Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(524,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.524");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.g (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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 32x^{14} + 386x^{12} + 2208x^{10} + 6263x^{8} + 8496x^{6} + 4790x^{4} + 704x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 524.10 | ||
Root | \(0.378617i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.524 |
Dual form | 525.2.g.f.524.9 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.09941 | 0.777403 | 0.388702 | − | 0.921364i | \(-0.372924\pi\) | ||||
0.388702 | + | 0.921364i | \(0.372924\pi\) | |||||||
\(3\) | −0.323042 | + | 1.70166i | −0.186508 | + | 0.982453i | ||||
\(4\) | −0.791288 | −0.395644 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.355157 | + | 1.87083i | −0.144992 | + | 0.763763i | ||||
\(7\) | −2.44949 | − | 1.00000i | −0.925820 | − | 0.377964i | ||||
\(8\) | −3.06878 | −1.08498 | ||||||||
\(9\) | −2.79129 | − | 1.09941i | −0.930429 | − | 0.366471i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.06878i | − | 0.925273i | −0.886548 | − | 0.462636i | \(-0.846904\pi\) | ||
0.886548 | − | 0.462636i | \(-0.153096\pi\) | |||||||
\(12\) | 0.255619 | − | 1.34650i | 0.0737909 | − | 0.388702i | ||||
\(13\) | −2.44949 | −0.679366 | −0.339683 | − | 0.940540i | \(-0.610320\pi\) | ||||
−0.339683 | + | 0.940540i | \(0.610320\pi\) | |||||||
\(14\) | −2.69300 | − | 1.09941i | −0.719736 | − | 0.293831i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.79129 | −0.447822 | ||||||||
\(17\) | 2.69300i | 0.653150i | 0.945171 | + | 0.326575i | \(0.105894\pi\) | ||||
−0.945171 | + | 0.326575i | \(0.894106\pi\) | |||||||
\(18\) | −3.06878 | − | 1.20871i | −0.723319 | − | 0.284896i | ||||
\(19\) | 4.38774i | 1.00662i | 0.864107 | + | 0.503308i | \(0.167884\pi\) | ||||
−0.864107 | + | 0.503308i | \(0.832116\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.49295 | − | 3.84515i | 0.544006 | − | 0.839082i | ||||
\(22\) | − | 3.37386i | − | 0.719310i | ||||||
\(23\) | −5.26761 | −1.09837 | −0.549186 | − | 0.835700i | \(-0.685062\pi\) | ||||
−0.549186 | + | 0.835700i | \(0.685062\pi\) | |||||||
\(24\) | 0.991345 | − | 5.22202i | 0.202358 | − | 1.06594i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.69300 | −0.528142 | ||||||||
\(27\) | 2.77253 | − | 4.39466i | 0.533574 | − | 0.845753i | ||||
\(28\) | 1.93825 | + | 0.791288i | 0.366295 | + | 0.149539i | ||||
\(29\) | − | 5.26761i | − | 0.978171i | −0.872236 | − | 0.489085i | \(-0.837331\pi\) | ||
0.872236 | − | 0.489085i | \(-0.162669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.83723i | − | 1.22800i | −0.789305 | − | 0.614001i | \(-0.789559\pi\) | ||
0.789305 | − | 0.614001i | \(-0.210441\pi\) | |||||||
\(32\) | 4.16820 | 0.736840 | ||||||||
\(33\) | 5.22202 | + | 0.991345i | 0.909037 | + | 0.172571i | ||||
\(34\) | 2.96073i | 0.507761i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.20871 | + | 0.869953i | 0.368119 | + | 0.144992i | ||||
\(37\) | 8.58258i | 1.41097i | 0.708726 | + | 0.705483i | \(0.249270\pi\) | ||||
−0.708726 | + | 0.705483i | \(0.750730\pi\) | |||||||
\(38\) | 4.82395i | 0.782547i | ||||||||
\(39\) | 0.791288 | − | 4.16820i | 0.126707 | − | 0.667446i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.2100 | −1.59453 | −0.797264 | − | 0.603631i | \(-0.793720\pi\) | ||||
−0.797264 | + | 0.603631i | \(0.793720\pi\) | |||||||
\(42\) | 2.74078 | − | 4.22742i | 0.422912 | − | 0.652305i | ||||
\(43\) | 6.58258i | 1.00383i | 0.864916 | + | 0.501917i | \(0.167372\pi\) | ||||
−0.864916 | + | 0.501917i | \(0.832628\pi\) | |||||||
\(44\) | 2.42829i | 0.366079i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.79129 | −0.853879 | ||||||||
\(47\) | 2.69300i | 0.392815i | 0.980522 | + | 0.196408i | \(0.0629276\pi\) | ||||
−0.980522 | + | 0.196408i | \(0.937072\pi\) | |||||||
\(48\) | 0.578661 | − | 3.04816i | 0.0835225 | − | 0.439964i | ||||
\(49\) | 5.00000 | + | 4.89898i | 0.714286 | + | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.58258 | − | 0.869953i | −0.641689 | − | 0.121818i | ||||
\(52\) | 1.93825 | 0.268787 | ||||||||
\(53\) | 3.93874 | 0.541027 | 0.270513 | − | 0.962716i | \(-0.412807\pi\) | ||||
0.270513 | + | 0.962716i | \(0.412807\pi\) | |||||||
\(54\) | 3.04816 | − | 4.83156i | 0.414802 | − | 0.657492i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.51695 | + | 3.06878i | 1.00449 | + | 0.410083i | ||||
\(57\) | −7.46644 | − | 1.41742i | −0.988954 | − | 0.187742i | ||||
\(58\) | − | 5.79129i | − | 0.760433i | ||||||
\(59\) | −7.51695 | −0.978624 | −0.489312 | − | 0.872109i | \(-0.662752\pi\) | ||||
−0.489312 | + | 0.872109i | \(0.662752\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.83723i | 0.875418i | 0.899117 | + | 0.437709i | \(0.144210\pi\) | ||||
−0.899117 | + | 0.437709i | \(0.855790\pi\) | |||||||
\(62\) | − | 7.51695i | − | 0.954654i | ||||||
\(63\) | 5.73782 | + | 5.48429i | 0.722897 | + | 0.690956i | ||||
\(64\) | 8.16515 | 1.02064 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.74117 | + | 1.08990i | 0.706689 | + | 0.134157i | ||||
\(67\) | 4.16515i | 0.508854i | 0.967092 | + | 0.254427i | \(0.0818869\pi\) | ||||
−0.967092 | + | 0.254427i | \(0.918113\pi\) | |||||||
\(68\) | − | 2.13094i | − | 0.258415i | ||||||
\(69\) | 1.70166 | − | 8.96368i | 0.204856 | − | 1.07910i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.06878i | − | 0.364197i | −0.983280 | − | 0.182099i | \(-0.941711\pi\) | ||
0.983280 | − | 0.182099i | \(-0.0582890\pi\) | |||||||
\(72\) | 8.56585 | + | 3.37386i | 1.00950 | + | 0.397614i | ||||
\(73\) | −16.1240 | −1.88717 | −0.943583 | − | 0.331136i | \(-0.892568\pi\) | ||||
−0.943583 | + | 0.331136i | \(0.892568\pi\) | |||||||
\(74\) | 9.43581i | 1.09689i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 3.47197i | − | 0.398262i | ||||||
\(77\) | −3.06878 | + | 7.51695i | −0.349720 | + | 0.856636i | ||||
\(78\) | 0.869953 | − | 4.58258i | 0.0985028 | − | 0.518875i | ||||
\(79\) | −0.582576 | −0.0655449 | −0.0327724 | − | 0.999463i | \(-0.510434\pi\) | ||||
−0.0327724 | + | 0.999463i | \(0.510434\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.58258 | + | 6.13756i | 0.731397 | + | 0.681952i | ||||
\(82\) | −11.2250 | −1.23959 | ||||||||
\(83\) | − | 15.5960i | − | 1.71188i | −0.517076 | − | 0.855940i | \(-0.672979\pi\) | ||
0.517076 | − | 0.855940i | \(-0.327021\pi\) | |||||||
\(84\) | −1.97264 | + | 3.04262i | −0.215233 | + | 0.331978i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.23698i | 0.780384i | ||||||||
\(87\) | 8.96368 | + | 1.70166i | 0.961007 | + | 0.182437i | ||||
\(88\) | 9.41742i | 1.00390i | ||||||||
\(89\) | 7.51695 | 0.796795 | 0.398398 | − | 0.917213i | \(-0.369566\pi\) | ||||
0.398398 | + | 0.917213i | \(0.369566\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | + | 2.44949i | 0.628971 | + | 0.256776i | ||||
\(92\) | 4.16820 | 0.434565 | ||||||||
\(93\) | 11.6346 | + | 2.20871i | 1.20646 | + | 0.229033i | ||||
\(94\) | 2.96073i | 0.305376i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.34650 | + | 7.09285i | −0.137427 | + | 0.723911i | ||||
\(97\) | −11.7362 | −1.19163 | −0.595816 | − | 0.803121i | \(-0.703171\pi\) | ||||
−0.595816 | + | 0.803121i | \(0.703171\pi\) | |||||||
\(98\) | 5.49707 | + | 5.38601i | 0.555288 | + | 0.544069i | ||||
\(99\) | −3.37386 | + | 8.56585i | −0.339086 | + | 0.860901i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.2890 | 1.81982 | 0.909910 | − | 0.414805i | \(-0.136150\pi\) | ||||
0.909910 | + | 0.414805i | \(0.136150\pi\) | |||||||
\(102\) | −5.03815 | − | 0.956439i | −0.498851 | − | 0.0947016i | ||||
\(103\) | 4.38774 | 0.432337 | 0.216168 | − | 0.976356i | \(-0.430644\pi\) | ||||
0.216168 | + | 0.976356i | \(0.430644\pi\) | |||||||
\(104\) | 7.51695 | 0.737098 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.33030 | 0.420596 | ||||||||
\(107\) | −10.5352 | −1.01848 | −0.509239 | − | 0.860625i | \(-0.670073\pi\) | ||||
−0.509239 | + | 0.860625i | \(0.670073\pi\) | |||||||
\(108\) | −2.19387 | + | 3.47744i | −0.211105 | + | 0.334617i | ||||
\(109\) | −5.00000 | −0.478913 | −0.239457 | − | 0.970907i | \(-0.576969\pi\) | ||||
−0.239457 | + | 0.970907i | \(0.576969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.6046 | − | 2.77253i | −1.38621 | − | 0.263157i | ||||
\(112\) | 4.38774 | + | 1.79129i | 0.414603 | + | 0.169261i | ||||
