Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(401,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.l (of order \(4\), degree \(2\), 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | 16.0.534694406811304329216.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 401.4 | ||
Root | \(1.32661 - 0.490008i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.401 |
Dual form | 1600.2.l.h.1201.4 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.183790 | − | 0.183790i | −0.106111 | − | 0.106111i | 0.652058 | − | 0.758169i | \(-0.273906\pi\) |
−0.758169 | + | 0.652058i | \(0.773906\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.84853i | − | 1.45461i | −0.686315 | − | 0.727304i | \(-0.740773\pi\) | ||
0.686315 | − | 0.727304i | \(-0.259227\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.93244i | − | 0.977481i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.60020 | + | 1.60020i | −0.482477 | + | 0.482477i | −0.905922 | − | 0.423445i | \(-0.860821\pi\) |
0.423445 | + | 0.905922i | \(0.360821\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.80775 | + | 1.80775i | 0.501379 | + | 0.501379i | 0.911866 | − | 0.410487i | \(-0.134641\pi\) |
−0.410487 | + | 0.911866i | \(0.634641\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.93886 | 1.19785 | 0.598924 | − | 0.800806i | \(-0.295595\pi\) | ||||
0.598924 | + | 0.800806i | \(0.295595\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.77162 | − | 4.77162i | −1.09468 | − | 1.09468i | −0.995021 | − | 0.0996636i | \(-0.968223\pi\) |
−0.0996636 | − | 0.995021i | \(-0.531777\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.707323 | + | 0.707323i | −0.154351 | + | 0.154351i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.134544i | 0.0280543i | 0.999902 | + | 0.0140272i | \(0.00446513\pi\) | ||||
−0.999902 | + | 0.0140272i | \(0.995535\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.09033 | + | 1.09033i | −0.209833 | + | 0.209833i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.17142 | − | 2.17142i | −0.403223 | − | 0.403223i | 0.476144 | − | 0.879367i | \(-0.342034\pi\) |
−0.879367 | + | 0.476144i | \(0.842034\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.26371 | −0.406574 | −0.203287 | − | 0.979119i | \(-0.565163\pi\) | ||||
−0.203287 | + | 0.979119i | \(0.565163\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.588201 | 0.102393 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.35066 | + | 4.35066i | −0.715243 | + | 0.715243i | −0.967627 | − | 0.252384i | \(-0.918785\pi\) |
0.252384 | + | 0.967627i | \(0.418785\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 0.664493i | − | 0.106404i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.34709i | − | 0.522727i | −0.965240 | − | 0.261364i | \(-0.915828\pi\) | ||
0.965240 | − | 0.261364i | \(-0.0841722\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.70896 | − | 2.70896i | 0.413112 | − | 0.413112i | −0.469709 | − | 0.882821i | \(-0.655641\pi\) |
0.882821 | + | 0.469709i | \(0.155641\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.03343 | −1.02593 | −0.512966 | − | 0.858409i | \(-0.671453\pi\) | ||||
−0.512966 | + | 0.858409i | \(0.671453\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.81119 | −1.11588 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.907714 | − | 0.907714i | −0.127105 | − | 0.127105i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.40020 | + | 3.40020i | −0.467053 | + | 0.467053i | −0.900958 | − | 0.433905i | \(-0.857135\pi\) |
0.433905 | + | 0.900958i | \(0.357135\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.75396i | 0.232317i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.107127 | + | 0.107127i | −0.0139468 | + | 0.0139468i | −0.714046 | − | 0.700099i | \(-0.753139\pi\) |
0.700099 | + | 0.714046i | \(0.253139\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.46410 | − | 3.46410i | −0.443533 | − | 0.443533i | 0.449665 | − | 0.893197i | \(-0.351543\pi\) |
−0.893197 | + | 0.449665i | \(0.851543\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.2856 | −1.42185 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.91078 | + | 1.91078i | 0.233440 | + | 0.233440i | 0.814127 | − | 0.580687i | \(-0.197216\pi\) |
−0.580687 | + | 0.814127i | \(0.697216\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0247279 | − | 0.0247279i | 0.00297689 | − | 0.00297689i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.32899i | − | 1.10715i | −0.832800 | − | 0.553573i | \(-0.813264\pi\) | ||
0.832800 | − | 0.553573i | \(-0.186736\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.82769i | − | 1.15024i | −0.818068 | − | 0.575122i | \(-0.804955\pi\) | ||
0.818068 | − | 0.575122i | \(-0.195045\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.15840 | + | 6.15840i | 0.701815 | + | 0.701815i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.0073 | −1.23842 | −0.619211 | − | 0.785224i | \(-0.712548\pi\) | ||||
−0.619211 | + | 0.785224i | \(0.712548\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.39654 | −0.932949 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.80967 | + | 8.80967i | 0.966987 | + | 0.966987i | 0.999472 | − | 0.0324850i | \(-0.0103421\pi\) |
−0.0324850 | + | 0.999472i | \(0.510342\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.798174i | 0.0855732i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.12125i | 0.118853i | 0.998233 | + | 0.0594263i | \(0.0189271\pi\) | ||||
−0.998233 | + | 0.0594263i | \(0.981073\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.95717 | − | 6.95717i | 0.729310 | − | 0.729310i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.416048 | + | 0.416048i | 0.0431422 | + | 0.0431422i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.10461 | −0.619829 | −0.309915 | − | 0.950764i | \(-0.600300\pi\) | ||||
−0.309915 | + | 0.950764i | \(0.600300\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.69248 | + | 4.69248i | 0.471612 | + | 0.471612i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.17142 | − | 2.17142i | 0.216065 | − | 0.216065i | −0.590773 | − | 0.806838i | \(-0.701177\pi\) |
0.806838 | + | 0.590773i | \(0.201177\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 15.3778i | − | 1.51522i | −0.652707 | − | 0.757610i | \(-0.726367\pi\) | ||
0.652707 | − | 0.757610i | \(-0.273633\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.98419 | − | 6.98419i | 0.675187 | − | 0.675187i | −0.283720 | − | 0.958907i | \(-0.591569\pi\) |
0.958907 | + | 0.283720i | \(0.0915688\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.59694 | − | 8.59694i | −0.823437 | − | 0.823437i | 0.163162 | − | 0.986599i | \(-0.447831\pi\) |
