Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(61,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.u (of order \(9\), degree \(6\), 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: | \(3.03431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 3 x^{17} + 21 x^{16} - 30 x^{15} + 192 x^{14} - 207 x^{13} + 1178 x^{12} - 705 x^{11} + \cdots + 5329 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 81.2 | ||
Root | \(-0.478554 - 0.828880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 380.81 |
Dual form | 380.2.u.b.61.2 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(e\left(\frac{8}{9}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.166200 | − | 0.942568i | 0.0959557 | − | 0.544192i | −0.898495 | − | 0.438984i | \(-0.855338\pi\) |
0.994450 | − | 0.105207i | \(-0.0335506\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.766044 | + | 0.642788i | 0.342585 | + | 0.287463i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.28066 | − | 3.95023i | −0.862010 | − | 1.49305i | −0.869985 | − | 0.493077i | \(-0.835872\pi\) |
0.00797511 | − | 0.999968i | \(-0.497461\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.95827 | + | 0.712751i | 0.652756 | + | 0.237584i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.558879 | + | 0.968007i | −0.168508 | + | 0.291865i | −0.937896 | − | 0.346918i | \(-0.887228\pi\) |
0.769387 | + | 0.638783i | \(0.220562\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.897380 | − | 5.08930i | −0.248889 | − | 1.41152i | −0.811286 | − | 0.584650i | \(-0.801232\pi\) |
0.562397 | − | 0.826867i | \(-0.309879\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.733187 | − | 0.615217i | 0.189308 | − | 0.158848i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.80290 | − | 2.47605i | 1.64994 | − | 0.600531i | 0.661209 | − | 0.750202i | \(-0.270044\pi\) |
0.988736 | + | 0.149671i | \(0.0478216\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.68742 | − | 2.32442i | −0.845953 | − | 0.533257i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.10240 | + | 1.49315i | −0.895218 | + | 0.325833i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.31875 | + | 2.78477i | −0.692008 | + | 0.580664i | −0.919488 | − | 0.393119i | \(-0.871396\pi\) |
0.227480 | + | 0.973783i | \(0.426952\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.173648 | + | 0.984808i | 0.0347296 | + | 0.196962i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.43294 | − | 4.21398i | 0.468220 | − | 0.810981i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.51115 | + | 0.913983i | 0.466308 | + | 0.169722i | 0.564479 | − | 0.825447i | \(-0.309077\pi\) |
−0.0981710 | + | 0.995170i | \(0.531299\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.37022 | + | 2.37328i | 0.246098 | + | 0.426254i | 0.962440 | − | 0.271495i | \(-0.0875181\pi\) |
−0.716342 | + | 0.697750i | \(0.754185\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.819526 | + | 0.687664i | 0.142661 | + | 0.119707i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.792067 | − | 4.49203i | 0.133884 | − | 0.759292i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.491893 | −0.0808666 | −0.0404333 | − | 0.999182i | \(-0.512874\pi\) | ||||
−0.0404333 | + | 0.999182i | \(0.512874\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.94615 | −0.792018 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.45408 | − | 8.24648i | 0.227089 | − | 1.28788i | −0.631563 | − | 0.775325i | \(-0.717586\pi\) |
0.858652 | − | 0.512560i | \(-0.171303\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.16372 | + | 2.65467i | 0.482462 | + | 0.404834i | 0.851316 | − | 0.524654i | \(-0.175805\pi\) |
−0.368853 | + | 0.929488i | \(0.620250\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.04197 | + | 1.80475i | 0.155328 | + | 0.269036i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.48547 | + | 0.904639i | 0.362544 | + | 0.131955i | 0.516868 | − | 0.856065i | \(-0.327098\pi\) |
−0.154324 | + | 0.988020i | \(0.549320\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.90286 | + | 11.9561i | −0.986124 | + | 1.70802i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.20320 | − | 6.82371i | −0.168482 | − | 0.955510i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.4500 | + | 8.76856i | −1.43541 | + | 1.20445i | −0.492988 | + | 0.870036i | \(0.664095\pi\) |
−0.942425 | + | 0.334418i | \(0.891460\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.05035 | + | 0.382296i | −0.141629 | + | 0.0515488i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.80377 | + | 3.08933i | −0.371368 | + | 0.409192i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.45313 | − | 0.892868i | 0.319371 | − | 0.116241i | −0.177360 | − | 0.984146i | \(-0.556756\pi\) |
0.496731 | + | 0.867905i | \(0.334534\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.64703 | − | 3.06022i | 0.466954 | − | 0.391821i | −0.378728 | − | 0.925508i | \(-0.623638\pi\) |
0.845682 | + | 0.533687i | \(0.179194\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.65062 | − | 9.36114i | −0.207959 | − | 1.17939i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.58390 | − | 4.47545i | 0.320494 | − | 0.555112i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.9079 | + | 4.33411i | 1.45478 | + | 0.529495i | 0.943921 | − | 0.330171i | \(-0.107107\pi\) |
0.510855 | + | 0.859667i | \(0.329329\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.07325 | + | 3.59098i | 0.249590 | + | 0.432303i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.524118 | + | 0.439787i | 0.0622013 | + | 0.0521931i | 0.673358 | − | 0.739316i | \(-0.264851\pi\) |
−0.611157 | + | 0.791509i | \(0.709296\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.28024 | + | 12.9319i | −0.266882 | + | 1.51356i | 0.496741 | + | 0.867899i | \(0.334530\pi\) |
−0.763623 | + | 0.645662i | \(0.776581\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.957108 | 0.110517 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.09846 | 0.581024 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.75095 | + | 15.6014i | −0.309506 | + | 1.75529i | 0.291993 | + | 0.956420i | \(0.405681\pi\) |
−0.601499 | + | 0.798874i | \(0.705430\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.22158 | + | 1.02502i | 0.135731 | + | 0.113892i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.88033 | + | 3.25683i | 0.206393 | + | 0.357484i | 0.950576 | − | 0.310493i | \(-0.100494\pi\) |
−0.744182 | + | 0.667976i | \(0.767161\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.80290 | + | 2.47605i | 0.737878 | + | 0.268565i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.27884 | − | 2.21502i | 0.137106 | − | 0.237475i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.04379 | + | 11.5909i | 0.216642 | + | 1.22864i | 0.878035 | + | 0.478597i | \(0.158854\pi\) |
−0.661393 | + | 0.750039i | \(0.730035\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.0573 | + | 15.1518i | −1.89292 | + | 1.58834i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.46471 | − | 0.897081i | 0.255579 | − | 0.0930230i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.33063 | − | 4.15084i | −0.136519 | − | 0.425867i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.27804 | − | 1.19311i | 0.332835 | − | 0.121142i | −0.170197 | − | 0.985410i | \(-0.554440\pi\) |
0.503031 | + | 0.864268i | \(0.332218\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.78438 | + | 1.49727i | −0.179337 | + | 0.150482i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.83378 | + | 10.3999i | 0.182468 | + | 1.03483i | 0.929165 | + | 0.369665i | \(0.120527\pi\) |
−0.746697 | + | 0.665164i | \(0.768362\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.77623 | − | 10.0047i | 0.569149 | − | 0.985794i | −0.427502 | − | 0.904015i | \(-0.640606\pi\) |
0.996650 | − | 0.0817799i | \(-0.0260605\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.10240 | − | 1.49315i | −0.400354 | − | 0.145717i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.88420 | − | 6.72763i | −0.375499 | − | 0.650384i | 0.614902 | − | 0.788603i | \(-0.289195\pi\) |
