Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [891,2,Mod(107,891)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(891, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([5, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("891.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 891 = 3^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 891.u (of order \(30\), degree \(8\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.11467082010\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{30})\) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{30}]$ |
Embedding invariants
Embedding label | 215.4 | ||
Character | \(\chi\) | \(=\) | 891.215 |
Dual form | 891.2.u.c.431.4 |
$q$-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 \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(650\) |
\(\chi(n)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.57299 | − | 1.74698i | 1.11227 | − | 1.23530i | 0.142893 | − | 0.989738i | \(-0.454359\pi\) |
0.969380 | − | 0.245566i | \(-0.0789738\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.368594 | − | 3.50694i | −0.184297 | − | 1.75347i | ||||
\(5\) | −1.67069 | + | 1.50430i | −0.747156 | + | 0.672742i | −0.952016 | − | 0.306049i | \(-0.900993\pi\) |
0.204860 | + | 0.978791i | \(0.434326\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.64772 | + | 3.70084i | −0.622780 | + | 1.39879i | 0.276330 | + | 0.961063i | \(0.410882\pi\) |
−0.899110 | + | 0.437723i | \(0.855785\pi\) | |||||||
\(8\) | −2.90269 | − | 2.10893i | −1.02626 | − | 0.745618i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.28492i | 1.67124i | ||||||||
\(11\) | 1.64091 | + | 2.88226i | 0.494754 | + | 0.869033i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.967343 | + | 4.55099i | −0.268293 | + | 1.26222i | 0.613165 | + | 0.789955i | \(0.289896\pi\) |
−0.881458 | + | 0.472263i | \(0.843437\pi\) | |||||||
\(14\) | 3.87346 | + | 8.69993i | 1.03523 | + | 2.32515i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.35177 | + | 0.287327i | −0.337942 | + | 0.0718317i | ||||
\(17\) | −0.0235753 | + | 0.0725574i | −0.00571786 | + | 0.0175978i | −0.953875 | − | 0.300205i | \(-0.902945\pi\) |
0.948157 | + | 0.317803i | \(0.102945\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.40822 | − | 1.93825i | 0.323068 | − | 0.444665i | −0.616333 | − | 0.787486i | \(-0.711382\pi\) |
0.939401 | + | 0.342821i | \(0.111382\pi\) | |||||||
\(20\) | 5.89128 | + | 5.30454i | 1.31733 | + | 1.18613i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.61640 | + | 1.66711i | 1.62382 | + | 0.355430i | ||||
\(23\) | −2.79482 | − | 1.61359i | −0.582759 | − | 0.336456i | 0.179470 | − | 0.983763i | \(-0.442562\pi\) |
−0.762229 | + | 0.647307i | \(0.775895\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.00565702 | − | 0.0538229i | 0.00113140 | − | 0.0107646i | ||||
\(26\) | 6.42889 | + | 8.84860i | 1.26081 | + | 1.73535i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 13.5860 | + | 4.41435i | 2.56750 | + | 0.834233i | ||||
\(29\) | −1.68021 | − | 0.748078i | −0.312007 | − | 0.138915i | 0.244759 | − | 0.969584i | \(-0.421291\pi\) |
−0.556766 | + | 0.830669i | \(0.687958\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.63816 | − | 0.348201i | −0.294222 | − | 0.0625388i | 0.0584358 | − | 0.998291i | \(-0.481389\pi\) |
−0.352658 | + | 0.935752i | \(0.614722\pi\) | |||||||
\(32\) | 1.96356 | − | 3.40098i | 0.347111 | − | 0.601214i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.0896728 | + | 0.155318i | 0.0153788 | + | 0.0266368i | ||||
\(35\) | −2.81433 | − | 8.66162i | −0.475709 | − | 1.46408i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.87906 | + | 4.27138i | −0.966511 | + | 0.702211i | −0.954654 | − | 0.297718i | \(-0.903774\pi\) |
−0.0118571 | + | 0.999930i | \(0.503774\pi\) | |||||||
\(38\) | −1.17097 | − | 5.50899i | −0.189957 | − | 0.893676i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.02195 | − | 0.843141i | 1.26838 | − | 0.133312i | ||||
\(41\) | 7.71224 | − | 3.43371i | 1.20445 | − | 0.536256i | 0.296378 | − | 0.955071i | \(-0.404221\pi\) |
0.908072 | + | 0.418815i | \(0.137554\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.70733 | + | 2.14043i | −0.565363 | + | 0.326413i | −0.755295 | − | 0.655385i | \(-0.772507\pi\) |
0.189932 | + | 0.981797i | \(0.439173\pi\) | |||||||
\(44\) | 9.50306 | − | 6.81697i | 1.43264 | − | 1.02770i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.21513 | + | 2.34434i | −1.06381 | + | 0.345654i | ||||
\(47\) | 6.18182 | + | 0.649735i | 0.901711 | + | 0.0947736i | 0.544026 | − | 0.839069i | \(-0.316899\pi\) |
0.357685 | + | 0.933842i | \(0.383566\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.29732 | − | 6.99389i | −0.899618 | − | 0.999127i | ||||
\(50\) | −0.0851293 | − | 0.0945457i | −0.0120391 | − | 0.0133708i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 16.3166 | + | 1.71494i | 2.26271 | + | 0.237820i | ||||
\(53\) | 1.16884 | − | 0.379779i | 0.160552 | − | 0.0521666i | −0.227638 | − | 0.973746i | \(-0.573100\pi\) |
0.388190 | + | 0.921579i | \(0.373100\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.07723 | − | 2.34694i | −0.954294 | − | 0.316461i | ||||
\(56\) | 12.5876 | − | 7.26746i | 1.68209 | − | 0.971156i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.94984 | + | 1.75858i | −0.518639 | + | 0.230913i | ||||
\(59\) | 0.577111 | − | 0.0606568i | 0.0751335 | − | 0.00789685i | −0.0668871 | − | 0.997761i | \(-0.521307\pi\) |
0.142021 | + | 0.989864i | \(0.454640\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.786366 | + | 3.69956i | 0.100684 | + | 0.473680i | 0.999383 | + | 0.0351153i | \(0.0111798\pi\) |
−0.898699 | + | 0.438565i | \(0.855487\pi\) | |||||||
\(62\) | −3.18511 | + | 2.31412i | −0.404510 | + | 0.293893i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.70690 | − | 11.4087i | −0.463363 | − | 1.42608i | ||||
\(65\) | −5.22991 | − | 9.05847i | −0.648691 | − | 1.12357i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.49920 | + | 11.2569i | −0.794003 | + | 1.37525i | 0.129467 | + | 0.991584i | \(0.458673\pi\) |
−0.923470 | + | 0.383670i | \(0.874660\pi\) | |||||||
\(68\) | 0.263144 | + | 0.0559330i | 0.0319109 | + | 0.00678287i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −19.5586 | − | 8.70807i | −2.33770 | − | 1.04081i | ||||
\(71\) | 1.06563 | + | 0.346245i | 0.126467 | + | 0.0410917i | 0.371567 | − | 0.928406i | \(-0.378821\pi\) |
−0.245100 | + | 0.969498i | \(0.578821\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.82153 | + | 10.7654i | 0.915441 | + | 1.26000i | 0.965274 | + | 0.261239i | \(0.0841309\pi\) |
−0.0498335 | + | 0.998758i | \(0.515869\pi\) | |||||||
\(74\) | −1.78566 | + | 16.9895i | −0.207579 | + | 1.97499i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.31639 | − | 4.22412i | −0.839247 | − | 0.484540i | ||||
\(77\) | −13.3705 | + | 1.32361i | −1.52371 | + | 0.150839i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.490373 | − | 0.441533i | −0.0551712 | − | 0.0496764i | 0.641084 | − | 0.767471i | \(-0.278485\pi\) |
−0.696255 | + | 0.717794i | \(0.745152\pi\) | |||||||
\(80\) | 1.82616 | − | 2.51349i | 0.204171 | − | 0.281017i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.13265 | − | 18.8744i | 0.677238 | − | 2.08432i | ||||
\(83\) | 9.98801 | − | 2.12302i | 1.09633 | − | 0.233031i | 0.375967 | − | 0.926633i | \(-0.377310\pi\) |
0.720359 | + | 0.693601i | \(0.243977\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0697608 | − | 0.156685i | −0.00756662 | − | 0.0169949i | ||||
\(86\) | −2.09231 | + | 9.84353i | −0.225619 | + | 1.06146i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.31540 | − | 11.8269i | 0.140222 | − | 1.26075i | ||||
\(89\) | − | 6.58983i | − | 0.698520i | −0.937026 | − | 0.349260i | \(-0.886433\pi\) | ||
0.937026 | − | 0.349260i | \(-0.113567\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.2486 | − | 11.0787i | −1.59849 | − | 1.16137i | ||||
\(92\) | −4.62860 | + | 10.3960i | −0.482565 | + | 1.08386i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.8590 | − | 9.77751i | 1.12002 | − | 1.00847i | ||||
\(95\) | 0.563001 | + | 5.35660i | 0.0577627 | + | 0.549576i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.0036 | − | 12.2208i | 1.11725 | − | 1.24083i | 0.149540 | − | 0.988756i | \(-0.452221\pi\) |
0.967708 | − | 0.252074i | \(-0.0811127\pi\) | |||||||
\(98\) | −22.1238 | −2.23485 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.190839 | −0.0190839 | ||||||||
\(101\) | 1.15217 | − | 1.27962i | 0.114646 | − | 0.127327i | −0.683090 | − | 0.730334i | \(-0.739364\pi\) |
0.797736 | + | 0.603007i | \(0.206031\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.337717 | + | 3.21316i | 0.0332762 | + | 0.316602i | 0.998481 | + | 0.0551054i | \(0.0175495\pi\) |
−0.965204 | + | 0.261497i | \(0.915784\pi\) | |||||||
\(104\) | 12.4056 | − | 11.1701i | 1.21647 | − | 1.09531i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.17511 | − | 2.63933i | 0.114136 | − | 0.256355i | ||||
\(107\) | 11.9884 | + | 8.71006i | 1.15896 | + | 0.842034i | 0.989646 | − | 0.143529i | \(-0.0458449\pi\) |
0.169314 | + | 0.985562i | \(0.445845\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 14.9258i | − | 1.42963i | −0.699313 | − | 0.714815i | \(-0.746511\pi\) | ||
