Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,2,Mod(35,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.l (of order \(18\), degree \(6\), 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: | \(2.58715302549\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 179.2 | ||
Character | \(\chi\) | \(=\) | 324.179 |
Dual form | 324.2.l.a.143.2 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{11}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32122 | − | 0.504364i | −0.934242 | − | 0.356639i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.49123 | + | 1.33275i | 0.745617 | + | 0.666375i | ||||
\(5\) | 3.39370 | + | 0.598401i | 1.51771 | + | 0.267613i | 0.869532 | − | 0.493877i | \(-0.164421\pi\) |
0.648177 | + | 0.761490i | \(0.275532\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.88319 | + | 2.24430i | 0.711781 | + | 0.848267i | 0.993805 | − | 0.111140i | \(-0.0354503\pi\) |
−0.282024 | + | 0.959407i | \(0.591006\pi\) | |||||||
\(8\) | −1.29805 | − | 2.51298i | −0.458931 | − | 0.888472i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.18200 | − | 2.50228i | −1.32247 | − | 0.791290i | ||||
\(11\) | 0.453915 | + | 2.57428i | 0.136861 | + | 0.776174i | 0.973546 | + | 0.228491i | \(0.0733791\pi\) |
−0.836686 | + | 0.547684i | \(0.815510\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.09721 | + | 1.85523i | −1.41371 | + | 0.514549i | −0.932217 | − | 0.361899i | \(-0.882128\pi\) |
−0.481496 | + | 0.876449i | \(0.659906\pi\) | |||||||
\(14\) | −1.35616 | − | 3.91503i | −0.362450 | − | 1.04634i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.447553 | + | 3.97488i | 0.111888 | + | 0.993721i | ||||
\(17\) | −1.15583 | − | 0.667320i | −0.280330 | − | 0.161849i | 0.353243 | − | 0.935532i | \(-0.385079\pi\) |
−0.633573 | + | 0.773683i | \(0.718412\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0790760 | − | 0.0456546i | 0.0181413 | − | 0.0104739i | −0.490902 | − | 0.871215i | \(-0.663333\pi\) |
0.509043 | + | 0.860741i | \(0.329999\pi\) | |||||||
\(20\) | 4.26328 | + | 5.41531i | 0.953298 | + | 1.21090i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.698654 | − | 3.63012i | 0.148954 | − | 0.773945i | ||||
\(23\) | −0.650322 | − | 0.545685i | −0.135602 | − | 0.113783i | 0.572464 | − | 0.819930i | \(-0.305988\pi\) |
−0.708066 | + | 0.706147i | \(0.750432\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.46065 | + | 2.35148i | 1.29213 | + | 0.470297i | ||||
\(26\) | 7.67024 | + | 0.119685i | 1.50426 | + | 0.0234721i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.182815 | + | 5.85661i | −0.0345487 | + | 1.10679i | ||||
\(29\) | 0.171418 | − | 0.470966i | 0.0318315 | − | 0.0874562i | −0.922759 | − | 0.385378i | \(-0.874071\pi\) |
0.954590 | + | 0.297922i | \(0.0962934\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.28324 | − | 5.10457i | 0.769293 | − | 0.916807i | −0.229105 | − | 0.973402i | \(-0.573580\pi\) |
0.998397 | + | 0.0565946i | \(0.0180243\pi\) | |||||||
\(32\) | 1.41348 | − | 5.47742i | 0.249869 | − | 0.968280i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.19053 | + | 1.46464i | 0.204175 | + | 0.251183i | ||||
\(35\) | 5.04800 | + | 8.74340i | 0.853268 | + | 1.47790i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.75869 | − | 4.77819i | 0.453526 | − | 0.785530i | −0.545076 | − | 0.838387i | \(-0.683499\pi\) |
0.998602 | + | 0.0528563i | \(0.0168325\pi\) | |||||||
\(38\) | −0.127503 | + | 0.0204365i | −0.0206838 | + | 0.00331524i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.90143 | − | 9.30505i | −0.458756 | − | 1.47126i | ||||
\(41\) | 0.976880 | + | 2.68396i | 0.152563 | + | 0.419163i | 0.992304 | − | 0.123823i | \(-0.0395156\pi\) |
−0.839741 | + | 0.542987i | \(0.817293\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.59737 | − | 0.986968i | 0.853591 | − | 0.150511i | 0.270302 | − | 0.962776i | \(-0.412876\pi\) |
0.583289 | + | 0.812264i | \(0.301765\pi\) | |||||||
\(44\) | −2.75398 | + | 4.44381i | −0.415178 | + | 0.669929i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.583993 | + | 1.04897i | 0.0861051 | + | 0.154662i | ||||
\(47\) | −5.06200 | + | 4.24752i | −0.738369 | + | 0.619565i | −0.932399 | − | 0.361430i | \(-0.882288\pi\) |
0.194030 | + | 0.980996i | \(0.437844\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.274941 | + | 1.55927i | −0.0392772 | + | 0.222752i | ||||
\(50\) | −7.34992 | − | 6.36534i | −1.03944 | − | 0.900196i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10.0737 | − | 4.02673i | −1.39697 | − | 0.558407i | ||||
\(53\) | − | 7.37249i | − | 1.01269i | −0.862331 | − | 0.506345i | \(-0.830996\pi\) | ||
0.862331 | − | 0.506345i | \(-0.169004\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.00795i | 1.21463i | ||||||||
\(56\) | 3.19540 | − | 7.64565i | 0.427004 | − | 1.02169i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.464019 | + | 0.535792i | −0.0609286 | + | 0.0703529i | ||||
\(59\) | 0.528787 | − | 2.99890i | 0.0688422 | − | 0.390423i | −0.930845 | − | 0.365414i | \(-0.880927\pi\) |
0.999687 | − | 0.0250093i | \(-0.00796152\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.85759 | + | 1.55871i | −0.237841 | + | 0.199572i | −0.753915 | − | 0.656972i | \(-0.771837\pi\) |
0.516075 | + | 0.856544i | \(0.327393\pi\) | |||||||
\(62\) | −8.23365 | + | 4.58393i | −1.04568 | + | 0.582160i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.63012 | + | 6.52395i | −0.578765 | + | 0.815494i | ||||
\(65\) | −18.4086 | + | 3.24593i | −2.28330 | + | 0.402608i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.64904 | + | 4.53069i | 0.201462 | + | 0.553512i | 0.998744 | − | 0.0500945i | \(-0.0159522\pi\) |
−0.797283 | + | 0.603606i | \(0.793730\pi\) | |||||||
\(68\) | −0.834244 | − | 2.53557i | −0.101167 | − | 0.307482i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.25965 | − | 14.0980i | −0.270080 | − | 1.68503i | ||||
\(71\) | 5.91940 | − | 10.2527i | 0.702504 | − | 1.21677i | −0.265081 | − | 0.964226i | \(-0.585399\pi\) |
0.967585 | − | 0.252546i | \(-0.0812678\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.83049 | − | 10.0987i | −0.682408 | − | 1.18197i | −0.974244 | − | 0.225497i | \(-0.927600\pi\) |
0.291836 | − | 0.956468i | \(-0.405734\pi\) | |||||||
\(74\) | −6.05478 | + | 4.92165i | −0.703854 | + | 0.572130i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.178767 | + | 0.0373070i | 0.0205060 | + | 0.00427941i | ||||
\(77\) | −4.92266 | + | 5.86659i | −0.560989 | + | 0.668560i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.576990 | + | 1.58527i | −0.0649165 | + | 0.178357i | −0.967910 | − | 0.251298i | \(-0.919143\pi\) |
0.902993 | + | 0.429655i | \(0.141365\pi\) | |||||||
\(80\) | −0.859714 | + | 13.7574i | −0.0961190 | + | 1.53812i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.0630204 | − | 4.03879i | 0.00695944 | − | 0.446010i | ||||
\(83\) | −2.02940 | − | 0.738640i | −0.222755 | − | 0.0810763i | 0.228232 | − | 0.973607i | \(-0.426706\pi\) |
−0.450987 | + | 0.892531i | \(0.648928\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.52322 | − | 2.95633i | −0.382147 | − | 0.320659i | ||||
\(86\) | −7.89314 | − | 1.51912i | −0.851139 | − | 0.163810i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.87990 | − | 4.48223i | 0.626800 | − | 0.477807i | ||||
\(89\) | 12.5801 | − | 7.26310i | 1.33348 | − | 0.769887i | 0.347652 | − | 0.937624i | \(-0.386979\pi\) |
0.985832 | + | 0.167737i | \(0.0536458\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.7628 | − | 7.94593i | −1.44273 | − | 0.832960i | ||||
\(92\) | −0.242520 | − | 1.68046i | −0.0252844 | − | 0.175200i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.83031 | − | 3.05881i | 0.910777 | − | 0.315492i | ||||
\(95\) | 0.295680 | − | 0.107619i | 0.0303361 | − | 0.0110414i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.14607 | + | 6.49971i | 0.116366 | + | 0.659946i | 0.986065 | + | 0.166362i | \(0.0532021\pi\) |
−0.869698 | + | 0.493583i | \(0.835687\pi\) | |||||||
\(98\) | 1.14969 | − | 1.92146i | 0.116137 | − | 0.194097i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.50039 | + | 12.1170i | 0.650039 | + | 1.21170i | ||||
\(101\) | 5.29995 | + | 6.31623i | 0.527365 | + | 0.628489i | 0.962306 | − | 0.271970i | \(-0.0876752\pi\) |
−0.434941 | + | 0.900459i | \(0.643231\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.8523 | − | 2.79519i | −1.56197 | − | 0.275418i | −0.675203 | − | 0.737632i | \(-0.735944\pi\) |
−0.886769 | + | 0.462214i | \(0.847055\pi\) | |||||||
\(104\) | 11.2786 | + | 10.4010i | 1.10596 | + | 1.01990i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.71842 | + | 9.74067i | −0.361165 | + | 0.946097i | ||||
\(107\) | −9.71808 | −0.939482 | −0.469741 | − | 0.882804i | \(-0.655653\pi\) | ||||
−0.469741 | + | 0.882804i | \(0.655653\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.69860 | −0.450044 | −0.225022 | − | 0.974354i | \(-0.572245\pi\) | ||||
−0.225022 | + | 0.974354i | \(0.572245\pi\) | |||||||
\(110\) | 4.54329 | − | 11.9015i | 0.433186 | − | 1.13476i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.07802 | + | 8.48992i | −0.763301 | + | 0.802222i | ||||
\(113\) | −0.555886 | − | 0.0980178i | −0.0522934 | − | 0.00922074i | 0.147440 | − | 0.989071i | \(-0.452897\pi\) |
