | 1.81381i | −0.421335 | − | 0.906905i | \(-0.638438\pi\) | ||
0.421335 | − | 0.906905i | \(-0.361562\pi\) | |||||||
\(578\) | 6.83013 | − | 1.83013i | 0.284096 | − | 0.0761232i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.9282i | 0.536352i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 9.07180i | − | 0.375715i | ||||||
\(584\) | −1.07180 | − | 1.07180i | −0.0443513 | − | 0.0443513i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.1962 | + | 4.33975i | −0.669057 | + | 0.179273i | ||||
\(587\) | −14.1962 | −0.585938 | −0.292969 | − | 0.956122i | \(-0.594643\pi\) | ||||
−0.292969 | + | 0.956122i | \(0.594643\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 10.9282i | − | 0.450289i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.00000 | − | 6.92820i | 0.164399 | − | 0.284747i | ||||
\(593\) | − | 36.6410i | − | 1.50467i | −0.658783 | − | 0.752333i | \(-0.728928\pi\) | ||
0.658783 | − | 0.752333i | \(-0.271072\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.8564 | + | 34.3923i | 0.813350 | + | 1.40876i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.32051 | + | 19.8564i | 0.217572 | + | 0.811989i | ||||
\(599\) | 34.6410 | 1.41539 | 0.707697 | − | 0.706516i | \(-0.249734\pi\) | ||||
0.707697 | + | 0.706516i | \(0.249734\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.4641 | 1.03870 | 0.519351 | − | 0.854561i | \(-0.326174\pi\) | ||||
0.519351 | + | 0.854561i | \(0.326174\pi\) | |||||||
\(602\) | 8.73205 | + | 32.5885i | 0.355892 | + | 1.32821i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.5359 | − | 8.39230i | 0.591457 | − | 0.341478i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 20.9808i | − | 0.851583i | −0.904821 | − | 0.425791i | \(-0.859996\pi\) | ||
0.904821 | − | 0.425791i | \(-0.140004\pi\) | |||||||
\(608\) | −40.7846 | − | 10.9282i | −1.65403 | − | 0.443197i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 23.3205i | − | 0.943447i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.60770 | 0.226493 | 0.113246 | − | 0.993567i | \(-0.463875\pi\) | ||||
0.113246 | + | 0.993567i | \(0.463875\pi\) | |||||||
\(614\) | −36.8564 | + | 9.87564i | −1.48740 | + | 0.398549i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.9282 | − | 10.9282i | 0.440310 | − | 0.440310i | ||||
\(617\) | 27.4641i | 1.10566i | 0.833293 | + | 0.552832i | \(0.186453\pi\) | ||||
−0.833293 | + | 0.552832i | \(0.813547\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.3205i | 1.33926i | 0.742693 | + | 0.669632i | \(0.233548\pi\) | ||||
−0.742693 | + | 0.669632i | \(0.766452\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.53590 | − | 1.21539i | 0.181873 | − | 0.0487327i | ||||
\(623\) | 13.4641i | 0.539428i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 11.6603 | + | 43.5167i | 0.466037 | + | 1.73928i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 29.3205 | − | 16.9282i | 1.17002 | − | 0.675509i | ||||
\(629\) | 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 | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.60770 | −0.0636992 | ||||||||
\(638\) | 18.9282 | − | 5.07180i | 0.749375 | − | 0.200794i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.3923 | 0.805448 | 0.402724 | − | 0.915322i | \(-0.368064\pi\) | ||||
0.402724 | + | 0.915322i | \(0.368064\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.8756 | 0.586638 | 0.293319 | − | 0.956015i | \(-0.405240\pi\) | ||||
0.293319 | + | 0.956015i | \(0.405240\pi\) | |||||||
\(644\) | 19.8564 | − | 11.4641i | 0.782452 | − | 0.451749i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 35.3205 | − | 9.46410i | 1.38967 | − | 0.372360i | ||||
\(647\) | − | 13.2679i | − | 0.521617i | −0.965391 | − | 0.260808i | \(-0.916011\pi\) | ||
