Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [891,2,Mod(82,891)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(891, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("891.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 891 = 3^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 891.f (of order \(5\), degree \(4\), 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: | \(7.11467082010\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{5})\) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 487.8 | ||
Character | \(\chi\) | \(=\) | 891.487 |
Dual form | 891.2.f.e.730.8 |
$q$-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 \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(650\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.25085 | − | 0.908796i | 0.884485 | − | 0.642616i | −0.0499492 | − | 0.998752i | \(-0.515906\pi\) |
0.934434 | + | 0.356136i | \(0.115906\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.120683 | − | 0.371424i | 0.0603415 | − | 0.185712i | ||||
\(5\) | 0.478964 | + | 0.347988i | 0.214199 | + | 0.155625i | 0.689712 | − | 0.724084i | \(-0.257737\pi\) |
−0.475512 | + | 0.879709i | \(0.657737\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.223095 | − | 0.686616i | 0.0843220 | − | 0.259516i | −0.900002 | − | 0.435886i | \(-0.856435\pi\) |
0.984324 | + | 0.176369i | \(0.0564353\pi\) | |||||||
\(8\) | 0.768973 | + | 2.36665i | 0.271873 | + | 0.836739i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.915362 | 0.289463 | ||||||||
\(11\) | 0.539627 | − | 3.27243i | 0.162704 | − | 0.986675i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.27417 | − | 0.925741i | 0.353392 | − | 0.256754i | −0.396899 | − | 0.917862i | \(-0.629914\pi\) |
0.750291 | + | 0.661108i | \(0.229914\pi\) | |||||||
\(14\) | −0.344935 | − | 1.06160i | −0.0921878 | − | 0.283725i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.74458 | + | 2.72060i | 0.936145 | + | 0.680149i | ||||
\(17\) | 3.71501 | + | 2.69911i | 0.901022 | + | 0.654631i | 0.938728 | − | 0.344658i | \(-0.112005\pi\) |
−0.0377065 | + | 0.999289i | \(0.512005\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.775200 | + | 2.38582i | 0.177843 | + | 0.547345i | 0.999752 | − | 0.0222743i | \(-0.00709072\pi\) |
−0.821909 | + | 0.569619i | \(0.807091\pi\) | |||||||
\(20\) | 0.187054 | − | 0.135902i | 0.0418265 | − | 0.0303887i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.29898 | − | 4.58373i | −0.490144 | − | 0.977255i | ||||
\(23\) | 4.45200 | 0.928306 | 0.464153 | − | 0.885755i | \(-0.346359\pi\) | ||||
0.464153 | + | 0.885755i | \(0.346359\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.43677 | − | 4.42194i | −0.287355 | − | 0.884387i | ||||
\(26\) | 0.752490 | − | 2.31593i | 0.147576 | − | 0.454191i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.228102 | − | 0.165726i | −0.0431072 | − | 0.0313192i | ||||
\(29\) | −2.15651 | + | 6.63706i | −0.400454 | + | 1.23247i | 0.524177 | + | 0.851609i | \(0.324373\pi\) |
−0.924632 | + | 0.380863i | \(0.875627\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.38490 | − | 5.36545i | 1.32637 | − | 0.963662i | 0.326538 | − | 0.945184i | \(-0.394118\pi\) |
0.999829 | − | 0.0184785i | \(-0.00588222\pi\) | |||||||
\(32\) | 2.17948 | 0.385282 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.09986 | 1.21762 | ||||||||
\(35\) | 0.345788 | − | 0.251230i | 0.0584489 | − | 0.0424656i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.893583 | − | 2.75017i | 0.146904 | − | 0.452125i | −0.850347 | − | 0.526223i | \(-0.823608\pi\) |
0.997251 | + | 0.0740981i | \(0.0236078\pi\) | |||||||
\(38\) | 3.13788 | + | 2.27981i | 0.509032 | + | 0.369833i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.455256 | + | 1.40114i | −0.0719824 | + | 0.221539i | ||||
\(41\) | 0.356643 | + | 1.09763i | 0.0556982 | + | 0.171421i | 0.975036 | − | 0.222049i | \(-0.0712744\pi\) |
−0.919337 | + | 0.393470i | \(0.871274\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.21448 | −0.642702 | −0.321351 | − | 0.946960i | \(-0.604137\pi\) | ||||
−0.321351 | + | 0.946960i | \(0.604137\pi\) | |||||||
\(44\) | −1.15033 | − | 0.595357i | −0.173419 | − | 0.0897534i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.56879 | − | 4.04596i | 0.821073 | − | 0.596544i | ||||
\(47\) | 0.0703185 | + | 0.216418i | 0.0102570 | + | 0.0315678i | 0.956054 | − | 0.293191i | \(-0.0947170\pi\) |
−0.945797 | + | 0.324758i | \(0.894717\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.24145 | + | 3.80814i | 0.748778 | + | 0.544019i | ||||
\(50\) | −5.81583 | − | 4.22545i | −0.822482 | − | 0.597568i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.190071 | − | 0.584979i | −0.0263581 | − | 0.0811220i | ||||
\(53\) | −4.61430 | + | 3.35249i | −0.633823 | + | 0.460500i | −0.857723 | − | 0.514113i | \(-0.828121\pi\) |
0.223899 | + | 0.974612i | \(0.428121\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.39723 | − | 1.37959i | 0.188402 | − | 0.186024i | ||||
\(56\) | 1.79654 | 0.240072 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.33426 | + | 10.2618i | 0.437810 | + | 1.34744i | ||||
\(59\) | −2.20439 | + | 6.78441i | −0.286987 | + | 0.883255i | 0.698809 | + | 0.715308i | \(0.253714\pi\) |
−0.985796 | + | 0.167947i | \(0.946286\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.68827 | − | 2.67969i | −0.472235 | − | 0.343099i | 0.326077 | − | 0.945343i | \(-0.394273\pi\) |
−0.798312 | + | 0.602244i | \(0.794273\pi\) | |||||||
\(62\) | 4.36131 | − | 13.4227i | 0.553887 | − | 1.70469i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.76295 | + | 3.46049i | −0.595369 | + | 0.432561i | ||||
\(65\) | 0.932429 | 0.115654 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.09142 | −0.988524 | −0.494262 | − | 0.869313i | \(-0.664562\pi\) | ||||
−0.494262 | + | 0.869313i | \(0.664562\pi\) | |||||||
\(68\) | 1.45085 | − | 1.05411i | 0.175942 | − | 0.127829i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.204213 | − | 0.628502i | 0.0244081 | − | 0.0751204i | ||||
\(71\) | −9.95852 | − | 7.23528i | −1.18186 | − | 0.858670i | −0.189478 | − | 0.981885i | \(-0.560680\pi\) |
−0.992380 | + | 0.123215i | \(0.960680\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.78461 | − | 14.7255i | 0.559996 | − | 1.72349i | −0.122373 | − | 0.992484i | \(-0.539050\pi\) |
0.682370 | − | 0.731007i | \(-0.260950\pi\) | |||||||
\(74\) | −1.38160 | − | 4.25213i | −0.160608 | − | 0.494300i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.979704 | 0.112380 | ||||||||
\(77\) | −2.12651 | − | 1.10058i | −0.242339 | − | 0.125423i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.8275 | − | 8.59316i | 1.33069 | − | 0.966806i | 0.330962 | − | 0.943644i | \(-0.392627\pi\) |
0.999732 | − | 0.0231619i | \(-0.00737332\pi\) | |||||||
\(80\) | 0.846785 | + | 2.60614i | 0.0946734 | + | 0.291375i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.44363 | + | 1.04886i | 0.159422 | + | 0.115827i | ||||
\(83\) | −5.62510 | − | 4.08687i | −0.617435 | − | 0.448593i | 0.234590 | − | 0.972094i | \(-0.424625\pi\) |
−0.852024 | + | 0.523502i | \(0.824625\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.840097 | + | 2.58555i | 0.0911214 | + | 0.280443i | ||||
\(86\) | −5.27169 | + | 3.83010i | −0.568461 | + | 0.413011i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.15967 | − | 1.23930i | 0.869824 | − | 0.132110i | ||||
\(89\) | −12.4803 | −1.32291 | −0.661453 | − | 0.749986i | \(-0.730060\pi\) | ||||
−0.661453 | + | 0.749986i | \(0.730060\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.351367 | − | 1.08140i | −0.0368332 | − | 0.113361i | ||||
\(92\) | 0.537280 | − | 1.65358i | 0.0560153 | − | 0.172397i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.284638 | + | 0.206802i | 0.0293582 | + | 0.0213300i | ||||
\(95\) | −0.458943 | + | 1.41248i | −0.0470866 | + | 0.144918i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.4722 | + | 8.33507i | −1.16483 | + | 0.846298i | −0.990381 | − | 0.138368i | \(-0.955814\pi\) |
−0.174449 | + | 0.984666i | \(0.555814\pi\) | |||||||
\(98\) | 10.0171 | 1.01188 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.81581 | −0.181581 | ||||||||
\(101\) | −11.6244 | + | 8.44561i | −1.15667 | + | 0.840370i | −0.989353 | − | 0.145533i | \(-0.953510\pi\) |
−0.167317 | + | 0.985903i | \(0.553510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.36859 | + | 4.21209i | −0.134851 | + | 0.415029i | −0.995567 | − | 0.0940566i | \(-0.970017\pi\) |
0.860716 | + | 0.509086i | \(0.170017\pi\) | |||||||
\(104\) | 3.17071 | + | 2.30366i | 0.310914 | + | 0.225892i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.72508 | + | 8.38693i | −0.264683 | + | 0.814610i | ||||
\(107\) | 4.86529 | + | 14.9738i | 0.470345 | + | 1.44757i | 0.852134 | + | 0.523324i | \(0.175308\pi\) |
−0.381788 | + | 0.924250i | \(0.624692\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.6970 | −1.31194 | −0.655969 | − | 0.754788i | \(-0.727740\pi\) | ||||
