Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,2,Mod(129,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.2208514587\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 640) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.1 | ||
Root | \(1.45161 - 1.45161i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.129 |
Dual form | 1280.2.f.j.129.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.90321 | −1.67617 | −0.838085 | − | 0.545540i | \(-0.816325\pi\) | ||||
−0.838085 | + | 0.545540i | \(0.816325\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.21432 | − | 0.311108i | −0.990274 | − | 0.139132i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.52543i | 1.33249i | 0.745735 | + | 0.666243i | \(0.232099\pi\) | ||||
−0.745735 | + | 0.666243i | \(0.767901\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.42864 | 1.80955 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.80642i | − | 1.14768i | −0.818967 | − | 0.573840i | \(-0.805453\pi\) | ||
0.818967 | − | 0.573840i | \(-0.194547\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.62222 | 0.727272 | 0.363636 | − | 0.931541i | \(-0.381535\pi\) | ||||
0.363636 | + | 0.931541i | \(0.381535\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.42864 | + | 0.903212i | 1.65987 | + | 0.233208i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.80642i | − | 1.40826i | −0.710069 | − | 0.704132i | \(-0.751336\pi\) | ||
0.710069 | − | 0.704132i | \(-0.248664\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.05086i | 1.15875i | 0.815063 | + | 0.579373i | \(0.196702\pi\) | ||||
−0.815063 | + | 0.579373i | \(0.803298\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 10.2351i | − | 2.23347i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 0.474572i | − | 0.0989552i | −0.998775 | − | 0.0494776i | \(-0.984244\pi\) | ||
0.998775 | − | 0.0494776i | \(-0.0157556\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.80642 | + | 1.37778i | 0.961285 | + | 0.275557i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.05086 | −1.35694 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.00000i | − | 0.371391i | −0.982607 | − | 0.185695i | \(-0.940546\pi\) | ||
0.982607 | − | 0.185695i | \(-0.0594537\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.75557 | −0.494915 | −0.247457 | − | 0.968899i | \(-0.579595\pi\) | ||||
−0.247457 | + | 0.968899i | \(0.579595\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 11.0509i | 1.92371i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.09679 | − | 7.80642i | 0.185391 | − | 1.31953i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.18421 | 1.18108 | 0.590538 | − | 0.807010i | \(-0.298915\pi\) | ||||
0.590538 | + | 0.807010i | \(0.298915\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.61285 | −1.21903 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.18421 | −0.809637 | −0.404819 | − | 0.914397i | \(-0.632665\pi\) | ||||
−0.404819 | + | 0.914397i | \(0.632665\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.95407 | −0.297992 | −0.148996 | − | 0.988838i | \(-0.547604\pi\) | ||||
−0.148996 | + | 0.988838i | \(0.547604\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −12.0207 | − | 1.68889i | −1.79195 | − | 0.251765i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.33185i | 0.777730i | 0.921295 | + | 0.388865i | \(0.127133\pi\) | ||||
−0.921295 | + | 0.388865i | \(0.872867\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.42864 | −0.775520 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 16.8573i | 2.36049i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.37778 | −0.738695 | −0.369348 | − | 0.929291i | \(-0.620419\pi\) | ||||
−0.369348 | + | 0.929291i | \(0.620419\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.18421 | + | 8.42864i | −0.159679 | + | 1.13652i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 14.6637i | − | 1.94225i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.05086i | 0.657565i | 0.944406 | + | 0.328783i | \(0.106638\pi\) | ||||
−0.944406 | + | 0.328783i | \(0.893362\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.2351i | 1.56654i | 0.621682 | + | 0.783270i | \(0.286450\pi\) | ||||
−0.621682 | + | 0.783270i | \(0.713550\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 19.1383i | 2.41120i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.80642 | − | 0.815792i | −0.720198 | − | 0.101187i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.76049 | −0.948095 | −0.474047 | − | 0.880499i | \(-0.657207\pi\) | ||||
−0.474047 | + | 0.880499i | \(0.657207\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.37778i | 0.165866i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.85728 | 0.576453 | 0.288226 | − | 0.957562i | \(-0.406934\pi\) | ||||
0.288226 | + | 0.957562i | \(0.406934\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.66370i | 0.779927i | 0.920830 | + | 0.389964i | \(0.127512\pi\) | ||||
−0.920830 | + | 0.389964i | \(0.872488\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13.9541 | − | 4.00000i | −1.61128 | − | 0.461880i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.4193 | 1.52927 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.24443 | 0.590045 | 0.295022 | − | 0.955490i | \(-0.404673\pi\) | ||||
0.295022 | + | 0.955490i | \(0.404673\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.18421 | 0.464912 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.1476 | −1.33338 | −0.666689 | − | 0.745336i | \(-0.732289\pi\) | ||||
−0.666689 | + | 0.745336i | \(0.732289\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.80642 | + | 12.8573i | −0.195934 | + | 1.39457i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.80642i | 0.622514i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.1017 | −1.28278 | −0.641389 | − | 0.767216i | \(-0.721642\pi\) | ||||
−0.641389 | + | 0.767216i | \(0.721642\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.24443i | 0.969080i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.00000 | 0.829561 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.57136 | − | 11.1842i | 0.161218 | − | 1.14748i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.8064i | − | 1.40183i | −0.713245 | − | 0.700915i | \(-0.752775\pi\) | ||
0.713245 | − | 0.700915i | \(-0.247225\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 20.6637i | − | 2.07678i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.7146i | 1.96167i | 0.194836 | + | 0.980836i | \(0.437583\pi\) | ||||
−0.194836 | + | 0.980836i | \(0.562417\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.13828i | 0.309223i | 0.987975 | + | 0.154612i | \(0.0494127\pi\) | ||||
−0.987975 | + | 0.154612i | \(0.950587\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.18421 | + | 22.6637i | −0.310747 | + | 2.21175i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.39207 | 0.521272 | 0.260636 | − | 0.965437i | \(-0.416068\pi\) | ||||
0.260636 | + | 0.965437i | \(0.416068\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.62222i | 0.825858i | 0.910763 | + | 0.412929i | \(0.135494\pi\) | ||||