0.965391 | − | 0.260808i | \(-0.0839891\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.07180 | 0.0420717 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.6603 | − | 10.1962i | 0.691629 | − | 0.399312i | ||||
\(653\) | 36.2487 | 1.41852 | 0.709261 | − | 0.704946i | \(-0.249029\pi\) | ||||
0.709261 | + | 0.704946i | \(0.249029\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 10.9282 | − | 18.9282i | 0.426675 | − | 0.739022i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −25.1244 | + | 6.73205i | −0.979449 | + | 0.262443i | ||||
\(659\) | 17.3205i | 0.674711i | 0.941377 | + | 0.337356i | \(0.109532\pi\) | ||||
−0.941377 | + | 0.337356i | \(0.890468\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 35.8564i | − | 1.39465i | −0.716754 | − | 0.697326i | \(-0.754373\pi\) | ||
0.716754 | − | 0.697326i | \(-0.245627\pi\) | |||||||
\(662\) | −5.12436 | − | 19.1244i | −0.199164 | − | 0.743289i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.46410 | + | 9.46410i | −0.367278 | + | 0.367278i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.0718 | 1.12566 | ||||||||
\(668\) | 20.1962 | + | 34.9808i | 0.781413 | + | 1.35345i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.85641 | −0.380502 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 19.4641i | − | 0.750286i | −0.926967 | − | 0.375143i | \(-0.877594\pi\) | ||
0.926967 | − | 0.375143i | \(-0.122406\pi\) | |||||||
\(674\) | 2.87564 | + | 10.7321i | 0.110766 | + | 0.413383i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.73205 | + | 1.00000i | −0.0666173 | + | 0.0384615i | ||||
\(677\) | 38.3923 | 1.47554 | 0.737768 | − | 0.675054i | \(-0.235880\pi\) | ||||
0.737768 | + | 0.675054i | \(0.235880\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.4641 | 0.670211 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.07180 | + | 4.00000i | 0.0410412 | + | 0.153168i | ||||
\(683\) | −34.9808 | −1.33850 | −0.669251 | − | 0.743037i | \(-0.733385\pi\) | ||||
−0.669251 | + | 0.743037i | \(0.733385\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.53590 | − | 24.3923i | −0.249542 | − | 0.931303i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −17.4641 | + | 30.2487i | −0.665813 | + | 1.15322i | ||||
\(689\) | −15.7128 | −0.598610 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.0000i | 0.684752i | 0.939563 | + | 0.342376i | \(0.111232\pi\) | ||||
−0.939563 | + | 0.342376i | \(0.888768\pi\) | |||||||
\(692\) | −3.46410 | + | 2.00000i | −0.131685 | + | 0.0760286i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.3923 | − | 5.73205i | 0.812041 | − | 0.217586i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.9282i | 0.716957i | ||||||||
\(698\) | 10.2487 | + | 38.2487i | 0.387919 | + | 1.44774i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 32.9282i | − | 1.24368i | −0.783144 | − | 0.621841i | \(-0.786385\pi\) | ||
0.783144 | − | 0.621841i | \(-0.213615\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 14.9282i | − | 0.563028i | ||||||
\(704\) | 16.0000 | 0.603023 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.339746 | − | 1.26795i | −0.0127865 | − | 0.0477199i | ||||
\(707\) | 29.8564 | 1.12287 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 28.7846i | − | 1.08103i | −0.841335 | − | 0.540514i | \(-0.818230\pi\) | ||
0.841335 | − | 0.540514i | \(-0.181770\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.85641 | + | 9.85641i | −0.369384 | + | 0.369384i | ||||
\(713\) | 6.14359i | 0.230079i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15.4641 | − | 26.7846i | −0.577921 | − | 1.00099i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.92820 | − | 1.85641i | 0.258558 | − | 0.0692805i | ||||
