Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,2,Mod(1088,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.1088");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.69570878012\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1088.6 | ||
Root | \(1.90184 - 0.0324487i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.1088 |
Dual form | 1089.2.d.g.1088.5 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.688291 | −0.486695 | −0.243348 | − | 0.969939i | \(-0.578246\pi\) | ||||
−0.243348 | + | 0.969939i | \(0.578246\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.52626 | −0.763128 | ||||||||
\(5\) | 0.0401087i | 0.0179372i | 0.999960 | + | 0.00896859i | \(0.00285483\pi\) | ||||
−0.999960 | + | 0.00896859i | \(0.997145\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 0.246848i | − 0.0932998i | −0.998911 | − | 0.0466499i | \(-0.985145\pi\) | ||||
0.998911 | − | 0.0466499i | \(-0.0148545\pi\) | |||||||
\(8\) | 2.42709 | 0.858106 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 0.0276065i | − 0.00872994i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.30152i | 0.638327i | 0.947700 | + | 0.319164i | \(0.103402\pi\) | ||||
−0.947700 | + | 0.319164i | \(0.896598\pi\) | |||||||
\(14\) | 0.169903i | 0.0454086i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.38197 | 0.345492 | ||||||||
\(17\) | −4.27621 | −1.03713 | −0.518567 | − | 0.855037i | \(-0.673534\pi\) | ||||
−0.518567 | + | 0.855037i | \(0.673534\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 6.20004i | − 1.42239i | −0.702997 | − | 0.711193i | \(-0.748155\pi\) | ||||
0.702997 | − | 0.711193i | \(-0.251845\pi\) | |||||||
\(20\) | − 0.0612162i | − 0.0136884i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.79984i | 1.41786i | 0.705277 | + | 0.708932i | \(0.250823\pi\) | ||||
−0.705277 | + | 0.708932i | \(0.749177\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.99839 | 0.999678 | ||||||||
\(26\) | − 1.58412i | − 0.310671i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.376753i | 0.0711997i | ||||||||
\(29\) | −5.59574 | −1.03910 | −0.519552 | − | 0.854439i | \(-0.673901\pi\) | ||||
−0.519552 | + | 0.854439i | \(0.673901\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.79738 | 0.861635 | 0.430817 | − | 0.902439i | \(-0.358225\pi\) | ||||
0.430817 | + | 0.902439i | \(0.358225\pi\) | |||||||
\(32\) | −5.80538 | −1.02626 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.94328 | 0.504768 | ||||||||
\(35\) | 0.00990077 | 0.00167354 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.03084 | −0.662667 | −0.331333 | − | 0.943514i | \(-0.607498\pi\) | ||||
−0.331333 | + | 0.943514i | \(0.607498\pi\) | |||||||
\(38\) | 4.26743i | 0.692268i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.0973475i | 0.0153920i | ||||||||
\(41\) | 9.60293 | 1.49973 | 0.749863 | − | 0.661593i | \(-0.230119\pi\) | ||||
0.749863 | + | 0.661593i | \(0.230119\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.03166i | 0.157327i | 0.996901 | + | 0.0786636i | \(0.0250653\pi\) | ||||
−0.996901 | + | 0.0786636i | \(0.974935\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − 4.68027i | − 0.690068i | ||||||||
\(47\) | 11.1262i | 1.62292i | 0.584405 | + | 0.811462i | \(0.301328\pi\) | ||||
−0.584405 | + | 0.811462i | \(0.698672\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.93907 | 0.991295 | ||||||||
\(50\) | −3.44035 | −0.486539 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 3.51271i | − 0.487125i | ||||||||
\(53\) | 8.96776i | 1.23182i | 0.787818 | + | 0.615908i | \(0.211211\pi\) | ||||
−0.787818 | + | 0.615908i | \(0.788789\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 0.599123i | − 0.0800611i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.85150 | 0.505727 | ||||||||
\(59\) | 2.78832i | 0.363008i | 0.983390 | + | 0.181504i | \(0.0580966\pi\) | ||||
−0.983390 | + | 0.181504i | \(0.941903\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.48450i | 1.08633i | 0.839627 | + | 0.543164i | \(0.182774\pi\) | ||||
−0.839627 | + | 0.543164i | \(0.817226\pi\) | |||||||
\(62\) | −3.30199 | −0.419354 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.23186 | 0.153982 | ||||||||
\(65\) | −0.0923111 | −0.0114498 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.94588 | 0.970744 | 0.485372 | − | 0.874308i | \(-0.338684\pi\) | ||||
0.485372 | + | 0.874308i | \(0.338684\pi\) | |||||||
\(68\) | 6.52659 | 0.791465 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.00681461 | −0.000814502 0 | ||||||||
\(71\) | 3.32850i | 0.395020i | 0.980301 | + | 0.197510i | \(0.0632855\pi\) | ||||
−0.980301 | + | 0.197510i | \(0.936714\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.8537i | 1.38737i | 0.720278 | + | 0.693685i | \(0.244014\pi\) | ||||
−0.720278 | + | 0.693685i | \(0.755986\pi\) | |||||||
\(74\) | 2.77439 | 0.322517 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.46284i | 1.08546i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.01100i | 0.338764i | 0.985550 | + | 0.169382i | \(0.0541772\pi\) | ||||
−0.985550 | + | 0.169382i | \(0.945823\pi\) | |||||||
\(80\) | 0.0554289i | 0.00619714i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.60961 | −0.729909 | ||||||||
\(83\) | −5.29380 | −0.581070 | −0.290535 | − | 0.956864i | \(-0.593833\pi\) | ||||
−0.290535 | + | 0.956864i | \(0.593833\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 0.171513i | − 0.0186032i | ||||||||
\(86\) | − 0.710085i | − 0.0765704i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.54422i | 0.905686i | 0.891590 | + | 0.452843i | \(0.149590\pi\) | ||||
−0.891590 | + | 0.452843i | \(0.850410\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.568126 | 0.0595558 | ||||||||
\(92\) | − 10.3783i | − 1.08201i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 7.65807i | − 0.789870i | ||||||||
\(95\) | 0.248676 | 0.0255136 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.02824 | −0.307471 | −0.153736 | − | 0.988112i | \(-0.549130\pi\) | ||||
−0.153736 | + | 0.988112i | \(0.549130\pi\) | |||||||
\(98\) | −4.77610 | −0.482459 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.62882 | −0.762882 | ||||||||
\(101\) | −6.95198 | −0.691747 | −0.345874 | − | 0.938281i | \(-0.612417\pi\) | ||||
−0.345874 | + | 0.938281i | \(0.612417\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.1194 | 1.29269 | 0.646347 | − | 0.763044i | \(-0.276296\pi\) | ||||
0.646347 | + | 0.763044i | \(0.276296\pi\) | |||||||
\(104\) | 5.58600i | 0.547752i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − 6.17243i | − 0.599519i | ||||||||
\(107\) | 1.36847 | 0.132295 | 0.0661476 | − | 0.997810i | \(-0.478929\pi\) | ||||
0.0661476 | + | 0.997810i | \(0.478929\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 7.34454i | − 0.703480i | −0.936098 | − | 0.351740i | \(-0.885590\pi\) | ||||
