Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,3,Mod(685,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("882.685");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.0327593166\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 685.1 | ||
Root | \(-0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.685 |
Dual form | 882.3.c.b.685.2 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | − 8.36308i | − 1.67262i | −0.548260 | − | 0.836308i | \(-0.684709\pi\) | ||||
0.548260 | − | 0.836308i | \(-0.315291\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 11.8272i | 1.18272i | ||||||||
\(11\) | −6.00000 | −0.545455 | −0.272727 | − | 0.962091i | \(-0.587926\pi\) | ||||
−0.272727 | + | 0.962091i | \(0.587926\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.8639i | 1.37414i | 0.726590 | + | 0.687072i | \(0.241104\pi\) | ||||
−0.726590 | + | 0.687072i | \(0.758896\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − 18.7554i | − 1.10326i | −0.834090 | − | 0.551629i | \(-0.814006\pi\) | ||||
0.834090 | − | 0.551629i | \(-0.185994\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 17.0233i | − 0.895965i | −0.894042 | − | 0.447983i | \(-0.852143\pi\) | ||||
0.894042 | − | 0.447983i | \(-0.147857\pi\) | |||||||
\(20\) | − 16.7262i | − 0.836308i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.48528 | 0.385695 | ||||||||
\(23\) | −13.4558 | −0.585037 | −0.292518 | − | 0.956260i | \(-0.594493\pi\) | ||||
−0.292518 | + | 0.956260i | \(0.594493\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −44.9411 | −1.79765 | ||||||||
\(26\) | − 25.2633i | − 0.971666i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −33.9411 | −1.17038 | −0.585192 | − | 0.810895i | \(-0.698981\pi\) | ||||
−0.585192 | + | 0.810895i | \(0.698981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 14.7479i | − 0.475740i | −0.971297 | − | 0.237870i | \(-0.923551\pi\) | ||||
0.971297 | − | 0.237870i | \(-0.0764491\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 26.5241i | 0.780121i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.97056 | 0.161367 | 0.0806833 | − | 0.996740i | \(-0.474290\pi\) | ||||
0.0806833 | + | 0.996740i | \(0.474290\pi\) | |||||||
\(38\) | 24.0746i | 0.633543i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 23.6544i | 0.591359i | ||||||||
\(41\) | 35.2354i | 0.859399i | 0.902972 | + | 0.429700i | \(0.141381\pi\) | ||||
−0.902972 | + | 0.429700i | \(0.858619\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 15.4853 | 0.360123 | 0.180061 | − | 0.983655i | \(-0.442370\pi\) | ||||
0.180061 | + | 0.983655i | \(0.442370\pi\) | |||||||
\(44\) | −12.0000 | −0.272727 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 19.0294 | 0.413683 | ||||||||
\(47\) | 33.2061i | 0.706514i | 0.935526 | + | 0.353257i | \(0.114926\pi\) | ||||
−0.935526 | + | 0.353257i | \(0.885074\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 63.5563 | 1.27113 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 35.7277i | 0.687072i | ||||||||
\(53\) | 34.5442 | 0.651777 | 0.325888 | − | 0.945408i | \(-0.394337\pi\) | ||||
0.325888 | + | 0.945408i | \(0.394337\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 50.1785i | 0.912336i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 48.0000 | 0.827586 | ||||||||
\(59\) | 27.3647i | 0.463808i | 0.972739 | + | 0.231904i | \(0.0744955\pi\) | ||||
−0.972739 | + | 0.231904i | \(0.925505\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 40.3805i | − 0.661976i | −0.943635 | − | 0.330988i | \(-0.892618\pi\) | ||||
0.943635 | − | 0.330988i | \(-0.107382\pi\) | |||||||
\(62\) | 20.8567i | 0.336399i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 149.397 | 2.29841 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −114.397 | −1.70742 | −0.853709 | − | 0.520751i | \(-0.825652\pi\) | ||||
−0.853709 | + | 0.520751i | \(0.825652\pi\) | |||||||
\(68\) | − 37.5108i | − 0.551629i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −18.6030 | −0.262015 | −0.131007 | − | 0.991381i | \(-0.541821\pi\) | ||||
−0.131007 | + | 0.991381i | \(0.541821\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 117.032i | 1.60318i | 0.597874 | + | 0.801590i | \(0.296012\pi\) | ||||
−0.597874 | + | 0.801590i | \(0.703988\pi\) | |||||||
\(74\) | −8.44365 | −0.114103 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 34.0467i | − 0.447983i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −88.3381 | −1.11820 | −0.559102 | − | 0.829099i | \(-0.688854\pi\) | ||||
−0.559102 | + | 0.829099i | \(0.688854\pi\) | |||||||
\(80\) | − 33.4523i | − 0.418154i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 49.8303i | − 0.607687i | ||||||||
\(83\) | 75.7601i | 0.912772i | 0.889782 | + | 0.456386i | \(0.150856\pi\) | ||||
−0.889782 | + | 0.456386i | \(0.849144\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −156.853 | −1.84533 | ||||||||
\(86\) | −21.8995 | −0.254645 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 16.9706 | 0.192847 | ||||||||
\(89\) | 20.7846i | 0.233535i | 0.993159 | + | 0.116767i | \(0.0372532\pi\) | ||||
−0.993159 | + | 0.116767i | \(0.962747\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −26.9117 | −0.292518 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 46.9606i | − 0.499581i | ||||||||
\(95\) | −142.368 | −1.49861 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 30.5826i | − 0.315284i | −0.987496 | − | 0.157642i | \(-0.949611\pi\) | ||||
0.987496 | − | 0.157642i | \(-0.0503892\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −89.8823 | −0.898823 | ||||||||
\(101\) | 127.968i | 1.26701i | 0.773739 | + | 0.633504i | \(0.218384\pi\) | ||||
−0.773739 | + | 0.633504i | \(0.781616\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 80.9563i | − 0.785983i | −0.919542 | − | 0.392992i | \(-0.871440\pi\) | ||||
0.919542 | − | 0.392992i | \(-0.128560\pi\) | |||||||
\(104\) | − 50.5266i | − 0.485833i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −48.8528 | −0.460876 | ||||||||
\(107\) | −169.456 | −1.58370 | −0.791850 | − | 0.610716i | \(-0.790882\pi\) | ||||
−0.791850 | + | 0.610716i | \(0.790882\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 178.941 | 1.64166 | 0.820831 | − | 0.571171i | \(-0.193511\pi\) | ||||
0.820831 | + | 0.571171i | \(0.193511\pi\) | |||||||
\(110\) | − 70.9631i | − 0.645119i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3970 | 0.153955 | 0.0769777 | − | 0.997033i | \(-0.475473\pi\) | ||||
0.0769777 | + | 0.997033i | \(0.475473\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 112.532i | 0.978542i | ||||||||
