Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,3,Mod(2161,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4140.2161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.d (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: | \(112.806829445\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2161.6 | ||
Character | \(\chi\) | \(=\) | 4140.2161 |
Dual form | 4140.3.d.b.2161.27 |
$q$-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 \(\left(\mathbb{Z}/4140\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(2071\) | \(3961\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.50512i | − | 0.643588i | −0.946810 | − | 0.321794i | \(-0.895714\pi\) | ||
0.946810 | − | 0.321794i | \(-0.104286\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 16.7256i | − | 1.52051i | −0.649626 | − | 0.760254i | \(-0.725075\pi\) | ||
0.649626 | − | 0.760254i | \(-0.274925\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.28056 | 0.252351 | 0.126175 | − | 0.992008i | \(-0.459730\pi\) | ||||
0.126175 | + | 0.992008i | \(0.459730\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 7.91035i | − | 0.465315i | −0.972559 | − | 0.232657i | \(-0.925258\pi\) | ||
0.972559 | − | 0.232657i | \(-0.0747421\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.02586i | 0.264519i | 0.991215 | + | 0.132259i | \(0.0422232\pi\) | ||||
−0.991215 | + | 0.132259i | \(0.957777\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.32297 | − | 21.0258i | −0.405347 | − | 0.914163i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 46.6444 | 1.60843 | 0.804213 | − | 0.594341i | \(-0.202587\pi\) | ||||
0.804213 | + | 0.594341i | \(0.202587\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −19.2951 | −0.622423 | −0.311211 | − | 0.950341i | \(-0.600735\pi\) | ||||
−0.311211 | + | 0.950341i | \(0.600735\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.0737 | −0.287821 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.65403i | − | 0.206866i | −0.994636 | − | 0.103433i | \(-0.967017\pi\) | ||
0.994636 | − | 0.103433i | \(-0.0329827\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 44.7331 | 1.09105 | 0.545525 | − | 0.838094i | \(-0.316330\pi\) | ||||
0.545525 | + | 0.838094i | \(0.316330\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 33.2928i | − | 0.774251i | −0.922027 | − | 0.387126i | \(-0.873468\pi\) | ||
0.922027 | − | 0.387126i | \(-0.126532\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 34.0399 | 0.724252 | 0.362126 | − | 0.932129i | \(-0.382051\pi\) | ||||
0.362126 | + | 0.932129i | \(0.382051\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 28.7039 | 0.585794 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 55.1208i | − | 1.04001i | −0.854162 | − | 0.520007i | \(-0.825929\pi\) | ||
0.854162 | − | 0.520007i | \(-0.174071\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −37.3995 | −0.679992 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −41.8005 | −0.708484 | −0.354242 | − | 0.935154i | \(-0.615261\pi\) | ||||
−0.354242 | + | 0.935154i | \(0.615261\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 60.8160i | − | 0.996983i | −0.866895 | − | 0.498492i | \(-0.833887\pi\) | ||
0.866895 | − | 0.498492i | \(-0.166113\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 7.33555i | − | 0.112855i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 99.3338i | − | 1.48259i | −0.671177 | − | 0.741297i | \(-0.734211\pi\) | ||
0.671177 | − | 0.741297i | \(-0.265789\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −75.5229 | −1.06370 | −0.531852 | − | 0.846838i | \(-0.678504\pi\) | ||||
−0.531852 | + | 0.846838i | \(0.678504\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.63517 | −0.0634955 | −0.0317477 | − | 0.999496i | \(-0.510107\pi\) | ||||
−0.0317477 | + | 0.999496i | \(0.510107\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −75.3507 | −0.978581 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 146.747i | 1.85755i | 0.370640 | + | 0.928777i | \(0.379138\pi\) | ||||
−0.370640 | + | 0.928777i | \(0.620862\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 95.3465i | 1.14875i | 0.818591 | + | 0.574377i | \(0.194756\pi\) | ||||
−0.818591 | + | 0.574377i | \(0.805244\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.6881 | −0.208095 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 18.9550i | − | 0.212977i | −0.994314 | − | 0.106489i | \(-0.966039\pi\) | ||
0.994314 | − | 0.106489i | \(-0.0339608\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 14.7793i | − | 0.162410i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.2382 | 0.118296 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 39.5365i | 0.407593i | 0.979013 | + | 0.203796i | \(0.0653280\pi\) | ||||
−0.979013 | + | 0.203796i | \(0.934672\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 106.867 | 1.05809 | 0.529046 | − | 0.848593i | \(-0.322550\pi\) | ||||
0.529046 | + | 0.848593i | \(0.322550\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 63.2367i | − | 0.613949i | −0.951718 | − | 0.306974i | \(-0.900683\pi\) | ||
0.951718 | − | 0.306974i | \(-0.0993166\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 69.0952i | 0.645749i | 0.946442 | + | 0.322875i | \(0.104649\pi\) | ||||