−0.990402 | + | 0.138219i | \(0.955862\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.1216 | − | 8.49299i | −0.969469 | − | 0.813481i | 0.0129986 | − | 0.999916i | \(-0.495862\pi\) |
−0.982467 | + | 0.186435i | \(0.940307\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0817526 | + | 0.463642i | −0.00775961 | + | 0.0440070i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.84103 | −0.173190 | −0.0865950 | − | 0.996244i | \(-0.527599\pi\) | ||||
−0.0865950 | + | 0.996244i | \(0.527599\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.33233 | −0.403991 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.87009 | − | 10.6058i | 0.172890 | − | 0.980507i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −25.2961 | − | 21.2259i | −2.31889 | − | 1.94578i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.87531 | + | 8.44428i | 0.443210 | + | 0.767662i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.53120 | − | 2.74113i | −0.679066 | − | 0.247160i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.500000 | + | 0.866025i | −0.0447214 | + | 0.0774597i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.731989 | − | 4.15132i | −0.0649536 | − | 0.368370i | −0.999908 | − | 0.0136008i | \(-0.995671\pi\) |
0.934954 | − | 0.354769i | \(-0.115441\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.02802 | − | 2.54081i | 0.266602 | − | 0.223706i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.58430 | + | 0.940609i | −0.225791 | + | 0.0821814i | −0.452439 | − | 0.891796i | \(-0.649446\pi\) |
0.226647 | + | 0.973977i | \(0.427224\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.772191 | + | 19.8674i | −0.0669574 | + | 1.72272i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.57244 | − | 1.66423i | 0.393533 | − | 0.143234i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.69224 | − | 1.41996i | 0.144578 | − | 0.121315i | −0.567630 | − | 0.823284i | \(-0.692140\pi\) |
0.712208 | + | 0.701968i | \(0.247695\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.53264 | + | 8.69203i | 0.129997 | + | 0.737248i | 0.978214 | + | 0.207600i | \(0.0665651\pi\) |
−0.848217 | + | 0.529649i | \(0.822324\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.26577 | − | 2.19238i | 0.106597 | − | 0.184631i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.42800 | + | 1.97563i | 0.453912 | + | 0.165211i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.33615 | + | 2.31429i | 0.110962 | + | 0.192191i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.1222 | + | 8.49352i | 0.834864 | + | 0.700534i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.62671 | − | 20.5681i | 0.297111 | − | 1.68500i | −0.361383 | − | 0.932417i | \(-0.617695\pi\) |
0.658495 | − | 0.752585i | \(-0.271194\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.73130 | 0.466407 | 0.233203 | − | 0.972428i | \(-0.425079\pi\) | ||||
0.233203 | + | 0.972428i | \(0.425079\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.0867 | 1.21969 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.475871 | + | 2.69880i | −0.0382229 | + | 0.216773i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.1251 | − | 11.8523i | −1.12730 | − | 0.945919i | −0.128352 | − | 0.991729i | \(-0.540969\pi\) |
−0.998950 | + | 0.0458101i | \(0.985413\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.52818 | + | 11.3071i | 0.517718 | + | 0.896714i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.5694 | + | 6.75872i | 1.46348 | + | 0.532661i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.74094 | + | 3.01540i | −0.136361 | + | 0.236185i | −0.926117 | − | 0.377237i | \(-0.876874\pi\) |
0.789755 | + | 0.613422i | \(0.210207\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.185772 | + | 1.05356i | 0.0144623 | + | 0.0820198i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.4620 | − | 13.8132i | 1.27387 | − | 1.06890i | 0.279806 | − | 0.960056i | \(-0.409730\pi\) |
0.994059 | − | 0.108843i | \(-0.0347147\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8797 | + | 4.68781i | −0.990742 | + | 0.360601i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.56423 | − | 7.18004i | −0.425507 | − | 0.549071i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.3262 | + | 3.75842i | −0.785084 | + | 0.285747i | −0.703291 | − | 0.710902i | \(-0.748287\pi\) |
−0.0817929 | + | 0.996649i | \(0.526065\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.49418 | − | 2.93197i | 0.264135 | − | 0.221636i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.433877 | − | 2.46064i | −0.0326122 | − | 0.184953i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.54852 | − | 14.8065i | 0.638946 | − | 1.10669i | −0.346718 | − | 0.937969i | \(-0.612704\pi\) |
0.985664 | − | 0.168718i | \(-0.0539627\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.8910 | − | 3.96399i | −0.809519 | − | 0.294641i | −0.0960938 | − | 0.995372i | \(-0.530635\pi\) |
−0.713425 | + | 0.700732i | \(0.752857\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.27833 | − | 3.94618i | −0.168419 | − | 0.291710i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.376812 | − | 0.316182i | −0.0277037 | − | 0.0232462i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.40516 | + | 7.96907i | −0.102756 | + | 0.582756i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −22.1949 | −1.61444 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.8688 | 1.87180 | 0.935901 | − | 0.352262i | \(-0.114587\pi\) | ||||
0.935901 | + | 0.352262i | \(0.114587\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.44272 | − | 13.8534i | 0.175831 | − | 0.997187i | −0.761349 | − | 0.648342i | \(-0.775463\pi\) |
0.937180 | − | 0.348845i | \(-0.113426\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.78897 | − | 3.17932i | −0.271334 | − | 0.227676i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.70220 | − | 2.94830i | −0.121277 | − | 0.210057i | 0.798995 | − | 0.601338i | \(-0.205365\pi\) |
−0.920271 | + | 0.391281i | \(0.872032\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.3891 | + | 6.32911i | 1.23268 | + | 0.448659i | 0.874515 | − | 0.484999i | \(-0.161180\pi\) |
0.358166 | + | 0.933658i | \(0.383402\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.06427 | − | 10.5036i | 0.427741 | − | 0.740869i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.11665 | − | 12.0041i | −0.148559 | − | 0.842522i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.41463 | − | 5.38251i | 0.448017 | − | 0.375931i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.48385 | + | 3.08787i | −0.589668 | + | 0.214622i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.31087 | − | 2.27039i | 0.298189 | − | 0.157046i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.8432 | + | 5.40250i | −1.02185 | + | 0.371923i | −0.797972 | − | 0.602694i | \(-0.794094\pi\) |
−0.223878 | + | 0.974617i | \(0.571872\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.501638 | − | 0.420924i | 0.0343716 | − | 0.0288412i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.717156 | + | 4.06720i | 0.0489097 | + | 0.277380i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.25001 | − | 10.8253i | 0.424278 | − | 0.734871i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.8102 | + | 4.29856i | 0.798058 | + | 0.290469i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.7061 | − | 32.4000i | −1.25831 | − | 2.17946i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.0138 | − | 14.2763i | −1.13933 | − | 0.956008i | −0.139910 | − | 0.990164i | \(-0.544681\pi\) |
−0.999417 | + | 0.0341558i | \(0.989126\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.361873 | + | 2.05228i | −0.0241249 | + | 0.136819i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.60932 | −0.372304 | −0.186152 | − | 0.982521i | \(-0.559602\pi\) | ||||
−0.186152 | + | 0.982521i | \(0.559602\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.04017 | 0.0687366 | 0.0343683 | − | 0.999409i | \(-0.489058\pi\) | ||||
0.0343683 | + | 0.999409i | \(0.489058\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.847365 | − | 4.80565i | 0.0557525 | − | 0.316188i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.15779 | + | 7.68430i | 0.599947 | + | 0.503415i | 0.891428 | − | 0.453161i | \(-0.149704\pi\) |
