Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,3,Mod(351,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.351");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.b (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: | \(21.7984211488\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.1827904.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 14x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 351.4 | ||
Root | \(0.273891i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 800.351 |
Dual form | 800.3.b.i.351.3 |
$q$-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 \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0.547781i | 0.182594i | 0.995824 | + | 0.0912969i | \(0.0291012\pi\) | ||||
−0.995824 | + | 0.0912969i | \(0.970899\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.0566i | 1.43666i | 0.695705 | + | 0.718328i | \(0.255092\pi\) | ||||
−0.695705 | + | 0.718328i | \(0.744908\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.69994 | 0.966660 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 17.2087i | − 1.56443i | −0.623008 | − | 0.782216i | \(-0.714089\pi\) | ||||
0.623008 | − | 0.782216i | \(-0.285911\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.41325 | −0.339481 | −0.169740 | − | 0.985489i | \(-0.554293\pi\) | ||||
−0.169740 | + | 0.985489i | \(0.554293\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 27.0176 | 1.58927 | 0.794636 | − | 0.607086i | \(-0.207662\pi\) | ||||
0.794636 | + | 0.607086i | \(0.207662\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.82650i | 0.254026i | 0.991901 | + | 0.127013i | \(0.0405390\pi\) | ||||
−0.991901 | + | 0.127013i | \(0.959461\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.50881 | −0.262324 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 15.2653i | − 0.663710i | −0.943330 | − | 0.331855i | \(-0.892325\pi\) | ||||
0.943330 | − | 0.331855i | \(-0.107675\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.69569i | 0.359100i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.38225 | 0.0821465 | 0.0410733 | − | 0.999156i | \(-0.486922\pi\) | ||||
0.0410733 | + | 0.999156i | \(0.486922\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 38.0352i | 1.22694i | 0.789717 | + | 0.613472i | \(0.210228\pi\) | ||||
−0.789717 | + | 0.613472i | \(0.789772\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.42663 | 0.285655 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 16.5691 | 0.447814 | 0.223907 | − | 0.974610i | \(-0.428119\pi\) | ||||
0.223907 | + | 0.974610i | \(0.428119\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 2.41749i | − 0.0619870i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −13.3177 | −0.324822 | −0.162411 | − | 0.986723i | \(-0.551927\pi\) | ||||
−0.162411 | + | 0.986723i | \(0.551927\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 59.7918i | 1.39051i | 0.718765 | + | 0.695253i | \(0.244708\pi\) | ||||
−0.718765 | + | 0.695253i | \(0.755292\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 62.4388i | 1.32849i | 0.747517 | + | 0.664243i | \(0.231246\pi\) | ||||
−0.747517 | + | 0.664243i | \(0.768754\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −52.1351 | −1.06398 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.7997i | 0.290191i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 71.5952 | 1.35085 | 0.675427 | − | 0.737427i | \(-0.263959\pi\) | ||||
0.675427 | + | 0.737427i | \(0.263959\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.64386 | −0.0463836 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 68.8265i | − 1.16655i | −0.812274 | − | 0.583275i | \(-0.801771\pi\) | ||||
0.812274 | − | 0.583275i | \(-0.198229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 40.9439 | 0.671212 | 0.335606 | − | 0.942002i | \(-0.391059\pi\) | ||||
0.335606 | + | 0.942002i | \(0.391059\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 87.4917i | 1.38876i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 51.0080i | 0.761313i | 0.924717 | + | 0.380656i | \(0.124302\pi\) | ||||
−0.924717 | + | 0.380656i | \(0.875698\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.36206 | 0.121189 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 40.4527i | − 0.569757i | −0.958564 | − | 0.284878i | \(-0.908047\pi\) | ||||
0.958564 | − | 0.284878i | \(-0.0919532\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 35.8441 | 0.491015 | 0.245508 | − | 0.969395i | \(-0.421045\pi\) | ||||
0.245508 | + | 0.969395i | \(0.421045\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 173.061 | 2.24755 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 126.800i | 1.60506i | 0.596612 | + | 0.802530i | \(0.296513\pi\) | ||||
−0.596612 | + | 0.802530i | \(0.703487\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 72.9883 | 0.901090 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 75.1490i | − 0.905409i | −0.891661 | − | 0.452705i | \(-0.850459\pi\) | ||||
0.891661 | − | 0.452705i | \(-0.149541\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.30495i | 0.0149994i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 106.523 | 1.19689 | 0.598445 | − | 0.801164i | \(-0.295785\pi\) | ||||
0.598445 | + | 0.801164i | \(0.295785\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 44.3822i | − 0.487717i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −20.8350 | −0.224032 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 85.4351 | 0.880774 | 0.440387 | − | 0.897808i | \(-0.354841\pi\) | ||||
0.440387 | + | 0.897808i | \(0.354841\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 149.715i | − 1.51227i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −83.2877 | −0.824631 | −0.412315 | − | 0.911041i | \(-0.635280\pi\) | ||||
−0.412315 | + | 0.911041i | \(0.635280\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 47.2653i | − 0.458887i | −0.973322 | − | 0.229443i | \(-0.926309\pi\) | ||||
0.973322 | − | 0.229443i | \(-0.0736906\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 189.628i | 1.77223i | 0.463467 | + | 0.886114i | \(0.346605\pi\) | ||||
