Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,3,Mod(1023,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.1023");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.d (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: | \(48.8284633734\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.157351936.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1023.6 | ||
Root | \(-1.28897 - 0.581861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.1023 |
Dual form | 1792.3.d.g.1023.4 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.585786i | 0.195262i | 0.995223 | + | 0.0976311i | \(0.0311265\pi\) | ||||
−0.995223 | + | 0.0976311i | \(0.968873\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9.03316 | 1.80663 | 0.903316 | − | 0.428976i | \(-0.141125\pi\) | ||||
0.903316 | + | 0.428976i | \(0.141125\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.64575i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.65685 | 0.961873 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 12.4853i | − 1.13503i | −0.823365 | − | 0.567513i | \(-0.807906\pi\) | ||||
0.823365 | − | 0.567513i | \(-0.192094\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.03316 | 0.694858 | 0.347429 | − | 0.937706i | \(-0.387055\pi\) | ||||
0.347429 | + | 0.937706i | \(0.387055\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.29150i | 0.352767i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 12.3431 | 0.726067 | 0.363034 | − | 0.931776i | \(-0.381741\pi\) | ||||
0.363034 | + | 0.931776i | \(0.381741\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 28.8701i | 1.51948i | 0.650229 | + | 0.759738i | \(0.274673\pi\) | ||||
−0.650229 | + | 0.759738i | \(0.725327\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.54985 | 0.0738022 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 24.6418i | 1.07138i | 0.844414 | + | 0.535690i | \(0.179949\pi\) | ||||
−0.844414 | + | 0.535690i | \(0.820051\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 56.5980 | 2.26392 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.3431i | 0.383079i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −22.4499 | −0.774136 | −0.387068 | − | 0.922051i | \(-0.626512\pi\) | ||||
−0.387068 | + | 0.922051i | \(0.626512\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 16.7824i | − 0.541367i | −0.962668 | − | 0.270684i | \(-0.912750\pi\) | ||||
0.962668 | − | 0.270684i | \(-0.0872497\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.31371 | 0.221628 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 23.8995i | − 0.682843i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 16.2506 | 0.439204 | 0.219602 | − | 0.975589i | \(-0.429524\pi\) | ||||
0.219602 | + | 0.975589i | \(0.429524\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.29150i | 0.135680i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.97056 | −0.170014 | −0.0850069 | − | 0.996380i | \(-0.527091\pi\) | ||||
−0.0850069 | + | 0.996380i | \(0.527091\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 22.8284i | 0.530894i | 0.964126 | + | 0.265447i | \(0.0855195\pi\) | ||||
−0.964126 | + | 0.265447i | \(0.914481\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 78.1987 | 1.73775 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 6.19938i | − 0.131902i | −0.997823 | − | 0.0659509i | \(-0.978992\pi\) | ||||
0.997823 | − | 0.0659509i | \(-0.0210081\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.23045i | 0.141773i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.01514 | 0.151229 | 0.0756145 | − | 0.997137i | \(-0.475908\pi\) | ||||
0.0756145 | + | 0.997137i | \(0.475908\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 112.782i | − 2.05057i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.9117 | −0.296696 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 30.4437i | − 0.515994i | −0.966146 | − | 0.257997i | \(-0.916938\pi\) | ||||
0.966146 | − | 0.257997i | \(-0.0830625\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.2325 | 0.249714 | 0.124857 | − | 0.992175i | \(-0.460153\pi\) | ||||
0.124857 | + | 0.992175i | \(0.460153\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 22.9039i | − 0.363554i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 81.5980 | 1.25535 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 78.6274i | − 1.17354i | −0.809752 | − | 0.586772i | \(-0.800399\pi\) | ||||
0.809752 | − | 0.586772i | \(-0.199601\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14.4348 | −0.209200 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 17.5345i | 0.246965i | 0.992347 | + | 0.123482i | \(0.0394062\pi\) | ||||
−0.992347 | + | 0.123482i | \(0.960594\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −46.6863 | −0.639538 | −0.319769 | − | 0.947495i | \(-0.603605\pi\) | ||||
−0.319769 | + | 0.947495i | \(0.603605\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 33.1543i | 0.442058i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −33.0329 | −0.428999 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 81.0325i | − 1.02573i | −0.858470 | − | 0.512864i | \(-0.828584\pi\) | ||||
0.858470 | − | 0.512864i | \(-0.171416\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 71.8528 | 0.887072 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 40.3848i | 0.486564i | 0.969956 | + | 0.243282i | \(0.0782240\pi\) | ||||
−0.969956 | + | 0.243282i | \(0.921776\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 111.498 | 1.31174 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 13.1509i | − 0.151159i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −111.941 | −1.25777 | −0.628883 | − | 0.777500i | \(-0.716487\pi\) | ||||
−0.628883 | + | 0.777500i | \(0.716487\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 23.8995i | − 0.262632i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.83089 | 0.105709 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 260.788i | 2.74514i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −164.108 | −1.69183 | −0.845916 | − | 0.533317i | \(-0.820945\pi\) | ||||
−0.845916 | + | 0.533317i | \(0.820945\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 108.083i | − 1.09175i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.1329 | 0.120127 | 0.0600636 | − | 0.998195i | \(-0.480870\pi\) | ||||
0.0600636 | + | 0.998195i | \(0.480870\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 106.582i | 1.03478i | 0.855750 | + | 0.517389i | \(0.173096\pi\) | ||||
−0.855750 | + | 0.517389i | \(0.826904\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14.0000 | 0.133333 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 63.5980i | 0.594374i | 0.954819 | + | 0.297187i | \(0.0960484\pi\) | ||||
−0.954819 | + | 0.297187i | \(0.903952\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 130.848 | 1.20044 | 0.600220 | − | 0.799835i | \(-0.295080\pi\) | ||||
