Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,3,Mod(1279,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1440.1279");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.j (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: | \(39.2371580679\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
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 | 1279.5 | ||
Root | \(2.65109i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1440.1279 |
Dual form | 1440.3.j.b.1279.6 |
$q$-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 \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.75441 | − | 3.30219i | 0.750881 | − | 0.660437i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.0566 | 1.43666 | 0.718328 | − | 0.695705i | \(-0.244908\pi\) | ||||
0.718328 | + | 0.695705i | \(0.244908\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 17.2087i | − | 1.56443i | −0.623008 | − | 0.782216i | \(-0.714089\pi\) | ||
0.623008 | − | 0.782216i | \(-0.285911\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.41325i | 0.339481i | 0.985489 | + | 0.169740i | \(0.0542929\pi\) | ||||
−0.985489 | + | 0.169740i | \(0.945707\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 27.0176i | − | 1.58927i | −0.607086 | − | 0.794636i | \(-0.707662\pi\) | ||
0.607086 | − | 0.794636i | \(-0.292338\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.82650i | 0.254026i | 0.991901 | + | 0.127013i | \(0.0405390\pi\) | ||||
−0.991901 | + | 0.127013i | \(0.959461\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −15.2653 | −0.663710 | −0.331855 | − | 0.943330i | \(-0.607675\pi\) | ||||
−0.331855 | + | 0.943330i | \(0.607675\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.19112 | − | 24.7955i | 0.127645 | − | 0.991820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 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 | \(-0.789772\pi\) | ||
0.789717 | − | 0.613472i | \(-0.210228\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 37.7565 | − | 33.2087i | 1.07876 | − | 0.948821i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 16.5691i | 0.447814i | 0.974610 | + | 0.223907i | \(0.0718812\pi\) | ||||
−0.974610 | + | 0.223907i | \(0.928119\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13.3177 | 0.324822 | 0.162411 | − | 0.986723i | \(-0.448073\pi\) | ||||
0.162411 | + | 0.986723i | \(0.448073\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −59.7918 | −1.39051 | −0.695253 | − | 0.718765i | \(-0.744708\pi\) | ||||
−0.695253 | + | 0.718765i | \(0.744708\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −62.4388 | −1.32849 | −0.664243 | − | 0.747517i | \(-0.731246\pi\) | ||||
−0.664243 | + | 0.747517i | \(0.731246\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 52.1351 | 1.06398 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 71.5952i | 1.35085i | 0.737427 | + | 0.675427i | \(0.236041\pi\) | ||||
−0.737427 | + | 0.675427i | \(0.763959\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −56.8265 | − | 64.6086i | −1.03321 | − | 1.17470i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 68.8265i | 1.16655i | 0.812274 | + | 0.583275i | \(0.198229\pi\) | ||||
−0.812274 | + | 0.583275i | \(0.801771\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 40.9439 | 0.671212 | 0.335606 | − | 0.942002i | \(-0.391059\pi\) | ||||
0.335606 | + | 0.942002i | \(0.391059\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.5734 | + | 16.5691i | 0.224206 | + | 0.254910i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 51.0080 | 0.761313 | 0.380656 | − | 0.924717i | \(-0.375698\pi\) | ||||
0.380656 | + | 0.924717i | \(0.375698\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 40.4527i | − | 0.569757i | −0.958564 | − | 0.284878i | \(-0.908047\pi\) | ||
0.958564 | − | 0.284878i | \(-0.0919532\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 35.8441i | − | 0.491015i | −0.969395 | − | 0.245508i | \(-0.921045\pi\) | ||
0.969395 | − | 0.245508i | \(-0.0789547\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 173.061i | − | 2.24755i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 126.800i | 1.60506i | 0.596612 | + | 0.802530i | \(0.296513\pi\) | ||||
−0.596612 | + | 0.802530i | \(0.703487\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −75.1490 | −0.905409 | −0.452705 | − | 0.891661i | \(-0.649541\pi\) | ||||
−0.452705 | + | 0.891661i | \(0.649541\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −89.2172 | − | 101.435i | −1.04961 | − | 1.19335i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 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 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.9380 | + | 18.1206i | 0.167768 | + | 0.190744i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 85.4351i | 0.880774i | 0.897808 | + | 0.440387i | \(0.145159\pi\) | ||||
−0.897808 | + | 0.440387i | \(0.854841\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 83.2877 | 0.824631 | 0.412315 | − | 0.911041i | \(-0.364720\pi\) | ||||
0.412315 | + | 0.911041i | \(0.364720\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 47.2653 | 0.458887 | 0.229443 | − | 0.973322i | \(-0.426309\pi\) | ||||
0.229443 | + | 0.973322i | \(0.426309\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −189.628 | −1.77223 | −0.886114 | − | 0.463467i | \(-0.846605\pi\) | ||||
−0.886114 | + | 0.463467i | \(0.846605\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 84.5617 | 0.775795 | 0.387898 | − | 0.921702i | \(-0.373201\pi\) | ||||
