Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1520,3,Mod(721,1520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1520.721");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1520 = 2^{4} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1520.h (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: | \(41.4170001828\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 62x^{10} + 1445x^{8} + 15924x^{6} + 83244x^{4} + 170640x^{2} + 55600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{9}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 721.11 | ||
Root | \(3.53755i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1520.721 |
Dual form | 1520.3.h.b.721.2 |
$q$-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 \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(401\) | \(1141\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 3.53755i | 1.17918i | 0.807701 | + | 0.589592i | \(0.200712\pi\) | ||||
−0.807701 | + | 0.589592i | \(0.799288\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.23607 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.468611 | −0.0669444 | −0.0334722 | − | 0.999440i | \(-0.510657\pi\) | ||||
−0.0334722 | + | 0.999440i | \(0.510657\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.51429 | −0.390477 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.1082 | 1.28256 | 0.641281 | − | 0.767306i | \(-0.278403\pi\) | ||||
0.641281 | + | 0.767306i | \(0.278403\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 11.0914i | − | 0.853185i | −0.904444 | − | 0.426593i | \(-0.859714\pi\) | ||
0.904444 | − | 0.426593i | \(-0.140286\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 7.91021i | − | 0.527347i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −22.0318 | −1.29599 | −0.647995 | − | 0.761644i | \(-0.724392\pi\) | ||||
−0.647995 | + | 0.761644i | \(0.724392\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −16.8411 | − | 8.79644i | −0.886374 | − | 0.462971i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.65774i | − | 0.0789398i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 41.1864 | 1.79071 | 0.895357 | − | 0.445348i | \(-0.146920\pi\) | ||||
0.895357 | + | 0.445348i | \(0.146920\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19.4060i | 0.718740i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 46.7187i | 1.61099i | 0.592604 | + | 0.805494i | \(0.298100\pi\) | ||||
−0.592604 | + | 0.805494i | \(0.701900\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 33.9265i | 1.09440i | 0.837001 | + | 0.547201i | \(0.184307\pi\) | ||||
−0.837001 | + | 0.547201i | \(0.815693\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 49.9085i | 1.51238i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.04785 | 0.0299384 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 62.6340i | 1.69281i | 0.532540 | + | 0.846405i | \(0.321238\pi\) | ||||
−0.532540 | + | 0.846405i | \(0.678762\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 39.2365 | 1.00606 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 23.5359i | 0.574046i | 0.957924 | + | 0.287023i | \(0.0926656\pi\) | ||||
−0.957924 | + | 0.287023i | \(0.907334\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 32.8769 | 0.764579 | 0.382289 | − | 0.924043i | \(-0.375136\pi\) | ||||
0.382289 | + | 0.924043i | \(0.375136\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.85820 | 0.174627 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −43.2839 | −0.920935 | −0.460468 | − | 0.887677i | \(-0.652318\pi\) | ||||
−0.460468 | + | 0.887677i | \(0.652318\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.7804 | −0.995518 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 77.9388i | − | 1.52821i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 99.9844i | − | 1.88650i | −0.332086 | − | 0.943249i | \(-0.607752\pi\) | ||
0.332086 | − | 0.943249i | \(-0.392248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −31.5469 | −0.573579 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 31.1179 | − | 59.5763i | 0.545928 | − | 1.04520i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 66.7119i | − | 1.13071i | −0.824848 | − | 0.565355i | \(-0.808739\pi\) | ||
0.824848 | − | 0.565355i | \(-0.191261\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −36.0483 | −0.590956 | −0.295478 | − | 0.955350i | \(-0.595479\pi\) | ||||
−0.295478 | + | 0.955350i | \(0.595479\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.64684 | 0.0261402 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 24.8011i | 0.381556i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 93.5215i | 1.39584i | 0.716174 | + | 0.697921i | \(0.245892\pi\) | ||||
−0.716174 | + | 0.697921i | \(0.754108\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 145.699i | 2.11158i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 124.406i | 1.75220i | 0.482128 | + | 0.876101i | \(0.339864\pi\) | ||||
−0.482128 | + | 0.876101i | \(0.660136\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 41.3341 | 0.566220 | 0.283110 | − | 0.959087i | \(-0.408634\pi\) | ||||
0.283110 | + | 0.959087i | \(0.408634\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 17.6878i | 0.235837i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.61125 | −0.0858604 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 27.2511i | 0.344950i | 0.985014 | + | 0.172475i | \(0.0551764\pi\) | ||||
−0.985014 | + | 0.172475i | \(0.944824\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −100.278 | −1.23800 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 32.9101 | 0.396507 | 0.198253 | − | 0.980151i | \(-0.436473\pi\) | ||||
0.198253 | + | 0.980151i | \(0.436473\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 49.2647 | 0.579585 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −165.270 | −1.89965 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 86.3670i | − | 0.970416i | −0.874399 | − | 0.485208i | \(-0.838744\pi\) | ||
0.874399 | − | 0.485208i | \(-0.161256\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.19755i | 0.0571160i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −120.017 | −1.29050 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 37.6578 | + | 19.6694i | 0.396398 | + | 0.207047i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 20.8071i | − | 0.214506i | −0.994232 | − | 0.107253i | \(-0.965795\pi\) | ||
0.994232 | − | 0.107253i | \(-0.0342054\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −49.5803 | −0.500811 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −118.267 | −1.17096 | −0.585482 | − | 0.810685i | \(-0.699095\pi\) | ||||
−0.585482 | + | 0.810685i | \(0.699095\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 107.875i | 1.04733i | 0.851924 | + | 0.523666i | \(0.175436\pi\) | ||||