−0.291482 | + | 0.956576i | \(0.594148\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.32249 | + | 2.29063i | 0.0862699 | + | 0.149424i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.2482 | + | 5.18591i | 0.925517 | + | 0.336861i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.50416 | − | 7.80144i | 0.291350 | − | 0.504633i | −0.682779 | − | 0.730625i | \(-0.739229\pi\) |
0.974129 | + | 0.225992i | \(0.0725622\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.31012 | − | 13.1014i | −0.148808 | − | 0.843933i | −0.964230 | − | 0.265066i | \(-0.914606\pi\) |
0.815422 | − | 0.578867i | \(-0.196505\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.3516 | − | 10.3642i | 0.792358 | − | 0.664867i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.9731 | + | 4.72184i | −0.828824 | + | 0.301667i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.52062 | + | 20.8523i | −0.542154 | + | 1.32680i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.38230 | − | 1.23105i | 0.214344 | − | 0.0780149i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.0043 | + | 14.2683i | −1.07330 | + | 0.900609i | −0.995348 | − | 0.0963480i | \(-0.969284\pi\) |
−0.0779560 | + | 0.996957i | \(0.524839\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.840890 | − | 4.76892i | −0.0528663 | − | 0.299820i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.46449 | − | 6.00067i | 0.216955 | − | 0.375776i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.37388 | + | 0.864022i | 0.148079 | + | 0.0538962i | 0.414996 | − | 0.909823i | \(-0.363783\pi\) |
−0.266918 | + | 0.963719i | \(0.586005\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.12184 | + | 1.94309i | 0.0697079 | + | 0.120738i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.26605 | + | 3.57964i | 0.264062 | + | 0.221574i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.18211 | + | 12.3753i | −0.134554 | + | 0.763096i | 0.840615 | + | 0.541634i | \(0.182194\pi\) |
−0.975169 | + | 0.221462i | \(0.928917\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.6415 | −0.837988 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.2649 | 0.689401 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.59540 | + | 20.3905i | −0.219216 | + | 1.24323i | 0.654224 | + | 0.756301i | \(0.272995\pi\) |
−0.873439 | + | 0.486933i | \(0.838116\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.02160 | − | 0.857226i | −0.0620579 | − | 0.0520728i | 0.611231 | − | 0.791452i | \(-0.290675\pi\) |
−0.673289 | + | 0.739379i | \(0.735119\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.2805 | + | 19.5384i | 0.682728 | + | 1.18252i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.05035 | − | 0.382296i | −0.0633384 | − | 0.0230533i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.1070 | + | 24.4340i | −0.847606 | + | 1.46810i | 0.0357322 | + | 0.999361i | \(0.488624\pi\) |
−0.883338 | + | 0.468736i | \(0.844710\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.991688 | + | 5.62414i | 0.0593708 | + | 0.336709i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.31199 | − | 7.81369i | 0.555507 | − | 0.466126i | −0.321294 | − | 0.946980i | \(-0.604118\pi\) |
0.876801 | + | 0.480854i | \(0.159673\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.65082 | + | 0.600850i | −0.0981312 | + | 0.0357168i | −0.390619 | − | 0.920552i | \(-0.627739\pi\) |
0.292488 | + | 0.956269i | \(0.405517\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.13359 | + | 0.564335i | −0.244853 | + | 0.0334283i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −35.8918 | + | 13.0635i | −2.11862 | + | 0.771116i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 27.1258 | − | 22.7612i | 1.59564 | − | 1.33890i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.579775 | − | 3.28807i | −0.0339870 | − | 0.192750i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.85056 | − | 6.66937i | 0.224952 | − | 0.389629i | −0.731353 | − | 0.681999i | \(-0.761111\pi\) |
0.956305 | + | 0.292370i | \(0.0944440\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.45313 | + | 0.892868i | 0.142827 | + | 0.0519848i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.71944 | + | 4.71021i | 0.157798 | + | 0.273314i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.1507 | + | 14.3911i | 0.991850 | + | 0.832261i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.27119 | − | 18.5518i | 0.188548 | − | 1.06931i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.1074 | 0.580654 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.76086 | 0.272606 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.11720 | + | 6.33598i | −0.0637623 | + | 0.361614i | 0.936187 | + | 0.351503i | \(0.114329\pi\) |
−0.999949 | + | 0.0101104i | \(0.996782\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.47012 | − | 7.10727i | −0.481848 | − | 0.404319i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.5028 | + | 25.1196i | 0.822379 | + | 1.42440i | 0.903906 | + | 0.427731i | \(0.140687\pi\) |
−0.0815274 | + | 0.996671i | \(0.525980\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.8655 | − | 4.68265i | −0.727200 | − | 0.264679i | −0.0482209 | − | 0.998837i | \(-0.515355\pi\) |
−0.678979 | + | 0.734158i | \(0.737577\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.75278 | − | 8.23205i | 0.267789 | − | 0.463824i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.782232 | − | 4.43626i | −0.0439345 | − | 0.249165i | 0.954929 | − | 0.296836i | \(-0.0959314\pi\) |
−0.998863 | + | 0.0476705i | \(0.984820\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.28817 | + | 1.92000i | −0.128113 | + | 0.107500i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.98680 | + | 2.54299i | −0.389965 | + | 0.141936i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −30.8405 | − | 6.68250i | −1.71601 | − | 0.371824i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.85615 | − | 1.76749i | 0.269371 | − | 0.0980430i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.68742 | + | 8.12871i | −0.535715 | + | 0.449519i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.09501 | − | 11.8814i | −0.115501 | − | 0.655041i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.72326 | + | 13.3771i | −0.424509 | + | 0.735271i | −0.996374 | − | 0.0850767i | \(-0.972886\pi\) |
0.571866 | + | 0.820347i | \(0.306220\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.963257 | − | 0.350597i | −0.0527862 | − | 0.0192126i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.33604 | + | 10.9743i | 0.346175 | + | 0.599592i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.3175 | − | 13.6920i | −0.888869 | − | 0.745850i | 0.0791136 | − | 0.996866i | \(-0.474791\pi\) |
−0.967983 | + | 0.251016i | \(0.919235\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.305980 | + | 1.73530i | −0.0166186 | + | 0.0942485i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.06314 | −0.165878 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 31.0432 | 1.67617 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.720033 | + | 4.08351i | −0.0387653 | + | 0.219849i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.69463 | + | 2.26106i | 0.144655 | + | 0.121380i | 0.712244 | − | 0.701932i | \(-0.247679\pi\) |
−0.567588 | + | 0.823312i | \(0.692124\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.55638 | − | 7.89188i | −0.243897 | − | 0.422443i | 0.717924 | − | 0.696122i | \(-0.245093\pi\) |
−0.961821 | + | 0.273679i | \(0.911759\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −23.6295 | − | 8.60042i | −1.26125 | − | 0.459057i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.4350 | + | 21.5381i | −0.661850 | + | 1.14636i | 0.318279 | + | 0.947997i | \(0.396895\pi\) |
−0.980129 | + | 0.198361i | \(0.936438\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.118808 | + | 0.673793i | 0.00630567 | + | 0.0357612i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −24.2111 | + | 20.3155i | −1.28139 | + | 1.07521i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.2882 | + | 6.65634i | −0.965212 | + | 0.351308i | −0.776074 | − | 0.630642i | \(-0.782792\pi\) |
