Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(47,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.be (of order \(18\), 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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 239.4 | ||
Character | \(\chi\) | \(=\) | 432.239 |
Dual form | 432.2.be.c.47.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.939092 | + | 1.45537i | 0.542185 | + | 0.840259i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.07086 | − | 0.188822i | −0.478904 | − | 0.0844436i | −0.0710149 | − | 0.997475i | \(-0.522624\pi\) |
−0.407889 | + | 0.913032i | \(0.633735\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0466102 | + | 0.0555478i | 0.0176170 | + | 0.0209951i | 0.774781 | − | 0.632230i | \(-0.217860\pi\) |
−0.757164 | + | 0.653225i | \(0.773416\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.23621 | + | 2.73346i | −0.412071 | + | 0.911152i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.889704 | + | 5.04576i | 0.268256 | + | 1.52135i | 0.759601 | + | 0.650389i | \(0.225394\pi\) |
−0.491346 | + | 0.870965i | \(0.663495\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.31632 | + | 1.93498i | −1.47448 | + | 0.536668i | −0.949314 | − | 0.314331i | \(-0.898220\pi\) |
−0.525168 | + | 0.850998i | \(0.675998\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.730832 | − | 1.73582i | −0.188700 | − | 0.448187i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.79605 | + | 2.19165i | 0.920678 | + | 0.531554i | 0.883851 | − | 0.467768i | \(-0.154942\pi\) |
0.0368269 | + | 0.999322i | \(0.488275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.96707 | − | 2.86774i | 1.13952 | − | 0.657905i | 0.193212 | − | 0.981157i | \(-0.438110\pi\) |
0.946313 | + | 0.323252i | \(0.104776\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0370715 | + | 0.120000i | −0.00808966 | + | 0.0261861i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.14687 | + | 2.64054i | 0.656168 | + | 0.550590i | 0.908935 | − | 0.416937i | \(-0.136896\pi\) |
−0.252768 | + | 0.967527i | \(0.581341\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.58737 | − | 1.30570i | −0.717475 | − | 0.261139i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.13911 | + | 0.767820i | −0.989022 | + | 0.147767i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.30353 | + | 3.58141i | −0.242059 | + | 0.665051i | 0.757862 | + | 0.652415i | \(0.226244\pi\) |
−0.999920 | + | 0.0126352i | \(0.995978\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.61088 | − | 3.11153i | 0.468929 | − | 0.558847i | −0.478800 | − | 0.877924i | \(-0.658928\pi\) |
0.947729 | + | 0.319076i | \(0.103373\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.50794 | + | 6.03328i | −1.13289 | + | 1.05026i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0394244 | − | 0.0682850i | −0.00666394 | − | 0.0115423i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.14643 | + | 1.98567i | −0.188471 | + | 0.326442i | −0.944741 | − | 0.327818i | \(-0.893687\pi\) |
0.756269 | + | 0.654260i | \(0.227020\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.80863 | − | 5.92009i | −1.25038 | − | 0.947974i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.494495 | − | 1.35861i | −0.0772271 | − | 0.212180i | 0.895071 | − | 0.445923i | \(-0.147125\pi\) |
−0.972298 | + | 0.233744i | \(0.924902\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.128831 | + | 0.0227164i | −0.0196466 | + | 0.00346422i | −0.183463 | − | 0.983027i | \(-0.558731\pi\) |
0.163816 | + | 0.986491i | \(0.447620\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.83995 | − | 2.69373i | 0.274283 | − | 0.401557i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.26138 | − | 3.57572i | 0.621586 | − | 0.521573i | −0.276716 | − | 0.960952i | \(-0.589246\pi\) |
0.898302 | + | 0.439379i | \(0.144802\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.21462 | − | 6.88848i | 0.173518 | − | 0.984068i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.375176 | + | 7.58283i | 0.0525351 | + | 1.06181i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 10.4743i | − | 1.43876i | −0.694619 | − | 0.719378i | \(-0.744427\pi\) | ||
0.694619 | − | 0.719378i | \(-0.255573\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.57130i | − | 0.751234i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.83817 | + | 4.53586i | 1.17064 | + | 0.600790i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.69171 | + | 9.59417i | −0.220242 | + | 1.24905i | 0.651333 | + | 0.758792i | \(0.274210\pi\) |
−0.871575 | + | 0.490262i | \(0.836901\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.96656 | − | 4.16744i | 0.635903 | − | 0.533586i | −0.266854 | − | 0.963737i | \(-0.585984\pi\) |
0.902757 | + | 0.430151i | \(0.141540\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.209458 | + | 0.0587379i | −0.0263892 | + | 0.00740029i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.05841 | − | 1.06826i | 0.751453 | − | 0.132501i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.28472 | + | 6.27722i | 0.279123 | + | 0.766885i | 0.997463 | + | 0.0711921i | \(0.0226803\pi\) |
−0.718339 | + | 0.695693i | \(0.755097\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.887762 | + | 7.05957i | −0.106874 | + | 0.849873i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.47730 | + | 6.02286i | −0.412680 | + | 0.714782i | −0.995182 | − | 0.0980471i | \(-0.968740\pi\) |
0.582502 | + | 0.812829i | \(0.302074\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.77130 | + | 4.80004i | 0.324356 | + | 0.561802i | 0.981382 | − | 0.192067i | \(-0.0615190\pi\) |
−0.657026 | + | 0.753868i | \(0.728186\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.46860 | − | 6.44713i | −0.169579 | − | 0.744450i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.238812 | + | 0.284605i | −0.0272151 | + | 0.0324337i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.83670 | − | 13.2887i | 0.544171 | − | 1.49510i | −0.297294 | − | 0.954786i | \(-0.596084\pi\) |
0.841465 | − | 0.540312i | \(-0.181694\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.94356 | − | 6.75826i | −0.660396 | − | 0.750918i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.77579 | + | 1.37428i | 0.414447 | + | 0.150846i | 0.540824 | − | 0.841136i | \(-0.318113\pi\) |
−0.126377 | + | 0.991982i | \(0.540335\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.65122 | − | 3.06373i | −0.396030 | − | 0.332309i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.43641 | + | 1.46616i | −0.690055 | + | 0.157189i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.4547 | − | 8.34541i | 1.53219 | − | 0.884612i | 0.532932 | − | 0.846158i | \(-0.321090\pi\) |
0.999260 | − | 0.0384538i | \(-0.0122432\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.355279 | − | 0.205120i | −0.0372433 | − | 0.0215024i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.98029 | + | 0.877792i | 0.723823 | + | 0.0910228i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.86054 | + | 2.13306i | −0.601278 | + | 0.218847i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.74888 | − | 15.5897i | −0.279106 | − | 1.58289i | −0.725608 | − | 0.688108i | \(-0.758442\pi\) |
0.446502 | − | 0.894783i | \(-0.352670\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14.8922 | − | 3.80566i | −1.49672 | − | 0.382483i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.40951 | + | 6.44680i | 0.538266 | + | 0.641481i | 0.964798 | − | 0.262992i | \(-0.0847092\pi\) |
−0.426532 | + | 0.904473i | \(0.640265\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.918166 | + | 0.161897i | 0.0904696 | + | 0.0159522i | 0.218700 | − | 0.975792i | \(-0.429818\pi\) |
−0.128230 | + | 0.991744i | \(0.540930\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0623569 | − | 0.121503i | 0.00608541 | − | 0.0118575i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.2973 | 1.09215 | 0.546076 | − | 0.837736i | \(-0.316121\pi\) | ||||
0.546076 | + | 0.837736i | \(0.316121\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.80915 | 0.747981 | 0.373991 | − | 0.927433i | \(-0.377989\pi\) | ||||