−0.851924 | + | 0.523666i | \(0.824564\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.70681i | 0.0353030i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 16.6498i | − | 0.155606i | −0.996969 | − | 0.0778029i | \(-0.975210\pi\) | ||
0.996969 | − | 0.0778029i | \(-0.0247905\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 34.4048i | − | 0.315640i | −0.987468 | − | 0.157820i | \(-0.949553\pi\) | ||
0.987468 | − | 0.157820i | \(-0.0504466\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −221.571 | −1.99614 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 34.2888i | 0.303441i | 0.988423 | + | 0.151720i | \(0.0484813\pi\) | ||||
−0.988423 | + | 0.151720i | \(0.951519\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −92.0957 | −0.800832 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 38.9784i | 0.333149i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.3244 | 0.0867593 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 78.0409 | 0.644966 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −83.2594 | −0.676906 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1803 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 245.621i | 1.93402i | 0.254733 | + | 0.967012i | \(0.418013\pi\) | ||||
−0.254733 | + | 0.967012i | \(0.581987\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 116.304i | 0.901580i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −196.826 | −1.50249 | −0.751245 | − | 0.660024i | \(-0.770546\pi\) | ||||
−0.751245 | + | 0.660024i | \(0.770546\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.89192 | + | 4.12211i | 0.0593377 | + | 0.0309933i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 43.3931i | − | 0.321430i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 249.410 | 1.82051 | 0.910255 | − | 0.414049i | \(-0.135886\pi\) | ||||
0.910255 | + | 0.414049i | \(0.135886\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −116.069 | −0.835030 | −0.417515 | − | 0.908670i | \(-0.637099\pi\) | ||||
−0.417515 | + | 0.908670i | \(0.637099\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 153.119i | − | 1.08595i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 156.480i | − | 1.09426i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 104.466i | − | 0.720456i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 172.563i | − | 1.17390i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −220.978 | −1.48308 | −0.741538 | − | 0.670911i | \(-0.765903\pi\) | ||||
−0.741538 | + | 0.670911i | \(0.765903\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 237.670i | − | 1.57397i | −0.616972 | − | 0.786985i | \(-0.711641\pi\) | ||
0.616972 | − | 0.786985i | \(-0.288359\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 77.4263 | 0.506054 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 75.8619i | − | 0.489431i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 35.3231 | 0.224988 | 0.112494 | − | 0.993652i | \(-0.464116\pi\) | ||||
0.112494 | + | 0.993652i | \(0.464116\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 353.700 | 2.22453 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.3004 | −0.119878 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −71.4216 | −0.438169 | −0.219085 | − | 0.975706i | \(-0.570307\pi\) | ||||
−0.219085 | + | 0.975706i | \(0.570307\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 111.599i | − | 0.676356i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 185.054i | 1.10811i | 0.832481 | + | 0.554054i | \(0.186920\pi\) | ||||
−0.832481 | + | 0.554054i | \(0.813080\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 45.9807 | 0.272075 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 59.1845 | + | 30.9133i | 0.346108 | + | 0.180779i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 231.572i | 1.33857i | 0.743006 | + | 0.669284i | \(0.233399\pi\) | ||||
−0.743006 | + | 0.669284i | \(0.766601\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.34305 | −0.0133889 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 235.997 | 1.33332 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 165.841i | 0.926487i | 0.886231 | + | 0.463244i | \(0.153315\pi\) | ||||
−0.886231 | + | 0.463244i | \(0.846685\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 25.0838i | − | 0.138585i | −0.997596 | − | 0.0692923i | \(-0.977926\pi\) | ||
0.997596 | − | 0.0692923i | \(-0.0220741\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 127.523i | − | 0.696846i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 140.054i | − | 0.757048i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −310.829 | −1.66219 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 9.09386i | − | 0.0481156i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 52.0646 | 0.272590 | 0.136295 | − | 0.990668i | \(-0.456481\pi\) | ||||
0.136295 | + | 0.990668i | \(0.456481\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 70.3184i | 0.364344i | 0.983267 | + | 0.182172i | \(0.0583128\pi\) | ||||
−0.983267 | + | 0.182172i | \(0.941687\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −87.7354 | −0.449925 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −131.361 | −0.666809 | −0.333404 | − | 0.942784i | \(-0.608197\pi\) | ||||
−0.333404 | + | 0.942784i | \(0.608197\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 120.966 | 0.607870 | 0.303935 | − | 0.952693i | \(-0.401699\pi\) | ||||
0.303935 | + | 0.952693i | \(0.401699\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −330.837 | −1.64596 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 21.8929i | − | 0.107847i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 52.6278i | − | 0.256721i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −144.741 | −0.699233 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −237.597 | − | 124.102i | −1.13683 | − | 0.593789i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 381.578i | − | 1.80843i | −0.427082 | − | 0.904213i | \(-0.640459\pi\) | ||
0.427082 | − | 0.904213i | \(-0.359541\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −440.094 | −2.06617 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −73.5150 | −0.341930 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 15.8983i | − | 0.0732641i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 146.222i | 0.667678i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 244.364i | 1.10572i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 155.025i | 0.695181i | 0.937646 | + | 0.347591i | \(0.113000\pi\) | ||||
−0.937646 | + | 0.347591i | \(0.887000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −17.5715 | −0.0780954 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 237.583i | 1.04662i | 0.852142 | + | 0.523310i | \(0.175303\pi\) | ||||
−0.852142 | + | 0.523310i | \(0.824697\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −275.640 | −1.20367 | −0.601834 | − | 0.798621i | \(-0.705563\pi\) | ||||