0.600220 | + | 0.799835i | \(0.295080\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.51936i | 0.0857600i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −138.225 | −1.22323 | −0.611617 | − | 0.791154i | \(-0.709481\pi\) | ||||
−0.611617 | + | 0.791154i | \(0.709481\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 222.593i | 1.93559i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 78.1987 | 0.668365 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 32.6569i | − 0.274428i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −34.8823 | −0.288283 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 4.08326i | − 0.0331972i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 285.430 | 2.28344 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 114.442i | − 0.901114i | −0.892748 | − | 0.450557i | \(-0.851225\pi\) | ||||
0.892748 | − | 0.450557i | \(-0.148775\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.3726 | −0.103663 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 168.350i | − 1.28512i | −0.766237 | − | 0.642558i | \(-0.777873\pi\) | ||||
0.766237 | − | 0.642558i | \(-0.222127\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 76.3830 | 0.574308 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 93.4313i | 0.692084i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −34.6863 | −0.253185 | −0.126592 | − | 0.991955i | \(-0.540404\pi\) | ||||
−0.126592 | + | 0.991955i | \(0.540404\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 107.664i | − 0.774561i | −0.921962 | − | 0.387281i | \(-0.873414\pi\) | ||||
0.921962 | − | 0.387281i | \(-0.126586\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.63151 | 0.0257554 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 112.782i | − 0.788682i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −202.794 | −1.39858 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 4.10051i | − 0.0278946i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 252.176 | 1.69246 | 0.846229 | − | 0.532819i | \(-0.178867\pi\) | ||||
0.846229 | + | 0.532819i | \(0.178867\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 234.486i | 1.55289i | 0.630186 | + | 0.776444i | \(0.282979\pi\) | ||||
−0.630186 | + | 0.776444i | \(0.717021\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 106.853 | 0.698384 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 151.598i | − 0.978051i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0968 | 0.0643109 | 0.0321554 | − | 0.999483i | \(-0.489763\pi\) | ||||
0.0321554 | + | 0.999483i | \(0.489763\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.69516i | 0.0295293i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 65.1960 | 0.404944 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 104.534i | 0.641313i | 0.947196 | + | 0.320657i | \(0.103904\pi\) | ||||
−0.947196 | + | 0.320657i | \(0.896096\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 66.0659 | 0.400399 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 296.765i | − 1.77703i | −0.458843 | − | 0.888517i | \(-0.651736\pi\) | ||||
0.458843 | − | 0.888517i | \(-0.348264\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −87.4020 | −0.517172 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 249.924i | 1.46154i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 40.0301 | 0.231388 | 0.115694 | − | 0.993285i | \(-0.463091\pi\) | ||||
0.115694 | + | 0.993285i | \(0.463091\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 149.744i | − 0.855681i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.8335 | 0.100754 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 294.794i | 1.64689i | 0.567394 | + | 0.823447i | \(0.307952\pi\) | ||||
−0.567394 | + | 0.823447i | \(0.692048\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −40.4706 | −0.223595 | −0.111797 | − | 0.993731i | \(-0.535661\pi\) | ||||
−0.111797 | + | 0.993731i | \(0.535661\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.92302i | 0.0487596i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 146.794 | 0.793481 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 154.108i | − 0.824105i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 27.3654 | 0.144790 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 156.929i | 0.821619i | 0.911721 | + | 0.410810i | \(0.134754\pi\) | ||||
−0.911721 | + | 0.410810i | \(0.865246\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −261.304 | −1.35390 | −0.676952 | − | 0.736027i | \(-0.736700\pi\) | ||||
−0.676952 | + | 0.736027i | \(0.736700\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 47.7990i | 0.245123i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 145.283 | 0.737475 | 0.368738 | − | 0.929533i | \(-0.379790\pi\) | ||||
0.368738 | + | 0.929533i | \(0.379790\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 390.508i | − 1.96235i | −0.193122 | − | 0.981175i | \(-0.561861\pi\) | ||||
0.193122 | − | 0.981175i | \(-0.438139\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 46.0589 | 0.229149 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 59.3970i | 0.292596i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −62.9662 | −0.307152 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 213.320i | 1.03053i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 360.451 | 1.72464 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 164.049i | − 0.777482i | −0.921347 | − | 0.388741i | \(-0.872910\pi\) | ||||
0.921347 | − | 0.388741i | \(-0.127090\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.2715 | −0.0482229 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 206.213i | 0.959129i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −44.4020 | −0.204618 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 27.3482i | − 0.124878i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 111.498 | 0.504514 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.5830i | 0.0474574i | 0.999718 | + | 0.0237287i | \(0.00755379\pi\) | ||||
−0.999718 | + | 0.0237287i | \(0.992446\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 489.960 | 2.17760 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 213.806i | − 0.941877i | −0.882166 | − | 0.470939i | \(-0.843915\pi\) | ||||
0.882166 | − | 0.470939i | \(-0.156085\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 232.028 | 1.01322 | 0.506612 | − | 0.862174i | \(-0.330898\pi\) | ||||
0.506612 | + | 0.862174i | \(0.330898\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 19.3503i | − 0.0837673i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 192.863 | 0.827738 | 0.413869 | − | 0.910336i | \(-0.364177\pi\) | ||||
0.413869 | + | 0.910336i | \(0.364177\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 56.0000i | − 0.238298i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 47.4678 | 0.200286 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 327.917i | − 1.37204i | −0.727583 | − | 0.686020i | \(-0.759356\pi\) | ||||