0.373991 | + | 0.927433i | \(0.377989\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.96649 | + | 0.196250i | −0.376482 | + | 0.0186272i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.09837 | − | 1.42796i | −0.761830 | − | 0.134331i | −0.220782 | − | 0.975323i | \(-0.570861\pi\) |
−0.541048 | + | 0.840992i | \(0.681972\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.87127 | − | 3.42185i | −0.267747 | − | 0.319089i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.28291 | − | 16.9240i | 0.118605 | − | 1.56462i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0551931 | + | 0.313016i | 0.00505955 | + | 0.0286941i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.3315 | + | 5.21624i | −1.30286 | + | 0.474203i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.51291 | − | 1.99554i | 0.136415 | − | 0.179931i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.30353 | + | 4.79405i | 0.742690 | + | 0.428793i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.34261 | − | 2.50721i | 0.385344 | − | 0.222479i | −0.294797 | − | 0.955560i | \(-0.595252\pi\) |
0.680141 | + | 0.733081i | \(0.261919\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.154045 | − | 0.166164i | −0.0135629 | − | 0.0146300i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.94960 | − | 1.63591i | −0.170337 | − | 0.142930i | 0.553634 | − | 0.832760i | \(-0.313241\pi\) |
−0.723971 | + | 0.689830i | \(0.757685\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.390813 | + | 0.142244i | 0.0338878 | + | 0.0123341i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.64825 | + | 0.148147i | 0.486124 | + | 0.0127505i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.44548 | + | 9.46638i | −0.294367 | + | 0.808767i | 0.701048 | + | 0.713115i | \(0.252716\pi\) |
−0.995415 | + | 0.0956528i | \(0.969506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.17758 | + | 2.59514i | −0.184700 | + | 0.220117i | −0.850447 | − | 0.526060i | \(-0.823669\pi\) |
0.665747 | + | 0.746178i | \(0.268113\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.20583 | + | 2.84396i | 0.775271 | + | 0.239504i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.4934 | − | 25.1033i | −1.21200 | − | 2.09924i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.07214 | − | 3.58906i | 0.172082 | − | 0.298055i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.1659 | − | 4.70118i | 0.920951 | − | 0.387747i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.17252 | − | 19.7063i | −0.587596 | − | 1.61441i | −0.774886 | − | 0.632101i | \(-0.782193\pi\) |
0.187290 | − | 0.982305i | \(-0.440030\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.2553 | + | 3.57156i | −1.64835 | + | 0.290649i | −0.919227 | − | 0.393728i | \(-0.871185\pi\) |
−0.729128 | + | 0.684377i | \(0.760074\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.6835 | + | 7.66700i | −0.863711 | + | 0.619840i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.38342 | + | 2.83903i | −0.271763 | + | 0.228036i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.28433 | + | 24.2976i | −0.341927 | + | 1.93916i | 0.00154349 | + | 0.999999i | \(0.499509\pi\) |
−0.343470 | + | 0.939164i | \(0.611602\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.2440 | − | 9.83633i | 1.20893 | − | 0.780072i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.297878i | 0.0234761i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 12.2188i | − | 0.957048i | −0.878074 | − | 0.478524i | \(-0.841172\pi\) | ||
0.878074 | − | 0.478524i | \(-0.158828\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.10832 | − | 5.23197i | 0.631231 | − | 0.407308i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.673297 | + | 3.81846i | −0.0521013 | + | 0.295481i | −0.999713 | − | 0.0239425i | \(-0.992378\pi\) |
0.947612 | + | 0.319423i | \(0.103489\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.5605 | − | 12.2177i | 1.12004 | − | 0.939826i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.69849 | + | 17.1224i | 0.129887 | + | 1.30938i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.4083 | + | 2.71690i | −1.17147 | + | 0.206562i | −0.725330 | − | 0.688401i | \(-0.758313\pi\) |
−0.446141 | + | 0.894963i | \(0.647202\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0946794 | − | 0.260130i | −0.00715709 | − | 0.0196639i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.5518 | + | 6.54774i | −1.16894 | + | 0.492158i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.03273 | + | 10.4490i | −0.450907 | + | 0.780994i | −0.998443 | − | 0.0557882i | \(-0.982233\pi\) |
0.547535 | + | 0.836783i | \(0.315566\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.1241 | + | 17.5354i | 0.752515 | + | 1.30339i | 0.946600 | + | 0.322410i | \(0.104493\pi\) |
−0.194085 | + | 0.980985i | \(0.562174\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.7292 | + | 3.31458i | 0.793127 | + | 0.245021i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.60260 | − | 1.90991i | 0.117826 | − | 0.140419i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.68119 | + | 21.1039i | −0.561704 | + | 1.54327i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.282186 | − | 0.249678i | −0.0205260 | − | 0.0181614i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.5661 | + | 8.57737i | 1.70518 | + | 0.620636i | 0.996399 | − | 0.0847874i | \(-0.0270211\pi\) |
0.708786 | + | 0.705424i | \(0.249243\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.3801 | − | 9.54906i | −0.819160 | − | 0.687357i | 0.133615 | − | 0.991033i | \(-0.457341\pi\) |
−0.952775 | + | 0.303677i | \(0.901786\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.24412 | + | 7.81404i | 0.518762 | + | 0.559575i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.3982 | + | 8.31282i | −1.02583 | + | 0.592264i | −0.915788 | − | 0.401663i | \(-0.868432\pi\) |
−0.110043 | + | 0.993927i | \(0.535099\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.6909 | + | 10.2138i | 1.25407 | + | 0.724039i | 0.971916 | − | 0.235329i | \(-0.0756167\pi\) |
0.282157 | + | 0.959368i | \(0.408950\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.99013 | + | 9.22001i | −0.493046 | + | 0.650330i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.259697 | + | 0.0945220i | −0.0182272 | + | 0.00663414i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.272999 | + | 1.54826i | 0.0190671 | + | 0.108135i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.1080 | + | 5.33757i | −0.772059 | + | 0.370987i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.8892 | + | 22.5112i | 1.30659 | + | 1.55713i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.6769 | + | 3.11691i | 1.21693 | + | 0.214577i | 0.745002 | − | 0.667062i | \(-0.232448\pi\) |
0.471924 | + | 0.881639i | \(0.343559\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.0310 | + | 0.595258i | −0.824351 | + | 0.0407864i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.142250 | 0.00970134 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.294533 | 0.0199942 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.38333 | + | 8.54095i | −0.296198 | + | 0.577144i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.4218 | − | 4.30623i | −1.64279 | − | 0.289668i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.193902 | − | 0.231084i | −0.0129846 | − | 0.0154745i | 0.759513 | − | 0.650492i | \(-0.225437\pi\) |
−0.772498 | + | 0.635018i | \(0.780993\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.00382 | − | 8.19181i | 0.533588 | − | 0.546121i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.55254 | − | 20.1475i | −0.235790 | − | 1.33723i | −0.840943 | − | 0.541124i | \(-0.817999\pi\) |
0.605152 | − | 0.796110i | \(-0.293112\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.31957 | − | 2.30013i | 0.417609 | − | 0.151997i | −0.124665 | − | 0.992199i | \(-0.539786\pi\) |
0.542274 | + | 0.840202i | \(0.317563\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.638472 | − | 0.0802897i | −0.0420084 | − | 0.00528267i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.00964 | + | 2.89232i | 0.328193 | + | 0.189482i | 0.655038 | − | 0.755596i | \(-0.272652\pi\) |