−0.986599 | + | 0.163162i | \(0.947831\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.59922 | 0.151791 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.5329 | 1.36714 | 0.683572 | − | 0.729883i | \(-0.260426\pi\) | ||||
0.683572 | + | 0.729883i | \(0.260426\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.30111 | − | 5.30111i | 0.490088 | − | 0.490088i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 19.0073i | − | 1.74240i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.87875i | 0.534432i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.615163 | + | 0.615163i | −0.0554673 | + | 0.0554673i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.96617 | 0.529412 | 0.264706 | − | 0.964329i | \(-0.414725\pi\) | ||||
0.264706 | + | 0.964329i | \(0.414725\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.995761 | −0.0876719 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.37084 | − | 2.37084i | −0.207141 | − | 0.207141i | 0.595910 | − | 0.803051i | \(-0.296791\pi\) |
−0.803051 | + | 0.595910i | \(0.796791\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.3637 | + | 18.3637i | −1.59234 | + | 1.59234i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 18.2745i | − | 1.56129i | −0.624973 | − | 0.780646i | \(-0.714890\pi\) | ||
0.624973 | − | 0.780646i | \(-0.285110\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.136094 | + | 0.136094i | −0.0115433 | + | 0.0115433i | −0.712855 | − | 0.701312i | \(-0.752598\pi\) |
0.701312 | + | 0.712855i | \(0.252598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.29268 | + | 1.29268i | 0.108863 | + | 0.108863i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.78550 | −0.483808 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.43562 | + | 1.43562i | 0.118408 | + | 0.118408i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.40078 | − | 2.40078i | 0.196680 | − | 0.196680i | −0.601895 | − | 0.798575i | \(-0.705588\pi\) |
0.798575 | + | 0.601895i | \(0.205588\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.9935i | 1.46429i | 0.681150 | + | 0.732144i | \(0.261480\pi\) | ||||
−0.681150 | + | 0.732144i | \(0.738520\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 14.4829i | − | 1.17087i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.6359 | − | 12.6359i | −1.00846 | − | 1.00846i | −0.999964 | − | 0.00849213i | \(-0.997297\pi\) |
−0.00849213 | − | 0.999964i | \(-0.502703\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.24985 | 0.0991193 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.517796 | 0.0408081 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.8470 | + | 15.8470i | 1.24123 | + | 1.24123i | 0.959490 | + | 0.281743i | \(0.0909126\pi\) |
0.281743 | + | 0.959490i | \(0.409087\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.7559i | 0.987083i | 0.869722 | + | 0.493541i | \(0.164298\pi\) | ||||
−0.869722 | + | 0.493541i | \(0.835702\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 6.46410i | − | 0.497239i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.9925 | + | 13.9925i | −1.07003 | + | 1.07003i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.64673 | − | 2.64673i | −0.201227 | − | 0.201227i | 0.599299 | − | 0.800525i | \(-0.295446\pi\) |
−0.800525 | + | 0.599299i | \(0.795446\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.0393779 | 0.00295983 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.6497 | − | 11.6497i | −0.870736 | − | 0.870736i | 0.121817 | − | 0.992553i | \(-0.461128\pi\) |
−0.992553 | + | 0.121817i | \(0.961128\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.24322 | − | 1.24322i | 0.0924079 | − | 0.0924079i | −0.659392 | − | 0.751800i | \(-0.729186\pi\) |
0.751800 | + | 0.659392i | \(0.229186\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.27334i | 0.0941278i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.90314 | + | 7.90314i | −0.577935 | + | 0.577935i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.19615 | + | 4.19615i | 0.305225 | + | 0.305225i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.07180 | −0.366982 | −0.183491 | − | 0.983021i | \(-0.558740\pi\) | ||||
−0.183491 | + | 0.983021i | \(0.558740\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.30278 | 0.165758 | 0.0828788 | − | 0.996560i | \(-0.473589\pi\) | ||||
0.0828788 | + | 0.996560i | \(0.473589\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.06997 | + | 8.06997i | −0.574961 | + | 0.574961i | −0.933511 | − | 0.358549i | \(-0.883271\pi\) |
0.358549 | + | 0.933511i | \(0.383271\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.8564i | 1.54936i | 0.632354 | + | 0.774680i | \(0.282089\pi\) | ||||
−0.632354 | + | 0.774680i | \(0.717911\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 0.702368i | − | 0.0495412i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.35679 | + | 8.35679i | −0.586532 | + | 0.586532i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.394542 | 0.0274226 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.2711 | 1.05632 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.478227 | − | 0.478227i | −0.0329225 | − | 0.0329225i | 0.690454 | − | 0.723376i | \(-0.257411\pi\) |
−0.723376 | + | 0.690454i | \(0.757411\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.71458 | + | 1.71458i | −0.117481 | + | 0.117481i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.71196i | 0.591406i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.80623 | + | 1.80623i | −0.122054 | + | 0.122054i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.92820 | + | 8.92820i | 0.600576 | + | 0.600576i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.50859 | −0.502813 | −0.251406 | − | 0.967882i | \(-0.580893\pi\) | ||||
−0.251406 | + | 0.967882i | \(0.580893\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.8788 | + | 12.8788i | 0.854798 | + | 0.854798i | 0.990720 | − | 0.135922i | \(-0.0433997\pi\) |
−0.135922 | + | 0.990720i | \(0.543400\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.62166 | + | 8.62166i | −0.569736 | + | 0.569736i | −0.932054 | − | 0.362319i | \(-0.881985\pi\) |
0.362319 | + | 0.932054i | \(0.381985\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 2.26371i | − | 0.148941i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4.63429i | − | 0.303602i | −0.988411 | − | 0.151801i | \(-0.951493\pi\) | ||
0.988411 | − | 0.151801i | \(-0.0485073\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.02304 | + | 2.02304i | 0.131411 | + | 0.131411i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.4220 | 1.19162 | 0.595810 | − | 0.803126i | \(-0.296831\pi\) | ||||