−0.601834 | + | 0.798621i | \(0.705563\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 23.3877i | − | 0.101245i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −271.591 | −1.16562 | −0.582812 | − | 0.812607i | \(-0.698048\pi\) | ||||
−0.582812 | + | 0.812607i | \(0.698048\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 96.7858 | 0.411855 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −96.4021 | −0.406760 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 236.246 | 0.988476 | 0.494238 | − | 0.869327i | \(-0.335447\pi\) | ||||
0.494238 | + | 0.869327i | \(0.335447\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 346.159i | − | 1.43634i | −0.695866 | − | 0.718171i | \(-0.744979\pi\) | ||
0.695866 | − | 0.718171i | \(-0.255021\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 180.086i | − | 0.741096i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 109.076 | 0.445209 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −97.5649 | + | 186.791i | −0.395000 | + | 0.756241i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 116.421i | 0.467555i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −222.337 | −0.885805 | −0.442903 | − | 0.896570i | \(-0.646051\pi\) | ||||
−0.442903 | + | 0.896570i | \(0.646051\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 581.066 | 2.29670 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 174.277i | 0.683437i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 143.232i | 0.557324i | 0.960389 | + | 0.278662i | \(0.0898909\pi\) | ||||
−0.960389 | + | 0.278662i | \(0.910109\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 29.3510i | − | 0.113324i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 164.183i | − | 0.629054i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 240.308 | 0.913718 | 0.456859 | − | 0.889539i | \(-0.348974\pi\) | ||||
0.456859 | + | 0.889539i | \(0.348974\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 223.572i | 0.843668i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 305.528 | 1.14430 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 261.289i | 0.971335i | 0.874144 | + | 0.485668i | \(0.161423\pi\) | ||||
−0.874144 | + | 0.485668i | \(0.838577\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 234.829 | 0.866527 | 0.433263 | − | 0.901267i | \(-0.357362\pi\) | ||||
0.433263 | + | 0.901267i | \(0.357362\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.3866 | −0.0673503 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 70.5409 | 0.256512 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.6370 | −0.103383 | −0.0516913 | − | 0.998663i | \(-0.516461\pi\) | ||||
−0.0516913 | + | 0.998663i | \(0.516461\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 119.227i | − | 0.427339i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 35.2442i | − | 0.125424i | −0.998032 | − | 0.0627121i | \(-0.980025\pi\) | ||
0.998032 | − | 0.0627121i | \(-0.0199750\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 159.486 | 0.563554 | 0.281777 | − | 0.959480i | \(-0.409076\pi\) | ||||
0.281777 | + | 0.959480i | \(0.409076\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −69.5817 | + | 133.217i | −0.244146 | + | 0.467427i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 11.0292i | − | 0.0384291i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 196.402 | 0.679591 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 73.6061 | 0.252942 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 79.8129i | 0.272399i | 0.990681 | + | 0.136199i | \(0.0434888\pi\) | ||||
−0.990681 | + | 0.136199i | \(0.956511\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 149.172i | 0.505669i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 273.783i | 0.921829i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 456.816i | − | 1.52781i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.4065 | −0.0511843 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 418.377i | − | 1.38078i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 80.6065 | 0.264284 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 135.726i | − | 0.442105i | −0.975262 | − | 0.221052i | \(-0.929051\pi\) | ||
0.975262 | − | 0.221052i | \(-0.0709492\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −381.614 | −1.23500 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −131.701 | −0.423475 | −0.211737 | − | 0.977327i | \(-0.567912\pi\) | ||||
−0.211737 | + | 0.977327i | \(0.567912\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 570.037 | 1.82120 | 0.910602 | − | 0.413285i | \(-0.135619\pi\) | ||||
0.910602 | + | 0.413285i | \(0.135619\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.68244 | −0.0116903 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 334.101i | 1.05395i | 0.849882 | + | 0.526974i | \(0.176673\pi\) | ||||
−0.849882 | + | 0.526974i | \(0.823327\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 659.116i | 2.06619i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 58.8997 | 0.183488 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 371.040 | + | 193.802i | 1.14873 | + | 0.600006i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 55.4570i | − | 0.170637i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 121.709 | 0.372198 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.2833 | 0.0616514 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 63.3605i | − | 0.191421i | −0.995409 | − | 0.0957107i | \(-0.969488\pi\) | ||
0.995409 | − | 0.0957107i | \(-0.0305124\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 220.114i | − | 0.661003i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 209.120i | − | 0.624240i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 153.496i | − | 0.455479i | −0.973722 | − | 0.227739i | \(-0.926867\pi\) | ||
0.973722 | − | 0.227739i | \(-0.0731335\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −121.298 | −0.357812 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 478.641i | 1.40364i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 45.8210 | 0.133589 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 325.794i | − | 0.944329i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 272.066 | 0.784052 | 0.392026 | − | 0.919954i | \(-0.371774\pi\) | ||||
0.392026 | + | 0.919954i | \(0.371774\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 187.833 | 0.538205 | 0.269102 | − | 0.963112i | \(-0.413273\pi\) | ||||
0.269102 | + | 0.963112i | \(0.413273\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 215.240 | 0.613219 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.8460 | −0.0873825 | −0.0436913 | − | 0.999045i | \(-0.513912\pi\) | ||||
−0.0436913 | + | 0.999045i | \(0.513912\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 278.181i | − | 0.783609i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 36.5230i | 0.102305i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −513.758 | −1.43108 | −0.715541 | − | 0.698571i | \(-0.753820\pi\) | ||||