0.699313 | − | 0.714815i | \(-0.253489\pi\) | |||||||
\(110\) | −15.2325 | + | 8.67210i | −1.45236 | + | 0.826852i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.16398 | − | 5.47611i | 0.109986 | − | 0.517444i | ||||
\(113\) | 4.57438 | + | 10.2742i | 0.430321 | + | 0.966518i | 0.990420 | + | 0.138091i | \(0.0440967\pi\) |
−0.560098 | + | 0.828426i | \(0.689237\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.09659 | − | 1.50843i | 0.661760 | − | 0.140662i | ||||
\(116\) | −2.00415 | + | 6.16813i | −0.186080 | + | 0.572697i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.801825 | − | 1.10362i | 0.0738139 | − | 0.101596i | ||||
\(119\) | −0.229678 | − | 0.206803i | −0.0210545 | − | 0.0189576i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.61480 | + | 9.45907i | −0.510436 | + | 0.859916i | ||||
\(122\) | 7.70002 | + | 4.44561i | 0.697127 | + | 0.402487i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.617305 | + | 5.87327i | −0.0554356 | + | 0.527435i | ||||
\(125\) | −6.53559 | − | 8.99547i | −0.584561 | − | 0.804580i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.76481 | − | 1.87310i | −0.511544 | − | 0.166211i | 0.0418604 | − | 0.999123i | \(-0.486672\pi\) |
−0.553404 | + | 0.832913i | \(0.686672\pi\) | |||||||
\(128\) | −18.5865 | − | 8.27524i | −1.64283 | − | 0.731435i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −24.0516 | − | 5.11233i | −2.10947 | − | 0.448381i | ||||
\(131\) | 3.57541 | − | 6.19280i | 0.312385 | − | 0.541067i | −0.666493 | − | 0.745511i | \(-0.732205\pi\) |
0.978878 | + | 0.204444i | \(0.0655387\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.85280 | + | 8.40530i | 0.420791 | + | 0.728832i | ||||
\(134\) | 9.44251 | + | 29.0611i | 0.815709 | + | 2.51049i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.221450 | − | 0.160893i | 0.0189892 | − | 0.0137964i | ||||
\(137\) | −2.20853 | − | 10.3903i | −0.188688 | − | 0.887706i | −0.965990 | − | 0.258579i | \(-0.916746\pi\) |
0.777302 | − | 0.629127i | \(-0.216587\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.0527856 | − | 0.00554799i | 0.00447722 | − | 0.000470575i | −0.102290 | − | 0.994755i | \(-0.532617\pi\) |
0.106767 | + | 0.994284i | \(0.465950\pi\) | |||||||
\(140\) | −29.3384 | + | 13.0623i | −2.47955 | + | 1.10397i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.28111 | − | 1.31700i | 0.191427 | − | 0.110520i | ||||
\(143\) | −14.7044 | + | 4.67966i | −1.22965 | + | 0.391333i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.93244 | − | 1.27773i | 0.326572 | − | 0.106110i | ||||
\(146\) | 31.1102 | + | 3.26981i | 2.57470 | + | 0.270612i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 17.1465 | + | 19.0431i | 1.40943 | + | 1.56533i | ||||
\(149\) | −13.6469 | − | 15.1564i | −1.11800 | − | 1.24166i | −0.967451 | − | 0.253057i | \(-0.918564\pi\) |
−0.150545 | − | 0.988603i | \(-0.548103\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.18266 | − | 0.124303i | −0.0962436 | − | 0.0101156i | 0.0562842 | − | 0.998415i | \(-0.482075\pi\) |
−0.152528 | + | 0.988299i | \(0.548741\pi\) | |||||||
\(152\) | −8.17525 | + | 2.65630i | −0.663101 | + | 0.215454i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −18.7194 | + | 25.4401i | −1.50845 | + | 2.05003i | ||||
\(155\) | 3.26066 | − | 1.88254i | 0.261902 | − | 0.151209i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.58325 | + | 0.704910i | −0.126357 | + | 0.0562580i | −0.468942 | − | 0.883229i | \(-0.655365\pi\) |
0.342584 | + | 0.939487i | \(0.388698\pi\) | |||||||
\(158\) | −1.54270 | + | 0.162145i | −0.122731 | + | 0.0128995i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.83559 | + | 8.63576i | 0.145116 | + | 0.682717i | ||||
\(161\) | 10.5767 | − | 7.68443i | 0.833561 | − | 0.605618i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.309821 | − | 0.953532i | −0.0242671 | − | 0.0746864i | 0.938190 | − | 0.346122i | \(-0.112502\pi\) |
−0.962457 | + | 0.271435i | \(0.912502\pi\) | |||||||
\(164\) | −14.8845 | − | 25.7807i | −1.16228 | − | 2.01314i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.0022 | − | 20.7884i | 0.931550 | − | 1.61349i | ||||
\(167\) | 13.2227 | + | 2.81058i | 1.02321 | + | 0.217489i | 0.688809 | − | 0.724943i | \(-0.258134\pi\) |
0.334398 | + | 0.942432i | \(0.391467\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.89967 | − | 3.51716i | −0.607667 | − | 0.270551i | ||||
\(170\) | −0.383460 | − | 0.124594i | −0.0294100 | − | 0.00955590i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.87286 | + | 12.2124i | 0.676549 | + | 0.931190i | ||||
\(173\) | −0.786362 | + | 7.48173i | −0.0597860 | + | 0.568826i | 0.923093 | + | 0.384576i | \(0.125652\pi\) |
−0.982879 | + | 0.184250i | \(0.941014\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.189869 | + | 0.109621i | 0.0143527 | + | 0.00828655i | ||||
\(176\) | −3.04628 | − | 3.42466i | −0.229622 | − | 0.258143i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.5123 | − | 10.3657i | −0.862885 | − | 0.776945i | ||||
\(179\) | 7.34750 | − | 10.1130i | 0.549178 | − | 0.755879i | −0.440722 | − | 0.897643i | \(-0.645278\pi\) |
0.989900 | + | 0.141765i | \(0.0452777\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.56261 | + | 17.1200i | −0.413466 | + | 1.27252i | 0.500150 | + | 0.865939i | \(0.333278\pi\) |
−0.913616 | + | 0.406578i | \(0.866722\pi\) | |||||||
\(182\) | −43.3403 | + | 9.21226i | −3.21259 | + | 0.682858i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.70954 | + | 10.5778i | 0.347192 | + | 0.779806i | ||||
\(185\) | 3.39666 | − | 15.9800i | 0.249727 | − | 1.17487i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.247814 | + | 0.0511104i | −0.0181220 | + | 0.00373756i | ||||
\(188\) | − | 21.9187i | − | 1.59859i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.2435 | + | 7.44233i | 0.743141 | + | 0.539924i | ||||
\(191\) | −8.80869 | + | 19.7846i | −0.637374 | + | 1.43157i | 0.248957 | + | 0.968514i | \(0.419912\pi\) |
−0.886331 | + | 0.463051i | \(0.846755\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.85464 | − | 3.47073i | 0.277463 | − | 0.249829i | −0.518636 | − | 0.854995i | \(-0.673560\pi\) |
0.796099 | + | 0.605166i | \(0.206893\pi\) | |||||||
\(194\) | −4.04087 | − | 38.4463i | −0.290117 | − | 2.76028i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −22.2060 | + | 24.6622i | −1.58614 | + | 1.76159i | ||||
\(197\) | −5.14679 | −0.366693 | −0.183347 | − | 0.983048i | \(-0.558693\pi\) | ||||
−0.183347 | + | 0.983048i | \(0.558693\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.2595 | 1.71971 | 0.859855 | − | 0.510539i | \(-0.170554\pi\) | ||||
0.859855 | + | 0.510539i | \(0.170554\pi\) | |||||||
\(200\) | −0.129929 | + | 0.144301i | −0.00918737 | + | 0.0102036i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.423114 | − | 4.02566i | −0.0297702 | − | 0.283244i | ||||
\(203\) | 5.53703 | − | 4.98557i | 0.388624 | − | 0.349918i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.71945 | + | 17.3382i | −0.539150 | + | 1.21095i | ||||
\(206\) | 6.14457 | + | 4.46429i | 0.428113 | + | 0.311042i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 6.42982i | − | 0.445828i | ||||||
\(209\) | 7.89730 | + | 0.878351i | 0.546268 | + | 0.0607568i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.89702 | − | 18.3340i | 0.268282 | − | 1.26217i | −0.613192 | − | 0.789934i | \(-0.710115\pi\) |
0.881474 | − | 0.472233i | \(-0.156552\pi\) | |||||||
\(212\) | −1.76269 | − | 3.95906i | −0.121062 | − | 0.271909i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 34.0739 | − | 7.24264i | 2.32925 | − | 0.495097i | ||||
\(215\) | 2.97397 | − | 9.15293i | 0.202823 | − | 0.624225i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.98787 | − | 5.48883i | 0.270714 | − | 0.372606i | ||||
\(218\) | −26.0751 | − | 23.4781i | −1.76603 | − | 1.59014i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.62194 | + | 25.6845i | −0.379031 | + | 1.73165i | ||||
\(221\) | −0.307403 | − | 0.177479i | −0.0206781 | − | 0.0119385i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.573715 | − | 5.45853i | 0.0384188 | − | 0.365530i | −0.958375 | − | 0.285513i | \(-0.907836\pi\) |
0.996794 | − | 0.0800168i | \(-0.0254974\pi\) | |||||||
\(224\) | 9.35109 | + | 12.8707i | 0.624796 | + | 0.859958i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 25.1444 | + | 8.16990i | 1.67258 | + | 0.543454i | ||||
\(227\) | 12.5739 | + | 5.59824i | 0.834557 | + | 0.371569i | 0.779105 | − | 0.626893i | \(-0.215674\pi\) |
0.0554511 | + | 0.998461i | \(0.482340\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.6708 | + | 4.39372i | 1.36597 | + | 0.290346i | 0.831820 | − | 0.555045i | \(-0.187299\pi\) |
0.534148 | + | 0.845391i | \(0.320632\pi\) | |||||||
\(230\) | 8.52768 | − | 14.7704i | 0.562298 | − | 0.973929i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.29949 | + | 5.71488i | 0.216622 | + | 0.375200i | ||||
\(233\) | −4.62458 | − | 14.2330i | −0.302967 | − | 0.932435i | −0.980428 | − | 0.196877i | \(-0.936920\pi\) |
0.677462 | − | 0.735558i | \(-0.263080\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.3053 | + | 8.21378i | −0.737477 | + | 0.535808i | ||||