−0.946442 | + | 0.322875i | \(0.895351\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 73.7413i | − | 0.676526i | −0.941052 | − | 0.338263i | \(-0.890161\pi\) | ||
0.941052 | − | 0.338263i | \(-0.109839\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.2883i | 0.0910467i | 0.998963 | + | 0.0455234i | \(0.0144955\pi\) | ||||
−0.998963 | + | 0.0455234i | \(0.985504\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −47.0150 | + | 20.8468i | −0.408826 | + | 0.181276i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −35.6370 | −0.299471 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −158.745 | −1.31194 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 149.110 | 1.17410 | 0.587049 | − | 0.809551i | \(-0.300290\pi\) | ||||
0.587049 | + | 0.809551i | \(0.300290\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 31.3444 | 0.239271 | 0.119635 | − | 0.992818i | \(-0.461827\pi\) | ||||
0.119635 | + | 0.992818i | \(0.461827\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 22.6421 | 0.170241 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 20.4938i | − | 0.149590i | −0.997199 | − | 0.0747951i | \(-0.976170\pi\) | ||
0.997199 | − | 0.0747951i | \(-0.0238303\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.55870 | −0.0256021 | −0.0128011 | − | 0.999918i | \(-0.504075\pi\) | ||||
−0.0128011 | + | 0.999918i | \(0.504075\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 54.8693i | − | 0.383701i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 104.300i | − | 0.719310i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 43.7333i | − | 0.293512i | −0.989173 | − | 0.146756i | \(-0.953117\pi\) | ||
0.989173 | − | 0.146756i | \(-0.0468833\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −241.291 | −1.59795 | −0.798976 | − | 0.601363i | \(-0.794625\pi\) | ||||
−0.798976 | + | 0.601363i | \(0.794625\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 43.1452i | 0.278356i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 237.304i | 1.51149i | 0.654865 | + | 0.755746i | \(0.272725\pi\) | ||||
−0.654865 | + | 0.755746i | \(0.727275\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −94.7235 | + | 42.0011i | −0.588344 | + | 0.260876i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −268.485 | −1.64715 | −0.823573 | − | 0.567211i | \(-0.808023\pi\) | ||||
−0.823573 | + | 0.567211i | \(0.808023\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 129.062 | 0.772824 | 0.386412 | − | 0.922326i | \(-0.373714\pi\) | ||||
0.386412 | + | 0.922326i | \(0.373714\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −158.238 | −0.936319 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −261.404 | −1.51101 | −0.755504 | − | 0.655144i | \(-0.772608\pi\) | ||||
−0.755504 | + | 0.655144i | \(0.772608\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.5256i | 0.128718i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 212.837 | 1.18903 | 0.594517 | − | 0.804083i | \(-0.297343\pi\) | ||||
0.594517 | + | 0.804083i | \(0.297343\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 142.181i | − | 0.785530i | −0.919639 | − | 0.392765i | \(-0.871519\pi\) | ||
0.919639 | − | 0.392765i | \(-0.128481\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −17.1149 | −0.0925132 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −132.305 | −0.707515 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 374.861i | 1.96262i | 0.192431 | + | 0.981310i | \(0.438363\pi\) | ||||
−0.192431 | + | 0.981310i | \(0.561637\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 62.3779 | 0.323202 | 0.161601 | − | 0.986856i | \(-0.448334\pi\) | ||||
0.161601 | + | 0.986856i | \(0.448334\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 65.4646 | 0.332308 | 0.166154 | − | 0.986100i | \(-0.446865\pi\) | ||||
0.166154 | + | 0.986100i | \(0.446865\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 11.2001i | − | 0.0562818i | −0.999604 | − | 0.0281409i | \(-0.991041\pi\) | ||
0.999604 | − | 0.0281409i | \(-0.00895871\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 210.138i | − | 1.03516i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 100.026i | − | 0.487933i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 84.0604 | 0.402203 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −122.214 | −0.579214 | −0.289607 | − | 0.957146i | \(-0.593525\pi\) | ||||
−0.289607 | + | 0.957146i | \(0.593525\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −74.4450 | −0.346256 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 86.9267i | 0.400584i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 25.9504i | − | 0.117423i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −56.4834 | −0.253289 | −0.126644 | − | 0.991948i | \(-0.540421\pi\) | ||||
−0.126644 | + | 0.991948i | \(0.540421\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 50.9497i | − | 0.224448i | −0.993683 | − | 0.112224i | \(-0.964203\pi\) | ||
0.993683 | − | 0.112224i | \(-0.0357974\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 250.713i | − | 1.09482i | −0.836865 | − | 0.547409i | \(-0.815614\pi\) | ||
