Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [869,2,Mod(315,869)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(869, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([7, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("869.315");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 869 = 11 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 869.l (of order \(10\), 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: | \(6.93899993565\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.484000000.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 710.2 | ||
Root | \(1.73855 - 1.26313i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 869.710 |
Dual form | 869.2.l.a.552.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/869\mathbb{Z}\right)^\times\).
\(n\) | \(475\) | \(793\) |
\(\chi(n)\) | \(e\left(\frac{9}{10}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.80902 | − | 0.587785i | 1.27917 | − | 0.415627i | 0.410881 | − | 0.911689i | \(-0.365221\pi\) |
0.868287 | + | 0.496062i | \(0.165221\pi\) | |||||||
\(3\) | 1.48490 | − | 2.04378i | 0.857305 | − | 1.17998i | −0.124901 | − | 0.992169i | \(-0.539861\pi\) |
0.982205 | − | 0.187810i | \(-0.0601388\pi\) | |||||||
\(4\) | 1.30902 | − | 0.951057i | 0.654508 | − | 0.475528i | ||||
\(5\) | 1.19098 | − | 3.66547i | 0.532624 | − | 1.63925i | −0.216104 | − | 0.976370i | \(-0.569335\pi\) |
0.748728 | − | 0.662877i | \(-0.230665\pi\) | |||||||
\(6\) | 1.48490 | − | 4.57004i | 0.606206 | − | 1.86571i | ||||
\(7\) | −1.07448 | + | 0.780656i | −0.406115 | + | 0.295060i | −0.772027 | − | 0.635589i | \(-0.780757\pi\) |
0.365912 | + | 0.930650i | \(0.380757\pi\) | |||||||
\(8\) | −0.427051 | + | 0.587785i | −0.150985 | + | 0.207813i | ||||
\(9\) | −1.04508 | − | 3.21644i | −0.348362 | − | 1.07215i | ||||
\(10\) | − | 7.33094i | − | 2.31825i | ||||||
\(11\) | 2.54508 | + | 2.12663i | 0.767372 | + | 0.641202i | ||||
\(12\) | − | 4.08757i | − | 1.17998i | ||||||
\(13\) | −1.38197 | + | 0.449028i | −0.383288 | + | 0.124538i | −0.494322 | − | 0.869279i | \(-0.664584\pi\) |
0.111034 | + | 0.993817i | \(0.464584\pi\) | |||||||
\(14\) | −1.48490 | + | 2.04378i | −0.396855 | + | 0.546224i | ||||
\(15\) | −5.72294 | − | 7.87695i | −1.47766 | − | 2.03382i | ||||
\(16\) | −1.42705 | + | 4.39201i | −0.356763 | + | 1.09800i | ||||
\(17\) | −1.99220 | + | 6.13135i | −0.483179 | + | 1.48707i | 0.351423 | + | 0.936217i | \(0.385698\pi\) |
−0.834602 | + | 0.550854i | \(0.814302\pi\) | |||||||
\(18\) | −3.78115 | − | 5.20431i | −0.891226 | − | 1.22667i | ||||
\(19\) | 4.47214 | − | 6.15537i | 1.02598 | − | 1.41214i | 0.118052 | − | 0.993007i | \(-0.462335\pi\) |
0.907926 | − | 0.419131i | \(-0.137665\pi\) | |||||||
\(20\) | −1.92705 | − | 5.93085i | −0.430902 | − | 1.32618i | ||||
\(21\) | 3.35520i | 0.732164i | ||||||||
\(22\) | 5.85410 | + | 2.35114i | 1.24810 | + | 0.501265i | ||||
\(23\) | 4.09017 | 0.852859 | 0.426430 | − | 0.904521i | \(-0.359771\pi\) | ||||
0.426430 | + | 0.904521i | \(0.359771\pi\) | |||||||
\(24\) | 0.567180 | + | 1.74560i | 0.115775 | + | 0.356319i | ||||
\(25\) | −7.97214 | − | 5.79210i | −1.59443 | − | 1.15842i | ||||
\(26\) | −2.23607 | + | 1.62460i | −0.438529 | + | 0.318610i | ||||
\(27\) | −0.917716 | − | 0.298184i | −0.176615 | − | 0.0573855i | ||||
\(28\) | −0.664066 | + | 2.04378i | −0.125497 | + | 0.386239i | ||||
\(29\) | −3.88751 | + | 2.82444i | −0.721892 | + | 0.524485i | −0.886988 | − | 0.461792i | \(-0.847207\pi\) |
0.165096 | + | 0.986277i | \(0.447207\pi\) | |||||||
\(30\) | −14.9828 | − | 10.8857i | −2.73548 | − | 1.98744i | ||||
\(31\) | 1.11803 | + | 3.44095i | 0.200805 | + | 0.618014i | 0.999860 | + | 0.0167555i | \(0.00533369\pi\) |
−0.799055 | + | 0.601258i | \(0.794666\pi\) | |||||||
\(32\) | 7.33094i | 1.29594i | ||||||||
\(33\) | 8.12555 | − | 2.04378i | 1.41448 | − | 0.355777i | ||||
\(34\) | 12.2627i | 2.10304i | ||||||||
\(35\) | 1.58178 | + | 4.86822i | 0.267370 | + | 0.822880i | ||||
\(36\) | −4.42705 | − | 3.21644i | −0.737842 | − | 0.536073i | ||||
\(37\) | −5.37240 | − | 7.39448i | −0.883218 | − | 1.21564i | −0.975519 | − | 0.219914i | \(-0.929422\pi\) |
0.0923018 | − | 0.995731i | \(-0.470578\pi\) | |||||||
\(38\) | 4.47214 | − | 13.7638i | 0.725476 | − | 2.23279i | ||||
\(39\) | −1.13436 | + | 3.49120i | −0.181643 | + | 0.559039i | ||||
\(40\) | 1.64590 | + | 2.26538i | 0.260239 | + | 0.358189i | ||||
\(41\) | 8.84950 | + | 6.42953i | 1.38206 | + | 1.00412i | 0.996684 | + | 0.0813643i | \(0.0259277\pi\) |
0.385375 | + | 0.922760i | \(0.374072\pi\) | |||||||
\(42\) | 1.97214 | + | 6.06961i | 0.304307 | + | 0.936561i | ||||
\(43\) | −11.5656 | −1.76374 | −0.881871 | − | 0.471490i | \(-0.843716\pi\) | ||||
−0.881871 | + | 0.471490i | \(0.843716\pi\) | |||||||
\(44\) | 5.35410 | + | 0.363271i | 0.807161 | + | 0.0547652i | ||||
\(45\) | −13.0344 | −1.94306 | ||||||||
\(46\) | 7.39919 | − | 2.40414i | 1.09095 | − | 0.354471i | ||||
\(47\) | 2.05208 | − | 2.82444i | 0.299326 | − | 0.411987i | −0.632689 | − | 0.774406i | \(-0.718049\pi\) |
0.932015 | + | 0.362419i | \(0.118049\pi\) | |||||||
\(48\) | 6.85730 | + | 9.43826i | 0.989766 | + | 1.36230i | ||||
\(49\) | −1.61803 | + | 4.97980i | −0.231148 | + | 0.711400i | ||||
\(50\) | −17.8262 | − | 5.79210i | −2.52101 | − | 0.819126i | ||||
\(51\) | 9.57295 | + | 13.1760i | 1.34048 | + | 1.84501i | ||||
\(52\) | −1.38197 | + | 1.90211i | −0.191644 | + | 0.263776i | ||||
\(53\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(54\) | −1.83543 | −0.249771 | ||||||||
\(55\) | 10.8262 | − | 6.79615i | 1.45981 | − | 0.916393i | ||||
\(56\) | − | 0.964944i | − | 0.128946i | ||||||
\(57\) | −5.93958 | − | 18.2802i | −0.786717 | − | 2.42127i | ||||
\(58\) | −5.37240 | + | 7.39448i | −0.705431 | + | 0.970943i | ||||
\(59\) | −2.40261 | − | 3.30691i | −0.312793 | − | 0.430523i | 0.623456 | − | 0.781858i | \(-0.285728\pi\) |
−0.936250 | + | 0.351335i | \(0.885728\pi\) | |||||||
\(60\) | −14.9828 | − | 4.86822i | −1.93428 | − | 0.628485i | ||||
\(61\) | 2.81303 | − | 8.65761i | 0.360171 | − | 1.10849i | −0.592779 | − | 0.805365i | \(-0.701969\pi\) |
0.952950 | − | 0.303128i | \(-0.0980308\pi\) | |||||||
\(62\) | 4.04508 | + | 5.56758i | 0.513726 | + | 0.707084i | ||||
\(63\) | 3.63386 | + | 2.64015i | 0.457823 | + | 0.332628i | ||||
\(64\) | 1.45492 | + | 4.47777i | 0.181864 | + | 0.559721i | ||||
\(65\) | 5.60034i | 0.694636i | ||||||||
\(66\) | 13.4980 | − | 8.47332i | 1.66148 | − | 1.04299i | ||||
\(67\) | −11.9443 | −1.45923 | −0.729613 | − | 0.683861i | \(-0.760300\pi\) | ||||
−0.729613 | + | 0.683861i | \(0.760300\pi\) | |||||||
\(68\) | 3.22344 | + | 9.92073i | 0.390900 | + | 1.20307i | ||||
\(69\) | 6.07348 | − | 8.35942i | 0.731161 | − | 1.00636i | ||||
\(70\) | 5.72294 | + | 7.87695i | 0.684022 | + | 0.941476i | ||||
\(71\) | 10.7448 | + | 3.49120i | 1.27517 | + | 0.414329i | 0.866878 | − | 0.498521i | \(-0.166123\pi\) |
0.408296 | + | 0.912850i | \(0.366123\pi\) | |||||||
\(72\) | 2.33688 | + | 0.759299i | 0.275404 | + | 0.0894842i | ||||
\(73\) | −0.427051 | − | 0.587785i | −0.0499825 | − | 0.0687951i | 0.783294 | − | 0.621651i | \(-0.213538\pi\) |
−0.833277 | + | 0.552856i | \(0.813538\pi\) | |||||||
\(74\) | −14.0651 | − | 10.2189i | −1.63504 | − | 1.18793i | ||||
\(75\) | −23.6756 | + | 7.69266i | −2.73382 | + | 0.888272i | ||||
\(76\) | − | 12.3107i | − | 1.41214i | ||||||
\(77\) | −4.39481 | − | 0.298184i | −0.500835 | − | 0.0339812i | ||||
\(78\) | 6.98240i | 0.790601i | ||||||||
\(79\) | 8.01334 | + | 3.84530i | 0.901572 | + | 0.432630i | ||||
\(80\) | 14.3992 | + | 10.4616i | 1.60988 | + | 1.16964i | ||||
\(81\) | 6.23607 | − | 4.53077i | 0.692896 | − | 0.503419i | ||||
\(82\) | 19.7881 | + | 6.42953i | 2.18523 | + | 0.710023i | ||||
\(83\) | −7.39919 | − | 2.40414i | −0.812166 | − | 0.263889i | −0.126651 | − | 0.991947i | \(-0.540423\pi\) |
−0.685515 | + | 0.728058i | \(0.740423\pi\) | |||||||
\(84\) | 3.19098 | + | 4.39201i | 0.348165 | + | 0.479208i | ||||
\(85\) | 20.1016 | + | 14.6047i | 2.18032 | + | 1.58410i | ||||
\(86\) | −20.9224 | + | 6.79811i | −2.25612 | + | 0.733059i | ||||
\(87\) | 12.1392i | 1.30146i | ||||||||
\(88\) | −2.33688 | + | 0.587785i | −0.249112 | + | 0.0626581i | ||||
\(89\) | −2.23607 | −0.237023 | −0.118511 | − | 0.992953i | \(-0.537812\pi\) | ||||
−0.118511 | + | 0.992953i | \(0.537812\pi\) | |||||||
\(90\) | −23.5795 | + | 7.66145i | −2.48550 | + | 0.807588i | ||||
\(91\) | 1.13436 | − | 1.56131i | 0.118913 | − | 0.163670i | ||||
\(92\) | 5.35410 | − | 3.88998i | 0.558204 | − | 0.405559i | ||||
\(93\) | 8.69273 | + | 2.82444i | 0.901394 | + | 0.292881i | ||||
\(94\) | 2.05208 | − | 6.31564i | 0.211655 | − | 0.651408i | ||||
\(95\) | −17.2361 | − | 23.7234i | −1.76838 | − | 2.43397i | ||||
\(96\) | 14.9828 | + | 10.8857i | 1.52918 | + | 1.11101i | ||||
\(97\) | −0.618034 | − | 1.90211i | −0.0627518 | − | 0.193130i | 0.914766 | − | 0.403985i | \(-0.132375\pi\) |
−0.977517 | + | 0.210855i | \(0.932375\pi\) | |||||||
\(98\) | 9.95959i | 1.00607i | ||||||||
\(99\) | 4.18034 | − | 10.4086i | 0.420140 | − | 1.04611i | ||||
\(100\) | −15.9443 | −1.59443 | ||||||||
\(101\) | −0.163119 | + | 0.0530006i | −0.0162309 | + | 0.00527375i | −0.317121 | − | 0.948385i | \(-0.602716\pi\) |
0.300890 | + | 0.953659i | \(0.402716\pi\) | |||||||
\(102\) | 25.0623 | + | 18.2088i | 2.48154 | + | 1.80294i | ||||
\(103\) | −3.53697 | − | 4.86822i | −0.348508 | − | 0.479680i | 0.598394 | − | 0.801202i | \(-0.295806\pi\) |
−0.946902 | + | 0.321522i | \(0.895806\pi\) | |||||||
\(104\) | 0.326238 | − | 1.00406i | 0.0319903 | − | 0.0984559i | ||||
\(105\) | 12.2984 | + | 3.99598i | 1.20020 | + | 0.389968i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.29792 | + | 3.12262i | 0.415496 | + | 0.301875i | 0.775823 | − | 0.630951i | \(-0.217335\pi\) |
−0.360327 | + | 0.932826i | \(0.617335\pi\) | |||||||
\(108\) | −1.48490 | + | 0.482472i | −0.142884 | + | 0.0464259i | ||||
