Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2178,3,Mod(485,2178)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2178, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2178.485");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2178 = 2 \cdot 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2178.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: | \(59.3462015777\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 102x^{6} + 3599x^{4} + 51708x^{2} + 249001 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 198) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 485.6 | ||
Root | \(3.15782i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2178.485 |
Dual form | 2178.3.c.p.485.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2178\mathbb{Z}\right)^\times\).
\(n\) | \(1333\) | \(1937\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | − 2.82122i | − 0.564244i | −0.959378 | − | 0.282122i | \(-0.908962\pi\) | ||||
0.959378 | − | 0.282122i | \(-0.0910384\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.22977 | −0.318539 | −0.159269 | − | 0.987235i | \(-0.550914\pi\) | ||||
−0.159269 | + | 0.987235i | \(0.550914\pi\) | |||||||
\(8\) | − 2.82843i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.98981 | 0.398981 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.52397 | −0.347998 | −0.173999 | − | 0.984746i | \(-0.555669\pi\) | ||||
−0.173999 | + | 0.984746i | \(0.555669\pi\) | |||||||
\(14\) | − 3.15337i | − 0.225241i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − 14.7266i | − 0.866269i | −0.901329 | − | 0.433134i | \(-0.857408\pi\) | ||||
0.901329 | − | 0.433134i | \(-0.142592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.0878 | 0.583567 | 0.291783 | − | 0.956484i | \(-0.405751\pi\) | ||||
0.291783 | + | 0.956484i | \(0.405751\pi\) | |||||||
\(20\) | 5.64244i | 0.282122i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 11.0813i | − 0.481796i | −0.970550 | − | 0.240898i | \(-0.922558\pi\) | ||||
0.970550 | − | 0.240898i | \(-0.0774419\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 17.0407 | 0.681628 | ||||||||
\(26\) | − 6.39786i | − 0.246072i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.45954 | 0.159269 | ||||||||
\(29\) | 22.6350i | 0.780517i | 0.920705 | + | 0.390259i | \(0.127614\pi\) | ||||
−0.920705 | + | 0.390259i | \(0.872386\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −23.0257 | −0.742766 | −0.371383 | − | 0.928480i | \(-0.621116\pi\) | ||||
−0.371383 | + | 0.928480i | \(0.621116\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 20.8265 | 0.612545 | ||||||||
\(35\) | 6.29068i | 0.179734i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 20.0315 | 0.541391 | 0.270695 | − | 0.962665i | \(-0.412746\pi\) | ||||
0.270695 | + | 0.962665i | \(0.412746\pi\) | |||||||
\(38\) | 15.6805i | 0.412644i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.97962 | −0.199491 | ||||||||
\(41\) | 40.5345i | 0.988646i | 0.869278 | + | 0.494323i | \(0.164584\pi\) | ||||
−0.869278 | + | 0.494323i | \(0.835416\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −45.6612 | −1.06189 | −0.530944 | − | 0.847407i | \(-0.678163\pi\) | ||||
−0.530944 | + | 0.847407i | \(0.678163\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 15.6713 | 0.340681 | ||||||||
\(47\) | 11.5931i | 0.246662i | 0.992366 | + | 0.123331i | \(0.0393577\pi\) | ||||
−0.992366 | + | 0.123331i | \(0.960642\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −44.0281 | −0.898533 | ||||||||
\(50\) | 24.0992i | 0.481984i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.04794 | 0.173999 | ||||||||
\(53\) | − 39.1410i | − 0.738510i | −0.929328 | − | 0.369255i | \(-0.879613\pi\) | ||||
0.929328 | − | 0.369255i | \(-0.120387\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.30674i | 0.112620i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −32.0107 | −0.551909 | ||||||||
\(59\) | − 93.1486i | − 1.57879i | −0.613885 | − | 0.789395i | \(-0.710394\pi\) | ||||
0.613885 | − | 0.789395i | \(-0.289606\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −74.1575 | −1.21570 | −0.607849 | − | 0.794053i | \(-0.707967\pi\) | ||||
−0.607849 | + | 0.794053i | \(0.707967\pi\) | |||||||
\(62\) | − 32.5633i | − 0.525215i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 12.7631i | 0.196356i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 87.7093 | 1.30909 | 0.654547 | − | 0.756021i | \(-0.272859\pi\) | ||||
0.654547 | + | 0.756021i | \(0.272859\pi\) | |||||||
\(68\) | 29.4531i | 0.433134i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.89636 | −0.127091 | ||||||||
\(71\) | 67.1772i | 0.946158i | 0.881020 | + | 0.473079i | \(0.156857\pi\) | ||||
−0.881020 | + | 0.473079i | \(0.843143\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 35.6952 | 0.488976 | 0.244488 | − | 0.969652i | \(-0.421380\pi\) | ||||
0.244488 | + | 0.969652i | \(0.421380\pi\) | |||||||
\(74\) | 28.3288i | 0.382821i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −22.1755 | −0.291783 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 25.4014 | 0.321537 | 0.160768 | − | 0.986992i | \(-0.448603\pi\) | ||||
0.160768 | + | 0.986992i | \(0.448603\pi\) | |||||||
\(80\) | − 11.2849i | − 0.141061i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −57.3244 | −0.699078 | ||||||||
\(83\) | − 21.9098i | − 0.263974i | −0.991251 | − | 0.131987i | \(-0.957864\pi\) | ||||
0.991251 | − | 0.131987i | \(-0.0421357\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −41.5469 | −0.488787 | ||||||||
\(86\) | − 64.5747i | − 0.750868i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 34.9908i | − 0.393155i | −0.980488 | − | 0.196577i | \(-0.937017\pi\) | ||||
0.980488 | − | 0.196577i | \(-0.0629827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.0874 | 0.110851 | ||||||||
\(92\) | 22.1626i | 0.240898i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −16.3951 | −0.174416 | ||||||||
\(95\) | − 31.2810i | − 0.329274i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −109.118 | −1.12493 | −0.562463 | − | 0.826823i | \(-0.690146\pi\) | ||||
−0.562463 | + | 0.826823i | \(0.690146\pi\) | |||||||
\(98\) | − 62.2652i | − 0.635359i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −34.0814 | −0.340814 | ||||||||
\(101\) | 180.838i | 1.79047i | 0.445592 | + | 0.895236i | \(0.352993\pi\) | ||||
−0.445592 | + | 0.895236i | \(0.647007\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −201.556 | −1.95685 | −0.978427 | − | 0.206594i | \(-0.933762\pi\) | ||||
−0.978427 | + | 0.206594i | \(0.933762\pi\) | |||||||
\(104\) | 12.7957i | 0.123036i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 55.3538 | 0.522205 | ||||||||
