Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(491,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.491");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.q (of order \(6\), degree \(2\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - x^{2} - 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 589.2 | ||
Root | \(-0.895644 + 1.09445i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.589 |
Dual form | 637.2.q.e.491.2 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.89564 | + | 1.09445i | 1.34042 | + | 0.773893i | 0.986869 | − | 0.161521i | \(-0.0516399\pi\) |
0.353553 | + | 0.935414i | \(0.384973\pi\) | |||||||
\(3\) | 0.895644 | − | 1.55130i | 0.517100 | − | 0.895644i | −0.482703 | − | 0.875784i | \(-0.660345\pi\) |
0.999803 | − | 0.0198595i | \(-0.00632191\pi\) | |||||||
\(4\) | 1.39564 | + | 2.41733i | 0.697822 | + | 1.20866i | ||||
\(5\) | − | 2.18890i | − | 0.978906i | −0.872030 | − | 0.489453i | \(-0.837196\pi\) | ||
0.872030 | − | 0.489453i | \(-0.162804\pi\) | |||||||
\(6\) | 3.39564 | − | 1.96048i | 1.38627 | − | 0.800361i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.73205i | 0.612372i | ||||||||
\(9\) | −0.104356 | − | 0.180750i | −0.0347854 | − | 0.0602500i | ||||
\(10\) | 2.39564 | − | 4.14938i | 0.757569 | − | 1.31215i | ||||
\(11\) | −1.10436 | − | 0.637600i | −0.332976 | − | 0.192244i | 0.324186 | − | 0.945993i | \(-0.394910\pi\) |
−0.657162 | + | 0.753750i | \(0.728243\pi\) | |||||||
\(12\) | 5.00000 | 1.44338 | ||||||||
\(13\) | 3.50000 | − | 0.866025i | 0.970725 | − | 0.240192i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.39564 | − | 1.96048i | −0.876751 | − | 0.506193i | ||||
\(16\) | 0.895644 | − | 1.55130i | 0.223911 | − | 0.387825i | ||||
\(17\) | −1.50000 | − | 2.59808i | −0.363803 | − | 0.630126i | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | − | 0.456850i | − | 0.107681i | ||||||
\(19\) | −5.68693 | + | 3.28335i | −1.30467 | + | 0.753253i | −0.981202 | − | 0.192986i | \(-0.938183\pi\) |
−0.323470 | + | 0.946238i | \(0.604850\pi\) | |||||||
\(20\) | 5.29129 | − | 3.05493i | 1.18317 | − | 0.683102i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.39564 | − | 2.41733i | −0.297552 | − | 0.515376i | ||||
\(23\) | −3.79129 | + | 6.56670i | −0.790538 | + | 1.36925i | 0.135096 | + | 0.990833i | \(0.456866\pi\) |
−0.925634 | + | 0.378420i | \(0.876468\pi\) | |||||||
\(24\) | 2.68693 | + | 1.55130i | 0.548468 | + | 0.316658i | ||||
\(25\) | 0.208712 | 0.0417424 | ||||||||
\(26\) | 7.58258 | + | 2.18890i | 1.48707 | + | 0.429279i | ||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.10436 | − | 1.91280i | 0.205074 | − | 0.355198i | −0.745082 | − | 0.666972i | \(-0.767590\pi\) |
0.950156 | + | 0.311774i | \(0.100923\pi\) | |||||||
\(30\) | −4.29129 | − | 7.43273i | −0.783478 | − | 1.35702i | ||||
\(31\) | 8.66025i | 1.55543i | 0.628619 | + | 0.777714i | \(0.283621\pi\) | ||||
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 6.39564 | − | 3.69253i | 1.13060 | − | 0.652753i | ||||
