Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(593,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.593");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.bm (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: | \(18.1100711784\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 593.1 | ||
Root | \(1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.593 |
Dual form | 2268.2.bm.g.1025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.44949 | −1.09545 | −0.547723 | − | 0.836660i | \(-0.684505\pi\) | ||||
−0.547723 | + | 0.836660i | \(0.684505\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | − | 0.866025i | −0.944911 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.24264i | 1.27920i | 0.768706 | + | 0.639602i | \(0.220901\pi\) | ||||
−0.768706 | + | 0.639602i | \(0.779099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.50000 | + | 0.866025i | −0.416025 | + | 0.240192i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) |
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.44949 | − | 4.24264i | −0.594089 | − | 1.02899i | −0.993675 | − | 0.112296i | \(-0.964180\pi\) |
0.399586 | − | 0.916696i | \(-0.369154\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.50000 | + | 2.59808i | 1.03237 | + | 0.596040i | 0.917663 | − | 0.397360i | \(-0.130073\pi\) |
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.34847 | − | 4.24264i | −1.36458 | − | 0.787839i | −0.374347 | − | 0.927289i | \(-0.622133\pi\) |
−0.990229 | + | 0.139450i | \(0.955467\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.50000 | + | 0.866025i | 0.269408 | + | 0.155543i | 0.628619 | − | 0.777714i | \(-0.283621\pi\) |
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.12372 | + | 2.12132i | 1.03510 | + | 0.358569i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.50000 | − | 4.33013i | 0.410997 | − | 0.711868i | −0.584002 | − | 0.811752i | \(-0.698514\pi\) |
0.994999 | + | 0.0998840i | \(0.0318472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.12372 | + | 10.6066i | 0.956365 | + | 1.65647i | 0.731213 | + | 0.682149i | \(0.238955\pi\) |
0.225152 | + | 0.974324i | \(0.427712\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.50000 | − | 9.52628i | 0.838742 | − | 1.45274i | −0.0522047 | − | 0.998636i | \(-0.516625\pi\) |
0.890947 | − | 0.454108i | \(-0.150042\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.22474 | + | 2.12132i | 0.178647 | + | 0.309426i | 0.941417 | − | 0.337243i | \(-0.109495\pi\) |
−0.762770 | + | 0.646670i | \(0.776161\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.34847 | + | 4.24264i | −1.00939 | + | 0.582772i | −0.911013 | − | 0.412378i | \(-0.864698\pi\) |
−0.0983769 | + | 0.995149i | \(0.531365\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 10.3923i | − | 1.40130i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.44949 | − | 4.24264i | 0.318896 | − | 0.552345i | −0.661362 | − | 0.750067i | \(-0.730021\pi\) |
0.980258 | + | 0.197722i | \(0.0633545\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00000 | − | 1.73205i | 0.384111 | − | 0.221766i | −0.295495 | − | 0.955344i | \(-0.595484\pi\) |
0.679605 | + | 0.733578i | \(0.262151\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.67423 | − | 2.12132i | 0.455733 | − | 0.263117i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50000 | − | 6.06218i | 0.427593 | − | 0.740613i | −0.569066 | − | 0.822292i | \(-0.692695\pi\) |
0.996659 | + | 0.0816792i | \(0.0260283\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.7279i | 1.51053i | 0.655422 | + | 0.755263i | \(0.272491\pi\) | ||||
−0.655422 | + | 0.755263i | \(0.727509\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.5000 | − | 7.79423i | 1.58006 | − | 0.912245i | 0.585206 | − | 0.810885i | \(-0.301014\pi\) |
0.994850 | − | 0.101361i | \(-0.0323196\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.67423 | − | 10.6066i | 0.418718 | − | 1.20873i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.50000 | − | 9.52628i | −0.618798 | − | 1.07179i | −0.989705 | − | 0.143120i | \(-0.954286\pi\) |
0.370907 | − | 0.928670i | \(-0.379047\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.12372 | − | 10.6066i | 0.672166 | − | 1.16423i | −0.305123 | − | 0.952313i | \(-0.598697\pi\) |
0.977289 | − | 0.211913i | \(-0.0679692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.00000 | + | 10.3923i | 0.650791 | + | 1.12720i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.34847 | − | 12.7279i | 0.778936 | − | 1.34916i | −0.153619 | − | 0.988130i | \(-0.549093\pi\) |
0.932555 | − | 0.361027i | \(-0.117574\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.50000 | − | 0.866025i | 0.471728 | − | 0.0907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.0227 | − | 6.36396i | −1.13091 | − | 0.652929i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.00000 | + | 1.73205i | 0.304604 | + | 0.175863i | 0.644509 | − | 0.764597i | \(-0.277062\pi\) |
−0.339905 | + | 0.940460i | \(0.610395\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.34847 | 0.731200 | 0.365600 | − | 0.930772i | \(-0.380864\pi\) | ||||
0.365600 | + | 0.930772i | \(0.380864\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.66025i | − | 0.853320i | −0.904412 | − | 0.426660i | \(-0.859690\pi\) | ||
0.904412 | − | 0.426660i | \(-0.140310\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.34847 | − | 4.24264i | −0.710403 | − | 0.410152i | 0.100807 | − | 0.994906i | \(-0.467858\pi\) |