−0.199734 | + | 0.979850i | \(0.564008\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.88046 | − | 2.24104i | −0.175354 | − | 0.208978i | ||||
\(116\) | 0.883304 | − | 0.473863i | 0.0820127 | − | 0.0439971i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.21118 | + | 3.69550i | −0.203556 | + | 0.340198i | ||||
\(119\) | −0.678988 | − | 3.85073i | −0.0622427 | − | 0.352996i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.91574 | − | 1.42521i | 0.355977 | − | 0.129565i | ||||
\(122\) | 3.24044 | − | 1.12249i | 0.293376 | − | 0.101625i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 13.1904 | − | 1.90361i | 1.18453 | − | 0.170949i | ||||
\(125\) | 5.59652 | + | 3.23116i | 0.500568 | + | 0.289003i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.63141 | − | 5.56070i | 0.854649 | − | 0.493432i | −0.00756758 | − | 0.999971i | \(-0.502409\pi\) |
0.862217 | + | 0.506539i | \(0.169076\pi\) | |||||||
\(128\) | 9.40785 | − | 6.28430i | 0.831544 | − | 0.555458i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 25.9589 | + | 4.99605i | 2.27674 | + | 0.438183i | ||||
\(131\) | −2.37648 | − | 1.99411i | −0.207634 | − | 0.174226i | 0.533040 | − | 0.846090i | \(-0.321049\pi\) |
−0.740675 | + | 0.671864i | \(0.765494\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.251378 | + | 0.0914942i | 0.0217973 | + | 0.00793355i | ||||
\(134\) | 0.106382 | − | 6.81774i | 0.00919004 | − | 0.588963i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.176631 | + | 3.77080i | −0.0151459 | + | 0.323343i | ||||
\(137\) | 5.90609 | − | 16.2268i | 0.504591 | − | 1.38635i | −0.382156 | − | 0.924098i | \(-0.624818\pi\) |
0.886747 | − | 0.462255i | \(-0.152959\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.19280 | − | 8.57205i | 0.610085 | − | 0.727071i | −0.369246 | − | 0.929332i | \(-0.620384\pi\) |
0.979332 | + | 0.202260i | \(0.0648286\pi\) | |||||||
\(140\) | −4.12502 | + | 19.7662i | −0.348628 | + | 1.67055i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.9919 | + | 10.5605i | −1.09026 | + | 0.886219i | ||||
\(143\) | −7.08959 | − | 12.2795i | −0.592862 | − | 1.02687i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.863567 | − | 1.49574i | 0.0717153 | − | 0.124215i | ||||
\(146\) | 2.60992 | + | 16.2833i | 0.215999 | + | 1.34762i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.4820 | − | 3.44875i | 0.861615 | − | 0.283486i | ||||
\(149\) | 6.24250 | + | 17.1511i | 0.511406 | + | 1.40508i | 0.879773 | + | 0.475395i | \(0.157695\pi\) |
−0.368367 | + | 0.929680i | \(0.620083\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.9571 | + | 3.34265i | −1.54271 | + | 0.272021i | −0.879311 | − | 0.476248i | \(-0.841996\pi\) |
−0.663396 | + | 0.748269i | \(0.730885\pi\) | |||||||
\(152\) | −0.217374 | − | 0.139454i | −0.0176313 | − | 0.0113112i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 9.46280 | − | 5.26823i | 0.762534 | − | 0.424526i | ||||
\(155\) | 17.5906 | − | 14.7603i | 1.41291 | − | 1.18557i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.92425 | + | 16.5843i | −0.233381 | + | 1.32357i | 0.612617 | + | 0.790380i | \(0.290117\pi\) |
−0.845997 | + | 0.533187i | \(0.820994\pi\) | |||||||
\(158\) | 1.56188 | − | 1.80347i | 0.124257 | − | 0.143476i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.07460 | − | 17.7429i | 0.638353 | − | 1.40270i | ||||
\(161\) | − | 2.48715i | − | 0.196015i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 8.02606i | − | 0.628650i | −0.949315 | − | 0.314325i | \(-0.898222\pi\) | ||
0.949315 | − | 0.314325i | \(-0.101778\pi\) | |||||||
\(164\) | −2.12029 | + | 5.30434i | −0.165567 | + | 0.414199i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.30873 | + | 1.99946i | 0.179192 | + | 0.155188i | ||||
\(167\) | −0.226727 | + | 1.28583i | −0.0175447 | + | 0.0995008i | −0.992323 | − | 0.123676i | \(-0.960532\pi\) |
0.974778 | + | 0.223177i | \(0.0716427\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5811 | − | 10.5568i | 0.967779 | − | 0.812063i | ||||
\(170\) | 3.16387 | + | 5.68295i | 0.242658 | + | 0.435862i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.66237 | + | 5.98810i | 0.736749 | + | 0.456588i | ||||
\(173\) | −11.2769 | + | 1.98842i | −0.857366 | + | 0.151177i | −0.585016 | − | 0.811022i | \(-0.698912\pi\) |
−0.272350 | + | 0.962198i | \(0.587801\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.88921 | + | 18.9280i | 0.520776 | + | 1.43082i | ||||
\(176\) | −10.0293 | + | 2.95638i | −0.755988 | + | 0.222846i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −20.2842 | + | 3.25120i | −1.52037 | + | 0.243688i | ||||
\(179\) | −10.7064 | + | 18.5441i | −0.800237 | + | 1.38605i | 0.119222 | + | 0.992868i | \(0.461960\pi\) |
−0.919460 | + | 0.393184i | \(0.871373\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.31416 | + | 12.6685i | 0.543657 | + | 0.941641i | 0.998690 | + | 0.0511670i | \(0.0162941\pi\) |
−0.455033 | + | 0.890474i | \(0.650373\pi\) | |||||||
\(182\) | 14.1760 | + | 17.4397i | 1.05079 | + | 1.29272i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.527143 | + | 2.34257i | −0.0388615 | + | 0.172697i | ||||
\(185\) | 12.2214 | − | 14.5650i | 0.898539 | − | 1.07084i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.19322 | − | 3.27834i | 0.0872568 | − | 0.239736i | ||||
\(188\) | −13.2095 | − | 0.412337i | −0.963403 | − | 0.0300728i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.444937 | − | 0.00694269i | −0.0322791 | − | 0.000503676i | ||||
\(191\) | 1.80607 | + | 0.657357i | 0.130683 | + | 0.0475647i | 0.406534 | − | 0.913636i | \(-0.366737\pi\) |
−0.275851 | + | 0.961200i | \(0.588960\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.79657 | − | 4.02480i | −0.345264 | − | 0.289711i | 0.453621 | − | 0.891195i | \(-0.350132\pi\) |
−0.798885 | + | 0.601484i | \(0.794577\pi\) | |||||||
\(194\) | 1.76401 | − | 9.16557i | 0.126648 | − | 0.658050i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.48811 | + | 1.95880i | −0.177722 | + | 0.139914i | ||||
\(197\) | −13.1022 | + | 7.56456i | −0.933494 | + | 0.538953i | −0.887915 | − | 0.460008i | \(-0.847847\pi\) |
−0.0455788 | + | 0.998961i | \(0.514513\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.4427 | + | 12.9573i | 1.59092 | + | 0.918517i | 0.993150 | + | 0.116849i | \(0.0372792\pi\) |
0.597769 | + | 0.801669i | \(0.296054\pi\) | |||||||
\(200\) | −2.47703 | − | 19.2878i | −0.175152 | − | 1.36385i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.81670 | − | 11.0182i | −0.268542 | − | 0.775240i | ||||
\(203\) | 1.37980 | − | 0.502208i | 0.0968433 | − | 0.0352481i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.70916 | + | 9.69310i | 0.119373 | + | 0.676996i | ||||
\(206\) | 19.5345 | + | 11.6884i | 1.36104 | + | 0.814368i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −9.65561 | − | 19.4305i | −0.669496 | − | 1.34726i | ||||
\(209\) | 0.153421 | + | 0.182841i | 0.0106124 | + | 0.0126473i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.1836 | − | 3.02993i | −1.18297 | − | 0.208589i | −0.452645 | − | 0.891691i | \(-0.649519\pi\) |
−0.730323 | + | 0.683102i | \(0.760631\pi\) | |||||||
\(212\) | 9.82569 | − | 10.9941i | 0.674831 | − | 0.755078i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.8397 | + | 4.90145i | 0.877704 | + | 0.335056i | ||||
\(215\) | 19.5864 | 1.33578 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.5224 | 1.32526 | ||||||||
\(218\) | 6.20788 | + | 2.36981i | 0.420450 | + | 0.160504i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −12.0054 | + | 13.4330i | −0.809401 | + | 0.905650i | ||||
\(221\) | 7.12956 | + | 1.25713i | 0.479586 | + | 0.0845639i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.3619 | − | 13.5406i | −0.760850 | − | 0.906746i | 0.237051 | − | 0.971497i | \(-0.423819\pi\) |
−0.997901 | + | 0.0647513i | \(0.979375\pi\) | |||||||
\(224\) | 14.9548 | − | 7.14277i | 0.999212 | − | 0.477247i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.685010 | + | 0.409872i | 0.0455662 | + | 0.0272643i | ||||
\(227\) | −1.62005 | − | 9.18776i | −0.107527 | − | 0.609813i | −0.990181 | − | 0.139791i | \(-0.955357\pi\) |
0.882654 | − | 0.470022i | \(-0.155754\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.8029 | + | 5.75180i | −1.04429 | + | 0.380090i | −0.806504 | − | 0.591228i | \(-0.798643\pi\) |
−0.237784 | + | 0.971318i | \(0.576421\pi\) | |||||||
\(230\) | 1.35419 | + | 3.90934i | 0.0892929 | + | 0.257775i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.40604 | + | 0.180570i | −0.0923109 | + | 0.0118550i | ||||
\(233\) | −15.2659 | − | 8.81379i | −1.00010 | − | 0.577410i | −0.0918250 | − | 0.995775i | \(-0.529270\pi\) |
−0.908279 | + | 0.418365i | \(0.862603\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.7206 | + | 11.3857i | −1.28643 | + | 0.742722i | ||||
\(236\) | 4.78533 | − | 3.76732i | 0.311498 | − | 0.245231i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.04508 | + | 5.43011i | −0.0677425 | + | 0.351982i | ||||
\(239\) | 7.05862 | + | 5.92289i | 0.456584 | + | 0.383120i | 0.841872 | − | 0.539677i | \(-0.181453\pi\) |
−0.385288 | + | 0.922796i | \(0.625898\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.85117 | − | 2.12965i | −0.376907 | − | 0.137183i | 0.146618 | − | 0.989193i | \(-0.453161\pi\) |