0.727583 | − | 0.686020i | \(-0.240644\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 71.8721 | 0.298225 | 0.149112 | − | 0.988820i | \(-0.452358\pi\) | ||||
0.149112 | + | 0.988820i | \(0.452358\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 135.179i | 0.556291i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −63.2321 | −0.258090 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 260.788i | 1.05582i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −23.6569 | −0.0950074 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 256.919i | 1.02358i | 0.859110 | + | 0.511790i | \(0.171018\pi\) | ||||
−0.859110 | + | 0.511790i | \(0.828982\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 307.659 | 1.21604 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 65.3138i | 0.256133i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 319.352 | 1.24262 | 0.621308 | − | 0.783566i | \(-0.286602\pi\) | ||||
0.621308 | + | 0.783566i | \(0.286602\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 42.9949i | − 0.166004i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −194.346 | −0.744620 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 377.357i | 1.43482i | 0.696653 | + | 0.717408i | \(0.254672\pi\) | ||||
−0.696653 | + | 0.717408i | \(0.745328\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 72.4020 | 0.273215 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 65.5736i | − 0.245594i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −28.1631 | −0.104696 | −0.0523478 | − | 0.998629i | \(-0.516670\pi\) | ||||
−0.0523478 | + | 0.998629i | \(0.516670\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 399.715i | 1.47496i | 0.675367 | + | 0.737482i | \(0.263985\pi\) | ||||
−0.675367 | + | 0.737482i | \(0.736015\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.0000 | 0.0512821 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 706.642i | − 2.56961i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −102.951 | −0.371663 | −0.185831 | − | 0.982582i | \(-0.559498\pi\) | ||||
−0.185831 | + | 0.982582i | \(0.559498\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 145.283i | − 0.520726i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 150.235 | 0.534646 | 0.267323 | − | 0.963607i | \(-0.413861\pi\) | ||||
0.267323 | + | 0.963607i | \(0.413861\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 178.561i | 0.630959i | 0.948932 | + | 0.315480i | \(0.102165\pi\) | ||||
−0.948932 | + | 0.315480i | \(0.897835\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −152.766 | −0.536021 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.4424i | 0.0642591i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −136.647 | −0.472826 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 96.1320i | − 0.330351i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −219.189 | −0.748085 | −0.374043 | − | 0.927411i | \(-0.622029\pi\) | ||||
−0.374043 | + | 0.927411i | \(0.622029\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 275.002i | − 0.932211i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 129.137 | 0.434805 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 222.593i | 0.744458i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 60.3983 | 0.200659 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.10726i | 0.0234563i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 137.598 | 0.451141 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 316.669i | 1.03150i | 0.856741 | + | 0.515748i | \(0.172486\pi\) | ||||
−0.856741 | + | 0.515748i | \(0.827514\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −62.4344 | −0.202053 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 72.2653i | − 0.232364i | −0.993228 | − | 0.116182i | \(-0.962934\pi\) | ||||
0.993228 | − | 0.116182i | \(-0.0370656\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −81.9512 | −0.261825 | −0.130913 | − | 0.991394i | \(-0.541791\pi\) | ||||
−0.130913 | + | 0.991394i | \(0.541791\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 206.894i | − 0.656808i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 109.150 | 0.344322 | 0.172161 | − | 0.985069i | \(-0.444925\pi\) | ||||
0.172161 | + | 0.985069i | \(0.444925\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 280.294i | 0.878664i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −37.2548 | −0.116059 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 356.347i | 1.10324i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 511.259 | 1.57310 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 76.6489i | 0.234400i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.4020 | −0.0498542 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 321.740i | − 0.972025i | −0.873952 | − | 0.486012i | \(-0.838451\pi\) | ||||
0.873952 | − | 0.486012i | \(-0.161549\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 140.679 | 0.422459 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 710.254i | − 2.12016i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −164.049 | −0.486792 | −0.243396 | − | 0.969927i | \(-0.578261\pi\) | ||||
−0.243396 | + | 0.969927i | \(0.578261\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 80.9706i | − 0.238851i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −209.533 | −0.614466 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −130.392 | −0.377948 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 330.309i | 0.951898i | 0.879473 | + | 0.475949i | \(0.157895\pi\) | ||||
−0.879473 | + | 0.475949i | \(0.842105\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −262.402 | −0.751869 | −0.375934 | − | 0.926646i | \(-0.622678\pi\) | ||||
−0.375934 | + | 0.926646i | \(0.622678\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 93.4313i | 0.266186i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −578.098 | −1.63767 | −0.818835 | − | 0.574029i | \(-0.805380\pi\) | ||||
−0.818835 | + | 0.574029i | \(0.805380\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 158.392i | 0.446174i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.1300 | 0.0535853 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 365.114i | − 1.01703i | −0.861053 | − | 0.508515i | \(-0.830195\pi\) | ||||
0.861053 | − | 0.508515i | \(-0.169805\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −472.480 | −1.30881 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 20.4335i | − 0.0562908i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −421.725 | −1.15541 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 520.071i | − 1.41709i | −0.705666 | − | 0.708544i | \(-0.749352\pi\) | ||||
0.705666 | − | 0.708544i | \(-0.250648\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −60.3431 | −0.163532 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 21.2061i | − 0.0571592i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 526.711 | 1.41210 | 0.706048 | − | 0.708164i | \(-0.250476\pi\) | ||||