\(107\) | 91.4378i | 0.854559i | 0.904120 | + | 0.427279i | \(0.140528\pi\) | ||||
−0.904120 | + | 0.427279i | \(0.859472\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −207.818 | −1.90659 | −0.953295 | − | 0.302040i | \(-0.902332\pi\) | ||||
−0.953295 | + | 0.302040i | \(0.902332\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.91908 | −0.0796347 | ||||||||
\(113\) | 63.4902i | 0.561860i | 0.959728 | + | 0.280930i | \(0.0906429\pi\) | ||||
−0.959728 | + | 0.280930i | \(0.909357\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −31.2628 | −0.271851 | ||||||||
\(116\) | − 45.2700i | − 0.390259i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 131.732 | 1.11637 | ||||||||
\(119\) | 32.8369i | 0.275940i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − 104.875i | − 0.859628i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 46.0515 | 0.371383 | ||||||||
\(125\) | − 118.606i | − 0.948849i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 65.9902 | 0.519608 | 0.259804 | − | 0.965661i | \(-0.416342\pi\) | ||||
0.259804 | + | 0.965661i | \(0.416342\pi\) | |||||||
\(128\) | − 11.3137i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −18.0498 | −0.138845 | ||||||||
\(131\) | 59.5648i | 0.454693i | 0.973814 | + | 0.227347i | \(0.0730050\pi\) | ||||
−0.973814 | + | 0.227347i | \(0.926995\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.7232 | −0.185888 | ||||||||
\(134\) | 124.040i | 0.925669i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −41.6530 | −0.306272 | ||||||||
\(137\) | − 190.202i | − 1.38834i | −0.719811 | − | 0.694170i | \(-0.755772\pi\) | ||||
0.719811 | − | 0.694170i | \(-0.244228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −234.628 | −1.68797 | −0.843986 | − | 0.536365i | \(-0.819797\pi\) | ||||
−0.843986 | + | 0.536365i | \(0.819797\pi\) | |||||||
\(140\) | − 12.5814i | − 0.0898668i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −95.0029 | −0.669035 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 63.8583 | 0.440402 | ||||||||
\(146\) | 50.4807i | 0.345758i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −40.0629 | −0.270695 | ||||||||
\(149\) | − 150.403i | − 1.00942i | −0.863290 | − | 0.504708i | \(-0.831600\pi\) | ||||
0.863290 | − | 0.504708i | \(-0.168400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −50.8256 | −0.336593 | −0.168297 | − | 0.985736i | \(-0.553827\pi\) | ||||
−0.168297 | + | 0.985736i | \(0.553827\pi\) | |||||||
\(152\) | − 31.3609i | − 0.206322i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 64.9607i | 0.419101i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −103.192 | −0.657277 | −0.328638 | − | 0.944456i | \(-0.606590\pi\) | ||||
−0.328638 | + | 0.944456i | \(0.606590\pi\) | |||||||
\(158\) | 35.9230i | 0.227361i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 15.9592 | 0.0997453 | ||||||||
\(161\) | 24.7088i | 0.153471i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −269.471 | −1.65319 | −0.826597 | − | 0.562794i | \(-0.809726\pi\) | ||||
−0.826597 | + | 0.562794i | \(0.809726\pi\) | |||||||
\(164\) | − 81.0690i | − 0.494323i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 30.9852 | 0.186658 | ||||||||
\(167\) | 211.841i | 1.26851i | 0.773124 | + | 0.634255i | \(0.218693\pi\) | ||||
−0.773124 | + | 0.634255i | \(0.781307\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −148.534 | −0.878898 | ||||||||
\(170\) | − 58.7562i | − 0.345625i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 91.3224 | 0.530944 | ||||||||
\(173\) | 120.944i | 0.699099i | 0.936918 | + | 0.349549i | \(0.113665\pi\) | ||||
−0.936918 | + | 0.349549i | \(0.886335\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −37.9969 | −0.217125 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 49.4844 | 0.278002 | ||||||||
\(179\) | 46.7700i | 0.261285i | 0.991430 | + | 0.130642i | \(0.0417040\pi\) | ||||
−0.991430 | + | 0.130642i | \(0.958296\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −282.456 | −1.56053 | −0.780264 | − | 0.625450i | \(-0.784916\pi\) | ||||
−0.780264 | + | 0.625450i | \(0.784916\pi\) | |||||||
\(182\) | 14.2658i | 0.0783833i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −31.3427 | −0.170341 | ||||||||
\(185\) | − 56.5132i | − 0.305477i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − 23.1862i | − 0.123331i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 44.2381 | 0.232832 | ||||||||
\(191\) | − 357.599i | − 1.87224i | −0.351676 | − | 0.936122i | \(-0.614388\pi\) | ||||
0.351676 | − | 0.936122i | \(-0.385612\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −37.1925 | −0.192707 | −0.0963537 | − | 0.995347i | \(-0.530718\pi\) | ||||
−0.0963537 | + | 0.995347i | \(0.530718\pi\) | |||||||
\(194\) | − 154.316i | − 0.795442i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 88.0562 | 0.449267 | ||||||||
\(197\) | − 129.220i | − 0.655937i | −0.944689 | − | 0.327969i | \(-0.893636\pi\) | ||||
0.944689 | − | 0.327969i | \(-0.106364\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −93.6837 | −0.470772 | −0.235386 | − | 0.971902i | \(-0.575635\pi\) | ||||
−0.235386 | + | 0.971902i | \(0.575635\pi\) | |||||||
\(200\) | − 48.1984i | − 0.240992i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −255.743 | −1.26606 | ||||||||
\(203\) | − 50.4708i | − 0.248625i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 114.357 | 0.557838 | ||||||||
\(206\) | − 285.043i | − 1.38370i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −18.0959 | −0.0869995 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 289.622 | 1.37261 | 0.686307 | − | 0.727312i | \(-0.259231\pi\) | ||||
0.686307 | + | 0.727312i | \(0.259231\pi\) | |||||||
\(212\) | 78.2821i | 0.369255i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −129.313 | −0.604264 | ||||||||
\(215\) | 128.820i | 0.599164i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 51.3421 | 0.236600 | ||||||||
\(218\) | − 293.900i | − 1.34816i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 66.6226i | 0.301460i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 143.972 | 0.645612 | 0.322806 | − | 0.946465i | \(-0.395374\pi\) | ||||
0.322806 | + | 0.946465i | \(0.395374\pi\) | |||||||
\(224\) | − 12.6135i | − 0.0563102i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −89.7887 | −0.397295 | ||||||||
\(227\) | 41.5246i | 0.182928i | 0.995808 | + | 0.0914639i | \(0.0291546\pi\) | ||||
−0.995808 | + | 0.0914639i | \(0.970845\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −126.536 | −0.552561 | −0.276280 | − | 0.961077i | \(-0.589102\pi\) | ||||
−0.276280 | + | 0.961077i | \(0.589102\pi\) | |||||||
