Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(2431,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4560.2431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.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: | \(36.4117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.792772608.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 22x^{4} + 62x^{2} + 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2431.4 | ||
Root | \(-4.32698i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.2431 |
Dual form | 4560.2.d.f.2431.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4560\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(1711\) | \(1921\) | \(2737\) | \(3041\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.624069i | 0.235876i | 0.993021 | + | 0.117938i | \(0.0376284\pi\) | ||||
−0.993021 | + | 0.117938i | \(0.962372\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.32698i | − | 1.30463i | −0.757946 | − | 0.652317i | \(-0.773797\pi\) | ||
0.757946 | − | 0.652317i | \(-0.226203\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.624069i | − | 0.173086i | −0.996248 | − | 0.0865429i | \(-0.972418\pi\) | ||
0.996248 | − | 0.0865429i | \(-0.0275820\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.41188 | −1.07004 | −0.535019 | − | 0.844840i | \(-0.679696\pi\) | ||||
−0.535019 | + | 0.844840i | \(0.679696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.29966 | + | 3.70291i | −0.527579 | + | 0.849506i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.624069i | − | 0.136183i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.92071i | − | 0.400496i | −0.979745 | − | 0.200248i | \(-0.935825\pi\) | ||
0.979745 | − | 0.200248i | \(-0.0641747\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.16840i | 1.51683i | 0.651770 | + | 0.758417i | \(0.274027\pi\) | ||||
−0.651770 | + | 0.758417i | \(0.725973\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.700336 | −0.125784 | −0.0628920 | − | 0.998020i | \(-0.520032\pi\) | ||||
−0.0628920 | + | 0.998020i | \(0.520032\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.32698i | 0.753230i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.624069i | 0.105487i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.40627i | 0.395588i | 0.980244 | + | 0.197794i | \(0.0633778\pi\) | ||||
−0.980244 | + | 0.197794i | \(0.936622\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.624069i | 0.0999311i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.89138i | 1.23243i | 0.787579 | + | 0.616213i | \(0.211334\pi\) | ||||
−0.787579 | + | 0.616213i | \(0.788666\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.40627i | − | 0.366953i | −0.983024 | − | 0.183476i | \(-0.941265\pi\) | ||
0.983024 | − | 0.183476i | \(-0.0587351\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.64369i | 0.239757i | 0.992789 | + | 0.119878i | \(0.0382505\pi\) | ||||
−0.992789 | + | 0.119878i | \(0.961750\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.61054 | 0.944362 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.41188 | 0.617787 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.92071i | 0.263830i | 0.991261 | + | 0.131915i | \(0.0421126\pi\) | ||||
−0.991261 | + | 0.131915i | \(0.957887\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.32698i | − | 0.583450i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.29966 | − | 3.70291i | 0.304598 | − | 0.490462i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.0224 | −1.30481 | −0.652404 | − | 0.757871i | \(-0.726239\pi\) | ||||
−0.652404 | + | 0.757871i | \(0.726239\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.3221 | 1.44964 | 0.724822 | − | 0.688936i | \(-0.241922\pi\) | ||||
0.724822 | + | 0.688936i | \(0.241922\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.624069i | 0.0786254i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 0.624069i | − | 0.0774063i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.31087 | 0.526657 | 0.263328 | − | 0.964706i | \(-0.415180\pi\) | ||||
0.263328 | + | 0.964706i | \(0.415180\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.92071i | 0.231226i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0224 | 1.18944 | 0.594721 | − | 0.803932i | \(-0.297262\pi\) | ||||
0.594721 | + | 0.803932i | \(0.297262\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.31087 | 0.738632 | 0.369316 | − | 0.929304i | \(-0.379592\pi\) | ||||
0.369316 | + | 0.929304i | \(0.379592\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.70034 | 0.307732 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.71155 | −0.417581 | −0.208791 | − | 0.977960i | \(-0.566953\pi\) | ||||
−0.208791 | + | 0.977960i | \(0.566953\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 4.23697i | − | 0.465068i | −0.972588 | − | 0.232534i | \(-0.925298\pi\) | ||
0.972588 | − | 0.232534i | \(-0.0747017\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.41188 | −0.478536 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 8.16840i | − | 0.875744i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.61290i | 0.382967i | 0.981496 | + | 0.191483i | \(0.0613298\pi\) | ||||
−0.981496 | + | 0.191483i | \(0.938670\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.389463 | 0.0408268 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.700336 | 0.0726214 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.29966 | + | 3.70291i | −0.235941 | + | 0.379911i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.94033i | 0.298545i | 0.988796 | + | 0.149273i | \(0.0476932\pi\) | ||||
−0.988796 | + | 0.149273i | \(0.952307\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 4.32698i | − | 0.434878i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.599328 | 0.0596354 | 0.0298177 | − | 0.999555i | \(-0.490507\pi\) | ||||
0.0298177 | + | 0.999555i | \(0.490507\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.8238 | 1.26356 | 0.631781 | − | 0.775147i | \(-0.282324\pi\) | ||||
0.631781 | + | 0.775147i | \(0.282324\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 0.624069i | − | 0.0609029i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.71155 | −0.745503 | −0.372752 | − | 0.927931i | \(-0.621586\pi\) | ||||
−0.372752 | + | 0.927931i | \(0.621586\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.2184i | 1.17031i | 0.810923 | + | 0.585153i | \(0.198966\pi\) | ||||
−0.810923 | + | 0.585153i | \(0.801034\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 2.40627i | − | 0.228393i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.01027i | 0.659471i | 0.944073 | + | 0.329735i | \(0.106960\pi\) | ||||