−0.655969 | + | 0.754788i | \(0.727740\pi\) | |||||||
\(110\) | 0.493954 | − | 2.99546i | 0.0470967 | − | 0.285606i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.70340 | − | 1.96414i | 0.255447 | − | 0.185593i | ||||
\(113\) | −2.48145 | − | 7.63711i | −0.233435 | − | 0.718439i | −0.997325 | − | 0.0730926i | \(-0.976713\pi\) |
0.763890 | − | 0.645346i | \(-0.223287\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.13235 | + | 1.54924i | 0.198842 | + | 0.144467i | ||||
\(116\) | 2.20491 | + | 1.60196i | 0.204721 | + | 0.148738i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.40829 | + | 10.4896i | 0.313758 | + | 0.965648i | ||||
\(119\) | 2.68205 | − | 1.94862i | 0.245863 | − | 0.178630i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4176 | − | 3.53178i | −0.947055 | − | 0.321071i | ||||
\(122\) | −7.04877 | −0.638166 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.10162 | − | 3.39045i | −0.0989286 | − | 0.304471i | ||||
\(125\) | 1.76536 | − | 5.43321i | 0.157898 | − | 0.485961i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.70522 | + | 7.05126i | 0.861199 | + | 0.625698i | 0.928211 | − | 0.372054i | \(-0.121347\pi\) |
−0.0670118 | + | 0.997752i | \(0.521347\pi\) | |||||||
\(128\) | −4.15986 | + | 12.8027i | −0.367683 | + | 1.13161i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.16633 | − | 0.847388i | 0.102294 | − | 0.0743209i | ||||
\(131\) | 6.89109 | 0.602077 | 0.301039 | − | 0.953612i | \(-0.402667\pi\) | ||||
0.301039 | + | 0.953612i | \(0.402667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.81109 | 0.157041 | ||||||||
\(134\) | −10.1212 | + | 7.35345i | −0.874335 | + | 0.635242i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.53112 | + | 10.8677i | −0.302791 | + | 0.931896i | ||||
\(137\) | 7.48062 | + | 5.43499i | 0.639112 | + | 0.464342i | 0.859545 | − | 0.511060i | \(-0.170747\pi\) |
−0.220433 | + | 0.975402i | \(0.570747\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.67826 | − | 20.5536i | 0.566442 | − | 1.74333i | −0.0971841 | − | 0.995266i | \(-0.530984\pi\) |
0.663627 | − | 0.748064i | \(-0.269016\pi\) | |||||||
\(140\) | −0.0515820 | − | 0.158753i | −0.00435948 | − | 0.0134171i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −19.0320 | −1.59713 | ||||||||
\(143\) | −2.34184 | − | 4.66920i | −0.195835 | − | 0.390458i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.34251 | + | 2.42847i | −0.277580 | + | 0.201674i | ||||
\(146\) | −7.39766 | − | 22.7677i | −0.612235 | − | 1.88426i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.913637 | − | 0.663796i | −0.0751005 | − | 0.0545637i | ||||
\(149\) | −0.927483 | − | 0.673856i | −0.0759824 | − | 0.0552044i | 0.549146 | − | 0.835727i | \(-0.314953\pi\) |
−0.625128 | + | 0.780522i | \(0.714953\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.272133 | + | 0.837539i | 0.0221459 | + | 0.0681579i | 0.961519 | − | 0.274740i | \(-0.0885916\pi\) |
−0.939373 | + | 0.342898i | \(0.888592\pi\) | |||||||
\(152\) | −5.05031 | + | 3.66926i | −0.409634 | + | 0.297616i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.66015 | + | 0.555908i | −0.294944 | + | 0.0447963i | ||||
\(155\) | 5.40421 | 0.434077 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.02411 | − | 9.30724i | −0.241350 | − | 0.742799i | −0.996215 | − | 0.0869191i | \(-0.972298\pi\) |
0.754865 | − | 0.655880i | \(-0.227702\pi\) | |||||||
\(158\) | 6.98497 | − | 21.4975i | 0.555694 | − | 1.71025i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.04389 | + | 0.758434i | 0.0825271 | + | 0.0599594i | ||||
\(161\) | 0.993219 | − | 3.05681i | 0.0782766 | − | 0.240911i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.74555 | + | 2.72130i | −0.293374 | + | 0.213149i | −0.724730 | − | 0.689033i | \(-0.758035\pi\) |
0.431355 | + | 0.902182i | \(0.358035\pi\) | |||||||
\(164\) | 0.450728 | 0.0351959 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.7503 | −0.834384 | ||||||||
\(167\) | −13.7431 | + | 9.98493i | −1.06347 | + | 0.772657i | −0.974727 | − | 0.223397i | \(-0.928285\pi\) |
−0.0887440 | + | 0.996054i | \(0.528285\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.25070 | + | 10.0046i | −0.250054 | + | 0.769587i | ||||
\(170\) | 3.40058 | + | 2.47066i | 0.260812 | + | 0.189491i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.508616 | + | 1.56536i | −0.0387816 | + | 0.119357i | ||||
\(173\) | 0.182646 | + | 0.562127i | 0.0138863 | + | 0.0427378i | 0.957760 | − | 0.287570i | \(-0.0928474\pi\) |
−0.943873 | + | 0.330308i | \(0.892847\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.35671 | −0.253743 | ||||||||
\(176\) | 10.9236 | − | 10.7858i | 0.823401 | − | 0.813008i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.6110 | + | 11.3420i | −1.17009 | + | 0.850121i | ||||
\(179\) | 2.97921 | + | 9.16907i | 0.222677 | + | 0.685328i | 0.998519 | + | 0.0544017i | \(0.0173251\pi\) |
−0.775842 | + | 0.630927i | \(0.782675\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.85243 | + | 2.79896i | 0.286349 | + | 0.208045i | 0.721682 | − | 0.692225i | \(-0.243369\pi\) |
−0.435333 | + | 0.900270i | \(0.643369\pi\) | |||||||
\(182\) | −1.42228 | − | 1.03334i | −0.105426 | − | 0.0765965i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.42347 | + | 10.5363i | 0.252381 | + | 0.776750i | ||||
\(185\) | 1.38502 | − | 1.00627i | 0.101829 | − | 0.0739828i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.8374 | − | 10.7006i | 0.792507 | − | 0.782505i | ||||
\(188\) | 0.0888691 | 0.00648144 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.709589 | + | 2.18389i | 0.0514790 | + | 0.158436i | ||||
\(191\) | 1.60628 | − | 4.94362i | 0.116226 | − | 0.357707i | −0.875975 | − | 0.482357i | \(-0.839781\pi\) |
0.992201 | + | 0.124650i | \(0.0397807\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.64390 | − | 1.92091i | −0.190312 | − | 0.138270i | 0.488549 | − | 0.872536i | \(-0.337526\pi\) |
−0.678861 | + | 0.734266i | \(0.737526\pi\) | |||||||
\(194\) | −6.77518 | + | 20.8519i | −0.486430 | + | 1.49708i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.04699 | − | 1.48722i | 0.146213 | − | 0.106230i | ||||
\(197\) | 22.4626 | 1.60039 | 0.800197 | − | 0.599737i | \(-0.204728\pi\) | ||||
0.800197 | + | 0.599737i | \(0.204728\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.8291 | −1.47654 | −0.738269 | − | 0.674507i | \(-0.764356\pi\) | ||||
−0.738269 | + | 0.674507i | \(0.764356\pi\) | |||||||
\(200\) | 9.36035 | − | 6.80070i | 0.661877 | − | 0.480882i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.86504 | + | 21.1284i | −0.483022 | + | 1.48659i | ||||
\(203\) | 4.07600 | + | 2.96139i | 0.286079 | + | 0.207849i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.211144 | + | 0.649834i | −0.0147469 | + | 0.0453864i | ||||
\(206\) | 2.11603 | + | 6.51246i | 0.147431 | + | 0.453745i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.28981 | 0.505457 | ||||||||
\(209\) | 8.22575 | − | 1.24934i | 0.568987 | − | 0.0864183i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.74420 | + | 1.99378i | −0.188919 | + | 0.137258i | −0.678224 | − | 0.734855i | \(-0.737250\pi\) |
0.489306 | + | 0.872112i | \(0.337250\pi\) | |||||||
\(212\) | 0.688326 | + | 2.11845i | 0.0472744 | + | 0.145496i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 19.6939 | + | 14.3085i | 1.34625 | + | 0.978106i | ||||
\(215\) | −2.01858 | − | 1.46659i | −0.137666 | − | 0.100020i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.03646 | − | 6.26759i | −0.138244 | − | 0.425472i | ||||
\(218\) | −17.1329 | + | 12.4478i | −1.16039 | + | 0.843072i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.343792 | − | 0.685457i | −0.0231785 | − | 0.0462135i | ||||
\(221\) | 7.23224 | 0.486493 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.40734 | − | 10.4867i | −0.228172 | − | 0.702243i | −0.997954 | − | 0.0639353i | \(-0.979635\pi\) |
0.769782 | − | 0.638307i | \(-0.220365\pi\) | |||||||
\(224\) | 0.486232 | − | 1.49647i | 0.0324877 | − | 0.0999870i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.0445 | − | 7.29775i | −0.668150 | − | 0.485439i | ||||
\(227\) | 1.84387 | − | 5.67485i | 0.122382 | − | 0.376653i | −0.871033 | − | 0.491224i | \(-0.836549\pi\) |
0.993415 | + | 0.114571i | \(0.0365495\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.0237 | + | 14.5481i | −1.32320 | + | 0.961364i | −0.323318 | + | 0.946290i | \(0.604798\pi\) |
−0.999886 | + | 0.0150739i | \(0.995202\pi\) | |||||||
\(230\) | 4.07519 | 0.268710 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −17.3659 | −1.14013 | ||||||||
\(233\) | 3.38850 | − | 2.46189i | 0.221988 | − | 0.161284i | −0.471233 | − | 0.882009i | \(-0.656191\pi\) |
0.693221 | + | 0.720725i | \(0.256191\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.0416308 | + | 0.128126i | −0.00271569 | + | 0.00835805i | ||||