\(113\) | 18.0017 | 1.69345 | 0.846727 | − | 0.532028i | \(-0.178570\pi\) | ||||
0.846727 | + | 0.532028i | \(0.178570\pi\) | |||||||
\(114\) | −8.20871 | − | 1.55834i | −0.768816 | − | 0.145952i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.16820i | 0.387007i | ||||||||
\(117\) | 6.83723 | + | 2.69300i | 0.632102 | + | 0.248968i | ||||
\(118\) | −8.26424 | −0.760785 | ||||||||
\(119\) | 2.69300 | − | 6.59649i | 0.246867 | − | 0.604699i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.58258 | 0.143871 | ||||||||
\(122\) | 7.51695i | 0.680553i | ||||||||
\(123\) | 3.29824 | − | 17.3739i | 0.297393 | − | 1.56655i | ||||
\(124\) | 5.41022i | 0.485852i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.30824 | + | 6.02951i | 0.561983 | + | 0.537151i | ||||
\(127\) | − | 8.16515i | − | 0.724540i | −0.932073 | − | 0.362270i | \(-0.882002\pi\) | ||
0.932073 | − | 0.362270i | \(-0.117998\pi\) | |||||||
\(128\) | 0.640492 | 0.0566120 | ||||||||
\(129\) | −11.2013 | − | 2.12645i | −0.986219 | − | 0.187223i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.69300 | −0.235289 | −0.117644 | − | 0.993056i | \(-0.537534\pi\) | ||||
−0.117644 | + | 0.993056i | \(0.537534\pi\) | |||||||
\(132\) | −4.13212 | − | 0.784439i | −0.359655 | − | 0.0682767i | ||||
\(133\) | 4.38774 | − | 10.7477i | 0.380465 | − | 0.931946i | ||||
\(134\) | 4.57923i | 0.395585i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 8.26424i | − | 0.708653i | ||||||
\(137\) | −10.5352 | −0.900085 | −0.450042 | − | 0.893007i | \(-0.648591\pi\) | ||||
−0.450042 | + | 0.893007i | \(0.648591\pi\) | |||||||
\(138\) | 1.87083 | − | 9.85480i | 0.159256 | − | 0.838896i | ||||
\(139\) | − | 2.44949i | − | 0.207763i | −0.994590 | − | 0.103882i | \(-0.966874\pi\) | ||
0.994590 | − | 0.103882i | \(-0.0331263\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.58258 | − | 0.869953i | −0.385922 | − | 0.0732633i | ||||
\(142\) | − | 3.37386i | − | 0.283128i | ||||||
\(143\) | 7.51695i | 0.628599i | ||||||||
\(144\) | 5.00000 | + | 1.96937i | 0.416667 | + | 0.164114i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −17.7269 | −1.46709 | ||||||||
\(147\) | −9.95160 | + | 6.92572i | −0.820794 | + | 0.571224i | ||||
\(148\) | − | 6.79129i | − | 0.558240i | ||||||
\(149\) | 18.0017i | 1.47475i | 0.675482 | + | 0.737377i | \(0.263936\pi\) | ||||
−0.675482 | + | 0.737377i | \(0.736064\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.16515 | −0.338955 | −0.169478 | − | 0.985534i | \(-0.554208\pi\) | ||||
−0.169478 | + | 0.985534i | \(0.554208\pi\) | |||||||
\(152\) | − | 13.4650i | − | 1.09216i | ||||||
\(153\) | 2.96073 | − | 7.51695i | 0.239361 | − | 0.607709i | ||||
\(154\) | −3.37386 | + | 8.26424i | −0.271874 | + | 0.665952i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.626136 | + | 3.29824i | −0.0501310 | + | 0.264071i | ||||
\(157\) | 1.93825 | 0.154689 | 0.0773447 | − | 0.997004i | \(-0.475356\pi\) | ||||
0.0773447 | + | 0.997004i | \(0.475356\pi\) | |||||||
\(158\) | −0.640492 | −0.0509548 | ||||||||
\(159\) | −1.27238 | + | 6.70239i | −0.100906 | + | 0.531534i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.9030 | + | 5.26761i | 1.01690 | + | 0.415146i | ||||
\(162\) | 7.23698 | + | 6.74773i | 0.568591 | + | 0.530152i | ||||
\(163\) | − | 4.00000i | − | 0.313304i | −0.987654 | − | 0.156652i | \(-0.949930\pi\) | ||
0.987654 | − | 0.156652i | \(-0.0500701\pi\) | |||||||
\(164\) | 8.07901 | 0.630865 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 17.1464i | − | 1.33082i | ||||||
\(167\) | − | 18.2890i | − | 1.41524i | −0.706592 | − | 0.707621i | \(-0.749768\pi\) | ||
0.706592 | − | 0.707621i | \(-0.250232\pi\) | |||||||
\(168\) | −7.65031 | + | 11.7999i | −0.590234 | + | 0.910385i | ||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.82395 | − | 12.2474i | 0.368896 | − | 0.936586i | ||||
\(172\) | − | 5.20871i | − | 0.397161i | ||||||
\(173\) | − | 8.07901i | − | 0.614236i | −0.951671 | − | 0.307118i | \(-0.900635\pi\) | ||
0.951671 | − | 0.307118i | \(-0.0993646\pi\) | |||||||
\(174\) | 9.85480 | + | 1.87083i | 0.747090 | + | 0.141827i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.49707i | 0.414357i | ||||||||
\(177\) | 2.42829 | − | 12.7913i | 0.182521 | − | 0.961452i | ||||
\(178\) | 8.26424 | 0.619431 | ||||||||
\(179\) | − | 14.4740i | − | 1.08183i | −0.841076 | − | 0.540917i | \(-0.818077\pi\) | ||
0.841076 | − | 0.540917i | \(-0.181923\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.2474i | 0.910346i | 0.890403 | + | 0.455173i | \(0.150423\pi\) | ||||
−0.890403 | + | 0.455173i | \(0.849577\pi\) | |||||||
\(182\) | 6.59649 | + | 2.69300i | 0.488964 | + | 0.199619i | ||||
\(183\) | −11.6346 | − | 2.20871i | −0.860057 | − | 0.163273i | ||||
\(184\) | 16.1652 | 1.19171 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 12.7913 | + | 2.42829i | 0.937903 | + | 0.178051i | ||||
\(187\) | 8.26424 | 0.604341 | ||||||||
\(188\) | − | 2.13094i | − | 0.155415i | ||||||
\(189\) | −11.1860 | + | 7.99215i | −0.813658 | + | 0.581343i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 17.1317i | − | 1.23961i | −0.784757 | − | 0.619803i | \(-0.787212\pi\) | ||
0.784757 | − | 0.619803i | \(-0.212788\pi\) | |||||||
\(192\) | −2.63769 | + | 13.8943i | −0.190359 | + | 1.00274i | ||||
\(193\) | 11.0000i | 0.791797i | 0.918294 | + | 0.395899i | \(0.129567\pi\) | ||||
−0.918294 | + | 0.395899i | \(0.870433\pi\) | |||||||
\(194\) | −12.9030 | −0.926379 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.95644 | − | 3.87650i | −0.282603 | − | 0.276893i | ||||
\(197\) | 3.52770 | 0.251339 | 0.125669 | − | 0.992072i | \(-0.459892\pi\) | ||||
0.125669 | + | 0.992072i | \(0.459892\pi\) | |||||||
\(198\) | −3.70927 | + | 9.41742i | −0.263607 | + | 0.669267i | ||||
\(199\) | − | 7.85971i | − | 0.557160i | −0.960413 | − | 0.278580i | \(-0.910136\pi\) | ||
0.960413 | − | 0.278580i | \(-0.0898637\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.08767 | − | 1.34552i | −0.499926 | − | 0.0949056i | ||||
\(202\) | 20.1072 | 1.41473 | ||||||||
\(203\) | −5.26761 | + | 12.9030i | −0.369714 | + | 0.905610i | ||||
\(204\) | 3.62614 | + | 0.688383i | 0.253880 | + | 0.0481965i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.82395 | 0.336100 | ||||||||
\(207\) | 14.7034 | + | 5.79129i | 1.02196 | + | 0.402522i | ||||
\(208\) | 4.38774 | 0.304235 | ||||||||
\(209\) | 13.4650 | 0.931395 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.7477 | −1.01528 | −0.507638 | − | 0.861571i | \(-0.669481\pi\) | ||||
−0.507638 | + | 0.861571i | \(0.669481\pi\) | |||||||
\(212\) | −3.11667 | −0.214054 | ||||||||
\(213\) | 5.22202 | + | 0.991345i | 0.357807 | + | 0.0679259i | ||||
\(214\) | −11.5826 | −0.791769 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −8.50830 | + | 13.4863i | −0.578916 | + | 0.917624i | ||||
\(217\) | −6.83723 | + | 16.7477i | −0.464141 | + | 1.13691i | ||||
\(218\) | −5.49707 | −0.372309 | ||||||||
\(219\) | 5.20871 | − | 27.4375i | 0.351972 | − | 1.85405i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 6.59649i | − | 0.443728i | ||||||
\(222\) | −16.0565 | − | 3.04816i | −1.07764 | − | 0.204579i | ||||
\(223\) | −2.44949 | −0.164030 | −0.0820150 | − | 0.996631i | \(-0.526136\pi\) | ||||
−0.0820150 | + | 0.996631i | \(0.526136\pi\) | |||||||
\(224\) | −10.2100 | − | 4.16820i | −0.682181 | − | 0.278499i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.7913 | 1.31650 | ||||||||
\(227\) | 2.69300i | 0.178741i | 0.995998 | + | 0.0893705i | \(0.0284855\pi\) | ||||
−0.995998 | + | 0.0893705i | \(0.971514\pi\) | |||||||
\(228\) | 5.90810 | + | 1.12159i | 0.391274 | + | 0.0742792i | ||||
\(229\) | − | 3.87650i | − | 0.256167i | −0.991763 | − | 0.128083i | \(-0.959118\pi\) | ||
0.991763 | − | 0.128083i | \(-0.0408825\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.7999 | − | 7.65031i | −0.776379 | − | 0.503354i | ||||
\(232\) | 16.1652i | 1.06129i | ||||||||
\(233\) | −5.26761 | −0.345093 | −0.172546 | − | 0.985001i | \(-0.555199\pi\) | ||||
−0.172546 | + | 0.985001i | \(0.555199\pi\) | |||||||
\(234\) | 7.51695 | + | 2.96073i | 0.491398 | + | 0.193549i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.94807 | 0.387186 | ||||||||
\(237\) | 0.188196 | − | 0.991345i | 0.0122247 | − | 0.0643948i | ||||
\(238\) | 2.96073 | − | 7.25227i | 0.191915 | − | 0.470095i | ||||