−0.811210 | + | 0.584754i | \(0.801191\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.50000 | + | 4.33013i | 0.239457 | + | 0.414751i | 0.960558 | − | 0.278078i | \(-0.0896974\pi\) |
−0.721102 | + | 0.692829i | \(0.756364\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.67423 | + | 2.12132i | −0.345643 | + | 0.199557i | −0.662765 | − | 0.748828i | \(-0.730617\pi\) |
0.317122 | + | 0.948385i | \(0.397284\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.44949 | + | 12.7279i | 0.224544 | + | 1.16677i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.79796 | 0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.00000 | 0.443678 | 0.221839 | − | 0.975083i | \(-0.428794\pi\) | ||||
0.221839 | + | 0.975083i | \(0.428794\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.34847 | −0.642039 | −0.321019 | − | 0.947073i | \(-0.604025\pi\) | ||||
−0.321019 | + | 0.947073i | \(0.604025\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.00000 | − | 10.3923i | −0.780399 | − | 0.901127i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.50000 | − | 0.866025i | 0.127228 | − | 0.0734553i | −0.435035 | − | 0.900414i | \(-0.643264\pi\) |
0.562263 | + | 0.826958i | \(0.309931\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.67423 | − | 6.36396i | −0.307255 | − | 0.532181i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.0000 | + | 10.3923i | 1.49482 | + | 0.863034i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 16.9706i | − | 1.39028i | −0.718873 | − | 0.695141i | \(-0.755342\pi\) | ||
0.718873 | − | 0.695141i | \(-0.244658\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.00000 | −0.162758 | −0.0813788 | − | 0.996683i | \(-0.525932\pi\) | ||||
−0.0813788 | + | 0.996683i | \(0.525932\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.67423 | − | 2.12132i | −0.295122 | − | 0.170389i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00000 | + | 5.19615i | 0.718278 | + | 0.414698i | 0.814119 | − | 0.580699i | \(-0.197221\pi\) |
−0.0958404 | + | 0.995397i | \(0.530554\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.0000 | − | 19.0526i | 0.861586 | − | 1.49231i | −0.00881059 | − | 0.999961i | \(-0.502805\pi\) |
0.870397 | − | 0.492350i | \(-0.163862\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.57321 | + | 14.8492i | 0.663415 | + | 1.14907i | 0.979712 | + | 0.200409i | \(0.0642270\pi\) |
−0.316297 | + | 0.948660i | \(0.602440\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | + | 8.66025i | −0.384615 | + | 0.666173i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.50000 | − | 0.866025i | −0.188982 | − | 0.0654654i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.0227 | − | 6.36396i | 0.823876 | − | 0.475665i | −0.0278755 | − | 0.999611i | \(-0.508874\pi\) |
0.851751 | + | 0.523947i | \(0.175541\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.19615i | 0.386227i | 0.981176 | + | 0.193113i | \(0.0618586\pi\) | ||||
−0.981176 | + | 0.193113i | \(0.938141\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.12372 | + | 10.6066i | −0.450225 | + | 0.779813i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.0000 | − | 10.3923i | 1.31629 | − | 0.759961i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.67423 | − | 2.12132i | 0.265858 | − | 0.153493i | −0.361146 | − | 0.932509i | \(-0.617614\pi\) |
0.627004 | + | 0.779016i | \(0.284281\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.50000 | + | 16.4545i | −0.683825 | + | 1.18442i | 0.289980 | + | 0.957033i | \(0.406351\pi\) |
−0.973805 | + | 0.227387i | \(0.926982\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.48528i | 0.604551i | 0.953221 | + | 0.302276i | \(0.0977463\pi\) | ||||
−0.953221 | + | 0.302276i | \(0.902254\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.0000 | + | 6.92820i | −0.850657 | + | 0.491127i | −0.860873 | − | 0.508821i | \(-0.830082\pi\) |
0.0102152 | + | 0.999948i | \(0.496748\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.6969 | + | 16.9706i | 1.03152 | + | 1.19110i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.0000 | − | 25.9808i | −1.04765 | − | 1.81458i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.0227 | + | 19.0919i | −0.762456 | + | 1.32061i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.00000 | + | 1.73205i | 0.0688428 | + | 0.119239i | 0.898392 | − | 0.439194i | \(-0.144736\pi\) |
−0.829549 | + | 0.558433i | \(0.811403\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.4722 | + | 23.3345i | −0.918796 | + | 1.59140i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | − | 3.46410i | −0.203653 | − | 0.235159i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.34847 | + | 4.24264i | 0.494312 | + | 0.285391i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.0000 | + | 10.3923i | 1.20537 | + | 0.695920i | 0.961744 | − | 0.273949i | \(-0.0883300\pi\) |
0.243625 | + | 0.969870i | \(0.421663\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.0454 | −1.46321 | −0.731603 | − | 0.681731i | \(-0.761227\pi\) | ||||
−0.731603 | + | 0.681731i | \(0.761227\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.73205i | − | 0.114457i | −0.998361 | − | 0.0572286i | \(-0.981774\pi\) | ||
0.998361 | − | 0.0572286i | \(-0.0182264\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.67423 | − | 2.12132i | −0.240707 | − | 0.138972i | 0.374795 | − | 0.927108i | \(-0.377713\pi\) |
