Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(37,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.y (of order \(12\), degree \(4\), 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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 253.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 432.253 |
Dual form | 432.2.y.c.181.1 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36603 | + | 0.366025i | 0.965926 | + | 0.258819i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.73205 | + | 1.00000i | 0.866025 | + | 0.500000i | ||||
\(5\) | 0.267949 | + | 1.00000i | 0.119831 | + | 0.447214i | 0.999603 | − | 0.0281817i | \(-0.00897171\pi\) |
−0.879772 | + | 0.475395i | \(0.842305\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.36603 | + | 1.36603i | −0.894274 | + | 0.516309i | −0.875338 | − | 0.483512i | \(-0.839361\pi\) |
−0.0189356 | + | 0.999821i | \(0.506028\pi\) | |||||||
\(8\) | 2.00000 | + | 2.00000i | 0.707107 | + | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.46410i | 0.462990i | ||||||||
\(11\) | 4.23205 | + | 1.13397i | 1.27601 | + | 0.341906i | 0.832331 | − | 0.554279i | \(-0.187006\pi\) |
0.443680 | + | 0.896185i | \(0.353673\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.36603 | + | 0.901924i | −0.933567 | + | 0.250149i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) |
−0.240192 | + | 0.970725i | \(0.577210\pi\) | |||||||
\(14\) | −3.73205 | + | 1.00000i | −0.997433 | + | 0.267261i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | 5.73205 | 1.39023 | 0.695113 | − | 0.718900i | \(-0.255354\pi\) | ||||
0.695113 | + | 0.718900i | \(0.255354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.36603 | − | 2.36603i | −0.542803 | − | 0.542803i | 0.381546 | − | 0.924350i | \(-0.375392\pi\) |
−0.924350 | + | 0.381546i | \(0.875392\pi\) | |||||||
\(20\) | −0.535898 | + | 2.00000i | −0.119831 | + | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.36603 | + | 3.09808i | 1.14404 | + | 0.660512i | ||||
\(23\) | −4.09808 | − | 2.36603i | −0.854508 | − | 0.493350i | 0.00766135 | − | 0.999971i | \(-0.497561\pi\) |
−0.862169 | + | 0.506620i | \(0.830895\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.40192 | − | 1.96410i | 0.680385 | − | 0.392820i | ||||
\(26\) | −4.92820 | −0.966500 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.46410 | −1.03262 | ||||||||
\(29\) | 0.633975 | − | 2.36603i | 0.117726 | − | 0.439360i | −0.881750 | − | 0.471717i | \(-0.843635\pi\) |
0.999476 | + | 0.0323566i | \(0.0103012\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.267949 | + | 0.464102i | −0.0481251 | + | 0.0833551i | −0.889085 | − | 0.457743i | \(-0.848658\pi\) |
0.840959 | + | 0.541098i | \(0.181991\pi\) | |||||||
\(32\) | 1.46410 | + | 5.46410i | 0.258819 | + | 0.965926i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.83013 | + | 2.09808i | 1.34286 | + | 0.359817i | ||||
\(35\) | −2.00000 | − | 2.00000i | −0.338062 | − | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.73205 | − | 4.73205i | 0.777944 | − | 0.777944i | −0.201537 | − | 0.979481i | \(-0.564594\pi\) |
0.979481 | + | 0.201537i | \(0.0645935\pi\) | |||||||
\(38\) | −2.36603 | − | 4.09808i | −0.383820 | − | 0.664796i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.46410 | + | 2.53590i | −0.231495 | + | 0.400961i | ||||
\(41\) | −2.59808 | − | 1.50000i | −0.405751 | − | 0.234261i | 0.283211 | − | 0.959058i | \(-0.408600\pi\) |
−0.688963 | + | 0.724797i | \(0.741934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.33013 | − | 2.23205i | −1.27033 | − | 0.340385i | −0.440174 | − | 0.897912i | \(-0.645083\pi\) |
−0.830158 | + | 0.557528i | \(0.811750\pi\) | |||||||
\(44\) | 6.19615 | + | 6.19615i | 0.934105 | + | 0.934105i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.73205 | − | 4.73205i | −0.697703 | − | 0.697703i | ||||
\(47\) | −3.83013 | − | 6.63397i | −0.558681 | − | 0.967665i | −0.997607 | − | 0.0691412i | \(-0.977974\pi\) |
0.438925 | − | 0.898523i | \(-0.355359\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.232051 | − | 0.401924i | 0.0331501 | − | 0.0574177i | ||||
\(50\) | 5.36603 | − | 1.43782i | 0.758871 | − | 0.203339i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.73205 | − | 1.80385i | −0.933567 | − | 0.250149i | ||||
\(53\) | 7.46410 | − | 7.46410i | 1.02527 | − | 1.02527i | 0.0256010 | − | 0.999672i | \(-0.491850\pi\) |
0.999672 | − | 0.0256010i | \(-0.00814993\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.53590i | 0.611620i | ||||||||
\(56\) | −7.46410 | − | 2.00000i | −0.997433 | − | 0.267261i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.73205 | − | 3.00000i | 0.227429 | − | 0.393919i | ||||
\(59\) | 1.96410 | + | 7.33013i | 0.255704 | + | 0.954301i | 0.967697 | + | 0.252115i | \(0.0811261\pi\) |
−0.711993 | + | 0.702186i | \(0.752207\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | + | 11.1962i | −0.384111 | + | 1.43352i | 0.455453 | + | 0.890260i | \(0.349477\pi\) |
−0.839564 | + | 0.543261i | \(0.817189\pi\) | |||||||
\(62\) | −0.535898 | + | 0.535898i | −0.0680592 | + | 0.0680592i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | −1.80385 | − | 3.12436i | −0.223740 | − | 0.387529i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.59808 | − | 1.76795i | 0.806083 | − | 0.215989i | 0.167830 | − | 0.985816i | \(-0.446324\pi\) |
0.638253 | + | 0.769827i | \(0.279657\pi\) | |||||||
\(68\) | 9.92820 | + | 5.73205i | 1.20397 | + | 0.695113i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.00000 | − | 3.46410i | −0.239046 | − | 0.414039i | ||||
\(71\) | − | 2.92820i | − | 0.347514i | −0.984789 | − | 0.173757i | \(-0.944409\pi\) | ||
0.984789 | − | 0.173757i | \(-0.0555907\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.26795i | − | 0.733608i | −0.930298 | − | 0.366804i | \(-0.880452\pi\) | ||
0.930298 | − | 0.366804i | \(-0.119548\pi\) | |||||||
\(74\) | 8.19615 | − | 4.73205i | 0.952783 | − | 0.550090i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.73205 | − | 6.46410i | −0.198680 | − | 0.741483i | ||||
\(77\) | −11.5622 | + | 3.09808i | −1.31763 | + | 0.353059i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.00000 | − | 10.3923i | −0.675053 | − | 1.16923i | −0.976453 | − | 0.215728i | \(-0.930788\pi\) |
0.301401 | − | 0.953498i | \(-0.402546\pi\) | |||||||
\(80\) | −2.92820 | + | 2.92820i | −0.327383 | + | 0.327383i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.00000 | − | 3.00000i | −0.331295 | − | 0.331295i | ||||
\(83\) | −0.366025 | + | 1.36603i | −0.0401765 | + | 0.149941i | −0.983100 | − | 0.183068i | \(-0.941397\pi\) |
0.942924 | + | 0.333009i | \(0.108064\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.53590 | + | 5.73205i | 0.166592 | + | 0.621728i | ||||
\(86\) | −10.5622 | − | 6.09808i | −1.13895 | − | 0.657572i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.19615 | + | 10.7321i | 0.660512 | + | 1.14404i | ||||
\(89\) | 2.00000i | 0.212000i | 0.994366 | + | 0.106000i | \(0.0338043\pi\) | ||||
−0.994366 | + | 0.106000i | \(0.966196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.73205 | − | 6.73205i | 0.705711 | − | 0.705711i | ||||
\(92\) | −4.73205 | − | 8.19615i | −0.493350 | − | 0.854508i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.80385 | − | 10.4641i | −0.289195 | − | 1.07929i | ||||
\(95\) | 1.73205 | − | 3.00000i | 0.177705 | − | 0.307794i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.86603 | − | 10.1603i | −0.595605 | − | 1.03162i | −0.993461 | − | 0.114170i | \(-0.963579\pi\) |
0.397857 | − | 0.917448i | \(-0.369754\pi\) | |||||||
\(98\) | 0.464102 | − | 0.464102i | 0.0468813 | − | 0.0468813i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.85641 | 0.785641 | ||||||||
\(101\) | 2.00000 | + | 0.535898i | 0.199007 | + | 0.0533239i | 0.356946 | − | 0.934125i | \(-0.383818\pi\) |
−0.157938 | + | 0.987449i | \(0.550485\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.0981 | − | 7.56218i | −1.29059 | − | 0.745124i | −0.311833 | − | 0.950137i | \(-0.600943\pi\) |
−0.978759 | + | 0.205014i | \(0.934276\pi\) | |||||||
\(104\) | −8.53590 | − | 4.92820i | −0.837014 | − | 0.483250i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.9282 | − | 7.46410i | 1.25570 | − | 0.724978i | ||||
\(107\) | −12.4904 | + | 12.4904i | −1.20749 | + | 1.20749i | −0.235654 | + | 0.971837i | \(0.575723\pi\) |
−0.971837 | + | 0.235654i | \(0.924277\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.7321 | + | 10.7321i | 1.02794 | + | 1.02794i | 0.999598 | + | 0.0283459i | \(0.00902398\pi\) |
0.0283459 | + | 0.999598i | \(0.490976\pi\) | |||||||
\(110\) | −1.66025 | + | 6.19615i | −0.158299 | + | 0.590780i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.46410 | − | 5.46410i | −0.894274 | − | 0.516309i | ||||
\(113\) | 6.92820 | − | 12.0000i | 0.651751 | − | 1.12887i | −0.330947 | − | 0.943649i | \(-0.607368\pi\) |
