Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(17,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.bt (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.2 | ||
Root | \(-1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.17 |
Dual form | 1008.2.bt.b.593.2 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.22474 | + | 2.12132i | 0.547723 | + | 0.948683i | 0.998430 | + | 0.0560116i | \(0.0178384\pi\) |
−0.450708 | + | 0.892672i | \(0.648828\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 2.59808i | 0.188982 | − | 0.981981i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.22474 | − | 0.707107i | −0.369274 | − | 0.213201i | 0.303867 | − | 0.952714i | \(-0.401722\pi\) |
−0.673141 | + | 0.739514i | \(0.735055\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.19615i | − | 1.44115i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) | ||
0.693375 | − | 0.720577i | \(-0.256123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.44949 | − | 4.24264i | 0.594089 | − | 1.02899i | −0.399586 | − | 0.916696i | \(-0.630846\pi\) |
0.993675 | − | 0.112296i | \(-0.0358205\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.50000 | + | 0.866025i | −0.344124 | + | 0.198680i | −0.662094 | − | 0.749421i | \(-0.730332\pi\) |
0.317970 | + | 0.948101i | \(0.396999\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.89898 | − | 2.82843i | 1.02151 | − | 0.589768i | 0.106967 | − | 0.994263i | \(-0.465886\pi\) |
0.914540 | + | 0.404495i | \(0.132553\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82843i | 0.525226i | 0.964901 | + | 0.262613i | \(0.0845842\pi\) | ||||
−0.964901 | + | 0.262613i | \(0.915416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | − | 0.866025i | −0.269408 | − | 0.155543i | 0.359211 | − | 0.933257i | \(-0.383046\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.12372 | − | 2.12132i | 1.03510 | − | 0.358569i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.500000 | + | 0.866025i | 0.0821995 | + | 0.142374i | 0.904194 | − | 0.427121i | \(-0.140472\pi\) |
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.34847 | 1.14764 | 0.573819 | − | 0.818982i | \(-0.305461\pi\) | ||||
0.573819 | + | 0.818982i | \(0.305461\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | 0.152499 | 0.0762493 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762493 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.12372 | + | 10.6066i | 0.893237 | + | 1.54713i | 0.835971 | + | 0.548773i | \(0.184905\pi\) |
0.0572655 | + | 0.998359i | \(0.481762\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.44949 | − | 1.41421i | −0.336463 | − | 0.194257i | 0.322244 | − | 0.946657i | \(-0.395563\pi\) |
−0.658707 | + | 0.752400i | \(0.728896\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.46410i | − | 0.467099i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.44949 | + | 4.24264i | −0.318896 | + | 0.552345i | −0.980258 | − | 0.197722i | \(-0.936646\pi\) |
0.661362 | + | 0.750067i | \(0.269979\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | + | 1.73205i | −0.384111 | + | 0.221766i | −0.679605 | − | 0.733578i | \(-0.737849\pi\) |
0.295495 | + | 0.955344i | \(0.404516\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.0227 | − | 6.36396i | 1.36720 | − | 0.789352i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.50000 | − | 9.52628i | 0.671932 | − | 1.16382i | −0.305424 | − | 0.952217i | \(-0.598798\pi\) |
0.977356 | − | 0.211604i | \(-0.0678686\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.07107i | − | 0.839181i | −0.907713 | − | 0.419591i | \(-0.862174\pi\) | ||
0.907713 | − | 0.419591i | \(-0.137826\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.50000 | + | 0.866025i | 0.175562 | + | 0.101361i | 0.585206 | − | 0.810885i | \(-0.301014\pi\) |
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.44949 | + | 2.82843i | −0.279145 | + | 0.322329i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.50000 | + | 4.33013i | 0.281272 | + | 0.487177i | 0.971698 | − | 0.236225i | \(-0.0759104\pi\) |
−0.690426 | + | 0.723403i | \(0.742577\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.34847 | 0.806599 | 0.403300 | − | 0.915068i | \(-0.367863\pi\) | ||||
0.403300 | + | 0.915068i | \(0.367863\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0000 | 1.30158 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.44949 | − | 4.24264i | −0.259645 | − | 0.449719i | 0.706502 | − | 0.707712i | \(-0.250272\pi\) |
−0.966147 | + | 0.257993i | \(0.916939\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.5000 | − | 2.59808i | −1.41518 | − | 0.272352i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.67423 | − | 2.12132i | −0.376969 | − | 0.217643i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.3923i | − | 1.05518i | −0.849500 | − | 0.527589i | \(-0.823096\pi\) | ||
0.849500 | − | 0.527589i | \(-0.176904\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.57321 | + | 14.8492i | −0.853067 | + | 1.47755i | 0.0253604 | + | 0.999678i | \(0.491927\pi\) |
−0.878427 | + | 0.477876i | \(0.841407\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.50000 | − | 4.33013i | 0.738997 | − | 0.426660i | −0.0827075 | − | 0.996574i | \(-0.526357\pi\) |
0.821705 | + | 0.569914i | \(0.193023\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.44949 | + | 1.41421i | −0.236801 | + | 0.136717i | −0.613706 | − | 0.789535i | \(-0.710322\pi\) |
0.376905 | + | 0.926252i | \(0.376988\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.500000 | − | 0.866025i | 0.0478913 | − | 0.0829502i | −0.841086 | − | 0.540901i | \(-0.818083\pi\) |