\(230\) | − 44.2123i | − 0.192227i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 64.0214 | 0.275954 | ||||||||
\(233\) | − 199.110i | − 0.854547i | −0.904122 | − | 0.427274i | \(-0.859474\pi\) | ||||
0.904122 | − | 0.427274i | \(-0.140526\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.7068 | 0.139178 | ||||||||
\(236\) | 186.297i | 0.789395i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −46.4384 | −0.195119 | ||||||||
\(239\) | 246.440i | 1.03113i | 0.856850 | + | 0.515566i | \(0.172418\pi\) | ||||
−0.856850 | + | 0.515566i | \(0.827582\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −439.621 | −1.82415 | −0.912076 | − | 0.410021i | \(-0.865521\pi\) | ||||
−0.912076 | + | 0.410021i | \(0.865521\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 148.315 | 0.607849 | ||||||||
\(245\) | 124.213i | 0.506992i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −50.1607 | −0.203080 | ||||||||
\(248\) | 65.1266i | 0.262607i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 167.734 | 0.670938 | ||||||||
\(251\) | − 161.114i | − 0.641887i | −0.947098 | − | 0.320944i | \(-0.896000\pi\) | ||||
0.947098 | − | 0.320944i | \(-0.104000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 93.3242i | 0.367418i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − 108.341i | − 0.421562i | −0.977533 | − | 0.210781i | \(-0.932399\pi\) | ||||
0.977533 | − | 0.210781i | \(-0.0676007\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −44.6655 | −0.172454 | ||||||||
\(260\) | − 25.5263i | − 0.0981779i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −84.2373 | −0.321517 | ||||||||
\(263\) | − 263.126i | − 1.00048i | −0.865887 | − | 0.500240i | \(-0.833245\pi\) | ||||
0.865887 | − | 0.500240i | \(-0.166755\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −110.426 | −0.416700 | ||||||||
\(266\) | − 34.9638i | − 0.131443i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −175.419 | −0.654547 | ||||||||
\(269\) | − 317.693i | − 1.18101i | −0.807033 | − | 0.590507i | \(-0.798928\pi\) | ||||
0.807033 | − | 0.590507i | \(-0.201072\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 43.4187 | 0.160216 | 0.0801082 | − | 0.996786i | \(-0.474473\pi\) | ||||
0.0801082 | + | 0.996786i | \(0.474473\pi\) | |||||||
\(272\) | − 58.9063i | − 0.216567i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 268.987 | 0.981704 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 352.762 | 1.27351 | 0.636754 | − | 0.771067i | \(-0.280277\pi\) | ||||
0.636754 | + | 0.771067i | \(0.280277\pi\) | |||||||
\(278\) | − 331.814i | − 1.19358i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 17.7927 | 0.0635454 | ||||||||
\(281\) | 179.361i | 0.638294i | 0.947705 | + | 0.319147i | \(0.103396\pi\) | ||||
−0.947705 | + | 0.319147i | \(0.896604\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 207.445 | 0.733021 | 0.366510 | − | 0.930414i | \(-0.380552\pi\) | ||||
0.366510 | + | 0.930414i | \(0.380552\pi\) | |||||||
\(284\) | − 134.354i | − 0.473079i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 90.3826i | − 0.314922i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 72.1281 | 0.249578 | ||||||||
\(290\) | 90.3093i | 0.311412i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −71.3905 | −0.244488 | ||||||||
\(293\) | 391.679i | 1.33679i | 0.743807 | + | 0.668395i | \(0.233018\pi\) | ||||
−0.743807 | + | 0.668395i | \(0.766982\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −262.793 | −0.890823 | ||||||||
\(296\) | − 56.6575i | − 0.191411i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 212.702 | 0.713764 | ||||||||
\(299\) | 50.1315i | 0.167664i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 101.814 | 0.338252 | ||||||||
\(302\) | − 71.8782i | − 0.238007i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 44.3511 | 0.145892 | ||||||||
\(305\) | 209.215i | 0.685950i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 82.4090 | 0.268433 | 0.134217 | − | 0.990952i | \(-0.457148\pi\) | ||||
0.134217 | + | 0.990952i | \(0.457148\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −91.8683 | −0.296349 | ||||||||
\(311\) | − 358.954i | − 1.15419i | −0.816676 | − | 0.577097i | \(-0.804186\pi\) | ||||
0.816676 | − | 0.577097i | \(-0.195814\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 422.642 | 1.35029 | 0.675147 | − | 0.737684i | \(-0.264080\pi\) | ||||
0.675147 | + | 0.737684i | \(0.264080\pi\) | |||||||
\(314\) | − 145.936i | − 0.464765i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −50.8028 | −0.160768 | ||||||||
\(317\) | 374.953i | 1.18282i | 0.806372 | + | 0.591409i | \(0.201428\pi\) | ||||
−0.806372 | + | 0.591409i | \(0.798572\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 22.5698i | 0.0705305i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −34.9435 | −0.108520 | ||||||||
\(323\) | − 163.285i | − 0.505526i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −77.0917 | −0.237205 | ||||||||
\(326\) | − 381.089i | − 1.16898i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 114.649 | 0.349539 | ||||||||
\(329\) | − 25.8500i | − 0.0785714i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −166.263 | −0.502305 | −0.251152 | − | 0.967948i | \(-0.580810\pi\) | ||||
−0.251152 | + | 0.967948i | \(0.580810\pi\) | |||||||
\(332\) | 43.8197i | 0.131987i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −299.589 | −0.896972 | ||||||||
\(335\) | − 247.447i | − 0.738649i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −628.279 | −1.86433 | −0.932165 | − | 0.362034i | \(-0.882082\pi\) | ||||
−0.932165 | + | 0.362034i | \(0.882082\pi\) | |||||||
\(338\) | − 210.058i | − 0.621474i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 83.0939 | 0.244394 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 207.431 | 0.604756 | ||||||||
\(344\) | 129.149i | 0.375434i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −171.041 | −0.494337 | ||||||||
\(347\) | − 569.371i | − 1.64084i | −0.571763 | − | 0.820419i | \(-0.693740\pi\) | ||||
0.571763 | − | 0.820419i | \(-0.306260\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −89.1980 | −0.255582 | −0.127791 | − | 0.991801i | \(-0.540789\pi\) | ||||
−0.127791 | + | 0.991801i | \(0.540789\pi\) | |||||||
\(350\) | − 53.7357i | − 0.153531i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 490.203i | 1.38868i | 0.719649 | + | 0.694338i | \(0.244303\pi\) | ||||
−0.719649 | + | 0.694338i | \(0.755697\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 189.522 | 0.533864 | ||||||||
\(356\) | 69.9815i | 0.196577i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −66.1427 | −0.184756 | ||||||||
