Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [240,3,Mod(209,240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("240.209");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.53952634465\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 16x^{2} + 81 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 30) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.3 | ||
Root | \(0.707107 - 2.91548i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 240.209 |
Dual form | 240.3.c.c.209.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(161\) | \(181\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.707107 | − | 2.91548i | 0.235702 | − | 0.971825i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.82843 | − | 4.12311i | −0.565685 | − | 0.824621i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.83095i | 0.832993i | 0.909137 | + | 0.416497i | \(0.136742\pi\) | ||||
−0.909137 | + | 0.416497i | \(0.863258\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.00000 | − | 4.12311i | −0.888889 | − | 0.458123i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 16.4924i | − | 1.49931i | −0.661828 | − | 0.749656i | \(-0.730219\pi\) | ||
0.661828 | − | 0.749656i | \(-0.269781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −14.0208 | + | 5.33074i | −0.934721 | + | 0.355382i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −11.3137 | −0.665512 | −0.332756 | − | 0.943013i | \(-0.607979\pi\) | ||||
−0.332756 | + | 0.943013i | \(0.607979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −12.0000 | −0.631579 | −0.315789 | − | 0.948829i | \(-0.602269\pi\) | ||||
−0.315789 | + | 0.948829i | \(0.602269\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 17.0000 | + | 4.12311i | 0.809524 | + | 0.196338i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −24.0416 | −1.04529 | −0.522644 | − | 0.852551i | \(-0.675054\pi\) | ||||
−0.522644 | + | 0.852551i | \(0.675054\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.00000 | + | 23.3238i | −0.360000 | + | 0.932952i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −17.6777 | + | 20.4083i | −0.654729 | + | 0.755864i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 32.0000 | 1.03226 | 0.516129 | − | 0.856511i | \(-0.327372\pi\) | ||||
0.516129 | + | 0.856511i | \(0.327372\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −48.0833 | − | 11.6619i | −1.45707 | − | 0.353391i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 24.0416 | − | 16.4924i | 0.686904 | − | 0.471212i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 23.3238i | − | 0.630373i | −0.949030 | − | 0.315187i | \(-0.897933\pi\) | ||
0.949030 | − | 0.315187i | \(-0.102067\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 57.7235i | − | 1.40789i | −0.710255 | − | 0.703945i | \(-0.751420\pi\) | ||
0.710255 | − | 0.703945i | \(-0.248580\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 40.8167i | − | 0.949225i | −0.880195 | − | 0.474612i | \(-0.842588\pi\) | ||
0.880195 | − | 0.474612i | \(-0.157412\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.62742 | + | 44.6467i | 0.125054 | + | 0.992150i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 35.3553 | 0.752241 | 0.376121 | − | 0.926571i | \(-0.377258\pi\) | ||||
0.376121 | + | 0.926571i | \(0.377258\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.0000 | 0.306122 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.00000 | + | 32.9848i | −0.156863 | + | 0.646762i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 67.8823 | 1.28080 | 0.640399 | − | 0.768043i | \(-0.278769\pi\) | ||||
0.640399 | + | 0.768043i | \(0.278769\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −68.0000 | + | 46.6476i | −1.23636 | + | 0.848138i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.48528 | + | 34.9857i | −0.148865 | + | 0.613784i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 16.4924i | − | 0.279533i | −0.990185 | − | 0.139766i | \(-0.955365\pi\) | ||
0.990185 | − | 0.139766i | \(-0.0446351\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −16.0000 | −0.262295 | −0.131148 | − | 0.991363i | \(-0.541866\pi\) | ||||
−0.131148 | + | 0.991363i | \(0.541866\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 24.0416 | − | 46.6476i | 0.381613 | − | 0.740438i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5.83095i | − | 0.0870291i | −0.999053 | − | 0.0435146i | \(-0.986145\pi\) | ||
0.999053 | − | 0.0435146i | \(-0.0138555\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −17.0000 | + | 70.0928i | −0.246377 | + | 1.01584i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 116.619i | − | 1.59752i | −0.601649 | − | 0.798761i | \(-0.705489\pi\) | ||
0.601649 | − | 0.798761i | \(-0.294511\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 61.6360 | + | 42.7317i | 0.821814 | + | 0.569756i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 96.1665 | 1.24892 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 72.0000 | 0.911392 | 0.455696 | − | 0.890135i | \(-0.349390\pi\) | ||||
0.455696 | + | 0.890135i | \(0.349390\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 47.0000 | + | 65.9697i | 0.580247 | + | 0.814441i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 43.8406 | 0.528200 | 0.264100 | − | 0.964495i | \(-0.414925\pi\) | ||||