\(236\) | −0.425440 | − | 2.00154i | −0.0276938 | − | 0.130289i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.722562 | + | 0.0759444i | −0.0468368 | + | 0.00492274i | ||||
\(239\) | −4.93771 | + | 2.19841i | −0.319394 | + | 0.142203i | −0.560171 | − | 0.828377i | \(-0.689265\pi\) |
0.240777 | + | 0.970581i | \(0.422598\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.1404 | + | 5.85457i | −0.653202 | + | 0.377126i | −0.789682 | − | 0.613517i | \(-0.789754\pi\) |
0.136480 | + | 0.990643i | \(0.456421\pi\) | |||||||
\(242\) | 7.69281 | + | 24.6880i | 0.494513 | + | 1.58700i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.6843 | − | 4.12137i | 0.812028 | − | 0.263844i | ||||
\(245\) | 21.0418 | + | 2.21158i | 1.34431 | + | 0.141293i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.45873 | + | 8.28376i | 0.474587 | + | 0.527083i | ||||
\(248\) | 4.02073 | + | 4.46548i | 0.255317 | + | 0.283558i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −25.9954 | − | 2.73222i | −1.64409 | − | 0.172801i | ||||
\(251\) | 21.4920 | − | 6.98319i | 1.35657 | − | 0.440775i | 0.461671 | − | 0.887051i | \(-0.347250\pi\) |
0.894895 | + | 0.446276i | \(0.147250\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0647190 | − | 10.7031i | 0.00406885 | − | 0.672900i | ||||
\(254\) | −12.3403 | + | 7.12466i | −0.774297 | + | 0.447041i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −21.7757 | + | 9.69518i | −1.36098 | + | 0.605949i | ||||
\(257\) | −27.3656 | + | 2.87624i | −1.70702 | + | 0.179415i | −0.907165 | − | 0.420775i | \(-0.861758\pi\) |
−0.799857 | + | 0.600191i | \(0.795091\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.12067 | − | 28.7955i | −0.380320 | − | 1.78926i | ||||
\(260\) | −29.8398 | + | 21.6799i | −1.85059 | + | 1.34453i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.19462 | − | 15.9874i | −0.320925 | − | 0.987705i | ||||
\(263\) | −16.0193 | − | 27.7463i | −0.987793 | − | 1.71091i | −0.628800 | − | 0.777567i | \(-0.716453\pi\) |
−0.358993 | − | 0.933340i | \(-0.616880\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.38147 | + | 2.39277i | −0.0848630 | + | 0.146987i | ||||
\(266\) | 22.3173 | + | 4.74370i | 1.36836 | + | 0.290855i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 41.8729 | + | 18.6430i | 2.55780 | + | 1.13880i | ||||
\(269\) | −25.7177 | − | 8.35619i | −1.56804 | − | 0.509486i | −0.609097 | − | 0.793096i | \(-0.708468\pi\) |
−0.958940 | + | 0.283610i | \(0.908468\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.74690 | + | 12.0391i | 0.531336 | + | 0.731322i | 0.987333 | − | 0.158660i | \(-0.0507172\pi\) |
−0.455997 | + | 0.889981i | \(0.650717\pi\) | |||||||
\(272\) | 0.0110207 | − | 0.104855i | 0.000668225 | − | 0.00635774i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −21.6257 | − | 12.4856i | −1.30646 | − | 0.754284i | ||||
\(275\) | 0.164414 | − | 0.0720138i | 0.00991454 | − | 0.00434260i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.85587 | + | 5.27265i | 0.351845 | + | 0.316803i | 0.826034 | − | 0.563621i | \(-0.190592\pi\) |
−0.474189 | + | 0.880423i | \(0.657259\pi\) | |||||||
\(278\) | 0.0733391 | − | 0.100943i | 0.00439859 | − | 0.00605414i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −10.0976 | + | 31.0772i | −0.603447 | + | 1.85722i | ||||
\(281\) | −20.7658 | + | 4.41390i | −1.23878 | + | 0.263311i | −0.780308 | − | 0.625396i | \(-0.784937\pi\) |
−0.458475 | + | 0.888707i | \(0.651604\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.74698 | − | 3.92378i | −0.103847 | − | 0.233244i | 0.854147 | − | 0.520031i | \(-0.174080\pi\) |
−0.957994 | + | 0.286787i | \(0.907413\pi\) | |||||||
\(284\) | 0.821474 | − | 3.86473i | 0.0487455 | − | 0.229329i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.9547 | + | 33.0495i | −0.884289 | + | 1.95426i | ||||
\(287\) | 34.1996i | 2.01874i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.7486 | + | 9.98893i | 0.808740 | + | 0.587584i | ||||
\(290\) | 3.95353 | − | 8.87977i | 0.232159 | − | 0.521438i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 34.8707 | − | 31.3977i | 2.04065 | − | 1.83741i | ||||
\(293\) | 1.99603 | + | 18.9909i | 0.116609 | + | 1.10946i | 0.883742 | + | 0.467974i | \(0.155016\pi\) |
−0.767133 | + | 0.641488i | \(0.778317\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.872929 | + | 0.969486i | −0.0508239 | + | 0.0564456i | ||||
\(296\) | 26.0731 | 1.51547 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −47.9444 | −2.77735 | ||||||||
\(299\) | 10.0470 | − | 11.1583i | 0.581031 | − | 0.645300i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.81274 | − | 17.2471i | −0.104485 | − | 0.994105i | ||||
\(302\) | −2.07747 | + | 1.87056i | −0.119545 | + | 0.107639i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.34668 | + | 3.02468i | −0.0772371 | + | 0.173477i | ||||
\(305\) | −6.87902 | − | 4.99790i | −0.393891 | − | 0.286179i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.86240i | − | 0.106293i | −0.998587 | − | 0.0531463i | \(-0.983075\pi\) | ||
0.998587 | − | 0.0531463i | \(-0.0169250\pi\) | |||||||
\(308\) | 9.57012 | + | 46.4018i | 0.545308 | + | 2.64399i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.84022 | − | 8.65753i | 0.104517 | − | 0.491715i | ||||
\(311\) | 3.64217 | + | 8.18044i | 0.206528 | + | 0.463870i | 0.986877 | − | 0.161475i | \(-0.0516250\pi\) |
−0.780348 | + | 0.625345i | \(0.784958\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.7624 | + | 3.56295i | −0.947466 | + | 0.201390i | −0.655633 | − | 0.755079i | \(-0.727598\pi\) |
−0.291832 | + | 0.956469i | \(0.594265\pi\) | |||||||
\(314\) | −1.25898 | + | 3.87474i | −0.0710483 | + | 0.218664i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.36768 | + | 1.88245i | −0.0769381 | + | 0.105896i | ||||
\(317\) | 20.2910 | + | 18.2701i | 1.13965 | + | 1.02615i | 0.999350 | + | 0.0360411i | \(0.0114747\pi\) |
0.140304 | + | 0.990108i | \(0.455192\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.600930 | − | 6.07033i | −0.0336456 | − | 0.339873i | ||||
\(320\) | 23.3551 | + | 13.4841i | 1.30559 | + | 0.753783i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.21250 | − | 30.5649i | 0.179025 | − | 1.70331i | ||||
\(323\) | 0.107435 | + | 0.147872i | 0.00597785 | + | 0.00822781i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.239475 | + | 0.0778102i | 0.0132837 | + | 0.00431614i | ||||
\(326\) | −2.15315 | − | 0.958645i | −0.119252 | − | 0.0530944i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −29.6277 | − | 6.29756i | −1.63591 | − | 0.347724i | ||||
\(329\) | −12.5905 | + | 21.8073i | −0.694135 | + | 1.20228i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.93609 | + | 5.08545i | 0.161382 | + | 0.279522i | 0.935365 | − | 0.353685i | \(-0.115072\pi\) |
−0.773983 | + | 0.633207i | \(0.781738\pi\) | |||||||
\(332\) | −11.1268 | − | 34.2448i | −0.610663 | − | 1.87943i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 25.7093 | − | 18.6789i | 1.40675 | − | 1.02206i | ||||
\(335\) | −6.07563 | − | 28.5836i | −0.331947 | − | 1.56169i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.4800 | − | 1.73212i | 0.897721 | − | 0.0943543i | 0.355584 | − | 0.934644i | \(-0.384282\pi\) |
0.542137 | + | 0.840290i | \(0.317615\pi\) | |||||||
\(338\) | −18.5705 | + | 8.26814i | −1.01010 | + | 0.449727i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.523772 | + | 0.302400i | −0.0284055 | + | 0.0163999i | ||||
\(341\) | −1.68447 | − | 5.29296i | −0.0912193 | − | 0.286630i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.28988 | − | 3.01847i | 0.501606 | − | 0.162982i | ||||
\(344\) | 15.2752 | + | 1.60549i | 0.823586 | + | 0.0865624i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.8335 | + | 13.1425i | 0.636174 | + | 0.706543i | ||||
\(347\) | 1.68499 | + | 1.87137i | 0.0904548 | + | 0.100460i | 0.786673 | − | 0.617370i | \(-0.211802\pi\) |
−0.696218 | + | 0.717830i | \(0.745135\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.68163 | − | 0.912476i | −0.464717 | − | 0.0488437i | −0.130723 | − | 0.991419i | \(-0.541730\pi\) |
−0.333994 | + | 0.942575i | \(0.608397\pi\) | |||||||
\(350\) | 0.490168 | − | 0.159265i | 0.0262006 | − | 0.00851308i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.0245 | + | 0.0787558i | 0.694210 | + | 0.00419770i | ||||
\(353\) | 0.464623 | − | 0.268250i | 0.0247294 | − | 0.0142775i | −0.487584 | − | 0.873076i | \(-0.662122\pi\) |
0.512314 | + | 0.858798i | \(0.328789\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.30120 | + | 1.02456i | −0.122135 | + | 0.0543779i | ||||
\(356\) | −23.1101 | + | 2.42897i | −1.22483 | + | 0.128735i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.10964 | − | 28.7436i | −0.322904 | − | 1.51915i | ||||
\(359\) | −12.7871 | + | 9.29040i | −0.674880 | + | 0.490329i | −0.871655 | − | 0.490120i | \(-0.836953\pi\) |
0.196775 | + | 0.980449i | \(0.436953\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.09760 | + | 12.6111i | 0.215663 | + | 0.663742i | ||||
\(362\) | 21.1584 | + | 36.6474i | 1.11206 | + | 1.92614i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −33.2319 | + | 57.5594i | −1.74183 | + | 3.01693i | ||||
\(365\) | −29.2617 | − | 6.21977i | −1.53163 | − | 0.325558i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.4318 | + | 11.7682i | 1.37973 | + | 0.614296i | 0.956502 | − | 0.291727i | \(-0.0942299\pi\) |