\(109\) | 8.78962 | 0.841893 | 0.420946 | − | 0.907086i | \(-0.361698\pi\) | ||||
0.420946 | + | 0.907086i | \(0.361698\pi\) | |||||||
\(110\) | 15.5902 | − | 18.6579i | 1.48646 | − | 1.77896i | ||||
\(111\) | −23.0902 | −2.19162 | ||||||||
\(112\) | −1.89531 | − | 5.83317i | −0.179090 | − | 0.551182i | ||||
\(113\) | 3.88751 | − | 5.35069i | 0.365706 | − | 0.503351i | −0.586022 | − | 0.810296i | \(-0.699307\pi\) |
0.951727 | + | 0.306944i | \(0.0993066\pi\) | |||||||
\(114\) | −21.4896 | − | 29.5779i | −2.01269 | − | 2.77023i | ||||
\(115\) | 4.87132 | − | 14.9924i | 0.454253 | − | 1.39805i | ||||
\(116\) | −2.40261 | + | 7.39448i | −0.223077 | + | 0.686560i | ||||
\(117\) | 2.88854 | + | 3.97574i | 0.267046 | + | 0.367557i | ||||
\(118\) | −6.29012 | − | 4.57004i | −0.579052 | − | 0.420706i | ||||
\(119\) | −2.64590 | − | 8.14324i | −0.242549 | − | 0.746489i | ||||
\(120\) | 7.07394 | 0.645760 | ||||||||
\(121\) | 1.95492 | + | 10.8249i | 0.177720 | + | 0.984081i | ||||
\(122\) | − | 17.3152i | − | 1.56765i | ||||||
\(123\) | 26.2812 | − | 8.53926i | 2.36969 | − | 0.769960i | ||||
\(124\) | 4.73607 | + | 3.44095i | 0.425311 | + | 0.309007i | ||||
\(125\) | −15.1353 | + | 10.9964i | −1.35374 | + | 0.983548i | ||||
\(126\) | 8.12555 | + | 2.64015i | 0.723882 | + | 0.235203i | ||||
\(127\) | 3.73074 | − | 11.4820i | 0.331050 | − | 1.01887i | −0.637585 | − | 0.770380i | \(-0.720067\pi\) |
0.968635 | − | 0.248487i | \(-0.0799333\pi\) | |||||||
\(128\) | −3.35410 | − | 4.61653i | −0.296464 | − | 0.408047i | ||||
\(129\) | −17.1738 | + | 23.6377i | −1.51207 | + | 2.08118i | ||||
\(130\) | 3.29180 | + | 10.1311i | 0.288710 | + | 0.888557i | ||||
\(131\) | 4.42477i | 0.386594i | 0.981140 | + | 0.193297i | \(0.0619180\pi\) | ||||
−0.981140 | + | 0.193297i | \(0.938082\pi\) | |||||||
\(132\) | 8.69273 | − | 10.4032i | 0.756605 | − | 0.905483i | ||||
\(133\) | 10.1050i | 0.876216i | ||||||||
\(134\) | −21.6074 | + | 7.02067i | −1.86659 | + | 0.606493i | ||||
\(135\) | −2.18597 | + | 3.00873i | −0.188138 | + | 0.258950i | ||||
\(136\) | −2.75315 | − | 3.78938i | −0.236080 | − | 0.324937i | ||||
\(137\) | −14.6323 | − | 4.75433i | −1.25012 | − | 0.406190i | −0.392158 | − | 0.919898i | \(-0.628271\pi\) |
−0.857965 | + | 0.513708i | \(0.828271\pi\) | |||||||
\(138\) | 6.07348 | − | 18.6922i | 0.517009 | − | 1.59119i | ||||
\(139\) | 5.62605 | − | 4.08757i | 0.477196 | − | 0.346703i | −0.323043 | − | 0.946384i | \(-0.604706\pi\) |
0.800239 | + | 0.599681i | \(0.204706\pi\) | |||||||
\(140\) | 6.70053 | + | 4.86822i | 0.566298 | + | 0.411440i | ||||
\(141\) | −2.72542 | − | 8.38800i | −0.229522 | − | 0.706397i | ||||
\(142\) | 21.4896 | 1.80337 | ||||||||
\(143\) | −4.47214 | − | 1.79611i | −0.373979 | − | 0.150198i | ||||
\(144\) | 15.6180 | 1.30150 | ||||||||
\(145\) | 5.72294 | + | 17.6134i | 0.475264 | + | 1.46271i | ||||
\(146\) | −1.11803 | − | 0.812299i | −0.0925292 | − | 0.0672264i | ||||
\(147\) | 7.77501 | + | 10.7014i | 0.641272 | + | 0.882636i | ||||
\(148\) | −14.0651 | − | 4.57004i | −1.15615 | − | 0.375655i | ||||
\(149\) | 0.0968859 | − | 0.298184i | 0.00793720 | − | 0.0244282i | −0.947009 | − | 0.321206i | \(-0.895912\pi\) |
0.954947 | + | 0.296777i | \(0.0959119\pi\) | |||||||
\(150\) | −38.3079 | + | 27.8323i | −3.12783 | + | 2.27250i | ||||
\(151\) | −11.0172 | + | 15.1639i | −0.896569 | + | 1.23402i | 0.0749809 | + | 0.997185i | \(0.476110\pi\) |
−0.971550 | + | 0.236836i | \(0.923890\pi\) | |||||||
\(152\) | 1.70820 | + | 5.25731i | 0.138554 | + | 0.426424i | ||||
\(153\) | 21.8031 | 1.76268 | ||||||||
\(154\) | −8.12555 | + | 2.04378i | −0.654776 | + | 0.164693i | ||||
\(155\) | 13.9443 | 1.12003 | ||||||||
\(156\) | 1.83543 | + | 5.64888i | 0.146952 | + | 0.452272i | ||||
\(157\) | −6.07348 | + | 8.35942i | −0.484716 | + | 0.667154i | −0.979403 | − | 0.201917i | \(-0.935283\pi\) |
0.494687 | + | 0.869071i | \(0.335283\pi\) | |||||||
\(158\) | 16.7565 | + | 2.24608i | 1.33307 | + | 0.178689i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 26.8713 | + | 8.73102i | 2.12436 | + | 0.690248i | ||||
\(161\) | −4.39481 | + | 3.19302i | −0.346359 | + | 0.251645i | ||||
\(162\) | 8.61803 | − | 11.8617i | 0.677097 | − | 0.931944i | ||||
\(163\) | 6.07295 | + | 18.6906i | 0.475670 | + | 1.46396i | 0.845052 | + | 0.534684i | \(0.179569\pi\) |
−0.369382 | + | 0.929278i | \(0.620431\pi\) | |||||||
\(164\) | 17.6990 | 1.38206 | ||||||||
\(165\) | 2.18597 | − | 32.2181i | 0.170177 | − | 2.50817i | ||||
\(166\) | −14.7984 | −1.14858 | ||||||||
\(167\) | 0.590170 | − | 0.191758i | 0.0456687 | − | 0.0148387i | −0.286094 | − | 0.958202i | \(-0.592357\pi\) |
0.331762 | + | 0.943363i | \(0.392357\pi\) | |||||||
\(168\) | −1.97214 | − | 1.43284i | −0.152154 | − | 0.110546i | ||||
\(169\) | −8.80902 | + | 6.40013i | −0.677617 | + | 0.492317i | ||||
\(170\) | 44.9485 | + | 14.6047i | 3.44740 | + | 1.12013i | ||||
\(171\) | −24.4721 | − | 7.95148i | −1.87143 | − | 0.608065i | ||||
\(172\) | −15.1396 | + | 10.9996i | −1.15438 | + | 0.838710i | ||||
\(173\) | 7.11095 | + | 5.16641i | 0.540635 | + | 0.392795i | 0.824321 | − | 0.566123i | \(-0.191557\pi\) |
−0.283686 | + | 0.958917i | \(0.591557\pi\) | |||||||
\(174\) | 7.13525 | + | 21.9601i | 0.540922 | + | 1.66479i | ||||
\(175\) | 13.0875 | 0.989325 | ||||||||
\(176\) | −12.9721 | + | 8.14324i | −0.977812 | + | 0.613820i | ||||
\(177\) | −10.3262 | −0.776168 | ||||||||
\(178\) | −4.04508 | + | 1.31433i | −0.303192 | + | 0.0985130i | ||||
\(179\) | −15.0172 | − | 10.9106i | −1.12244 | − | 0.815500i | −0.137863 | − | 0.990451i | \(-0.544023\pi\) |
−0.984577 | + | 0.174951i | \(0.944023\pi\) | |||||||
\(180\) | −17.0623 | + | 12.3965i | −1.27175 | + | 0.923980i | ||||
\(181\) | 0.763932 | − | 2.35114i | 0.0567826 | − | 0.174759i | −0.918643 | − | 0.395089i | \(-0.870714\pi\) |
0.975425 | + | 0.220331i | \(0.0707136\pi\) | |||||||
\(182\) | 1.13436 | − | 3.49120i | 0.0840843 | − | 0.258785i | ||||
\(183\) | −13.5172 | − | 18.6049i | −0.999222 | − | 1.37531i | ||||
\(184\) | −1.74671 | + | 2.40414i | −0.128769 | + | 0.177236i | ||||
\(185\) | −33.5027 | + | 10.8857i | −2.46317 | + | 0.800331i | ||||
\(186\) | 17.3855 | 1.27476 | ||||||||
\(187\) | −18.1094 | + | 11.3681i | −1.32429 | + | 0.831321i | ||||
\(188\) | − | 5.64888i | − | 0.411987i | ||||||
\(189\) | 1.21885 | − | 0.396027i | 0.0886581 | − | 0.0288068i | ||||
\(190\) | −45.1246 | − | 32.7849i | −3.27368 | − | 2.37847i | ||||
\(191\) | −15.1995 | − | 20.9203i | −1.09980 | − | 1.51374i | −0.835654 | − | 0.549257i | \(-0.814911\pi\) |
−0.264143 | − | 0.964484i | \(-0.585089\pi\) | |||||||
\(192\) | 11.3120 | + | 3.67549i | 0.816372 | + | 0.265255i | ||||
\(193\) | −4.55157 | + | 14.0083i | −0.327629 | + | 1.00834i | 0.642610 | + | 0.766193i | \(0.277851\pi\) |
−0.970240 | + | 0.242146i | \(0.922149\pi\) | |||||||
\(194\) | −2.23607 | − | 3.07768i | −0.160540 | − | 0.220965i | ||||
\(195\) | 11.4459 | + | 8.31592i | 0.819656 | + | 0.595515i | ||||
\(196\) | 2.61803 | + | 8.05748i | 0.187002 | + | 0.575534i | ||||
\(197\) | 10.2375 | 0.729392 | 0.364696 | − | 0.931127i | \(-0.381173\pi\) | ||||
0.364696 | + | 0.931127i | \(0.381173\pi\) | |||||||
\(198\) | 1.44427 | − | 21.2865i | 0.102640 | − | 1.51277i | ||||
\(199\) | 15.3853i | 1.09064i | 0.838229 | + | 0.545318i | \(0.183591\pi\) | ||||
−0.838229 | + | 0.545318i | \(0.816409\pi\) | |||||||
\(200\) | 6.80902 | − | 2.21238i | 0.481470 | − | 0.156439i | ||||
\(201\) | −17.7360 | + | 24.4115i | −1.25100 | + | 1.72185i | ||||
\(202\) | −0.263932 | + | 0.191758i | −0.0185702 | + | 0.0134920i | ||||
\(203\) | 1.97214 | − | 6.06961i | 0.138417 | − | 0.426003i | ||||
\(204\) | 25.0623 | + | 8.14324i | 1.75471 | + | 0.570141i | ||||
\(205\) | 34.1069 | − | 24.7801i | 2.38213 | − | 1.73072i | ||||
\(206\) | −9.25991 | − | 6.72772i | −0.645169 | − | 0.468742i | ||||
\(207\) | −4.27458 | − | 13.1558i | −0.297104 | − | 0.914391i | ||||
\(208\) | − | 6.71040i | − | 0.465282i | ||||||
\(209\) | 24.4721 | − | 6.15537i | 1.69277 | − | 0.425776i | ||||
\(210\) | 24.5967 | 1.69734 | ||||||||
\(211\) | 1.32813 | + | 4.08757i | 0.0914323 | + | 0.281400i | 0.986307 | − | 0.164917i | \(-0.0527356\pi\) |
−0.894875 | + | 0.446317i | \(0.852736\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 23.0902 | − | 16.7760i | 1.58211 | − | 1.14947i | ||||
\(214\) | 9.61045 | + | 3.12262i | 0.656957 | + | 0.213458i | ||||
\(215\) | −13.7745 | + | 42.3935i | −0.939411 | + | 2.89121i | ||||
\(216\) | 0.567180 | − | 0.412080i | 0.0385917 | − | 0.0280385i | ||||
\(217\) | −3.88751 | − | 2.82444i | −0.263901 | − | 0.191735i | ||||
\(218\) | 15.9006 | − | 5.16641i | 1.07692 | − | 0.349913i | ||||
\(219\) | −1.83543 | −0.124027 | ||||||||
\(220\) | 7.70820 | − | 19.1926i | 0.519687 | − | 1.29397i | ||||
\(221\) | − | 9.36787i | − | 0.630151i | ||||||
\(222\) | −41.7705 | + | 13.5721i | −2.80345 | + | 0.910897i | ||||
\(223\) | 5.97214 | + | 4.33901i | 0.399924 | + | 0.290562i | 0.769510 | − | 0.638635i | \(-0.220501\pi\) |
−0.369586 | + | 0.929196i | \(0.620501\pi\) | |||||||
\(224\) | −5.72294 | − | 7.87695i | −0.382380 | − | 0.526301i | ||||
\(225\) | −10.2984 | + | 31.6951i | −0.686558 | + | 2.11301i | ||||
\(226\) | 3.88751 | − | 11.9645i | 0.258593 | − | 0.795868i | ||||
\(227\) | −18.3631 | + | 13.3415i | −1.21880 | + | 0.885509i | −0.996000 | − | 0.0893552i | \(-0.971519\pi\) |
−0.222799 | + | 0.974864i | \(0.571519\pi\) | |||||||
\(228\) | −25.1605 | − | 18.2802i | −1.66629 | − | 1.21063i | ||||
\(229\) | 21.2730 | − | 6.91201i | 1.40576 | − | 0.456758i | 0.494709 | − | 0.869059i | \(-0.335275\pi\) |
0.911048 | + | 0.412300i | \(0.135275\pi\) | |||||||
\(230\) | − | 29.9848i | − | 1.97714i | ||||||
\(231\) | −7.13525 | + | 8.53926i | −0.469465 | + | 0.561842i | ||||
\(232\) | − | 3.49120i | − | 0.229208i | ||||||
\(233\) | −7.67813 | − | 23.6308i | −0.503011 | − | 1.54811i | −0.804089 | − | 0.594509i | \(-0.797346\pi\) |