\(239\) | − | 14.4740i | − | 0.936242i | −0.883664 | − | 0.468121i | \(-0.844931\pi\) | ||
0.883664 | − | 0.468121i | \(-0.155069\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.0847i | 1.22935i | 0.788780 | + | 0.614676i | \(0.210713\pi\) | ||||
−0.788780 | + | 0.614676i | \(0.789287\pi\) | |||||||
\(242\) | 1.73991 | 0.111845 | ||||||||
\(243\) | −12.5705 | + | 9.21861i | −0.806397 | + | 0.591374i | ||||
\(244\) | − | 5.41022i | − | 0.346354i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.62614 | − | 19.1011i | 0.231194 | − | 1.21784i | ||||
\(247\) | − | 10.7477i | − | 0.683861i | ||||||
\(248\) | 20.9820i | 1.33236i | ||||||||
\(249\) | 26.5390 | + | 5.03815i | 1.68184 | + | 0.319280i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.7269 | −1.11891 | −0.559456 | − | 0.828860i | \(-0.688990\pi\) | ||||
−0.559456 | + | 0.828860i | \(0.688990\pi\) | |||||||
\(252\) | −4.54026 | − | 4.33965i | −0.286010 | − | 0.273372i | ||||
\(253\) | 16.1652i | 1.01629i | ||||||||
\(254\) | − | 8.97689i | − | 0.563260i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.6261 | −0.976634 | ||||||||
\(257\) | − | 4.82395i | − | 0.300909i | −0.988617 | − | 0.150455i | \(-0.951926\pi\) | ||
0.988617 | − | 0.150455i | \(-0.0480738\pi\) | |||||||
\(258\) | −12.3149 | − | 2.33785i | −0.766690 | − | 0.145548i | ||||
\(259\) | 8.58258 | − | 21.0229i | 0.533295 | − | 1.30630i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.79129 | + | 14.7034i | −0.358472 | + | 0.910119i | ||||
\(262\) | −2.96073 | −0.182914 | ||||||||
\(263\) | −28.5369 | −1.75966 | −0.879830 | − | 0.475289i | \(-0.842344\pi\) | ||||
−0.879830 | + | 0.475289i | \(0.842344\pi\) | |||||||
\(264\) | −16.0252 | − | 3.04222i | −0.986286 | − | 0.187236i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.82395 | − | 11.8162i | 0.295775 | − | 0.724498i | ||||
\(267\) | −2.42829 | + | 12.7913i | −0.148609 | + | 0.782814i | ||||
\(268\) | − | 3.29583i | − | 0.201325i | ||||||
\(269\) | −20.9820 | −1.27929 | −0.639647 | − | 0.768669i | \(-0.720919\pi\) | ||||
−0.639647 | + | 0.768669i | \(0.720919\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.9219i | 1.57464i | 0.616542 | + | 0.787322i | \(0.288533\pi\) | ||||
−0.616542 | + | 0.787322i | \(0.711467\pi\) | |||||||
\(272\) | − | 4.82395i | − | 0.292495i | ||||||
\(273\) | −6.10645 | + | 9.41867i | −0.369579 | + | 0.570044i | ||||
\(274\) | −11.5826 | −0.699729 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.34650 | + | 7.09285i | −0.0810499 | + | 0.426939i | ||||
\(277\) | − | 18.7477i | − | 1.12644i | −0.826306 | − | 0.563221i | \(-0.809562\pi\) | ||
0.826306 | − | 0.563221i | \(-0.190438\pi\) | |||||||
\(278\) | − | 2.69300i | − | 0.161516i | ||||||
\(279\) | −7.51695 | + | 19.0847i | −0.450028 | + | 1.14257i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.3439i | 0.915341i | 0.889122 | + | 0.457670i | \(0.151316\pi\) | ||||
−0.889122 | + | 0.457670i | \(0.848684\pi\) | |||||||
\(282\) | −5.03815 | − | 0.956439i | −0.300017 | − | 0.0569551i | ||||
\(283\) | 23.4724 | 1.39529 | 0.697645 | − | 0.716443i | \(-0.254231\pi\) | ||||
0.697645 | + | 0.716443i | \(0.254231\pi\) | |||||||
\(284\) | 2.42829i | 0.144093i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.26424i | 0.488675i | ||||||||
\(287\) | 25.0092 | + | 10.2100i | 1.47625 | + | 0.602675i | ||||
\(288\) | −11.6346 | − | 4.58258i | −0.685578 | − | 0.270031i | ||||
\(289\) | 9.74773 | 0.573396 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.79129 | − | 19.9710i | 0.222249 | − | 1.17072i | ||||
\(292\) | 12.7587 | 0.746646 | ||||||||
\(293\) | − | 2.13094i | − | 0.124491i | −0.998061 | − | 0.0622455i | \(-0.980174\pi\) | ||
0.998061 | − | 0.0622455i | \(-0.0198262\pi\) | |||||||
\(294\) | −10.9409 | + | 7.61424i | −0.638088 | + | 0.444071i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 26.3381i | − | 1.53087i | ||||||
\(297\) | −13.4863 | − | 8.50830i | −0.782552 | − | 0.493701i | ||||
\(298\) | 19.7913i | 1.14648i | ||||||||
\(299\) | 12.9030 | 0.746197 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.58258 | − | 16.1240i | 0.379413 | − | 0.929369i | ||||
\(302\) | −4.57923 | −0.263505 | ||||||||
\(303\) | −5.90810 | + | 31.1216i | −0.339412 | + | 1.78789i | ||||
\(304\) | − | 7.85971i | − | 0.450785i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.25507 | − | 8.26424i | 0.186080 | − | 0.472435i | ||||
\(307\) | −13.1632 | −0.751265 | −0.375632 | − | 0.926769i | \(-0.622574\pi\) | ||||
−0.375632 | + | 0.926769i | \(0.622574\pi\) | |||||||
\(308\) | 2.42829 | − | 5.94807i | 0.138365 | − | 0.338923i | ||||
\(309\) | −1.41742 | + | 7.46644i | −0.0806345 | + | 0.424751i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.3409 | 0.699788 | 0.349894 | − | 0.936789i | \(-0.386218\pi\) | ||||
0.349894 | + | 0.936789i | \(0.386218\pi\) | |||||||
\(312\) | −2.42829 | + | 12.7913i | −0.137475 | + | 0.724164i | ||||
\(313\) | −22.9612 | −1.29784 | −0.648921 | − | 0.760855i | \(-0.724780\pi\) | ||||
−0.648921 | + | 0.760855i | \(0.724780\pi\) | |||||||
\(314\) | 2.13094 | 0.120256 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.460985 | 0.0259324 | ||||||||
\(317\) | −1.32888 | −0.0746371 | −0.0373185 | − | 0.999303i | \(-0.511882\pi\) | ||||
−0.0373185 | + | 0.999303i | \(0.511882\pi\) | |||||||
\(318\) | −1.39887 | + | 7.36870i | −0.0784447 | + | 0.413216i | ||||
\(319\) | −16.1652 | −0.905075 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.40332 | − | 17.9274i | 0.189955 | − | 1.00061i | ||||
\(322\) | 14.1857 | + | 5.79129i | 0.790538 | + | 0.322736i | ||||
\(323\) | −11.8162 | −0.657471 | ||||||||
\(324\) | −5.20871 | − | 4.85658i | −0.289373 | − | 0.269810i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 4.39766i | − | 0.243564i | ||||||
\(327\) | 1.61521 | − | 8.50830i | 0.0893213 | − | 0.470510i | ||||
\(328\) | 31.3321 | 1.73003 | ||||||||
\(329\) | 2.69300 | − | 6.59649i | 0.148470 | − | 0.363676i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.0000 | 0.934405 | 0.467202 | − | 0.884150i | \(-0.345262\pi\) | ||||
0.467202 | + | 0.884150i | \(0.345262\pi\) | |||||||
\(332\) | 12.3409i | 0.677295i | ||||||||
\(333\) | 9.43581 | − | 23.9564i | 0.517079 | − | 1.31280i | ||||
\(334\) | − | 20.1072i | − | 1.10021i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.46559 | + | 6.88778i | −0.243618 | + | 0.375759i | ||||
\(337\) | − | 2.00000i | − | 0.108947i | −0.998515 | − | 0.0544735i | \(-0.982652\pi\) | ||
0.998515 | − | 0.0544735i | \(-0.0173480\pi\) | |||||||
\(338\) | −7.69590 | −0.418602 | ||||||||
\(339\) | −5.81529 | + | 30.6327i | −0.315843 | + | 1.66374i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.9820 | −1.13624 | ||||||||
\(342\) | 5.30352 | − | 13.4650i | 0.286781 | − | 0.728105i | ||||
\(343\) | −7.34847 | − | 17.0000i | −0.396780 | − | 0.917914i | ||||
\(344\) | − | 20.2005i | − | 1.08914i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 8.88218i | − | 0.477509i | ||||||
\(347\) | 3.52770 | 0.189377 | 0.0946886 | − | 0.995507i | \(-0.469814\pi\) | ||||
0.0946886 | + | 0.995507i | \(0.469814\pi\) | |||||||
\(348\) | −7.09285 | − | 1.34650i | −0.380217 | − | 0.0721801i | ||||
\(349\) | − | 9.28672i | − | 0.497107i | −0.968618 | − | 0.248553i | \(-0.920045\pi\) | ||
0.968618 | − | 0.248553i | \(-0.0799551\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.79129 | + | 10.7647i | −0.362492 | + | 0.574576i | ||||
\(352\) | − | 12.7913i | − | 0.681778i | ||||||
\(353\) | − | 30.6299i | − | 1.63026i | −0.579276 | − | 0.815132i | \(-0.696665\pi\) | ||
0.579276 | − | 0.815132i | \(-0.303335\pi\) | |||||||
\(354\) | 2.66970 | − | 14.0629i | 0.141893 | − | 0.747436i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.94807 | −0.315247 | ||||||||
\(357\) | 10.3550 | + | 6.71352i | 0.548046 | + | 0.355317i | ||||
\(358\) | − | 15.9129i | − | 0.841022i | ||||||
\(359\) | 18.0017i | 0.950091i | 0.879961 | + | 0.475046i | \(0.157568\pi\) | ||||
−0.879961 | + | 0.475046i | \(0.842432\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.252273 | −0.0132775 | ||||||||
\(362\) | 13.4650i | 0.707706i | ||||||||
\(363\) | −0.511238 | + | 2.69300i | −0.0268331 | + | 0.141346i | ||||
\(364\) | −4.74773 | − | 1.93825i | −0.248849 | − | 0.101592i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −12.7913 | − | 2.42829i | −0.668611 | − | 0.126929i | ||||
\(367\) | −0.915775 | −0.0478031 | −0.0239015 | − | 0.999714i | \(-0.507609\pi\) | ||||