\(359\) | 479.086i | 1.33450i | 0.744833 | + | 0.667251i | \(0.232529\pi\) | ||||
−0.744833 | + | 0.667251i | \(0.767471\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −238.061 | −0.659450 | ||||||||
\(362\) | − 399.453i | − 1.10346i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −20.1748 | −0.0554254 | ||||||||
\(365\) | − 100.704i | − 0.275902i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.59096 | 0.0125094 | 0.00625471 | − | 0.999980i | \(-0.498009\pi\) | ||||
0.00625471 | + | 0.999980i | \(0.498009\pi\) | |||||||
\(368\) | − 44.3252i | − 0.120449i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 79.9217 | 0.216005 | ||||||||
\(371\) | 87.2755i | 0.235244i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −127.560 | −0.341984 | −0.170992 | − | 0.985272i | \(-0.554697\pi\) | ||||
−0.170992 | + | 0.985272i | \(0.554697\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 32.7903 | 0.0872082 | ||||||||
\(377\) | − 102.400i | − 0.271618i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 315.967 | 0.833686 | 0.416843 | − | 0.908979i | \(-0.363137\pi\) | ||||
0.416843 | + | 0.908979i | \(0.363137\pi\) | |||||||
\(380\) | 62.5621i | 0.164637i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 505.721 | 1.32388 | ||||||||
\(383\) | 283.220i | 0.739478i | 0.929136 | + | 0.369739i | \(0.120553\pi\) | ||||
−0.929136 | + | 0.369739i | \(0.879447\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 52.5982i | − 0.136265i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 218.236 | 0.562463 | ||||||||
\(389\) | 294.629i | 0.757401i | 0.925519 | + | 0.378700i | \(0.123629\pi\) | ||||
−0.925519 | + | 0.378700i | \(0.876371\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −163.190 | −0.417365 | ||||||||
\(392\) | 124.530i | 0.317679i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 182.744 | 0.463818 | ||||||||
\(395\) | − 71.6630i | − 0.181425i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 354.576 | 0.893138 | 0.446569 | − | 0.894749i | \(-0.352646\pi\) | ||||
0.446569 | + | 0.894749i | \(0.352646\pi\) | |||||||
\(398\) | − 132.489i | − 0.332886i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 68.1628 | 0.170407 | ||||||||
\(401\) | − 40.8024i | − 0.101752i | −0.998705 | − | 0.0508758i | \(-0.983799\pi\) | ||||
0.998705 | − | 0.0508758i | \(-0.0162013\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 104.168 | 0.258481 | ||||||||
\(404\) | − 361.675i | − 0.895236i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 71.3765 | 0.175804 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −477.416 | −1.16728 | −0.583638 | − | 0.812014i | \(-0.698371\pi\) | ||||
−0.583638 | + | 0.812014i | \(0.698371\pi\) | |||||||
\(410\) | 161.725i | 0.394451i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 403.112 | 0.978427 | ||||||||
\(413\) | 207.700i | 0.502906i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −61.8125 | −0.148946 | ||||||||
\(416\) | − 25.5914i | − 0.0615179i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 75.9631i | 0.181296i | 0.995883 | + | 0.0906481i | \(0.0288938\pi\) | ||||
−0.995883 | + | 0.0906481i | \(0.971106\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −279.302 | −0.663425 | −0.331713 | − | 0.943381i | \(-0.607626\pi\) | ||||
−0.331713 | + | 0.943381i | \(0.607626\pi\) | |||||||
\(422\) | 409.587i | 0.970585i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −110.708 | −0.261103 | ||||||||
\(425\) | − 250.951i | − 0.590473i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 165.354 | 0.387247 | ||||||||
\(428\) | − 182.876i | − 0.427279i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −182.179 | −0.423673 | ||||||||
\(431\) | − 594.555i | − 1.37948i | −0.724058 | − | 0.689739i | \(-0.757725\pi\) | ||||
0.724058 | − | 0.689739i | \(-0.242275\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −157.674 | −0.364144 | −0.182072 | − | 0.983285i | \(-0.558280\pi\) | ||||
−0.182072 | + | 0.983285i | \(0.558280\pi\) | |||||||
\(434\) | 72.6087i | 0.167301i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 415.637 | 0.953295 | ||||||||
\(437\) | − 122.867i | − 0.281160i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 265.463 | 0.604699 | 0.302349 | − | 0.953197i | \(-0.402229\pi\) | ||||
0.302349 | + | 0.953197i | \(0.402229\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −94.2186 | −0.213164 | ||||||||
\(443\) | 59.7786i | 0.134940i | 0.997721 | + | 0.0674702i | \(0.0214928\pi\) | ||||
−0.997721 | + | 0.0674702i | \(0.978507\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −98.7167 | −0.221835 | ||||||||
\(446\) | 203.607i | 0.456517i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 17.8382 | 0.0398173 | ||||||||
\(449\) | − 278.016i | − 0.619189i | −0.950869 | − | 0.309595i | \(-0.899807\pi\) | ||||
0.950869 | − | 0.309595i | \(-0.100193\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − 126.980i | − 0.280930i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −58.7247 | −0.129350 | ||||||||
\(455\) | − 28.4588i | − 0.0625469i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 329.376 | 0.720736 | 0.360368 | − | 0.932810i | \(-0.382651\pi\) | ||||
0.360368 | + | 0.932810i | \(0.382651\pi\) | |||||||
\(458\) | − 178.949i | − 0.390719i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 62.5257 | 0.135925 | ||||||||
\(461\) | 628.919i | 1.36425i | 0.731236 | + | 0.682124i | \(0.238944\pi\) | ||||
−0.731236 | + | 0.682124i | \(0.761056\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −509.930 | −1.10136 | −0.550680 | − | 0.834716i | \(-0.685632\pi\) | ||||
−0.550680 | + | 0.834716i | \(0.685632\pi\) | |||||||
\(464\) | 90.5400i | 0.195129i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 281.583 | 0.604256 | ||||||||
\(467\) | 221.291i | 0.473856i | 0.971527 | + | 0.236928i | \(0.0761406\pi\) | ||||
−0.971527 | + | 0.236928i | \(0.923859\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −195.572 | −0.416997 | ||||||||
\(470\) | 46.2543i | 0.0984135i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −263.464 | −0.558187 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 188.943 | 0.397775 | ||||||||
\(476\) | − 65.6737i | − 0.137970i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −348.519 | −0.729120 | ||||||||
\(479\) | − 258.547i | − 0.539763i | −0.962894 | − | 0.269882i | \(-0.913015\pi\) | ||||
0.962894 | − | 0.269882i | \(-0.0869846\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −90.6217 | −0.188403 | ||||||||
\(482\) | − 621.718i | − 1.28987i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 307.845i | 0.634733i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −446.632 | −0.917108 | −0.458554 | − | 0.888667i | \(-0.651632\pi\) | ||||