0.595810 | + | 0.803126i | \(0.296831\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.3247 | 1.18040 | 0.590200 | − | 0.807257i | \(-0.299049\pi\) | ||||
0.590200 | + | 0.807257i | \(0.299049\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.81418 | + | 4.81418i | 0.308830 | + | 0.308830i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 17.2518i | − | 1.09770i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 3.23827i | − | 0.205217i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.0222 | − | 16.0222i | 1.01131 | − | 1.01131i | 0.0113760 | − | 0.999935i | \(-0.496379\pi\) |
0.999935 | − | 0.0113760i | \(-0.00362116\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.215297 | − | 0.215297i | −0.0135356 | − | 0.0135356i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.82098 | −0.363103 | −0.181551 | − | 0.983381i | \(-0.558112\pi\) | ||||
−0.181551 | + | 0.983381i | \(0.558112\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.7436 | + | 16.7436i | 1.04040 | + | 1.04040i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.36758 | + | 6.36758i | −0.394143 | + | 0.394143i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 0.806693i | − | 0.0497428i | −0.999691 | − | 0.0248714i | \(-0.992082\pi\) | ||
0.999691 | − | 0.0248714i | \(-0.00791763\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.206075 | − | 0.206075i | 0.0126116 | − | 0.0126116i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.1939 | + | 15.1939i | 0.926387 | + | 0.926387i | 0.997470 | − | 0.0710837i | \(-0.0226458\pi\) |
−0.0710837 | + | 0.997470i | \(0.522646\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.8491 | 0.659034 | 0.329517 | − | 0.944150i | \(-0.393114\pi\) | ||||
0.329517 | + | 0.944150i | \(0.393114\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.55732 | −0.154776 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.27334 | + | 1.27334i | −0.0765074 | + | 0.0765074i | −0.744325 | − | 0.667818i | \(-0.767229\pi\) |
0.667818 | + | 0.744325i | \(0.267229\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.63820i | 0.397419i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.2174i | − | 1.20607i | −0.797716 | − | 0.603033i | \(-0.793959\pi\) | ||
0.797716 | − | 0.603033i | \(-0.206041\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.3741 | − | 21.3741i | 1.27056 | − | 1.27056i | 0.324759 | − | 0.945797i | \(-0.394717\pi\) |
0.945797 | − | 0.324759i | \(-0.105283\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.8814 | −0.760363 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.39230 | 0.434841 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.12197 | + | 1.12197i | 0.0657710 | + | 0.0657710i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.1656 | − | 11.1656i | 0.652301 | − | 0.652301i | −0.301246 | − | 0.953547i | \(-0.597402\pi\) |
0.953547 | + | 0.301246i | \(0.0974024\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.48947i | − | 0.202480i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.243221 | + | 0.243221i | −0.0140659 | + | 0.0140659i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.4255 | − | 10.4255i | −0.600916 | − | 0.600916i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.798174 | −0.0458539 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.18143 | − | 2.18143i | −0.124501 | − | 0.124501i | 0.642111 | − | 0.766612i | \(-0.278059\pi\) |
−0.766612 | + | 0.642111i | \(0.778059\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.82629 | + | 2.82629i | −0.160782 | + | 0.160782i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 11.5517i | − | 0.655038i | −0.944845 | − | 0.327519i | \(-0.893787\pi\) | ||
0.944845 | − | 0.327519i | \(-0.106213\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.4265i | 0.589343i | 0.955599 | + | 0.294671i | \(0.0952102\pi\) | ||||
−0.955599 | + | 0.294671i | \(0.904790\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.0785 | + | 10.0785i | 0.566063 | + | 0.566063i | 0.931023 | − | 0.364960i | \(-0.118917\pi\) |
−0.364960 | + | 0.931023i | \(0.618917\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.94941 | 0.389092 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.56725 | −0.143290 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.5663 | − | 23.5663i | −1.31127 | − | 1.31127i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.16007i | 0.174752i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.0684i | 1.49233i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.77162 | + | 8.77162i | −0.482132 | + | 0.482132i | −0.905812 | − | 0.423680i | \(-0.860738\pi\) |
0.423680 | + | 0.905812i | \(0.360738\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.7580 | + | 12.7580i | 0.699137 | + | 0.699137i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.0226 | 1.79885 | 0.899427 | − | 0.437072i | \(-0.143984\pi\) | ||||
0.899427 | + | 0.437072i | \(0.143984\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.67101 | − | 2.67101i | −0.145070 | − | 0.145070i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.62238 | − | 3.62238i | 0.196163 | − | 0.196163i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.12189i | 0.168566i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.1412 | − | 11.1412i | 0.598090 | − | 0.598090i | −0.341714 | − | 0.939804i | \(-0.611007\pi\) |
0.939804 | + | 0.341714i | \(0.111007\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.8656 | + | 10.8656i | 0.581622 | + | 0.581622i | 0.935349 | − | 0.353727i | \(-0.115086\pi\) |
−0.353727 | + | 0.935349i | \(0.615086\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.94207 | −0.210412 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.3480 | −0.603995 | −0.301998 | − | 0.953309i | \(-0.597653\pi\) | ||||
−0.301998 | + | 0.953309i | \(0.597653\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.49337 | + | 3.49337i | −0.184889 | + | 0.184889i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.5788i | 1.40278i | 0.712779 | + | 0.701389i | \(0.247436\pi\) | ||||
−0.712779 | + | 0.701389i | \(0.752564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.5367i | 1.39667i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.08046 | − | 1.08046i | 0.0567093 | − | 0.0567093i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.90729 | 0.151760 | 0.0758798 | − | 0.997117i | \(-0.475823\pi\) | ||||
0.0758798 | + | 0.997117i | \(0.475823\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.81514 | −0.510956 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.0858 | + | 13.0858i | 0.679379 | + | 0.679379i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.65522 | − | 4.65522i | 0.241038 | − | 0.241038i | −0.576241 | − | 0.817280i | \(-0.695481\pi\) |