−0.910763 | + | 0.412929i | \(0.864506\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.8573 | −1.97969 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.51114i | 0.518444i | 0.965818 | + | 0.259222i | \(0.0834662\pi\) | ||||
−0.965818 | + | 0.259222i | \(0.916534\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.147643 | + | 1.05086i | −0.0137678 | + | 0.0979927i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.2351 | 1.31603 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 20.4701 | 1.87649 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.48886 | −0.317169 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.0509 | 1.35709 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.2143 | − | 4.54617i | −0.913597 | − | 0.406622i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.2810i | − | 0.912291i | −0.889905 | − | 0.456145i | \(-0.849230\pi\) | ||
0.889905 | − | 0.456145i | \(-0.150770\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.67307 | 0.499486 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 4.66370i | − | 0.407470i | −0.979026 | − | 0.203735i | \(-0.934692\pi\) | ||
0.979026 | − | 0.203735i | \(-0.0653080\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.8064 | −1.54401 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.6128 | + | 2.19358i | 1.34374 | + | 0.188793i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.3461i | 0.969366i | 0.874690 | + | 0.484683i | \(0.161065\pi\) | ||||
−0.874690 | + | 0.484683i | \(0.838935\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 11.8064i | − | 1.00141i | −0.865619 | − | 0.500704i | \(-0.833075\pi\) | ||
0.865619 | − | 0.500704i | \(-0.166925\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 15.4795i | − | 1.30361i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 9.98126i | − | 0.834675i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.622216 | + | 4.42864i | −0.0516722 | + | 0.367778i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.7605 | 1.29990 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.47949i | 0.448898i | 0.974486 | + | 0.224449i | \(0.0720582\pi\) | ||||
−0.974486 | + | 0.224449i | \(0.927942\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.6128 | −1.92159 | −0.960793 | − | 0.277266i | \(-0.910572\pi\) | ||||
−0.960793 | + | 0.277266i | \(0.910572\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 31.5210i | − | 2.54832i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.10171 | + | 0.857279i | 0.490101 | + | 0.0688583i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.815792 | −0.0651073 | −0.0325536 | − | 0.999470i | \(-0.510364\pi\) | ||||
−0.0325536 | + | 0.999470i | \(0.510364\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.6128 | 1.23818 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.67307 | 0.131856 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.9032 | −0.854005 | −0.427003 | − | 0.904250i | \(-0.640431\pi\) | ||||
−0.427003 | + | 0.904250i | \(0.640431\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.43801 | − | 24.4701i | 0.267649 | − | 1.90500i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 6.57628i | − | 0.508888i | −0.967088 | − | 0.254444i | \(-0.918108\pi\) | ||
0.967088 | − | 0.254444i | \(-0.0818925\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.12399 | −0.471076 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 27.4193i | 2.09680i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.5303 | −0.800608 | −0.400304 | − | 0.916382i | \(-0.631095\pi\) | ||||
−0.400304 | + | 0.916382i | \(0.631095\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.85728 | + | 16.9447i | −0.367176 | + | 1.28090i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 14.6637i | − | 1.10219i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 6.29529i | − | 0.470532i | −0.971931 | − | 0.235266i | \(-0.924404\pi\) | ||
0.971931 | − | 0.235266i | \(-0.0755961\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.488863i | − | 0.0363369i | −0.999835 | − | 0.0181684i | \(-0.994216\pi\) | ||
0.999835 | − | 0.0181684i | \(-0.00578351\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 35.5210i | − | 2.62579i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.9081 | − | 2.23506i | −1.16959 | − | 0.164325i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22.1017 | −1.61624 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 24.8573i | − | 1.80810i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.4889 | −0.758947 | −0.379474 | − | 0.925203i | \(-0.623895\pi\) | ||||
−0.379474 | + | 0.925203i | \(0.623895\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.8064i | 0.993808i | 0.867805 | + | 0.496904i | \(0.165530\pi\) | ||||
−0.867805 | + | 0.496904i | \(0.834470\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.8573 | + | 2.36842i | 1.20717 | + | 0.169606i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.7239 | 1.19153 | 0.595765 | − | 0.803159i | \(-0.296849\pi\) | ||||
0.595765 | + | 0.803159i | \(0.296849\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.8573 | 1.47853 | 0.739267 | − | 0.673413i | \(-0.235172\pi\) | ||||
0.739267 | + | 0.673413i | \(0.235172\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.5303 | 1.58917 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.05086 | 0.494873 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.4795 | + | 1.61285i | 0.801763 | + | 0.112646i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 2.57628i | − | 0.179064i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.2257 | 1.32987 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4.66370i | − | 0.321063i | −0.987031 | − | 0.160531i | \(-0.948679\pi\) | ||
0.987031 | − | 0.160531i | \(-0.0513207\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.1017 | −0.966233 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.32693 | + | 0.607926i | 0.295094 | + | 0.0414602i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 9.71456i | − | 0.659467i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 19.3461i | − | 1.30729i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 15.2257i | − | 1.02419i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.4558i | 1.77161i | 0.464054 | + | 0.885807i | \(0.346394\pi\) | ||||
−0.464054 | + | 0.885807i | \(0.653606\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 26.0923 | + | 7.47949i | 1.73949 | + | 0.498633i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.3225 | 0.817872 | 0.408936 | − | 0.912563i | \(-0.365900\pi\) | ||||
0.408936 | + | 0.912563i | \(0.365900\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 13.2257i | − | 0.873979i | −0.899467 | − | 0.436989i | \(-0.856045\pi\) | ||
0.899467 | − | 0.436989i | \(-0.143955\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −38.9590 | −2.56331 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.66370i | 0.436554i | 0.975887 | + | 0.218277i | \(0.0700436\pi\) | ||||
−0.975887 | + | 0.218277i | \(0.929956\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.65878 | − | 11.8064i | 0.108207 | − | 0.770166i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.2257 | −0.989015 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.9590 | −1.48509 | −0.742547 | − | 0.669794i | \(-0.766382\pi\) | ||||