\(236\) | 2.25386 | + | 1.63753i | 0.146714 | + | 0.106594i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.58394 | − | 4.87488i | 0.102672 | − | 0.315991i | ||||
\(239\) | 2.27833 | + | 7.01199i | 0.147373 | + | 0.453568i | 0.997309 | − | 0.0733190i | \(-0.0233591\pi\) |
−0.849935 | + | 0.526887i | \(0.823359\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.82924 | −0.568741 | −0.284371 | − | 0.958714i | \(-0.591785\pi\) | ||||
−0.284371 | + | 0.958714i | \(0.591785\pi\) | |||||||
\(242\) | −16.2405 | + | 5.04975i | −1.04398 | + | 0.324610i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.44041 | + | 1.04652i | −0.0922129 | + | 0.0669966i | ||||
\(245\) | 1.18528 | + | 3.64792i | 0.0757248 | + | 0.233057i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.19639 | + | 2.32231i | 0.203381 | + | 0.147765i | ||||
\(248\) | 18.3769 | + | 13.3516i | 1.16694 | + | 0.847829i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.72948 | − | 8.40048i | −0.172628 | − | 0.531293i | ||||
\(251\) | 16.6439 | − | 12.0925i | 1.05056 | − | 0.763274i | 0.0782385 | − | 0.996935i | \(-0.475070\pi\) |
0.972318 | + | 0.233661i | \(0.0750704\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.40242 | − | 14.5689i | 0.151039 | − | 0.915936i | ||||
\(254\) | 18.5479 | 1.16380 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.79314 | + | 8.59640i | 0.174571 | + | 0.537275i | ||||
\(257\) | 1.04521 | − | 3.21684i | 0.0651987 | − | 0.200661i | −0.913150 | − | 0.407623i | \(-0.866358\pi\) |
0.978349 | + | 0.206962i | \(0.0663577\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.68895 | − | 1.22710i | −0.104946 | − | 0.0762481i | ||||
\(260\) | 0.112528 | − | 0.346326i | 0.00697871 | − | 0.0214783i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.61973 | − | 6.26260i | 0.532528 | − | 0.386905i | ||||
\(263\) | 14.2822 | 0.880681 | 0.440341 | − | 0.897831i | \(-0.354858\pi\) | ||||
0.440341 | + | 0.897831i | \(0.354858\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.37671 | −0.207430 | ||||||||
\(266\) | 2.26540 | − | 1.64591i | 0.138900 | − | 0.100917i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.976496 | + | 3.00535i | −0.0596490 | + | 0.183581i | ||||
\(269\) | 5.43693 | + | 3.95016i | 0.331495 | + | 0.240845i | 0.741065 | − | 0.671433i | \(-0.234321\pi\) |
−0.409570 | + | 0.912279i | \(0.634321\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.23000 | + | 3.78554i | −0.0747170 | + | 0.229955i | −0.981439 | − | 0.191773i | \(-0.938576\pi\) |
0.906722 | + | 0.421728i | \(0.138576\pi\) | |||||||
\(272\) | 6.56795 | + | 20.2141i | 0.398241 | + | 1.22566i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.2964 | 0.863679 | ||||||||
\(275\) | −15.2458 | + | 2.31555i | −0.919356 | + | 0.139633i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.6240 | − | 7.71880i | 0.638335 | − | 0.463778i | −0.220943 | − | 0.975287i | \(-0.570913\pi\) |
0.859278 | + | 0.511509i | \(0.170913\pi\) | |||||||
\(278\) | −10.3255 | − | 31.7786i | −0.619282 | − | 1.90595i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.860476 | + | 0.625172i | 0.0514233 | + | 0.0373612i | ||||
\(281\) | −2.40106 | − | 1.74447i | −0.143235 | − | 0.104066i | 0.513860 | − | 0.857874i | \(-0.328215\pi\) |
−0.657095 | + | 0.753808i | \(0.728215\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.50081 | + | 7.69669i | 0.148657 | + | 0.457521i | 0.997463 | − | 0.0711843i | \(-0.0226778\pi\) |
−0.848806 | + | 0.528705i | \(0.822678\pi\) | |||||||
\(284\) | −3.88918 | + | 2.82565i | −0.230780 | + | 0.167672i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.17265 | − | 3.71221i | −0.424128 | − | 0.219508i | ||||
\(287\) | 0.833217 | 0.0491833 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.26279 | + | 3.88648i | 0.0742820 | + | 0.228616i | ||||
\(290\) | −1.97399 | + | 6.07532i | −0.115917 | + | 0.356755i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.89199 | − | 3.55424i | −0.286282 | − | 0.207996i | ||||
\(293\) | 4.85638 | − | 14.9464i | 0.283713 | − | 0.873178i | −0.703069 | − | 0.711122i | \(-0.748187\pi\) |
0.986782 | − | 0.162056i | \(-0.0518126\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.41671 | + | 2.48239i | −0.198929 | + | 0.144530i | ||||
\(296\) | 7.19584 | 0.418249 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.77254 | −0.102681 | ||||||||
\(299\) | 5.67262 | − | 4.12140i | 0.328056 | − | 0.238347i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.940229 | + | 2.89373i | −0.0541939 | + | 0.166792i | ||||
\(302\) | 1.10155 | + | 0.800323i | 0.0633871 | + | 0.0460534i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.58806 | + | 11.0429i | −0.205789 | + | 0.633354i | ||||
\(305\) | −0.834052 | − | 2.56695i | −0.0477577 | − | 0.146983i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.51315 | −0.200506 | −0.100253 | − | 0.994962i | \(-0.531965\pi\) | ||||
−0.100253 | + | 0.994962i | \(0.531965\pi\) | |||||||
\(308\) | −0.665415 | + | 0.657017i | −0.0379156 | + | 0.0374370i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.75986 | − | 4.91133i | 0.383934 | − | 0.278945i | ||||
\(311\) | −8.13778 | − | 25.0455i | −0.461451 | − | 1.42020i | −0.863391 | − | 0.504535i | \(-0.831664\pi\) |
0.401940 | − | 0.915666i | \(-0.368336\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.99111 | + | 1.44662i | 0.112544 | + | 0.0817679i | 0.642634 | − | 0.766174i | \(-0.277842\pi\) |
−0.530090 | + | 0.847942i | \(0.677842\pi\) | |||||||
\(314\) | −12.2411 | − | 8.89367i | −0.690805 | − | 0.501899i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.76433 | − | 5.43005i | −0.0992513 | − | 0.305464i | ||||
\(317\) | −21.4447 | + | 15.5805i | −1.20446 | + | 0.875089i | −0.994716 | − | 0.102669i | \(-0.967262\pi\) |
−0.209740 | + | 0.977757i | \(0.567262\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.5556 | + | 10.6386i | 1.15089 | + | 0.595646i | ||||
\(320\) | −3.48549 | −0.194845 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.53565 | − | 4.72625i | −0.0855785 | − | 0.263384i | ||||
\(323\) | −3.55972 | + | 10.9557i | −0.198068 | + | 0.609591i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.92427 | − | 4.30423i | −0.328619 | − | 0.238756i | ||||
\(326\) | −2.21202 | + | 6.80789i | −0.122512 | + | 0.377054i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.32347 | + | 1.68810i | −0.128292 | + | 0.0932097i | ||||
\(329\) | 0.164284 | 0.00905726 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.10397 | 0.445434 | 0.222717 | − | 0.974883i | \(-0.428507\pi\) | ||||
0.222717 | + | 0.974883i | \(0.428507\pi\) | |||||||
\(332\) | −2.19681 | + | 1.59608i | −0.120566 | + | 0.0875962i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.11627 | + | 24.9793i | −0.444103 | + | 1.36681i | ||||
\(335\) | −3.87550 | − | 2.81571i | −0.211741 | − | 0.153839i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.63910 | − | 23.5107i | 0.416128 | − | 1.28071i | −0.495110 | − | 0.868830i | \(-0.664872\pi\) |
0.911238 | − | 0.411880i | \(-0.135128\pi\) | |||||||
\(338\) | 5.02603 | + | 15.4685i | 0.273380 | + | 0.841376i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.06172 | 0.0575799 | ||||||||
\(341\) | −13.5730 | − | 27.0619i | −0.735017 | − | 1.46549i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.87256 | − | 5.71975i | 0.425078 | − | 0.308837i | ||||
\(344\) | −3.24082 | − | 9.97422i | −0.174733 | − | 0.537774i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.739322 | + | 0.537149i | 0.0397462 | + | 0.0288773i | ||||
\(347\) | −1.67438 | − | 1.21651i | −0.0898853 | − | 0.0653055i | 0.541935 | − | 0.840420i | \(-0.317692\pi\) |
−0.631820 | + | 0.775115i | \(0.717692\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.61130 | − | 4.95906i | −0.0862507 | − | 0.265452i | 0.898624 | − | 0.438719i | \(-0.144568\pi\) |
−0.984875 | + | 0.173267i | \(0.944568\pi\) | |||||||
\(350\) | −4.19874 | + | 3.05056i | −0.224432 | + | 0.163059i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.17611 | − | 7.13221i | 0.0626868 | − | 0.380148i | ||||
\(353\) | −21.6725 | −1.15351 | −0.576756 | − | 0.816917i | \(-0.695681\pi\) | ||||
−0.576756 | + | 0.816917i | \(0.695681\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.25198 | − | 6.93088i | −0.119523 | − | 0.367853i | ||||
\(356\) | −1.50616 | + | 4.63547i | −0.0798261 | + | 0.245680i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0594 | + | 8.76164i | 0.637357 | + | 0.463067i | ||||
\(359\) | −2.70478 | + | 8.32446i | −0.142753 | + | 0.439348i | −0.996715 | − | 0.0809868i | \(-0.974193\pi\) |
0.853962 | + | 0.520335i | \(0.174193\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.2801 | − | 7.46894i | 0.541059 | − | 0.393102i | ||||
\(362\) | 7.36250 | 0.386964 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.444060 | −0.0232751 | ||||||||
\(365\) | 7.41595 | − | 5.38801i | 0.388169 | − | 0.282021i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.09088 | + | 6.43506i | −0.109143 | + | 0.335908i | −0.990680 | − | 0.136206i | \(-0.956509\pi\) |