−0.944073 | + | 0.329735i | \(0.893040\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.92071i | − | 0.179107i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 0.624069i | − | 0.0576952i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.75332i | − | 0.252396i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.72275 | −0.702069 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 7.89138i | − | 0.711542i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.31087 | 0.382528 | 0.191264 | − | 0.981539i | \(-0.438741\pi\) | ||||
0.191264 | + | 0.981539i | \(0.438741\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.40627i | 0.211860i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.26776i | − | 0.198135i | −0.995081 | − | 0.0990676i | \(-0.968414\pi\) | ||
0.995081 | − | 0.0990676i | \(-0.0315860\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.31087 | − | 1.43515i | −0.200378 | − | 0.124443i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.68913 | 0.315183 | 0.157592 | − | 0.987504i | \(-0.449627\pi\) | ||||
0.157592 | + | 0.987504i | \(0.449627\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.3368i | 1.38567i | 0.721097 | + | 0.692835i | \(0.243638\pi\) | ||||
−0.721097 | + | 0.692835i | \(0.756362\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 1.64369i | − | 0.138424i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.70034 | −0.225813 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.16840i | 0.678349i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.61054 | −0.545228 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.82376 | −0.231332 | −0.115666 | − | 0.993288i | \(-0.536900\pi\) | ||||
−0.115666 | + | 0.993288i | \(0.536900\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.83497 | −0.800359 | −0.400179 | − | 0.916437i | \(-0.631052\pi\) | ||||
−0.400179 | + | 0.916437i | \(0.631052\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.41188 | −0.356679 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.700336 | −0.0562523 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.11222 | −0.727234 | −0.363617 | − | 0.931549i | \(-0.618458\pi\) | ||||
−0.363617 | + | 0.931549i | \(0.618458\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 1.92071i | − | 0.152322i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.19866 | 0.0944674 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 14.3676i | − | 1.12536i | −0.826676 | − | 0.562678i | \(-0.809771\pi\) | ||
0.826676 | − | 0.562678i | \(-0.190229\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.32698i | 0.336855i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.4343 | 1.58125 | 0.790627 | − | 0.612298i | \(-0.209755\pi\) | ||||
0.790627 | + | 0.612298i | \(0.209755\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6105 | 0.970041 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.29966 | + | 3.70291i | −0.175860 | + | 0.283169i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 20.1997i | − | 1.53576i | −0.640595 | − | 0.767879i | \(-0.721312\pi\) | ||
0.640595 | − | 0.767879i | \(-0.278688\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.624069i | 0.0471752i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.0224 | 0.753331 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.19866 | −0.0895918 | −0.0447959 | − | 0.998996i | \(-0.514264\pi\) | ||||
−0.0447959 | + | 0.998996i | \(0.514264\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.65396i | 0.643244i | 0.946868 | + | 0.321622i | \(0.104228\pi\) | ||||
−0.946868 | + | 0.321622i | \(0.895772\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.3221 | −0.836952 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.40627i | 0.176912i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.0901i | 1.39601i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 0.624069i | − | 0.0453944i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.5453i | 1.19718i | 0.801056 | + | 0.598589i | \(0.204272\pi\) | ||||
−0.801056 | + | 0.598589i | \(0.795728\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.02989i | 0.578004i | 0.957328 | + | 0.289002i | \(0.0933234\pi\) | ||||
−0.957328 | + | 0.289002i | \(0.906677\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.624069i | 0.0446905i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.4343 | 1.02840 | 0.514201 | − | 0.857670i | \(-0.328089\pi\) | ||||
0.514201 | + | 0.857670i | \(0.328089\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.31626i | 0.164195i | 0.996624 | + | 0.0820977i | \(0.0261620\pi\) | ||||
−0.996624 | + | 0.0820977i | \(0.973838\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.31087 | −0.304066 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.09765 | −0.357785 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.89138i | 0.551158i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.92071i | − | 0.133499i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0224 | + | 9.95060i | 1.10829 | + | 0.688297i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.08644 | 0.143636 | 0.0718182 | − | 0.997418i | \(-0.477120\pi\) | ||||
0.0718182 | + | 0.997418i | \(0.477120\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.0224 | −0.686725 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 2.40627i | − | 0.164106i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.437058i | − | 0.0296694i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.31087 | −0.426449 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.75332i | 0.185208i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.82376 | −0.323023 | −0.161511 | − | 0.986871i | \(-0.551637\pi\) | ||||
−0.161511 | + | 0.986871i | \(0.551637\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.81255 | −0.253048 | −0.126524 | − | 0.991964i | \(-0.540382\pi\) | ||||
−0.126524 | + | 0.991964i | \(0.540382\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.6105 | 0.899410 | 0.449705 | − | 0.893177i | \(-0.351529\pi\) | ||||
0.449705 | + | 0.893177i | \(0.351529\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.70034 | −0.177669 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.42309 | 0.617327 | 0.308664 | − | 0.951171i | \(-0.400118\pi\) | ||||
0.308664 | + | 0.951171i | \(0.400118\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.64369i | 0.107223i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.71155 | 0.241091 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.38620i | 0.413089i | 0.978437 | + | 0.206544i | \(0.0662218\pi\) | ||||
