Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,3,Mod(639,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.639");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(34.8774738381\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 639.4 | ||
Root | \(0.273891i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.639 |
Dual form | 1280.3.e.f.639.3 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | 3.30219 | − | 3.75441i | 0.660437 | − | 0.750881i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.0566 | −1.43666 | −0.718328 | − | 0.695705i | \(-0.755092\pi\) | ||||
−0.718328 | + | 0.695705i | \(0.755092\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.69994 | 0.966660 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 17.2087 | 1.56443 | 0.782216 | − | 0.623008i | \(-0.214089\pi\) | ||||
0.782216 | + | 0.623008i | \(0.214089\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.41325 | −0.339481 | −0.169740 | − | 0.985489i | \(-0.554293\pi\) | ||||
−0.169740 | + | 0.985489i | \(0.554293\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.05659 | + | 1.80888i | 0.137106 | + | 0.120592i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 27.0176i | − | 1.58927i | −0.607086 | − | 0.794636i | \(-0.707662\pi\) | ||
0.607086 | − | 0.794636i | \(-0.292338\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.82650 | −0.254026 | −0.127013 | − | 0.991901i | \(-0.540539\pi\) | ||||
−0.127013 | + | 0.991901i | \(0.540539\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 5.50881i | − | 0.262324i | ||||||
\(22\) | 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 | ||||||||
\(27\) | 9.69569i | 0.359100i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.38225i | 0.0821465i | 0.999156 | + | 0.0410733i | \(0.0130777\pi\) | ||||
−0.999156 | + | 0.0410733i | \(0.986922\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 38.0352i | 1.22694i | 0.789717 | + | 0.613472i | \(0.210228\pi\) | ||||
−0.789717 | + | 0.613472i | \(0.789772\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.42663i | 0.285655i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −33.2087 | + | 37.7565i | −0.948821 | + | 1.07876i | ||||
\(36\) | 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 | \(-0.448073\pi\) | ||||
0.162411 | + | 0.986723i | \(0.448073\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 59.7918i | − | 1.39051i | −0.718765 | − | 0.695253i | \(-0.755292\pi\) | ||
0.718765 | − | 0.695253i | \(-0.244708\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 28.7288 | − | 32.6631i | 0.638418 | − | 0.725846i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 62.4388 | 1.32849 | 0.664243 | − | 0.747517i | \(-0.268754\pi\) | ||||
0.664243 | + | 0.747517i | \(0.268754\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 52.1351 | 1.06398 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.7997 | 0.290191 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −71.5952 | −1.35085 | −0.675427 | − | 0.737427i | \(-0.736041\pi\) | ||||
−0.675427 | + | 0.737427i | \(0.736041\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 56.8265 | − | 64.6086i | 1.03321 | − | 1.17470i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.64386i | − | 0.0463836i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −68.8265 | −1.16655 | −0.583275 | − | 0.812274i | \(-0.698229\pi\) | ||||
−0.583275 | + | 0.812274i | \(0.698229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 40.9439i | − | 0.671212i | −0.942002 | − | 0.335606i | \(-0.891059\pi\) | ||
0.942002 | − | 0.335606i | \(-0.108941\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −87.4917 | −1.38876 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.5734 | + | 16.5691i | −0.224206 | + | 0.254910i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 51.0080i | − | 0.761313i | −0.924717 | − | 0.380656i | \(-0.875698\pi\) | ||
0.924717 | − | 0.380656i | \(-0.124302\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 8.36206i | − | 0.121189i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 40.4527i | 0.569757i | 0.958564 | + | 0.284878i | \(0.0919532\pi\) | ||||
−0.958564 | + | 0.284878i | \(0.908047\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 35.8441i | − | 0.491015i | −0.969395 | − | 0.245508i | \(-0.921045\pi\) | ||
0.969395 | − | 0.245508i | \(-0.0789547\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.5825 | − | 1.74804i | 0.181100 | − | 0.0233072i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −173.061 | −2.24755 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 126.800i | − | 1.60506i | −0.596612 | − | 0.802530i | \(-0.703487\pi\) | ||
0.596612 | − | 0.802530i | \(-0.296513\pi\) | |||||||
\(80\) | 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 | ||||||||
\(85\) | −101.435 | − | 89.2172i | −1.19335 | − | 1.04961i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.30495 | −0.0149994 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 106.523 | 1.19689 | 0.598445 | − | 0.801164i | \(-0.295785\pi\) | ||||
0.598445 | + | 0.801164i | \(0.295785\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 44.3822 | 0.487717 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −20.8350 | −0.224032 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.9380 | + | 18.1206i | −0.167768 | + | 0.190744i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 85.4351i | − | 0.880774i | −0.897808 | − | 0.440387i | \(-0.854841\pi\) | ||
0.897808 | − | 0.440387i | \(-0.145159\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 149.715 | 1.51227 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 83.2877i | − | 0.824631i | −0.911041 | − | 0.412315i | \(-0.864720\pi\) | ||
0.911041 | − | 0.412315i | \(-0.135280\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −47.2653 | −0.458887 | −0.229443 | − | 0.973322i | \(-0.573691\pi\) | ||||
−0.229443 | + | 0.973322i | \(0.573691\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −20.6823 | − | 18.1911i | −0.196974 | − | 0.173249i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 189.628i | 1.77223i | 0.463467 | + | 0.886114i | \(0.346605\pi\) | ||||