0.387898 | + | 0.921702i | \(0.373201\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 114.558i | − | 1.01379i | −0.862007 | − | 0.506896i | \(-0.830793\pi\) | ||
0.862007 | − | 0.506896i | \(-0.169207\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −57.3123 | + | 50.4090i | −0.498368 | + | 0.438339i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 271.705i | − | 2.28324i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −175.141 | −1.44745 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −69.8986 | − | 103.630i | −0.559189 | − | 0.829040i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 44.4121 | 0.349701 | 0.174851 | − | 0.984595i | \(-0.444056\pi\) | ||||
0.174851 | + | 0.984595i | \(0.444056\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 47.1200i | − | 0.359695i | −0.983695 | − | 0.179847i | \(-0.942440\pi\) | ||
0.983695 | − | 0.179847i | \(-0.0575604\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 48.5381i | 0.364948i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 62.8617i | − | 0.458845i | −0.973327 | − | 0.229422i | \(-0.926316\pi\) | ||
0.973327 | − | 0.229422i | \(-0.0736837\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 128.320i | − | 0.923167i | −0.887097 | − | 0.461584i | \(-0.847281\pi\) | ||
0.887097 | − | 0.461584i | \(-0.152719\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 75.9465 | 0.531094 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.94393 | − | 7.86663i | 0.0616823 | − | 0.0542526i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 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 | \(-0.742438\pi\) | ||
0.690111 | − | 0.723704i | \(-0.257562\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −125.599 | − | 142.800i | −0.810319 | − | 0.921289i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 174.293i | − | 1.11014i | −0.831802 | − | 0.555072i | \(-0.812691\pi\) | ||
0.831802 | − | 0.555072i | \(-0.187309\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −153.517 | −0.953524 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −52.6353 | −0.322916 | −0.161458 | − | 0.986880i | \(-0.551620\pi\) | ||||
−0.161458 | + | 0.986880i | \(0.551620\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 76.6812 | 0.459169 | 0.229584 | − | 0.973289i | \(-0.426263\pi\) | ||||
0.229584 | + | 0.973289i | \(0.426263\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 149.523 | 0.884753 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 9.72437i | − | 0.0562102i | −0.999605 | − | 0.0281051i | \(-0.991053\pi\) | ||
0.999605 | − | 0.0281051i | \(-0.00894731\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 32.0918 | − | 249.358i | 0.183382 | − | 1.42490i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 155.502i | 0.868728i | 0.900738 | + | 0.434364i | \(0.143027\pi\) | ||||
−0.900738 | + | 0.434364i | \(0.856973\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 250.346 | 1.38313 | 0.691563 | − | 0.722316i | \(-0.256923\pi\) | ||||
0.691563 | + | 0.722316i | \(0.256923\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 54.7144 | + | 62.2072i | 0.295753 | + | 0.336255i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −464.939 | −2.48631 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 111.128i | − | 0.581825i | −0.956750 | − | 0.290912i | \(-0.906041\pi\) | ||
0.956750 | − | 0.290912i | \(-0.0939588\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 10.2701i | − | 0.0532130i | −0.999646 | − | 0.0266065i | \(-0.991530\pi\) | ||
0.999646 | − | 0.0266065i | \(-0.00847011\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 163.213i | 0.828492i | 0.910165 | + | 0.414246i | \(0.135955\pi\) | ||||
−0.910165 | + | 0.414246i | \(0.864045\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 195.028i | − | 0.980041i | −0.871711 | − | 0.490021i | \(-0.836989\pi\) | ||
0.871711 | − | 0.490021i | \(-0.163011\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 23.9573 | 0.118016 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 50.0000 | − | 43.9775i | 0.243902 | − | 0.214524i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 83.0580 | 0.397407 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 297.038i | 1.40776i | 0.710317 | + | 0.703881i | \(0.248551\pi\) | ||||
−0.710317 | + | 0.703881i | \(0.751449\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −224.483 | + | 197.444i | −1.04411 | + | 0.918342i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 382.505i | − | 1.76270i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 119.236 | 0.539527 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 405.335 | 1.81764 | 0.908822 | − | 0.417184i | \(-0.136983\pi\) | ||||
0.908822 | + | 0.417184i | \(0.136983\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 36.6013 | 0.161239 | 0.0806196 | − | 0.996745i | \(-0.474310\pi\) | ||||
0.0806196 | + | 0.996745i | \(0.474310\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −91.1467 | −0.398021 | −0.199010 | − | 0.979997i | \(-0.563773\pi\) | ||||
−0.199010 | + | 0.979997i | \(0.563773\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 338.802i | − | 1.45409i | −0.686592 | − | 0.727043i | \(-0.740894\pi\) | ||
0.686592 | − | 0.727043i | \(-0.259106\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −234.421 | + | 206.185i | −0.997535 | + | 0.877382i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 30.7997i | − | 0.128869i | −0.997922 | − | 0.0644346i | \(-0.979476\pi\) | ||