0.888977 | + | 0.457951i | \(0.151417\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.41421i | − | 0.133038i | −0.997785 | − | 0.0665190i | \(-0.978811\pi\) | ||
0.997785 | − | 0.0665190i | \(-0.0211893\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.0000 | + | 6.92820i | 1.11901 | + | 0.646058i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.79796 | − | 8.48528i | −0.898177 | − | 0.777844i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.50000 | − | 7.79423i | −0.409091 | − | 0.708566i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.79796 | 0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.0000 | −0.976092 | −0.488046 | − | 0.872818i | \(-0.662290\pi\) | ||||
−0.488046 | + | 0.872818i | \(0.662290\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.22474 | − | 2.12132i | −0.107006 | − | 0.185341i | 0.807550 | − | 0.589799i | \(-0.200793\pi\) |
−0.914556 | + | 0.404459i | \(0.867460\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.50000 | + | 4.33013i | 0.130066 | + | 0.375470i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.79796 | − | 5.65685i | −0.837096 | − | 0.483298i | 0.0191800 | − | 0.999816i | \(-0.493894\pi\) |
−0.856276 | + | 0.516518i | \(0.827228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.19615i | 0.440732i | 0.975417 | + | 0.220366i | \(0.0707252\pi\) | ||||
−0.975417 | + | 0.220366i | \(0.929275\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.67423 | + | 6.36396i | −0.307255 | + | 0.532181i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | + | 3.46410i | −0.498273 | + | 0.287678i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.89898 | + | 2.82843i | −0.401340 | + | 0.231714i | −0.687062 | − | 0.726599i | \(-0.741100\pi\) |
0.285722 | + | 0.958313i | \(0.407767\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.0000 | + | 19.0526i | −0.895167 | + | 1.55048i | −0.0615699 | + | 0.998103i | \(0.519611\pi\) |
−0.833597 | + | 0.552372i | \(0.813723\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 4.24264i | − | 0.340777i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.0000 | + | 8.66025i | 1.19713 | + | 0.691164i | 0.959914 | − | 0.280293i | \(-0.0904318\pi\) |
0.237216 | + | 0.971457i | \(0.423765\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.89898 | − | 14.1421i | −0.386094 | − | 1.11456i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.00000 | − | 8.66025i | −0.391630 | − | 0.678323i | 0.601035 | − | 0.799223i | \(-0.294755\pi\) |
−0.992665 | + | 0.120900i | \(0.961422\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.34847 | −0.568642 | −0.284321 | − | 0.958729i | \(-0.591768\pi\) | ||||
−0.284321 | + | 0.958729i | \(0.591768\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.0000 | −1.07692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.89898 | + | 8.48528i | 0.372463 | + | 0.645124i | 0.989944 | − | 0.141462i | \(-0.0451802\pi\) |
−0.617481 | + | 0.786586i | \(0.711847\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | + | 1.73205i | 0.151186 | + | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.57321 | − | 4.94975i | −0.640792 | − | 0.369961i | 0.144127 | − | 0.989559i | \(-0.453962\pi\) |
−0.784920 | + | 0.619598i | \(0.787296\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.5885i | 1.15868i | 0.815086 | + | 0.579340i | \(0.196690\pi\) | ||||
−0.815086 | + | 0.579340i | \(0.803310\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.22474 | + | 2.12132i | −0.0900450 | + | 0.155963i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.00000 | + | 3.46410i | −0.438763 | + | 0.253320i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.22474 | − | 0.707107i | 0.0886194 | − | 0.0511645i | −0.455035 | − | 0.890473i | \(-0.650373\pi\) |
0.543655 | + | 0.839309i | \(0.317040\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.50000 | + | 9.52628i | −0.395899 | + | 0.685717i | −0.993215 | − | 0.116289i | \(-0.962900\pi\) |
0.597317 | + | 0.802005i | \(0.296234\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.7990i | 1.41062i | 0.708899 | + | 0.705310i | \(0.249192\pi\) | ||||
−0.708899 | + | 0.705310i | \(0.750808\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.0000 | + | 6.92820i | 0.850657 | + | 0.491127i | 0.860873 | − | 0.508821i | \(-0.169918\pi\) |
−0.0102152 | + | 0.999948i | \(0.503252\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.34847 | + | 1.41421i | 0.515761 | + | 0.0992583i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.00000 | + | 15.5885i | 0.628587 | + | 1.08875i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.44949 | 0.169435 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.0000 | 1.51454 | 0.757271 | − | 0.653101i | \(-0.226532\pi\) | ||||
0.757271 | + | 0.653101i | \(0.226532\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.22474 | + | 2.12132i | 0.0835269 | + | 0.144673i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | + | 3.46410i | −0.203653 | + | 0.235159i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.0454 | − | 12.7279i | −1.48293 | − | 0.856173i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 20.7846i | − | 1.39184i | −0.718119 | − | 0.695920i | \(-0.754997\pi\) | ||
0.718119 | − | 0.695920i | \(-0.245003\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.4722 | + | 23.3345i | −0.894181 | + | 1.54877i | −0.0593658 | + | 0.998236i | \(0.518908\pi\) |
−0.834815 | + | 0.550530i | \(0.814425\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.5000 | − | 11.2583i | 1.28860 | − | 0.743971i | 0.310192 | − | 0.950674i | \(-0.399607\pi\) |