−0.463467 | + | 0.886114i | \(0.653395\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 84.5617i | − | 0.775795i | −0.921702 | − | 0.387898i | \(-0.873201\pi\) | ||
0.921702 | − | 0.387898i | \(-0.126799\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.07626i | 0.0817681i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 114.558i | − | 1.01379i | −0.862007 | − | 0.506896i | \(-0.830793\pi\) | ||
0.862007 | − | 0.506896i | \(-0.169207\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −50.4090 | + | 57.3123i | −0.438339 | + | 0.498368i | ||||
\(116\) | 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 | ||||||||
\(125\) | −103.630 | − | 69.8986i | −0.829040 | − | 0.559189i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 44.4121 | 0.349701 | 0.174851 | − | 0.984595i | \(-0.444056\pi\) | ||||
0.174851 | + | 0.984595i | \(0.444056\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 32.7528 | 0.253898 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −47.1200 | −0.359695 | −0.179847 | − | 0.983695i | \(-0.557560\pi\) | ||||
−0.179847 | + | 0.983695i | \(0.557560\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 48.5381 | 0.364948 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 36.4016 | + | 32.0170i | 0.269641 | + | 0.237163i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 62.8617i | 0.458845i | 0.973327 | + | 0.229422i | \(0.0736837\pi\) | ||||
−0.973327 | + | 0.229422i | \(0.926316\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −128.320 | −0.923167 | −0.461584 | − | 0.887097i | \(-0.652719\pi\) | ||||
−0.461584 | + | 0.887097i | \(0.652719\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 34.2028i | 0.242573i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −75.9465 | −0.531094 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.94393 | + | 7.86663i | 0.0616823 | + | 0.0542526i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 28.5586i | 0.194276i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 165.561i | − | 1.11115i | −0.831467 | − | 0.555574i | \(-0.812499\pi\) | ||
0.831467 | − | 0.555574i | \(-0.187501\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 218.558i | − | 1.44741i | −0.690111 | − | 0.723704i | \(-0.742438\pi\) | ||
0.690111 | − | 0.723704i | \(-0.257562\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 235.052i | − | 1.53628i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 142.800 | + | 125.599i | 0.921289 | + | 0.810319i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 174.293 | 1.11014 | 0.555072 | − | 0.831802i | \(-0.312691\pi\) | ||||
0.555072 | + | 0.831802i | \(0.312691\pi\) | |||||||
\(158\) | 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 | ||||||||
\(165\) | 35.3914 | + | 31.1285i | 0.214493 | + | 0.188657i | ||||
\(166\) | 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 | ||||||||
\(171\) | −41.9902 | −0.245557 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.72437 | −0.0562102 | −0.0281051 | − | 0.999605i | \(-0.508947\pi\) | ||||
−0.0281051 | + | 0.999605i | \(0.508947\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 32.0918 | + | 249.358i | 0.183382 | + | 1.42490i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 37.7019i | − | 0.213005i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 155.502 | 0.868728 | 0.434364 | − | 0.900738i | \(-0.356973\pi\) | ||||
0.434364 | + | 0.900738i | \(0.356973\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 250.346i | 1.38313i | 0.722316 | + | 0.691563i | \(0.243077\pi\) | ||||
−0.722316 | + | 0.691563i | \(0.756923\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 22.4283 | 0.122559 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 54.7144 | − | 62.2072i | 0.295753 | − | 0.336255i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 464.939i | − | 2.48631i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 97.5056i | − | 0.515903i | ||||||
\(190\) | 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 | \(0.00847011\pi\) | ||||
−0.999646 | + | 0.0266065i | \(0.991530\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.07626 | − | 7.98302i | −0.0465449 | − | 0.0409386i | ||||
\(196\) | 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 | ||||||||
\(205\) | 43.9775 | − | 50.0000i | 0.214524 | − | 0.243902i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −132.807 | −0.641582 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −83.0580 | −0.397407 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −297.038 | −1.40776 | −0.703881 | − | 0.710317i | \(-0.748551\pi\) | ||||
−0.703881 | + | 0.710317i | \(0.748551\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −22.1592 | −0.104034 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −224.483 | − | 197.444i | −1.04411 | − | 0.918342i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 382.505i | − | 1.76270i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.6347 | 0.0896563 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 119.236i | 0.539527i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 405.335 | 1.81764 | 0.908822 | − | 0.417184i | \(-0.136983\pi\) | ||||
0.908822 | + | 0.417184i | \(0.136983\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −27.7626 | − | 215.719i | −0.123389 | − | 0.958752i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 36.6013i | 0.161239i | 0.996745 | + | 0.0806196i | \(0.0256899\pi\) | ||||
−0.996745 | + | 0.0806196i | \(0.974310\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 91.1467i | − | 0.398021i | −0.979997 | − | 0.199010i | \(-0.936227\pi\) | ||
0.979997 | − | 0.199010i | \(-0.0637727\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 94.7997i | − | 0.410388i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 338.802i | 1.45409i | 0.686592 | + | 0.727043i | \(0.259106\pi\) | ||||