0.997922 | − | 0.0644346i | \(-0.0205244\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 240.282 | 0.997020 | 0.498510 | − | 0.866884i | \(-0.333881\pi\) | ||||
0.498510 | + | 0.866884i | \(0.333881\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 195.736 | − | 172.160i | 0.798923 | − | 0.702693i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.3005 | −0.0862370 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 86.0268i | 0.342736i | 0.985207 | + | 0.171368i | \(0.0548187\pi\) | ||||
−0.985207 | + | 0.171368i | \(0.945181\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 262.697i | 1.03833i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 355.963i | 1.38507i | 0.721383 | + | 0.692536i | \(0.243507\pi\) | ||||
−0.721383 | + | 0.692536i | \(0.756493\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 166.629i | 0.643355i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 73.1254 | 0.278043 | 0.139022 | − | 0.990289i | \(-0.455604\pi\) | ||||
0.139022 | + | 0.990289i | \(0.455604\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 236.421 | + | 268.798i | 0.892154 | + | 1.01433i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 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 | \(-0.860883\pi\) | ||
0.906004 | − | 0.423269i | \(-0.139117\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −426.699 | − | 54.9153i | −1.55163 | − | 0.199692i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 126.327i | 0.456053i | 0.973655 | + | 0.228026i | \(0.0732272\pi\) | ||||
−0.973655 | + | 0.228026i | \(0.926773\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 458.746 | 1.63255 | 0.816275 | − | 0.577664i | \(-0.196036\pi\) | ||||
0.816275 | + | 0.577664i | \(0.196036\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 465.558 | 1.64508 | 0.822541 | − | 0.568706i | \(-0.192556\pi\) | ||||
0.822541 | + | 0.568706i | \(0.192556\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 133.931 | 0.466657 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −440.952 | −1.52579 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 165.218i | 0.563884i | 0.959431 | + | 0.281942i | \(0.0909786\pi\) | ||||
−0.959431 | + | 0.281942i | \(0.909021\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 227.278 | + | 258.403i | 0.770434 | + | 0.875941i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 67.3697i | − | 0.225317i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −601.302 | −1.99768 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 153.720 | − | 135.205i | 0.504000 | − | 0.443293i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −235.339 | −0.766577 | −0.383288 | − | 0.923629i | \(-0.625208\pi\) | ||||
−0.383288 | + | 0.923629i | \(0.625208\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 210.665i | − | 0.677381i | −0.940898 | − | 0.338691i | \(-0.890016\pi\) | ||
0.940898 | − | 0.338691i | \(-0.109984\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 318.738i | 1.01833i | 0.860668 | + | 0.509166i | \(0.170046\pi\) | ||||
−0.860668 | + | 0.509166i | \(0.829954\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 70.3950i | − | 0.222066i | −0.993817 | − | 0.111033i | \(-0.964584\pi\) | ||
0.993817 | − | 0.111033i | \(-0.0354160\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 40.9955i | − | 0.128513i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 130.401 | 0.403717 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 109.429 | + | 14.0832i | 0.336704 | + | 0.0433330i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −627.922 | −1.90858 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 280.807i | 0.848359i | 0.905578 | + | 0.424180i | \(0.139438\pi\) | ||||
−0.905578 | + | 0.424180i | \(0.860562\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 191.505 | − | 168.438i | 0.571656 | − | 0.502800i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 120.969i | − | 0.358959i | −0.983762 | − | 0.179480i | \(-0.942559\pi\) | ||
0.983762 | − | 0.179480i | \(-0.0574414\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −654.539 | −1.91947 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 31.5280 | 0.0919182 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 214.333 | 0.617675 | 0.308838 | − | 0.951115i | \(-0.400060\pi\) | ||||
0.308838 | + | 0.951115i | \(0.400060\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −418.041 | −1.19782 | −0.598912 | − | 0.800815i | \(-0.704400\pi\) | ||||
−0.598912 | + | 0.800815i | \(0.704400\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 364.929i | 1.03379i | 0.856048 | + | 0.516897i | \(0.172913\pi\) | ||||
−0.856048 | + | 0.516897i | \(0.827087\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −133.583 | − | 151.876i | −0.376289 | − | 0.427820i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 242.169i | 0.674567i | 0.941403 | + | 0.337283i | \(0.109508\pi\) | ||||
−0.941403 | + | 0.337283i | \(0.890492\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 337.705 | 0.935471 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −118.364 | − | 134.573i | −0.324285 | − | 0.368694i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −224.564 | −0.611891 | −0.305945 | − | 0.952049i | \(-0.598972\pi\) | ||||
−0.305945 | + | 0.952049i | \(0.598972\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 720.004i | 1.94071i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 572.174i | 1.53398i | 0.641660 | + | 0.766989i | \(0.278246\pi\) | ||||