0.936098 | − | 0.351740i | \(-0.114410\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 0.341136i | − 0.0322343i | ||||||||
\(113\) | 0.528542i | 0.0497211i | 0.999691 | + | 0.0248605i | \(0.00791417\pi\) | ||||
−0.999691 | + | 0.0248605i | \(0.992086\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.272733 | −0.0254325 | ||||||||
\(116\) | 8.54053 | 0.792968 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 1.91917i | − 0.176674i | ||||||||
\(119\) | 1.05557i | 0.0967644i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − 5.83980i | − 0.528711i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.32203 | −0.657537 | ||||||||
\(125\) | 0.401023i | 0.0358686i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.7719i | 1.13332i | 0.823952 | + | 0.566660i | \(0.191765\pi\) | ||||
−0.823952 | + | 0.566660i | \(0.808235\pi\) | |||||||
\(128\) | 10.7629 | 0.951313 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.0635369 | 0.00557256 | ||||||||
\(131\) | 18.1534 | 1.58607 | 0.793033 | − | 0.609178i | \(-0.208501\pi\) | ||||
0.793033 | + | 0.609178i | \(0.208501\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.53047 | −0.132708 | ||||||||
\(134\) | −5.46908 | −0.472456 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.3787 | −0.889970 | ||||||||
\(137\) | − 16.0730i | − 1.37321i | −0.727032 | − | 0.686604i | \(-0.759101\pi\) | ||||
0.727032 | − | 0.686604i | \(-0.240899\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 3.85730i | − 0.327172i | −0.986529 | − | 0.163586i | \(-0.947694\pi\) | ||||
0.986529 | − | 0.163586i | \(-0.0523061\pi\) | |||||||
\(140\) | −0.0151111 | −0.00127712 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 2.29098i | − 0.192255i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 0.224438i | − 0.0186386i | ||||||||
\(146\) | − 8.15879i | − 0.675227i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.15210 | 0.505699 | ||||||||
\(149\) | 10.2700 | 0.841350 | 0.420675 | − | 0.907211i | \(-0.361793\pi\) | ||||
0.420675 | + | 0.907211i | \(0.361793\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.77042i | 0.713726i | 0.934157 | + | 0.356863i | \(0.116154\pi\) | ||||
−0.934157 | + | 0.356863i | \(0.883846\pi\) | |||||||
\(152\) | − 15.0480i | − 1.22056i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.192417i | 0.0154553i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.0308 | −1.03997 | −0.519987 | − | 0.854174i | \(-0.674063\pi\) | ||||
−0.519987 | + | 0.854174i | \(0.674063\pi\) | |||||||
\(158\) | − 2.07245i | − 0.164875i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 0.232846i | − 0.0184081i | ||||||||
\(161\) | 1.67853 | 0.132287 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.17774 | −0.718856 | −0.359428 | − | 0.933173i | \(-0.617028\pi\) | ||||
−0.359428 | + | 0.933173i | \(0.617028\pi\) | |||||||
\(164\) | −14.6565 | −1.14448 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.64367 | 0.282804 | ||||||||
\(167\) | −7.60934 | −0.588828 | −0.294414 | − | 0.955678i | \(-0.595124\pi\) | ||||
−0.294414 | + | 0.955678i | \(0.595124\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.70300 | 0.592538 | ||||||||
\(170\) | 0.118051i | 0.00905411i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 1.57458i | − 0.120061i | ||||||||
\(173\) | −16.6204 | −1.26363 | −0.631813 | − | 0.775121i | \(-0.717689\pi\) | ||||
−0.631813 | + | 0.775121i | \(0.717689\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 1.23384i | − 0.0932698i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 5.88091i | − 0.440793i | ||||||||
\(179\) | − 7.04979i | − 0.526926i | −0.964669 | − | 0.263463i | \(-0.915135\pi\) | ||||
0.964669 | − | 0.263463i | \(-0.0848647\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.1236 | −1.57011 | −0.785053 | − | 0.619429i | \(-0.787364\pi\) | ||||
−0.785053 | + | 0.619429i | \(0.787364\pi\) | |||||||
\(182\) | −0.391036 | −0.0289855 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 16.5038i | 1.21668i | ||||||||
\(185\) | − 0.161672i | − 0.0118864i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − 16.9814i | − 1.23850i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.171161 | −0.0124173 | ||||||||
\(191\) | 13.6683i | 0.989000i | 0.869178 | + | 0.494500i | \(0.164649\pi\) | ||||
−0.869178 | + | 0.494500i | \(0.835351\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 25.0349i | − 1.80205i | −0.433767 | − | 0.901025i | \(-0.642816\pi\) | ||||
0.433767 | − | 0.901025i | \(-0.357184\pi\) | |||||||
\(194\) | 2.08431 | 0.149645 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.5908 | −0.756485 | ||||||||
\(197\) | 21.0442 | 1.49934 | 0.749668 | − | 0.661814i | \(-0.230213\pi\) | ||||
0.749668 | + | 0.661814i | \(0.230213\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.3709 | −0.735176 | −0.367588 | − | 0.929989i | \(-0.619816\pi\) | ||||
−0.367588 | + | 0.929989i | \(0.619816\pi\) | |||||||
\(200\) | 12.1315 | 0.857830 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.78498 | 0.336670 | ||||||||
\(203\) | 1.38130i | 0.0969481i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.385161i | 0.0269008i | ||||||||
\(206\) | −9.02997 | −0.629148 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.18062i | 0.220537i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.7436i | 1.29036i | 0.764029 | + | 0.645182i | \(0.223218\pi\) | ||||
−0.764029 | + | 0.645182i | \(0.776782\pi\) | |||||||
\(212\) | − 13.6871i | − 0.940033i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.941908 | −0.0643875 | ||||||||
\(215\) | −0.0413787 | −0.00282201 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 1.18422i | − 0.0803904i | ||||||||
\(218\) | 5.05518i | 0.342380i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 9.84179i | − 0.662031i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.66894 | 0.647480 | 0.323740 | − | 0.946146i | \(-0.395060\pi\) | ||||
0.323740 | + | 0.946146i | \(0.395060\pi\) | |||||||
\(224\) | 1.43305i | 0.0957494i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − 0.363791i | − 0.0241990i | ||||||||
\(227\) | 11.7162 | 0.777630 | 0.388815 | − | 0.921316i | \(-0.372884\pi\) | ||||
0.388815 | + | 0.921316i | \(0.372884\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.4802 | 1.35337 | 0.676684 | − | 0.736274i | \(-0.263416\pi\) | ||||
0.676684 | + | 0.736274i | \(0.263416\pi\) | |||||||
\(230\) | 0.187720 | 0.0123779 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.5814 | −0.891661 | ||||||||
\(233\) | 16.1429 | 1.05755 | 0.528777 | − | 0.848761i | \(-0.322651\pi\) | ||||
0.528777 | + | 0.848761i | \(0.322651\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.446258 | −0.0291107 | ||||||||