−0.715541 | + | 0.698571i | \(0.753820\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 206.245 | + | 296.284i | 0.571316 | + | 0.820730i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 276.074i | 0.760535i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −92.4258 | −0.253221 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.6982 | 0.0618481 | 0.0309240 | − | 0.999522i | \(-0.490155\pi\) | ||||
0.0309240 | + | 0.999522i | \(0.490155\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 82.7119i | − | 0.224152i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 46.8538i | 0.126290i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 108.632i | 0.291238i | 0.989341 | + | 0.145619i | \(0.0465174\pi\) | ||||
−0.989341 | + | 0.145619i | \(0.953483\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 39.5511i | − | 0.105469i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 518.176 | 1.37447 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 203.467i | − | 0.536852i | −0.963300 | − | 0.268426i | \(-0.913497\pi\) | ||
0.963300 | − | 0.268426i | \(-0.0865035\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −868.897 | −2.28057 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 38.4623i | − | 0.100424i | −0.998739 | − | 0.0502119i | \(-0.984010\pi\) | ||
0.998739 | − | 0.0502119i | \(-0.0159897\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.7832 | 0.0383979 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −115.539 | −0.298550 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 521.954 | 1.34179 | 0.670893 | − | 0.741555i | \(-0.265911\pi\) | ||||
0.670893 | + | 0.741555i | \(0.265911\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −907.413 | −2.32075 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 696.283i | − | 1.77171i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 60.9352i | − | 0.154266i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 369.352 | 0.930357 | 0.465179 | − | 0.885217i | \(-0.345990\pi\) | ||||
0.465179 | + | 0.885217i | \(0.345990\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −14.5822 | + | 27.9181i | −0.0365468 | + | 0.0699702i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 128.575i | − | 0.320636i | −0.987065 | − | 0.160318i | \(-0.948748\pi\) | ||
0.987065 | − | 0.160318i | \(-0.0512520\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 376.292 | 0.933727 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 224.229 | 0.553653 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 883.652i | 2.17113i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 611.222i | 1.49443i | 0.664583 | + | 0.747215i | \(0.268609\pi\) | ||||
−0.664583 | + | 0.747215i | \(0.731391\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 882.301i | 2.14672i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 31.2619i | 0.0756947i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −73.5891 | −0.177323 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 410.601i | − | 0.984655i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 218.656 | 0.521853 | 0.260927 | − | 0.965359i | \(-0.415972\pi\) | ||||
0.260927 | + | 0.965359i | \(0.415972\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 534.615i | − | 1.26987i | −0.772566 | − | 0.634935i | \(-0.781027\pi\) | ||
0.772566 | − | 0.634935i | \(-0.218973\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 152.112 | 0.359604 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −110.159 | −0.259198 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.8926 | 0.0395612 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 553.555 | 1.29034 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 81.6513i | 0.189446i | 0.995504 | + | 0.0947231i | \(0.0301966\pi\) | ||||
−0.995504 | + | 0.0947231i | \(0.969803\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 90.7988i | − | 0.209697i | −0.994488 | − | 0.104848i | \(-0.966564\pi\) | ||
0.994488 | − | 0.104848i | \(-0.0334357\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 369.555 | 0.849551 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −693.625 | − | 362.294i | −1.58724 | − | 0.829048i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 89.4005i | 0.203646i | 0.994803 | + | 0.101823i | \(0.0324675\pi\) | ||||
−0.994803 | + | 0.101823i | \(0.967533\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 171.429 | 0.388727 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −127.590 | −0.288013 | −0.144007 | − | 0.989577i | \(-0.545999\pi\) | ||||
−0.144007 | + | 0.989577i | \(0.545999\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 193.123i | 0.433983i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 781.723i | − | 1.74882i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 441.576i | − | 0.983465i | −0.870746 | − | 0.491733i | \(-0.836364\pi\) | ||
0.870746 | − | 0.491733i | \(-0.163636\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 332.049i | 0.736250i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 840.769 | 1.85600 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 11.6221i | − | 0.0255430i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 166.817 | 0.365027 | 0.182513 | − | 0.983203i | \(-0.441577\pi\) | ||||
0.182513 | + | 0.983203i | \(0.441577\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 427.550i | − | 0.931481i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −377.705 | −0.819317 | −0.409659 | − | 0.912239i | \(-0.634352\pi\) | ||||
−0.409659 | + | 0.912239i | \(0.634352\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 161.036 | 0.347810 | 0.173905 | − | 0.984762i | \(-0.444361\pi\) | ||||
0.173905 | + | 0.984762i | \(0.444361\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 268.365 | 0.577130 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 63.1149 | 0.135150 | 0.0675749 | − | 0.997714i | \(-0.478474\pi\) | ||||
0.0675749 | + | 0.997714i | \(0.478474\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 43.8252i | − | 0.0934438i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 124.958i | 0.265303i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 463.833 | 0.980620 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −84.2055 | − | 43.9822i | −0.177275 | − | 0.0925941i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 351.374i | 0.736634i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 536.087 | 1.11918 | 0.559589 | − | 0.828770i | \(-0.310959\pi\) | ||||
0.559589 | + | 0.828770i | \(0.310959\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 694.699 | 1.44428 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 68.2763i | − | 0.141359i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 46.5260i | 0.0959299i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 247.634i | − | 0.508490i | −0.967140 | − | 0.254245i | \(-0.918173\pi\) | ||
