Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,3,Mod(101,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("150.101");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.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: | \(4.08720396540\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 30) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 101.2 | ||
Root | \(-2.91548 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 150.101 |
Dual form | 150.3.d.d.101.4 |
$q$-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 \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | 2.91548 | − | 0.707107i | 0.971825 | − | 0.235702i | ||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | − | 4.12311i | −0.166667 | − | 0.687184i | ||||
\(7\) | 5.83095 | 0.832993 | 0.416497 | − | 0.909137i | \(-0.363258\pi\) | ||||
0.416497 | + | 0.909137i | \(0.363258\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 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 | \(-0.269781\pi\) | |||||||
\(12\) | −5.83095 | + | 1.41421i | −0.485913 | + | 0.117851i | ||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | − | 8.24621i | − | 0.589015i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 11.3137i | 0.665512i | 0.943013 | + | 0.332756i | \(0.107979\pi\) | ||||
−0.943013 | + | 0.332756i | \(0.892021\pi\) | |||||||
\(18\) | −5.83095 | − | 11.3137i | −0.323942 | − | 0.628539i | ||||
\(19\) | −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 | ||||
\(22\) | −23.3238 | −1.06017 | ||||||||
\(23\) | 24.0416i | 1.04529i | 0.852551 | + | 0.522644i | \(0.175054\pi\) | ||||
−0.852551 | + | 0.522644i | \(0.824946\pi\) | |||||||
\(24\) | 2.00000 | + | 8.24621i | 0.0833333 | + | 0.343592i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 20.4083 | − | 17.6777i | 0.755864 | − | 0.654729i | ||||
\(28\) | −11.6619 | −0.416497 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −32.0000 | −1.03226 | −0.516129 | − | 0.856511i | \(-0.672628\pi\) | ||||
−0.516129 | + | 0.856511i | \(0.672628\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | −11.6619 | − | 48.0833i | −0.353391 | − | 1.45707i | ||||
\(34\) | 16.0000 | 0.470588 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −16.0000 | + | 8.24621i | −0.444444 | + | 0.229061i | ||||
\(37\) | 23.3238 | 0.630373 | 0.315187 | − | 0.949030i | \(-0.397933\pi\) | ||||
0.315187 | + | 0.949030i | \(0.397933\pi\) | |||||||
\(38\) | 16.9706i | 0.446594i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 57.7235i | 1.40789i | 0.710255 | + | 0.703945i | \(0.248580\pi\) | ||||
−0.710255 | + | 0.703945i | \(0.751420\pi\) | |||||||
\(42\) | −5.83095 | − | 24.0416i | −0.138832 | − | 0.572420i | ||||
\(43\) | 40.8167 | 0.949225 | 0.474612 | − | 0.880195i | \(-0.342588\pi\) | ||||
0.474612 | + | 0.880195i | \(0.342588\pi\) | |||||||
\(44\) | 32.9848i | 0.749656i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 34.0000 | 0.739130 | ||||||||
\(47\) | 35.3553i | 0.752241i | 0.926571 | + | 0.376121i | \(0.122742\pi\) | ||||
−0.926571 | + | 0.376121i | \(0.877258\pi\) | |||||||
\(48\) | 11.6619 | − | 2.82843i | 0.242956 | − | 0.0589256i | ||||
\(49\) | −15.0000 | −0.306122 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.00000 | + | 32.9848i | 0.156863 | + | 0.646762i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 67.8823i | 1.28080i | 0.768043 | + | 0.640399i | \(0.221231\pi\) | ||||
−0.768043 | + | 0.640399i | \(0.778769\pi\) | |||||||
\(54\) | −25.0000 | − | 28.8617i | −0.462963 | − | 0.534477i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 16.4924i | 0.294508i | ||||||||
\(57\) | −34.9857 | + | 8.48528i | −0.613784 | + | 0.148865i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 16.4924i | 0.279533i | 0.990185 | + | 0.139766i | \(0.0446351\pi\) | ||||
−0.990185 | + | 0.139766i | \(0.955365\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −16.0000 | −0.262295 | −0.131148 | − | 0.991363i | \(-0.541866\pi\) | ||||
−0.131148 | + | 0.991363i | \(0.541866\pi\) | |||||||
\(62\) | 45.2548i | 0.729917i | ||||||||
\(63\) | 46.6476 | − | 24.0416i | 0.740438 | − | 0.381613i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −68.0000 | + | 16.4924i | −1.03030 | + | 0.249885i | ||||
\(67\) | −5.83095 | −0.0870291 | −0.0435146 | − | 0.999053i | \(-0.513855\pi\) | ||||
−0.0435146 | + | 0.999053i | \(0.513855\pi\) | |||||||
\(68\) | − | 22.6274i | − | 0.332756i | ||||||
\(69\) | 17.0000 | + | 70.0928i | 0.246377 | + | 1.01584i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 11.6619 | + | 22.6274i | 0.161971 | + | 0.314270i | ||||
\(73\) | −116.619 | −1.59752 | −0.798761 | − | 0.601649i | \(-0.794511\pi\) | ||||
−0.798761 | + | 0.601649i | \(0.794511\pi\) | |||||||
\(74\) | − | 32.9848i | − | 0.445741i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 24.0000 | 0.315789 | ||||||||
\(77\) | − | 96.1665i | − | 1.24892i | ||||||
\(78\) | 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 | ||||
\(82\) | 81.6333 | 0.995528 | ||||||||
\(83\) | − | 43.8406i | − | 0.528200i | −0.964495 | − | 0.264100i | \(-0.914925\pi\) | ||
0.964495 | − | 0.264100i | \(-0.0850749\pi\) | |||||||
\(84\) | −34.0000 | + | 8.24621i | −0.404762 | + | 0.0981692i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 57.7235i | − | 0.671203i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 46.6476 | 0.530087 | ||||||||
\(89\) | − | 65.9697i | − | 0.741232i | −0.928786 | − | 0.370616i | \(-0.879147\pi\) | ||
0.928786 | − | 0.370616i | \(-0.120853\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 48.0833i | − | 0.522644i | ||||||
\(93\) | −93.2952 | + | 22.6274i | −1.00317 | + | 0.243306i | ||||
\(94\) | 50.0000 | 0.531915 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.00000 | − | 16.4924i | −0.0416667 | − | 0.171796i | ||||
\(97\) | −163.267 | −1.68316 | −0.841581 | − | 0.540131i | \(-0.818375\pi\) | ||||
−0.841581 | + | 0.540131i | \(0.818375\pi\) | |||||||
\(98\) | 21.2132i | 0.216461i | ||||||||
\(99\) | −68.0000 | − | 131.939i | −0.686869 | − | 1.33272i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 131.939i | − | 1.30633i | −0.757215 | − | 0.653165i | \(-0.773441\pi\) | ||
0.757215 | − | 0.653165i | \(-0.226559\pi\) | |||||||
\(102\) | 46.6476 | − | 11.3137i | 0.457330 | − | 0.110919i | ||||
\(103\) | 99.1262 | 0.962390 | 0.481195 | − | 0.876614i | \(-0.340203\pi\) | ||||
0.481195 | + | 0.876614i | \(0.340203\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 96.0000 | 0.905660 | ||||||||
\(107\) | 55.1543i | 0.515461i | 0.966217 | + | 0.257731i | \(0.0829747\pi\) | ||||
−0.966217 | + | 0.257731i | \(0.917025\pi\) | |||||||
\(108\) | −40.8167 | + | 35.3553i | −0.377932 | + | 0.327364i | ||||
\(109\) | −80.0000 | −0.733945 | −0.366972 | − | 0.930232i | \(-0.619606\pi\) | ||||
−0.366972 | + | 0.930232i | \(0.619606\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 68.0000 | − | 16.4924i | 0.612613 | − | 0.148580i | ||||
\(112\) | 23.3238 | 0.208248 | ||||||||
\(113\) | − | 152.735i | − | 1.35164i | −0.737068 | − | 0.675819i | \(-0.763790\pi\) | ||