−0.641660 | + | 0.766989i | \(0.721754\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.5135i | 0.0278872i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 122.896i | − | 0.324263i | −0.986769 | − | 0.162132i | \(-0.948163\pi\) | ||
0.986769 | − | 0.162132i | \(-0.0518369\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 289.717 | 0.756442 | 0.378221 | − | 0.925715i | \(-0.376536\pi\) | ||||
0.378221 | + | 0.925715i | \(0.376536\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −571.481 | − | 649.743i | −1.48437 | − | 1.68764i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 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 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 418.716 | + | 476.058i | 1.06004 | + | 1.20521i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 705.314i | − | 1.77661i | −0.459253 | − | 0.888305i | \(-0.651883\pi\) | ||
0.459253 | − | 0.888305i | \(-0.348117\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −432.052 | −1.07744 | −0.538718 | − | 0.842486i | \(-0.681091\pi\) | ||||
−0.538718 | + | 0.842486i | \(0.681091\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 167.859 | 0.416524 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 285.134 | 0.700575 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −98.8102 | −0.241590 | −0.120795 | − | 0.992677i | \(-0.538544\pi\) | ||||
−0.120795 | + | 0.992677i | \(0.538544\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 692.160i | 1.67593i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −282.140 | + | 248.156i | −0.679855 | + | 0.597966i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 204.980i | − | 0.489213i | −0.969622 | − | 0.244607i | \(-0.921341\pi\) | ||
0.969622 | − | 0.244607i | \(-0.0786588\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 449.956 | 1.06878 | 0.534390 | − | 0.845238i | \(-0.320541\pi\) | ||||
0.534390 | + | 0.845238i | \(0.320541\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −669.915 | − | 86.2166i | −1.57627 | − | 0.202863i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 411.756 | 0.964301 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 314.588i | − | 0.729903i | −0.931026 | − | 0.364952i | \(-0.881086\pi\) | ||
0.931026 | − | 0.364952i | \(-0.118914\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 330.441i | 0.763143i | 0.924339 | + | 0.381571i | \(0.124617\pi\) | ||||
−0.924339 | + | 0.381571i | \(0.875383\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 73.6781i | − | 0.168600i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 664.815i | − | 1.51439i | −0.653191 | − | 0.757193i | \(-0.726570\pi\) | ||
0.653191 | − | 0.757193i | \(-0.273430\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 312.860 | 0.706229 | 0.353115 | − | 0.935580i | \(-0.385123\pi\) | ||||
0.353115 | + | 0.935580i | \(0.385123\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 399.931 | − | 351.760i | 0.898722 | − | 0.790471i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 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 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 146.558 | + | 166.629i | 0.322107 | + | 0.366218i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 707.094i | 1.54725i | 0.633642 | + | 0.773626i | \(0.281559\pi\) | ||||
−0.633642 | + | 0.773626i | \(0.718441\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 611.288 | 1.32600 | 0.663002 | − | 0.748618i | \(-0.269282\pi\) | ||||
0.663002 | + | 0.748618i | \(0.269282\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 334.063 | 0.721519 | 0.360760 | − | 0.932659i | \(-0.382518\pi\) | ||||
0.360760 | + | 0.932659i | \(0.382518\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 128.864 | 0.275939 | 0.137970 | − | 0.990436i | \(-0.455942\pi\) | ||||
0.137970 | + | 0.990436i | \(0.455942\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 512.966 | 1.09374 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1028.94i | 2.17535i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 119.675 | + | 15.4020i | 0.251948 | + | 0.0324252i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 510.257i | 1.06525i | 0.846350 | + | 0.532627i | \(0.178795\pi\) | ||||
−0.846350 | + | 0.532627i | \(0.821205\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −73.1237 | −0.152024 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 282.123 | + | 320.758i | 0.581696 | + | 0.661357i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 616.472 | 1.26586 | 0.632928 | − | 0.774211i | \(-0.281853\pi\) | ||||
0.632928 | + | 0.774211i | \(0.281853\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 603.190i | 1.22849i | 0.789114 | + | 0.614247i | \(0.210540\pi\) | ||||
−0.789114 | + | 0.614247i | \(0.789460\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 64.3627i | − | 0.130553i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 406.817i | − | 0.818545i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 867.976i | 1.73943i | 0.493553 | + | 0.869716i | \(0.335698\pi\) | ||||
−0.493553 | + | 0.869716i | \(0.664302\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −57.8408 | −0.114992 | −0.0574958 | − | 0.998346i | \(-0.518312\pi\) | ||||