−0.326846 | + | 0.945078i | \(0.605986\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.23852 | + | 3.02446i | −0.341723 | + | 0.197294i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 23.8821 | − | 5.44014i | 1.55131 | − | 0.353375i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.92638 | + | 1.61642i | 0.124607 | + | 0.104558i | 0.702962 | − | 0.711228i | \(-0.251861\pi\) |
−0.578355 | + | 0.815785i | \(0.696305\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.855851 | + | 0.311504i | 0.0551302 | + | 0.0200657i | 0.369438 | − | 0.929255i | \(-0.379550\pi\) |
−0.314308 | + | 0.949321i | \(0.601772\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.25423 | − | 14.9967i | 0.272909 | − | 0.962040i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.60139 | + | 7.14725i | −0.166197 | + | 0.456621i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.8575 | + | 24.8570i | −1.32713 | + | 1.58161i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.54573 | + | 6.78575i | 0.0979569 | + | 0.430029i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.85499 | − | 17.0693i | −0.622041 | − | 1.07741i | −0.989105 | − | 0.147212i | \(-0.952970\pi\) |
0.367064 | − | 0.930196i | \(-0.380363\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.5237 | + | 18.2276i | −0.661622 | + | 1.14596i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.03004 | − | 8.19100i | 0.0645037 | − | 0.512940i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.84779 | + | 10.5717i | 0.240018 | + | 0.659445i | 0.999955 | + | 0.00944810i | \(0.00300747\pi\) |
−0.759937 | + | 0.649997i | \(0.774770\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.163735 | + | 0.0288709i | −0.0101740 | + | 0.00179395i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.17818 | − | 7.99051i | −0.506217 | − | 0.494600i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.08262 | − | 6.78213i | 0.498396 | − | 0.418204i | −0.358628 | − | 0.933481i | \(-0.616755\pi\) |
0.857024 | + | 0.515277i | \(0.172311\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.97778 | + | 11.2165i | −0.121494 | + | 0.689025i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 25.7199 | + | 13.1998i | 1.57404 | + | 0.807815i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 28.9612i | − | 1.76580i | −0.469564 | − | 0.882898i | \(-0.655589\pi\) | ||
0.469564 | − | 0.882898i | \(-0.344411\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.5660i | 1.79600i | 0.439991 | + | 0.898002i | \(0.354982\pi\) | ||||
−0.439991 | + | 0.898002i | \(0.645018\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.0351133 | − | 0.709689i | −0.00212515 | − | 0.0429523i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.39653 | − | 19.2627i | 0.204819 | − | 1.16158i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.54306 | + | 1.29478i | −0.0927134 | + | 0.0777958i | −0.687966 | − | 0.725743i | \(-0.741496\pi\) |
0.595253 | + | 0.803538i | \(0.297052\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.27763 | + | 10.9832i | 0.315963 | + | 0.657550i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.06067 | + | 0.716005i | −0.242239 | + | 0.0427133i | −0.293449 | − | 0.955975i | \(-0.594803\pi\) |
0.0512103 | + | 0.998688i | \(0.483692\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.21065 | + | 6.07372i | 0.131410 | + | 0.361045i | 0.987895 | − | 0.155127i | \(-0.0495787\pi\) |
−0.856485 | + | 0.516172i | \(0.827356\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.60798 | − | 6.52612i | −0.509893 | − | 0.386574i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.0524195 | − | 0.0907933i | 0.00309423 | − | 0.00535936i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.10668 | + | 1.91683i | 0.0650990 | + | 0.112755i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20.1073 | − | 18.6408i | 1.17871 | − | 1.09274i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.8278 | + | 23.6299i | −1.15835 | + | 1.38047i | −0.246915 | + | 0.969037i | \(0.579417\pi\) |
−0.911439 | + | 0.411435i | \(0.865028\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.62318 | − | 9.95459i | 0.210949 | − | 0.579579i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.44652 | − | 25.2476i | −0.490117 | − | 1.46501i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −21.8392 | − | 7.94881i | −1.26299 | − | 0.459691i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.00726669 | − | 0.00609748i | −0.000418845 | − | 0.000351453i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.30246 | + | 13.9270i | −0.247170 | + | 0.800084i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.10540 | + | 3.52495i | −0.349594 | + | 0.201838i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.5367 | − | 15.8983i | −1.57160 | − | 0.907364i | −0.995973 | − | 0.0896520i | \(-0.971425\pi\) |
−0.575628 | − | 0.817712i | \(-0.695242\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.626622 | + | 1.48831i | 0.0356473 | + | 0.0846670i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.5550 | + | 4.93361i | −0.768633 | + | 0.279759i | −0.696424 | − | 0.717630i | \(-0.745227\pi\) |
−0.0722083 | + | 0.997390i | \(0.523005\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.513567 | + | 2.91258i | 0.0290285 | + | 0.164629i | 0.995876 | − | 0.0907261i | \(-0.0289188\pi\) |
−0.966847 | + | 0.255355i | \(0.917808\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.235391 | − | 0.0233501i | 0.0132628 | − | 0.00131563i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.9386 | − | 17.8031i | −0.839035 | − | 0.999923i | −0.999916 | − | 0.0129495i | \(-0.995878\pi\) |
0.160881 | − | 0.986974i | \(-0.448567\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.2307 | − | 3.39089i | −1.07671 | − | 0.189853i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.6092 | + | 16.4418i | 0.592148 | + | 0.917690i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.1404 | 1.39885 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.5981 | 1.19805 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.33351 | + | 11.3652i | 0.405544 | + | 0.628498i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.397247 | + | 0.0700454i | 0.0219010 | + | 0.00386173i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.74589 | − | 5.65593i | −0.260857 | − | 0.310878i | 0.619680 | − | 0.784855i | \(-0.287262\pi\) |
−0.880537 | + | 0.473977i | \(0.842818\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.01051 | − | 5.58842i | −0.219775 | − | 0.306243i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.26134 | − | 7.15344i | −0.0689146 | − | 0.390834i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.45078 | − | 3.07583i | 0.460343 | − | 0.167551i | −0.101430 | − | 0.994843i | \(-0.532342\pi\) |
0.561773 | + | 0.827292i | \(0.310119\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.52690 | − | 13.1271i | −0.300180 | − | 0.712967i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.0230 | + | 10.4056i | 0.975997 | + | 0.563492i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.878838 | − | 0.507397i | 0.0474528 | − | 0.0273969i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.28367 | − | 7.39219i | 0.122949 | − | 0.397982i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.3234 | − | 9.50146i | −0.607872 | − | 0.510065i | 0.286093 | − | 0.958202i | \(-0.407643\pi\) |
−0.893965 | + | 0.448137i | \(0.852088\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.57893 | + | 2.39453i | 0.352162 | + | 0.128176i | 0.512043 | − | 0.858960i | \(-0.328889\pi\) |
−0.159881 | + | 0.987136i | \(0.551111\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25.8354 | − | 14.0261i | 1.37899 | − | 0.748656i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.61218 | + | 9.92437i | −0.192257 | + | 0.528221i | −0.997942 | − | 0.0641228i | \(-0.979575\pi\) |
0.805685 | + | 0.592344i | \(0.201797\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.86095 | − | 5.79306i | 0.257993 | − | 0.307464i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.403723 | + | 0.374277i | −0.0213673 | + | 0.0198089i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.6210 | − | 21.8603i | −0.666112 | − | 1.15374i | −0.978983 | − | 0.203944i | \(-0.934624\pi\) |