−0.742547 | + | 0.669794i | \(0.766382\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0415 | −0.904492 | −0.452246 | − | 0.891893i | \(-0.649377\pi\) | ||||
−0.452246 | + | 0.891893i | \(0.649377\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.00492 | 0.577666 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.0207 | + | 1.68889i | 0.767977 | + | 0.107899i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.2444i | 0.842723i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 35.2672 | 2.23497 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.9304i | 1.57359i | 0.617212 | + | 0.786797i | \(0.288262\pi\) | ||||
−0.617212 | + | 0.786797i | \(0.711738\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.80642 | −0.113569 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.24443 | − | 37.3274i | 0.328419 | − | 2.33753i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.7146i | 1.60403i | 0.597304 | + | 0.802015i | \(0.296239\pi\) | ||||
−0.597304 | + | 0.802015i | \(0.703761\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 25.3274i | 1.57377i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 10.8573i | − | 0.672049i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 2.57628i | − | 0.158860i | −0.996840 | − | 0.0794302i | \(-0.974690\pi\) | ||
0.996840 | − | 0.0794302i | \(-0.0253101\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.9081 | + | 1.67307i | 0.731511 | + | 0.102776i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 35.1338 | 2.15016 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.7462i | 1.56977i | 0.619639 | + | 0.784887i | \(0.287279\pi\) | ||||
−0.619639 | + | 0.784887i | \(0.712721\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.1847 | 1.83359 | 0.916795 | − | 0.399359i | \(-0.130767\pi\) | ||||
0.916795 | + | 0.399359i | \(0.130767\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 26.8385i | − | 1.62434i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.24443 | − | 18.2953i | 0.316251 | − | 1.10325i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.5303 | −0.632707 | −0.316354 | − | 0.948641i | \(-0.602459\pi\) | ||||
−0.316354 | + | 0.948641i | \(0.602459\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.9590 | −0.895571 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.93978 | 0.473647 | 0.236824 | − | 0.971553i | \(-0.423894\pi\) | ||||
0.236824 | + | 0.971553i | \(0.423894\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.9032 | 0.648129 | 0.324064 | − | 0.946035i | \(-0.394951\pi\) | ||||
0.324064 | + | 0.946035i | \(0.394951\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.56199 | + | 32.4701i | −0.270229 | + | 1.92336i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 18.2766i | − | 1.07883i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7146 | −0.983209 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 40.0830i | 2.34971i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.42864 | −0.258724 | −0.129362 | − | 0.991597i | \(-0.541293\pi\) | ||||
−0.129362 | + | 0.991597i | \(0.541293\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.57136 | − | 11.1842i | 0.0914881 | − | 0.651170i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 26.8385i | 1.55733i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 1.24443i | − | 0.0719673i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 6.88892i | − | 0.397071i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 57.2355i | − | 3.28810i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.80642 | − | 27.0923i | 0.217955 | − | 1.55130i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.27163 | −0.300868 | −0.150434 | − | 0.988620i | \(-0.548067\pi\) | ||||
−0.150434 | + | 0.988620i | \(0.548067\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 9.11108i | − | 0.518311i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.387152 | −0.0219534 | −0.0109767 | − | 0.999940i | \(-0.503494\pi\) | ||||
−0.0109767 | + | 0.999940i | \(0.503494\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 11.3461i | − | 0.641322i | −0.947194 | − | 0.320661i | \(-0.896095\pi\) | ||
0.947194 | − | 0.320661i | \(-0.103905\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.95407 | − | 42.3783i | 0.335474 | − | 2.38774i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.7239 | 0.939309 | 0.469655 | − | 0.882850i | \(-0.344378\pi\) | ||||
0.469655 | + | 0.882850i | \(0.344378\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.61285 | −0.426238 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.6543 | −0.873740 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.3274 | 1.63182 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.6035 | + | 3.61285i | 0.699115 | + | 0.200405i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 25.0321i | − | 1.38428i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18.7971 | −1.03632 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.33630i | 0.183379i | 0.995788 | + | 0.0916897i | \(0.0292268\pi\) | ||||
−0.995788 | + | 0.0916897i | \(0.970773\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 39.0005 | 2.13721 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.1842 | + | 2.41435i | 0.938874 | + | 0.131910i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.61285i | 0.196804i | 0.995147 | + | 0.0984022i | \(0.0313732\pi\) | ||||
−0.995147 | + | 0.0984022i | \(0.968627\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 16.0000i | − | 0.869001i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.4889i | 0.568004i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.53972i | 0.299117i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.428639 | − | 3.05086i | 0.0230772 | − | 0.164253i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.7605 | 0.846067 | 0.423034 | − | 0.906114i | \(-0.360965\pi\) | ||||
0.423034 | + | 0.906114i | \(0.360965\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 0.285442i | − | 0.0152794i | −0.999971 | − | 0.00763968i | \(-0.997568\pi\) | ||
0.999971 | − | 0.00763968i | \(-0.00243181\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.4889 | −0.986862 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 4.38715i | − | 0.233505i | −0.993161 | − | 0.116752i | \(-0.962752\pi\) | ||
0.993161 | − | 0.116752i | \(-0.0372484\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.7556 | − | 1.51114i | −0.570846 | − | 0.0802028i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −59.4291 | −3.14532 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.5906 | −1.08673 | −0.543364 | − | 0.839497i | \(-0.682850\pi\) | ||||
−0.543364 | + | 0.839497i | \(0.682850\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.51114 | −0.342691 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.1289 | 0.531630 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.07313 | − | 14.7556i | 0.108513 | − | 0.772342i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.5575i | 0.864297i | 0.901802 | + | 0.432148i | \(0.142244\pi\) | ||||