0.706048 | + | 0.708164i | \(0.250476\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 167.201i | 0.445869i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −202.794 | −0.537915 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 121.976i | − 0.321835i | −0.986968 | − | 0.160918i | \(-0.948555\pi\) | ||||
0.986968 | − | 0.160918i | \(-0.0514454\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 67.0383 | 0.175954 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 316.427i | 0.826179i | 0.910690 | + | 0.413089i | \(0.135550\pi\) | ||||
−0.910690 | + | 0.413089i | \(0.864450\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −298.392 | −0.775044 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 197.622i | 0.510652i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −92.1474 | −0.236883 | −0.118441 | − | 0.992961i | \(-0.537790\pi\) | ||||
−0.118441 | + | 0.992961i | \(0.537790\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 304.157i | 0.777895i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 98.6173 | 0.250935 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 731.980i | − 1.85311i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 562.267 | 1.41629 | 0.708144 | − | 0.706068i | \(-0.249533\pi\) | ||||
0.708144 | + | 0.706068i | \(0.249533\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 44.7441i | 0.112141i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 81.2061 | 0.202509 | 0.101254 | − | 0.994861i | \(-0.467714\pi\) | ||||
0.101254 | + | 0.994861i | \(0.467714\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 151.598i | − 0.376174i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 649.058 | 1.60261 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 202.893i | − 0.498508i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −450.735 | −1.10204 | −0.551021 | − | 0.834491i | \(-0.685762\pi\) | ||||
−0.551021 | + | 0.834491i | \(0.685762\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 20.3188i | − 0.0494374i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −80.5463 | −0.195027 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 364.802i | 0.879041i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 63.0681 | 0.151242 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 624.988i | 1.49162i | 0.666160 | + | 0.745809i | \(0.267937\pi\) | ||||
−0.666160 | + | 0.745809i | \(0.732063\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −566.476 | −1.34555 | −0.672774 | − | 0.739848i | \(-0.734897\pi\) | ||||
−0.672774 | + | 0.739848i | \(0.734897\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 53.6671i | − 0.126873i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 698.597 | 1.64376 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 40.3015i | − 0.0943829i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 66.0659 | 0.154000 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 289.528i | − 0.671760i | −0.941905 | − | 0.335880i | \(-0.890966\pi\) | ||||
0.941905 | − | 0.335880i | \(-0.109034\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −597.696 | −1.38036 | −0.690180 | − | 0.723638i | \(-0.742468\pi\) | ||||
−0.690180 | + | 0.723638i | \(0.742468\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 118.794i | − 0.273090i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −711.409 | −1.62794 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 38.3890i | − 0.0874464i | −0.999044 | − | 0.0437232i | \(-0.986078\pi\) | ||||
0.999044 | − | 0.0437232i | \(-0.0139220\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −60.5980 | −0.137410 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 599.058i | − 1.35228i | −0.736775 | − | 0.676138i | \(-0.763652\pi\) | ||||
0.736775 | − | 0.676138i | \(-0.236348\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1011.18 | −2.27232 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 147.721i | 0.330473i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −460.039 | −1.02459 | −0.512293 | − | 0.858811i | \(-0.671204\pi\) | ||||
−0.512293 | + | 0.858811i | \(0.671204\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 87.0294i | 0.192970i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −137.359 | −0.303220 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 215.888i | − 0.474479i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −266.323 | −0.582764 | −0.291382 | − | 0.956607i | \(-0.594115\pi\) | ||||
−0.291382 | + | 0.956607i | \(0.594115\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 127.667i | 0.278142i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −763.123 | −1.65537 | −0.827683 | − | 0.561196i | \(-0.810341\pi\) | ||||
−0.827683 | + | 0.561196i | \(0.810341\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 123.988i | − 0.267792i | −0.990995 | − | 0.133896i | \(-0.957251\pi\) | ||||
0.990995 | − | 0.133896i | \(-0.0427488\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 88.8040 | 0.190976 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 768.718i | − 1.64608i | −0.567986 | − | 0.823038i | \(-0.692277\pi\) | ||||
0.567986 | − | 0.823038i | \(-0.307723\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −208.029 | −0.443558 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.91457i | 0.0125575i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 285.019 | 0.602578 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1633.99i | 3.43997i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 69.3859 | 0.145463 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 118.981i | 0.248394i | 0.992258 | + | 0.124197i | \(0.0396355\pi\) | ||||
−0.992258 | + | 0.124197i | \(0.960364\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 146.794 | 0.305185 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 38.1909i | 0.0790702i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1482.41 | −3.05652 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 282.577i | − 0.580240i | −0.956990 | − | 0.290120i | \(-0.906305\pi\) | ||||
0.956990 | − | 0.290120i | \(-0.0936952\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −61.2346 | −0.125224 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 388.049i | 0.790323i | 0.918612 | + | 0.395162i | \(0.129311\pi\) | ||||
−0.918612 | + | 0.395162i | \(0.870689\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −277.103 | −0.562075 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 976.333i | − 1.97239i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 46.3919 | 0.0933439 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 27.7157i | − 0.0555425i | −0.999614 | − | 0.0277713i | \(-0.991159\pi\) | ||||
0.999614 | − | 0.0277713i | \(-0.00884101\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 173.841 | 0.346988 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 727.477i | 1.44628i | 0.690703 | + | 0.723138i | \(0.257301\pi\) | ||||