−0.978437 | + | 0.206544i | \(0.933778\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.34514i | 0.0866482i | 0.999061 | + | 0.0433241i | \(0.0137948\pi\) | ||||
−0.999061 | + | 0.0433241i | \(0.986205\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.61054 | 0.422332 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.31087 | + | 1.43515i | 0.147037 | + | 0.0913164i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.23697i | 0.268507i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.01962i | 0.0643579i | 0.999482 | + | 0.0321790i | \(0.0102447\pi\) | ||||
−0.999482 | + | 0.0321790i | \(0.989755\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.31087 | −0.522500 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.41188 | 0.276283 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.3863i | 1.58355i | 0.610810 | + | 0.791777i | \(0.290844\pi\) | ||||
−0.610810 | + | 0.791777i | \(0.709156\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.50168 | −0.0933098 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.16840i | 0.505611i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 6.73325i | − | 0.415190i | −0.978215 | − | 0.207595i | \(-0.933436\pi\) | ||
0.978215 | − | 0.207595i | \(-0.0665636\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.92071i | 0.117988i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 3.61290i | − | 0.221106i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.2669i | 0.747924i | 0.927444 | + | 0.373962i | \(0.122001\pi\) | ||||
−0.927444 | + | 0.373962i | \(0.877999\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.1886i | 1.40861i | 0.709899 | + | 0.704303i | \(0.248740\pi\) | ||||
−0.709899 | + | 0.704303i | \(0.751260\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.389463 | −0.0235714 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 4.32698i | − | 0.260927i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.40067 | −0.204327 | −0.102163 | − | 0.994768i | \(-0.532576\pi\) | ||||
−0.102163 | + | 0.994768i | \(0.532576\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.700336 | −0.0419280 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.4469i | 0.742518i | 0.928529 | + | 0.371259i | \(0.121074\pi\) | ||||
−0.928529 | + | 0.371259i | \(0.878926\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.3378i | 1.50618i | 0.657920 | + | 0.753088i | \(0.271437\pi\) | ||||
−0.657920 | + | 0.753088i | \(0.728563\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.29966 | − | 3.70291i | 0.136220 | − | 0.219341i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.92477 | −0.290700 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.46469 | 0.144982 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 2.94033i | − | 0.172365i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 7.28729i | − | 0.425728i | −0.977082 | − | 0.212864i | \(-0.931721\pi\) | ||
0.977082 | − | 0.212864i | \(-0.0682791\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.0224 | −0.583528 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.32698i | 0.251077i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.19866 | −0.0693201 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.50168 | 0.0865554 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.599328 | −0.0344305 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.3221 | 0.648301 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.0224 | 0.800302 | 0.400151 | − | 0.916449i | \(-0.368958\pi\) | ||||
0.400151 | + | 0.916449i | \(0.368958\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.8238 | −0.729518 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.2594i | 0.978692i | 0.872090 | + | 0.489346i | \(0.162764\pi\) | ||||
−0.872090 | + | 0.489346i | \(0.837236\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.1346 | 0.855460 | 0.427730 | − | 0.903907i | \(-0.359313\pi\) | ||||
0.427730 | + | 0.903907i | \(0.359313\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.624069i | 0.0351623i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 15.1102i | − | 0.848673i | −0.905505 | − | 0.424336i | \(-0.860507\pi\) | ||
0.905505 | − | 0.424336i | \(-0.139493\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 35.3445 | 1.97891 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.71155 | 0.430416 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.1458 | − | 16.3368i | 0.564530 | − | 0.909004i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 0.624069i | − | 0.0346171i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 12.2184i | − | 0.675677i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.02578 | −0.0565529 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.8092 | 0.923917 | 0.461958 | − | 0.886902i | \(-0.347147\pi\) | ||||
0.461958 | + | 0.886902i | \(0.347147\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.40627i | 0.131863i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.31087 | 0.235528 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.9829i | 1.90564i | 0.303539 | + | 0.952819i | \(0.401832\pi\) | ||||
−0.303539 | + | 0.952819i | \(0.598168\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 7.01027i | − | 0.380746i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.03034i | 0.164102i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.49392i | 0.458629i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.92071i | 0.103408i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 20.4768i | − | 1.09925i | −0.835411 | − | 0.549625i | \(-0.814771\pi\) | ||
0.835411 | − | 0.549625i | \(-0.185229\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.50953 | 0.294918 | 0.147459 | − | 0.989068i | \(-0.452890\pi\) | ||||
0.147459 | + | 0.989068i | \(0.452890\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.624069i | 0.0333104i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.0448 | −1.38623 | −0.693113 | − | 0.720829i | \(-0.743761\pi\) | ||||
−0.693113 | + | 0.720829i | \(0.743761\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.0224 | 0.531935 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.75332i | 0.145721i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 17.0994i | − | 0.902471i | −0.892405 | − | 0.451235i | \(-0.850984\pi\) | ||
0.892405 | − | 0.451235i | \(-0.149016\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.42309 | − | 17.0309i | −0.443321 | − | 0.896363i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.72275 | 0.405339 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.31087 | 0.330326 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.0995i | 0.683787i | 0.939739 | + | 0.341893i | \(0.111068\pi\) | ||||