−0.458554 | + | 0.888667i | \(0.651632\pi\) | |||||||
\(488\) | 209.749i | 0.429814i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −175.664 | −0.358498 | ||||||||
\(491\) | − 444.393i | − 0.905078i | −0.891745 | − | 0.452539i | \(-0.850518\pi\) | ||||
0.891745 | − | 0.452539i | \(-0.149482\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 333.336 | 0.676138 | ||||||||
\(494\) | − 70.9380i | − 0.143599i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −92.1030 | −0.185691 | ||||||||
\(497\) | − 149.790i | − 0.301388i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 752.146 | 1.50731 | 0.753654 | − | 0.657272i | \(-0.228290\pi\) | ||||
0.753654 | + | 0.657272i | \(0.228290\pi\) | |||||||
\(500\) | 237.212i | 0.474425i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 227.849 | 0.453883 | ||||||||
\(503\) | 333.651i | 0.663321i | 0.943399 | + | 0.331661i | \(0.107609\pi\) | ||||
−0.943399 | + | 0.331661i | \(0.892391\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 510.183 | 1.01026 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −131.980 | −0.259804 | ||||||||
\(509\) | 353.913i | 0.695310i | 0.937622 | + | 0.347655i | \(0.113022\pi\) | ||||
−0.937622 | + | 0.347655i | \(0.886978\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −79.5922 | −0.155758 | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 153.218 | 0.298089 | ||||||||
\(515\) | 568.634i | 1.10414i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − 63.1666i | − 0.121943i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 36.0996 | 0.0694223 | ||||||||
\(521\) | − 783.964i | − 1.50473i | −0.658747 | − | 0.752365i | \(-0.728913\pi\) | ||||
0.658747 | − | 0.752365i | \(-0.271087\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 417.872 | 0.798990 | 0.399495 | − | 0.916735i | \(-0.369185\pi\) | ||||
0.399495 | + | 0.916735i | \(0.369185\pi\) | |||||||
\(524\) | − 119.130i | − 0.227347i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 372.117 | 0.707446 | ||||||||
\(527\) | 339.090i | 0.643435i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 406.205 | 0.767873 | ||||||||
\(530\) | − 156.165i | − 0.294652i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 49.4463 | 0.0929442 | ||||||||
\(533\) | − 183.377i | − 0.344047i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 257.966 | 0.482180 | ||||||||
\(536\) | − 248.079i | − 0.462835i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 449.285 | 0.835103 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.1922 | −0.0705956 | −0.0352978 | − | 0.999377i | \(-0.511238\pi\) | ||||
−0.0352978 | + | 0.999377i | \(0.511238\pi\) | |||||||
\(542\) | 61.4033i | 0.113290i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 83.3061 | 0.153136 | ||||||||
\(545\) | 586.302i | 1.07578i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −916.000 | −1.67459 | −0.837294 | − | 0.546752i | \(-0.815864\pi\) | ||||
−0.837294 | + | 0.546752i | \(0.815864\pi\) | |||||||
\(548\) | 380.405i | 0.694170i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 250.972i | 0.455484i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −56.6393 | −0.102422 | ||||||||
\(554\) | 498.880i | 0.900506i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 469.256 | 0.843986 | ||||||||
\(557\) | 776.071i | 1.39330i | 0.717409 | + | 0.696652i | \(0.245328\pi\) | ||||
−0.717409 | + | 0.696652i | \(0.754672\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 206.570 | 0.369535 | ||||||||
\(560\) | 25.1627i | 0.0449334i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −253.654 | −0.451342 | ||||||||
\(563\) | 390.137i | 0.692961i | 0.938057 | + | 0.346481i | \(0.112623\pi\) | ||||
−0.938057 | + | 0.346481i | \(0.887377\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 179.120 | 0.317026 | ||||||||
\(566\) | 293.371i | 0.518324i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 190.006 | 0.334517 | ||||||||
\(569\) | − 104.399i | − 0.183479i | −0.995783 | − | 0.0917393i | \(-0.970757\pi\) | ||||
0.995783 | − | 0.0917393i | \(-0.0292427\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −66.1095 | −0.115778 | −0.0578892 | − | 0.998323i | \(-0.518437\pi\) | ||||
−0.0578892 | + | 0.998323i | \(0.518437\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 127.820 | 0.222683 | ||||||||
\(575\) | − 188.833i | − 0.328406i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 961.516 | 1.66641 | 0.833203 | − | 0.552967i | \(-0.186505\pi\) | ||||
0.833203 | + | 0.552967i | \(0.186505\pi\) | |||||||
\(578\) | 102.004i | 0.176478i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −127.717 | −0.220201 | ||||||||
\(581\) | 48.8539i | 0.0840859i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − 100.961i | − 0.172879i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −553.918 | −0.945253 | ||||||||
\(587\) | 660.093i | 1.12452i | 0.826961 | + | 0.562260i | \(0.190068\pi\) | ||||
−0.826961 | + | 0.562260i | \(0.809932\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −255.304 | −0.433453 | ||||||||
\(590\) | − 371.645i | − 0.629907i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 80.1258 | 0.135348 | ||||||||
\(593\) | 883.670i | 1.49017i | 0.666970 | + | 0.745084i | \(0.267591\pi\) | ||||
−0.666970 | + | 0.745084i | \(0.732409\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 92.6401 | 0.155698 | ||||||||
\(596\) | 300.806i | 0.504708i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −70.8967 | −0.118556 | ||||||||
\(599\) | 234.670i | 0.391769i | 0.980627 | + | 0.195885i | \(0.0627578\pi\) | ||||
−0.980627 | + | 0.195885i | \(0.937242\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −155.942 | −0.259470 | −0.129735 | − | 0.991549i | \(-0.541413\pi\) | ||||
−0.129735 | + | 0.991549i | \(0.541413\pi\) | |||||||
\(602\) | 143.987i | 0.239180i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 101.651 | 0.168297 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1043.58 | −1.71924 | −0.859618 | − | 0.510937i | \(-0.829298\pi\) | ||||
−0.859618 | + | 0.510937i | \(0.829298\pi\) | |||||||
\(608\) | 62.7219i | 0.103161i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −295.874 | −0.485040 | ||||||||
\(611\) | − 52.4469i | − 0.0858379i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −824.714 | −1.34537 | −0.672686 | − | 0.739928i | \(-0.734860\pi\) | ||||
−0.672686 | + | 0.739928i | \(0.734860\pi\) | |||||||
\(614\) | 116.544i | 0.189811i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 513.392i | − 0.832078i | −0.909347 | − | 0.416039i | \(-0.863418\pi\) | ||||