\(719\) | 25.8564 | 0.964281 | 0.482141 | − | 0.876094i | \(-0.339859\pi\) | ||||
0.482141 | + | 0.876094i | \(0.339859\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.53590 | 0.168926 | ||||||||
\(722\) | −50.1506 | + | 13.4378i | −1.86641 | + | 0.500104i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16.0000 | + | 27.7128i | 0.594635 | + | 1.02994i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0526i | 0.521181i | 0.965449 | + | 0.260590i | \(0.0839172\pi\) | ||||
−0.965449 | + | 0.260590i | \(0.916083\pi\) | |||||||
\(728\) | −18.9282 | − | 18.9282i | −0.701526 | − | 0.701526i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 30.2487i | − | 1.11879i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −48.9282 | −1.80720 | −0.903602 | − | 0.428373i | \(-0.859087\pi\) | ||||
−0.903602 | + | 0.428373i | \(0.859087\pi\) | |||||||
\(734\) | 9.92820 | + | 37.0526i | 0.366457 | + | 1.36763i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.9282 | + | 6.14359i | 0.845145 | + | 0.226456i | ||||
\(737\) | − | 14.5359i | − | 0.535437i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.32051i | 0.195718i | 0.995200 | + | 0.0978590i | \(0.0311994\pi\) | ||||
−0.995200 | + | 0.0978590i | \(0.968801\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.53590 | + | 16.9282i | 0.166518 | + | 0.621454i | ||||
\(743\) | − | 40.9808i | − | 1.50344i | −0.659483 | − | 0.751719i | \(-0.729225\pi\) | ||
0.659483 | − | 0.751719i | \(-0.270775\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 40.5885 | − | 10.8756i | 1.48605 | − | 0.398186i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12.0000 | + | 6.92820i | −0.438763 | + | 0.253320i | ||||
\(749\) | 2.00000i | 0.0730784i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.2487 | −0.811867 | −0.405934 | − | 0.913903i | \(-0.633054\pi\) | ||||
−0.405934 | + | 0.913903i | \(0.633054\pi\) | |||||||
\(752\) | −23.3205 | − | 13.4641i | −0.850411 | − | 0.490985i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.78461 | − | 32.7846i | −0.319917 | − | 1.19395i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.9282 | 1.19680 | 0.598398 | − | 0.801199i | \(-0.295804\pi\) | ||||
0.598398 | + | 0.801199i | \(0.295804\pi\) | |||||||
\(758\) | −4.48334 | − | 16.7321i | −0.162842 | − | 0.607735i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −49.7128 | −1.80209 | −0.901044 | − | 0.433728i | \(-0.857198\pi\) | ||||
−0.901044 | + | 0.433728i | \(0.857198\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.39230 | −0.303822 | ||||||||
\(764\) | 33.4641 | − | 19.3205i | 1.21069 | − | 0.698991i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.14359 | − | 4.26795i | −0.0413197 | − | 0.154207i | ||||
\(767\) | − | 1.85641i | − | 0.0670310i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.928203 | 0.0334719 | 0.0167359 | − | 0.999860i | \(-0.494673\pi\) | ||||
0.0167359 | + | 0.999860i | \(0.494673\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.46410 | − | 12.9282i | −0.268639 | − | 0.465296i | ||||
\(773\) | 1.60770 | 0.0578248 | 0.0289124 | − | 0.999582i | \(-0.490796\pi\) | ||||
0.0289124 | + | 0.999582i | \(0.490796\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 12.7846 | + | 12.7846i | 0.458941 | + | 0.458941i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.7321 | − | 47.5167i | −0.456466 | − | 1.70355i | ||||
\(779\) | − | 40.7846i | − | 1.46126i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.92820i | 0.104779i | ||||||||
\(782\) | −19.8564 | + | 5.32051i | −0.710064 | + | 0.190261i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.928203 | + | 1.60770i | −0.0331501 | + | 0.0574177i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.5885 | 0.520022 | 0.260011 | − | 0.965606i | \(-0.416274\pi\) | ||||