0.978404 | + | 0.206702i | \(0.0662732\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.57321 | + | 4.94975i | −0.561650 | + | 0.324269i | −0.753807 | − | 0.657095i | \(-0.771785\pi\) |
0.192158 | + | 0.981364i | \(0.438452\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.0000 | + | 25.9808i | −0.978492 | + | 1.69480i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.8701i | 1.73808i | 0.494742 | + | 0.869040i | \(0.335262\pi\) | ||||
−0.494742 | + | 0.869040i | \(0.664738\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.0000 | − | 6.92820i | −0.772988 | − | 0.446285i | 0.0609515 | − | 0.998141i | \(-0.480586\pi\) |
−0.833939 | + | 0.551856i | \(0.813920\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.44949 | − | 16.9706i | −0.156492 | − | 1.08421i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.50000 | + | 7.79423i | 0.286328 | + | 0.495935i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.00000 | −0.502956 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.22474 | + | 2.12132i | 0.0763975 | + | 0.132324i | 0.901693 | − | 0.432377i | \(-0.142325\pi\) |
−0.825296 | + | 0.564701i | \(0.808992\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.50000 | − | 0.866025i | 0.155342 | − | 0.0538122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.2474 | − | 7.07107i | −0.755210 | − | 0.436021i | 0.0723633 | − | 0.997378i | \(-0.476946\pi\) |
−0.827573 | + | 0.561358i | \(0.810279\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 6.92820i | − | 0.425596i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.57321 | + | 14.8492i | −0.522718 | + | 0.905374i | 0.476932 | + | 0.878940i | \(0.341749\pi\) |
−0.999651 | + | 0.0264343i | \(0.991585\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | − | 6.92820i | 0.728948 | − | 0.420858i | −0.0890891 | − | 0.996024i | \(-0.528396\pi\) |
0.818037 | + | 0.575165i | \(0.195062\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.22474 | − | 0.707107i | 0.0738549 | − | 0.0426401i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.5000 | + | 19.9186i | −0.690968 | + | 1.19679i | 0.280553 | + | 0.959839i | \(0.409482\pi\) |
−0.971521 | + | 0.236953i | \(0.923851\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 22.6274i | − | 1.34984i | −0.737892 | − | 0.674919i | \(-0.764178\pi\) | ||
0.737892 | − | 0.674919i | \(-0.235822\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.50000 | − | 0.866025i | −0.0891657 | − | 0.0514799i | 0.454754 | − | 0.890617i | \(-0.349727\pi\) |
−0.543920 | + | 0.839137i | \(0.683060\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.67423 | − | 19.0919i | 0.216883 | − | 1.12696i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.50000 | − | 6.06218i | −0.205882 | − | 0.356599i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.6969 | −0.858604 | −0.429302 | − | 0.903161i | \(-0.641240\pi\) | ||||
−0.429302 | + | 0.903161i | \(0.641240\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.0000 | −0.698667 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.6969 | − | 25.4558i | −0.849946 | − | 1.47215i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.500000 | − | 2.59808i | 0.0288195 | − | 0.149751i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.34847 | − | 4.24264i | −0.420772 | − | 0.242933i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.5885i | 0.889680i | 0.895610 | + | 0.444840i | \(0.146740\pi\) | ||||
−0.895610 | + | 0.444840i | \(0.853260\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.57321 | − | 14.8492i | 0.486142 | − | 0.842023i | −0.513731 | − | 0.857951i | \(-0.671737\pi\) |
0.999873 | + | 0.0159282i | \(0.00507031\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.5000 | − | 6.06218i | 0.593495 | − | 0.342655i | −0.172983 | − | 0.984925i | \(-0.555341\pi\) |
0.766478 | + | 0.642270i | \(0.222007\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.2474 | + | 7.07107i | −0.687885 | + | 0.397151i | −0.802819 | − | 0.596222i | \(-0.796668\pi\) |
0.114934 | + | 0.993373i | \(0.463334\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.00000 | − | 3.46410i | 0.111979 | − | 0.193952i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.48528i | 0.472134i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.50000 | + | 2.59808i | 0.249615 | + | 0.144115i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.6186 | − | 10.6066i | 1.68806 | − | 0.584761i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.5000 | − | 26.8468i | −0.851957 | − | 1.47563i | −0.879440 | − | 0.476011i | \(-0.842082\pi\) |
0.0274825 | − | 0.999622i | \(-0.491251\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 26.9444 | 1.47213 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.0000 | 1.25289 | 0.626445 | − | 0.779466i | \(-0.284509\pi\) | ||||
0.626445 | + | 0.779466i | \(0.284509\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.22474 | + | 2.12132i | 0.0663237 | + | 0.114876i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.9444 | − | 15.5563i | −1.44645 | − | 0.835109i | −0.448183 | − | 0.893942i | \(-0.647929\pi\) |
−0.998268 | + | 0.0588334i | \(0.981262\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 10.3923i | − | 0.556287i | −0.960539 | − | 0.278144i | \(-0.910281\pi\) | ||
0.960539 | − | 0.278144i | \(-0.0897191\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.57321 | + | 14.8492i | −0.456306 | + | 0.790345i | −0.998762 | − | 0.0497387i | \(-0.984161\pi\) |
0.542456 | + | 0.840084i | \(0.317494\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.0000 | − | 8.66025i | 0.796117 | − | 0.459639i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.4949 | + | 14.1421i | −1.29279 | + | 0.746393i | −0.979148 | − | 0.203148i | \(-0.934883\pi\) |