0.301078 | − | 0.953599i | \(-0.402654\pi\) | |||||||
\(234\) | 7.56231 | + | 5.49434i | 0.494363 | + | 0.359176i | ||||
\(235\) | −7.90891 | − | 10.8857i | −0.515920 | − | 0.710103i | ||||
\(236\) | −6.29012 | − | 2.04378i | −0.409452 | − | 0.133039i | ||||
\(237\) | 19.7579 | − | 10.6677i | 1.28342 | − | 0.692940i | ||||
\(238\) | −9.57295 | − | 13.1760i | −0.620522 | − | 0.854075i | ||||
\(239\) | 5.22542 | − | 7.19218i | 0.338005 | − | 0.465223i | −0.605853 | − | 0.795577i | \(-0.707168\pi\) |
0.943857 | + | 0.330353i | \(0.107168\pi\) | |||||||
\(240\) | 42.7626 | − | 13.8944i | 2.76031 | − | 0.896880i | ||||
\(241\) | 20.0252i | 1.28994i | 0.764210 | + | 0.644968i | \(0.223129\pi\) | ||||
−0.764210 | + | 0.644968i | \(0.776871\pi\) | |||||||
\(242\) | 9.89919 | + | 18.4333i | 0.636344 | + | 1.18494i | ||||
\(243\) | − | 22.3677i | − | 1.43489i | ||||||
\(244\) | −4.55157 | − | 14.0083i | −0.291385 | − | 0.896790i | ||||
\(245\) | 16.3262 | + | 11.8617i | 1.04305 | + | 0.757817i | ||||
\(246\) | 42.5238 | − | 30.8953i | 2.71122 | − | 1.96982i | ||||
\(247\) | −3.41641 | + | 10.5146i | −0.217381 | + | 0.669029i | ||||
\(248\) | −2.50000 | − | 0.812299i | −0.158750 | − | 0.0515811i | ||||
\(249\) | −15.9006 | + | 11.5524i | −1.00766 | + | 0.732106i | ||||
\(250\) | −20.9164 | + | 28.7890i | −1.32287 | + | 1.82077i | ||||
\(251\) | −3.32033 | + | 1.07884i | −0.209577 | + | 0.0680958i | −0.411924 | − | 0.911218i | \(-0.635143\pi\) |
0.202347 | + | 0.979314i | \(0.435143\pi\) | |||||||
\(252\) | 7.26771 | 0.457823 | ||||||||
\(253\) | 10.4098 | + | 8.69827i | 0.654460 | + | 0.546855i | ||||
\(254\) | − | 22.9641i | − | 1.44090i | ||||||
\(255\) | 59.6976 | − | 19.3969i | 3.73841 | − | 1.21468i | ||||
\(256\) | −16.3992 | − | 11.9147i | −1.02495 | − | 0.744669i | ||||
\(257\) | −6.47214 | + | 4.70228i | −0.403721 | + | 0.293320i | −0.771055 | − | 0.636769i | \(-0.780271\pi\) |
0.367334 | + | 0.930089i | \(0.380271\pi\) | |||||||
\(258\) | −17.1738 | + | 52.8554i | −1.06919 | + | 3.29063i | ||||
\(259\) | 11.5451 | + | 3.75123i | 0.717377 | + | 0.233090i | ||||
\(260\) | 5.32624 | + | 7.33094i | 0.330319 | + | 0.454645i | ||||
\(261\) | 13.1474 | + | 9.55216i | 0.813805 | + | 0.591264i | ||||
\(262\) | 2.60081 | + | 8.00448i | 0.160679 | + | 0.494518i | ||||
\(263\) | 12.0332i | 0.742000i | 0.928633 | + | 0.371000i | \(0.120985\pi\) | ||||
−0.928633 | + | 0.371000i | \(0.879015\pi\) | |||||||
\(264\) | −2.26872 | + | 5.64888i | −0.139630 | + | 0.347664i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.93958 | + | 18.2802i | 0.364179 | + | 1.12083i | ||||
\(267\) | −3.32033 | + | 4.57004i | −0.203201 | + | 0.279682i | ||||
\(268\) | −15.6353 | + | 11.3597i | −0.955075 | + | 0.693903i | ||||
\(269\) | 4.25329 | − | 13.0903i | 0.259328 | − | 0.798128i | −0.733618 | − | 0.679562i | \(-0.762170\pi\) |
0.992946 | − | 0.118567i | \(-0.0378300\pi\) | |||||||
\(270\) | −2.18597 | + | 6.72772i | −0.133034 | + | 0.409436i | ||||
\(271\) | −9.61045 | + | 6.98240i | −0.583793 | + | 0.424150i | −0.840090 | − | 0.542448i | \(-0.817498\pi\) |
0.256297 | + | 0.966598i | \(0.417498\pi\) | |||||||
\(272\) | −24.0860 | − | 17.4995i | −1.46043 | − | 1.06106i | ||||
\(273\) | −1.50658 | − | 4.63677i | −0.0911822 | − | 0.280630i | ||||
\(274\) | −29.2646 | −1.76794 | ||||||||
\(275\) | −7.97214 | − | 31.6951i | −0.480738 | − | 1.91129i | ||||
\(276\) | − | 16.7188i | − | 1.00636i | ||||||
\(277\) | 7.56231 | − | 2.45714i | 0.454375 | − | 0.147635i | −0.0728833 | − | 0.997340i | \(-0.523220\pi\) |
0.527258 | + | 0.849705i | \(0.323220\pi\) | |||||||
\(278\) | 7.77501 | − | 10.7014i | 0.466314 | − | 0.641827i | ||||
\(279\) | 9.89919 | − | 7.19218i | 0.592649 | − | 0.430585i | ||||
\(280\) | −3.53697 | − | 1.14923i | −0.211374 | − | 0.0686797i | ||||
\(281\) | 13.3541 | + | 4.33901i | 0.796639 | + | 0.258844i | 0.678929 | − | 0.734204i | \(-0.262445\pi\) |
0.117710 | + | 0.993048i | \(0.462445\pi\) | |||||||
\(282\) | −9.86068 | − | 13.5721i | −0.587195 | − | 0.808204i | ||||
\(283\) | −3.68034 | + | 5.06555i | −0.218773 | + | 0.301116i | −0.904271 | − | 0.426959i | \(-0.859585\pi\) |
0.685497 | + | 0.728075i | \(0.259585\pi\) | |||||||
\(284\) | 17.3855 | − | 5.64888i | 1.03164 | − | 0.335199i | ||||
\(285\) | −74.0793 | −4.38808 | ||||||||
\(286\) | −9.14590 | − | 0.620541i | −0.540808 | − | 0.0366934i | ||||
\(287\) | −14.5279 | −0.857553 | ||||||||
\(288\) | 23.5795 | − | 7.66145i | 1.38944 | − | 0.451455i | ||||
\(289\) | −19.8713 | − | 14.4374i | −1.16890 | − | 0.849257i | ||||
\(290\) | 20.7058 | + | 28.4991i | 1.21589 | + | 1.67352i | ||||
\(291\) | −4.80522 | − | 1.56131i | −0.281687 | − | 0.0915257i | ||||
\(292\) | −1.11803 | − | 0.363271i | −0.0654280 | − | 0.0212588i | ||||
\(293\) | 6.19323 | − | 4.49965i | 0.361813 | − | 0.262872i | −0.391995 | − | 0.919967i | \(-0.628215\pi\) |
0.753808 | + | 0.657095i | \(0.228215\pi\) | |||||||
\(294\) | 20.3553 | + | 14.7890i | 1.18714 | + | 0.862509i | ||||
\(295\) | −14.9828 | + | 4.86822i | −0.872335 | + | 0.283439i | ||||
\(296\) | 6.64066 | 0.385980 | ||||||||
\(297\) | −1.70154 | − | 2.71054i | −0.0987333 | − | 0.157282i | ||||
\(298\) | − | 0.596368i | − | 0.0345467i | ||||||
\(299\) | −5.65248 | + | 1.83660i | −0.326891 | + | 0.106213i | ||||
\(300\) | −23.6756 | + | 32.5866i | −1.36691 | + | 1.88139i | ||||
\(301\) | 12.4271 | − | 9.02878i | 0.716283 | − | 0.520410i | ||||
\(302\) | −11.0172 | + | 33.9075i | −0.633970 | + | 1.95116i | ||||
\(303\) | −0.133893 | + | 0.412080i | −0.00769195 | + | 0.0236734i | ||||
\(304\) | 20.6525 | + | 28.4257i | 1.18450 | + | 1.63033i | ||||
\(305\) | −28.3839 | − | 20.6221i | −1.62526 | − | 1.18082i | ||||
\(306\) | 39.4423 | − | 12.8156i | 2.25476 | − | 0.732617i | ||||
\(307\) | −7.96879 | −0.454803 | −0.227401 | − | 0.973801i | \(-0.573023\pi\) | ||||
−0.227401 | + | 0.973801i | \(0.573023\pi\) | |||||||
\(308\) | −6.03647 | + | 3.78938i | −0.343960 | + | 0.215920i | ||||
\(309\) | −15.2016 | −0.864790 | ||||||||
\(310\) | 25.2254 | − | 8.19624i | 1.43271 | − | 0.465515i | ||||
\(311\) | −7.07394 | + | 9.73645i | −0.401126 | + | 0.552103i | −0.961026 | − | 0.276457i | \(-0.910840\pi\) |
0.559900 | + | 0.828560i | \(0.310840\pi\) | |||||||
\(312\) | −1.56765 | − | 2.15768i | −0.0887505 | − | 0.122155i | ||||
\(313\) | 1.85410 | − | 5.70634i | 0.104800 | − | 0.322541i | −0.884883 | − | 0.465813i | \(-0.845762\pi\) |
0.989683 | + | 0.143271i | \(0.0457621\pi\) | |||||||
\(314\) | −6.07348 | + | 18.6922i | −0.342746 | + | 1.05486i | ||||
\(315\) | 14.0053 | − | 10.1754i | 0.789107 | − | 0.573320i | ||||
\(316\) | 14.1467 | − | 2.58758i | 0.795814 | − | 0.145563i | ||||
\(317\) | −4.60739 | − | 14.1801i | −0.258777 | − | 0.796433i | −0.993062 | − | 0.117592i | \(-0.962482\pi\) |
0.734285 | − | 0.678841i | \(-0.237518\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.9006 | − | 1.07884i | −0.890261 | − | 0.0604034i | ||||
\(320\) | 18.1459 | 1.01439 | ||||||||
\(321\) | 12.7639 | − | 4.14725i | 0.712413 | − | 0.231477i | ||||
\(322\) | −6.07348 | + | 8.35942i | −0.338462 | + | 0.465852i | ||||
\(323\) | 28.8313 | + | 39.6829i | 1.60422 | + | 2.20802i | ||||
\(324\) | 3.85410 | − | 11.8617i | 0.214117 | − | 0.658984i | ||||
\(325\) | 13.6180 | + | 4.42477i | 0.755393 | + | 0.245442i | ||||
\(326\) | 21.9721 | + | 30.2421i | 1.21692 | + | 1.67495i | ||||
\(327\) | 13.0517 | − | 17.9641i | 0.721759 | − | 0.993415i | ||||
\(328\) | −7.55837 | + | 2.45586i | −0.417341 | + | 0.135602i | ||||
\(329\) | 4.63677i | 0.255633i | ||||||||
\(330\) | −14.9828 | − | 59.5679i | −0.824779 | − | 3.27911i | ||||
\(331\) | 9.36787i | 0.514905i | 0.966291 | + | 0.257452i | \(0.0828830\pi\) | ||||
−0.966291 | + | 0.257452i | \(0.917117\pi\) | |||||||
\(332\) | −11.9721 | + | 3.88998i | −0.657056 | + | 0.213491i | ||||
\(333\) | −18.1693 | + | 25.0079i | −0.995671 | + | 1.37042i | ||||
\(334\) | 0.954915 | − | 0.693786i | 0.0522506 | − | 0.0379623i | ||||
\(335\) | −14.2254 | + | 43.7814i | −0.777218 | + | 2.39203i | ||||
\(336\) | −14.7361 | − | 4.78804i | −0.803918 | − | 0.261209i | ||||
\(337\) | 6.70820 | + | 9.23305i | 0.365419 | + | 0.502956i | 0.951649 | − | 0.307189i | \(-0.0993883\pi\) |
−0.586229 | + | 0.810145i | \(0.699388\pi\) | |||||||
\(338\) | −12.1738 | + | 16.7557i | −0.662165 | + | 0.911392i | ||||
\(339\) | −5.16312 | − | 15.8904i | −0.280422 | − | 0.863051i | ||||
\(340\) | 40.2032 | 2.18032 | ||||||||
\(341\) | −4.47214 | + | 11.1352i | −0.242180 | + | 0.603003i | ||||
\(342\) | −48.9443 | −2.64660 | ||||||||
\(343\) | −5.02187 | − | 15.4557i | −0.271155 | − | 0.834530i | ||||
\(344\) | 4.93912 | − | 6.79811i | 0.266299 | − | 0.366530i | ||||
\(345\) | −23.4078 | − | 32.2181i | −1.26023 | − | 1.73456i | ||||
\(346\) | 15.9006 | + | 5.16641i | 0.854820 | + | 0.277748i | ||||
\(347\) | 20.4894 | + | 6.65740i | 1.09993 | + | 0.357388i | 0.802074 | − | 0.597224i | \(-0.203730\pi\) |
0.297852 | + | 0.954612i | \(0.403730\pi\) | |||||||
\(348\) | 11.5451 | + | 15.8904i | 0.618882 | + | 0.851817i | ||||
\(349\) | −13.8115 | − | 10.0346i | −0.739312 | − | 0.537141i | 0.153184 | − | 0.988198i | \(-0.451047\pi\) |
−0.892495 | + | 0.451056i | \(0.851047\pi\) | |||||||
\(350\) | 23.6756 | − | 7.69266i | 1.26551 | − | 0.411190i | ||||
\(351\) | 1.40215 | 0.0748410 | ||||||||
\(352\) | −15.5902 | + | 18.6579i | −0.830959 | + | 0.994467i | ||||
\(353\) | 2.75405i | 0.146583i | 0.997311 | + | 0.0732916i | \(0.0233504\pi\) | ||||
−0.997311 | + | 0.0732916i | \(0.976650\pi\) | |||||||
\(354\) | −18.6803 | + | 6.06961i | −0.992849 | + | 0.322596i | ||||
\(355\) | 25.5938 | − | 35.2268i | 1.35838 | − | 1.86964i | ||||
\(356\) | −2.92705 | + | 2.12663i | −0.155133 | + | 0.112711i | ||||
\(357\) | −20.5719 | − | 6.68421i | −1.08878 | − | 0.353766i | ||||
\(358\) | −33.5795 | − | 10.9106i | −1.77473 | − | 0.576646i | ||||
\(359\) | −26.0782 | + | 18.9469i | −1.37635 | + | 0.999980i | −0.379144 | + | 0.925338i | \(0.623781\pi\) |