0.737068 | − | 0.675819i | \(-0.236210\pi\) | |||||||
\(114\) | 12.0000 | + | 49.4773i | 0.105263 | + | 0.434011i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 23.3238 | 0.197659 | ||||||||
\(119\) | 65.9697i | 0.554367i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −151.000 | −1.24793 | ||||||||
\(122\) | 22.6274i | 0.185471i | ||||||||
\(123\) | 40.8167 | + | 168.291i | 0.331843 | + | 1.36822i | ||||
\(124\) | 64.0000 | 0.516129 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −34.0000 | − | 65.9697i | −0.269841 | − | 0.523569i | ||||
\(127\) | 40.8167 | 0.321391 | 0.160696 | − | 0.987004i | \(-0.448626\pi\) | ||||
0.160696 | + | 0.987004i | \(0.448626\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 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 | \(-0.0604742\pi\) | |||||||
\(132\) | 23.3238 | + | 96.1665i | 0.176696 | + | 0.728534i | ||||
\(133\) | −69.9714 | −0.526101 | ||||||||
\(134\) | 8.24621i | 0.0615389i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −32.0000 | −0.235294 | ||||||||
\(137\) | 50.9117i | 0.371618i | 0.982586 | + | 0.185809i | \(0.0594906\pi\) | ||||
−0.982586 | + | 0.185809i | \(0.940509\pi\) | |||||||
\(138\) | 99.1262 | − | 24.0416i | 0.718306 | − | 0.174215i | ||||
\(139\) | −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 | ||||||||
\(144\) | 32.0000 | − | 16.4924i | 0.222222 | − | 0.114531i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 164.924i | 1.12962i | ||||||||
\(147\) | −43.7321 | + | 10.6066i | −0.297498 | + | 0.0721538i | ||||
\(148\) | −46.6476 | −0.315187 | ||||||||
\(149\) | − | 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 | \(-0.351306\pi\) | ||||
0.450331 | + | 0.892862i | \(0.351306\pi\) | |||||||
\(152\) | − | 33.9411i | − | 0.223297i | ||||||
\(153\) | 46.6476 | + | 90.5097i | 0.304886 | + | 0.591566i | ||||
\(154\) | −136.000 | −0.883117 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 116.619 | 0.742796 | 0.371398 | − | 0.928474i | \(-0.378878\pi\) | ||||
0.371398 | + | 0.928474i | \(0.378878\pi\) | |||||||
\(158\) | − | 101.823i | − | 0.644452i | ||||||
\(159\) | 48.0000 | + | 197.909i | 0.301887 | + | 1.24471i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 140.186i | 0.870718i | ||||||||
\(162\) | −93.2952 | − | 66.4680i | −0.575896 | − | 0.410297i | ||||
\(163\) | 99.1262 | 0.608136 | 0.304068 | − | 0.952650i | \(-0.401655\pi\) | ||||
0.304068 | + | 0.952650i | \(0.401655\pi\) | |||||||
\(164\) | − | 115.447i | − | 0.703945i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −62.0000 | −0.373494 | ||||||||
\(167\) | − | 292.742i | − | 1.75295i | −0.481450 | − | 0.876474i | \(-0.659890\pi\) | ||
0.481450 | − | 0.876474i | \(-0.340110\pi\) | |||||||
\(168\) | 11.6619 | + | 48.0833i | 0.0694161 | + | 0.286210i | ||||
\(169\) | −169.000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −96.0000 | + | 49.4773i | −0.561404 | + | 0.289341i | ||||
\(172\) | −81.6333 | −0.474612 | ||||||||
\(173\) | − | 164.049i | − | 0.948259i | −0.880455 | − | 0.474129i | \(-0.842763\pi\) | ||
0.880455 | − | 0.474129i | \(-0.157237\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 65.9697i | − | 0.374828i | ||||||
\(177\) | 11.6619 | + | 48.0833i | 0.0658865 | + | 0.271657i | ||||
\(178\) | −93.2952 | −0.524131 | ||||||||
\(179\) | 16.4924i | 0.0921364i | 0.998938 | + | 0.0460682i | \(0.0146692\pi\) | ||||
−0.998938 | + | 0.0460682i | \(0.985331\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −82.0000 | −0.453039 | −0.226519 | − | 0.974007i | \(-0.572735\pi\) | ||||
−0.226519 | + | 0.974007i | \(0.572735\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −46.6476 | + | 11.3137i | −0.254905 | + | 0.0618235i | ||||
\(184\) | −68.0000 | −0.369565 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 32.0000 | + | 131.939i | 0.172043 | + | 0.709352i | ||||
\(187\) | 186.590 | 0.997810 | ||||||||
\(188\) | − | 70.7107i | − | 0.376121i | ||||||
\(189\) | 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 | \(0.716675\pi\) | |||||||
\(192\) | −23.3238 | + | 5.65685i | −0.121478 | + | 0.0294628i | ||||
\(193\) | −116.619 | −0.604244 | −0.302122 | − | 0.953269i | \(-0.597695\pi\) | ||||
−0.302122 | + | 0.953269i | \(0.597695\pi\) | |||||||
\(194\) | 230.894i | 1.19017i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 30.0000 | 0.153061 | ||||||||
\(197\) | 192.333i | 0.976310i | 0.872757 | + | 0.488155i | \(0.162330\pi\) | ||||
−0.872757 | + | 0.488155i | \(0.837670\pi\) | |||||||
\(198\) | −186.590 | + | 96.1665i | −0.942376 | + | 0.485690i | ||||
\(199\) | 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 | ||||
\(202\) | −186.590 | −0.923715 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −16.0000 | − | 65.9697i | −0.0784314 | − | 0.323381i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 140.186i | − | 0.680513i | ||||||
\(207\) | 99.1262 | + | 192.333i | 0.478870 | + | 0.929145i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 197.909i | 0.946933i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.0568720 | −0.0284360 | − | 0.999596i | \(-0.509053\pi\) | ||||
−0.0284360 | + | 0.999596i | \(0.509053\pi\) | |||||||
\(212\) | − | 135.765i | − | 0.640399i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 78.0000 | 0.364486 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 50.0000 | + | 57.7235i | 0.231481 | + | 0.267238i | ||||
\(217\) | −186.590 | −0.859864 | ||||||||
\(218\) | 113.137i | 0.518977i | ||||||||
\(219\) | −340.000 | + | 82.4621i | −1.55251 | + | 0.376539i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −23.3238 | − | 96.1665i | −0.105062 | − | 0.433183i | ||||
\(223\) | 40.8167 | 0.183034 | 0.0915172 | − | 0.995803i | \(-0.470828\pi\) | ||||
0.0915172 | + | 0.995803i | \(0.470828\pi\) | |||||||
\(224\) | − | 32.9848i | − | 0.147254i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −216.000 | −0.955752 | ||||||||
\(227\) | 159.806i | 0.703992i | 0.936002 | + | 0.351996i | \(0.114497\pi\) | ||||
−0.936002 | + | 0.351996i | \(0.885503\pi\) | |||||||
\(228\) | 69.9714 | − | 16.9706i | 0.306892 | − | 0.0744323i | ||||
\(229\) | −82.0000 | −0.358079 | −0.179039 | − | 0.983842i | \(-0.557299\pi\) | ||||
−0.179039 | + | 0.983842i | \(0.557299\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −68.0000 | − | 280.371i | −0.294372 | − | 1.21373i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 192.333i | 0.825464i | 0.910853 | + | 0.412732i | \(0.135425\pi\) | ||||
−0.910853 | + | 0.412732i | \(0.864575\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 32.9848i | − | 0.139766i | ||||||
\(237\) | 209.914 | − | 50.9117i | 0.885714 | − | 0.214817i | ||||
\(238\) | 93.2952 | 0.391997 | ||||||||
\(239\) | − | 461.788i | − | 1.93217i | −0.258231 | − | 0.966083i | \(-0.583139\pi\) | ||
0.258231 | − | 0.966083i | \(-0.416861\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 304.000 | 1.26141 | 0.630705 | − | 0.776022i | \(-0.282766\pi\) | ||||
0.630705 | + | 0.776022i | \(0.282766\pi\) | |||||||
\(242\) | 213.546i | 0.882423i | ||||||||