0.836865 | − | 0.547409i | \(-0.184386\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −105.830 | −0.454206 | −0.227103 | − | 0.973871i | \(-0.572925\pi\) | ||||
−0.227103 | + | 0.973871i | \(0.572925\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 76.1154i | − | 0.323895i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −198.228 | −0.829405 | −0.414703 | − | 0.909957i | \(-0.636114\pi\) | ||||
−0.414703 | + | 0.909957i | \(0.636114\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 141.253i | − | 0.586111i | −0.956095 | − | 0.293056i | \(-0.905328\pi\) | ||
0.956095 | − | 0.293056i | \(-0.0946721\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 64.1839i | − | 0.261975i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.4876i | 0.0667515i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 313.146i | − | 1.24759i | −0.781587 | − | 0.623797i | \(-0.785589\pi\) | ||
0.781587 | − | 0.623797i | \(-0.214411\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −351.668 | + | 155.932i | −1.38999 | + | 0.616333i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 220.699 | 0.858751 | 0.429376 | − | 0.903126i | \(-0.358734\pi\) | ||||
0.429376 | + | 0.903126i | \(0.358734\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −34.4823 | −0.133136 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.3556i | 0.0888047i | 0.999014 | + | 0.0444023i | \(0.0141384\pi\) | ||||
−0.999014 | + | 0.0444023i | \(0.985862\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −123.254 | −0.465109 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −36.7299 | −0.136542 | −0.0682712 | − | 0.997667i | \(-0.521748\pi\) | ||||
−0.0682712 | + | 0.997667i | \(0.521748\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −409.730 | −1.51192 | −0.755959 | − | 0.654619i | \(-0.772829\pi\) | ||||
−0.755959 | + | 0.654619i | \(0.772829\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 83.6279i | 0.304102i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 81.7757 | 0.295219 | 0.147610 | − | 0.989046i | \(-0.452842\pi\) | ||||
0.147610 | + | 0.989046i | \(0.452842\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 162.029i | 0.576617i | 0.957538 | + | 0.288308i | \(0.0930928\pi\) | ||||
−0.957538 | + | 0.288308i | \(0.906907\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 390.052i | 1.37828i | 0.724630 | + | 0.689138i | \(0.242011\pi\) | ||||
−0.724630 | + | 0.689138i | \(0.757989\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 201.528i | − | 0.702187i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 226.426 | 0.783482 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 9.07936i | − | 0.0309876i | −0.999880 | − | 0.0154938i | \(-0.995068\pi\) | ||
0.999880 | − | 0.0154938i | \(-0.00493203\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 93.4689i | 0.316844i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −30.5846 | − | 68.9762i | −0.102290 | − | 0.230690i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −149.988 | −0.498299 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −135.989 | −0.445864 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −347.241 | −1.13108 | −0.565538 | − | 0.824722i | \(-0.691332\pi\) | ||||
−0.565538 | + | 0.824722i | \(0.691332\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 446.607 | 1.43604 | 0.718018 | − | 0.696024i | \(-0.245049\pi\) | ||||
0.718018 | + | 0.696024i | \(0.245049\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 196.972i | − | 0.629303i | −0.949207 | − | 0.314652i | \(-0.898112\pi\) | ||
0.949207 | − | 0.314652i | \(-0.101888\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −267.299 | −0.843214 | −0.421607 | − | 0.906779i | \(-0.638534\pi\) | ||||
−0.421607 | + | 0.906779i | \(0.638534\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 780.154i | − | 2.44563i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 39.7563 | 0.123085 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.4028 | −0.0504702 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 153.354i | − | 0.466120i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −323.583 | −0.977591 | −0.488796 | − | 0.872398i | \(-0.662564\pi\) | ||||
−0.488796 | + | 0.872398i | \(0.662564\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −222.117 | −0.663036 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 429.028i | − | 1.27308i | −0.771243 | − | 0.636540i | \(-0.780365\pi\) | ||
0.771243 | − | 0.636540i | \(-0.219635\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 322.722i | 0.946399i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 350.065i | − | 1.02060i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.9140 | −0.0833257 | −0.0416628 | − | 0.999132i | \(-0.513266\pi\) | ||||
−0.0416628 | + | 0.999132i | \(0.513266\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −459.116 | −1.31552 | −0.657760 | − | 0.753228i | \(-0.728496\pi\) | ||||
−0.657760 | + | 0.753228i | \(0.728496\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 497.975 | 1.41069 | 0.705347 | − | 0.708862i | \(-0.250791\pi\) | ||||