−0.686592 | + | 0.727043i | \(0.740894\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 206.185 | − | 234.421i | 0.877382 | − | 0.997535i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 69.4585 | 0.293074 | ||||||||
\(238\) | 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 | ||||||||
\(243\) | 127.243i | 0.523633i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 172.160 | − | 195.736i | 0.702693 | − | 0.798923i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.3005 | 0.0862370 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 41.1652 | 0.165322 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −86.0268 | −0.342736 | −0.171368 | − | 0.985207i | \(-0.554819\pi\) | ||||
−0.171368 | + | 0.985207i | \(0.554819\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −262.697 | −1.03833 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 48.8715 | − | 55.5642i | 0.191653 | − | 0.217899i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 355.963i | 1.38507i | 0.721383 | + | 0.692536i | \(0.243507\pi\) | ||||
−0.721383 | + | 0.692536i | \(0.756493\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −166.629 | −0.643355 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.7254i | 0.0794077i | ||||||||
\(262\) | 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 | ||||||||
\(267\) | 58.3514i | 0.218545i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 268.002i | − | 0.996290i | −0.867094 | − | 0.498145i | \(-0.834015\pi\) | ||
0.867094 | − | 0.498145i | \(-0.165985\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 229.412i | 0.846538i | 0.906004 | + | 0.423269i | \(0.139117\pi\) | ||||
−0.906004 | + | 0.423269i | \(0.860883\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 24.3118i | 0.0890541i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −54.9153 | − | 426.699i | −0.199692 | − | 1.55163i | ||||
\(276\) | 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 | \(-0.196036\pi\) | ||||
0.816275 | + | 0.577664i | \(0.196036\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 465.558i | 1.64508i | 0.568706 | + | 0.822541i | \(0.307444\pi\) | ||||
−0.568706 | + | 0.822541i | \(0.692556\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.92614 | − | 8.73053i | −0.0348286 | − | 0.0306335i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −133.931 | −0.466657 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −440.952 | −1.52579 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 46.7997 | 0.160824 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −165.218 | −0.563884 | −0.281942 | − | 0.959431i | \(-0.590979\pi\) | ||||
−0.281942 | + | 0.959431i | \(0.590979\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −227.278 | + | 258.403i | −0.770434 | + | 0.875941i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 166.851i | 0.561787i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 67.3697 | 0.225317 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 601.302i | 1.99768i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 45.6234 | 0.150572 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −153.720 | − | 135.205i | −0.504000 | − | 0.443293i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 235.339i | 0.766577i | 0.923629 | + | 0.383288i | \(0.125208\pi\) | ||||
−0.923629 | + | 0.383288i | \(0.874792\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 25.8911i | − | 0.0837898i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 210.665i | 0.677381i | 0.940898 | + | 0.338691i | \(0.109984\pi\) | ||||
−0.940898 | + | 0.338691i | \(0.890016\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 318.738i | 1.01833i | 0.860668 | + | 0.509166i | \(0.170046\pi\) | ||||
−0.860668 | + | 0.509166i | \(0.829954\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −288.914 | + | 328.479i | −0.917187 | + | 1.04279i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −70.3950 | −0.222066 | −0.111033 | − | 0.993817i | \(-0.535416\pi\) | ||||
−0.111033 | + | 0.993817i | \(0.535416\pi\) | |||||||
\(318\) | 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 | ||||||||
\(325\) | 14.0832 | + | 109.429i | 0.0433330 | + | 0.336704i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 46.3213 | 0.141655 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −627.922 | −1.90858 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 280.807 | 0.848359 | 0.424180 | − | 0.905578i | \(-0.360562\pi\) | ||||
0.424180 | + | 0.905578i | \(0.360562\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 144.150 | 0.432884 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −191.505 | − | 168.438i | −0.571656 | − | 0.502800i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 120.969i | 0.358959i | 0.983762 | + | 0.179480i | \(0.0574414\pi\) | ||||
−0.983762 | + | 0.179480i | \(0.942559\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 62.7530 | 0.185112 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 654.539i | 1.91947i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −31.5280 | −0.0919182 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −31.3946 | − | 27.6131i | −0.0909988 | − | 0.0800380i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 214.333i | − | 0.617675i | −0.951115 | − | 0.308838i | \(-0.900060\pi\) | ||
0.951115 | − | 0.308838i | \(-0.0999399\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 418.041i | 1.19782i | 0.800815 | + | 0.598912i | \(0.204400\pi\) | ||||
−0.800815 | + | 0.598912i | \(0.795600\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 42.7895i | − | 0.121907i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 364.929i | 1.03379i | 0.856048 | + | 0.516897i | \(0.172913\pi\) | ||||
−0.856048 | + | 0.516897i | \(0.827087\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 151.876 | + | 133.583i | 0.427820 | + | 0.376289i | ||||
\(356\) | 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 | ||||||||
\(365\) | −134.573 | − | 118.364i | −0.368694 | − | 0.324285i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −224.564 | −0.611891 | −0.305945 | − | 0.952049i | \(-0.598972\pi\) | ||||