\(33\) | −1.97822 | + | 1.14213i | −0.344364 | + | 0.198819i | ||||
\(34\) | − | 6.56670i | − | 1.12618i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.291288 | − | 0.504525i | 0.0485480 | − | 0.0840876i | ||||
\(37\) | 6.00000 | + | 3.46410i | 0.986394 | + | 0.569495i | 0.904194 | − | 0.427121i | \(-0.140472\pi\) |
0.0821995 | + | 0.996616i | \(0.473806\pi\) | |||||||
\(38\) | −14.3739 | −2.33175 | ||||||||
\(39\) | 1.79129 | − | 6.20520i | 0.286836 | − | 0.993628i | ||||
\(40\) | 3.79129 | 0.599455 | ||||||||
\(41\) | 2.20871 | + | 1.27520i | 0.344943 | + | 0.199153i | 0.662456 | − | 0.749101i | \(-0.269514\pi\) |
−0.317513 | + | 0.948254i | \(0.602848\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.18693 | + | 3.78788i | 0.333504 | + | 0.577646i | 0.983196 | − | 0.182551i | \(-0.0584356\pi\) |
−0.649692 | + | 0.760197i | \(0.725102\pi\) | |||||||
\(44\) | − | 3.55945i | − | 0.536608i | ||||||
\(45\) | −0.395644 | + | 0.228425i | −0.0589791 | + | 0.0340516i | ||||
\(46\) | −14.3739 | + | 8.29875i | −2.11931 | + | 1.22358i | ||||
\(47\) | − | 4.28245i | − | 0.624660i | −0.949974 | − | 0.312330i | \(-0.898891\pi\) | ||
0.949974 | − | 0.312330i | \(-0.101109\pi\) | |||||||
\(48\) | −1.60436 | − | 2.77883i | −0.231569 | − | 0.401089i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.395644 | + | 0.228425i | 0.0559525 | + | 0.0323042i | ||||
\(51\) | −5.37386 | −0.752491 | ||||||||
\(52\) | 6.97822 | + | 7.25198i | 0.967705 | + | 1.00567i | ||||
\(53\) | −12.1652 | −1.67101 | −0.835506 | − | 0.549481i | \(-0.814825\pi\) | ||||
−0.835506 | + | 0.549481i | \(0.814825\pi\) | |||||||
\(54\) | 9.47822 | + | 5.47225i | 1.28982 | + | 0.744679i | ||||
\(55\) | −1.39564 | + | 2.41733i | −0.188189 | + | 0.325952i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.7629i | 1.55803i | ||||||||
\(58\) | 4.18693 | − | 2.41733i | 0.549771 | − | 0.317410i | ||||
\(59\) | −7.66515 | + | 4.42548i | −0.997918 | + | 0.576148i | −0.907632 | − | 0.419768i | \(-0.862112\pi\) |
−0.0902862 | + | 0.995916i | \(0.528778\pi\) | |||||||
\(60\) | − | 10.9445i | − | 1.41293i | ||||||
\(61\) | −6.37386 | − | 11.0399i | −0.816090 | − | 1.41351i | −0.908543 | − | 0.417792i | \(-0.862804\pi\) |
0.0924533 | − | 0.995717i | \(-0.470529\pi\) | |||||||
\(62\) | −9.47822 | + | 16.4168i | −1.20374 | + | 2.08493i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12.5826 | 1.57282 | ||||||||
\(65\) | −1.89564 | − | 7.66115i | −0.235126 | − | 0.950249i | ||||
\(66\) | −5.00000 | −0.615457 | ||||||||
\(67\) | 9.87386 | + | 5.70068i | 1.20628 | + | 0.696449i | 0.961946 | − | 0.273241i | \(-0.0880957\pi\) |
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 4.18693 | − | 7.25198i | 0.507740 | − | 0.879432i | ||||
\(69\) | 6.79129 | + | 11.7629i | 0.817575 | + | 1.41608i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.791288 | + | 0.456850i | −0.0939086 | + | 0.0542181i | −0.546219 | − | 0.837643i | \(-0.683933\pi\) |
0.452310 | + | 0.891861i | \(0.350600\pi\) | |||||||