0.982698 | − | 0.185216i | \(-0.0592984\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.26795 | − | 4.73205i | 0.118237 | − | 0.441266i | ||||
\(116\) | 3.46410 | − | 3.46410i | 0.321634 | − | 0.321634i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.7321i | 0.987965i | ||||||||
\(119\) | −13.5622 | + | 7.83013i | −1.24324 | + | 0.717787i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.09808 | + | 4.09808i | 0.645280 | + | 0.372552i | ||||
\(122\) | −8.19615 | + | 14.1962i | −0.742045 | + | 1.28526i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.928203 | + | 0.535898i | −0.0833551 | + | 0.0481251i | ||||
\(125\) | 6.53590 | + | 6.53590i | 0.584589 | + | 0.584589i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.19615 | 0.372348 | 0.186174 | − | 0.982517i | \(-0.440391\pi\) | ||||
0.186174 | + | 0.982517i | \(0.440391\pi\) | |||||||
\(128\) | −2.92820 | + | 10.9282i | −0.258819 | + | 0.965926i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.32051 | − | 4.92820i | −0.115816 | − | 0.432232i | ||||
\(131\) | 7.83013 | − | 2.09808i | 0.684121 | − | 0.183310i | 0.100014 | − | 0.994986i | \(-0.468111\pi\) |
0.584108 | + | 0.811676i | \(0.301445\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.83013 | + | 2.36603i | 0.765669 | + | 0.205160i | ||||
\(134\) | 9.66025 | 0.834519 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.4641 | + | 11.4641i | 0.983039 | + | 0.983039i | ||||
\(137\) | 8.25833 | − | 4.76795i | 0.705557 | − | 0.407353i | −0.103857 | − | 0.994592i | \(-0.533118\pi\) |
0.809414 | + | 0.587239i | \(0.199785\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.06218 | + | 11.4282i | 0.259731 | + | 0.969328i | 0.965397 | + | 0.260784i | \(0.0839809\pi\) |
−0.705667 | + | 0.708544i | \(0.749352\pi\) | |||||||
\(140\) | −1.46410 | − | 5.46410i | −0.123739 | − | 0.461801i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.07180 | − | 4.00000i | 0.0899432 | − | 0.335673i | ||||
\(143\) | −15.2679 | −1.27677 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.53590 | 0.210595 | ||||||||
\(146\) | 2.29423 | − | 8.56218i | 0.189872 | − | 0.708611i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 12.9282 | − | 3.46410i | 1.06269 | − | 0.284747i | ||||
\(149\) | 2.09808 | + | 7.83013i | 0.171881 | + | 0.641469i | 0.997062 | + | 0.0766003i | \(0.0244065\pi\) |
−0.825181 | + | 0.564869i | \(0.808927\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.633975 | + | 0.366025i | −0.0515921 | + | 0.0297867i | −0.525574 | − | 0.850748i | \(-0.676149\pi\) |
0.473982 | + | 0.880534i | \(0.342816\pi\) | |||||||
\(152\) | − | 9.46410i | − | 0.767640i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −16.9282 | −1.36411 | ||||||||
\(155\) | −0.535898 | − | 0.143594i | −0.0430444 | − | 0.0115337i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.73205 | + | 1.26795i | −0.377659 | + | 0.101193i | −0.442655 | − | 0.896692i | \(-0.645963\pi\) |
0.0649959 | + | 0.997886i | \(0.479297\pi\) | |||||||
\(158\) | −4.39230 | − | 16.3923i | −0.349433 | − | 1.30410i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.07180 | + | 2.92820i | −0.400961 | + | 0.231495i | ||||
\(161\) | 12.9282 | 1.01889 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.00000 | − | 7.00000i | −0.548282 | − | 0.548282i | 0.377661 | − | 0.925944i | \(-0.376728\pi\) |
−0.925944 | + | 0.377661i | \(0.876728\pi\) | |||||||
\(164\) | −3.00000 | − | 5.19615i | −0.234261 | − | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.00000 | + | 1.73205i | −0.0776151 | + | 0.134433i | ||||
\(167\) | 6.46410 | + | 3.73205i | 0.500207 | + | 0.288795i | 0.728799 | − | 0.684728i | \(-0.240079\pi\) |
−0.228592 | + | 0.973522i | \(0.573412\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.741670 | + | 0.428203i | −0.0570515 | + | 0.0329387i | ||||
\(170\) | 8.39230i | 0.643660i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.1962 | − | 12.1962i | −0.929948 | − | 0.929948i | ||||
\(173\) | 0.437822 | − | 1.63397i | 0.0332870 | − | 0.124229i | −0.947283 | − | 0.320398i | \(-0.896183\pi\) |
0.980570 | + | 0.196169i | \(0.0628501\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.36603 | + | 9.29423i | −0.405633 | + | 0.702578i | ||||
\(176\) | 4.53590 | + | 16.9282i | 0.341906 | + | 1.27601i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.732051 | + | 2.73205i | −0.0548695 | + | 0.204776i | ||||
\(179\) | 1.92820 | + | 1.92820i | 0.144121 | + | 0.144121i | 0.775486 | − | 0.631365i | \(-0.217505\pi\) |
−0.631365 | + | 0.775486i | \(0.717505\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.39230 | + | 7.39230i | −0.549466 | + | 0.549466i | −0.926286 | − | 0.376821i | \(-0.877017\pi\) |
0.376821 | + | 0.926286i | \(0.377017\pi\) | |||||||
\(182\) | 11.6603 | − | 6.73205i | 0.864316 | − | 0.499013i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.46410 | − | 12.9282i | −0.255377 | − | 0.953080i | ||||
\(185\) | 6.00000 | + | 3.46410i | 0.441129 | + | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.2583 | + | 6.50000i | 1.77394 | + | 0.475327i | ||||
\(188\) | − | 15.3205i | − | 1.11736i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.46410 | − | 3.46410i | 0.251312 | − | 0.251312i | ||||
\(191\) | 12.0263 | + | 20.8301i | 0.870191 | + | 1.50722i | 0.861799 | + | 0.507250i | \(0.169338\pi\) |
0.00839227 | + | 0.999965i | \(0.497329\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.8660 | + | 18.8205i | −0.782154 | + | 1.35473i | 0.148531 | + | 0.988908i | \(0.452545\pi\) |
−0.930685 | + | 0.365822i | \(0.880788\pi\) | |||||||
\(194\) | −4.29423 | − | 16.0263i | −0.308308 | − | 1.15062i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.803848 | − | 0.464102i | 0.0574177 | − | 0.0331501i | ||||
\(197\) | −13.6603 | + | 13.6603i | −0.973253 | + | 0.973253i | −0.999651 | − | 0.0263987i | \(-0.991596\pi\) |
0.0263987 | + | 0.999651i | \(0.491596\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.1244i | 1.78102i | 0.454965 | + | 0.890509i | \(0.349652\pi\) | ||||
−0.454965 | + | 0.890509i | \(0.650348\pi\) | |||||||
\(200\) | 10.7321 | + | 2.87564i | 0.758871 | + | 0.203339i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.53590 | + | 1.46410i | 0.178425 | + | 0.103014i | ||||
\(203\) | 1.73205 | + | 6.46410i | 0.121566 | + | 0.453691i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.803848 | − | 3.00000i | 0.0561432 | − | 0.209529i | ||||
\(206\) | −15.1244 | − | 15.1244i | −1.05376 | − | 1.05376i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −9.85641 | − | 9.85641i | −0.683419 | − | 0.683419i | ||||
\(209\) | −7.33013 | − | 12.6962i | −0.507035 | − | 0.878211i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.09808 | − | 1.09808i | 0.282123 | − | 0.0755947i | −0.114983 | − | 0.993367i | \(-0.536681\pi\) |
0.397106 | + | 0.917773i | \(0.370015\pi\) | |||||||
\(212\) | 20.3923 | − | 5.46410i | 1.40055 | − | 0.375276i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −21.6340 | + | 12.4904i | −1.47887 | + | 0.853825i | ||||
\(215\) | − | 8.92820i | − | 0.608898i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.46410i | − | 0.0993897i | ||||||
\(218\) | 10.7321 | + | 18.5885i | 0.726866 | + | 1.25897i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.53590 | + | 7.85641i | −0.305810 | + | 0.529679i | ||||
\(221\) | −19.2942 | + | 5.16987i | −1.29787 | + | 0.347763i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.02628 | − | 13.9019i | −0.537479 | − | 0.930942i | −0.999039 | − | 0.0438324i | \(-0.986043\pi\) |
0.461559 | − | 0.887109i | \(-0.347290\pi\) | |||||||
\(224\) | −10.9282 | − | 10.9282i | −0.730171 | − | 0.730171i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.8564 | − | 13.8564i | 0.921714 | − | 0.921714i | ||||
\(227\) | 0.571797 | − | 2.13397i | 0.0379515 | − | 0.141637i | −0.944351 | − | 0.328941i | \(-0.893308\pi\) |
0.982302 | + | 0.187304i | \(0.0599750\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.83013 | − | 6.83013i | −0.120938 | − | 0.451347i | 0.878724 | − | 0.477330i | \(-0.158395\pi\) |
−0.999662 | + | 0.0259823i | \(0.991729\pi\) | |||||||
\(230\) | 3.46410 | − | 6.00000i | 0.228416 | − | 0.395628i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.00000 | − | 3.46410i | 0.393919 | − | 0.227429i | ||||
\(233\) | 3.19615i | 0.209387i | 0.994505 | + | 0.104693i | \(0.0333861\pi\) | ||||
−0.994505 | + | 0.104693i | \(0.966614\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.60770 | − | 5.60770i | 0.365806 | − | 0.365806i | ||||
\(236\) | −3.92820 | + | 14.6603i | −0.255704 | + | 0.954301i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −21.3923 | + | 5.73205i | −1.38666 | + | 0.371554i | ||||
\(239\) | 7.90192 | − | 13.6865i | 0.511133 | − | 0.885308i | −0.488784 | − | 0.872405i | \(-0.662559\pi\) |