0.967140 | − | 0.254245i | \(-0.0818269\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 252.658i | − | 0.516683i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −895.324 | −1.82347 | −0.911735 | − | 0.410779i | \(-0.865257\pi\) | ||||
−0.911735 | + | 0.410779i | \(0.865257\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1029.30i | − | 2.08783i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 110.865 | 0.223969 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 58.2982i | − | 0.117300i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −78.2101 | −0.156734 | −0.0783669 | − | 0.996925i | \(-0.524971\pi\) | ||||
−0.0783669 | + | 0.996925i | \(0.524971\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −654.638 | −1.30666 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 568.406 | 1.13003 | 0.565015 | − | 0.825080i | \(-0.308870\pi\) | ||||
0.565015 | + | 0.825080i | \(0.308870\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 264.454 | 0.523671 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 162.659i | 0.320827i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 528.251i | 1.03782i | 0.854829 | + | 0.518911i | \(0.173662\pi\) | ||||
−0.854829 | + | 0.518911i | \(0.826338\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.3696 | −0.0379053 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 170.704 | − | 326.818i | 0.332756 | − | 0.637073i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 241.216i | − | 0.468381i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −610.658 | −1.18116 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −819.200 | −1.57842 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1004.23i | 1.92750i | 0.266807 | + | 0.963750i | \(0.414031\pi\) | ||||
−0.266807 | + | 0.963750i | \(0.585969\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 588.915i | 1.12603i | 0.826446 | + | 0.563016i | \(0.190359\pi\) | ||||
−0.826446 | + | 0.563016i | \(0.809641\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 8.28868i | − | 0.0157880i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 747.462i | − | 1.41833i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1167.32 | 2.20666 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 234.445i | 0.441516i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 261.046 | 0.489767 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 37.2301i | 0.0695891i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −586.672 | −1.09250 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −688.203 | −1.27681 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 431.404 | 0.797420 | 0.398710 | − | 0.917077i | \(-0.369458\pi\) | ||||
0.398710 | + | 0.917077i | \(0.369458\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 88.7353 | 0.163417 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 76.9314i | 0.141159i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 257.771i | − | 0.471244i | −0.971845 | − | 0.235622i | \(-0.924287\pi\) | ||
0.971845 | − | 0.235622i | \(-0.0757127\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 126.684 | 0.230755 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 410.958 | − | 786.794i | 0.745840 | − | 1.42794i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 12.7701i | − | 0.0230925i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 495.448 | 0.892699 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −616.514 | −1.10685 | −0.553424 | − | 0.832900i | \(-0.686679\pi\) | ||||
−0.553424 | + | 0.832900i | \(0.686679\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 364.651i | − | 0.652327i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 1099.58i | − | 1.96003i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 79.5657i | 0.141324i | 0.997500 | + | 0.0706622i | \(0.0225113\pi\) | ||||
−0.997500 | + | 0.0706622i | \(0.977489\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 76.6720i | − | 0.135703i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 46.9915 | 0.0828775 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 118.993i | 0.209127i | 0.994518 | + | 0.104563i | \(0.0333445\pi\) | ||||
−0.994518 | + | 0.104563i | \(0.966655\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1004.19 | 1.75865 | 0.879323 | − | 0.476227i | \(-0.157996\pi\) | ||||
0.879323 | + | 0.476227i | \(0.157996\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 184.181i | 0.321434i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 205.932 | 0.358143 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −795.249 | −1.37825 | −0.689123 | − | 0.724644i | \(-0.742004\pi\) | ||||
−0.689123 | + | 0.724644i | \(0.742004\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −248.755 | −0.429629 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.4220 | −0.0265439 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1410.60i | − | 2.41955i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 87.1584i | − | 0.148989i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −192.221 | −0.327463 | −0.163732 | − | 0.986505i | \(-0.552353\pi\) | ||||
−0.163732 | + | 0.986505i | \(0.552353\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 298.432 | − | 571.359i | 0.506676 | − | 0.970049i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 464.698i | − | 0.786290i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −83.5456 | −0.140886 | −0.0704432 | − | 0.997516i | \(-0.522441\pi\) | ||||
−0.0704432 | + | 0.997516i | \(0.522441\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.0860 | −0.0387999 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 427.924i | 0.716791i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 665.445i | 1.11093i | 0.831541 | + | 0.555463i | \(0.187459\pi\) | ||||
−0.831541 | + | 0.555463i | \(0.812541\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 648.842i | 1.07960i | 0.841792 | + | 0.539802i | \(0.181501\pi\) | ||||
−0.841792 | + | 0.539802i | \(0.818499\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 328.662i | − | 0.545044i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −174.505 | −0.288438 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 212.490i | − | 0.350066i | −0.984563 | − | 0.175033i | \(-0.943997\pi\) | ||
0.984563 | − | 0.175033i | \(-0.0560032\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 77.4472 | 0.127171 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 480.080i | 0.785728i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 878.692 | 1.43343 | 0.716715 | − | 0.697366i | \(-0.245645\pi\) | ||||
0.716715 | + | 0.697366i | \(0.245645\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 186.174 | 0.302722 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −77.9272 | −0.126300 | −0.0631501 | − | 0.998004i | \(-0.520115\pi\) | ||||
−0.0631501 | + | 0.998004i | \(0.520115\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 744.679 | 1.20304 | 0.601518 | − | 0.798860i | \(-0.294563\pi\) | ||||