−0.523525 | + | 0.852010i | \(0.675383\pi\) | |||||||
\(242\) | −5.89238 | − | 0.0919433i | −0.378776 | − | 0.00591034i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.84747 | − | 0.151315i | −0.310328 | − | 0.00968692i | ||||
\(245\) | −1.86613 | + | 5.12716i | −0.119223 | + | 0.327562i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.318368 | + | 0.379416i | −0.0202572 | + | 0.0241416i | ||||
\(248\) | −18.3875 | − | 4.13770i | −1.16761 | − | 0.262744i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.76455 | − | 7.09175i | −0.364582 | − | 0.448522i | ||||
\(251\) | −14.1765 | − | 24.5545i | −0.894814 | − | 1.54986i | −0.834034 | − | 0.551713i | \(-0.813974\pi\) |
−0.0607805 | − | 0.998151i | \(-0.519359\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.10955 | − | 1.92181i | 0.0697571 | − | 0.120823i | ||||
\(254\) | −15.5298 | + | 2.48915i | −0.974427 | + | 0.156183i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.5994 | + | 3.55794i | −0.974962 | + | 0.222371i | ||||
\(257\) | −5.64266 | − | 15.5031i | −0.351979 | − | 0.967056i | −0.981734 | − | 0.190261i | \(-0.939067\pi\) |
0.629754 | − | 0.776795i | \(-0.283156\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.9189 | − | 2.80693i | 0.989151 | − | 0.174414i | ||||
\(260\) | −31.7775 | − | 19.6936i | −1.97076 | − | 1.22135i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.13410 | + | 3.83326i | 0.131845 | + | 0.236820i | ||||
\(263\) | −18.5512 | + | 15.5663i | −1.14391 | + | 0.959859i | −0.999560 | − | 0.0296674i | \(-0.990555\pi\) |
−0.144355 | + | 0.989526i | \(0.546111\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.41171 | − | 25.0200i | 0.271009 | − | 1.53697i | ||||
\(266\) | −0.285979 | − | 0.247670i | −0.0175345 | − | 0.0151856i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.57918 | + | 8.95406i | −0.218633 | + | 0.546956i | ||||
\(269\) | 12.1956i | 0.743578i | 0.928317 | + | 0.371789i | \(0.121255\pi\) | ||||
−0.928317 | + | 0.371789i | \(0.878745\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 25.0009i | − | 1.51870i | −0.650683 | − | 0.759349i | \(-0.725517\pi\) | ||
0.650683 | − | 0.759349i | \(-0.274483\pi\) | |||||||
\(272\) | 2.13522 | − | 4.89296i | 0.129467 | − | 0.296679i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.9875 | + | 18.4604i | −0.965838 | + | 1.11523i | ||||
\(275\) | −3.12079 | + | 17.6989i | −0.188191 | + | 1.06728i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.69358 | + | 5.61658i | −0.402178 | + | 0.337468i | −0.821335 | − | 0.570446i | \(-0.806770\pi\) |
0.419157 | + | 0.907914i | \(0.362326\pi\) | |||||||
\(278\) | −13.8267 | + | 7.69775i | −0.829270 | + | 0.461680i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 15.4194 | − | 24.0349i | 0.921485 | − | 1.43636i | ||||
\(281\) | 21.5554 | − | 3.80080i | 1.28589 | − | 0.226737i | 0.511409 | − | 0.859338i | \(-0.329124\pi\) |
0.774478 | + | 0.632601i | \(0.218013\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.2956 | + | 28.2869i | 0.612010 | + | 1.68148i | 0.725737 | + | 0.687972i | \(0.241499\pi\) |
−0.113727 | + | 0.993512i | \(0.536279\pi\) | |||||||
\(284\) | 22.4915 | − | 7.40009i | 1.33462 | − | 0.439114i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.17354 | + | 19.7997i | 0.187655 | + | 1.17078i | ||||
\(287\) | −4.18396 | + | 7.24682i | −0.246971 | + | 0.427766i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.60937 | − | 13.1798i | −0.447610 | − | 0.775283i | ||||
\(290\) | −1.89536 | + | 1.54065i | −0.111299 | + | 0.0904700i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.76444 | − | 22.8301i | 0.278818 | − | 1.33603i | ||||
\(293\) | −8.50981 | + | 10.1416i | −0.497148 | + | 0.592478i | −0.955021 | − | 0.296540i | \(-0.904167\pi\) |
0.457872 | + | 0.889018i | \(0.348612\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.58909 | − | 9.86094i | 0.208965 | − | 0.574126i | ||||
\(296\) | −15.5884 | − | 0.730189i | −0.906059 | − | 0.0424413i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.402716 | − | 25.8089i | 0.0233287 | − | 1.49507i | ||||
\(299\) | 4.32720 | + | 1.57497i | 0.250249 | + | 0.0910831i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.7560 | + | 10.7036i | 0.735243 | + | 0.616942i | ||||
\(302\) | 26.7324 | + | 5.14492i | 1.53827 | + | 0.296057i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.216862 | + | 0.293885i | 0.0124379 | + | 0.0168555i | ||||
\(305\) | −7.23685 | + | 4.17820i | −0.414381 | + | 0.239243i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.4064 | + | 6.58546i | 0.650995 | + | 0.375852i | 0.788837 | − | 0.614602i | \(-0.210683\pi\) |
−0.137842 | + | 0.990454i | \(0.544017\pi\) | |||||||
\(308\) | −15.1595 | + | 2.18779i | −0.863794 | + | 0.124661i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −30.6856 | + | 10.6295i | −1.74282 | + | 0.603713i | ||||
\(311\) | −5.80348 | + | 2.11230i | −0.329085 | + | 0.119777i | −0.501279 | − | 0.865286i | \(-0.667137\pi\) |
0.172193 | + | 0.985063i | \(0.444915\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.72249 | − | 21.1113i | −0.210407 | − | 1.19328i | −0.888701 | − | 0.458488i | \(-0.848391\pi\) |
0.678293 | − | 0.734791i | \(-0.262720\pi\) | |||||||
\(314\) | 12.2281 | − | 20.4365i | 0.690070 | − | 1.15330i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.97319 | + | 1.59502i | −0.167255 | + | 0.0897269i | ||||
\(317\) | 9.45061 | + | 11.2628i | 0.530799 | + | 0.632582i | 0.963099 | − | 0.269148i | \(-0.0867422\pi\) |
−0.432300 | + | 0.901730i | \(0.642298\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.29021 | + | 0.227498i | 0.0722378 | + | 0.0127375i | ||||
\(320\) | −19.6172 | + | 19.3697i | −1.09663 | + | 1.08280i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.25443 | + | 3.28607i | −0.0699067 | + | 0.183125i | ||||
\(323\) | −0.121865 | −0.00678074 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −37.2939 | −2.06869 | ||||||||
\(326\) | −4.04806 | + | 10.6042i | −0.224201 | + | 0.587311i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.47668 | − | 5.93879i | 0.302399 | − | 0.327915i | ||||
\(329\) | −19.0655 | − | 3.36176i | −1.05111 | − | 0.185340i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.0491 | + | 20.3184i | 0.937106 | + | 1.11680i | 0.992971 | + | 0.118361i | \(0.0377639\pi\) |
−0.0558649 | + | 0.998438i | \(0.517792\pi\) | |||||||
\(332\) | −2.04188 | − | 3.80616i | −0.112063 | − | 0.208890i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.948085 | − | 1.58451i | 0.0518769 | − | 0.0867007i | ||||
\(335\) | 2.88516 | + | 16.3626i | 0.157633 | + | 0.893983i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.4992 | − | 5.27727i | 0.789820 | − | 0.287471i | 0.0845588 | − | 0.996418i | \(-0.473052\pi\) |
0.705261 | + | 0.708948i | \(0.250830\pi\) | |||||||
\(338\) | −21.9469 | + | 7.60238i | −1.19375 | + | 0.413515i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.31389 | − | 9.10416i | −0.0712557 | − | 0.493742i | ||||
\(341\) | 15.0848 | + | 8.70922i | 0.816888 | + | 0.471631i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.7433 | − | 7.93471i | 0.742069 | − | 0.428434i | ||||
\(344\) | −9.74591 | − | 12.7849i | −0.525464 | − | 0.689318i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.9021 | + | 3.06052i | 0.854903 | + | 0.164535i | ||||
\(347\) | 16.4887 | + | 13.8357i | 0.885162 | + | 0.742739i | 0.967234 | − | 0.253888i | \(-0.0817093\pi\) |
−0.0820721 | + | 0.996626i | \(0.526154\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.8787 | − | 4.32349i | −0.635851 | − | 0.231431i | 0.00392469 | − | 0.999992i | \(-0.498751\pi\) |
−0.639776 | + | 0.768561i | \(0.720973\pi\) | |||||||
\(350\) | 0.444436 | − | 28.4826i | 0.0237561 | − | 1.52246i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 14.7420 | + | 1.15240i | 0.785751 | + | 0.0614231i | ||||
\(353\) | −3.82687 | + | 10.5142i | −0.203684 | + | 0.559617i | −0.998909 | − | 0.0466973i | \(-0.985130\pi\) |
0.795225 | + | 0.606314i | \(0.207353\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.2239 | − | 31.2524i | 1.39182 | − | 1.65871i | ||||
\(356\) | 28.4397 | + | 5.93510i | 1.50730 | + | 0.314560i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 23.4985 | − | 19.1009i | 1.24194 | − | 1.00951i | ||||
\(359\) | 16.1699 | + | 28.0070i | 0.853413 | + | 1.47816i | 0.878109 | + | 0.478460i | \(0.158805\pi\) |
−0.0246959 | + | 0.999695i | \(0.507862\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.49583 | + | 16.4473i | −0.499781 | + | 0.865645i | ||||
\(362\) | −3.27406 | − | 20.4268i | −0.172081 | − | 1.07361i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.93353 | − | 30.1916i | −0.520659 | − | 1.58247i | ||||
\(365\) | −13.7439 | − | 37.7610i | −0.719387 | − | 1.97650i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.656339 | − | 0.115730i | 0.0342606 | − | 0.00604107i | −0.156492 | − | 0.987679i | \(-0.550018\pi\) |
0.190752 | + | 0.981638i | \(0.438907\pi\) | |||||||
\(368\) | 1.87798 | − | 2.82918i | 0.0978965 | − | 0.147481i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −23.4932 | + | 13.0794i | −1.22136 | + | 0.679966i | ||||