−0.189138 | + | 0.981951i | \(0.560569\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.19419 | + | 17.1422i | 0.431273 | + | 0.902221i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.76958 | − | 3.19187i | 0.460284 | − | 0.167530i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.0592 | + | 8.44068i | −0.526523 | + | 0.441805i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.57276 | + | 20.2622i | 0.186497 | + | 1.05768i | 0.924017 | + | 0.382351i | \(0.124885\pi\) |
−0.737520 | + | 0.675325i | \(0.764003\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.72516 | − | 15.1124i | 0.454214 | − | 0.786721i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 58.4707 | + | 21.2816i | 3.03565 | + | 1.10488i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.84938 | + | 3.20322i | 0.0957572 | + | 0.165856i | 0.909924 | − | 0.414774i | \(-0.136139\pi\) |
−0.814167 | + | 0.580630i | \(0.802806\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.733187 | + | 0.615217i | 0.0378616 | + | 0.0317697i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.39808 | − | 13.6002i | 0.123507 | − | 0.700444i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.68304 | −0.343285 | −0.171642 | − | 0.985159i | \(-0.554907\pi\) | ||||
−0.171642 | + | 0.985159i | \(0.554907\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.03456 | −0.206697 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.39114 | − | 30.5747i | 0.275474 | − | 1.56229i | −0.461977 | − | 0.886892i | \(-0.652860\pi\) |
0.737451 | − | 0.675400i | \(-0.236029\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.90565 | + | 3.27723i | 0.199050 | + | 0.167023i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.30328 | + | 7.45350i | 0.218748 | + | 0.378883i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.2323 | + | 4.08822i | 0.569500 | + | 0.207281i | 0.610689 | − | 0.791870i | \(-0.290892\pi\) |
−0.0411892 | + | 0.999151i | \(0.513115\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.6819 | + | 27.1619i | −0.793068 | + | 1.37363i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.457076 | + | 2.59221i | 0.0230564 | + | 0.130760i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.1357 | + | 10.1831i | −0.610615 | + | 0.512367i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.00480 | − | 1.45763i | 0.200995 | − | 0.0731562i | −0.239561 | − | 0.970881i | \(-0.577004\pi\) |
0.440556 | + | 0.897725i | \(0.354781\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18.5980 | + | 4.02980i | 0.931065 | + | 0.201742i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.433821 | − | 0.157898i | 0.0216640 | − | 0.00788506i | −0.331165 | − | 0.943573i | \(-0.607442\pi\) |
0.352829 | + | 0.935688i | \(0.385220\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.8487 | − | 9.10317i | 0.540414 | − | 0.453461i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.276909 | + | 1.57043i | 0.0137597 | + | 0.0780352i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.274909 | − | 0.476156i | 0.0136267 | − | 0.0236022i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.7422 | + | 10.8253i | 1.47066 | + | 0.535276i | 0.948279 | − | 0.317438i | \(-0.102823\pi\) |
0.522378 | + | 0.852714i | \(0.325045\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.05715 | − | 1.83104i | −0.0521456 | − | 0.0903188i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.12181 | − | 7.65411i | −0.448855 | − | 0.376634i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.653033 | + | 3.70353i | −0.0320561 | + | 0.181799i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.44755 | 0.413678 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.8430 | 1.16481 | 0.582403 | − | 0.812900i | \(-0.302112\pi\) | ||||
0.582403 | + | 0.812900i | \(0.302112\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.32252 | − | 7.50041i | 0.0644559 | − | 0.365547i | −0.935470 | − | 0.353405i | \(-0.885024\pi\) |
0.999926 | − | 0.0121424i | \(-0.00386514\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.22244 | + | 3.54305i | 0.205302 | + | 0.172269i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.61975 | + | 6.26958i | 0.175583 | + | 0.304119i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.4062 | − | 7.42726i | −0.987526 | − | 0.359430i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.76430 | − | 4.78791i | 0.133462 | − | 0.231162i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.04802 | − | 5.94360i | −0.0504812 | − | 0.286293i | 0.949108 | − | 0.314950i | \(-0.101988\pi\) |
−0.999589 | + | 0.0286575i | \(0.990877\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.2376 | + | 11.9468i | −0.684216 | + | 0.574126i | −0.917235 | − | 0.398347i | \(-0.869584\pi\) |
0.233019 | + | 0.972472i | \(0.425140\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.40344 | − | 0.874781i | 0.115236 | − | 0.0419425i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.7106 | − | 2.55445i | 0.895049 | − | 0.122196i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.0999 | + | 4.76797i | −0.625223 | + | 0.227563i | −0.635151 | − | 0.772388i | \(-0.719062\pi\) |
0.00992755 | + | 0.999951i | \(0.496840\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −22.0394 | + | 18.4932i | −1.04949 | + | 0.880630i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.65351 | − | 15.0488i | −0.126072 | − | 0.714991i | −0.980665 | − | 0.195692i | \(-0.937305\pi\) |
0.854593 | − | 0.519298i | \(-0.173807\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.88487 | + | 10.1929i | −0.278970 | + | 0.483189i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.7840 | − | 6.83683i | −0.888455 | − | 0.323371i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.3149 | + | 28.2582i | 0.769947 | + | 1.33359i | 0.937591 | + | 0.347739i | \(0.113051\pi\) |
−0.167645 | + | 0.985847i | \(0.553616\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.17000 | + | 6.01635i | 0.337622 | + | 0.283299i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.952543 | − | 5.40214i | 0.0447544 | − | 0.253815i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −23.5721 | −1.10508 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.5721 | −0.915546 | −0.457773 | − | 0.889069i | \(-0.651353\pi\) | ||||
−0.457773 | + | 0.889069i | \(0.651353\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.11702 | − | 34.6914i | 0.285518 | − | 1.61925i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.0645 | − | 20.1925i | −1.12079 | − | 0.940457i | −0.122149 | − | 0.992512i | \(-0.538979\pi\) |
−0.998644 | + | 0.0520545i | \(0.983423\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.2496 | + | 26.4132i | 0.708711 | + | 1.22752i | 0.965335 | + | 0.261012i | \(0.0840563\pi\) |
−0.256624 | + | 0.966511i | \(0.582610\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.46471 | + | 0.897081i | 0.114298 | + | 0.0416011i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.74239 | − | 6.48201i | 0.173177 | − | 0.299952i | −0.766352 | − | 0.642421i | \(-0.777930\pi\) |
0.939529 | + | 0.342469i | \(0.111263\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.0371 | − | 56.9234i | −0.463472 | − | 2.62848i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.5192 | + | 11.3440i | −0.622932 | + | 0.522702i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.33788 | + | 1.57886i | −0.199456 | + | 0.0725960i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.64879 | − | 4.03503i | 0.0756516 | − | 0.185140i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −26.7136 | + | 9.72296i | −1.22313 | + | 0.445184i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.59620 | + | 3.85667i | −0.210006 | + | 0.176216i | −0.741723 | − | 0.670706i | \(-0.765991\pi\) |
0.531718 | + | 0.846922i | \(0.321547\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.441415 | + | 2.50339i | 0.0201268 | + | 0.114145i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.45679 | − | 16.3796i | 0.430299 | − | 0.745299i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.27804 | + | 1.19311i | 0.148848 | + | 0.0541763i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.24803 | − | 5.62576i | −0.147182 | − | 0.254927i | 0.783003 | − | 0.622018i | \(-0.213687\pi\) |