0.817280 | + | 0.576241i | \(0.195481\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7.85077i | − | 0.404335i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.52106 | − | 9.52106i | 0.489064 | − | 0.489064i | −0.418947 | − | 0.908011i | \(-0.637601\pi\) |
0.908011 | + | 0.418947i | \(0.137601\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.09652 | − | 1.09652i | −0.0561767 | − | 0.0561767i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.92429 | 0.353815 | 0.176907 | − | 0.984228i | \(-0.443391\pi\) | ||||
0.176907 | + | 0.984228i | \(0.443391\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.94386 | − | 7.94386i | −0.403809 | − | 0.403809i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.0232 | − | 20.0232i | 1.01521 | − | 1.01521i | 0.0153322 | − | 0.999882i | \(-0.495119\pi\) |
0.999882 | − | 0.0153322i | \(-0.00488057\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.664493i | 0.0336049i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.871474i | 0.0439601i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.81625 | − | 3.81625i | −0.191532 | − | 0.191532i | 0.604826 | − | 0.796358i | \(-0.293243\pi\) |
−0.796358 | + | 0.604826i | \(0.793243\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.75015 | 0.337930 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.68031 | 0.0839108 | 0.0419554 | − | 0.999119i | \(-0.486641\pi\) | ||||
0.0419554 | + | 0.999119i | \(0.486641\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.09222 | − | 4.09222i | −0.203848 | − | 0.203848i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 13.9238i | − | 0.690177i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.1317i | 0.995448i | 0.867335 | + | 0.497724i | \(0.165831\pi\) | ||||
−0.867335 | + | 0.497724i | \(0.834169\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.35867 | + | 3.35867i | −0.165671 | + | 0.165671i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.412282 | + | 0.412282i | 0.0202871 | + | 0.0202871i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.0500256 | 0.00244976 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.6570 | + | 22.6570i | 1.10687 | + | 1.10687i | 0.993560 | + | 0.113306i | \(0.0361442\pi\) |
0.113306 | + | 0.993560i | \(0.463856\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.1583 | + | 10.1583i | −0.495084 | + | 0.495084i | −0.909904 | − | 0.414820i | \(-0.863845\pi\) |
0.414820 | + | 0.909904i | \(0.363845\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20.6251i | 1.00283i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.3317 | + | 13.3317i | −0.645166 | + | 0.645166i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.06332 | + | 1.06332i | 0.0513375 | + | 0.0513375i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.1518 | 1.25969 | 0.629843 | − | 0.776723i | \(-0.283119\pi\) | ||||
0.629843 | + | 0.776723i | \(0.283119\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.30795 | −0.447312 | −0.223656 | − | 0.974668i | \(-0.571799\pi\) | ||||
−0.223656 | + | 0.974668i | \(0.571799\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.641992 | − | 0.641992i | 0.0307107 | − | 0.0307107i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 30.4799i | − | 1.45473i | −0.686252 | − | 0.727364i | \(-0.740745\pi\) | ||
0.686252 | − | 0.727364i | \(-0.259255\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 22.9059i | 1.09076i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.7437 | + | 16.7437i | −0.795516 | + | 0.795516i | −0.982385 | − | 0.186869i | \(-0.940166\pi\) |
0.186869 | + | 0.982385i | \(0.440166\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.882482 | −0.0417399 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.40502 | −0.255079 | −0.127539 | − | 0.991834i | \(-0.540708\pi\) | ||||
−0.127539 | + | 0.991834i | \(0.540708\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.35600 | + | 5.35600i | 0.252204 | + | 0.252204i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.30703 | − | 3.30703i | 0.155378 | − | 0.155378i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.5929i | 1.61819i | 0.587678 | + | 0.809095i | \(0.300042\pi\) | ||||
−0.587678 | + | 0.809095i | \(0.699958\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.38496 | + | 5.38496i | −0.251349 | + | 0.251349i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.3876 | + | 14.3876i | 0.670099 | + | 0.670099i | 0.957739 | − | 0.287640i | \(-0.0928706\pi\) |
−0.287640 | + | 0.957739i | \(0.592871\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.6591 | 0.960108 | 0.480054 | − | 0.877239i | \(-0.340617\pi\) | ||||
0.480054 | + | 0.877239i | \(0.340617\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.3222 | − | 16.3222i | −0.755300 | − | 0.755300i | 0.220163 | − | 0.975463i | \(-0.429341\pi\) |
−0.975463 | + | 0.220163i | \(0.929341\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.35371 | − | 7.35371i | 0.339563 | − | 0.339563i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.64472i | 0.214017i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.66973i | 0.398635i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.97088 | + | 9.97088i | 0.456535 | + | 0.456535i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.5136 | −0.891597 | −0.445799 | − | 0.895133i | \(-0.647080\pi\) | ||||
−0.445799 | + | 0.895133i | \(0.647080\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.7298 | −0.717216 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.0951660 | − | 0.0951660i | −0.00433020 | − | 0.00433020i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 15.6638i | − | 0.709794i | −0.934905 | − | 0.354897i | \(-0.884516\pi\) | ||
0.934905 | − | 0.354897i | \(-0.115484\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 5.82505i | − | 0.263418i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.9076 | − | 17.9076i | 0.808157 | − | 0.808157i | −0.176198 | − | 0.984355i | \(-0.556380\pi\) |
0.984355 | + | 0.176198i | \(0.0563799\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.7244 | − | 10.7244i | −0.483001 | − | 0.483001i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −35.9029 | −1.61046 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.32067 | − | 2.32067i | −0.103887 | − | 0.103887i | 0.653253 | − | 0.757140i | \(-0.273404\pi\) |
−0.757140 | + | 0.653253i | \(0.773404\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.34441 | − | 2.34441i | 0.104741 | − | 0.104741i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 6.18913i | − | 0.275960i | −0.990435 | − | 0.137980i | \(-0.955939\pi\) | ||