−0.0574958 | + | 0.998346i | \(0.518312\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 312.696 | − | 275.032i | 0.619200 | − | 0.544617i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 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 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 177.453 | − | 156.079i | 0.344569 | − | 0.303066i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1074.49i | 2.07833i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 87.1060 | 0.167190 | 0.0835951 | − | 0.996500i | \(-0.473360\pi\) | ||||
0.0835951 | + | 0.996500i | \(0.473360\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −243.469 | −0.465524 | −0.232762 | − | 0.972534i | \(-0.574776\pi\) | ||||
−0.232762 | + | 0.972534i | \(0.574776\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1027.62 | −1.94995 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −295.969 | −0.559488 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 58.7743i | 0.110271i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −711.942 | + | 626.189i | −1.33073 | + | 1.17045i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 317.479 | − | 279.238i | 0.582530 | − | 0.512364i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 104.713 | 0.191431 | 0.0957155 | − | 0.995409i | \(-0.469486\pi\) | ||||
0.0957155 | + | 0.995409i | \(0.469486\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.4979i | 0.0208674i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1275.17i | 2.30592i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 260.018i | − | 0.466818i | −0.972379 | − | 0.233409i | \(-0.925012\pi\) | ||
0.972379 | − | 0.233409i | \(-0.0749882\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 263.876i | − | 0.472050i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 39.9073 | 0.0708833 | 0.0354416 | − | 0.999372i | \(-0.488716\pi\) | ||||
0.0354416 | + | 0.999372i | \(0.488716\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −378.293 | − | 430.099i | −0.669546 | − | 0.761237i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 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 | \(0.162159\pi\) | ||||
−0.873019 | + | 0.487686i | \(0.837841\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −48.7136 | + | 378.512i | −0.0847193 | + | 0.658281i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 516.233i | − | 0.894684i | −0.894363 | − | 0.447342i | \(-0.852371\pi\) | ||
0.894363 | − | 0.447342i | \(-0.147629\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −755.742 | −1.30076 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1232.06 | 2.11332 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −934.677 | −1.59229 | −0.796147 | − | 0.605103i | \(-0.793132\pi\) | ||||
−0.796147 | + | 0.605103i | \(0.793132\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 183.577 | 0.311676 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 634.665i | 1.07026i | 0.844769 | + | 0.535131i | \(0.179738\pi\) | ||||
−0.844769 | + | 0.535131i | \(0.820262\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −897.221 | − | 1020.09i | −1.50794 | − | 1.71444i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 914.029i | 1.52593i | 0.646443 | + | 0.762963i | \(0.276256\pi\) | ||||
−0.646443 | + | 0.762963i | \(0.723744\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −598.569 | −0.995955 | −0.497977 | − | 0.867190i | \(-0.665924\pi\) | ||||
−0.497977 | + | 0.867190i | \(0.665924\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −657.550 | + | 578.348i | −1.08686 | + | 0.955948i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −201.830 | −0.332504 | −0.166252 | − | 0.986083i | \(-0.553166\pi\) | ||||
−0.166252 | + | 0.986083i | \(0.553166\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 275.558i | − | 0.450995i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 71.9205i | − | 0.117325i | −0.998278 | − | 0.0586627i | \(-0.981316\pi\) | ||
0.998278 | − | 0.0586627i | \(-0.0186836\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 204.485i | − | 0.331418i | −0.986175 | − | 0.165709i | \(-0.947009\pi\) | ||
0.986175 | − | 0.165709i | \(-0.0529912\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 287.512i | 0.464479i | 0.972659 | + | 0.232239i | \(0.0746053\pi\) | ||||
−0.972659 | + | 0.232239i | \(0.925395\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1071.26 | 1.71952 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −604.633 | − | 158.251i | −0.967414 | − | 0.253202i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 447.658 | 0.711699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 274.203i | − | 0.434554i | −0.976110 | − | 0.217277i | \(-0.930283\pi\) | ||
0.976110 | − | 0.217277i | \(-0.0697175\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 166.741 | − | 146.657i | 0.262584 | − | 0.230956i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 230.085i | 0.361201i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −681.328 | −1.06291 | −0.531457 | − | 0.847085i | \(-0.678355\pi\) | ||||
−0.531457 | + | 0.847085i | \(0.678355\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 527.270 | 0.820016 | 0.410008 | − | 0.912082i | \(-0.365526\pi\) | ||||
0.410008 | + | 0.912082i | \(0.365526\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 551.627 | 0.852592 | 0.426296 | − | 0.904584i | \(-0.359818\pi\) | ||||
0.426296 | + | 0.904584i | \(0.359818\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1184.42 | 1.82499 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 699.422i | − | 1.07109i | −0.844507 | − | 0.535545i | \(-0.820106\pi\) | ||