0.999917 | − | 0.0129033i | \(-0.00410736\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.5981 | − | 20.0885i | −0.747098 | − | 1.29401i | −0.949208 | − | 0.314649i | \(-0.898113\pi\) |
0.202110 | − | 0.979363i | \(-0.435220\pi\) | |||||||
\(242\) | 8.19615 | + | 8.19615i | 0.526869 | + | 0.526869i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −16.3923 | + | 16.3923i | −1.04941 | + | 1.04941i | ||||
\(245\) | 0.464102 | + | 0.124356i | 0.0296504 | + | 0.00794479i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.0981 | + | 5.83013i | 0.642525 | + | 0.370962i | ||||
\(248\) | −1.46410 | + | 0.392305i | −0.0929705 | + | 0.0249114i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.53590 | + | 11.3205i | 0.413367 | + | 0.715972i | ||||
\(251\) | 5.83013 | − | 5.83013i | 0.367994 | − | 0.367994i | −0.498751 | − | 0.866745i | \(-0.666208\pi\) |
0.866745 | + | 0.498751i | \(0.166208\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.6603 | − | 14.6603i | −0.921682 | − | 0.921682i | ||||
\(254\) | 5.73205 | + | 1.53590i | 0.359661 | + | 0.0963708i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −9.42820 | + | 16.3301i | −0.588115 | + | 1.01865i | 0.406364 | + | 0.913711i | \(0.366796\pi\) |
−0.994479 | + | 0.104934i | \(0.966537\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.73205 | + | 17.6603i | −0.294035 | + | 1.09735i | ||||
\(260\) | − | 7.21539i | − | 0.447480i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.4641 | 0.708255 | ||||||||
\(263\) | −2.49038 | + | 1.43782i | −0.153563 | + | 0.0886599i | −0.574813 | − | 0.818285i | \(-0.694925\pi\) |
0.421249 | + | 0.906945i | \(0.361592\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.46410 | + | 5.46410i | 0.581375 | + | 0.335657i | ||||
\(266\) | 11.1962 | + | 6.46410i | 0.686480 | + | 0.396339i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.1962 | + | 3.53590i | 0.806083 | + | 0.215989i | ||||
\(269\) | −1.26795 | − | 1.26795i | −0.0773082 | − | 0.0773082i | 0.667395 | − | 0.744704i | \(-0.267409\pi\) |
−0.744704 | + | 0.667395i | \(0.767409\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.392305 | −0.0238308 | −0.0119154 | − | 0.999929i | \(-0.503793\pi\) | ||||
−0.0119154 | + | 0.999929i | \(0.503793\pi\) | |||||||
\(272\) | 11.4641 | + | 19.8564i | 0.695113 | + | 1.20397i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.0263 | − | 3.49038i | 0.786946 | − | 0.210862i | ||||
\(275\) | 16.6244 | − | 4.45448i | 1.00249 | − | 0.268615i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.2224 | + | 6.75833i | 1.51547 | + | 0.406069i | 0.918247 | − | 0.396007i | \(-0.129605\pi\) |
0.597222 | + | 0.802076i | \(0.296271\pi\) | |||||||
\(278\) | 16.7321i | 1.00352i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 8.00000i | − | 0.478091i | ||||||
\(281\) | −8.66025 | + | 5.00000i | −0.516627 | + | 0.298275i | −0.735554 | − | 0.677466i | \(-0.763078\pi\) |
0.218926 | + | 0.975741i | \(0.429745\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.24167 | + | 19.5622i | 0.311585 | + | 1.16285i | 0.927127 | + | 0.374747i | \(0.122270\pi\) |
−0.615542 | + | 0.788104i | \(0.711063\pi\) | |||||||
\(284\) | 2.92820 | − | 5.07180i | 0.173757 | − | 0.300956i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.8564 | − | 5.58846i | −1.23327 | − | 0.330452i | ||||
\(287\) | 8.19615 | 0.483804 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.8564 | 0.932730 | ||||||||
\(290\) | 3.46410 | + | 0.928203i | 0.203419 | + | 0.0545060i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.26795 | − | 10.8564i | 0.366804 | − | 0.635323i | ||||
\(293\) | −1.43782 | − | 5.36603i | −0.0839985 | − | 0.313487i | 0.911124 | − | 0.412132i | \(-0.135216\pi\) |
−0.995123 | + | 0.0986454i | \(0.968549\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.80385 | + | 3.92820i | −0.396135 | + | 0.228709i | ||||
\(296\) | 18.9282 | 1.10018 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.4641i | 0.664098i | ||||||||
\(299\) | 15.9282 | + | 4.26795i | 0.921152 | + | 0.246822i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.7583 | − | 6.09808i | 1.31177 | − | 0.351487i | ||||
\(302\) | −1.00000 | + | 0.267949i | −0.0575435 | + | 0.0154187i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.46410 | − | 12.9282i | 0.198680 | − | 0.741483i | ||||
\(305\) | −12.0000 | −0.687118 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.02628 | + | 3.02628i | 0.172719 | + | 0.172719i | 0.788173 | − | 0.615454i | \(-0.211027\pi\) |
−0.615454 | + | 0.788173i | \(0.711027\pi\) | |||||||
\(308\) | −23.1244 | − | 6.19615i | −1.31763 | − | 0.353059i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.679492 | − | 0.392305i | −0.0385925 | − | 0.0222814i | ||||
\(311\) | −19.0981 | − | 11.0263i | −1.08295 | − | 0.625243i | −0.151261 | − | 0.988494i | \(-0.548333\pi\) |
−0.931691 | + | 0.363251i | \(0.881667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.6506 | + | 10.7679i | −1.05420 | + | 0.608640i | −0.923821 | − | 0.382824i | \(-0.874951\pi\) |
−0.130375 | + | 0.991465i | \(0.541618\pi\) | |||||||
\(314\) | −6.92820 | −0.390981 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 24.0000i | − | 1.35011i | ||||||
\(317\) | −5.50962 | + | 20.5622i | −0.309451 | + | 1.15489i | 0.619595 | + | 0.784922i | \(0.287297\pi\) |
−0.929046 | + | 0.369965i | \(0.879370\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.36603 | − | 9.29423i | 0.300440 | − | 0.520377i | ||||
\(320\) | −8.00000 | + | 2.14359i | −0.447214 | + | 0.119831i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 17.6603 | + | 4.73205i | 0.984167 | + | 0.263707i | ||||
\(323\) | −13.5622 | − | 13.5622i | −0.754620 | − | 0.754620i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.67949 | + | 9.67949i | −0.536922 | + | 0.536922i | ||||
\(326\) | −7.00000 | − | 12.1244i | −0.387694 | − | 0.671506i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.19615 | − | 8.19615i | −0.121262 | − | 0.452557i | ||||
\(329\) | 18.1244 | + | 10.4641i | 0.999228 | + | 0.576905i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.0980762 | − | 0.0262794i | −0.00539076 | − | 0.00144445i | 0.256123 | − | 0.966644i | \(-0.417555\pi\) |
−0.261513 | + | 0.965200i | \(0.584222\pi\) | |||||||
\(332\) | −2.00000 | + | 2.00000i | −0.109764 | + | 0.109764i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.46410 | + | 7.46410i | 0.408417 | + | 0.408417i | ||||
\(335\) | 3.53590 | + | 6.12436i | 0.193187 | + | 0.334609i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.89230 | − | 15.4019i | 0.484395 | − | 0.838996i | −0.515445 | − | 0.856923i | \(-0.672373\pi\) |
0.999839 | + | 0.0179267i | \(0.00570654\pi\) | |||||||
\(338\) | −1.16987 | + | 0.313467i | −0.0636327 | + | 0.0170503i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.07180 | + | 11.4641i | −0.166592 | + | 0.621728i | ||||
\(341\) | −1.66025 | + | 1.66025i | −0.0899078 | + | 0.0899078i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.8564i | − | 0.964155i | ||||||
\(344\) | −12.1962 | − | 21.1244i | −0.657572 | − | 1.13895i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.19615 | − | 2.07180i | 0.0643056 | − | 0.111380i | ||||
\(347\) | −4.72243 | − | 17.6244i | −0.253513 | − | 0.946125i | −0.968911 | − | 0.247408i | \(-0.920421\pi\) |
0.715398 | − | 0.698717i | \(-0.246245\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.26795 | + | 15.9282i | −0.228458 | + | 0.852617i | 0.752531 | + | 0.658556i | \(0.228833\pi\) |
−0.980989 | + | 0.194061i | \(0.937834\pi\) | |||||||
\(350\) | −10.7321 | + | 10.7321i | −0.573652 | + | 0.573652i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 24.7846i | 1.32102i | ||||||||
\(353\) | −7.16025 | − | 12.4019i | −0.381102 | − | 0.660088i | 0.610118 | − | 0.792310i | \(-0.291122\pi\) |
−0.991220 | + | 0.132223i | \(0.957789\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.92820 | − | 0.784610i | 0.155413 | − | 0.0416428i | ||||
\(356\) | −2.00000 | + | 3.46410i | −0.106000 | + | 0.183597i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.92820 | + | 3.33975i | 0.101909 | + | 0.176511i | ||||
\(359\) | − | 11.2679i | − | 0.594700i | −0.954769 | − | 0.297350i | \(-0.903897\pi\) | ||
0.954769 | − | 0.297350i | \(-0.0961028\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 7.80385i | − | 0.410729i | ||||||
\(362\) | −12.8038 | + | 7.39230i | −0.672955 | + | 0.388531i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 18.3923 | − | 4.92820i | 0.964019 | − | 0.258308i | ||||
\(365\) | 6.26795 | − | 1.67949i | 0.328079 | − | 0.0879086i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.1244 | + | 24.4641i | 0.737285 | + | 1.27702i | 0.953713 | + | 0.300717i | \(0.0972260\pi\) |
−0.216428 | + | 0.976299i | \(0.569441\pi\) | |||||||
\(368\) | − | 18.9282i | − | 0.986701i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.92820 | + | 6.92820i | 0.360180 | + | 0.360180i | ||||