\(116\) | −67.8823 | −0.585192 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 38.6995i | − 0.327962i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −85.0000 | −0.702479 | ||||||||
\(122\) | 57.1067i | 0.468088i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 29.4959i | − 0.237870i | ||||||||
\(125\) | 166.769i | 1.33415i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 167.426 | 1.31832 | 0.659159 | − | 0.752004i | \(-0.270912\pi\) | ||||
0.659159 | + | 0.752004i | \(0.270912\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −211.279 | −1.62522 | ||||||||
\(131\) | 1.78304i | 0.0136110i | 0.999977 | + | 0.00680549i | \(0.00216627\pi\) | ||||
−0.999977 | + | 0.00680549i | \(0.997834\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 161.782 | 1.20733 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 53.0482i | 0.390061i | ||||||||
\(137\) | −100.971 | −0.737011 | −0.368506 | − | 0.929625i | \(-0.620130\pi\) | ||||
−0.368506 | + | 0.929625i | \(0.620130\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 140.542i | 1.01110i | 0.862799 | + | 0.505548i | \(0.168710\pi\) | ||||
−0.862799 | + | 0.505548i | \(0.831290\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 26.3087 | 0.185272 | ||||||||
\(143\) | − 107.183i | − 0.749533i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 283.852i | 1.95760i | ||||||||
\(146\) | − 165.508i | − 1.13362i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.9411 | 0.0806833 | ||||||||
\(149\) | −182.912 | −1.22760 | −0.613798 | − | 0.789463i | \(-0.710359\pi\) | ||||
−0.613798 | + | 0.789463i | \(0.710359\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −288.794 | −1.91254 | −0.956271 | − | 0.292481i | \(-0.905519\pi\) | ||||
−0.956271 | + | 0.292481i | \(0.905519\pi\) | |||||||
\(152\) | 48.1493i | 0.316771i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −123.338 | −0.795730 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 187.061i | − 1.19147i | −0.803179 | − | 0.595737i | \(-0.796860\pi\) | ||||
0.803179 | − | 0.595737i | \(-0.203140\pi\) | |||||||
\(158\) | 124.929 | 0.790689 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 47.3087i | 0.295680i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.0589 | 0.0985207 | 0.0492604 | − | 0.998786i | \(-0.484314\pi\) | ||||
0.0492604 | + | 0.998786i | \(0.484314\pi\) | |||||||
\(164\) | 70.4707i | 0.429700i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 107.141i | − 0.645427i | ||||||||
\(167\) | − 176.117i | − 1.05459i | −0.849681 | − | 0.527297i | \(-0.823206\pi\) | ||||
0.849681 | − | 0.527297i | \(-0.176794\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −150.118 | −0.888271 | ||||||||
\(170\) | 221.823 | 1.30484 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 30.9706 | 0.180061 | ||||||||
\(173\) | 231.152i | 1.33614i | 0.744098 | + | 0.668070i | \(0.232879\pi\) | ||||
−0.744098 | + | 0.668070i | \(0.767121\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −24.0000 | −0.136364 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 29.3939i | − 0.165134i | ||||||||
\(179\) | 85.2792 | 0.476420 | 0.238210 | − | 0.971214i | \(-0.423439\pi\) | ||||
0.238210 | + | 0.971214i | \(0.423439\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.58655i | 0.0308649i | 0.999881 | + | 0.0154325i | \(0.00491250\pi\) | ||||
−0.999881 | + | 0.0154325i | \(0.995087\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 38.0589 | 0.206842 | ||||||||
\(185\) | − 49.9323i | − 0.269904i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 112.532i | 0.601777i | ||||||||
\(188\) | 66.4123i | 0.353257i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 201.338 | 1.05967 | ||||||||
\(191\) | −185.397 | −0.970665 | −0.485332 | − | 0.874330i | \(-0.661301\pi\) | ||||
−0.485332 | + | 0.874330i | \(0.661301\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 227.794 | 1.18028 | 0.590140 | − | 0.807301i | \(-0.299073\pi\) | ||||
0.590140 | + | 0.807301i | \(0.299073\pi\) | |||||||
\(194\) | 43.2503i | 0.222940i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −123.161 | −0.625185 | −0.312593 | − | 0.949887i | \(-0.601197\pi\) | ||||
−0.312593 | + | 0.949887i | \(0.601197\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 6.23188i | − 0.0313160i | −0.999877 | − | 0.0156580i | \(-0.995016\pi\) | ||||
0.999877 | − | 0.0156580i | \(-0.00498430\pi\) | |||||||
\(200\) | 127.113 | 0.635563 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 180.974i | − 0.895910i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 294.676 | 1.43744 | ||||||||
\(206\) | 114.489i | 0.555774i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 71.4555i | 0.343536i | ||||||||
\(209\) | 102.140i | 0.488708i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −124.912 | −0.591999 | −0.295999 | − | 0.955188i | \(-0.595653\pi\) | ||||
−0.295999 | + | 0.955188i | \(0.595653\pi\) | |||||||
\(212\) | 69.0883 | 0.325888 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 239.647 | 1.11984 | ||||||||
\(215\) | − 129.505i | − 0.602347i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −253.061 | −1.16083 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 100.357i | 0.456168i | ||||||||
\(221\) | 335.044 | 1.51603 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 228.631i | 1.02525i | 0.858613 | + | 0.512625i | \(0.171327\pi\) | ||||
−0.858613 | + | 0.512625i | \(0.828673\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −24.6030 | −0.108863 | ||||||||
\(227\) | − 169.537i | − 0.746859i | −0.927659 | − | 0.373430i | \(-0.878182\pi\) | ||||
0.927659 | − | 0.373430i | \(-0.121818\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 34.6920i | 0.151493i | 0.997127 | + | 0.0757467i | \(0.0241340\pi\) | ||||
−0.997127 | + | 0.0757467i | \(0.975866\pi\) | |||||||
\(230\) | − 159.145i | − 0.691934i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 96.0000 | 0.413793 | ||||||||
\(233\) | 254.485 | 1.09221 | 0.546106 | − | 0.837716i | \(-0.316110\pi\) | ||||
0.546106 | + | 0.837716i | \(0.316110\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 277.706 | 1.18173 | ||||||||
\(236\) | 54.7293i | 0.231904i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −197.147 | −0.824884 | −0.412442 | − | 0.910984i | \(-0.635324\pi\) | ||||
−0.412442 | + | 0.910984i | \(0.635324\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 88.4701i | − 0.367096i | −0.983011 | − | 0.183548i | \(-0.941242\pi\) | ||||
0.983011 | − | 0.183548i | \(-0.0587582\pi\) | |||||||