−0.690703 | + | 0.723138i | \(0.742699\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 109.598 | 0.217026 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 51.1989i | − 0.100984i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −634.183 | −1.24594 | −0.622969 | − | 0.782246i | \(-0.714074\pi\) | ||||
−0.622969 | + | 0.782246i | \(0.714074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 123.520i | 0.241723i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −298.607 | −0.582080 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 962.774i | 1.86946i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −77.4010 | −0.149712 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.4491i | 0.0451813i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −833.127 | −1.59909 | −0.799546 | − | 0.600605i | \(-0.794927\pi\) | ||||
−0.799546 | + | 0.600605i | \(0.794927\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 876.434i | − 1.67578i | −0.545838 | − | 0.837891i | \(-0.683789\pi\) | ||||
0.545838 | − | 0.837891i | \(-0.316211\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 87.7181 | 0.167082 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 207.147i | − 0.393069i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −78.2162 | −0.147857 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 263.546i | − 0.496321i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −62.9662 | −0.118135 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 574.491i | 1.07381i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −172.686 | −0.321576 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 87.3970i | 0.162147i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 405.915 | 0.750305 | 0.375152 | − | 0.926963i | \(-0.377590\pi\) | ||||
0.375152 | + | 0.926963i | \(0.377590\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 23.7072i | − 0.0436596i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1181.97 | 2.16875 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 606.024i | − 1.10791i | −0.832548 | − | 0.553953i | \(-0.813119\pi\) | ||||
0.832548 | − | 0.553953i | \(-0.186881\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 131.866 | 0.240193 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 648.131i | − 1.17628i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −214.392 | −0.387689 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 85.9899i | 0.154937i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.4442 | −0.0654294 | −0.0327147 | − | 0.999465i | \(-0.510415\pi\) | ||||
−0.0327147 | + | 0.999465i | \(0.510415\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 206.213i | 0.368896i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 90.2742 | 0.160917 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 186.389i | − 0.331064i | −0.986204 | − | 0.165532i | \(-0.947066\pi\) | ||||
0.986204 | − | 0.165532i | \(-0.0529341\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1248.61 | −2.20993 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 190.105i | − 0.335282i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 670.891 | 1.17907 | 0.589536 | − | 0.807742i | \(-0.299311\pi\) | ||||
0.589536 | + | 0.807742i | \(0.299311\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 677.082i | 1.18578i | 0.805282 | + | 0.592892i | \(0.202014\pi\) | ||||
−0.805282 | + | 0.592892i | \(0.797986\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −91.9271 | −0.160431 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1394.67i | 2.42552i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 927.901 | 1.60815 | 0.804073 | − | 0.594530i | \(-0.202662\pi\) | ||||
0.804073 | + | 0.594530i | \(0.202662\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 153.068i | − 0.264366i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 106.848 | 0.183904 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 100.071i | − 0.171649i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 706.382 | 1.20749 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 321.120i | 0.547053i | 0.961865 | + | 0.273526i | \(0.0881900\pi\) | ||||
−0.961865 | + | 0.273526i | \(0.911810\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 484.508 | 0.822595 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 85.1046i | 0.144001i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −219.255 | −0.369738 | −0.184869 | − | 0.982763i | \(-0.559186\pi\) | ||||
−0.184869 | + | 0.982763i | \(0.559186\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 294.995i | − 0.495790i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 228.754 | 0.383173 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 154.802i | − 0.258434i | −0.991616 | − | 0.129217i | \(-0.958754\pi\) | ||||
0.991616 | − | 0.129217i | \(-0.0412464\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −205.862 | −0.342533 | −0.171266 | − | 0.985225i | \(-0.554786\pi\) | ||||
−0.171266 | + | 0.985225i | \(0.554786\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 680.666i | − 1.12880i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −315.097 | −0.520821 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 790.663i | 1.30258i | 0.758831 | + | 0.651288i | \(0.225771\pi\) | ||||
−0.758831 | + | 0.651288i | \(0.774229\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −34.7939 | −0.0571329 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 56.0000i | − 0.0916530i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 741.471 | 1.20958 | 0.604789 | − | 0.796386i | \(-0.293257\pi\) | ||||
0.604789 | + | 0.796386i | \(0.293257\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 36.8848i | − 0.0599752i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −171.578 | −0.278084 | −0.139042 | − | 0.990286i | \(-0.544402\pi\) | ||||
−0.139042 | + | 0.990286i | \(0.544402\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 540.198i | 0.872695i | 0.899778 | + | 0.436347i | \(0.143728\pi\) | ||||
−0.899778 | + | 0.436347i | \(0.856272\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −254.873 | −0.410424 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 296.168i | 0.475391i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1163.38 | 1.86141 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 211.147i | 0.336758i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 200.583 | 0.318892 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 269.399i | − 0.426940i | −0.976950 | − | 0.213470i | \(-0.931523\pi\) | ||||
0.976950 | − | 0.213470i | \(-0.0684766\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 96.0975 | 0.151813 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1033.77i | − 1.62798i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −63.2321 | −0.0992655 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 151.794i | 0.237549i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.1867 | 0.0564535 | 0.0282268 | − | 0.999602i | \(-0.491014\pi\) | ||||