−0.939739 | + | 0.341893i | \(0.888932\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.89138i | 0.410809i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.19866 | −0.0622311 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 10.3462i | − | 0.535703i | −0.963460 | − | 0.267852i | \(-0.913686\pi\) | ||
0.963460 | − | 0.267852i | \(-0.0863137\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.09765 | 0.262542 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.8092 | 0.863430 | 0.431715 | − | 0.902010i | \(-0.357909\pi\) | ||||
0.431715 | + | 0.902010i | \(0.357909\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.31087 | −0.220853 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.8462 | −1.57617 | −0.788083 | − | 0.615569i | \(-0.788926\pi\) | ||||
−0.788083 | + | 0.615569i | \(0.788926\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.70034 | 0.137622 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 2.40627i | − | 0.122318i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.97758 | 0.404479 | 0.202240 | − | 0.979336i | \(-0.435178\pi\) | ||||
0.202240 | + | 0.979336i | \(0.435178\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.47394i | 0.428546i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.26776i | 0.114393i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.71155 | −0.186748 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.1987 | −0.562044 | −0.281022 | − | 0.959701i | \(-0.590673\pi\) | ||||
−0.281022 | + | 0.959701i | \(0.590673\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.31087 | + | 1.43515i | 0.115688 | + | 0.0718474i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 24.4082i | − | 1.21889i | −0.792829 | − | 0.609444i | \(-0.791393\pi\) | ||
0.792829 | − | 0.609444i | \(-0.208607\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.437058i | 0.0217714i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.4119 | 0.516098 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.5337i | 1.21311i | 0.795040 | + | 0.606557i | \(0.207450\pi\) | ||||
−0.795040 | + | 0.606557i | \(0.792550\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.68913 | −0.181971 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 6.25469i | − | 0.307773i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4.23697i | − | 0.207985i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 16.3368i | − | 0.800017i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 37.7917i | − | 1.84624i | −0.384507 | − | 0.923122i | \(-0.625628\pi\) | ||
0.384507 | − | 0.923122i | \(-0.374372\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 15.9628i | − | 0.777978i | −0.921242 | − | 0.388989i | \(-0.872824\pi\) | ||
0.921242 | − | 0.388989i | \(-0.127176\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.64369i | 0.0799190i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.41188 | −0.214008 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.06577i | 0.341936i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.70034 | 0.130373 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.82376 | −0.425026 | −0.212513 | − | 0.977158i | \(-0.568165\pi\) | ||||
−0.212513 | + | 0.977158i | \(0.568165\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.39737i | − | 0.163267i | −0.996662 | − | 0.0816335i | \(-0.973986\pi\) | ||
0.996662 | − | 0.0816335i | \(-0.0260137\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 8.16840i | − | 0.391645i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.11222 | + | 4.41699i | 0.340223 | + | 0.211293i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0000 | 0.763638 | 0.381819 | − | 0.924237i | \(-0.375298\pi\) | ||||
0.381819 | + | 0.924237i | \(0.375298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.61054 | 0.314787 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 27.9796i | − | 1.32935i | −0.747132 | − | 0.664675i | \(-0.768570\pi\) | ||
0.747132 | − | 0.664675i | \(-0.231430\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.61290i | 0.171268i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.82376 | 0.133559 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.5165i | 0.826653i | 0.910583 | + | 0.413326i | \(0.135633\pi\) | ||||
−0.910583 | + | 0.413326i | \(0.864367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.1458 | 1.60787 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.83497 | 0.462087 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.389463 | 0.0182583 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.535307 | −0.0250406 | −0.0125203 | − | 0.999922i | \(-0.503985\pi\) | ||||
−0.0125203 | + | 0.999922i | \(0.503985\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.41188 | 0.205929 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.6475 | 0.542479 | 0.271240 | − | 0.962512i | \(-0.412566\pi\) | ||||
0.271240 | + | 0.962512i | \(0.412566\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.8326i | 1.10760i | 0.832651 | + | 0.553798i | \(0.186822\pi\) | ||||
−0.832651 | + | 0.553798i | \(0.813178\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.700336 | 0.0324773 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 39.0328i | 1.80622i | 0.429405 | + | 0.903112i | \(0.358723\pi\) | ||||
−0.429405 | + | 0.903112i | \(0.641277\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.69028i | 0.124226i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.11222 | 0.419869 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.4119 | −0.478739 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.29966 | + | 3.70291i | −0.105516 | + | 0.169901i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.92071i | 0.0879433i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.9423i | 1.13964i | 0.821769 | + | 0.569820i | \(0.192987\pi\) | ||||
−0.821769 | + | 0.569820i | \(0.807013\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.50168 | 0.0684707 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.19866 | −0.0545408 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.94033i | 0.133514i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.3333 | −1.01202 | −0.506009 | − | 0.862528i | \(-0.668880\pi\) | ||||
−0.506009 | + | 0.862528i | \(0.668880\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.3676i | 0.649725i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 12.4269i | − | 0.560818i | −0.959881 | − | 0.280409i | \(-0.909530\pi\) | ||