−0.463467 | + | 0.886114i | \(0.653395\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −84.5617 | −0.775795 | −0.387898 | − | 0.921702i | \(-0.626799\pi\) | ||||
−0.387898 | + | 0.921702i | \(0.626799\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.07626i | 0.0817681i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −114.558 | −1.01379 | −0.506896 | − | 0.862007i | \(-0.669207\pi\) | ||||
−0.506896 | + | 0.862007i | \(0.669207\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −38.3950 | −0.328162 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 271.705i | 2.28324i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −175.141 | −1.44745 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 7.29518i | − 0.0593104i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 44.4121i | 0.349701i | 0.984595 | + | 0.174851i | \(0.0559443\pi\) | ||||
−0.984595 | + | 0.174851i | \(0.944056\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −32.7528 | −0.253898 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 47.1200i | − 0.359695i | −0.983695 | − | 0.179847i | \(-0.942440\pi\) | ||||
0.983695 | − | 0.179847i | \(-0.0575604\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −48.5381 | −0.364948 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 62.8617 | 0.458845 | 0.229422 | − | 0.973327i | \(-0.426316\pi\) | ||||
0.229422 | + | 0.973327i | \(0.426316\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 128.320i | − 0.923167i | −0.887097 | − | 0.461584i | \(-0.847281\pi\) | ||||
0.887097 | − | 0.461584i | \(-0.152719\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −34.2028 | −0.242573 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 75.9465i | 0.531094i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 28.5586i | − 0.194276i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 165.561 | 1.11115 | 0.555574 | − | 0.831467i | \(-0.312499\pi\) | ||||
0.555574 | + | 0.831467i | \(0.312499\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 218.558i | 1.44741i | 0.690111 | + | 0.723704i | \(0.257562\pi\) | ||||
−0.690111 | + | 0.723704i | \(0.742438\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 235.052 | 1.53628 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −174.293 | −1.11014 | −0.555072 | − | 0.831802i | \(-0.687309\pi\) | ||||
−0.555072 | + | 0.831802i | \(0.687309\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 39.2185i | 0.246657i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 153.517 | 0.953524 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 52.6353i | 0.322916i | 0.986880 | + | 0.161458i | \(0.0516196\pi\) | ||||
−0.986880 | + | 0.161458i | \(0.948380\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 76.6812i | − 0.459169i | −0.973289 | − | 0.229584i | \(-0.926263\pi\) | ||||
0.973289 | − | 0.229584i | \(-0.0737367\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −149.523 | −0.884753 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 41.9902i | 0.245557i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.72437 | −0.0562102 | −0.0281051 | − | 0.999605i | \(-0.508947\pi\) | ||||
−0.0281051 | + | 0.999605i | \(0.508947\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 37.7019 | 0.213005 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 155.502i | − 0.868728i | −0.900738 | − | 0.434364i | \(-0.856973\pi\) | ||||
0.900738 | − | 0.434364i | \(-0.143027\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 250.346 | 1.38313 | 0.691563 | − | 0.722316i | \(-0.256923\pi\) | ||||
0.691563 | + | 0.722316i | \(0.256923\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 22.4283i | 0.122559i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 464.939i | − 2.48631i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −97.5056 | −0.515903 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 111.128i | − 0.581825i | −0.956750 | − | 0.290912i | \(-0.906041\pi\) | ||||
0.956750 | − | 0.290912i | \(-0.0939588\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.2701 | 0.0532130 | 0.0266065 | − | 0.999646i | \(-0.491530\pi\) | ||||
0.0266065 | + | 0.999646i | \(0.491530\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −163.213 | −0.828492 | −0.414246 | − | 0.910165i | \(-0.635955\pi\) | ||||
−0.414246 | + | 0.910165i | \(0.635955\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 195.028i | − 0.980041i | −0.871711 | − | 0.490021i | \(-0.836989\pi\) | ||||
0.871711 | − | 0.490021i | \(-0.163011\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −27.9412 | −0.139011 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 23.9573i | 0.118016i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 132.807i | − 0.641582i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 83.0580 | 0.397407 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 297.038i | − 1.40776i | −0.710317 | − | 0.703881i | \(-0.751449\pi\) | ||||
0.710317 | − | 0.703881i | \(-0.248551\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 22.1592 | 0.104034 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −382.505 | −1.76270 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.6347i | 0.0896563i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −119.236 | −0.539527 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 405.335i | − 1.81764i | −0.417184 | − | 0.908822i | \(-0.636983\pi\) | ||||
0.417184 | − | 0.908822i | \(-0.363017\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 36.6013i | − 0.161239i | −0.996745 | − | 0.0806196i | \(-0.974310\pi\) | ||||
0.996745 | − | 0.0806196i | \(-0.0256899\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 91.1467 | 0.398021 | 0.199010 | − | 0.979997i | \(-0.436227\pi\) | ||||
0.199010 | + | 0.979997i | \(0.436227\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 94.7997i | 0.410388i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −338.802 | −1.45409 | −0.727043 | − | 0.686592i | \(-0.759106\pi\) | ||||