\(72\) | 0.313068 | − | 0.180750i | 0.0368954 | − | 0.0213016i | ||||
\(73\) | − | 3.46410i | − | 0.405442i | −0.979236 | − | 0.202721i | \(-0.935021\pi\) | ||
0.979236 | − | 0.202721i | \(-0.0649785\pi\) | |||||||
\(74\) | 7.58258 | + | 13.1334i | 0.881457 | + | 1.52673i | ||||
\(75\) | 0.186932 | − | 0.323775i | 0.0215850 | − | 0.0373864i | ||||
\(76\) | −15.8739 | − | 9.16478i | −1.82086 | − | 1.05127i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 10.1869 | − | 9.80238i | 1.15344 | − | 1.10990i | ||||
\(79\) | −6.00000 | −0.675053 | −0.337526 | − | 0.941316i | \(-0.609590\pi\) | ||||
−0.337526 | + | 0.941316i | \(0.609590\pi\) | |||||||
\(80\) | −3.39564 | − | 1.96048i | −0.379645 | − | 0.219188i | ||||
\(81\) | 4.79129 | − | 8.29875i | 0.532365 | − | 0.922084i | ||||
\(82\) | 2.79129 | + | 4.83465i | 0.308246 | + | 0.533898i | ||||
\(83\) | 3.55945i | 0.390701i | 0.980734 | + | 0.195350i | \(0.0625844\pi\) | ||||
−0.980734 | + | 0.195350i | \(0.937416\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.68693 | + | 3.28335i | −0.616834 | + | 0.356129i | ||||
\(86\) | 9.57395i | 1.03239i | ||||||||
\(87\) | −1.97822 | − | 3.42638i | −0.212087 | − | 0.367346i | ||||
\(88\) | 1.10436 | − | 1.91280i | 0.117725 | − | 0.203905i | ||||
\(89\) | −2.52178 | − | 1.45595i | −0.267308 | − | 0.154330i | 0.360356 | − | 0.932815i | \(-0.382655\pi\) |
−0.627664 | + | 0.778485i | \(0.715989\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −21.1652 | −2.20662 | ||||||||
\(93\) | 13.4347 | + | 7.75650i | 1.39311 | + | 0.804312i | ||||
\(94\) | 4.68693 | − | 8.11800i | 0.483420 | − | 0.837308i | ||||
\(95\) | 7.18693 | + | 12.4481i | 0.737364 | + | 1.27715i | ||||
\(96\) | − | 13.2288i | − | 1.35015i | ||||||
\(97\) | −13.1869 | + | 7.61348i | −1.33893 | + | 0.773032i | −0.986649 | − | 0.162863i | \(-0.947927\pi\) |
−0.352281 | + | 0.935894i | \(0.614594\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.266150i | 0.0267491i | ||||||||
\(100\) | 0.291288 | + | 0.504525i | 0.0291288 | + | 0.0504525i | ||||
\(101\) | −4.89564 | + | 8.47950i | −0.487135 | + | 0.843742i | −0.999891 | − | 0.0147923i | \(-0.995291\pi\) |
0.512756 | + | 0.858534i | \(0.328625\pi\) | |||||||
\(102\) | −10.1869 | − | 5.88143i | −1.00866 | − | 0.582348i | ||||
\(103\) | −4.58258 | −0.451535 | −0.225767 | − | 0.974181i | \(-0.572489\pi\) | ||||
−0.225767 | + | 0.974181i | \(0.572489\pi\) | |||||||
\(104\) | 1.50000 | + | 6.06218i | 0.147087 | + | 0.594445i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −23.0608 | − | 13.3142i | −2.23986 | − | 1.29319i | ||||
\(107\) | 4.89564 | − | 8.47950i | 0.473280 | − | 0.819745i | −0.526252 | − | 0.850328i | \(-0.676403\pi\) |
0.999532 | + | 0.0305838i | \(0.00973664\pi\) | |||||||
\(108\) | 6.97822 | + | 12.0866i | 0.671479 | + | 1.16304i | ||||
\(109\) | 7.93725i | 0.760251i | 0.924935 | + | 0.380126i | \(0.124119\pi\) | ||||
−0.924935 | + | 0.380126i | \(0.875881\pi\) | |||||||
\(110\) | −5.29129 | + | 3.05493i | −0.504505 | + | 0.291276i | ||||