0.844507 | − | 0.535545i | \(-0.179894\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −155.599 | − | 176.908i | −0.237556 | − | 0.270088i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.3257i | 0.0581574i | 0.999577 | + | 0.0290787i | \(0.00925734\pi\) | ||||
−0.999577 | + | 0.0290787i | \(0.990743\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 392.364 | 0.593591 | 0.296796 | − | 0.954941i | \(-0.404082\pi\) | ||||
0.296796 | + | 0.954941i | \(0.404082\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 160.282 | + | 182.232i | 0.241026 | + | 0.274033i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −36.3658 | −0.0545215 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 704.594i | − | 1.05007i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 427.290i | − | 0.634904i | −0.948274 | − | 0.317452i | \(-0.897173\pi\) | ||
0.948274 | − | 0.317452i | \(-0.102827\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 131.234i | 0.193847i | 0.995292 | + | 0.0969233i | \(0.0309002\pi\) | ||||
−0.995292 | + | 0.0969233i | \(0.969100\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 859.186i | 1.26537i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 896.229 | 1.31219 | 0.656097 | − | 0.754676i | \(-0.272206\pi\) | ||||
0.656097 | + | 0.754676i | \(0.272206\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −207.581 | − | 236.008i | −0.303038 | − | 0.344538i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −315.968 | −0.458589 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 520.465i | − | 0.753206i | −0.926375 | − | 0.376603i | \(-0.877092\pi\) | ||
0.926375 | − | 0.376603i | \(-0.122908\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −423.737 | − | 481.766i | −0.609694 | − | 0.693189i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 359.812i | − | 0.516230i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −80.7527 | −0.115196 | −0.0575982 | − | 0.998340i | \(-0.518344\pi\) | ||||
−0.0575982 | + | 0.998340i | \(0.518344\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −79.9709 | −0.113757 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 837.591 | 1.18471 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −174.828 | −0.246584 | −0.123292 | − | 0.992370i | \(-0.539345\pi\) | ||||
−0.123292 | + | 0.992370i | \(0.539345\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 580.621i | 0.814335i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 285.134 | − | 250.789i | 0.398789 | − | 0.350755i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 889.905i | 1.23770i | 0.785510 | + | 0.618849i | \(0.212401\pi\) | ||||
−0.785510 | + | 0.618849i | \(0.787599\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 475.328 | 0.659263 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.60205 | − | 59.0690i | 0.0104856 | − | 0.0814745i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −408.818 | −0.562335 | −0.281168 | − | 0.959659i | \(-0.590722\pi\) | ||||
−0.281168 | + | 0.959659i | \(0.590722\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1615.43i | 2.20989i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 388.369i | 0.529835i | 0.964271 | + | 0.264917i | \(0.0853446\pi\) | ||||
−0.964271 | + | 0.264917i | \(0.914655\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 877.783i | − | 1.19102i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 109.561i | − | 0.148256i | −0.997249 | − | 0.0741280i | \(-0.976383\pi\) | ||
0.997249 | − | 0.0741280i | \(-0.0236173\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 732.717 | 0.986160 | 0.493080 | − | 0.869984i | \(-0.335871\pi\) | ||||
0.493080 | + | 0.869984i | \(0.335871\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 621.583 | − | 546.713i | 0.834340 | − | 0.733844i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1907.02 | −2.54608 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 420.809i | 0.560332i | 0.959952 | + | 0.280166i | \(0.0903895\pi\) | ||||
−0.959952 | + | 0.280166i | \(0.909610\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −721.721 | − | 820.557i | −0.955922 | − | 1.08683i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1306.99i | − | 1.72654i | −0.504744 | − | 0.863269i | \(-0.668413\pi\) | ||
0.504744 | − | 0.863269i | \(-0.331587\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1402.25 | 1.84264 | 0.921320 | − | 0.388804i | \(-0.127112\pi\) | ||||
0.921320 | + | 0.388804i | \(0.127112\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 850.402 | 1.11455 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −303.748 | −0.396021 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −359.952 | −0.468078 | −0.234039 | − | 0.972227i | \(-0.575194\pi\) | ||||
−0.234039 | + | 0.972227i | \(0.575194\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 437.539i | − | 0.566027i | −0.959116 | − | 0.283013i | \(-0.908666\pi\) | ||
0.959116 | − | 0.283013i | \(-0.0913341\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −943.103 | − | 121.375i | −1.21691 | − | 0.156613i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 64.2778i | 0.0825132i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −696.141 | −0.891346 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −575.547 | − | 654.365i | −0.733181 | − | 0.833586i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 438.946 | 0.557746 | 0.278873 | − | 0.960328i | \(-0.410039\pi\) | ||||