\(236\) | − 4.25569i | − 0.277022i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 0.726543i | − 0.0470948i | ||||||||
\(239\) | −28.3875 | −1.83624 | −0.918118 | − | 0.396306i | \(-0.870292\pi\) | ||||
−0.918118 | + | 0.396306i | \(0.870292\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 14.3654i | − 0.925357i | −0.886526 | − | 0.462679i | \(-0.846888\pi\) | ||||
0.886526 | − | 0.462679i | \(-0.153112\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 12.9495i | − 0.829007i | ||||||||
\(245\) | 0.278317i | 0.0177810i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.2695 | 0.907948 | ||||||||
\(248\) | 11.6437 | 0.739374 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 0.276021i | − 0.0174571i | ||||||||
\(251\) | − 6.94278i | − 0.438225i | −0.975700 | − | 0.219112i | \(-0.929684\pi\) | ||||
0.975700 | − | 0.219112i | \(-0.0703161\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − 8.79077i | − 0.551582i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.87170 | −0.616981 | ||||||||
\(257\) | 10.4183i | 0.649875i | 0.945735 | + | 0.324938i | \(0.105343\pi\) | ||||
−0.945735 | + | 0.324938i | \(0.894657\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.995006i | 0.0618267i | ||||||||
\(260\) | 0.140890 | 0.00873765 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.4948 | −0.771931 | ||||||||
\(263\) | −4.26110 | −0.262751 | −0.131375 | − | 0.991333i | \(-0.541939\pi\) | ||||
−0.131375 | + | 0.991333i | \(0.541939\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.359686 | −0.0220953 | ||||||||
\(266\) | 1.05341 | 0.0645885 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.1274 | −0.740801 | ||||||||
\(269\) | − 11.0638i | − 0.674569i | −0.941403 | − | 0.337285i | \(-0.890492\pi\) | ||||
0.941403 | − | 0.337285i | \(-0.109508\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 15.8957i | − 0.965596i | −0.875732 | − | 0.482798i | \(-0.839621\pi\) | ||||
0.875732 | − | 0.482798i | \(-0.160379\pi\) | |||||||
\(272\) | −5.90958 | −0.358321 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.0629i | 0.668334i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 11.3410i | − 0.681417i | −0.940169 | − | 0.340709i | \(-0.889333\pi\) | ||||
0.940169 | − | 0.340709i | \(-0.110667\pi\) | |||||||
\(278\) | 2.65495i | 0.159233i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.0240301 | 0.00143607 | ||||||||
\(281\) | 1.56030 | 0.0930794 | 0.0465397 | − | 0.998916i | \(-0.485181\pi\) | ||||
0.0465397 | + | 0.998916i | \(0.485181\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.5654i | 1.57915i | 0.613653 | + | 0.789576i | \(0.289699\pi\) | ||||
−0.613653 | + | 0.789576i | \(0.710301\pi\) | |||||||
\(284\) | − 5.08014i | − 0.301451i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 2.37046i | − 0.139924i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.28598 | 0.0756456 | ||||||||
\(290\) | 0.154479i | 0.00907131i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 18.0918i | − 1.05874i | ||||||||
\(293\) | −26.3345 | −1.53848 | −0.769240 | − | 0.638960i | \(-0.779365\pi\) | ||||
−0.769240 | + | 0.638960i | \(0.779365\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.111836 | −0.00651134 | ||||||||
\(296\) | −9.78322 | −0.568638 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.06874 | −0.409481 | ||||||||
\(299\) | −15.6500 | −0.905062 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.254664 | 0.0146786 | ||||||||
\(302\) | − 6.03660i | − 0.347367i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 8.56824i | − 0.491422i | ||||||||
\(305\) | −0.340302 | −0.0194857 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 26.0083i | − 1.48437i | −0.670195 | − | 0.742185i | \(-0.733789\pi\) | ||||
0.670195 | − | 0.742185i | \(-0.266211\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − 0.132439i | − 0.00752202i | ||||||||
\(311\) | − 13.3248i | − 0.755578i | −0.925892 | − | 0.377789i | \(-0.876684\pi\) | ||||
0.925892 | − | 0.377789i | \(-0.123316\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.2483 | −0.635792 | −0.317896 | − | 0.948126i | \(-0.602976\pi\) | ||||
−0.317896 | + | 0.948126i | \(0.602976\pi\) | |||||||
\(314\) | 8.96901 | 0.506151 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − 4.59556i | − 0.258520i | ||||||||
\(317\) | − 10.9526i | − 0.615161i | −0.951522 | − | 0.307580i | \(-0.900481\pi\) | ||||
0.951522 | − | 0.307580i | \(-0.0995193\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.0494082i | 0.00276200i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.15532 | −0.0643832 | ||||||||
\(323\) | 26.5127i | 1.47520i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.5039i | 0.638122i | ||||||||
\(326\) | 6.31695 | 0.349864 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 23.3072 | 1.28692 | ||||||||
\(329\) | 2.74648 | 0.151419 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.23285 | 0.232659 | 0.116329 | − | 0.993211i | \(-0.462887\pi\) | ||||
0.116329 | + | 0.993211i | \(0.462887\pi\) | |||||||
\(332\) | 8.07968 | 0.443430 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.23744 | 0.286580 | ||||||||
\(335\) | 0.318699i | 0.0174124i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.66238i | 0.145029i | 0.997367 | + | 0.0725146i | \(0.0231024\pi\) | ||||
−0.997367 | + | 0.0725146i | \(0.976898\pi\) | |||||||
\(338\) | −5.30191 | −0.288386 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.261773i | 0.0141966i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 3.44083i | − 0.185787i | ||||||||
\(344\) | 2.50394i | 0.135003i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.4397 | 0.615001 | ||||||||
\(347\) | −16.6032 | −0.891304 | −0.445652 | − | 0.895206i | \(-0.647028\pi\) | ||||
−0.445652 | + | 0.895206i | \(0.647028\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 13.7748i | − 0.737346i | −0.929559 | − | 0.368673i | \(-0.879812\pi\) | ||||
0.929559 | − | 0.368673i | \(-0.120188\pi\) | |||||||
\(350\) | 0.849243i | 0.0453940i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 11.0249i | − 0.586795i | −0.955990 | − | 0.293398i | \(-0.905214\pi\) | ||||
0.955990 | − | 0.293398i | \(-0.0947860\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.133502 | −0.00708555 | ||||||||
\(356\) | − 13.0407i | − 0.691154i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.85231i | 0.256452i | ||||||||
\(359\) | 19.0142 | 1.00353 | 0.501766 | − | 0.865003i | \(-0.332684\pi\) | ||||
0.501766 | + | 0.865003i | \(0.332684\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.4404 | −1.02318 | ||||||||
\(362\) | 14.5392 | 0.764163 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.867106 | −0.0454487 | ||||||||
\(365\) | −0.475437 | −0.0248855 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.69718 | −0.297390 | −0.148695 | − | 0.988883i | \(-0.547507\pi\) | ||||