0.264100 | + | 0.964495i | \(0.414925\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 32.0000 | + | 46.6476i | 0.376471 | + | 0.548795i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 65.9697i | − | 0.741232i | −0.928786 | − | 0.370616i | \(-0.879147\pi\) | ||
0.928786 | − | 0.370616i | \(-0.120853\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 22.6274 | − | 93.2952i | 0.243306 | − | 1.00317i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 33.9411 | + | 49.4773i | 0.357275 | + | 0.520813i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 163.267i | 1.68316i | 0.540131 | + | 0.841581i | \(0.318375\pi\) | ||||
−0.540131 | + | 0.841581i | \(0.681625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −68.0000 | + | 131.939i | −0.686869 | + | 1.33272i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 131.939i | 1.30633i | 0.757215 | + | 0.653165i | \(0.226559\pi\) | ||||
−0.757215 | + | 0.653165i | \(0.773441\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 99.1262i | − | 0.962390i | −0.876614 | − | 0.481195i | \(-0.840203\pi\) | ||
0.876614 | − | 0.481195i | \(-0.159797\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −31.0833 | − | 81.7547i | −0.296031 | − | 0.778616i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 55.1543 | 0.515461 | 0.257731 | − | 0.966217i | \(-0.417025\pi\) | ||||
0.257731 | + | 0.966217i | \(0.417025\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 80.0000 | 0.733945 | 0.366972 | − | 0.930232i | \(-0.380394\pi\) | ||||
0.366972 | + | 0.930232i | \(0.380394\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −68.0000 | − | 16.4924i | −0.612613 | − | 0.148580i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −152.735 | −1.35164 | −0.675819 | − | 0.737068i | \(-0.736210\pi\) | ||||
−0.675819 | + | 0.737068i | \(0.736210\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 68.0000 | + | 99.1262i | 0.591304 | + | 0.861967i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 65.9697i | − | 0.554367i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −151.000 | −1.24793 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −168.291 | − | 40.8167i | −1.36822 | − | 0.331843i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 121.622 | − | 28.8617i | 0.972979 | − | 0.230894i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 40.8167i | 0.321391i | 0.987004 | + | 0.160696i | \(0.0513737\pi\) | ||||
−0.987004 | + | 0.160696i | \(0.948626\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −119.000 | − | 28.8617i | −0.922481 | − | 0.223734i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 49.4773i | − | 0.377689i | −0.982007 | − | 0.188845i | \(-0.939526\pi\) | ||
0.982007 | − | 0.188845i | \(-0.0604742\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 69.9714i | − | 0.526101i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 134.146 | + | 15.1634i | 0.993672 | + | 0.112322i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −50.9117 | −0.371618 | −0.185809 | − | 0.982586i | \(-0.559491\pi\) | ||||
−0.185809 | + | 0.982586i | \(0.559491\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −44.0000 | −0.316547 | −0.158273 | − | 0.987395i | \(-0.550593\pi\) | ||||
−0.158273 | + | 0.987395i | \(0.550593\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 25.0000 | − | 103.078i | 0.177305 | − | 0.731047i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.6066 | − | 43.7321i | 0.0721538 | − | 0.297498i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 8.24621i | − | 0.0553437i | −0.999617 | − | 0.0276718i | \(-0.991191\pi\) | ||
0.999617 | − | 0.0276718i | \(-0.00880935\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −136.000 | −0.900662 | −0.450331 | − | 0.892862i | \(-0.648694\pi\) | ||||
−0.450331 | + | 0.892862i | \(0.648694\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 90.5097 | + | 46.6476i | 0.591566 | + | 0.304886i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −90.5097 | − | 131.939i | −0.583933 | − | 0.851222i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 116.619i | − | 0.742796i | −0.928474 | − | 0.371398i | \(-0.878878\pi\) | ||
0.928474 | − | 0.371398i | \(-0.121122\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 48.0000 | − | 197.909i | 0.301887 | − | 1.24471i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 140.186i | − | 0.870718i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 99.1262i | − | 0.608136i | −0.952650 | − | 0.304068i | \(-0.901655\pi\) | ||
0.952650 | − | 0.304068i | \(-0.0983450\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 87.9167 | + | 231.237i | 0.532829 | + | 1.40144i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −292.742 | −1.75295 | −0.876474 | − | 0.481450i | \(-0.840110\pi\) | ||||
−0.876474 | + | 0.481450i | \(0.840110\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 96.0000 | + | 49.4773i | 0.561404 | + | 0.289341i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −164.049 | −0.948259 | −0.474129 | − | 0.880455i | \(-0.657237\pi\) | ||||
−0.474129 | + | 0.880455i | \(0.657237\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −136.000 | − | 52.4786i | −0.777143 | − | 0.299878i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −48.0833 | − | 11.6619i | −0.271657 | − | 0.0658865i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 16.4924i | − | 0.0921364i | −0.998938 | − | 0.0460682i | \(-0.985331\pi\) | ||
0.998938 | − | 0.0460682i | \(-0.0146692\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −82.0000 | −0.453039 | −0.226519 | − | 0.974007i | \(-0.572735\pi\) | ||||