−0.0239015 | + | 0.999714i | \(0.507609\pi\) | |||||||
\(368\) | 9.43581 | 0.491875 | ||||||||
\(369\) | 28.4989 | + | 11.2250i | 1.48359 | + | 0.584349i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.64789 | − | 3.93874i | −0.500894 | − | 0.204489i | ||||
\(372\) | −9.20635 | − | 1.74773i | −0.477327 | − | 0.0906154i | ||||
\(373\) | − | 26.9129i | − | 1.39350i | −0.717316 | − | 0.696748i | \(-0.754630\pi\) | ||
0.717316 | − | 0.696748i | \(-0.245370\pi\) | |||||||
\(374\) | 9.08583 | 0.469817 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 8.26424i | − | 0.426196i | ||||||
\(377\) | 12.9030i | 0.664536i | ||||||||
\(378\) | −12.2980 | + | 8.78669i | −0.632541 | + | 0.451938i | ||||
\(379\) | −17.3303 | −0.890198 | −0.445099 | − | 0.895481i | \(-0.646831\pi\) | ||||
−0.445099 | + | 0.895481i | \(0.646831\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.8943 | + | 2.63769i | 0.711827 | + | 0.135133i | ||||
\(382\) | − | 18.8348i | − | 0.963675i | ||||||
\(383\) | 27.9369i | 1.42751i | 0.700397 | + | 0.713753i | \(0.253006\pi\) | ||||
−0.700397 | + | 0.713753i | \(0.746994\pi\) | |||||||
\(384\) | −0.206906 | + | 1.08990i | −0.0105586 | + | 0.0556187i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.0936i | 0.615546i | ||||||||
\(387\) | 7.23698 | − | 18.3739i | 0.367876 | − | 0.933996i | ||||
\(388\) | 9.28672 | 0.471462 | ||||||||
\(389\) | 13.1451i | 0.666482i | 0.942842 | + | 0.333241i | \(0.108142\pi\) | ||||
−0.942842 | + | 0.333241i | \(0.891858\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 14.1857i | − | 0.717402i | ||||||
\(392\) | −15.3439 | − | 15.0339i | −0.774985 | − | 0.759327i | ||||
\(393\) | 0.869953 | − | 4.58258i | 0.0438833 | − | 0.231160i | ||||
\(394\) | 3.87841 | 0.195391 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.66970 | − | 6.77806i | 0.134157 | − | 0.340610i | ||||
\(397\) | 8.77548 | 0.440429 | 0.220214 | − | 0.975451i | \(-0.429324\pi\) | ||||
0.220214 | + | 0.975451i | \(0.429324\pi\) | |||||||
\(398\) | − | 8.64108i | − | 0.433138i | ||||||
\(399\) | 16.8715 | + | 10.9384i | 0.844634 | + | 0.547605i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.2005i | 1.00876i | 0.863481 | + | 0.504382i | \(0.168280\pi\) | ||||
−0.863481 | + | 0.504382i | \(0.831720\pi\) | |||||||
\(402\) | −7.79228 | − | 1.47928i | −0.388644 | − | 0.0737799i | ||||
\(403\) | 16.7477i | 0.834264i | ||||||||
\(404\) | −14.4718 | −0.720001 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.79129 | + | 14.1857i | −0.287417 | + | 0.704024i | ||||
\(407\) | 26.3381 | 1.30553 | ||||||||
\(408\) | 14.0629 | + | 2.66970i | 0.696219 | + | 0.132170i | ||||
\(409\) | 31.7367i | 1.56928i | 0.619954 | + | 0.784639i | \(0.287151\pi\) | ||||
−0.619954 | + | 0.784639i | \(0.712849\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.40332 | − | 17.9274i | 0.167873 | − | 0.884291i | ||||
\(412\) | −3.47197 | −0.171052 | ||||||||
\(413\) | 18.4127 | + | 7.51695i | 0.906029 | + | 0.369885i | ||||
\(414\) | 16.1652 | + | 6.36703i | 0.794474 | + | 0.312922i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −10.2100 | −0.500584 | ||||||||
\(417\) | 4.16820 | + | 0.791288i | 0.204117 | + | 0.0387495i | ||||
\(418\) | 14.8036 | 0.724070 | ||||||||
\(419\) | −20.9820 | −1.02504 | −0.512518 | − | 0.858676i | \(-0.671287\pi\) | ||||
−0.512518 | + | 0.858676i | \(0.671287\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.16515 | 0.397945 | 0.198973 | − | 0.980005i | \(-0.436240\pi\) | ||||
0.198973 | + | 0.980005i | \(0.436240\pi\) | |||||||
\(422\) | −16.2139 | −0.789279 | ||||||||
\(423\) | 2.96073 | − | 7.51695i | 0.143956 | − | 0.365487i | ||||
\(424\) | −12.0871 | −0.587003 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.74117 | + | 1.08990i | 0.278160 | + | 0.0528058i | ||||
\(427\) | 6.83723 | − | 16.7477i | 0.330877 | − | 0.810479i | ||||
\(428\) | 8.33639 | 0.402955 | ||||||||
\(429\) | −12.7913 | − | 2.42829i | −0.617569 | − | 0.117239i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.2634i | 1.65041i | 0.564833 | + | 0.825205i | \(0.308941\pi\) | ||||
−0.564833 | + | 0.825205i | \(0.691059\pi\) | |||||||
\(432\) | −4.96640 | + | 7.87211i | −0.238946 | + | 0.378747i | ||||
\(433\) | −1.02248 | −0.0491371 | −0.0245685 | − | 0.999698i | \(-0.507821\pi\) | ||||
−0.0245685 | + | 0.999698i | \(0.507821\pi\) | |||||||
\(434\) | −7.51695 | + | 18.4127i | −0.360825 | + | 0.883838i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.95644 | 0.189479 | ||||||||
\(437\) | − | 23.1129i | − | 1.10564i | ||||||
\(438\) | 5.72653 | − | 30.1652i | 0.273624 | − | 1.44135i | ||||
\(439\) | − | 26.9444i | − | 1.28599i | −0.765872 | − | 0.642993i | \(-0.777693\pi\) | ||
0.765872 | − | 0.642993i | \(-0.222307\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.57043 | − | 19.1715i | −0.408116 | − | 0.912930i | ||||
\(442\) | − | 7.25227i | − | 0.344955i | ||||||
\(443\) | 3.93874 | 0.187135 | 0.0935675 | − | 0.995613i | \(-0.470173\pi\) | ||||
0.0935675 | + | 0.995613i | \(0.470173\pi\) | |||||||
\(444\) | 11.5565 | + | 2.19387i | 0.548445 | + | 0.104116i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.69300 | −0.127517 | ||||||||
\(447\) | −30.6327 | − | 5.81529i | −1.44888 | − | 0.275054i | ||||
\(448\) | −20.0005 | − | 8.16515i | −0.944933 | − | 0.385767i | ||||
\(449\) | 36.4144i | 1.71850i | 0.511556 | + | 0.859250i | \(0.329069\pi\) | ||||
−0.511556 | + | 0.859250i | \(0.670931\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.3321i | 1.47537i | ||||||||
\(452\) | −14.2445 | −0.670005 | ||||||||
\(453\) | 1.34552 | − | 7.08767i | 0.0632180 | − | 0.333008i | ||||
\(454\) | 2.96073i | 0.138954i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 22.9129 | + | 4.34977i | 1.07299 | + | 0.203696i | ||||
\(457\) | 34.1652i | 1.59818i | 0.601213 | + | 0.799089i | \(0.294685\pi\) | ||||
−0.601213 | + | 0.799089i | \(0.705315\pi\) | |||||||
\(458\) | − | 4.26188i | − | 0.199145i | ||||||
\(459\) | 11.8348 | + | 7.46644i | 0.552403 | + | 0.348504i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.3229 | 1.55200 | 0.776000 | − | 0.630732i | \(-0.217245\pi\) | ||||
0.776000 | + | 0.630732i | \(0.217245\pi\) | |||||||
\(462\) | −12.9730 | − | 8.41086i | −0.603560 | − | 0.391309i | ||||
\(463\) | 12.7477i | 0.592437i | 0.955120 | + | 0.296219i | \(0.0957257\pi\) | ||||
−0.955120 | + | 0.296219i | \(0.904274\pi\) | |||||||
\(464\) | 9.43581i | 0.438046i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.79129 | −0.268276 | ||||||||
\(467\) | 16.1580i | 0.747704i | 0.927488 | + | 0.373852i | \(0.121963\pi\) | ||||
−0.927488 | + | 0.373852i | \(0.878037\pi\) | |||||||
\(468\) | −5.41022 | − | 2.13094i | −0.250087 | − | 0.0985028i | ||||
\(469\) | 4.16515 | − | 10.2025i | 0.192329 | − | 0.471107i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.626136 | + | 3.29824i | −0.0288508 | + | 0.151975i | ||||
\(472\) | 23.0679 | 1.06179 | ||||||||
\(473\) | 20.2005 | 0.928820 | ||||||||
\(474\) | 0.206906 | − | 1.08990i | 0.00950350 | − | 0.0500607i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.13094 | + | 5.21972i | −0.0976716 | + | 0.239245i | ||||
\(477\) | −10.9941 | − | 4.33030i | −0.503387 | − | 0.198271i | ||||
\(478\) | − | 15.9129i | − | 0.727838i | ||||||
\(479\) | −7.51695 | −0.343458 | −0.171729 | − | 0.985144i | \(-0.554935\pi\) | ||||
−0.171729 | + | 0.985144i | \(0.554935\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 21.0229i | − | 0.958563i | ||||||
\(482\) | 20.9820i | 0.955703i | ||||||||
\(483\) | −13.1319 | + | 20.2548i | −0.597521 | + | 0.921624i | ||||
\(484\) | −1.25227 | −0.0569215 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −13.8202 | + | 10.1351i | −0.626896 | + | 0.459736i | ||||
\(487\) | 21.8348i | 0.989431i | 0.869055 | + | 0.494716i | \(0.164728\pi\) | ||||
−0.869055 | + | 0.494716i | \(0.835272\pi\) | |||||||
\(488\) | − | 20.9820i | − | 0.949809i | ||||||
\(489\) | 6.80664 | + | 1.29217i | 0.307807 | + | 0.0584338i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 26.3381i | − | 1.18862i | −0.804236 | − | 0.594310i | \(-0.797425\pi\) | ||
0.804236 | − | 0.594310i | \(-0.202575\pi\) | |||||||
\(492\) | −2.60986 | + | 13.7477i | −0.117662 | + | 0.619795i | ||||
\(493\) | 14.1857 | 0.638892 | ||||||||
\(494\) | − | 11.8162i | − | 0.531636i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.2474i | 0.549927i | ||||||||
\(497\) | −3.06878 | + | 7.51695i | −0.137654 | + | 0.337181i | ||||