−0.727043 | + | 0.686592i | \(0.759106\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −69.4585 | −0.293074 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 30.7997i | 0.128869i | 0.997922 | + | 0.0644346i | \(0.0205244\pi\) | ||||
−0.997922 | + | 0.0644346i | \(0.979476\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 240.282 | 0.997020 | 0.498510 | − | 0.866884i | \(-0.333881\pi\) | ||||
0.498510 | + | 0.866884i | \(0.333881\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 127.243i | 0.523633i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 21.3005i | − 0.0862370i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 41.1652 | 0.165322 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 86.0268i | 0.342736i | 0.985207 | + | 0.171368i | \(0.0548187\pi\) | ||||
−0.985207 | + | 0.171368i | \(0.945181\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −262.697 | −1.03833 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −355.963 | −1.38507 | −0.692536 | − | 0.721383i | \(-0.743507\pi\) | ||||
−0.692536 | + | 0.721383i | \(0.743507\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 166.629i | 0.643355i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.7254 | 0.0794077 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 73.1254i | 0.278043i | 0.990289 | + | 0.139022i | \(0.0443958\pi\) | ||||
−0.990289 | + | 0.139022i | \(0.955604\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 58.3514i | 0.218545i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −268.002 | −0.996290 | −0.498145 | − | 0.867094i | \(-0.665985\pi\) | ||||
−0.498145 | + | 0.867094i | \(0.665985\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 229.412i | 0.846538i | 0.906004 | + | 0.423269i | \(0.139117\pi\) | ||||
−0.906004 | + | 0.423269i | \(0.860883\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 24.3118 | 0.0890541 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 126.327 | 0.456053 | 0.228026 | − | 0.973655i | \(-0.426773\pi\) | ||||
0.228026 | + | 0.973655i | \(0.426773\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 330.904i | 1.18604i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −458.746 | −1.63255 | −0.816275 | − | 0.577664i | \(-0.803964\pi\) | ||||
−0.816275 | + | 0.577664i | \(0.803964\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 465.558i | − 1.64508i | −0.568706 | − | 0.822541i | \(-0.692556\pi\) | ||||
0.568706 | − | 0.822541i | \(-0.307444\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 133.931i | − 0.466657i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 440.952 | 1.52579 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 46.7997i | 0.160824i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 165.218 | 0.563884 | 0.281942 | − | 0.959431i | \(-0.409021\pi\) | ||||
0.281942 | + | 0.959431i | \(0.409021\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 166.851 | 0.561787 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 67.3697i | 0.225317i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −601.302 | −1.99768 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 45.6234i | − 0.150572i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 235.339i | − 0.766577i | −0.923629 | − | 0.383288i | \(-0.874792\pi\) | ||||
0.923629 | − | 0.383288i | \(-0.125208\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 25.8911 | 0.0837898 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 210.665i | − 0.677381i | −0.940898 | − | 0.338691i | \(-0.890016\pi\) | ||||
0.940898 | − | 0.338691i | \(-0.109984\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −318.738 | −1.01833 | −0.509166 | − | 0.860668i | \(-0.670046\pi\) | ||||
−0.509166 | + | 0.860668i | \(0.670046\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 70.3950 | 0.222066 | 0.111033 | − | 0.993817i | \(-0.464584\pi\) | ||||
0.111033 | + | 0.993817i | \(0.464584\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 40.9955i | − 0.128513i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −103.875 | −0.323598 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 130.401i | 0.403717i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 46.3213i | − 0.141655i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −627.922 | −1.90858 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 280.807i | − 0.848359i | −0.905578 | − | 0.424180i | \(-0.860562\pi\) | ||||
0.905578 | − | 0.424180i | \(-0.139438\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 144.150 | 0.432884 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −120.969 | −0.358959 | −0.179480 | − | 0.983762i | \(-0.557441\pi\) | ||||
−0.179480 | + | 0.983762i | \(0.557441\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 62.7530i | − 0.185112i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 654.539 | 1.91947 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 31.5280i | − 0.0919182i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 214.333i | − 0.617675i | −0.951115 | − | 0.308838i | \(-0.900060\pi\) | ||||
0.951115 | − | 0.308838i | \(-0.0999399\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 418.041 | 1.19782 | 0.598912 | − | 0.800815i | \(-0.295600\pi\) | ||||
0.598912 | + | 0.800815i | \(0.295600\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 42.7895i | − 0.121907i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 364.929 | 1.03379 | 0.516897 | − | 0.856048i | \(-0.327087\pi\) | ||||
0.516897 | + | 0.856048i | \(0.327087\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −148.835 | −0.416905 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 242.169i | − 0.674567i | −0.941403 | − | 0.337283i | \(-0.890492\pi\) | ||||
0.941403 | − | 0.337283i | \(-0.109508\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 337.705 | 0.935471 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 95.9389i | − 0.264295i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 224.564i | − 0.611891i | −0.952049 | − | 0.305945i | \(-0.901028\pi\) | ||||