\(111\) | 10.7477 | − | 6.20520i | 1.02013 | − | 0.588972i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.708712 | − | 1.22753i | −0.0666700 | − | 0.115476i | 0.830764 | − | 0.556625i | \(-0.187904\pi\) |
−0.897434 | + | 0.441150i | \(0.854571\pi\) | |||||||
\(114\) | −12.8739 | + | 22.2982i | −1.20575 | + | 2.08842i | ||||
\(115\) | 14.3739 | + | 8.29875i | 1.34037 | + | 0.773863i | ||||
\(116\) | 6.16515 | 0.572420 | ||||||||
\(117\) | −0.521780 | − | 0.542250i | −0.0482386 | − | 0.0501310i | ||||
\(118\) | −19.3739 | −1.78351 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.39564 | − | 5.88143i | 0.309978 | − | 0.536898i | ||||
\(121\) | −4.68693 | − | 8.11800i | −0.426085 | − | 0.738000i | ||||
\(122\) | − | 27.9035i | − | 2.52627i | ||||||
\(123\) | 3.95644 | − | 2.28425i | 0.356740 | − | 0.205964i | ||||
\(124\) | −20.9347 | + | 12.0866i | −1.87999 | + | 1.08541i | ||||
\(125\) | − | 11.4014i | − | 1.01977i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.97822 | − | 13.8187i | 0.707953 | − | 1.22621i | −0.257663 | − | 0.966235i | \(-0.582952\pi\) |
0.965615 | − | 0.259975i | \(-0.0837143\pi\) | |||||||
\(128\) | 11.0608 | + | 6.38595i | 0.977645 | + | 0.564444i | ||||
\(129\) | 7.83485 | 0.689820 | ||||||||
\(130\) | 4.79129 | − | 16.5975i | 0.420224 | − | 1.45570i | ||||
\(131\) | −3.62614 | −0.316817 | −0.158409 | − | 0.987374i | \(-0.550636\pi\) | ||||
−0.158409 | + | 0.987374i | \(0.550636\pi\) | |||||||
\(132\) | −5.52178 | − | 3.18800i | −0.480609 | − | 0.277480i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.4782 | + | 21.6129i | 1.07795 | + | 1.86707i | ||||
\(135\) | − | 10.9445i | − | 0.941953i | ||||||
\(136\) | 4.50000 | − | 2.59808i | 0.385872 | − | 0.222783i | ||||
\(137\) | −14.8521 | + | 8.57485i | −1.26890 | + | 0.732599i | −0.974780 | − | 0.223169i | \(-0.928360\pi\) |
−0.294119 | + | 0.955769i | \(0.595026\pi\) | |||||||
\(138\) | 29.7309i | 2.53086i | ||||||||
\(139\) | 0.395644 | + | 0.685275i | 0.0335581 | + | 0.0581243i | 0.882317 | − | 0.470656i | \(-0.155983\pi\) |
−0.848759 | + | 0.528781i | \(0.822649\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.64337 | − | 3.83555i | −0.559473 | − | 0.323012i | ||||
\(142\) | −2.00000 | −0.167836 | ||||||||
\(143\) | −4.41742 | − | 1.27520i | −0.369404 | − | 0.106638i | ||||
\(144\) | −0.373864 | −0.0311553 | ||||||||
\(145\) | −4.18693 | − | 2.41733i | −0.347706 | − | 0.200748i | ||||
\(146\) | 3.79129 | − | 6.56670i | 0.313769 | − | 0.543464i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 19.3386i | 1.58962i | ||||||||
\(149\) | 1.89564 | − | 1.09445i | 0.155297 | − | 0.0896609i | −0.420338 | − | 0.907368i | \(-0.638088\pi\) |
0.575635 | + | 0.817707i | \(0.304755\pi\) | |||||||
\(150\) | 0.708712 | − | 0.409175i | 0.0578661 | − | 0.0334090i | ||||
\(151\) | − | 12.1244i | − | 0.986666i | −0.869841 | − | 0.493333i | \(-0.835778\pi\) | ||
0.869841 | − | 0.493333i | \(-0.164222\pi\) | |||||||
\(152\) | −5.68693 | − | 9.85005i | −0.461271 | − | 0.798945i | ||||