−0.615502 | + | 0.788136i | \(0.711047\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.00000 | − | 5.19615i | −0.195698 | − | 0.338960i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.67423 | + | 2.12132i | −0.237666 | + | 0.137217i | −0.614104 | − | 0.789225i | \(-0.710482\pi\) |
0.376437 | + | 0.926442i | \(0.377149\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.8564i | 0.892570i | 0.894891 | + | 0.446285i | \(0.147253\pi\) | ||||
−0.894891 | + | 0.446285i | \(0.852747\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.4722 | − | 10.6066i | −0.860707 | − | 0.677631i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.00000 | −0.572656 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.79796 | −0.618442 | −0.309221 | − | 0.950990i | \(-0.600068\pi\) | ||||
−0.309221 | + | 0.950990i | \(0.600068\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.34847 | 0.458385 | 0.229192 | − | 0.973381i | \(-0.426391\pi\) | ||||
0.229192 | + | 0.973381i | \(0.426391\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.0000 | + | 8.66025i | −0.621370 | + | 0.538122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 25.4558i | − | 1.56967i | −0.619702 | − | 0.784837i | \(-0.712746\pi\) | ||
0.619702 | − | 0.784837i | \(-0.287254\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.0000 | − | 10.3923i | 1.10573 | − | 0.638394i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.12372 | + | 10.6066i | 0.373370 | + | 0.646696i | 0.990082 | − | 0.140493i | \(-0.0448688\pi\) |
−0.616712 | + | 0.787189i | \(0.711536\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.0000 | − | 13.8564i | −1.45790 | − | 0.841717i | −0.458988 | − | 0.888442i | \(-0.651788\pi\) |
−0.998908 | + | 0.0467255i | \(0.985121\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.24264i | 0.255841i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0000 | 0.660926 | 0.330463 | − | 0.943819i | \(-0.392795\pi\) | ||||
0.330463 | + | 0.943819i | \(0.392795\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.6969 | + | 8.48528i | 0.876746 | + | 0.506189i | 0.869584 | − | 0.493785i | \(-0.164387\pi\) |
0.00716177 | + | 0.999974i | \(0.497720\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.50000 | + | 4.33013i | 0.445829 | + | 0.257399i | 0.706067 | − | 0.708145i | \(-0.250468\pi\) |
−0.260238 | + | 0.965544i | \(0.583801\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.12372 | − | 31.8198i | −0.361472 | − | 1.87826i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.50000 | + | 6.06218i | −0.205882 | + | 0.356599i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.2474 | − | 21.2132i | −0.715504 | − | 1.23929i | −0.962765 | − | 0.270340i | \(-0.912864\pi\) |
0.247261 | − | 0.968949i | \(-0.420469\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.00000 | + | 10.3923i | −0.349334 | + | 0.605063i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.0000 | + | 19.0526i | −1.26806 | + | 1.09817i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.34847 | + | 4.24264i | −0.420772 | + | 0.242933i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.0526i | 1.08739i | 0.839284 | + | 0.543693i | \(0.182975\pi\) | ||||
−0.839284 | + | 0.543693i | \(0.817025\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | 13.5000 | − | 7.79423i | 0.763065 | − | 0.440556i | −0.0673300 | − | 0.997731i | \(-0.521448\pi\) |
0.830395 | + | 0.557175i | \(0.188115\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.34847 | + | 4.24264i | −0.412731 | + | 0.238290i | −0.691963 | − | 0.721933i | \(-0.743254\pi\) |
0.279231 | + | 0.960224i | \(0.409920\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.0000 | − | 31.1769i | 1.00781 | − | 1.74557i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 25.4558i | − | 1.41640i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.50000 | + | 0.866025i | −0.0832050 | + | 0.0480384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.22474 | − | 6.36396i | −0.0675224 | − | 0.350857i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.50000 | + | 4.33013i | 0.137412 | + | 0.238005i | 0.926516 | − | 0.376254i | \(-0.122788\pi\) |
−0.789104 | + | 0.614260i | \(0.789455\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.57321 | + | 14.8492i | −0.468405 | + | 0.811301i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.50000 | − | 6.06218i | −0.190657 | − | 0.330228i | 0.754811 | − | 0.655942i | \(-0.227729\pi\) |
−0.945468 | + | 0.325714i | \(0.894395\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.67423 | + | 6.36396i | −0.198971 | + | 0.344628i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.34847 | − | 4.24264i | −0.394486 | − | 0.227757i | 0.289616 | − | 0.957143i | \(-0.406472\pi\) |
−0.684102 | + | 0.729386i | \(0.739806\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.0000 | − | 12.1244i | −1.12410 | − | 0.649002i | −0.181659 | − | 0.983362i | \(-0.558147\pi\) |
−0.942446 | + | 0.334360i | \(0.891480\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.9444 | 1.43411 | 0.717053 | − | 0.697019i | \(-0.245491\pi\) | ||||
0.717053 | + | 0.697019i | \(0.245491\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 31.1769i | − | 1.65470i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.6969 | + | 8.48528i | 0.775675 | + | 0.447836i | 0.834895 | − | 0.550409i | \(-0.185528\pi\) |