0.959881 | − | 0.280409i | \(-0.0904701\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 36.0380i | − | 1.62307i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 4.32698i | − | 0.194483i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.25469i | 0.280561i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.3472i | 0.866098i | 0.901370 | + | 0.433049i | \(0.142562\pi\) | ||||
−0.901370 | + | 0.433049i | \(0.857438\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.4343 | −0.912937 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 0.395552i | − | 0.0176368i | −0.999961 | − | 0.00881839i | \(-0.997193\pi\) | ||
0.999961 | − | 0.00881839i | \(-0.00280702\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.599328 | 0.0266698 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.6105 | −0.560054 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.1889i | 0.983507i | 0.870734 | + | 0.491754i | \(0.163644\pi\) | ||||
−0.870734 | + | 0.491754i | \(0.836356\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.93842i | 0.174226i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.29966 | − | 3.70291i | 0.101533 | − | 0.163487i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.8238 | 0.565082 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.11222 | 0.312795 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.1997i | 0.886671i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 23.5141i | − | 1.03017i | −0.857139 | − | 0.515086i | \(-0.827760\pi\) | ||
0.857139 | − | 0.515086i | \(-0.172240\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.1604 | −0.969007 | −0.484504 | − | 0.874789i | \(-0.661000\pi\) | ||||
−0.484504 | + | 0.874789i | \(0.661000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 0.624069i | − | 0.0272366i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.08980 | 0.134594 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.3109 | 0.839603 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.0224 | −0.434936 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.92477 | 0.213315 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.71155 | −0.333399 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.19866 | 0.0517258 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 28.6037i | − | 1.23205i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.19866 | −0.395481 | −0.197741 | − | 0.980254i | \(-0.563360\pi\) | ||||
−0.197741 | + | 0.980254i | \(0.563360\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 8.65396i | − | 0.371377i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.2184i | 0.523377i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.55449 | 0.109222 | 0.0546111 | − | 0.998508i | \(-0.482608\pi\) | ||||
0.0546111 | + | 0.998508i | \(0.482608\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.3221 | 0.483215 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −30.2469 | − | 18.7846i | −1.28856 | − | 0.800250i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.31626i | − | 0.0984975i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 2.40627i | − | 0.102140i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −40.3557 | −1.70993 | −0.854963 | − | 0.518689i | \(-0.826420\pi\) | ||||
−0.854963 | + | 0.518689i | \(0.826420\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.50168 | −0.0635143 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 19.0901i | − | 0.805985i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −41.0112 | −1.72842 | −0.864208 | − | 0.503134i | \(-0.832180\pi\) | ||||
−0.864208 | + | 0.503134i | \(0.832180\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.01027i | 0.294924i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.624069i | 0.0262085i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.4147i | 1.23313i | 0.787304 | + | 0.616565i | \(0.211476\pi\) | ||||
−0.787304 | + | 0.616565i | \(0.788524\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.5635i | 0.567615i | 0.958881 | + | 0.283807i | \(0.0915977\pi\) | ||||
−0.958881 | + | 0.283807i | \(0.908402\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 16.5453i | − | 0.691191i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1.92071i | − | 0.0800991i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.91020 | −0.204414 | −0.102207 | − | 0.994763i | \(-0.532590\pi\) | ||||
−0.102207 | + | 0.994763i | \(0.532590\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 8.02989i | − | 0.333711i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.64416 | 0.109698 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.31087 | 0.344201 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 0.624069i | − | 0.0258021i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.2968i | 0.837737i | 0.908047 | + | 0.418868i | \(0.137573\pi\) | ||||
−0.908047 | + | 0.418868i | \(0.862427\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.61054 | − | 2.59328i | 0.0663610 | − | 0.106854i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.4343 | −0.593748 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.1571 | 1.11521 | 0.557603 | − | 0.830108i | \(-0.311721\pi\) | ||||
0.557603 | + | 0.830108i | \(0.311721\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 2.75332i | − | 0.112875i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 2.31626i | − | 0.0947983i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.7980 | −0.808924 | −0.404462 | − | 0.914555i | \(-0.632541\pi\) | ||||
−0.404462 | + | 0.914555i | \(0.632541\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.2315i | 1.27396i | 0.770881 | + | 0.636979i | \(0.219816\pi\) | ||||
−0.770881 | + | 0.636979i | \(0.780184\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.31087 | 0.175552 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.72275 | −0.313975 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.31087 | 0.174973 | 0.0874865 | − | 0.996166i | \(-0.472117\pi\) | ||||
0.0874865 | + | 0.996166i | \(0.472117\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.09765 | 0.206567 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.02578 | 0.0414985 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −43.1346 | −1.74219 | −0.871096 | − | 0.491113i | \(-0.836590\pi\) | ||||
−0.871096 | + | 0.491113i | \(0.836590\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 7.89138i | − | 0.318211i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.38946 | 0.257230 | 0.128615 | − | 0.991695i | \(-0.458947\pi\) | ||||
0.128615 | + | 0.991695i | \(0.458947\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.0878i | 1.00836i | 0.863598 | + | 0.504181i | \(0.168206\pi\) | ||||