\(371\) | −7.46410 | + | 27.8564i | −0.387517 | + | 1.44623i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.36603 | − | 27.4904i | −0.381398 | − | 1.42340i | −0.843767 | − | 0.536710i | \(-0.819667\pi\) |
0.462368 | − | 0.886688i | \(-0.347000\pi\) | |||||||
\(374\) | 30.7583 | + | 17.7583i | 1.59048 | + | 0.918261i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.60770 | − | 20.9282i | 0.289195 | − | 1.07929i | ||||
\(377\) | 8.53590i | 0.439621i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.75833 | − | 3.75833i | 0.193052 | − | 0.193052i | −0.603961 | − | 0.797014i | \(-0.706412\pi\) |
0.797014 | + | 0.603961i | \(0.206412\pi\) | |||||||
\(380\) | 6.00000 | − | 3.46410i | 0.307794 | − | 0.177705i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.80385 | + | 32.8564i | 0.450444 | + | 1.68108i | ||||
\(383\) | 6.73205 | − | 11.6603i | 0.343992 | − | 0.595811i | −0.641178 | − | 0.767392i | \(-0.721554\pi\) |
0.985170 | + | 0.171581i | \(0.0548874\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.19615 | − | 10.7321i | −0.315785 | − | 0.546956i | ||||
\(386\) | −21.7321 | + | 21.7321i | −1.10613 | + | 1.10613i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 23.4641i | − | 1.19121i | ||||||
\(389\) | −19.7583 | − | 5.29423i | −1.00179 | − | 0.268428i | −0.279593 | − | 0.960119i | \(-0.590200\pi\) |
−0.722194 | + | 0.691691i | \(0.756866\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.4904 | − | 13.5622i | −1.18796 | − | 0.685869i | ||||
\(392\) | 1.26795 | − | 0.339746i | 0.0640411 | − | 0.0171598i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −23.6603 | + | 13.6603i | −1.19199 | + | 0.688194i | ||||
\(395\) | 8.78461 | − | 8.78461i | 0.442002 | − | 0.442002i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.26795 | − | 9.26795i | −0.465145 | − | 0.465145i | 0.435192 | − | 0.900337i | \(-0.356680\pi\) |
−0.900337 | + | 0.435192i | \(0.856680\pi\) | |||||||
\(398\) | −9.19615 | + | 34.3205i | −0.460961 | + | 1.72033i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.6077 | + | 7.85641i | 0.680385 | + | 0.392820i | ||||
\(401\) | 1.79423 | − | 3.10770i | 0.0895995 | − | 0.155191i | −0.817742 | − | 0.575584i | \(-0.804775\pi\) |
0.907342 | + | 0.420393i | \(0.138108\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.483340 | − | 1.80385i | 0.0240769 | − | 0.0898560i | ||||
\(404\) | 2.92820 | + | 2.92820i | 0.145684 | + | 0.145684i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.46410i | 0.469695i | ||||||||
\(407\) | 25.3923 | − | 14.6603i | 1.25865 | − | 0.726682i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.8660 | − | 16.0885i | −1.37789 | − | 0.795523i | −0.385981 | − | 0.922507i | \(-0.626137\pi\) |
−0.991905 | + | 0.126984i | \(0.959470\pi\) | |||||||
\(410\) | 2.19615 | − | 3.80385i | 0.108460 | − | 0.187859i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15.1244 | − | 26.1962i | −0.745124 | − | 1.29059i | ||||
\(413\) | −14.6603 | − | 14.6603i | −0.721384 | − | 0.721384i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.46410 | −0.0718699 | ||||||||
\(416\) | −9.85641 | − | 17.0718i | −0.483250 | − | 0.837014i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.36603 | − | 20.0263i | −0.262461 | − | 0.979517i | ||||
\(419\) | 6.63397 | − | 1.77757i | 0.324091 | − | 0.0868399i | −0.0931055 | − | 0.995656i | \(-0.529679\pi\) |
0.417196 | + | 0.908816i | \(0.363013\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.5885 | − | 8.19615i | −1.49079 | − | 0.399456i | −0.580786 | − | 0.814056i | \(-0.697255\pi\) |
−0.910004 | + | 0.414600i | \(0.863922\pi\) | |||||||
\(422\) | 6.00000 | 0.292075 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 29.8564 | 1.44996 | ||||||||
\(425\) | 19.5000 | − | 11.2583i | 0.945889 | − | 0.546109i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.19615 | − | 30.5885i | −0.396640 | − | 1.48028i | ||||
\(428\) | −34.1244 | + | 9.14359i | −1.64946 | + | 0.441972i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.26795 | − | 12.1962i | 0.157595 | − | 0.588151i | ||||
\(431\) | 16.1962 | 0.780141 | 0.390071 | − | 0.920785i | \(-0.372451\pi\) | ||||
0.390071 | + | 0.920785i | \(0.372451\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.73205 | −0.275465 | −0.137732 | − | 0.990469i | \(-0.543981\pi\) | ||||
−0.137732 | + | 0.990469i | \(0.543981\pi\) | |||||||
\(434\) | 0.535898 | − | 2.00000i | 0.0257239 | − | 0.0960031i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.85641 | + | 29.3205i | 0.376254 | + | 1.40420i | ||||
\(437\) | 4.09808 | + | 15.2942i | 0.196038 | + | 0.731622i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.8564 | − | 13.1962i | 1.09088 | − | 0.629818i | 0.157067 | − | 0.987588i | \(-0.449796\pi\) |
0.933810 | + | 0.357770i | \(0.116463\pi\) | |||||||
\(440\) | −9.07180 | + | 9.07180i | −0.432481 | + | 0.432481i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −28.2487 | −1.34365 | ||||||||
\(443\) | −17.2583 | − | 4.62436i | −0.819968 | − | 0.219710i | −0.175636 | − | 0.984455i | \(-0.556198\pi\) |
−0.644332 | + | 0.764745i | \(0.722865\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.00000 | + | 0.535898i | −0.0948091 | + | 0.0254040i | ||||
\(446\) | −5.87564 | − | 21.9282i | −0.278220 | − | 1.03833i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10.9282 | − | 18.9282i | −0.516309 | − | 0.894274i | ||||
\(449\) | 3.33975 | 0.157612 | 0.0788062 | − | 0.996890i | \(-0.474889\pi\) | ||||
0.0788062 | + | 0.996890i | \(0.474889\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.29423 | − | 9.29423i | −0.437648 | − | 0.437648i | ||||
\(452\) | 24.0000 | − | 13.8564i | 1.12887 | − | 0.651751i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.56218 | − | 2.70577i | 0.0733166 | − | 0.126988i | ||||
\(455\) | 8.53590 | + | 4.92820i | 0.400169 | + | 0.231038i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.25833 | + | 1.30385i | −0.105640 | + | 0.0609914i | −0.551889 | − | 0.833917i | \(-0.686093\pi\) |
0.446249 | + | 0.894909i | \(0.352760\pi\) | |||||||
\(458\) | − | 10.0000i | − | 0.467269i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.92820 | − | 6.92820i | 0.323029 | − | 0.323029i | ||||
\(461\) | 9.56218 | − | 35.6865i | 0.445355 | − | 1.66209i | −0.269642 | − | 0.962961i | \(-0.586906\pi\) |
0.714997 | − | 0.699127i | \(-0.246428\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.19615 | − | 2.07180i | 0.0555899 | − | 0.0962846i | −0.836891 | − | 0.547369i | \(-0.815629\pi\) |
0.892481 | + | 0.451085i | \(0.148963\pi\) | |||||||
\(464\) | 9.46410 | − | 2.53590i | 0.439360 | − | 0.117726i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.16987 | + | 4.36603i | −0.0541933 | + | 0.202252i | ||||
\(467\) | −2.63397 | − | 2.63397i | −0.121886 | − | 0.121886i | 0.643533 | − | 0.765419i | \(-0.277468\pi\) |
−0.765419 | + | 0.643533i | \(0.777468\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.1962 | + | 13.1962i | −0.609342 | + | 0.609342i | ||||
\(470\) | 9.71281 | − | 5.60770i | 0.448019 | − | 0.258664i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10.7321 | + | 18.5885i | −0.493983 | + | 0.855603i | ||||
\(473\) | −32.7224 | − | 18.8923i | −1.50458 | − | 0.868669i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.6962 | − | 3.40192i | −0.582539 | − | 0.156091i | ||||
\(476\) | −31.3205 | −1.43557 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.8038 | − | 15.8038i | 0.722851 | − | 0.722851i | ||||
\(479\) | −4.16987 | − | 7.22243i | −0.190526 | − | 0.330001i | 0.754898 | − | 0.655842i | \(-0.227686\pi\) |
−0.945425 | + | 0.325840i | \(0.894353\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.6603 | + | 20.1962i | −0.531662 | + | 0.920865i | ||||
\(482\) | −8.49038 | − | 31.6865i | −0.386726 | − | 1.44328i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.19615 | + | 14.1962i | 0.372552 | + | 0.645280i | ||||
\(485\) | 8.58846 | − | 8.58846i | 0.389982 | − | 0.389982i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.80385i | 0.262997i | 0.991316 | + | 0.131499i | \(0.0419789\pi\) | ||||
−0.991316 | + | 0.131499i | \(0.958021\pi\) | |||||||
\(488\) | −28.3923 | + | 16.3923i | −1.28526 | + | 0.742045i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.588457 | + | 0.339746i | 0.0265838 | + | 0.0153482i | ||||
\(491\) | −3.72243 | − | 13.8923i | −0.167991 | − | 0.626951i | −0.997640 | − | 0.0686652i | \(-0.978126\pi\) |
0.829649 | − | 0.558286i | \(-0.188541\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.63397 | − | 13.5622i | 0.163666 | − | 0.610810i | ||||
\(494\) | 11.6603 | + | 11.6603i | 0.524620 | + | 0.524620i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.14359 | −0.0962502 | ||||||||