0.601518 | + | 0.798860i | \(0.294563\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 799.264i | 1.28706i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 40.4725i | 0.0649639i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 439.017 | − | 840.514i | 0.700187 | − | 1.34053i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1379.94i | − | 2.19387i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −583.634 | −0.924934 | −0.462467 | − | 0.886636i | \(-0.653036\pi\) | ||||
−0.462467 | + | 0.886636i | \(0.653036\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1349.85 | 2.13247 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 549.225i | − | 0.864921i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 541.043i | 0.849361i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 437.200i | − | 0.684194i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 835.068i | − | 1.30276i | −0.758753 | − | 0.651379i | \(-0.774191\pi\) | ||
0.758753 | − | 0.651379i | \(-0.225809\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 348.076 | 0.541331 | 0.270666 | − | 0.962673i | \(-0.412756\pi\) | ||||
0.270666 | + | 0.962673i | \(0.412756\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 260.063i | − | 0.403199i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 667.701 | 1.03199 | 0.515997 | − | 0.856590i | \(-0.327421\pi\) | ||||
0.515997 | + | 0.856590i | \(0.327421\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 941.184i | − | 1.45021i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 56.2411 | 0.0863919 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −913.560 | −1.39902 | −0.699510 | − | 0.714623i | \(-0.746598\pi\) | ||||
−0.699510 | + | 0.714623i | \(0.746598\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 440.117 | 0.671934 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −145.260 | −0.221096 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 654.040i | 0.992474i | 0.868187 | + | 0.496237i | \(0.165285\pi\) | ||||
−0.868187 | + | 0.496237i | \(0.834715\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 284.200i | 0.429955i | 0.976619 | + | 0.214977i | \(0.0689678\pi\) | ||||
−0.976619 | + | 0.214977i | \(0.931032\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −864.451 | −1.30385 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17.6469 | − | 9.21731i | −0.0265366 | − | 0.0138606i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1924.18i | 2.88482i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −548.411 | −0.819747 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −508.576 | −0.757938 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 652.742i | − | 0.969899i | −0.874542 | − | 0.484950i | \(-0.838838\pi\) | ||
0.874542 | − | 0.484950i | \(-0.161162\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 97.0300i | 0.143748i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 548.221i | − | 0.809781i | −0.914365 | − | 0.404890i | \(-0.867310\pi\) | ||
0.914365 | − | 0.404890i | \(-0.132690\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.75041i | 0.0143600i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −840.462 | −1.23416 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 183.490i | − | 0.268653i | −0.990937 | − | 0.134327i | \(-0.957113\pi\) | ||
0.990937 | − | 0.134327i | \(-0.0428872\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −557.697 | −0.814156 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 975.092i | − | 1.41935i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1108.97 | −1.60953 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 700.503 | 1.01375 | 0.506876 | − | 0.862019i | \(-0.330800\pi\) | ||||
0.506876 | + | 0.862019i | \(0.330800\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.2339 | 0.0335265 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 259.539 | 0.373437 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 518.539i | − | 0.743958i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 960.766i | − | 1.37449i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 353.859 | 0.504791 | 0.252396 | − | 0.967624i | \(-0.418782\pi\) | ||||
0.252396 | + | 0.967624i | \(0.418782\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 550.956 | − | 1054.83i | 0.783721 | − | 1.50046i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 342.385i | 0.485653i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 55.4214 | 0.0783895 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −592.019 | −0.835006 | −0.417503 | − | 0.908676i | \(-0.637095\pi\) | ||||
−0.417503 | + | 0.908676i | \(0.637095\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 95.7682i | − | 0.134695i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1397.31i | 1.95976i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 349.899i | 0.489369i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 835.732i | 1.16560i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −385.615 | −0.536321 | −0.268160 | − | 0.963374i | \(-0.586416\pi\) | ||||
−0.268160 | + | 0.963374i | \(0.586416\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 50.5515i | − | 0.0701130i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1224.55 | 1.69371 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 233.593i | 0.322198i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1136.34 | 1.56306 | 0.781530 | − | 0.623867i | \(-0.214439\pi\) | ||||
0.781530 | + | 0.623867i | \(0.214439\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −265.440 | −0.364116 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −724.338 | −0.990887 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −871.591 | −1.18907 | −0.594537 | − | 0.804068i | \(-0.702665\pi\) | ||||
−0.594537 | + | 0.804068i | \(0.702665\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 385.863i | 0.524984i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1319.42i | 1.79026i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −605.269 | −0.819038 | −0.409519 | − | 0.912301i | \(-0.634304\pi\) | ||||
−0.409519 | + | 0.912301i | \(0.634304\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −660.785 | − | 345.141i | −0.891748 | − | 0.465778i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 490.677i | 0.660400i | 0.943911 | + | 0.330200i | \(0.107116\pi\) | ||||
−0.943911 | + | 0.330200i | \(0.892884\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 494.122 | 0.663252 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −115.656 | −0.154827 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.80229i | 0.0104169i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1075.66i | 1.43230i | 0.697948 | + | 0.716149i | \(0.254097\pi\) | ||||