\(243\) | 90.3798 | − | 225.567i | 0.371933 | − | 0.928260i | ||||
\(244\) | 32.0000 | 0.131148 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 238.000 | − | 57.7235i | 0.967480 | − | 0.234648i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 90.5097i | − | 0.364958i | ||||||
\(249\) | −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 | \(-0.242355\pi\) | |||||||
\(252\) | −93.2952 | + | 48.0833i | −0.370219 | + | 0.190807i | ||||
\(253\) | 396.505 | 1.56721 | ||||||||
\(254\) | − | 57.7235i | − | 0.227258i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 390.323i | − | 1.51877i | −0.650644 | − | 0.759383i | \(-0.725501\pi\) | ||
0.650644 | − | 0.759383i | \(-0.274499\pi\) | |||||||
\(258\) | −40.8167 | − | 168.291i | −0.158204 | − | 0.652292i | ||||
\(259\) | 136.000 | 0.525097 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −69.9714 | −0.267066 | ||||||||
\(263\) | 295.571i | 1.12384i | 0.827191 | + | 0.561921i | \(0.189938\pi\) | ||||
−0.827191 | + | 0.561921i | \(0.810062\pi\) | |||||||
\(264\) | 136.000 | − | 32.9848i | 0.515152 | − | 0.124943i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 98.9545i | 0.372010i | ||||||||
\(267\) | −46.6476 | − | 192.333i | −0.174710 | − | 0.720348i | ||||
\(268\) | 11.6619 | 0.0435146 | ||||||||
\(269\) | 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 | \(-0.476487\pi\) | ||||
0.0738007 | + | 0.997273i | \(0.476487\pi\) | |||||||
\(272\) | 45.2548i | 0.166378i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 72.0000 | 0.262774 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −34.0000 | − | 140.186i | −0.123188 | − | 0.507919i | ||||
\(277\) | 443.152 | 1.59983 | 0.799914 | − | 0.600115i | \(-0.204878\pi\) | ||||
0.799914 | + | 0.600115i | \(0.204878\pi\) | |||||||
\(278\) | 62.2254i | 0.223832i | ||||||||
\(279\) | −256.000 | + | 131.939i | −0.917563 | + | 0.472901i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 519.511i | − | 1.84879i | −0.381431 | − | 0.924397i | \(-0.624569\pi\) | ||
0.381431 | − | 0.924397i | \(-0.375431\pi\) | |||||||
\(282\) | 145.774 | − | 35.3553i | 0.516928 | − | 0.125374i | ||||
\(283\) | −320.702 | −1.13322 | −0.566612 | − | 0.823985i | \(-0.691746\pi\) | ||||
−0.566612 | + | 0.823985i | \(0.691746\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 336.583i | 1.17276i | ||||||||
\(288\) | −23.3238 | − | 45.2548i | −0.0809854 | − | 0.157135i | ||||
\(289\) | 161.000 | 0.557093 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −476.000 | + | 115.447i | −1.63574 | + | 0.396725i | ||||
\(292\) | 233.238 | 0.798761 | ||||||||
\(293\) | 84.8528i | 0.289600i | 0.989461 | + | 0.144800i | \(0.0462539\pi\) | ||||
−0.989461 | + | 0.144800i | \(0.953746\pi\) | |||||||
\(294\) | 15.0000 | + | 61.8466i | 0.0510204 | + | 0.210363i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 65.9697i | 0.222871i | ||||||||
\(297\) | −291.548 | − | 336.583i | −0.981642 | − | 1.13328i | ||||
\(298\) | −11.6619 | −0.0391339 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 238.000 | 0.790698 | ||||||||
\(302\) | − | 192.333i | − | 0.636864i | ||||||
\(303\) | −93.2952 | − | 384.666i | −0.307905 | − | 1.26953i | ||||
\(304\) | −48.0000 | −0.157895 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 128.000 | − | 65.9697i | 0.418301 | − | 0.215587i | ||||
\(307\) | −367.350 | −1.19658 | −0.598290 | − | 0.801280i | \(-0.704153\pi\) | ||||
−0.598290 | + | 0.801280i | \(0.704153\pi\) | |||||||
\(308\) | 192.333i | 0.624458i | ||||||||
\(309\) | 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 | ||||||||
\(313\) | −186.590 | −0.596136 | −0.298068 | − | 0.954545i | \(-0.596342\pi\) | ||||
−0.298068 | + | 0.954545i | \(0.596342\pi\) | |||||||
\(314\) | − | 164.924i | − | 0.525236i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −144.000 | −0.455696 | ||||||||
\(317\) | 520.431i | 1.64174i | 0.571117 | + | 0.820868i | \(0.306510\pi\) | ||||
−0.571117 | + | 0.820868i | \(0.693490\pi\) | |||||||
\(318\) | 279.886 | − | 67.8823i | 0.880144 | − | 0.213466i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 39.0000 | + | 160.801i | 0.121495 | + | 0.500938i | ||||
\(322\) | 198.252 | 0.615691 | ||||||||
\(323\) | − | 135.765i | − | 0.420324i | ||||||
\(324\) | −94.0000 | + | 131.939i | −0.290123 | + | 0.407220i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 140.186i | − | 0.430017i | ||||||
\(327\) | −233.238 | + | 56.5685i | −0.713266 | + | 0.172992i | ||||
\(328\) | −163.267 | −0.497764 | ||||||||
\(329\) | 206.155i | 0.626612i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 292.000 | 0.882175 | 0.441088 | − | 0.897464i | \(-0.354593\pi\) | ||||
0.441088 | + | 0.897464i | \(0.354593\pi\) | |||||||
\(332\) | 87.6812i | 0.264100i | ||||||||
\(333\) | 186.590 | − | 96.1665i | 0.560332 | − | 0.288788i | ||||
\(334\) | −414.000 | −1.23952 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 68.0000 | − | 16.4924i | 0.202381 | − | 0.0490846i | ||||
\(337\) | −326.533 | −0.968942 | −0.484471 | − | 0.874807i | \(-0.660988\pi\) | ||||
−0.484471 | + | 0.874807i | \(0.660988\pi\) | |||||||
\(338\) | 239.002i | 0.707107i | ||||||||
\(339\) | −108.000 | − | 445.295i | −0.318584 | − | 1.31356i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 527.758i | 1.54768i | ||||||||
\(342\) | 69.9714 | + | 135.765i | 0.204595 | + | 0.396972i | ||||
\(343\) | −373.181 | −1.08799 | ||||||||
\(344\) | 115.447i | 0.335602i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −232.000 | −0.670520 | ||||||||
\(347\) | − | 394.566i | − | 1.13708i | −0.822657 | − | 0.568538i | \(-0.807509\pi\) | ||
0.822657 | − | 0.568538i | \(-0.192491\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −254.000 | −0.727794 | −0.363897 | − | 0.931439i | \(-0.618554\pi\) | ||||
−0.363897 | + | 0.931439i | \(0.618554\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −93.2952 | −0.265043 | ||||||||
\(353\) | 345.068i | 0.977530i | 0.872415 | + | 0.488765i | \(0.162552\pi\) | ||||
−0.872415 | + | 0.488765i | \(0.837448\pi\) | |||||||
\(354\) | 68.0000 | − | 16.4924i | 0.192090 | − | 0.0465888i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 131.939i | 0.370616i | ||||||||
\(357\) | 46.6476 | + | 192.333i | 0.130666 | + | 0.538748i | ||||
\(358\) | 23.3238 | 0.0651503 | ||||||||
\(359\) | 395.818i | 1.10256i | 0.834321 | + | 0.551279i | \(0.185860\pi\) | ||||
−0.834321 | + | 0.551279i | \(0.814140\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −217.000 | −0.601108 | ||||||||
\(362\) | 115.966i | 0.320347i | ||||||||
\(363\) | −440.237 | + | 106.773i | −1.21277 | + | 0.294141i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 16.0000 | + | 65.9697i | 0.0437158 | + | 0.180245i | ||||
\(367\) | −413.998 | −1.12806 | −0.564029 | − | 0.825755i | \(-0.690750\pi\) | ||||
−0.564029 | + | 0.825755i | \(0.690750\pi\) | |||||||
\(368\) | 96.1665i | 0.261322i | ||||||||
\(369\) | 238.000 | + | 461.788i | 0.644986 | + | 1.25146i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 395.818i | 1.06690i | ||||||||
\(372\) | 186.590 | − | 45.2548i | 0.501587 | − | 0.121653i | ||||