\(371\) | 16.5461 | − | 13.8838i | 0.859031 | − | 0.720813i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.61725 | − | 20.5144i | 0.187294 | − | 1.06220i | −0.735678 | − | 0.677331i | \(-0.763136\pi\) |
0.922972 | − | 0.384867i | \(-0.125753\pi\) | |||||||
\(374\) | −3.22998 | + | 3.72959i | −0.167018 | + | 0.192852i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 17.2447 | + | 7.20720i | 0.889326 | + | 0.371683i | ||||
\(377\) | 2.71864i | 0.140017i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.1904i | 0.985744i | 0.870102 | + | 0.492872i | \(0.164053\pi\) | ||||
−0.870102 | + | 0.492872i | \(0.835947\pi\) | |||||||
\(380\) | 0.584357 | + | 0.233583i | 0.0299769 | + | 0.0119826i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.05467 | − | 1.77943i | −0.105126 | − | 0.0910436i | ||||
\(383\) | 1.37744 | − | 7.81186i | 0.0703840 | − | 0.399168i | −0.929180 | − | 0.369629i | \(-0.879485\pi\) |
0.999564 | − | 0.0295390i | \(-0.00940393\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.2166 | + | 16.9637i | −1.03033 | + | 0.864552i | ||||
\(386\) | 4.30735 | + | 7.73685i | 0.219238 | + | 0.393795i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.95343 | + | 11.2200i | −0.353007 | + | 0.569610i | ||||
\(389\) | 12.1585 | − | 2.14387i | 0.616461 | − | 0.108699i | 0.143307 | − | 0.989678i | \(-0.454226\pi\) |
0.473154 | + | 0.880980i | \(0.343115\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.387517 | + | 1.06469i | 0.0195976 | + | 0.0538438i | ||||
\(392\) | 4.27529 | − | 1.33309i | 0.215935 | − | 0.0673311i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 21.1262 | − | 3.38615i | 1.06432 | − | 0.170592i | ||||
\(395\) | −2.90676 | + | 5.03465i | −0.146255 | + | 0.253321i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.5959 | + | 20.0847i | 0.581982 | + | 1.00802i | 0.995244 | + | 0.0974099i | \(0.0310558\pi\) |
−0.413263 | + | 0.910612i | \(0.635611\pi\) | |||||||
\(398\) | −23.1165 | − | 28.4387i | −1.15872 | − | 1.42550i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.45539 | + | 26.7327i | −0.322770 | + | 1.33664i | ||||
\(401\) | −4.36829 | + | 5.20593i | −0.218142 | + | 0.259972i | −0.864007 | − | 0.503480i | \(-0.832053\pi\) |
0.645865 | + | 0.763452i | \(0.276497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.3624 | + | 33.9655i | −0.615816 | + | 1.69194i | ||||
\(404\) | −0.514503 | + | 16.4825i | −0.0255975 | + | 0.820034i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.07632 | − | 0.0323984i | −0.103046 | − | 0.00160790i | ||||
\(407\) | 13.5526 | + | 4.93275i | 0.671778 | + | 0.244507i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.9170 | + | 11.6777i | 0.688149 | + | 0.577426i | 0.918375 | − | 0.395712i | \(-0.129502\pi\) |
−0.230226 | + | 0.973137i | \(0.573946\pi\) | |||||||
\(410\) | 2.63069 | − | 13.6687i | 0.129920 | − | 0.675051i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −19.9142 | − | 25.2954i | −0.981101 | − | 1.24622i | ||||
\(413\) | 7.72625 | − | 4.46075i | 0.380184 | − | 0.219499i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.44516 | − | 3.72111i | −0.316380 | − | 0.182662i | ||||
\(416\) | 2.95711 | + | 30.5419i | 0.144984 | + | 1.49744i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.110485 | − | 0.318952i | −0.00540399 | − | 0.0156005i | ||||
\(419\) | 4.62462 | − | 1.68322i | 0.225927 | − | 0.0822309i | −0.226576 | − | 0.973993i | \(-0.572753\pi\) |
0.452504 | + | 0.891763i | \(0.350531\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.04359 | − | 11.5898i | −0.0995984 | − | 0.564851i | −0.993241 | − | 0.116071i | \(-0.962970\pi\) |
0.893642 | − | 0.448780i | \(-0.148141\pi\) | |||||||
\(422\) | 21.1751 | + | 12.6700i | 1.03079 | + | 0.616766i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −18.5269 | + | 9.56988i | −0.899747 | + | 0.464754i | ||||
\(425\) | −5.89823 | − | 7.02924i | −0.286106 | − | 0.340968i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.99642 | − | 1.23366i | −0.338581 | − | 0.0597009i | ||||
\(428\) | −14.4919 | − | 12.9518i | −0.700494 | − | 0.626048i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −25.8779 | − | 9.87868i | −1.24794 | − | 0.476392i | ||||
\(431\) | −4.40894 | −0.212371 | −0.106186 | − | 0.994346i | \(-0.533864\pi\) | ||||
−0.106186 | + | 0.994346i | \(0.533864\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.5232 | 1.37074 | 0.685369 | − | 0.728196i | \(-0.259641\pi\) | ||||
0.685369 | + | 0.728196i | \(0.259641\pi\) | |||||||
\(434\) | −25.7933 | − | 9.84639i | −1.23812 | − | 0.472642i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.00671 | − | 6.26206i | −0.335561 | − | 0.299898i | ||||
\(437\) | −0.0763379 | − | 0.0134604i | −0.00365174 | − | 0.000643900i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.10907 | − | 3.70524i | −0.148388 | − | 0.176842i | 0.686730 | − | 0.726912i | \(-0.259045\pi\) |
−0.835118 | + | 0.550071i | \(0.814601\pi\) | |||||||
\(440\) | 22.6368 | − | 11.6928i | 1.07917 | − | 0.557432i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.78565 | − | 5.25684i | −0.417891 | − | 0.250042i | ||||
\(443\) | 1.26185 | + | 7.15628i | 0.0599521 | + | 0.340005i | 0.999999 | − | 0.00103872i | \(-0.000330635\pi\) |
−0.940047 | + | 0.341044i | \(0.889220\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 47.0392 | − | 17.1209i | 2.22987 | − | 0.811607i | ||||
\(446\) | 8.18217 | + | 23.6206i | 0.387437 | + | 1.11847i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −23.3612 | + | 1.89447i | −1.10371 | + | 0.0895054i | ||||
\(449\) | 5.50442 | + | 3.17798i | 0.259769 | + | 0.149978i | 0.624229 | − | 0.781241i | \(-0.285413\pi\) |
−0.364460 | + | 0.931219i | \(0.618746\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.46583 | + | 3.73305i | −0.304464 | + | 0.175782i | ||||
\(452\) | −0.698323 | − | 0.887025i | −0.0328463 | − | 0.0417222i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.49354 | + | 12.9561i | −0.117028 | + | 0.608062i | ||||
\(455\) | −41.9518 | − | 35.2017i | −1.96673 | − | 1.65028i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.840235 | + | 0.305821i | 0.0393045 | + | 0.0143057i | 0.361598 | − | 0.932334i | \(-0.382231\pi\) |
−0.322293 | + | 0.946640i | \(0.604454\pi\) | |||||||
\(458\) | 23.7801 | + | 0.371060i | 1.11117 | + | 0.0173385i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.182549 | − | 5.84810i | 0.00851140 | − | 0.272669i | ||||
\(461\) | 4.48102 | − | 12.3115i | 0.208702 | − | 0.573404i | −0.790537 | − | 0.612415i | \(-0.790198\pi\) |
0.999239 | + | 0.0390104i | \(0.0124206\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.866856 | + | 1.03308i | −0.0402862 | + | 0.0480112i | −0.785811 | − | 0.618466i | \(-0.787754\pi\) |
0.745525 | + | 0.666478i | \(0.232199\pi\) | |||||||
\(464\) | 1.94875 | + | 0.470583i | 0.0904686 | + | 0.0218463i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.7243 | + | 19.3445i | 0.728412 | + | 0.896118i | ||||
\(467\) | 9.81172 | + | 16.9944i | 0.454032 | + | 0.786407i | 0.998632 | − | 0.0522890i | \(-0.0166517\pi\) |
−0.544600 | + | 0.838696i | \(0.683318\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.06278 | + | 12.2331i | −0.326129 | + | 0.564872i | ||||
\(470\) | 31.7978 | − | 5.09662i | 1.46672 | − | 0.235090i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.22256 | + | 2.56390i | −0.378474 | + | 0.118013i | ||||
\(473\) | 5.08146 | + | 13.9612i | 0.233646 | + | 0.641937i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.618239 | − | 0.109012i | 0.0283667 | − | 0.00500182i | ||||
\(476\) | 4.11953 | − | 6.64726i | 0.188819 | − | 0.304677i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.33869 | − | 11.3855i | −0.289925 | − | 0.520763i | ||||
\(479\) | −14.6017 | + | 12.2523i | −0.667170 | + | 0.559822i | −0.912226 | − | 0.409687i | \(-0.865638\pi\) |
0.245056 | + | 0.969509i | \(0.421194\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.19697 | + | 29.4735i | −0.236962 | + | 1.34388i | ||||
\(482\) | 6.65655 | + | 5.76486i | 0.303198 | + | 0.262582i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.73874 | + | 3.09338i | 0.351761 | + | 0.140608i | ||||
\(485\) | 22.7439i | 1.03275i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.7440i | 0.577486i | 0.957407 | + | 0.288743i | \(0.0932373\pi\) | ||||
−0.957407 | + | 0.288743i | \(0.906763\pi\) | |||||||
\(488\) | 6.32825 | + | 2.64481i | 0.286466 | + | 0.119725i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.05152 | − | 5.83288i | 0.228204 | − | 0.263503i | ||||
\(491\) | 4.29474 | − | 24.3567i | 0.193819 | − | 1.09920i | −0.720272 | − | 0.693692i | \(-0.755983\pi\) |
0.914091 | − | 0.405510i | \(-0.132906\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.512415 | + | 0.429967i | −0.0230780 | + | 0.0193648i | ||||
\(494\) | 0.611997 | − | 0.340718i | 0.0275350 | − | 0.0153296i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 22.2070 | + | 14.7408i | 0.997125 | + | 0.661882i | ||||
\(497\) | 34.1576 | − | 6.02290i | 1.53218 | − | 0.270164i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.5128 | − | 37.1262i | −0.604917 | − | 1.66199i | −0.741167 | − | 0.671320i | \(-0.765727\pi\) |
0.136251 | − | 0.990674i | \(-0.456495\pi\) | |||||||
\(500\) | 4.03940 | + | 12.2772i | 0.180647 | + | 0.549052i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.34588 | + | 39.5919i | 0.283231 | + | 1.76707i | ||||