0.312871 | − | 0.949796i | \(-0.398709\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.94788 | − | 12.0341i | 0.365678 | − | 0.633373i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.0502 | − | 15.9591i | −1.10485 | − | 0.837637i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.06133 | − | 5.66345i | −0.107895 | − | 0.296439i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.2545 | − | 1.98448i | 0.587483 | − | 0.103589i | 0.127997 | − | 0.991774i | \(-0.459145\pi\) |
0.459485 | + | 0.888185i | \(0.348034\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.32501 | + | 0.327854i | 0.225151 | + | 0.0170674i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.581825 | − | 0.488209i | 0.0302068 | − | 0.0253465i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.86274 | − | 16.2354i | 0.148227 | − | 0.840639i | −0.816492 | − | 0.577357i | \(-0.804084\pi\) |
0.964719 | − | 0.263282i | \(-0.0848048\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.820664 | + | 16.5868i | 0.0423789 | + | 0.856537i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 21.5622i | − | 1.11051i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 15.7412i | − | 0.808572i | −0.914633 | − | 0.404286i | \(-0.867520\pi\) | ||
0.914633 | − | 0.404286i | \(-0.132480\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.72703 | + | 3.96561i | 0.395868 | + | 0.203164i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.45535 | + | 30.9388i | −0.278756 | + | 1.58090i | 0.448018 | + | 0.894024i | \(0.352130\pi\) |
−0.726774 | + | 0.686877i | \(0.758981\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.309474 | − | 0.259679i | 0.0157722 | − | 0.0132345i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.0971683 | − | 0.380237i | 0.00493934 | − | 0.0193285i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.4122 | − | 1.83595i | 0.527918 | − | 0.0930862i | 0.0966646 | − | 0.995317i | \(-0.469183\pi\) |
0.431253 | + | 0.902231i | \(0.358071\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.15855 | + | 16.9205i | 0.311451 | + | 0.855705i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.550001 | − | 4.37366i | 0.0277439 | − | 0.220622i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.68863 | + | 13.3171i | −0.386857 | + | 0.670056i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.12129 | + | 3.67419i | 0.106465 | + | 0.184402i | 0.914336 | − | 0.404957i | \(-0.132714\pi\) |
−0.807871 | + | 0.589359i | \(0.799380\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.159991 | + | 0.702358i | 0.00800957 | + | 0.0351619i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.6057 | − | 20.9817i | 0.879189 | − | 1.04778i | −0.119302 | − | 0.992858i | \(-0.538066\pi\) |
0.998491 | − | 0.0549188i | \(-0.0174900\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.85954 | + | 21.5939i | −0.391512 | + | 1.07567i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.08862 | + | 8.35943i | 0.252856 | + | 0.415384i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.0392 | − | 4.01794i | −0.547193 | − | 0.199162i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.397716 | + | 0.333723i | 0.0196658 | + | 0.0165016i | 0.652568 | − | 0.757731i | \(-0.273692\pi\) |
−0.632902 | + | 0.774232i | \(0.718136\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.0127 | + | 3.87535i | −0.839176 | + | 0.191157i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.611786 | + | 0.353215i | −0.0301040 | + | 0.0173806i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.78385 | − | 2.18461i | −0.185742 | − | 0.107238i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.82185 | − | 0.732114i | −0.285097 | − | 0.0358518i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.8567 | − | 4.31547i | 0.579236 | − | 0.210825i | −0.0357528 | − | 0.999361i | \(-0.511383\pi\) |
0.614988 | + | 0.788536i | \(0.289161\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.43676 | − | 13.8196i | −0.118760 | − | 0.673524i | −0.984819 | − | 0.173582i | \(-0.944466\pi\) |
0.866059 | − | 0.499942i | \(-0.166645\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.50611 | + | 16.0686i | 0.219095 | + | 0.781284i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.7562 | − | 12.8188i | −0.521754 | − | 0.621802i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.462984 | + | 0.0816366i | 0.0224054 | + | 0.00395067i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 22.9240 | − | 44.6676i | 1.10678 | − | 2.15657i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.28837 | 0.206564 | 0.103282 | − | 0.994652i | \(-0.467066\pi\) | ||||
0.103282 | + | 0.994652i | \(0.467066\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.60769 | 0.269488 | 0.134744 | − | 0.990880i | \(-0.456979\pi\) | ||||
0.134744 | + | 0.990880i | \(0.456979\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.16934 | − | 0.354718i | 0.343744 | − | 0.0170074i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23.2031 | + | 4.09133i | 1.10996 | + | 0.195715i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.51341 | − | 5.37887i | −0.215413 | − | 0.256719i | 0.647507 | − | 0.762059i | \(-0.275812\pi\) |
−0.862920 | + | 0.505340i | \(0.831367\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.3278 | + | 11.8357i | 0.825134 | + | 0.563606i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.26637 | + | 29.8670i | 0.250213 | + | 1.41903i | 0.808069 | + | 0.589088i | \(0.200513\pi\) |
−0.557856 | + | 0.829938i | \(0.688376\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.0547 | + | 6.20742i | −0.808472 | + | 0.294260i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.9444 | − | 28.9447i | 1.03793 | − | 1.36904i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.7669 | + | 14.2991i | 1.16882 | + | 0.674819i | 0.953402 | − | 0.301703i | \(-0.0975552\pi\) |
0.215418 | + | 0.976522i | \(0.430889\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.41528 | − | 3.70386i | 0.302084 | − | 0.174408i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −24.2196 | − | 26.1250i | −1.13793 | − | 1.22746i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.341723 | + | 0.286740i | 0.0160202 | + | 0.0134426i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.676715 | − | 0.246304i | −0.0316554 | − | 0.0115216i | 0.326144 | − | 0.945320i | \(-0.394251\pi\) |
−0.357799 | + | 0.933799i | \(0.616473\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −21.1911 | − | 8.34846i | −0.989117 | − | 0.389673i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.907267 | − | 2.49269i | 0.0422556 | − | 0.116096i | −0.916770 | − | 0.399415i | \(-0.869213\pi\) |
0.959026 | + | 0.283319i | \(0.0914354\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.24403 | − | 7.44135i | 0.290185 | − | 0.345829i | −0.601181 | − | 0.799113i | \(-0.705303\pi\) |
0.891366 | + | 0.453284i | \(0.149748\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.30918 | − | 2.25802i | −0.338955 | − | 0.104713i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.87482 | − | 17.1037i | −0.456952 | − | 0.791464i | 0.541846 | − | 0.840478i | \(-0.317726\pi\) |
−0.998798 | + | 0.0490137i | \(0.984392\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.242195 | + | 0.419494i | −0.0111835 | + | 0.0193704i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −39.3855 | + | 16.5824i | −1.81479 | + | 0.764078i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.229243 | − | 0.629840i | −0.0105406 | − | 0.0289601i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.5631 | + | 3.80216i | −0.989385 | + | 0.174455i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 28.6310 | + | 12.9485i | 1.31093 | + | 0.592869i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.2243 | − | 12.7747i | 0.695616 | − | 0.583691i | −0.224906 | − | 0.974380i | \(-0.572208\pi\) |
0.920523 | + | 0.390689i | \(0.127763\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.25254 | − | 12.7748i | 0.102707 | − | 0.582480i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.433523 | + | 0.279735i | −0.0197260 | + | 0.0127284i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.2134i | 0.781621i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 3.34369i | − | 0.151517i | −0.997126 | − | 0.0757584i | \(-0.975862\pi\) | ||