−0.313643 | + | 0.949541i | \(0.601550\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.00000 | + | 13.8564i | −0.421053 | + | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.24264i | 0.222070i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.50000 | − | 0.866025i | −0.0782994 | − | 0.0452062i | 0.460339 | − | 0.887743i | \(-0.347728\pi\) |
−0.538639 | + | 0.842537i | \(0.681061\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.89898 | + | 5.65685i | −0.254342 | + | 0.293689i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.5000 | − | 25.1147i | −0.750782 | − | 1.30039i | −0.947444 | − | 0.319921i | \(-0.896344\pi\) |
0.196663 | − | 0.980471i | \(-0.436990\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.6969 | 0.756931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.00000 | 0.359566 | 0.179783 | − | 0.983706i | \(-0.442460\pi\) | ||||
0.179783 | + | 0.983706i | \(0.442460\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.79796 | + | 16.9706i | 0.500652 | + | 0.867155i | 1.00000 | 0.000753393i | \(0.000239813\pi\) | |
−0.499347 | + | 0.866402i | \(0.666427\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.00000 | − | 1.73205i | −0.458682 | − | 0.0882735i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.2702 | + | 13.4350i | 1.17984 | + | 0.681183i | 0.955978 | − | 0.293437i | \(-0.0947991\pi\) |
0.223865 | + | 0.974620i | \(0.428132\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 27.7128i | − | 1.40150i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.12372 | + | 10.6066i | −0.308118 | + | 0.533676i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.50000 | − | 0.866025i | 0.0752828 | − | 0.0434646i | −0.461886 | − | 0.886939i | \(-0.652827\pi\) |
0.537169 | + | 0.843475i | \(0.319494\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.1464 | − | 9.89949i | 0.856252 | − | 0.494357i | −0.00650355 | − | 0.999979i | \(-0.502070\pi\) |
0.862755 | + | 0.505622i | \(0.168737\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.50000 | + | 7.79423i | −0.224161 | + | 0.388258i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.41421i | − | 0.0701000i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.5000 | + | 16.4545i | 1.40923 | + | 0.813622i | 0.995314 | − | 0.0966915i | \(-0.0308260\pi\) |
0.413920 | + | 0.910313i | \(0.364159\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.79796 | + | 8.48528i | 0.482126 | + | 0.417533i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.00000 | + | 15.5885i | 0.441793 | + | 0.765207i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.7423 | 1.79498 | 0.897491 | − | 0.441034i | \(-0.145388\pi\) | ||||
0.897491 | + | 0.441034i | \(0.145388\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00000 | −0.0487370 | −0.0243685 | − | 0.999703i | \(-0.507758\pi\) | ||||
−0.0243685 | + | 0.999703i | \(0.507758\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.44949 | + | 4.24264i | 0.118818 | + | 0.205798i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.00000 | + | 8.66025i | 0.145180 | + | 0.419099i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.4722 | + | 7.77817i | 0.648933 | + | 0.374661i | 0.788047 | − | 0.615615i | \(-0.211092\pi\) |
−0.139114 | + | 0.990276i | \(0.544426\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.5885i | 0.749133i | 0.927200 | + | 0.374567i | \(0.122209\pi\) | ||||
−0.927200 | + | 0.374567i | \(0.877791\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.89898 | + | 8.48528i | −0.234350 | + | 0.405906i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.0000 | + | 13.8564i | −1.14546 | + | 0.661330i | −0.947776 | − | 0.318936i | \(-0.896674\pi\) |
−0.197681 | + | 0.980266i | \(0.563341\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.2929 | − | 19.7990i | 1.62930 | − | 0.940678i | 0.645002 | − | 0.764181i | \(-0.276857\pi\) |
0.984301 | − | 0.176497i | \(-0.0564767\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | − | 10.3923i | 0.284427 | − | 0.492642i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.07107i | 0.333704i | 0.985982 | + | 0.166852i | \(0.0533603\pi\) | ||||
−0.985982 | + | 0.166852i | \(0.946640\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00000 | − | 5.19615i | −0.423793 | − | 0.244677i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.0227 | − | 31.8198i | −0.516752 | − | 1.49174i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.50000 | − | 4.33013i | −0.116945 | − | 0.202555i | 0.801611 | − | 0.597847i | \(-0.203977\pi\) |
−0.918556 | + | 0.395292i | \(0.870643\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.6969 | 0.684505 | 0.342252 | − | 0.939608i | \(-0.388810\pi\) | ||||
0.342252 | + | 0.939608i | \(0.388810\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.0000 | 0.604161 | 0.302081 | − | 0.953282i | \(-0.402319\pi\) | ||||
0.302081 | + | 0.953282i | \(0.402319\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.4722 | + | 23.3345i | 0.623419 | + | 1.07979i | 0.988844 | + | 0.148952i | \(0.0475901\pi\) |
−0.365426 | + | 0.930841i | \(0.619077\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.0000 | − | 19.0526i | −1.01587 | − | 0.879765i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.22474 | − | 0.707107i | −0.0563138 | − | 0.0325128i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.73205i | − | 0.0794719i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.44949 | + | 4.24264i | −0.111920 | + | 0.193851i | −0.916544 | − | 0.399933i | \(-0.869033\pi\) |