\(503\) | 18.2058 | − | 31.5334i | 0.811757 | − | 1.40600i | −0.0998757 | − | 0.995000i | \(-0.531845\pi\) |
0.911633 | − | 0.411005i | \(-0.134822\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.2068 | + | 24.6069i | 0.632194 | + | 1.09499i | ||||
\(506\) | −2.43525 | + | 1.97950i | −0.108260 | + | 0.0879997i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 21.7737 | + | 4.54397i | 0.966051 | + | 0.201606i | ||||
\(509\) | 2.32891 | − | 2.77549i | 0.103227 | − | 0.123021i | −0.711957 | − | 0.702223i | \(-0.752191\pi\) |
0.815184 | + | 0.579201i | \(0.196636\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.6846 | − | 32.1032i | 0.516897 | − | 1.42016i | ||||
\(512\) | 22.4047 | + | 3.16697i | 0.990157 | + | 0.139961i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.364019 | + | 23.3289i | −0.0160562 | + | 1.02899i | ||||
\(515\) | −52.1252 | − | 18.9720i | −2.29691 | − | 0.836008i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.2320 | − | 11.1030i | −0.581944 | − | 0.488309i | ||||
\(518\) | −22.4480 | − | 4.32035i | −0.986309 | − | 0.189825i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 32.0523 | + | 42.0470i | 1.40558 | + | 1.84388i | ||||
\(521\) | −18.0443 | + | 10.4179i | −0.790534 | + | 0.456415i | −0.840151 | − | 0.542353i | \(-0.817534\pi\) |
0.0496162 | + | 0.998768i | \(0.484200\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.0780 | − | 11.0147i | −0.834223 | − | 0.481639i | 0.0210733 | − | 0.999778i | \(-0.493292\pi\) |
−0.855296 | + | 0.518139i | \(0.826625\pi\) | |||||||
\(524\) | −0.886245 | − | 6.14094i | −0.0387158 | − | 0.268268i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 32.3612 | − | 11.2099i | 1.41102 | − | 0.488775i | ||||
\(527\) | −8.35708 | + | 3.04173i | −0.364040 | + | 0.132500i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.86876 | − | 21.9408i | −0.168207 | − | 0.953949i | ||||
\(530\) | −18.4480 | + | 30.8318i | −0.801331 | + | 1.33925i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.252925 | + | 0.471464i | 0.0109657 | + | 0.0204405i | ||||
\(533\) | −9.95873 | − | 11.8684i | −0.431361 | − | 0.514075i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −32.9802 | − | 5.81531i | −1.42586 | − | 0.251418i | ||||
\(536\) | 9.24499 | − | 10.0251i | 0.399323 | − | 0.433017i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.15102 | − | 16.1130i | 0.265189 | − | 0.694682i | ||||
\(539\) | −4.13879 | −0.178270 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.2610 | −0.570135 | −0.285067 | − | 0.958507i | \(-0.592016\pi\) | ||||
−0.285067 | + | 0.958507i | \(0.592016\pi\) | |||||||
\(542\) | −12.6096 | + | 33.0317i | −0.541628 | + | 1.41883i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.28893 | + | 5.38773i | −0.226761 | + | 0.230997i | ||||
\(545\) | −15.9456 | − | 2.81165i | −0.683036 | − | 0.120438i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.19354 | + | 10.9564i | 0.393087 | + | 0.468463i | 0.925899 | − | 0.377770i | \(-0.123309\pi\) |
−0.532812 | + | 0.846234i | \(0.678865\pi\) | |||||||
\(548\) | 30.4337 | − | 16.3267i | 1.30006 | − | 0.697440i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 13.0499 | − | 21.8101i | 0.556451 | − | 0.929985i | ||||
\(551\) | −0.00794673 | − | 0.0450681i | −0.000338542 | − | 0.00191997i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.64441 | + | 1.69043i | −0.197500 | + | 0.0718842i | ||||
\(554\) | 11.6765 | − | 4.04472i | 0.496086 | − | 0.171844i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22.1505 | − | 3.19671i | 0.939392 | − | 0.135571i | ||||
\(557\) | −6.40425 | − | 3.69750i | −0.271357 | − | 0.156668i | 0.358147 | − | 0.933665i | \(-0.383409\pi\) |
−0.629504 | + | 0.776997i | \(0.716742\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.6999 | + | 15.4152i | −1.12929 | + | 0.651994i | ||||
\(560\) | −32.4947 | + | 23.9784i | −1.37315 | + | 1.01327i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −30.3964 | − | 5.85009i | −1.28219 | − | 0.246771i | ||||
\(563\) | 16.2270 | + | 13.6161i | 0.683887 | + | 0.573850i | 0.917139 | − | 0.398567i | \(-0.130492\pi\) |
−0.233252 | + | 0.972416i | \(0.574937\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.82786 | − | 0.665286i | −0.0768985 | − | 0.0279888i | ||||
\(566\) | 0.664189 | − | 42.5660i | 0.0279180 | − | 1.78918i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −33.4485 | − | 1.56679i | −1.40347 | − | 0.0657409i | ||||
\(569\) | 1.52428 | − | 4.18793i | 0.0639012 | − | 0.175567i | −0.903633 | − | 0.428308i | \(-0.859110\pi\) |
0.967534 | + | 0.252741i | \(0.0813320\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.38240 | − | 1.64748i | 0.0578516 | − | 0.0689449i | −0.736343 | − | 0.676609i | \(-0.763449\pi\) |
0.794194 | + | 0.607664i | \(0.207893\pi\) | |||||||
\(572\) | 5.79332 | − | 27.7603i | 0.242231 | − | 1.16072i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.18296 | − | 7.46439i | 0.383289 | − | 0.311558i | ||||
\(575\) | −2.91833 | − | 5.05470i | −0.121703 | − | 0.210796i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.0706 | + | 27.8351i | −0.669028 | + | 1.15879i | 0.309148 | + | 0.951014i | \(0.399956\pi\) |
−0.978176 | + | 0.207777i | \(0.933377\pi\) | |||||||
\(578\) | 3.40621 | + | 21.2513i | 0.141679 | + | 0.883937i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.28123 | − | 1.07958i | 0.136246 | − | 0.0448271i | ||||
\(581\) | −2.16402 | − | 5.94559i | −0.0897785 | − | 0.246664i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.9789 | − | 3.34648i | 0.786024 | − | 0.138597i | ||||
\(584\) | −17.8096 | + | 27.7606i | −0.736965 | + | 1.14874i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.3584 | − | 9.10721i | 0.675758 | − | 0.376215i | ||||
\(587\) | −27.6154 | + | 23.1721i | −1.13981 | + | 0.956414i | −0.999433 | − | 0.0336838i | \(-0.989276\pi\) |
−0.140378 | + | 0.990098i | \(0.544832\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.105655 | − | 0.599198i | 0.00435343 | − | 0.0246895i | ||||
\(590\) | −9.71547 | + | 11.2182i | −0.399980 | + | 0.461848i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 20.2274 | + | 8.82698i | 0.831342 | + | 0.362787i | ||||
\(593\) | 4.09387i | 0.168115i | 0.996461 | + | 0.0840576i | \(0.0267880\pi\) | ||||
−0.996461 | + | 0.0840576i | \(0.973212\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 13.4745i | − | 0.552402i | ||||||
\(596\) | −13.5491 | + | 33.8960i | −0.554995 | + | 1.38844i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.92282 | − | 4.26337i | −0.201309 | − | 0.174342i | ||||
\(599\) | 1.46823 | − | 8.32677i | 0.0599904 | − | 0.340223i | −0.940009 | − | 0.341149i | \(-0.889184\pi\) |
1.00000 | 0.000926605i | \(0.000294948\pi\) | ||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.3724 | − | 18.7727i | 0.912590 | − | 0.765754i | −0.0600202 | − | 0.998197i | \(-0.519116\pi\) |
0.972610 | + | 0.232443i | \(0.0746721\pi\) | |||||||
\(602\) | −11.4550 | − | 20.5754i | −0.466869 | − | 0.838590i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −32.7244 | − | 20.2804i | −1.33154 | − | 0.825198i | ||||
\(605\) | 14.1417 | − | 2.49356i | 0.574942 | − | 0.101378i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.2715 | + | 36.4633i | 0.538675 | + | 1.48000i | 0.848495 | + | 0.529203i | \(0.177509\pi\) |
−0.309820 | + | 0.950795i | \(0.600269\pi\) | |||||||
\(608\) | −0.138297 | − | 0.497664i | −0.00560869 | − | 0.0201829i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.6688 | − | 1.87030i | 0.472455 | − | 0.0757262i | ||||
\(611\) | 17.9220 | − | 31.0417i | 0.725045 | − | 1.25581i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.677216 | − | 1.17297i | −0.0273525 | − | 0.0473759i | 0.852025 | − | 0.523501i | \(-0.175374\pi\) |
−0.879378 | + | 0.476125i | \(0.842041\pi\) | |||||||
\(614\) | −11.7488 | − | 14.4538i | −0.474143 | − | 0.583307i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 21.1325 | + | 4.75539i | 0.851452 | + | 0.191600i | ||||
\(617\) | 14.2746 | − | 17.0118i | 0.574675 | − | 0.684871i | −0.397909 | − | 0.917425i | \(-0.630264\pi\) |
0.972583 | + | 0.232554i | \(0.0747083\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.757138 | + | 2.08022i | −0.0304320 | + | 0.0836111i | −0.953978 | − | 0.299876i | \(-0.903055\pi\) |
0.923546 | + | 0.383487i | \(0.125277\pi\) | |||||||
\(620\) | 45.9034 | + | 1.43288i | 1.84353 | + | 0.0575459i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.73303 | + | 0.136268i | 0.350163 | + | 0.00546386i | ||||
\(623\) | 39.9913 | + | 14.5556i | 1.60222 | + | 0.583160i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.27445 | − | 7.78219i | −0.370978 | − | 0.311287i | ||||
\(626\) | −5.72956 | + | 29.7701i | −0.228999 | + | 1.18985i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −26.4634 | + | 20.8337i | −1.05601 | + | 0.831355i | ||||
\(629\) | −6.37717 | + | 3.68186i | −0.254274 | + | 0.146805i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.3534 | − | 5.97752i | −0.412161 | − | 0.237961i | 0.279557 | − | 0.960129i | \(-0.409813\pi\) |
−0.691718 | + | 0.722168i | \(0.743146\pi\) | |||||||