0.909347 | − | 0.416039i | \(-0.136582\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 812.562 | 1.31270 | 0.656350 | − | 0.754456i | \(-0.272099\pi\) | ||||
0.656350 | + | 0.754456i | \(0.272099\pi\) | |||||||
\(620\) | − 129.921i | − 0.209551i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 507.638 | 0.816138 | ||||||||
\(623\) | 78.0214i | 0.125235i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 91.4034 | 0.146245 | ||||||||
\(626\) | 597.706i | 0.954802i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 206.385 | 0.328638 | ||||||||
\(629\) | − 294.995i | − 0.468990i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 597.643 | 0.947136 | 0.473568 | − | 0.880757i | \(-0.342966\pi\) | ||||
0.473568 | + | 0.880757i | \(0.342966\pi\) | |||||||
\(632\) | − 71.8460i | − 0.113680i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −530.264 | −0.836378 | ||||||||
\(635\) | − 186.173i | − 0.293186i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 199.182 | 0.312688 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −31.9185 | −0.0498726 | ||||||||
\(641\) | 815.883i | 1.27283i | 0.771347 | + | 0.636414i | \(0.219583\pi\) | ||||
−0.771347 | + | 0.636414i | \(0.780417\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −463.073 | −0.720176 | −0.360088 | − | 0.932918i | \(-0.617253\pi\) | ||||
−0.360088 | + | 0.932918i | \(0.617253\pi\) | |||||||
\(644\) | − 49.4175i | − 0.0767353i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 230.920 | 0.357461 | ||||||||
\(647\) | 993.955i | 1.53625i | 0.640298 | + | 0.768126i | \(0.278811\pi\) | ||||
−0.640298 | + | 0.768126i | \(0.721189\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − 109.024i | − 0.167729i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 538.941 | 0.826597 | ||||||||
\(653\) | 610.848i | 0.935449i | 0.883874 | + | 0.467725i | \(0.154926\pi\) | ||||
−0.883874 | + | 0.467725i | \(0.845074\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 168.045 | 0.256558 | ||||||||
\(656\) | 162.138i | 0.247161i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 36.5574 | 0.0555584 | ||||||||
\(659\) | − 249.471i | − 0.378560i | −0.981923 | − | 0.189280i | \(-0.939385\pi\) | ||||
0.981923 | − | 0.189280i | \(-0.0606154\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1210.43 | −1.83121 | −0.915604 | − | 0.402081i | \(-0.868287\pi\) | ||||
−0.915604 | + | 0.402081i | \(0.868287\pi\) | |||||||
\(662\) | − 235.131i | − 0.355183i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −61.9704 | −0.0933289 | ||||||||
\(665\) | 69.7495i | 0.104887i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 250.825 | 0.376050 | ||||||||
\(668\) | − 423.682i | − 0.634255i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 349.943 | 0.522304 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1121.51 | −1.66643 | −0.833214 | − | 0.552950i | \(-0.813502\pi\) | ||||
−0.833214 | + | 0.552950i | \(0.813502\pi\) | |||||||
\(674\) | − 888.521i | − 1.31828i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 297.067 | 0.439449 | ||||||||
\(677\) | − 238.834i | − 0.352782i | −0.984320 | − | 0.176391i | \(-0.943558\pi\) | ||||
0.984320 | − | 0.176391i | \(-0.0564424\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 243.308 | 0.358332 | ||||||||
\(680\) | 117.512i | 0.172812i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1328.40i | − 1.94494i | −0.233023 | − | 0.972471i | \(-0.574862\pi\) | ||||
0.233023 | − | 0.972471i | \(-0.425138\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −536.603 | −0.783363 | ||||||||
\(686\) | 293.352i | 0.427627i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −182.645 | −0.265472 | ||||||||
\(689\) | 177.073i | 0.257000i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.9558 | −0.0592703 | −0.0296352 | − | 0.999561i | \(-0.509435\pi\) | ||||
−0.0296352 | + | 0.999561i | \(0.509435\pi\) | |||||||
\(692\) | − 241.888i | − 0.349549i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 805.212 | 1.16025 | ||||||||
\(695\) | 661.938i | 0.952429i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 596.934 | 0.856433 | ||||||||
\(698\) | − 126.145i | − 0.180724i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 75.9937 | 0.108562 | ||||||||
\(701\) | − 232.085i | − 0.331078i | −0.986203 | − | 0.165539i | \(-0.947064\pi\) | ||||
0.986203 | − | 0.165539i | \(-0.0529363\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 222.104 | 0.315938 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −693.251 | −0.981942 | ||||||||
\(707\) | − 403.227i | − 0.570335i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 215.214 | 0.303546 | 0.151773 | − | 0.988415i | \(-0.451502\pi\) | ||||
0.151773 | + | 0.988415i | \(0.451502\pi\) | |||||||
\(710\) | 268.024i | 0.377499i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −98.9688 | −0.139001 | ||||||||
\(713\) | 255.155i | 0.357862i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − 93.5399i | − 0.130642i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −677.530 | −0.943636 | ||||||||
\(719\) | − 152.742i | − 0.212437i | −0.994343 | − | 0.106218i | \(-0.966126\pi\) | ||||
0.994343 | − | 0.106218i | \(-0.0338743\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 449.423 | 0.623333 | ||||||||
\(722\) | − 336.670i | − 0.466302i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 564.911 | 0.780264 | ||||||||
\(725\) | 385.716i | 0.532023i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 610.733 | 0.840073 | 0.420037 | − | 0.907507i | \(-0.362017\pi\) | ||||
0.420037 | + | 0.907507i | \(0.362017\pi\) | |||||||
\(728\) | − 28.5315i | − 0.0391917i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 142.417 | 0.195092 | ||||||||
\(731\) | 672.433i | 0.919881i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −222.773 | −0.303920 | −0.151960 | − | 0.988387i | \(-0.548558\pi\) | ||||
−0.151960 | + | 0.988387i | \(0.548558\pi\) | |||||||
\(734\) | 6.49259i | 0.00884550i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 62.6853 | 0.0851703 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −320.857 | −0.434178 | −0.217089 | − | 0.976152i | \(-0.569656\pi\) | ||||
−0.217089 | + | 0.976152i | \(0.569656\pi\) | |||||||
\(740\) | 113.026i | 0.152738i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −123.426 | −0.166343 | ||||||||
\(743\) | − 276.852i | − 0.372614i | −0.982492 | − | 0.186307i | \(-0.940348\pi\) | ||||
0.982492 | − | 0.186307i | \(-0.0596518\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −424.320 | −0.569557 | ||||||||
\(746\) | − 180.397i | − 0.241819i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 203.885i | − 0.272210i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 535.544 | 0.713107 | 0.356554 | − | 0.934275i | \(-0.383952\pi\) | ||||