0.881537 | + | 0.472114i | \(0.156509\pi\) | |||||||
\(368\) | 16.6709 | + | 12.1121i | 0.869029 | + | 0.631387i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.817952 | − | 2.51740i | 0.0425233 | − | 0.130873i | ||||
\(371\) | 1.27244 | + | 3.91618i | 0.0660620 | + | 0.203318i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.8933 | −1.13359 | −0.566797 | − | 0.823857i | \(-0.691818\pi\) | ||||
−0.566797 | + | 0.823857i | \(0.691818\pi\) | |||||||
\(374\) | 3.83128 | − | 23.2338i | 0.198111 | − | 1.20139i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.458114 | + | 0.332839i | −0.0236254 | + | 0.0171649i | ||||
\(377\) | 3.39643 | + | 10.4531i | 0.174925 | + | 0.538364i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.3639 | + | 19.8810i | 1.40559 | + | 1.02122i | 0.993946 | + | 0.109873i | \(0.0350445\pi\) |
0.411642 | + | 0.911346i | \(0.364955\pi\) | |||||||
\(380\) | 0.469243 | + | 0.340925i | 0.0240716 | + | 0.0174891i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.48353 | − | 7.64350i | −0.127068 | − | 0.391076i | ||||
\(383\) | −14.8648 | + | 10.7999i | −0.759555 | + | 0.551849i | −0.898774 | − | 0.438413i | \(-0.855541\pi\) |
0.139219 | + | 0.990262i | \(0.455541\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.635536 | − | 1.26714i | −0.0323899 | − | 0.0645794i | ||||
\(386\) | −5.05284 | −0.257183 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.71134 | + | 5.26696i | 0.0868801 | + | 0.267390i | ||||
\(389\) | 9.51975 | − | 29.2988i | 0.482670 | − | 1.48551i | −0.352657 | − | 0.935753i | \(-0.614722\pi\) |
0.835327 | − | 0.549754i | \(-0.185278\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.5392 | + | 12.0164i | 0.836424 | + | 0.607698i | ||||
\(392\) | −4.98201 | + | 15.3331i | −0.251630 | + | 0.774436i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 28.0974 | − | 20.4139i | 1.41552 | − | 1.02844i | ||||
\(395\) | 8.65524 | 0.435493 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.29578 | −0.416353 | −0.208177 | − | 0.978091i | \(-0.566753\pi\) | ||||
−0.208177 | + | 0.978091i | \(0.566753\pi\) | |||||||
\(398\) | −26.0541 | + | 18.9294i | −1.30598 | + | 0.948847i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.65019 | − | 20.4672i | 0.332509 | − | 1.02336i | ||||
\(401\) | −3.18237 | − | 2.31212i | −0.158920 | − | 0.115462i | 0.505483 | − | 0.862836i | \(-0.331314\pi\) |
−0.664403 | + | 0.747374i | \(0.731314\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.44263 | − | 13.6730i | 0.221303 | − | 0.681101i | ||||
\(404\) | 1.73404 | + | 5.33682i | 0.0862716 | + | 0.265517i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.78977 | 0.386600 | ||||||||
\(407\) | −8.51753 | − | 4.40825i | −0.422198 | − | 0.218509i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.02598 | − | 1.47196i | 0.100178 | − | 0.0727839i | −0.536568 | − | 0.843857i | \(-0.680280\pi\) |
0.636747 | + | 0.771073i | \(0.280280\pi\) | |||||||
\(410\) | 0.326457 | + | 1.00473i | 0.0161226 | + | 0.0496202i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.39930 | + | 1.01665i | 0.0689388 | + | 0.0500870i | ||||
\(413\) | 4.16650 | + | 3.02714i | 0.205020 | + | 0.148956i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.27204 | − | 3.91493i | −0.0624419 | − | 0.192176i | ||||
\(416\) | 2.77704 | − | 2.01764i | 0.136156 | − | 0.0989228i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.15380 | − | 9.03826i | 0.447727 | − | 0.442076i | ||||
\(419\) | −10.7394 | −0.524654 | −0.262327 | − | 0.964979i | \(-0.584490\pi\) | ||||
−0.262327 | + | 0.964979i | \(0.584490\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.85630 | + | 21.1015i | 0.334156 | + | 1.02843i | 0.967136 | + | 0.254258i | \(0.0818311\pi\) |
−0.632981 | + | 0.774167i | \(0.718169\pi\) | |||||||
\(422\) | −1.62065 | + | 4.98785i | −0.0788920 | + | 0.242805i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.4825 | − | 8.34249i | −0.557637 | − | 0.405147i | ||||
\(425\) | 6.59767 | − | 20.3055i | 0.320034 | − | 0.984963i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.66275 | + | 1.93460i | −0.128860 | + | 0.0936219i | ||||
\(428\) | 6.14879 | 0.297213 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.85778 | −0.186038 | ||||||||
\(431\) | −14.9330 | + | 10.8495i | −0.719297 | + | 0.522600i | −0.886160 | − | 0.463380i | \(-0.846636\pi\) |
0.166862 | + | 0.985980i | \(0.446636\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.67130 | − | 14.3768i | 0.224488 | − | 0.690904i | −0.773855 | − | 0.633363i | \(-0.781674\pi\) |
0.998343 | − | 0.0575408i | \(-0.0183259\pi\) | |||||||
\(434\) | −8.24328 | − | 5.98909i | −0.395690 | − | 0.287486i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.65300 | + | 5.08740i | −0.0791642 | + | 0.243642i | ||||
\(437\) | 3.45119 | + | 10.6217i | 0.165093 | + | 0.508103i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.9553 | 1.14333 | 0.571663 | − | 0.820488i | \(-0.306298\pi\) | ||||
0.571663 | + | 0.820488i | \(0.306298\pi\) | |||||||
\(440\) | 4.33945 | + | 2.24589i | 0.206875 | + | 0.107068i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.04645 | − | 6.57263i | 0.430296 | − | 0.312628i | ||||
\(443\) | −7.87922 | − | 24.2498i | −0.374353 | − | 1.15214i | −0.943914 | − | 0.330192i | \(-0.892887\pi\) |
0.569561 | − | 0.821949i | \(-0.307113\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.97760 | − | 4.34298i | −0.283366 | − | 0.205877i | ||||
\(446\) | −13.7924 | − | 10.0207i | −0.653088 | − | 0.474496i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.31343 | + | 4.04234i | 0.0620539 | + | 0.190982i | ||||
\(449\) | −18.1886 | + | 13.2148i | −0.858375 | + | 0.623646i | −0.927442 | − | 0.373966i | \(-0.877998\pi\) |
0.0690672 | + | 0.997612i | \(0.477998\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.78438 | − | 0.574776i | 0.178200 | − | 0.0270651i | ||||
\(452\) | −3.13607 | −0.147508 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.85087 | − | 8.77409i | −0.133798 | − | 0.411788i | ||||
\(455\) | 0.208020 | − | 0.640221i | 0.00975214 | − | 0.0300140i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.5472 | − | 12.7488i | −0.820825 | − | 0.596364i | 0.0961237 | − | 0.995369i | \(-0.469356\pi\) |
−0.916949 | + | 0.399005i | \(0.869356\pi\) | |||||||
\(458\) | −11.8254 | + | 36.3950i | −0.552566 | + | 1.70062i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.832763 | − | 0.605037i | 0.0388278 | − | 0.0282100i | ||||
\(461\) | 12.1036 | 0.563722 | 0.281861 | − | 0.959455i | \(-0.409048\pi\) | ||||
0.281861 | + | 0.959455i | \(0.409048\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.0308 | 0.930910 | 0.465455 | − | 0.885071i | \(-0.345891\pi\) | ||||
0.465455 | + | 0.885071i | \(0.345891\pi\) | |||||||
\(464\) | −26.1320 | + | 18.9860i | −1.21315 | + | 0.881404i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.00115 | − | 6.15891i | 0.0927015 | − | 0.285306i | ||||
\(467\) | 4.90871 | + | 3.56639i | 0.227148 | + | 0.165033i | 0.695538 | − | 0.718489i | \(-0.255166\pi\) |
−0.468390 | + | 0.883522i | \(0.655166\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.80516 | + | 5.55570i | −0.0833543 | + | 0.256538i | ||||
\(470\) | 0.0643669 | + | 0.198101i | 0.00296902 | + | 0.00913772i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −17.7515 | −0.817078 | ||||||||
\(473\) | −2.27425 | + | 13.7916i | −0.104570 | + | 0.634138i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.43616 | − | 6.85577i | 0.432961 | − | 0.314564i | ||||
\(476\) | −0.400088 | − | 1.23134i | −0.0183380 | − | 0.0564385i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.22233 | + | 6.70041i | 0.421819 | + | 0.306470i | ||||
\(479\) | 29.3453 | + | 21.3206i | 1.34082 | + | 0.974164i | 0.999413 | + | 0.0342489i | \(0.0109039\pi\) |
0.341408 | + | 0.939915i | \(0.389096\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.40736 | − | 4.33141i | −0.0641702 | − | 0.197496i | ||||
\(482\) | −11.0441 | + | 8.02398i | −0.503043 | + | 0.365482i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.56902 | + | 3.44312i | −0.116773 | + | 0.156505i | ||||
\(485\) | −8.39529 | −0.381211 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.68379 | − | 8.25986i | −0.121614 | − | 0.374290i | 0.871655 | − | 0.490120i | \(-0.163047\pi\) |
−0.993269 | + | 0.115830i | \(0.963047\pi\) | |||||||
\(488\) | 3.50571 | − | 10.7895i | 0.158696 | − | 0.488417i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.79782 | + | 3.48582i | 0.216744 | + | 0.157473i | ||||
\(491\) | 10.2585 | − | 31.5725i | 0.462961 | − | 1.42485i | −0.398567 | − | 0.917139i | \(-0.630492\pi\) |
0.861529 | − | 0.507709i | \(-0.169508\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.9256 | + | 18.8361i | −1.16763 | + | 0.848334i | ||||
\(494\) | 6.10872 | 0.274844 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 42.2506 | 1.89711 | ||||||||