−0.930185 | + | 0.367091i | \(0.880354\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.55288 | + | 2.14212i | 0.115445 | + | 0.0968699i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.01124 | − | 28.4202i | 0.226154 | − | 1.28258i | −0.634312 | − | 0.773077i | \(-0.718717\pi\) |
0.860467 | − | 0.509507i | \(-0.170172\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.3461 | 0.871306 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.32935 | −0.104696 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.541922 | − | 3.07339i | 0.0243085 | − | 0.137860i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.63514 | − | 8.08484i | −0.431328 | − | 0.361927i | 0.401124 | − | 0.916024i | \(-0.368619\pi\) |
−0.832453 | + | 0.554096i | \(0.813064\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.2839 | − | 17.8123i | −0.459452 | − | 0.795794i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.4854 | − | 5.27226i | −0.645872 | − | 0.235078i | −0.00174715 | − | 0.999998i | \(-0.500556\pi\) |
−0.644125 | + | 0.764920i | \(0.722778\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.28017 | + | 9.14552i | −0.234964 | + | 0.406970i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.27798 | + | 12.9191i | 0.101169 | + | 0.573755i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.58561 | + | 3.84778i | −0.203254 | + | 0.170550i | −0.738733 | − | 0.673998i | \(-0.764575\pi\) |
0.535479 | + | 0.844548i | \(0.320131\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 56.2843 | − | 20.4858i | 2.48987 | − | 0.906239i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.7663 | + | 9.88356i | −0.828554 | + | 0.436370i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.8558 | − | 3.95117i | 0.478362 | − | 0.174109i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.26478 | + | 1.90037i | −0.0996047 | + | 0.0835783i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.82635 | + | 10.3578i | 0.0801680 | + | 0.454655i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.62104 | − | 14.9321i | 0.377695 | − | 0.654187i | −0.613032 | − | 0.790058i | \(-0.710050\pi\) |
0.990726 | + | 0.135872i | \(0.0433835\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.113607 | + | 0.0413496i | 0.00496770 | + | 0.00180809i | 0.344503 | − | 0.938785i | \(-0.388048\pi\) |
−0.339535 | + | 0.940593i | \(0.610270\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.18284 | − | 3.78080i | −0.0952671 | − | 0.165007i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.1978 | + | 12.7525i | 0.662027 | + | 0.555507i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.734698 | + | 4.16668i | −0.0319434 | + | 0.181160i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.44028 | 0.236088 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −43.2737 | −1.87439 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.34897 | − | 7.65037i | 0.0583209 | − | 0.330754i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.5353 | − | 10.5184i | −0.540940 | − | 0.453902i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.71574 | − | 13.3640i | −0.332340 | − | 0.575630i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.3600 | + | 13.2340i | 1.56324 | + | 0.568973i | 0.971476 | − | 0.237139i | \(-0.0762097\pi\) |
0.591764 | + | 0.806112i | \(0.298432\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.54640 | + | 9.60665i | −0.238019 | + | 0.412261i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.29437 | − | 13.0120i | −0.0982800 | − | 0.557373i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.34449 | + | 6.16276i | −0.314028 | + | 0.263501i | −0.786154 | − | 0.618030i | \(-0.787931\pi\) |
0.472127 | + | 0.881531i | \(0.343486\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.32303 | − | 3.39331i | 0.397897 | − | 0.144823i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.13519 | − | 9.20719i | −0.303969 | − | 0.392240i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 67.9030 | − | 24.7147i | 2.88753 | − | 1.05098i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.360649 | + | 0.302621i | −0.0153087 | + | 0.0128455i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.99528 | + | 34.0009i | 0.254028 | + | 1.44067i | 0.798555 | + | 0.601922i | \(0.205598\pi\) |
−0.544527 | + | 0.838744i | \(0.683291\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.6714 | − | 18.4834i | 0.451351 | − | 0.781762i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.27784 | + | 2.64892i | 0.307271 | + | 0.111837i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.6196 | + | 37.4463i | 0.911158 | + | 1.57817i | 0.812431 | + | 0.583057i | \(0.198144\pi\) |
0.0987270 | + | 0.995115i | \(0.468523\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.41031 | − | 1.18339i | −0.0593324 | − | 0.0497858i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.26307 | − | 7.16324i | 0.0530440 | − | 0.300828i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.172138 | −0.00721638 | −0.00360819 | − | 0.999993i | \(-0.501149\pi\) | ||||
−0.00360819 | + | 0.999993i | \(0.501149\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.8203 | −1.20609 | −0.603046 | − | 0.797706i | \(-0.706046\pi\) | ||||
−0.603046 | + | 0.797706i | \(0.706046\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.29940 | − | 24.3831i | 0.179610 | − | 1.01862i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.31875 | − | 2.78477i | −0.138402 | − | 0.116133i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.03745 | − | 1.79692i | −0.0431898 | − | 0.0748069i | 0.843622 | − | 0.536937i | \(-0.180419\pi\) |
−0.886812 | + | 0.462130i | \(0.847085\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.6517 | − | 4.60486i | −0.525789 | − | 0.191371i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.57682 | − | 14.8555i | 0.355826 | − | 0.616309i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.64776 | − | 15.0162i | −0.109659 | − | 0.621908i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.24986 | − | 6.92245i | 0.341090 | − | 0.286208i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.5583 | + | 10.3944i | −1.17873 | + | 0.429022i | −0.855752 | − | 0.517385i | \(-0.826905\pi\) |
−0.322975 | + | 0.946407i | \(0.604683\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.463930 | − | 11.9363i | 0.0191159 | − | 0.491825i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.06187 | + | 1.11443i | −0.125949 | + | 0.0458416i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.44741 | + | 7.08822i | −0.346894 | + | 0.291078i | −0.799541 | − | 0.600611i | \(-0.794924\pi\) |
0.452648 | + | 0.891689i | \(0.350480\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.73416 | − | 32.5200i | −0.235078 | − | 1.33319i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.85569 | − | 15.3385i | 0.362439 | − | 0.627763i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.2641 | − | 8.46746i | −0.950547 | − | 0.345971i | −0.180225 | − | 0.983625i | \(-0.557683\pi\) |
−0.770322 | + | 0.637655i | \(0.779905\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.6916 | − | 35.8388i | −0.844026 | − | 1.46190i | −0.886464 | − | 0.462797i | \(-0.846846\pi\) |
0.0424380 | − | 0.999099i | \(-0.486487\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.2296 | + | 16.9747i | 0.823814 | + | 0.691262i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.69318 | + | 9.60248i | −0.0688374 | + | 0.390396i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.0263 | 1.09696 | 0.548481 | − | 0.836163i | \(-0.315206\pi\) | ||||
0.548481 | + | 0.836163i | \(0.315206\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.6665 | −0.472749 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.37356 | − | 13.4611i | 0.0960239 | − | 0.544579i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.62519 | + | 4.72010i | 0.227199 | + | 0.190643i | 0.749280 | − | 0.662253i | \(-0.230400\pi\) |