0.260011 | + | 0.965606i | \(0.416274\pi\) | |||||||
\(788\) | −21.7128 | + | 12.5359i | −0.773487 | + | 0.446573i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.53590 | 0.0901662 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.0718i | 0.606237i | ||||||||
\(794\) | 22.1962 | − | 5.94744i | 0.787712 | − | 0.211067i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −44.7846 | + | 25.8564i | −1.58735 | + | 0.916456i | ||||
\(797\) | −26.1051 | −0.924691 | −0.462345 | − | 0.886700i | \(-0.652992\pi\) | ||||
−0.462345 | + | 0.886700i | \(0.652992\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.3205 | 0.825020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −27.1244 | + | 7.26795i | −0.957794 | + | 0.256640i | ||||
\(803\) | 1.07180 | 0.0378229 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 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 | \(-0.521595\pi\) | ||||
−0.0677920 | + | 0.997699i | \(0.521595\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 15.0718i | − | 0.529242i | −0.964352 | − | 0.264621i | \(-0.914753\pi\) | ||
0.964352 | − | 0.264621i | \(-0.0852469\pi\) | |||||||
\(812\) | −32.7846 | + | 18.9282i | −1.15051 | + | 0.664250i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.46410 | + | 5.46410i | 0.0513167 | + | 0.191517i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 65.1769i | 2.28025i | ||||||||
\(818\) | −31.8564 | + | 8.53590i | −1.11383 | + | 0.298451i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.78461i | 0.236785i | 0.992967 | + | 0.118392i | \(0.0377740\pi\) | ||||
−0.992967 | + | 0.118392i | \(0.962226\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 15.1244i | − | 0.527202i | −0.964632 | − | 0.263601i | \(-0.915090\pi\) | ||
0.964632 | − | 0.263601i | \(-0.0849102\pi\) | |||||||
\(824\) | 3.32051 | + | 3.32051i | 0.115675 | + | 0.115675i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.00000 | + | 0.535898i | −0.0695889 | + | 0.0186463i | ||||
\(827\) | −1.12436 | −0.0390977 | −0.0195488 | − | 0.999809i | \(-0.506223\pi\) | ||||
−0.0195488 | + | 0.999809i | \(0.506223\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 15.0718i | − | 0.523465i | −0.965140 | − | 0.261733i | \(-0.915706\pi\) | ||
0.965140 | − | 0.261733i | \(-0.0842938\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 27.7128i | − | 0.960769i | ||||||
\(833\) | − | 1.60770i | − | 0.0557033i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 25.8564 | − | 14.9282i | 0.894263 | − | 0.516303i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.875644 | − | 3.26795i | −0.0302486 | − | 0.112889i | ||||
\(839\) | −16.7846 | −0.579469 | −0.289735 | − | 0.957107i | \(-0.593567\pi\) | ||||
−0.289735 | + | 0.957107i | \(0.593567\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.0000 | −0.655172 | ||||||||
\(842\) | 10.1962 | + | 38.0526i | 0.351383 | + | 1.31138i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14.7846 | − | 25.6077i | −0.508907 | − | 0.881453i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 19.1244i | − | 0.657121i | ||||||
\(848\) | −9.07180 | + | 15.7128i | −0.311527 | + | 0.539580i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.39230i | 0.287685i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.3923 | −1.45148 | −0.725742 | − | 0.687967i | \(-0.758504\pi\) | ||||
−0.725742 | + | 0.687967i | \(0.758504\pi\) | |||||||
\(854\) | 18.3923 | − | 4.92820i | 0.629372 | − | 0.168640i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.46410 | + | 1.46410i | −0.0500420 | + | 0.0500420i | ||||
\(857\) | − | 7.85641i | − | 0.268370i | −0.990956 | − | 0.134185i | \(-0.957158\pi\) | ||