\(497\) | −7.18956 | + | 5.22352i | −0.322496 | + | 0.234307i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.45131 | − | 19.8551i | 0.288800 | − | 0.888837i | −0.696433 | − | 0.717622i | \(-0.745231\pi\) |
0.985234 | − | 0.171215i | \(-0.0547692\pi\) | |||||||
\(500\) | −1.80497 | − | 1.31139i | −0.0807209 | − | 0.0586472i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.82944 | − | 30.2519i | 0.438710 | − | 1.35021i | ||||
\(503\) | −7.20593 | − | 22.1776i | −0.321297 | − | 0.988850i | −0.973085 | − | 0.230448i | \(-0.925981\pi\) |
0.651788 | − | 0.758401i | \(-0.274019\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.50663 | −0.378540 | ||||||||
\(506\) | −10.2351 | − | 20.4068i | −0.455004 | − | 0.907192i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.79026 | − | 2.75378i | 0.168166 | − | 0.122179i | ||||
\(509\) | −2.00280 | − | 6.16400i | −0.0887728 | − | 0.273214i | 0.896808 | − | 0.442420i | \(-0.145880\pi\) |
−0.985581 | + | 0.169205i | \(0.945880\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.04335 | − | 6.57038i | −0.400054 | − | 0.290656i | ||||
\(512\) | −10.4751 | − | 7.61063i | −0.462940 | − | 0.336346i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.61605 | − | 4.97368i | −0.0712807 | − | 0.219379i | ||||
\(515\) | −2.12126 | + | 1.54119i | −0.0934739 | + | 0.0679128i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.746159 | − | 0.113327i | 0.0328160 | − | 0.00498413i | ||||
\(518\) | −3.22781 | −0.141822 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.717013 | + | 2.20674i | 0.0314431 | + | 0.0967719i | ||||
\(521\) | 10.2625 | − | 31.5848i | 0.449610 | − | 1.38376i | −0.427738 | − | 0.903903i | \(-0.640689\pi\) |
0.877348 | − | 0.479855i | \(-0.159311\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.4728 | + | 23.5929i | 1.41994 | + | 1.03164i | 0.991782 | + | 0.127938i | \(0.0408359\pi\) |
0.428154 | + | 0.903706i | \(0.359164\pi\) | |||||||
\(524\) | 0.831637 | − | 2.55952i | 0.0363302 | − | 0.111813i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.8650 | − | 12.9797i | 0.778949 | − | 0.565940i | ||||
\(527\) | 41.9169 | 1.82593 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.17970 | −0.138248 | ||||||||
\(530\) | −4.22376 | + | 3.06874i | −0.183468 | + | 0.133298i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.218567 | − | 0.672680i | 0.00947608 | − | 0.0291644i | ||||
\(533\) | 1.47055 | + | 1.06842i | 0.0636965 | + | 0.0462782i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.88041 | + | 8.86498i | −0.124531 | + | 0.383267i | ||||
\(536\) | −6.22208 | − | 19.1496i | −0.268753 | − | 0.827137i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.3907 | 0.447974 | ||||||||
\(539\) | 15.2903 | − | 15.0973i | 0.658599 | − | 0.650287i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.9410 | + | 14.4880i | −0.857332 | + | 0.622888i | −0.927158 | − | 0.374671i | \(-0.877756\pi\) |
0.0698260 | + | 0.997559i | \(0.477756\pi\) | |||||||
\(542\) | 1.90174 | + | 5.85296i | 0.0816868 | + | 0.251406i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.09680 | + | 5.88267i | 0.347147 | + | 0.252217i | ||||
\(545\) | −6.56038 | − | 4.76640i | −0.281016 | − | 0.204170i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.94803 | + | 24.4615i | 0.339833 | + | 1.04590i | 0.964292 | + | 0.264841i | \(0.0853195\pi\) |
−0.624459 | + | 0.781058i | \(0.714681\pi\) | |||||||
\(548\) | 2.92147 | − | 2.12257i | 0.124799 | − | 0.0906716i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −16.9659 | + | 16.7517i | −0.723427 | + | 0.714296i | ||||
\(551\) | −17.5066 | −0.745805 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.26155 | − | 10.0380i | −0.138695 | − | 0.426860i | ||||
\(554\) | 6.27424 | − | 19.3101i | 0.266567 | − | 0.820409i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.82813 | − | 4.96093i | −0.289577 | − | 0.210390i | ||||
\(557\) | −3.60979 | + | 11.1098i | −0.152952 | + | 0.470737i | −0.997948 | − | 0.0640357i | \(-0.979603\pi\) |
0.844996 | + | 0.534773i | \(0.179603\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.36998 | + | 3.90152i | −0.227126 | + | 0.165017i | ||||
\(560\) | 1.97833 | 0.0835996 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.58873 | −0.193564 | ||||||||
\(563\) | 6.57092 | − | 4.77405i | 0.276931 | − | 0.201202i | −0.440647 | − | 0.897681i | \(-0.645251\pi\) |
0.717578 | + | 0.696478i | \(0.245251\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.46910 | − | 4.52141i | 0.0618053 | − | 0.190217i | ||||
\(566\) | 10.1229 | + | 7.35468i | 0.425495 | + | 0.309140i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.46559 | − | 29.1321i | 0.397167 | − | 1.22236i | ||||
\(569\) | 5.56435 | + | 17.1253i | 0.233270 | + | 0.717930i | 0.997346 | + | 0.0728046i | \(0.0231950\pi\) |
−0.764077 | + | 0.645126i | \(0.776805\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.60645 | −0.109076 | −0.0545382 | − | 0.998512i | \(-0.517369\pi\) | ||||
−0.0545382 | + | 0.998512i | \(0.517369\pi\) | |||||||
\(572\) | −2.01687 | + | 0.306324i | −0.0843296 | + | 0.0128081i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.04223 | − | 0.757225i | 0.0435019 | − | 0.0316059i | ||||
\(575\) | −6.39652 | − | 19.6865i | −0.266753 | − | 0.820982i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.4684 | − | 20.6835i | −1.18515 | − | 0.861064i | −0.192409 | − | 0.981315i | \(-0.561630\pi\) |
−0.992744 | + | 0.120251i | \(0.961630\pi\) | |||||||
\(578\) | 5.11158 | + | 3.71378i | 0.212614 | + | 0.154473i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.498609 | + | 1.53456i | 0.0207036 | + | 0.0637192i | ||||
\(581\) | −4.06104 | + | 2.95052i | −0.168480 | + | 0.122408i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.48078 | + | 16.9091i | 0.351238 | + | 0.700303i | ||||
\(584\) | 38.5294 | 1.59436 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.50863 | − | 23.1092i | −0.310179 | − | 0.954631i | ||||
\(587\) | −7.27809 | + | 22.3997i | −0.300399 | + | 0.924533i | 0.680955 | + | 0.732325i | \(0.261565\pi\) |
−0.981354 | + | 0.192208i | \(0.938435\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.5258 | + | 13.4598i | 0.763341 | + | 0.554600i | ||||
\(590\) | −2.01781 | + | 6.21019i | −0.0830721 | + | 0.255670i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.8282 | − | 7.86714i | 0.445036 | − | 0.323337i | ||||
\(593\) | −13.1828 | −0.541354 | −0.270677 | − | 0.962670i | \(-0.587248\pi\) | ||||
−0.270677 | + | 0.962670i | \(0.587248\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.96270 | 0.0804630 | ||||||||
\(596\) | −0.362218 | + | 0.263166i | −0.0148370 | + | 0.0107797i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.35009 | − | 10.3105i | 0.136995 | − | 0.421628i | ||||
\(599\) | 27.6817 | + | 20.1119i | 1.13104 | + | 0.821750i | 0.985846 | − | 0.167653i | \(-0.0536188\pi\) |
0.145196 | + | 0.989403i | \(0.453619\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.97030 | − | 27.6077i | 0.365906 | − | 1.12614i | −0.583505 | − | 0.812109i | \(-0.698319\pi\) |
0.949412 | − | 0.314034i | \(-0.101681\pi\) | |||||||
\(602\) | 1.45372 | + | 4.47410i | 0.0592493 | + | 0.182351i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.343924 | 0.0139941 | ||||||||
\(605\) | −3.76064 | − | 5.31680i | −0.152892 | − | 0.216158i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.55354 | − | 1.85526i | 0.103645 | − | 0.0753026i | −0.534756 | − | 0.845007i | \(-0.679596\pi\) |
0.638401 | + | 0.769704i | \(0.279596\pi\) | |||||||
\(608\) | 1.68954 | + | 5.19986i | 0.0685197 | + | 0.210882i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.37611 | − | 2.45288i | −0.136695 | − | 0.0993144i | ||||
\(611\) | 0.289945 | + | 0.210657i | 0.0117299 | + | 0.00852229i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.4884 | + | 32.2798i | 0.423620 | + | 1.30377i | 0.904309 | + | 0.426878i | \(0.140387\pi\) |
−0.480689 | + | 0.876891i | \(0.659613\pi\) | |||||||
\(614\) | −4.39443 | + | 3.19274i | −0.177345 | + | 0.128848i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.969460 | − | 5.87904i | 0.0390606 | − | 0.236873i | ||||
\(617\) | 21.6077 | 0.869895 | 0.434948 | − | 0.900456i | \(-0.356767\pi\) | ||||
0.434948 | + | 0.900456i | \(0.356767\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.33874 | + | 19.5086i | 0.254775 | + | 0.784118i | 0.993874 | + | 0.110521i | \(0.0352519\pi\) |
−0.739098 | + | 0.673598i | \(0.764748\pi\) | |||||||
\(620\) | 0.652196 | − | 2.00725i | 0.0261928 | − | 0.0806132i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −32.9404 | − | 23.9326i | −1.32079 | − | 0.959611i | ||||
\(623\) | −2.78429 | + | 8.56915i | −0.111550 | + | 0.343316i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.0714 | + | 11.6765i | −0.642855 | + | 0.467062i | ||||
\(626\) | 3.80526 | 0.152089 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.82189 | −0.152510 | ||||||||