0.990435 | − | 0.137980i | \(-0.0440609\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.18804 | + | 1.18804i | −0.0527627 | + | 0.0527627i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.6217 | − | 18.6217i | −0.825391 | − | 0.825391i | 0.161485 | − | 0.986875i | \(-0.448372\pi\) |
−0.986875 | + | 0.161485i | \(0.948372\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −37.8222 | −1.67315 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.4052 | 0.459403 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.2549 | − | 11.2549i | 0.494988 | − | 0.494988i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.972885i | 0.0427049i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 24.0232i | − | 1.05247i | −0.850338 | − | 0.526237i | \(-0.823603\pi\) | ||
0.850338 | − | 0.526237i | \(-0.176397\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.1791 | + | 16.1791i | −0.707463 | + | 0.707463i | −0.966001 | − | 0.258538i | \(-0.916759\pi\) |
0.258538 | + | 0.966001i | \(0.416759\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.1801 | −0.487015 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.9819 | 0.999213 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.314144 | + | 0.314144i | 0.0136327 | + | 0.0136327i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.05069 | − | 6.05069i | 0.262084 | − | 0.262084i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.28219i | 0.184790i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.4994 | − | 12.4994i | 0.538389 | − | 0.538389i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.76526 | + | 6.76526i | 0.290861 | + | 0.290861i | 0.837420 | − | 0.546559i | \(-0.184063\pi\) |
−0.546559 | + | 0.837420i | \(0.684063\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.456984 | −0.0196111 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.38359 | − | 4.38359i | −0.187429 | − | 0.187429i | 0.607155 | − | 0.794584i | \(-0.292311\pi\) |
−0.794584 | + | 0.607155i | \(0.792311\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.1583 | + | 10.1583i | −0.433545 | + | 0.433545i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.7224i | 0.882805i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 42.3621i | 1.80142i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.92396 | − | 3.92396i | −0.166264 | − | 0.166264i | 0.619071 | − | 0.785335i | \(-0.287509\pi\) |
−0.785335 | + | 0.619071i | \(0.787509\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.79422 | 0.414252 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.90504 | 0.122651 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.61660 | − | 6.61660i | −0.278857 | − | 0.278857i | 0.553796 | − | 0.832652i | \(-0.313179\pi\) |
−0.832652 | + | 0.553796i | \(0.813179\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 32.3144i | 1.35708i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 40.2900i | − | 1.68904i | −0.535521 | − | 0.844522i | \(-0.679885\pi\) | ||
0.535521 | − | 0.844522i | \(-0.320115\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.6010 | + | 22.6010i | −0.945823 | + | 0.945823i | −0.998606 | − | 0.0527829i | \(-0.983191\pi\) |
0.0527829 | + | 0.998606i | \(0.483191\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.932147 | + | 0.932147i | 0.0389410 | + | 0.0389410i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.8020 | 0.782737 | 0.391368 | − | 0.920234i | \(-0.372002\pi\) | ||||
0.391368 | + | 0.920234i | \(0.372002\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.423229 | − | 0.423229i | −0.0175888 | − | 0.0175888i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 33.9043 | − | 33.9043i | 1.40659 | − | 1.40659i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 10.8820i | − | 0.450685i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.71961 | − | 2.71961i | 0.112250 | − | 0.112250i | −0.648751 | − | 0.761001i | \(-0.724708\pi\) |
0.761001 | + | 0.648751i | \(0.224708\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.8016 | + | 10.8016i | 0.445071 | + | 0.445071i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.96636 | 0.122020 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.04894 | −0.166270 | −0.0831350 | − | 0.996538i | \(-0.526493\pi\) | ||||
−0.0831350 | + | 0.996538i | \(0.526493\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.01700 | − | 4.01700i | 0.164405 | − | 0.164405i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 19.0455i | − | 0.778178i | −0.921200 | − | 0.389089i | \(-0.872790\pi\) | ||
0.921200 | − | 0.389089i | \(-0.127210\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 14.4406i | − | 0.589045i | −0.955645 | − | 0.294522i | \(-0.904839\pi\) | ||
0.955645 | − | 0.294522i | \(-0.0951606\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.60327 | − | 5.60327i | 0.228183 | − | 0.228183i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.3473 | 1.88118 | 0.940589 | − | 0.339546i | \(-0.110273\pi\) | ||||
0.940589 | + | 0.339546i | \(0.110273\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.07180 | 0.124475 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.7147 | − | 12.7147i | −0.514380 | − | 0.514380i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.961106 | − | 0.961106i | 0.0388187 | − | 0.0388187i | −0.687431 | − | 0.726250i | \(-0.741262\pi\) |
0.726250 | + | 0.687431i | \(0.241262\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.44724i | 0.138781i | 0.997590 | + | 0.0693903i | \(0.0221054\pi\) | ||||
−0.997590 | + | 0.0693903i | \(0.977895\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.5574 | + | 24.5574i | −0.987044 | + | 0.987044i | −0.999917 | − | 0.0128733i | \(-0.995902\pi\) |
0.0128733 | + | 0.999917i | \(0.495902\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.146697 | − | 0.146697i | −0.00588673 | − | 0.00588673i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.31517 | 0.172884 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.80667 | − | 2.80667i | −0.112088 | − | 0.112088i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.4873 | + | 21.4873i | −0.856753 | + | 0.856753i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 22.7950i | − | 0.907456i | −0.891140 | − | 0.453728i | \(-0.850094\pi\) | ||
0.891140 | − | 0.453728i | \(-0.149906\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.175787i | 0.00698691i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.1207 | − | 14.1207i | −0.559481 | − | 0.559481i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27.3567 | −1.08221 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.4468 | 1.20258 | 0.601289 | − | 0.799032i | \(-0.294654\pi\) | ||||