\(373\) | 629.743 | 1.68832 | 0.844159 | − | 0.536092i | \(-0.180100\pi\) | ||||
0.844159 | + | 0.536092i | \(0.180100\pi\) | |||||||
\(374\) | − | 263.879i | − | 0.705558i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −100.000 | −0.265957 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −145.774 | − | 168.291i | −0.385645 | − | 0.445215i | ||||
\(379\) | 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 | ||||
\(382\) | 419.829 | 1.09903 | ||||||||
\(383\) | − | 193.747i | − | 0.505868i | −0.967484 | − | 0.252934i | \(-0.918605\pi\) | ||
0.967484 | − | 0.252934i | \(-0.0813955\pi\) | |||||||
\(384\) | 8.00000 | + | 32.9848i | 0.0208333 | + | 0.0858980i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 164.924i | 0.427265i | ||||||||
\(387\) | 326.533 | − | 168.291i | 0.843755 | − | 0.434862i | ||||
\(388\) | 326.533 | 0.841581 | ||||||||
\(389\) | − | 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 | ||||||||
\(392\) | − | 42.4264i | − | 0.108231i | ||||||
\(393\) | −34.9857 | − | 144.250i | −0.0890222 | − | 0.367048i | ||||
\(394\) | 272.000 | 0.690355 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 136.000 | + | 263.879i | 0.343434 | + | 0.666361i | ||||
\(397\) | 513.124 | 1.29250 | 0.646252 | − | 0.763124i | \(-0.276336\pi\) | ||||
0.646252 | + | 0.763124i | \(0.276336\pi\) | |||||||
\(398\) | − | 441.235i | − | 1.10863i | ||||||
\(399\) | −204.000 | + | 49.4773i | −0.511278 | + | 0.124003i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 65.9697i | 0.164513i | 0.996611 | + | 0.0822565i | \(0.0262127\pi\) | ||||
−0.996611 | + | 0.0822565i | \(0.973787\pi\) | |||||||
\(402\) | 5.83095 | + | 24.0416i | 0.0145049 | + | 0.0598051i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 263.879i | 0.653165i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 384.666i | − | 0.945126i | ||||||
\(408\) | −93.2952 | + | 22.6274i | −0.228665 | + | 0.0554594i | ||||
\(409\) | −640.000 | −1.56479 | −0.782396 | − | 0.622781i | \(-0.786003\pi\) | ||||
−0.782396 | + | 0.622781i | \(0.786003\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 36.0000 | + | 148.432i | 0.0875912 | + | 0.361148i | ||||
\(412\) | −198.252 | −0.481195 | ||||||||
\(413\) | 96.1665i | 0.232849i | ||||||||
\(414\) | 272.000 | − | 140.186i | 0.657005 | − | 0.338613i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −128.281 | + | 31.1127i | −0.307628 | + | 0.0746108i | ||||
\(418\) | 279.886 | 0.669583 | ||||||||
\(419\) | 577.235i | 1.37765i | 0.724928 | + | 0.688824i | \(0.241873\pi\) | ||||
−0.724928 | + | 0.688824i | \(0.758127\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −656.000 | −1.55819 | −0.779097 | − | 0.626903i | \(-0.784322\pi\) | ||||
−0.779097 | + | 0.626903i | \(0.784322\pi\) | |||||||
\(422\) | 16.9706i | 0.0402146i | ||||||||
\(423\) | 145.774 | + | 282.843i | 0.344619 | + | 0.668659i | ||||
\(424\) | −192.000 | −0.452830 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −93.2952 | −0.218490 | ||||||||
\(428\) | − | 110.309i | − | 0.257731i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 362.833i | − | 0.841841i | −0.907098 | − | 0.420920i | \(-0.861707\pi\) | ||
0.907098 | − | 0.420920i | \(-0.138293\pi\) | |||||||
\(432\) | 81.6333 | − | 70.7107i | 0.188966 | − | 0.163682i | ||||
\(433\) | 163.267 | 0.377059 | 0.188530 | − | 0.982068i | \(-0.439628\pi\) | ||||
0.188530 | + | 0.982068i | \(0.439628\pi\) | |||||||
\(434\) | 263.879i | 0.608016i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 160.000 | 0.366972 | ||||||||
\(437\) | − | 288.500i | − | 0.660182i | ||||||
\(438\) | 116.619 | + | 480.833i | 0.266254 | + | 1.09779i | ||||
\(439\) | −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 | ||||||||
\(443\) | 123.037i | 0.277735i | 0.990311 | + | 0.138867i | \(0.0443462\pi\) | ||||
−0.990311 | + | 0.138867i | \(0.955654\pi\) | |||||||
\(444\) | −136.000 | + | 32.9848i | −0.306306 | + | 0.0742902i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 57.7235i | − | 0.129425i | ||||||
\(447\) | −5.83095 | − | 24.0416i | −0.0130446 | − | 0.0537844i | ||||
\(448\) | −46.6476 | −0.104124 | ||||||||
\(449\) | − | 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 | ||||||||
\(452\) | 305.470i | 0.675819i | ||||||||
\(453\) | 396.505 | − | 96.1665i | 0.875286 | − | 0.212288i | ||||
\(454\) | 226.000 | 0.497797 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −24.0000 | − | 98.9545i | −0.0526316 | − | 0.217006i | ||||
\(457\) | −466.476 | −1.02074 | −0.510368 | − | 0.859956i | \(-0.670491\pi\) | ||||
−0.510368 | + | 0.859956i | \(0.670491\pi\) | |||||||
\(458\) | 115.966i | 0.253200i | ||||||||
\(459\) | 200.000 | + | 230.894i | 0.435730 | + | 0.503037i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | −396.505 | + | 96.1665i | −0.858235 | + | 0.208153i | ||||
\(463\) | −612.250 | −1.32235 | −0.661177 | − | 0.750230i | \(-0.729943\pi\) | ||||
−0.661177 | + | 0.750230i | \(0.729943\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 272.000 | 0.583691 | ||||||||
\(467\) | 767.918i | 1.64436i | 0.569225 | + | 0.822182i | \(0.307243\pi\) | ||||
−0.569225 | + | 0.822182i | \(0.692757\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −34.0000 | −0.0724947 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 340.000 | − | 82.4621i | 0.721868 | − | 0.175079i | ||||
\(472\) | −46.6476 | −0.0988297 | ||||||||
\(473\) | − | 673.166i | − | 1.42318i | ||||||
\(474\) | −72.0000 | − | 296.864i | −0.151899 | − | 0.626295i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 131.939i | − | 0.277184i | ||||||
\(477\) | 279.886 | + | 543.058i | 0.586762 | + | 1.13849i | ||||
\(478\) | −653.067 | −1.36625 | ||||||||
\(479\) | − | 560.742i | − | 1.17065i | −0.810798 | − | 0.585326i | \(-0.800967\pi\) | ||
0.810798 | − | 0.585326i | \(-0.199033\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 429.921i | − | 0.891952i | ||||||
\(483\) | 99.1262 | + | 408.708i | 0.205230 | + | 0.846186i | ||||
\(484\) | 302.000 | 0.623967 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −319.000 | − | 127.816i | −0.656379 | − | 0.262996i | ||||
\(487\) | 647.236 | 1.32903 | 0.664513 | − | 0.747277i | \(-0.268639\pi\) | ||||
0.664513 | + | 0.747277i | \(0.268639\pi\) | |||||||
\(488\) | − | 45.2548i | − | 0.0927353i | ||||||
\(489\) | 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 | \(-0.114733\pi\) | |||||||
\(492\) | −81.6333 | − | 336.583i | −0.165921 | − | 0.684111i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −128.000 | −0.258065 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −180.760 | + | 43.8406i | −0.362971 | + | 0.0880334i | ||||
\(499\) | 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 | ||||
\(502\) | −489.800 | −0.975697 | ||||||||
\(503\) | − | 182.434i | − | 0.362691i | −0.983419 | − | 0.181345i | \(-0.941955\pi\) | ||
0.983419 | − | 0.181345i | \(-0.0580452\pi\) | |||||||
\(504\) | 68.0000 | + | 131.939i | 0.134921 | + | 0.261784i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 560.742i | − | 1.10819i | ||||||