0.705347 | + | 0.708862i | \(0.250791\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 168.874i | 0.475702i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.5119i | 0.0682782i | 0.999417 | + | 0.0341391i | \(0.0108689\pi\) | ||||
−0.999417 | + | 0.0341391i | \(0.989131\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 335.741 | 0.930030 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.3646i | 0.0283960i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 506.076i | − | 1.37895i | −0.724308 | − | 0.689477i | \(-0.757841\pi\) | ||
0.724308 | − | 0.689477i | \(-0.242159\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −248.325 | −0.669341 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 141.697i | − | 0.379885i | −0.981795 | − | 0.189942i | \(-0.939170\pi\) | ||
0.981795 | − | 0.189942i | \(-0.0608302\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 153.020 | 0.405888 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 488.878i | 1.28992i | 0.764218 | + | 0.644958i | \(0.223125\pi\) | ||||
−0.764218 | + | 0.644958i | \(0.776875\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.6483i | 0.0382462i | 0.999817 | + | 0.0191231i | \(0.00608744\pi\) | ||||
−0.999817 | + | 0.0191231i | \(0.993913\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 168.489i | 0.437635i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 172.342i | 0.443037i | 0.975156 | + | 0.221519i | \(0.0711014\pi\) | ||||
−0.975156 | + | 0.221519i | \(0.928899\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −166.321 | + | 73.7480i | −0.425374 | + | 0.188614i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 328.136 | 0.830723 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 175.371 | 0.441742 | 0.220871 | − | 0.975303i | \(-0.429110\pi\) | ||||
0.220871 | + | 0.975303i | \(0.429110\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 449.214i | 1.12024i | 0.828413 | + | 0.560118i | \(0.189244\pi\) | ||||
−0.828413 | + | 0.560118i | \(0.810756\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −63.2987 | −0.157069 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −128.018 | −0.314541 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −620.134 | −1.51622 | −0.758110 | − | 0.652127i | \(-0.773877\pi\) | ||||
−0.758110 | + | 0.652127i | \(0.773877\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 188.316i | 0.455972i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 213.201 | 0.513738 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 206.896i | 0.493784i | 0.969043 | + | 0.246892i | \(0.0794093\pi\) | ||||
−0.969043 | + | 0.246892i | \(0.920591\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 220.733i | 0.524307i | 0.965026 | + | 0.262153i | \(0.0844327\pi\) | ||||
−0.965026 | + | 0.262153i | \(0.915567\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 39.5517i | 0.0930629i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −273.983 | −0.641646 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 90.1264i | 0.209110i | 0.994519 | + | 0.104555i | \(0.0333418\pi\) | ||||
−0.994519 | + | 0.104555i | \(0.966658\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 348.623i | − | 0.805133i | −0.915391 | − | 0.402567i | \(-0.868118\pi\) | ||
0.915391 | − | 0.402567i | \(-0.131882\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 105.672 | − | 46.8559i | 0.241813 | − | 0.107222i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −193.342 | −0.440414 | −0.220207 | − | 0.975453i | \(-0.570673\pi\) | ||||
−0.220207 | + | 0.975453i | \(0.570673\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −639.655 | −1.44392 | −0.721958 | − | 0.691937i | \(-0.756757\pi\) | ||||
−0.721958 | + | 0.691937i | \(0.756757\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −42.3846 | −0.0952464 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 354.736 | 0.790058 | 0.395029 | − | 0.918669i | \(-0.370735\pi\) | ||||
0.395029 | + | 0.918669i | \(0.370735\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 748.187i | − | 1.65895i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −33.0475 | −0.0726319 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 592.163i | 1.29576i | 0.761742 | + | 0.647881i | \(0.224345\pi\) | ||||
−0.761742 | + | 0.647881i | \(0.775655\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −340.832 | −0.739332 | −0.369666 | − | 0.929165i | \(-0.620528\pi\) | ||||
−0.369666 | + | 0.929165i | \(0.620528\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −180.466 | −0.389776 | −0.194888 | − | 0.980826i | \(-0.562434\pi\) | ||||
−0.194888 | + | 0.980826i | \(0.562434\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 641.661i | − | 1.37401i | −0.726654 | − | 0.687003i | \(-0.758926\pi\) | ||
0.726654 | − | 0.687003i | \(-0.241074\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −447.510 | −0.954180 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −556.842 | −1.17725 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 25.1293i | − | 0.0529038i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.67841i | 0.0139424i | 0.999976 | + | 0.00697120i | \(0.00221902\pi\) | ||||