−0.901802 | + | 0.432148i | \(0.857756\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −28.1432 | −1.46508 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 18.9590i | − | 0.984302i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.8988 | 1.28921 | 0.644605 | − | 0.764516i | \(-0.277022\pi\) | ||||
0.644605 | + | 0.764516i | \(0.277022\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 29.6543 | + | 13.1985i | 1.53134 | + | 0.681568i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 5.24443i | − | 0.270102i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.31756i | − | 0.478611i | −0.970944 | − | 0.239305i | \(-0.923080\pi\) | ||
0.970944 | − | 0.239305i | \(-0.0769197\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 29.8479i | 1.52915i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.5575i | 1.66361i | 0.555066 | + | 0.831806i | \(0.312693\pi\) | ||||
−0.555066 | + | 0.831806i | \(0.687307\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −29.7146 | − | 4.17484i | −1.51439 | − | 0.212770i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.6079 | −0.539231 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.9906i | 0.962863i | 0.876484 | + | 0.481432i | \(0.159883\pi\) | ||||
−0.876484 | + | 0.481432i | \(0.840117\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.75557 | −0.139355 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.5397i | 0.682988i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.6128 | − | 1.63158i | −0.584306 | − | 0.0820939i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.9906 | −1.65575 | −0.827876 | − | 0.560911i | \(-0.810451\pi\) | ||||
−0.827876 | + | 0.560911i | \(0.810451\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 51.6958 | 2.58803 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.1017 | −0.804081 | −0.402041 | − | 0.915622i | \(-0.631699\pi\) | ||||
−0.402041 | + | 0.915622i | \(0.631699\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.22570 | −0.359938 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.26517 | − | 1.30174i | −0.460390 | − | 0.0646840i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 27.3461i | − | 1.35550i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.3876 | −1.65091 | −0.825456 | − | 0.564466i | \(-0.809082\pi\) | ||||
−0.825456 | + | 0.564466i | \(0.809082\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 32.9403i | − | 1.62482i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.8064 | −0.876197 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.8988 | + | 3.77923i | 1.32041 | + | 0.185515i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 34.2766i | 1.67853i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.4193i | 1.33952i | 0.742578 | + | 0.669760i | \(0.233603\pi\) | ||||
−0.742578 | + | 0.669760i | \(0.766397\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 12.2351i | − | 0.596301i | −0.954519 | − | 0.298150i | \(-0.903630\pi\) | ||
0.954519 | − | 0.298150i | \(-0.0963696\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 28.9447i | 1.40734i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.00000 | − | 27.9081i | 0.388057 | − | 1.35374i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −43.1338 | −2.08739 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 28.9777i | 1.39906i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.4701 | −1.37136 | −0.685679 | − | 0.727904i | \(-0.740495\pi\) | ||||
−0.685679 | + | 0.727904i | \(0.740495\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.0098i | 1.63441i | 0.576348 | + | 0.817204i | \(0.304477\pi\) | ||||
−0.576348 | + | 0.817204i | \(0.695523\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.80642 | − | 12.8573i | 0.0866114 | − | 0.616459i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.39700 | 0.114664 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.8385 | −0.708205 | −0.354103 | − | 0.935207i | \(-0.615214\pi\) | ||||
−0.354103 | + | 0.935207i | \(0.615214\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −29.4701 | −1.40334 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.0968 | −0.622247 | −0.311124 | − | 0.950369i | \(-0.600705\pi\) | ||||
−0.311124 | + | 0.950369i | \(0.600705\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.7971 | + | 3.76494i | 1.27030 | + | 0.178475i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 15.9081i | − | 0.752429i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.3876 | 1.00934 | 0.504672 | − | 0.863311i | \(-0.331613\pi\) | ||||
0.504672 | + | 0.863311i | \(0.331613\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.7333i | 0.929205i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 68.5531 | 3.22091 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.87601 | − | 20.4701i | 0.134830 | − | 0.959654i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.9813i | 0.841128i | 0.907263 | + | 0.420564i | \(0.138168\pi\) | ||||
−0.907263 | + | 0.420564i | \(0.861832\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 40.9403i | 1.91093i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.7368i | 0.500064i | 0.968238 | + | 0.250032i | \(0.0804412\pi\) | ||||
−0.968238 | + | 0.250032i | \(0.919559\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 9.30327i | − | 0.432360i | −0.976354 | − | 0.216180i | \(-0.930640\pi\) | ||
0.976354 | − | 0.216180i | \(-0.0693598\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17.7146 | − | 2.48886i | −0.821493 | − | 0.115418i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.70964 | 0.403034 | 0.201517 | − | 0.979485i | \(-0.435413\pi\) | ||||
0.201517 | + | 0.979485i | \(0.435413\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 27.3590i | − | 1.26332i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.36842 | 0.109131 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.43801i | 0.342000i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.95899 | + | 24.2766i | −0.319300 | + | 1.11388i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −29.1941 | −1.33670 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −23.2257 | −1.06121 | −0.530605 | − | 0.847619i | \(-0.678035\pi\) | ||||
−0.530605 | + | 0.847619i | \(0.678035\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.8385 | 0.858964 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.85728 | −0.221014 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.29529 | + | 30.5718i | −0.195039 | + | 1.38820i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.8528i | 1.48870i | 0.667787 | + | 0.744352i | \(0.267241\pi\) | ||||
−0.667787 | + | 0.744352i | \(0.732759\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 31.6543 | 1.43146 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.94914i | − | 0.133093i | −0.997783 | − | 0.0665465i | \(-0.978802\pi\) | ||
0.997783 | − | 0.0665465i | \(-0.0211981\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.6128 | −0.523016 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.42864 | + | 45.7560i | −0.288946 | + | 2.05658i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.1240i | 0.768116i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 35.0321i | − | 1.56825i | −0.620601 | − | 0.784127i | \(-0.713111\pi\) | ||