\(629\) | 10.7427 | − | 7.80501i | 0.428339 | − | 0.311206i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.22863 | − | 28.4028i | 0.367386 | − | 1.13070i | −0.581087 | − | 0.813841i | \(-0.697372\pi\) |
0.948473 | − | 0.316857i | \(-0.102628\pi\) | |||||||
\(632\) | 29.4320 | + | 21.3836i | 1.17074 | + | 0.850595i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.6646 | + | 38.9778i | −0.502977 | + | 1.54801i | ||||
\(635\) | 2.19470 | + | 6.75459i | 0.0870940 | + | 0.268048i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.2039 | 0.404292 | ||||||||
\(638\) | 35.3803 | − | 5.37360i | 1.40072 | − | 0.212743i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.44762 | + | 4.68447i | −0.254864 | + | 0.185170i | ||||
\(641\) | 11.7797 | + | 36.2543i | 0.465272 | + | 1.43196i | 0.858640 | + | 0.512579i | \(0.171310\pi\) |
−0.393368 | + | 0.919381i | \(0.628690\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.6118 | + | 9.88957i | 0.536798 | + | 0.390006i | 0.822894 | − | 0.568194i | \(-0.192358\pi\) |
−0.286097 | + | 0.958201i | \(0.592358\pi\) | |||||||
\(644\) | −1.01551 | − | 0.737810i | −0.0400166 | − | 0.0290738i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.50381 | + | 16.9390i | 0.216545 | + | 0.666456i | ||||
\(647\) | −16.9687 | + | 12.3285i | −0.667109 | + | 0.484683i | −0.869056 | − | 0.494713i | \(-0.835273\pi\) |
0.201947 | + | 0.979396i | \(0.435273\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.0120 | + | 10.8748i | 0.824792 | + | 0.426872i | ||||
\(650\) | −11.3220 | −0.444087 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.558733 | + | 1.71960i | 0.0218817 | + | 0.0673449i | ||||
\(653\) | −6.10818 | + | 18.7990i | −0.239031 | + | 0.735663i | 0.757530 | + | 0.652801i | \(0.226406\pi\) |
−0.996561 | + | 0.0828623i | \(0.973594\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.30058 | + | 2.39801i | 0.128964 | + | 0.0936982i | ||||
\(656\) | −1.65074 | + | 5.08046i | −0.0644506 | + | 0.198358i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.205494 | − | 0.149300i | 0.00801101 | − | 0.00582034i | ||||
\(659\) | 11.8055 | 0.459879 | 0.229939 | − | 0.973205i | \(-0.426147\pi\) | ||||
0.229939 | + | 0.973205i | \(0.426147\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.8076 | 0.692637 | 0.346318 | − | 0.938117i | \(-0.387432\pi\) | ||||
0.346318 | + | 0.938117i | \(0.387432\pi\) | |||||||
\(662\) | 10.1369 | − | 7.36485i | 0.393980 | − | 0.286243i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.34667 | − | 16.4554i | 0.207491 | − | 0.638592i | ||||
\(665\) | 0.867445 | + | 0.630235i | 0.0336381 | + | 0.0244395i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.60079 | + | 29.5482i | −0.371744 | + | 1.14411i | ||||
\(668\) | 2.05009 | + | 6.30952i | 0.0793202 | + | 0.244123i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.40658 | −0.286141 | ||||||||
\(671\) | −10.7594 | + | 10.6236i | −0.415361 | + | 0.410119i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.9419 | + | 11.5825i | −0.614515 | + | 0.446472i | −0.851001 | − | 0.525163i | \(-0.824004\pi\) |
0.236486 | + | 0.971635i | \(0.424004\pi\) | |||||||
\(674\) | −11.8111 | − | 36.3508i | −0.454946 | − | 1.40018i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.32365 | + | 2.41477i | 0.127833 | + | 0.0928760i | ||||
\(677\) | −10.0431 | − | 7.29671i | −0.385986 | − | 0.280436i | 0.377822 | − | 0.925878i | \(-0.376673\pi\) |
−0.763809 | + | 0.645443i | \(0.776673\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.16359 | + | 9.73653i | 0.121408 | + | 0.373654i | ||||
\(680\) | −5.47310 | + | 3.97644i | −0.209884 | + | 0.152490i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −41.5715 | − | 21.5154i | −1.59186 | − | 0.823866i | ||||
\(683\) | −2.02837 | −0.0776135 | −0.0388068 | − | 0.999247i | \(-0.512356\pi\) | ||||
−0.0388068 | + | 0.999247i | \(0.512356\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.69164 | + | 5.20632i | 0.0646341 | + | 0.198923i | ||||
\(686\) | 4.64931 | − | 14.3091i | 0.177511 | − | 0.546324i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −15.7815 | − | 11.4659i | −0.601663 | − | 0.437133i | ||||
\(689\) | −2.77589 | + | 8.54330i | −0.105753 | + | 0.325474i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.89542 | + | 1.37710i | −0.0721052 | + | 0.0523875i | −0.623254 | − | 0.782020i | \(-0.714190\pi\) |
0.551149 | + | 0.834407i | \(0.314190\pi\) | |||||||
\(692\) | 0.230830 | 0.00877483 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.19995 | −0.121469 | ||||||||
\(695\) | 10.3510 | − | 7.52046i | 0.392637 | − | 0.285267i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.63770 | + | 5.04033i | −0.0620324 | + | 0.190916i | ||||
\(698\) | −6.52227 | − | 4.73871i | −0.246871 | − | 0.179363i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.405097 | + | 1.24676i | −0.0153112 | + | 0.0471231i | ||||
\(701\) | 1.37008 | + | 4.21668i | 0.0517473 | + | 0.159262i | 0.973591 | − | 0.228301i | \(-0.0733170\pi\) |
−0.921843 | + | 0.387563i | \(0.873317\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.25411 | 0.273594 | ||||||||
\(704\) | 8.75399 | + | 17.4538i | 0.329928 | + | 0.657815i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −27.1091 | + | 19.6959i | −1.02026 | + | 0.741265i | ||||
\(707\) | 3.20555 | + | 9.86566i | 0.120557 | + | 0.371037i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.1755 | − | 17.5645i | −0.907929 | − | 0.659649i | 0.0325612 | − | 0.999470i | \(-0.489634\pi\) |
−0.940490 | + | 0.339821i | \(0.889634\pi\) | |||||||
\(710\) | −9.11565 | − | 6.62291i | −0.342104 | − | 0.248553i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.59699 | − | 29.5365i | −0.359662 | − | 1.10693i | ||||
\(713\) | 32.8776 | − | 23.8870i | 1.23127 | − | 0.894574i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.503164 | − | 3.05131i | 0.0188173 | − | 0.114113i | ||||
\(716\) | 3.76515 | 0.140710 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.18196 | + | 12.8707i | 0.156069 | + | 0.480332i | ||||
\(719\) | 6.68469 | − | 20.5734i | 0.249297 | − | 0.767257i | −0.745603 | − | 0.666390i | \(-0.767838\pi\) |
0.994900 | − | 0.100867i | \(-0.0321616\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.58676 | + | 1.87939i | 0.0963360 | + | 0.0699922i | ||||
\(722\) | 6.07115 | − | 18.6851i | 0.225945 | − | 0.695386i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.50452 | − | 1.09310i | 0.0559151 | − | 0.0406247i | ||||
\(725\) | 32.4471 | 1.20505 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.4422 | −0.461455 | −0.230727 | − | 0.973018i | \(-0.574111\pi\) | ||||
−0.230727 | + | 0.973018i | \(0.574111\pi\) | |||||||
\(728\) | 2.28910 | − | 1.66313i | 0.0848396 | − | 0.0616396i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.37965 | − | 13.4792i | 0.162098 | − | 0.498887i | ||||
\(731\) | −15.6568 | − | 11.3754i | −0.579089 | − | 0.420733i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.1777 | + | 49.7899i | −0.597538 | + | 1.83903i | −0.0558724 | + | 0.998438i | \(0.517794\pi\) |
−0.541665 | + | 0.840594i | \(0.682206\pi\) | |||||||
\(734\) | 3.23278 | + | 9.94949i | 0.119324 | + | 0.367242i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.70306 | 0.357660 | ||||||||
\(737\) | −4.36635 | + | 26.4786i | −0.160837 | + | 0.975352i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.7617 | − | 27.4355i | 1.38909 | − | 1.00923i | 0.393122 | − | 0.919486i | \(-0.371395\pi\) |
0.995965 | − | 0.0897445i | \(-0.0286051\pi\) | |||||||
\(740\) | −0.206606 | − | 0.635869i | −0.00759500 | − | 0.0233750i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.15064 | + | 3.74216i | 0.189086 | + | 0.137379i | ||||
\(743\) | −17.6947 | − | 12.8560i | −0.649156 | − | 0.471640i | 0.213827 | − | 0.976871i | \(-0.431407\pi\) |
−0.862984 | + | 0.505232i | \(0.831407\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.209737 | − | 0.645506i | −0.00768419 | − | 0.0236495i | ||||
\(746\) | −27.3853 | + | 19.8966i | −1.00265 | + | 0.728466i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.66657 | − | 5.31664i | −0.0974994 | − | 0.194395i | ||||
\(749\) | 11.3667 | 0.415330 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.2346 | + | 37.6543i | 0.446448 | + | 1.37403i | 0.880888 | + | 0.473326i | \(0.156947\pi\) |
−0.434439 | + | 0.900701i | \(0.643053\pi\) | |||||||
\(752\) | −0.325473 | + | 1.00170i | −0.0118688 | + | 0.0365284i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13.7482 | + | 9.98865i | 0.500680 | + | 0.363765i | ||||
\(755\) | −0.161111 | + | 0.495850i | −0.00586344 | + | 0.0180458i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.7253 | + | 13.6047i | −0.680583 | + | 0.494472i | −0.873551 | − | 0.486733i | \(-0.838189\pi\) |
0.192968 | + | 0.981205i | \(0.438189\pi\) | |||||||
\(758\) | 52.2959 | 1.89947 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.69577 | −0.134060 | ||||||||