−0.863598 | + | 0.504181i | \(0.831794\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.92071i | 0.0770754i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.25470 | −0.0903327 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.0224 | − | 9.95060i | −0.639874 | − | 0.397389i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 10.6162i | − | 0.423295i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.9524i | 0.515627i | 0.966195 | + | 0.257814i | \(0.0830021\pi\) | ||||
−0.966195 | + | 0.257814i | \(0.916998\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.08644 | −0.0829285 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.31087 | 0.171072 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4.12543i | − | 0.163456i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.0224 | 0.396481 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 22.2660i | − | 0.879453i | −0.898132 | − | 0.439726i | \(-0.855075\pi\) | ||
0.898132 | − | 0.439726i | \(-0.144925\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.8430i | 1.05858i | 0.848440 | + | 0.529292i | \(0.177542\pi\) | ||||
−0.848440 | + | 0.529292i | \(0.822458\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.40627i | 0.0947468i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.78357i | 0.384632i | 0.981333 | + | 0.192316i | \(0.0615998\pi\) | ||||
−0.981333 | + | 0.192316i | \(0.938400\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 43.3668i | 1.70230i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.437058i | 0.0171297i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −47.4309 | −1.85612 | −0.928058 | − | 0.372436i | \(-0.878523\pi\) | ||||
−0.928058 | + | 0.372436i | \(0.878523\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2.26776i | − | 0.0886087i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.31087 | 0.246211 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.4679 | 0.446727 | 0.223363 | − | 0.974735i | \(-0.428296\pi\) | ||||
0.223363 | + | 0.974735i | \(0.428296\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 3.38438i | − | 0.131637i | −0.997832 | − | 0.0658187i | \(-0.979034\pi\) | ||
0.997832 | − | 0.0658187i | \(-0.0209659\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 2.75332i | − | 0.106930i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.31087 | − | 1.43515i | −0.0896118 | − | 0.0556527i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.6891 | 0.607485 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.82376 | 0.186497 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 48.9904i | − | 1.89125i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 38.2702i | − | 1.47521i | −0.675233 | − | 0.737605i | \(-0.735957\pi\) | ||
0.675233 | − | 0.737605i | \(-0.264043\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 39.8239i | − | 1.53056i | −0.643699 | − | 0.765279i | \(-0.722601\pi\) | ||
0.643699 | − | 0.765279i | \(-0.277399\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.83497 | −0.0704197 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.81255 | 0.146097 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.73732 | 0.334324 | 0.167162 | − | 0.985929i | \(-0.446540\pi\) | ||||
0.167162 | + | 0.985929i | \(0.446540\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.68913 | 0.140954 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.6105 | −0.519274 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.19866 | 0.0456652 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.50282i | 0.285421i | 0.989764 | + | 0.142710i | \(0.0455818\pi\) | ||||
−0.989764 | + | 0.142710i | \(0.954418\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.70034 | 0.102577 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.3368i | 0.619690i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 34.8158i | − | 1.31874i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.42309 | −0.356414 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.0673 | −1.81548 | −0.907738 | − | 0.419538i | \(-0.862192\pi\) | ||||
−0.907738 | + | 0.419538i | \(0.862192\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.91020 | − | 5.53361i | −0.336055 | − | 0.208704i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 1.64369i | − | 0.0619050i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.374022i | 0.0140666i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.3703 | 1.74147 | 0.870736 | − | 0.491750i | \(-0.163643\pi\) | ||||
0.870736 | + | 0.491750i | \(0.163643\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.71155 | −0.139194 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.34514i | 0.0503760i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.70034 | −0.100987 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 6.38620i | − | 0.238497i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 31.2800i | − | 1.16655i | −0.812276 | − | 0.583273i | \(-0.801772\pi\) | ||
0.812276 | − | 0.583273i | \(-0.198228\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.00292i | 0.298044i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 1.34514i | − | 0.0500264i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.16840i | 0.303367i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 18.7231i | − | 0.694401i | −0.937791 | − | 0.347201i | \(-0.887132\pi\) | ||
0.937791 | − | 0.347201i | \(-0.112868\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.6162i | 0.392653i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.86201 | −0.216518 | −0.108259 | − | 0.994123i | \(-0.534528\pi\) | ||||
−0.108259 | + | 0.994123i | \(0.534528\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.61054 | −0.243833 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 18.6531i | − | 0.687094i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.71554i | 0.173464i | 0.996232 | + | 0.0867319i | \(0.0276424\pi\) | ||||
−0.996232 | + | 0.0867319i | \(0.972358\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.31087 | − | 1.43515i | −0.0848920 | − | 0.0527216i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.8720 | 1.16927 | 0.584634 | − | 0.811297i | \(-0.301238\pi\) | ||||
0.584634 | + | 0.811297i | \(0.301238\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.82376 | −0.103455 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 4.23697i | − | 0.155023i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 4.81254i | − | 0.175846i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.9022 | 1.74798 | 0.873989 | − | 0.485947i | \(-0.161525\pi\) | ||||