0.620601 | − | 0.784127i | \(-0.286889\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.0923i | 0.852983i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 16.2908i | − | 0.726373i | −0.931717 | − | 0.363186i | \(-0.881689\pi\) | ||
0.931717 | − | 0.363186i | \(-0.118311\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.13335 | − | 43.6543i | 0.272931 | − | 1.94259i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.7792 | 0.789603 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 26.0000i | − | 1.15243i | −0.817298 | − | 0.576215i | \(-0.804529\pi\) | ||
0.817298 | − | 0.576215i | \(-0.195471\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.4924 | −1.03924 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 35.6128i | − | 1.57235i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.976342 | − | 6.94914i | 0.0430228 | − | 0.306216i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.2953 | 0.892586 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 30.5718 | 1.34195 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.7146 | −0.513224 | −0.256612 | − | 0.966514i | \(-0.582606\pi\) | ||||
−0.256612 | + | 0.966514i | \(0.582606\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −38.0370 | −1.66324 | −0.831622 | − | 0.555342i | \(-0.812587\pi\) | ||||
−0.831622 | + | 0.555342i | \(0.812587\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 14.1017 | − | 49.1941i | 0.615449 | − | 2.14700i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.0000i | 0.696971i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.7748 | 0.990208 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.4193i | 1.18990i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.5941 | −0.588826 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.9398 | − | 1.67752i | −0.516202 | − | 0.0725254i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.2766i | 0.788691i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.6637i | 0.890049i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.5111i | 0.494902i | 0.968900 | + | 0.247451i | \(0.0795930\pi\) | ||||
−0.968900 | + | 0.247451i | \(0.920407\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.41927i | 0.0609068i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.68244 | − | 19.0923i | 0.114903 | − | 0.817826i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.2208 | 1.29215 | 0.646073 | − | 0.763275i | \(-0.276410\pi\) | ||||
0.646073 | + | 0.763275i | \(0.276410\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 66.4197i | 2.83473i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.1017 | 0.430347 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.4889i | 0.786226i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 46.1847 | + | 6.48886i | 1.96043 | + | 0.275437i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.75605 | −0.413377 | −0.206688 | − | 0.978407i | \(-0.566269\pi\) | ||||
−0.206688 | + | 0.978407i | \(0.566269\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.12399 | −0.216721 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 64.1659 | 2.70909 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.50622 | 0.189914 | 0.0949572 | − | 0.995481i | \(-0.469729\pi\) | ||||
0.0949572 | + | 0.995481i | \(0.469729\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.71456 | − | 12.2034i | 0.0721320 | − | 0.513402i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.7511i | 0.619489i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.30465 | 0.222383 | 0.111191 | − | 0.993799i | \(-0.464533\pi\) | ||||
0.111191 | + | 0.993799i | \(0.464533\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.3970i | 0.686193i | 0.939300 | + | 0.343096i | \(0.111476\pi\) | ||||
−0.939300 | + | 0.343096i | \(0.888524\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 30.4514 | 1.27213 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.653858 | − | 2.28100i | 0.0272678 | − | 0.0951241i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 39.8163i | − | 1.65757i | −0.559565 | − | 0.828786i | \(-0.689032\pi\) | ||
0.559565 | − | 0.828786i | \(-0.310968\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 40.0830i | − | 1.66579i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 42.8256i | − | 1.77671i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.4701i | 0.847786i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −31.5210 | − | 4.42864i | −1.30323 | − | 0.183102i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.1699 | 0.626130 | 0.313065 | − | 0.949732i | \(-0.398644\pi\) | ||||
0.313065 | + | 0.949732i | \(0.398644\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 13.9180i | − | 0.573480i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −48.5531 | −1.99721 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 8.00000i | − | 0.328521i | −0.986417 | − | 0.164260i | \(-0.947476\pi\) | ||
0.986417 | − | 0.164260i | \(-0.0525237\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −45.3274 | − | 6.36842i | −1.85824 | − | 0.261080i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −60.5531 | −2.47827 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.83500 | 0.0749762 | 0.0374881 | − | 0.999297i | \(-0.488064\pi\) | ||||
0.0374881 | + | 0.999297i | \(0.488064\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.1432 | 1.47431 | 0.737156 | − | 0.675723i | \(-0.236168\pi\) | ||||
0.737156 | + | 0.675723i | \(0.236168\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −42.1289 | −1.71562 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.72546 | + | 1.08541i | 0.314084 | + | 0.0441283i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.5353i | 0.711735i | 0.934536 | + | 0.355867i | \(0.115815\pi\) | ||||
−0.934536 | + | 0.355867i | \(0.884185\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.4701 | −0.829491 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.9813i | 0.565621i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.9309 | −1.37046 | −0.685228 | − | 0.728329i | \(-0.740297\pi\) | ||||
−0.685228 | + | 0.728329i | \(0.740297\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −33.3274 | − | 4.68244i | −1.34389 | − | 0.188814i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 9.68598i | − | 0.389943i | −0.980809 | − | 0.194971i | \(-0.937539\pi\) | ||
0.980809 | − | 0.194971i | \(-0.0624614\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 41.4005i | − | 1.66403i | −0.554755 | − | 0.832014i | \(-0.687188\pi\) | ||
0.554755 | − | 0.832014i | \(-0.312812\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.34614i | 0.134276i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 42.6637i | − | 1.70929i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.2034 | + | 13.2444i | 0.848137 | + | 0.529777i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −55.8163 | −2.22909 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 41.7146i | − | 1.66327i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.8163 | 1.10735 | 0.553674 | − | 0.832733i | \(-0.313225\pi\) | ||||