\(242\) | 120.208 | 0.496728 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 80.7611i | − 0.330988i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 304.103 | 1.23118 | ||||||||
\(248\) | 41.7134i | 0.168199i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 235.847i | − 0.943389i | ||||||||
\(251\) | − 215.903i | − 0.860172i | −0.902788 | − | 0.430086i | \(-0.858483\pi\) | ||||
0.902788 | − | 0.430086i | \(-0.141517\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 80.7351 | 0.319111 | ||||||||
\(254\) | −236.777 | −0.932192 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 4.30463i | 0.0167495i | 0.999965 | + | 0.00837477i | \(0.00266580\pi\) | ||||
−0.999965 | + | 0.00837477i | \(0.997334\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 298.794 | 1.14921 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 2.52160i | − 0.00962441i | ||||||||
\(263\) | −282.676 | −1.07481 | −0.537407 | − | 0.843323i | \(-0.680596\pi\) | ||||
−0.537407 | + | 0.843323i | \(0.680596\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 288.896i | − 1.09017i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −228.794 | −0.853709 | ||||||||
\(269\) | − 381.934i | − 1.41983i | −0.704288 | − | 0.709914i | \(-0.748734\pi\) | ||||
0.704288 | − | 0.709914i | \(-0.251266\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 84.3271i | − 0.311170i | −0.987822 | − | 0.155585i | \(-0.950274\pi\) | ||||
0.987822 | − | 0.155585i | \(-0.0497263\pi\) | |||||||
\(272\) | − 75.0215i | − 0.275814i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 142.794 | 0.521146 | ||||||||
\(275\) | 269.647 | 0.980534 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −137.118 | −0.495010 | −0.247505 | − | 0.968887i | \(-0.579611\pi\) | ||||
−0.247505 | + | 0.968887i | \(0.579611\pi\) | |||||||
\(278\) | − 198.757i | − 0.714953i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 325.103 | 1.15695 | 0.578474 | − | 0.815701i | \(-0.303648\pi\) | ||||
0.578474 | + | 0.815701i | \(0.303648\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 194.575i | − 0.687545i | −0.939053 | − | 0.343773i | \(-0.888295\pi\) | ||||
0.939053 | − | 0.343773i | \(-0.111705\pi\) | |||||||
\(284\) | −37.2061 | −0.131007 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 151.580i | 0.530000i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −62.7645 | −0.217178 | ||||||||
\(290\) | − 401.428i | − 1.38423i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 234.064i | 0.801590i | ||||||||
\(293\) | − 239.702i | − 0.818095i | −0.912513 | − | 0.409048i | \(-0.865861\pi\) | ||||
0.912513 | − | 0.409048i | \(-0.134139\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 228.853 | 0.775772 | ||||||||
\(296\) | −16.8873 | −0.0570517 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 258.676 | 0.868041 | ||||||||
\(299\) | − 240.373i | − 0.803924i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 408.416 | 1.35237 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 68.0933i | − 0.223991i | ||||||||
\(305\) | −337.706 | −1.10723 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 540.272i | − 1.75984i | −0.475120 | − | 0.879921i | \(-0.657595\pi\) | ||||
0.475120 | − | 0.879921i | \(-0.342405\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 174.426 | 0.562666 | ||||||||
\(311\) | 404.196i | 1.29966i | 0.760078 | + | 0.649832i | \(0.225161\pi\) | ||||
−0.760078 | + | 0.649832i | \(0.774839\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 131.296i | − 0.419477i | −0.977757 | − | 0.209739i | \(-0.932739\pi\) | ||||
0.977757 | − | 0.209739i | \(-0.0672613\pi\) | |||||||
\(314\) | 264.545i | 0.842500i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −176.676 | −0.559102 | ||||||||
\(317\) | 93.9411 | 0.296344 | 0.148172 | − | 0.988962i | \(-0.452661\pi\) | ||||
0.148172 | + | 0.988962i | \(0.452661\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 203.647 | 0.638391 | ||||||||
\(320\) | − 66.9046i | − 0.209077i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −319.279 | −0.988481 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 802.822i | − 2.47022i | ||||||||
\(326\) | −22.7107 | −0.0696647 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 99.6607i | − 0.303843i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −261.368 | −0.789630 | −0.394815 | − | 0.918761i | \(-0.629191\pi\) | ||||
−0.394815 | + | 0.918761i | \(0.629191\pi\) | |||||||
\(332\) | 151.520i | 0.456386i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 249.067i | 0.745710i | ||||||||
\(335\) | 956.711i | 2.85585i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 136.265 | 0.404347 | 0.202173 | − | 0.979350i | \(-0.435200\pi\) | ||||
0.202173 | + | 0.979350i | \(0.435200\pi\) | |||||||
\(338\) | 212.299 | 0.628102 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −313.706 | −0.922664 | ||||||||
\(341\) | 88.4876i | 0.259494i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −43.7990 | −0.127323 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 326.899i | − 0.944794i | ||||||||
\(347\) | 322.191 | 0.928504 | 0.464252 | − | 0.885703i | \(-0.346323\pi\) | ||||
0.464252 | + | 0.885703i | \(0.346323\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 346.495i | − 0.992821i | −0.868088 | − | 0.496411i | \(-0.834651\pi\) | ||||
0.868088 | − | 0.496411i | \(-0.165349\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 33.9411 | 0.0964237 | ||||||||
\(353\) | − 620.591i | − 1.75805i | −0.476777 | − | 0.879025i | \(-0.658195\pi\) | ||||
0.476777 | − | 0.879025i | \(-0.341805\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 155.579i | 0.438250i | ||||||||
\(356\) | 41.5692i | 0.116767i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −120.603 | −0.336880 | ||||||||
\(359\) | −20.2355 | −0.0563663 | −0.0281831 | − | 0.999603i | \(-0.508972\pi\) | ||||
−0.0281831 | + | 0.999603i | \(0.508972\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 71.2061 | 0.197247 | ||||||||
\(362\) | − 7.90058i | − 0.0218248i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 978.749 | 2.68151 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 311.574i | 0.848975i | 0.905434 | + | 0.424488i | \(0.139546\pi\) | ||||
−0.905434 | + | 0.424488i | \(0.860454\pi\) | |||||||
\(368\) | −53.8234 | −0.146259 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 70.6149i | 0.190851i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −681.382 | −1.82676 | −0.913380 | − | 0.407107i | \(-0.866538\pi\) | ||||
−0.913380 | + | 0.407107i | \(0.866538\pi\) | |||||||