0.804624 | + | 0.593784i | \(0.202367\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.50000 | − | 2.59808i | 0.205182 | − | 0.118462i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.0454 | − | 12.7279i | 1.00103 | − | 0.577945i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.50000 | − | 14.7224i | 0.385172 | − | 0.667137i | −0.606621 | − | 0.794991i | \(-0.707476\pi\) |
0.991793 | + | 0.127854i | \(0.0408089\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 11.3137i | − | 0.510581i | −0.966864 | − | 0.255290i | \(-0.917829\pi\) | ||
0.966864 | − | 0.255290i | \(-0.0821710\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0000 | + | 6.92820i | 0.540453 | + | 0.312031i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.3712 | − | 3.53553i | −0.824060 | − | 0.158590i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.5000 | − | 21.6506i | −0.559577 | − | 0.969216i | −0.997532 | − | 0.0702185i | \(-0.977630\pi\) |
0.437955 | − | 0.898997i | \(-0.355703\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.0454 | 0.982956 | 0.491478 | − | 0.870890i | \(-0.336457\pi\) | ||||
0.491478 | + | 0.870890i | \(0.336457\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −42.0000 | −1.86898 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.22474 | + | 2.12132i | 0.0542859 | + | 0.0940259i | 0.891891 | − | 0.452250i | \(-0.149378\pi\) |
−0.837605 | + | 0.546276i | \(0.816045\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.00000 | − | 3.46410i | 0.132712 | − | 0.153243i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.3712 | + | 10.6066i | 0.809531 | + | 0.467383i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 17.3205i | − | 0.761755i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.44949 | − | 4.24264i | 0.107314 | − | 0.185873i | −0.807367 | − | 0.590049i | \(-0.799108\pi\) |
0.914681 | + | 0.404176i | \(0.132442\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.50000 | + | 0.866025i | −0.0655904 | + | 0.0378686i | −0.532437 | − | 0.846470i | \(-0.678724\pi\) |
0.466846 | + | 0.884339i | \(0.345390\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.34847 | + | 4.24264i | −0.320104 | + | 0.184812i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.50000 | − | 7.79423i | 0.195652 | − | 0.338880i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 38.1838i | − | 1.65392i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.00000 | − | 3.46410i | −0.259403 | − | 0.149766i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.12372 | + | 7.77817i | 0.263767 | + | 0.335030i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.50000 | − | 14.7224i | −0.365444 | − | 0.632967i | 0.623404 | − | 0.781900i | \(-0.285749\pi\) |
−0.988847 | + | 0.148933i | \(0.952416\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.44949 | 0.104925 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.0000 | 0.427569 | 0.213785 | − | 0.976881i | \(-0.431421\pi\) | ||||
0.213785 | + | 0.976881i | \(0.431421\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.44949 | − | 4.24264i | −0.104352 | − | 0.180743i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.5000 | − | 4.33013i | 0.531554 | − | 0.184136i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.4722 | − | 7.77817i | −0.570835 | − | 0.329572i | 0.186648 | − | 0.982427i | \(-0.440238\pi\) |
−0.757483 | + | 0.652855i | \(0.773571\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.19615i | − | 0.219774i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.4722 | + | 23.3345i | −0.567785 | + | 0.983433i | 0.428999 | + | 0.903305i | \(0.358866\pi\) |
−0.996785 | + | 0.0801281i | \(0.974467\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.00000 | − | 1.73205i | 0.126211 | − | 0.0728679i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.22474 | + | 0.707107i | −0.0513440 | + | 0.0296435i | −0.525452 | − | 0.850823i | \(-0.676104\pi\) |
0.474108 | + | 0.880467i | \(0.342771\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.50000 | − | 9.52628i | 0.230168 | − | 0.398662i | −0.727690 | − | 0.685907i | \(-0.759406\pi\) |
0.957857 | + | 0.287244i | \(0.0927391\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.65685i | 0.235907i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.50000 | + | 0.866025i | 0.0624458 | + | 0.0360531i | 0.530898 | − | 0.847436i | \(-0.321855\pi\) |
−0.468452 | + | 0.883489i | \(0.655188\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.67423 | − | 19.0919i | 0.152433 | − | 0.792065i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.00000 | + | 3.46410i | 0.0828315 | + | 0.143468i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.6969 | −0.606608 | −0.303304 | − | 0.952894i | \(-0.598090\pi\) | ||||
−0.303304 | + | 0.952894i | \(0.598090\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.00000 | 0.123613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.57321 | + | 14.8492i | 0.352060 | + | 0.609785i | 0.986610 | − | 0.163096i | \(-0.0521481\pi\) |
−0.634550 | + | 0.772881i | \(0.718815\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.00000 | − | 31.1769i | 0.245976 | − | 1.27813i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.89898 | − | 2.82843i | −0.200167 | − | 0.115566i | 0.396566 | − | 0.918006i | \(-0.370202\pi\) |
−0.596733 | + | 0.802440i | \(0.703535\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 25.9808i | − | 1.05978i | −0.848067 | − | 0.529889i | \(-0.822234\pi\) | ||
0.848067 | − | 0.529889i | \(-0.177766\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.0227 | − | 19.0919i | 0.448137 | − | 0.776195i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.5000 | − | 19.9186i | 1.40031 | − | 0.808470i | 0.405887 | − | 0.913923i | \(-0.366962\pi\) |