0.553674 | + | 0.832733i | \(0.313225\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.5397i | 0.538155i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.19850 | + | 22.7654i | −0.126929 | + | 0.903418i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.2351 | −0.564014 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 26.3684 | 1.04312 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.8988 | 1.69440 | 0.847200 | − | 0.531275i | \(-0.178287\pi\) | ||||
0.847200 | + | 0.531275i | \(0.178287\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.9639 | −1.10279 | −0.551395 | − | 0.834245i | \(-0.685904\pi\) | ||||
−0.551395 | + | 0.834245i | \(0.685904\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.5620 | − | 1.76494i | −0.494628 | − | 0.0694943i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.13828i | 0.280635i | 0.990107 | + | 0.140317i | \(0.0448123\pi\) | ||||
−0.990107 | + | 0.140317i | \(0.955188\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.2257 | 0.754675 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 28.2034i | 1.10538i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.7649 | −0.695196 | −0.347598 | − | 0.937644i | \(-0.613003\pi\) | ||||
−0.347598 | + | 0.937644i | \(0.613003\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.45091 | + | 10.3269i | −0.0566919 | + | 0.403507i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 36.1748i | 1.41131i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.1936i | 0.786630i | 0.919404 | + | 0.393315i | \(0.128672\pi\) | ||||
−0.919404 | + | 0.393315i | \(0.871328\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0701i | 0.858426i | 0.903203 | + | 0.429213i | \(0.141209\pi\) | ||||
−0.903203 | + | 0.429213i | \(0.858791\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 44.2034i | 1.71672i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 39.4291 | + | 5.53972i | 1.52900 | + | 0.214821i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.949145 | −0.0367510 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 76.8069i | − | 2.96953i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 46.5718 | 1.79789 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 26.0098i | − | 1.00261i | −0.865272 | − | 0.501303i | \(-0.832854\pi\) | ||
0.865272 | − | 0.501303i | \(-0.167146\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −33.8894 | − | 9.71456i | −1.30440 | − | 0.373914i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.86665 | −0.302340 | −0.151170 | − | 0.988508i | \(-0.548304\pi\) | ||||
−0.151170 | + | 0.988508i | \(0.548304\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 48.6735 | 1.86792 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −35.7748 | −1.37089 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.2494 | 0.698292 | 0.349146 | − | 0.937068i | \(-0.386472\pi\) | ||||
0.349146 | + | 0.937068i | \(0.386472\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.52987 | − | 25.1240i | 0.134870 | − | 0.959938i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 38.3970i | 1.46494i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.1017 | −0.537232 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.2543i | 0.960718i | 0.877072 | + | 0.480359i | \(0.159494\pi\) | ||||
−0.877072 | + | 0.480359i | \(0.840506\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 72.8484 | 2.76728 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.67307 | + | 26.1432i | −0.139328 | + | 0.991668i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.1017i | 1.14018i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 19.3461i | − | 0.731738i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 34.8069i | − | 1.31464i | −0.753612 | − | 0.657319i | \(-0.771690\pi\) | ||
0.753612 | − | 0.657319i | \(-0.228310\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.2864i | 1.36857i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.81579 | + | 34.2766i | −0.181373 | + | 1.29093i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −69.5022 | −2.61390 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.51114i | 0.282087i | 0.990003 | + | 0.141043i | \(0.0450457\pi\) | ||||
−0.990003 | + | 0.141043i | \(0.954954\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 28.4701 | 1.06771 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.30772i | 0.0489744i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.10525 | + | 22.1017i | −0.116130 | + | 0.826557i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 66.6548 | 2.48927 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.7556 | −0.997814 | −0.498907 | − | 0.866655i | \(-0.666265\pi\) | ||||
−0.498907 | + | 0.866655i | \(0.666265\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.0638 | −0.412036 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 40.7654 | 1.51608 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.75557 | − | 9.61285i | 0.102339 | − | 0.357012i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.6271i | 0.950458i | 0.879862 | + | 0.475229i | \(0.157635\pi\) | ||||
−0.879862 | + | 0.475229i | \(0.842365\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −38.6958 | −1.43318 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.3461i | 0.419652i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.6543 | −0.725949 | −0.362975 | − | 0.931799i | \(-0.618239\pi\) | ||||
−0.362975 | + | 0.931799i | \(0.618239\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −34.8988 | − | 4.90321i | −1.28726 | − | 0.180858i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.5397i | 1.08811i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 32.5433i | − | 1.19712i | −0.801077 | − | 0.598562i | \(-0.795739\pi\) | ||
0.801077 | − | 0.598562i | \(-0.204261\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 38.4514i | − | 1.41255i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.1383i | 0.848861i | 0.905461 | + | 0.424430i | \(0.139526\pi\) | ||||
−0.905461 | + | 0.424430i | \(0.860474\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.70471 | − | 12.1334i | 0.0624559 | − | 0.444532i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −65.9452 | −2.41281 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.0094i | 0.694587i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.48886 | −0.0908199 | −0.0454099 | − | 0.998968i | \(-0.514459\pi\) | ||||
−0.0454099 | + | 0.998968i | \(0.514459\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 72.3783i | − | 2.63761i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 52.2864 | + | 7.34614i | 1.90290 | + | 0.267353i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.2859 | 0.773650 | 0.386825 | − | 0.922153i | \(-0.373572\pi\) | ||||
0.386825 | + | 0.922153i | \(0.373572\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.24443 | 0.190361 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.1240 | −0.693244 | −0.346622 | − | 0.938005i | \(-0.612671\pi\) | ||||
−0.346622 | + | 0.938005i | \(0.612671\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.3970 | −1.10045 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.80642 | + | 69.7975i | −0.354552 | + | 2.52354i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.2444i | 0.478229i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.9625 | 1.22472 | 0.612360 | − | 0.790579i | \(-0.290220\pi\) | ||||