0.952049 | − | 0.305945i | \(-0.0989725\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −115.863 | −0.313992 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 720.004i | 1.94071i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −572.174 | −1.53398 | −0.766989 | − | 0.641660i | \(-0.778246\pi\) | ||||
−0.766989 | + | 0.641660i | \(0.778246\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.5135 | −0.0278872 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 122.896i | − 0.324263i | −0.986769 | − | 0.162132i | \(-0.948163\pi\) | ||||
0.986769 | − | 0.162132i | \(-0.0518369\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.3281 | −0.0638533 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 289.717i | 0.756442i | 0.925715 | + | 0.378221i | \(0.123464\pi\) | ||||
−0.925715 | + | 0.378221i | \(0.876536\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 520.185i | 1.34415i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −111.590 | −0.286863 | −0.143432 | − | 0.989660i | \(-0.545814\pi\) | ||||
−0.143432 | + | 0.989660i | \(0.545814\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 412.433i | − 1.05482i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 25.8114 | 0.0656780 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −705.314 | −1.77661 | −0.888305 | − | 0.459253i | \(-0.848117\pi\) | ||||
−0.888305 | + | 0.459253i | \(0.848117\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 26.5883i | − 0.0666373i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 432.052 | 1.07744 | 0.538718 | − | 0.842486i | \(-0.318909\pi\) | ||||
0.538718 | + | 0.842486i | \(0.318909\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 167.859i | − 0.416524i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 285.134i | − 0.700575i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 98.8102 | 0.241590 | 0.120795 | − | 0.992677i | \(-0.461456\pi\) | ||||
0.120795 | + | 0.992677i | \(0.461456\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 34.4345i | 0.0837822i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 692.160 | 1.67593 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 70.2914 | 0.168565 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 204.980i | 0.489213i | 0.969622 | + | 0.244607i | \(0.0786588\pi\) | ||||
−0.969622 | + | 0.244607i | \(0.921341\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 449.956 | 1.06878 | 0.534390 | − | 0.845238i | \(-0.320541\pi\) | ||||
0.534390 | + | 0.845238i | \(0.320541\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 543.214i | 1.28419i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 411.756i | 0.964301i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −41.6021 | −0.0969745 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 314.588i | − 0.729903i | −0.931026 | − | 0.364952i | \(-0.881086\pi\) | ||||
0.931026 | − | 0.364952i | \(-0.118914\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −330.441 | −0.763143 | −0.381571 | − | 0.924339i | \(-0.624617\pi\) | ||||
−0.381571 | + | 0.924339i | \(0.624617\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 73.6781 | 0.168600 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 664.815i | − 1.51439i | −0.653191 | − | 0.757193i | \(-0.726570\pi\) | ||||
0.653191 | − | 0.757193i | \(-0.273430\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −453.572 | −1.02851 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 312.860i | 0.706229i | 0.935580 | + | 0.353115i | \(0.114877\pi\) | ||||
−0.935580 | + | 0.353115i | \(0.885123\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 90.6912i | 0.202889i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 246.330 | 0.548620 | 0.274310 | − | 0.961641i | \(-0.411551\pi\) | ||||
0.274310 | + | 0.961641i | \(0.411551\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 229.181i | 0.508161i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −119.722 | −0.264287 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 707.094 | 1.54725 | 0.773626 | − | 0.633642i | \(-0.218441\pi\) | ||||
0.773626 | + | 0.633642i | \(0.218441\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 261.955i | 0.570707i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −611.288 | −1.32600 | −0.663002 | − | 0.748618i | \(-0.730718\pi\) | ||||
−0.663002 | + | 0.748618i | \(0.730718\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 334.063i | − 0.721519i | −0.932659 | − | 0.360760i | \(-0.882518\pi\) | ||||
0.932659 | − | 0.360760i | \(-0.117482\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 128.864i | − 0.275939i | −0.990436 | − | 0.137970i | \(-0.955942\pi\) | ||||
0.990436 | − | 0.137970i | \(-0.0440577\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −512.966 | −1.09374 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 95.4742i | − 0.202705i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1028.94 | 2.17535 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 622.874 | 1.30582 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 510.257i | − 1.06525i | −0.846350 | − | 0.532627i | \(-0.821205\pi\) | ||||
0.846350 | − | 0.532627i | \(-0.178795\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −73.1237 | −0.152024 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 84.0939i | 0.174107i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 616.472i | 1.26586i | 0.774211 | + | 0.632928i | \(0.218147\pi\) | ||||
−0.774211 | + | 0.632928i | \(0.781853\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −28.8326 | −0.0589624 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 603.190i | 1.22849i | 0.789114 | + | 0.614247i | \(0.210540\pi\) | ||||
−0.789114 | + | 0.614247i | \(0.789460\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 64.3627 | 0.130553 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 406.817 | 0.818545 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 867.976i | 1.73943i | 0.493553 | + | 0.869716i | \(0.335698\pi\) | ||||
−0.493553 | + | 0.869716i | \(0.664302\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 42.0045 | 0.0838413 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 57.8408i | − 0.114992i | −0.998346 | − | 0.0574958i | \(-0.981688\pi\) | ||||