−0.305945 | + | 0.952049i | \(0.598972\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 115.863 | 0.313992 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 720.004 | 1.94071 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 572.174 | 1.53398 | 0.766989 | − | 0.641660i | \(-0.221754\pi\) | ||||
0.766989 | + | 0.641660i | \(0.221754\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 38.2891 | − | 56.7666i | 0.102104 | − | 0.151378i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 10.5135i | − | 0.0278872i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −122.896 | −0.324263 | −0.162132 | − | 0.986769i | \(-0.551837\pi\) | ||||
−0.162132 | + | 0.986769i | \(0.551837\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.3281i | 0.0638533i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −289.717 | −0.756442 | −0.378221 | − | 0.925715i | \(-0.623464\pi\) | ||||
−0.378221 | + | 0.925715i | \(0.623464\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −571.481 | + | 649.743i | −1.48437 | + | 1.68764i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 520.185i | − | 1.34415i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 111.590i | 0.286863i | 0.989660 | + | 0.143432i | \(0.0458137\pi\) | ||||
−0.989660 | + | 0.143432i | \(0.954186\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 412.433i | 1.05482i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 25.8114i | − | 0.0656780i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −476.058 | − | 418.716i | −1.20521 | − | 1.06004i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 705.314 | 1.77661 | 0.888305 | − | 0.459253i | \(-0.151883\pi\) | ||||
0.888305 | + | 0.459253i | \(0.151883\pi\) | |||||||
\(398\) | 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 | ||||||||
\(405\) | 241.021 | − | 274.028i | 0.595114 | − | 0.676612i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 285.134 | 0.700575 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 98.8102 | 0.241590 | 0.120795 | − | 0.992677i | \(-0.461456\pi\) | ||||
0.120795 | + | 0.992677i | \(0.461456\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −34.4345 | −0.0837822 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 692.160 | 1.67593 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −282.140 | − | 248.156i | −0.679855 | − | 0.597966i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 70.2914i | − | 0.168565i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −204.980 | −0.489213 | −0.244607 | − | 0.969622i | \(-0.578659\pi\) | ||||
−0.244607 | + | 0.969622i | \(0.578659\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 449.956i | 1.06878i | 0.845238 | + | 0.534390i | \(0.179459\pi\) | ||||
−0.845238 | + | 0.534390i | \(0.820541\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 543.214 | 1.28419 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −669.915 | + | 86.2166i | −1.57627 | + | 0.202863i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 411.756i | 0.964301i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 41.6021i | − | 0.0969745i | ||||||
\(430\) | 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 | \(-0.875383\pi\) | ||
0.924339 | − | 0.381571i | \(-0.124617\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.30919 | + | 4.89932i | −0.00990619 | + | 0.0112628i | ||||
\(436\) | 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 | \(-0.885123\pi\) | ||
0.935580 | − | 0.353115i | \(-0.114877\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 351.760 | − | 399.931i | 0.790471 | − | 0.898722i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 90.6912 | 0.202889 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −246.330 | −0.548620 | −0.274310 | − | 0.961641i | \(-0.588449\pi\) | ||||
−0.274310 | + | 0.961641i | \(0.588449\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 229.181 | 0.508161 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 119.722 | 0.264287 | ||||||||
\(454\) | 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 | ||||||||
\(459\) | 261.955 | 0.570707 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 611.288i | 1.32600i | 0.748618 | + | 0.663002i | \(0.230718\pi\) | ||||
−0.748618 | + | 0.663002i | \(0.769282\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 334.063 | 0.721519 | 0.360760 | − | 0.932659i | \(-0.382518\pi\) | ||||
0.360760 | + | 0.932659i | \(0.382518\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −68.8010 | + | 78.2230i | −0.147959 | + | 0.168222i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 128.864i | 0.275939i | 0.990436 | + | 0.137970i | \(0.0440577\pi\) | ||||
−0.990436 | + | 0.137970i | \(0.955942\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 512.966i | 1.09374i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 95.4742i | 0.202705i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1028.94i | − | 2.17535i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.4020 | + | 119.675i | 0.0324252 | + | 0.251948i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −622.874 | −1.30582 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 84.0939i | 0.174107i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −320.758 | − | 282.123i | −0.661357 | − | 0.581696i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −616.472 | −1.26586 | −0.632928 | − | 0.774211i | \(-0.718147\pi\) | ||||
−0.632928 | + | 0.774211i | \(0.718147\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −28.8326 | −0.0589624 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −603.190 | −1.22849 | −0.614247 | − | 0.789114i | \(-0.710540\pi\) | ||||
−0.614247 | + | 0.789114i | \(0.710540\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 64.3627 | 0.130553 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 494.387 | − | 562.091i | 0.998761 | − | 1.13554i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 406.817i | − | 0.818545i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −867.976 | −1.73943 | −0.869716 | − | 0.493553i | \(-0.835698\pi\) | ||||