0.356554 | + | 0.934275i | \(0.383952\pi\) | |||||||
\(752\) | 46.3725i | 0.0616655i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 144.816 | 0.192063 | ||||||||
\(755\) | 143.390i | 0.189921i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 678.968 | 0.896919 | 0.448460 | − | 0.893803i | \(-0.351973\pi\) | ||||
0.448460 | + | 0.893803i | \(0.351973\pi\) | |||||||
\(758\) | 446.845i | 0.589505i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −88.4762 | −0.116416 | ||||||||
\(761\) | − 562.037i | − 0.738551i | −0.929320 | − | 0.369276i | \(-0.879606\pi\) | ||||
0.929320 | − | 0.369276i | \(-0.120394\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 463.387 | 0.607323 | ||||||||
\(764\) | 715.197i | 0.936122i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −400.534 | −0.522890 | ||||||||
\(767\) | 421.402i | 0.549416i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −113.242 | −0.147258 | −0.0736291 | − | 0.997286i | \(-0.523458\pi\) | ||||
−0.0736291 | + | 0.997286i | \(0.523458\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 74.3851 | 0.0963537 | ||||||||
\(773\) | − 1070.60i | − 1.38499i | −0.721422 | − | 0.692495i | \(-0.756511\pi\) | ||||
0.721422 | − | 0.692495i | \(-0.243489\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −392.375 | −0.506290 | ||||||||
\(776\) | 308.632i | 0.397721i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −416.668 | −0.535563 | ||||||||
\(779\) | 449.437i | 0.576941i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − 230.785i | − 0.295122i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −176.112 | −0.224633 | ||||||||
\(785\) | 291.129i | 0.370865i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 208.201 | 0.264550 | 0.132275 | − | 0.991213i | \(-0.457772\pi\) | ||||
0.132275 | + | 0.991213i | \(0.457772\pi\) | |||||||
\(788\) | 258.439i | 0.327969i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 101.347 | 0.128287 | ||||||||
\(791\) | − 141.569i | − 0.178974i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 335.487 | 0.423060 | ||||||||
\(794\) | 501.446i | 0.631544i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 187.367 | 0.235386 | ||||||||
\(797\) | 263.612i | 0.330755i | 0.986230 | + | 0.165377i | \(0.0528842\pi\) | ||||
−0.986230 | + | 0.165377i | \(0.947116\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 170.727 | 0.213676 | ||||||||
\(800\) | 96.3968i | 0.120496i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 57.7033 | 0.0719492 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 69.7089 | 0.0865949 | ||||||||
\(806\) | 147.316i | 0.182774i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 511.486 | 0.633028 | ||||||||
\(809\) | 967.704i | 1.19617i | 0.801431 | + | 0.598087i | \(0.204072\pi\) | ||||
−0.801431 | + | 0.598087i | \(0.795928\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −438.776 | −0.541030 | −0.270515 | − | 0.962716i | \(-0.587194\pi\) | ||||
−0.270515 | + | 0.962716i | \(0.587194\pi\) | |||||||
\(812\) | 100.942i | 0.124312i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 760.236i | 0.932805i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −506.280 | −0.619682 | ||||||||
\(818\) | − 675.169i | − 0.825389i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −228.714 | −0.278919 | ||||||||
\(821\) | − 275.623i | − 0.335716i | −0.985811 | − | 0.167858i | \(-0.946315\pi\) | ||||
0.985811 | − | 0.167858i | \(-0.0536850\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1210.40 | 1.47072 | 0.735360 | − | 0.677677i | \(-0.237013\pi\) | ||||
0.735360 | + | 0.677677i | \(0.237013\pi\) | |||||||
\(824\) | 570.086i | 0.691852i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −293.732 | −0.355608 | ||||||||
\(827\) | − 1090.50i | − 1.31862i | −0.751871 | − | 0.659311i | \(-0.770848\pi\) | ||||
0.751871 | − | 0.659311i | \(-0.229152\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1284.18 | 1.54907 | 0.774536 | − | 0.632530i | \(-0.217983\pi\) | ||||
0.774536 | + | 0.632530i | \(0.217983\pi\) | |||||||
\(830\) | − 87.4161i | − 0.105321i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 36.1918 | 0.0434997 | ||||||||
\(833\) | 648.383i | 0.778371i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 597.651 | 0.715750 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −107.428 | −0.128196 | ||||||||
\(839\) | 529.962i | 0.631659i | 0.948816 | + | 0.315829i | \(0.102283\pi\) | ||||
−0.948816 | + | 0.315829i | \(0.897717\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 328.657 | 0.390793 | ||||||||
\(842\) | − 394.993i | − 0.469112i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −579.243 | −0.686307 | ||||||||
\(845\) | 419.046i | 0.495913i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 156.564i | − 0.184628i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 354.899 | 0.417528 | ||||||||
\(851\) | − 221.975i | − 0.260840i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1222.42 | −1.43308 | −0.716542 | − | 0.697544i | \(-0.754276\pi\) | ||||
−0.716542 | + | 0.697544i | \(0.754276\pi\) | |||||||
\(854\) | 233.846i | 0.273825i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 258.625 | 0.302132 | ||||||||
\(857\) | 1479.73i | 1.72664i | 0.504653 | + | 0.863322i | \(0.331620\pi\) | ||||
−0.504653 | + | 0.863322i | \(0.668380\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 95.9499 | 0.111700 | 0.0558498 | − | 0.998439i | \(-0.482213\pi\) | ||||
0.0558498 | + | 0.998439i | \(0.482213\pi\) | |||||||
\(860\) | − 257.641i | − 0.299582i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 840.828 | 0.975439 | ||||||||
\(863\) | 1277.20i | 1.47996i | 0.672630 | + | 0.739979i | \(0.265165\pi\) | ||||
−0.672630 | + | 0.739979i | \(0.734835\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 341.210 | 0.394462 | ||||||||
\(866\) | − 222.985i | − 0.257488i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −102.684 | −0.118300 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −396.794 | −0.455562 | ||||||||
\(872\) | 587.799i | 0.674081i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 173.760 | 0.198810 | ||||||||
\(875\) | 264.464i | 0.302245i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 327.910 | 0.373900 | 0.186950 | − | 0.982369i | \(-0.440140\pi\) | ||||
0.186950 | + | 0.982369i | \(0.440140\pi\) | |||||||
\(878\) | 375.421i | 0.427586i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 768.903i | − 0.872761i | −0.899762 | − | 0.436381i | \(-0.856260\pi\) | ||||