\(497\) | 4.00000 | + | 6.92820i | 0.179425 | + | 0.310772i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.69615 | − | 2.33013i | 0.389293 | − | 0.104311i | −0.0588630 | − | 0.998266i | \(-0.518748\pi\) |
0.448156 | + | 0.893955i | \(0.352081\pi\) | |||||||
\(500\) | 4.78461 | + | 17.8564i | 0.213974 | + | 0.798563i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.0981 | − | 5.83013i | 0.450699 | − | 0.260211i | ||||
\(503\) | 27.7128i | 1.23565i | 0.786314 | + | 0.617827i | \(0.211987\pi\) | ||||
−0.786314 | + | 0.617827i | \(0.788013\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.14359i | 0.0953887i | ||||||||
\(506\) | −14.6603 | − | 25.3923i | −0.651728 | − | 1.12883i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.26795 | + | 4.19615i | 0.322463 | + | 0.186174i | ||||
\(509\) | 11.4641 | − | 3.07180i | 0.508137 | − | 0.136155i | 0.00436335 | − | 0.999990i | \(-0.498611\pi\) |
0.503774 | + | 0.863835i | \(0.331944\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.56218 | + | 14.8301i | 0.378768 | + | 0.656046i | ||||
\(512\) | −16.0000 | + | 16.0000i | −0.707107 | + | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.8564 | + | 18.8564i | −0.831720 | + | 0.831720i | ||||
\(515\) | 4.05256 | − | 15.1244i | 0.178577 | − | 0.666459i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.68653 | − | 32.4186i | −0.382033 | − | 1.42577i | ||||
\(518\) | −12.9282 | + | 22.3923i | −0.568033 | + | 0.983861i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.64102 | − | 9.85641i | 0.115816 | − | 0.432232i | ||||
\(521\) | − | 13.0000i | − | 0.569540i | −0.958596 | − | 0.284770i | \(-0.908083\pi\) | ||
0.958596 | − | 0.284770i | \(-0.0919173\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.53590 | + | 7.53590i | −0.329522 | + | 0.329522i | −0.852405 | − | 0.522883i | \(-0.824857\pi\) |
0.522883 | + | 0.852405i | \(0.324857\pi\) | |||||||
\(524\) | 15.6603 | + | 4.19615i | 0.684121 | + | 0.183310i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.92820 | + | 1.05256i | −0.171278 | + | 0.0458937i | ||||
\(527\) | −1.53590 | + | 2.66025i | −0.0669048 | + | 0.115882i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.303848 | − | 0.526279i | −0.0132108 | − | 0.0228817i | ||||
\(530\) | 10.9282 | + | 10.9282i | 0.474691 | + | 0.474691i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.9282 | + | 12.9282i | 0.560509 | + | 0.560509i | ||||
\(533\) | 10.0981 | + | 2.70577i | 0.437396 | + | 0.117200i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.8372 | − | 9.14359i | −0.684701 | − | 0.395312i | ||||
\(536\) | 16.7321 | + | 9.66025i | 0.722715 | + | 0.417259i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.26795 | − | 2.19615i | −0.0546652 | − | 0.0946829i | ||||
\(539\) | 1.43782 | − | 1.43782i | 0.0619314 | − | 0.0619314i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.19615 | + | 2.19615i | 0.0944200 | + | 0.0944200i | 0.752739 | − | 0.658319i | \(-0.228732\pi\) |
−0.658319 | + | 0.752739i | \(0.728732\pi\) | |||||||
\(542\) | −0.535898 | − | 0.143594i | −0.0230188 | − | 0.00616787i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.39230 | + | 31.3205i | 0.359817 | + | 1.34286i | ||||
\(545\) | −7.85641 | + | 13.6077i | −0.336531 | + | 0.582890i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.74167 | + | 32.6244i | −0.373767 | + | 1.39492i | 0.481371 | + | 0.876517i | \(0.340139\pi\) |
−0.855138 | + | 0.518400i | \(0.826528\pi\) | |||||||
\(548\) | 19.0718 | 0.814707 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 24.3397 | 1.03785 | ||||||||
\(551\) | −7.09808 | + | 4.09808i | −0.302388 | + | 0.174584i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.3923 | + | 16.3923i | 1.20736 | + | 0.697072i | ||||
\(554\) | 31.9808 | + | 18.4641i | 1.35873 | + | 0.784465i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.12436 | + | 22.8564i | −0.259731 | + | 0.969328i | ||||
\(557\) | 14.8038 | + | 14.8038i | 0.627259 | + | 0.627259i | 0.947378 | − | 0.320118i | \(-0.103723\pi\) |
−0.320118 | + | 0.947378i | \(0.603723\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.0526 | 1.27109 | ||||||||
\(560\) | 2.92820 | − | 10.9282i | 0.123739 | − | 0.461801i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.6603 | + | 3.66025i | −0.576223 | + | 0.154398i | ||||
\(563\) | −26.9904 | + | 7.23205i | −1.13751 | + | 0.304795i | −0.777949 | − | 0.628327i | \(-0.783740\pi\) |
−0.359560 | + | 0.933122i | \(0.617073\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.8564 | + | 3.71281i | 0.582943 | + | 0.156199i | ||||
\(566\) | 28.6410i | 1.20387i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.85641 | − | 5.85641i | 0.245729 | − | 0.245729i | ||||
\(569\) | −18.4019 | + | 10.6244i | −0.771449 | + | 0.445396i | −0.833391 | − | 0.552684i | \(-0.813604\pi\) |
0.0619424 | + | 0.998080i | \(0.480270\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.892305 | + | 3.33013i | 0.0373418 | + | 0.139361i | 0.982080 | − | 0.188464i | \(-0.0603509\pi\) |
−0.944738 | + | 0.327825i | \(0.893684\pi\) | |||||||
\(572\) | −26.4449 | − | 15.2679i | −1.10572 | − | 0.638385i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.1962 | + | 3.00000i | 0.467318 | + | 0.125218i | ||||
\(575\) | −18.5885 | −0.775192 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.78461 | −0.240816 | −0.120408 | − | 0.992724i | \(-0.538420\pi\) | ||||
−0.120408 | + | 0.992724i | \(0.538420\pi\) | |||||||
\(578\) | 21.6603 | + | 5.80385i | 0.900948 | + | 0.241408i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.39230 | + | 2.53590i | 0.182381 | + | 0.105297i | ||||
\(581\) | −1.00000 | − | 3.73205i | −0.0414870 | − | 0.154832i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 40.0526 | − | 23.1244i | 1.65881 | − | 0.957713i | ||||
\(584\) | 12.5359 | − | 12.5359i | 0.518739 | − | 0.518739i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 7.85641i | − | 0.324545i | ||||||
\(587\) | 26.9904 | + | 7.23205i | 1.11401 | + | 0.298499i | 0.768458 | − | 0.639900i | \(-0.221024\pi\) |
0.345554 | + | 0.938399i | \(0.387691\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.73205 | − | 0.464102i | 0.0713679 | − | 0.0191230i | ||||
\(590\) | −10.7321 | + | 2.87564i | −0.441832 | + | 0.118388i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 25.8564 | + | 6.92820i | 1.06269 | + | 0.284747i | ||||
\(593\) | −17.4641 | −0.717165 | −0.358582 | − | 0.933498i | \(-0.616740\pi\) | ||||
−0.358582 | + | 0.933498i | \(0.616740\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.4641 | − | 11.4641i | −0.469982 | − | 0.469982i | ||||
\(596\) | −4.19615 | + | 15.6603i | −0.171881 | + | 0.641469i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 20.1962 | + | 11.6603i | 0.825882 | + | 0.476823i | ||||
\(599\) | 11.3205 | + | 6.53590i | 0.462543 | + | 0.267050i | 0.713113 | − | 0.701049i | \(-0.247285\pi\) |
−0.250570 | + | 0.968099i | \(0.580618\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.5526 | − | 11.8660i | 0.838356 | − | 0.484025i | −0.0183488 | − | 0.999832i | \(-0.505841\pi\) |
0.856705 | + | 0.515806i | \(0.172508\pi\) | |||||||
\(602\) | 33.3205 | 1.35804 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.46410 | −0.0595734 | ||||||||
\(605\) | −2.19615 | + | 8.19615i | −0.0892863 | + | 0.333221i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.58846 | + | 14.8756i | −0.348595 | + | 0.603784i | −0.986000 | − | 0.166745i | \(-0.946674\pi\) |
0.637405 | + | 0.770529i | \(0.280008\pi\) | |||||||
\(608\) | 9.46410 | − | 16.3923i | 0.383820 | − | 0.664796i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −16.3923 | − | 4.39230i | −0.663705 | − | 0.177839i | ||||
\(611\) | 18.8756 | + | 18.8756i | 0.763627 | + | 0.763627i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.6603 | + | 15.6603i | −0.632512 | + | 0.632512i | −0.948697 | − | 0.316186i | \(-0.897598\pi\) |
0.316186 | + | 0.948697i | \(0.397598\pi\) | |||||||
\(614\) | 3.02628 | + | 5.24167i | 0.122131 | + | 0.211537i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −29.3205 | − | 16.9282i | −1.18136 | − | 0.682057i | ||||
\(617\) | −35.0885 | − | 20.2583i | −1.41261 | − | 0.815570i | −0.416975 | − | 0.908918i | \(-0.636910\pi\) |
−0.995633 | + | 0.0933485i | \(0.970243\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.5981 | − | 4.17949i | −0.626940 | − | 0.167988i | −0.0686590 | − | 0.997640i | \(-0.521872\pi\) |
−0.558281 | + | 0.829652i | \(0.688539\pi\) | |||||||
\(620\) | −0.784610 | − | 0.784610i | −0.0315107 | − | 0.0315107i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −22.0526 | − | 22.0526i | −0.884227 | − | 0.884227i | ||||
\(623\) | −2.73205 | − | 4.73205i | −0.109457 | − | 0.189586i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.03590 | − | 8.72243i | 0.201436 | − | 0.348897i | ||||
\(626\) | −29.4186 | + | 7.88269i | −1.17580 | + | 0.315055i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.46410 | − | 2.53590i | −0.377659 | − | 0.101193i | ||||