0.423229 | + | 0.906023i | \(0.360897\pi\) | |||||||
\(368\) | 4.24157 | + | 1.37817i | 0.221107 | + | 0.0718420i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −22.5739 | − | 31.0703i | −1.17356 | − | 1.61527i | ||||
\(371\) | −0.520419 | + | 4.95146i | −0.0270188 | + | 0.257067i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.72386 | − | 3.30467i | −0.296370 | − | 0.171109i | 0.344441 | − | 0.938808i | \(-0.388069\pi\) |
−0.640811 | + | 0.767699i | \(0.721402\pi\) | |||||||
\(374\) | −0.300520 | + | 0.513323i | −0.0155395 | + | 0.0265433i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −16.5736 | − | 14.9230i | −0.854720 | − | 0.769594i | ||||
\(377\) | 5.02984 | − | 6.92297i | 0.259050 | − | 0.356551i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.478524 | − | 1.47275i | 0.0245801 | − | 0.0756498i | −0.938014 | − | 0.346597i | \(-0.887337\pi\) |
0.962594 | + | 0.270948i | \(0.0873370\pi\) | |||||||
\(380\) | 18.5778 | − | 3.94882i | 0.953019 | − | 0.202570i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 20.7075 | + | 46.5097i | 1.05949 | + | 2.37964i | ||||
\(383\) | 2.80843 | − | 13.2126i | 0.143504 | − | 0.675135i | −0.846301 | − | 0.532705i | \(-0.821175\pi\) |
0.989805 | − | 0.142429i | \(-0.0454913\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.3469 | − | 22.3246i | 1.03698 | − | 1.13777i | ||||
\(386\) | − | 12.1934i | − | 0.620629i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −46.9133 | − | 34.0845i | −2.38166 | − | 1.73038i | ||||
\(389\) | −6.09270 | + | 13.6844i | −0.308912 | + | 0.693828i | −0.999569 | − | 0.0293547i | \(-0.990655\pi\) |
0.690657 | + | 0.723182i | \(0.257321\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.182966 | − | 0.164744i | 0.00925301 | − | 0.00833145i | ||||
\(392\) | 3.52957 | + | 33.5817i | 0.178270 | + | 1.69613i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.09585 | + | 8.99135i | −0.407863 | + | 0.452978i | ||||
\(395\) | 1.48346 | 0.0746409 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.7132 | −1.03956 | −0.519782 | − | 0.854299i | \(-0.673987\pi\) | ||||
−0.519782 | + | 0.854299i | \(0.673987\pi\) | |||||||
\(398\) | 38.1600 | − | 42.3809i | 1.91279 | − | 2.12436i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.00781780 | + | 0.0743814i | 0.000390890 | + | 0.00371907i | ||||
\(401\) | 20.0982 | − | 18.0965i | 1.00366 | − | 0.903695i | 0.00830020 | − | 0.999966i | \(-0.497358\pi\) |
0.995355 | + | 0.0962701i | \(0.0306913\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.16932 | − | 7.11842i | 0.157875 | − | 0.354594i | ||||
\(404\) | −4.91223 | − | 3.56894i | −0.244392 | − | 0.177561i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 17.5154i | − | 0.869273i | ||||||
\(407\) | −21.9583 | − | 9.93597i | −1.08843 | − | 0.492508i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.26941 | − | 5.97208i | 0.0627681 | − | 0.295300i | −0.935556 | − | 0.353180i | \(-0.885100\pi\) |
0.998324 | + | 0.0578791i | \(0.0184338\pi\) | |||||||
\(410\) | 18.1469 | + | 40.7586i | 0.896211 | + | 2.01292i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.1439 | − | 2.36871i | 0.549020 | − | 0.116698i | ||||
\(413\) | −0.726437 | + | 2.23574i | −0.0357456 | + | 0.110014i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.4932 | + | 18.5718i | −0.662357 | + | 0.911656i | ||||
\(416\) | 13.5784 | + | 12.2260i | 0.665736 | + | 0.599431i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 13.9569 | − | 12.4148i | 0.682652 | − | 0.607229i | ||||
\(419\) | 30.8841 | + | 17.8309i | 1.50879 | + | 0.871098i | 0.999948 | + | 0.0102354i | \(0.00325810\pi\) |
0.508838 | + | 0.860862i | \(0.330075\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.49556 | + | 14.2293i | −0.0728889 | + | 0.693492i | 0.895672 | + | 0.444715i | \(0.146695\pi\) |
−0.968561 | + | 0.248777i | \(0.919972\pi\) | |||||||
\(422\) | −25.8993 | − | 35.6473i | −1.26076 | − | 1.73528i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.19370 | − | 1.36262i | −0.203664 | − | 0.0661745i | ||||
\(425\) | 0.00377188 | + | 0.00167935i | 0.000182963 | + | 8.14605e-5i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.9872 | − | 3.18563i | −0.725282 | − | 0.154163i | ||||
\(428\) | 26.1268 | − | 45.2530i | 1.26289 | − | 2.18738i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.3120 | − | 19.5930i | −0.545513 | − | 0.944856i | ||||
\(431\) | −2.68944 | − | 8.27725i | −0.129546 | − | 0.398701i | 0.865156 | − | 0.501503i | \(-0.167219\pi\) |
−0.994702 | + | 0.102802i | \(0.967219\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.3812 | − | 22.0733i | 1.46003 | − | 1.06077i | 0.476673 | − | 0.879080i | \(-0.341842\pi\) |
0.983355 | − | 0.181693i | \(-0.0581576\pi\) | |||||||
\(434\) | −3.31601 | − | 15.6006i | −0.159174 | − | 0.748853i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −52.3438 | + | 5.50156i | −2.50681 | + | 0.263477i | ||||
\(437\) | −7.06326 | + | 3.14476i | −0.337881 | + | 0.150434i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.1171 | − | 16.2334i | 1.34196 | − | 0.774779i | 0.354863 | − | 0.934918i | \(-0.384528\pi\) |
0.987094 | + | 0.160139i | \(0.0511942\pi\) | |||||||
\(440\) | 15.5935 | + | 21.7378i | 0.743390 | + | 1.03631i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.793595 | + | 0.257855i | −0.0377474 | + | 0.0122649i | ||||
\(443\) | −18.7184 | − | 1.96738i | −0.889336 | − | 0.0934730i | −0.351170 | − | 0.936312i | \(-0.614216\pi\) |
−0.538166 | + | 0.842839i | \(0.680883\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.91306 | + | 11.0096i | 0.469924 | + | 0.521904i | ||||
\(446\) | −8.63351 | − | 9.58849i | −0.408809 | − | 0.454028i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 48.3296 | + | 5.07965i | 2.28336 | + | 0.239991i | ||||
\(449\) | 6.86840 | − | 2.23168i | 0.324140 | − | 0.105319i | −0.142427 | − | 0.989805i | \(-0.545491\pi\) |
0.466567 | + | 0.884486i | \(0.345491\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.5520 | + | 16.5942i | 1.06193 | + | 0.781392i | ||||
\(452\) | 34.3450 | − | 19.8291i | 1.61545 | − | 0.932681i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 29.5586 | − | 13.1603i | 1.38725 | − | 0.617646i | ||||
\(455\) | 42.1414 | − | 4.42924i | 1.97562 | − | 0.207646i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.877843 | − | 4.12993i | −0.0410638 | − | 0.193190i | 0.952835 | − | 0.303490i | \(-0.0981520\pi\) |
−0.993898 | + | 0.110301i | \(0.964819\pi\) | |||||||
\(458\) | 40.1908 | − | 29.2004i | 1.87799 | − | 1.36444i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.90572 | − | 24.3313i | −0.368606 | − | 1.13445i | ||||
\(461\) | 7.09611 | + | 12.2908i | 0.330499 | + | 0.572441i | 0.982610 | − | 0.185683i | \(-0.0594497\pi\) |
−0.652111 | + | 0.758123i | \(0.726116\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.1892 | − | 34.9687i | 0.938271 | − | 1.62513i | 0.169576 | − | 0.985517i | \(-0.445760\pi\) |
0.768695 | − | 0.639616i | \(-0.220906\pi\) | |||||||
\(464\) | 2.48620 | + | 0.528457i | 0.115419 | + | 0.0245330i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −32.1393 | − | 14.3093i | −1.48882 | − | 0.662867i | ||||
\(467\) | 10.7476 | + | 3.49210i | 0.497338 | + | 0.161595i | 0.546936 | − | 0.837174i | \(-0.315794\pi\) |
−0.0495980 | + | 0.998769i | \(0.515794\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.9513 | − | 42.6008i | −1.42920 | − | 1.96712i | ||||
\(470\) | −3.43380 | + | 32.6704i | −0.158389 | + | 1.50697i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.80309 | − | 1.04102i | −0.0829942 | − | 0.0479167i | ||||
\(473\) | −12.2527 | − | 7.17322i | −0.563379 | − | 0.329825i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.0963559 | − | 0.0867593i | −0.00442111 | − | 0.00398079i | ||||
\(476\) | −0.640587 | + | 0.881692i | −0.0293612 | + | 0.0404123i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.92639 | + | 12.0842i | −0.179589 | + | 0.552718i | ||||
\(479\) | 22.3979 | − | 4.76083i | 1.02339 | − | 0.217528i | 0.334500 | − | 0.942396i | \(-0.391433\pi\) |
0.688888 | + | 0.724868i | \(0.258099\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.7520 | − | 30.8874i | −0.627036 | − | 1.40835i | ||||
\(482\) | −5.72295 | + | 26.9243i | −0.260673 | + | 1.22637i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 35.2420 | + | 16.2042i | 1.60191 | + | 0.736554i | ||||
\(485\) | 36.9698i | 1.67871i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.10169 | + | 4.43314i | 0.276494 | + | 0.200885i | 0.717387 | − | 0.696675i | \(-0.245338\pi\) |
−0.440893 | + | 0.897560i | \(0.645338\pi\) | |||||||
\(488\) | 5.51953 | − | 12.3971i | 0.249857 | − | 0.561189i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 36.9621 | − | 33.2808i | 1.66978 | − | 1.50347i | ||||
\(491\) | −3.99196 | − | 37.9810i | −0.180155 | − | 1.71406i | −0.594632 | − | 0.803998i | \(-0.702702\pi\) |
0.414477 | − | 0.910060i | \(-0.363964\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.0938901 | − | 0.104276i | 0.00422860 | − | 0.00469633i | ||||
\(494\) | 26.2041 | 1.17898 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.31446 | 0.103922 | ||||||||