−0.697948 | + | 0.716149i | \(0.745903\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 786.530i | − | 1.04453i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 531.445i | 0.703901i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −775.132 | −1.02395 | −0.511976 | − | 0.859000i | \(-0.671086\pi\) | ||||
−0.511976 | + | 0.859000i | \(0.671086\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2055.55i | 2.70824i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 801.361 | 1.05304 | 0.526519 | − | 0.850164i | \(-0.323497\pi\) | ||||
0.526519 | + | 0.850164i | \(0.323497\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.1225i | 0.0211303i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −173.130 | −0.226314 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −739.929 | −0.964705 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 419.799 | 0.545902 | 0.272951 | − | 0.962028i | \(-0.412000\pi\) | ||||
0.272951 | + | 0.962028i | \(0.412000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −506.692 | −0.657188 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 518.154i | − | 0.670316i | −0.942162 | − | 0.335158i | \(-0.891210\pi\) | ||
0.942162 | − | 0.335158i | \(-0.108790\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 169.632i | 0.218880i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 103.831 | 0.133630 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 207.032 | − | 396.370i | 0.265766 | − | 0.508819i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1755.15i | 2.24731i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −906.622 | −1.15788 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −78.9849 | −0.100618 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 393.934i | − | 0.500551i | −0.968175 | − | 0.250276i | \(-0.919479\pi\) | ||
0.968175 | − | 0.250276i | \(-0.0805212\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 850.102i | 1.07744i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 16.0681i | − | 0.0203136i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 399.827i | 0.504195i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −790.898 | −0.994840 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 305.628i | − | 0.383474i | −0.981446 | − | 0.191737i | \(-0.938588\pi\) | ||
0.981446 | − | 0.191737i | \(-0.0614120\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 953.625 | 1.19352 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 303.519i | 0.378925i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 583.149 | 0.726213 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 43.1570 | 0.0536112 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −924.325 | −1.14538 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1186.46 | 1.46657 | 0.733285 | − | 0.679921i | \(-0.237986\pi\) | ||||
0.733285 | + | 0.679921i | \(0.237986\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1581.99i | − | 1.95067i | −0.220740 | − | 0.975333i | \(-0.570847\pi\) | ||
0.220740 | − | 0.975333i | \(-0.429153\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 830.719i | 1.02180i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 159.704 | 0.195955 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −553.683 | − | 289.200i | −0.677703 | − | 0.353978i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 18.2657i | − | 0.0223025i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −95.9928 | −0.116922 | −0.0584609 | − | 0.998290i | \(-0.518619\pi\) | ||||
−0.0584609 | + | 0.998290i | \(0.518619\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1292.87 | −1.57093 | −0.785464 | − | 0.618908i | \(-0.787576\pi\) | ||||
−0.785464 | + | 0.618908i | \(0.787576\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 249.542i | 0.302476i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44.7405i | 0.0540998i | 0.999634 | + | 0.0270499i | \(0.00861130\pi\) | ||||
−0.999634 | + | 0.0270499i | \(0.991389\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 802.912i | − | 0.968530i | −0.874921 | − | 0.484265i | \(-0.839087\pi\) | ||
0.874921 | − | 0.484265i | \(-0.160913\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 101.305i | − | 0.121907i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1074.72 | 1.29018 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 413.793i | − | 0.495561i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −658.377 | −0.786591 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 346.934i | 0.413509i | 0.978393 | + | 0.206754i | \(0.0662901\pi\) | ||||
−0.978393 | + | 0.206754i | \(0.933710\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1341.63 | −1.59528 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 124.678 | 0.147898 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −102.816 | −0.121676 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36.5708 | −0.0431769 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 564.190i | 0.664534i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2579.67i | 3.03134i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 766.503 | 0.898597 | 0.449298 | − | 0.893382i | \(-0.351674\pi\) | ||||
0.449298 | + | 0.893382i | \(0.351674\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −132.341 | − | 69.1242i | −0.154784 | − | 0.0808470i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1701.81i | − | 1.98577i | −0.119063 | − | 0.992887i | \(-0.537989\pi\) | ||
0.119063 | − | 0.992887i | \(-0.462011\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −436.740 | −0.508429 | −0.254214 | − | 0.967148i | \(-0.581817\pi\) | ||||
−0.254214 | + | 0.967148i | \(0.581817\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 39.0163 | 0.0453151 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 555.776i | − | 0.644004i | −0.946739 | − | 0.322002i | \(-0.895644\pi\) | ||
0.946739 | − | 0.322002i | \(-0.104356\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 517.812i | − | 0.598626i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 694.782i | 0.801364i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 384.463i | 0.442420i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1037.28 | 1.19091 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 73.1221i | 0.0837595i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.23923 | 0.00598769 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 506.241i | 0.577242i | 0.957443 | + | 0.288621i | \(0.0931967\pi\) | ||||
−0.957443 | + | 0.288621i | \(0.906803\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −282.342 | −0.321209 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1208.80 | 1.37208 | 0.686038 | − | 0.727566i | \(-0.259348\pi\) | ||||
0.686038 | + | 0.727566i | \(0.259348\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −221.477 | −0.250823 | −0.125412 | − | 0.992105i | \(-0.540025\pi\) | ||||
−0.125412 | + | 0.992105i | \(0.540025\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −527.705 | −0.596277 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1533.50i | − | 1.72886i | −0.502753 | − | 0.864430i | \(-0.667680\pi\) | ||