−0.226519 | + | 0.974007i | \(0.572735\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.3137 | + | 46.6476i | −0.0618235 | + | 0.254905i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −96.1665 | + | 65.9697i | −0.519819 | + | 0.356593i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 186.590i | 0.997810i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −119.000 | − | 103.078i | −0.629630 | − | 0.545384i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 296.864i | 1.55426i | 0.629340 | + | 0.777130i | \(0.283325\pi\) | ||||
−0.629340 | + | 0.777130i | \(0.716675\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 116.619i | − | 0.604244i | −0.953269 | − | 0.302122i | \(-0.902305\pi\) | ||
0.953269 | − | 0.302122i | \(-0.0976950\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −192.333 | −0.976310 | −0.488155 | − | 0.872757i | \(-0.662330\pi\) | ||||
−0.488155 | + | 0.872757i | \(0.662330\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 312.000 | 1.56784 | 0.783920 | − | 0.620862i | \(-0.213217\pi\) | ||||
0.783920 | + | 0.620862i | \(0.213217\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.0000 | − | 4.12311i | −0.0845771 | − | 0.0205130i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −238.000 | + | 163.267i | −1.16098 | + | 0.796423i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 192.333 | + | 99.1262i | 0.929145 | + | 0.478870i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 197.909i | 0.946933i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.0568720 | 0.0284360 | − | 0.999596i | \(-0.490947\pi\) | ||||
0.0284360 | + | 0.999596i | \(0.490947\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −168.291 | + | 115.447i | −0.782751 | + | 0.536963i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 186.590i | 0.859864i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −340.000 | − | 82.4621i | −1.55251 | − | 0.376539i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 40.8167i | − | 0.183034i | −0.995803 | − | 0.0915172i | \(-0.970828\pi\) | ||
0.995803 | − | 0.0915172i | \(-0.0291716\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 168.167 | − | 149.483i | 0.747407 | − | 0.664367i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 159.806 | 0.703992 | 0.351996 | − | 0.936002i | \(-0.385503\pi\) | ||||
0.351996 | + | 0.936002i | \(0.385503\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 82.0000 | 0.358079 | 0.179039 | − | 0.983842i | \(-0.442701\pi\) | ||||
0.179039 | + | 0.983842i | \(0.442701\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 68.0000 | − | 280.371i | 0.294372 | − | 1.21373i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 192.333 | 0.825464 | 0.412732 | − | 0.910853i | \(-0.364575\pi\) | ||||
0.412732 | + | 0.910853i | \(0.364575\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −100.000 | − | 145.774i | −0.425532 | − | 0.620314i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 50.9117 | − | 209.914i | 0.214817 | − | 0.885714i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 461.788i | 1.93217i | 0.258231 | + | 0.966083i | \(0.416861\pi\) | ||||
−0.258231 | + | 0.966083i | \(0.583139\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 304.000 | 1.26141 | 0.630705 | − | 0.776022i | \(-0.282766\pi\) | ||||
0.630705 | + | 0.776022i | \(0.282766\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 225.567 | − | 90.3798i | 0.928260 | − | 0.371933i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −42.4264 | − | 61.8466i | −0.173169 | − | 0.252435i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 31.0000 | − | 127.816i | 0.124498 | − | 0.513318i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 346.341i | − | 1.37984i | −0.723884 | − | 0.689922i | \(-0.757645\pi\) | ||
0.723884 | − | 0.689922i | \(-0.242355\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 396.505i | 1.56721i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 158.627 | − | 60.3104i | 0.622068 | − | 0.236511i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 390.323 | 1.51877 | 0.759383 | − | 0.650644i | \(-0.225501\pi\) | ||||
0.759383 | + | 0.650644i | \(0.225501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 136.000 | 0.525097 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −295.571 | −1.12384 | −0.561921 | − | 0.827191i | \(-0.689938\pi\) | ||||
−0.561921 | + | 0.827191i | \(0.689938\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −192.000 | − | 279.886i | −0.724528 | − | 1.05617i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −192.333 | − | 46.6476i | −0.720348 | − | 0.174710i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 74.2159i | 0.275896i | 0.990440 | + | 0.137948i | \(0.0440506\pi\) | ||||
−0.990440 | + | 0.137948i | \(0.955949\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −40.0000 | −0.147601 | −0.0738007 | − | 0.997273i | \(-0.523513\pi\) | ||||
−0.0738007 | + | 0.997273i | \(0.523513\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 384.666 | + | 148.432i | 1.39879 | + | 0.539752i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 443.152i | − | 1.59983i | −0.600115 | − | 0.799914i | \(-0.704878\pi\) | ||
0.600115 | − | 0.799914i | \(-0.295122\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −256.000 | − | 131.939i | −0.917563 | − | 0.472901i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 519.511i | 1.84879i | 0.381431 | + | 0.924397i | \(0.375431\pi\) | ||||