−0.869716 | + | 0.493553i | \(0.835698\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 42.0045i | 0.0838413i | ||||||||
\(502\) | 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 | ||||||||
\(507\) | − | 81.9060i | − | 0.161550i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 168.498i | 0.331038i | 0.986207 | + | 0.165519i | \(0.0529299\pi\) | ||||
−0.986207 | + | 0.165519i | \(0.947070\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 360.470i | 0.705420i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 46.7962i | − | 0.0912207i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −156.079 | + | 177.453i | −0.303066 | + | 0.344569i | ||||
\(516\) | 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 | \(-0.473360\pi\) | ||||
0.0835951 | + | 0.996500i | \(0.473360\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 243.469i | − | 0.465524i | −0.972534 | − | 0.232762i | \(-0.925224\pi\) | ||
0.972534 | − | 0.232762i | \(-0.0747763\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −136.594 | + | 17.5793i | −0.260179 | + | 0.0334844i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1027.62 | 1.94995 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −295.969 | −0.559488 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −598.786 | −1.12766 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −58.7743 | −0.110271 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 711.942 | + | 626.189i | 1.33073 | + | 1.17045i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 85.1812i | 0.158624i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 897.179 | 1.66452 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 812.616i | 1.50206i | 0.660266 | + | 0.751032i | \(0.270443\pi\) | ||||
−0.660266 | + | 0.751032i | \(0.729557\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −137.135 | −0.252550 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −317.479 | − | 279.238i | −0.582530 | − | 0.512364i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 104.713i | − | 0.191431i | −0.995409 | − | 0.0957155i | \(-0.969486\pi\) | ||
0.995409 | − | 0.0957155i | \(-0.0305139\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 356.210i | − | 0.648833i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 11.4979i | − | 0.0208674i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1275.17i | 2.30592i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 34.0759 | + | 29.9715i | 0.0613981 | + | 0.0540027i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −260.018 | −0.466818 | −0.233409 | − | 0.972379i | \(-0.574988\pi\) | ||||
−0.233409 | + | 0.972379i | \(0.574988\pi\) | |||||||
\(558\) | 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 | ||||||||
\(565\) | −430.099 | − | 378.293i | −0.761237 | − | 0.669546i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −734.014 | −1.29456 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 211.588 | 0.371860 | 0.185930 | − | 0.982563i | \(-0.440470\pi\) | ||||
0.185930 | + | 0.982563i | \(0.440470\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 556.938 | 0.975372 | 0.487686 | − | 0.873019i | \(-0.337841\pi\) | ||||
0.487686 | + | 0.873019i | \(0.337841\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 60.8741 | 0.106237 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 48.7136 | + | 378.512i | 0.0847193 | + | 0.658281i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 516.233i | 0.894684i | 0.894363 | + | 0.447342i | \(0.147629\pi\) | ||||
−0.894363 | + | 0.447342i | \(0.852371\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.62577 | −0.00971636 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 755.742i | 1.30076i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1232.06 | −2.11332 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −126.787 | + | 144.150i | −0.216731 | + | 0.246411i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 934.677i | 1.59229i | 0.605103 | + | 0.796147i | \(0.293132\pi\) | ||||
−0.605103 | + | 0.796147i | \(0.706868\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 183.577i | − | 0.311676i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 89.4050i | − | 0.151277i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 634.665i | 1.07026i | 0.844769 | + | 0.535131i | \(0.179738\pi\) | ||||
−0.844769 | + | 0.535131i | \(0.820262\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1020.09 | + | 897.221i | 1.71444 | + | 1.50794i | ||||
\(596\) | 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 | \(-0.334076\pi\) | ||||
0.497977 | + | 0.867190i | \(0.334076\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 443.766i | − | 0.735930i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 578.348 | − | 657.550i | 0.955948 | − | 1.08686i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −201.830 | −0.332504 | −0.166252 | − | 0.986083i | \(-0.553166\pi\) | ||||
−0.166252 | + | 0.986083i | \(0.553166\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.1234 | 0.0215490 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −275.558 | −0.450995 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −71.9205 | −0.117325 | −0.0586627 | − | 0.998278i | \(-0.518684\pi\) | ||||
−0.0586627 | + | 0.998278i | \(0.518684\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 27.3891 | + | 24.0900i | 0.0445350 | + | 0.0391708i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 204.485i | 0.331418i | 0.986175 | + | 0.165709i | \(0.0529912\pi\) | ||||
−0.986175 | + | 0.165709i | \(0.947009\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 287.512 | 0.464479 | 0.232239 | − | 0.972659i | \(-0.425395\pi\) | ||||
0.232239 | + | 0.972659i | \(0.425395\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 148.008i | − | 0.238338i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1071.26 | −1.71952 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −604.633 | + | 158.251i | −0.967414 | + | 0.253202i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 45.4976i | − | 0.0725640i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 447.658i | − | 0.711699i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 274.203i | − | 0.434554i | −0.976110 | − | 0.217277i | \(-0.930283\pi\) | ||