−0.999976 | + | 0.00697120i | \(0.997781\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 25.1095i | − | 0.0522027i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 88.4063 | 0.182281 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −315.161 | −0.647147 | −0.323574 | − | 0.946203i | \(-0.604884\pi\) | ||||
−0.323574 | + | 0.946203i | \(0.604884\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.8038 | −0.0566268 | −0.0283134 | − | 0.999599i | \(-0.509014\pi\) | ||||
−0.0283134 | + | 0.999599i | \(0.509014\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 368.973i | − | 0.748425i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 340.240i | 0.684587i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 210.058 | 0.420958 | 0.210479 | − | 0.977598i | \(-0.432498\pi\) | ||||
0.210479 | + | 0.977598i | \(0.432498\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 96.4559i | 0.191761i | 0.995393 | + | 0.0958807i | \(0.0305667\pi\) | ||||
−0.995393 | + | 0.0958807i | \(0.969433\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 238.963i | − | 0.473193i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −568.643 | −1.11718 | −0.558589 | − | 0.829445i | \(-0.688657\pi\) | ||||
−0.558589 | + | 0.829445i | \(0.688657\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.8820i | 0.0408649i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −141.402 | −0.274566 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 569.336i | − | 1.10123i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 40.7079i | − | 0.0781342i | −0.999237 | − | 0.0390671i | \(-0.987561\pi\) | ||
0.999237 | − | 0.0390671i | \(-0.0124386\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 768.320i | − | 1.46906i | −0.678575 | − | 0.734531i | \(-0.737402\pi\) | ||
0.678575 | − | 0.734531i | \(-0.262598\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 152.631i | 0.289622i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −355.164 | + | 392.045i | −0.671388 | + | 0.741106i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 146.750 | 0.275327 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 154.501 | 0.288788 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 480.090i | − | 0.890705i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 713.405 | 1.31868 | 0.659340 | − | 0.751845i | \(-0.270836\pi\) | ||||
0.659340 | + | 0.751845i | \(0.270836\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −164.891 | −0.302552 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −845.349 | −1.54543 | −0.772714 | − | 0.634755i | \(-0.781101\pi\) | ||||
−0.772714 | + | 0.634755i | \(0.781101\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 234.428i | 0.425459i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 661.111 | 1.19550 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.4984i | 0.0368014i | 0.999831 | + | 0.0184007i | \(0.00585745\pi\) | ||||
−0.999831 | + | 0.0184007i | \(0.994143\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 109.219i | − | 0.195383i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 696.419i | − | 1.23698i | −0.785794 | − | 0.618489i | \(-0.787745\pi\) | ||
0.785794 | − | 0.618489i | \(-0.212255\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.0053 | 0.0407173 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 164.123i | − | 0.288441i | −0.989546 | − | 0.144221i | \(-0.953932\pi\) | ||
0.989546 | − | 0.144221i | \(-0.0460675\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 356.989i | 0.625199i | 0.949885 | + | 0.312600i | \(0.101200\pi\) | ||||
−0.949885 | + | 0.312600i | \(0.898800\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 46.6149 | + | 105.129i | 0.0810693 | + | 0.182833i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −955.102 | −1.65529 | −0.827645 | − | 0.561252i | \(-0.810320\pi\) | ||||
−0.827645 | + | 0.561252i | \(0.810320\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 429.547 | 0.739324 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −921.927 | −1.58135 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 943.977 | 1.60814 | 0.804069 | − | 0.594536i | \(-0.202664\pi\) | ||||
0.804069 | + | 0.594536i | \(0.202664\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 96.9745i | − | 0.164643i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −282.505 | −0.476399 | −0.238199 | − | 0.971216i | \(-0.576557\pi\) | ||||
−0.238199 | + | 0.971216i | \(0.576557\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 79.6869i | 0.133928i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 872.279 | 1.45622 | 0.728112 | − | 0.685458i | \(-0.240398\pi\) | ||||
0.728112 | + | 0.685458i | \(0.240398\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 421.219 | 0.700863 | 0.350432 | − | 0.936588i | \(-0.386035\pi\) | ||||
0.350432 | + | 0.936588i | \(0.386035\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 354.965i | 0.586719i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −527.228 | −0.868581 | −0.434290 | − | 0.900773i | \(-0.643001\pi\) | ||||
−0.434290 | + | 0.900773i | \(0.643001\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 111.670 | 0.182766 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 932.715i | 1.52156i | 0.649011 | + | 0.760779i | \(0.275183\pi\) | ||||