−0.997210 | + | 0.0746422i | \(0.976219\pi\) | |||||||
\(360\) | 5.56637 | − | 7.66145i | 0.293374 | − | 0.403794i | ||||
\(361\) | −12.0172 | − | 36.9852i | −0.632485 | − | 1.94659i | ||||
\(362\) | − | 4.70228i | − | 0.247146i | ||||||
\(363\) | 25.0266 | + | 12.0784i | 1.31355 | + | 0.633952i | ||||
\(364\) | − | 3.12262i | − | 0.163670i | ||||||
\(365\) | −2.66312 | + | 0.865300i | −0.139394 | + | 0.0452919i | ||||
\(366\) | −35.3885 | − | 25.7113i | −1.84979 | − | 1.34395i | ||||
\(367\) | −0.763932 | + | 0.555029i | −0.0398769 | + | 0.0289723i | −0.607545 | − | 0.794285i | \(-0.707846\pi\) |
0.567668 | + | 0.823257i | \(0.307846\pi\) | |||||||
\(368\) | −5.83688 | + | 17.9641i | −0.304268 | + | 0.936442i | ||||
\(369\) | 11.4317 | − | 35.1833i | 0.595113 | − | 1.83157i | ||||
\(370\) | −54.2085 | + | 39.3847i | −2.81816 | + | 2.04752i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 14.0651 | − | 4.57004i | 0.729243 | − | 0.236945i | ||||
\(373\) | 12.8938 | 0.667614 | 0.333807 | − | 0.942641i | \(-0.391667\pi\) | ||||
0.333807 | + | 0.942641i | \(0.391667\pi\) | |||||||
\(374\) | −26.0782 | + | 31.2096i | −1.34847 | + | 1.61381i | ||||
\(375\) | 47.2617i | 2.44058i | ||||||||
\(376\) | 0.783823 | + | 2.41236i | 0.0404226 | + | 0.124408i | ||||
\(377\) | 4.10415 | − | 5.64888i | 0.211375 | − | 0.290932i | ||||
\(378\) | 1.97214 | − | 1.43284i | 0.101436 | − | 0.0736974i | ||||
\(379\) | 11.6625 | + | 3.78938i | 0.599063 | + | 0.194648i | 0.592823 | − | 0.805333i | \(-0.298013\pi\) |
0.00624079 | + | 0.999981i | \(0.498013\pi\) | |||||||
\(380\) | −45.1246 | − | 14.6619i | −2.31484 | − | 0.752138i | ||||
\(381\) | −17.9271 | − | 24.6745i | −0.918431 | − | 1.26411i | ||||
\(382\) | −39.7928 | − | 28.9112i | −2.03598 | − | 1.47922i | ||||
\(383\) | 5.60739 | + | 17.2578i | 0.286524 | + | 0.881831i | 0.985938 | + | 0.167114i | \(0.0534447\pi\) |
−0.699413 | + | 0.714717i | \(0.746555\pi\) | |||||||
\(384\) | −14.4157 | −0.735647 | ||||||||
\(385\) | −6.32713 | + | 15.7539i | −0.322460 | + | 0.802893i | ||||
\(386\) | 28.0166i | 1.42601i | ||||||||
\(387\) | 12.0871 | + | 37.2002i | 0.614420 | + | 1.89099i | ||||
\(388\) | −2.61803 | − | 1.90211i | −0.132911 | − | 0.0965652i | ||||
\(389\) | −3.61803 | + | 2.62866i | −0.183442 | + | 0.133278i | −0.675716 | − | 0.737162i | \(-0.736166\pi\) |
0.492275 | + | 0.870440i | \(0.336166\pi\) | |||||||
\(390\) | 25.5938 | + | 8.31592i | 1.29599 | + | 0.421093i | ||||
\(391\) | −8.14842 | + | 25.0783i | −0.412083 | + | 1.26826i | ||||
\(392\) | −2.23607 | − | 3.07768i | −0.112938 | − | 0.155446i | ||||
\(393\) | 9.04327 | + | 6.57032i | 0.456172 | + | 0.331429i | ||||
\(394\) | 18.5198 | − | 6.01745i | 0.933015 | − | 0.303155i | ||||
\(395\) | 23.6386 | − | 24.7930i | 1.18939 | − | 1.24747i | ||||
\(396\) | −4.42705 | − | 17.6008i | −0.222468 | − | 0.884474i | ||||
\(397\) | 18.7082 | 0.938938 | 0.469469 | − | 0.882949i | \(-0.344445\pi\) | ||||
0.469469 | + | 0.882949i | \(0.344445\pi\) | |||||||
\(398\) | 9.04327 | + | 27.8323i | 0.453298 | + | 1.39511i | ||||
\(399\) | 20.6525 | + | 15.0049i | 1.03392 | + | 0.751185i | ||||
\(400\) | 36.8156 | − | 26.7481i | 1.84078 | − | 1.33740i | ||||
\(401\) | 6.85730 | + | 2.22807i | 0.342437 | + | 0.111265i | 0.475187 | − | 0.879885i | \(-0.342381\pi\) |
−0.132749 | + | 0.991150i | \(0.542381\pi\) | |||||||
\(402\) | −17.7360 | + | 54.5858i | −0.884591 | + | 2.72249i | ||||
\(403\) | −3.09017 | − | 4.25325i | −0.153932 | − | 0.211870i | ||||
\(404\) | −0.163119 | + | 0.224514i | −0.00811547 | + | 0.0111700i | ||||
\(405\) | −9.18034 | − | 28.2542i | −0.456175 | − | 1.40396i | ||||
\(406\) | − | 12.1392i | − | 0.602459i | ||||||
\(407\) | 2.05208 | − | 30.2447i | 0.101718 | − | 1.49917i | ||||
\(408\) | −11.8328 | −0.585812 | ||||||||
\(409\) | −11.4459 | − | 35.2268i | −0.565962 | − | 1.74185i | −0.665075 | − | 0.746777i | \(-0.731600\pi\) |
0.0991128 | − | 0.995076i | \(-0.468400\pi\) | |||||||
\(410\) | 47.1345 | − | 64.8751i | 2.32781 | − | 3.20395i | ||||
\(411\) | −31.4443 | + | 22.8456i | −1.55103 | + | 1.12689i | ||||
\(412\) | −9.25991 | − | 3.00873i | −0.456203 | − | 0.148229i | ||||
\(413\) | 5.16312 | + | 1.67760i | 0.254060 | + | 0.0825493i | ||||
\(414\) | −15.4656 | − | 21.2865i | −0.760091 | − | 1.04618i | ||||
\(415\) | −17.6246 | + | 24.2582i | −0.865158 | + | 1.19079i | ||||
\(416\) | −3.29180 | − | 10.1311i | −0.161394 | − | 0.496718i | ||||
\(417\) | − | 17.5680i | − | 0.860311i | ||||||
\(418\) | 40.6525 | − | 25.5195i | 1.98838 | − | 1.24820i | ||||
\(419\) | − | 24.5254i | − | 1.19814i | −0.800695 | − | 0.599072i | \(-0.795536\pi\) | ||
0.800695 | − | 0.599072i | \(-0.204464\pi\) | |||||||
\(420\) | 19.8992 | − | 6.46564i | 0.970981 | − | 0.315491i | ||||
\(421\) | −14.9894 | − | 10.8904i | −0.730537 | − | 0.530766i | 0.159197 | − | 0.987247i | \(-0.449110\pi\) |
−0.889733 | + | 0.456481i | \(0.849110\pi\) | |||||||
\(422\) | 4.80522 | + | 6.61382i | 0.233915 | + | 0.321956i | ||||
\(423\) | −11.2292 | − | 3.64860i | −0.545984 | − | 0.177401i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 51.3954 | − | 37.3410i | 2.49304 | − | 1.81130i | ||||
\(426\) | 31.9098 | − | 43.9201i | 1.54604 | − | 2.12794i | ||||
\(427\) | 3.73607 | + | 11.4984i | 0.180801 | + | 0.556448i | ||||
\(428\) | 8.59584 | 0.415496 | ||||||||
\(429\) | −10.3115 | + | 6.47304i | −0.497845 | + | 0.312521i | ||||
\(430\) | 84.7870i | 4.08879i | ||||||||
\(431\) | 3.61803 | − | 1.17557i | 0.174275 | − | 0.0566252i | −0.220580 | − | 0.975369i | \(-0.570795\pi\) |
0.394855 | + | 0.918744i | \(0.370795\pi\) | |||||||
\(432\) | 2.61925 | − | 3.60510i | 0.126019 | − | 0.173450i | ||||
\(433\) | −14.1631 | + | 10.2901i | −0.680636 | + | 0.494511i | −0.873569 | − | 0.486701i | \(-0.838200\pi\) |
0.192933 | + | 0.981212i | \(0.438200\pi\) | |||||||
\(434\) | −8.69273 | − | 2.82444i | −0.417264 | − | 0.135577i | ||||
\(435\) | 44.4959 | + | 14.4576i | 2.13342 | + | 0.693189i | ||||
\(436\) | 11.5058 | − | 8.35942i | 0.551026 | − | 0.400344i | ||||
\(437\) | 18.2918 | − | 25.1765i | 0.875015 | − | 1.20436i | ||||
\(438\) | −3.32033 | + | 1.07884i | −0.158651 | + | 0.0515490i | ||||
\(439\) | − | 32.7849i | − | 1.56474i | −0.622814 | − | 0.782370i | \(-0.714011\pi\) | ||
0.622814 | − | 0.782370i | \(-0.285989\pi\) | |||||||
\(440\) | −0.628677 | + | 9.26581i | −0.0299710 | + | 0.441730i | ||||
\(441\) | 17.7082 | 0.843248 | ||||||||
\(442\) | −5.50630 | − | 16.9466i | −0.261908 | − | 0.806069i | ||||
\(443\) | −3.53697 | + | 4.86822i | −0.168047 | + | 0.231296i | −0.884732 | − | 0.466101i | \(-0.845658\pi\) |
0.716685 | + | 0.697397i | \(0.245658\pi\) | |||||||
\(444\) | −30.2254 | + | 21.9601i | −1.43444 | + | 1.04218i | ||||
\(445\) | −2.66312 | + | 8.19624i | −0.126244 | + | 0.388539i | ||||
\(446\) | 13.3541 | + | 4.33901i | 0.632335 | + | 0.205458i | ||||
\(447\) | −0.465558 | − | 0.640786i | −0.0220201 | − | 0.0303081i | ||||
\(448\) | −5.05887 | − | 3.67549i | −0.239009 | − | 0.173650i | ||||
\(449\) | 31.4506 | − | 10.2189i | 1.48425 | − | 0.482261i | 0.548867 | − | 0.835910i | \(-0.315059\pi\) |
0.935378 | + | 0.353649i | \(0.115059\pi\) | |||||||
\(450\) | 63.3903i | 2.98825i | ||||||||
\(451\) | 8.84950 | + | 35.1833i | 0.416706 | + | 1.65672i | ||||
\(452\) | − | 10.7014i | − | 0.503351i | ||||||
\(453\) | 14.6323 | + | 45.0336i | 0.687486 | + | 2.11586i | ||||
\(454\) | −25.3771 | + | 34.9286i | −1.19101 | + | 1.63928i | ||||
\(455\) | −4.37194 | − | 6.01745i | −0.204960 | − | 0.282103i | ||||
\(456\) | 13.2813 | + | 4.31536i | 0.621954 | + | 0.202085i | ||||
\(457\) | −32.8885 | − | 10.6861i | −1.53846 | − | 0.499876i | −0.587510 | − | 0.809217i | \(-0.699892\pi\) |
−0.950951 | + | 0.309341i | \(0.899892\pi\) | |||||||
\(458\) | 34.4204 | − | 25.0079i | 1.60836 | − | 1.16854i | ||||
\(459\) | 3.65654 | − | 5.03280i | 0.170673 | − | 0.234911i | ||||
\(460\) | −7.88197 | − | 24.2582i | −0.367499 | − | 1.13104i | ||||
\(461\) | 15.1167 | 0.704057 | 0.352028 | − | 0.935989i | \(-0.385492\pi\) | ||||
0.352028 | + | 0.935989i | \(0.385492\pi\) | |||||||
\(462\) | −7.88854 | + | 19.6417i | −0.367008 | + | 0.913813i | ||||
\(463\) | − | 26.8239i | − | 1.24661i | −0.781979 | − | 0.623305i | \(-0.785789\pi\) | ||
0.781979 | − | 0.623305i | \(-0.214211\pi\) | |||||||
\(464\) | −6.85730 | − | 21.1046i | −0.318342 | − | 0.979756i | ||||
\(465\) | 20.7058 | − | 28.4991i | 0.960208 | − | 1.32161i | ||||
\(466\) | −27.7797 | − | 38.2355i | −1.28687 | − | 1.77123i | ||||
\(467\) | 6.39261 | − | 19.6744i | 0.295815 | − | 0.910424i | −0.687132 | − | 0.726533i | \(-0.741131\pi\) |
0.982947 | − | 0.183891i | \(-0.0588694\pi\) | |||||||
\(468\) | 7.56231 | + | 2.45714i | 0.349568 | + | 0.113581i | ||||
\(469\) | 12.8339 | − | 9.32437i | 0.592614 | − | 0.430559i | ||||
\(470\) | −20.7058 | − | 15.0436i | −0.955087 | − | 0.693911i | ||||
\(471\) | 8.06637 | + | 24.8257i | 0.371679 | + | 1.14391i | ||||
\(472\) | 2.96979 | 0.136696 | ||||||||
\(473\) | −29.4355 | − | 24.5958i | −1.35345 | − | 1.13092i | ||||
\(474\) | 29.4721 | − | 30.9114i | 1.35370 | − | 1.41981i | ||||
\(475\) | −71.3050 | + | 23.1684i | −3.27170 | + | 1.06304i | ||||
\(476\) | −11.2082 | − | 8.14324i | −0.513727 | − | 0.373245i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.22542 | − | 16.0822i | 0.239005 | − | 0.735583i | ||||
\(479\) | −22.1353 | − | 7.19218i | −1.01139 | − | 0.328619i | −0.243979 | − | 0.969780i | \(-0.578453\pi\) |
−0.767406 | + | 0.641161i | \(0.778453\pi\) | |||||||
\(480\) | 57.7454 | − | 41.9545i | 2.63571 | − | 1.91495i | ||||
\(481\) | 10.7448 | + | 7.80656i | 0.489921 | + | 0.355948i | ||||
\(482\) | 11.7705 | + | 36.2259i | 0.536132 | + | 1.65004i | ||||
\(483\) | 13.7233i | 0.624433i | ||||||||
\(484\) | 12.8541 | + | 12.3107i | 0.584277 | + | 0.559579i | ||||
\(485\) | −7.70820 | −0.350012 | ||||||||
\(486\) | −13.1474 | − | 40.4636i | −0.596379 | − | 1.83547i | ||||