−0.522081 | + | 0.852896i | \(0.674844\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.00727 | − | 6.94079i | −0.161589 | − | 0.279880i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.4866 | − | 5.63667i | −0.623468 | − | 0.226924i | 0.0109180 | − | 0.999940i | \(-0.496525\pi\) |
−0.634386 | + | 0.773017i | \(0.718747\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.27186 | − | 9.13112i | 0.211894 | − | 0.367011i | −0.740413 | − | 0.672152i | \(-0.765370\pi\) |
0.952307 | + | 0.305141i | \(0.0987036\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.66061 | + | 20.7603i | 0.146895 | + | 0.833083i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 41.1256 | − | 34.5085i | 1.64766 | − | 1.38255i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.939693 | + | 0.342020i | −0.0375877 | + | 0.0136808i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.42352 | − | 4.44063i | −0.0568501 | − | 0.177342i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.34629 | + | 1.21795i | −0.133425 | + | 0.0485629i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.0300 | + | 10.0944i | −0.478907 | + | 0.401850i | −0.850031 | − | 0.526733i | \(-0.823417\pi\) |
0.371124 | + | 0.928583i | \(0.378972\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.62527 | + | 14.8886i | 0.104345 | + | 0.591771i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.10768 | − | 3.65061i | 0.0836407 | − | 0.144870i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 67.0427 | + | 24.4016i | 2.65633 | + | 0.966825i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.712904 | + | 1.23479i | 0.0282020 | + | 0.0488474i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.38617 | + | 2.00224i | 0.0942481 | + | 0.0790836i | 0.688694 | − | 0.725052i | \(-0.258184\pi\) |
−0.594446 | + | 0.804135i | \(0.702629\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.53665 | − | 20.0573i | 0.139472 | − | 0.790983i | −0.832169 | − | 0.554522i | \(-0.812901\pi\) |
0.971641 | − | 0.236462i | \(-0.0759877\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.95280 | 0.155641 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.01187 | −0.0790946 | −0.0395473 | − | 0.999218i | \(-0.512592\pi\) | ||||
−0.0395473 | + | 0.999218i | \(0.512592\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.506703 | + | 2.87366i | −0.0198898 | + | 0.112801i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.16485 | − | 7.69022i | −0.359199 | − | 0.301404i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.326876 | − | 0.566166i | −0.0127916 | − | 0.0221558i | 0.859559 | − | 0.511037i | \(-0.170738\pi\) |
−0.872350 | + | 0.488881i | \(0.837405\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.58430 | − | 0.940609i | −0.100977 | − | 0.0367526i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.6825 | + | 23.6988i | −0.533806 | + | 0.924579i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.256516 | − | 1.45477i | −0.00999243 | − | 0.0566699i | 0.979404 | − | 0.201911i | \(-0.0647153\pi\) |
−0.989396 | + | 0.145241i | \(0.953604\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.31742 | + | 1.10545i | −0.0512418 | + | 0.0429970i | −0.668049 | − | 0.744117i | \(-0.732870\pi\) |
0.616807 | + | 0.787114i | \(0.288426\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −33.6482 | + | 12.2469i | −1.30679 | + | 0.475631i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13.3620 | + | 14.7229i | −0.518157 | + | 0.570931i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.8791 | + | 3.95967i | −0.421241 | + | 0.153319i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.2840 | + | 13.6639i | −0.629577 | + | 0.528278i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.924067 | + | 5.24064i | 0.0356732 | + | 0.202313i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.1537 | − | 26.2469i | 0.584130 | − | 1.01174i | −0.410853 | − | 0.911702i | \(-0.634769\pi\) |
0.994983 | − | 0.100042i | \(-0.0318977\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.57244 | + | 1.66423i | 0.175993 | + | 0.0640563i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.5349 | + | 23.4432i | 0.520190 | + | 0.900995i | 0.999724 | + | 0.0234721i | \(0.00747210\pi\) |
−0.479535 | + | 0.877523i | \(0.659195\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.1892 | − | 10.2279i | −0.467777 | − | 0.392512i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.932270 | + | 5.28717i | −0.0357247 | + | 0.202605i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −49.3960 | −1.89008 | −0.945042 | − | 0.326948i | \(-0.893980\pi\) | ||||
−0.945042 | + | 0.326948i | \(0.893980\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.20906 | 0.0844038 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.172877 | − | 0.980433i | 0.00659566 | − | 0.0374059i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 54.0034 | + | 45.3142i | 2.05737 | + | 1.72633i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.99171 | + | 5.18179i | 0.113810 | + | 0.197125i | 0.917303 | − | 0.398189i | \(-0.130361\pi\) |
−0.803493 | + | 0.595314i | \(0.797028\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.98415 | + | 3.63393i | 0.379267 | + | 0.138042i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.41306 | + | 7.64364i | −0.167397 | + | 0.289940i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.5268 | − | 59.7003i | −0.398730 | − | 2.26131i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.76499 | − | 7.35470i | 0.331522 | − | 0.278180i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.2185 | − | 4.08320i | 0.423717 | − | 0.154220i | −0.121356 | − | 0.992609i | \(-0.538724\pi\) |
0.545073 | + | 0.838389i | \(0.316502\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.81382 | + | 1.14336i | 0.0684094 | + | 0.0431227i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.37887 | − | 0.865837i | 0.0895933 | − | 0.0326093i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 36.8997 | − | 30.9625i | 1.38776 | − | 1.16447i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.35271 | + | 24.6854i | 0.163469 | + | 0.927080i | 0.950629 | + | 0.310331i | \(0.100440\pi\) |
−0.787159 | + | 0.616750i | \(0.788449\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.5070 | + | 28.5909i | −0.619061 | + | 1.07224i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.1564 | − | 4.06061i | −0.417812 | − | 0.152071i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.88818 | + | 5.00248i | 0.108012 | + | 0.187082i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.60479 | − | 5.54208i | −0.246660 | − | 0.206973i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.32244 | − | 18.8425i | 0.123906 | − | 0.702706i | −0.858046 | − | 0.513574i | \(-0.828321\pi\) |
0.981952 | − | 0.189132i | \(-0.0605676\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −52.6946 | −1.96245 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.7329 | −0.473540 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.464041 | + | 2.63171i | −0.0172341 | + | 0.0977392i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.68566 | − | 4.77084i | −0.210870 | − | 0.176941i | 0.531235 | − | 0.847224i | \(-0.321728\pi\) |
−0.742105 | + | 0.670284i | \(0.766172\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.32418 | − | 9.22175i | −0.197192 | − | 0.341546i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.0955 | + | 10.2259i | 1.03915 | + | 0.378220i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.59766 | + | 2.76722i | −0.0590108 | + | 0.102210i | −0.894022 | − | 0.448024i | \(-0.852128\pi\) |
0.835011 | + | 0.550234i | \(0.185461\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.29451 | + | 13.0128i | 0.0846344 | + | 0.479986i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.8505 | + | 9.10465i | −0.399683 | + | 0.335374i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.47844 | − | 0.538109i | 0.0543853 | − | 0.0197946i | −0.314684 | − | 0.949196i | \(-0.601899\pi\) |
0.369070 | + | 0.929402i | \(0.379676\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.2386 | + | 11.4969i | 0.670010 | + | 0.422350i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.6647 | + | 3.88164i | −0.391251 | + | 0.142404i | −0.530152 | − | 0.847903i | \(-0.677865\pi\) |