\(374\) | − 159.145i | − 0.425521i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 93.9211i | − 0.249790i | ||||||||
\(377\) | − 606.320i | − 1.60828i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −624.779 | −1.64849 | −0.824246 | − | 0.566231i | \(-0.808401\pi\) | ||||
−0.824246 | + | 0.566231i | \(0.808401\pi\) | |||||||
\(380\) | −284.735 | −0.749303 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 262.191 | 0.686364 | ||||||||
\(383\) | − 138.300i | − 0.361098i | −0.983566 | − | 0.180549i | \(-0.942213\pi\) | ||||
0.983566 | − | 0.180549i | \(-0.0577874\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −322.149 | −0.834584 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 61.1651i | − 0.157642i | ||||||||
\(389\) | 563.574 | 1.44878 | 0.724388 | − | 0.689393i | \(-0.242123\pi\) | ||||
0.724388 | + | 0.689393i | \(0.242123\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 252.370i | 0.645446i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 174.177 | 0.442073 | ||||||||
\(395\) | 738.779i | 1.87033i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 453.338i | − 1.14191i | −0.820981 | − | 0.570955i | \(-0.806573\pi\) | ||||
0.820981 | − | 0.570955i | \(-0.193427\pi\) | |||||||
\(398\) | 8.81321i | 0.0221438i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −179.765 | −0.449411 | ||||||||
\(401\) | 275.750 | 0.687656 | 0.343828 | − | 0.939033i | \(-0.388276\pi\) | ||||
0.343828 | + | 0.939033i | \(0.388276\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 263.455 | 0.653734 | ||||||||
\(404\) | 255.936i | 0.633504i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −35.8234 | −0.0880181 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 435.831i | 1.06560i | 0.846240 | + | 0.532801i | \(0.178861\pi\) | ||||
−0.846240 | + | 0.532801i | \(0.821139\pi\) | |||||||
\(410\) | −416.735 | −1.01643 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 161.913i | − 0.392992i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 633.588 | 1.52672 | ||||||||
\(416\) | − 101.053i | − 0.242917i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 144.448i | − 0.345569i | ||||||||
\(419\) | − 301.257i | − 0.718991i | −0.933147 | − | 0.359496i | \(-0.882949\pi\) | ||||
0.933147 | − | 0.359496i | \(-0.117051\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −203.794 | −0.484071 | −0.242036 | − | 0.970267i | \(-0.577815\pi\) | ||||
−0.242036 | + | 0.970267i | \(0.577815\pi\) | |||||||
\(422\) | 176.652 | 0.418606 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −97.7056 | −0.230438 | ||||||||
\(425\) | 842.888i | 1.98327i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −338.912 | −0.791850 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 183.147i | 0.425924i | ||||||||
\(431\) | 395.720 | 0.918144 | 0.459072 | − | 0.888399i | \(-0.348182\pi\) | ||||
0.459072 | + | 0.888399i | \(0.348182\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 44.2685i | 0.102237i | 0.998693 | + | 0.0511184i | \(0.0162786\pi\) | ||||
−0.998693 | + | 0.0511184i | \(0.983721\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 357.882 | 0.820831 | ||||||||
\(437\) | 229.063i | 0.524172i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 397.862i | 0.906291i | 0.891437 | + | 0.453146i | \(0.149698\pi\) | ||||
−0.891437 | + | 0.453146i | \(0.850302\pi\) | |||||||
\(440\) | − 141.926i | − 0.322560i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −473.823 | −1.07200 | ||||||||
\(443\) | 118.544 | 0.267594 | 0.133797 | − | 0.991009i | \(-0.457283\pi\) | ||||
0.133797 | + | 0.991009i | \(0.457283\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 173.823 | 0.390614 | ||||||||
\(446\) | − 323.333i | − 0.724961i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −713.897 | −1.58997 | −0.794985 | − | 0.606629i | \(-0.792521\pi\) | ||||
−0.794985 | + | 0.606629i | \(0.792521\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 211.412i | − 0.468763i | ||||||||
\(452\) | 34.7939 | 0.0769777 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 239.762i | 0.528109i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −125.177 | −0.273909 | −0.136955 | − | 0.990577i | \(-0.543731\pi\) | ||||
−0.136955 | + | 0.990577i | \(0.543731\pi\) | |||||||
\(458\) | − 49.0619i | − 0.107122i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 225.065i | 0.489271i | ||||||||
\(461\) | 655.767i | 1.42249i | 0.702945 | + | 0.711244i | \(0.251868\pi\) | ||||
−0.702945 | + | 0.711244i | \(0.748132\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 869.396 | 1.87775 | 0.938873 | − | 0.344265i | \(-0.111872\pi\) | ||||
0.938873 | + | 0.344265i | \(0.111872\pi\) | |||||||
\(464\) | −135.765 | −0.292596 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −359.897 | −0.772310 | ||||||||
\(467\) | 267.372i | 0.572532i | 0.958150 | + | 0.286266i | \(0.0924141\pi\) | ||||
−0.958150 | + | 0.286266i | \(0.907586\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −392.735 | −0.835607 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 77.3989i | − 0.163981i | ||||||||
\(473\) | −92.9117 | −0.196431 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 765.048i | 1.61063i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 278.808 | 0.583281 | ||||||||
\(479\) | 271.737i | 0.567300i | 0.958928 | + | 0.283650i | \(0.0915454\pi\) | ||||
−0.958928 | + | 0.283650i | \(0.908455\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 106.657i | 0.221741i | ||||||||
\(482\) | 125.116i | 0.259576i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −170.000 | −0.351240 | ||||||||
\(485\) | −255.765 | −0.527349 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −561.514 | −1.15301 | −0.576503 | − | 0.817095i | \(-0.695583\pi\) | ||||
−0.576503 | + | 0.817095i | \(0.695583\pi\) | |||||||
\(488\) | 114.213i | 0.234044i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 406.441 | 0.827781 | 0.413891 | − | 0.910327i | \(-0.364170\pi\) | ||||
0.413891 | + | 0.910327i | \(0.364170\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 636.579i | 1.29124i | ||||||||
\(494\) | −430.066 | −0.870579 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 58.9917i | − 0.118935i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −371.426 | −0.744341 | −0.372171 | − | 0.928164i | \(-0.621386\pi\) | ||||
−0.372171 | + | 0.928164i | \(0.621386\pi\) | |||||||
\(500\) | 333.538i | 0.667077i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 305.333i | 0.608234i | ||||||||
\(503\) | 64.6292i | 0.128488i | 0.997934 | + | 0.0642438i | \(0.0204635\pi\) | ||||