\(487\) | 13.3262 | + | 9.68208i | 0.603869 | + | 0.438737i | 0.847250 | − | 0.531194i | \(-0.178256\pi\) |
−0.243381 | + | 0.969931i | \(0.578256\pi\) | |||||||
\(488\) | 3.88751 | + | 5.35069i | 0.175979 | + | 0.242215i | ||||
\(489\) | 47.2173 | + | 15.3418i | 2.13524 | + | 0.693781i | ||||
\(490\) | 36.5066 | + | 11.8617i | 1.64920 | + | 0.535857i | ||||
\(491\) | 5.72294 | − | 4.15796i | 0.258273 | − | 0.187646i | −0.451113 | − | 0.892467i | \(-0.648973\pi\) |
0.709385 | + | 0.704821i | \(0.248973\pi\) | |||||||
\(492\) | 26.2812 | − | 36.1729i | 1.18485 | − | 1.63080i | ||||
\(493\) | −9.57295 | − | 29.4625i | −0.431144 | − | 1.32692i | ||||
\(494\) | 21.0292i | 0.946150i | ||||||||
\(495\) | −33.1738 | − | 27.7194i | −1.49105 | − | 1.24589i | ||||
\(496\) | −16.7082 | −0.750221 | ||||||||
\(497\) | −14.2705 | + | 4.63677i | −0.640120 | + | 0.207988i | ||||
\(498\) | −21.9740 | + | 30.2447i | −0.984680 | + | 1.35530i | ||||
\(499\) | 9.69098 | − | 7.04091i | 0.433828 | − | 0.315194i | −0.349350 | − | 0.936992i | \(-0.613597\pi\) |
0.783178 | + | 0.621798i | \(0.213597\pi\) | |||||||
\(500\) | −9.35410 | + | 28.7890i | −0.418328 | + | 1.28748i | ||||
\(501\) | 0.484429 | − | 1.49092i | 0.0216427 | − | 0.0666094i | ||||
\(502\) | −5.37240 | + | 3.90328i | −0.239782 | + | 0.174212i | ||||
\(503\) | −28.2272 | − | 20.5082i | −1.25859 | − | 0.914417i | −0.259899 | − | 0.965636i | \(-0.583689\pi\) |
−0.998687 | + | 0.0512192i | \(0.983689\pi\) | |||||||
\(504\) | −3.10368 | + | 1.00845i | −0.138249 | + | 0.0449199i | ||||
\(505\) | 0.661030i | 0.0294155i | ||||||||
\(506\) | 23.9443 | + | 9.61657i | 1.06445 | + | 0.427509i | ||||
\(507\) | 27.5072i | 1.22164i | ||||||||
\(508\) | −6.03647 | − | 18.5783i | −0.267825 | − | 0.824281i | ||||
\(509\) | −5.72294 | + | 7.87695i | −0.253665 | + | 0.349140i | −0.916791 | − | 0.399368i | \(-0.869229\pi\) |
0.663126 | + | 0.748508i | \(0.269229\pi\) | |||||||
\(510\) | 96.5927 | − | 70.1787i | 4.27720 | − | 3.10756i | ||||
\(511\) | 0.917716 | + | 0.298184i | 0.0405974 | + | 0.0131909i | ||||
\(512\) | −25.8156 | − | 8.38800i | −1.14090 | − | 0.370701i | ||||
\(513\) | −5.93958 | + | 4.31536i | −0.262239 | + | 0.190528i | ||||
\(514\) | −8.94427 | + | 12.3107i | −0.394515 | + | 0.543003i | ||||
\(515\) | −22.0568 | + | 7.16669i | −0.971938 | + | 0.315802i | ||||
\(516\) | 47.2753i | 2.08118i | ||||||||
\(517\) | 11.2292 | − | 2.82444i | 0.493861 | − | 0.124219i | ||||
\(518\) | 23.0902 | 1.01452 | ||||||||
\(519\) | 21.1180 | − | 6.86167i | 0.926979 | − | 0.301194i | ||||
\(520\) | −3.29180 | − | 2.39163i | −0.144355 | − | 0.104880i | ||||
\(521\) | −6.99119 | − | 9.62255i | −0.306290 | − | 0.421572i | 0.627930 | − | 0.778270i | \(-0.283902\pi\) |
−0.934220 | + | 0.356698i | \(0.883902\pi\) | |||||||
\(522\) | 29.3985 | + | 9.55216i | 1.28674 | + | 0.418087i | ||||
\(523\) | −4.63525 | − | 1.50609i | −0.202686 | − | 0.0658565i | 0.205915 | − | 0.978570i | \(-0.433983\pi\) |
−0.408600 | + | 0.912713i | \(0.633983\pi\) | |||||||
\(524\) | 4.20820 | + | 5.79210i | 0.183836 | + | 0.253029i | ||||
\(525\) | 19.4336 | − | 26.7481i | 0.848153 | − | 1.16738i | ||||
\(526\) | 7.07295 | + | 21.7683i | 0.308395 | + | 0.949143i | ||||
\(527\) | −23.3250 | −1.01605 | ||||||||
\(528\) | −2.61925 | + | 38.6041i | −0.113988 | + | 1.68003i | ||||
\(529\) | −6.27051 | −0.272631 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.12555 | + | 11.1839i | −0.352619 | + | 0.485338i | ||||
\(532\) | 9.61045 | + | 13.2276i | 0.416666 | + | 0.573491i | ||||
\(533\) | −15.1167 | − | 4.91173i | −0.654779 | − | 0.212751i | ||||
\(534\) | −3.32033 | + | 10.2189i | −0.143685 | + | 0.442216i | ||||
\(535\) | 16.5646 | − | 12.0349i | 0.716151 | − | 0.520314i | ||||
\(536\) | 5.10081 | − | 7.02067i | 0.220322 | − | 0.303247i | ||||
\(537\) | −44.5980 | + | 14.4908i | −1.92455 | + | 0.625323i | ||||
\(538\) | − | 26.1806i | − | 1.12872i | ||||||
\(539\) | −14.7082 | + | 9.23305i | −0.633527 | + | 0.397696i | ||||
\(540\) | 6.01745i | 0.258950i | ||||||||
\(541\) | −14.0451 | + | 4.56352i | −0.603845 | + | 0.196201i | −0.594955 | − | 0.803759i | \(-0.702830\pi\) |
−0.00889065 | + | 0.999960i | \(0.502830\pi\) | |||||||
\(542\) | −13.2813 | + | 18.2802i | −0.570481 | + | 0.785200i | ||||
\(543\) | −3.67086 | − | 5.05251i | −0.157532 | − | 0.216824i | ||||
\(544\) | −44.9485 | − | 14.6047i | −1.92715 | − | 0.626170i | ||||
\(545\) | 10.4683 | − | 32.2181i | 0.448412 | − | 1.38007i | ||||
\(546\) | −5.45085 | − | 7.50245i | −0.233275 | − | 0.321075i | ||||
\(547\) | −7.33688 | + | 10.0984i | −0.313702 | + | 0.431774i | −0.936531 | − | 0.350584i | \(-0.885983\pi\) |
0.622829 | + | 0.782358i | \(0.285983\pi\) | |||||||
\(548\) | −23.6756 | + | 7.69266i | −1.01137 | + | 0.328614i | ||||
\(549\) | −30.7865 | −1.31394 | ||||||||
\(550\) | −33.0517 | − | 52.6511i | −1.40933 | − | 2.24505i | ||||
\(551\) | 36.5603i | 1.55752i | ||||||||
\(552\) | 2.31986 | + | 7.13980i | 0.0987398 | + | 0.303890i | ||||
\(553\) | −11.6120 | + | 2.12397i | −0.493794 | + | 0.0903203i | ||||
\(554\) | 12.2361 | − | 8.89002i | 0.519861 | − | 0.377701i | ||||
\(555\) | −27.5000 | + | 84.6363i | −1.16731 | + | 3.59261i | ||||
\(556\) | 3.47709 | − | 10.7014i | 0.147462 | − | 0.453840i | ||||
\(557\) | −14.6976 | − | 20.2295i | −0.622756 | − | 0.857150i | 0.374794 | − | 0.927108i | \(-0.377713\pi\) |
−0.997550 | + | 0.0699584i | \(0.977713\pi\) | |||||||
\(558\) | 13.6803 | − | 18.8294i | 0.579135 | − | 0.797111i | ||||
\(559\) | 15.9833 | − | 5.19329i | 0.676022 | − | 0.219653i | ||||
\(560\) | −23.6386 | −0.998912 | ||||||||
\(561\) | −3.65654 | + | 53.8922i | −0.154379 | + | 2.27533i | ||||
\(562\) | 26.7082 | 1.12662 | ||||||||
\(563\) | −21.1803 | + | 6.88191i | −0.892645 | + | 0.290038i | −0.719198 | − | 0.694805i | \(-0.755491\pi\) |
−0.173447 | + | 0.984843i | \(0.555491\pi\) | |||||||
\(564\) | −11.5451 | − | 8.38800i | −0.486136 | − | 0.353198i | ||||
\(565\) | −14.9828 | − | 20.6221i | −0.630333 | − | 0.867579i | ||||
\(566\) | −3.68034 | + | 11.3269i | −0.154696 | + | 0.476106i | ||||
\(567\) | −3.16356 | + | 9.73645i | −0.132857 | + | 0.408892i | ||||
\(568\) | −6.64066 | + | 4.82472i | −0.278636 | + | 0.202441i | ||||
\(569\) | 20.7148 | − | 28.5115i | 0.868409 | − | 1.19526i | −0.111090 | − | 0.993810i | \(-0.535434\pi\) |
0.979498 | − | 0.201452i | \(-0.0645659\pi\) | |||||||
\(570\) | −134.011 | + | 43.5427i | −5.61309 | + | 1.82380i | ||||
\(571\) | − | 31.8869i | − | 1.33442i | −0.744867 | − | 0.667212i | \(-0.767487\pi\) | ||
0.744867 | − | 0.667212i | \(-0.232513\pi\) | |||||||
\(572\) | −7.56231 | + | 1.90211i | −0.316196 | + | 0.0795313i | ||||
\(573\) | −65.3262 | −2.72904 | ||||||||
\(574\) | −26.2812 | + | 8.53926i | −1.09695 | + | 0.356422i | ||||
\(575\) | −32.6074 | − | 23.6907i | −1.35982 | − | 0.987969i | ||||
\(576\) | 12.8820 | − | 9.35930i | 0.536749 | − | 0.389971i | ||||
\(577\) | 26.6454 | + | 8.65761i | 1.10926 | + | 0.360421i | 0.805660 | − | 0.592378i | \(-0.201811\pi\) |
0.303601 | + | 0.952799i | \(0.401811\pi\) | |||||||
\(578\) | −44.4336 | − | 14.4374i | −1.84820 | − | 0.600515i | ||||
\(579\) | 21.8713 | + | 30.1033i | 0.908941 | + | 1.25105i | ||||
\(580\) | 24.2428 | + | 17.6134i | 1.00663 | + | 0.731356i | ||||
\(581\) | 9.82709 | − | 3.19302i | 0.407696 | − | 0.132469i | ||||
\(582\) | −9.61045 | −0.398366 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0.527864 | 0.0218432 | ||||||||
\(585\) | 18.0132 | − | 5.85283i | 0.744752 | − | 0.241985i | ||||
\(586\) | 8.55884 | − | 11.7802i | 0.353562 | − | 0.486637i | ||||
\(587\) | −14.2818 | − | 19.6572i | −0.589472 | − | 0.811339i | 0.405222 | − | 0.914218i | \(-0.367194\pi\) |
−0.994694 | + | 0.102880i | \(0.967194\pi\) | |||||||
\(588\) | 20.3553 | + | 6.61382i | 0.839436 | + | 0.272749i | ||||
\(589\) | 26.1803 | + | 8.50651i | 1.07874 | + | 0.350505i | ||||
\(590\) | −24.2428 | + | 17.6134i | −0.998059 | + | 0.725132i | ||||
\(591\) | 15.2016 | − | 20.9232i | 0.625311 | − | 0.860667i | ||||
\(592\) | 40.1433 | − | 13.0434i | 1.64988 | − | 0.536079i | ||||
\(593\) | 9.85359i | 0.404639i | 0.979320 | + | 0.202319i | \(0.0648479\pi\) | ||||
−0.979320 | + | 0.202319i | \(0.935152\pi\) | |||||||
\(594\) | −4.67133 | − | 3.90328i | −0.191667 | − | 0.160153i | ||||
\(595\) | −33.0000 | −1.35287 | ||||||||
\(596\) | −0.156765 | − | 0.482472i | −0.00642133 | − | 0.0197628i | ||||
\(597\) | 31.4443 | + | 22.8456i | 1.28693 | + | 0.935008i | ||||
\(598\) | −9.14590 | + | 6.64488i | −0.374004 | + | 0.271730i | ||||
\(599\) | −0.364745 | + | 1.12257i | −0.0149031 | + | 0.0458670i | −0.958232 | − | 0.285994i | \(-0.907676\pi\) |
0.943328 | + | 0.331861i | \(0.107676\pi\) | |||||||
\(600\) | 5.58905 | − | 17.2013i | 0.228172 | − | 0.702241i | ||||
\(601\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(602\) | 17.1738 | − | 23.6377i | 0.699950 | − | 0.963399i | ||||
\(603\) | 12.4828 | + | 38.4180i | 0.508338 | + | 1.56450i | ||||
\(604\) | 30.3278i | 1.23402i | ||||||||
\(605\) | 42.0066 | + | 5.72658i | 1.70781 | + | 0.232819i | ||||
\(606\) | 0.824160i | 0.0334792i | ||||||||
\(607\) | 4.61145 | + | 14.1926i | 0.187173 | + | 0.576059i | 0.999979 | − | 0.00647509i | \(-0.00206110\pi\) |
−0.812806 | + | 0.582534i | \(0.802061\pi\) | |||||||
\(608\) | 45.1246 | + | 32.7849i | 1.83004 | + | 1.32961i | ||||
\(609\) | −9.47655 | − | 13.0434i | −0.384009 | − | 0.528543i | ||||
\(610\) | −63.4684 | − | 20.6221i | −2.56976 | − | 0.834965i | ||||
\(611\) | −1.56765 | + | 4.82472i | −0.0634202 | + | 0.195187i | ||||
\(612\) | 28.5407 | − | 20.7360i | 1.15369 | − | 0.838204i | ||||
\(613\) | 5.27552 | + | 3.83289i | 0.213076 | + | 0.154809i | 0.689204 | − | 0.724567i | \(-0.257960\pi\) |
−0.476128 | + | 0.879376i | \(0.657960\pi\) | |||||||
\(614\) | −14.4157 | + | 4.68393i | −0.581769 | + | 0.189028i | ||||
\(615\) | − | 106.503i | − | 4.29461i | ||||||