0.997126 | − | 0.0757584i | \(-0.0241378\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.7829 | − | 11.4746i | 0.804169 | − | 0.518897i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.46183 | − | 36.6468i | 0.291618 | − | 1.65385i | −0.389020 | − | 0.921229i | \(-0.627186\pi\) |
0.680638 | − | 0.732620i | \(-0.261703\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.7975 | + | 10.7383i | −0.576368 | + | 0.483630i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.2289 | + | 6.88731i | 0.684489 | + | 0.309562i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.496634 | + | 0.0875700i | −0.0222771 | + | 0.00392805i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.25828 | − | 17.1945i | −0.280159 | − | 0.769731i | −0.997343 | − | 0.0728472i | \(-0.976791\pi\) |
0.717184 | − | 0.696884i | \(-0.245431\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.18956 | + | 2.60599i | −0.276529 | + | 0.116427i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.9327 | + | 34.5244i | −0.888754 | + | 1.53937i | −0.0474040 | + | 0.998876i | \(0.515095\pi\) |
−0.841350 | + | 0.540491i | \(0.818239\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.57554 | − | 7.92506i | −0.203609 | − | 0.352661i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 31.4550 | + | 9.71740i | 1.39697 | + | 0.431565i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.228853 | − | 0.272736i | 0.0101437 | − | 0.0120888i | −0.760949 | − | 0.648812i | \(-0.775266\pi\) |
0.771092 | + | 0.636723i | \(0.219711\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.137461 | + | 0.377670i | −0.00608091 | + | 0.0167072i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −23.3244 | + | 18.5515i | −1.02980 | + | 0.819067i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.952659 | − | 0.346739i | −0.0419792 | − | 0.0152792i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.8336 | + | 18.3206i | 0.960241 | + | 0.805738i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.4239 | − | 19.8734i | −0.808720 | − | 0.872344i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.3668 | + | 13.4908i | −1.02372 | + | 0.591044i | −0.915179 | − | 0.403049i | \(-0.867951\pi\) |
−0.108539 | + | 0.994092i | \(0.534617\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.8958 | + | 14.3736i | 1.08862 | + | 0.628513i | 0.933208 | − | 0.359337i | \(-0.116997\pi\) |
0.155408 | + | 0.987850i | \(0.450331\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.289672 | − | 0.382079i | 0.0126423 | − | 0.0166753i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.7305 | − | 6.08939i | 0.728790 | − | 0.265258i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.06356 | − | 6.03172i | −0.0462415 | − | 0.262249i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −24.1339 | − | 16.4846i | −1.04732 | − | 0.715373i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.25778 | + | 6.26598i | 0.227740 | + | 0.271410i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.0978 | − | 2.13318i | −0.523035 | − | 0.0922253i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.8725 | + | 1.03271i | −0.900713 | + | 0.0445646i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 35.8382 | 1.54366 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.2500 | −0.913608 | −0.456804 | − | 0.889567i | \(-0.651006\pi\) | ||||
−0.456804 | + | 0.889567i | \(0.651006\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.0131 | + | 31.2016i | −0.687186 | + | 1.33899i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.36252 | − | 1.47454i | −0.358211 | − | 0.0631622i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.82124 | + | 10.5127i | 0.377169 | + | 0.449492i | 0.920919 | − | 0.389755i | \(-0.127440\pi\) |
−0.543750 | + | 0.839247i | \(0.682996\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.25179 | + | 18.7277i | 0.224141 | + | 0.799279i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.79584 | + | 21.5273i | 0.161708 | + | 0.917093i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.963599 | − | 0.350721i | 0.0409764 | − | 0.0149142i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.28461 | + | 0.538803i | 0.181872 | + | 0.0228709i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.8867 | − | 17.2551i | −1.26634 | − | 0.731121i | −0.292046 | − | 0.956404i | \(-0.594336\pi\) |
−0.974293 | + | 0.225283i | \(0.927669\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.640952 | − | 0.370054i | 0.0271094 | − | 0.0156516i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −37.9274 | + | 8.63952i | −1.60129 | + | 0.364761i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.90869 | + | 6.63618i | 0.333312 | + | 0.279682i | 0.794048 | − | 0.607856i | \(-0.207970\pi\) |
−0.460736 | + | 0.887537i | \(0.652414\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.40260 | + | 3.05830i | 0.353500 | + | 0.128663i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.0983763 | − | 0.645156i | 0.00413142 | − | 0.0270940i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.3576 | − | 28.4573i | 0.434214 | − | 1.19299i | −0.508989 | − | 0.860773i | \(-0.669981\pi\) |
0.943202 | − | 0.332219i | \(-0.107797\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.6804 | − | 28.2212i | 0.990992 | − | 1.18102i | 0.00751760 | − | 0.999972i | \(-0.497607\pi\) |
0.983475 | − | 0.181047i | \(-0.0579485\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.64751 | + | 42.3524i | 0.403030 | + | 1.76930i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.84125 | − | 13.5815i | −0.327003 | − | 0.566386i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.46070 | − | 9.45821i | 0.227332 | − | 0.393750i | −0.729685 | − | 0.683784i | \(-0.760333\pi\) |
0.957016 | + | 0.290034i | \(0.0936665\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.21044 | − | 25.5298i | 0.133421 | − | 1.06098i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.0996522 | + | 0.273792i | 0.00413427 | + | 0.0113588i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 52.8508 | − | 9.31902i | 2.18886 | − | 0.385954i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.56943 | + | 17.8810i | −0.188923 | + | 0.739288i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.8588 | + | 21.6981i | −1.06730 | + | 0.895575i | −0.994806 | − | 0.101793i | \(-0.967542\pi\) |
−0.0724993 | + | 0.997368i | \(0.523098\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.04539 | − | 22.9425i | 0.166687 | − | 0.945331i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.6195 | − | 13.1483i | −1.05385 | − | 0.540847i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1.65720i | − | 0.0680529i | −0.999421 | − | 0.0340265i | \(-0.989167\pi\) | ||
0.999421 | − | 0.0340265i | \(-0.0108330\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 0.345618i | − | 0.0141690i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.74845 | + | 35.3385i | 0.0715591 | + | 1.44631i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.97543 | + | 16.8745i | −0.121573 | + | 0.689474i | 0.861712 | + | 0.507398i | \(0.169393\pi\) |
−0.983285 | + | 0.182076i | \(0.941718\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.6454 | + | 20.6799i | −1.00531 | + | 0.843552i | −0.987711 | − | 0.156294i | \(-0.950045\pi\) |
−0.0175950 | + | 0.999845i | \(0.505601\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.9829 | − | 1.51479i | −0.813767 | − | 0.0616870i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.3320 | − | 2.87977i | 0.663990 | − | 0.117079i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.5382 | − | 31.7008i | −0.468319 | − | 1.28670i | −0.919087 | − | 0.394055i | \(-0.871072\pi\) |
0.450768 | − | 0.892641i | \(-0.351150\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.381444 | − | 0.289191i | −0.0154569 | − | 0.0117186i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.7359 | + | 27.2554i | −0.636606 | + | 1.10263i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.7069 | − | 37.5975i | −0.876734 | − | 1.51855i | −0.854904 | − | 0.518787i | \(-0.826384\pi\) |
−0.0218308 | − | 0.999762i | \(-0.506949\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.99692 | + | 1.85127i | −0.0805235 | + | 0.0746505i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.65341 | + | 5.54572i | −0.187339 | + | 0.223262i | −0.851537 | − | 0.524295i | \(-0.824329\pi\) |