0.899762 | − | 0.436381i | \(-0.143740\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −698.075 | −0.790572 | −0.395286 | − | 0.918558i | \(-0.629355\pi\) | ||||
−0.395286 | + | 0.918558i | \(0.629355\pi\) | |||||||
\(884\) | − 133.245i | − 0.150730i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −84.5397 | −0.0954173 | ||||||||
\(887\) | − 836.619i | − 0.943200i | −0.881812 | − | 0.471600i | \(-0.843677\pi\) | ||||
0.881812 | − | 0.471600i | \(-0.156323\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −147.143 | −0.165515 | ||||||||
\(890\) | − 139.607i | − 0.156861i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −287.943 | −0.322806 | ||||||||
\(893\) | 128.542i | 0.143944i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 131.948 | 0.147428 | ||||||||
\(896\) | 25.2270i | 0.0281551i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 393.174 | 0.437833 | ||||||||
\(899\) | − 521.187i | − 0.579741i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −576.413 | −0.639748 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 179.577 | 0.198648 | ||||||||
\(905\) | 796.870i | 0.880520i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −109.786 | −0.121043 | −0.0605215 | − | 0.998167i | \(-0.519276\pi\) | ||||
−0.0605215 | + | 0.998167i | \(0.519276\pi\) | |||||||
\(908\) | − 83.0493i | − 0.0914639i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 40.2469 | 0.0442273 | ||||||||
\(911\) | − 1011.19i | − 1.10998i | −0.831858 | − | 0.554988i | \(-0.812723\pi\) | ||||
0.831858 | − | 0.554988i | \(-0.187277\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 465.808i | 0.509637i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 253.073 | 0.276280 | ||||||||
\(917\) | − 132.816i | − 0.144837i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 744.228 | 0.809823 | 0.404912 | − | 0.914356i | \(-0.367302\pi\) | ||||
0.404912 | + | 0.914356i | \(0.367302\pi\) | |||||||
\(920\) | 88.4246i | 0.0961137i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −889.425 | −0.964670 | ||||||||
\(923\) | − 303.908i | − 0.329261i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 341.350 | 0.369027 | ||||||||
\(926\) | − 721.150i | − 0.778779i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −128.043 | −0.137977 | ||||||||
\(929\) | 181.064i | 0.194902i | 0.995240 | + | 0.0974511i | \(0.0310690\pi\) | ||||
−0.995240 | + | 0.0974511i | \(0.968931\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −488.173 | −0.524354 | ||||||||
\(932\) | 398.219i | 0.427274i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −312.952 | −0.335067 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 808.409 | 0.862764 | 0.431382 | − | 0.902169i | \(-0.358026\pi\) | ||||
0.431382 | + | 0.902169i | \(0.358026\pi\) | |||||||
\(938\) | − 276.580i | − 0.294861i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −65.4135 | −0.0695888 | ||||||||
\(941\) | − 131.022i | − 0.139237i | −0.997574 | − | 0.0696185i | \(-0.977822\pi\) | ||||
0.997574 | − | 0.0696185i | \(-0.0221782\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 449.175 | 0.476326 | ||||||||
\(944\) | − 372.594i | − 0.394698i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 816.092i | 0.861765i | 0.902408 | + | 0.430883i | \(0.141798\pi\) | ||||
−0.902408 | + | 0.430883i | \(0.858202\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −161.484 | −0.170163 | ||||||||
\(950\) | 267.206i | 0.281270i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 92.8767 | 0.0975596 | ||||||||
\(953\) | 1000.66i | 1.05001i | 0.851098 | + | 0.525007i | \(0.175937\pi\) | ||||
−0.851098 | + | 0.525007i | \(0.824063\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1008.86 | −1.05640 | ||||||||
\(956\) | − 492.881i | − 0.515566i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 365.640 | 0.381670 | ||||||||
\(959\) | 424.108i | 0.442240i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −430.815 | −0.448299 | ||||||||
\(962\) | − 128.159i | − 0.133221i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 879.241 | 0.912076 | ||||||||
\(965\) | 104.928i | 0.108734i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1675.29 | 1.73247 | 0.866233 | − | 0.499640i | \(-0.166534\pi\) | ||||
0.866233 | + | 0.499640i | \(0.166534\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −435.359 | −0.448824 | ||||||||
\(971\) | − 1409.87i | − 1.45197i | −0.687709 | − | 0.725987i | \(-0.741383\pi\) | ||||
0.687709 | − | 0.725987i | \(-0.258617\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 523.167 | 0.537684 | ||||||||
\(974\) | − 631.633i | − 0.648493i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −296.630 | −0.303924 | ||||||||
\(977\) | − 653.115i | − 0.668490i | −0.942486 | − | 0.334245i | \(-0.891519\pi\) | ||||
0.942486 | − | 0.334245i | \(-0.108481\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − 248.426i | − 0.253496i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 628.467 | 0.639987 | ||||||||
\(983\) | 641.147i | 0.652235i | 0.945329 | + | 0.326118i | \(0.105741\pi\) | ||||
−0.945329 | + | 0.326118i | \(0.894259\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −364.557 | −0.370109 | ||||||||
\(986\) | 471.408i | 0.478102i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 100.321 | 0.101540 | ||||||||
\(989\) | 505.986i | 0.511613i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 435.813 | 0.439771 | 0.219886 | − | 0.975526i | \(-0.429432\pi\) | ||||
0.219886 | + | 0.975526i | \(0.429432\pi\) | |||||||
\(992\) | − 130.253i | − 0.131304i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 211.835 | 0.213113 | ||||||||
\(995\) | 264.302i | 0.265631i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 422.219 | 0.423490 | 0.211745 | − | 0.977325i | \(-0.432085\pi\) | ||||
0.211745 | + | 0.977325i | \(0.432085\pi\) | |||||||
\(998\) | 1063.70i | 1.06583i | ||||||||
\(999\) | 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 | 2178.3.c.p.485.6 | 8 | ||
3.2 | odd | 2 | inner | 2178.3.c.p.485.3 | 8 | ||
11.3 | even | 5 | 198.3.k.a.53.4 | yes | 16 | ||
11.4 | even | 5 | 198.3.k.a.71.1 | yes | 16 | ||
11.10 | odd | 2 | 2178.3.c.m.485.2 | 8 | |||
33.14 | odd | 10 | 198.3.k.a.53.1 | ✓ | 16 | ||
33.26 | odd | 10 | 198.3.k.a.71.4 | yes | 16 | ||
33.32 | even | 2 | 2178.3.c.m.485.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
198.3.k.a.53.1 | ✓ | 16 | 33.14 | odd | 10 | ||
198.3.k.a.53.4 | yes | 16 | 11.3 | even | 5 | ||
198.3.k.a.71.1 | yes | 16 | 11.4 | even | 5 | ||
198.3.k.a.71.4 | yes | 16 | 33.26 | odd | 10 | ||
2178.3.c.m.485.2 | 8 | 11.10 | odd | 2 | |||
2178.3.c.m.485.7 | 8 | 33.32 | even | 2 | |||
2178.3.c.p.485.3 | 8 | 3.2 | odd | 2 | inner | ||
2178.3.c.p.485.6 | 8 | 1.1 | even | 1 | trivial |