0.976110 | − | 0.217277i | \(-0.0697175\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 162.712i | − | 0.257049i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 146.657 | − | 166.741i | 0.230956 | − | 0.262584i | ||||
\(636\) | 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 | ||||||||
\(645\) | 108.156 | − | 122.967i | 0.167684 | − | 0.190647i | ||||
\(646\) | 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 | ||||||||
\(651\) | 209.529 | 0.321857 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −699.422 | −1.07109 | −0.535545 | − | 0.844507i | \(-0.679894\pi\) | ||||
−0.535545 | + | 0.844507i | \(0.679894\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −155.599 | + | 176.908i | −0.237556 | + | 0.270088i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 311.842i | − | 0.474645i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.3257 | 0.0581574 | 0.0290787 | − | 0.999577i | \(-0.490743\pi\) | ||||
0.0290787 | + | 0.999577i | \(0.490743\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 392.364i | 0.593591i | 0.954941 | + | 0.296796i | \(0.0959180\pi\) | ||||
−0.954941 | + | 0.296796i | \(0.904082\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −65.3150 | −0.0985143 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 160.282 | − | 182.232i | 0.241026 | − | 0.274033i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 36.3658i | − | 0.0545215i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 222.035i | 0.331890i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 704.594i | − | 1.05007i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 427.290i | 0.634904i | 0.948274 | + | 0.317452i | \(0.102827\pi\) | ||||
−0.948274 | + | 0.317452i | \(0.897173\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 240.409 | − | 30.9402i | 0.356162 | − | 0.0458373i | ||||
\(676\) | 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 | \(-0.772206\pi\) | ||
0.754676 | − | 0.656097i | \(-0.227794\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 236.008 | + | 207.581i | 0.344538 | + | 0.303038i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 49.9285 | 0.0726761 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 315.968 | 0.458589 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 520.465 | 0.753206 | 0.376603 | − | 0.926375i | \(-0.377092\pi\) | ||||
0.376603 | + | 0.926375i | \(0.377092\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1505.62 | −2.17262 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −423.737 | + | 481.766i | −0.609694 | + | 0.693189i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 359.812i | − | 0.516230i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −185.589 | −0.265507 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 80.7527i | − | 0.115196i | −0.998340 | − | 0.0575982i | \(-0.981656\pi\) | ||
0.998340 | − | 0.0575982i | \(-0.0183442\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −79.9709 | −0.113757 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 128.411 | + | 112.944i | 0.182144 | + | 0.160204i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 837.591i | 1.18471i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 174.828i | − | 0.246584i | −0.992370 | − | 0.123292i | \(-0.960655\pi\) | ||
0.992370 | − | 0.123292i | \(-0.0393452\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1103.15i | − | 1.55155i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 580.621i | − | 0.814335i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −250.789 | + | 285.134i | −0.350755 | + | 0.398789i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.8715 | 0.0235307 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 131.622i | 0.182050i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 59.0690 | − | 7.60205i | 0.0814745 | − | 0.0104856i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 408.818 | 0.562335 | 0.281168 | − | 0.959659i | \(-0.409278\pi\) | ||||
0.281168 | + | 0.959659i | \(0.409278\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 587.194 | 0.805478 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1615.43 | −2.20989 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −388.369 | −0.529835 | −0.264917 | − | 0.964271i | \(-0.585345\pi\) | ||||
−0.264917 | + | 0.964271i | \(0.585345\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 107.221 | + | 94.3058i | 0.145878 | + | 0.128307i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 877.783i | − | 1.19102i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 109.561 | 0.148256 | 0.0741280 | − | 0.997249i | \(-0.476383\pi\) | ||||
0.0741280 | + | 0.997249i | \(0.476383\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.6680i | 0.0157463i | ||||||||
\(742\) | 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 | ||||||||
\(747\) | − | 653.791i | − | 0.875222i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1907.02i | − | 2.54608i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 420.809i | − | 0.560332i | −0.959952 | − | 0.280166i | \(-0.909610\pi\) | ||
0.959952 | − | 0.280166i | \(-0.0903895\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 47.1238i | − | 0.0625814i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −820.557 | − | 721.721i | −1.08683 | − | 0.955922i | ||||
\(756\) | 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 | \(-0.127112\pi\) | ||||
0.921320 | + | 0.388804i | \(0.127112\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 850.402i | 1.11455i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −882.479 | − | 776.184i | −1.15357 | − | 1.01462i | ||||
\(766\) | 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 | ||||||||
\(771\) | −194.990 | −0.252905 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 437.539 | 0.566027 | 0.283013 | − | 0.959116i | \(-0.408666\pi\) | ||||