\(629\) | 27.1244 | − | 27.1244i | 1.08152 | − | 1.08152i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.6077i | 0.700951i | 0.936572 | + | 0.350476i | \(0.113980\pi\) | ||||
−0.936572 | + | 0.350476i | \(0.886020\pi\) | |||||||
\(632\) | 8.78461 | − | 32.7846i | 0.349433 | − | 1.30410i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15.0526 | + | 26.0718i | −0.597813 | + | 1.03544i | ||||
\(635\) | 1.12436 | + | 4.19615i | 0.0446187 | + | 0.166519i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.418584 | + | 1.56218i | −0.0165849 | + | 0.0618957i | ||||
\(638\) | 10.7321 | − | 10.7321i | 0.424886 | − | 0.424886i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.7128 | −0.462990 | ||||||||
\(641\) | 19.7942 | + | 34.2846i | 0.781825 | + | 1.35416i | 0.930878 | + | 0.365331i | \(0.119044\pi\) |
−0.149053 | + | 0.988829i | \(0.547622\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.76795 | − | 2.34936i | 0.345774 | − | 0.0926499i | −0.0817525 | − | 0.996653i | \(-0.526052\pi\) |
0.427527 | + | 0.904003i | \(0.359385\pi\) | |||||||
\(644\) | 22.3923 | + | 12.9282i | 0.882380 | + | 0.509443i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.5622 | − | 23.4904i | −0.533597 | − | 0.924217i | ||||
\(647\) | − | 16.7321i | − | 0.657805i | −0.944364 | − | 0.328902i | \(-0.893321\pi\) | ||
0.944364 | − | 0.328902i | \(-0.106679\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33.2487i | 1.30513i | ||||||||
\(650\) | −16.7654 | + | 9.67949i | −0.657592 | + | 0.379661i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.12436 | − | 19.1244i | −0.200685 | − | 0.748968i | ||||
\(653\) | 27.4904 | − | 7.36603i | 1.07578 | − | 0.288255i | 0.322915 | − | 0.946428i | \(-0.395337\pi\) |
0.752867 | + | 0.658173i | \(0.228671\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.19615 | + | 7.26795i | 0.163957 | + | 0.283982i | ||||
\(656\) | − | 12.0000i | − | 0.468521i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 20.9282 | + | 20.9282i | 0.815866 | + | 0.815866i | ||||
\(659\) | −4.02628 | + | 15.0263i | −0.156842 | + | 0.585341i | 0.842099 | + | 0.539323i | \(0.181320\pi\) |
−0.998941 | + | 0.0460178i | \(0.985347\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.19615 | + | 8.19615i | 0.0854204 | + | 0.318793i | 0.995393 | − | 0.0958740i | \(-0.0305646\pi\) |
−0.909973 | + | 0.414667i | \(0.863898\pi\) | |||||||
\(662\) | −0.124356 | − | 0.0717968i | −0.00483322 | − | 0.00279046i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.46410 | + | 2.00000i | −0.134433 | + | 0.0776151i | ||||
\(665\) | 9.46410i | 0.367002i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.19615 | + | 8.19615i | −0.317356 | + | 0.317356i | ||||
\(668\) | 7.46410 | + | 12.9282i | 0.288795 | + | 0.500207i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.58846 | + | 9.66025i | 0.100001 | + | 0.373208i | ||||
\(671\) | −25.3923 | + | 43.9808i | −0.980259 | + | 1.69786i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.1962 | + | 33.2487i | 0.739957 | + | 1.28164i | 0.952514 | + | 0.304495i | \(0.0984877\pi\) |
−0.212557 | + | 0.977149i | \(0.568179\pi\) | |||||||
\(674\) | 17.7846 | − | 17.7846i | 0.685038 | − | 0.685038i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.71281 | −0.0658774 | ||||||||
\(677\) | 4.73205 | + | 1.26795i | 0.181867 | + | 0.0487312i | 0.348603 | − | 0.937270i | \(-0.386656\pi\) |
−0.166736 | + | 0.986002i | \(0.553323\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.7583 | + | 16.0263i | 1.06527 | + | 0.615032i | ||||
\(680\) | −8.39230 | + | 14.5359i | −0.321830 | + | 0.557426i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.87564 | + | 1.66025i | −0.110114 | + | 0.0635744i | ||||
\(683\) | 20.2942 | − | 20.2942i | 0.776537 | − | 0.776537i | −0.202703 | − | 0.979240i | \(-0.564973\pi\) |
0.979240 | + | 0.202703i | \(0.0649726\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.98076 | + | 6.98076i | 0.266721 | + | 0.266721i | ||||
\(686\) | 6.53590 | − | 24.3923i | 0.249542 | − | 0.931303i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.92820 | − | 33.3205i | −0.340385 | − | 1.27033i | ||||
\(689\) | −18.3923 | + | 31.8564i | −0.700691 | + | 1.21363i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.49038 | + | 9.29423i | −0.0947386 | + | 0.353569i | −0.996980 | − | 0.0776628i | \(-0.975254\pi\) |
0.902241 | + | 0.431232i | \(0.141921\pi\) | |||||||
\(692\) | 2.39230 | − | 2.39230i | 0.0909418 | − | 0.0909418i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 25.8038i | − | 0.979501i | ||||||
\(695\) | −10.6077 | + | 6.12436i | −0.402373 | + | 0.232310i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.8923 | − | 8.59808i | −0.564086 | − | 0.325675i | ||||
\(698\) | −11.6603 | + | 20.1962i | −0.441347 | + | 0.764436i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −18.5885 | + | 10.7321i | −0.702578 | + | 0.405633i | ||||
\(701\) | 6.66025 | + | 6.66025i | 0.251554 | + | 0.251554i | 0.821608 | − | 0.570053i | \(-0.193077\pi\) |
−0.570053 | + | 0.821608i | \(0.693077\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.3923 | −0.844542 | ||||||||
\(704\) | −9.07180 | + | 33.8564i | −0.341906 | + | 1.27601i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.24167 | − | 19.5622i | −0.197273 | − | 0.736232i | ||||
\(707\) | −5.46410 | + | 1.46410i | −0.205499 | + | 0.0550632i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.5885 | + | 9.80385i | 1.37411 | + | 0.368191i | 0.868978 | − | 0.494852i | \(-0.164778\pi\) |
0.505131 | + | 0.863043i | \(0.331444\pi\) | |||||||
\(710\) | 4.28719 | 0.160895 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.00000 | + | 4.00000i | −0.149906 | + | 0.149906i | ||||
\(713\) | 2.19615 | − | 1.26795i | 0.0822466 | − | 0.0474851i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.09103 | − | 15.2679i | −0.152996 | − | 0.570989i | ||||
\(716\) | 1.41154 | + | 5.26795i | 0.0527518 | + | 0.196873i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.12436 | − | 15.3923i | 0.153920 | − | 0.574436i | ||||
\(719\) | −4.39230 | −0.163805 | −0.0819027 | − | 0.996640i | \(-0.526100\pi\) | ||||
−0.0819027 | + | 0.996640i | \(0.526100\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 41.3205 | 1.53886 | ||||||||
\(722\) | 2.85641 | − | 10.6603i | 0.106304 | − | 0.396734i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −20.1962 | + | 5.41154i | −0.750584 | + | 0.201118i | ||||
\(725\) | −2.49038 | − | 9.29423i | −0.0924904 | − | 0.345179i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.8109 | − | 16.6340i | 1.06854 | − | 0.616920i | 0.140755 | − | 0.990044i | \(-0.455047\pi\) |
0.927781 | + | 0.373124i | \(0.121714\pi\) | |||||||
\(728\) | 26.9282 | 0.998026 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.17691 | 0.339653 | ||||||||
\(731\) | −47.7487 | − | 12.7942i | −1.76605 | − | 0.473212i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.0263 | + | 2.95448i | −0.407265 | + | 0.109126i | −0.456635 | − | 0.889654i | \(-0.650945\pi\) |
0.0493698 | + | 0.998781i | \(0.484279\pi\) | |||||||
\(734\) | 10.3397 | + | 38.5885i | 0.381647 | + | 1.42433i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.92820 | − | 25.8564i | 0.255377 | − | 0.953080i | ||||
\(737\) | 29.9282 | 1.10242 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.22243 | − | 8.22243i | −0.302467 | − | 0.302467i | 0.539511 | − | 0.841978i | \(-0.318609\pi\) |
−0.841978 | + | 0.539511i | \(0.818609\pi\) | |||||||
\(740\) | 6.92820 | + | 12.0000i | 0.254686 | + | 0.441129i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −20.3923 | + | 35.3205i | −0.748625 | + | 1.29666i | ||||
\(743\) | 24.7583 | + | 14.2942i | 0.908295 | + | 0.524404i | 0.879882 | − | 0.475192i | \(-0.157621\pi\) |
0.0284129 | + | 0.999596i | \(0.490955\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.26795 | + | 4.19615i | −0.266277 | + | 0.153735i | ||||
\(746\) | − | 40.2487i | − | 1.47361i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 35.5167 | + | 35.5167i | 1.29862 | + | 1.29862i | ||||
\(749\) | 12.4904 | − | 46.6147i | 0.456389 | − | 1.70327i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.85641 | + | 15.3397i | −0.323175 | + | 0.559755i | −0.981141 | − | 0.193292i | \(-0.938084\pi\) |
0.657966 | + | 0.753047i | \(0.271417\pi\) | |||||||
\(752\) | 15.3205 | − | 26.5359i | 0.558681 | − | 0.967665i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.12436 | + | 11.6603i | −0.113782 | + | 0.424641i | ||||
\(755\) | −0.535898 | − | 0.535898i | −0.0195033 | − | 0.0195033i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.9282 | + | 19.9282i | −0.724303 | + | 0.724303i | −0.969479 | − | 0.245176i | \(-0.921154\pi\) |
0.245176 | + | 0.969479i | \(0.421154\pi\) | |||||||