\(497\) | −3.03726 | + | 3.37322i | −0.136240 | + | 0.151310i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.842404 | + | 8.01494i | 0.0377112 | + | 0.358798i | 0.997063 | + | 0.0765852i | \(0.0244017\pi\) |
−0.959352 | + | 0.282213i | \(0.908932\pi\) | |||||||
\(500\) | −29.1376 | + | 26.2356i | −1.30307 | + | 1.17329i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 21.6073 | − | 48.5308i | 0.964381 | − | 2.16603i | ||||
\(503\) | 21.0846 | + | 15.3188i | 0.940115 | + | 0.683033i | 0.948448 | − | 0.316932i | \(-0.102653\pi\) |
−0.00833362 | + | 0.999965i | \(0.502653\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.87106i | 0.172260i | ||||||||
\(506\) | −18.5964 | − | 16.9490i | −0.826711 | − | 0.753475i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.44397 | + | 20.9072i | −0.197169 | + | 0.927609i | ||||
\(509\) | −11.3737 | − | 25.5457i | −0.504130 | − | 1.13230i | −0.969033 | − | 0.246933i | \(-0.920577\pi\) |
0.464902 | − | 0.885362i | \(-0.346089\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −52.7288 | + | 11.2078i | −2.33258 | + | 0.495806i | ||||
\(512\) | −4.74153 | + | 14.5929i | −0.209548 | + | 0.644922i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −38.0212 | + | 52.3316i | −1.67704 | + | 2.30825i | ||||
\(515\) | −5.39777 | − | 4.86018i | −0.237854 | − | 0.214165i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.27113 | + | 18.8837i | 0.363764 | + | 0.830506i | ||||
\(518\) | −59.9330 | − | 34.6024i | −2.63331 | − | 1.52034i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.92285 | + | 37.3234i | −0.172028 | + | 1.63674i | ||||
\(521\) | 18.9804 | + | 26.1242i | 0.831545 | + | 1.14452i | 0.987633 | + | 0.156781i | \(0.0501117\pi\) |
−0.156088 | + | 0.987743i | \(0.549888\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.5104 | + | 5.36454i | 0.721948 | + | 0.234575i | 0.646868 | − | 0.762602i | \(-0.276079\pi\) |
0.0750804 | + | 0.997177i | \(0.476079\pi\) | |||||||
\(524\) | −23.0356 | − | 10.2561i | −1.00632 | − | 0.448041i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −73.6705 | − | 15.6591i | −3.21219 | − | 0.682771i | ||||
\(527\) | 0.0638847 | − | 0.110652i | 0.00278286 | − | 0.00482006i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.29267 | − | 10.8992i | −0.273594 | − | 0.473879i | ||||
\(530\) | 2.00710 | + | 6.17722i | 0.0871828 | + | 0.268321i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 27.6881 | − | 20.1166i | 1.20043 | − | 0.872166i | ||||
\(533\) | 8.16641 | + | 38.4199i | 0.353726 | + | 1.66415i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −33.1314 | + | 3.48225i | −1.43239 | + | 0.150551i | ||||
\(536\) | 42.6052 | − | 18.9690i | 1.84026 | − | 0.819338i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −55.0519 | + | 31.7842i | −2.37345 | + | 1.37031i | ||||
\(539\) | 9.82480 | − | 29.6269i | 0.423184 | − | 1.27612i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.58312 | + | 3.11375i | −0.412011 | + | 0.133870i | −0.507686 | − | 0.861542i | \(-0.669499\pi\) |
0.0956753 | + | 0.995413i | \(0.469499\pi\) | |||||||
\(542\) | 34.7909 | + | 3.65667i | 1.49440 | + | 0.157067i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.200475 | + | 0.222650i | 0.00859529 | + | 0.00954603i | ||||
\(545\) | 22.4528 | + | 24.9364i | 0.961773 | + | 1.06816i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.7290 | − | 2.49402i | −1.01458 | − | 0.106637i | −0.417382 | − | 0.908731i | \(-0.637052\pi\) |
−0.597197 | + | 0.802095i | \(0.703719\pi\) | |||||||
\(548\) | −35.6242 | + | 11.5750i | −1.52179 | + | 0.494460i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.132815 | − | 0.400506i | 0.00566325 | − | 0.0170776i | ||||
\(551\) | −3.81607 | + | 2.20321i | −0.162570 | + | 0.0938599i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.44204 | − | 1.08727i | 0.103846 | − | 0.0462353i | ||||
\(554\) | 18.4225 | − | 1.93628i | 0.782695 | − | 0.0822646i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.0389130 | − | 0.183071i | −0.00165028 | − | 0.00776394i | ||||
\(557\) | 31.6776 | − | 23.0151i | 1.34222 | − | 0.975181i | 0.342862 | − | 0.939386i | \(-0.388604\pi\) |
0.999359 | − | 0.0357950i | \(-0.0113963\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.15482 | − | 18.9426i | −0.260321 | − | 0.801185i | ||||
\(560\) | 6.29304 | + | 10.8999i | 0.265929 | + | 0.460603i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −24.9534 | + | 43.2205i | −1.05259 | + | 1.82315i | ||||
\(563\) | 4.91096 | + | 1.04386i | 0.206972 | + | 0.0439933i | 0.310231 | − | 0.950661i | \(-0.399594\pi\) |
−0.103259 | + | 0.994655i | \(0.532927\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23.0979 | − | 10.2838i | −0.971734 | − | 0.432644i | ||||
\(566\) | −9.60276 | − | 3.12012i | −0.403634 | − | 0.131149i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.36299 | − | 3.25238i | −0.0991489 | − | 0.136467i | ||||
\(569\) | −0.993979 | + | 9.45708i | −0.0416698 | + | 0.396461i | 0.953731 | + | 0.300662i | \(0.0972075\pi\) |
−0.995401 | + | 0.0957997i | \(0.969459\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.4930 | + | 19.9146i | 1.44349 | + | 0.833398i | 0.998081 | − | 0.0619297i | \(-0.0197254\pi\) |
0.445408 | + | 0.895328i | \(0.353059\pi\) | |||||||
\(572\) | 21.8312 | + | 49.8427i | 0.912810 | + | 2.08403i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 59.7461 | + | 53.7956i | 2.49375 | + | 2.24539i | ||||
\(575\) | −0.102658 | + | 0.141297i | −0.00428115 | + | 0.00589249i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.03506 | + | 12.4186i | −0.167982 | + | 0.516994i | −0.999244 | − | 0.0388866i | \(-0.987619\pi\) |
0.831262 | + | 0.555881i | \(0.187619\pi\) | |||||||
\(578\) | 39.0769 | − | 8.30605i | 1.62538 | − | 0.345486i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.93039 | − | 13.3199i | −0.246246 | − | 0.553078i | ||||
\(581\) | −8.60050 | + | 40.4622i | −0.356809 | + | 1.67865i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.01258 | + | 2.74571i | 0.124769 | + | 0.113716i | ||||
\(584\) | − | 47.7437i | − | 1.97565i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 36.3166 | + | 26.3855i | 1.50022 | + | 1.08998i | ||||
\(587\) | 9.66059 | − | 21.6980i | 0.398735 | − | 0.895574i | −0.596906 | − | 0.802311i | \(-0.703604\pi\) |
0.995642 | − | 0.0932631i | \(-0.0297298\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.98179 | + | 2.68482i | −0.122863 | + | 0.110626i | ||||
\(590\) | 0.320566 | + | 3.04999i | 0.0131975 | + | 0.125566i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.71983 | − | 7.46313i | 0.276183 | − | 0.306733i | ||||
\(593\) | −37.1489 | −1.52552 | −0.762761 | − | 0.646680i | \(-0.776157\pi\) | ||||
−0.762761 | + | 0.646680i | \(0.776157\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.694814 | 0.0284846 | ||||||||
\(596\) | −48.1224 | + | 53.4453i | −1.97117 | + | 2.18921i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.68956 | − | 35.1038i | −0.150877 | − | 1.43550i | ||||
\(599\) | 1.77298 | − | 1.59640i | 0.0724422 | − | 0.0652272i | −0.632114 | − | 0.774875i | \(-0.717813\pi\) |
0.704556 | + | 0.709648i | \(0.251146\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.76331 | − | 6.20650i | 0.112718 | − | 0.253168i | −0.848374 | − | 0.529397i | \(-0.822418\pi\) |
0.961092 | + | 0.276229i | \(0.0890848\pi\) | |||||||
\(602\) | −32.9818 | − | 23.9627i | −1.34424 | − | 0.976646i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.19334i | 0.170624i | ||||||||
\(605\) | −4.84866 | − | 24.2495i | −0.197126 | − | 0.985883i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.41966 | − | 39.6114i | 0.341744 | − | 1.60778i | −0.386386 | − | 0.922337i | \(-0.626277\pi\) |
0.728129 | − | 0.685440i | \(-0.240390\pi\) | |||||||
\(608\) | −3.82683 | − | 8.59520i | −0.155198 | − | 0.348581i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.5519 | + | 4.15588i | −0.791633 | + | 0.168267i | ||||
\(611\) | −8.93688 | + | 27.5049i | −0.361547 | + | 1.11273i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.119072 | − | 0.163888i | 0.00480926 | − | 0.00661938i | −0.806606 | − | 0.591090i | \(-0.798698\pi\) |
0.811415 | + | 0.584471i | \(0.198698\pi\) | |||||||
\(614\) | −3.25358 | − | 2.92953i | −0.131304 | − | 0.118226i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 41.6019 | + | 24.3554i | 1.67619 | + | 0.981309i | ||||
\(617\) | 7.00117 | + | 4.04213i | 0.281857 | + | 0.162730i | 0.634264 | − | 0.773117i | \(-0.281303\pi\) |
−0.352407 | + | 0.935847i | \(0.614637\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.19370 | + | 20.8716i | −0.0881722 | + | 0.838902i | 0.857654 | + | 0.514228i | \(0.171921\pi\) |
−0.945826 | + | 0.324674i | \(0.894745\pi\) | |||||||
\(620\) | −7.80381 | − | 10.7410i | −0.313409 | − | 0.431370i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.0202 | + | 6.50496i | 0.802737 | + | 0.260825i | ||||
\(623\) | 24.3879 | + | 10.8582i | 0.977081 | + | 0.435024i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.7155 | + | 5.25344i | 0.988620 | + | 0.210138i | ||||
\(626\) | −20.1427 | + | 34.8881i | −0.805062 | + | 1.39441i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.05565 | + | 5.29255i | 0.121934 | + | 0.211196i | ||||