\(498\) | 29.1774 | + | 5.53901i | 1.30747 | + | 0.248209i | ||||
\(499\) | −3.25227 | −0.145592 | −0.0727959 | − | 0.997347i | \(-0.523192\pi\) | ||||
−0.0727959 | + | 0.997347i | \(0.523192\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.1216 | + | 5.90810i | 1.39041 | + | 0.263955i | ||||
\(502\) | −19.4892 | −0.869846 | ||||||||
\(503\) | 5.38601i | 0.240150i | 0.992765 | + | 0.120075i | \(0.0383135\pi\) | ||||
−0.992765 | + | 0.120075i | \(0.961686\pi\) | |||||||
\(504\) | −17.6081 | − | 16.8301i | −0.784328 | − | 0.749672i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 17.7722i | 0.790071i | ||||||||
\(507\) | 2.26129 | − | 11.9116i | 0.100428 | − | 0.529013i | ||||
\(508\) | 6.46099i | 0.286660i | ||||||||
\(509\) | 22.5509 | 0.999549 | 0.499774 | − | 0.866156i | \(-0.333416\pi\) | ||||
0.499774 | + | 0.866156i | \(0.333416\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 39.4955 | + | 16.1240i | 1.74718 | + | 0.713282i | ||||
\(512\) | −18.4606 | −0.815850 | ||||||||
\(513\) | 19.2826 | + | 12.1652i | 0.851350 | + | 0.537105i | ||||
\(514\) | − | 5.30352i | − | 0.233928i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.86345 | + | 1.68263i | 0.390192 | + | 0.0740738i | ||||
\(517\) | 8.26424 | 0.363461 | ||||||||
\(518\) | 9.43581 | − | 23.1129i | 0.414586 | − | 1.01552i | ||||
\(519\) | 13.7477 | + | 2.60986i | 0.603458 | + | 0.114560i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.1580 | −0.707896 | −0.353948 | − | 0.935265i | \(-0.615161\pi\) | ||||
−0.353948 | + | 0.935265i | \(0.615161\pi\) | |||||||
\(522\) | −6.36703 | + | 16.1652i | −0.278677 | + | 0.707529i | ||||
\(523\) | −14.6969 | −0.642652 | −0.321326 | − | 0.946969i | \(-0.604129\pi\) | ||||
−0.321326 | + | 0.946969i | \(0.604129\pi\) | |||||||
\(524\) | 2.13094 | 0.0930906 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −31.3739 | −1.36797 | ||||||||
\(527\) | 18.4127 | 0.802070 | ||||||||
\(528\) | −9.35414 | − | 1.77578i | −0.407087 | − | 0.0772811i | ||||
\(529\) | 4.74773 | 0.206423 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.9820 | + | 8.26424i | 0.910540 | + | 0.358638i | ||||
\(532\) | −3.47197 | + | 8.50455i | −0.150529 | + | 0.368719i | ||||
\(533\) | 25.0092 | 1.08327 | ||||||||
\(534\) | −2.66970 | + | 14.0629i | −0.115529 | + | 0.608562i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 12.7819i | − | 0.552096i | ||||||
\(537\) | 24.6297 | + | 4.67569i | 1.06285 | + | 0.201771i | ||||
\(538\) | −23.0679 | −0.994527 | ||||||||
\(539\) | 15.0339 | − | 15.3439i | 0.647556 | − | 0.660909i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.58258 | −0.368994 | −0.184497 | − | 0.982833i | \(-0.559066\pi\) | ||||
−0.184497 | + | 0.982833i | \(0.559066\pi\) | |||||||
\(542\) | 28.4989i | 1.22413i | ||||||||
\(543\) | −20.8410 | − | 3.95644i | −0.894372 | − | 0.169787i | ||||
\(544\) | 11.2250i | 0.481267i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −6.71352 | + | 10.3550i | −0.287312 | + | 0.443154i | ||||
\(547\) | − | 4.66970i | − | 0.199662i | −0.995004 | − | 0.0998309i | \(-0.968170\pi\) | ||
0.995004 | − | 0.0998309i | \(-0.0318302\pi\) | |||||||
\(548\) | 8.33639 | 0.356113 | ||||||||
\(549\) | 7.51695 | − | 19.0847i | 0.320816 | − | 0.814514i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.1129 | 0.984643 | ||||||||
\(552\) | −5.22202 | + | 27.5076i | −0.222264 | + | 1.17080i | ||||
\(553\) | 1.42701 | + | 0.582576i | 0.0606828 | + | 0.0247736i | ||||
\(554\) | − | 20.6115i | − | 0.875700i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.93825i | 0.0822002i | ||||||||
\(557\) | −6.18546 | −0.262086 | −0.131043 | − | 0.991377i | \(-0.541833\pi\) | ||||
−0.131043 | + | 0.991377i | \(0.541833\pi\) | |||||||
\(558\) | −8.26424 | + | 20.9820i | −0.349853 | + | 0.888238i | ||||
\(559\) | − | 16.1240i | − | 0.681970i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.66970 | + | 14.0629i | −0.112715 | + | 0.593737i | ||||
\(562\) | 16.8693i | 0.711589i | ||||||||
\(563\) | − | 9.64789i | − | 0.406610i | −0.979115 | − | 0.203305i | \(-0.934832\pi\) | ||
0.979115 | − | 0.203305i | \(-0.0651683\pi\) | |||||||
\(564\) | 3.62614 | + | 0.688383i | 0.152688 | + | 0.0289862i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 25.8059 | 1.08470 | ||||||||
\(567\) | −9.98639 | − | 21.6165i | −0.419389 | − | 0.907807i | ||||
\(568\) | 9.41742i | 0.395146i | ||||||||
\(569\) | − | 0.411031i | − | 0.0172313i | −0.999963 | − | 0.00861566i | \(-0.997258\pi\) | ||
0.999963 | − | 0.00861566i | \(-0.00274248\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.7477 | −1.24490 | −0.622452 | − | 0.782658i | \(-0.713863\pi\) | ||||
−0.622452 | + | 0.782658i | \(0.713863\pi\) | |||||||
\(572\) | − | 5.94807i | − | 0.248701i | ||||||
\(573\) | 29.1523 | + | 5.53426i | 1.21786 | + | 0.231197i | ||||
\(574\) | 27.4955 | + | 11.2250i | 1.14764 | + | 0.468521i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −22.7913 | − | 8.97689i | −0.949637 | − | 0.374037i | ||||
\(577\) | −23.9837 | −0.998453 | −0.499226 | − | 0.866472i | \(-0.666382\pi\) | ||||
−0.499226 | + | 0.866472i | \(0.666382\pi\) | |||||||
\(578\) | 10.7168 | 0.445760 | ||||||||
\(579\) | −18.7183 | − | 3.55346i | −0.777904 | − | 0.147677i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.5960 | + | 38.2022i | −0.647030 | + | 1.58489i | ||||
\(582\) | 4.16820 | − | 21.9564i | 0.172777 | − | 0.910124i | ||||
\(583\) | − | 12.0871i | − | 0.500597i | ||||||
\(584\) | 49.4809 | 2.04753 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 2.34279i | − | 0.0967797i | ||||||
\(587\) | − | 3.25507i | − | 0.134351i | −0.997741 | − | 0.0671755i | \(-0.978601\pi\) | ||
0.997741 | − | 0.0671755i | \(-0.0213987\pi\) | |||||||
\(588\) | 7.87458 | − | 5.48024i | 0.324742 | − | 0.226001i | ||||
\(589\) | 30.0000 | 1.23613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.13960 | + | 6.00295i | −0.0468767 | + | 0.246928i | ||||
\(592\) | − | 15.3739i | − | 0.631862i | ||||||
\(593\) | 5.38601i | 0.221177i | 0.993866 | + | 0.110588i | \(0.0352735\pi\) | ||||
−0.993866 | + | 0.110588i | \(0.964726\pi\) | |||||||
\(594\) | −14.8270 | − | 9.35414i | −0.608359 | − | 0.383805i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 14.2445i | − | 0.583477i | ||||||
\(597\) | 13.3745 | + | 2.53901i | 0.547384 | + | 0.103915i | ||||
\(598\) | 14.1857 | 0.580096 | ||||||||
\(599\) | 36.4144i | 1.48785i | 0.668263 | + | 0.743925i | \(0.267038\pi\) | ||||
−0.668263 | + | 0.743925i | \(0.732962\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2.85403i | − | 0.116418i | −0.998304 | − | 0.0582091i | \(-0.981461\pi\) | ||
0.998304 | − | 0.0582091i | \(-0.0185390\pi\) | |||||||
\(602\) | 7.23698 | − | 17.7269i | 0.294957 | − | 0.722495i | ||||
\(603\) | 4.57923 | − | 11.6261i | 0.186481 | − | 0.473453i | ||||
\(604\) | 3.29583 | 0.134106 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.49545 | + | 34.2155i | −0.263860 | + | 1.38991i | ||||
\(607\) | 21.0229 | 0.853294 | 0.426647 | − | 0.904418i | \(-0.359695\pi\) | ||||
0.426647 | + | 0.904418i | \(0.359695\pi\) | |||||||
\(608\) | 18.2890i | 0.741716i | ||||||||
\(609\) | −20.2548 | − | 13.1319i | −0.820765 | − | 0.532130i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 6.59649i | − | 0.266865i | ||||||
\(612\) | −2.34279 | + | 5.94807i | −0.0947016 | + | 0.240437i | ||||
\(613\) | 36.5826i | 1.47756i | 0.673949 | + | 0.738778i | \(0.264597\pi\) | ||||
−0.673949 | + | 0.738778i | \(0.735403\pi\) | |||||||
\(614\) | −14.4718 | −0.584036 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.41742 | − | 23.0679i | 0.379439 | − | 0.929432i | ||||
\(617\) | −1.32888 | −0.0534985 | −0.0267493 | − | 0.999642i | \(-0.508516\pi\) | ||||
−0.0267493 | + | 0.999642i | \(0.508516\pi\) | |||||||
\(618\) | −1.55834 | + | 8.20871i | −0.0626855 | + | 0.330203i | ||||
\(619\) | − | 13.2699i | − | 0.533363i | −0.963785 | − | 0.266682i | \(-0.914073\pi\) | ||
0.963785 | − | 0.266682i | \(-0.0859272\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.6046 | + | 23.1494i | −0.586063 | + | 0.928953i | ||||
\(622\) | 13.5678 | 0.544018 | ||||||||
\(623\) | −18.4127 | − | 7.51695i | −0.737689 | − | 0.301160i | ||||
\(624\) | −1.41742 | + | 7.46644i | −0.0567424 | + | 0.298897i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −25.2439 | −1.00895 | ||||||||
\(627\) | −4.34977 | + | 22.9129i | −0.173713 | + | 0.915052i | ||||