−0.381431 | + | 0.924397i | \(0.624569\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 320.702i | 1.13322i | 0.823985 | + | 0.566612i | \(0.191746\pi\) | ||||
−0.823985 | + | 0.566612i | \(0.808254\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 168.250 | − | 63.9688i | 0.590350 | − | 0.224452i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 336.583 | 1.17276 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −161.000 | −0.557093 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 476.000 | + | 115.447i | 1.63574 | + | 0.396725i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 84.8528 | 0.289600 | 0.144800 | − | 0.989461i | \(-0.453746\pi\) | ||||
0.144800 | + | 0.989461i | \(0.453746\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −68.0000 | + | 46.6476i | −0.230508 | + | 0.158128i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 336.583 | + | 291.548i | 1.13328 | + | 0.981642i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 238.000 | 0.790698 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 384.666 | + | 93.2952i | 1.26953 | + | 0.307905i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 45.2548 | + | 65.9697i | 0.148377 | + | 0.216294i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 367.350i | − | 1.19658i | −0.801280 | − | 0.598290i | \(-0.795847\pi\) | ||
0.801280 | − | 0.598290i | \(-0.204153\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −289.000 | − | 70.0928i | −0.935275 | − | 0.226838i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 98.9545i | 0.318182i | 0.987264 | + | 0.159091i | \(0.0508563\pi\) | ||||
−0.987264 | + | 0.159091i | \(0.949144\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 186.590i | − | 0.596136i | −0.954545 | − | 0.298068i | \(-0.903658\pi\) | ||
0.954545 | − | 0.298068i | \(-0.0963422\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −260.333 | + | 32.8132i | −0.826454 | + | 0.104169i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −520.431 | −1.64174 | −0.820868 | − | 0.571117i | \(-0.806510\pi\) | ||||
−0.820868 | + | 0.571117i | \(0.806510\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 39.0000 | − | 160.801i | 0.121495 | − | 0.500938i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 135.765 | 0.420324 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 56.5685 | − | 233.238i | 0.172992 | − | 0.713266i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 206.155i | 0.626612i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −292.000 | −0.882175 | −0.441088 | − | 0.897464i | \(-0.645407\pi\) | ||||
−0.441088 | + | 0.897464i | \(0.645407\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −96.1665 | + | 186.590i | −0.288788 | + | 0.560332i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −24.0416 | + | 16.4924i | −0.0717661 | + | 0.0492311i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 326.533i | 0.968942i | 0.874807 | + | 0.484471i | \(0.160988\pi\) | ||||
−0.874807 | + | 0.484471i | \(0.839012\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −108.000 | + | 445.295i | −0.318584 | + | 1.31356i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 527.758i | − | 1.54768i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 373.181i | 1.08799i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 337.083 | − | 128.160i | 0.977053 | − | 0.371477i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −394.566 | −1.13708 | −0.568538 | − | 0.822657i | \(-0.692491\pi\) | ||||
−0.568538 | + | 0.822657i | \(0.692491\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 254.000 | 0.727794 | 0.363897 | − | 0.931439i | \(-0.381446\pi\) | ||||
0.363897 | + | 0.931439i | \(0.381446\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 345.068 | 0.977530 | 0.488765 | − | 0.872415i | \(-0.337448\pi\) | ||||
0.488765 | + | 0.872415i | \(0.337448\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −192.333 | − | 46.6476i | −0.538748 | − | 0.130666i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 395.818i | − | 1.10256i | −0.834321 | − | 0.551279i | \(-0.814140\pi\) | ||
0.834321 | − | 0.551279i | \(-0.185860\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −217.000 | −0.601108 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −106.773 | + | 440.237i | −0.294141 | + | 1.21277i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −480.833 | + | 329.848i | −1.31735 | + | 0.903694i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 413.998i | − | 1.12806i | −0.825755 | − | 0.564029i | \(-0.809250\pi\) | ||
0.825755 | − | 0.564029i | \(-0.190750\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −238.000 | + | 461.788i | −0.644986 | + | 1.25146i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 395.818i | 1.06690i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 629.743i | 1.68832i | 0.536092 | + | 0.844159i | \(0.319900\pi\) | ||||
−0.536092 | + | 0.844159i | \(0.680100\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.85429 | − | 374.995i | 0.00494478 | − | 0.999988i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 572.000 | 1.50923 | 0.754617 | − | 0.656165i | \(-0.227822\pi\) | ||||
0.754617 | + | 0.656165i | \(0.227822\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 119.000 | + | 28.8617i | 0.312336 | + | 0.0757526i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 193.747 | 0.505868 | 0.252934 | − | 0.967484i | \(-0.418605\pi\) | ||||