−0.997934 | + | 0.0642438i | \(0.979536\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1070.21 | 2.11922 | ||||||||
\(506\) | −114.177 | −0.225646 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 334.853 | 0.659159 | ||||||||
\(509\) | − 1006.77i | − 1.97794i | −0.148125 | − | 0.988969i | \(-0.547324\pi\) | ||||
0.148125 | − | 0.988969i | \(-0.452676\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 6.08767i | − 0.0118437i | ||||||||
\(515\) | −677.044 | −1.31465 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 199.237i | − 0.385371i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −422.558 | −0.812612 | ||||||||
\(521\) | − 372.153i | − 0.714306i | −0.934046 | − | 0.357153i | \(-0.883747\pi\) | ||||
0.934046 | − | 0.357153i | \(-0.116253\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 637.284i | − 1.21852i | −0.792972 | − | 0.609258i | \(-0.791467\pi\) | ||||
0.792972 | − | 0.609258i | \(-0.208533\pi\) | |||||||
\(524\) | 3.56608i | 0.00680549i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 399.765 | 0.760009 | ||||||||
\(527\) | −276.603 | −0.524863 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −347.940 | −0.657732 | ||||||||
\(530\) | 408.560i | 0.770868i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −629.440 | −1.18094 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1417.17i | 2.64892i | ||||||||
\(536\) | 323.563 | 0.603663 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 540.136i | 1.00397i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 220.823 | 0.408176 | 0.204088 | − | 0.978953i | \(-0.434577\pi\) | ||||
0.204088 | + | 0.978953i | \(0.434577\pi\) | |||||||
\(542\) | 119.257i | 0.220031i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 106.096i | 0.195030i | ||||||||
\(545\) | − 1496.50i | − 2.74587i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −160.676 | −0.293741 | −0.146870 | − | 0.989156i | \(-0.546920\pi\) | ||||
−0.146870 | + | 0.989156i | \(0.546920\pi\) | |||||||
\(548\) | −201.941 | −0.368506 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −381.338 | −0.693342 | ||||||||
\(551\) | 577.791i | 1.04862i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 193.914 | 0.350025 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 281.085i | 0.505548i | ||||||||
\(557\) | 474.353 | 0.851622 | 0.425811 | − | 0.904812i | \(-0.359989\pi\) | ||||
0.425811 | + | 0.904812i | \(0.359989\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 276.627i | 0.494860i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −459.765 | −0.818086 | ||||||||
\(563\) | − 496.868i | − 0.882537i | −0.897375 | − | 0.441269i | \(-0.854529\pi\) | ||||
0.897375 | − | 0.441269i | \(-0.145471\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 145.492i | − 0.257508i | ||||||||
\(566\) | 275.171i | 0.486168i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 52.6173 | 0.0926361 | ||||||||
\(569\) | −785.294 | −1.38013 | −0.690065 | − | 0.723748i | \(-0.742418\pi\) | ||||
−0.690065 | + | 0.723748i | \(0.742418\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −715.043 | −1.25226 | −0.626132 | − | 0.779717i | \(-0.715363\pi\) | ||||
−0.626132 | + | 0.779717i | \(0.715363\pi\) | |||||||
\(572\) | − 214.366i | − 0.374766i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 604.721 | 1.05169 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 772.630i | − 1.33905i | −0.742791 | − | 0.669524i | \(-0.766498\pi\) | ||||
0.742791 | − | 0.669524i | \(-0.233502\pi\) | |||||||
\(578\) | 88.7624 | 0.153568 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 567.705i | 0.978801i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −207.265 | −0.355514 | ||||||||
\(584\) | − 331.017i | − 0.566810i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 338.990i | 0.578481i | ||||||||
\(587\) | − 436.477i | − 0.743572i | −0.928318 | − | 0.371786i | \(-0.878746\pi\) | ||||
0.928318 | − | 0.371786i | \(-0.121254\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −251.059 | −0.426246 | ||||||||
\(590\) | −323.647 | −0.548554 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 23.8823 | 0.0403416 | ||||||||
\(593\) | − 834.152i | − 1.40666i | −0.710861 | − | 0.703332i | \(-0.751695\pi\) | ||||
0.710861 | − | 0.703332i | \(-0.248305\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −365.823 | −0.613798 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 339.939i | 0.568460i | ||||||||
\(599\) | −873.588 | −1.45841 | −0.729205 | − | 0.684295i | \(-0.760110\pi\) | ||||
−0.729205 | + | 0.684295i | \(0.760110\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 198.982i | − 0.331085i | −0.986203 | − | 0.165542i | \(-0.947063\pi\) | ||||
0.986203 | − | 0.165542i | \(-0.0529375\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −577.588 | −0.956271 | ||||||||
\(605\) | 710.862i | 1.17498i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 158.950i | 0.261861i | 0.991392 | + | 0.130930i | \(0.0417964\pi\) | ||||
−0.991392 | + | 0.130930i | \(0.958204\pi\) | |||||||
\(608\) | 96.2985i | 0.158386i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 477.588 | 0.782931 | ||||||||
\(611\) | −593.190 | −0.970851 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −714.735 | −1.16596 | −0.582981 | − | 0.812486i | \(-0.698114\pi\) | ||||
−0.582981 | + | 0.812486i | \(0.698114\pi\) | |||||||
\(614\) | 764.059i | 1.24440i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 639.381 | 1.03627 | 0.518137 | − | 0.855298i | \(-0.326626\pi\) | ||||
0.518137 | + | 0.855298i | \(0.326626\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 172.025i | − 0.277908i | −0.990299 | − | 0.138954i | \(-0.955626\pi\) | ||||
0.990299 | − | 0.138954i | \(-0.0443740\pi\) | |||||||
\(620\) | −246.676 | −0.397865 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 571.619i | − 0.919002i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 271.177 | 0.433883 | ||||||||
\(626\) | 185.681i | 0.296615i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 374.123i | − 0.595737i | ||||||||
\(629\) | − 111.980i | − 0.178029i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1141.06 | −1.80833 | −0.904166 | − | 0.427180i | \(-0.859507\pi\) | ||||
−0.904166 | + | 0.427180i | \(0.859507\pi\) | |||||||
\(632\) | 249.858 | 0.395345 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −132.853 | −0.209547 | ||||||||
\(635\) | − 1400.20i | − 2.20504i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −288.000 | −0.451411 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 94.6175i | 0.147840i | ||||||||