0.502753 | − | 0.864430i | \(-0.332320\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 115.101i | − | 0.129472i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1414.75 | −1.58782 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 728.949 | + | 380.745i | 0.816292 | + | 0.426366i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 370.832i | − | 0.414338i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1616.01 | 1.80157 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1585.00 | −1.76307 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2202.84i | 2.44488i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 54.5012i | − | 0.0603557i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 56.0891i | 0.0619769i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 670.343i | − | 0.739077i | −0.929215 | − | 0.369539i | \(-0.879516\pi\) | ||
0.929215 | − | 0.369539i | \(-0.120484\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 415.626 | 0.457234 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 351.217i | 0.385529i | 0.981245 | + | 0.192765i | \(0.0617454\pi\) | ||||
−0.981245 | + | 0.192765i | \(0.938255\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 464.301 | 0.508545 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 285.150i | 0.311639i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 92.2348 | 0.100583 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 701.167 | 0.762967 | 0.381484 | − | 0.924376i | \(-0.375413\pi\) | ||||
0.381484 | + | 0.924376i | \(0.375413\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 480.139 | 0.521323 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1379.84 | 1.49495 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 313.170i | 0.338562i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 379.105i | − | 0.408959i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1521.71 | −1.63801 | −0.819004 | − | 0.573787i | \(-0.805474\pi\) | ||||
−0.819004 | + | 0.573787i | \(0.805474\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 821.516 | + | 429.094i | 0.882401 | + | 0.460896i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 465.898i | − | 0.499355i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 695.035 | 0.743353 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1462.89 | 1.56125 | 0.780624 | − | 0.625001i | \(-0.214902\pi\) | ||||
0.780624 | + | 0.625001i | \(0.214902\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2016.54i | 2.14754i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 460.939i | − | 0.489840i | −0.969543 | − | 0.244920i | \(-0.921238\pi\) | ||
0.969543 | − | 0.244920i | \(-0.0787617\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 969.359i | 1.02795i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 20.3345i | 0.0215180i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −707.825 | −0.747439 | −0.373719 | − | 0.927542i | \(-0.621918\pi\) | ||||
−0.373719 | + | 0.927542i | \(0.621918\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 458.453i | − | 0.483091i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1181.90 | −1.24280 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1553.32i | − | 1.62993i | −0.579511 | − | 0.814964i | \(-0.696757\pi\) | ||
0.579511 | − | 0.814964i | \(-0.303243\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −116.420 | −0.121906 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2331.66 | −2.43642 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −116.876 | −0.121873 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −190.004 | −0.197715 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 58.5124i | 0.0607605i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 157.237i | − | 0.162940i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −155.746 | −0.161061 | −0.0805307 | − | 0.996752i | \(-0.525661\pi\) | ||||
−0.0805307 | + | 0.996752i | \(0.525661\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −685.584 | + | 1312.58i | −0.707517 | + | 1.35457i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 297.557i | 0.306444i | 0.988192 | + | 0.153222i | \(0.0489649\pi\) | ||||
−0.988192 | + | 0.153222i | \(0.951035\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 54.3913 | 0.0559006 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 196.182 | 0.201213 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 618.917i | − | 0.633487i | −0.948511 | − | 0.316744i | \(-0.897411\pi\) | ||
0.948511 | − | 0.316744i | \(-0.102589\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1218.48i | − | 1.24462i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 120.908i | 0.123250i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 632.754i | − | 0.643697i | −0.946791 | − | 0.321848i | \(-0.895696\pi\) | ||
0.946791 | − | 0.321848i | \(-0.104304\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 293.733 | 0.298206 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 71.7534i | 0.0726984i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1354.08 | 1.36914 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1876.53i | 1.89358i | 0.321858 | + | 0.946788i | \(0.395692\pi\) | ||||
−0.321858 | + | 0.946788i | \(0.604308\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 224.141 | 0.225721 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −270.489 | −0.271848 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −270.045 | −0.270857 | −0.135429 | − | 0.990787i | \(-0.543241\pi\) | ||||
−0.135429 | + | 0.990787i | \(0.543241\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1215.47 | −1.21669 |
(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 | 1520.3.h.b.721.11 | 12 | ||
4.3 | odd | 2 | 380.3.e.a.341.2 | ✓ | 12 | ||
12.11 | even | 2 | 3420.3.o.a.721.9 | 12 | |||
19.18 | odd | 2 | inner | 1520.3.h.b.721.2 | 12 | ||
20.3 | even | 4 | 1900.3.g.c.949.21 | 24 | |||
20.7 | even | 4 | 1900.3.g.c.949.4 | 24 | |||
20.19 | odd | 2 | 1900.3.e.f.1101.11 | 12 | |||
76.75 | even | 2 | 380.3.e.a.341.11 | yes | 12 | ||
228.227 | odd | 2 | 3420.3.o.a.721.10 | 12 | |||
380.227 | odd | 4 | 1900.3.g.c.949.22 | 24 | |||
380.303 | odd | 4 | 1900.3.g.c.949.3 | 24 | |||
380.379 | even | 2 | 1900.3.e.f.1101.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.3.e.a.341.2 | ✓ | 12 | 4.3 | odd | 2 | ||
380.3.e.a.341.11 | yes | 12 | 76.75 | even | 2 | ||
1520.3.h.b.721.2 | 12 | 19.18 | odd | 2 | inner | ||
1520.3.h.b.721.11 | 12 | 1.1 | even | 1 | trivial | ||
1900.3.e.f.1101.2 | 12 | 380.379 | even | 2 | |||
1900.3.e.f.1101.11 | 12 | 20.19 | odd | 2 | |||
1900.3.g.c.949.3 | 24 | 380.303 | odd | 4 | |||
1900.3.g.c.949.4 | 24 | 20.7 | even | 4 | |||
1900.3.g.c.949.21 | 24 | 20.3 | even | 4 | |||
1900.3.g.c.949.22 | 24 | 380.227 | odd | 4 | |||
3420.3.o.a.721.9 | 12 | 12.11 | even | 2 | |||
3420.3.o.a.721.10 | 12 | 228.227 | odd | 2 |