\(153\) | −0.313068 | + | 0.542250i | −0.0253101 | + | 0.0438383i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.9564 | 1.52262 | ||||||||
\(156\) | 17.5000 | − | 4.33013i | 1.40112 | − | 0.346688i | ||||
\(157\) | 21.9564 | 1.75231 | 0.876157 | − | 0.482025i | \(-0.160099\pi\) | ||||
0.876157 | + | 0.482025i | \(0.160099\pi\) | |||||||
\(158\) | −11.3739 | − | 6.56670i | −0.904856 | − | 0.522419i | ||||
\(159\) | −10.8956 | + | 18.8718i | −0.864081 | + | 1.49663i | ||||
\(160\) | −8.08258 | − | 13.9994i | −0.638984 | − | 1.10675i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 18.1652 | − | 10.4877i | 1.42719 | − | 0.823988i | ||||
\(163\) | 6.00000 | − | 3.46410i | 0.469956 | − | 0.271329i | −0.246265 | − | 0.969202i | \(-0.579203\pi\) |
0.716221 | + | 0.697873i | \(0.245870\pi\) | |||||||
\(164\) | 7.11890i | 0.555893i | ||||||||
\(165\) | 2.50000 | + | 4.33013i | 0.194625 | + | 0.337100i | ||||
\(166\) | −3.89564 | + | 6.74745i | −0.302361 | + | 0.523704i | ||||
\(167\) | 17.2913 | + | 9.98313i | 1.33804 | + | 0.772518i | 0.986517 | − | 0.163661i | \(-0.0523304\pi\) |
0.351523 | + | 0.936179i | \(0.385664\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5000 | − | 6.06218i | 0.884615 | − | 0.466321i | ||||
\(170\) | −14.3739 | −1.10243 | ||||||||
\(171\) | 1.18693 | + | 0.685275i | 0.0907669 | + | 0.0524043i | ||||
\(172\) | −6.10436 | + | 10.5731i | −0.465453 | + | 0.806188i | ||||
\(173\) | 3.87386 | + | 6.70973i | 0.294524 | + | 0.510131i | 0.974874 | − | 0.222756i | \(-0.0715054\pi\) |
−0.680350 | + | 0.732888i | \(0.738172\pi\) | |||||||
\(174\) | − | 8.66025i | − | 0.656532i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.97822 | + | 1.14213i | −0.149114 | + | 0.0860910i | ||||
\(177\) | 15.8546i | 1.19171i | ||||||||
\(178\) | −3.18693 | − | 5.51993i | −0.238871 | − | 0.413736i | ||||
\(179\) | 4.50000 | − | 7.79423i | 0.336346 | − | 0.582568i | −0.647397 | − | 0.762153i | \(-0.724142\pi\) |
0.983742 | + | 0.179585i | \(0.0574756\pi\) | |||||||
\(180\) | −1.10436 | − | 0.637600i | −0.0823138 | − | 0.0475239i | ||||
\(181\) | 9.16515 | 0.681240 | 0.340620 | − | 0.940201i | \(-0.389363\pi\) | ||||
0.340620 | + | 0.940201i | \(0.389363\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −22.8348 | −1.68800 | ||||||||
\(184\) | −11.3739 | − | 6.56670i | −0.838492 | − | 0.484104i | ||||
\(185\) | 7.58258 | − | 13.1334i | 0.557482 | − | 0.965587i | ||||
\(186\) | 16.9782 | + | 29.4071i | 1.24490 | + | 2.15624i | ||||
\(187\) | 3.82560i | 0.279756i | ||||||||
\(188\) | 10.3521 | − | 5.97678i | 0.755003 | − | 0.435901i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 31.4630i | 2.28256i | ||||||||
\(191\) | 0.313068 | + | 0.542250i | 0.0226528 | + | 0.0392358i | 0.877130 | − | 0.480254i | \(-0.159455\pi\) |
−0.854477 | + | 0.519490i | \(0.826122\pi\) | |||||||
\(192\) | 11.2695 | − | 19.5194i | 0.813307 | − | 1.40869i | ||||
\(193\) | −10.7477 | − | 6.20520i | −0.773638 | − | 0.446660i | 0.0605327 | − | 0.998166i | \(-0.480720\pi\) |
−0.834171 | + | 0.551506i | \(0.814053\pi\) | |||||||