−0.0592205 | + | 0.998245i | \(0.518862\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.00000 | + | 6.92820i | 0.210526 | + | 0.364642i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −33.0681 | + | 19.0919i | −1.73086 | + | 0.999315i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.9808i | 1.35618i | 0.734977 | + | 0.678092i | \(0.237193\pi\) | ||||
−0.734977 | + | 0.678092i | \(0.762807\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.0454 | − | 4.24264i | 1.14454 | − | 0.220267i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.00000 | −0.362446 | −0.181223 | − | 0.983442i | \(-0.558006\pi\) | ||||
−0.181223 | + | 0.983442i | \(0.558006\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.6969 | 0.756931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.00000 | −0.256833 | −0.128416 | − | 0.991720i | \(-0.540989\pi\) | ||||
−0.128416 | + | 0.991720i | \(0.540989\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.79796 | 0.500652 | 0.250326 | − | 0.968162i | \(-0.419462\pi\) | ||||
0.250326 | + | 0.968162i | \(0.419462\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.00000 | + | 25.9808i | −0.458682 | + | 1.32410i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.24264i | 0.215110i | 0.994199 | + | 0.107555i | \(0.0343022\pi\) | ||||
−0.994199 | + | 0.107555i | \(0.965698\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.4722 | + | 23.3345i | 0.677860 | + | 1.17409i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.50000 | + | 4.33013i | 0.376414 | + | 0.217323i | 0.676257 | − | 0.736666i | \(-0.263601\pi\) |
−0.299843 | + | 0.953989i | \(0.596934\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.48528i | 0.423735i | 0.977298 | + | 0.211867i | \(0.0679545\pi\) | ||||
−0.977298 | + | 0.211867i | \(0.932046\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.00000 | −0.149441 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.3712 | + | 10.6066i | 0.910625 | + | 0.525750i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.50000 | + | 4.33013i | 0.370851 | + | 0.214111i | 0.673830 | − | 0.738886i | \(-0.264648\pi\) |
−0.302979 | + | 0.952997i | \(0.597981\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.79796 | + | 8.48528i | −0.482126 | + | 0.417533i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.0000 | + | 25.9808i | −0.736321 | + | 1.27535i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.4722 | − | 23.3345i | −0.658160 | − | 1.13997i | −0.981092 | − | 0.193544i | \(-0.938002\pi\) |
0.322932 | − | 0.946422i | \(-0.395332\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.5000 | + | 30.3109i | −0.852898 | + | 1.47726i | 0.0256838 | + | 0.999670i | \(0.491824\pi\) |
−0.878582 | + | 0.477592i | \(0.841510\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.44949 | − | 4.24264i | −0.118818 | − | 0.205798i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.00000 | + | 1.73205i | −0.435541 | + | 0.0838198i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.3712 | − | 10.6066i | 0.884908 | − | 0.510902i | 0.0126347 | − | 0.999920i | \(-0.495978\pi\) |
0.872274 | + | 0.489018i | \(0.162645\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.1244i | 0.582659i | 0.956623 | + | 0.291330i | \(0.0940977\pi\) | ||||
−0.956623 | + | 0.291330i | \(0.905902\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.0000 | − | 20.7846i | 1.71819 | − | 0.991995i | 0.795956 | − | 0.605355i | \(-0.206969\pi\) |
0.922231 | − | 0.386640i | \(-0.126365\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.0000 | + | 31.1769i | −0.853282 | + | 1.47793i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 12.7279i | − | 0.600668i | −0.953834 | − | 0.300334i | \(-0.902902\pi\) | ||
0.953834 | − | 0.300334i | \(-0.0970981\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −45.0000 | + | 25.9808i | −2.11897 | + | 1.22339i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.0227 | + | 2.12132i | −0.516752 | + | 0.0994490i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.50000 | − | 11.2583i | −0.304057 | − | 0.526642i | 0.672994 | − | 0.739648i | \(-0.265008\pi\) |
−0.977051 | + | 0.213006i | \(0.931675\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.44949 | − | 4.24264i | 0.114084 | − | 0.197599i | −0.803329 | − | 0.595535i | \(-0.796940\pi\) |
0.917413 | + | 0.397936i | \(0.130273\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.5000 | − | 25.1147i | −0.673872 | − | 1.16718i | −0.976797 | − | 0.214166i | \(-0.931297\pi\) |
0.302925 | − | 0.953014i | \(-0.402037\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.67423 | − | 6.36396i | 0.170023 | − | 0.294489i | −0.768404 | − | 0.639965i | \(-0.778949\pi\) |
0.938428 | + | 0.345476i | \(0.112282\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.0000 | + | 12.1244i | −0.646460 | + | 0.559851i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 40.4166 | + | 23.3345i | 1.85836 | + | 1.07292i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.50000 | + | 2.59808i | 0.206474 | + | 0.119208i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.89898 | −0.223840 | −0.111920 | − | 0.993717i | \(-0.535700\pi\) | ||||
−0.111920 | + | 0.993717i | \(0.535700\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.66025i | 0.394874i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.34847 | − | 4.24264i | −0.333677 | − | 0.192648i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.50000 | − | 6.06218i | −0.158600 | − | 0.274703i | 0.775764 | − | 0.631023i | \(-0.217365\pi\) |