0.873989 | + | 0.485947i | \(0.161525\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1.01962i | − | 0.0371571i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.83497 | −0.357931 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.7980 | −0.646879 | −0.323439 | − | 0.946249i | \(-0.604839\pi\) | ||||
−0.323439 | + | 0.946249i | \(0.604839\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.31087 | 0.301666 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.0482 | 0.617997 | 0.308998 | − | 0.951063i | \(-0.400006\pi\) | ||||
0.308998 | + | 0.951063i | \(0.400006\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.62511 | −0.276047 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.41188 | −0.159512 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.25469i | 0.225844i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.02578 | −0.325478 | −0.162739 | − | 0.986669i | \(-0.552033\pi\) | ||||
−0.162739 | + | 0.986669i | \(0.552033\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 25.3863i | − | 0.914266i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 21.9189i | − | 0.788369i | −0.919031 | − | 0.394184i | \(-0.871027\pi\) | ||
0.919031 | − | 0.394184i | \(-0.128973\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.700336 | −0.0251568 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.50168 | 0.0538725 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29.2211 | − | 18.1475i | −1.04695 | − | 0.650203i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 43.3668i | − | 1.55179i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 8.16840i | − | 0.291915i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.11222 | −0.325229 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.4039 | −1.54718 | −0.773591 | − | 0.633685i | \(-0.781541\pi\) | ||||
−0.773591 | + | 0.633685i | \(0.781541\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.73325i | 0.239710i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.37489 | −0.155553 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 7.06577i | − | 0.250913i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 1.92071i | − | 0.0681206i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 44.0394i | − | 1.55995i | −0.625808 | − | 0.779977i | \(-0.715231\pi\) | ||
0.625808 | − | 0.779977i | \(-0.284769\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 7.25177i | − | 0.256549i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.61290i | 0.127656i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 27.3070i | − | 0.963644i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.19866 | 0.0422471 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 12.2669i | − | 0.431814i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.8428 | 0.767953 | 0.383976 | − | 0.923343i | \(-0.374554\pi\) | ||||
0.383976 | + | 0.923343i | \(0.374554\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.84618 | −0.0999429 | −0.0499714 | − | 0.998751i | \(-0.515913\pi\) | ||||
−0.0499714 | + | 0.998751i | \(0.515913\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 23.1886i | − | 0.813259i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 14.3676i | − | 0.503275i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.91020 | + | 5.53361i | 0.311728 | + | 0.193597i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.389463 | 0.0136089 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.6666 | −1.07027 | −0.535136 | − | 0.844766i | \(-0.679739\pi\) | ||||
−0.535136 | + | 0.844766i | \(0.679739\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 15.3587i | − | 0.535370i | −0.963506 | − | 0.267685i | \(-0.913741\pi\) | ||
0.963506 | − | 0.267685i | \(-0.0862587\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.32698i | 0.150646i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.389463 | −0.0135429 | −0.00677147 | − | 0.999977i | \(-0.502155\pi\) | ||||
−0.00677147 | + | 0.999977i | \(0.502155\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 24.0196i | − | 0.834237i | −0.908852 | − | 0.417118i | \(-0.863040\pi\) | ||
0.908852 | − | 0.417118i | \(-0.136960\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.40067 | 0.117968 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29.1649 | −1.01050 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.4343 | 0.707158 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.700336 | 0.0242071 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.44551 | 0.0499045 | 0.0249522 | − | 0.999689i | \(-0.492057\pi\) | ||||
0.0249522 | + | 0.999689i | \(0.492057\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −37.7228 | −1.30078 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 12.4469i | − | 0.428693i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.6105 | 0.433816 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4.81953i | − | 0.165601i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 25.3378i | − | 0.869591i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.62175 | 0.158431 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.9966 | −0.650433 | −0.325216 | − | 0.945640i | \(-0.605437\pi\) | ||||
−0.325216 | + | 0.945640i | \(0.605437\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.29966 | + | 3.70291i | −0.0786469 | + | 0.126637i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.5365i | 1.24806i | 0.781399 | + | 0.624032i | \(0.214507\pi\) | ||||
−0.781399 | + | 0.624032i | \(0.785493\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.9610i | 1.22697i | 0.789705 | + | 0.613486i | \(0.210233\pi\) | ||||
−0.789705 | + | 0.613486i | \(0.789767\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.92477 | 0.167836 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.5577 | 0.495551 | 0.247775 | − | 0.968818i | \(-0.420301\pi\) | ||||
0.247775 | + | 0.968818i | \(0.420301\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 20.1997i | − | 0.686812i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.46469 | −0.0837054 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.0598i | 0.544791i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2.69028i | − | 0.0911568i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.94033i | 0.0995151i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.624069i | 0.0210974i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 52.2078i | − | 1.76293i | −0.472248 | − | 0.881466i | \(-0.656557\pi\) | ||
0.472248 | − | 0.881466i | \(-0.343443\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.28729i | 0.245794i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.46793 | 0.184219 | 0.0921096 | − | 0.995749i | \(-0.470639\pi\) | ||||