\(194\) | −33.3303 | −2.39298 | ||||||||
\(195\) | −13.5826 | − | 3.92095i | −0.972668 | − | 0.280785i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.47822 | − | 5.47225i | −0.675295 | − | 0.389882i | 0.122785 | − | 0.992433i | \(-0.460817\pi\) |
−0.798080 | + | 0.602551i | \(0.794151\pi\) | |||||||
\(198\) | −0.291288 | + | 0.504525i | −0.0207009 | + | 0.0358551i | ||||
\(199\) | 5.50000 | + | 9.52628i | 0.389885 | + | 0.675300i | 0.992434 | − | 0.122782i | \(-0.0391815\pi\) |
−0.602549 | + | 0.798082i | \(0.705848\pi\) | |||||||
\(200\) | 0.361500i | 0.0255619i | ||||||||
\(201\) | 17.6869 | − | 10.2116i | 1.24754 | − | 0.720268i | ||||
\(202\) | −18.5608 | + | 10.7161i | −1.30593 | + | 0.753981i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7.50000 | − | 12.9904i | −0.525105 | − | 0.909509i | ||||
\(205\) | 2.79129 | − | 4.83465i | 0.194952 | − | 0.337667i | ||||
\(206\) | −8.68693 | − | 5.01540i | −0.605247 | − | 0.349440i | ||||
\(207\) | 1.58258 | 0.109997 | ||||||||
\(208\) | 1.79129 | − | 6.20520i | 0.124203 | − | 0.430253i | ||||
\(209\) | 8.37386 | 0.579232 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.708712 | + | 1.22753i | −0.0487898 | + | 0.0845063i | −0.889389 | − | 0.457151i | \(-0.848870\pi\) |
0.840599 | + | 0.541658i | \(0.182203\pi\) | |||||||
\(212\) | −16.9782 | − | 29.4071i | −1.16607 | − | 2.01969i | ||||
\(213\) | 1.63670i | 0.112145i | ||||||||
\(214\) | 18.5608 | − | 10.7161i | 1.26879 | − | 0.732536i | ||||
\(215\) | 8.29129 | − | 4.78698i | 0.565461 | − | 0.326469i | ||||
\(216\) | 8.66025i | 0.589256i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −8.68693 | + | 15.0462i | −0.588353 | + | 1.01906i | ||||
\(219\) | −5.37386 | − | 3.10260i | −0.363132 | − | 0.209654i | ||||
\(220\) | −7.79129 | −0.525289 | ||||||||
\(221\) | −7.50000 | − | 7.79423i | −0.504505 | − | 0.524297i | ||||
\(222\) | 27.1652 | 1.82321 | ||||||||
\(223\) | −17.9347 | − | 10.3546i | −1.20099 | − | 0.693394i | −0.240217 | − | 0.970719i | \(-0.577219\pi\) |
−0.960776 | + | 0.277325i | \(0.910552\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.0217804 | − | 0.0377247i | −0.00145203 | − | 0.00251498i | ||||
\(226\) | − | 3.10260i | − | 0.206382i | ||||||
\(227\) | 10.6652 | − | 6.15753i | 0.707871 | − | 0.408689i | −0.102401 | − | 0.994743i | \(-0.532653\pi\) |
0.810272 | + | 0.586054i | \(0.199319\pi\) | |||||||
\(228\) | −28.4347 | + | 16.4168i | −1.88313 | + | 1.08723i | ||||
\(229\) | − | 6.92820i | − | 0.457829i | −0.973447 | − | 0.228914i | \(-0.926482\pi\) | ||
0.973447 | − | 0.228914i | \(-0.0735176\pi\) | |||||||
\(230\) | 18.1652 | + | 31.4630i | 1.19777 | + | 2.07461i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.31307 | + | 1.91280i | 0.217514 | + | 0.125582i | ||||
\(233\) | −6.95644 | −0.455731 | −0.227866 | − | 0.973693i | \(-0.573175\pi\) | ||||
−0.227866 | + | 0.973693i | \(0.573175\pi\) | |||||||
\(234\) | −0.395644 | − | 1.59898i | −0.0258641 | − | 0.104528i | ||||
\(235\) | −9.37386 | −0.611483 | ||||||||