0.278873 | + | 0.960328i | \(0.410039\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1152.07i | − | 1.45647i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 180.696i | 0.227864i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 982.414i | 1.23264i | 0.787496 | + | 0.616320i | \(0.211377\pi\) | ||||
−0.787496 | + | 0.616320i | \(0.788623\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1686.95i | 2.11133i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −616.832 | −0.768160 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −576.366 | + | 506.943i | −0.715983 | + | 0.629743i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 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 | \(-0.877250\pi\) | ||
0.926561 | − | 0.376144i | \(-0.122750\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −197.614 | + | 173.811i | −0.242471 | + | 0.213266i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 288.585i | − | 0.353225i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1099.76 | 1.33954 | 0.669770 | − | 0.742568i | \(-0.266393\pi\) | ||||
0.669770 | + | 0.742568i | \(0.266393\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −236.092 | −0.286867 | −0.143434 | − | 0.989660i | \(-0.545814\pi\) | ||||
−0.143434 | + | 0.989660i | \(0.545814\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1266.81 | −1.53182 | −0.765908 | − | 0.642950i | \(-0.777710\pi\) | ||||
−0.765908 | + | 0.642950i | \(0.777710\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −41.7642 | −0.0503790 | −0.0251895 | − | 0.999683i | \(-0.508019\pi\) | ||||
−0.0251895 | + | 0.999683i | \(0.508019\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1408.57i | − | 1.69095i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 287.892 | − | 253.215i | 0.344781 | − | 0.303252i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 816.273i | − | 0.972912i | −0.873705 | − | 0.486456i | \(-0.838289\pi\) | ||
0.873705 | − | 0.486456i | \(-0.161711\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −835.325 | −0.993252 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 561.371 | − | 493.754i | 0.664344 | − | 0.584324i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1761.32 | −2.07948 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 252.933i | − | 0.297219i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1215.58i | 1.42507i | 0.701639 | + | 0.712533i | \(0.252452\pi\) | ||||
−0.701639 | + | 0.712533i | \(0.747548\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 997.998i | 1.16452i | 0.813001 | + | 0.582262i | \(0.197832\pi\) | ||||
−0.813001 | + | 0.582262i | \(0.802168\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1110.42i | − | 1.29269i | −0.763044 | − | 0.646347i | \(-0.776296\pi\) | ||
0.763044 | − | 0.646347i | \(-0.223704\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1372.33 | −1.59019 | −0.795094 | − | 0.606486i | \(-0.792578\pi\) | ||||
−0.795094 | + | 0.606486i | \(0.792578\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.1117 | − | 36.5092i | −0.0371233 | − | 0.0422072i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2182.06 | 2.51101 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 225.111i | 0.258451i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −702.942 | − | 1042.17i | −0.803362 | − | 1.19105i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 776.337i | 0.885219i | 0.896714 | + | 0.442609i | \(0.145947\pi\) | ||||
−0.896714 | + | 0.442609i | \(0.854053\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1047.38 | −1.18885 | −0.594427 | − | 0.804150i | \(-0.702621\pi\) | ||||
−0.594427 | + | 0.804150i | \(0.702621\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1175.41 | 1.33116 | 0.665579 | − | 0.746327i | \(-0.268185\pi\) | ||||
0.665579 | + | 0.746327i | \(0.268185\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 109.768 | 0.123752 | 0.0618762 | − | 0.998084i | \(-0.480292\pi\) | ||||
0.0618762 | + | 0.998084i | \(0.480292\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 446.634 | 0.502401 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 301.361i | − | 0.337470i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 513.497 | + | 583.818i | 0.573740 | + | 0.652311i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 90.6094i | − | 0.100789i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1934.33 | 2.14687 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 939.899 | − | 826.688i | 1.03856 | − | 0.913468i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1639.15 | −1.80722 | −0.903609 | − | 0.428358i | \(-0.859092\pi\) | ||||
−0.903609 | + | 0.428358i | \(0.859092\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.82023i | 0.00748654i | 0.999993 | + | 0.00374327i | \(0.00119152\pi\) | ||||
−0.999993 | + | 0.00374327i | \(0.998808\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1293.22i | 1.41645i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 473.867i | − | 0.516757i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 72.4188i | 0.0788017i | 0.999223 | + | 0.0394009i | \(0.0125449\pi\) | ||||
−0.999223 | + | 0.0394009i | \(0.987455\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 178.528 | 0.193421 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 410.840 | + | 52.8741i | 0.444151 | + | 0.0571612i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 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 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1745.57 | + | 1535.32i | −1.86692 | + | 1.64205i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 590.172i | − | 0.629852i | −0.949116 | − | 0.314926i | \(-0.898020\pi\) | ||