0.0282268 | + | 0.999602i | \(0.491014\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 266.297i | 0.414148i | 0.978325 | + | 0.207074i | \(0.0663941\pi\) | ||||
−0.978325 | + | 0.207074i | \(0.933606\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −120.797 | −0.187282 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1086.24i | 1.67888i | 0.543452 | + | 0.839440i | \(0.317117\pi\) | ||||
−0.543452 | + | 0.839440i | \(0.682883\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −380.098 | −0.585666 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 26.0101i | − 0.0399541i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1195.35 | −1.83055 | −0.915274 | − | 0.402832i | \(-0.868026\pi\) | ||||
−0.915274 | + | 0.402832i | \(0.868026\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 1520.74i | − 2.32173i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −404.156 | −0.615154 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 685.220i | − 1.03979i | −0.854231 | − | 0.519894i | \(-0.825971\pi\) | ||||
0.854231 | − | 0.519894i | \(-0.174029\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −993.382 | −1.50285 | −0.751423 | − | 0.659820i | \(-0.770632\pi\) | ||||
−0.751423 | + | 0.659820i | \(0.770632\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 65.3138i | 0.0985125i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 689.980 | 1.03756 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 553.206i | − 0.829394i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.19938 | −0.00926664 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 190.183i | − 0.283432i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 106.569 | 0.158349 | 0.0791743 | − | 0.996861i | \(-0.474772\pi\) | ||||
0.0791743 | + | 0.996861i | \(0.474772\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 585.401i | 0.867261i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1004.18 | 1.48329 | 0.741643 | − | 0.670795i | \(-0.234047\pi\) | ||||
0.741643 | + | 0.670795i | \(0.234047\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 434.188i | 0.639452i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 125.245 | 0.183913 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 678.225i | 0.993009i | 0.868034 | + | 0.496505i | \(0.165383\pi\) | ||||
−0.868034 | + | 0.496505i | \(0.834617\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −313.327 | −0.457411 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 135.919i | 0.197844i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 72.4020 | 0.105083 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 365.175i | − 0.528473i | −0.964458 | − | 0.264236i | \(-0.914880\pi\) | ||||
0.964458 | − | 0.264236i | \(-0.0851199\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −285.961 | −0.412643 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 972.546i | − 1.39935i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −86.0387 | −0.123441 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 112.976i | 0.161626i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −940.292 | −1.34136 | −0.670679 | − | 0.741748i | \(-0.733997\pi\) | ||||
−0.670679 | + | 0.741748i | \(0.733997\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 469.155i | 0.667361i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 32.8040 | 0.0465306 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 32.1005i | − 0.0454038i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1057.46 | −1.49148 | −0.745738 | − | 0.666239i | \(-0.767903\pi\) | ||||
−0.745738 | + | 0.666239i | \(0.767903\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 701.487i | − 0.986620i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 413.547 | 0.580010 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1018.77i | − 1.42486i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 192.090 | 0.267907 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1034.82i | − 1.43926i | −0.694360 | − | 0.719628i | \(-0.744312\pi\) | ||||
0.694360 | − | 0.719628i | \(-0.255688\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 281.990 | 0.391109 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 42.1017i | 0.0582320i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1270.62 | −1.75258 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 495.145i | 0.681080i | 0.940230 | + | 0.340540i | \(0.110610\pi\) | ||||
−0.940230 | + | 0.340540i | \(0.889390\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 567.489 | 0.778449 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 281.775i | 0.385465i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 567.494 | 0.774207 | 0.387103 | − | 0.922036i | \(-0.373476\pi\) | ||||
0.387103 | + | 0.922036i | \(0.373476\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 37.0405i | − 0.0503953i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −981.685 | −1.33200 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 544.701i | − 0.737078i | −0.929612 | − | 0.368539i | \(-0.879858\pi\) | ||||
0.929612 | − | 0.368539i | \(-0.120142\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −152.766 | −0.206162 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 731.264i | 0.984205i | 0.870537 | + | 0.492102i | \(0.163771\pi\) | ||||
−0.870537 | + | 0.492102i | \(0.836229\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2277.95 | 3.05765 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 349.605i | 0.468012i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 168.264 | 0.224652 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 666.262i | − 0.887166i | −0.896233 | − | 0.443583i | \(-0.853707\pi\) | ||||
0.896233 | − | 0.443583i | \(-0.146293\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −150.500 | −0.199867 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2118.15i | 2.80550i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 238.623 | 0.315222 | 0.157611 | − | 0.987501i | \(-0.449621\pi\) | ||||
0.157611 | + | 0.987501i | \(0.449621\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 180.223i | 0.237447i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −614.930 | −0.808055 | −0.404028 | − | 0.914747i | \(-0.632390\pi\) | ||||
−0.404028 | + | 0.914747i | \(0.632390\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 346.191i | − 0.453723i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 965.219 | 1.26172 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 275.002i | − 0.358543i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 178.950 | 0.232705 | 0.116353 | − | 0.993208i | \(-0.462880\pi\) | ||||