\(507\) | −492.715 | + | 119.501i | −0.971825 | + | 0.235702i | ||||
\(508\) | −81.6333 | −0.160696 | ||||||||
\(509\) | 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 | ||||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | −244.900 | + | 212.132i | −0.477388 | + | 0.413513i | ||||
\(514\) | −552.000 | −1.07393 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −238.000 | + | 57.7235i | −0.461240 | + | 0.111867i | ||||
\(517\) | 583.095 | 1.12784 | ||||||||
\(518\) | − | 192.333i | − | 0.371299i | ||||||
\(519\) | −116.000 | − | 478.280i | −0.223507 | − | 0.921542i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 131.939i | − | 0.253243i | −0.991951 | − | 0.126621i | \(-0.959587\pi\) | ||
0.991951 | − | 0.126621i | \(-0.0404133\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −145.774 | −0.278726 | −0.139363 | − | 0.990241i | \(-0.544506\pi\) | ||||
−0.139363 | + | 0.990241i | \(0.544506\pi\) | |||||||
\(524\) | 98.9545i | 0.188845i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 418.000 | 0.794677 | ||||||||
\(527\) | − | 362.039i | − | 0.686980i | ||||||
\(528\) | −46.6476 | − | 192.333i | −0.0883478 | − | 0.364267i | ||||
\(529\) | −49.0000 | −0.0926276 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 68.0000 | + | 131.939i | 0.128060 | + | 0.248473i | ||||
\(532\) | 139.943 | 0.263050 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −272.000 | + | 65.9697i | −0.509363 | + | 0.123539i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 16.4924i | − | 0.0307694i | ||||||
\(537\) | 11.6619 | + | 48.0833i | 0.0217168 | + | 0.0895405i | ||||
\(538\) | 104.957 | 0.195088 | ||||||||
\(539\) | 247.386i | 0.458973i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 418.000 | 0.772643 | 0.386322 | − | 0.922364i | \(-0.373745\pi\) | ||||
0.386322 | + | 0.922364i | \(0.373745\pi\) | |||||||
\(542\) | − | 56.5685i | − | 0.104370i | ||||||
\(543\) | −239.069 | + | 57.9828i | −0.440274 | + | 0.106782i | ||||
\(544\) | 64.0000 | 0.117647 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 285.717 | 0.522334 | 0.261167 | − | 0.965294i | \(-0.415893\pi\) | ||||
0.261167 | + | 0.965294i | \(0.415893\pi\) | |||||||
\(548\) | − | 101.823i | − | 0.185809i | ||||||
\(549\) | −128.000 | + | 65.9697i | −0.233151 | + | 0.120163i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −198.252 | + | 48.0833i | −0.359153 | + | 0.0871074i | ||||
\(553\) | 419.829 | 0.759184 | ||||||||
\(554\) | − | 626.712i | − | 1.13125i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 88.0000 | 0.158273 | ||||||||
\(557\) | − | 424.264i | − | 0.761695i | −0.924638 | − | 0.380847i | \(-0.875632\pi\) | ||
0.924638 | − | 0.380847i | \(-0.124368\pi\) | |||||||
\(558\) | 186.590 | + | 362.039i | 0.334392 | + | 0.648815i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 544.000 | − | 131.939i | 0.969697 | − | 0.235186i | ||||
\(562\) | −734.700 | −1.30730 | ||||||||
\(563\) | − | 813.173i | − | 1.44436i | −0.691707 | − | 0.722178i | \(-0.743141\pi\) | ||
0.691707 | − | 0.722178i | \(-0.256859\pi\) | |||||||
\(564\) | −50.0000 | − | 206.155i | −0.0886525 | − | 0.365524i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 453.542i | 0.801310i | ||||||||
\(567\) | 274.055 | − | 384.666i | 0.483342 | − | 0.678423i | ||||
\(568\) | 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 | \(-0.438294\pi\) | ||||
0.192644 | + | 0.981269i | \(0.438294\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 209.914 | + | 865.499i | 0.366343 | + | 1.51047i | ||||
\(574\) | 476.000 | 0.829268 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −64.0000 | + | 32.9848i | −0.111111 | + | 0.0572654i | ||||
\(577\) | −46.6476 | −0.0808451 | −0.0404225 | − | 0.999183i | \(-0.512870\pi\) | ||||
−0.0404225 | + | 0.999183i | \(0.512870\pi\) | |||||||
\(578\) | − | 227.688i | − | 0.393925i | ||||||
\(579\) | −340.000 | + | 82.4621i | −0.587219 | + | 0.142422i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 255.633i | − | 0.439987i | ||||||
\(582\) | 163.267 | + | 673.166i | 0.280527 | + | 1.15664i | ||||
\(583\) | 1119.54 | 1.92031 | ||||||||
\(584\) | − | 329.848i | − | 0.564809i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 120.000 | 0.204778 | ||||||||
\(587\) | − | 55.1543i | − | 0.0939597i | −0.998896 | − | 0.0469798i | \(-0.985040\pi\) | ||
0.998896 | − | 0.0469798i | \(-0.0149597\pi\) | |||||||
\(588\) | 87.4643 | − | 21.2132i | 0.148749 | − | 0.0360769i | ||||
\(589\) | 384.000 | 0.651952 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 136.000 | + | 560.742i | 0.230118 | + | 0.948803i | ||||
\(592\) | 93.2952 | 0.157593 | ||||||||
\(593\) | 390.323i | 0.658217i | 0.944292 | + | 0.329109i | \(0.106748\pi\) | ||||
−0.944292 | + | 0.329109i | \(0.893252\pi\) | |||||||
\(594\) | −476.000 | + | 412.311i | −0.801347 | + | 0.694126i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.4924i | 0.0276718i | ||||||||
\(597\) | 909.628 | − | 220.617i | 1.52367 | − | 0.369543i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 98.9545i | − | 0.165200i | −0.996583 | − | 0.0825998i | \(-0.973678\pi\) | ||
0.996583 | − | 0.0825998i | \(-0.0263223\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −880.000 | −1.46423 | −0.732113 | − | 0.681183i | \(-0.761466\pi\) | ||||
−0.732113 | + | 0.681183i | \(0.761466\pi\) | |||||||
\(602\) | − | 336.583i | − | 0.559108i | ||||||
\(603\) | −46.6476 | + | 24.0416i | −0.0773592 | + | 0.0398700i | ||||
\(604\) | −272.000 | −0.450331 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −544.000 | + | 131.939i | −0.897690 | + | 0.217722i | ||||
\(607\) | −425.659 | −0.701251 | −0.350626 | − | 0.936516i | \(-0.614031\pi\) | ||||
−0.350626 | + | 0.936516i | \(0.614031\pi\) | |||||||
\(608\) | 67.8823i | 0.111648i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −93.2952 | − | 181.019i | −0.152443 | − | 0.295783i | ||||
\(613\) | −606.419 | −0.989264 | −0.494632 | − | 0.869102i | \(-0.664697\pi\) | ||||
−0.494632 | + | 0.869102i | \(0.664697\pi\) | |||||||
\(614\) | 519.511i | 0.846110i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 272.000 | 0.441558 | ||||||||
\(617\) | 113.137i | 0.183366i | 0.995788 | + | 0.0916832i | \(0.0292247\pi\) | ||||
−0.995788 | + | 0.0916832i | \(0.970775\pi\) | |||||||
\(618\) | −99.1262 | − | 408.708i | −0.160398 | − | 0.661339i | ||||
\(619\) | −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 | ||||
\(622\) | 139.943 | 0.224988 | ||||||||
\(623\) | − | 384.666i | − | 0.617442i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 263.879i | 0.421532i | ||||||||
\(627\) | 139.943 | + | 576.999i | 0.223194 | + | 0.920254i | ||||
\(628\) | −233.238 | −0.371398 | ||||||||
\(629\) | 263.879i | 0.419521i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −544.000 | −0.862124 | −0.431062 | − | 0.902322i | \(-0.641861\pi\) | ||||
−0.431062 | + | 0.902322i | \(0.641861\pi\) | |||||||
\(632\) | 203.647i | 0.322226i | ||||||||
\(633\) | −34.9857 | + | 8.48528i | −0.0552697 | + | 0.0134049i | ||||