0.601289 | + | 0.799032i | \(0.294654\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.4452 | − | 20.4452i | −0.806282 | − | 0.806282i | 0.177787 | − | 0.984069i | \(-0.443106\pi\) |
−0.984069 | + | 0.177787i | \(0.943106\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.5876i | 1.16321i | 0.813472 | + | 0.581604i | \(0.197575\pi\) | ||||
−0.813472 | + | 0.581604i | \(0.802425\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 0.342849i | − | 0.0134580i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.60117 | − | 1.60117i | 0.0627550 | − | 0.0627550i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.2334 | − | 21.2334i | −0.830928 | − | 0.830928i | 0.156716 | − | 0.987644i | \(-0.449909\pi\) |
−0.987644 | + | 0.156716i | \(0.949909\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −28.8191 | −1.12434 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.0222 | − | 20.0222i | −0.779954 | − | 0.779954i | 0.199869 | − | 0.979823i | \(-0.435948\pi\) |
−0.979823 | + | 0.199869i | \(0.935948\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.9536 | + | 19.9536i | −0.776107 | + | 0.776107i | −0.979166 | − | 0.203059i | \(-0.934912\pi\) |
0.203059 | + | 0.979166i | \(0.434912\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 3.28184i | − | 0.127456i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.292152 | − | 0.292152i | 0.0113122 | − | 0.0113122i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.38001 | + | 1.38001i | 0.0533542 | + | 0.0533542i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.0865 | 0.427989 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.91192 | −0.112246 | −0.0561231 | − | 0.998424i | \(-0.517874\pi\) | ||||
−0.0561231 | + | 0.998424i | \(0.517874\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.6045 | − | 34.6045i | 1.32996 | − | 1.32996i | 0.424558 | − | 0.905401i | \(-0.360430\pi\) |
0.905401 | − | 0.424558i | \(-0.139570\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.4938i | 0.901609i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 4.73401i | − | 0.181408i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.7435 | − | 24.7435i | 0.946785 | − | 0.946785i | −0.0518690 | − | 0.998654i | \(-0.516518\pi\) |
0.998654 | + | 0.0518690i | \(0.0165178\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.16916 | 0.120911 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.2934 | −0.468341 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.3782 | − | 25.3782i | −0.965431 | − | 0.965431i | 0.0339907 | − | 0.999422i | \(-0.489178\pi\) |
−0.999422 | + | 0.0339907i | \(0.989178\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.0592 | − | 18.0592i | 0.686011 | − | 0.686011i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 16.5308i | − | 0.626148i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.851738 | + | 0.851738i | −0.0322157 | + | 0.0322157i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.3544 | − | 32.3544i | −1.22201 | − | 1.22201i | −0.966916 | − | 0.255094i | \(-0.917894\pi\) |
−0.255094 | − | 0.966916i | \(-0.582106\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.5194 | 1.56593 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.35679 | − | 8.35679i | −0.314290 | − | 0.314290i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.64939 | + | 6.64939i | −0.249723 | + | 0.249723i | −0.820857 | − | 0.571134i | \(-0.806504\pi\) |
0.571134 | + | 0.820857i | \(0.306504\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 32.2784i | 1.21053i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 0.304568i | − | 0.0114062i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.38578 | − | 3.38578i | −0.126444 | − | 0.126444i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.0785 | 1.68115 | 0.840573 | − | 0.541699i | \(-0.182219\pi\) | ||||
0.840573 | + | 0.541699i | \(0.182219\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −59.1820 | −2.20405 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.36791 | − | 3.36791i | −0.125254 | − | 0.125254i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.6075i | 0.690116i | 0.938581 | + | 0.345058i | \(0.112141\pi\) | ||||
−0.938581 | + | 0.345058i | \(0.887859\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.4200i | 0.867409i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.3792 | − | 13.3792i | 0.494846 | − | 0.494846i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.95550 | − | 7.95550i | −0.293843 | − | 0.293843i | 0.544753 | − | 0.838596i | \(-0.316623\pi\) |
−0.838596 | + | 0.544753i | \(0.816623\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.11526 | −0.225258 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.2636 | − | 15.2636i | −0.561479 | − | 0.561479i | 0.368249 | − | 0.929727i | \(-0.379958\pi\) |
−0.929727 | + | 0.368249i | \(0.879958\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.17071 | + | 3.17071i | −0.116479 | + | 0.116479i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.3017i | 1.22172i | 0.791738 | + | 0.610861i | \(0.209177\pi\) | ||||
−0.791738 | + | 0.610861i | \(0.790823\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.8339 | − | 25.8339i | 0.945211 | − | 0.945211i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −26.8789 | − | 26.8789i | −0.982132 | − | 0.982132i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.17214 | −0.0427720 | −0.0213860 | − | 0.999771i | \(-0.506808\pi\) | ||||
−0.0213860 | + | 0.999771i | \(0.506808\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.88945 | −0.214623 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.9408 | + | 17.9408i | −0.652069 | + | 0.652069i | −0.953491 | − | 0.301422i | \(-0.902539\pi\) |
0.301422 | + | 0.953491i | \(0.402539\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.0791389i | 0.00287256i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.4641i | 0.560573i | 0.959916 | + | 0.280287i | \(0.0904295\pi\) | ||||
−0.959916 | + | 0.280287i | \(0.909570\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.0856 | + | 33.0856i | −1.19778 | + | 1.19778i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.387318 | −0.0139852 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.9777 | −0.540108 | −0.270054 | − | 0.962845i | \(-0.587042\pi\) | ||||
−0.270054 | + | 0.962845i | \(0.587042\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.06984 | + | 1.06984i | 0.0385293 | + | 0.0385293i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.0120 | − | 33.0120i | 1.18736 | − | 1.18736i | 0.209566 | − | 0.977794i | \(-0.432795\pi\) |