0.116353 | + | 0.993208i | \(0.462880\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 187.072i | 0.242636i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 631.615 | 0.817095 | 0.408548 | − | 0.912737i | \(-0.366035\pi\) | ||||
0.408548 | + | 0.912737i | \(0.366035\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 949.849i | − 1.22561i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 25.1859 | 0.0324142 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 201.241i | − 0.258332i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 218.923 | 0.280311 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 232.203i | − 0.296556i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 91.2061 | 0.116186 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 456.655i | 0.580247i | 0.956989 | + | 0.290124i | \(0.0936965\pi\) | ||||
−0.956989 | + | 0.290124i | \(0.906304\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −221.050 | −0.280165 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 365.710i | 0.462339i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 137.598 | 0.173516 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 42.4121i | 0.0533486i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 218.566 | 0.274236 | 0.137118 | − | 0.990555i | \(-0.456216\pi\) | ||||
0.137118 | + | 0.990555i | \(0.456216\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 76.5199i | − 0.0957695i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −969.058 | −1.20981 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 582.891i | 0.725892i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 588.926 | 0.731585 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 16.4976i | − 0.0204431i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1347.46 | −1.66559 | −0.832794 | − | 0.553584i | \(-0.813260\pi\) | ||||
−0.832794 | + | 0.553584i | \(0.813260\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 672.620i | 0.829371i | 0.909965 | + | 0.414686i | \(0.136108\pi\) | ||||
−0.909965 | + | 0.414686i | \(0.863892\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −234.148 | −0.288005 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 944.273i | 1.15862i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −659.058 | −0.806681 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 206.894i | − 0.252618i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1162.57 | 1.41604 | 0.708022 | − | 0.706190i | \(-0.249588\pi\) | ||||
0.708022 | + | 0.706190i | \(0.249588\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1041.65i | − 1.26567i | −0.774286 | − | 0.632835i | \(-0.781891\pi\) | ||||
0.774286 | − | 0.632835i | \(-0.218109\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 413.941 | 0.501747 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 278.432i | − 0.336678i | −0.985729 | − | 0.168339i | \(-0.946160\pi\) | ||||
0.985729 | − | 0.168339i | \(-0.0538403\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1065.74 | −1.28557 | −0.642785 | − | 0.766046i | \(-0.722221\pi\) | ||||
−0.642785 | + | 0.766046i | \(0.722221\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 60.3071i | − 0.0725717i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −86.4020 | −0.103724 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 2680.72i | − 3.21045i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 173.583 | 0.207387 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 305.844i | 0.364533i | 0.983249 | + | 0.182267i | \(0.0583434\pi\) | ||||
−0.983249 | + | 0.182267i | \(0.941657\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −337.000 | −0.400713 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 88.0059i | 0.104396i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −789.516 | −0.934339 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 92.2898i | 0.108961i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −104.599 | −0.123202 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 400.442i | 0.470555i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 164.018 | 0.192283 | 0.0961417 | − | 0.995368i | \(-0.469350\pi\) | ||||
0.0961417 | + | 0.995368i | \(0.469350\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2257.60i | 2.64047i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −851.068 | −0.993078 | −0.496539 | − | 0.868014i | \(-0.665396\pi\) | ||||
−0.496539 | + | 0.868014i | \(0.665396\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1179.69i | 1.37333i | 0.726973 | + | 0.686666i | \(0.240927\pi\) | ||||
−0.726973 | + | 0.686666i | \(0.759073\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.8033 | −0.0125474 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 279.048i | − 0.323346i | −0.986844 | − | 0.161673i | \(-0.948311\pi\) | ||||
0.986844 | − | 0.161673i | \(-0.0516890\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 361.598 | 0.418032 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 80.0458i | − 0.0923250i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1011.71 | −1.16423 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 710.254i | − 0.815447i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1420.66 | −1.62733 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 755.176i | − 0.863058i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −674.159 | −0.768711 | −0.384355 | − | 0.923185i | \(-0.625576\pi\) | ||||
−0.384355 | + | 0.923185i | \(0.625576\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 128.398i | − 0.146073i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1001.29 | −1.13654 | −0.568271 | − | 0.822841i | \(-0.692387\pi\) | ||||
−0.568271 | + | 0.822841i | \(0.692387\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 882.010i | 0.998879i | 0.866349 | + | 0.499439i | \(0.166461\pi\) | ||||
−0.866349 | + | 0.499439i | \(0.833539\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 161.093 | 0.182026 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.08053i | 0.00798256i | 0.999992 | + | 0.00399128i | \(0.00127047\pi\) | ||||
−0.999992 | + | 0.00399128i | \(0.998730\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −302.784 | −0.340589 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 897.103i | − 1.00685i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 178.976 | 0.200422 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2662.92i | 2.97533i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −130.392 | −0.145364 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 376.764i | 0.419092i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 98.9320 | 0.109802 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 35.3805i | 0.0391811i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −365.578 | −0.403953 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 450.372i | − 0.496551i | −0.968689 | − | 0.248275i | \(-0.920136\pi\) | ||||