0.612360 | + | 0.790579i | \(0.290220\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 74.6548i | − | 2.68863i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.133353 | 0.00479638 | 0.00239819 | − | 0.999997i | \(-0.499237\pi\) | ||||
0.00239819 | + | 0.999997i | \(0.499237\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.2444 | − | 3.79658i | −0.475754 | − | 0.136377i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 73.5308i | − | 2.63790i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 26.1847i | − | 0.938164i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 18.4889i | − | 0.661584i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.1017i | 0.503954i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.80642 | + | 0.253799i | 0.0644740 | + | 0.00905848i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.12537 | −0.0401150 | −0.0200575 | − | 0.999799i | \(-0.506385\pi\) | ||||
−0.0200575 | + | 0.999799i | \(0.506385\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.47949i | 0.266277i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.4291 | −0.690820 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.0830i | 1.13930i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −34.5718 | − | 4.85728i | −1.22614 | − | 0.172270i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.11108 | 0.181044 | 0.0905218 | − | 0.995894i | \(-0.471147\pi\) | ||||
0.0905218 | + | 0.995894i | \(0.471147\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.9590 | 1.09525 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −65.6958 | −2.32125 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.3649 | 0.895107 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.70471 | − | 0.520505i | −0.130574 | − | 0.0183454i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 74.7467i | − | 2.63121i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.7368 | 0.658752 | 0.329376 | − | 0.944199i | \(-0.393162\pi\) | ||||
0.329376 | + | 0.944199i | \(0.393162\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 37.5210i | − | 1.31754i | −0.752344 | − | 0.658770i | \(-0.771077\pi\) | ||
0.752344 | − | 0.658770i | \(-0.228923\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −87.6325 | −3.07341 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.1432 | + | 3.39207i | 0.845699 | + | 0.118819i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 9.86971i | − | 0.345297i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 50.1847i | 1.75359i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.4001i | 0.642166i | 0.947051 | + | 0.321083i | \(0.104047\pi\) | ||||
−0.947051 | + | 0.321083i | \(0.895953\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.649413i | 0.0226371i | 0.999936 | + | 0.0113186i | \(0.00360288\pi\) | ||||
−0.999936 | + | 0.0113186i | \(0.996397\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −15.2257 | + | 53.1151i | −0.530091 | + | 1.84923i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.8622 | 1.03841 | 0.519205 | − | 0.854650i | \(-0.326228\pi\) | ||||
0.519205 | + | 0.854650i | \(0.326228\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.1753i | 0.735449i | 0.929935 | + | 0.367725i | \(0.119863\pi\) | ||||
−0.929935 | + | 0.367725i | \(0.880137\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30.5718 | 1.06053 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31.5210i | 1.09214i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.04593 | + | 14.5620i | −0.0708024 | + | 0.503939i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.4291 | 0.671568 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −43.8163 | −1.51271 | −0.756353 | − | 0.654164i | \(-0.773021\pi\) | ||||
−0.756353 | + | 0.654164i | \(0.773021\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23.0509 | −0.793914 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.5605 | + | 1.90522i | 0.466494 | + | 0.0655415i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 12.2997i | − | 0.422624i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −31.6543 | −1.08637 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 3.40943i | − | 0.116874i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.7846 | −1.29372 | −0.646860 | − | 0.762608i | \(-0.723918\pi\) | ||||
−0.646860 | + | 0.762608i | \(0.723918\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.53035 | − | 60.7150i | 0.291732 | − | 2.07641i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 19.5299i | − | 0.667128i | −0.942727 | − | 0.333564i | \(-0.891749\pi\) | ||
0.942727 | − | 0.333564i | \(-0.108251\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.2543i | 1.13462i | 0.823504 | + | 0.567311i | \(0.192016\pi\) | ||||
−0.823504 | + | 0.567311i | \(0.807984\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 53.0607i | 1.80830i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 44.9733i | − | 1.53091i | −0.643490 | − | 0.765454i | \(-0.722514\pi\) | ||
0.643490 | − | 0.765454i | \(-0.277486\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.3176 | + | 3.27607i | 0.792821 | + | 0.111390i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 48.5259 | 1.64803 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 19.9625i | − | 0.677182i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.3497 | −0.689523 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 74.9501i | − | 2.53668i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.0272 | − | 36.0098i | 0.541818 | − | 1.21735i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.30819 | 0.280548 | 0.140274 | − | 0.990113i | \(-0.455202\pi\) | ||||
0.140274 | + | 0.990113i | \(0.455202\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.8573 | 0.433665 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.3689 | −1.32637 | −0.663186 | − | 0.748455i | \(-0.730796\pi\) | ||||
−0.663186 | + | 0.748455i | \(0.730796\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.29036 | −0.245340 | −0.122670 | − | 0.992447i | \(-0.539146\pi\) | ||||
−0.122670 | + | 0.992447i | \(0.539146\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.56199 | + | 32.4701i | −0.153350 | + | 1.09147i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 11.1097i | − | 0.373027i | −0.982452 | − | 0.186514i | \(-0.940281\pi\) | ||
0.982452 | − | 0.186514i | \(-0.0597188\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.2449 | 1.21562 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 15.9269i | − | 0.533570i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.9304 | −0.901192 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.95851 | + | 13.9398i | −0.0654659 | + | 0.465955i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.61285i | 0.120629i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.51114i | 0.183807i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.2257i | 1.04028i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.0000i | 0.665558i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.152089 | + | 1.08250i | −0.00505561 | + | 0.0359835i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.5383 | 0.582351 | 0.291175 | − | 0.956670i | \(-0.405954\pi\) | ||||