0.0921096 | + | 0.995749i | \(0.470639\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.07658i | 0.170840i | 0.996345 | + | 0.0854202i | \(0.0272233\pi\) | ||||
−0.996345 | + | 0.0854202i | \(0.972777\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.0224 | 0.336900 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.42309 | −0.114936 | −0.0574681 | − | 0.998347i | \(-0.518303\pi\) | ||||
−0.0574681 | + | 0.998347i | \(0.518303\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.69028i | 0.0902292i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 4.32698i | − | 0.144959i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.08644 | − | 3.77994i | −0.203675 | − | 0.126491i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.19866 | −0.0400667 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.19866 | 0.0400220 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 5.72062i | − | 0.190793i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 8.47394i | − | 0.282308i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.50168 | −0.0499728 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.65396i | 0.287667i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.7788 | 1.71929 | 0.859643 | − | 0.510895i | \(-0.170686\pi\) | ||||
0.859643 | + | 0.510895i | \(0.170686\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.599328 | 0.0198785 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.0224 | 0.729635 | 0.364818 | − | 0.931079i | \(-0.381131\pi\) | ||||
0.364818 | + | 0.931079i | \(0.381131\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.3333 | −0.606743 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.3221 | −0.374296 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.41524 | 0.0467353 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 16.1568i | − | 0.532963i | −0.963840 | − | 0.266482i | \(-0.914139\pi\) | ||
0.963840 | − | 0.266482i | \(-0.0858611\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.0224 | −0.462054 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 6.25469i | − | 0.205875i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.40627i | 0.0791177i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.8238 | 0.421188 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.8462 | −0.421469 | −0.210735 | − | 0.977543i | \(-0.567586\pi\) | ||||
−0.210735 | + | 0.977543i | \(0.567586\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.2020 | + | 24.4782i | −0.498226 | + | 0.802241i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 17.2594i | − | 0.565048i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.0901i | 0.624314i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.8428 | 0.582900 | 0.291450 | − | 0.956586i | \(-0.405862\pi\) | ||||
0.291450 | + | 0.956586i | \(0.405862\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.1346 | −0.493900 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 57.9499i | − | 1.88911i | −0.328348 | − | 0.944557i | \(-0.606492\pi\) | ||
0.328348 | − | 0.944557i | \(-0.393508\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.1571 | 0.493582 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 0.624069i | − | 0.0203010i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.7035i | 0.575286i | 0.957738 | + | 0.287643i | \(0.0928716\pi\) | ||||
−0.957738 | + | 0.287643i | \(0.907128\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 3.93842i | − | 0.127847i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.1102i | 0.489981i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 30.0188i | − | 0.972405i | −0.873846 | − | 0.486203i | \(-0.838382\pi\) | ||
0.873846 | − | 0.486203i | \(-0.161618\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.5453i | 0.535395i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −35.3445 | −1.14253 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.30227i | 0.0743442i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5095 | −0.984178 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.71155 | −0.248501 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.02989i | 0.258491i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 30.2474i | − | 0.972689i | −0.873767 | − | 0.486345i | \(-0.838330\pi\) | ||
0.873767 | − | 0.486345i | \(-0.161670\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.1458 | + | 16.3368i | −0.325931 | + | 0.524814i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.22443 | −0.0713855 | −0.0356927 | − | 0.999363i | \(-0.511364\pi\) | ||||
−0.0356927 | + | 0.999363i | \(0.511364\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.1953 | −0.326846 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.624069i | 0.0199862i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.12216i | 0.195865i | 0.995193 | + | 0.0979327i | \(0.0312230\pi\) | ||||
−0.995193 | + | 0.0979327i | \(0.968777\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.6330 | 0.499631 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.2184i | 0.390102i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.26142 | −0.263498 | −0.131749 | − | 0.991283i | \(-0.542059\pi\) | ||||
−0.131749 | + | 0.991283i | \(0.542059\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.4343 | 0.459915 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.02578 | 0.0326508 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.62175 | −0.146963 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.55449 | −0.271742 | −0.135871 | − | 0.990727i | \(-0.543383\pi\) | ||||
−0.135871 | + | 0.990727i | \(0.543383\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.8092 | −0.533424 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.31626i | 0.0734304i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.66335 | −0.147690 | −0.0738449 | − | 0.997270i | \(-0.523527\pi\) | ||||
−0.0738449 | + | 0.997270i | \(0.523527\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 2.40627i | − | 0.0761310i |
(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 | 4560.2.d.f.2431.4 | yes | 6 | |
4.3 | odd | 2 | 4560.2.d.h.2431.3 | yes | 6 | ||
19.18 | odd | 2 | 4560.2.d.h.2431.4 | yes | 6 | ||
76.75 | even | 2 | inner | 4560.2.d.f.2431.3 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4560.2.d.f.2431.3 | ✓ | 6 | 76.75 | even | 2 | inner | |
4560.2.d.f.2431.4 | yes | 6 | 1.1 | even | 1 | trivial | |
4560.2.d.h.2431.3 | yes | 6 | 4.3 | odd | 2 | ||
4560.2.d.h.2431.4 | yes | 6 | 19.18 | odd | 2 |