\(629\) | −0.171320 | − | 0.527268i | −0.00683097 | − | 0.0210236i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.6268 | − | 14.2597i | 0.781332 | − | 0.567671i | −0.124047 | − | 0.992276i | \(-0.539587\pi\) |
0.905378 | + | 0.424606i | \(0.139587\pi\) | |||||||
\(632\) | 0.492237 | + | 2.31579i | 0.0195801 | + | 0.0921173i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 63.8351 | − | 6.70933i | 2.53521 | − | 0.266462i | ||||
\(635\) | 12.4489 | − | 5.54261i | 0.494020 | − | 0.219952i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 37.9208 | − | 21.8936i | 1.50248 | − | 0.867455i | ||||
\(638\) | −11.5500 | − | 8.49876i | −0.457270 | − | 0.336469i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 43.5007 | − | 14.1342i | 1.71952 | − | 0.558705i | ||||
\(641\) | −16.0507 | − | 1.68700i | −0.633965 | − | 0.0666324i | −0.217905 | − | 0.975970i | \(-0.569922\pi\) |
−0.416059 | + | 0.909338i | \(0.636589\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.42032 | + | 9.35171i | 0.332065 | + | 0.368796i | 0.885936 | − | 0.463807i | \(-0.153517\pi\) |
−0.553871 | + | 0.832602i | \(0.686850\pi\) | |||||||
\(644\) | −30.8473 | − | 34.2594i | −1.21555 | − | 1.35001i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.427324 | + | 0.0449136i | 0.0168128 | + | 0.00176710i | ||||
\(647\) | −28.7701 | + | 9.34797i | −1.13107 | + | 0.367507i | −0.813982 | − | 0.580890i | \(-0.802705\pi\) |
−0.317087 | + | 0.948396i | \(0.602705\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.12182 | + | 1.56385i | 0.0440352 | + | 0.0613865i | ||||
\(650\) | 0.512626 | − | 0.295965i | 0.0201068 | − | 0.0116087i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.22978 | + | 1.43799i | −0.126488 | + | 0.0563161i | ||||
\(653\) | −19.4852 | + | 2.04798i | −0.762516 | + | 0.0801436i | −0.477800 | − | 0.878468i | \(-0.658566\pi\) |
−0.284715 | + | 0.958612i | \(0.591899\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.34240 | + | 15.7247i | 0.130598 | + | 0.614416i | ||||
\(656\) | −9.43855 | + | 6.85751i | −0.368514 | + | 0.267741i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 18.2924 | + | 56.2981i | 0.713111 | + | 2.19473i | ||||
\(659\) | 0.674716 | + | 1.16864i | 0.0262832 | + | 0.0455238i | 0.878868 | − | 0.477065i | \(-0.158300\pi\) |
−0.852585 | + | 0.522589i | \(0.824966\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.3929 | + | 24.9293i | −0.559821 | + | 0.969638i | 0.437690 | + | 0.899126i | \(0.355797\pi\) |
−0.997511 | + | 0.0705120i | \(0.977537\pi\) | |||||||
\(662\) | 13.5026 | + | 2.87007i | 0.524795 | + | 0.111549i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −33.4694 | − | 14.9015i | −1.29886 | − | 0.578291i | ||||
\(665\) | −20.7516 | − | 6.74260i | −0.804712 | − | 0.261467i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.48879 | + | 4.80191i | 0.135086 | + | 0.185931i | ||||
\(668\) | 4.98271 | − | 47.4073i | 0.192787 | − | 1.83424i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −59.4920 | − | 34.3477i | −2.29838 | − | 1.32697i | ||||
\(671\) | −9.37273 | + | 8.33718i | −0.361830 | + | 0.321853i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.1641 | − | 14.5542i | −0.623080 | − | 0.561023i | 0.295954 | − | 0.955202i | \(-0.404362\pi\) |
−0.919034 | + | 0.394179i | \(0.871029\pi\) | |||||||
\(674\) | 22.8969 | − | 31.5149i | 0.881955 | − | 1.21391i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.42270 | + | 29.0001i | −0.362411 | + | 1.11539i | ||||
\(677\) | −18.4922 | + | 3.93065i | −0.710714 | + | 0.151067i | −0.549063 | − | 0.835781i | \(-0.685015\pi\) |
−0.161651 | + | 0.986848i | \(0.551682\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.0962 | + | 60.8590i | 1.03986 | + | 2.33555i | ||||
\(680\) | −0.127944 | + | 0.601929i | −0.00490643 | + | 0.0230829i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −11.8964 | − | 5.38304i | −0.455536 | − | 0.206127i | ||||
\(683\) | 33.7466i | 1.29128i | 0.763642 | + | 0.645640i | \(0.223409\pi\) | ||||
−0.763642 | + | 0.645640i | \(0.776591\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.3199 | + | 14.0367i | 0.738176 | + | 0.536316i | ||||
\(686\) | 9.33969 | − | 20.9773i | 0.356591 | − | 0.800917i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.39645 | − | 3.95858i | 0.167613 | − | 0.150919i | ||||
\(689\) | 0.597702 | + | 5.68675i | 0.0227706 | + | 0.216648i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.4231 | + | 20.4609i | −0.700849 | + | 0.778371i | −0.983511 | − | 0.180848i | \(-0.942116\pi\) |
0.282662 | + | 0.959219i | \(0.408782\pi\) | |||||||
\(692\) | 26.5278 | 1.00844 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.91971 | 0.224709 | ||||||||
\(695\) | −0.0798427 | + | 0.0886743i | −0.00302861 | + | 0.00336361i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.0673225 | + | 0.640531i | 0.00255002 | + | 0.0242618i | ||||
\(698\) | −15.2502 | + | 13.7314i | −0.577229 | + | 0.519739i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.314449 | − | 0.706264i | 0.0118851 | − | 0.0266943i | ||||
\(701\) | 8.43699 | + | 6.12983i | 0.318661 | + | 0.231521i | 0.735604 | − | 0.677412i | \(-0.236899\pi\) |
−0.416943 | + | 0.908933i | \(0.636899\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.4101i | 0.656636i | ||||||||
\(704\) | 26.8000 | − | 29.4049i | 1.01006 | − | 1.10824i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.262219 | − | 1.23364i | 0.00986875 | − | 0.0464288i | ||||
\(707\) | 2.83720 | + | 6.37246i | 0.106704 | + | 0.239661i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.6086 | − | 4.16794i | 0.736417 | − | 0.156530i | 0.175590 | − | 0.984463i | \(-0.443817\pi\) |
0.560827 | + | 0.827933i | \(0.310483\pi\) | |||||||
\(710\) | −1.82988 | + | 5.63178i | −0.0686740 | + | 0.211357i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13.8975 | + | 19.1282i | −0.520829 | + | 0.716860i | ||||
\(713\) | 4.01650 | + | 3.61647i | 0.150419 | + | 0.135438i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.5270 | − | 29.9381i | 0.655473 | − | 1.11962i | ||||
\(716\) | −38.1738 | − | 22.0397i | −1.42662 | − | 0.823660i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.88388 | + | 36.9527i | −0.144945 | + | 1.37906i | ||||
\(719\) | 6.01752 | + | 8.28241i | 0.224416 | + | 0.308882i | 0.906347 | − | 0.422535i | \(-0.138860\pi\) |
−0.681931 | + | 0.731417i | \(0.738860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.4479 | − | 4.04456i | −0.463583 | − | 0.150627i | ||||
\(722\) | 28.4769 | + | 12.6787i | 1.05980 | + | 0.471853i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 62.0890 | + | 13.1974i | 2.30752 | + | 0.490478i | ||||
\(725\) | −0.0497687 | + | 0.0862019i | −0.00184836 | + | 0.00320146i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.22282 | + | 12.5103i | 0.267880 | + | 0.463981i | 0.968314 | − | 0.249736i | \(-0.0803437\pi\) |
−0.700434 | + | 0.713717i | \(0.747010\pi\) | |||||||
\(728\) | 20.8976 | + | 64.3163i | 0.774517 | + | 2.38372i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −56.8943 | + | 41.3361i | −2.10575 | + | 1.52992i | ||||
\(731\) | −0.0679024 | − | 0.319456i | −0.00251146 | − | 0.0118155i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.26913 | + | 0.764016i | −0.268491 | + | 0.0282196i | −0.237817 | − | 0.971310i | \(-0.576432\pi\) |
−0.0306739 | + | 0.999529i | \(0.509765\pi\) | |||||||
\(734\) | 62.1359 | − | 27.6647i | 2.29348 | − | 1.02112i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −10.9756 | + | 6.33674i | −0.404565 | + | 0.233575i | ||||
\(737\) | −43.1100 | − | 0.260675i | −1.58798 | − | 0.00960207i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.4909 | + | 4.05854i | −0.459485 | + | 0.149296i | −0.529608 | − | 0.848243i | \(-0.677661\pi\) |
0.0701229 | + | 0.997538i | \(0.477661\pi\) | |||||||
\(740\) | −57.2929 | − | 6.02173i | −2.10613 | − | 0.221363i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.83150 | + | 8.69776i | 0.287503 | + | 0.319305i | ||||
\(743\) | 23.6688 | + | 26.2868i | 0.868323 | + | 0.964370i | 0.999636 | − | 0.0269705i | \(-0.00858600\pi\) |
−0.131313 | + | 0.991341i | \(0.541919\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 45.5995 | + | 4.79270i | 1.67063 | + | 0.175591i | ||||
\(746\) | −14.7768 | + | 4.80127i | −0.541017 | + | 0.175787i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.270584 | + | 0.850230i | 0.00989352 | + | 0.0310875i | ||||
\(749\) | −51.9880 | + | 30.0153i | −1.89960 | + | 1.09674i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.0742 | + | 9.38284i | −0.769009 | + | 0.342385i | −0.753460 | − | 0.657494i | \(-0.771616\pi\) |
−0.0155493 | + | 0.999879i | \(0.504950\pi\) | |||||||
\(752\) | −8.54306 | + | 0.897912i | −0.311533 | + | 0.0327435i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.18244 | − | 19.6768i | −0.152315 | − | 0.716588i | ||||
\(755\) | 2.16285 | − | 1.57140i | 0.0787141 | − | 0.0571892i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.02640 | + | 9.31430i | 0.109996 | + | 0.338534i | 0.990871 | − | 0.134816i | \(-0.0430445\pi\) |
−0.880874 | + | 0.473350i | \(0.843044\pi\) | |||||||
\(758\) | −1.82015 | − | 3.15259i | −0.0661108 | − | 0.114507i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.66246 | − | 16.7359i | 0.350494 | − | 0.607074i | ||||