0.252934 | + | 0.967484i | \(0.418605\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −272.000 | − | 396.505i | −0.706494 | − | 1.02988i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −168.291 | + | 326.533i | −0.434862 | + | 0.843755i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 387.572i | − | 0.996329i | −0.867083 | − | 0.498164i | \(-0.834008\pi\) | ||
0.867083 | − | 0.498164i | \(-0.165992\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 272.000 | 0.695652 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −144.250 | − | 34.9857i | −0.367048 | − | 0.0890222i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −203.647 | − | 296.864i | −0.515561 | − | 0.751553i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 513.124i | − | 1.29250i | −0.763124 | − | 0.646252i | \(-0.776336\pi\) | ||
0.763124 | − | 0.646252i | \(-0.223664\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −204.000 | − | 49.4773i | −0.511278 | − | 0.124003i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 65.9697i | − | 0.164513i | −0.996611 | − | 0.0822565i | \(-0.973787\pi\) | ||
0.996611 | − | 0.0822565i | \(-0.0262127\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 139.064 | − | 380.376i | 0.343368 | − | 0.939201i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −384.666 | −0.945126 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 640.000 | 1.56479 | 0.782396 | − | 0.622781i | \(-0.213997\pi\) | ||||
0.782396 | + | 0.622781i | \(0.213997\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −36.0000 | + | 148.432i | −0.0875912 | + | 0.361148i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 96.1665 | 0.232849 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −124.000 | − | 180.760i | −0.298795 | − | 0.435565i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −31.1127 | + | 128.281i | −0.0746108 | + | 0.307628i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 577.235i | − | 1.37765i | −0.724928 | − | 0.688824i | \(-0.758127\pi\) | ||
0.724928 | − | 0.688824i | \(-0.241873\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −656.000 | −1.55819 | −0.779097 | − | 0.626903i | \(-0.784322\pi\) | ||||
−0.779097 | + | 0.626903i | \(0.784322\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −282.843 | − | 145.774i | −0.668659 | − | 0.344619i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 101.823 | − | 263.879i | 0.239584 | − | 0.620891i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 93.2952i | − | 0.218490i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 362.833i | − | 0.841841i | −0.907098 | − | 0.420920i | \(-0.861707\pi\) | ||
0.907098 | − | 0.420920i | \(-0.138293\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 163.267i | 0.377059i | 0.982068 | + | 0.188530i | \(0.0603722\pi\) | ||||
−0.982068 | + | 0.188530i | \(0.939628\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 288.500 | 0.660182 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −432.000 | −0.984055 | −0.492027 | − | 0.870580i | \(-0.663744\pi\) | ||||
−0.492027 | + | 0.870580i | \(0.663744\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −120.000 | − | 61.8466i | −0.272109 | − | 0.140242i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −123.037 | −0.277735 | −0.138867 | − | 0.990311i | \(-0.544346\pi\) | ||||
−0.138867 | + | 0.990311i | \(0.544346\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −272.000 | + | 186.590i | −0.611236 | + | 0.419304i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.0416 | − | 5.83095i | −0.0537844 | − | 0.0130446i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 865.852i | − | 1.92840i | −0.265174 | − | 0.964201i | \(-0.585429\pi\) | ||
0.265174 | − | 0.964201i | \(-0.414571\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −952.000 | −2.11086 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −96.1665 | + | 396.505i | −0.212288 | + | 0.875286i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 466.476i | 1.02074i | 0.859956 | + | 0.510368i | \(0.170491\pi\) | ||||
−0.859956 | + | 0.510368i | \(0.829509\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 200.000 | − | 230.894i | 0.435730 | − | 0.503037i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 612.250i | 1.32235i | 0.750230 | + | 0.661177i | \(0.229943\pi\) | ||||
−0.750230 | + | 0.661177i | \(0.770057\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −448.666 | + | 170.584i | −0.964873 | + | 0.366846i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 767.918 | 1.64436 | 0.822182 | − | 0.569225i | \(-0.192757\pi\) | ||||
0.822182 | + | 0.569225i | \(0.192757\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 34.0000 | 0.0724947 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −340.000 | − | 82.4621i | −0.721868 | − | 0.175079i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −673.166 | −1.42318 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 108.000 | − | 279.886i | 0.227368 | − | 0.589233i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −543.058 | − | 279.886i | −1.13849 | − | 0.586762i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 560.742i | 1.17065i | 0.810798 | + | 0.585326i | \(0.199033\pi\) | ||||