0.949116 | − | 0.314926i | \(-0.101980\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 189.017 | 0.200869 | 0.100434 | − | 0.994944i | \(-0.467977\pi\) | ||||
0.100434 | + | 0.994944i | \(0.467977\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −203.299 | −0.215588 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 664.319 | 0.701498 | 0.350749 | − | 0.936470i | \(-0.385927\pi\) | ||||
0.350749 | + | 0.936470i | \(0.385927\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 158.189 | 0.166690 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 173.943i | 0.182522i | 0.995827 | + | 0.0912610i | \(0.0290898\pi\) | ||||
−0.995827 | + | 0.0912610i | \(0.970910\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −366.967 | − | 417.221i | −0.384259 | − | 0.436881i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 632.175i | − | 0.659202i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −485.680 | −0.505390 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −33.9138 | − | 38.5581i | −0.0351438 | − | 0.0399566i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −255.364 | −0.264078 | −0.132039 | − | 0.991245i | \(-0.542152\pi\) | ||||
−0.132039 | + | 0.991245i | \(0.542152\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1623.60i | − | 1.67209i | −0.548659 | − | 0.836046i | \(-0.684861\pi\) | ||
0.548659 | − | 0.836046i | \(-0.315139\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1290.46i | − | 1.32627i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 104.946i | − | 0.107416i | −0.998557 | − | 0.0537082i | \(-0.982896\pi\) | ||
0.998557 | − | 0.0537082i | \(-0.0171041\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1833.13i | − | 1.87245i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −889.933 | −0.905323 | −0.452662 | − | 0.891682i | \(-0.649525\pi\) | ||||
−0.452662 | + | 0.891682i | \(0.649525\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 538.960 | + | 612.768i | 0.547167 | + | 0.622099i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 912.742 | 0.922894 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1509.57i | − | 1.52328i | −0.648001 | − | 0.761639i | \(-0.724395\pi\) | ||
0.648001 | − | 0.761639i | \(-0.275605\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −644.020 | − | 732.215i | −0.647256 | − | 0.735894i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1599.93i | − | 1.60474i | −0.596825 | − | 0.802371i | \(-0.703571\pi\) | ||
0.596825 | − | 0.802371i | \(-0.296429\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1440.3.j.b.1279.5 | 6 | ||
3.2 | odd | 2 | 160.3.h.b.159.4 | yes | 6 | ||
4.3 | odd | 2 | 1440.3.j.a.1279.5 | 6 | |||
5.4 | even | 2 | 1440.3.j.a.1279.6 | 6 | |||
12.11 | even | 2 | 160.3.h.a.159.4 | yes | 6 | ||
15.2 | even | 4 | 800.3.b.h.351.4 | 6 | |||
15.8 | even | 4 | 800.3.b.i.351.3 | 6 | |||
15.14 | odd | 2 | 160.3.h.a.159.3 | ✓ | 6 | ||
20.19 | odd | 2 | inner | 1440.3.j.b.1279.6 | 6 | ||
24.5 | odd | 2 | 320.3.h.f.319.3 | 6 | |||
24.11 | even | 2 | 320.3.h.g.319.3 | 6 | |||
48.5 | odd | 4 | 1280.3.e.h.639.4 | 6 | |||
48.11 | even | 4 | 1280.3.e.i.639.3 | 6 | |||
48.29 | odd | 4 | 1280.3.e.f.639.3 | 6 | |||
48.35 | even | 4 | 1280.3.e.g.639.4 | 6 | |||
60.23 | odd | 4 | 800.3.b.i.351.4 | 6 | |||
60.47 | odd | 4 | 800.3.b.h.351.3 | 6 | |||
60.59 | even | 2 | 160.3.h.b.159.3 | yes | 6 | ||
120.29 | odd | 2 | 320.3.h.g.319.4 | 6 | |||
120.53 | even | 4 | 1600.3.b.w.1151.4 | 6 | |||
120.59 | even | 2 | 320.3.h.f.319.4 | 6 | |||
120.77 | even | 4 | 1600.3.b.v.1151.3 | 6 | |||
120.83 | odd | 4 | 1600.3.b.w.1151.3 | 6 | |||
120.107 | odd | 4 | 1600.3.b.v.1151.4 | 6 | |||
240.29 | odd | 4 | 1280.3.e.i.639.4 | 6 | |||
240.59 | even | 4 | 1280.3.e.f.639.4 | 6 | |||
240.149 | odd | 4 | 1280.3.e.g.639.3 | 6 | |||
240.179 | even | 4 | 1280.3.e.h.639.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.3.h.a.159.3 | ✓ | 6 | 15.14 | odd | 2 | ||
160.3.h.a.159.4 | yes | 6 | 12.11 | even | 2 | ||
160.3.h.b.159.3 | yes | 6 | 60.59 | even | 2 | ||
160.3.h.b.159.4 | yes | 6 | 3.2 | odd | 2 | ||
320.3.h.f.319.3 | 6 | 24.5 | odd | 2 | |||
320.3.h.f.319.4 | 6 | 120.59 | even | 2 | |||
320.3.h.g.319.3 | 6 | 24.11 | even | 2 | |||
320.3.h.g.319.4 | 6 | 120.29 | odd | 2 | |||
800.3.b.h.351.3 | 6 | 60.47 | odd | 4 | |||
800.3.b.h.351.4 | 6 | 15.2 | even | 4 | |||
800.3.b.i.351.3 | 6 | 15.8 | even | 4 | |||
800.3.b.i.351.4 | 6 | 60.23 | odd | 4 | |||
1280.3.e.f.639.3 | 6 | 48.29 | odd | 4 | |||
1280.3.e.f.639.4 | 6 | 240.59 | even | 4 | |||
1280.3.e.g.639.3 | 6 | 240.149 | odd | 4 | |||
1280.3.e.g.639.4 | 6 | 48.35 | even | 4 | |||
1280.3.e.h.639.3 | 6 | 240.179 | even | 4 | |||
1280.3.e.h.639.4 | 6 | 48.5 | odd | 4 | |||
1280.3.e.i.639.3 | 6 | 48.11 | even | 4 | |||
1280.3.e.i.639.4 | 6 | 240.29 | odd | 4 | |||
1440.3.j.a.1279.5 | 6 | 4.3 | odd | 2 | |||
1440.3.j.a.1279.6 | 6 | 5.4 | even | 2 | |||
1440.3.j.b.1279.5 | 6 | 1.1 | even | 1 | trivial | ||
1440.3.j.b.1279.6 | 6 | 20.19 | odd | 2 | inner | ||
1600.3.b.v.1151.3 | 6 | 120.77 | even | 4 | |||
1600.3.b.v.1151.4 | 6 | 120.107 | odd | 4 | |||
1600.3.b.w.1151.3 | 6 | 120.83 | odd | 4 | |||
1600.3.b.w.1151.4 | 6 | 120.53 | even | 4 |