−0.148695 | + | 0.988883i | \(0.547507\pi\) | |||||||
\(368\) | 9.39715i | 0.489860i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.111277i | 0.00578504i | ||||||||
\(371\) | 2.21367 | 0.114928 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.1594i | 1.14737i | 0.819076 | + | 0.573684i | \(0.194486\pi\) | ||||
−0.819076 | + | 0.573684i | \(0.805514\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 27.0043i | 1.39264i | ||||||||
\(377\) | − 12.8787i | − 0.663288i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.381352 | −0.0195887 | −0.00979436 | − | 0.999952i | \(-0.503118\pi\) | ||||
−0.00979436 | + | 0.999952i | \(0.503118\pi\) | |||||||
\(380\) | −0.379542 | −0.0194701 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 9.40774i | − 0.481342i | ||||||||
\(383\) | 12.6644i | 0.647122i | 0.946207 | + | 0.323561i | \(0.104880\pi\) | ||||
−0.946207 | + | 0.323561i | \(0.895120\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.2313i | 0.877049i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.62187 | 0.234640 | ||||||||
\(389\) | − 23.7986i | − 1.20664i | −0.797500 | − | 0.603318i | \(-0.793845\pi\) | ||||
0.797500 | − | 0.603318i | \(-0.206155\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 29.0775i | − 1.47051i | ||||||||
\(392\) | 16.8417 | 0.850636 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.4845 | −0.729720 | ||||||||
\(395\) | −0.120768 | −0.00607647 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.00497 | 0.251192 | 0.125596 | − | 0.992081i | \(-0.459916\pi\) | ||||
0.125596 | + | 0.992081i | \(0.459916\pi\) | |||||||
\(398\) | 7.13823 | 0.357807 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.90761 | 0.345380 | ||||||||
\(401\) | − 4.24415i | − 0.211943i | −0.994369 | − | 0.105971i | \(-0.966205\pi\) | ||||
0.994369 | − | 0.105971i | \(-0.0337952\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.0413i | 0.550005i | ||||||||
\(404\) | 10.6105 | 0.527892 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − 0.950735i | − 0.0471842i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.8056i | 0.583748i | 0.956457 | + | 0.291874i | \(0.0942788\pi\) | ||||
−0.956457 | + | 0.291874i | \(0.905721\pi\) | |||||||
\(410\) | − 0.265103i | − 0.0130925i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −20.0236 | −0.986490 | ||||||||
\(413\) | 0.688291 | 0.0338686 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 0.212328i | − 0.0104227i | ||||||||
\(416\) | − 13.3612i | − 0.655087i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.9795i | 1.02492i | 0.858712 | + | 0.512459i | \(0.171265\pi\) | ||||
−0.858712 | + | 0.512459i | \(0.828735\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.77978 | −0.135478 | −0.0677390 | − | 0.997703i | \(-0.521579\pi\) | ||||
−0.0677390 | + | 0.997703i | \(0.521579\pi\) | |||||||
\(422\) | − 12.9011i | − 0.628014i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 21.7656i | 1.05703i | ||||||||
\(425\) | −21.3742 | −1.03680 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.09438 | 0.101354 | ||||||||
\(428\) | −2.08864 | −0.100958 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.0284806 | 0.00137346 | ||||||||
\(431\) | −27.9292 | −1.34530 | −0.672652 | − | 0.739959i | \(-0.734845\pi\) | ||||
−0.672652 | + | 0.739959i | \(0.734845\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.16809 | −0.440590 | −0.220295 | − | 0.975433i | \(-0.570702\pi\) | ||||
−0.220295 | + | 0.975433i | \(0.570702\pi\) | |||||||
\(434\) | 0.815091i | 0.0391256i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.2096i | 0.536845i | ||||||||
\(437\) | 42.1592 | 2.01675 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 2.93111i | − 0.139894i | −0.997551 | − | 0.0699472i | \(-0.977717\pi\) | ||||
0.997551 | − | 0.0699472i | \(-0.0222831\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.77402i | 0.322207i | ||||||||
\(443\) | 35.8414i | 1.70288i | 0.524455 | + | 0.851438i | \(0.324269\pi\) | ||||
−0.524455 | + | 0.851438i | \(0.675731\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.342698 | −0.0162454 | ||||||||
\(446\) | −6.65504 | −0.315125 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 0.304081i | − 0.0143665i | ||||||||
\(449\) | 14.2141i | 0.670806i | 0.942075 | + | 0.335403i | \(0.108872\pi\) | ||||
−0.942075 | + | 0.335403i | \(0.891128\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − 0.806691i | − 0.0379435i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.06414 | −0.378469 | ||||||||
\(455\) | 0.0227868i | 0.00106826i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.3993i | 0.954238i | 0.878839 | + | 0.477119i | \(0.158319\pi\) | ||||
−0.878839 | + | 0.477119i | \(0.841681\pi\) | |||||||
\(458\) | −14.0963 | −0.658678 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.416260 | 0.0194082 | ||||||||
\(461\) | −0.770354 | −0.0358790 | −0.0179395 | − | 0.999839i | \(-0.505711\pi\) | ||||
−0.0179395 | + | 0.999839i | \(0.505711\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.7948 | 1.75647 | 0.878236 | − | 0.478228i | \(-0.158721\pi\) | ||||
0.878236 | + | 0.478228i | \(0.158721\pi\) | |||||||
\(464\) | −7.73312 | −0.359001 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.1110 | −0.514707 | ||||||||
\(467\) | 17.6026i | 0.814551i | 0.913305 | + | 0.407276i | \(0.133521\pi\) | ||||
−0.913305 | + | 0.407276i | \(0.866479\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 1.96143i | − 0.0905702i | ||||||||
\(470\) | 0.307156 | 0.0141680 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.76750i | 0.311499i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 30.9902i | − 1.42193i | ||||||||
\(476\) | − 1.61108i | − 0.0738436i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 19.5389 | 0.893688 | ||||||||
\(479\) | 2.40586 | 0.109927 | 0.0549633 | − | 0.998488i | \(-0.482496\pi\) | ||||
0.0549633 | + | 0.998488i | \(0.482496\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 9.27708i | − 0.422998i | ||||||||
\(482\) | 9.88758i | 0.450367i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 0.121459i | − 0.00551517i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.5978 | 0.661491 | 0.330745 | − | 0.943720i | \(-0.392700\pi\) | ||||
0.330745 | + | 0.943720i | \(0.392700\pi\) | |||||||
\(488\) | 20.5926i | 0.932185i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − 0.191563i | − 0.00865395i | ||||||||
\(491\) | 25.0424 | 1.13015 | 0.565073 | − | 0.825041i | \(-0.308848\pi\) | ||||
0.565073 | + | 0.825041i | \(0.308848\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.9286 | 1.07769 | ||||||||
\(494\) | −9.82158 | −0.441894 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.62982 | 0.297688 | ||||||||
\(497\) | 0.821634 | 0.0368553 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.7116 | 1.01671 | 0.508355 | − | 0.861148i | \(-0.330254\pi\) | ||||