−0.649011 | + | 0.760779i | \(0.724817\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 666.640i | − | 1.08045i | −0.841519 | − | 0.540227i | \(-0.818338\pi\) | ||
0.841519 | − | 0.540227i | \(-0.181662\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 368.300i | 0.594992i | 0.954723 | + | 0.297496i | \(0.0961515\pi\) | ||||
−0.954723 | + | 0.297496i | \(0.903849\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −85.3944 | −0.137070 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −60.5461 | −0.0962577 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 668.239i | − | 1.05902i | −0.848305 | − | 0.529508i | \(-0.822376\pi\) | ||
0.848305 | − | 0.529508i | \(-0.177624\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 333.421i | − | 0.525073i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 94.1649 | 0.147826 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 7.09640i | − | 0.0110708i | −0.999985 | − | 0.00553541i | \(-0.998238\pi\) | ||
0.999985 | − | 0.00553541i | \(-0.00176199\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 349.594i | 0.543692i | 0.962341 | + | 0.271846i | \(0.0876342\pi\) | ||||
−0.962341 | + | 0.271846i | \(0.912366\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1161.51 | 1.79523 | 0.897613 | − | 0.440785i | \(-0.145300\pi\) | ||||
0.897613 | + | 0.440785i | \(0.145300\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 699.138i | 1.07725i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 973.812 | 1.49129 | 0.745644 | − | 0.666344i | \(-0.232142\pi\) | ||||
0.745644 | + | 0.666344i | \(0.232142\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 70.0883i | − | 0.107005i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 643.261i | − | 0.976117i | −0.872811 | − | 0.488059i | \(-0.837705\pi\) | ||
0.872811 | − | 0.488059i | \(-0.162295\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 709.808i | 1.07384i | 0.843633 | + | 0.536919i | \(0.180412\pi\) | ||||
−0.843633 | + | 0.536919i | \(0.819588\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 50.6292i | − | 0.0761342i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −434.864 | − | 980.733i | −0.651970 | − | 1.47036i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1017.18 | −1.51592 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −171.463 | −0.254774 | −0.127387 | − | 0.991853i | \(-0.540659\pi\) | ||||
−0.127387 | + | 0.991853i | \(0.540659\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1311.57i | − | 1.93732i | −0.248392 | − | 0.968660i | \(-0.579902\pi\) | ||
0.248392 | − | 0.968660i | \(-0.420098\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 178.117 | 0.262322 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1251.08 | 1.83174 | 0.915872 | − | 0.401470i | \(-0.131501\pi\) | ||||
0.915872 | + | 0.401470i | \(0.131501\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −45.8256 | −0.0668987 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 180.827i | − | 0.262448i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 458.895 | 0.664103 | 0.332052 | − | 0.943261i | \(-0.392259\pi\) | ||||
0.332052 | + | 0.943261i | \(0.392259\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.95748i | 0.0114496i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 353.854i | − | 0.507682i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1065.87i | 1.52050i | 0.649629 | + | 0.760252i | \(0.274924\pi\) | ||||
−0.649629 | + | 0.760252i | \(0.725076\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 38.4681 | 0.0547199 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 481.450i | − | 0.680976i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1291.74i | − | 1.82192i | −0.412490 | − | 0.910962i | \(-0.635341\pi\) | ||
0.412490 | − | 0.910962i | \(-0.364659\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 179.888 | + | 405.694i | 0.252297 | + | 0.568996i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −122.691 | −0.171596 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −832.051 | −1.15723 | −0.578617 | − | 0.815599i | \(-0.696407\pi\) | ||||
−0.578617 | + | 0.815599i | \(0.696407\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −284.889 | −0.395130 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −233.222 | −0.321685 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 254.392i | 0.349920i | 0.984576 | + | 0.174960i | \(0.0559796\pi\) | ||||
−0.984576 | + | 0.174960i | \(0.944020\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −263.358 | −0.360270 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1009.28i | 1.37691i | 0.725277 | + | 0.688457i | \(0.241712\pi\) | ||||
−0.725277 | + | 0.688457i | \(0.758288\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1661.42 | −2.25430 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 421.530 | 0.570407 | 0.285203 | − | 0.958467i | \(-0.407939\pi\) | ||||
0.285203 | + | 0.958467i | \(0.407939\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 232.509i | 0.312932i | 0.987683 | + | 0.156466i | \(0.0500102\pi\) | ||||