0.138901 | + | 0.990306i | \(0.455643\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.9991 | − | 13.4249i | 0.586163 | − | 0.491849i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.36088 | + | 7.71795i | 0.0497921 | + | 0.282385i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.7171 | + | 30.6869i | −0.647369 | + | 1.12128i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.5103 | − | 10.0129i | −1.00386 | − | 0.365377i | −0.212791 | − | 0.977098i | \(-0.568255\pi\) |
−0.791074 | + | 0.611721i | \(0.790478\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.6227 | + | 18.3991i | 0.387114 | + | 0.670501i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.39043 | + | 3.68401i | 0.159784 | + | 0.134075i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.71567 | − | 38.0865i | 0.244085 | − | 1.38428i | −0.578522 | − | 0.815667i | \(-0.696370\pi\) |
0.822607 | − | 0.568610i | \(-0.192519\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.63479 | −0.168232 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.8253 | 1.15367 | 0.576833 | − | 0.816862i | \(-0.304288\pi\) | ||||
0.576833 | + | 0.816862i | \(0.304288\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.4654 | + | 59.3521i | −0.378872 | + | 2.14869i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.5571 | + | 9.69754i | 0.417847 | + | 0.350615i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.74546 | − | 11.6835i | −0.243565 | − | 0.421866i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.83346 | − | 3.21512i | −0.318543 | − | 0.115940i | 0.177800 | − | 0.984067i | \(-0.443102\pi\) |
−0.496343 | + | 0.868127i | \(0.665324\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.20894 | − | 2.09394i | 0.0435388 | − | 0.0754115i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.61084 | + | 14.8068i | 0.0939054 | + | 0.532564i | 0.995077 | + | 0.0991019i | \(0.0315970\pi\) |
−0.901172 | + | 0.433462i | \(0.857292\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.09929 | + | 1.76152i | −0.0754088 | + | 0.0632755i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.01794 | − | 0.734471i | 0.0723933 | − | 0.0263490i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.5301 | + | 27.0284i | −0.878880 | + | 0.968393i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.718636 | + | 0.261562i | −0.0257148 | + | 0.00935942i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.96098 | − | 8.35826i | 0.355976 | − | 0.298700i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.20189 | − | 18.1588i | −0.114280 | − | 0.648116i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.6930 | + | 23.7170i | −0.488104 | + | 0.845421i | −0.999906 | − | 0.0136825i | \(-0.995645\pi\) |
0.511803 | + | 0.859103i | \(0.328978\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.3019 | + | 4.11356i | 0.402359 | + | 0.146447i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.19878 | + | 7.27251i | 0.149292 | + | 0.258581i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.8471 | − | 15.8146i | −0.669282 | − | 0.561594i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.26721 | + | 12.8580i | −0.0804097 | + | 0.456026i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.1496 | 0.713736 | 0.356868 | − | 0.934155i | \(-0.383845\pi\) | ||||
0.356868 | + | 0.934155i | \(0.383845\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.1484 | 0.677420 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.25915 | + | 24.1548i | −0.150490 | + | 0.853470i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.2438 | − | 9.43464i | −0.396784 | − | 0.332941i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.88058 | + | 17.1137i | 0.348245 | + | 0.603178i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.6219 | + | 6.77782i | 0.655522 | + | 0.238591i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.1867 | + | 33.2323i | −0.674568 | + | 1.16839i | 0.302027 | + | 0.953299i | \(0.402337\pi\) |
−0.976595 | + | 0.215087i | \(0.930997\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.88099 | + | 39.0241i | 0.241624 | + | 1.37032i | 0.828203 | + | 0.560428i | \(0.189363\pi\) |
−0.586579 | + | 0.809892i | \(0.699526\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.977784 | + | 0.820458i | −0.0342924 | + | 0.0287747i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.27191 | + | 1.19088i | −0.114610 | + | 0.0417146i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.49540 | − | 17.1427i | −0.192260 | − | 0.599747i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −46.1604 | + | 16.8010i | −1.61298 | + | 0.587075i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.94984 | − | 8.34891i | 0.347252 | − | 0.291379i | −0.452434 | − | 0.891798i | \(-0.649444\pi\) |
0.799685 | + | 0.600419i | \(0.205000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.71731 | − | 38.0958i | −0.234151 | − | 1.32793i | −0.844395 | − | 0.535721i | \(-0.820040\pi\) |
0.610244 | − | 0.792213i | \(-0.291071\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.534908 | + | 0.926488i | −0.0186231 | + | 0.0322562i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.2916 | − | 13.5730i | −1.29675 | − | 0.471980i | −0.400816 | − | 0.916158i | \(-0.631273\pi\) |
−0.895938 | + | 0.444178i | \(0.853496\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.8732 | − | 46.5457i | −0.933344 | − | 1.61660i | −0.777561 | − | 0.628807i | \(-0.783543\pi\) |
−0.155783 | − | 0.987791i | \(-0.549790\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.6861 | + | 17.3577i | 0.717594 | + | 0.602132i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.3555 | + | 98.4280i | −0.601333 | + | 3.41033i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.4896 | 0.743677 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.3346 | 0.460912 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.947486 | + | 5.37346i | −0.0327109 | + | 0.185512i | −0.996785 | − | 0.0801200i | \(-0.974470\pi\) |
0.964074 | + | 0.265632i | \(0.0855808\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.7448 | − | 14.0505i | −0.577407 | − | 0.484502i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.81728 | − | 10.0758i | −0.200358 | − | 0.347030i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.8797 | − | 4.68781i | −0.443073 | − | 0.161266i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.2379 | − | 38.5172i | 0.764103 | − | 1.32347i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.291975 | + | 1.65587i | 0.0100206 | + | 0.0568294i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.63247 | − | 1.36981i | 0.0559604 | − | 0.0469563i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.6665 | + | 10.4338i | −0.981524 | + | 0.357245i | −0.782432 | − | 0.622736i | \(-0.786021\pi\) |
−0.199091 | + | 0.979981i | \(0.563799\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.352792 | − | 9.07685i | 0.0120652 | − | 0.310422i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.6050 | − | 15.5070i | 1.45536 | − | 0.529707i | 0.511276 | − | 0.859416i | \(-0.329173\pi\) |
0.944083 | + | 0.329709i | \(0.106951\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.97862 | + | 4.17756i | −0.169868 | + | 0.142536i | −0.723759 | − | 0.690053i | \(-0.757587\pi\) |
0.553890 | + | 0.832590i | \(0.313143\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.34805 | + | 36.0016i | 0.216341 | + | 1.22693i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.8754 | − | 18.8367i | 0.370203 | − | 0.641210i | −0.619394 | − | 0.785080i | \(-0.712622\pi\) |
0.989597 | + | 0.143871i | \(0.0459549\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.3262 | − | 3.75842i | −0.351100 | − | 0.127790i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.9457 | − | 29.3508i | −0.575506 | − | 0.996806i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.5648 | − | 11.3822i | −0.460155 | − | 0.386116i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.3717 | − | 64.4920i | 0.385314 | − | 2.18523i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.26967 | 0.246041 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.56133 | 0.154201 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.34817 | + | 41.6736i | −0.248130 | + | 1.40722i | 0.564979 | + | 0.825105i | \(0.308884\pi\) |