0.508355 | + | 0.861148i | \(0.330254\pi\) | |||||||
\(500\) | − 0.612063i | − 0.0273723i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.77866i | 0.213282i | ||||||||
\(503\) | 10.4071 | 0.464030 | 0.232015 | − | 0.972712i | \(-0.425468\pi\) | ||||
0.232015 | + | 0.972712i | \(0.425468\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − 0.278835i | − 0.0124080i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 19.4931i | − 0.864868i | ||||||||
\(509\) | 8.08550i | 0.358383i | 0.983814 | + | 0.179192i | \(0.0573482\pi\) | ||||
−0.983814 | + | 0.179192i | \(0.942652\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.92606 | 0.129441 | ||||||||
\(512\) | −14.7311 | −0.651031 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 7.17082i | − 0.316291i | ||||||||
\(515\) | 0.526203i | 0.0231873i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − 0.684854i | − 0.0300908i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.224047 | −0.00982513 | ||||||||
\(521\) | − 35.0206i | − 1.53428i | −0.641479 | − | 0.767141i | \(-0.721679\pi\) | ||||
0.641479 | − | 0.767141i | \(-0.278321\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.2956i | 1.89318i | 0.322434 | + | 0.946592i | \(0.395499\pi\) | ||||
−0.322434 | + | 0.946592i | \(0.604501\pi\) | |||||||
\(524\) | −27.7067 | −1.21037 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.93288 | 0.127880 | ||||||||
\(527\) | −20.5146 | −0.893630 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.2378 | −1.01034 | ||||||||
\(530\) | 0.247568 | 0.0107537 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.33588 | 0.101273 | ||||||||
\(533\) | 22.1013i | 0.957316i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.0548877i | 0.00237300i | ||||||||
\(536\) | 19.2854 | 0.833001 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.61509i | 0.328310i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.226329i | 0.00973066i | 0.999988 | + | 0.00486533i | \(0.00154869\pi\) | ||||
−0.999988 | + | 0.00486533i | \(0.998451\pi\) | |||||||
\(542\) | 10.9409i | 0.469951i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 24.8250 | 1.06436 | ||||||||
\(545\) | 0.294580 | 0.0126184 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 16.4633i | − 0.703918i | −0.936015 | − | 0.351959i | \(-0.885516\pi\) | ||||
0.936015 | − | 0.351959i | \(-0.114484\pi\) | |||||||
\(548\) | 24.5315i | 1.04793i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.6938i | 1.47801i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.743260 | 0.0316066 | ||||||||
\(554\) | 7.80594i | 0.331643i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.88723i | 0.249674i | ||||||||
\(557\) | −26.2818 | −1.11360 | −0.556798 | − | 0.830648i | \(-0.687970\pi\) | ||||
−0.556798 | + | 0.830648i | \(0.687970\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.37440 | −0.100426 | ||||||||
\(560\) | 0.0136825 | 0.000578192 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.07394 | −0.0453013 | ||||||||
\(563\) | 36.3658 | 1.53263 | 0.766317 | − | 0.642463i | \(-0.222087\pi\) | ||||
0.766317 | + | 0.642463i | \(0.222087\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.0211992 | −0.000891856 0 | ||||||||
\(566\) | − 18.2848i | − 0.768565i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.07857i | 0.338969i | ||||||||
\(569\) | 20.2307 | 0.848114 | 0.424057 | − | 0.905636i | \(-0.360606\pi\) | ||||
0.424057 | + | 0.905636i | \(0.360606\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.4002i | 1.02112i | 0.859843 | + | 0.510558i | \(0.170561\pi\) | ||||
−0.859843 | + | 0.510558i | \(0.829439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.63157i | 0.0681004i | ||||||||
\(575\) | 33.9883i | 1.41741i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.3030 | −0.803593 | −0.401796 | − | 0.915729i | \(-0.631614\pi\) | ||||
−0.401796 | + | 0.915729i | \(0.631614\pi\) | |||||||
\(578\) | −0.885126 | −0.0368164 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.342550i | 0.0142236i | ||||||||
\(581\) | 1.30676i | 0.0542137i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 28.7700i | 1.19051i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.1258 | 0.748771 | ||||||||
\(587\) | − 19.1363i | − 0.789840i | −0.918715 | − | 0.394920i | \(-0.870772\pi\) | ||||
0.918715 | − | 0.394920i | \(-0.129228\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 29.7439i | − 1.22558i | ||||||||
\(590\) | 0.0769757 | 0.00316904 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.57049 | −0.228946 | ||||||||
\(593\) | −14.9885 | −0.615503 | −0.307751 | − | 0.951467i | \(-0.599577\pi\) | ||||
−0.307751 | + | 0.951467i | \(0.599577\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0423378 | −0.00173568 | ||||||||
\(596\) | −15.6746 | −0.642058 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.7717 | 0.440489 | ||||||||
\(599\) | 33.3409i | 1.36227i | 0.732158 | + | 0.681135i | \(0.238513\pi\) | ||||
−0.732158 | + | 0.681135i | \(0.761487\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.2730i | 1.72435i | 0.506610 | + | 0.862175i | \(0.330898\pi\) | ||||
−0.506610 | + | 0.862175i | \(0.669102\pi\) | |||||||
\(602\) | −0.175283 | −0.00714401 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − 13.3859i | − 0.544664i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.8859i | 1.25362i | 0.779172 | + | 0.626810i | \(0.215640\pi\) | ||||
−0.779172 | + | 0.626810i | \(0.784360\pi\) | |||||||
\(608\) | 35.9935i | 1.45973i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.234227 | 0.00948358 | ||||||||
\(611\) | −25.6072 | −1.03596 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 15.9745i | − 0.645204i | −0.946535 | − | 0.322602i | \(-0.895442\pi\) | ||||
0.946535 | − | 0.322602i | \(-0.104558\pi\) | |||||||
\(614\) | 17.9013i | 0.722436i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.63374i | 0.106030i | 0.998594 | + | 0.0530151i | \(0.0168831\pi\) | ||||
−0.998594 | + | 0.0530151i | \(0.983117\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.2495 | 0.813894 | 0.406947 | − | 0.913452i | \(-0.366593\pi\) | ||||
0.406947 | + | 0.913452i | \(0.366593\pi\) | |||||||
\(620\) | − 0.293677i | − 0.0117944i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9.17132i | 0.367736i | ||||||||
\(623\) | 2.10913 | 0.0845003 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9759 | 0.999035 | ||||||||
\(626\) | 7.74212 | 0.309437 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19.8884 | 0.793633 | ||||||||
\(629\) | 17.2367 | 0.687274 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.44044 | 0.336009 | 0.168004 | − | 0.985786i | \(-0.446268\pi\) | ||||
0.168004 | + | 0.985786i | \(0.446268\pi\) | |||||||