−0.810798 | + | 0.585326i | \(0.800967\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −408.708 | − | 99.1262i | −0.846186 | − | 0.205230i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 673.166 | − | 461.788i | 1.38797 | − | 0.952140i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 647.236i | 1.32903i | 0.747277 | + | 0.664513i | \(0.231361\pi\) | ||||
−0.747277 | + | 0.664513i | \(0.768639\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −289.000 | − | 70.0928i | −0.591002 | − | 0.143339i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 346.341i | − | 0.705379i | −0.935740 | − | 0.352689i | \(-0.885267\pi\) | ||
0.935740 | − | 0.352689i | \(-0.114733\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 736.333 | − | 92.8097i | 1.48754 | − | 0.187494i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 660.000 | 1.32265 | 0.661323 | − | 0.750102i | \(-0.269995\pi\) | ||||
0.661323 | + | 0.750102i | \(0.269995\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −207.000 | + | 853.483i | −0.413174 | + | 1.70356i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 182.434 | 0.362691 | 0.181345 | − | 0.983419i | \(-0.441955\pi\) | ||||
0.181345 | + | 0.983419i | \(0.441955\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 544.000 | − | 373.181i | 1.07723 | − | 0.738972i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 119.501 | − | 492.715i | 0.235702 | − | 0.971825i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 395.818i | 0.777639i | 0.921314 | + | 0.388819i | \(0.127117\pi\) | ||||
−0.921314 | + | 0.388819i | \(0.872883\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 680.000 | 1.33072 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 212.132 | − | 244.900i | 0.413513 | − | 0.477388i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −408.708 | + | 280.371i | −0.793607 | + | 0.544410i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 583.095i | − | 1.12784i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −116.000 | + | 478.280i | −0.223507 | + | 0.921542i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 131.939i | 0.253243i | 0.991951 | + | 0.126621i | \(0.0404133\pi\) | ||||
−0.991951 | + | 0.126621i | \(0.959587\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 145.774i | 0.278726i | 0.990241 | + | 0.139363i | \(0.0445055\pi\) | ||||
−0.990241 | + | 0.139363i | \(0.955494\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −249.167 | + | 359.397i | −0.474603 | + | 0.684565i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −362.039 | −0.686980 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 49.0000 | 0.0926276 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −68.0000 | + | 131.939i | −0.128060 | + | 0.248473i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −156.000 | − | 227.407i | −0.291589 | − | 0.425060i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −48.0833 | − | 11.6619i | −0.0895405 | − | 0.0217168i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 247.386i | − | 0.458973i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 418.000 | 0.772643 | 0.386322 | − | 0.922364i | \(-0.373745\pi\) | ||||
0.386322 | + | 0.922364i | \(0.373745\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −57.9828 | + | 239.069i | −0.106782 | + | 0.440274i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −226.274 | − | 329.848i | −0.415182 | − | 0.605227i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 285.717i | 0.522334i | 0.965294 | + | 0.261167i | \(0.0841073\pi\) | ||||
−0.965294 | + | 0.261167i | \(0.915893\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 128.000 | + | 65.9697i | 0.233151 | + | 0.120163i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 419.829i | 0.759184i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 124.333 | + | 327.019i | 0.224024 | + | 0.589223i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 424.264 | 0.761695 | 0.380847 | − | 0.924638i | \(-0.375632\pi\) | ||||
0.380847 | + | 0.924638i | \(0.375632\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 544.000 | + | 131.939i | 0.969697 | + | 0.235186i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 813.173 | 1.44436 | 0.722178 | − | 0.691707i | \(-0.243141\pi\) | ||||
0.722178 | + | 0.691707i | \(0.243141\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 432.000 | + | 629.743i | 0.764602 | + | 1.11459i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −384.666 | + | 274.055i | −0.678423 | + | 0.483342i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 453.542i | 0.797085i | 0.917150 | + | 0.398543i | \(0.130484\pi\) | ||||
−0.917150 | + | 0.398543i | \(0.869516\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −220.000 | −0.385289 | −0.192644 | − | 0.981269i | \(-0.561706\pi\) | ||||
−0.192644 | + | 0.981269i | \(0.561706\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 865.499 | + | 209.914i | 1.51047 | + | 0.366343i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 216.375 | − | 560.742i | 0.376304 | − | 0.975204i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 46.6476i | 0.0808451i | 0.999183 | + | 0.0404225i | \(0.0128704\pi\) | ||||
−0.999183 | + | 0.0404225i | \(0.987130\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −340.000 | − | 82.4621i | −0.587219 | − | 0.142422i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 255.633i | 0.439987i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1119.54i | − | 1.92031i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −55.1543 | −0.0939597 | −0.0469798 | − | 0.998896i | \(-0.514960\pi\) | ||||