0.998346 | − | 0.0574958i | \(-0.0183116\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 81.9060i | − 0.161550i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 168.498 | 0.331038 | 0.165519 | − | 0.986207i | \(-0.447070\pi\) | ||||
0.165519 | + | 0.986207i | \(0.447070\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 360.470i | 0.705420i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −46.7962 | −0.0912207 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1074.49 | 2.07833 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 5.32682i | − 0.0102636i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −87.1060 | −0.167190 | −0.0835951 | − | 0.996500i | \(-0.526640\pi\) | ||||
−0.0835951 | + | 0.996500i | \(0.526640\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 243.469i | 0.465524i | 0.972534 | + | 0.232762i | \(0.0747763\pi\) | ||||
−0.972534 | + | 0.232762i | \(0.925224\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1027.62i | 1.94995i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 295.969 | 0.559488 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 598.786i | − 1.12766i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 58.7743 | 0.110271 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 85.1812 | 0.158624 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 897.179i | 1.66452i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −812.616 | −1.50206 | −0.751032 | − | 0.660266i | \(-0.770443\pi\) | ||||
−0.751032 | + | 0.660266i | \(0.770443\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 137.135i | 0.252550i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 104.713i | 0.191431i | 0.995409 | + | 0.0957155i | \(0.0305139\pi\) | ||||
−0.995409 | + | 0.0957155i | \(0.969486\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 356.210 | 0.648833 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.4979i | 0.0208674i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1275.17 | −2.30592 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 260.018 | 0.466818 | 0.233409 | − | 0.972379i | \(-0.425012\pi\) | ||||
0.233409 | + | 0.972379i | \(0.425012\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 263.876i | − 0.472050i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 254.685 | 0.453984 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 39.9073i | 0.0708833i | 0.999372 | + | 0.0354416i | \(0.0112838\pi\) | ||||
−0.999372 | + | 0.0354416i | \(0.988716\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 734.014i | 1.29456i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 211.588 | 0.371860 | 0.185930 | − | 0.982563i | \(-0.440470\pi\) | ||||
0.185930 | + | 0.982563i | \(0.440470\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 556.938i | − 0.975372i | −0.873019 | − | 0.487686i | \(-0.837841\pi\) | ||||
0.873019 | − | 0.487686i | \(-0.162159\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 60.8741 | 0.106237 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −516.233 | −0.894684 | −0.447342 | − | 0.894363i | \(-0.647629\pi\) | ||||
−0.447342 | + | 0.894363i | \(0.647629\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.62577i | 0.00971636i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 755.742 | 1.30076 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1232.06i | − 2.11332i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 934.677i | 1.59229i | 0.605103 | + | 0.796147i | \(0.293132\pi\) | ||||
−0.605103 | + | 0.796147i | \(0.706868\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −183.577 | −0.311676 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 89.4050i | − 0.151277i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 634.665 | 1.07026 | 0.535131 | − | 0.844769i | \(-0.320262\pi\) | ||||
0.535131 | + | 0.844769i | \(0.320262\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 106.833 | 0.178949 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 914.029i | − 1.52593i | −0.646443 | − | 0.762963i | \(-0.723744\pi\) | ||||
0.646443 | − | 0.762963i | \(-0.276256\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −598.569 | −0.995955 | −0.497977 | − | 0.867190i | \(-0.665924\pi\) | ||||
−0.497977 | + | 0.867190i | \(0.665924\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 443.766i | 0.735930i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 201.830i | − 0.332504i | −0.986083 | − | 0.166252i | \(-0.946834\pi\) | ||||
0.986083 | − | 0.166252i | \(-0.0531664\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.1234 | −0.0215490 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 275.558i | − 0.450995i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 71.9205 | 0.117325 | 0.0586627 | − | 0.998278i | \(-0.481316\pi\) | ||||
0.0586627 | + | 0.998278i | \(0.481316\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 204.485 | 0.331418 | 0.165709 | − | 0.986175i | \(-0.447009\pi\) | ||||
0.165709 | + | 0.986175i | \(0.447009\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 287.512i | 0.464479i | 0.972659 | + | 0.232239i | \(0.0746053\pi\) | ||||
−0.972659 | + | 0.232239i | \(0.925395\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 148.008 | 0.238338 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1071.26i | 1.71952i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 45.4976i | 0.0725640i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 447.658 | 0.711699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 274.203i | 0.434554i | 0.976110 | + | 0.217277i | \(0.0697175\pi\) | ||||
−0.976110 | + | 0.217277i | \(0.930283\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 162.712 | 0.257049 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 230.085 | 0.361201 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 351.936i | − 0.550761i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 681.328 | 1.06291 | 0.531457 | − | 0.847085i | \(-0.321645\pi\) | ||||