−0.813109 | + | 0.582111i | \(0.802227\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.64637 | − | 4.73787i | −0.190447 | − | 0.159804i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.18932 | + | 8.98817i | 0.174833 | + | 0.302819i | 0.940103 | − | 0.340890i | \(-0.110728\pi\) |
−0.765271 | + | 0.643709i | \(0.777395\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.3004 | + | 6.29684i | 0.582206 | + | 0.211906i | 0.616298 | − | 0.787513i | \(-0.288632\pi\) |
−0.0340920 | + | 0.999419i | \(0.510854\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.24930 | − | 2.16385i | 0.0419947 | − | 0.0727370i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.62268 | + | 37.5591i | 0.222368 | + | 1.26111i | 0.867653 | + | 0.497170i | \(0.165627\pi\) |
−0.645285 | + | 0.763942i | \(0.723262\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.7292 | + | 12.3593i | −0.494003 | + | 0.414517i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.67494 | + | 0.609630i | −0.0561127 | + | 0.0204234i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.06224 | − | 9.11306i | −0.236329 | − | 0.304957i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.0660 | − | 5.84753i | 0.537026 | − | 0.195461i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.4151 | − | 13.7739i | 0.548083 | − | 0.459896i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.27167 | + | 7.21202i | 0.0424127 | + | 0.240534i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −49.3786 | + | 85.5262i | −1.64504 | + | 2.84929i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.9427 | − | 6.16663i | −0.563817 | − | 0.205213i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.79496 | − | 10.0372i | −0.192631 | − | 0.333647i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.7640 | − | 28.3314i | −1.12112 | − | 0.940728i | −0.122455 | − | 0.992474i | \(-0.539077\pi\) |
−0.998660 | + | 0.0517465i | \(0.983521\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.82150 | + | 21.6728i | −0.126751 | + | 0.718842i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.0351 | −0.995107 | −0.497553 | − | 0.867433i | \(-0.665768\pi\) | ||||
−0.497553 | + | 0.867433i | \(0.665768\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.20352 | −0.139116 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.791255 | − | 4.48743i | 0.0261581 | − | 0.148350i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.60955 | + | 8.06337i | 0.317335 | + | 0.266276i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.9301 | + | 43.1803i | 0.822370 | + | 1.42439i | 0.903913 | + | 0.427716i | \(0.140682\pi\) |
−0.0815433 | + | 0.996670i | \(0.525985\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.78641 | + | 2.10608i | 0.190669 | + | 0.0693978i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.76787 | − | 3.06205i | 0.0581903 | − | 0.100789i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.0854163 | − | 0.484420i | −0.00280847 | − | 0.0159276i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.4423 | − | 15.4749i | 0.605724 | − | 0.508262i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.3651 | − | 11.7799i | 1.06187 | − | 0.386487i | 0.248737 | − | 0.968571i | \(-0.419985\pi\) |
0.813129 | + | 0.582084i | \(0.197762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 53.2448 | − | 28.0421i | 1.74503 | − | 0.919044i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26.0873 | − | 9.49500i | 0.854059 | − | 0.310852i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.19883 | + | 5.20144i | −0.202723 | + | 0.170105i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.119594 | + | 0.678251i | 0.00390696 | + | 0.0221575i | 0.986699 | − | 0.162558i | \(-0.0519746\pi\) |
−0.982792 | + | 0.184716i | \(0.940863\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.55196 | + | 11.3483i | −0.213815 | + | 0.370339i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.2750 | + | 6.28758i | 0.563148 | + | 0.204969i | 0.607879 | − | 0.794030i | \(-0.292021\pi\) |
−0.0447304 | + | 0.998999i | \(0.514243\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.1388 | + | 31.4173i | 0.590680 | + | 1.02309i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −17.0023 | − | 14.2666i | −0.553084 | − | 0.464093i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.93867 | + | 22.3373i | −0.127989 | + | 0.725864i | 0.851498 | + | 0.524358i | \(0.175695\pi\) |
−0.979487 | + | 0.201506i | \(0.935416\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 67.8604 | 2.20284 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.31148 | −0.139809 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.59020 | + | 54.3887i | −0.310657 | + | 1.76182i | 0.284945 | + | 0.958544i | \(0.408025\pi\) |
−0.595602 | + | 0.803280i | \(0.703086\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.8167 | + | 16.6282i | 0.641252 | + | 0.538075i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.42944 | + | 2.47586i | 0.0462072 | + | 0.0800332i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.46857 | − | 3.44628i | −0.305756 | − | 0.111286i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.7450 | − | 20.3430i | 0.378872 | − | 0.656225i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.81117 | − | 15.9429i | −0.0905888 | − | 0.513754i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.7760 | − | 9.04214i | 0.346892 | − | 0.291077i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.4162 | − | 12.1625i | 1.07459 | − | 0.391120i | 0.256701 | − | 0.966491i | \(-0.417365\pi\) |
0.817893 | + | 0.575371i | \(0.195142\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.4244 | + | 27.9587i | −0.367005 | + | 0.898161i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.8615 | + | 18.1481i | −1.60013 | + | 0.582400i | −0.979454 | − | 0.201667i | \(-0.935364\pi\) |
−0.620676 | + | 0.784067i | \(0.713142\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.8401 | − | 25.8779i | 0.988687 | − | 0.829607i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.858890 | − | 4.87101i | −0.0275065 | − | 0.155997i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.62779 | + | 2.81942i | −0.0520777 | + | 0.0902012i | −0.890889 | − | 0.454221i | \(-0.849918\pi\) |
0.838811 | + | 0.544422i | \(0.183251\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.3623 | − | 4.49952i | −0.395102 | − | 0.143805i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.7673 | − | 23.8457i | −0.439556 | − | 0.761334i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.4044 | − | 12.9258i | −0.491324 | − | 0.412270i | 0.363176 | − | 0.931720i | \(-0.381692\pi\) |
−0.854501 | + | 0.519450i | \(0.826137\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.591168 | − | 3.35268i | 0.0188362 | − | 0.106825i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.5472 | −0.367551 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.8922 | −0.568940 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.942702 | − | 5.34633i | 0.0299459 | − | 0.169832i | −0.966167 | − | 0.257917i | \(-0.916964\pi\) |
0.996113 | + | 0.0880856i | \(0.0280749\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.3252 | + | 9.50296i | 0.359394 | + | 0.301567i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.25255 | + | 16.0259i | 0.293325 | + | 0.508054i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.85246 | + | 2.85806i | 0.248690 | + | 0.0905157i | 0.463358 | − | 0.886171i | \(-0.346645\pi\) |
−0.214668 | + | 0.976687i | \(0.568867\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.19675 | + | 2.07283i | −0.0378634 | + | 0.0655813i |
(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 | 380.2.u.b.81.2 | yes | 18 | |
19.2 | odd | 18 | 7220.2.a.y.1.4 | 9 | |||
19.4 | even | 9 | inner | 380.2.u.b.61.2 | ✓ | 18 | |
19.17 | even | 9 | 7220.2.a.w.1.6 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.u.b.61.2 | ✓ | 18 | 19.4 | even | 9 | inner | |
380.2.u.b.81.2 | yes | 18 | 1.1 | even | 1 | trivial | |
7220.2.a.w.1.6 | 9 | 19.17 | even | 9 | |||
7220.2.a.y.1.4 | 9 | 19.2 | odd | 18 |