\(641\) | −229.103 | −0.357414 | −0.178707 | − | 0.983902i | \(-0.557191\pi\) | ||||
−0.178707 | + | 0.983902i | \(0.557191\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 707.670i | − 1.10058i | −0.834975 | − | 0.550288i | \(-0.814518\pi\) | ||||
0.834975 | − | 0.550288i | \(-0.185482\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 451.529 | 0.698961 | ||||||||
\(647\) | 1179.37i | 1.82283i | 0.411484 | + | 0.911417i | \(0.365011\pi\) | ||||
−0.411484 | + | 0.911417i | \(0.634989\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 164.188i | − 0.252986i | ||||||||
\(650\) | 1135.36i | 1.74671i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 32.1177 | 0.0492604 | ||||||||
\(653\) | 154.764 | 0.237004 | 0.118502 | − | 0.992954i | \(-0.462191\pi\) | ||||
0.118502 | + | 0.992954i | \(0.462191\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.9117 | 0.0227659 | ||||||||
\(656\) | 140.941i | 0.214850i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −591.308 | −0.897280 | −0.448640 | − | 0.893712i | \(-0.648092\pi\) | ||||
−0.448640 | + | 0.893712i | \(0.648092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 162.167i | − 0.245337i | −0.992448 | − | 0.122668i | \(-0.960855\pi\) | ||||
0.992448 | − | 0.122668i | \(-0.0391451\pi\) | |||||||
\(662\) | 369.630 | 0.558353 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − 214.282i | − 0.322714i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 456.706 | 0.684717 | ||||||||
\(668\) | − 352.234i | − 0.527297i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 1352.99i | − 2.01939i | ||||||||
\(671\) | 242.283i | 0.361078i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.3238 | 0.0628883 | 0.0314441 | − | 0.999506i | \(-0.489989\pi\) | ||||
0.0314441 | + | 0.999506i | \(0.489989\pi\) | |||||||
\(674\) | −192.708 | −0.285916 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −300.235 | −0.444135 | ||||||||
\(677\) | − 497.354i | − 0.734643i | −0.930094 | − | 0.367322i | \(-0.880275\pi\) | ||||
0.930094 | − | 0.367322i | \(-0.119725\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 443.647 | 0.652422 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 125.140i | − 0.183490i | ||||||||
\(683\) | −1216.16 | −1.78062 | −0.890308 | − | 0.455359i | \(-0.849511\pi\) | ||||
−0.890308 | + | 0.455359i | \(0.849511\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 844.425i | 1.23274i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 61.9411 | 0.0900307 | ||||||||
\(689\) | 617.092i | 0.895635i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1076.39i | − 1.55773i | −0.627191 | − | 0.778865i | \(-0.715796\pi\) | ||||
0.627191 | − | 0.778865i | \(-0.284204\pi\) | |||||||
\(692\) | 462.305i | 0.668070i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −455.647 | −0.656552 | ||||||||
\(695\) | 1175.37 | 1.69118 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 660.853 | 0.948139 | ||||||||
\(698\) | 490.017i | 0.702031i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 695.897 | 0.992720 | 0.496360 | − | 0.868117i | \(-0.334670\pi\) | ||||
0.496360 | + | 0.868117i | \(0.334670\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 101.639i | − 0.144579i | ||||||||
\(704\) | −48.0000 | −0.0681818 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 877.649i | 1.24313i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 254.824 | 0.359414 | 0.179707 | − | 0.983720i | \(-0.442485\pi\) | ||||
0.179707 | + | 0.983720i | \(0.442485\pi\) | |||||||
\(710\) | − 220.021i | − 0.309889i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 58.7878i | − 0.0825671i | ||||||||
\(713\) | 198.446i | 0.278325i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −896.382 | −1.25368 | ||||||||
\(716\) | 170.558 | 0.238210 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.6173 | 0.0398570 | ||||||||
\(719\) | 1114.20i | 1.54965i | 0.632175 | + | 0.774826i | \(0.282162\pi\) | ||||
−0.632175 | + | 0.774826i | \(0.717838\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −100.701 | −0.139474 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.1731i | 0.0154325i | ||||||||
\(725\) | 1525.35 | 2.10393 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 398.345i | 0.547930i | 0.961740 | + | 0.273965i | \(0.0883353\pi\) | ||||
−0.961740 | + | 0.273965i | \(0.911665\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1384.16 | −1.89611 | ||||||||
\(731\) | − 290.432i | − 0.397308i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 945.139i | 1.28941i | 0.764431 | + | 0.644706i | \(0.223020\pi\) | ||||
−0.764431 | + | 0.644706i | \(0.776980\pi\) | |||||||
\(734\) | − 440.632i | − 0.600316i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 76.1177 | 0.103421 | ||||||||
\(737\) | 686.382 | 0.931319 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 192.632 | 0.260666 | 0.130333 | − | 0.991470i | \(-0.458395\pi\) | ||||
0.130333 | + | 0.991470i | \(0.458395\pi\) | |||||||
\(740\) | − 99.8646i | − 0.134952i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 911.616 | 1.22694 | 0.613470 | − | 0.789718i | \(-0.289773\pi\) | ||||
0.613470 | + | 0.789718i | \(0.289773\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1529.71i | 2.05330i | ||||||||
\(746\) | 963.619 | 1.29172 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 225.065i | 0.300889i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −391.662 | −0.521521 | −0.260760 | − | 0.965404i | \(-0.583973\pi\) | ||||
−0.260760 | + | 0.965404i | \(0.583973\pi\) | |||||||
\(752\) | 132.825i | 0.176628i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 857.466i | 1.13722i | ||||||||
\(755\) | 2415.21i | 3.19895i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −152.823 | −0.201879 | −0.100940 | − | 0.994893i | \(-0.532185\pi\) | ||||
−0.100940 | + | 0.994893i | \(0.532185\pi\) | |||||||
\(758\) | 883.571 | 1.16566 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 402.676 | 0.529837 | ||||||||
\(761\) | 126.245i | 0.165893i | 0.996554 | + | 0.0829465i | \(0.0264330\pi\) | ||||
−0.996554 | + | 0.0829465i | \(0.973567\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −370.794 | −0.485332 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 195.586i | 0.255335i | ||||||||
\(767\) | −488.839 | −0.637338 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 369.148i | 0.480037i | 0.970768 | + | 0.240018i | \(0.0771535\pi\) | ||||
−0.970768 | + | 0.240018i | \(0.922847\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 455.588 | 0.590140 | ||||||||
\(773\) | − 1403.71i | − 1.81592i | −0.419056 | − | 0.907961i | \(-0.637639\pi\) | ||||