\(758\) | 6.50962 | − | 3.75833i | 0.236440 | − | 0.136509i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.46410 | − | 2.53590i | 0.343299 | − | 0.0919867i | ||||
\(761\) | 45.3731 | + | 26.1962i | 1.64477 | + | 0.949610i | 0.979104 | + | 0.203363i | \(0.0651870\pi\) |
0.665669 | + | 0.746247i | \(0.268146\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −40.0526 | − | 10.7321i | −1.45000 | − | 0.388526i | ||||
\(764\) | 48.1051i | 1.74038i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.4641 | − | 13.4641i | 0.486478 | − | 0.486478i | ||||
\(767\) | −13.2224 | − | 22.9019i | −0.477434 | − | 0.826941i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.1244 | + | 24.4641i | −0.509337 | + | 0.882198i | 0.490604 | + | 0.871383i | \(0.336776\pi\) |
−0.999942 | + | 0.0108155i | \(0.996557\pi\) | |||||||
\(770\) | −4.53590 | − | 16.9282i | −0.163462 | − | 0.610050i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −37.6410 | + | 21.7321i | −1.35473 | + | 0.782154i | ||||
\(773\) | −35.5885 | + | 35.5885i | −1.28003 | + | 1.28003i | −0.339378 | + | 0.940650i | \(0.610216\pi\) |
−0.940650 | + | 0.339378i | \(0.889784\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.10512i | 0.0756181i | ||||||||
\(776\) | 8.58846 | − | 32.0526i | 0.308308 | − | 1.15062i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25.0526 | − | 14.4641i | −0.898178 | − | 0.518563i | ||||
\(779\) | 2.59808 | + | 9.69615i | 0.0930857 | + | 0.347401i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.32051 | − | 12.3923i | 0.118817 | − | 0.443432i | ||||
\(782\) | −27.1244 | − | 27.1244i | −0.969965 | − | 0.969965i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.85641 | 0.0663002 | ||||||||
\(785\) | −2.53590 | − | 4.39230i | −0.0905101 | − | 0.156768i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 40.3468 | − | 10.8109i | 1.43821 | − | 0.385367i | 0.546302 | − | 0.837588i | \(-0.316035\pi\) |
0.891906 | + | 0.452222i | \(0.149368\pi\) | |||||||
\(788\) | −37.3205 | + | 10.0000i | −1.32949 | + | 0.356235i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 15.2154 | − | 8.78461i | 0.541339 | − | 0.312542i | ||||
\(791\) | 37.8564i | 1.34602i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 40.3923i | − | 1.43437i | ||||||
\(794\) | −9.26795 | − | 16.0526i | −0.328907 | − | 0.569684i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −25.1244 | + | 43.5167i | −0.890509 | + | 1.54241i | ||||
\(797\) | 30.5167 | − | 8.17691i | 1.08096 | − | 0.289641i | 0.325968 | − | 0.945381i | \(-0.394310\pi\) |
0.754987 | + | 0.655740i | \(0.227643\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.9545 | − | 38.0263i | −0.776694 | − | 1.34527i | ||||
\(800\) | 15.7128 | + | 15.7128i | 0.555532 | + | 0.555532i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.58846 | − | 3.58846i | 0.126713 | − | 0.126713i | ||||
\(803\) | 7.10770 | − | 26.5263i | 0.250825 | − | 0.936092i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.46410 | + | 12.9282i | 0.122094 | + | 0.455659i | ||||
\(806\) | 1.32051 | − | 2.28719i | 0.0465129 | − | 0.0805627i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.92820 | + | 5.07180i | 0.103014 | + | 0.178425i | ||||
\(809\) | 6.32051i | 0.222217i | 0.993808 | + | 0.111109i | \(0.0354401\pi\) | ||||
−0.993808 | + | 0.111109i | \(0.964560\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.0263 | + | 14.0263i | −0.492529 | + | 0.492529i | −0.909102 | − | 0.416573i | \(-0.863231\pi\) |
0.416573 | + | 0.909102i | \(0.363231\pi\) | |||||||
\(812\) | −3.46410 | + | 12.9282i | −0.121566 | + | 0.453691i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 40.0526 | − | 10.7321i | 1.40384 | − | 0.376158i | ||||
\(815\) | 5.12436 | − | 8.87564i | 0.179498 | − | 0.310900i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.4282 | + | 24.9904i | 0.504779 | + | 0.874303i | ||||
\(818\) | −32.1769 | − | 32.1769i | −1.12504 | − | 1.12504i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.39230 | − | 4.39230i | 0.153386 | − | 0.153386i | ||||
\(821\) | 10.3660 | + | 2.77757i | 0.361777 | + | 0.0969378i | 0.435129 | − | 0.900368i | \(-0.356703\pi\) |
−0.0733518 | + | 0.997306i | \(0.523370\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.26795 | − | 4.19615i | −0.253345 | − | 0.146269i | 0.367950 | − | 0.929846i | \(-0.380060\pi\) |
−0.621295 | + | 0.783577i | \(0.713393\pi\) | |||||||
\(824\) | −11.0718 | − | 41.3205i | −0.385704 | − | 1.43947i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −14.6603 | − | 25.3923i | −0.510095 | − | 0.883511i | ||||
\(827\) | −17.5359 | + | 17.5359i | −0.609783 | + | 0.609783i | −0.942889 | − | 0.333106i | \(-0.891903\pi\) |
0.333106 | + | 0.942889i | \(0.391903\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.5167 | − | 20.5167i | −0.712573 | − | 0.712573i | 0.254500 | − | 0.967073i | \(-0.418089\pi\) |
−0.967073 | + | 0.254500i | \(0.918089\pi\) | |||||||
\(830\) | −2.00000 | − | 0.535898i | −0.0694210 | − | 0.0186013i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.21539 | − | 26.9282i | −0.250149 | − | 0.933567i | ||||
\(833\) | 1.33013 | − | 2.30385i | 0.0460862 | − | 0.0798236i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.00000 | + | 7.46410i | −0.0692129 | + | 0.258306i | ||||
\(836\) | − | 29.3205i | − | 1.01407i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9.71281 | 0.335524 | ||||||||
\(839\) | 23.4449 | − | 13.5359i | 0.809407 | − | 0.467311i | −0.0373432 | − | 0.999303i | \(-0.511889\pi\) |
0.846750 | + | 0.531991i | \(0.178556\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.9186 | + | 11.5000i | 0.686848 | + | 0.396552i | ||||
\(842\) | −38.7846 | − | 22.3923i | −1.33661 | − | 0.771690i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.19615 | + | 2.19615i | 0.282123 | + | 0.0755947i | ||||
\(845\) | −0.626933 | − | 0.626933i | −0.0215672 | − | 0.0215672i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.3923 | −0.769409 | ||||||||
\(848\) | 40.7846 | + | 10.9282i | 1.40055 | + | 0.375276i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 30.7583 | − | 8.24167i | 1.05500 | − | 0.282687i | ||||
\(851\) | −30.5885 | + | 8.19615i | −1.04856 | + | 0.280960i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.63397 | + | 0.437822i | 0.0559462 | + | 0.0149907i | 0.286684 | − | 0.958025i | \(-0.407447\pi\) |
−0.230737 | + | 0.973016i | \(0.574114\pi\) | |||||||
\(854\) | − | 44.7846i | − | 1.53250i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −49.9615 | −1.70765 | ||||||||
\(857\) | −44.9090 | + | 25.9282i | −1.53406 | + | 0.885691i | −0.534892 | + | 0.844920i | \(0.679648\pi\) |
−0.999169 | + | 0.0407704i | \(0.987019\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.82051 | − | 14.2583i | −0.130354 | − | 0.486488i | 0.869620 | − | 0.493722i | \(-0.164364\pi\) |
−0.999974 | + | 0.00723407i | \(0.997697\pi\) | |||||||
\(860\) | 8.92820 | − | 15.4641i | 0.304449 | − | 0.527321i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 22.1244 | + | 5.92820i | 0.753559 | + | 0.201915i | ||||
\(863\) | 15.4641 | 0.526404 | 0.263202 | − | 0.964741i | \(-0.415221\pi\) | ||||
0.263202 | + | 0.964741i | \(0.415221\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.75129 | 0.0595456 | ||||||||
\(866\) | −7.83013 | − | 2.09808i | −0.266079 | − | 0.0712955i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.46410 | − | 2.53590i | 0.0496948 | − | 0.0860740i | ||||
\(869\) | −13.6077 | − | 50.7846i | −0.461609 | − | 1.72275i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.6147 | + | 11.9019i | −0.698504 | + | 0.403281i | ||||
\(872\) | 42.9282i | 1.45373i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 22.3923i | 0.757431i | ||||||||
\(875\) | −24.3923 | − | 6.53590i | −0.824610 | − | 0.220954i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.5885 | − | 8.46410i | 1.06667 | − | 0.285812i | 0.317544 | − | 0.948244i | \(-0.397142\pi\) |
0.749123 | + | 0.662431i | \(0.230475\pi\) | |||||||
\(878\) | 36.0526 | − | 9.66025i | 1.21671 | − | 0.326018i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −15.7128 | + | 9.07180i | −0.529679 | + | 0.305810i | ||||
\(881\) | −27.3205 | −0.920451 | −0.460226 | − | 0.887802i | \(-0.652231\pi\) | ||||
−0.460226 | + | 0.887802i | \(0.652231\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.6340 | − | 12.6340i | −0.425167 | − | 0.425167i | 0.461811 | − | 0.886978i | \(-0.347200\pi\) |
−0.886978 | + | 0.461811i | \(0.847200\pi\) | |||||||
\(884\) | −38.5885 | − | 10.3397i | −1.29787 | − | 0.347763i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21.8827 | − | 12.6340i | −0.735163 | − | 0.424447i | ||||
\(887\) | 8.87564 | + | 5.12436i | 0.298015 | + | 0.172059i | 0.641551 | − | 0.767081i | \(-0.278291\pi\) |
−0.343536 | + | 0.939140i | \(0.611625\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.92820 | + | 5.73205i | −0.332981 | + | 0.192247i | ||||