\(634\) | 736.000 | 1.16088 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −96.0000 | − | 395.818i | −0.150943 | − | 0.622356i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 849.360i | 1.32505i | 0.749038 | + | 0.662527i | \(0.230516\pi\) | ||||
−0.749038 | + | 0.662527i | \(0.769484\pi\) | |||||||
\(642\) | 227.407 | − | 55.1543i | 0.354217 | − | 0.0859102i | ||||
\(643\) | 367.350 | 0.571306 | 0.285653 | − | 0.958333i | \(-0.407789\pi\) | ||||
0.285653 | + | 0.958333i | \(0.407789\pi\) | |||||||
\(644\) | − | 280.371i | − | 0.435359i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −192.000 | −0.297214 | ||||||||
\(647\) | 971.565i | 1.50165i | 0.660504 | + | 0.750823i | \(0.270343\pi\) | ||||
−0.660504 | + | 0.750823i | \(0.729657\pi\) | |||||||
\(648\) | 186.590 | + | 132.936i | 0.287948 | + | 0.205148i | ||||
\(649\) | 272.000 | 0.419106 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −544.000 | + | 131.939i | −0.835637 | + | 0.202672i | ||||
\(652\) | −198.252 | −0.304068 | ||||||||
\(653\) | 350.725i | 0.537098i | 0.963266 | + | 0.268549i | \(0.0865441\pi\) | ||||
−0.963266 | + | 0.268549i | \(0.913456\pi\) | |||||||
\(654\) | 80.0000 | + | 329.848i | 0.122324 | + | 0.504355i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 230.894i | 0.351972i | ||||||||
\(657\) | −932.952 | + | 480.833i | −1.42002 | + | 0.731861i | ||||
\(658\) | 291.548 | 0.443081 | ||||||||
\(659\) | − | 577.235i | − | 0.875925i | −0.898993 | − | 0.437963i | \(-0.855700\pi\) | ||
0.898993 | − | 0.437963i | \(-0.144300\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 80.0000 | 0.121029 | 0.0605144 | − | 0.998167i | \(-0.480726\pi\) | ||||
0.0605144 | + | 0.998167i | \(0.480726\pi\) | |||||||
\(662\) | − | 412.950i | − | 0.623792i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 124.000 | 0.186747 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −136.000 | − | 263.879i | −0.204204 | − | 0.396214i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 585.484i | 0.876474i | ||||||||
\(669\) | 119.000 | − | 28.8617i | 0.177877 | − | 0.0431416i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 263.879i | 0.393262i | ||||||||
\(672\) | −23.3238 | − | 96.1665i | −0.0347080 | − | 0.143105i | ||||
\(673\) | −489.800 | −0.727786 | −0.363893 | − | 0.931441i | \(-0.618553\pi\) | ||||
−0.363893 | + | 0.931441i | \(0.618553\pi\) | |||||||
\(674\) | 461.788i | 0.685145i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 338.000 | 0.500000 | ||||||||
\(677\) | − | 192.333i | − | 0.284096i | −0.989860 | − | 0.142048i | \(-0.954631\pi\) | ||
0.989860 | − | 0.142048i | \(-0.0453687\pi\) | |||||||
\(678\) | −629.743 | + | 152.735i | −0.928824 | + | 0.225273i | ||||
\(679\) | −952.000 | −1.40206 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 113.000 | + | 465.911i | 0.165932 | + | 0.684157i | ||||
\(682\) | 746.362 | 1.09437 | ||||||||
\(683\) | 236.174i | 0.345789i | 0.984940 | + | 0.172894i | \(0.0553119\pi\) | ||||
−0.984940 | + | 0.172894i | \(0.944688\pi\) | |||||||
\(684\) | 192.000 | − | 98.9545i | 0.280702 | − | 0.144670i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 527.758i | 0.769326i | ||||||||
\(687\) | −239.069 | + | 57.9828i | −0.347990 | + | 0.0843999i | ||||
\(688\) | 163.267 | 0.237306 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −548.000 | −0.793054 | −0.396527 | − | 0.918023i | \(-0.629785\pi\) | ||||
−0.396527 | + | 0.918023i | \(0.629785\pi\) | |||||||
\(692\) | 328.098i | 0.474129i | ||||||||
\(693\) | −396.505 | − | 769.332i | −0.572157 | − | 1.11015i | ||||
\(694\) | −558.000 | −0.804035 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −653.067 | −0.936968 | ||||||||
\(698\) | 359.210i | 0.514628i | ||||||||
\(699\) | 136.000 | + | 560.742i | 0.194564 | + | 0.802207i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 57.7235i | 0.0823445i | 0.999152 | + | 0.0411722i | \(0.0131092\pi\) | ||||
−0.999152 | + | 0.0411722i | \(0.986891\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −279.886 | −0.398130 | ||||||||
\(704\) | 131.939i | 0.187414i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 488.000 | 0.691218 | ||||||||
\(707\) | − | 769.332i | − | 1.08816i | ||||||
\(708\) | −23.3238 | − | 96.1665i | −0.0329432 | − | 0.135828i | ||||
\(709\) | −1230.00 | −1.73484 | −0.867419 | − | 0.497579i | \(-0.834223\pi\) | ||||
−0.867419 | + | 0.497579i | \(0.834223\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 576.000 | − | 296.864i | 0.810127 | − | 0.417530i | ||||
\(712\) | 186.590 | 0.262065 | ||||||||
\(713\) | − | 769.332i | − | 1.07901i | ||||||
\(714\) | 272.000 | − | 65.9697i | 0.380952 | − | 0.0923945i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 32.9848i | − | 0.0460682i | ||||||
\(717\) | −326.533 | − | 1346.33i | −0.455416 | − | 1.87773i | ||||
\(718\) | 559.771 | 0.779626 | ||||||||
\(719\) | 626.712i | 0.871644i | 0.900033 | + | 0.435822i | \(0.143542\pi\) | ||||
−0.900033 | + | 0.435822i | \(0.856458\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 578.000 | 0.801664 | ||||||||
\(722\) | 306.884i | 0.425048i | ||||||||
\(723\) | 886.305 | − | 214.960i | 1.22587 | − | 0.297317i | ||||
\(724\) | 164.000 | 0.226519 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 151.000 | + | 622.589i | 0.207989 | + | 0.857561i | ||||
\(727\) | 367.350 | 0.505296 | 0.252648 | − | 0.967558i | \(-0.418699\pi\) | ||||
0.252648 | + | 0.967558i | \(0.418699\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 104.000 | − | 721.543i | 0.142661 | − | 0.989772i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 461.788i | 0.631721i | ||||||||
\(732\) | 93.2952 | − | 22.6274i | 0.127453 | − | 0.0309118i | ||||
\(733\) | −1002.92 | −1.36825 | −0.684123 | − | 0.729367i | \(-0.739815\pi\) | ||||
−0.684123 | + | 0.729367i | \(0.739815\pi\) | |||||||
\(734\) | 585.481i | 0.797658i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 136.000 | 0.184783 | ||||||||
\(737\) | 96.1665i | 0.130484i | ||||||||
\(738\) | 653.067 | − | 336.583i | 0.884914 | − | 0.456074i | ||||
\(739\) | 340.000 | 0.460081 | 0.230041 | − | 0.973181i | \(-0.426114\pi\) | ||||
0.230041 | + | 0.973181i | \(0.426114\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 559.771 | 0.754409 | ||||||||
\(743\) | 1243.09i | 1.67307i | 0.547911 | + | 0.836537i | \(0.315423\pi\) | ||||
−0.547911 | + | 0.836537i | \(0.684577\pi\) | |||||||
\(744\) | −64.0000 | − | 263.879i | −0.0860215 | − | 0.354676i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 890.591i | − | 1.19382i | ||||||
\(747\) | −180.760 | − | 350.725i | −0.241981 | − | 0.469511i | ||||
\(748\) | −373.181 | −0.498905 | ||||||||
\(749\) | 321.602i | 0.429375i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −520.000 | −0.692410 | −0.346205 | − | 0.938159i | \(-0.612530\pi\) | ||||
−0.346205 | + | 0.938159i | \(0.612530\pi\) | |||||||
\(752\) | 141.421i | 0.188060i | ||||||||
\(753\) | −244.900 | − | 1009.75i | −0.325232 | − | 1.34097i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −238.000 | + | 206.155i | −0.314815 | + | 0.272692i | ||||
\(757\) | −816.333 | −1.07838 | −0.539190 | − | 0.842184i | \(-0.681269\pi\) | ||||