\(628\) | −1.53371 | −0.0612019 | ||||||||
\(629\) | −23.1129 | −0.921572 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.7477 | 1.34348 | 0.671738 | − | 0.740789i | \(-0.265548\pi\) | ||||
0.671738 | + | 0.740789i | \(0.265548\pi\) | |||||||
\(632\) | 1.78780 | 0.0711148 | ||||||||
\(633\) | 4.76413 | − | 25.0956i | 0.189357 | − | 0.997461i | ||||
\(634\) | −1.46099 | −0.0580231 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.00682 | − | 5.30352i | 0.0399229 | − | 0.210298i | ||||
\(637\) | −12.2474 | − | 12.0000i | −0.485262 | − | 0.475457i | ||||
\(638\) | −17.7722 | −0.703608 | ||||||||
\(639\) | −3.37386 | + | 8.56585i | −0.133468 | + | 0.338860i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.78780i | 0.0706138i | 0.999377 | + | 0.0353069i | \(0.0112409\pi\) | ||||
−0.999377 | + | 0.0353069i | \(0.988759\pi\) | |||||||
\(642\) | 3.74166 | − | 19.7096i | 0.147671 | − | 0.777876i | ||||
\(643\) | 20.6184 | 0.813110 | 0.406555 | − | 0.913626i | \(-0.366730\pi\) | ||||
0.406555 | + | 0.913626i | \(0.366730\pi\) | |||||||
\(644\) | −10.2100 | − | 4.16820i | −0.402329 | − | 0.164250i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.9909 | −0.511120 | ||||||||
\(647\) | − | 40.8398i | − | 1.60558i | −0.596263 | − | 0.802790i | \(-0.703348\pi\) | ||
0.596263 | − | 0.802790i | \(-0.296652\pi\) | |||||||
\(648\) | −20.2005 | − | 18.8348i | −0.793550 | − | 0.739903i | ||||
\(649\) | 23.0679i | 0.905494i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.2902 | − | 17.0449i | −1.03039 | − | 0.668041i | ||||
\(652\) | 3.16515i | 0.123957i | ||||||||
\(653\) | −14.4740 | −0.566410 | −0.283205 | − | 0.959059i | \(-0.591398\pi\) | ||||
−0.283205 | + | 0.959059i | \(0.591398\pi\) | |||||||
\(654\) | 1.77578 | − | 9.35414i | 0.0694387 | − | 0.365776i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 18.2890 | 0.714064 | ||||||||
\(657\) | 45.0066 | + | 17.7269i | 1.75587 | + | 0.691592i | ||||
\(658\) | 2.96073 | − | 7.25227i | 0.115421 | − | 0.282723i | ||||
\(659\) | − | 14.4740i | − | 0.563825i | −0.959440 | − | 0.281913i | \(-0.909031\pi\) | ||
0.959440 | − | 0.281913i | \(-0.0909688\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 43.5796i | − | 1.69505i | −0.530756 | − | 0.847525i | \(-0.678092\pi\) | ||
0.530756 | − | 0.847525i | \(-0.321908\pi\) | |||||||
\(662\) | 18.6900 | 0.726409 | ||||||||
\(663\) | 11.2250 | + | 2.13094i | 0.435942 | + | 0.0827589i | ||||
\(664\) | 47.8606i | 1.85735i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.3739 | − | 26.3381i | 0.401979 | − | 1.02058i | ||||
\(667\) | 27.7477i | 1.07440i | ||||||||
\(668\) | 14.4718i | 0.559932i | ||||||||
\(669\) | 0.791288 | − | 4.16820i | 0.0305930 | − | 0.161152i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.9820 | 0.810000 | ||||||||
\(672\) | 10.3911 | − | 16.0274i | 0.400845 | − | 0.618269i | ||||
\(673\) | − | 7.49545i | − | 0.288929i | −0.989510 | − | 0.144464i | \(-0.953854\pi\) | ||
0.989510 | − | 0.144464i | \(-0.0461459\pi\) | |||||||
\(674\) | − | 2.19883i | − | 0.0846957i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.53901 | 0.213039 | ||||||||
\(677\) | − | 10.7720i | − | 0.414002i | −0.978341 | − | 0.207001i | \(-0.933630\pi\) | ||
0.978341 | − | 0.207001i | \(-0.0663704\pi\) | |||||||
\(678\) | −6.39342 | + | 33.6780i | −0.245538 | + | 1.29340i | ||||
\(679\) | 28.7477 | + | 11.7362i | 1.10324 | + | 0.450394i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.58258 | − | 0.869953i | −0.175605 | − | 0.0333367i | ||||
\(682\) | −23.0679 | −0.883315 | ||||||||
\(683\) | −10.1242 | −0.387391 | −0.193696 | − | 0.981062i | \(-0.562047\pi\) | ||||
−0.193696 | + | 0.981062i | \(0.562047\pi\) | |||||||
\(684\) | −3.81713 | + | 9.69126i | −0.145952 | + | 0.370554i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.07901 | − | 18.6900i | −0.308458 | − | 0.713589i | ||||
\(687\) | 6.59649 | + | 1.25227i | 0.251672 | + | 0.0477772i | ||||
\(688\) | − | 11.7913i | − | 0.449539i | ||||||
\(689\) | −9.64789 | −0.367555 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.83723i | 0.260101i | 0.991507 | + | 0.130050i | \(0.0415139\pi\) | ||||
−0.991507 | + | 0.130050i | \(0.958486\pi\) | |||||||
\(692\) | 6.39283i | 0.243019i | ||||||||
\(693\) | 16.8301 | − | 17.6081i | 0.639323 | − | 0.668877i | ||||
\(694\) | 3.87841 | 0.147222 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −27.5076 | − | 5.22202i | −1.04267 | − | 0.197940i | ||||
\(697\) | − | 27.4955i | − | 1.04146i | ||||||
\(698\) | − | 10.2100i | − | 0.386452i | ||||||
\(699\) | 1.70166 | − | 8.96368i | 0.0643627 | − | 0.339037i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 17.1317i | − | 0.647056i | −0.946219 | − | 0.323528i | \(-0.895131\pi\) | ||
0.946219 | − | 0.323528i | \(-0.104869\pi\) | |||||||
\(702\) | −7.46644 | + | 11.8348i | −0.281803 | + | 0.446678i | ||||
\(703\) | −37.6581 | −1.42030 | ||||||||
\(704\) | − | 25.0571i | − | 0.944374i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 33.6749i | − | 1.26737i | ||||||
\(707\) | −44.7986 | − | 18.2890i | −1.68483 | − | 0.687827i | ||||
\(708\) | −1.92148 | + | 10.1216i | −0.0722135 | + | 0.380393i | ||||
\(709\) | −23.4955 | −0.882390 | −0.441195 | − | 0.897411i | \(-0.645445\pi\) | ||||
−0.441195 | + | 0.897411i | \(0.645445\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.62614 | + | 0.640492i | 0.0609849 | + | 0.0240203i | ||||
\(712\) | −23.0679 | −0.864506 | ||||||||
\(713\) | 36.0159i | 1.34881i | ||||||||
\(714\) | 11.3845 | + | 7.38094i | 0.426053 | + | 0.276225i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.4531i | 0.428021i | ||||||||
\(717\) | 24.6297 | + | 4.67569i | 0.919815 | + | 0.174617i | ||||
\(718\) | 19.7913i | 0.738604i | ||||||||
\(719\) | −5.94807 | −0.221826 | −0.110913 | − | 0.993830i | \(-0.535377\pi\) | ||||
−0.110913 | + | 0.993830i | \(0.535377\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.7477 | − | 4.38774i | −0.400266 | − | 0.163408i | ||||
\(722\) | −0.277352 | −0.0103220 | ||||||||
\(723\) | −32.4756 | − | 6.16515i | −1.20778 | − | 0.229284i | ||||
\(724\) | − | 9.69126i | − | 0.360173i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.562063 | + | 2.96073i | −0.0208601 | + | 0.109883i | ||||
\(727\) | 11.3317 | 0.420269 | 0.210134 | − | 0.977673i | \(-0.432610\pi\) | ||||
0.210134 | + | 0.977673i | \(0.432610\pi\) | |||||||
\(728\) | −18.4127 | − | 7.51695i | −0.682420 | − | 0.278597i | ||||
\(729\) | −11.6261 | − | 24.3687i | −0.430598 | − | 0.902544i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.7269 | −0.655653 | ||||||||
\(732\) | 9.20635 | + | 1.74773i | 0.340276 | + | 0.0645979i | ||||
\(733\) | 12.6520 | 0.467312 | 0.233656 | − | 0.972319i | \(-0.424931\pi\) | ||||
0.233656 | + | 0.972319i | \(0.424931\pi\) | |||||||
\(734\) | −1.00682 | −0.0371623 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −21.9564 | −0.809325 | ||||||||
\(737\) | 12.7819 | 0.470829 | ||||||||
\(738\) | 31.3321 | + | 12.3409i | 1.15335 | + | 0.454275i | ||||
\(739\) | −50.8258 | −1.86966 | −0.934828 | − | 0.355101i | \(-0.884446\pi\) | ||||
−0.934828 | + | 0.355101i | \(0.884446\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.2890 | + | 3.47197i | 0.671862 | + | 0.127546i | ||||
\(742\) | −10.6070 | − | 4.33030i | −0.389396 | − | 0.158970i | ||||
\(743\) | −14.4740 | −0.530998 | −0.265499 | − | 0.964111i | \(-0.585537\pi\) | ||||
−0.265499 | + | 0.964111i | \(0.585537\pi\) | |||||||
\(744\) | −35.7042 | − | 6.77806i | −1.30898 | − | 0.248496i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 29.5884i | − | 1.08331i | ||||||
\(747\) | −17.1464 | + | 43.5328i | −0.627355 | + | 1.59278i | ||||
\(748\) | −6.53940 | −0.239104 | ||||||||
\(749\) | 25.8059 | + | 10.5352i | 0.942928 | + | 0.384949i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.2523 | −0.410601 | −0.205301 | − | 0.978699i | \(-0.565817\pi\) | ||||
−0.205301 | + | 0.978699i | \(0.565817\pi\) | |||||||
\(752\) | − | 4.82395i | − | 0.175911i | ||||||
\(753\) | 5.72653 | − | 30.1652i | 0.208686 | − | 1.09928i | ||||
\(754\) | 14.1857i | 0.516613i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.85131 | − | 6.32409i | 0.321919 | − | 0.230005i | ||||
\(757\) | − | 33.7477i | − | 1.22658i | −0.789857 | − | 0.613291i | \(-0.789845\pi\) | ||
0.789857 | − | 0.613291i | \(-0.210155\pi\) | |||||||
\(758\) | −19.0532 | −0.692043 | ||||||||