\(761\) | −12.0486 | + | 8.75381i | −0.436761 | + | 0.317325i | −0.784346 | − | 0.620323i | \(-0.787002\pi\) |
0.347586 | + | 0.937648i | \(0.387002\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.05574 | + | 9.40460i | −0.110625 | + | 0.340469i | ||||
\(764\) | −1.64233 | − | 1.19322i | −0.0594173 | − | 0.0431692i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.77872 | + | 27.0181i | −0.317188 | + | 0.976204i | ||||
\(767\) | 3.47183 | + | 10.6852i | 0.125361 | + | 0.385820i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.6233 | 0.779757 | 0.389879 | − | 0.920866i | \(-0.372517\pi\) | ||||
0.389879 | + | 0.920866i | \(0.372517\pi\) | |||||||
\(770\) | −1.94653 | − | 1.00743i | −0.0701481 | − | 0.0363052i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.03255 | + | 0.750188i | −0.0371621 | + | 0.0269999i | ||||
\(773\) | 1.87664 | + | 5.77569i | 0.0674979 | + | 0.207737i | 0.979117 | − | 0.203300i | \(-0.0651666\pi\) |
−0.911619 | + | 0.411037i | \(0.865167\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34.3361 | − | 24.9466i | −1.23339 | − | 0.896109i | ||||
\(776\) | −28.5481 | − | 20.7414i | −1.02482 | − | 0.744572i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.7188 | − | 45.2999i | −0.527695 | − | 1.62408i | ||||
\(779\) | −2.34229 | + | 1.70177i | −0.0839211 | + | 0.0609722i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.0509 | + | 28.6842i | −1.03952 | + | 1.02640i | ||||
\(782\) | 31.6086 | 1.13032 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.26663 | + | 28.5197i | 0.330951 | + | 1.01856i | ||||
\(785\) | 1.79037 | − | 5.51018i | 0.0639010 | − | 0.196667i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.3856 | − | 30.0684i | −1.47524 | − | 1.07182i | −0.979053 | − | 0.203604i | \(-0.934735\pi\) |
−0.496183 | − | 0.868218i | \(-0.665265\pi\) | |||||||
\(788\) | 2.71085 | − | 8.34314i | 0.0965701 | − | 0.297212i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.8264 | − | 7.86585i | 0.385187 | − | 0.279854i | ||||
\(791\) | −5.79736 | −0.206130 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.18019 | −0.254976 | ||||||||
\(794\) | −10.3768 | + | 7.53917i | −0.368258 | + | 0.267555i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.51372 | + | 7.73643i | −0.0890964 | + | 0.274211i | ||||
\(797\) | −20.4368 | − | 14.8482i | −0.723907 | − | 0.525949i | 0.163723 | − | 0.986506i | \(-0.447650\pi\) |
−0.887630 | + | 0.460557i | \(0.847650\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.322903 | + | 0.993792i | −0.0114235 | + | 0.0351579i | ||||
\(800\) | −3.13143 | − | 9.63754i | −0.110713 | − | 0.340738i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.08192 | −0.214760 | ||||||||
\(803\) | −45.6063 | − | 23.6036i | −1.60941 | − | 0.832953i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.53945 | − | 1.11848i | 0.0542584 | − | 0.0394211i | ||||
\(806\) | −6.86891 | − | 21.1403i | −0.241947 | − | 0.744637i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −28.9267 | − | 21.0165i | −1.01764 | − | 0.739357i | ||||
\(809\) | 41.5248 | + | 30.1696i | 1.45994 | + | 1.06071i | 0.983380 | + | 0.181561i | \(0.0581150\pi\) |
0.476556 | + | 0.879144i | \(0.341885\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.40476 | + | 4.32339i | 0.0493276 | + | 0.151815i | 0.972686 | − | 0.232124i | \(-0.0745674\pi\) |
−0.923359 | + | 0.383939i | \(0.874567\pi\) | |||||||
\(812\) | 1.59184 | − | 1.15654i | 0.0558625 | − | 0.0405865i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −14.6604 | + | 2.22663i | −0.513845 | + | 0.0780433i | ||||
\(815\) | −2.74097 | −0.0960119 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.26707 | − | 10.0550i | −0.114300 | − | 0.351780i | ||||
\(818\) | 1.19649 | − | 3.68241i | 0.0418342 | − | 0.128753i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.215882 | + | 0.156848i | 0.00753894 | + | 0.00547736i | ||||
\(821\) | −3.36019 | + | 10.3416i | −0.117271 | + | 0.360924i | −0.992414 | − | 0.122941i | \(-0.960767\pi\) |
0.875143 | + | 0.483865i | \(0.160767\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.1059 | − | 13.8812i | 0.665988 | − | 0.483869i | −0.202692 | − | 0.979243i | \(-0.564969\pi\) |
0.868680 | + | 0.495374i | \(0.164969\pi\) | |||||||
\(824\) | −11.0210 | −0.383934 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.96271 | 0.277058 | ||||||||
\(827\) | −22.3321 | + | 16.2252i | −0.776564 | + | 0.564207i | −0.903946 | − | 0.427647i | \(-0.859343\pi\) |
0.127382 | + | 0.991854i | \(0.459343\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.97546 | + | 15.3129i | −0.172805 | + | 0.531839i | −0.999526 | − | 0.0307727i | \(-0.990203\pi\) |
0.826722 | + | 0.562611i | \(0.190203\pi\) | |||||||
\(830\) | −5.14900 | − | 3.74097i | −0.178724 | − | 0.129851i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.86531 | + | 8.81852i | −0.0993368 | + | 0.305727i | ||||
\(833\) | 9.19344 | + | 28.2945i | 0.318534 | + | 0.980347i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.0571 | −0.348039 | ||||||||
\(836\) | 0.528675 | − | 3.20601i | 0.0182846 | − | 0.110882i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.4334 | + | 9.75993i | −0.464049 | + | 0.337151i | ||||
\(839\) | 6.00479 | + | 18.4809i | 0.207309 | + | 0.638030i | 0.999611 | + | 0.0279012i | \(0.00888236\pi\) |
−0.792302 | + | 0.610129i | \(0.791118\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.9386 | − | 11.5800i | −0.549606 | − | 0.399312i | ||||
\(842\) | 27.7532 | + | 20.1639i | 0.956438 | + | 0.694893i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.409359 | + | 1.25988i | 0.0140907 | + | 0.0433668i | ||||
\(845\) | −5.03845 | + | 3.66065i | −0.173328 | + | 0.125930i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.74909 | + | 6.36497i | −0.163181 | + | 0.218703i | ||||
\(848\) | −26.3994 | −0.906559 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10.2009 | − | 31.3951i | −0.349888 | − | 1.07684i | ||||
\(851\) | 3.97823 | − | 12.2437i | 0.136372 | − | 0.419710i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.0068 | + | 11.6296i | 0.548063 | + | 0.398191i | 0.827071 | − | 0.562098i | \(-0.190006\pi\) |
−0.279008 | + | 0.960289i | \(0.590006\pi\) | |||||||
\(854\) | −1.57255 | + | 4.83980i | −0.0538114 | + | 0.165614i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −31.6966 | + | 23.0289i | −1.08337 | + | 0.787112i | ||||
\(857\) | 4.34065 | 0.148274 | 0.0741369 | − | 0.997248i | \(-0.476380\pi\) | ||||
0.0741369 | + | 0.997248i | \(0.476380\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.17935 | −0.176717 | −0.0883586 | − | 0.996089i | \(-0.528162\pi\) | ||||
−0.0883586 | + | 0.996089i | \(0.528162\pi\) | |||||||
\(860\) | −0.788334 | + | 0.572758i | −0.0268820 | + | 0.0195309i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.81901 | + | 27.1421i | −0.300377 | + | 0.924464i | ||||
\(863\) | −2.17943 | − | 1.58345i | −0.0741886 | − | 0.0539011i | 0.550073 | − | 0.835117i | \(-0.314600\pi\) |
−0.624261 | + | 0.781216i | \(0.714600\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.108132 | + | 0.332797i | −0.00367661 | + | 0.0113155i | ||||
\(866\) | −7.22246 | − | 22.2285i | −0.245429 | − | 0.755354i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.57370 | −0.0873571 | ||||||||
\(869\) | −21.7381 | − | 43.3417i | −0.737414 | − | 1.47027i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.3099 | + | 7.49056i | −0.349337 | + | 0.253808i | ||||
\(872\) | −10.5326 | − | 32.4161i | −0.356680 | − | 1.09775i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.9699 | + | 10.1497i | 0.472538 | + | 0.343319i | ||||
\(875\) | −3.33668 | − | 2.42424i | −0.112800 | − | 0.0819543i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.44139 | − | 19.8246i | −0.217510 | − | 0.669428i | −0.998966 | − | 0.0454669i | \(-0.985522\pi\) |
0.781456 | − | 0.623961i | \(-0.214478\pi\) | |||||||
\(878\) | 29.9646 | − | 21.7705i | 1.01125 | − | 0.734720i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.98535 | − | 1.36470i | 0.302896 | − | 0.0460041i | ||||
\(881\) | −11.5843 | −0.390286 | −0.195143 | − | 0.980775i | \(-0.562517\pi\) | ||||
−0.195143 | + | 0.980775i | \(0.562517\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.75801 | + | 14.6437i | 0.160120 | + | 0.492798i | 0.998644 | − | 0.0520667i | \(-0.0165808\pi\) |
−0.838524 | + | 0.544865i | \(0.816581\pi\) | |||||||
\(884\) | 0.872808 | − | 2.68623i | 0.0293557 | − | 0.0903476i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −31.8938 | − | 23.1722i | −1.07149 | − | 0.778486i | ||||
\(887\) | 1.82628 | − | 5.62070i | 0.0613204 | − | 0.188725i | −0.915703 | − | 0.401855i | \(-0.868366\pi\) |
0.977024 | + | 0.213130i | \(0.0683657\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.00669 | − | 5.09066i | 0.234997 | − | 0.170735i | ||||
\(890\) | −11.4240 | −0.382932 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.30623 | −0.144183 | ||||||||