−0.934364 | + | 0.356320i | \(0.884031\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.3939 | − | 16.9706i | 1.32653 | − | 0.765871i | 0.341766 | − | 0.939785i | \(-0.388975\pi\) |
0.984761 | + | 0.173914i | \(0.0556415\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 41.5692i | 1.87218i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.0227 | − | 31.8198i | 0.494436 | − | 1.42731i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.0000 | −1.56682 | −0.783408 | − | 0.621508i | \(-0.786520\pi\) | ||||
−0.783408 | + | 0.621508i | \(0.786520\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.44949 | 0.109217 | 0.0546087 | − | 0.998508i | \(-0.482609\pi\) | ||||
0.0546087 | + | 0.998508i | \(0.482609\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.0000 | −0.800989 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.1464 | 0.760002 | 0.380001 | − | 0.924986i | \(-0.375924\pi\) | ||||
0.380001 | + | 0.924986i | \(0.375924\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −40.5000 | + | 7.79423i | −1.79161 | + | 0.344796i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 21.2132i | 0.934765i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.00000 | + | 5.19615i | −0.395820 | + | 0.228527i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.44949 | + | 4.24264i | 0.107314 | + | 0.185873i | 0.914681 | − | 0.404176i | \(-0.132442\pi\) |
−0.807367 | + | 0.590049i | \(0.799108\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.50000 | − | 4.33013i | −0.327952 | − | 0.189343i | 0.326979 | − | 0.945031i | \(-0.393969\pi\) |
−0.654932 | + | 0.755688i | \(0.727303\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 8.48528i | − | 0.369625i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.3712 | − | 10.6066i | −0.795744 | − | 0.459423i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.0000 | + | 10.3923i | 0.778208 | + | 0.449299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.3712 | + | 23.3345i | −0.791302 | + | 1.00509i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.50000 | − | 16.4545i | 0.408437 | − | 0.707433i | −0.586278 | − | 0.810110i | \(-0.699407\pi\) |
0.994715 | + | 0.102677i | \(0.0327407\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.12372 | − | 10.6066i | −0.262312 | − | 0.454337i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.00000 | + | 1.73205i | −0.0427569 | + | 0.0740571i | −0.886612 | − | 0.462514i | \(-0.846947\pi\) |
0.843855 | + | 0.536571i | \(0.180281\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.0454 | − | 38.1838i | −0.939166 | − | 1.62668i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.50000 | + | 28.5788i | 0.233884 | + | 1.21530i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.3712 | + | 10.6066i | −0.778412 | + | 0.449416i | −0.835867 | − | 0.548932i | \(-0.815035\pi\) |
0.0574555 | + | 0.998348i | \(0.481701\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.0526i | 0.805837i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.67423 | + | 6.36396i | −0.154851 | + | 0.268209i | −0.933005 | − | 0.359864i | \(-0.882823\pi\) |
0.778154 | + | 0.628073i | \(0.216156\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.00000 | − | 5.19615i | 0.378633 | − | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.3712 | + | 10.6066i | −0.770160 | + | 0.444652i | −0.832932 | − | 0.553376i | \(-0.813339\pi\) |
0.0627719 | + | 0.998028i | \(0.480006\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.50000 | − | 6.06218i | 0.146470 | − | 0.253694i | −0.783450 | − | 0.621455i | \(-0.786542\pi\) |
0.929921 | + | 0.367760i | \(0.119875\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.5000 | + | 19.9186i | −1.43625 | + | 0.829222i | −0.997587 | − | 0.0694283i | \(-0.977883\pi\) |
−0.438667 | + | 0.898650i | \(0.644549\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.4949 | + | 21.2132i | −1.01622 | + | 0.880072i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.0000 | − | 31.1769i | −0.745484 | − | 1.29122i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.34847 | − | 12.7279i | 0.303304 | − | 0.525338i | −0.673578 | − | 0.739116i | \(-0.735244\pi\) |
0.976882 | + | 0.213778i | \(0.0685770\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.50000 | + | 7.79423i | 0.185419 | + | 0.321156i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.22474 | + | 2.12132i | −0.0502942 | + | 0.0871122i | −0.890077 | − | 0.455811i | \(-0.849349\pi\) |
0.839782 | + | 0.542923i | \(0.182683\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.00000 | − | 31.1769i | −0.245976 | − | 1.27813i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.6969 | − | 8.48528i | −0.600501 | − | 0.346699i | 0.168738 | − | 0.985661i | \(-0.446031\pi\) |
−0.769238 | + | 0.638962i | \(0.779364\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.5000 | + | 21.6506i | 1.52966 | + | 0.883148i | 0.999376 | + | 0.0353259i | \(0.0112469\pi\) |
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.1464 | 0.697101 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 25.9808i | − | 1.05453i | −0.849702 | − | 0.527263i | \(-0.823218\pi\) | ||