−0.987683 | + | 0.156466i | \(0.949990\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −97.7907 | −0.131263 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 311.282 | 0.415596 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 497.992i | 0.663105i | 0.943437 | + | 0.331552i | \(0.107572\pi\) | ||||
−0.943437 | + | 0.331552i | \(0.892428\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 539.543i | 0.714626i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 75.3812i | 0.0995788i | 0.998760 | + | 0.0497894i | \(0.0158550\pi\) | ||||
−0.998760 | + | 0.0497894i | \(0.984145\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1074.06 | −1.41138 | −0.705688 | − | 0.708523i | \(-0.749362\pi\) | ||||
−0.705688 | + | 0.708523i | \(0.749362\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −332.213 | −0.435404 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −137.129 | −0.178786 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 107.714i | 0.140070i | 0.997545 | + | 0.0700349i | \(0.0223111\pi\) | ||||
−0.997545 | + | 0.0700349i | \(0.977689\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 796.138i | − | 1.02993i | −0.857210 | − | 0.514966i | \(-0.827804\pi\) | ||
0.857210 | − | 0.514966i | \(-0.172196\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 96.4755 | 0.124485 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 224.822i | 0.288604i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1263.16i | 1.61737i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 530.628 | 0.675960 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 92.6042i | − | 0.117667i | −0.998268 | − | 0.0588337i | \(-0.981262\pi\) | ||
0.998268 | − | 0.0588337i | \(-0.0187382\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 46.3499 | 0.0585966 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 199.510i | − | 0.251589i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 796.483i | − | 0.999352i | −0.866213 | − | 0.499676i | \(-0.833452\pi\) | ||
0.866213 | − | 0.499676i | \(-0.166548\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 269.267i | − | 0.337005i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 77.5259i | 0.0965454i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 93.9172 | + | 211.808i | 0.116667 | + | 0.263116i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −279.321 | −0.345268 | −0.172634 | − | 0.984986i | \(-0.555228\pi\) | ||||
−0.172634 | + | 0.984986i | \(0.555228\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 359.059 | 0.442736 | 0.221368 | − | 0.975190i | \(-0.428948\pi\) | ||||
0.221368 | + | 0.975190i | \(0.428948\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 600.350i | 0.736626i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 167.325 | 0.204804 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −566.638 | −0.690180 | −0.345090 | − | 0.938570i | \(-0.612152\pi\) | ||||
−0.345090 | + | 0.938570i | \(0.612152\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −127.948 | −0.155466 | −0.0777329 | − | 0.996974i | \(-0.524768\pi\) | ||||
−0.0777329 | + | 0.996974i | \(0.524768\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.0636i | 0.0145872i | 0.999973 | + | 0.00729360i | \(0.00232164\pi\) | ||||
−0.999973 | + | 0.00729360i | \(0.997678\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 840.795 | 1.01423 | 0.507114 | − | 0.861879i | \(-0.330712\pi\) | ||||
0.507114 | + | 0.861879i | \(0.330712\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 227.058i | − | 0.272579i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 288.591i | − | 0.345617i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 158.463i | − | 0.188872i | −0.995531 | − | 0.0944358i | \(-0.969895\pi\) | ||
0.995531 | − | 0.0944358i | \(-0.0301047\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1334.70 | 1.58704 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 353.831i | 0.418735i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 715.166i | 0.844351i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −160.932 | + | 71.3583i | −0.189109 | + | 0.0838523i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 450.469 | 0.528099 | 0.264050 | − | 0.964509i | \(-0.414942\pi\) | ||||
0.264050 | + | 0.964509i | \(0.414942\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 838.563 | 0.978487 | 0.489243 | − | 0.872147i | \(-0.337273\pi\) | ||||
0.489243 | + | 0.872147i | \(0.337273\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −743.346 | −0.865362 | −0.432681 | − | 0.901547i | \(-0.642432\pi\) | ||||
−0.432681 | + | 0.901547i | \(0.642432\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −920.734 | −1.06690 | −0.533450 | − | 0.845832i | \(-0.679105\pi\) | ||||
−0.533450 | + | 0.845832i | \(0.679105\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 584.518i | 0.675743i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2454.42 | 2.82442 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 325.870i | − | 0.374134i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 50.3687 | 0.0575643 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 952.517 | 1.08611 | 0.543054 | − | 0.839698i | \(-0.317268\pi\) | ||||