\(632\) | 7.30797i | 0.290696i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.53859i | 0.299396i | ||||||||
\(635\) | −0.512264 | −0.0203286 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.9704i | 0.632771i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.431685i | 0.0170639i | ||||||||
\(641\) | − 32.3145i | − 1.27634i | −0.769894 | − | 0.638172i | \(-0.779691\pi\) | ||||
0.769894 | − | 0.638172i | \(-0.220309\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.7767 | 0.543300 | 0.271650 | − | 0.962396i | \(-0.412431\pi\) | ||||
0.271650 | + | 0.962396i | \(0.412431\pi\) | |||||||
\(644\) | −2.56186 | −0.100951 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − 18.2484i | − 0.717975i | ||||||||
\(647\) | − 8.52739i | − 0.335246i | −0.985851 | − | 0.167623i | \(-0.946391\pi\) | ||||
0.985851 | − | 0.167623i | \(-0.0536092\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − 7.91804i | − 0.310571i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.0076 | 0.548579 | ||||||||
\(653\) | − 1.20799i | − 0.0472722i | −0.999721 | − | 0.0236361i | \(-0.992476\pi\) | ||||
0.999721 | − | 0.0236361i | \(-0.00752430\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.728108i | 0.0284496i | ||||||||
\(656\) | 13.2709 | 0.518142 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.89038 | −0.0736947 | ||||||||
\(659\) | −9.41054 | −0.366583 | −0.183291 | − | 0.983059i | \(-0.558675\pi\) | ||||
−0.183291 | + | 0.983059i | \(0.558675\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.1027 | 0.587425 | 0.293713 | − | 0.955894i | \(-0.405109\pi\) | ||||
0.293713 | + | 0.955894i | \(0.405109\pi\) | |||||||
\(662\) | −2.91343 | −0.113234 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.8485 | −0.498619 | ||||||||
\(665\) | − 0.0613851i | − 0.00238041i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 38.0501i | − 1.47331i | ||||||||
\(668\) | 11.6138 | 0.449351 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 0.219358i | − 0.00847453i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 41.5989i | − 1.60352i | −0.597647 | − | 0.801759i | \(-0.703898\pi\) | ||||
0.597647 | − | 0.801759i | \(-0.296102\pi\) | |||||||
\(674\) | − 1.83249i | − 0.0705850i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.7567 | −0.452182 | ||||||||
\(677\) | −4.52056 | −0.173739 | −0.0868696 | − | 0.996220i | \(-0.527686\pi\) | ||||
−0.0868696 | + | 0.996220i | \(0.527686\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.747516i | 0.0286870i | ||||||||
\(680\) | − 0.416279i | − 0.0159636i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 34.7783i | − 1.33075i | −0.746507 | − | 0.665377i | \(-0.768271\pi\) | ||||
0.746507 | − | 0.665377i | \(-0.231729\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.644667 | 0.0246315 | ||||||||
\(686\) | 2.36829i | 0.0904219i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.42572i | 0.0543552i | ||||||||
\(689\) | −20.6395 | −0.786302 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.8835 | −0.680320 | −0.340160 | − | 0.940368i | \(-0.610481\pi\) | ||||
−0.340160 | + | 0.940368i | \(0.610481\pi\) | |||||||
\(692\) | 25.3670 | 0.964308 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.4278 | 0.433794 | ||||||||
\(695\) | 0.154712 | 0.00586854 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −41.0641 | −1.55542 | ||||||||
\(698\) | 9.48105i | 0.358863i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.88316i | 0.0711768i | ||||||||
\(701\) | 17.4712 | 0.659878 | 0.329939 | − | 0.944002i | \(-0.392972\pi\) | ||||
0.329939 | + | 0.944002i | \(0.392972\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.9914i | 0.942568i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.58833i | 0.285591i | ||||||||
\(707\) | 1.71608i | 0.0645399i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.33849 | 0.313158 | 0.156579 | − | 0.987665i | \(-0.449953\pi\) | ||||
0.156579 | + | 0.987665i | \(0.449953\pi\) | |||||||
\(710\) | 0.0918882 | 0.00344850 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 20.7376i | 0.777174i | ||||||||
\(713\) | 32.6214i | 1.22168i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.7598i | 0.402112i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −13.0873 | −0.488415 | ||||||||
\(719\) | 23.6031i | 0.880249i | 0.897937 | + | 0.440124i | \(0.145066\pi\) | ||||
−0.897937 | + | 0.440124i | \(0.854934\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − 3.23850i | − 0.120608i | ||||||||
\(722\) | 13.3807 | 0.497977 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 32.2400 | 1.19819 | ||||||||
\(725\) | −27.9697 | −1.03877 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.90462 | 0.0706386 | 0.0353193 | − | 0.999376i | \(-0.488755\pi\) | ||||
0.0353193 | + | 0.999376i | \(0.488755\pi\) | |||||||
\(728\) | 1.37889 | 0.0511052 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.327239 | 0.0121117 | ||||||||
\(731\) | − 4.41161i | − 0.163169i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.6118i | 0.650506i | 0.945627 | + | 0.325253i | \(0.105450\pi\) | ||||
−0.945627 | + | 0.325253i | \(0.894550\pi\) | |||||||
\(734\) | 3.92132 | 0.144738 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − 39.4756i | − 1.45509i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.77737i | 0.175738i | 0.996132 | + | 0.0878692i | \(0.0280058\pi\) | ||||
−0.996132 | + | 0.0878692i | \(0.971994\pi\) | |||||||
\(740\) | 0.246753i | 0.00907082i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.52365 | −0.0559350 | ||||||||
\(743\) | 1.83777 | 0.0674211 | 0.0337105 | − | 0.999432i | \(-0.489268\pi\) | ||||
0.0337105 | + | 0.999432i | \(0.489268\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.411916i | 0.0150914i | ||||||||
\(746\) | − 15.2521i | − 0.558419i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 0.337805i | − 0.0123431i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.9446 | −1.38462 | −0.692308 | − | 0.721602i | \(-0.743406\pi\) | ||||
−0.692308 | + | 0.721602i | \(0.743406\pi\) | |||||||
\(752\) | 15.3760i | 0.560707i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.86431i | 0.322819i | ||||||||
\(755\) | −0.351770 | −0.0128022 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.6265 | −1.11314 | −0.556569 | − | 0.830802i | \(-0.687882\pi\) | ||||
−0.556569 | + | 0.830802i | \(0.687882\pi\) | |||||||
\(758\) | 0.262481 | 0.00953373 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.603558 | 0.0218934 | ||||||||
\(761\) | −30.8652 | −1.11886 | −0.559432 | − | 0.828876i | \(-0.688981\pi\) | ||||
−0.559432 | + | 0.828876i | \(0.688981\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.81299 | −0.0656345 | ||||||||
\(764\) | − 20.8613i | − 0.754734i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 8.71682i | − 0.314951i | ||||||||