0.968689 | − | 0.248275i | \(-0.0798638\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 105.032 | 0.115547 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 202.426i | − 0.222201i | −0.993809 | − | 0.111101i | \(-0.964562\pi\) | ||||
0.993809 | − | 0.111101i | \(-0.0354376\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 504.215 | 0.552262 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 80.6030i | 0.0880907i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −445.413 | −0.485728 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1593.73i | 1.73420i | 0.498138 | + | 0.867098i | \(0.334017\pi\) | ||||
−0.498138 | + | 0.867098i | \(0.665983\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −185.500 | −0.201412 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 158.392i | 0.171606i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 919.749 | 0.994323 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 922.666i | 0.995325i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1039.40 | −1.11884 | −0.559419 | − | 0.828885i | \(-0.688976\pi\) | ||||
−0.559419 | + | 0.828885i | \(0.688976\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 202.090i | − 0.217068i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 42.3320 | 0.0453719 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 1392.08i | − 1.48885i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −881.765 | −0.941051 | −0.470525 | − | 0.882386i | \(-0.655936\pi\) | ||||
−0.470525 | + | 0.882386i | \(0.655936\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 48.0059i | − 0.0511245i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 953.344 | 1.01312 | 0.506559 | − | 0.862205i | \(-0.330917\pi\) | ||||
0.506559 | + | 0.862205i | \(0.330917\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 171.767i | − 0.182149i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 247.196 | 0.261583 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.8957i | 0.0178413i | 0.999960 | + | 0.00892063i | \(0.00283956\pi\) | ||||
−0.999960 | + | 0.00892063i | \(0.997160\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −421.725 | −0.444389 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 63.9386i | 0.0672330i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1526.31 | −1.60159 | −0.800794 | − | 0.598940i | \(-0.795589\pi\) | ||||
−0.800794 | + | 0.598940i | \(0.795589\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1417.57i | 1.48436i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −164.192 | −0.171570 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 91.7713i | 0.0956948i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 679.352 | 0.706921 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 550.558i | 0.571712i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2360.40 | −2.44601 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1410.39i | − 1.45852i | −0.684235 | − | 0.729262i | \(-0.739864\pi\) | ||||
0.684235 | − | 0.729262i | \(-0.260136\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −208.743 | −0.215421 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 596.497i | 0.614312i | 0.951659 | + | 0.307156i | \(0.0993773\pi\) | ||||
−0.951659 | + | 0.307156i | \(0.900623\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −284.852 | −0.292757 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 299.488i | 0.307168i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 146.686 | 0.150140 | 0.0750698 | − | 0.997178i | \(-0.476082\pi\) | ||||
0.0750698 | + | 0.997178i | \(0.476082\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1397.62i | 1.42760i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1132.73 | 1.15467 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 169.457i | − 0.172388i | −0.996278 | − | 0.0861939i | \(-0.972530\pi\) | ||||
0.996278 | − | 0.0861939i | \(-0.0274704\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1312.36 | 1.33235 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 9.60808i | − 0.00973463i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −562.533 | −0.568789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 1686.90i | − 1.70222i | −0.524988 | − | 0.851109i | \(-0.675930\pi\) | ||||
0.524988 | − | 0.851109i | \(-0.324070\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 188.471 | 0.189800 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 3527.52i | − 3.54524i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1736.14 | 1.74136 | 0.870680 | − | 0.491849i | \(-0.163679\pi\) | ||||
0.870680 | + | 0.491849i | \(0.163679\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 168.082i | 0.168250i |
(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 | 1792.3.d.g.1023.6 | 8 | ||
4.3 | odd | 2 | inner | 1792.3.d.g.1023.4 | 8 | ||
8.3 | odd | 2 | inner | 1792.3.d.g.1023.5 | 8 | ||
8.5 | even | 2 | inner | 1792.3.d.g.1023.3 | 8 | ||
16.3 | odd | 4 | 56.3.g.a.43.1 | ✓ | 4 | ||
16.5 | even | 4 | 56.3.g.a.43.2 | yes | 4 | ||
16.11 | odd | 4 | 224.3.g.a.15.4 | 4 | |||
16.13 | even | 4 | 224.3.g.a.15.3 | 4 | |||
48.5 | odd | 4 | 504.3.g.a.379.3 | 4 | |||
48.11 | even | 4 | 2016.3.g.a.1135.1 | 4 | |||
48.29 | odd | 4 | 2016.3.g.a.1135.4 | 4 | |||
48.35 | even | 4 | 504.3.g.a.379.4 | 4 | |||
112.3 | even | 12 | 392.3.k.j.275.4 | 8 | |||
112.5 | odd | 12 | 392.3.k.j.67.4 | 8 | |||
112.13 | odd | 4 | 1568.3.g.h.687.2 | 4 | |||
112.19 | even | 12 | 392.3.k.j.67.2 | 8 | |||
112.27 | even | 4 | 1568.3.g.h.687.1 | 4 | |||
112.37 | even | 12 | 392.3.k.i.67.4 | 8 | |||
112.51 | odd | 12 | 392.3.k.i.67.2 | 8 | |||
112.53 | even | 12 | 392.3.k.i.275.2 | 8 | |||
112.67 | odd | 12 | 392.3.k.i.275.4 | 8 | |||
112.69 | odd | 4 | 392.3.g.h.99.2 | 4 | |||
112.83 | even | 4 | 392.3.g.h.99.1 | 4 | |||
112.101 | odd | 12 | 392.3.k.j.275.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.a.43.1 | ✓ | 4 | 16.3 | odd | 4 | ||
56.3.g.a.43.2 | yes | 4 | 16.5 | even | 4 | ||
224.3.g.a.15.3 | 4 | 16.13 | even | 4 | |||
224.3.g.a.15.4 | 4 | 16.11 | odd | 4 | |||
392.3.g.h.99.1 | 4 | 112.83 | even | 4 | |||
392.3.g.h.99.2 | 4 | 112.69 | odd | 4 | |||
392.3.k.i.67.2 | 8 | 112.51 | odd | 12 | |||
392.3.k.i.67.4 | 8 | 112.37 | even | 12 | |||
392.3.k.i.275.2 | 8 | 112.53 | even | 12 | |||
392.3.k.i.275.4 | 8 | 112.67 | odd | 12 | |||
392.3.k.j.67.2 | 8 | 112.19 | even | 12 | |||
392.3.k.j.67.4 | 8 | 112.5 | odd | 12 | |||
392.3.k.j.275.2 | 8 | 112.101 | odd | 12 | |||
392.3.k.j.275.4 | 8 | 112.3 | even | 12 | |||
504.3.g.a.379.3 | 4 | 48.5 | odd | 4 | |||
504.3.g.a.379.4 | 4 | 48.35 | even | 4 | |||
1568.3.g.h.687.1 | 4 | 112.27 | even | 4 | |||
1568.3.g.h.687.2 | 4 | 112.13 | odd | 4 | |||
1792.3.d.g.1023.3 | 8 | 8.5 | even | 2 | inner | ||
1792.3.d.g.1023.4 | 8 | 4.3 | odd | 2 | inner | ||
1792.3.d.g.1023.5 | 8 | 8.3 | odd | 2 | inner | ||
1792.3.d.g.1023.6 | 8 | 1.1 | even | 1 | trivial | ||
2016.3.g.a.1135.1 | 4 | 48.11 | even | 4 | |||
2016.3.g.a.1135.4 | 4 | 48.29 | odd | 4 |