\(236\) | −21.3956 | − | 12.3528i | −1.39274 | − | 0.804098i | ||||
\(237\) | −5.37386 | + | 9.30780i | −0.349070 | + | 0.604607i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 13.2288i | − | 0.855697i | −0.903850 | − | 0.427849i | \(-0.859272\pi\) | ||
0.903850 | − | 0.427849i | \(-0.140728\pi\) | |||||||
\(240\) | −6.08258 | + | 3.51178i | −0.392629 | + | 0.226684i | ||||
\(241\) | −3.56080 | + | 2.05583i | −0.229371 | + | 0.132427i | −0.610282 | − | 0.792184i | \(-0.708944\pi\) |
0.380911 | + | 0.924612i | \(0.375610\pi\) | |||||||
\(242\) | − | 20.5185i | − | 1.31898i | ||||||
\(243\) | −1.08258 | − | 1.87508i | −0.0694473 | − | 0.120286i | ||||
\(244\) | 17.7913 | − | 30.8154i | 1.13897 | − | 1.97275i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.0000 | 0.637577 | ||||||||
\(247\) | −17.0608 | + | 16.4168i | −1.08555 | + | 1.04457i | ||||
\(248\) | −15.0000 | −0.952501 | ||||||||
\(249\) | 5.52178 | + | 3.18800i | 0.349929 | + | 0.202031i | ||||
\(250\) | 12.4782 | − | 21.6129i | 0.789192 | − | 1.36692i | ||||
\(251\) | −10.5826 | − | 18.3296i | −0.667966 | − | 1.15695i | −0.978472 | − | 0.206380i | \(-0.933832\pi\) |
0.310506 | − | 0.950572i | \(-0.399502\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.37386 | − | 4.83465i | 0.526460 | − | 0.303952i | ||||
\(254\) | 30.2477 | − | 17.4635i | 1.89791 | − | 1.09576i | ||||
\(255\) | 11.7629i | 0.736619i | ||||||||
\(256\) | 1.39564 | + | 2.41733i | 0.0872277 | + | 0.151083i | ||||
\(257\) | 13.9782 | − | 24.2110i | 0.871937 | − | 1.51024i | 0.0119476 | − | 0.999929i | \(-0.496197\pi\) |
0.859990 | − | 0.510311i | \(-0.170470\pi\) | |||||||
\(258\) | 14.8521 | + | 8.57485i | 0.924650 | + | 0.533847i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 15.8739 | − | 15.2746i | 0.984455 | − | 0.947292i | ||||
\(261\) | −0.460985 | −0.0285343 | ||||||||
\(262\) | −6.87386 | − | 3.96863i | −0.424669 | − | 0.245183i | ||||
\(263\) | 13.6652 | − | 23.6687i | 0.842629 | − | 1.45948i | −0.0450348 | − | 0.998985i | \(-0.514340\pi\) |
0.887664 | − | 0.460491i | \(-0.152327\pi\) | |||||||
\(264\) | −1.97822 | − | 3.42638i | −0.121751 | − | 0.210879i | ||||
\(265\) | 26.6283i | 1.63576i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.51723 | + | 2.60803i | −0.276450 | + | 0.159609i | ||||
\(268\) | 31.8245i | 1.94399i | ||||||||
\(269\) | −5.60436 | − | 9.70703i | −0.341704 | − | 0.591848i | 0.643046 | − | 0.765828i | \(-0.277671\pi\) |
−0.984749 | + | 0.173980i | \(0.944337\pi\) | |||||||
\(270\) | 11.9782 | − | 20.7469i | 0.728971 | − | 1.26262i | ||||
\(271\) | 24.8739 | + | 14.3609i | 1.51098 | + | 0.872364i | 0.999918 | + | 0.0128205i | \(0.00408101\pi\) |
0.511062 | + | 0.859544i | \(0.329252\pi\) | |||||||
\(272\) | −5.37386 | −0.325838 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −37.5390 | −2.26781 | ||||||||
\(275\) | −0.230493 | − | 0.133075i | −0.0138992 | − | 0.00802472i | ||||
\(276\) | −18.9564 | + | 32.8335i | −1.14104 | + | 1.97635i | ||||