\(616\) | 2.05208 | − | 2.45586i | 0.0826805 | − | 0.0989496i | ||||
\(617\) | 48.3050 | 1.94468 | 0.972342 | − | 0.233561i | \(-0.0750380\pi\) | ||||
0.972342 | + | 0.233561i | \(0.0750380\pi\) | |||||||
\(618\) | −27.5000 | + | 8.93529i | −1.10621 | + | 0.359430i | ||||
\(619\) | 2.61925 | − | 3.60510i | 0.105277 | − | 0.144901i | −0.753128 | − | 0.657874i | \(-0.771456\pi\) |
0.858405 | + | 0.512973i | \(0.171456\pi\) | |||||||
\(620\) | 18.2533 | − | 13.2618i | 0.733070 | − | 0.532606i | ||||
\(621\) | −3.75361 | − | 1.21962i | −0.150627 | − | 0.0489418i | ||||
\(622\) | −7.07394 | + | 21.7714i | −0.283639 | + | 0.872952i | ||||
\(623\) | 2.40261 | − | 1.74560i | 0.0962586 | − | 0.0699360i | ||||
\(624\) | −13.7146 | − | 9.96424i | −0.549023 | − | 0.398889i | ||||
\(625\) | 7.05573 | + | 21.7153i | 0.282229 | + | 0.868612i | ||||
\(626\) | − | 11.4127i | − | 0.456142i | ||||||
\(627\) | 23.7583 | − | 59.1558i | 0.948816 | − | 2.36246i | ||||
\(628\) | 16.7188i | 0.667154i | ||||||||
\(629\) | 56.0410 | − | 18.2088i | 2.23450 | − | 0.726034i | ||||
\(630\) | 19.3548 | − | 26.6396i | 0.771113 | − | 1.06135i | ||||
\(631\) | 21.2730 | + | 29.2797i | 0.846863 | + | 1.16561i | 0.984545 | + | 0.175131i | \(0.0560349\pi\) |
−0.137682 | + | 0.990477i | \(0.543965\pi\) | |||||||
\(632\) | −5.68232 | + | 3.06799i | −0.226030 | + | 0.122038i | ||||
\(633\) | 10.3262 | + | 3.35520i | 0.410431 | + | 0.133357i | ||||
\(634\) | −16.6697 | − | 22.9439i | −0.662038 | − | 0.911217i | ||||
\(635\) | −37.6438 | − | 27.3498i | −1.49385 | − | 1.08535i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 7.60845i | − | 0.301458i | ||||||
\(638\) | −29.3985 | + | 7.39448i | −1.16390 | + | 0.292750i | ||||
\(639\) | − | 38.2086i | − | 1.51151i | ||||||
\(640\) | −20.9164 | + | 6.79615i | −0.826794 | + | 0.268642i | ||||
\(641\) | −19.3992 | − | 14.0943i | −0.766222 | − | 0.556693i | 0.134591 | − | 0.990901i | \(-0.457028\pi\) |
−0.900812 | + | 0.434209i | \(0.857028\pi\) | |||||||
\(642\) | 20.6525 | − | 15.0049i | 0.815088 | − | 0.592196i | ||||
\(643\) | 3.83688 | − | 11.8087i | 0.151312 | − | 0.465690i | −0.846457 | − | 0.532458i | \(-0.821269\pi\) |
0.997769 | + | 0.0667676i | \(0.0212686\pi\) | |||||||
\(644\) | −2.71614 | + | 8.35942i | −0.107031 | + | 0.329407i | ||||
\(645\) | 66.1894 | + | 91.1019i | 2.60621 | + | 3.58714i | ||||
\(646\) | 75.4814 | + | 54.8405i | 2.96978 | + | 2.15767i | ||||
\(647\) | 7.99166 | − | 2.59665i | 0.314184 | − | 0.102085i | −0.147680 | − | 0.989035i | \(-0.547181\pi\) |
0.461865 | + | 0.886950i | \(0.347181\pi\) | |||||||
\(648\) | 5.60034i | 0.220002i | ||||||||
\(649\) | 0.917716 | − | 13.5258i | 0.0360235 | − | 0.530935i | ||||
\(650\) | 27.2361 | 1.06829 | ||||||||
\(651\) | −11.5451 | + | 3.75123i | −0.452488 | + | 0.147022i | ||||
\(652\) | 25.7254 | + | 18.6906i | 1.00749 | + | 0.731981i | ||||
\(653\) | 32.3156 | − | 23.4787i | 1.26461 | − | 0.918791i | 0.265633 | − | 0.964074i | \(-0.414419\pi\) |
0.998974 | + | 0.0452836i | \(0.0144191\pi\) | |||||||
\(654\) | 13.0517 | − | 40.1689i | 0.510360 | − | 1.57073i | ||||
\(655\) | 16.2188 | + | 5.26982i | 0.633723 | + | 0.205909i | ||||
\(656\) | −40.8673 | + | 29.6918i | −1.59560 | + | 1.15927i | ||||
\(657\) | −1.44427 | + | 1.98787i | −0.0563464 | + | 0.0775542i | ||||
\(658\) | 2.72542 | + | 8.38800i | 0.106248 | + | 0.326998i | ||||
\(659\) | −5.81983 | −0.226708 | −0.113354 | − | 0.993555i | \(-0.536159\pi\) | ||||
−0.113354 | + | 0.993555i | \(0.536159\pi\) | |||||||
\(660\) | −27.7797 | − | 44.2530i | −1.08132 | − | 1.72254i | ||||
\(661\) | 18.5079i | 0.719876i | 0.932976 | + | 0.359938i | \(0.117202\pi\) | ||||
−0.932976 | + | 0.359938i | \(0.882798\pi\) | |||||||
\(662\) | 5.50630 | + | 16.9466i | 0.214008 | + | 0.658650i | ||||
\(663\) | −19.1459 | − | 13.9103i | −0.743565 | − | 0.540232i | ||||
\(664\) | 4.57295 | − | 3.32244i | 0.177465 | − | 0.128936i | ||||
\(665\) | 37.0396 | + | 12.0349i | 1.43634 | + | 0.466694i | ||||
\(666\) | −18.1693 | + | 55.9193i | −0.704045 | + | 2.16683i | ||||
\(667\) | −15.9006 | + | 11.5524i | −0.615672 | + | 0.447312i | ||||
\(668\) | 0.590170 | − | 0.812299i | 0.0228344 | − | 0.0314288i | ||||
\(669\) | 17.7360 | − | 5.76277i | 0.685713 | − | 0.222802i | ||||
\(670\) | 87.5627i | 3.38284i | ||||||||
\(671\) | 25.5709 | − | 16.0521i | 0.987153 | − | 0.619684i | ||||
\(672\) | −24.5967 | −0.948840 | ||||||||
\(673\) | −7.87190 | − | 24.2272i | −0.303439 | − | 0.933891i | −0.980255 | − | 0.197738i | \(-0.936641\pi\) |
0.676815 | − | 0.736153i | \(-0.263359\pi\) | |||||||
\(674\) | 17.5623 | + | 12.7598i | 0.676475 | + | 0.491488i | ||||
\(675\) | 5.58905 | + | 7.69266i | 0.215122 | + | 0.296091i | ||||
\(676\) | −5.44427 | + | 16.7557i | −0.209395 | + | 0.644452i | ||||
\(677\) | 8.55573 | + | 2.77992i | 0.328823 | + | 0.106841i | 0.468776 | − | 0.883317i | \(-0.344695\pi\) |
−0.139953 | + | 0.990158i | \(0.544695\pi\) | |||||||
\(678\) | −18.6803 | − | 25.7113i | −0.717414 | − | 0.987436i | ||||
\(679\) | 2.14896 | + | 1.56131i | 0.0824696 | + | 0.0599176i | ||||
\(680\) | −17.1688 | + | 5.57849i | −0.658394 | + | 0.213925i | ||||
\(681\) | 57.3409i | 2.19731i | ||||||||
\(682\) | −1.54508 | + | 22.7724i | −0.0591644 | + | 0.871999i | ||||
\(683\) | 1.65248 | 0.0632302 | 0.0316151 | − | 0.999500i | \(-0.489935\pi\) | ||||
0.0316151 | + | 0.999500i | \(0.489935\pi\) | |||||||
\(684\) | −39.5967 | + | 12.8658i | −1.51402 | + | 0.491935i | ||||
\(685\) | −34.8537 | + | 47.9720i | −1.33169 | + | 1.83291i | ||||
\(686\) | −18.1693 | − | 25.0079i | −0.693706 | − | 0.954805i | ||||
\(687\) | 17.4615 | − | 53.7409i | 0.666198 | − | 2.05035i | ||||
\(688\) | 16.5048 | − | 50.7964i | 0.629238 | − | 1.93659i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −61.2824 | − | 44.5243i | −2.33298 | − | 1.69501i | ||||
\(691\) | 35.3381 | − | 11.4820i | 1.34432 | − | 0.436798i | 0.453545 | − | 0.891233i | \(-0.350159\pi\) |
0.890780 | + | 0.454436i | \(0.150159\pi\) | |||||||
\(692\) | 14.2219 | 0.540635 | ||||||||
\(693\) | 3.63386 | + | 14.4473i | 0.138039 | + | 0.548806i | ||||
\(694\) | 40.9787 | 1.55553 | ||||||||
\(695\) | −8.28232 | − | 25.4903i | −0.314166 | − | 0.966904i | ||||
\(696\) | −7.13525 | − | 5.18407i | −0.270461 | − | 0.196502i | ||||
\(697\) | −57.0517 | + | 41.4505i | −2.16099 | + | 1.57005i | ||||
\(698\) | −30.8834 | − | 10.0346i | −1.16895 | − | 0.379816i | ||||
\(699\) | −59.6976 | − | 19.3969i | −2.25797 | − | 0.733659i | ||||
\(700\) | 17.1318 | − | 12.4470i | 0.647522 | − | 0.470452i | ||||
\(701\) | 13.1474 | + | 9.55216i | 0.496571 | + | 0.360780i | 0.807706 | − | 0.589586i | \(-0.200709\pi\) |
−0.311135 | + | 0.950366i | \(0.600709\pi\) | |||||||
\(702\) | 2.53650 | − | 0.824160i | 0.0957342 | − | 0.0311059i | ||||
\(703\) | −69.5418 | −2.62282 | ||||||||
\(704\) | −5.81966 | + | 14.4904i | −0.219337 | + | 0.546126i | ||||
\(705\) | −33.9919 | −1.28021 | ||||||||
\(706\) | 1.61879 | + | 4.98212i | 0.0609239 | + | 0.187505i | ||||
\(707\) | 0.133893 | − | 0.184288i | 0.00503556 | − | 0.00693086i | ||||
\(708\) | −13.5172 | + | 9.82084i | −0.508008 | + | 0.369090i | ||||
\(709\) | 16.4677 | + | 5.35069i | 0.618459 | + | 0.200950i | 0.601456 | − | 0.798906i | \(-0.294587\pi\) |
0.0170031 | + | 0.999855i | \(0.494587\pi\) | |||||||
\(710\) | 25.5938 | − | 78.7695i | 0.960517 | − | 2.95617i | ||||
\(711\) | 3.99354 | − | 29.7931i | 0.149770 | − | 1.11733i | ||||
\(712\) | 0.954915 | − | 1.31433i | 0.0357870 | − | 0.0492565i | ||||
\(713\) | 4.57295 | + | 14.0741i | 0.171258 | + | 0.527079i | ||||
\(714\) | −41.1438 | −1.53977 | ||||||||
\(715\) | −11.9098 | + | 14.2533i | −0.445402 | + | 0.533045i | ||||
\(716\) | −30.0344 | −1.12244 | ||||||||
\(717\) | −6.94005 | − | 21.3593i | −0.259181 | − | 0.797677i | ||||
\(718\) | −36.0392 | + | 49.6037i | −1.34497 | + | 1.85119i | ||||
\(719\) | −26.0344 | + | 18.9151i | −0.970921 | + | 0.705415i | −0.955661 | − | 0.294468i | \(-0.904857\pi\) |
−0.0152596 | + | 0.999884i | \(0.504857\pi\) | |||||||
\(720\) | 18.6008 | − | 57.2474i | 0.693211 | − | 2.13349i | ||||
\(721\) | 7.60081 | + | 2.46965i | 0.283069 | + | 0.0919747i | ||||
\(722\) | −43.4787 | − | 59.8433i | −1.61811 | − | 2.22714i | ||||
\(723\) | 40.9271 | + | 29.7353i | 1.52210 | + | 1.10587i | ||||
\(724\) | −1.23607 | − | 3.80423i | −0.0459381 | − | 0.141383i | ||||
\(725\) | 47.3512 | 1.75858 | ||||||||
\(726\) | 52.3730 | + | 7.13980i | 1.94375 | + | 0.264983i | ||||
\(727\) | 26.5967 | 0.986419 | 0.493209 | − | 0.869911i | \(-0.335824\pi\) | ||||
0.493209 | + | 0.869911i | \(0.335824\pi\) | |||||||
\(728\) | 0.433287 | + | 1.33352i | 0.0160587 | + | 0.0494235i | ||||
\(729\) | −27.0066 | − | 19.6214i | −1.00024 | − | 0.726720i | ||||
\(730\) | −4.30902 | + | 3.13068i | −0.159484 | + | 0.115872i | ||||
\(731\) | 23.0410 | − | 70.9130i | 0.852203 | − | 2.62281i | ||||
\(732\) | −35.3885 | − | 11.4984i | −1.30800 | − | 0.424994i | ||||
\(733\) | −21.0795 | − | 29.0135i | −0.778590 | − | 1.07164i | −0.995436 | − | 0.0954315i | \(-0.969577\pi\) |
0.216846 | − | 0.976206i | \(-0.430423\pi\) | |||||||
\(734\) | −1.05573 | + | 1.45309i | −0.0389676 | + | 0.0536343i | ||||
\(735\) | 48.4855 | − | 15.7539i | 1.78842 | − | 0.581091i | ||||
\(736\) | 29.9848i | 1.10525i | ||||||||
\(737\) | −30.3992 | − | 25.4010i | −1.11977 | − | 0.935658i | ||||
\(738\) | − | 70.3666i | − | 2.59023i | ||||||
\(739\) | 9.39380 | + | 28.9112i | 0.345557 | + | 1.06351i | 0.961285 | + | 0.275556i | \(0.0888618\pi\) |
−0.615729 | + | 0.787958i | \(0.711138\pi\) | |||||||
\(740\) | −33.5027 | + | 46.1125i | −1.23158 | + | 1.69513i | ||||
\(741\) | 16.4166 | + | 22.5955i | 0.603079 | + | 0.830067i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.47214 | + | 1.45309i | 0.164067 | + | 0.0533085i | 0.389899 | − | 0.920858i | \(-0.372510\pi\) |
−0.225832 | + | 0.974166i | \(0.572510\pi\) | |||||||
\(744\) | −5.37240 | + | 3.90328i | −0.196962 | + | 0.143101i | ||||