0.283013 | + | 0.959116i | \(0.408666\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 943.103 | − | 121.375i | 1.21691 | − | 0.156613i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 91.2762i | − | 0.117473i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −64.2778 | −0.0825132 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 696.141i | 0.891346i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −23.0975 | −0.0294988 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 575.547 | − | 654.365i | 0.733181 | − | 0.833586i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 438.946i | − | 0.557746i | −0.960328 | − | 0.278873i | \(-0.910039\pi\) | ||
0.960328 | − | 0.278873i | \(-0.0899608\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 40.0567i | 0.0507690i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1152.07i | 1.45647i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 180.696i | 0.227864i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −147.242 | − | 129.507i | −0.185210 | − | 0.162902i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 982.414 | 1.23264 | 0.616320 | − | 0.787496i | \(-0.288623\pi\) | ||||
0.616320 | + | 0.787496i | \(0.288623\pi\) | |||||||
\(798\) | 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 | ||||||||
\(805\) | 506.943 | − | 576.366i | 0.629743 | − | 0.715983i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 146.806 | 0.181916 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 449.408 | 0.555510 | 0.277755 | − | 0.960652i | \(-0.410410\pi\) | ||||
0.277755 | + | 0.960652i | \(0.410410\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −610.106 | −0.752288 | −0.376144 | − | 0.926561i | \(-0.622750\pi\) | ||||
−0.376144 | + | 0.926561i | \(0.622750\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −125.667 | −0.154572 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 197.614 | + | 173.811i | 0.242471 | + | 0.213266i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 288.585i | 0.353225i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 386.123 | 0.471456 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1099.76i | − | 1.33954i | −0.742568 | − | 0.669770i | \(-0.766393\pi\) | ||
0.742568 | − | 0.669770i | \(-0.233607\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 236.092 | 0.286867 | 0.143434 | − | 0.989660i | \(-0.454186\pi\) | ||||
0.143434 | + | 0.989660i | \(0.454186\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 233.738 | − | 30.0815i | 0.283319 | − | 0.0364625i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1266.81i | 1.53182i | 0.642950 | + | 0.765908i | \(0.277710\pi\) | ||||
−0.642950 | + | 0.765908i | \(0.722290\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.7642i | 0.0503790i | 0.999683 | + | 0.0251895i | \(0.00801891\pi\) | ||||
−0.999683 | + | 0.0251895i | \(0.991981\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 69.1993i | 0.0832723i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1408.57i | − | 1.69095i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 253.215 | − | 287.892i | 0.303252 | − | 0.344781i | ||||
\(836\) | 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 | ||||||||
\(845\) | −493.754 | + | 561.371i | −0.584324 | + | 0.664344i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1761.32 | −2.07948 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −255.024 | −0.300381 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −252.933 | −0.297219 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1215.58 | 1.42507 | 0.712533 | − | 0.701639i | \(-0.247548\pi\) | ||||
0.712533 | + | 0.701639i | \(0.247548\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −138.660 | + | 157.648i | −0.162175 | + | 0.184384i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 997.998i | − | 1.16452i | −0.813001 | − | 0.582262i | \(-0.802168\pi\) | ||
0.813001 | − | 0.582262i | \(-0.197832\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1110.42 | −1.29269 | −0.646347 | − | 0.763044i | \(-0.723704\pi\) | ||||
−0.646347 | + | 0.763044i | \(0.723704\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 73.3646i | − | 0.0852086i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1372.33 | 1.59019 | 0.795094 | − | 0.606486i | \(-0.207422\pi\) | ||||
0.795094 | + | 0.606486i | \(0.207422\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.1117 | + | 36.5092i | −0.0371233 | + | 0.0422072i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 241.545i | − | 0.278599i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2182.06i | − | 2.51101i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 225.111i | 0.258451i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 743.280i | − | 0.851409i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1042.17 | + | 702.942i | 1.19105 | + | 0.803362i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −776.337 | −0.885219 | −0.442609 | − | 0.896714i | \(-0.645947\pi\) | ||||
−0.442609 | + | 0.896714i | \(0.645947\pi\) | |||||||
\(878\) | 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 | ||||||||
\(885\) | −141.548 | − | 124.499i | −0.159941 | − | 0.140676i | ||||
\(886\) | 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 | ||||||||
\(891\) | 1256.04 | 1.40969 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −301.361 | −0.337470 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 513.497 | − | 583.818i | 0.573740 | − | 0.652311i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 36.9039i | 0.0411414i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −90.6094 | −0.100789 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1934.33i | 2.14687i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −329.382 | −0.364764 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 939.899 | + | 826.688i | 1.03856 | + | 0.913468i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1639.15i | − | 1.80722i | −0.428358 | − | 0.903609i | \(-0.640908\pi\) | ||