\(759\) | −27.5076 | − | 5.22202i | −0.998462 | − | 0.189547i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.26188 | −0.154493 | −0.0772466 | − | 0.997012i | \(-0.524613\pi\) | ||||
−0.0772466 | + | 0.997012i | \(0.524613\pi\) | |||||||
\(762\) | 15.2756 | + | 2.89991i | 0.553377 | + | 0.105053i | ||||
\(763\) | 12.2474 | + | 5.00000i | 0.443387 | + | 0.181012i | ||||
\(764\) | 13.5561i | 0.490443i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30.7142i | 1.10975i | ||||||||
\(767\) | 18.4127 | 0.664844 | ||||||||
\(768\) | 5.04790 | − | 26.5904i | 0.182150 | − | 0.959497i | ||||
\(769\) | 30.3097i | 1.09299i | 0.837461 | + | 0.546497i | \(0.184039\pi\) | ||||
−0.837461 | + | 0.546497i | \(0.815961\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.20871 | + | 1.55834i | 0.295630 | + | 0.0561221i | ||||
\(772\) | − | 8.70417i | − | 0.313270i | ||||||
\(773\) | − | 15.5960i | − | 0.560948i | −0.959862 | − | 0.280474i | \(-0.909508\pi\) | ||
0.959862 | − | 0.280474i | \(-0.0904916\pi\) | |||||||
\(774\) | 7.95644 | − | 20.2005i | 0.285988 | − | 0.726092i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 36.0159 | 1.29289 | ||||||||
\(777\) | 33.0013 | + | 21.3959i | 1.18392 | + | 0.767574i | ||||
\(778\) | 14.4519i | 0.518125i | ||||||||
\(779\) | − | 44.7986i | − | 1.60508i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.41742 | −0.336982 | ||||||||
\(782\) | − | 15.5960i | − | 0.557711i | ||||||
\(783\) | −23.1494 | − | 14.6046i | −0.827291 | − | 0.521926i | ||||
\(784\) | −8.95644 | − | 8.77548i | −0.319873 | − | 0.313410i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.956439 | − | 5.03815i | 0.0341151 | − | 0.179705i | ||||
\(787\) | −6.32599 | −0.225497 | −0.112749 | − | 0.993624i | \(-0.535965\pi\) | ||||
−0.112749 | + | 0.993624i | \(0.535965\pi\) | |||||||
\(788\) | −2.79143 | −0.0994406 | ||||||||
\(789\) | 9.21861 | − | 48.5601i | 0.328191 | − | 1.72878i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −44.0949 | − | 18.0017i | −1.56783 | − | 0.640065i | ||||
\(792\) | 10.3537 | − | 26.2867i | 0.367901 | − | 0.934059i | ||||
\(793\) | − | 16.7477i | − | 0.594729i | ||||||
\(794\) | 9.64789 | 0.342391 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.21929i | 0.220437i | ||||||||
\(797\) | 17.7269i | 0.627919i | 0.949436 | + | 0.313960i | \(0.101656\pi\) | ||||
−0.949436 | + | 0.313960i | \(0.898344\pi\) | |||||||
\(798\) | 18.5488 | + | 12.0258i | 0.656621 | + | 0.425710i | ||||
\(799\) | −7.25227 | −0.256567 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.9820 | − | 8.26424i | −0.741362 | − | 0.292003i | ||||
\(802\) | 22.2087i | 0.784217i | ||||||||
\(803\) | 49.4809i | 1.74614i | ||||||||
\(804\) | 5.60839 | + | 1.06469i | 0.197793 | + | 0.0375488i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 18.4127i | 0.648559i | ||||||||
\(807\) | 6.77806 | − | 35.7042i | 0.238599 | − | 1.25685i | ||||
\(808\) | −56.1249 | −1.97447 | ||||||||
\(809\) | − | 28.5369i | − | 1.00330i | −0.865070 | − | 0.501652i | \(-0.832726\pi\) | ||
0.865070 | − | 0.501652i | \(-0.167274\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.6745i | 0.480175i | 0.970751 | + | 0.240088i | \(0.0771762\pi\) | ||||
−0.970751 | + | 0.240088i | \(0.922824\pi\) | |||||||
\(812\) | 4.16820 | − | 10.2100i | 0.146275 | − | 0.358299i | ||||
\(813\) | −44.1103 | − | 8.37386i | −1.54701 | − | 0.293684i | ||||
\(814\) | 28.9564 | 1.01492 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.20871 | + | 1.55834i | 0.287362 | + | 0.0545527i | ||||
\(817\) | −28.8826 | −1.01048 | ||||||||
\(818\) | 34.8917i | 1.21996i | ||||||||
\(819\) | −14.0547 | − | 13.4337i | −0.491112 | − | 0.469412i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 17.1317i | − | 0.597901i | −0.954269 | − | 0.298950i | \(-0.903363\pi\) | ||
0.954269 | − | 0.298950i | \(-0.0966365\pi\) | |||||||
\(822\) | 3.74166 | − | 19.7096i | 0.130505 | − | 0.687451i | ||||
\(823\) | − | 2.25227i | − | 0.0785093i | −0.999229 | − | 0.0392546i | \(-0.987502\pi\) | ||
0.999229 | − | 0.0392546i | \(-0.0124984\pi\) | |||||||
\(824\) | −13.4650 | −0.469076 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 20.2432 | + | 8.26424i | 0.704350 | + | 0.287550i | ||||
\(827\) | −14.8850 | −0.517602 | −0.258801 | − | 0.965931i | \(-0.583327\pi\) | ||||
−0.258801 | + | 0.965931i | \(0.583327\pi\) | |||||||
\(828\) | −11.6346 | − | 4.58258i | −0.404332 | − | 0.159256i | ||||
\(829\) | 15.2082i | 0.528202i | 0.964495 | + | 0.264101i | \(0.0850752\pi\) | ||||
−0.964495 | + | 0.264101i | \(0.914925\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 31.9022 | + | 6.05630i | 1.10668 | + | 0.210091i | ||||
\(832\) | −20.0005 | −0.693391 | ||||||||
\(833\) | −13.1930 | + | 13.4650i | −0.457109 | + | 0.466535i | ||||
\(834\) | 4.58258 | + | 0.869953i | 0.158682 | + | 0.0301240i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10.6547 | −0.368501 | ||||||||
\(837\) | −30.0473 | − | 18.9564i | −1.03859 | − | 0.655230i | ||||
\(838\) | −23.0679 | −0.796867 | ||||||||
\(839\) | −7.51695 | −0.259514 | −0.129757 | − | 0.991546i | \(-0.541420\pi\) | ||||
−0.129757 | + | 0.991546i | \(0.541420\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.25227 | 0.0431818 | ||||||||
\(842\) | 8.97689 | 0.309364 | ||||||||
\(843\) | −26.1101 | − | 4.95673i | −0.899280 | − | 0.170719i | ||||
\(844\) | 11.6697 | 0.401688 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.25507 | − | 8.26424i | 0.111912 | − | 0.284131i | ||||
\(847\) | −3.87650 | − | 1.58258i | −0.133198 | − | 0.0543779i | ||||
\(848\) | −7.05541 | −0.242284 | ||||||||
\(849\) | −7.58258 | + | 39.9421i | −0.260233 | + | 1.37081i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 45.2097i | − | 1.54977i | ||||||
\(852\) | −4.13212 | − | 0.784439i | −0.141564 | − | 0.0268745i | ||||
\(853\) | −17.5510 | −0.600934 | −0.300467 | − | 0.953792i | \(-0.597142\pi\) | ||||
−0.300467 | + | 0.953792i | \(0.597142\pi\) | |||||||
\(854\) | 7.51695 | − | 18.4127i | 0.257225 | − | 0.630069i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 32.3303 | 1.10503 | ||||||||
\(857\) | − | 46.7879i | − | 1.59824i | −0.601169 | − | 0.799122i | \(-0.705298\pi\) | ||
0.601169 | − | 0.799122i | \(-0.294702\pi\) | |||||||
\(858\) | −14.0629 | − | 2.66970i | −0.480100 | − | 0.0911420i | ||||
\(859\) | 47.9673i | 1.63662i | 0.574774 | + | 0.818312i | \(0.305090\pi\) | ||||
−0.574774 | + | 0.818312i | \(0.694910\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −25.4529 | + | 39.2589i | −0.867432 | + | 1.33794i | ||||
\(862\) | 37.6697i | 1.28303i | ||||||||
\(863\) | 22.8582 | 0.778104 | 0.389052 | − | 0.921216i | \(-0.372803\pi\) | ||||
0.389052 | + | 0.921216i | \(0.372803\pi\) | |||||||
\(864\) | 11.5565 | − | 18.3178i | 0.393159 | − | 0.623185i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.12413 | −0.0381993 | ||||||||
\(867\) | −3.14892 | + | 16.5873i | −0.106943 | + | 0.563335i | ||||
\(868\) | 5.41022 | − | 13.2523i | 0.183635 | − | 0.449811i | ||||
\(869\) | 1.78780i | 0.0606469i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 10.2025i | − | 0.345698i | ||||||
\(872\) | 15.3439 | 0.519610 | ||||||||
\(873\) | 32.7591 | + | 12.9030i | 1.10873 | + | 0.436699i | ||||
\(874\) | − | 25.4107i | − | 0.859529i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.12159 | + | 21.7109i | −0.139256 | + | 0.733545i | ||||
\(877\) | 31.4955i | 1.06353i | 0.846893 | + | 0.531763i | \(0.178470\pi\) | ||||
−0.846893 | + | 0.531763i | \(0.821530\pi\) | |||||||
\(878\) | − | 29.6230i | − | 0.999729i | ||||||
\(879\) | 3.62614 | + | 0.688383i | 0.122307 | + | 0.0232186i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.8917 | 1.17553 | 0.587766 | − | 0.809031i | \(-0.300007\pi\) | ||||
0.587766 | + | 0.809031i | \(0.300007\pi\) | |||||||
\(882\) | −9.42246 | − | 21.0775i | −0.317271 | − | 0.709715i | ||||
\(883\) | 15.4174i | 0.518838i | 0.965765 | + | 0.259419i | \(0.0835310\pi\) | ||||
−0.965765 | + | 0.259419i | \(0.916469\pi\) | |||||||
\(884\) | 5.21972i | 0.175558i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.33030 | 0.145479 | ||||||||
\(887\) | 40.2778i | 1.35239i | 0.736721 | + | 0.676197i | \(0.236373\pi\) | ||||
−0.736721 | + | 0.676197i | \(0.763627\pi\) | |||||||
\(888\) | 44.8184 | + | 8.50830i | 1.50401 | + | 0.285520i | ||||
\(889\) | −8.16515 | + | 20.0005i | −0.273850 | + | 0.670794i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.8348 | − | 20.2005i | 0.630991 | − | 0.676742i | ||||