0.849702 | − | 0.527263i | \(-0.176782\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.67423 | − | 2.12132i | −0.148644 | − | 0.0858194i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.00000 | − | 6.92820i | −0.161558 | − | 0.279827i | 0.773869 | − | 0.633345i | \(-0.218319\pi\) |
−0.935428 | + | 0.353518i | \(0.884985\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.3712 | − | 10.6066i | 0.739596 | − | 0.427006i | −0.0823267 | − | 0.996605i | \(-0.526235\pi\) |
0.821922 | + | 0.569600i | \(0.192902\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.66025i | 0.348085i | 0.984738 | + | 0.174042i | \(0.0556830\pi\) | ||||
−0.984738 | + | 0.174042i | \(0.944317\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29.3939 | + | 25.4558i | −1.17764 | + | 1.01987i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.4949 | −0.976676 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.0000 | −0.875806 | −0.437903 | − | 0.899022i | \(-0.644279\pi\) | ||||
−0.437903 | + | 0.899022i | \(0.644279\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.2474 | −0.486025 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.0000 | − | 1.73205i | −0.475457 | − | 0.0686264i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.48528i | 0.335148i | 0.985859 | + | 0.167574i | \(0.0535934\pi\) | ||||
−0.985859 | + | 0.167574i | \(0.946407\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.5000 | − | 16.4545i | 1.12393 | − | 0.648901i | 0.181529 | − | 0.983386i | \(-0.441895\pi\) |
0.942401 | + | 0.334484i | \(0.108562\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.0227 | − | 19.0919i | −0.433347 | − | 0.750579i | 0.563812 | − | 0.825903i | \(-0.309334\pi\) |
−0.997159 | + | 0.0753238i | \(0.976001\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.0000 | + | 10.3923i | 0.706562 | + | 0.407934i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.2132i | 0.830137i | 0.909790 | + | 0.415068i | \(0.136242\pi\) | ||||
−0.909790 | + | 0.415068i | \(0.863758\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.0000 | 0.703318 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.6969 | + | 8.48528i | 0.572511 | + | 0.330540i | 0.758152 | − | 0.652078i | \(-0.226103\pi\) |
−0.185640 | + | 0.982618i | \(0.559436\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.50000 | − | 2.59808i | −0.175030 | − | 0.101053i | 0.409926 | − | 0.912119i | \(-0.365555\pi\) |
−0.584955 | + | 0.811065i | \(0.698888\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 22.0454 | + | 25.4558i | 0.854884 | + | 0.987135i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.34847 | + | 12.7279i | 0.283685 | + | 0.491356i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.50000 | + | 16.4545i | −0.366198 | + | 0.634274i | −0.988968 | − | 0.148132i | \(-0.952674\pi\) |
0.622770 | + | 0.782405i | \(0.286007\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.6969 | + | 25.4558i | 0.564849 | + | 0.978348i | 0.997064 | + | 0.0765767i | \(0.0243990\pi\) |
−0.432214 | + | 0.901771i | \(0.642268\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.00000 | − | 6.92820i | −0.230259 | − | 0.265880i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.34847 | + | 4.24264i | −0.281181 | + | 0.162340i | −0.633958 | − | 0.773367i | \(-0.718571\pi\) |
0.352777 | + | 0.935708i | \(0.385238\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.34847 | − | 12.7279i | 0.279954 | − | 0.484895i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.5000 | + | 9.52628i | −0.627690 | + | 0.362397i | −0.779857 | − | 0.625958i | \(-0.784708\pi\) |
0.152167 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.67423 | + | 2.12132i | −0.139372 | + | 0.0804663i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.0000 | − | 51.9615i | 1.13633 | − | 1.96818i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 33.9411i | − | 1.28194i | −0.767567 | − | 0.640969i | \(-0.778533\pi\) | ||
0.767567 | − | 0.640969i | \(-0.221467\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.5000 | − | 12.9904i | 0.848604 | − | 0.489942i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.3712 | − | 6.36396i | −0.690919 | − | 0.239341i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.00000 | − | 13.8564i | −0.300446 | − | 0.520388i | 0.675791 | − | 0.737093i | \(-0.263802\pi\) |
−0.976237 | + | 0.216705i | \(0.930469\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.00000 | + | 15.5885i | 0.336581 | + | 0.582975i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.4722 | − | 23.3345i | 0.502428 | − | 0.870231i | −0.497568 | − | 0.867425i | \(-0.665774\pi\) |
0.999996 | − | 0.00280593i | \(-0.000893157\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.50000 | + | 21.6506i | −0.279315 | + | 0.806312i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.34847 | − | 4.24264i | −0.272915 | − | 0.157568i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.5000 | + | 19.9186i | 1.27953 | + | 0.738739i | 0.976763 | − | 0.214324i | \(-0.0687548\pi\) |
0.302772 | + | 0.953063i | \(0.402088\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −53.8888 | −1.99315 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 8.66025i | − | 0.319874i | −0.987127 | − | 0.159937i | \(-0.948871\pi\) | ||
0.987127 | − | 0.159937i | \(-0.0511291\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.7196 | + | 14.8492i | 0.947395 | + | 0.546979i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.50000 | + | 16.4545i | 0.349463 | + | 0.605288i | 0.986154 | − | 0.165831i | \(-0.0530307\pi\) |