0.990956 | − | 0.134185i | \(-0.0428416\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.2487i | 0.690877i | 0.938441 | + | 0.345439i | \(0.112270\pi\) | ||||
−0.938441 | + | 0.345439i | \(0.887730\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.8564 | − | 5.32051i | 0.676312 | − | 0.181217i | ||||
\(863\) | 30.3397i | 1.03278i | 0.856354 | + | 0.516388i | \(0.172724\pi\) | ||||
−0.856354 | + | 0.516388i | \(0.827276\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.58846 | + | 17.1244i | 0.155922 | + | 0.581909i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.00000 | − | 6.92820i | −0.135769 | − | 0.235159i | ||||
\(869\) | 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 | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −53.7128 | −1.81375 | −0.906876 | − | 0.421397i | \(-0.861540\pi\) | ||||
−0.906876 | + | 0.421397i | \(0.861540\pi\) | |||||||
\(878\) | 1.07180 | − | 0.287187i | 0.0361714 | − | 0.00969209i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.53590 | −0.0854366 | −0.0427183 | − | 0.999087i | \(-0.513602\pi\) | ||||
−0.0427183 | + | 0.999087i | \(0.513602\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.9090 | 1.27574 | 0.637869 | − | 0.770145i | \(-0.279816\pi\) | ||||
0.637869 | + | 0.770145i | \(0.279816\pi\) | |||||||
\(884\) | 12.0000 | + | 20.7846i | 0.403604 | + | 0.699062i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 42.3205 | − | 11.3397i | 1.42179 | − | 0.380966i | ||||
\(887\) | − | 51.9090i | − | 1.74293i | −0.490455 | − | 0.871466i | \(-0.663170\pi\) | ||
0.490455 | − | 0.871466i | \(-0.336830\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.2487 | 1.21574 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.1962 | + | 28.0526i | 0.542287 | + | 0.939269i | ||||
\(893\) | −50.2487 | −1.68151 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −29.8564 | + | 8.00000i | −0.997433 | + | 0.267261i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.4641 | − | 4.14359i | 0.516044 | − | 0.138274i | ||||
\(899\) | − | 10.1436i | − | 0.338308i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 15.7128i | − | 0.523470i | ||||||
\(902\) | 4.00000 | + | 14.9282i | 0.133185 | + | 0.497055i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.85641 | + | 1.85641i | 0.0617432 | + | 0.0617432i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.1244 | −0.967058 | −0.483529 | − | 0.875328i | \(-0.660645\pi\) | ||||
−0.483529 | + | 0.875328i | \(0.660645\pi\) | |||||||
\(908\) | −48.5885 | + | 28.0526i | −1.61246 | + | 0.930957i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.1769 | −0.436571 | −0.218285 | − | 0.975885i | \(-0.570046\pi\) | ||||
−0.218285 | + | 0.975885i | \(0.570046\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 9.46410i | − | 0.313216i | ||||||
\(914\) | 5.41154 | + | 20.1962i | 0.178998 | + | 0.668029i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.00000 | + | 6.92820i | 0.132164 | + | 0.228914i | ||||
\(917\) | −21.4641 | −0.708807 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.0718 | 0.827042 | 0.413521 | − | 0.910495i | \(-0.364299\pi\) | ||||
0.413521 | + | 0.910495i | \(0.364299\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.07180 | − | 4.00000i | −0.0352977 | − | 0.131733i | ||||
\(923\) | 5.07180 | 0.166940 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 5.39230 | + | 20.1244i | 0.177202 | + | 0.661327i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −37.8564 | − | 10.1436i | −1.24270 | − | 0.332980i | ||||
\(929\) | −10.5359 | −0.345672 | −0.172836 | − | 0.984951i | \(-0.555293\pi\) | ||||
−0.172836 | + | 0.984951i | \(0.555293\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.46410i | 0.113531i | ||||||||