\(892\) | 1.93825 | 0.0648975 | ||||||||
\(893\) | −11.8162 | −0.395414 | ||||||||
\(894\) | −33.6780 | − | 6.39342i | −1.12636 | − | 0.213828i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.56888 | − | 0.640492i | −0.0524126 | − | 0.0213973i | ||||
\(897\) | −4.16820 | + | 21.9564i | −0.139172 | + | 0.733104i | ||||
\(898\) | 40.0345i | 1.33597i | ||||||||
\(899\) | −36.0159 | −1.20120 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.6070i | 0.353371i | ||||||||
\(902\) | 34.4470i | 1.14696i | ||||||||
\(903\) | 25.3110 | + | 16.4100i | 0.842298 | + | 0.546091i | ||||
\(904\) | −55.2432 | −1.83736 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.47928 | − | 7.79228i | 0.0491459 | − | 0.258881i | ||||
\(907\) | 1.49545i | 0.0496557i | 0.999692 | + | 0.0248279i | \(0.00790377\pi\) | ||||
−0.999692 | + | 0.0248279i | \(0.992096\pi\) | |||||||
\(908\) | − | 2.13094i | − | 0.0707178i | ||||||
\(909\) | −51.0498 | − | 20.1072i | −1.69321 | − | 0.666912i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.4873i | 0.347461i | 0.984793 | + | 0.173730i | \(0.0555821\pi\) | ||||
−0.984793 | + | 0.173730i | \(0.944418\pi\) | |||||||
\(912\) | 13.3745 | + | 2.53901i | 0.442875 | + | 0.0840752i | ||||
\(913\) | −47.8606 | −1.58396 | ||||||||
\(914\) | 37.5617i | 1.24243i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.06743i | 0.101351i | ||||||||
\(917\) | 6.59649 | + | 2.69300i | 0.217835 | + | 0.0889308i | ||||
\(918\) | 13.0114 | + | 8.20871i | 0.429440 | + | 0.270928i | ||||
\(919\) | 24.0780 | 0.794261 | 0.397130 | − | 0.917762i | \(-0.370006\pi\) | ||||
0.397130 | + | 0.917762i | \(0.370006\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.25227 | − | 22.3993i | 0.140117 | − | 0.738083i | ||||
\(922\) | 36.6356 | 1.20653 | ||||||||
\(923\) | 7.51695i | 0.247423i | ||||||||
\(924\) | 9.33715 | + | 6.05360i | 0.307170 | + | 0.199149i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 14.0150i | 0.460563i | ||||||||
\(927\) | −12.2474 | − | 4.82395i | −0.402259 | − | 0.158439i | ||||
\(928\) | − | 21.9564i | − | 0.720755i | ||||||
\(929\) | 7.51695 | 0.246623 | 0.123312 | − | 0.992368i | \(-0.460649\pi\) | ||||
0.123312 | + | 0.992368i | \(0.460649\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.4955 | + | 21.9387i | −0.704485 | + | 0.719012i | ||||
\(932\) | 4.16820 | 0.136534 | ||||||||
\(933\) | −3.98663 | + | 21.0000i | −0.130516 | + | 0.687509i | ||||
\(934\) | 17.7644i | 0.581268i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −20.9820 | − | 8.26424i | −0.685817 | − | 0.270125i | ||||
\(937\) | −36.2311 | −1.18362 | −0.591809 | − | 0.806078i | \(-0.701586\pi\) | ||||
−0.591809 | + | 0.806078i | \(0.701586\pi\) | |||||||
\(938\) | 4.57923 | − | 11.2168i | 0.149517 | − | 0.366241i | ||||
\(939\) | 7.41742 | − | 39.0721i | 0.242058 | − | 1.27507i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.2439 | −0.822926 | −0.411463 | − | 0.911426i | \(-0.634982\pi\) | ||||
−0.411463 | + | 0.911426i | \(0.634982\pi\) | |||||||
\(942\) | −0.688383 | + | 3.62614i | −0.0224287 | + | 0.118146i | ||||
\(943\) | 53.7821 | 1.75139 | ||||||||
\(944\) | 13.4650 | 0.438249 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.2087 | 0.722068 | ||||||||
\(947\) | −28.9479 | −0.940681 | −0.470340 | − | 0.882485i | \(-0.655869\pi\) | ||||
−0.470340 | + | 0.882485i | \(0.655869\pi\) | |||||||
\(948\) | −0.148917 | + | 0.784439i | −0.00483662 | + | 0.0254774i | ||||
\(949\) | 39.4955 | 1.28208 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.429283 | − | 2.26129i | 0.0139204 | − | 0.0733275i | ||||
\(952\) | −8.26424 | + | 20.2432i | −0.267846 | + | 0.656085i | ||||
\(953\) | −5.26761 | −0.170635 | −0.0853173 | − | 0.996354i | \(-0.527190\pi\) | ||||
−0.0853173 | + | 0.996354i | \(0.527190\pi\) | |||||||
\(954\) | −12.0871 | − | 4.76080i | −0.391335 | − | 0.154137i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.4531i | 0.370419i | ||||||||
\(957\) | 5.22202 | − | 27.5076i | 0.168804 | − | 0.889194i | ||||
\(958\) | −8.26424 | −0.267006 | ||||||||
\(959\) | 25.8059 | + | 10.5352i | 0.833317 | + | 0.340200i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.7477 | −0.507991 | ||||||||
\(962\) | − | 23.1129i | − | 0.745190i | ||||||
\(963\) | 29.4068 | + | 11.5826i | 0.947622 | + | 0.373243i | ||||
\(964\) | − | 15.1015i | − | 0.486386i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −14.4374 | + | 22.2684i | −0.464515 | + | 0.716474i | ||||
\(967\) | 14.7477i | 0.474255i | 0.971479 | + | 0.237127i | \(0.0762059\pi\) | ||||
−0.971479 | + | 0.237127i | \(0.923794\pi\) | |||||||
\(968\) | −4.85658 | −0.156096 | ||||||||
\(969\) | 3.81713 | − | 20.1072i | 0.122624 | − | 0.645935i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.3748 | 0.878499 | 0.439250 | − | 0.898365i | \(-0.355244\pi\) | ||||
0.439250 | + | 0.898365i | \(0.355244\pi\) | |||||||
\(972\) | 9.94688 | − | 7.29457i | 0.319046 | − | 0.233974i | ||||
\(973\) | −2.44949 | + | 6.00000i | −0.0785270 | + | 0.192351i | ||||
\(974\) | 24.0055i | 0.769187i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 12.2474i | − | 0.392031i | ||||||
\(977\) | −1.32888 | −0.0425145 | −0.0212572 | − | 0.999774i | \(-0.506767\pi\) | ||||
−0.0212572 | + | 0.999774i | \(0.506767\pi\) | |||||||
\(978\) | 7.48331 | + | 1.42063i | 0.239290 | + | 0.0454267i | ||||
\(979\) | − | 23.0679i | − | 0.737253i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.9564 | + | 5.49707i | 0.445595 | + | 0.175508i | ||||
\(982\) | − | 28.9564i | − | 0.924037i | ||||||
\(983\) | − | 15.5960i | − | 0.497434i | −0.968576 | − | 0.248717i | \(-0.919991\pi\) | ||
0.968576 | − | 0.248717i | \(-0.0800089\pi\) | |||||||
\(984\) | −10.1216 | + | 53.3166i | −0.322665 | + | 1.69967i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 15.5960 | 0.496677 | ||||||||
\(987\) | 10.3550 | + | 6.71352i | 0.329604 | + | 0.213694i | ||||
\(988\) | 8.50455i | 0.270566i | ||||||||
\(989\) | − | 34.6744i | − | 1.10258i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.0780 | −1.33665 | −0.668326 | − | 0.743868i | \(-0.732989\pi\) | ||||
−0.668326 | + | 0.743868i | \(0.732989\pi\) | |||||||
\(992\) | − | 28.4989i | − | 0.904842i | ||||||
\(993\) | −5.49171 | + | 28.9282i | −0.174274 | + | 0.918009i | ||||
\(994\) | −3.37386 | + | 8.26424i | −0.107012 | + | 0.262126i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −21.0000 | − | 3.98663i | −0.665410 | − | 0.126321i | ||||
\(997\) | 25.0061 | 0.791952 | 0.395976 | − | 0.918261i | \(-0.370406\pi\) | ||||
0.395976 | + | 0.918261i | \(0.370406\pi\) | |||||||
\(998\) | −3.57560 | −0.113184 | ||||||||
\(999\) | 37.7175 | + | 23.7955i | 1.19333 | + | 0.752855i |
(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 | 525.2.g.f.524.10 | 16 | ||
3.2 | odd | 2 | inner | 525.2.g.f.524.5 | 16 | ||
5.2 | odd | 4 | 525.2.b.i.251.6 | yes | 8 | ||
5.3 | odd | 4 | 525.2.b.h.251.3 | ✓ | 8 | ||
5.4 | even | 2 | inner | 525.2.g.f.524.7 | 16 | ||
7.6 | odd | 2 | inner | 525.2.g.f.524.11 | 16 | ||
15.2 | even | 4 | 525.2.b.i.251.3 | yes | 8 | ||
15.8 | even | 4 | 525.2.b.h.251.6 | yes | 8 | ||
15.14 | odd | 2 | inner | 525.2.g.f.524.12 | 16 | ||
21.20 | even | 2 | inner | 525.2.g.f.524.8 | 16 | ||
35.13 | even | 4 | 525.2.b.h.251.4 | yes | 8 | ||
35.27 | even | 4 | 525.2.b.i.251.5 | yes | 8 | ||
35.34 | odd | 2 | inner | 525.2.g.f.524.6 | 16 | ||
105.62 | odd | 4 | 525.2.b.i.251.4 | yes | 8 | ||
105.83 | odd | 4 | 525.2.b.h.251.5 | yes | 8 | ||
105.104 | even | 2 | inner | 525.2.g.f.524.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.b.h.251.3 | ✓ | 8 | 5.3 | odd | 4 | ||
525.2.b.h.251.4 | yes | 8 | 35.13 | even | 4 | ||
525.2.b.h.251.5 | yes | 8 | 105.83 | odd | 4 | ||
525.2.b.h.251.6 | yes | 8 | 15.8 | even | 4 | ||
525.2.b.i.251.3 | yes | 8 | 15.2 | even | 4 | ||
525.2.b.i.251.4 | yes | 8 | 105.62 | odd | 4 | ||
525.2.b.i.251.5 | yes | 8 | 35.27 | even | 4 | ||
525.2.b.i.251.6 | yes | 8 | 5.2 | odd | 4 | ||
525.2.g.f.524.5 | 16 | 3.2 | odd | 2 | inner | ||
525.2.g.f.524.6 | 16 | 35.34 | odd | 2 | inner | ||
525.2.g.f.524.7 | 16 | 5.4 | even | 2 | inner | ||
525.2.g.f.524.8 | 16 | 21.20 | even | 2 | inner | ||
525.2.g.f.524.9 | 16 | 105.104 | even | 2 | inner | ||
525.2.g.f.524.10 | 16 | 1.1 | even | 1 | trivial | ||
525.2.g.f.524.11 | 16 | 7.6 | odd | 2 | inner | ||
525.2.g.f.524.12 | 16 | 15.14 | odd | 2 | inner |