−0.636691 | + | 0.771119i | \(0.719697\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.0227 | − | 6.36396i | 0.404384 | − | 0.233471i | −0.283990 | − | 0.958827i | \(-0.591658\pi\) |
0.688374 | + | 0.725356i | \(0.258325\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 41.5692i | 1.52298i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.6969 | + | 16.9706i | 0.537014 | + | 0.620091i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.00000 | −0.182453 | −0.0912263 | − | 0.995830i | \(-0.529079\pi\) | ||||
−0.0912263 | + | 0.995830i | \(0.529079\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.89898 | 0.178292 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.0000 | −0.508839 | −0.254419 | − | 0.967094i | \(-0.581884\pi\) | ||||
−0.254419 | + | 0.967094i | \(0.581884\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.2929 | −1.24312 | −0.621558 | − | 0.783369i | \(-0.713500\pi\) | ||||
−0.621558 | + | 0.783369i | \(0.713500\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.50000 | − | 12.9904i | −0.0905061 | − | 0.470283i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.48528i | 0.306386i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.5000 | − | 7.79423i | 0.486822 | − | 0.281067i | −0.236433 | − | 0.971648i | \(-0.575978\pi\) |
0.723255 | + | 0.690581i | \(0.242645\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.8207 | − | 36.0624i | −0.748867 | − | 1.29708i | −0.948366 | − | 0.317178i | \(-0.897265\pi\) |
0.199499 | − | 0.979898i | \(-0.436069\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.50000 | + | 0.866025i | 0.0538816 | + | 0.0311086i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 63.6396i | 2.28013i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.0000 | −1.93227 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.0454 | − | 12.7279i | −0.786834 | − | 0.454279i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.0000 | − | 8.66025i | −0.534692 | − | 0.308705i | 0.208233 | − | 0.978079i | \(-0.433229\pi\) |
−0.742925 | + | 0.669375i | \(0.766562\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.0227 | − | 2.12132i | 0.391922 | − | 0.0754255i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.00000 | + | 5.19615i | −0.106533 | + | 0.184521i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.00000 | − | 10.3923i | 0.212265 | − | 0.367653i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 33.0681 | + | 57.2756i | 1.16695 | + | 2.02121i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.3712 | − | 10.6066i | 0.645896 | − | 0.372908i | −0.140986 | − | 0.990012i | \(-0.545027\pi\) |
0.786882 | + | 0.617103i | \(0.211694\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31.1769i | − | 1.09477i | −0.836881 | − | 0.547385i | \(-0.815623\pi\) | ||
0.836881 | − | 0.547385i | \(-0.184377\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −26.9444 | + | 46.6690i | −0.943821 | + | 1.63475i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 49.5000 | − | 28.5788i | 1.73179 | − | 0.999847i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.3712 | − | 10.6066i | 0.641158 | − | 0.370173i | −0.143902 | − | 0.989592i | \(-0.545965\pi\) |
0.785061 | + | 0.619419i | \(0.212632\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.0000 | + | 22.5167i | −0.453152 | + | 0.784881i | −0.998580 | − | 0.0532760i | \(-0.983034\pi\) |
0.545428 | + | 0.838157i | \(0.316367\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.6985i | 1.03272i | 0.856372 | + | 0.516359i | \(0.172713\pi\) | ||||
−0.856372 | + | 0.516359i | \(0.827287\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.5000 | − | 18.1865i | 1.09404 | − | 0.631644i | 0.159391 | − | 0.987216i | \(-0.449047\pi\) |
0.934649 | + | 0.355571i | \(0.115714\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.89898 | − | 33.9411i | 0.169740 | − | 1.17599i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.0000 | − | 36.3731i | −0.726735 | − | 1.25874i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.9444 | − | 46.6690i | 0.930224 | − | 1.61119i | 0.147286 | − | 0.989094i | \(-0.452946\pi\) |
0.782937 | − | 0.622101i | \(-0.213720\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.5000 | + | 37.2391i | 0.741379 | + | 1.28411i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.2474 | − | 21.2132i | 0.421325 | − | 0.729756i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.5000 | + | 6.06218i | 0.601307 | + | 0.208299i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.5000 | − | 12.9904i | −0.770385 | − | 0.444782i | 0.0626267 | − | 0.998037i | \(-0.480052\pi\) |
−0.833012 | + | 0.553255i | \(0.813386\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39.1918 | −1.33877 | −0.669384 | − | 0.742917i | \(-0.733442\pi\) | ||||
−0.669384 | + | 0.742917i | \(0.733442\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 45.0333i | − | 1.53652i | −0.640140 | − | 0.768259i | \(-0.721124\pi\) | ||
0.640140 | − | 0.768259i | \(-0.278876\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.0681 | + | 19.0919i | 1.12565 | + | 0.649895i | 0.942838 | − | 0.333252i | \(-0.108146\pi\) |