0.664198 | + | 0.747557i | \(0.268773\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.37729 | − | 23.0164i | 0.336712 | − | 0.925108i | −0.649609 | − | 0.760269i | \(-0.725067\pi\) |
0.986320 | − | 0.164839i | \(-0.0527105\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.1996 | − | 11.1538i | −0.730324 | − | 0.447586i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.13730 | + | 0.413945i | 0.0455651 | + | 0.0165844i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.63556 | + | 5.56789i | 0.265422 | + | 0.222716i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.0235 | + | 48.6308i | −0.599982 | + | 1.94213i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.70380 | + | 5.02514i | −0.347043 | + | 0.200365i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.68103 | + | 5.58935i | 0.385396 | + | 0.222508i | 0.680163 | − | 0.733061i | \(-0.261909\pi\) |
−0.294768 | + | 0.955569i | \(0.595242\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.0640 | + | 28.6535i | 0.479499 | + | 1.13887i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.12375 | + | 1.86489i | −0.203330 | + | 0.0740060i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.87175 | + | 38.9716i | 0.272269 | + | 1.54411i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.1645 | − | 16.9506i | −0.481222 | − | 0.670554i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.72355 | − | 9.20457i | −0.305062 | − | 0.363559i | 0.591633 | − | 0.806207i | \(-0.298483\pi\) |
−0.896695 | + | 0.442649i | \(0.854039\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.71839 | + | 1.36096i | 0.304384 | + | 0.0536711i | 0.323754 | − | 0.946141i | \(-0.395055\pi\) |
−0.0193702 | + | 0.999812i | \(0.506166\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.133586 | + | 0.207026i | 0.00525992 | + | 0.00815164i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 44.0555 | 1.73200 | 0.866000 | − | 0.500044i | \(-0.166683\pi\) | ||||
0.866000 | + | 0.500044i | \(0.166683\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −49.9150 | −1.95933 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.276593 | + | 0.428654i | 0.0108405 | + | 0.0168003i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.0561 | + | 6.88664i | 1.52838 | + | 0.269495i | 0.873721 | − | 0.486428i | \(-0.161700\pi\) |
0.654661 | + | 0.755923i | \(0.272811\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.77886 | + | 2.11996i | 0.0695057 | + | 0.0828336i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.5466 | + | 1.64137i | −0.645544 | + | 0.0640360i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.66439 | + | 9.43924i | 0.0648355 | + | 0.367701i | 0.999912 | + | 0.0132549i | \(0.00421930\pi\) |
−0.935077 | + | 0.354446i | \(0.884670\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.0924 | + | 3.67332i | −0.392547 | + | 0.142876i | −0.530750 | − | 0.847528i | \(-0.678090\pi\) |
0.138203 | + | 0.990404i | \(0.455867\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.6672 | − | 39.5868i | −0.647301 | − | 1.53742i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.391648 | − | 0.226118i | −0.0151874 | − | 0.00876847i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.5589 | + | 7.82821i | −0.525001 | + | 0.303110i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.154220 | − | 0.499208i | 0.00596250 | − | 0.0193005i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.4467 | + | 21.3523i | 0.982357 | + | 0.824296i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.534095 | − | 0.194395i | −0.0205878 | − | 0.00749336i | 0.331706 | − | 0.943383i | \(-0.392376\pi\) |
−0.352294 | + | 0.935890i | \(0.614598\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 19.4384 | + | 3.95566i | 0.748186 | + | 0.152254i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.40412 | − | 6.60528i | 0.0923980 | − | 0.253861i | −0.884881 | − | 0.465816i | \(-0.845761\pi\) |
0.977279 | + | 0.211955i | \(0.0679830\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.737846 | − | 0.879331i | 0.0283159 | − | 0.0337456i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.9859 | − | 24.0906i | 0.995781 | − | 0.923153i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.1061 | + | 41.7529i | 0.922393 | + | 1.59763i | 0.795701 | + | 0.605690i | \(0.207103\pi\) |
0.126693 | + | 0.991942i | \(0.459564\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.47709 | − | 9.48660i | 0.209269 | − | 0.362464i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.28220 | + | 7.03728i | 0.354138 | + | 0.268489i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.2676 | + | 55.6847i | 0.772134 | + | 2.12142i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.0430 | − | 3.71046i | 0.800515 | − | 0.141152i | 0.241599 | − | 0.970376i | \(-0.422328\pi\) |
0.558917 | + | 0.829224i | \(0.311217\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.482733 | − | 1.00461i | −0.0183375 | − | 0.0381621i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.82191 | − | 2.36786i | 0.107041 | − | 0.0898182i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.10048 | − | 6.24113i | 0.0416836 | − | 0.236400i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.495119 | + | 10.0070i | 0.0187271 | + | 0.378501i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.4157i | 0.468935i | 0.972124 | + | 0.234468i | \(0.0753347\pi\) | ||||
−0.972124 | + | 0.234468i | \(0.924665\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.1506i | 0.495985i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.32117 | − | 4.78375i | −0.351056 | − | 0.180166i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.105968 | + | 0.600973i | −0.00398533 | + | 0.0226019i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.976912 | + | 0.819726i | −0.0366887 | + | 0.0307855i | −0.660948 | − | 0.750432i | \(-0.729845\pi\) |
0.624259 | + | 0.781218i | \(0.285401\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 30.3449 | + | 29.6486i | 1.13802 | + | 1.11191i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.4322 | − | 2.89745i | 0.615392 | − | 0.108510i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.7804 | + | 29.6188i | 0.403163 | + | 1.10768i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.543449 | + | 4.32157i | −0.0202955 | + | 0.161392i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.5684 | + | 25.2332i | −0.543310 | + | 0.941041i | 0.455401 | + | 0.890287i | \(0.349496\pi\) |
−0.998711 | + | 0.0507546i | \(0.983837\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.0338028 | + | 0.0585482i | 0.00125888 | + | 0.00218045i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.350368 | + | 1.53811i | 0.0130303 | + | 0.0572030i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.35246 | − | 11.1458i | 0.347342 | − | 0.413946i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.73821 | − | 7.52317i | 0.101555 | − | 0.279019i | −0.878502 | − | 0.477739i | \(-0.841456\pi\) |
0.980056 | + | 0.198720i | \(0.0636786\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.8209 | − | 7.89182i | 0.956330 | − | 0.292290i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.538836 | − | 0.196120i | −0.0199296 | − | 0.00725378i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.12619 | + | 1.78409i | 0.0785326 | + | 0.0658967i | 0.681209 | − | 0.732089i | \(-0.261455\pi\) |
−0.602676 | + | 0.797986i | \(0.705899\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.8449 | + | 2.92595i | −0.473790 | + | 0.107925i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.6406 | + | 17.1130i | −1.09183 | + | 0.630367i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.0458 | − | 12.7281i | −0.810967 | − | 0.468212i | 0.0363245 | − | 0.999340i | \(-0.488435\pi\) |
−0.847292 | + | 0.531128i | \(0.821768\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −55.7634 | − | 7.01240i | −2.04852 | − | 0.257607i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.02834 | − | 0.738257i | 0.0744127 | − | 0.0270840i | −0.304546 | − | 0.952498i | \(-0.598505\pi\) |