\(932\) | 29.3205 | + | 50.7846i | 0.960425 | + | 1.66351i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −11.3923 | + | 3.05256i | −0.372768 | + | 0.0998828i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 44.2487i | − | 1.44554i | −0.691087 | − | 0.722771i | \(-0.742868\pi\) | ||
0.691087 | − | 0.722771i | \(-0.257132\pi\) | |||||||
\(938\) | 7.26795 | + | 27.1244i | 0.237307 | + | 0.885642i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.0000i | 1.04317i | 0.853199 | + | 0.521585i | \(0.174659\pi\) | ||||
−0.853199 | + | 0.521585i | \(0.825341\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.9282i | 0.746645i | ||||||||
\(944\) | −1.85641 | − | 1.07180i | −0.0604209 | − | 0.0348840i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.39230 | − | 23.8564i | −0.207832 | − | 0.775639i | ||||
\(947\) | 21.1244 | 0.686449 | 0.343225 | − | 0.939253i | \(-0.388481\pi\) | ||||
0.343225 | + | 0.939253i | \(0.388481\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.85641i | − | 0.0602615i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 18.9282 | − | 18.9282i | 0.613467 | − | 0.613467i | ||||
\(953\) | − | 58.7846i | − | 1.90422i | −0.305755 | − | 0.952110i | \(-0.598909\pi\) | ||
0.305755 | − | 0.952110i | \(-0.401091\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −34.6410 | + | 20.0000i | −1.12037 | + | 0.646846i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −29.8564 | + | 8.00000i | −0.964617 | + | 0.258468i | ||||
\(959\) | 24.3923 | 0.787669 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.8564 | −0.930852 | ||||||||
\(962\) | 9.46410 | − | 2.53590i | 0.305135 | − | 0.0817606i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.60770 | + | 4.39230i | −0.245027 | + | 0.141467i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.6603i | 1.08244i | 0.840881 | + | 0.541220i | \(0.182038\pi\) | ||||
−0.840881 | + | 0.541220i | \(0.817962\pi\) | |||||||
\(968\) | 14.0000 | − | 14.0000i | 0.449977 | − | 0.449977i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 23.0718i | − | 0.740409i | −0.928950 | − | 0.370205i | \(-0.879288\pi\) | ||
0.928950 | − | 0.370205i | \(-0.120712\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.3923 | 0.653747 | ||||||||
\(974\) | −9.00000 | − | 33.5885i | −0.288379 | − | 1.07624i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 17.0718 | + | 9.85641i | 0.546455 | + | 0.315496i | ||||
\(977\) | 31.4641i | 1.00663i | 0.864104 | + | 0.503313i | \(0.167886\pi\) | ||||
−0.864104 | + | 0.503313i | \(0.832114\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 9.85641i | − | 0.315012i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.12436 | + | 4.19615i | 0.0358796 | + | 0.133905i | ||||
\(983\) | − | 45.2679i | − | 1.44382i | −0.691985 | − | 0.721912i | \(-0.743264\pi\) | ||
0.691985 | − | 0.721912i | \(-0.256736\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 32.7846 | − | 8.78461i | 1.04407 | − | 0.279759i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −25.8564 | − | 44.7846i | −0.822602 | − | 1.42479i | ||||
\(989\) | − | 36.6410i | − | 1.16512i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.5359 | 1.09707 | 0.548534 | − | 0.836128i | \(-0.315186\pi\) | ||||
0.548534 | + | 0.836128i | \(0.315186\pi\) | |||||||
\(992\) | 2.14359 | − | 8.00000i | 0.0680592 | − | 0.254000i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.46410 | − | 5.46410i | −0.0464385 | − | 0.173311i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −51.1769 | −1.62079 | −0.810395 | − | 0.585884i | \(-0.800747\pi\) | ||||
−0.810395 | + | 0.585884i | \(0.800747\pi\) | |||||||
\(998\) | −8.98076 | − | 33.5167i | −0.284281 | − | 1.06095i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))