0.182814 | + | 0.983148i | \(0.441479\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 40.4166 | − | 23.3345i | 1.37104 | − | 0.791570i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.1244i | 0.410818i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.4949 | − | 8.48528i | −0.828079 | − | 0.286855i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.0000 | −0.945493 | −0.472746 | − | 0.881199i | \(-0.656737\pi\) | ||||
−0.472746 | + | 0.881199i | \(0.656737\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.3939 | −0.990305 | −0.495152 | − | 0.868806i | \(-0.664888\pi\) | ||||
−0.495152 | + | 0.868806i | \(0.664888\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.00000 | 0.0336527 | 0.0168263 | − | 0.999858i | \(-0.494644\pi\) | ||||
0.0168263 | + | 0.999858i | \(0.494644\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 56.3383 | 1.89165 | 0.945827 | − | 0.324671i | \(-0.105254\pi\) | ||||
0.945827 | + | 0.324671i | \(0.105254\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.5000 | − | 4.33013i | −0.419237 | − | 0.145228i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.7279i | 0.425924i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.0000 | + | 15.5885i | −0.902510 | + | 0.521065i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.34847 | − | 12.7279i | −0.245085 | − | 0.424500i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.0000 | + | 20.7846i | 1.19933 | + | 0.692436i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 12.7279i | − | 0.423090i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.00000 | 0.232431 | 0.116216 | − | 0.993224i | \(-0.462924\pi\) | ||||
0.116216 | + | 0.993224i | \(0.462924\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.34847 | + | 4.24264i | 0.243466 | + | 0.140565i | 0.616769 | − | 0.787145i | \(-0.288441\pi\) |
−0.373303 | + | 0.927710i | \(0.621775\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 45.0000 | + | 25.9808i | 1.48928 | + | 0.859838i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.3712 | + | 6.36396i | 0.606670 | + | 0.210157i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.5000 | − | 35.5070i | 0.676233 | − | 1.17127i | −0.299874 | − | 0.953979i | \(-0.596945\pi\) |
0.976107 | − | 0.217291i | \(-0.0697219\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.0227 | − | 19.0919i | −0.362817 | − | 0.628417i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.50000 | − | 4.33013i | 0.0821995 | − | 0.142374i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.4722 | − | 23.3345i | −0.442008 | − | 0.765581i | 0.555830 | − | 0.831296i | \(-0.312401\pi\) |
−0.997838 | + | 0.0657150i | \(0.979067\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.5000 | + | 33.7750i | 0.442445 | + | 1.10693i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −44.0908 | + | 25.4558i | −1.44192 | + | 0.832495i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19.0526i | − | 0.622420i | −0.950341 | − | 0.311210i | \(-0.899266\pi\) | ||
0.950341 | − | 0.311210i | \(-0.100734\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.79796 | − | 16.9706i | 0.319404 | − | 0.553225i | −0.660960 | − | 0.750422i | \(-0.729851\pi\) |
0.980364 | + | 0.197197i | \(0.0631839\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.7650 | − | 27.5772i | 1.55216 | − | 0.896137i | 0.554189 | − | 0.832391i | \(-0.313028\pi\) |
0.997966 | − | 0.0637469i | \(-0.0203050\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.5000 | + | 23.3827i | −0.438229 | + | 0.759034i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.9411i | 1.09946i | 0.835342 | + | 0.549730i | \(0.185270\pi\) | ||||
−0.835342 | + | 0.549730i | \(0.814730\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.00000 | + | 5.19615i | −0.291233 | + | 0.168144i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | − | 24.2487i | −0.451613 | − | 0.782216i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.2702 | − | 40.3051i | 0.749093 | − | 1.29747i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.5000 | + | 37.2391i | 0.691393 | + | 1.19753i | 0.971381 | + | 0.237525i | \(0.0763362\pi\) |
−0.279988 | + | 0.960003i | \(0.590331\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.89898 | + | 8.48528i | −0.157216 | + | 0.272306i | −0.933864 | − | 0.357629i | \(-0.883585\pi\) |
0.776648 | + | 0.629935i | \(0.216918\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.50000 | + | 0.866025i | −0.144263 | + | 0.0277635i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.0681 | − | 19.0919i | −1.05794 | − | 0.610803i | −0.133080 | − | 0.991105i | \(-0.542487\pi\) |
−0.924862 | + | 0.380302i | \(0.875820\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 54.0000 | + | 31.1769i | 1.72585 | + | 0.996419i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53.8888 | 1.71878 | 0.859392 | − | 0.511316i | \(-0.170842\pi\) | ||||
0.859392 | + | 0.511316i | \(0.170842\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 20.7846i | − | 0.662253i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.50000 | − | 11.2583i | −0.206479 | − | 0.357633i | 0.744124 | − | 0.668042i | \(-0.232867\pi\) |
−0.950603 | + | 0.310409i | \(0.899534\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 29.3939 | − | 16.9706i | 0.931849 | − | 0.538003i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 50.2295i | − | 1.59078i | −0.606096 | − | 0.795392i | \(-0.707265\pi\) | ||
0.606096 | − | 0.795392i | \(-0.292735\pi\) | |||||||
\(998\) | 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 \(a_p\))