0.378958 | + | 0.925414i | \(0.376282\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.95979 | + | 22.4571i | 0.145075 | + | 0.822764i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.42420 | + | 8.62206i | −0.308225 | + | 0.315465i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.526569 | + | 0.627541i | 0.0192404 | + | 0.0229298i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.26718 | − | 0.576092i | −0.119221 | − | 0.0210219i | 0.113719 | − | 0.993513i | \(-0.463724\pi\) |
−0.232940 | + | 0.972491i | \(0.574835\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.5875 | − | 30.3724i | 0.568040 | − | 1.10683i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.3650 | 0.813947 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.4846 | −0.780869 | −0.390435 | − | 0.920631i | \(-0.627675\pi\) | ||||
−0.390435 | + | 0.920631i | \(0.627675\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −36.4108 | + | 1.80150i | −1.32163 | + | 0.0653901i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.57062 | − | 1.15858i | −0.238185 | − | 0.0419984i | 0.0532815 | − | 0.998580i | \(-0.483032\pi\) |
−0.291466 | + | 0.956581i | \(0.594143\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.363986 | + | 0.433781i | 0.0131772 | + | 0.0157039i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.8883 | − | 6.19301i | 0.465976 | − | 0.223909i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.57087 | − | 54.2791i | −0.345584 | − | 1.95991i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.8560 | − | 13.7784i | 1.36512 | − | 0.496863i | 0.447487 | − | 0.894290i | \(-0.352319\pi\) |
0.917634 | + | 0.397427i | \(0.130097\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.7723 | + | 15.5278i | −0.423970 | + | 0.559219i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.8074 | + | 9.12640i | 0.568552 | + | 0.328254i | 0.756571 | − | 0.653912i | \(-0.226873\pi\) |
−0.188019 | + | 0.982165i | \(0.560207\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.4289 | + | 7.75320i | −0.482382 | + | 0.278503i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.195780 | − | 0.211183i | −0.00702357 | − | 0.00757613i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.35234 | − | 5.33025i | −0.227596 | − | 0.190976i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.4837 | − | 12.1871i | −1.19814 | − | 0.436087i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.94909 | − | 19.4061i | 0.141129 | − | 0.693518i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.17584 | − | 25.2104i | 0.327500 | − | 0.899798i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.4720 | − | 14.8636i | 0.444580 | − | 0.529830i | −0.496490 | − | 0.868043i | \(-0.665378\pi\) |
0.941070 | + | 0.338213i | \(0.109822\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.4608 | + | 5.39418i | 0.621622 | + | 0.192038i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.298146 | − | 0.516404i | −0.0106009 | − | 0.0183612i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.3399 | + | 31.7656i | −0.651269 | + | 1.12803i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18.1815 | + | 7.65495i | −0.644832 | + | 0.271493i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.34972 | − | 9.20329i | −0.118653 | − | 0.325997i | 0.866121 | − | 0.499834i | \(-0.166606\pi\) |
−0.984774 | + | 0.173837i | \(0.944383\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0132 | − | 4.23417i | 0.849525 | − | 0.149794i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.94277 | + | 49.8279i | 0.174644 | + | 1.76058i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.7542 | + | 18.2539i | −0.767689 | + | 0.644167i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0562458 | − | 0.318986i | 0.00198240 | − | 0.0112428i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 42.1493 | − | 27.1973i | 1.48373 | − | 0.957389i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 25.9021i | − | 0.910671i | −0.890320 | − | 0.455336i | \(-0.849519\pi\) | ||
0.890320 | − | 0.455336i | \(-0.150481\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 28.6572i | − | 1.00629i | −0.864202 | − | 0.503145i | \(-0.832176\pi\) | ||
0.864202 | − | 0.503145i | \(-0.167824\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −43.0295 | + | 27.7652i | −1.50911 | + | 0.973767i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.30717 | + | 13.0846i | −0.0808166 | + | 0.458334i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.574769 | + | 0.482288i | −0.0201086 | + | 0.0168731i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.999887 | − | 0.717566i | 0.0349389 | − | 0.0250738i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.2292 | + | 4.97757i | −0.985205 | + | 0.173718i | −0.642966 | − | 0.765895i | \(-0.722296\pi\) |
−0.342239 | + | 0.939613i | \(0.611185\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.22536 | − | 19.8515i | −0.251860 | − | 0.691980i | −0.999608 | − | 0.0279972i | \(-0.991087\pi\) |
0.747748 | − | 0.663983i | \(-0.231135\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 31.2240 | − | 13.1462i | 1.08708 | − | 0.457693i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.73569 | + | 16.8627i | −0.338543 | + | 0.586374i | −0.984159 | − | 0.177288i | \(-0.943267\pi\) |
0.645616 | + | 0.763662i | \(0.276601\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.1430 | − | 34.8887i | −0.699595 | − | 1.21173i | −0.968607 | − | 0.248597i | \(-0.920031\pi\) |
0.269012 | − | 0.963137i | \(-0.413303\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.33346 | − | 1.02981i | −0.115636 | − | 0.0357236i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.7079 | − | 23.4870i | 0.682839 | − | 0.813776i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.44201 | − | 3.96190i | 0.0499030 | − | 0.137107i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.0285 | + | 17.9952i | −0.381202 | + | 0.622005i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.3185 | + | 8.48725i | 0.805045 | + | 0.293012i | 0.711575 | − | 0.702610i | \(-0.247982\pi\) |
0.0934694 | + | 0.995622i | \(0.470204\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0880 | + | 9.30393i | 0.382345 | + | 0.320825i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.85540 | − | 5.23739i | −0.167229 | − | 0.180385i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.8993 | + | 10.3342i | −0.615754 | + | 0.355506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.957744 | − | 0.552954i | −0.0329085 | − | 0.0189997i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.76351 | + | 8.92110i | −0.232123 | + | 0.306171i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.85089 | + | 3.22146i | −0.303405 | + | 0.110430i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.33230 | − | 24.5697i | −0.148335 | − | 0.841250i | −0.964629 | − | 0.263613i | \(-0.915086\pi\) |
0.816294 | − | 0.577637i | \(-0.196025\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.41424 | − | 18.6564i | 0.0483659 | − | 0.638037i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.1320 | − | 23.9924i | −0.687696 | − | 0.819564i | 0.303379 | − | 0.952870i | \(-0.401885\pi\) |
−0.991075 | + | 0.133306i | \(0.957441\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.8494 | + | 7.55550i | 1.46200 | + | 0.257790i | 0.847361 | − | 0.531017i | \(-0.178190\pi\) |
0.614640 | + | 0.788808i | \(0.289301\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.181365 | − | 0.00897338i | 0.00618089 | − | 0.000305812i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.1195 | −0.548714 | −0.274357 | − | 0.961628i | \(-0.588465\pi\) | ||||
−0.274357 | + | 0.961628i | \(0.588465\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.0132 | 0.578465 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.75042 | + | 3.41072i | −0.0594475 | + | 0.115834i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 71.3549 | + | 12.5818i | 2.42055 | + | 0.426808i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.2926 | − | 28.9508i | −0.823125 | − | 0.980962i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 46.0118 | + | 11.7582i | 1.55727 | + | 0.397954i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.120730 | + | 0.684695i | 0.00408142 | + | 0.0231469i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.9396 | − | 19.2684i | 1.78764 | − | 0.650649i | 0.788266 | − | 0.615334i | \(-0.210979\pi\) |