0.531457 | + | 0.847085i | \(0.321645\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 527.270i | − 0.820016i | −0.912082 | − | 0.410008i | \(-0.865526\pi\) | ||||
0.912082 | − | 0.410008i | \(-0.134474\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 551.627i | − 0.852592i | −0.904584 | − | 0.426296i | \(-0.859818\pi\) | ||||
0.904584 | − | 0.426296i | \(-0.140182\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1184.42 | −1.82499 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 209.529i | − 0.321857i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −699.422 | −1.07109 | −0.535545 | − | 0.844507i | \(-0.679894\pi\) | ||||
−0.535545 | + | 0.844507i | \(0.679894\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 311.842 | 0.474645 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 38.3257i | − 0.0581574i | −0.999577 | − | 0.0290787i | \(-0.990743\pi\) | ||||
0.999577 | − | 0.0290787i | \(-0.00925734\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 392.364 | 0.593591 | 0.296796 | − | 0.954941i | \(-0.404082\pi\) | ||||
0.296796 | + | 0.954941i | \(0.404082\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 65.3150i | − 0.0985143i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 36.3658i | − 0.0545215i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 222.035 | 0.331890 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 704.594i | − 1.05007i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 427.290 | 0.634904 | 0.317452 | − | 0.948274i | \(-0.397173\pi\) | ||||
0.317452 | + | 0.948274i | \(0.397173\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −131.234 | −0.193847 | −0.0969233 | − | 0.995292i | \(-0.530900\pi\) | ||||
−0.0969233 | + | 0.995292i | \(0.530900\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 859.186i | 1.26537i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.0495 | 0.0294413 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 896.229i | 1.31219i | 0.754676 | + | 0.656097i | \(0.227794\pi\) | ||||
−0.754676 | + | 0.656097i | \(0.772206\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 49.9285i | 0.0726761i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −315.968 | −0.458589 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 520.465i | 0.753206i | 0.926375 | + | 0.376603i | \(0.122908\pi\) | ||||
−0.926375 | + | 0.376603i | \(0.877092\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1505.62 | 2.17262 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −359.812 | −0.516230 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 185.589i | − 0.265507i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 80.7527 | 0.115196 | 0.0575982 | − | 0.998340i | \(-0.481656\pi\) | ||||
0.0575982 | + | 0.998340i | \(0.481656\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 79.9709i | 0.113757i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 837.591i | − 1.18471i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 174.828 | 0.246584 | 0.123292 | − | 0.992370i | \(-0.460655\pi\) | ||||
0.123292 | + | 0.992370i | \(0.460655\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1103.15i | 1.55155i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 580.621 | 0.814335 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.8715 | −0.0235307 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 889.905i | − 1.23770i | −0.785510 | − | 0.618849i | \(-0.787599\pi\) | ||||
0.785510 | − | 0.618849i | \(-0.212401\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 475.328 | 0.659263 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 131.622i | 0.182050i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 408.818i | − 0.562335i | −0.959659 | − | 0.281168i | \(-0.909278\pi\) | ||||
0.959659 | − | 0.281168i | \(-0.0907217\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 587.194 | 0.805478 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1615.43i | 2.20989i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −388.369 | −0.529835 | −0.264917 | − | 0.964271i | \(-0.585345\pi\) | ||||
−0.264917 | + | 0.964271i | \(0.585345\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 877.783 | 1.19102 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 109.561i | − 0.148256i | −0.997249 | − | 0.0741280i | \(-0.976383\pi\) | ||||
0.997249 | − | 0.0741280i | \(-0.0236173\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.6680 | 0.0157463 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 732.717i | 0.986160i | 0.869984 | + | 0.493080i | \(0.164129\pi\) | ||||
−0.869984 | + | 0.493080i | \(0.835871\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 653.791i | − 0.875222i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1907.02 | −2.54608 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 420.809i | − 0.560332i | −0.959952 | − | 0.280166i | \(-0.909610\pi\) | ||||
0.959952 | − | 0.280166i | \(-0.0903895\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −47.1238 | −0.0625814 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1306.99 | −1.72654 | −0.863269 | − | 0.504744i | \(-0.831587\pi\) | ||||
−0.863269 | + | 0.504744i | \(0.831587\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 143.901i | − 0.189592i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1402.25 | −1.84264 | −0.921320 | − | 0.388804i | \(-0.872888\pi\) | ||||
−0.921320 | + | 0.388804i | \(0.872888\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 850.402i | − 1.11455i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 303.748i | 0.396021i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 359.952 | 0.468078 | 0.234039 | − | 0.972227i | \(-0.424806\pi\) | ||||
0.234039 | + | 0.972227i | \(0.424806\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 194.990i | − 0.252905i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −437.539 | −0.566027 | −0.283013 | − | 0.959116i | \(-0.591334\pi\) | ||||