0.994424 | + | 0.105453i | \(0.0336291\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 55.1135 | − | 31.8198i | 2.22965 | − | 1.28729i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.00000 | + | 6.92820i | −0.161558 | + | 0.279827i | −0.935428 | − | 0.353518i | \(-0.884985\pi\) |
0.773869 | + | 0.633345i | \(0.218319\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.0416i | 0.967880i | 0.875101 | + | 0.483940i | \(0.160795\pi\) | ||||
−0.875101 | + | 0.483940i | \(0.839205\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.5000 | + | 14.7224i | 1.02493 | + | 0.591744i | 0.915529 | − | 0.402253i | \(-0.131773\pi\) |
0.109403 | + | 0.993997i | \(0.465106\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.2474 | + | 4.24264i | −0.490684 | + | 0.169978i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.89898 | 0.195335 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.0000 | −1.51276 | −0.756378 | − | 0.654135i | \(-0.773033\pi\) | ||||
−0.756378 | + | 0.654135i | \(0.773033\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.4722 | − | 23.3345i | −0.534628 | − | 0.926002i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.5000 | + | 33.7750i | −0.534889 | + | 1.33821i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.2474 | + | 7.07107i | 0.483745 | + | 0.279290i | 0.721976 | − | 0.691918i | \(-0.243234\pi\) |
−0.238231 | + | 0.971209i | \(0.576567\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 25.9808i | − | 1.02458i | −0.858812 | − | 0.512291i | \(-0.828797\pi\) | ||
0.858812 | − | 0.512291i | \(-0.171203\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.57321 | − | 14.8492i | 0.337048 | − | 0.583784i | −0.646828 | − | 0.762636i | \(-0.723905\pi\) |
0.983876 | + | 0.178852i | \(0.0572383\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.00000 | − | 3.46410i | 0.235521 | − | 0.135978i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.12372 | − | 3.53553i | 0.239640 | − | 0.138356i | −0.375371 | − | 0.926875i | \(-0.622485\pi\) |
0.615011 | + | 0.788518i | \(0.289151\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.00000 | − | 5.19615i | 0.117220 | − | 0.203030i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.6274i | 0.881439i | 0.897645 | + | 0.440720i | \(0.145277\pi\) | ||||
−0.897645 | + | 0.440720i | \(0.854723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.5000 | − | 14.7224i | −0.991835 | − | 0.572636i | −0.0860127 | − | 0.996294i | \(-0.527413\pi\) |
−0.905822 | + | 0.423658i | \(0.860746\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.34847 | + | 8.48528i | −0.284961 | + | 0.329045i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.00000 | + | 13.8564i | 0.309761 | + | 0.536522i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.89898 | 0.189123 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.0000 | 1.34915 | 0.674575 | − | 0.738206i | \(-0.264327\pi\) | ||||
0.674575 | + | 0.738206i | \(0.264327\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.89898 | + | 8.48528i | 0.188283 | + | 0.326116i | 0.944678 | − | 0.327999i | \(-0.106374\pi\) |
−0.756395 | + | 0.654115i | \(0.773041\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.0000 | − | 5.19615i | −1.03616 | − | 0.199410i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.6413 | − | 24.0416i | −1.59336 | − | 0.919927i | −0.992725 | − | 0.120405i | \(-0.961581\pi\) |
−0.600636 | − | 0.799522i | \(-0.705086\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 27.7128i | − | 1.05885i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.34847 | + | 12.7279i | −0.279954 | + | 0.484895i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.5000 | + | 21.6506i | −1.42657 | + | 0.823629i | −0.996848 | − | 0.0793336i | \(-0.974721\pi\) |
−0.429719 | + | 0.902963i | \(0.641387\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.0227 | + | 6.36396i | −0.418115 | + | 0.241399i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | − | 31.1769i | 0.681799 | − | 1.18091i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 5.65685i | − | 0.213656i | −0.994277 | − | 0.106828i | \(-0.965931\pi\) | ||
0.994277 | − | 0.106828i | \(-0.0340695\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.50000 | − | 0.866025i | −0.0565736 | − | 0.0326628i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 34.2929 | + | 29.6985i | 1.28972 | + | 1.11693i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.0000 | + | 34.6410i | 0.751116 | + | 1.30097i | 0.947282 | + | 0.320400i | \(0.103817\pi\) |
−0.196167 | + | 0.980571i | \(0.562849\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.79796 | −0.366936 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.0000 | −0.673162 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.4722 | + | 23.3345i | 0.502428 | + | 0.870231i | 0.999996 | + | 0.00280593i | \(0.000893157\pi\) |
−0.497568 | + | 0.867425i | \(0.665774\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.50000 | − | 21.6506i | −0.279315 | − | 0.806312i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.44949 | − | 1.41421i | −0.0909718 | − | 0.0525226i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.9808i | 0.963573i | 0.876289 | + | 0.481787i | \(0.160012\pi\) | ||||
−0.876289 | + | 0.481787i | \(0.839988\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.44949 | − | 4.24264i | 0.0905977 | − | 0.156920i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.5000 | + | 19.9186i | −1.27429 | + | 0.735710i | −0.975792 | − | 0.218702i | \(-0.929818\pi\) |