0.419056 | − | 0.907961i | \(-0.362361\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 662.788i | 0.855211i | ||||||||
\(776\) | 86.5006i | 0.111470i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −797.013 | −1.02444 | ||||||||
\(779\) | 599.823 | 0.769991 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 111.618 | 0.142917 | ||||||||
\(782\) | − 356.904i | − 0.456400i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1564.41 | −1.99288 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 226.507i | − 0.287810i | −0.989591 | − | 0.143905i | \(-0.954034\pi\) | ||||
0.989591 | − | 0.143905i | \(-0.0459660\pi\) | |||||||
\(788\) | −246.323 | −0.312593 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 1044.79i | − 1.32252i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 721.352 | 0.909650 | ||||||||
\(794\) | 641.117i | 0.807453i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 12.4638i | − 0.0156580i | ||||||||
\(797\) | − 688.414i | − 0.863756i | −0.901932 | − | 0.431878i | \(-0.857851\pi\) | ||||
0.901932 | − | 0.431878i | \(-0.142149\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 622.794 | 0.779467 | ||||||||
\(800\) | 254.225 | 0.317782 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −389.970 | −0.486247 | ||||||||
\(803\) | − 702.193i | − 0.874462i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −372.582 | −0.462260 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 361.948i | − 0.447955i | ||||||||
\(809\) | −25.2792 | −0.0312475 | −0.0156237 | − | 0.999878i | \(-0.504973\pi\) | ||||
−0.0156237 | + | 0.999878i | \(0.504973\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1527.62i | − 1.88362i | −0.336145 | − | 0.941810i | \(-0.609123\pi\) | ||||
0.336145 | − | 0.941810i | \(-0.390877\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 50.6619 | 0.0622382 | ||||||||
\(815\) | − 134.302i | − 0.164787i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 263.611i | − 0.322657i | ||||||||
\(818\) | − 616.359i | − 0.753495i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 589.352 | 0.718722 | ||||||||
\(821\) | 116.662 | 0.142097 | 0.0710487 | − | 0.997473i | \(-0.477365\pi\) | ||||
0.0710487 | + | 0.997473i | \(0.477365\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 125.911 | 0.152990 | 0.0764950 | − | 0.997070i | \(-0.475627\pi\) | ||||
0.0764950 | + | 0.997070i | \(0.475627\pi\) | |||||||
\(824\) | 228.979i | 0.277887i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1434.40 | 1.73446 | 0.867229 | − | 0.497910i | \(-0.165899\pi\) | ||||
0.867229 | + | 0.497910i | \(0.165899\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.3228i | 0.0450215i | 0.999747 | + | 0.0225107i | \(0.00716600\pi\) | ||||
−0.999747 | + | 0.0225107i | \(0.992834\pi\) | |||||||
\(830\) | −896.029 | −1.07955 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 142.911i | 0.171768i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1472.88 | −1.76393 | ||||||||
\(836\) | 204.280i | 0.244354i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 426.042i | 0.508404i | ||||||||
\(839\) | 3.07370i | 0.00366353i | 0.999998 | + | 0.00183177i | \(0.000583069\pi\) | ||||
−0.999998 | + | 0.00183177i | \(0.999417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 311.000 | 0.369798 | ||||||||
\(842\) | 288.208 | 0.342290 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −249.823 | −0.295999 | ||||||||
\(845\) | 1255.45i | 1.48574i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 138.177 | 0.162944 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 1192.02i | − 1.40238i | ||||||||
\(851\) | −80.3390 | −0.0944054 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 155.257i | 0.182013i | 0.995850 | + | 0.0910063i | \(0.0290083\pi\) | ||||
−0.995850 | + | 0.0910063i | \(0.970992\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 479.294 | 0.559922 | ||||||||
\(857\) | − 1603.86i | − 1.87148i | −0.352686 | − | 0.935742i | \(-0.614731\pi\) | ||||
0.352686 | − | 0.935742i | \(-0.385269\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 629.735i | 0.733103i | 0.930398 | + | 0.366551i | \(0.119462\pi\) | ||||
−0.930398 | + | 0.366551i | \(0.880538\pi\) | |||||||
\(860\) | − 259.009i | − 0.301174i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −559.632 | −0.649226 | ||||||||
\(863\) | −1029.41 | −1.19283 | −0.596414 | − | 0.802677i | \(-0.703408\pi\) | ||||
−0.596414 | + | 0.802677i | \(0.703408\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1933.15 | 2.23485 | ||||||||
\(866\) | − 62.6051i | − 0.0722923i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 530.029 | 0.609929 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 2043.57i | − 2.34624i | ||||||||
\(872\) | −506.122 | −0.580415 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − 323.944i | − 0.370646i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 648.441 | 0.739385 | 0.369693 | − | 0.929154i | \(-0.379463\pi\) | ||||
0.369693 | + | 0.929154i | \(0.379463\pi\) | |||||||
\(878\) | − 562.662i | − 0.640845i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 200.714i | 0.228084i | ||||||||
\(881\) | − 363.857i | − 0.413005i | −0.978446 | − | 0.206502i | \(-0.933792\pi\) | ||||
0.978446 | − | 0.206502i | \(-0.0662082\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1536.16 | 1.73971 | 0.869853 | − | 0.493312i | \(-0.164214\pi\) | ||||
0.869853 | + | 0.493312i | \(0.164214\pi\) | |||||||
\(884\) | 670.087 | 0.758017 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −167.647 | −0.189218 | ||||||||
\(887\) | − 1125.51i | − 1.26889i | −0.772966 | − | 0.634447i | \(-0.781228\pi\) | ||||
0.772966 | − | 0.634447i | \(-0.218772\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −245.823 | −0.276206 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 457.261i | 0.512625i | ||||||||
\(893\) | 565.279 | 0.633011 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 713.197i | − 0.796868i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1009.60 | 1.12428 | ||||||||
\(899\) | 500.561i | 0.556798i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 647.889i | − 0.719078i | ||||||||
\(902\) | 298.982i | 0.331466i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −49.2061 | −0.0544315 | ||||||||
\(905\) | 46.7208 | 0.0516252 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 234.897 | 0.258982 | 0.129491 | − | 0.991581i | \(-0.458666\pi\) | ||||
0.129491 | + | 0.991581i | \(0.458666\pi\) | |||||||