\(632\) | 4.73271 | − | 0.607796i | 0.188257 | − | 0.0241768i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.80576 | − | 19.6472i | −0.270291 | − | 0.780288i | ||||
\(635\) | 36.0136 | − | 13.1079i | 1.42916 | − | 0.520171i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.49137 | − | 8.45799i | −0.0590903 | − | 0.335118i | ||||
\(638\) | −1.58990 | − | 0.951310i | −0.0629449 | − | 0.0376627i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 35.6879 | − | 15.6973i | 1.41069 | − | 0.620492i | ||||
\(641\) | −8.66598 | − | 10.3277i | −0.342286 | − | 0.407920i | 0.567250 | − | 0.823545i | \(-0.308007\pi\) |
−0.909536 | + | 0.415625i | \(0.863563\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.1966 | + | 4.79550i | 1.07253 | + | 0.189116i | 0.681910 | − | 0.731436i | \(-0.261150\pi\) |
0.390620 | + | 0.920552i | \(0.372261\pi\) | |||||||
\(644\) | 3.31475 | − | 3.70892i | 0.130620 | − | 0.146152i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.161010 | + | 0.0614643i | 0.00633485 | + | 0.00241828i | ||||
\(647\) | 15.2634 | 0.600064 | 0.300032 | − | 0.953929i | \(-0.403003\pi\) | ||||
0.300032 | + | 0.953929i | \(0.403003\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.96003 | 0.312458 | ||||||||
\(650\) | 49.2733 | + | 18.8097i | 1.93266 | + | 0.737777i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.6967 | − | 11.9687i | 0.418917 | − | 0.468732i | ||||
\(653\) | 30.1302 | + | 5.31277i | 1.17909 | + | 0.207905i | 0.728639 | − | 0.684898i | \(-0.240153\pi\) |
0.450448 | + | 0.892803i | \(0.351264\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.87180 | − | 8.18949i | −0.268503 | − | 0.319990i | ||||
\(656\) | −10.2312 | + | 5.08419i | −0.399461 | + | 0.198504i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 23.4941 | + | 14.0576i | 0.915895 | + | 0.548021i | ||||
\(659\) | −7.25464 | − | 41.1431i | −0.282601 | − | 1.60271i | −0.713732 | − | 0.700418i | \(-0.752997\pi\) |
0.431132 | − | 0.902289i | \(-0.358114\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.7435 | + | 11.1897i | −1.19578 | + | 0.435230i | −0.861751 | − | 0.507331i | \(-0.830632\pi\) |
−0.334033 | + | 0.942561i | \(0.608410\pi\) | |||||||
\(662\) | −12.2778 | − | 35.4440i | −0.477189 | − | 1.37757i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.778076 | + | 6.05862i | 0.0301952 | + | 0.235120i | ||||
\(665\) | 0.798352 | + | 0.460929i | 0.0309588 | + | 0.0178741i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.368476 | + | 0.212740i | −0.0142674 | + | 0.00823731i | ||||
\(668\) | −2.05180 | + | 1.61531i | −0.0793865 | + | 0.0624981i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.44077 | − | 23.0737i | 0.171562 | − | 0.891415i | ||||
\(671\) | −4.85574 | − | 4.07445i | −0.187454 | − | 0.157292i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.6470 | − | 9.69872i | −1.02717 | − | 0.373858i | −0.227166 | − | 0.973856i | \(-0.572946\pi\) |
−0.800002 | + | 0.599998i | \(0.795168\pi\) | |||||||
\(674\) | −21.8182 | − | 0.340446i | −0.840407 | − | 0.0131135i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 32.8310 | + | 1.02482i | 1.26273 | + | 0.0394163i | ||||
\(677\) | −13.7737 | + | 37.8429i | −0.529366 | + | 1.45442i | 0.330453 | + | 0.943822i | \(0.392799\pi\) |
−0.859819 | + | 0.510599i | \(0.829424\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.4290 | + | 14.8124i | −0.476983 | + | 0.568446i | ||||
\(680\) | −2.85588 | + | 12.6913i | −0.109518 | + | 0.486687i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −15.5377 | − | 19.1150i | −0.594969 | − | 0.731952i | ||||
\(683\) | 2.35647 | + | 4.08153i | 0.0901678 | + | 0.156175i | 0.907582 | − | 0.419876i | \(-0.137926\pi\) |
−0.817414 | + | 0.576051i | \(0.804593\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29.7536 | − | 51.5348i | 1.13683 | − | 1.96904i | ||||
\(686\) | −22.1599 | + | 3.55184i | −0.846069 | + | 0.135610i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.42820 | + | 21.8072i | 0.245073 | + | 0.831391i | ||||
\(689\) | 13.6777 | + | 37.5792i | 0.521079 | + | 1.43165i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −47.8656 | + | 8.44000i | −1.82089 | + | 0.321073i | −0.976642 | − | 0.214875i | \(-0.931066\pi\) |
−0.844251 | + | 0.535947i | \(0.819955\pi\) | |||||||
\(692\) | −19.4665 | − | 12.0641i | −0.740006 | − | 0.458607i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.8070 | − | 26.5963i | −0.562065 | − | 1.00958i | ||||
\(695\) | 29.5397 | − | 24.7868i | 1.12051 | − | 0.940216i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.661948 | − | 3.75409i | 0.0250731 | − | 0.142196i | ||||
\(698\) | 13.5137 | + | 11.7035i | 0.511502 | + | 0.442982i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −14.9528 | + | 37.4076i | −0.565164 | + | 1.41387i | ||||
\(701\) | − | 5.10945i | − | 0.192981i | −0.995334 | − | 0.0964906i | \(-0.969238\pi\) | ||
0.995334 | − | 0.0964906i | \(-0.0307618\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.503788i | − | 0.0190007i | ||||||
\(704\) | −18.8962 | − | 8.95791i | −0.712176 | − | 0.337614i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.3591 | − | 11.9615i | 0.389871 | − | 0.450176i | ||||
\(707\) | −4.19471 | + | 23.7894i | −0.157758 | + | 0.894692i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.00392 | + | 5.87699i | −0.263038 | + | 0.220715i | −0.764762 | − | 0.644313i | \(-0.777144\pi\) |
0.501725 | + | 0.865027i | \(0.332699\pi\) | |||||||
\(710\) | −50.4101 | + | 28.0649i | −1.89186 | + | 1.05326i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −34.5816 | − | 22.1855i | −1.29600 | − | 0.831438i | ||||
\(713\) | −5.57097 | + | 0.982312i | −0.208634 | + | 0.0367879i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.7119 | − | 45.9155i | −0.624988 | − | 1.71714i | ||||
\(716\) | −40.6805 | + | 13.3846i | −1.52030 | + | 0.500205i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.23817 | − | 45.1589i | −0.270126 | − | 1.68532i | ||||
\(719\) | −11.2528 | + | 19.4904i | −0.419658 | + | 0.726869i | −0.995905 | − | 0.0904064i | \(-0.971183\pi\) |
0.576247 | + | 0.817276i | \(0.304517\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.5797 | − | 40.8412i | −0.878153 | − | 1.52101i | ||||
\(722\) | 20.8415 | − | 16.9411i | 0.775639 | − | 0.630481i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.97682 | + | 28.6396i | −0.222127 | + | 1.06438i | ||||
\(725\) | 2.21494 | − | 2.63966i | 0.0822608 | − | 0.0980346i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.99428 | + | 16.4691i | −0.222316 | + | 0.610807i | −0.999837 | − | 0.0180494i | \(-0.994254\pi\) |
0.777522 | + | 0.628856i | \(0.216477\pi\) | |||||||
\(728\) | −2.10318 | + | 44.8997i | −0.0779491 | + | 1.66409i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.886643 | + | 56.8224i | −0.0328161 | + | 2.10309i | ||||
\(731\) | −7.12825 | − | 2.59447i | −0.263648 | − | 0.0959599i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.2190 | − | 14.4484i | −0.635998 | − | 0.533666i | 0.266788 | − | 0.963755i | \(-0.414038\pi\) |
−0.902786 | + | 0.430089i | \(0.858482\pi\) | |||||||
\(734\) | −0.925538 | − | 0.178129i | −0.0341622 | − | 0.00657487i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.90816 | + | 2.79077i | −0.144057 | + | 0.102869i | ||||
\(737\) | −10.9147 | + | 6.30162i | −0.402049 | + | 0.232123i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.76664 | − | 4.48407i | −0.285700 | − | 0.164949i | 0.350301 | − | 0.936637i | \(-0.386079\pi\) |
−0.636001 | + | 0.771688i | \(0.719413\pi\) | |||||||
\(740\) | 37.6365 | − | 5.43160i | 1.38354 | − | 0.199670i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −28.8635 | + | 9.99830i | −1.05961 | + | 0.367049i | ||||
\(743\) | −44.6168 | + | 16.2392i | −1.63683 | + | 0.595758i | −0.986481 | − | 0.163875i | \(-0.947601\pi\) |
−0.650352 | + | 0.759633i | \(0.725378\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.9219 | + | 61.9413i | 0.400148 | + | 2.26935i | ||||
\(746\) | −15.1259 | + | 25.2796i | −0.553800 | + | 0.925554i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.14858 | − | 3.29851i | 0.224814 | − | 0.120605i | ||||
\(749\) | −18.3010 | − | 21.8103i | −0.668705 | − | 0.796932i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.7230 | + | 2.41974i | 0.500761 | + | 0.0882976i | 0.418323 | − | 0.908299i | \(-0.362618\pi\) |
0.0824383 | + | 0.996596i | \(0.473729\pi\) | |||||||
\(752\) | −19.1489 | − | 18.2199i | −0.698289 | − | 0.664411i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.37118 | − | 3.59191i | 0.0499355 | − | 0.130810i | ||||
\(755\) | −66.3349 | −2.41418 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.8098 | 0.465582 | 0.232791 | − | 0.972527i | \(-0.425214\pi\) | ||||
0.232791 | + | 0.972527i | \(0.425214\pi\) | |||||||
\(758\) | 9.67895 | − | 25.3547i | 0.351555 | − | 0.920924i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.654252 | − | 0.603343i | −0.0237322 | − | 0.0218855i | ||||
\(761\) | −30.5200 | − | 5.38149i | −1.10635 | − | 0.195079i | −0.409508 | − | 0.912306i | \(-0.634300\pi\) |
−0.696839 | + | 0.717227i | \(0.745411\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.84838 | − | 10.5451i | −0.320333 | − | 0.381758i | ||||
\(764\) | 1.81718 | + | 3.38732i | 0.0657434 | + | 0.122549i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.75993 | + | 9.62644i | −0.208115 | + | 0.347817i | ||||