−0.0469798 | + | 0.998896i | \(0.514960\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −384.000 | −0.651952 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −136.000 | + | 560.742i | −0.230118 | + | 0.948803i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 390.323 | 0.658217 | 0.329109 | − | 0.944292i | \(-0.393252\pi\) | ||||
0.329109 | + | 0.944292i | \(0.393252\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −272.000 | + | 186.590i | −0.457143 | + | 0.313597i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 220.617 | − | 909.628i | 0.369543 | − | 1.52367i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 98.9545i | 0.165200i | 0.996583 | + | 0.0825998i | \(0.0263223\pi\) | ||||
−0.996583 | + | 0.0825998i | \(0.973678\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −880.000 | −1.46423 | −0.732113 | − | 0.681183i | \(-0.761466\pi\) | ||||
−0.732113 | + | 0.681183i | \(0.761466\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24.0416 | + | 46.6476i | −0.0398700 | + | 0.0773592i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 427.092 | + | 622.589i | 0.705938 | + | 1.02907i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 425.659i | − | 0.701251i | −0.936516 | − | 0.350626i | \(-0.885969\pi\) | ||
0.936516 | − | 0.350626i | \(-0.114031\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 606.419i | − | 0.989264i | −0.869102 | − | 0.494632i | \(-0.835303\pi\) | ||
0.869102 | − | 0.494632i | \(-0.164697\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 307.709 | + | 809.330i | 0.500339 | + | 1.31598i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −113.137 | −0.183366 | −0.0916832 | − | 0.995788i | \(-0.529225\pi\) | ||||
−0.0916832 | + | 0.995788i | \(0.529225\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −52.0000 | −0.0840065 | −0.0420032 | − | 0.999117i | \(-0.513374\pi\) | ||||
−0.0420032 | + | 0.999117i | \(0.513374\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 425.000 | − | 490.650i | 0.684380 | − | 0.790096i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 384.666 | 0.617442 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −463.000 | − | 419.829i | −0.740800 | − | 0.671726i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 576.999 | + | 139.943i | 0.920254 | + | 0.223194i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 263.879i | 0.419521i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 544.000 | 0.862124 | 0.431062 | − | 0.902322i | \(-0.358139\pi\) | ||||
0.431062 | + | 0.902322i | \(0.358139\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.48528 | − | 34.9857i | 0.0134049 | − | 0.0552697i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 168.291 | − | 115.447i | 0.265026 | − | 0.181806i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 849.360i | − | 1.32505i | −0.749038 | − | 0.662527i | \(-0.769484\pi\) | ||
0.749038 | − | 0.662527i | \(-0.230516\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 367.350i | − | 0.571306i | −0.958333 | − | 0.285653i | \(-0.907789\pi\) | ||
0.958333 | − | 0.285653i | \(-0.0922105\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 217.583 | + | 572.283i | 0.337338 | + | 0.887260i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 971.565 | 1.50165 | 0.750823 | − | 0.660504i | \(-0.229657\pi\) | ||||
0.750823 | + | 0.660504i | \(0.229657\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −272.000 | −0.419106 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 544.000 | + | 131.939i | 0.835637 | + | 0.202672i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 350.725 | 0.537098 | 0.268549 | − | 0.963266i | \(-0.413456\pi\) | ||||
0.268549 | + | 0.963266i | \(0.413456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −204.000 | + | 139.943i | −0.311450 | + | 0.213653i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −480.833 | + | 932.952i | −0.731861 | + | 1.42002i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 577.235i | 0.875925i | 0.898993 | + | 0.437963i | \(0.144300\pi\) | ||||
−0.898993 | + | 0.437963i | \(0.855700\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 80.0000 | 0.121029 | 0.0605144 | − | 0.998167i | \(-0.480726\pi\) | ||||
0.0605144 | + | 0.998167i | \(0.480726\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −288.500 | + | 197.909i | −0.433834 | + | 0.297608i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −119.000 | − | 28.8617i | −0.177877 | − | 0.0431416i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 263.879i | 0.393262i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 489.800i | − | 0.727786i | −0.931441 | − | 0.363893i | \(-0.881447\pi\) | ||
0.931441 | − | 0.363893i | \(-0.118553\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −316.901 | − | 595.986i | −0.469483 | − | 0.882942i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 192.333 | 0.284096 | 0.142048 | − | 0.989860i | \(-0.454631\pi\) | ||||
0.142048 | + | 0.989860i | \(0.454631\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −952.000 | −1.40206 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 113.000 | − | 465.911i | 0.165932 | − | 0.684157i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −236.174 | −0.345789 | −0.172894 | − | 0.984940i | \(-0.555312\pi\) | ||||