0.977794 | − | 0.209566i | \(-0.0672052\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 6.15464i | − | 0.220796i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.9710 | + | 15.9710i | −0.572222 | + | 0.572222i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.9282 | + | 14.9282i | 0.534173 | + | 0.534173i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.73512 | 0.169219 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.8326 | + | 28.8326i | 1.02777 | + | 1.02777i | 0.999603 | + | 0.0281690i | \(0.00896767\pi\) |
0.0281690 | + | 0.999603i | \(0.491032\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.148262 | + | 0.148262i | −0.00527828 | + | 0.00527828i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 55.9305i | − | 1.98866i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 12.5244i | − | 0.444756i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.1556 | + | 23.1556i | 0.820214 | + | 0.820214i | 0.986139 | − | 0.165924i | \(-0.0530607\pi\) |
−0.165924 | + | 0.986139i | \(0.553061\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.7371 | −1.22891 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.28801 | 0.116176 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.7262 | + | 15.7262i | 0.554966 | + | 0.554966i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 5.58497i | − | 0.196600i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 36.2210i | − | 1.27346i | −0.771086 | − | 0.636731i | \(-0.780286\pi\) | ||
0.771086 | − | 0.636731i | \(-0.219714\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.17312 | + | 9.17312i | −0.322112 | + | 0.322112i | −0.849577 | − | 0.527465i | \(-0.823143\pi\) |
0.527465 | + | 0.849577i | \(0.323143\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.99395 | − | 1.99395i | −0.0699310 | − | 0.0699310i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.8522 | −0.904456 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −20.4015 | − | 20.4015i | −0.712886 | − | 0.712886i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.26795 | − | 7.26795i | 0.253653 | − | 0.253653i | −0.568813 | − | 0.822467i | \(-0.692597\pi\) |
0.822467 | + | 0.568813i | \(0.192597\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.2974i | 0.986384i | 0.869920 | + | 0.493192i | \(0.164170\pi\) | ||||
−0.869920 | + | 0.493192i | \(0.835830\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.1661 | + | 18.1661i | −0.631697 | + | 0.631697i | −0.948494 | − | 0.316797i | \(-0.897393\pi\) |
0.316797 | + | 0.948494i | \(0.397393\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.0865 | − | 11.0865i | −0.385049 | − | 0.385049i | 0.487868 | − | 0.872917i | \(-0.337775\pi\) |
−0.872917 | + | 0.487868i | \(0.837775\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.468054 | 0.0162366 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −38.5783 | −1.33666 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.46818 | − | 2.46818i | 0.0853128 | − | 0.0853128i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 11.9093i | − | 0.411153i | −0.978641 | − | 0.205577i | \(-0.934093\pi\) | ||
0.978641 | − | 0.205577i | \(-0.0659069\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 19.5698i | − | 0.674822i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.71576 | + | 3.71576i | −0.127977 | + | 0.127977i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.6245 | 0.777388 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.85669 | −0.269641 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.585354 | − | 0.585354i | −0.0200657 | − | 0.0200657i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.44597 | − | 2.44597i | 0.0837485 | − | 0.0837485i | −0.663992 | − | 0.747740i | \(-0.731139\pi\) |
0.747740 | + | 0.663992i | \(0.231139\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.57862i | 0.0880839i | 0.999030 | + | 0.0440419i | \(0.0140235\pi\) | ||||
−0.999030 | + | 0.0440419i | \(0.985976\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.0076 | − | 33.0076i | 1.12620 | − | 1.12620i | 0.135416 | − | 0.990789i | \(-0.456763\pi\) |
0.990789 | − | 0.135416i | \(-0.0432371\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.36747 | + | 2.36747i | 0.0806832 | + | 0.0806832i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.5500 | 0.801652 | 0.400826 | − | 0.916154i | \(-0.368723\pi\) | ||||
0.400826 | + | 0.916154i | \(0.368723\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.35863 | − | 1.35863i | −0.0461416 | − | 0.0461416i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.6139 | − | 17.6139i | 0.597511 | − | 0.597511i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.90843i | 0.234083i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.9014i | 0.605871i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.2135 | − | 34.2135i | −1.15531 | − | 1.15531i | −0.985472 | − | 0.169836i | \(-0.945676\pi\) |
−0.169836 | − | 0.985472i | \(-0.554324\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.10426 | −0.138433 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.6823 | 1.37062 | 0.685310 | − | 0.728251i | \(-0.259667\pi\) | ||||
0.685310 | + | 0.728251i | \(0.259667\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.8531 | − | 35.8531i | −1.20655 | − | 1.20655i | −0.972137 | − | 0.234415i | \(-0.924682\pi\) |
−0.234415 | − | 0.972137i | \(-0.575318\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.33231i | 0.313348i | 0.987650 | + | 0.156674i | \(0.0500773\pi\) | ||||
−0.987650 | + | 0.156674i | \(0.949923\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 22.9610i | − | 0.770087i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.4361 | − | 13.4361i | 0.450127 | − | 0.450127i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 33.5609 | + | 33.5609i | 1.12307 | + | 1.12307i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.0894035 | 0.00298510 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.91548 | + | 4.91548i | 0.163940 | + | 0.163940i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.7931 | + | 16.7931i | −0.559459 | + | 0.559459i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.83222i | 0.127528i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.2170 | + | 33.2170i | −1.10295 | + | 1.10295i | −0.108899 | + | 0.994053i | \(0.534733\pi\) |
−0.994053 | + | 0.108899i | \(0.965267\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.36758 | − | 6.36758i | −0.211199 | − | 0.211199i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.77870 | −0.191457 | −0.0957284 | − | 0.995407i | \(-0.530518\pi\) | ||||
−0.0957284 | + | 0.995407i | \(0.530518\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.1944 | −0.933098 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.12424 | + | 9.12424i | −0.301309 | + | 0.301309i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 50.8572i | − | 1.67763i | −0.544420 | − | 0.838813i | \(-0.683250\pi\) | ||