\(767\) | 2.86832 | + | 16.2671i | 0.103569 | + | 0.587369i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.0889 | + | 5.85587i | −0.580179 | + | 0.211168i | −0.615404 | − | 0.788211i | \(-0.711007\pi\) |
0.0352254 | + | 0.999379i | \(0.488785\pi\) | |||||||
\(770\) | 35.2664 | − | 12.2163i | 1.27091 | − | 0.440243i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.78875 | − | 12.3945i | −0.0643785 | − | 0.446089i | ||||
\(773\) | −37.1476 | − | 21.4472i | −1.33610 | − | 0.771401i | −0.349877 | − | 0.936795i | \(-0.613777\pi\) |
−0.986227 | + | 0.165395i | \(0.947110\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.6758 | − | 22.9068i | 1.42520 | − | 0.822838i | ||||
\(776\) | 14.8460 | − | 11.3170i | 0.532939 | − | 0.406257i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17.1453 | − | 3.29980i | −0.614690 | − | 0.118303i | ||||
\(779\) | 0.199783 | + | 0.167638i | 0.00715795 | + | 0.00600624i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.0802 | + | 10.5843i | 1.04057 | + | 0.378737i | ||||
\(782\) | 0.0249994 | − | 1.60214i | 0.000893978 | − | 0.0572924i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.32095 | − | 0.395004i | −0.225748 | − | 0.0141073i | ||||
\(785\) | −19.8481 | + | 54.5321i | −0.708408 | + | 1.94633i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.83079 | − | 4.56536i | 0.136553 | − | 0.162737i | −0.693434 | − | 0.720520i | \(-0.743903\pi\) |
0.829987 | + | 0.557783i | \(0.188348\pi\) | |||||||
\(788\) | −29.6201 | − | 6.18145i | −1.05517 | − | 0.220205i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.37976 | − | 5.18580i | 0.226982 | − | 0.184503i | ||||
\(791\) | −0.826860 | − | 1.43216i | −0.0293998 | − | 0.0509219i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.57679 | − | 11.3913i | 0.233549 | − | 0.404518i | ||||
\(794\) | −5.19071 | − | 32.3848i | −0.184211 | − | 1.14929i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.1984 | + | 49.2328i | 0.574138 | + | 1.74501i | ||||
\(797\) | −14.1501 | − | 38.8770i | −0.501221 | − | 1.37709i | −0.890084 | − | 0.455797i | \(-0.849354\pi\) |
0.388863 | − | 0.921296i | \(-0.372868\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.68528 | − | 1.53145i | 0.307263 | − | 0.0541788i | ||||
\(800\) | 22.0120 | − | 32.0639i | 0.778243 | − | 1.13363i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.39715 | − | 4.67495i | 0.296514 | − | 0.165078i | ||||
\(803\) | 23.3504 | − | 19.5933i | 0.824016 | − | 0.691432i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.48831 | − | 8.44064i | 0.0524561 | − | 0.297494i | ||||
\(806\) | 33.4644 | − | 38.6406i | 1.17873 | − | 1.36106i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.99295 | − | 21.5175i | 0.316371 | − | 0.756982i | ||||
\(809\) | − | 45.8780i | − | 1.61298i | −0.591245 | − | 0.806492i | \(-0.701363\pi\) | ||
0.591245 | − | 0.806492i | \(-0.298637\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.4302i | 0.892974i | 0.894790 | + | 0.446487i | \(0.147325\pi\) | ||||
−0.894790 | + | 0.446487i | \(0.852675\pi\) | |||||||
\(812\) | 2.72693 | + | 1.09003i | 0.0956964 | + | 0.0382524i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.4181 | − | 13.3527i | −0.540403 | − | 0.468012i | ||||
\(815\) | 4.80280 | − | 27.2380i | 0.168235 | − | 0.954107i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.397558 | − | 0.333591i | 0.0139088 | − | 0.0116709i | ||||
\(818\) | −12.4975 | − | 22.4480i | −0.436965 | − | 0.784877i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.3697 | + | 16.7326i | −0.362127 | + | 0.584326i | ||||
\(821\) | 7.72253 | − | 1.36169i | 0.269518 | − | 0.0475233i | −0.0372556 | − | 0.999306i | \(-0.511862\pi\) |
0.306774 | + | 0.951782i | \(0.400750\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.99728 | + | 8.23497i | 0.104479 | + | 0.287053i | 0.980906 | − | 0.194481i | \(-0.0623021\pi\) |
−0.876428 | + | 0.481534i | \(0.840080\pi\) | |||||||
\(824\) | 13.5528 | + | 43.4647i | 0.472136 | + | 1.51417i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.4579 | + | 1.99678i | −0.433466 | + | 0.0694769i | ||||
\(827\) | −9.57006 | + | 16.5758i | −0.332784 | + | 0.576398i | −0.983057 | − | 0.183303i | \(-0.941321\pi\) |
0.650273 | + | 0.759701i | \(0.274655\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.0258029 | − | 0.0446919i | −0.000896172 | − | 0.00155222i | 0.865577 | − | 0.500776i | \(-0.166952\pi\) |
−0.866473 | + | 0.499224i | \(0.833619\pi\) | |||||||
\(830\) | 6.63866 | + | 8.16711i | 0.230431 | + | 0.283485i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11.4973 | − | 41.8440i | 0.398596 | − | 1.45068i | ||||
\(833\) | 1.35831 | − | 1.61878i | 0.0470628 | − | 0.0560873i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.53889 | + | 4.22806i | −0.0532554 | + | 0.146318i | ||||
\(836\) | −0.0148937 | + | 0.477130i | −0.000515109 | + | 0.0165019i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.95909 | − | 0.108588i | −0.240398 | − | 0.00375111i | ||||
\(839\) | −10.1094 | − | 3.67952i | −0.349015 | − | 0.127031i | 0.161563 | − | 0.986862i | \(-0.448346\pi\) |
−0.510578 | + | 0.859831i | \(0.670569\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.0229 | + | 18.4794i | 0.759409 | + | 0.637220i | ||||
\(842\) | −3.14544 | + | 16.3433i | −0.108399 | + | 0.563228i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −21.5866 | − | 27.4198i | −0.743042 | − | 0.943828i | ||||
\(845\) | 49.0137 | − | 28.2981i | 1.68612 | − | 0.973484i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.5727 | + | 6.10416i | 0.363283 | + | 0.209741i | ||||
\(848\) | 29.3048 | − | 3.29958i | 1.00633 | − | 0.113308i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.24755 | + | 12.2620i | 0.145690 | + | 0.420584i | ||||
\(851\) | −4.40143 | + | 1.60199i | −0.150879 | + | 0.0549155i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.86844 | + | 38.9529i | 0.235171 | + | 1.33372i | 0.842254 | + | 0.539082i | \(0.181229\pi\) |
−0.607083 | + | 0.794639i | \(0.707660\pi\) | |||||||
\(854\) | 8.62159 | + | 5.15868i | 0.295025 | + | 0.176526i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.6146 | + | 24.4213i | 0.431157 | + | 0.834704i | ||||
\(857\) | 6.59420 | + | 7.85866i | 0.225253 | + | 0.268447i | 0.866820 | − | 0.498620i | \(-0.166160\pi\) |
−0.641567 | + | 0.767067i | \(0.721715\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.49071 | + | 0.615507i | 0.119102 | + | 0.0210008i | 0.232881 | − | 0.972505i | \(-0.425185\pi\) |
−0.113780 | + | 0.993506i | \(0.536296\pi\) | |||||||
\(860\) | 29.2079 | + | 26.1038i | 0.995981 | + | 0.890132i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.82517 | + | 2.22371i | 0.198406 | + | 0.0757400i | ||||
\(863\) | 6.36151 | 0.216548 | 0.108274 | − | 0.994121i | \(-0.465468\pi\) | ||||
0.108274 | + | 0.994121i | \(0.465468\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39.4602 | −1.34169 | ||||||||
\(866\) | −37.6854 | − | 14.3861i | −1.28060 | − | 0.488860i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 29.1124 | + | 26.0184i | 0.988139 | + | 0.883124i | ||||
\(869\) | −4.34283 | − | 0.765757i | −0.147320 | − | 0.0259765i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.8110 | − | 20.0345i | −0.569618 | − | 0.678844i | ||||
\(872\) | 6.09903 | + | 11.8075i | 0.206539 | + | 0.399852i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.0940700 | + | 0.0562863i | 0.00318197 | + | 0.00190391i | ||||
\(875\) | 3.28765 | + | 18.6452i | 0.111143 | + | 0.630323i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.3450 | − | 5.58514i | 0.518165 | − | 0.188597i | −0.0696811 | − | 0.997569i | \(-0.522198\pi\) |
0.587846 | + | 0.808973i | \(0.299976\pi\) | |||||||
\(878\) | 2.23896 | + | 6.46354i | 0.0755614 | + | 0.218134i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −35.8056 | + | 4.03153i | −1.20701 | + | 0.135903i | ||||
\(881\) | 43.1593 | + | 24.9180i | 1.45407 | + | 0.839509i | 0.998709 | − | 0.0507963i | \(-0.0161759\pi\) |
0.455364 | + | 0.890306i | \(0.349509\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.2077 | − | 22.0592i | 1.28579 | − | 0.742352i | 0.307890 | − | 0.951422i | \(-0.400377\pi\) |
0.977901 | + | 0.209070i | \(0.0670437\pi\) | |||||||
\(884\) | 8.95639 | + | 11.3766i | 0.301236 | + | 0.382636i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.94220 | − | 10.0914i | 0.0652495 | − | 0.339028i | ||||
\(887\) | −1.84120 | − | 1.54495i | −0.0618215 | − | 0.0518744i | 0.611353 | − | 0.791358i | \(-0.290625\pi\) |
−0.673175 | + | 0.739483i | \(0.735070\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.6177 | + | 11.1439i | 1.02688 | + | 0.373756i | ||||
\(890\) | −70.7842 | − | 1.10450i | −2.37269 | − | 0.0370229i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.10298 | − | 35.3348i | 0.0369305 | − | 1.18310i | ||||
\(893\) | −0.206364 | + | 0.566981i | −0.00690571 | + | 0.0189733i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −47.4313 | + | 56.5264i | −1.58545 | + | 1.88947i | ||||
\(896\) | 31.8207 | + | 9.27952i | 1.06305 | + | 0.310007i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.66967 | − | 6.97503i | −0.189199 | − | 0.232760i | ||||