\(893\) | −0.461824 | + | 0.335535i | −0.0154543 | + | 0.0112282i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.76379 | + | 5.42838i | −0.0589569 | + | 0.181451i | ||||
\(896\) | 7.86251 | + | 5.71245i | 0.262668 | + | 0.190840i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.7417 | + | 33.0595i | −0.358455 | + | 1.10321i | ||||
\(899\) | 19.6852 | + | 60.5847i | 0.656537 | + | 2.02061i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.1909 | −0.872546 | ||||||||
\(902\) | 4.21134 | − | 4.15819i | 0.140222 | − | 0.138453i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.1662 | − | 11.7455i | 0.537681 | − | 0.390648i | ||||
\(905\) | 0.871174 | + | 2.68120i | 0.0289588 | + | 0.0891260i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.98132 | + | 4.34568i | 0.198606 | + | 0.144296i | 0.682644 | − | 0.730751i | \(-0.260830\pi\) |
−0.484037 | + | 0.875047i | \(0.660830\pi\) | |||||||
\(908\) | −1.88525 | − | 1.36971i | −0.0625642 | − | 0.0454556i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.321628 | − | 0.989869i | −0.0106619 | − | 0.0328138i | ||||
\(911\) | −11.4871 | + | 8.34585i | −0.380584 | + | 0.276510i | −0.761586 | − | 0.648064i | \(-0.775579\pi\) |
0.381002 | + | 0.924574i | \(0.375579\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.4095 | + | 16.2024i | −0.543074 | + | 0.536220i | ||||
\(914\) | −33.5350 | −1.10924 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.98698 | + | 9.19299i | 0.0986927 | + | 0.303745i | ||||
\(917\) | 1.53737 | − | 4.73153i | 0.0507684 | − | 0.156249i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.6895 | + | 24.4769i | 1.11132 | + | 0.807418i | 0.982870 | − | 0.184299i | \(-0.0590013\pi\) |
0.128445 | + | 0.991717i | \(0.459001\pi\) | |||||||
\(920\) | −2.02680 | + | 6.23785i | −0.0668217 | + | 0.205656i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.1398 | − | 10.9997i | 0.498604 | − | 0.362257i | ||||
\(923\) | −19.3869 | −0.638127 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.4449 | −0.442067 | ||||||||
\(926\) | 25.0555 | − | 18.2039i | 0.823376 | − | 0.598218i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.70008 | + | 14.4654i | −0.154288 | + | 0.474849i | ||||
\(929\) | −27.6140 | − | 20.0627i | −0.905986 | − | 0.658237i | 0.0340108 | − | 0.999421i | \(-0.489172\pi\) |
−0.939996 | + | 0.341184i | \(0.889172\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.02236 | + | 15.4572i | −0.164601 | + | 0.506590i | ||||
\(932\) | −0.505470 | − | 1.55568i | −0.0165572 | − | 0.0509579i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.38118 | 0.306962 | ||||||||
\(935\) | 8.91439 | − | 1.35393i | 0.291532 | − | 0.0442781i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.8118 | + | 30.3780i | −1.36593 | + | 0.992407i | −0.367889 | + | 0.929870i | \(0.619919\pi\) |
−0.998043 | + | 0.0625376i | \(0.980081\pi\) | |||||||
\(938\) | 2.79102 | + | 8.58987i | 0.0911299 | + | 0.280469i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.0425651 | + | 0.0309253i | 0.00138832 | + | 0.00100867i | ||||
\(941\) | 14.5673 | + | 10.5838i | 0.474881 | + | 0.345021i | 0.799340 | − | 0.600878i | \(-0.205182\pi\) |
−0.324460 | + | 0.945900i | \(0.605182\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.58777 | + | 4.88666i | 0.0517050 | + | 0.159132i | ||||
\(944\) | −26.7122 | + | 19.4075i | −0.869407 | + | 0.631661i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.68901 | + | 19.3181i | 0.315017 | + | 0.628084i | ||||
\(947\) | −28.6303 | −0.930360 | −0.465180 | − | 0.885216i | \(-0.654010\pi\) | ||||
−0.465180 | + | 0.885216i | \(0.654010\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.53559 | − | 23.1922i | −0.244616 | − | 0.752850i | ||||
\(950\) | 5.57273 | − | 17.1511i | 0.180803 | − | 0.556455i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.67415 | + | 4.84905i | 0.216310 | + | 0.157159i | ||||
\(953\) | −5.15728 | + | 15.8725i | −0.167061 | + | 0.514160i | −0.999182 | − | 0.0404331i | \(-0.987126\pi\) |
0.832121 | + | 0.554594i | \(0.187126\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.48967 | − | 1.80885i | 0.0805637 | − | 0.0585330i | ||||
\(956\) | 2.87938 | 0.0931257 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 56.0827 | 1.81195 | ||||||||
\(959\) | 5.40063 | − | 3.92379i | 0.174396 | − | 0.126706i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.1692 | − | 49.7638i | 0.521589 | − | 1.60528i | ||||
\(962\) | −5.69677 | − | 4.13895i | −0.183671 | − | 0.133445i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.06554 | + | 3.27939i | −0.0343187 | + | 0.105622i | ||||
\(965\) | −0.597882 | − | 1.84009i | −0.0192465 | − | 0.0592347i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.3193 | 0.782057 | 0.391029 | − | 0.920379i | \(-0.372119\pi\) | ||||
0.391029 | + | 0.920379i | \(0.372119\pi\) | |||||||
\(968\) | 0.347660 | − | 27.3707i | 0.0111742 | − | 0.879728i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10.5013 | + | 7.62961i | −0.337175 | + | 0.244972i | ||||
\(971\) | −2.33367 | − | 7.18229i | −0.0748910 | − | 0.230491i | 0.906603 | − | 0.421985i | \(-0.138667\pi\) |
−0.981494 | + | 0.191495i | \(0.938667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.6225 | − | 9.17079i | −0.404659 | − | 0.294002i | ||||
\(974\) | −10.8635 | − | 7.89283i | −0.348091 | − | 0.252903i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.52069 | − | 20.0686i | −0.208722 | − | 0.642381i | ||||
\(977\) | 1.64415 | − | 1.19455i | 0.0526011 | − | 0.0382170i | −0.561174 | − | 0.827698i | \(-0.689650\pi\) |
0.613775 | + | 0.789481i | \(0.289650\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.73470 | + | 40.8408i | −0.215242 | + | 1.30528i | ||||
\(980\) | 1.49797 | 0.0478508 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15.8611 | − | 48.8154i | −0.506148 | − | 1.55776i | ||||
\(983\) | −10.3334 | + | 31.8030i | −0.329584 | + | 1.01436i | 0.639744 | + | 0.768588i | \(0.279040\pi\) |
−0.969329 | + | 0.245769i | \(0.920960\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.7588 | + | 7.81671i | 0.342803 | + | 0.249061i | ||||
\(986\) | −15.3109 | + | 47.1222i | −0.487600 | + | 1.50068i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.24831 | − | 0.906952i | 0.0397141 | − | 0.0288540i | ||||
\(989\) | −18.7629 | −0.596624 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.1009 | 1.27385 | 0.636923 | − | 0.770927i | \(-0.280207\pi\) | ||||
0.636923 | + | 0.770927i | \(0.280207\pi\) | |||||||
\(992\) | 16.0953 | − | 11.6939i | 0.511026 | − | 0.371282i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.24595 | + | 13.0677i | −0.134673 | + | 0.414482i | ||||
\(995\) | −9.97640 | − | 7.24828i | −0.316273 | − | 0.229786i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.98448 | − | 15.3406i | 0.157860 | − | 0.485843i | −0.840580 | − | 0.541688i | \(-0.817785\pi\) |
0.998439 | + | 0.0558453i | \(0.0177854\pi\) | |||||||
\(998\) | −9.97461 | − | 30.6987i | −0.315741 | − | 0.971750i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 891.2.f.e.487.8 | 36 | ||
3.2 | odd | 2 | 891.2.f.f.487.2 | 36 | |||
9.2 | odd | 6 | 99.2.m.b.58.8 | yes | 72 | ||
9.4 | even | 3 | 297.2.n.b.289.8 | 72 | |||
9.5 | odd | 6 | 99.2.m.b.25.2 | yes | 72 | ||
9.7 | even | 3 | 297.2.n.b.91.2 | 72 | |||
11.2 | odd | 10 | 9801.2.a.cn.1.15 | 18 | |||
11.4 | even | 5 | inner | 891.2.f.e.730.8 | 36 | ||
11.9 | even | 5 | 9801.2.a.cp.1.4 | 18 | |||
33.2 | even | 10 | 9801.2.a.co.1.4 | 18 | |||
33.20 | odd | 10 | 9801.2.a.cm.1.15 | 18 | |||
33.26 | odd | 10 | 891.2.f.f.730.2 | 36 | |||
99.2 | even | 30 | 1089.2.e.o.364.15 | 36 | |||
99.4 | even | 15 | 297.2.n.b.235.2 | 72 | |||
99.20 | odd | 30 | 1089.2.e.p.364.4 | 36 | |||
99.59 | odd | 30 | 99.2.m.b.70.8 | yes | 72 | ||
99.68 | even | 30 | 1089.2.e.o.727.15 | 36 | |||
99.70 | even | 15 | 297.2.n.b.37.8 | 72 | |||
99.86 | odd | 30 | 1089.2.e.p.727.4 | 36 | |||
99.92 | odd | 30 | 99.2.m.b.4.2 | ✓ | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.m.b.4.2 | ✓ | 72 | 99.92 | odd | 30 | ||
99.2.m.b.25.2 | yes | 72 | 9.5 | odd | 6 | ||
99.2.m.b.58.8 | yes | 72 | 9.2 | odd | 6 | ||
99.2.m.b.70.8 | yes | 72 | 99.59 | odd | 30 | ||
297.2.n.b.37.8 | 72 | 99.70 | even | 15 | |||
297.2.n.b.91.2 | 72 | 9.7 | even | 3 | |||
297.2.n.b.235.2 | 72 | 99.4 | even | 15 | |||
297.2.n.b.289.8 | 72 | 9.4 | even | 3 | |||
891.2.f.e.487.8 | 36 | 1.1 | even | 1 | trivial | ||
891.2.f.e.730.8 | 36 | 11.4 | even | 5 | inner | ||
891.2.f.f.487.2 | 36 | 3.2 | odd | 2 | |||
891.2.f.f.730.2 | 36 | 33.26 | odd | 10 | |||
1089.2.e.o.364.15 | 36 | 99.2 | even | 30 | |||
1089.2.e.o.727.15 | 36 | 99.68 | even | 30 | |||
1089.2.e.p.364.4 | 36 | 99.20 | odd | 30 | |||
1089.2.e.p.727.4 | 36 | 99.86 | odd | 30 | |||
9801.2.a.cm.1.15 | 18 | 33.20 | odd | 10 | |||
9801.2.a.cn.1.15 | 18 | 11.2 | odd | 10 | |||
9801.2.a.co.1.4 | 18 | 33.2 | even | 10 | |||
9801.2.a.cp.1.4 | 18 | 11.9 | even | 5 |