−0.283013 | + | 0.959116i | \(0.591334\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −91.2762 | −0.117473 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 64.2778i | − 0.0825132i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −696.141 | −0.891346 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 23.0975i | 0.0294988i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 438.946i | 0.557746i | 0.960328 | + | 0.278873i | \(0.0899608\pi\) | ||||
−0.960328 | + | 0.278873i | \(0.910039\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −40.0567 | −0.0507690 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 1152.07i | − 1.45647i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −180.696 | −0.227864 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −982.414 | −1.23264 | −0.616320 | − | 0.787496i | \(-0.711377\pi\) | ||||
−0.616320 | + | 0.787496i | \(0.711377\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1686.95i | 2.11133i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 926.745 | 1.15699 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 616.832i | − 0.768160i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 146.806i | − 0.181916i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 449.408 | 0.555510 | 0.277755 | − | 0.960652i | \(-0.410410\pi\) | ||||
0.277755 | + | 0.960652i | \(0.410410\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 610.106i | 0.752288i | 0.926561 | + | 0.376144i | \(0.122750\pi\) | ||||
−0.926561 | + | 0.376144i | \(0.877250\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −125.667 | −0.154572 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −288.585 | −0.353225 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 386.123i | − 0.471456i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1099.76 | −1.33954 | −0.669770 | − | 0.742568i | \(-0.733607\pi\) | ||||
−0.669770 | + | 0.742568i | \(0.733607\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 236.092i | 0.286867i | 0.989660 | + | 0.143434i | \(0.0458143\pi\) | ||||
−0.989660 | + | 0.143434i | \(0.954186\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1266.81i | 1.53182i | 0.642950 | + | 0.765908i | \(0.277710\pi\) | ||||
−0.642950 | + | 0.765908i | \(0.722290\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.7642 | 0.0503790 | 0.0251895 | − | 0.999683i | \(-0.491981\pi\) | ||||
0.0251895 | + | 0.999683i | \(0.491981\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 69.1993i | 0.0832723i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1408.57 | −1.69095 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −368.778 | −0.440595 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 816.273i | 0.972912i | 0.873705 | + | 0.486456i | \(0.161711\pi\) | ||||
−0.873705 | + | 0.486456i | \(0.838289\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −835.325 | −0.993252 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 251.293i | − 0.298093i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 1761.32i | − 2.07948i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 255.024 | 0.300381 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 252.933i | − 0.297219i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1215.58 | −1.42507 | −0.712533 | − | 0.701639i | \(-0.752452\pi\) | ||||
−0.712533 | + | 0.701639i | \(0.752452\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −997.998 | −1.16452 | −0.582262 | − | 0.813001i | \(-0.697832\pi\) | ||||
−0.582262 | + | 0.813001i | \(0.697832\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1110.42i | − 1.29269i | −0.763044 | − | 0.646347i | \(-0.776296\pi\) | ||||
0.763044 | − | 0.646347i | \(-0.223704\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 73.3646 | 0.0852086 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1372.33i | − 1.59019i | −0.606486 | − | 0.795094i | \(-0.707422\pi\) | ||||
0.606486 | − | 0.795094i | \(-0.292578\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 241.545i | 0.278599i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2182.06 | 2.51101 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 225.111i | − 0.258451i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 743.280 | 0.851409 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 776.337 | 0.885219 | 0.442609 | − | 0.896714i | \(-0.354053\pi\) | ||||
0.442609 | + | 0.896714i | \(0.354053\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 90.5034i | 0.102962i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1047.38 | 1.18885 | 0.594427 | − | 0.804150i | \(-0.297379\pi\) | ||||
0.594427 | + | 0.804150i | \(0.297379\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1175.41i | − 1.33116i | −0.746327 | − | 0.665579i | \(-0.768185\pi\) | ||||
0.746327 | − | 0.665579i | \(-0.231815\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 109.768i | − 0.123752i | −0.998084 | − | 0.0618762i | \(-0.980292\pi\) | ||||
0.998084 | − | 0.0618762i | \(-0.0197084\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −446.634 | −0.502401 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 1256.04i | − 1.40969i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −301.361 | −0.337470 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −36.9039 | −0.0411414 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 90.6094i | 0.100789i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1934.33 | 2.14687 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 329.382i | − 0.364764i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1639.15i | − 1.80722i | −0.428358 | − | 0.903609i | \(-0.640908\pi\) | ||||
0.428358 | − | 0.903609i | \(-0.359092\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −724.598 | −0.797137 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.82023i | 0.00748654i | 0.999993 | + | 0.00374327i | \(0.00119152\pi\) | ||||
−0.999993 | + | 0.00374327i | \(0.998808\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1293.22 | −1.41645 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 473.867 | 0.516757 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 72.4188i | 0.0788017i | 0.999223 | + | 0.0394009i | \(0.0125449\pi\) | ||||