\(767\) | −6.41738 | −0.231718 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 19.3154i | − 0.696532i | −0.937396 | − | 0.348266i | \(-0.886771\pi\) | ||||
0.937396 | − | 0.348266i | \(-0.113229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 38.2096i | 1.37519i | ||||||||
\(773\) | − 2.94203i | − 0.105818i | −0.998599 | − | 0.0529088i | \(-0.983151\pi\) | ||||
0.998599 | − | 0.0529088i | \(-0.0168493\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.9792 | 0.861358 | ||||||||
\(776\) | −7.34982 | −0.263843 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.3804i | 0.587265i | ||||||||
\(779\) | − 59.5385i | − 2.13319i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 20.0138i | 0.715693i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.58955 | 0.342484 | ||||||||
\(785\) | − 0.522651i | − 0.0186542i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 8.04569i | − 0.286798i | −0.989665 | − | 0.143399i | \(-0.954197\pi\) | ||||
0.989665 | − | 0.143399i | \(-0.0458032\pi\) | |||||||
\(788\) | −32.1188 | −1.14419 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.0831232 | 0.00295739 | ||||||||
\(791\) | 0.130470 | 0.00463897 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.5272 | −0.693433 | ||||||||
\(794\) | −3.44487 | −0.122254 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.8287 | 0.561033 | ||||||||
\(797\) | − 54.9219i | − 1.94543i | −0.231996 | − | 0.972717i | \(-0.574526\pi\) | ||||
0.231996 | − | 0.972717i | \(-0.425474\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 47.5780i | − 1.68319i | ||||||||
\(800\) | −29.0175 | −1.02592 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.92121i | 0.103152i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0673236i | 0.00237285i | ||||||||
\(806\) | − 7.59961i | − 0.267685i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −16.8731 | −0.593593 | ||||||||
\(809\) | 24.3526 | 0.856193 | 0.428096 | − | 0.903733i | \(-0.359184\pi\) | ||||
0.428096 | + | 0.903733i | \(0.359184\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 20.7604i | − 0.728996i | −0.931204 | − | 0.364498i | \(-0.881241\pi\) | ||||
0.931204 | − | 0.364498i | \(-0.118759\pi\) | |||||||
\(812\) | − 2.10821i | − 0.0739838i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 0.368107i | − 0.0128942i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.39635 | 0.223780 | ||||||||
\(818\) | − 8.12567i | − 0.284107i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − 0.587855i | − 0.0205288i | ||||||||
\(821\) | 28.6373 | 0.999449 | 0.499725 | − | 0.866184i | \(-0.333435\pi\) | ||||
0.499725 | + | 0.866184i | \(0.333435\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.48784 | 0.0867207 | 0.0433603 | − | 0.999059i | \(-0.486194\pi\) | ||||
0.0433603 | + | 0.999059i | \(0.486194\pi\) | |||||||
\(824\) | 31.8420 | 1.10927 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.473745 | −0.0164837 | ||||||||
\(827\) | −23.8333 | −0.828765 | −0.414383 | − | 0.910103i | \(-0.636002\pi\) | ||||
−0.414383 | + | 0.910103i | \(0.636002\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.6340 | −1.41128 | −0.705639 | − | 0.708572i | \(-0.749340\pi\) | ||||
−0.705639 | + | 0.708572i | \(0.749340\pi\) | |||||||
\(830\) | 0.146143i | 0.00507270i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.83514i | 0.0982909i | ||||||||
\(833\) | −29.6729 | −1.02811 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 0.305201i | − 0.0105619i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 14.4400i | − 0.498822i | ||||||||
\(839\) | − 57.2232i | − 1.97556i | −0.155842 | − | 0.987782i | \(-0.549809\pi\) | ||||
0.155842 | − | 0.987782i | \(-0.450191\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.31232 | 0.0797352 | ||||||||
\(842\) | 1.91330 | 0.0659365 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − 28.6075i | − 0.984712i | ||||||||
\(845\) | 0.308958i | 0.0106285i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.3931i | 0.425582i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 14.7117 | 0.504606 | ||||||||
\(851\) | − 27.4091i | − 0.939572i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 30.5412i | − 1.04571i | −0.852422 | − | 0.522855i | \(-0.824867\pi\) | ||||
0.852422 | − | 0.522855i | \(-0.175133\pi\) | |||||||
\(854\) | −1.44154 | −0.0493286 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.32141 | 0.113523 | ||||||||
\(857\) | −6.14781 | −0.210005 | −0.105003 | − | 0.994472i | \(-0.533485\pi\) | ||||
−0.105003 | + | 0.994472i | \(0.533485\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.5988 | −0.941660 | −0.470830 | − | 0.882224i | \(-0.656045\pi\) | ||||
−0.470830 | + | 0.882224i | \(0.656045\pi\) | |||||||
\(860\) | 0.0631545 | 0.00215355 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.2234 | 0.654753 | ||||||||
\(863\) | 42.8009i | 1.45696i | 0.685067 | + | 0.728481i | \(0.259773\pi\) | ||||
−0.685067 | + | 0.728481i | \(0.740227\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 0.666624i | − 0.0226659i | ||||||||
\(866\) | 6.31032 | 0.214433 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.80743i | 0.0613481i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.2876i | 0.619652i | ||||||||
\(872\) | − 17.8259i | − 0.603660i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −29.0178 | −0.981543 | ||||||||
\(875\) | 0.0989917 | 0.00334653 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.2305i | 0.379227i | 0.981859 | + | 0.189613i | \(0.0607235\pi\) | ||||
−0.981859 | + | 0.189613i | \(0.939277\pi\) | |||||||
\(878\) | 2.01746i | 0.0680860i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 47.3136i | − 1.59403i | −0.603957 | − | 0.797017i | \(-0.706410\pi\) | ||||
0.603957 | − | 0.797017i | \(-0.293590\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.2617 | 0.614555 | 0.307278 | − | 0.951620i | \(-0.400582\pi\) | ||||
0.307278 | + | 0.951620i | \(0.400582\pi\) | |||||||
\(884\) | 15.0211i | 0.505214i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − 24.6693i | − 0.828782i | ||||||||
\(887\) | 40.7104 | 1.36692 | 0.683460 | − | 0.729988i | \(-0.260474\pi\) | ||||
0.683460 | + | 0.729988i | \(0.260474\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.15271 | 0.105739 | ||||||||
\(890\) | 0.235876 | 0.00790658 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.7573 | −0.494110 | ||||||||
\(893\) | 68.9829 | 2.30842 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.282758 | 0.00945157 | ||||||||
\(896\) | − 2.65680i | − 0.0887573i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 9.78345i | − 0.326478i | ||||||||
\(899\) | −26.8449 | −0.895327 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 38.3480i | − 1.27756i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.28282i | 0.0426660i | ||||||||