0.544420 | − | 0.838813i | \(-0.316750\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.801852i | 0.0264219i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.8644 | − | 16.8644i | 0.555100 | − | 0.555100i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −45.0945 | −1.48110 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.6815 | −0.711346 | −0.355673 | − | 0.934611i | \(-0.615748\pi\) | ||||
−0.355673 | + | 0.934611i | \(0.615748\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.2720 | + | 37.2720i | 1.22154 | + | 1.22154i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.12309 | + | 2.12309i | −0.0695070 | + | 0.0695070i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.7948i | 0.646668i | 0.946285 | + | 0.323334i | \(0.104804\pi\) | ||||
−0.946285 | + | 0.323334i | \(0.895196\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.91630 | − | 1.91630i | 0.0625360 | − | 0.0625360i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.4510 | − | 29.4510i | −0.960074 | − | 0.960074i | 0.0391593 | − | 0.999233i | \(-0.487532\pi\) |
−0.999233 | + | 0.0391593i | \(0.987532\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.450330 | 0.0146648 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.11783 | + | 4.11783i | 0.133811 | + | 0.133811i | 0.770840 | − | 0.637029i | \(-0.219837\pi\) |
−0.637029 | + | 0.770840i | \(0.719837\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.7660 | − | 17.7660i | 0.576708 | − | 0.576708i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 3.70465i | − | 0.120131i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.3245i | 1.30624i | 0.757255 | + | 0.653119i | \(0.226540\pi\) | ||||
−0.757255 | + | 0.653119i | \(0.773460\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.27723 | − | 1.27723i | −0.0412871 | − | 0.0412871i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −70.3298 | −2.27107 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.8756 | −0.834697 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.4807 | − | 20.4807i | −0.659982 | − | 0.659982i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 58.1740i | − | 1.87075i | −0.353656 | − | 0.935375i | \(-0.615062\pi\) | ||
0.353656 | − | 0.935375i | \(-0.384938\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.66254i | 0.278281i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.70830 | − | 1.70830i | 0.0548220 | − | 0.0548220i | −0.679164 | − | 0.733986i | \(-0.737658\pi\) |
0.733986 | + | 0.679164i | \(0.237658\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.523762 | + | 0.523762i | 0.0167910 | + | 0.0167910i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 35.1811 | 1.12554 | 0.562772 | − | 0.826612i | \(-0.309735\pi\) | ||||
0.562772 | + | 0.826612i | \(0.309735\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.79422 | − | 1.79422i | −0.0573436 | − | 0.0573436i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.2100 | + | 25.2100i | −0.804894 | + | 0.804894i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.7257i | 0.884312i | 0.896938 | + | 0.442156i | \(0.145786\pi\) | ||||
−0.896938 | + | 0.442156i | \(0.854214\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.97491 | − | 4.97491i | 0.158353 | − | 0.158353i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.364474 | + | 0.364474i | 0.0115896 | + | 0.0115896i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.02711 | 0.223224 | 0.111612 | − | 0.993752i | \(-0.464399\pi\) | ||||
0.111612 | + | 0.993752i | \(0.464399\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.22428 | 0.102319 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.2467 | + | 14.2467i | −0.451197 | + | 0.451197i | −0.895752 | − | 0.444555i | \(-0.853362\pi\) |
0.444555 | + | 0.895752i | \(0.353362\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 9.48726i | − | 0.300164i |
(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 | 1600.2.l.h.401.4 | 16 | ||
4.3 | odd | 2 | 400.2.l.i.301.4 | 16 | |||
5.2 | odd | 4 | 320.2.q.c.209.4 | 16 | |||
5.3 | odd | 4 | 320.2.q.c.209.5 | 16 | |||
5.4 | even | 2 | inner | 1600.2.l.h.401.5 | 16 | ||
16.5 | even | 4 | inner | 1600.2.l.h.1201.4 | 16 | ||
16.11 | odd | 4 | 400.2.l.i.101.4 | 16 | |||
20.3 | even | 4 | 80.2.q.c.29.1 | ✓ | 16 | ||
20.7 | even | 4 | 80.2.q.c.29.8 | yes | 16 | ||
20.19 | odd | 2 | 400.2.l.i.301.5 | 16 | |||
40.3 | even | 4 | 640.2.q.e.289.5 | 16 | |||
40.13 | odd | 4 | 640.2.q.f.289.4 | 16 | |||
40.27 | even | 4 | 640.2.q.e.289.4 | 16 | |||
40.37 | odd | 4 | 640.2.q.f.289.5 | 16 | |||
60.23 | odd | 4 | 720.2.bm.f.109.8 | 16 | |||
60.47 | odd | 4 | 720.2.bm.f.109.1 | 16 | |||
80.3 | even | 4 | 640.2.q.e.609.4 | 16 | |||
80.13 | odd | 4 | 640.2.q.f.609.5 | 16 | |||
80.27 | even | 4 | 80.2.q.c.69.1 | yes | 16 | ||
80.37 | odd | 4 | 320.2.q.c.49.5 | 16 | |||
80.43 | even | 4 | 80.2.q.c.69.8 | yes | 16 | ||
80.53 | odd | 4 | 320.2.q.c.49.4 | 16 | |||
80.59 | odd | 4 | 400.2.l.i.101.5 | 16 | |||
80.67 | even | 4 | 640.2.q.e.609.5 | 16 | |||
80.69 | even | 4 | inner | 1600.2.l.h.1201.5 | 16 | ||
80.77 | odd | 4 | 640.2.q.f.609.4 | 16 | |||
240.107 | odd | 4 | 720.2.bm.f.469.8 | 16 | |||
240.203 | odd | 4 | 720.2.bm.f.469.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.q.c.29.1 | ✓ | 16 | 20.3 | even | 4 | ||
80.2.q.c.29.8 | yes | 16 | 20.7 | even | 4 | ||
80.2.q.c.69.1 | yes | 16 | 80.27 | even | 4 | ||
80.2.q.c.69.8 | yes | 16 | 80.43 | even | 4 | ||
320.2.q.c.49.4 | 16 | 80.53 | odd | 4 | |||
320.2.q.c.49.5 | 16 | 80.37 | odd | 4 | |||
320.2.q.c.209.4 | 16 | 5.2 | odd | 4 | |||
320.2.q.c.209.5 | 16 | 5.3 | odd | 4 | |||
400.2.l.i.101.4 | 16 | 16.11 | odd | 4 | |||
400.2.l.i.101.5 | 16 | 80.59 | odd | 4 | |||
400.2.l.i.301.4 | 16 | 4.3 | odd | 2 | |||
400.2.l.i.301.5 | 16 | 20.19 | odd | 2 | |||
640.2.q.e.289.4 | 16 | 40.27 | even | 4 | |||
640.2.q.e.289.5 | 16 | 40.3 | even | 4 | |||
640.2.q.e.609.4 | 16 | 80.3 | even | 4 | |||
640.2.q.e.609.5 | 16 | 80.67 | even | 4 | |||
640.2.q.f.289.4 | 16 | 40.13 | odd | 4 | |||
640.2.q.f.289.5 | 16 | 40.37 | odd | 4 | |||
640.2.q.f.609.4 | 16 | 80.77 | odd | 4 | |||
640.2.q.f.609.5 | 16 | 80.13 | odd | 4 | |||
720.2.bm.f.109.1 | 16 | 60.47 | odd | 4 | |||
720.2.bm.f.109.8 | 16 | 60.23 | odd | 4 | |||
720.2.bm.f.469.1 | 16 | 240.203 | odd | 4 | |||
720.2.bm.f.469.8 | 16 | 240.107 | odd | 4 | |||
1600.2.l.h.401.4 | 16 | 1.1 | even | 1 | trivial | ||
1600.2.l.h.401.5 | 16 | 5.4 | even | 2 | inner | ||
1600.2.l.h.1201.4 | 16 | 16.5 | even | 4 | inner | ||
1600.2.l.h.1201.5 | 16 | 80.69 | even | 4 | inner |