−0.999223 | + | 0.0394009i | \(0.987455\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 128.914 | 0.139972 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 178.528i | 0.193421i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 411.205i | − 0.443587i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 368.537 | 0.396703 | 0.198352 | − | 0.980131i | \(-0.436441\pi\) | ||||
0.198352 | + | 0.980131i | \(0.436441\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 251.630i | − 0.270279i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 115.399 | 0.123686 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −590.172 | −0.629852 | −0.314926 | − | 0.949116i | \(-0.601980\pi\) | ||||
−0.314926 | + | 0.949116i | \(0.601980\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 174.599i | − 0.185941i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −189.017 | −0.200869 | −0.100434 | − | 0.994944i | \(-0.532023\pi\) | ||||
−0.100434 | + | 0.994944i | \(0.532023\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 203.299i | 0.215588i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 664.319i | − 0.701498i | −0.936470 | − | 0.350749i | \(-0.885927\pi\) | ||||
0.936470 | − | 0.350749i | \(-0.114073\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −158.189 | −0.166690 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 38.5610i | 0.0405479i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 173.943 | 0.182522 | 0.0912610 | − | 0.995827i | \(-0.470910\pi\) | ||||
0.0912610 | + | 0.995827i | \(0.470910\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22.4566 | 0.0234656 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 632.175i | 0.659202i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −485.680 | −0.505390 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1649.76i | 1.71314i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 255.364i | − 0.264078i | −0.991245 | − | 0.132039i | \(-0.957848\pi\) | ||||
0.991245 | − | 0.132039i | \(-0.0421524\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −71.4309 | −0.0737161 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1623.60i | − 1.67209i | −0.548659 | − | 0.836046i | \(-0.684861\pi\) | ||||
0.548659 | − | 0.836046i | \(-0.315139\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1290.46 | 1.32627 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 104.946 | 0.107416 | 0.0537082 | − | 0.998557i | \(-0.482896\pi\) | ||||
0.0537082 | + | 0.998557i | \(0.482896\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1833.13i | − 1.87245i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −735.681 | −0.749930 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 889.933i | − 0.905323i | −0.891682 | − | 0.452662i | \(-0.850475\pi\) | ||||
0.891682 | − | 0.452662i | \(-0.149525\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 343.964i | − 0.348494i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 912.742 | 0.922894 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1509.57i | 1.52328i | 0.648001 | + | 0.761639i | \(0.275605\pi\) | ||||
−0.648001 | + | 0.761639i | \(0.724395\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 153.821 | 0.154905 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1599.93 | −1.60474 | −0.802371 | − | 0.596825i | \(-0.796429\pi\) | ||||
−0.802371 | + | 0.596825i | \(0.796429\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 160.649i | 0.160810i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 800.3.b.i.351.4 | 6 | ||
4.3 | odd | 2 | inner | 800.3.b.i.351.3 | 6 | ||
5.2 | odd | 4 | 160.3.h.a.159.4 | yes | 6 | ||
5.3 | odd | 4 | 160.3.h.b.159.3 | yes | 6 | ||
5.4 | even | 2 | 800.3.b.h.351.3 | 6 | |||
8.3 | odd | 2 | 1600.3.b.w.1151.4 | 6 | |||
8.5 | even | 2 | 1600.3.b.w.1151.3 | 6 | |||
15.2 | even | 4 | 1440.3.j.a.1279.5 | 6 | |||
15.8 | even | 4 | 1440.3.j.b.1279.6 | 6 | |||
20.3 | even | 4 | 160.3.h.a.159.3 | ✓ | 6 | ||
20.7 | even | 4 | 160.3.h.b.159.4 | yes | 6 | ||
20.19 | odd | 2 | 800.3.b.h.351.4 | 6 | |||
40.3 | even | 4 | 320.3.h.g.319.4 | 6 | |||
40.13 | odd | 4 | 320.3.h.f.319.4 | 6 | |||
40.19 | odd | 2 | 1600.3.b.v.1151.3 | 6 | |||
40.27 | even | 4 | 320.3.h.f.319.3 | 6 | |||
40.29 | even | 2 | 1600.3.b.v.1151.4 | 6 | |||
40.37 | odd | 4 | 320.3.h.g.319.3 | 6 | |||
60.23 | odd | 4 | 1440.3.j.a.1279.6 | 6 | |||
60.47 | odd | 4 | 1440.3.j.b.1279.5 | 6 | |||
80.3 | even | 4 | 1280.3.e.i.639.4 | 6 | |||
80.13 | odd | 4 | 1280.3.e.h.639.3 | 6 | |||
80.27 | even | 4 | 1280.3.e.h.639.4 | 6 | |||
80.37 | odd | 4 | 1280.3.e.i.639.3 | 6 | |||
80.43 | even | 4 | 1280.3.e.g.639.3 | 6 | |||
80.53 | odd | 4 | 1280.3.e.f.639.4 | 6 | |||
80.67 | even | 4 | 1280.3.e.f.639.3 | 6 | |||
80.77 | odd | 4 | 1280.3.e.g.639.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.3.h.a.159.3 | ✓ | 6 | 20.3 | even | 4 | ||
160.3.h.a.159.4 | yes | 6 | 5.2 | odd | 4 | ||
160.3.h.b.159.3 | yes | 6 | 5.3 | odd | 4 | ||
160.3.h.b.159.4 | yes | 6 | 20.7 | even | 4 | ||
320.3.h.f.319.3 | 6 | 40.27 | even | 4 | |||
320.3.h.f.319.4 | 6 | 40.13 | odd | 4 | |||
320.3.h.g.319.3 | 6 | 40.37 | odd | 4 | |||
320.3.h.g.319.4 | 6 | 40.3 | even | 4 | |||
800.3.b.h.351.3 | 6 | 5.4 | even | 2 | |||
800.3.b.h.351.4 | 6 | 20.19 | odd | 2 | |||
800.3.b.i.351.3 | 6 | 4.3 | odd | 2 | inner | ||
800.3.b.i.351.4 | 6 | 1.1 | even | 1 | trivial | ||
1280.3.e.f.639.3 | 6 | 80.67 | even | 4 | |||
1280.3.e.f.639.4 | 6 | 80.53 | odd | 4 | |||
1280.3.e.g.639.3 | 6 | 80.43 | even | 4 | |||
1280.3.e.g.639.4 | 6 | 80.77 | odd | 4 | |||
1280.3.e.h.639.3 | 6 | 80.13 | odd | 4 | |||
1280.3.e.h.639.4 | 6 | 80.27 | even | 4 | |||
1280.3.e.i.639.3 | 6 | 80.37 | odd | 4 | |||
1280.3.e.i.639.4 | 6 | 80.3 | even | 4 | |||
1440.3.j.a.1279.5 | 6 | 15.2 | even | 4 | |||
1440.3.j.a.1279.6 | 6 | 60.23 | odd | 4 | |||
1440.3.j.b.1279.5 | 6 | 60.47 | odd | 4 | |||
1440.3.j.b.1279.6 | 6 | 15.8 | even | 4 | |||
1600.3.b.v.1151.3 | 6 | 40.19 | odd | 2 | |||
1600.3.b.v.1151.4 | 6 | 40.29 | even | 2 | |||
1600.3.b.w.1151.3 | 6 | 8.5 | even | 2 | |||
1600.3.b.w.1151.4 | 6 | 8.3 | odd | 2 |