\(905\) | − 0.847242i | − 0.0281633i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.18171 | 0.0392380 | 0.0196190 | − | 0.999808i | \(-0.493755\pi\) | ||||
0.0196190 | + | 0.999808i | \(0.493755\pi\) | |||||||
\(908\) | −17.8819 | −0.593431 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | − 0.0156840i | 0 0.000519919i | ||||||||
\(911\) | − 21.1641i | − 0.701198i | −0.936526 | − | 0.350599i | \(-0.885978\pi\) | ||||
0.936526 | − | 0.350599i | \(-0.114022\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − 14.0406i | − 0.464423i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −31.2580 | −1.03279 | ||||||||
\(917\) | − 4.48112i | − 0.147980i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 14.0906i | − 0.464805i | −0.972620 | − | 0.232402i | \(-0.925341\pi\) | ||||
0.972620 | − | 0.232402i | \(-0.0746586\pi\) | |||||||
\(920\) | −0.661948 | −0.0218238 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.530228 | 0.0174621 | ||||||||
\(923\) | −7.66061 | −0.252152 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.1477 | −0.662454 | ||||||||
\(926\) | −26.0138 | −0.854867 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 32.4854 | 1.06638 | ||||||||
\(929\) | − 34.0857i | − 1.11832i | −0.829061 | − | 0.559158i | \(-0.811125\pi\) | ||||
0.829061 | − | 0.559158i | \(-0.188875\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 43.0225i | − 1.41000i | ||||||||
\(932\) | −24.6381 | −0.807049 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 12.1157i | − 0.396438i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 6.75011i | − 0.220517i | −0.993903 | − | 0.110258i | \(-0.964832\pi\) | ||||
0.993903 | − | 0.110258i | \(-0.0351678\pi\) | |||||||
\(938\) | 1.35003i | 0.0440801i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.681104 | 0.0222152 | ||||||||
\(941\) | 33.2979 | 1.08548 | 0.542740 | − | 0.839901i | \(-0.317387\pi\) | ||||
0.542740 | + | 0.839901i | \(0.317387\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 65.2984i | 2.12641i | ||||||||
\(944\) | 3.85336i | 0.125416i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 0.751232i | − 0.0244117i | −0.999926 | − | 0.0122059i | \(-0.996115\pi\) | ||||
0.999926 | − | 0.0122059i | \(-0.00388535\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.2815 | −0.885596 | ||||||||
\(950\) | 21.3303i | 0.692046i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.56197i | 0.0830341i | ||||||||
\(953\) | 4.65369 | 0.150748 | 0.0753739 | − | 0.997155i | \(-0.475985\pi\) | ||||
0.0753739 | + | 0.997155i | \(0.475985\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.548217 | −0.0177399 | ||||||||
\(956\) | 43.3266 | 1.40128 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.65593 | −0.0535007 | ||||||||
\(959\) | −3.96758 | −0.128120 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.98515 | −0.257585 | ||||||||
\(962\) | 6.38533i | 0.205871i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 21.9253i | 0.706166i | ||||||||
\(965\) | 1.00412 | 0.0323237 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.7529i | 0.699525i | 0.936838 | + | 0.349763i | \(0.113738\pi\) | ||||
−0.936838 | + | 0.349763i | \(0.886262\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.0835991i | 0.00268421i | ||||||||
\(971\) | 5.87314i | 0.188478i | 0.995550 | + | 0.0942391i | \(0.0300418\pi\) | ||||
−0.995550 | + | 0.0942391i | \(0.969958\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.952168 | −0.0305251 | ||||||||
\(974\) | −10.0476 | −0.321944 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.7253i | 0.375317i | ||||||||
\(977\) | 0.919993i | 0.0294332i | 0.999892 | + | 0.0147166i | \(0.00468460\pi\) | ||||
−0.999892 | + | 0.0147166i | \(0.995315\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − 0.424783i | − 0.0135692i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17.2364 | −0.550037 | ||||||||
\(983\) | 46.6359i | 1.48745i | 0.668483 | + | 0.743727i | \(0.266944\pi\) | ||||
−0.668483 | + | 0.743727i | \(0.733056\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.844056i | 0.0268939i | ||||||||
\(986\) | −16.4698 | −0.524506 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21.7789 | −0.692880 | ||||||||
\(989\) | −7.01515 | −0.223069 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.21090 | 0.197296 | 0.0986478 | − | 0.995122i | \(-0.468548\pi\) | ||||
0.0986478 | + | 0.995122i | \(0.468548\pi\) | |||||||
\(992\) | −27.8506 | −0.884257 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.565523 | −0.0179373 | ||||||||
\(995\) | − 0.415965i | − 0.0131870i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.5668i | 0.904719i | 0.891836 | + | 0.452360i | \(0.149418\pi\) | ||||
−0.891836 | + | 0.452360i | \(0.850582\pi\) | |||||||
\(998\) | −15.6322 | −0.494828 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1089.2.d.g.1088.6 | 16 | ||
3.2 | odd | 2 | inner | 1089.2.d.g.1088.11 | 16 | ||
11.4 | even | 5 | 99.2.j.a.17.2 | ✓ | 16 | ||
11.8 | odd | 10 | 99.2.j.a.35.3 | yes | 16 | ||
11.10 | odd | 2 | inner | 1089.2.d.g.1088.12 | 16 | ||
33.8 | even | 10 | 99.2.j.a.35.2 | yes | 16 | ||
33.26 | odd | 10 | 99.2.j.a.17.3 | yes | 16 | ||
33.32 | even | 2 | inner | 1089.2.d.g.1088.5 | 16 | ||
44.15 | odd | 10 | 1584.2.cd.c.17.3 | 16 | |||
44.19 | even | 10 | 1584.2.cd.c.1025.2 | 16 | |||
99.4 | even | 15 | 891.2.u.c.512.3 | 32 | |||
99.41 | even | 30 | 891.2.u.c.431.2 | 32 | |||
99.52 | odd | 30 | 891.2.u.c.134.2 | 32 | |||
99.59 | odd | 30 | 891.2.u.c.512.2 | 32 | |||
99.70 | even | 15 | 891.2.u.c.215.2 | 32 | |||
99.74 | even | 30 | 891.2.u.c.134.3 | 32 | |||
99.85 | odd | 30 | 891.2.u.c.431.3 | 32 | |||
99.92 | odd | 30 | 891.2.u.c.215.3 | 32 | |||
132.59 | even | 10 | 1584.2.cd.c.17.2 | 16 | |||
132.107 | odd | 10 | 1584.2.cd.c.1025.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.j.a.17.2 | ✓ | 16 | 11.4 | even | 5 | ||
99.2.j.a.17.3 | yes | 16 | 33.26 | odd | 10 | ||
99.2.j.a.35.2 | yes | 16 | 33.8 | even | 10 | ||
99.2.j.a.35.3 | yes | 16 | 11.8 | odd | 10 | ||
891.2.u.c.134.2 | 32 | 99.52 | odd | 30 | |||
891.2.u.c.134.3 | 32 | 99.74 | even | 30 | |||
891.2.u.c.215.2 | 32 | 99.70 | even | 15 | |||
891.2.u.c.215.3 | 32 | 99.92 | odd | 30 | |||
891.2.u.c.431.2 | 32 | 99.41 | even | 30 | |||
891.2.u.c.431.3 | 32 | 99.85 | odd | 30 | |||
891.2.u.c.512.2 | 32 | 99.59 | odd | 30 | |||
891.2.u.c.512.3 | 32 | 99.4 | even | 15 | |||
1089.2.d.g.1088.5 | 16 | 33.32 | even | 2 | inner | ||
1089.2.d.g.1088.6 | 16 | 1.1 | even | 1 | trivial | ||
1089.2.d.g.1088.11 | 16 | 3.2 | odd | 2 | inner | ||
1089.2.d.g.1088.12 | 16 | 11.10 | odd | 2 | inner | ||
1584.2.cd.c.17.2 | 16 | 132.59 | even | 10 | |||
1584.2.cd.c.17.3 | 16 | 44.15 | odd | 10 | |||
1584.2.cd.c.1025.2 | 16 | 44.19 | even | 10 | |||
1584.2.cd.c.1025.3 | 16 | 132.107 | odd | 10 |