0.543054 | + | 0.839698i | \(0.317268\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1233.48i | 1.40009i | 0.714099 | + | 0.700045i | \(0.246837\pi\) | ||||
−0.714099 | + | 0.700045i | \(0.753163\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1645.24 | −1.86324 | −0.931622 | − | 0.363428i | \(-0.881606\pi\) | ||||
−0.931622 | + | 0.363428i | \(0.881606\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1412.37 | −1.59230 | −0.796148 | − | 0.605102i | \(-0.793132\pi\) | ||||
−0.796148 | + | 0.605102i | \(0.793132\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 671.760i | − | 0.755636i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 171.079i | 0.191578i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 475.918i | − | 0.531752i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −900.008 | −1.00112 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −436.025 | −0.483934 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −317.926 | −0.351300 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 23.7746i | − | 0.0262124i | −0.999914 | − | 0.0131062i | \(-0.995828\pi\) | ||
0.999914 | − | 0.0131062i | \(-0.00417195\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 907.624i | 0.996295i | 0.867092 | + | 0.498147i | \(0.165986\pi\) | ||||
−0.867092 | + | 0.498147i | \(0.834014\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1594.73 | 1.74669 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 141.210i | − | 0.153992i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 443.884i | − | 0.483008i | −0.970400 | − | 0.241504i | \(-0.922359\pi\) | ||
0.970400 | − | 0.241504i | \(-0.0776407\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −247.757 | −0.268426 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.2702i | 0.0413732i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 687.674 | 0.740230 | 0.370115 | − | 0.928986i | \(-0.379318\pi\) | ||||
0.370115 | + | 0.928986i | \(0.379318\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 144.262i | 0.154954i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 295.843i | 0.316410i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 335.833i | 0.358413i | 0.983811 | + | 0.179207i | \(0.0573530\pi\) | ||||
−0.983811 | + | 0.179207i | \(0.942647\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 0.00945708i | − | 1.00500e-5i | −1.00000 | 5.02502e-6i | \(-0.999998\pi\) | |||
1.00000 | 5.02502e-6i | \(-1.59951e-6\pi\) | ||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −417.045 | − | 940.547i | −0.442254 | − | 0.997398i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1303.23 | 1.37617 | 0.688084 | − | 0.725631i | \(-0.258452\pi\) | ||||
0.688084 | + | 0.725631i | \(0.258452\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.2060 | −0.0160231 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1053.25i | 1.10519i | 0.833449 | + | 0.552597i | \(0.186363\pi\) | ||||
−0.833449 | + | 0.552597i | \(0.813637\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 838.214 | 0.877711 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −92.3272 | −0.0962744 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −588.699 | −0.612590 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 139.481i | − | 0.144540i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1599.40 | 1.65398 | 0.826990 | − | 0.562216i | \(-0.190051\pi\) | ||||
0.826990 | + | 0.562216i | \(0.190051\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1031.90i | 1.06272i | 0.847146 | + | 0.531361i | \(0.178319\pi\) | ||||
−0.847146 | + | 0.531361i | \(0.821681\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.0323i | 0.0164772i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 443.622i | − | 0.454066i | −0.973887 | − | 0.227033i | \(-0.927097\pi\) | ||
0.973887 | − | 0.227033i | \(-0.0729025\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −317.033 | −0.323834 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 528.007i | 0.537138i | 0.963260 | + | 0.268569i | \(0.0865507\pi\) | ||||
−0.963260 | + | 0.268569i | \(0.913449\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 146.383i | − | 0.148613i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −700.006 | + | 310.388i | −0.707792 | + | 0.313840i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1185.02 | −1.19578 | −0.597890 | − | 0.801578i | \(-0.703994\pi\) | ||||
−0.597890 | + | 0.801578i | \(0.703994\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.0441 | −0.0251700 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1381.72 | 1.38588 | 0.692939 | − | 0.720996i | \(-0.256315\pi\) | ||||
0.692939 | + | 0.720996i | \(0.256315\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4140.3.d.b.2161.6 | ✓ | 32 | |
3.2 | odd | 2 | inner | 4140.3.d.b.2161.22 | yes | 32 | |
23.22 | odd | 2 | inner | 4140.3.d.b.2161.27 | yes | 32 | |
69.68 | even | 2 | inner | 4140.3.d.b.2161.11 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.3.d.b.2161.6 | ✓ | 32 | 1.1 | even | 1 | trivial | |
4140.3.d.b.2161.11 | yes | 32 | 69.68 | even | 2 | inner | |
4140.3.d.b.2161.22 | yes | 32 | 3.2 | odd | 2 | inner | |
4140.3.d.b.2161.27 | yes | 32 | 23.22 | odd | 2 | inner |