−0.298495 | + | 0.954411i | \(0.596485\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.4722 | + | 7.77817i | −0.496255 | + | 0.286513i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.500000 | + | 0.866025i | −0.0183928 | + | 0.0318573i | −0.875075 | − | 0.483987i | \(-0.839188\pi\) |
0.856683 | + | 0.515844i | \(0.172522\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 24.0416i | − | 0.882002i | −0.897507 | − | 0.441001i | \(-0.854624\pi\) | ||
0.897507 | − | 0.441001i | \(-0.145376\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.0000 | − | 6.92820i | −0.439646 | − | 0.253830i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.44949 | + | 7.07107i | 0.0895024 | + | 0.258371i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.5000 | + | 25.1147i | 0.529113 | + | 0.916450i | 0.999424 | + | 0.0339490i | \(0.0108084\pi\) |
−0.470311 | + | 0.882501i | \(0.655858\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −53.8888 | −1.96121 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.2474 | + | 21.2132i | 0.443970 | + | 0.768978i | 0.997980 | − | 0.0635319i | \(-0.0202365\pi\) |
−0.554010 | + | 0.832510i | \(0.686903\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.00000 | − | 1.73205i | −0.0724049 | − | 0.0627044i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.0454 | + | 12.7279i | 0.796014 | + | 0.459579i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.9808i | 0.936890i | 0.883493 | + | 0.468445i | \(0.155186\pi\) | ||||
−0.883493 | + | 0.468445i | \(0.844814\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.4722 | − | 23.3345i | 0.484561 | − | 0.839284i | −0.515282 | − | 0.857021i | \(-0.672313\pi\) |
0.999843 | + | 0.0177365i | \(0.00564599\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.50000 | − | 0.866025i | 0.0538816 | − | 0.0311086i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.0227 | + | 6.36396i | −0.394929 | + | 0.228013i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.00000 | + | 8.66025i | −0.178914 | + | 0.309888i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 42.4264i | 1.51426i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.0000 | + | 22.5167i | 1.39020 | + | 0.802632i | 0.993337 | − | 0.115246i | \(-0.0367655\pi\) |
0.396863 | + | 0.917878i | \(0.370099\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.67423 | − | 0.707107i | −0.130641 | − | 0.0251418i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.00000 | + | 15.5885i | 0.319599 | + | 0.553562i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.3939 | 1.04118 | 0.520592 | − | 0.853805i | \(-0.325711\pi\) | ||||
0.520592 | + | 0.853805i | \(0.325711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 60.0000 | 2.12265 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.22474 | − | 2.12132i | −0.0432203 | − | 0.0748598i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.0000 | − | 27.7128i | 0.845889 | − | 0.976748i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.5176 | − | 20.5061i | −1.24873 | − | 0.720956i | −0.277876 | − | 0.960617i | \(-0.589630\pi\) |
−0.970857 | + | 0.239661i | \(0.922964\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.1769i | 1.09477i | 0.836881 | + | 0.547385i | \(0.184377\pi\) | ||||
−0.836881 | + | 0.547385i | \(0.815623\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.2474 | − | 21.2132i | 0.429009 | − | 0.743066i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.50000 | + | 0.866025i | −0.0524784 | + | 0.0302984i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.8207 | − | 12.0208i | 0.726646 | − | 0.419529i | −0.0905478 | − | 0.995892i | \(-0.528862\pi\) |
0.817194 | + | 0.576363i | \(0.195528\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.0000 | + | 29.4449i | −0.592583 | + | 1.02638i | 0.401300 | + | 0.915947i | \(0.368558\pi\) |
−0.993883 | + | 0.110437i | \(0.964775\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 7.07107i | − | 0.245885i | −0.992414 | − | 0.122943i | \(-0.960767\pi\) | ||
0.992414 | − | 0.122943i | \(-0.0392331\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.50000 | + | 0.866025i | 0.0520972 | + | 0.0300783i | 0.525822 | − | 0.850594i | \(-0.323758\pi\) |
−0.473725 | + | 0.880673i | \(0.657091\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26.9444 | + | 21.2132i | −0.933568 | + | 0.734994i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.00000 | − | 15.5885i | −0.311458 | − | 0.539461i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.6969 | −0.507395 | −0.253697 | − | 0.967284i | \(-0.581647\pi\) | ||||
−0.253697 | + | 0.967284i | \(0.581647\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.1464 | − | 29.6985i | −0.589855 | − | 1.02166i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.5000 | + | 7.79423i | −0.773109 | + | 0.267813i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.89898 | + | 2.82843i | 0.167935 | + | 0.0969572i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.3731i | 1.24539i | 0.782465 | + | 0.622695i | \(0.213962\pi\) | ||||
−0.782465 | + | 0.622695i | \(0.786038\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.5959 | + | 33.9411i | −0.669384 | + | 1.15941i | 0.308693 | + | 0.951162i | \(0.400108\pi\) |
−0.978077 | + | 0.208245i | \(0.933225\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.0000 | + | 19.0526i | −1.12595 | + | 0.650065i | −0.942912 | − | 0.333042i | \(-0.891925\pi\) |
−0.183033 | + | 0.983107i | \(0.558592\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.5176 | + | 20.5061i | −1.20903 | + | 0.698036i | −0.962548 | − | 0.271111i | \(-0.912609\pi\) |