\(908\) | − 339.074i | − 0.373430i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −224.278 | −0.246189 | −0.123095 | − | 0.992395i | \(-0.539282\pi\) | ||||
−0.123095 | + | 0.992395i | \(0.539282\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 454.561i | − 0.497876i | ||||||||
\(914\) | 177.026 | 0.193683 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 69.3840i | 0.0757467i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −932.161 | −1.01432 | −0.507161 | − | 0.861851i | \(-0.669305\pi\) | ||||
−0.507161 | + | 0.861851i | \(0.669305\pi\) | |||||||
\(920\) | − 318.289i | − 0.345967i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 927.394i | − 1.00585i | ||||||||
\(923\) | − 332.322i | − 0.360046i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −268.324 | −0.290080 | ||||||||
\(926\) | −1229.51 | −1.32777 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 192.000 | 0.206897 | ||||||||
\(929\) | 714.055i | 0.768628i | 0.923203 | + | 0.384314i | \(0.125562\pi\) | ||||
−0.923203 | + | 0.384314i | \(0.874438\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 508.971 | 0.546106 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 378.122i | − 0.404841i | ||||||||
\(935\) | 941.117 | 1.00654 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1723.25i | 1.83912i | 0.392952 | + | 0.919559i | \(0.371454\pi\) | ||||
−0.392952 | + | 0.919559i | \(0.628546\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 555.411 | 0.590863 | ||||||||
\(941\) | 964.761i | 1.02525i | 0.858612 | + | 0.512625i | \(0.171327\pi\) | ||||
−0.858612 | + | 0.512625i | \(0.828673\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 474.122i | − 0.502780i | ||||||||
\(944\) | 109.459i | 0.115952i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 131.397 | 0.138897 | ||||||||
\(947\) | −1451.76 | −1.53301 | −0.766506 | − | 0.642237i | \(-0.778007\pi\) | ||||
−0.766506 | + | 0.642237i | \(0.778007\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2090.65 | −2.20300 | ||||||||
\(950\) | − 1081.94i | − 1.13889i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1147.43 | −1.20401 | −0.602007 | − | 0.798491i | \(-0.705632\pi\) | ||||
−0.602007 | + | 0.798491i | \(0.705632\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1550.49i | 1.62355i | ||||||||
\(956\) | −394.294 | −0.412442 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 384.294i | − 0.401142i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 743.499 | 0.773672 | ||||||||
\(962\) | − 150.836i | − 0.156794i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 176.940i | − 0.183548i | ||||||||
\(965\) | − 1905.06i | − 1.97415i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 412.190 | 0.426257 | 0.213128 | − | 0.977024i | \(-0.431635\pi\) | ||||
0.213128 | + | 0.977024i | \(0.431635\pi\) | |||||||
\(968\) | 240.416 | 0.248364 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 361.706 | 0.372892 | ||||||||
\(971\) | − 1004.12i | − 1.03411i | −0.855952 | − | 0.517056i | \(-0.827028\pi\) | ||||
0.855952 | − | 0.517056i | \(-0.172972\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 794.101 | 0.815298 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 161.522i | − 0.165494i | ||||||||
\(977\) | 1588.23 | 1.62562 | 0.812812 | − | 0.582527i | \(-0.197936\pi\) | ||||
0.812812 | + | 0.582527i | \(0.197936\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 124.708i | − 0.127383i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −574.794 | −0.585330 | ||||||||
\(983\) | 833.533i | 0.847948i | 0.905674 | + | 0.423974i | \(0.139365\pi\) | ||||
−0.905674 | + | 0.423974i | \(0.860635\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1030.01i | 1.04569i | ||||||||
\(986\) | − 900.259i | − 0.913041i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 608.205 | 0.615592 | ||||||||
\(989\) | −208.368 | −0.210685 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 66.8965 | 0.0675041 | 0.0337520 | − | 0.999430i | \(-0.489254\pi\) | ||||
0.0337520 | + | 0.999430i | \(0.489254\pi\) | |||||||
\(992\) | 83.4269i | 0.0840997i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −52.1177 | −0.0523796 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1464.91i | − 1.46931i | −0.678439 | − | 0.734657i | \(-0.737343\pi\) | ||||
0.678439 | − | 0.734657i | \(-0.262657\pi\) | |||||||
\(998\) | 525.276 | 0.526329 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 882.3.c.b.685.1 | 4 | ||
3.2 | odd | 2 | 294.3.c.a.97.3 | 4 | |||
7.2 | even | 3 | 126.3.n.a.73.2 | 4 | |||
7.3 | odd | 6 | 126.3.n.a.19.2 | 4 | |||
7.4 | even | 3 | 882.3.n.e.19.2 | 4 | |||
7.5 | odd | 6 | 882.3.n.e.325.2 | 4 | |||
7.6 | odd | 2 | inner | 882.3.c.b.685.2 | 4 | ||
12.11 | even | 2 | 2352.3.f.e.97.4 | 4 | |||
21.2 | odd | 6 | 42.3.g.a.31.1 | yes | 4 | ||
21.5 | even | 6 | 294.3.g.a.31.1 | 4 | |||
21.11 | odd | 6 | 294.3.g.a.19.1 | 4 | |||
21.17 | even | 6 | 42.3.g.a.19.1 | ✓ | 4 | ||
21.20 | even | 2 | 294.3.c.a.97.4 | 4 | |||
28.3 | even | 6 | 1008.3.cg.h.145.1 | 4 | |||
28.23 | odd | 6 | 1008.3.cg.h.577.1 | 4 | |||
84.23 | even | 6 | 336.3.bh.e.241.2 | 4 | |||
84.59 | odd | 6 | 336.3.bh.e.145.2 | 4 | |||
84.83 | odd | 2 | 2352.3.f.e.97.1 | 4 | |||
105.2 | even | 12 | 1050.3.q.a.199.4 | 8 | |||
105.17 | odd | 12 | 1050.3.q.a.649.1 | 8 | |||
105.23 | even | 12 | 1050.3.q.a.199.1 | 8 | |||
105.38 | odd | 12 | 1050.3.q.a.649.4 | 8 | |||
105.44 | odd | 6 | 1050.3.p.a.451.2 | 4 | |||
105.59 | even | 6 | 1050.3.p.a.901.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.3.g.a.19.1 | ✓ | 4 | 21.17 | even | 6 | ||
42.3.g.a.31.1 | yes | 4 | 21.2 | odd | 6 | ||
126.3.n.a.19.2 | 4 | 7.3 | odd | 6 | |||
126.3.n.a.73.2 | 4 | 7.2 | even | 3 | |||
294.3.c.a.97.3 | 4 | 3.2 | odd | 2 | |||
294.3.c.a.97.4 | 4 | 21.20 | even | 2 | |||
294.3.g.a.19.1 | 4 | 21.11 | odd | 6 | |||
294.3.g.a.31.1 | 4 | 21.5 | even | 6 | |||
336.3.bh.e.145.2 | 4 | 84.59 | odd | 6 | |||
336.3.bh.e.241.2 | 4 | 84.23 | even | 6 | |||
882.3.c.b.685.1 | 4 | 1.1 | even | 1 | trivial | ||
882.3.c.b.685.2 | 4 | 7.6 | odd | 2 | inner | ||
882.3.n.e.19.2 | 4 | 7.4 | even | 3 | |||
882.3.n.e.325.2 | 4 | 7.5 | odd | 6 | |||
1008.3.cg.h.145.1 | 4 | 28.3 | even | 6 | |||
1008.3.cg.h.577.1 | 4 | 28.23 | odd | 6 | |||
1050.3.p.a.451.2 | 4 | 105.44 | odd | 6 | |||
1050.3.p.a.901.2 | 4 | 105.59 | even | 6 | |||
1050.3.q.a.199.1 | 8 | 105.23 | even | 12 | |||
1050.3.q.a.199.4 | 8 | 105.2 | even | 12 | |||
1050.3.q.a.649.1 | 8 | 105.17 | odd | 12 | |||
1050.3.q.a.649.4 | 8 | 105.38 | odd | 12 | |||
2352.3.f.e.97.1 | 4 | 84.83 | odd | 2 | |||
2352.3.f.e.97.4 | 4 | 12.11 | even | 2 |