\(761\) | −47.3669 | − | 10.0682i | −1.71705 | − | 0.364970i | −0.758894 | − | 0.651215i | \(-0.774260\pi\) |
−0.958157 | + | 0.286244i | \(0.907593\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 55.2379 | + | 24.5935i | 1.99975 | + | 0.890345i | ||||
\(764\) | 72.6303 | + | 23.5990i | 2.62767 | + | 0.853783i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.6646 | − | 25.6897i | −0.674381 | − | 0.928205i | ||||
\(767\) | −0.282216 | + | 2.68510i | −0.0101902 | + | 0.0969535i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.9445 | − | 16.7111i | −1.04377 | − | 0.602619i | −0.122869 | − | 0.992423i | \(-0.539209\pi\) |
−0.920898 | + | 0.389804i | \(0.872543\pi\) | |||||||
\(770\) | −6.99517 | − | 70.6622i | −0.252089 | − | 2.54649i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.5924 | − | 12.2387i | −0.489203 | − | 0.440480i | ||||
\(773\) | −3.82924 | + | 5.27050i | −0.137728 | + | 0.189567i | −0.872310 | − | 0.488954i | \(-0.837379\pi\) |
0.734581 | + | 0.678521i | \(0.237379\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.0280083 | + | 0.0862007i | −0.00100609 | + | 0.00309642i | ||||
\(776\) | −57.7127 | + | 12.2672i | −2.07177 | + | 0.440368i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.3227 | + | 32.1693i | 0.513494 | + | 1.15333i | ||||
\(779\) | 4.20515 | − | 19.7837i | 0.150665 | − | 0.708824i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.750645 | + | 3.63958i | 0.0268602 | + | 0.130234i | ||||
\(782\) | − | 0.578780i | − | 0.0206971i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.5220 | + | 7.64471i | 0.375787 | + | 0.273025i | ||||
\(785\) | 1.58473 | − | 3.55937i | 0.0565616 | − | 0.127039i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.5467 | + | 19.4007i | −0.768057 | + | 0.691562i | −0.956891 | − | 0.290447i | \(-0.906196\pi\) |
0.188834 | + | 0.982009i | \(0.439529\pi\) | |||||||
\(788\) | 1.89707 | + | 18.0495i | 0.0675805 | + | 0.642985i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.33347 | − | 2.59158i | 0.0830211 | − | 0.0922042i | ||||
\(791\) | −45.5606 | −1.61995 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.5974 | −0.624901 | ||||||||
\(794\) | −32.5816 | + | 36.1856i | −1.15628 | + | 1.28418i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.94190 | − | 85.0765i | −0.316937 | − | 3.01546i | ||||
\(797\) | −20.1023 | + | 18.1002i | −0.712059 | + | 0.641141i | −0.943371 | − | 0.331738i | \(-0.892365\pi\) |
0.231312 | + | 0.972880i | \(0.425698\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.192881 | + | 0.433219i | −0.00682366 | + | 0.0153262i | ||||
\(800\) | −0.171943 | − | 0.124924i | −0.00607910 | − | 0.00441672i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 63.5768i | − | 2.24498i | ||||||
\(803\) | −18.1942 | + | 40.2088i | −0.642060 | + | 1.41894i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.11075 | + | 28.7488i | −0.215376 | + | 1.01326i | ||||
\(806\) | −7.45044 | − | 16.7340i | −0.262431 | − | 0.589429i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.04302 | + | 1.28448i | −0.212593 | + | 0.0451880i | ||||
\(809\) | 12.9385 | − | 39.8205i | 0.454892 | − | 1.40001i | −0.416370 | − | 0.909195i | \(-0.636698\pi\) |
0.871262 | − | 0.490818i | \(-0.163302\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.51871 | + | 10.3486i | −0.264018 | + | 0.363389i | −0.920359 | − | 0.391075i | \(-0.872103\pi\) |
0.656341 | + | 0.754464i | \(0.272103\pi\) | |||||||
\(812\) | −19.5250 | − | 17.5804i | −0.685193 | − | 0.616951i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −51.8981 | + | 22.7315i | −1.81903 | + | 0.796739i | ||||
\(815\) | 1.95201 | + | 1.12699i | 0.0683760 | + | 0.0394769i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.07206 | + | 10.1999i | −0.0375065 | + | 0.356851i | ||||
\(818\) | −8.43637 | − | 11.6117i | −0.294971 | − | 0.405992i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 63.6493 | + | 20.6809i | 2.22273 | + | 0.722208i | ||||
\(821\) | −10.8368 | − | 4.82484i | −0.378206 | − | 0.168388i | 0.208824 | − | 0.977953i | \(-0.433036\pi\) |
−0.587030 | + | 0.809565i | \(0.699703\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.7019 | − | 5.46311i | −0.895912 | − | 0.190432i | −0.263128 | − | 0.964761i | \(-0.584754\pi\) |
−0.632783 | + | 0.774329i | \(0.718088\pi\) | |||||||
\(824\) | 5.79604 | − | 10.0390i | 0.201914 | − | 0.349726i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.76313 | + | 4.78588i | 0.0961415 | + | 0.166522i | ||||
\(827\) | 7.99992 | + | 24.6212i | 0.278184 | + | 0.856163i | 0.988359 | + | 0.152138i | \(0.0486159\pi\) |
−0.710175 | + | 0.704025i | \(0.751384\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.0195 | + | 10.1858i | −0.486918 | + | 0.353766i | −0.803998 | − | 0.594632i | \(-0.797298\pi\) |
0.317080 | + | 0.948399i | \(0.397298\pi\) | |||||||
\(830\) | 11.2200 | + | 52.7858i | 0.389451 | + | 1.83222i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 55.5066 | − | 5.83398i | 1.92435 | − | 0.202257i | ||||
\(833\) | 0.655920 | − | 0.292034i | 0.0227263 | − | 0.0101184i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.3191 | + | 15.1953i | −0.910809 | + | 0.525856i | ||||
\(836\) | 0.169424 | − | 28.0191i | 0.00585965 | − | 0.969061i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 79.7307 | − | 25.9061i | 2.75425 | − | 0.894911i | ||||
\(839\) | −30.8808 | − | 3.24571i | −1.06612 | − | 0.112054i | −0.444818 | − | 0.895621i | \(-0.646731\pi\) |
−0.621307 | + | 0.783567i | \(0.713398\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.1413 | − | 19.0373i | −0.591079 | − | 0.656460i | ||||
\(842\) | 22.5058 | + | 24.9952i | 0.775601 | + | 0.861392i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −65.7327 | − | 6.90879i | −2.26261 | − | 0.237810i | ||||
\(845\) | 18.4888 | − | 6.00737i | 0.636033 | − | 0.206660i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.7549 | − | 36.3654i | −0.884949 | − | 1.24953i | ||||
\(848\) | −1.47088 | + | 0.849211i | −0.0505101 | + | 0.0291620i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.00886694 | − | 0.00394782i | 0.000304134 | − | 0.000135409i | ||||
\(851\) | 23.3231 | − | 2.45136i | 0.799507 | − | 0.0840315i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.0664004 | − | 0.312389i | −0.00227351 | − | 0.0106960i | 0.976996 | − | 0.213257i | \(-0.0684070\pi\) |
−0.979270 | + | 0.202561i | \(0.935074\pi\) | |||||||
\(854\) | −29.1400 | + | 21.1714i | −0.997150 | + | 0.724472i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.4296 | − | 50.5652i | −0.561553 | − | 1.72828i | ||||
\(857\) | −6.62378 | − | 11.4727i | −0.226264 | − | 0.391901i | 0.730434 | − | 0.682983i | \(-0.239318\pi\) |
−0.956698 | + | 0.291083i | \(0.905985\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.29076 | − | 7.43181i | 0.146399 | − | 0.253570i | −0.783495 | − | 0.621398i | \(-0.786565\pi\) |
0.929894 | + | 0.367828i | \(0.119898\pi\) | |||||||
\(860\) | −33.1949 | − | 7.05580i | −1.13194 | − | 0.240601i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −18.6907 | − | 8.32163i | −0.636607 | − | 0.283436i | ||||
\(863\) | 51.0889 | + | 16.5998i | 1.73909 | + | 0.565063i | 0.994712 | − | 0.102700i | \(-0.0327482\pi\) |
0.744374 | + | 0.667763i | \(0.232748\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.94098 | − | 13.6826i | −0.338004 | − | 0.465222i | ||||
\(866\) | 9.22779 | − | 87.7966i | 0.313573 | − | 2.98345i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −20.7189 | − | 11.9620i | −0.703245 | − | 0.406018i | ||||
\(869\) | 0.467953 | − | 2.13790i | 0.0158742 | − | 0.0725232i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −44.9433 | − | 40.4671i | −1.52284 | − | 1.37118i | ||||
\(872\) | −31.4774 | + | 43.3249i | −1.06596 | + | 1.46717i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.61659 | + | 17.2861i | −0.189984 | + | 0.584710i | ||||
\(875\) | 44.0596 | − | 9.36517i | 1.48949 | − | 0.316600i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.9027 | − | 40.2101i | −0.604531 | − | 1.35780i | −0.913544 | − | 0.406741i | \(-0.866665\pi\) |
0.309013 | − | 0.951058i | \(-0.400001\pi\) | |||||||
\(878\) | 15.8685 | − | 74.6552i | 0.535535 | − | 2.51949i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.2411 | + | 1.13903i | 0.345228 | + | 0.0383968i | ||||
\(881\) | 7.44194i | 0.250725i | 0.992111 | + | 0.125363i | \(0.0400095\pi\) | ||||
−0.992111 | + | 0.125363i | \(0.959991\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.59369 | + | 5.51714i | 0.255548 | + | 0.185667i | 0.708182 | − | 0.706030i | \(-0.249516\pi\) |
−0.452634 | + | 0.891696i | \(0.649516\pi\) | |||||||
\(884\) | −0.509101 | + | 1.14346i | −0.0171229 | + | 0.0384587i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32.8808 | + | 29.6060i | −1.10465 | + | 0.994633i | ||||
\(887\) | −2.52799 | − | 24.0522i | −0.0848816 | − | 0.807595i | −0.951298 | − | 0.308273i | \(-0.900249\pi\) |
0.866416 | − | 0.499322i | \(-0.166418\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.4308 | − | 18.2483i | 0.551072 | − | 0.612028i | ||||
\(890\) | 34.8267 | 1.16739 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.3542 | −0.648026 | ||||||||