\(890\) | −2.92820 | −0.0981536 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 32.1051i | − | 1.07496i | ||||||
\(893\) | −6.63397 | + | 24.7583i | −0.221997 | + | 0.828506i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.41154 | + | 2.44486i | −0.0471827 | + | 0.0817228i | ||||
\(896\) | −8.00000 | − | 29.8564i | −0.267261 | − | 0.997433i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.56218 | + | 1.22243i | 0.152242 | + | 0.0407931i | ||||
\(899\) | 0.928203 | + | 0.928203i | 0.0309573 | + | 0.0309573i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.7846 | − | 42.7846i | 1.42536 | − | 1.42536i | ||||
\(902\) | −9.29423 | − | 16.0981i | −0.309464 | − | 0.536007i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 37.8564 | − | 10.1436i | 1.25909 | − | 0.337371i | ||||
\(905\) | −9.37307 | − | 5.41154i | −0.311571 | − | 0.179886i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.50000 | + | 1.20577i | 0.149420 | + | 0.0400370i | 0.332754 | − | 0.943014i | \(-0.392022\pi\) |
−0.183334 | + | 0.983051i | \(0.558689\pi\) | |||||||
\(908\) | 3.12436 | − | 3.12436i | 0.103685 | − | 0.103685i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 9.85641 | + | 9.85641i | 0.326737 | + | 0.326737i | ||||
\(911\) | −2.46410 | − | 4.26795i | −0.0816393 | − | 0.141403i | 0.822315 | − | 0.569033i | \(-0.192682\pi\) |
−0.903954 | + | 0.427629i | \(0.859349\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.09808 | + | 5.36603i | −0.102531 | + | 0.177590i | ||||
\(914\) | −3.56218 | + | 0.954483i | −0.117826 | + | 0.0315715i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.66025 | − | 13.6603i | 0.120938 | − | 0.451347i | ||||
\(917\) | −15.6603 | + | 15.6603i | −0.517147 | + | 0.517147i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.9808i | 0.626118i | 0.949734 | + | 0.313059i | \(0.101354\pi\) | ||||
−0.949734 | + | 0.313059i | \(0.898646\pi\) | |||||||
\(920\) | 12.0000 | − | 6.92820i | 0.395628 | − | 0.228416i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 26.1244 | − | 45.2487i | 0.860360 | − | 1.49019i | ||||
\(923\) | 2.64102 | + | 9.85641i | 0.0869301 | + | 0.324428i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.80385 | − | 25.3923i | 0.223709 | − | 0.834894i | ||||
\(926\) | 2.39230 | − | 2.39230i | 0.0786160 | − | 0.0786160i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13.8564 | 0.454859 | ||||||||
\(929\) | 11.5359 | + | 19.9808i | 0.378481 | + | 0.655548i | 0.990841 | − | 0.135031i | \(-0.0431134\pi\) |
−0.612361 | + | 0.790578i | \(0.709780\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.50000 | + | 0.401924i | −0.0491605 | + | 0.0131725i | ||||
\(932\) | −3.19615 | + | 5.53590i | −0.104693 | + | 0.181334i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.63397 | − | 4.56218i | −0.0861863 | − | 0.149279i | ||||
\(935\) | 26.0000i | 0.850291i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 11.1769i | − | 0.365134i | −0.983193 | − | 0.182567i | \(-0.941559\pi\) | ||
0.983193 | − | 0.182567i | \(-0.0584406\pi\) | |||||||
\(938\) | −22.8564 | + | 13.1962i | −0.746288 | + | 0.430870i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15.3205 | − | 4.10512i | 0.499700 | − | 0.133894i | ||||
\(941\) | −6.73205 | + | 1.80385i | −0.219459 | + | 0.0588038i | −0.366873 | − | 0.930271i | \(-0.619572\pi\) |
0.147414 | + | 0.989075i | \(0.452905\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.09808 | + | 12.2942i | 0.231145 | + | 0.400355i | ||||
\(944\) | −21.4641 | + | 21.4641i | −0.698597 | + | 0.698597i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −37.7846 | − | 37.7846i | −1.22848 | − | 1.22848i | ||||
\(947\) | 10.9904 | − | 41.0167i | 0.357139 | − | 1.33286i | −0.520631 | − | 0.853782i | \(-0.674303\pi\) |
0.877771 | − | 0.479081i | \(-0.159030\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.65321 | + | 21.0981i | 0.183511 | + | 0.684873i | ||||
\(950\) | −16.0981 | − | 9.29423i | −0.522291 | − | 0.301545i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −42.7846 | − | 11.4641i | −1.38666 | − | 0.371554i | ||||
\(953\) | − | 17.1051i | − | 0.554089i | −0.960857 | − | 0.277045i | \(-0.910645\pi\) | ||
0.960857 | − | 0.277045i | \(-0.0893550\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.6077 | + | 17.6077i | −0.569772 | + | 0.569772i | ||||
\(956\) | 27.3731 | − | 15.8038i | 0.885308 | − | 0.511133i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.05256 | − | 11.3923i | −0.0986237 | − | 0.368069i | ||||
\(959\) | −13.0263 | + | 22.5622i | −0.420641 | + | 0.728571i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3564 | + | 26.5981i | 0.495368 | + | 0.858002i | ||||
\(962\) | −23.3205 | + | 23.3205i | −0.751883 | + | 0.751883i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 46.3923i | − | 1.49420i | ||||||
\(965\) | −21.7321 | − | 5.82309i | −0.699579 | − | 0.187452i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.8301 | − | 10.2942i | −0.573378 | − | 0.331040i | 0.185119 | − | 0.982716i | \(-0.440733\pi\) |
−0.758497 | + | 0.651676i | \(0.774066\pi\) | |||||||
\(968\) | 6.00000 | + | 22.3923i | 0.192847 | + | 0.719716i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14.8756 | − | 8.58846i | 0.477628 | − | 0.275759i | ||||
\(971\) | −15.5359 | + | 15.5359i | −0.498571 | + | 0.498571i | −0.910993 | − | 0.412422i | \(-0.864683\pi\) |
0.412422 | + | 0.910993i | \(0.364683\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.8564 | − | 22.8564i | −0.732743 | − | 0.732743i | ||||
\(974\) | −2.12436 | + | 7.92820i | −0.0680687 | + | 0.254036i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −44.7846 | + | 12.0000i | −1.43352 | + | 0.384111i | ||||
\(977\) | 22.0622 | − | 38.2128i | 0.705832 | − | 1.22254i | −0.260559 | − | 0.965458i | \(-0.583907\pi\) |
0.966391 | − | 0.257078i | \(-0.0827598\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.26795 | + | 8.46410i | −0.0724840 | + | 0.270514i | ||||
\(980\) | 0.679492 | + | 0.679492i | 0.0217056 | + | 0.0217056i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 20.3397i | − | 0.649067i | ||||||
\(983\) | 13.8564 | − | 8.00000i | 0.441951 | − | 0.255160i | −0.262474 | − | 0.964939i | \(-0.584538\pi\) |
0.704425 | + | 0.709779i | \(0.251205\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.3205 | − | 10.0000i | −0.551877 | − | 0.318626i | ||||
\(986\) | 9.92820 | − | 17.1962i | 0.316178 | − | 0.547637i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.6603 | + | 20.1962i | 0.370962 | + | 0.642525i | ||||
\(989\) | 28.8564 | + | 28.8564i | 0.917580 | + | 0.917580i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.6410 | 1.16394 | 0.581970 | − | 0.813210i | \(-0.302282\pi\) | ||||
0.581970 | + | 0.813210i | \(0.302282\pi\) | |||||||
\(992\) | −2.92820 | − | 0.784610i | −0.0929705 | − | 0.0249114i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.92820 | + | 10.9282i | 0.0928770 | + | 0.346622i | ||||
\(995\) | −25.1244 | + | 6.73205i | −0.796496 | + | 0.213420i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.3923 | − | 7.87564i | −0.930864 | − | 0.249424i | −0.238641 | − | 0.971108i | \(-0.576702\pi\) |
−0.692223 | + | 0.721684i | \(0.743368\pi\) | |||||||
\(998\) | 12.7321 | 0.403026 | ||||||||
\(999\) | 0 | 0 |
(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 | 432.2.y.c.253.1 | 4 | ||
3.2 | odd | 2 | 144.2.x.b.13.1 | ✓ | 4 | ||
4.3 | odd | 2 | 1728.2.bc.d.145.1 | 4 | |||
9.2 | odd | 6 | 144.2.x.c.61.1 | yes | 4 | ||
9.7 | even | 3 | 432.2.y.b.397.1 | 4 | |||
12.11 | even | 2 | 576.2.bb.d.337.1 | 4 | |||
16.5 | even | 4 | 432.2.y.b.37.1 | 4 | |||
16.11 | odd | 4 | 1728.2.bc.a.1009.1 | 4 | |||
36.7 | odd | 6 | 1728.2.bc.a.721.1 | 4 | |||
36.11 | even | 6 | 576.2.bb.c.529.1 | 4 | |||
48.5 | odd | 4 | 144.2.x.c.85.1 | yes | 4 | ||
48.11 | even | 4 | 576.2.bb.c.49.1 | 4 | |||
144.11 | even | 12 | 576.2.bb.d.241.1 | 4 | |||
144.43 | odd | 12 | 1728.2.bc.d.1585.1 | 4 | |||
144.101 | odd | 12 | 144.2.x.b.133.1 | yes | 4 | ||
144.133 | even | 12 | inner | 432.2.y.c.181.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.b.13.1 | ✓ | 4 | 3.2 | odd | 2 | ||
144.2.x.b.133.1 | yes | 4 | 144.101 | odd | 12 | ||
144.2.x.c.61.1 | yes | 4 | 9.2 | odd | 6 | ||
144.2.x.c.85.1 | yes | 4 | 48.5 | odd | 4 | ||
432.2.y.b.37.1 | 4 | 16.5 | even | 4 | |||
432.2.y.b.397.1 | 4 | 9.7 | even | 3 | |||
432.2.y.c.181.1 | 4 | 144.133 | even | 12 | inner | ||
432.2.y.c.253.1 | 4 | 1.1 | even | 1 | trivial | ||
576.2.bb.c.49.1 | 4 | 48.11 | even | 4 | |||
576.2.bb.c.529.1 | 4 | 36.11 | even | 6 | |||
576.2.bb.d.241.1 | 4 | 144.11 | even | 12 | |||
576.2.bb.d.337.1 | 4 | 12.11 | even | 2 | |||
1728.2.bc.a.721.1 | 4 | 36.7 | odd | 6 | |||
1728.2.bc.a.1009.1 | 4 | 16.11 | odd | 4 | |||
1728.2.bc.d.145.1 | 4 | 4.3 | odd | 2 | |||
1728.2.bc.d.1585.1 | 4 | 144.43 | odd | 12 |