−0.539190 | + | 0.842184i | \(0.681269\pi\) | |||||||
\(758\) | − | 808.930i | − | 1.06719i | ||||||
\(759\) | 1156.00 | − | 280.371i | 1.52306 | − | 0.369395i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 395.818i | − | 0.520129i | −0.965591 | − | 0.260064i | \(-0.916256\pi\) | ||
0.965591 | − | 0.260064i | \(-0.0837438\pi\) | |||||||
\(762\) | −40.8167 | − | 168.291i | −0.0535652 | − | 0.220855i | ||||
\(763\) | −466.476 | −0.611371 | ||||||||
\(764\) | − | 593.727i | − | 0.777130i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −274.000 | −0.357702 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 46.6476 | − | 11.3137i | 0.0607391 | − | 0.0147314i | ||||
\(769\) | 306.000 | 0.397919 | 0.198960 | − | 0.980008i | \(-0.436244\pi\) | ||||
0.198960 | + | 0.980008i | \(0.436244\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −276.000 | − | 1137.98i | −0.357977 | − | 1.47598i | ||||
\(772\) | 233.238 | 0.302122 | ||||||||
\(773\) | 305.470i | 0.395175i | 0.980285 | + | 0.197587i | \(0.0633106\pi\) | ||||
−0.980285 | + | 0.197587i | \(0.936689\pi\) | |||||||
\(774\) | −238.000 | − | 461.788i | −0.307494 | − | 0.596625i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 461.788i | − | 0.595087i | ||||||
\(777\) | 396.505 | − | 96.1665i | 0.510302 | − | 0.123766i | ||||
\(778\) | −548.109 | −0.704511 | ||||||||
\(779\) | − | 692.682i | − | 0.889194i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 384.666i | 0.491900i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −60.0000 | −0.0765306 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −204.000 | + | 49.4773i | −0.259542 | + | 0.0629482i | ||||
\(787\) | 565.602 | 0.718681 | 0.359341 | − | 0.933206i | \(-0.383002\pi\) | ||||
0.359341 | + | 0.933206i | \(0.383002\pi\) | |||||||
\(788\) | − | 384.666i | − | 0.488155i | ||||||
\(789\) | 209.000 | + | 861.729i | 0.264892 | + | 1.09218i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 890.591i | − | 1.12590i | ||||||
\(792\) | 373.181 | − | 192.333i | 0.471188 | − | 0.242845i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | − | 725.667i | − | 0.913938i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −624.000 | −0.783920 | ||||||||
\(797\) | 1063.49i | 1.33436i | 0.744894 | + | 0.667182i | \(0.232500\pi\) | ||||
−0.744894 | + | 0.667182i | \(0.767500\pi\) | |||||||
\(798\) | 69.9714 | + | 288.500i | 0.0876835 | + | 0.361528i | ||||
\(799\) | −400.000 | −0.500626 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −272.000 | − | 527.758i | −0.339576 | − | 0.658873i | ||||
\(802\) | 93.2952 | 0.116328 | ||||||||
\(803\) | 1923.33i | 2.39518i | ||||||||
\(804\) | 34.0000 | − | 8.24621i | 0.0422886 | − | 0.0102565i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 52.4786 | + | 216.375i | 0.0650292 | + | 0.268122i | ||||
\(808\) | 373.181 | 0.461858 | ||||||||
\(809\) | − | 791.636i | − | 0.978537i | −0.872133 | − | 0.489268i | \(-0.837264\pi\) | ||
0.872133 | − | 0.489268i | \(-0.162736\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 436.000 | 0.537608 | 0.268804 | − | 0.963195i | \(-0.413372\pi\) | ||||
0.268804 | + | 0.963195i | \(0.413372\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 116.619 | − | 28.2843i | 0.143443 | − | 0.0347900i | ||||
\(814\) | −544.000 | −0.668305 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 32.0000 | + | 131.939i | 0.0392157 | + | 0.161690i | ||||
\(817\) | −489.800 | −0.599510 | ||||||||
\(818\) | 905.097i | 1.10648i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 799.882i | − | 0.974278i | −0.873324 | − | 0.487139i | \(-0.838040\pi\) | ||
0.873324 | − | 0.487139i | \(-0.161960\pi\) | |||||||
\(822\) | 209.914 | − | 50.9117i | 0.255370 | − | 0.0619364i | ||||
\(823\) | 1311.96 | 1.59412 | 0.797062 | − | 0.603897i | \(-0.206386\pi\) | ||||
0.797062 | + | 0.603897i | \(0.206386\pi\) | |||||||
\(824\) | 280.371i | 0.340256i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 136.000 | 0.164649 | ||||||||
\(827\) | − | 985.707i | − | 1.19191i | −0.803019 | − | 0.595953i | \(-0.796774\pi\) | ||
0.803019 | − | 0.595953i | \(-0.203226\pi\) | |||||||
\(828\) | −198.252 | − | 384.666i | −0.239435 | − | 0.464573i | ||||
\(829\) | 1488.00 | 1.79493 | 0.897467 | − | 0.441082i | \(-0.145405\pi\) | ||||
0.897467 | + | 0.441082i | \(0.145405\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1292.00 | − | 313.356i | 1.55475 | − | 0.377083i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 169.706i | − | 0.203728i | ||||||
\(834\) | 44.0000 | + | 181.417i | 0.0527578 | + | 0.217526i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 395.818i | − | 0.473467i | ||||||
\(837\) | −653.067 | + | 565.685i | −0.780247 | + | 0.675849i | ||||
\(838\) | 816.333 | 0.974145 | ||||||||
\(839\) | 461.788i | 0.550403i | 0.961387 | + | 0.275201i | \(0.0887445\pi\) | ||||
−0.961387 | + | 0.275201i | \(0.911255\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 1.00000 | ||||||||
\(842\) | 927.724i | 1.10181i | ||||||||
\(843\) | −367.350 | − | 1514.62i | −0.435765 | − | 1.79671i | ||||
\(844\) | 24.0000 | 0.0284360 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 400.000 | − | 206.155i | 0.472813 | − | 0.243682i | ||||
\(847\) | −880.474 | −1.03952 | ||||||||
\(848\) | 271.529i | 0.320199i | ||||||||
\(849\) | −935.000 | + | 226.771i | −1.10130 | + | 0.267103i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 560.742i | 0.658922i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 326.533 | 0.382806 | 0.191403 | − | 0.981512i | \(-0.438696\pi\) | ||||
0.191403 | + | 0.981512i | \(0.438696\pi\) | |||||||
\(854\) | 131.939i | 0.154496i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −156.000 | −0.182243 | ||||||||
\(857\) | 288.500i | 0.336639i | 0.985732 | + | 0.168319i | \(0.0538340\pi\) | ||||
−0.985732 | + | 0.168319i | \(0.946166\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −796.000 | −0.926659 | −0.463329 | − | 0.886186i | \(-0.653345\pi\) | ||||
−0.463329 | + | 0.886186i | \(0.653345\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 238.000 | + | 981.299i | 0.276423 | + | 1.13972i | ||||
\(862\) | −513.124 | −0.595271 | ||||||||
\(863\) | − | 352.139i | − | 0.408041i | −0.978967 | − | 0.204020i | \(-0.934599\pi\) | ||
0.978967 | − | 0.204020i | \(-0.0654009\pi\) | |||||||
\(864\) | −100.000 | − | 115.447i | −0.115741 | − | 0.133619i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 230.894i | − | 0.266621i | ||||||
\(867\) | 469.392 | − | 113.844i | 0.541397 | − | 0.131308i | ||||
\(868\) | 373.181 | 0.429932 | ||||||||
\(869\) | − | 1187.45i | − | 1.36646i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 226.274i | − | 0.259489i | ||||||
\(873\) | −1306.13 | + | 673.166i | −1.49614 | + | 0.771095i | ||||
\(874\) | −408.000 | −0.466819 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 680.000 | − | 164.924i | 0.776256 | − | 0.188270i | ||||
\(877\) | 676.390 | 0.771255 | 0.385627 | − | 0.922655i | \(-0.373985\pi\) | ||||
0.385627 | + | 0.922655i | \(0.373985\pi\) | |||||||