\(745\) | −0.977595 | − | 0.710264i | −0.0358163 | − | 0.0260221i | ||||
\(746\) | 23.3250 | − | 7.57877i | 0.853991 | − | 0.277478i | ||||
\(747\) | 26.3116i | 0.962690i | ||||||||
\(748\) | −12.8938 | + | 32.1042i | −0.471443 | + | 1.17384i | ||||
\(749\) | −7.05573 | −0.257811 | ||||||||
\(750\) | 27.7797 | + | 85.4972i | 1.01437 | + | 3.12192i | ||||
\(751\) | 25.7533 | + | 18.7109i | 0.939751 | + | 0.682769i | 0.948361 | − | 0.317194i | \(-0.102741\pi\) |
−0.00860982 | + | 0.999963i | \(0.502741\pi\) | |||||||
\(752\) | 9.47655 | + | 13.0434i | 0.345574 | + | 0.475642i | ||||
\(753\) | −2.72542 | + | 8.38800i | −0.0993200 | + | 0.305676i | ||||
\(754\) | 4.10415 | − | 12.6313i | 0.149464 | − | 0.460004i | ||||
\(755\) | 42.4615 | + | 58.4432i | 1.54533 | + | 2.12697i | ||||
\(756\) | 1.21885 | − | 1.67760i | 0.0443290 | − | 0.0610137i | ||||
\(757\) | −4.11146 | − | 12.6538i | −0.149433 | − | 0.459909i | 0.848121 | − | 0.529803i | \(-0.177734\pi\) |
−0.997554 | + | 0.0698938i | \(0.977734\pi\) | |||||||
\(758\) | 23.3250 | 0.847204 | ||||||||
\(759\) | 33.2349 | − | 8.35942i | 1.20635 | − | 0.303428i | ||||
\(760\) | 21.3050 | 0.772812 | ||||||||
\(761\) | 0.892609 | − | 0.290026i | 0.0323571 | − | 0.0105134i | −0.292794 | − | 0.956176i | \(-0.594585\pi\) |
0.325151 | + | 0.945662i | \(0.394585\pi\) | |||||||
\(762\) | −46.9336 | − | 34.0993i | −1.70023 | − | 1.23529i | ||||
\(763\) | −9.44427 | + | 6.86167i | −0.341906 | + | 0.248409i | ||||
\(764\) | −39.7928 | − | 12.9295i | −1.43965 | − | 0.467771i | ||||
\(765\) | 25.9672 | − | 79.9187i | 0.938845 | − | 2.88947i | ||||
\(766\) | 20.2877 | + | 27.9237i | 0.733026 | + | 1.00892i | ||||
\(767\) | 4.80522 | + | 3.49120i | 0.173507 | + | 0.126060i | ||||
\(768\) | −48.7022 | + | 15.8243i | −1.75739 | + | 0.571010i | ||||
\(769\) | 12.9678 | 0.467630 | 0.233815 | − | 0.972281i | \(-0.424879\pi\) | ||||
0.233815 | + | 0.972281i | \(0.424879\pi\) | |||||||
\(770\) | −2.18597 | + | 32.2181i | −0.0787768 | + | 1.16106i | ||||
\(771\) | 20.2100i | 0.727847i | ||||||||
\(772\) | 7.36460 | + | 22.6659i | 0.265058 | + | 0.815764i | ||||
\(773\) | 28.9615 | + | 21.0418i | 1.04167 | + | 0.756819i | 0.970611 | − | 0.240653i | \(-0.0773614\pi\) |
0.0710612 | + | 0.997472i | \(0.477361\pi\) | |||||||
\(774\) | 43.7314 | + | 60.1912i | 1.57189 | + | 2.16353i | ||||
\(775\) | 11.0172 | − | 33.9075i | 0.395750 | − | 1.21799i | ||||
\(776\) | 1.38197 | + | 0.449028i | 0.0496097 | + | 0.0161192i | ||||
\(777\) | 24.8099 | − | 18.0255i | 0.890052 | − | 0.646660i | ||||
\(778\) | −5.00000 | + | 6.88191i | −0.179259 | + | 0.246728i | ||||
\(779\) | 79.1523 | − | 25.7181i | 2.83593 | − | 0.921448i | ||||
\(780\) | 22.8918 | 0.819656 | ||||||||
\(781\) | 19.9220 | + | 31.7356i | 0.712864 | + | 1.13559i | ||||
\(782\) | 50.1565i | 1.79359i | ||||||||
\(783\) | 4.40983 | − | 1.43284i | 0.157594 | − | 0.0512055i | ||||
\(784\) | −19.5623 | − | 14.2128i | −0.698654 | − | 0.507602i | ||||
\(785\) | 23.4078 | + | 32.2181i | 0.835460 | + | 1.14991i | ||||
\(786\) | 20.2214 | + | 6.57032i | 0.721272 | + | 0.234355i | ||||
\(787\) | 10.9164 | + | 3.54696i | 0.389128 | + | 0.126435i | 0.497045 | − | 0.867725i | \(-0.334418\pi\) |
−0.107917 | + | 0.994160i | \(0.534418\pi\) | |||||||
\(788\) | 13.4011 | − | 9.73645i | 0.477393 | − | 0.346847i | ||||
\(789\) | 24.5933 | + | 17.8681i | 0.875545 | + | 0.636120i | ||||
\(790\) | 28.1896 | − | 58.7453i | 1.00294 | − | 2.09007i | ||||
\(791\) | 8.78402i | 0.312324i | ||||||||
\(792\) | 4.33282 | + | 6.90215i | 0.153960 | + | 0.245257i | ||||
\(793\) | 13.2276i | 0.469727i | ||||||||
\(794\) | 33.8435 | − | 10.9964i | 1.20106 | − | 0.390248i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.6323 | + | 20.1397i | 0.518629 | + | 0.713831i | ||||
\(797\) | −21.4896 | − | 6.98240i | −0.761201 | − | 0.247329i | −0.0974070 | − | 0.995245i | \(-0.531055\pi\) |
−0.663794 | + | 0.747915i | \(0.731055\pi\) | |||||||
\(798\) | 46.1803 | + | 15.0049i | 1.63477 | + | 0.531168i | ||||
\(799\) | 13.2295 | + | 18.2088i | 0.468026 | + | 0.644182i | ||||
\(800\) | 42.4615 | − | 58.4432i | 1.50124 | − | 2.06628i | ||||
\(801\) | 2.33688 | + | 7.19218i | 0.0825696 | + | 0.254123i | ||||
\(802\) | 13.7146 | 0.484279 | ||||||||
\(803\) | 0.163119 | − | 2.40414i | 0.00575634 | − | 0.0848403i | ||||
\(804\) | 48.8230i | 1.72185i | ||||||||
\(805\) | 6.46976 | + | 19.9119i | 0.228029 | + | 0.701801i | ||||
\(806\) | −8.09017 | − | 5.87785i | −0.284964 | − | 0.207039i | ||||
\(807\) | −20.4380 | − | 28.1305i | −0.719452 | − | 0.990240i | ||||
\(808\) | 0.0385072 | − | 0.118513i | 0.00135468 | − | 0.00416927i | ||||
\(809\) | 17.2361 | + | 5.60034i | 0.605988 | + | 0.196897i | 0.595909 | − | 0.803052i | \(-0.296792\pi\) |
0.0100787 | + | 0.999949i | \(0.496792\pi\) | |||||||
\(810\) | −33.2148 | − | 45.7162i | −1.16705 | − | 1.60630i | ||||
\(811\) | −22.9894 | + | 31.6421i | −0.807266 | + | 1.11111i | 0.184474 | + | 0.982837i | \(0.440942\pi\) |
−0.991740 | + | 0.128268i | \(0.959058\pi\) | |||||||
\(812\) | −3.19098 | − | 9.82084i | −0.111982 | − | 0.344644i | ||||
\(813\) | 30.0098i | 1.05249i | ||||||||
\(814\) | −14.0651 | − | 55.9193i | −0.492983 | − | 1.95997i | ||||
\(815\) | 75.7426 | 2.65315 | ||||||||
\(816\) | −71.5304 | + | 23.2416i | −2.50406 | + | 0.813620i | ||||
\(817\) | −51.7231 | + | 71.1907i | −1.80956 | + | 2.49065i | ||||
\(818\) | −41.4116 | − | 56.9981i | −1.44792 | − | 1.99289i | ||||
\(819\) | −6.20737 | − | 2.01690i | −0.216903 | − | 0.0704761i | ||||
\(820\) | 21.0792 | − | 64.8751i | 0.736117 | − | 2.26554i | ||||
\(821\) | −27.3369 | − | 37.6260i | −0.954064 | − | 1.31316i | −0.949699 | − | 0.313166i | \(-0.898611\pi\) |
−0.00436519 | − | 0.999990i | \(-0.501389\pi\) | |||||||
\(822\) | −43.4549 | + | 59.8106i | −1.51566 | + | 2.08613i | ||||
\(823\) | 10.9614 | − | 3.56159i | 0.382092 | − | 0.124149i | −0.111672 | − | 0.993745i | \(-0.535621\pi\) |
0.493764 | + | 0.869596i | \(0.335621\pi\) | |||||||
\(824\) | 4.37194 | 0.152304 | ||||||||
\(825\) | −76.6158 | − | 30.7706i | −2.66742 | − | 1.07130i | ||||
\(826\) | 10.3262 | 0.359296 | ||||||||
\(827\) | −5.91671 | − | 18.2098i | −0.205744 | − | 0.633216i | −0.999682 | − | 0.0252166i | \(-0.991972\pi\) |
0.793938 | − | 0.607999i | \(-0.208028\pi\) | |||||||
\(828\) | −18.1074 | − | 13.1558i | −0.629275 | − | 0.457195i | ||||
\(829\) | 5.58905 | + | 7.69266i | 0.194116 | + | 0.267177i | 0.894969 | − | 0.446128i | \(-0.147197\pi\) |
−0.700854 | + | 0.713305i | \(0.747197\pi\) | |||||||
\(830\) | −17.6246 | + | 54.2430i | −0.611759 | + | 1.88280i | ||||
\(831\) | 6.20737 | − | 19.1043i | 0.215331 | − | 0.662721i | ||||
\(832\) | −4.02129 | − | 5.53483i | −0.139413 | − | 0.191886i | ||||
\(833\) | −27.3094 | − | 19.8415i | −0.946216 | − | 0.687466i | ||||
\(834\) | −10.3262 | − | 31.7809i | −0.357568 | − | 1.10048i | ||||
\(835\) | − | 2.39163i | − | 0.0827658i | ||||||
\(836\) | 26.1803 | − | 31.3319i | 0.905466 | − | 1.08364i | ||||
\(837\) | − | 3.49120i | − | 0.120673i | ||||||
\(838\) | −14.4157 | − | 44.3669i | −0.497981 | − | 1.53263i | ||||
\(839\) | −17.2984 | − | 12.5680i | −0.597206 | − | 0.433896i | 0.247680 | − | 0.968842i | \(-0.420332\pi\) |
−0.844886 | + | 0.534946i | \(0.820332\pi\) | |||||||
\(840\) | −7.60081 | + | 5.52231i | −0.262253 | + | 0.190538i | ||||
\(841\) | −1.82624 | + | 5.62058i | −0.0629737 | + | 0.193813i | ||||
\(842\) | −33.5172 | − | 10.8904i | −1.15508 | − | 0.375308i | ||||
\(843\) | 28.6974 | − | 20.8499i | 0.988393 | − | 0.718109i | ||||
\(844\) | 5.62605 | + | 4.08757i | 0.193657 | + | 0.140700i | ||||
\(845\) | 12.9681 | + | 39.9116i | 0.446115 | + | 1.37300i | ||||
\(846\) | −22.4585 | −0.772138 | ||||||||
\(847\) | −10.5510 | − | 10.1050i | −0.362538 | − | 0.347213i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.88797 | + | 15.0436i | 0.167755 | + | 0.516296i | ||||
\(850\) | 71.0267 | − | 97.7599i | 2.43620 | − | 3.35314i | ||||
\(851\) | −21.9740 | − | 30.2447i | −0.753260 | − | 1.03677i | ||||
\(852\) | 14.2705 | − | 43.9201i | 0.488900 | − | 1.50468i | ||||
\(853\) | −2.36560 | + | 7.28058i | −0.0809968 | + | 0.249282i | −0.983352 | − | 0.181711i | \(-0.941837\pi\) |
0.902355 | + | 0.430993i | \(0.141837\pi\) | |||||||
\(854\) | 13.5172 | + | 18.6049i | 0.462550 | + | 0.636645i | ||||
\(855\) | −58.2918 | + | 80.2318i | −1.99354 | + | 2.74387i | ||||
\(856\) | −3.67086 | + | 1.19274i | −0.125468 | + | 0.0407669i | ||||
\(857\) | 48.3449i | 1.65143i | 0.564088 | + | 0.825715i | \(0.309228\pi\) | ||||
−0.564088 | + | 0.825715i | \(0.690772\pi\) | |||||||
\(858\) | −14.8490 | + | 17.7708i | −0.506935 | + | 0.606685i | ||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | 22.2876 | + | 68.5941i | 0.760000 | + | 2.33904i | ||||
\(861\) | −21.5724 | + | 29.6918i | −0.735184 | + | 1.01189i | ||||
\(862\) | 5.85410 | − | 4.25325i | 0.199392 | − | 0.144866i | ||||
\(863\) | −15.2467 | + | 46.9246i | −0.519004 | + | 1.59733i | 0.256872 | + | 0.966445i | \(0.417308\pi\) |
−0.775876 | + | 0.630885i | \(0.782692\pi\) | |||||||
\(864\) | 2.18597 | − | 6.72772i | 0.0743681 | − | 0.228882i | ||||
\(865\) | 27.4063 | − | 19.9119i | 0.931843 | − | 0.677024i | ||||
\(866\) | −19.5729 | + | 26.9399i | −0.665116 | + | 0.915453i | ||||
\(867\) | −59.0137 | + | 19.1747i | −2.00421 | + | 0.651207i | ||||
\(868\) | −7.77501 | −0.263901 | ||||||||
\(869\) | 12.2171 | + | 26.8280i | 0.414438 | + | 0.910078i | ||||
\(870\) | 88.9919 | 3.01711 | ||||||||
\(871\) | 16.5066 | − | 5.36331i | 0.559304 | − | 0.181729i | ||||
\(872\) | −3.75361 | + | 5.16641i | −0.127113 | + | 0.174957i | ||||
\(873\) | −5.47214 | + | 3.97574i | −0.185204 | + | 0.134558i | ||||
\(874\) | 18.2918 | − | 56.2964i | 0.618729 | − | 1.90425i | ||||
\(875\) | 7.67813 | − | 23.6308i | 0.259568 | − | 0.798869i | ||||
\(876\) | −2.40261 | + | 1.74560i | −0.0811767 | + | 0.0589783i | ||||