0.428358 | − | 0.903609i | \(-0.359092\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 724.598i | − | 0.797137i | ||||||
\(910\) | 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 | ||||||||
\(915\) | 74.0625 | − | 84.2050i | 0.0809426 | − | 0.0920273i | ||||
\(916\) | 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 | ||||||||
\(925\) | −52.8741 | − | 410.840i | −0.0571612 | − | 0.444151i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −411.205 | −0.443587 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −368.537 | −0.396703 | −0.198352 | − | 0.980131i | \(-0.563559\pi\) | ||||
−0.198352 | + | 0.980131i | \(0.563559\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −251.630 | −0.270279 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −115.399 | −0.123686 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | −174.599 | −0.185941 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 189.017i | 0.200869i | 0.994944 | + | 0.100434i | \(0.0320232\pi\) | ||||
−0.994944 | + | 0.100434i | \(0.967977\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −203.299 | −0.215588 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −366.076 | − | 321.982i | −0.387382 | − | 0.340721i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 664.319i | 0.701498i | 0.936470 | + | 0.350749i | \(0.114073\pi\) | ||||
−0.936470 | + | 0.350749i | \(0.885927\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 158.189i | 0.166690i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 38.5610i | − | 0.0405479i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 173.943i | − | 0.182522i | −0.995827 | − | 0.0912610i | \(-0.970910\pi\) | ||
0.995827 | − | 0.0912610i | \(-0.0290898\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −417.221 | − | 366.967i | −0.436881 | − | 0.384259i | ||||
\(956\) | 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 | ||||||||
\(965\) | 38.5581 | + | 33.9138i | 0.0399566 | + | 0.0351438i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 255.364 | 0.264078 | 0.132039 | − | 0.991245i | \(-0.457848\pi\) | ||||
0.132039 | + | 0.991245i | \(0.457848\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −71.4309 | −0.0737161 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1623.60 | 1.67209 | 0.836046 | − | 0.548659i | \(-0.184861\pi\) | ||||
0.836046 | + | 0.548659i | \(0.184861\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1290.46 | 1.32627 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −59.9430 | + | 7.71453i | −0.0614800 | + | 0.00791233i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 104.946i | − | 0.107416i | −0.998557 | − | 0.0537082i | \(-0.982896\pi\) | ||
0.998557 | − | 0.0537082i | \(-0.0171041\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1833.13 | 1.87245 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 735.681i | − | 0.749930i | ||||||
\(982\) | 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 | ||||||||
\(987\) | − | 343.964i | − | 0.348494i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 912.742i | 0.922894i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1509.57i | 1.52328i | 0.648001 | + | 0.761639i | \(0.275605\pi\) | ||||
−0.648001 | + | 0.761639i | \(0.724395\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 153.821i | 0.154905i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −732.215 | − | 644.020i | −0.735894 | − | 0.647256i | ||||
\(996\) | 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 | 1280.3.e.f.639.4 | 6 | ||
4.3 | odd | 2 | 1280.3.e.g.639.3 | 6 | |||
5.4 | even | 2 | 1280.3.e.i.639.3 | 6 | |||
8.3 | odd | 2 | 1280.3.e.i.639.4 | 6 | |||
8.5 | even | 2 | 1280.3.e.h.639.3 | 6 | |||
16.3 | odd | 4 | 160.3.h.a.159.3 | ✓ | 6 | ||
16.5 | even | 4 | 320.3.h.f.319.4 | 6 | |||
16.11 | odd | 4 | 320.3.h.g.319.4 | 6 | |||
16.13 | even | 4 | 160.3.h.b.159.3 | yes | 6 | ||
20.19 | odd | 2 | 1280.3.e.h.639.4 | 6 | |||
40.19 | odd | 2 | inner | 1280.3.e.f.639.3 | 6 | ||
40.29 | even | 2 | 1280.3.e.g.639.4 | 6 | |||
48.29 | odd | 4 | 1440.3.j.b.1279.6 | 6 | |||
48.35 | even | 4 | 1440.3.j.a.1279.6 | 6 | |||
80.3 | even | 4 | 800.3.b.h.351.4 | 6 | |||
80.13 | odd | 4 | 800.3.b.h.351.3 | 6 | |||
80.19 | odd | 4 | 160.3.h.b.159.4 | yes | 6 | ||
80.27 | even | 4 | 1600.3.b.w.1151.4 | 6 | |||
80.29 | even | 4 | 160.3.h.a.159.4 | yes | 6 | ||
80.37 | odd | 4 | 1600.3.b.w.1151.3 | 6 | |||
80.43 | even | 4 | 1600.3.b.v.1151.3 | 6 | |||
80.53 | odd | 4 | 1600.3.b.v.1151.4 | 6 | |||
80.59 | odd | 4 | 320.3.h.f.319.3 | 6 | |||
80.67 | even | 4 | 800.3.b.i.351.3 | 6 | |||
80.69 | even | 4 | 320.3.h.g.319.3 | 6 | |||
80.77 | odd | 4 | 800.3.b.i.351.4 | 6 | |||
240.29 | odd | 4 | 1440.3.j.a.1279.5 | 6 | |||
240.179 | even | 4 | 1440.3.j.b.1279.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.3.h.a.159.3 | ✓ | 6 | 16.3 | odd | 4 | ||
160.3.h.a.159.4 | yes | 6 | 80.29 | even | 4 | ||
160.3.h.b.159.3 | yes | 6 | 16.13 | even | 4 | ||
160.3.h.b.159.4 | yes | 6 | 80.19 | odd | 4 | ||
320.3.h.f.319.3 | 6 | 80.59 | odd | 4 | |||
320.3.h.f.319.4 | 6 | 16.5 | even | 4 | |||
320.3.h.g.319.3 | 6 | 80.69 | even | 4 | |||
320.3.h.g.319.4 | 6 | 16.11 | odd | 4 | |||
800.3.b.h.351.3 | 6 | 80.13 | odd | 4 | |||
800.3.b.h.351.4 | 6 | 80.3 | even | 4 | |||
800.3.b.i.351.3 | 6 | 80.67 | even | 4 | |||
800.3.b.i.351.4 | 6 | 80.77 | odd | 4 | |||
1280.3.e.f.639.3 | 6 | 40.19 | odd | 2 | inner | ||
1280.3.e.f.639.4 | 6 | 1.1 | even | 1 | trivial | ||
1280.3.e.g.639.3 | 6 | 4.3 | odd | 2 | |||
1280.3.e.g.639.4 | 6 | 40.29 | even | 2 | |||
1280.3.e.h.639.3 | 6 | 8.5 | even | 2 | |||
1280.3.e.h.639.4 | 6 | 20.19 | odd | 2 | |||
1280.3.e.i.639.3 | 6 | 5.4 | even | 2 | |||
1280.3.e.i.639.4 | 6 | 8.3 | odd | 2 | |||
1440.3.j.a.1279.5 | 6 | 240.29 | odd | 4 | |||
1440.3.j.a.1279.6 | 6 | 48.35 | even | 4 | |||
1440.3.j.b.1279.5 | 6 | 240.179 | even | 4 | |||
1440.3.j.b.1279.6 | 6 | 48.29 | odd | 4 | |||
1600.3.b.v.1151.3 | 6 | 80.43 | even | 4 | |||
1600.3.b.v.1151.4 | 6 | 80.53 | odd | 4 | |||
1600.3.b.w.1151.3 | 6 | 80.37 | odd | 4 | |||
1600.3.b.w.1151.4 | 6 | 80.27 | even | 4 |