\(878\) | 610.940i | 0.695832i | ||||||||
\(879\) | 60.0000 | + | 247.386i | 0.0682594 | + | 0.281441i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 519.511i | 0.589684i | 0.955546 | + | 0.294842i | \(0.0952670\pi\) | ||||
−0.955546 | + | 0.294842i | \(0.904733\pi\) | |||||||
\(882\) | 87.4643 | + | 169.706i | 0.0991658 | + | 0.192410i | ||||
\(883\) | 1591.85 | 1.80277 | 0.901387 | − | 0.433014i | \(-0.142550\pi\) | ||||
0.901387 | + | 0.433014i | \(0.142550\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 174.000 | 0.196388 | ||||||||
\(887\) | 767.918i | 0.865747i | 0.901455 | + | 0.432874i | \(0.142500\pi\) | ||||
−0.901455 | + | 0.432874i | \(0.857500\pi\) | |||||||
\(888\) | 46.6476 | + | 192.333i | 0.0525311 | + | 0.216591i | ||||
\(889\) | 238.000 | 0.267717 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1088.00 | − | 775.144i | −1.22110 | − | 0.869971i | ||||
\(892\) | −81.6333 | −0.0915172 | ||||||||
\(893\) | − | 424.264i | − | 0.475100i | ||||||
\(894\) | −34.0000 | + | 8.24621i | −0.0380313 | + | 0.00922395i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 65.9697i | 0.0736269i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1224.50 | −1.36359 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −768.000 | −0.852386 | ||||||||
\(902\) | − | 1346.33i | − | 1.49261i | ||||||
\(903\) | 693.883 | − | 168.291i | 0.768420 | − | 0.186369i | ||||
\(904\) | 432.000 | 0.477876 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −136.000 | − | 560.742i | −0.150110 | − | 0.618921i | ||||
\(907\) | −332.364 | −0.366444 | −0.183222 | − | 0.983072i | \(-0.558653\pi\) | ||||
−0.183222 | + | 0.983072i | \(0.558653\pi\) | |||||||
\(908\) | − | 319.612i | − | 0.351996i | ||||||
\(909\) | −544.000 | − | 1055.52i | −0.598460 | − | 1.16118i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 692.682i | − | 0.760353i | −0.924914 | − | 0.380177i | \(-0.875863\pi\) | ||
0.924914 | − | 0.380177i | \(-0.124137\pi\) | |||||||
\(912\) | −139.943 | + | 33.9411i | −0.153446 | + | 0.0372161i | ||||
\(913\) | −723.038 | −0.791937 | ||||||||
\(914\) | 659.697i | 0.721769i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 164.000 | 0.179039 | ||||||||
\(917\) | − | 288.500i | − | 0.314612i | ||||||
\(918\) | 326.533 | − | 282.843i | 0.355701 | − | 0.308108i | ||||
\(919\) | 912.000 | 0.992383 | 0.496192 | − | 0.868213i | \(-0.334731\pi\) | ||||
0.496192 | + | 0.868213i | \(0.334731\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1071.00 | + | 259.756i | −1.16287 | + | 0.282037i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 136.000 | + | 560.742i | 0.147186 | + | 0.606864i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 865.852i | 0.935046i | ||||||||
\(927\) | 793.009 | − | 408.708i | 0.855458 | − | 0.440893i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1261.67i | 1.35810i | 0.734094 | + | 0.679048i | \(0.237607\pi\) | ||||
−0.734094 | + | 0.679048i | \(0.762393\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 180.000 | 0.193340 | ||||||||
\(932\) | − | 384.666i | − | 0.412732i | ||||||
\(933\) | 69.9714 | + | 288.500i | 0.0749962 | + | 0.309217i | ||||
\(934\) | 1086.00 | 1.16274 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 816.333 | 0.871220 | 0.435610 | − | 0.900135i | \(-0.356533\pi\) | ||||
0.435610 | + | 0.900135i | \(0.356533\pi\) | |||||||
\(938\) | 48.0833i | 0.0512615i | ||||||||
\(939\) | −544.000 | + | 131.939i | −0.579340 | + | 0.140511i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1055.52i | − | 1.12170i | −0.827919 | − | 0.560848i | \(-0.810475\pi\) | ||
0.827919 | − | 0.560848i | \(-0.189525\pi\) | |||||||
\(942\) | −116.619 | − | 480.833i | −0.123799 | − | 0.510438i | ||||
\(943\) | −1387.77 | −1.47165 | ||||||||
\(944\) | 65.9697i | 0.0698831i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −952.000 | −1.00634 | ||||||||
\(947\) | 114.551i | 0.120962i | 0.998169 | + | 0.0604812i | \(0.0192635\pi\) | ||||
−0.998169 | + | 0.0604812i | \(0.980736\pi\) | |||||||
\(948\) | −419.829 | + | 101.823i | −0.442857 | + | 0.107409i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 368.000 | + | 1517.30i | 0.386961 | + | 1.59548i | ||||
\(952\) | −186.590 | −0.195998 | ||||||||
\(953\) | 243.245i | 0.255241i | 0.991823 | + | 0.127621i | \(0.0407340\pi\) | ||||
−0.991823 | + | 0.127621i | \(0.959266\pi\) | |||||||
\(954\) | 768.000 | − | 395.818i | 0.805031 | − | 0.414904i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 923.576i | 0.966083i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −793.009 | −0.827776 | ||||||||
\(959\) | 296.864i | 0.309555i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 63.0000 | 0.0655567 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 227.407 | + | 441.235i | 0.236144 | + | 0.458188i | ||||
\(964\) | −608.000 | −0.630705 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 578.000 | − | 140.186i | 0.598344 | − | 0.145120i | ||||
\(967\) | 938.783 | 0.970820 | 0.485410 | − | 0.874287i | \(-0.338670\pi\) | ||||
0.485410 | + | 0.874287i | \(0.338670\pi\) | |||||||
\(968\) | − | 427.092i | − | 0.441211i | ||||||
\(969\) | −96.0000 | − | 395.818i | −0.0990712 | − | 0.408481i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1335.89i | 1.37578i | 0.725813 | + | 0.687892i | \(0.241464\pi\) | ||||
−0.725813 | + | 0.687892i | \(0.758536\pi\) | |||||||
\(972\) | −180.760 | + | 451.134i | −0.185967 | + | 0.464130i | ||||
\(973\) | −256.562 | −0.263681 | ||||||||
\(974\) | − | 915.329i | − | 0.939763i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −64.0000 | −0.0655738 | ||||||||
\(977\) | − | 305.470i | − | 0.312661i | −0.987705 | − | 0.156331i | \(-0.950033\pi\) | ||
0.987705 | − | 0.156331i | \(-0.0499665\pi\) | |||||||
\(978\) | −99.1262 | − | 408.708i | −0.101356 | − | 0.417902i | ||||
\(979\) | −1088.00 | −1.11134 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −640.000 | + | 329.848i | −0.652396 | + | 0.336237i | ||||
\(982\) | −489.800 | −0.498778 | ||||||||
\(983\) | − | 1110.16i | − | 1.12936i | −0.825311 | − | 0.564678i | \(-0.809000\pi\) | ||
0.825311 | − | 0.564678i | \(-0.191000\pi\) | |||||||
\(984\) | −476.000 | + | 115.447i | −0.483740 | + | 0.117324i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 145.774 | + | 601.041i | 0.147694 | + | 0.608957i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 981.299i | 0.992213i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 640.000 | 0.645812 | 0.322906 | − | 0.946431i | \(-0.395340\pi\) | ||||
0.322906 | + | 0.946431i | \(0.395340\pi\) | |||||||
\(992\) | 181.019i | 0.182479i | ||||||||
\(993\) | 851.319 | − | 206.475i | 0.857320 | − | 0.207931i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 62.0000 | + | 255.633i | 0.0622490 | + | 0.256659i | ||||
\(997\) | 279.886 | 0.280728 | 0.140364 | − | 0.990100i | \(-0.455173\pi\) | ||||
0.140364 | + | 0.990100i | \(0.455173\pi\) | |||||||
\(998\) | − | 933.381i | − | 0.935251i | ||||||
\(999\) | 476.000 | − | 412.311i | 0.476476 | − | 0.412723i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))