0.291175 | + | 0.956670i | \(0.405954\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 107.023i | 3.54974i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.4701 | 1.47336 | 0.736681 | − | 0.676241i | \(-0.236392\pi\) | ||||
0.736681 | + | 0.676241i | \(0.236392\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 46.2391i | 1.53029i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.0509 | + | 78.6548i | −0.365330 | + | 2.60025i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.4415 | 0.542948 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.87955 | 0.259922 | 0.129961 | − | 0.991519i | \(-0.458515\pi\) | ||||
0.129961 | + | 0.991519i | \(0.458515\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.3047 | 0.504306 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.7368 | 0.419238 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.5303 | + | 9.89829i | 1.13535 | + | 0.325454i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.0366i | 0.559554i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.7560 | −0.516939 | −0.258470 | − | 0.966019i | \(-0.583218\pi\) | ||||
−0.258470 | + | 0.966019i | \(0.583218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 27.4193i | − | 0.898630i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.12399 | 0.0367976 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 48.9403 | + | 6.87601i | 1.60052 | + | 0.224870i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 10.2766i | − | 0.335720i | −0.985811 | − | 0.167860i | \(-0.946314\pi\) | ||
0.985811 | − | 0.167860i | \(-0.0536857\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.9403i | 1.07496i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 2.53341i | − | 0.0825869i | −0.999147 | − | 0.0412934i | \(-0.986852\pi\) | ||
0.999147 | − | 0.0412934i | \(-0.0131478\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.46028i | 0.0801178i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.73329 | + | 55.0420i | −0.251564 | + | 1.79052i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.06821 | −0.0347121 | −0.0173560 | − | 0.999849i | \(-0.505525\pi\) | ||||
−0.0173560 | + | 0.999849i | \(0.505525\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.4737i | 0.567219i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −48.5531 | −1.57444 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.6958i | 1.67459i | 0.546750 | + | 0.837296i | \(0.315865\pi\) | ||||
−0.546750 | + | 0.837296i | \(0.684135\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.2257 | + | 3.26317i | 0.751566 | + | 0.105594i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22.1017 | 0.714447 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −40.0000 | −1.29167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.4068 | −0.755059 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 29.2716 | 0.943265 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.29529 | − | 30.5718i | 0.138270 | − | 0.984142i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.2623i | 1.68064i | 0.542090 | + | 0.840320i | \(0.317633\pi\) | ||||
−0.542090 | + | 0.840320i | \(0.682367\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −85.1437 | −2.73521 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 59.3560i | − | 1.90482i | −0.304813 | − | 0.952412i | \(-0.598594\pi\) | ||
0.304813 | − | 0.952412i | \(-0.401406\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 41.6227 | 1.33436 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −36.5906 | − | 10.4889i | −1.17184 | − | 0.335912i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 47.8707i | − | 1.53152i | −0.643128 | − | 0.765759i | \(-0.722363\pi\) | ||
0.643128 | − | 0.765759i | \(-0.277637\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 46.0642i | 1.47222i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 46.8069i | 1.49443i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.01429i | 0.191826i | 0.995390 | + | 0.0959130i | \(0.0305771\pi\) | ||||
−0.995390 | + | 0.0959130i | \(0.969423\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −37.0321 | − | 5.20294i | −1.17994 | − | 0.165780i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 54.5718 | 1.73704 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.927346i | 0.0294879i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.4291 | −0.617186 | −0.308593 | − | 0.951194i | \(-0.599858\pi\) | ||||
−0.308593 | + | 0.951194i | \(0.599858\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 9.68598i | − | 0.307375i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −46.1847 | − | 6.48886i | −1.46415 | − | 0.205711i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.1334 | 1.01767 | 0.508837 | − | 0.860863i | \(-0.330076\pi\) | ||||
0.508837 | + | 0.860863i | \(0.330076\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −50.6548 | −1.60265 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1280.2.f.j.129.1 | 6 | ||
4.3 | odd | 2 | 1280.2.f.l.129.5 | 6 | |||
5.4 | even | 2 | 1280.2.f.k.129.5 | 6 | |||
8.3 | odd | 2 | 1280.2.f.i.129.2 | 6 | |||
8.5 | even | 2 | 1280.2.f.k.129.6 | 6 | |||
16.3 | odd | 4 | 640.2.c.a.129.6 | yes | 6 | ||
16.5 | even | 4 | 640.2.c.c.129.6 | yes | 6 | ||
16.11 | odd | 4 | 640.2.c.d.129.1 | yes | 6 | ||
16.13 | even | 4 | 640.2.c.b.129.1 | yes | 6 | ||
20.19 | odd | 2 | 1280.2.f.i.129.1 | 6 | |||
40.19 | odd | 2 | 1280.2.f.l.129.6 | 6 | |||
40.29 | even | 2 | inner | 1280.2.f.j.129.2 | 6 | ||
80.3 | even | 4 | 3200.2.a.bq.1.1 | 3 | |||
80.13 | odd | 4 | 3200.2.a.bt.1.3 | 3 | |||
80.19 | odd | 4 | 640.2.c.a.129.1 | ✓ | 6 | ||
80.27 | even | 4 | 3200.2.a.bp.1.1 | 3 | |||
80.29 | even | 4 | 640.2.c.b.129.6 | yes | 6 | ||
80.37 | odd | 4 | 3200.2.a.bu.1.3 | 3 | |||
80.43 | even | 4 | 3200.2.a.bv.1.3 | 3 | |||
80.53 | odd | 4 | 3200.2.a.bo.1.1 | 3 | |||
80.59 | odd | 4 | 640.2.c.d.129.6 | yes | 6 | ||
80.67 | even | 4 | 3200.2.a.bs.1.3 | 3 | |||
80.69 | even | 4 | 640.2.c.c.129.1 | yes | 6 | ||
80.77 | odd | 4 | 3200.2.a.br.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
640.2.c.a.129.1 | ✓ | 6 | 80.19 | odd | 4 | ||
640.2.c.a.129.6 | yes | 6 | 16.3 | odd | 4 | ||
640.2.c.b.129.1 | yes | 6 | 16.13 | even | 4 | ||
640.2.c.b.129.6 | yes | 6 | 80.29 | even | 4 | ||
640.2.c.c.129.1 | yes | 6 | 80.69 | even | 4 | ||
640.2.c.c.129.6 | yes | 6 | 16.5 | even | 4 | ||
640.2.c.d.129.1 | yes | 6 | 16.11 | odd | 4 | ||
640.2.c.d.129.6 | yes | 6 | 80.59 | odd | 4 | ||
1280.2.f.i.129.1 | 6 | 20.19 | odd | 2 | |||
1280.2.f.i.129.2 | 6 | 8.3 | odd | 2 | |||
1280.2.f.j.129.1 | 6 | 1.1 | even | 1 | trivial | ||
1280.2.f.j.129.2 | 6 | 40.29 | even | 2 | inner | ||
1280.2.f.k.129.5 | 6 | 5.4 | even | 2 | |||
1280.2.f.k.129.6 | 6 | 8.5 | even | 2 | |||
1280.2.f.l.129.5 | 6 | 4.3 | odd | 2 | |||
1280.2.f.l.129.6 | 6 | 40.19 | odd | 2 | |||
3200.2.a.bo.1.1 | 3 | 80.53 | odd | 4 | |||
3200.2.a.bp.1.1 | 3 | 80.27 | even | 4 | |||
3200.2.a.bq.1.1 | 3 | 80.3 | even | 4 | |||
3200.2.a.br.1.1 | 3 | 80.77 | odd | 4 | |||
3200.2.a.bs.1.3 | 3 | 80.67 | even | 4 | |||
3200.2.a.bt.1.3 | 3 | 80.13 | odd | 4 | |||
3200.2.a.bu.1.3 | 3 | 80.37 | odd | 4 | |||
3200.2.a.bv.1.3 | 3 | 80.43 | even | 4 |