\(893\) | 9.96472 | − | 11.0669i | 0.333457 | − | 0.370341i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.93750 | + | 27.9485i | 0.0981899 | + | 0.934214i | ||||
\(896\) | 61.2507 | − | 55.1504i | 2.04624 | − | 1.84244i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.90523 | − | 15.5094i | 0.230431 | − | 0.517555i | ||||
\(899\) | 2.49197 | + | 1.81052i | 0.0831119 | + | 0.0603843i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.0937613i | 0.00312364i | ||||||||
\(902\) | 64.4639 | − | 13.2953i | 2.14641 | − | 0.442686i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.38958 | − | 39.4699i | 0.279033 | − | 1.31275i | ||||
\(905\) | −16.4601 | − | 36.9700i | −0.547152 | − | 1.22892i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.0511 | − | 7.45035i | 1.16385 | − | 0.247385i | 0.414812 | − | 0.909907i | \(-0.363848\pi\) |
0.749042 | + | 0.662523i | \(0.230514\pi\) | |||||||
\(908\) | 14.9980 | − | 46.1592i | 0.497728 | − | 1.53185i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 58.5502 | − | 80.5875i | 1.94092 | − | 2.67145i | ||||
\(911\) | −6.50944 | − | 5.86113i | −0.215668 | − | 0.194188i | 0.554215 | − | 0.832374i | \(-0.313019\pi\) |
−0.769883 | + | 0.638186i | \(0.779685\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.5085 | + | 25.3043i | 0.744924 | + | 0.837450i | ||||
\(914\) | −8.59575 | − | 4.96276i | −0.284322 | − | 0.164154i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.78937 | − | 74.1109i | 0.257368 | − | 2.44869i | ||||
\(917\) | 17.0273 | + | 23.4360i | 0.562290 | + | 0.773926i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.4876 | − | 12.8303i | −1.30258 | − | 0.423233i | −0.426100 | − | 0.904676i | \(-0.640113\pi\) |
−0.876477 | + | 0.481443i | \(0.840113\pi\) | |||||||
\(920\) | −23.7803 | − | 10.5877i | −0.784015 | − | 0.349066i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 32.6340 | + | 6.93657i | 1.07474 | + | 0.228444i | ||||
\(923\) | −2.60659 | + | 4.51474i | −0.0857969 | + | 0.148605i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.196640 | + | 0.340591i | 0.00646550 | + | 0.0111986i | ||||
\(926\) | −29.3323 | − | 90.2756i | −0.963920 | − | 2.96664i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.84339 | + | 4.24547i | −0.191819 | + | 0.139364i | ||||
\(929\) | −11.2664 | − | 53.0043i | −0.369639 | − | 1.73901i | −0.632849 | − | 0.774276i | \(-0.718114\pi\) |
0.263210 | − | 0.964739i | \(-0.415219\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.4239 | + | 2.35685i | −0.734915 | + | 0.0772426i | ||||
\(932\) | −48.2097 | + | 21.4643i | −1.57916 | + | 0.703088i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 23.0065 | − | 13.2828i | 0.752795 | − | 0.434626i | ||||
\(935\) | 0.337136 | − | 0.458176i | 0.0110255 | − | 0.0149839i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.5444 | + | 5.37559i | −0.540480 | + | 0.175613i | −0.566520 | − | 0.824048i | \(-0.691710\pi\) |
0.0260393 | + | 0.999661i | \(0.491710\pi\) | |||||||
\(938\) | −123.109 | − | 12.9393i | −4.01965 | − | 0.422482i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 32.9723 | + | 36.6194i | 1.07544 | + | 1.19439i | ||||
\(941\) | −14.3933 | − | 15.9854i | −0.469207 | − | 0.521108i | 0.461368 | − | 0.887209i | \(-0.347359\pi\) |
−0.930575 | + | 0.366101i | \(0.880692\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.0949 | − | 2.84779i | −0.882331 | − | 0.0927367i | ||||
\(944\) | −0.762692 | + | 0.247814i | −0.0248235 | + | 0.00806564i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −31.8049 | + | 10.1218i | −1.03407 | + | 0.329089i | ||||
\(947\) | −38.7882 | + | 22.3944i | −1.26045 | + | 0.727719i | −0.973161 | − | 0.230126i | \(-0.926086\pi\) |
−0.287286 | + | 0.957845i | \(0.592753\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −56.5594 | + | 25.1819i | −1.83600 | + | 0.817438i | ||||
\(950\) | −0.303134 | + | 0.0318607i | −0.00983497 | + | 0.00103370i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.230551 | + | 1.08466i | 0.00747220 | + | 0.0351540i | ||||
\(953\) | 8.11741 | − | 5.89765i | 0.262949 | − | 0.191043i | −0.448497 | − | 0.893784i | \(-0.648041\pi\) |
0.711446 | + | 0.702741i | \(0.248041\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.0454 | − | 46.3049i | −0.486857 | − | 1.49839i | ||||
\(956\) | 9.52970 | + | 16.5059i | 0.308213 | + | 0.533840i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 26.9147 | − | 46.6176i | 0.869574 | − | 1.50615i | ||||
\(959\) | 42.0920 | + | 8.94693i | 1.35922 | + | 0.288911i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.7576 | − | 11.4680i | −0.830890 | − | 0.369936i | ||||
\(962\) | −75.5916 | − | 24.5612i | −2.43717 | − | 0.791884i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 24.2693 | + | 33.4039i | 0.781662 | + | 1.07587i | ||||
\(965\) | −1.21890 | + | 11.5970i | −0.0392377 | + | 0.373322i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.74268 | − | 2.16084i | −0.120356 | − | 0.0694878i | 0.438613 | − | 0.898676i | \(-0.355470\pi\) |
−0.558970 | + | 0.829188i | \(0.688803\pi\) | |||||||
\(968\) | 36.2465 | − | 15.6155i | 1.16501 | − | 0.501902i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 64.5857 | + | 58.1532i | 2.07372 | + | 1.86719i | ||||
\(971\) | −33.7344 | + | 46.4314i | −1.08259 | + | 1.49005i | −0.225947 | + | 0.974140i | \(0.572548\pi\) |
−0.856640 | + | 0.515914i | \(0.827452\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.0664437 | + | 0.204493i | −0.00213009 | + | 0.00655574i | ||||
\(974\) | 17.3425 | − | 3.68627i | 0.555690 | − | 0.118116i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.12597 | − | 4.77500i | −0.0680506 | − | 0.152844i | ||||
\(977\) | 0.717330 | − | 3.37477i | 0.0229494 | − | 0.107969i | −0.965182 | − | 0.261579i | \(-0.915757\pi\) |
0.988131 | + | 0.153611i | \(0.0490901\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.9936 | − | 10.8133i | 0.607037 | − | 0.345596i | ||||
\(980\) | − | 74.6073i | − | 2.38324i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −72.6315 | − | 52.7699i | −2.31776 | − | 1.68395i | ||||
\(983\) | −0.420841 | + | 0.945223i | −0.0134227 | + | 0.0301479i | −0.920132 | − | 0.391607i | \(-0.871919\pi\) |
0.906710 | + | 0.421755i | \(0.138586\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.59869 | − | 7.74230i | 0.273977 | − | 0.246690i | ||||
\(986\) | −0.0344793 | − | 0.328049i | −0.00109805 | − | 0.0104472i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 26.3014 | − | 29.2106i | 0.836758 | − | 0.929314i | ||||
\(989\) | 13.8151 | 0.439294 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.78910 | 0.310961 | 0.155481 | − | 0.987839i | \(-0.450307\pi\) | ||||
0.155481 | + | 0.987839i | \(0.450307\pi\) | |||||||
\(992\) | −4.40085 | + | 4.88763i | −0.139727 | + | 0.155183i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.11538 | + | 10.6121i | 0.0353776 | + | 0.336595i | ||||
\(995\) | −40.5301 | + | 36.4935i | −1.28489 | + | 1.15692i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.72409 | + | 10.6105i | −0.149613 | + | 0.336037i | −0.972768 | − | 0.231780i | \(-0.925545\pi\) |
0.823155 | + | 0.567817i | \(0.192212\pi\) | |||||||
\(998\) | 15.3271 | + | 11.1358i | 0.485170 | + | 0.352496i | ||||
\(999\) | 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.u.c.215.4 | 32 | ||
3.2 | odd | 2 | inner | 891.2.u.c.215.1 | 32 | ||
9.2 | odd | 6 | inner | 891.2.u.c.512.4 | 32 | ||
9.4 | even | 3 | 99.2.j.a.17.4 | yes | 16 | ||
9.5 | odd | 6 | 99.2.j.a.17.1 | ✓ | 16 | ||
9.7 | even | 3 | inner | 891.2.u.c.512.1 | 32 | ||
11.2 | odd | 10 | inner | 891.2.u.c.134.4 | 32 | ||
33.2 | even | 10 | inner | 891.2.u.c.134.1 | 32 | ||
36.23 | even | 6 | 1584.2.cd.c.17.1 | 16 | |||
36.31 | odd | 6 | 1584.2.cd.c.17.4 | 16 | |||
99.2 | even | 30 | inner | 891.2.u.c.431.4 | 32 | ||
99.13 | odd | 30 | 99.2.j.a.35.1 | yes | 16 | ||
99.14 | odd | 30 | 1089.2.d.g.1088.3 | 16 | |||
99.41 | even | 30 | 1089.2.d.g.1088.13 | 16 | |||
99.58 | even | 15 | 1089.2.d.g.1088.14 | 16 | |||
99.68 | even | 30 | 99.2.j.a.35.4 | yes | 16 | ||
99.79 | odd | 30 | inner | 891.2.u.c.431.1 | 32 | ||
99.85 | odd | 30 | 1089.2.d.g.1088.4 | 16 | |||
396.167 | odd | 30 | 1584.2.cd.c.1025.4 | 16 | |||
396.211 | even | 30 | 1584.2.cd.c.1025.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.j.a.17.1 | ✓ | 16 | 9.5 | odd | 6 | ||
99.2.j.a.17.4 | yes | 16 | 9.4 | even | 3 | ||
99.2.j.a.35.1 | yes | 16 | 99.13 | odd | 30 | ||
99.2.j.a.35.4 | yes | 16 | 99.68 | even | 30 | ||
891.2.u.c.134.1 | 32 | 33.2 | even | 10 | inner | ||
891.2.u.c.134.4 | 32 | 11.2 | odd | 10 | inner | ||
891.2.u.c.215.1 | 32 | 3.2 | odd | 2 | inner | ||
891.2.u.c.215.4 | 32 | 1.1 | even | 1 | trivial | ||
891.2.u.c.431.1 | 32 | 99.79 | odd | 30 | inner | ||
891.2.u.c.431.4 | 32 | 99.2 | even | 30 | inner | ||
891.2.u.c.512.1 | 32 | 9.7 | even | 3 | inner | ||
891.2.u.c.512.4 | 32 | 9.2 | odd | 6 | inner | ||
1089.2.d.g.1088.3 | 16 | 99.14 | odd | 30 | |||
1089.2.d.g.1088.4 | 16 | 99.85 | odd | 30 | |||
1089.2.d.g.1088.13 | 16 | 99.41 | even | 30 | |||
1089.2.d.g.1088.14 | 16 | 99.58 | even | 15 | |||
1584.2.cd.c.17.1 | 16 | 36.23 | even | 6 | |||
1584.2.cd.c.17.4 | 16 | 36.31 | odd | 6 | |||
1584.2.cd.c.1025.1 | 16 | 396.211 | even | 30 | |||
1584.2.cd.c.1025.4 | 16 | 396.167 | odd | 30 |