0.999376 | − | 0.0353144i | \(-0.0112432\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −53.0104 | − | 6.66621i | −1.78800 | − | 0.224846i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.5381 | + | 11.8577i | 0.691946 | + | 0.399495i | 0.804341 | − | 0.594168i | \(-0.202519\pi\) |
−0.112394 | + | 0.993664i | \(0.535852\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.3285 | + | 6.54053i | −0.381235 | + | 0.220106i | −0.678356 | − | 0.734734i | \(-0.737307\pi\) |
0.297120 | + | 0.954840i | \(0.403974\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.8901 | − | 4.07521i | 0.601370 | − | 0.136987i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.2454 | − | 21.1834i | −0.847659 | − | 0.711270i | 0.111614 | − | 0.993752i | \(-0.464398\pi\) |
−0.959273 | + | 0.282482i | \(0.908842\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.341680 | + | 0.124361i | 0.0114596 | + | 0.00417094i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.8125 | − | 36.0026i | 0.965257 | − | 1.20613i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.9123 | − | 29.9814i | 0.365168 | − | 1.00329i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.43321 | − | 10.0503i | 0.281891 | − | 0.335945i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.94052 | − | 39.2488i | −0.298515 | − | 1.31048i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.74030 | + | 13.4066i | 0.258154 | + | 0.447135i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.9560 | − | 39.7610i | 0.764776 | − | 1.32463i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.00205000 | − | 0.0163018i | 6.82198e−5 | − | 0.000542491i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.53040 | − | 20.6896i | −0.250319 | − | 0.687746i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.1995 | + | 6.73561i | −1.26839 | + | 0.223652i | −0.767045 | − | 0.641593i | \(-0.778274\pi\) |
−0.501349 | + | 0.865245i | \(0.667163\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −24.3093 | + | 6.81704i | −0.806290 | + | 0.226107i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.4658 | + | 18.0119i | −0.711192 | + | 0.596761i | −0.924933 | − | 0.380129i | \(-0.875880\pi\) |
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.57493 | + | 20.2744i | −0.118313 | + | 0.670986i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.8636 | − | 5.57537i | −0.359141 | − | 0.184316i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 0.184546i | − | 0.00609425i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.63307i | 0.0538701i | 0.999637 | + | 0.0269351i | \(0.00857473\pi\) | ||||
−0.999637 | + | 0.0269351i | \(0.991425\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.72154 | − | 55.0061i | −0.0896776 | − | 1.81251i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.83231 | − | 38.7480i | 0.224888 | − | 1.27540i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.70535 | − | 5.62645i | 0.220470 | − | 0.184997i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.57759 | + | 2.30963i | −0.0518148 | + | 0.0758581i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.8733 | + | 2.44623i | −0.455167 | + | 0.0802582i | −0.396531 | − | 0.918021i | \(-0.629786\pi\) |
−0.0586356 | + | 0.998279i | \(0.518675\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.7212 | − | 37.6988i | −0.449695 | − | 1.23553i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.9096 | − | 15.0944i | −0.651812 | − | 0.494169i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.2104 | − | 21.1490i | 0.399322 | − | 0.691645i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.05418 | + | 15.6823i | 0.295787 | + | 0.512318i | 0.975168 | − | 0.221468i | \(-0.0710847\pi\) |
−0.679381 | + | 0.733786i | \(0.737751\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.75660 | + | 3.48261i | −0.122592 | + | 0.113651i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.18751 | − | 6.18223i | 0.169108 | − | 0.201535i | −0.674834 | − | 0.737970i | \(-0.735785\pi\) |
0.843942 | + | 0.536435i | \(0.180229\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.03136 | − | 5.58111i | 0.0661501 | − | 0.181746i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.255037 | + | 0.320653i | 0.00829635 | + | 0.0104309i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.27726 | − | 1.19283i | −0.106497 | − | 0.0387617i | 0.288222 | − | 0.957564i | \(-0.406936\pi\) |
−0.394719 | + | 0.918802i | \(0.629158\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.0211 | − | 20.1561i | −0.779758 | − | 0.654295i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.8814 | − | 38.4600i | 0.385282 | − | 1.24715i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.9114 | + | 25.9296i | −1.45482 | + | 0.839942i | −0.998749 | − | 0.0500006i | \(-0.984078\pi\) |
−0.456073 | + | 0.889942i | \(0.650744\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.6165 | − | 13.6350i | −0.764210 | − | 0.441217i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.1244 | − | 31.1721i | −0.424251 | − | 1.00765i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.686431 | + | 0.249841i | −0.0221660 | + | 0.00806777i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.51819 | + | 14.2813i | 0.0812318 | + | 0.460688i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.9659 | + | 30.8807i | −0.450044 | + | 0.995116i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.3835 | + | 12.3745i | 0.334256 | + | 0.398350i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −51.8699 | − | 9.14607i | −1.66802 | − | 0.294118i | −0.741669 | − | 0.670766i | \(-0.765965\pi\) |
−0.926356 | + | 0.376649i | \(0.877076\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 23.6091 | + | 36.5886i | 0.758434 | + | 1.17539i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.1045 | 1.03028 | 0.515142 | − | 0.857105i | \(-0.327739\pi\) | ||||
0.515142 | + | 0.857105i | \(0.327739\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.245652 | −0.00787525 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20.2826 | + | 31.4333i | 0.649564 | + | 1.00667i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.4436 | − | 4.13374i | −0.750028 | − | 0.132250i | −0.214449 | − | 0.976735i | \(-0.568796\pi\) |
−0.535579 | + | 0.844485i | \(0.679907\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 54.9693 | + | 65.5099i | 1.75683 | + | 2.09370i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.65377 | + | 21.3460i | −0.308221 | + | 0.681524i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.141641 | − | 0.803287i | −0.00451765 | − | 0.0256209i | 0.982466 | − | 0.186444i | \(-0.0596963\pi\) |
−0.986983 | + | 0.160823i | \(0.948585\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.9881 | − | 6.18318i | 0.541287 | − | 0.197012i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.271110 | + | 0.643921i | 0.00862952 | + | 0.0204962i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.465398 | − | 0.268698i | −0.0147988 | − | 0.00854410i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.2917 | − | 12.2928i | 0.676353 | − | 0.390492i | −0.122127 | − | 0.992515i | \(-0.538971\pi\) |
0.798479 | + | 0.602022i | \(0.205638\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.77465 | − | 12.2185i | 0.119785 | − | 0.387741i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −17.0159 | − | 14.2780i | −0.539440 | − | 0.452644i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.0212 | + | 10.1989i | 0.887440 | + | 0.323002i | 0.745208 | − | 0.666832i | \(-0.232350\pi\) |
0.142232 | + | 0.989833i | \(0.454572\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.36698 | − | 11.0848i | 0.138165 | − | 0.350708i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 432.2.be.c.239.4 | yes | 36 | |
4.3 | odd | 2 | 432.2.be.b.239.3 | yes | 36 | ||
27.20 | odd | 18 | 432.2.be.b.47.3 | ✓ | 36 | ||
108.47 | even | 18 | inner | 432.2.be.c.47.4 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.be.b.47.3 | ✓ | 36 | 27.20 | odd | 18 | ||
432.2.be.b.239.3 | yes | 36 | 4.3 | odd | 2 | ||
432.2.be.c.47.4 | yes | 36 | 108.47 | even | 18 | inner | |
432.2.be.c.239.4 | yes | 36 | 1.1 | even | 1 | trivial |