−0.172894 | + | 0.984940i | \(0.555312\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 144.000 | + | 209.914i | 0.210219 | + | 0.306444i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 57.9828 | − | 239.069i | 0.0843999 | − | 0.347990i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 548.000 | 0.793054 | 0.396527 | − | 0.918023i | \(-0.370215\pi\) | ||||
0.396527 | + | 0.918023i | \(0.370215\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −769.332 | − | 396.505i | −1.11015 | − | 0.572157i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 124.451 | + | 181.417i | 0.179066 | + | 0.261031i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 653.067i | 0.936968i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 136.000 | − | 560.742i | 0.194564 | − | 0.802207i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 57.7235i | − | 0.0823445i | −0.999152 | − | 0.0411722i | \(-0.986891\pi\) | ||
0.999152 | − | 0.0411722i | \(-0.0131092\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 279.886i | 0.398130i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −495.711 | + | 188.470i | −0.703136 | + | 0.267333i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −769.332 | −1.08816 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1230.00 | 1.73484 | 0.867419 | − | 0.497579i | \(-0.165777\pi\) | ||||
0.867419 | + | 0.497579i | \(0.165777\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −576.000 | − | 296.864i | −0.810127 | − | 0.417530i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −769.332 | −1.07901 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1346.33 | + | 326.533i | 1.87773 | + | 0.455416i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 626.712i | − | 0.871644i | −0.900033 | − | 0.435822i | \(-0.856458\pi\) | ||
0.900033 | − | 0.435822i | \(-0.143542\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 578.000 | 0.801664 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 214.960 | − | 886.305i | 0.297317 | − | 1.22587i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 367.350i | 0.505296i | 0.967558 | + | 0.252648i | \(0.0813014\pi\) | ||||
−0.967558 | + | 0.252648i | \(0.918699\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −104.000 | − | 721.543i | −0.142661 | − | 0.989772i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 461.788i | 0.631721i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1002.92i | − | 1.36825i | −0.729367 | − | 0.684123i | \(-0.760185\pi\) | ||
0.729367 | − | 0.684123i | \(-0.239815\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −210.312 | + | 79.9610i | −0.286139 | + | 0.108791i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −96.1665 | −0.130484 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 340.000 | 0.460081 | 0.230041 | − | 0.973181i | \(-0.426114\pi\) | ||||
0.230041 | + | 0.973181i | \(0.426114\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1243.09 | −1.67307 | −0.836537 | − | 0.547911i | \(-0.815423\pi\) | ||||
−0.836537 | + | 0.547911i | \(0.815423\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −34.0000 | + | 23.3238i | −0.0456376 | + | 0.0313071i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −350.725 | − | 180.760i | −0.469511 | − | 0.241981i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 321.602i | 0.429375i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 520.000 | 0.692410 | 0.346205 | − | 0.938159i | \(-0.387470\pi\) | ||||
0.346205 | + | 0.938159i | \(0.387470\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1009.75 | − | 244.900i | −1.34097 | − | 0.325232i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 384.666 | + | 560.742i | 0.509492 | + | 0.742705i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 816.333i | 1.07838i | 0.842184 | + | 0.539190i | \(0.181269\pi\) | ||||
−0.842184 | + | 0.539190i | \(0.818731\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1156.00 | + | 280.371i | 1.52306 | + | 0.369395i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 395.818i | 0.520129i | 0.965591 | + | 0.260064i | \(0.0837438\pi\) | ||||
−0.965591 | + | 0.260064i | \(0.916256\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 466.476i | 0.611371i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −63.6670 | − | 505.120i | −0.0832248 | − | 0.660288i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −306.000 | −0.397919 | −0.198960 | − | 0.980008i | \(-0.563756\pi\) | ||||
−0.198960 | + | 0.980008i | \(0.563756\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 276.000 | − | 1137.98i | 0.357977 | − | 1.47598i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 305.470 | 0.395175 | 0.197587 | − | 0.980285i | \(-0.436689\pi\) | ||||
0.197587 | + | 0.980285i | \(0.436689\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −288.000 | + | 746.362i | −0.371613 | + | 0.963048i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 96.1665 | − | 396.505i | 0.123766 | − | 0.510302i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 692.682i | 0.889194i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −480.833 | + | 329.848i | −0.612526 | + | 0.420189i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 565.602i | 0.718681i | 0.933206 | + | 0.359341i | \(0.116998\pi\) | ||||
−0.933206 | + | 0.359341i | \(0.883002\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −209.000 | + | 861.729i | −0.264892 | + | 1.09218i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 890.591i | − | 1.12590i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 |