\(877\) | −5.65248 | + | 7.77997i | −0.190871 | + | 0.262711i | −0.893717 | − | 0.448630i | \(-0.851912\pi\) |
0.702847 | + | 0.711341i | \(0.251912\pi\) | |||||||
\(878\) | −19.2705 | − | 59.3085i | −0.650348 | − | 2.00157i | ||||
\(879\) | − | 19.3391i | − | 0.652293i | ||||||
\(880\) | 14.3992 | + | 57.2474i | 0.485396 | + | 1.92981i | ||||
\(881\) | 19.6137i | 0.660801i | 0.943841 | + | 0.330401i | \(0.107184\pi\) | ||||
−0.943841 | + | 0.330401i | \(0.892816\pi\) | |||||||
\(882\) | 32.0344 | − | 10.4086i | 1.07866 | − | 0.350477i | ||||
\(883\) | −3.75361 | + | 5.16641i | −0.126319 | + | 0.173863i | −0.867492 | − | 0.497450i | \(-0.834270\pi\) |
0.741173 | + | 0.671314i | \(0.234270\pi\) | |||||||
\(884\) | −8.90937 | − | 12.2627i | −0.299655 | − | 0.412439i | ||||
\(885\) | −12.2984 | + | 37.8505i | −0.413405 | + | 1.27233i | ||||
\(886\) | −3.53697 | + | 10.8857i | −0.118827 | + | 0.365711i | ||||
\(887\) | −6.80902 | − | 9.37181i | −0.228624 | − | 0.314675i | 0.679258 | − | 0.733900i | \(-0.262302\pi\) |
−0.907882 | + | 0.419225i | \(0.862302\pi\) | |||||||
\(888\) | 9.86068 | − | 13.5721i | 0.330903 | − | 0.455449i | ||||
\(889\) | 4.95492 | + | 15.2497i | 0.166183 | + | 0.511457i | ||||
\(890\) | 16.3925i | 0.549477i | ||||||||
\(891\) | 25.5066 | + | 1.73060i | 0.854503 | + | 0.0579773i | ||||
\(892\) | 11.9443 | 0.399924 | ||||||||
\(893\) | −8.20830 | − | 25.2626i | −0.274680 | − | 0.845379i | ||||
\(894\) | −1.21885 | − | 0.885544i | −0.0407643 | − | 0.0296170i | ||||
\(895\) | −57.8779 | + | 42.0508i | −1.93464 | + | 1.40560i | ||||
\(896\) | 7.20783 | + | 2.34197i | 0.240797 | + | 0.0782396i | ||||
\(897\) | −4.63972 | + | 14.2796i | −0.154916 | + | 0.476782i | ||||
\(898\) | 50.8881 | − | 36.9724i | 1.69816 | − | 1.23378i | ||||
\(899\) | −14.0651 | − | 10.2189i | −0.469098 | − | 0.340820i | ||||
\(900\) | 16.6631 | + | 51.2838i | 0.555437 | + | 1.70946i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 36.6891 | + | 58.4456i | 1.22161 | + | 1.94602i | ||||
\(903\) | − | 38.8050i | − | 1.29135i | ||||||
\(904\) | 1.48490 | + | 4.57004i | 0.0493869 | + | 0.151997i | ||||
\(905\) | −7.70820 | − | 5.60034i | −0.256229 | − | 0.186162i | ||||
\(906\) | 52.9402 | + | 72.8659i | 1.75882 | + | 2.42081i | ||||
\(907\) | −4.87132 | + | 14.9924i | −0.161750 | + | 0.497814i | −0.998782 | − | 0.0493391i | \(-0.984289\pi\) |
0.837032 | + | 0.547153i | \(0.184289\pi\) | |||||||
\(908\) | −11.3490 | + | 34.9286i | −0.376630 | + | 1.15915i | ||||
\(909\) | 0.340946 | + | 0.469272i | 0.0113085 | + | 0.0155648i | ||||
\(910\) | −11.4459 | − | 8.31592i | −0.379427 | − | 0.275670i | ||||
\(911\) | −4.89919 | − | 15.0781i | −0.162317 | − | 0.499561i | 0.836511 | − | 0.547950i | \(-0.184591\pi\) |
−0.998829 | + | 0.0483884i | \(0.984591\pi\) | |||||||
\(912\) | 88.7627 | 2.93923 | ||||||||
\(913\) | −13.7188 | − | 21.8541i | −0.454028 | − | 0.723264i | ||||
\(914\) | −65.7771 | −2.17571 | ||||||||
\(915\) | −84.2943 | + | 27.3889i | −2.78668 | + | 0.905448i | ||||
\(916\) | 21.2730 | − | 29.2797i | 0.702879 | − | 0.967429i | ||||
\(917\) | −3.45422 | − | 4.75433i | −0.114068 | − | 0.157002i | ||||
\(918\) | 3.65654 | − | 11.2537i | 0.120684 | − | 0.371427i | ||||
\(919\) | 24.8369 | + | 8.06999i | 0.819293 | + | 0.266204i | 0.688529 | − | 0.725209i | \(-0.258257\pi\) |
0.130764 | + | 0.991413i | \(0.458257\pi\) | |||||||
\(920\) | 6.73200 | + | 9.26581i | 0.221948 | + | 0.305485i | ||||
\(921\) | −11.8328 | + | 16.2865i | −0.389905 | + | 0.536658i | ||||
\(922\) | 27.3464 | − | 8.88540i | 0.900607 | − | 0.292625i | ||||
\(923\) | −16.4166 | −0.540359 | ||||||||
\(924\) | −1.21885 | + | 17.9641i | −0.0400971 | + | 0.590975i | ||||
\(925\) | 90.0673i | 2.96139i | ||||||||
\(926\) | −15.7667 | − | 48.5248i | −0.518125 | − | 1.59462i | ||||
\(927\) | −11.9619 | + | 16.4642i | −0.392881 | + | 0.540754i | ||||
\(928\) | −20.7058 | − | 28.4991i | −0.679701 | − | 0.935528i | ||||
\(929\) | 30.1823 | + | 9.80684i | 0.990251 | + | 0.321752i | 0.758963 | − | 0.651134i | \(-0.225706\pi\) |
0.231287 | + | 0.972885i | \(0.425706\pi\) | |||||||
\(930\) | 20.7058 | − | 63.7259i | 0.678970 | − | 2.08965i | ||||
\(931\) | 23.4164 | + | 32.2299i | 0.767442 | + | 1.05629i | ||||
\(932\) | −32.5251 | − | 23.6308i | −1.06539 | − | 0.774054i | ||||
\(933\) | 9.39512 | + | 28.9152i | 0.307582 | + | 0.946642i | ||||
\(934\) | − | 39.3489i | − | 1.28753i | ||||||
\(935\) | 20.1016 | + | 79.9187i | 0.657393 | + | 2.61362i | ||||
\(936\) | −3.57044 | −0.116703 | ||||||||
\(937\) | 11.7224 | + | 36.0778i | 0.382954 | + | 1.17861i | 0.937954 | + | 0.346761i | \(0.112718\pi\) |
−0.554999 | + | 0.831851i | \(0.687282\pi\) | |||||||
\(938\) | 17.7360 | − | 24.4115i | 0.579101 | − | 0.797064i | ||||
\(939\) | −8.90937 | − | 12.2627i | −0.290746 | − | 0.400178i | ||||
\(940\) | −20.7058 | − | 6.72772i | −0.675348 | − | 0.219434i | ||||
\(941\) | 56.2426 | + | 18.2743i | 1.83346 | + | 0.595727i | 0.999003 | + | 0.0446508i | \(0.0142175\pi\) |
0.834455 | + | 0.551076i | \(0.185782\pi\) | |||||||
\(942\) | 29.1844 | + | 40.1689i | 0.950879 | + | 1.30877i | ||||
\(943\) | 36.1959 | + | 26.2979i | 1.17870 | + | 0.856377i | ||||
\(944\) | 17.9526 | − | 5.83317i | 0.584309 | − | 0.189853i | ||||
\(945\) | − | 4.93931i | − | 0.160676i | ||||||
\(946\) | −67.7064 | − | 27.1924i | −2.20133 | − | 0.884103i | ||||
\(947\) | 28.1574i | 0.914992i | 0.889212 | + | 0.457496i | \(0.151254\pi\) | ||||
−0.889212 | + | 0.457496i | \(0.848746\pi\) | |||||||
\(948\) | 15.7179 | − | 32.7551i | 0.510494 | − | 1.06384i | ||||
\(949\) | 0.854102 | + | 0.620541i | 0.0277253 | + | 0.0201436i | ||||
\(950\) | −115.374 | + | 83.8240i | −3.74322 | + | 2.71961i | ||||
\(951\) | −35.8225 | − | 11.6394i | −1.16163 | − | 0.377435i | ||||
\(952\) | 5.91641 | + | 1.92236i | 0.191752 | + | 0.0623040i | ||||
\(953\) | −4.53444 | − | 6.24112i | −0.146885 | − | 0.202170i | 0.729234 | − | 0.684264i | \(-0.239876\pi\) |
−0.876119 | + | 0.482094i | \(0.839876\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −94.7851 | + | 30.7975i | −3.06717 | + | 0.996585i | ||||
\(956\) | − | 14.3844i | − | 0.465223i | ||||||
\(957\) | −25.8156 | + | 30.8953i | −0.834500 | + | 0.998705i | ||||
\(958\) | −44.2705 | −1.43032 | ||||||||
\(959\) | 19.4336 | − | 6.31437i | 0.627545 | − | 0.203902i | ||||
\(960\) | 26.9448 | − | 37.0863i | 0.869639 | − | 1.19695i | ||||
\(961\) | 14.4894 | − | 10.5271i | 0.467399 | − | 0.339585i | ||||
\(962\) | 24.0261 | + | 7.80656i | 0.774633 | + | 0.251694i | ||||
\(963\) | 5.55204 | − | 17.0874i | 0.178912 | − | 0.550634i | ||||
\(964\) | 19.0451 | + | 26.2133i | 0.613401 | + | 0.844274i | ||||
\(965\) | 45.9261 | + | 33.3673i | 1.47841 | + | 1.07413i | ||||
\(966\) | 8.06637 | + | 24.8257i | 0.259531 | + | 0.798755i | ||||
\(967\) | − | 34.6871i | − | 1.11546i | −0.830022 | − | 0.557730i | \(-0.811672\pi\) | ||
0.830022 | − | 0.557730i | \(-0.188328\pi\) | |||||||
\(968\) | −7.19756 | − | 3.47371i | −0.231338 | − | 0.111649i | ||||
\(969\) | 123.915 | 3.98072 | ||||||||
\(970\) | −13.9443 | + | 4.53077i | −0.447724 | + | 0.145474i | ||||
\(971\) | −12.8262 | − | 9.31881i | −0.411614 | − | 0.299055i | 0.362641 | − | 0.931929i | \(-0.381875\pi\) |
−0.774255 | + | 0.632874i | \(0.781875\pi\) | |||||||
\(972\) | −21.2730 | − | 29.2797i | −0.682331 | − | 0.939148i | ||||
\(973\) | −2.85410 | + | 8.78402i | −0.0914983 | + | 0.281603i | ||||
\(974\) | 29.7984 | + | 9.68208i | 0.954801 | + | 0.310234i | ||||
\(975\) | 29.2646 | − | 21.2620i | 0.937218 | − | 0.680929i | ||||
\(976\) | 34.0100 | + | 24.7097i | 1.08863 | + | 0.790938i | ||||
\(977\) | 2.96979 | − | 0.964944i | 0.0950120 | − | 0.0308713i | −0.261125 | − | 0.965305i | \(-0.584094\pi\) |
0.356137 | + | 0.934434i | \(0.384094\pi\) | |||||||
\(978\) | 94.4345 | 3.01968 | ||||||||
\(979\) | −5.69098 | − | 4.75528i | −0.181885 | − | 0.151979i | ||||
\(980\) | 32.6525 | 1.04305 | ||||||||
\(981\) | −9.18590 | − | 28.2713i | −0.293283 | − | 0.902633i | ||||
\(982\) | 7.90891 | − | 10.8857i | 0.252383 | − | 0.347376i | ||||
\(983\) | 0.834966 | + | 1.14923i | 0.0266313 | + | 0.0366548i | 0.822125 | − | 0.569307i | \(-0.192788\pi\) |
−0.795494 | + | 0.605962i | \(0.792788\pi\) | |||||||
\(984\) | −6.20414 | + | 19.0944i | −0.197781 | + | 0.608706i | ||||
\(985\) | 12.1927 | − | 37.5253i | 0.388492 | − | 1.19565i | ||||
\(986\) | −34.6353 | − | 47.6713i | −1.10301 | − | 1.51816i | ||||
\(987\) | 9.47655 | + | 6.88512i | 0.301642 | + | 0.219156i | ||||
\(988\) | 5.52786 | + | 17.0130i | 0.175865 | + | 0.541256i | ||||
\(989\) | −47.3054 | −1.50422 | ||||||||
\(990\) | −76.3050 | − | 30.6458i | −2.42513 | − | 0.973988i | ||||
\(991\) | − | 24.8940i | − | 0.790783i | −0.918513 | − | 0.395392i | \(-0.870609\pi\) | ||
0.918513 | − | 0.395392i | \(-0.129391\pi\) | |||||||
\(992\) | −25.2254 | + | 8.19624i | −0.800908 | + | 0.260231i | ||||
\(993\) | 19.1459 | + | 13.9103i | 0.607577 | + | 0.441430i | ||||
\(994\) | −23.0902 | + | 16.7760i | −0.732376 | + | 0.532102i | ||||
\(995\) | 56.3944 | + | 18.3237i | 1.78782 | + | 0.580899i | ||||
\(996\) | −9.82709 | + | 30.2447i | −0.311383 | + | 0.958339i | ||||
\(997\) | −6.34346 | − | 8.73102i | −0.200899 | − | 0.276514i | 0.696666 | − | 0.717396i | \(-0.254666\pi\) |
−0.897565 | + | 0.440881i | \(0.854666\pi\) | |||||||
\(998\) | 13.3926 | − | 18.4333i | 0.423936 | − | 0.583497i | ||||
\(999\) | 2.72542 | + | 8.38800i | 0.0862286 | + | 0.265384i |
(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 | 869.2.l.a.710.2 | yes | 8 | |
11.2 | odd | 10 | inner | 869.2.l.a.552.1 | ✓ | 8 | |
79.78 | odd | 2 | inner | 869.2.l.a.710.1 | yes | 8 | |
869.552 | even | 10 | inner | 869.2.l.a.552.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
869.2.l.a.552.1 | ✓ | 8 | 11.2 | odd | 10 | inner | |
869.2.l.a.552.2 | yes | 8 | 869.552 | even | 10 | inner | |
869.2.l.a.710.1 | yes | 8 | 79.78 | odd | 2 | inner | |
869.2.l.a.710.2 | yes | 8 | 1.1 | even | 1 | trivial |