−0.246485 | + | 0.969147i | \(0.579276\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.0000 | + | 20.7846i | −0.408012 | + | 0.706698i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 7.07107i | − | 0.239870i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −49.5000 | − | 28.5788i | −1.67724 | − | 0.968357i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.89898 | − | 25.4558i | 0.165616 | − | 0.860565i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.0000 | − | 17.3205i | −0.337676 | − | 0.584872i | 0.646319 | − | 0.763067i | \(-0.276307\pi\) |
−0.983995 | + | 0.178195i | \(0.942974\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.0000 | −0.370179 | −0.185090 | − | 0.982722i | \(-0.559258\pi\) | ||||
−0.185090 | + | 0.982722i | \(0.559258\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.8207 | + | 36.0624i | 0.699089 | + | 1.21086i | 0.968783 | + | 0.247912i | \(0.0797444\pi\) |
−0.269693 | + | 0.962946i | \(0.586922\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.50000 | + | 28.5788i | −0.184464 | + | 0.958503i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.3712 | − | 10.6066i | −0.614768 | − | 0.354936i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 24.2487i | − | 0.810545i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.44949 | − | 4.24264i | 0.0816951 | − | 0.141500i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0000 | + | 6.92820i | −0.399778 | + | 0.230812i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −33.0681 | + | 19.0919i | −1.09922 | + | 0.634636i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.50000 | − | 4.33013i | 0.0830111 | − | 0.143780i | −0.821531 | − | 0.570164i | \(-0.806880\pi\) |
0.904542 | + | 0.426385i | \(0.140213\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 53.7401i | − | 1.78049i | −0.455483 | − | 0.890245i | \(-0.650533\pi\) | ||
0.455483 | − | 0.890245i | \(-0.349467\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.00000 | − | 5.19615i | −0.297857 | − | 0.171968i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.12372 | + | 2.12132i | −0.202223 | + | 0.0700522i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.50000 | + | 14.7224i | 0.280389 | + | 0.485648i | 0.971481 | − | 0.237119i | \(-0.0762032\pi\) |
−0.691091 | + | 0.722767i | \(0.742870\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −36.7423 | −1.20939 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.00000 | −0.0328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.1691 | − | 48.7904i | −0.924199 | − | 1.60076i | −0.792844 | − | 0.609425i | \(-0.791400\pi\) |
−0.131355 | − | 0.991335i | \(-0.541933\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.0000 | − | 1.73205i | 0.393284 | − | 0.0567657i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.6969 | − | 8.48528i | −0.480641 | − | 0.277498i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.7654i | 1.52776i | 0.645359 | + | 0.763879i | \(0.276708\pi\) | ||||
−0.645359 | + | 0.763879i | \(0.723292\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.4949 | − | 42.4264i | 0.798511 | − | 1.38306i | −0.122075 | − | 0.992521i | \(-0.538955\pi\) |
0.920586 | − | 0.390540i | \(-0.127712\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.0000 | − | 20.7846i | 1.17232 | − | 0.676840i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.8661 | + | 24.7487i | −1.39296 | + | 0.804226i | −0.993642 | − | 0.112586i | \(-0.964086\pi\) |
−0.399318 | + | 0.916812i | \(0.630753\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.50000 | − | 7.79423i | 0.146076 | − | 0.253011i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 5.65685i | − | 0.183243i | −0.995794 | − | 0.0916217i | \(-0.970795\pi\) | ||
0.995794 | − | 0.0916217i | \(-0.0292051\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.00000 | + | 1.73205i | 0.0970777 | + | 0.0560478i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.5959 | + | 22.6274i | −0.632785 | + | 0.730677i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | − | 24.2487i | −0.451613 | − | 0.782216i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −26.9444 | −0.867371 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.0000 | 0.418052 | 0.209026 | − | 0.977910i | \(-0.432971\pi\) | ||||
0.209026 | + | 0.977910i | \(0.432971\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.5959 | − | 33.9411i | −0.628863 | − | 1.08922i | −0.987780 | − | 0.155853i | \(-0.950187\pi\) |
0.358917 | − | 0.933369i | \(-0.383146\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.5000 | + | 2.59808i | 0.432790 | + | 0.0832905i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.12372 | − | 3.53553i | −0.195915 | − | 0.113112i | 0.398833 | − | 0.917023i | \(-0.369415\pi\) |
−0.594749 | + | 0.803912i | \(0.702748\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.92820i | 0.221426i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.44949 | + | 4.24264i | −0.0781266 | + | 0.135319i | −0.902442 | − | 0.430812i | \(-0.858227\pi\) |
0.824315 | + | 0.566131i | \(0.191561\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −42.0000 | + | 24.2487i | −1.33823 | + | 0.772628i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.89898 | − | 2.82843i | 0.155778 | − | 0.0899388i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.5000 | − | 30.3109i | 0.555906 | − | 0.962857i | −0.441927 | − | 0.897051i | \(-0.645705\pi\) |
0.997832 | − | 0.0658059i | \(-0.0209618\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33.9411i | 1.07601i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.5000 | − | 14.7224i | −0.807593 | − | 0.466264i | 0.0385262 | − | 0.999258i | \(-0.487734\pi\) |
−0.846119 | + | 0.532993i | \(0.821067\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))