\(899\) | −1.66986 | − | 2.89227i | −0.0556928 | − | 0.0964627i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.91981 | + | 8.52136i | −0.163903 | + | 0.283888i | ||||
\(902\) | 10.4256 | − | 1.67104i | 0.347134 | − | 0.0556394i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.475253 | + | 1.52416i | 0.0158067 | + | 0.0506929i | ||||
\(905\) | 17.2412 | + | 47.3698i | 0.573117 | + | 1.57463i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.5531 | − | 6.09265i | 1.14732 | − | 0.202303i | 0.432513 | − | 0.901628i | \(-0.357627\pi\) |
0.714804 | + | 0.699324i | \(0.246516\pi\) | |||||||
\(908\) | 9.82912 | − | 15.8602i | 0.326191 | − | 0.526340i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 37.6730 | + | 67.6682i | 1.24885 | + | 2.24318i | ||||
\(911\) | −8.27443 | + | 6.94307i | −0.274144 | + | 0.230034i | −0.769486 | − | 0.638664i | \(-0.779487\pi\) |
0.495342 | + | 0.868698i | \(0.335043\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.980292 | − | 5.55951i | 0.0324429 | − | 0.183993i | ||||
\(914\) | −0.955888 | − | 0.827840i | −0.0316180 | − | 0.0273825i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −31.2316 | − | 12.4841i | −1.03192 | − | 0.412486i | ||||
\(917\) | − | 9.08884i | − | 0.300140i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.9319i | 0.690481i | 0.938514 | + | 0.345241i | \(0.112203\pi\) | ||||
−0.938514 | + | 0.345241i | \(0.887797\pi\) | |||||||
\(920\) | −3.19076 | + | 7.63455i | −0.105196 | + | 0.251704i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.1299 | + | 14.0061i | −0.399477 | + | 0.461267i | ||||
\(923\) | −11.1513 | + | 63.2421i | −0.367049 | + | 2.08164i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.0588 | − | 24.3832i | 0.955447 | − | 0.801715i | ||||
\(926\) | 1.66635 | − | 0.927710i | 0.0547598 | − | 0.0304865i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.33738 | − | 1.60463i | −0.0767284 | − | 0.0526744i | ||||
\(929\) | −33.1245 | + | 5.84075i | −1.08678 | + | 0.191629i | −0.688212 | − | 0.725510i | \(-0.741604\pi\) |
−0.398568 | + | 0.917139i | \(0.630493\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0494464 | + | 0.135853i | 0.00162054 | + | 0.00445240i | ||||
\(932\) | −11.0185 | − | 33.4891i | −0.360922 | − | 1.09697i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.39205 | − | 27.4020i | −0.143712 | − | 0.896621i | ||||
\(935\) | 6.01119 | − | 10.4117i | 0.196587 | − | 0.340498i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.5767 | − | 21.7834i | −0.410862 | − | 0.711634i | 0.584122 | − | 0.811666i | \(-0.301439\pi\) |
−0.994984 | + | 0.100032i | \(0.968106\pi\) | |||||||
\(938\) | 15.5014 | − | 12.6004i | 0.506139 | − | 0.411417i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −44.5824 | − | 9.30393i | −1.45412 | − | 0.303461i | ||||
\(941\) | −26.6235 | + | 31.7286i | −0.867901 | + | 1.03432i | 0.131175 | + | 0.991359i | \(0.458125\pi\) |
−0.999077 | + | 0.0429652i | \(0.986320\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.829308 | − | 2.27850i | 0.0270060 | − | 0.0741983i | ||||
\(944\) | 12.1569 | + | 0.759701i | 0.395675 | + | 0.0247262i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.327815 | − | 21.0087i | 0.0106582 | − | 0.683052i | ||||
\(947\) | 53.1276 | + | 19.3369i | 1.72642 | + | 0.628364i | 0.998365 | − | 0.0571597i | \(-0.0182044\pi\) |
0.728050 | + | 0.685524i | \(0.240427\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 48.4548 | + | 40.6584i | 1.57291 | + | 1.31983i | ||||
\(950\) | −0.871810 | − | 0.167789i | −0.0282852 | − | 0.00544378i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.79544 | + | 6.70473i | −0.285062 | + | 0.217302i | ||||
\(953\) | 31.8569 | − | 18.3926i | 1.03195 | − | 0.595795i | 0.114405 | − | 0.993434i | \(-0.463504\pi\) |
0.917542 | + | 0.397639i | \(0.130170\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.73591 | + | 3.31163i | 0.185610 | + | 0.107162i | ||||
\(956\) | 2.63232 | + | 18.2398i | 0.0851354 | + | 0.589917i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25.4717 | − | 8.82338i | 0.822953 | − | 0.285070i | ||||
\(959\) | 47.5403 | − | 17.3032i | 1.53516 | − | 0.558751i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.32736 | − | 13.1991i | −0.0750761 | − | 0.425778i | ||||
\(962\) | 21.7317 | − | 36.3197i | 0.700659 | − | 1.17100i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.88716 | − | 10.9740i | −0.189613 | − | 0.353447i | ||||
\(965\) | −13.8697 | − | 16.5292i | −0.446480 | − | 0.532094i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.3616 | + | 7.82215i | 1.42657 | + | 0.251543i | 0.833016 | − | 0.553249i | \(-0.186612\pi\) |
0.593557 | + | 0.804792i | \(0.297723\pi\) | |||||||
\(968\) | −8.66437 | − | 7.99018i | −0.278483 | − | 0.256814i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11.4712 | − | 30.0496i | 0.368318 | − | 0.964835i | ||||
\(971\) | 40.1053 | 1.28704 | 0.643520 | − | 0.765429i | \(-0.277473\pi\) | ||||
0.643520 | + | 0.765429i | \(0.277473\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.7837 | 1.05100 | ||||||||
\(974\) | 6.42762 | − | 16.8376i | 0.205954 | − | 0.539512i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.02705 | − | 6.68612i | −0.224930 | − | 0.214017i | ||||
\(977\) | 36.1734 | + | 6.37835i | 1.15729 | + | 0.204062i | 0.719157 | − | 0.694848i | \(-0.244528\pi\) |
0.438134 | + | 0.898910i | \(0.355639\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.4075 | + | 29.0878i | 0.780068 | + | 0.929649i | ||||
\(980\) | −9.61606 | + | 5.15870i | −0.307174 | + | 0.164788i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17.9589 | + | 30.0144i | −0.573093 | + | 0.957797i | ||||
\(983\) | 3.28853 | + | 18.6502i | 0.104888 | + | 0.594848i | 0.991265 | + | 0.131884i | \(0.0421028\pi\) |
−0.886377 | + | 0.462963i | \(0.846786\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −48.9916 | + | 17.8315i | −1.56100 | + | 0.568158i | ||||
\(986\) | 0.893872 | − | 0.309637i | 0.0284667 | − | 0.00986084i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.980427 | + | 0.141493i | −0.0311915 | + | 0.00450148i | ||||
\(989\) | −4.17867 | − | 2.41256i | −0.132874 | − | 0.0767148i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.3997 | − | 17.5513i | 0.965680 | − | 0.557535i | 0.0677633 | − | 0.997701i | \(-0.478414\pi\) |
0.897916 | + | 0.440166i | \(0.145080\pi\) | |||||||
\(992\) | −21.9056 | − | 30.6763i | −0.695503 | − | 0.973972i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −48.1673 | − | 9.27029i | −1.52777 | − | 0.294036i | ||||
\(995\) | 68.4100 | + | 57.4028i | 2.16874 | + | 1.81979i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.5603 | − | 8.21129i | −0.714493 | − | 0.260054i | −0.0409071 | − | 0.999163i | \(-0.513025\pi\) |
−0.673586 | + | 0.739109i | \(0.735247\pi\) | |||||||
\(998\) | −0.871737 | + | 55.8671i | −0.0275944 | + | 1.76844i | ||||
\(999\) | 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 | 324.2.l.a.179.2 | 96 | ||
3.2 | odd | 2 | 108.2.l.a.23.15 | yes | 96 | ||
4.3 | odd | 2 | inner | 324.2.l.a.179.15 | 96 | ||
9.2 | odd | 6 | 972.2.l.c.215.7 | 96 | |||
9.4 | even | 3 | 972.2.l.a.863.12 | 96 | |||
9.5 | odd | 6 | 972.2.l.d.863.5 | 96 | |||
9.7 | even | 3 | 972.2.l.b.215.10 | 96 | |||
12.11 | even | 2 | 108.2.l.a.23.2 | ✓ | 96 | ||
27.2 | odd | 18 | 972.2.l.a.107.4 | 96 | |||
27.7 | even | 9 | 108.2.l.a.47.2 | yes | 96 | ||
27.11 | odd | 18 | 972.2.l.b.755.8 | 96 | |||
27.16 | even | 9 | 972.2.l.c.755.9 | 96 | |||
27.20 | odd | 18 | inner | 324.2.l.a.143.15 | 96 | ||
27.25 | even | 9 | 972.2.l.d.107.13 | 96 | |||
36.7 | odd | 6 | 972.2.l.b.215.8 | 96 | |||
36.11 | even | 6 | 972.2.l.c.215.9 | 96 | |||
36.23 | even | 6 | 972.2.l.d.863.13 | 96 | |||
36.31 | odd | 6 | 972.2.l.a.863.4 | 96 | |||
108.7 | odd | 18 | 108.2.l.a.47.15 | yes | 96 | ||
108.11 | even | 18 | 972.2.l.b.755.10 | 96 | |||
108.43 | odd | 18 | 972.2.l.c.755.7 | 96 | |||
108.47 | even | 18 | inner | 324.2.l.a.143.2 | 96 | ||
108.79 | odd | 18 | 972.2.l.d.107.5 | 96 | |||
108.83 | even | 18 | 972.2.l.a.107.12 | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.2.l.a.23.2 | ✓ | 96 | 12.11 | even | 2 | ||
108.2.l.a.23.15 | yes | 96 | 3.2 | odd | 2 | ||
108.2.l.a.47.2 | yes | 96 | 27.7 | even | 9 | ||
108.2.l.a.47.15 | yes | 96 | 108.7 | odd | 18 | ||
324.2.l.a.143.2 | 96 | 108.47 | even | 18 | inner | ||
324.2.l.a.143.15 | 96 | 27.20 | odd | 18 | inner | ||
324.2.l.a.179.2 | 96 | 1.1 | even | 1 | trivial | ||
324.2.l.a.179.15 | 96 | 4.3 | odd | 2 | inner | ||
972.2.l.a.107.4 | 96 | 27.2 | odd | 18 | |||
972.2.l.a.107.12 | 96 | 108.83 | even | 18 | |||
972.2.l.a.863.4 | 96 | 36.31 | odd | 6 | |||
972.2.l.a.863.12 | 96 | 9.4 | even | 3 | |||
972.2.l.b.215.8 | 96 | 36.7 | odd | 6 | |||
972.2.l.b.215.10 | 96 | 9.7 | even | 3 | |||
972.2.l.b.755.8 | 96 | 27.11 | odd | 18 | |||
972.2.l.b.755.10 | 96 | 108.11 | even | 18 | |||
972.2.l.c.215.7 | 96 | 9.2 | odd | 6 | |||
972.2.l.c.215.9 | 96 | 36.11 | even | 6 | |||
972.2.l.c.755.7 | 96 | 108.43 | odd | 18 | |||
972.2.l.c.755.9 | 96 | 27.16 | even | 9 | |||
972.2.l.d.107.5 | 96 | 108.79 | odd | 18 | |||
972.2.l.d.107.13 | 96 | 27.25 | even | 9 | |||
972.2.l.d.863.5 | 96 | 9.5 | odd | 6 | |||
972.2.l.d.863.13 | 96 | 36.23 | even | 6 |