\(277\) | 7.87386 | + | 13.6379i | 0.473095 | + | 0.819424i | 0.999526 | − | 0.0307939i | \(-0.00980354\pi\) |
−0.526431 | + | 0.850218i | \(0.676470\pi\) | |||||||
\(278\) | 1.73205i | 0.103882i | ||||||||
\(279\) | 1.56534 | − | 0.903750i | 0.0937145 | − | 0.0541061i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.39590i | − | 0.381548i | −0.981634 | − | 0.190774i | \(-0.938900\pi\) | ||
0.981634 | − | 0.190774i | \(-0.0610997\pi\) | |||||||
\(282\) | −8.39564 | − | 14.5417i | −0.499953 | − | 0.865945i | ||||
\(283\) | −12.3739 | + | 21.4322i | −0.735550 | + | 1.27401i | 0.218932 | + | 0.975740i | \(0.429743\pi\) |
−0.954482 | + | 0.298270i | \(0.903591\pi\) | |||||||
\(284\) | −2.20871 | − | 1.27520i | −0.131063 | − | 0.0756692i | ||||
\(285\) | 25.7477 | 1.52516 | ||||||||
\(286\) | −6.97822 | − | 7.25198i | −0.412631 | − | 0.428818i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.33485 | − | 0.770675i | −0.0786567 | − | 0.0454125i | ||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | −5.29129 | − | 9.16478i | −0.310715 | − | 0.538174i | ||||
\(291\) | 27.2759i | 1.59894i | ||||||||
\(292\) | 8.37386 | − | 4.83465i | 0.490043 | − | 0.282927i | ||||
\(293\) | −6.79129 | + | 3.92095i | −0.396751 | + | 0.229064i | −0.685081 | − | 0.728467i | \(-0.740233\pi\) |
0.288330 | + | 0.957531i | \(0.406900\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.68693 | + | 16.7783i | 0.563995 | + | 0.976868i | ||||
\(296\) | −6.00000 | + | 10.3923i | −0.348743 | + | 0.604040i | ||||
\(297\) | −5.52178 | − | 3.18800i | −0.320406 | − | 0.184987i | ||||
\(298\) | 4.79129 | 0.277552 | ||||||||
\(299\) | −7.58258 | + | 26.2668i | −0.438512 | + | 1.51905i | ||||
\(300\) | 1.04356 | 0.0602500 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 13.2695 | − | 22.9835i | 0.763574 | − | 1.32255i | ||||
\(303\) | 8.76951 | + | 15.1892i | 0.503795 | + | 0.872599i | ||||
\(304\) | 11.7629i | 0.674646i | ||||||||
\(305\) | −24.1652 | + | 13.9518i | −1.38369 | + | 0.798875i | ||||
\(306\) | −1.18693 | + | 0.685275i | −0.0678524 | + | 0.0391746i | ||||
\(307\) | 24.1733i | 1.37964i | 0.723980 | + | 0.689820i | \(0.242311\pi\) | ||||
−0.723980 | + | 0.689820i | \(0.757689\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.10436 | + | 7.10895i | −0.233489 | + | 0.404414i | ||||
\(310\) | 35.9347 | + | 20.7469i | 2.04095 | + | 1.17834i | ||||
\(311\) | 5.53901 | 0.314089 | 0.157044 | − | 0.987592i | \(-0.449803\pi\) | ||||
0.157044 | + | 0.987592i | \(0.449803\pi\) | |||||||
\(312\) | 10.7477 | + | 3.10260i | 0.608470 | + | 0.175650i | ||||
\(313\) | −20.7477 | −1.17273 | −0.586365 | − | 0.810047i | \(-0.699442\pi\) | ||||
−0.586365 | + | 0.810047i | \(0.699442\pi\) | |||||||
\(314\) | 41.6216 | + | 24.0302i | 2.34884 | + | 1.35610i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.37386 | − | 14.5040i | −0.471067 | − | 0.815911i | ||||
\(317\) | 18.5203i | 1.04020i | 0.854105 | + | 0.520101i | \(0.174106\pi\) | ||||
−0.854105 | + | 0.520101i | \(0.825894\pi\) | |||||||
\(318\) | −41.3085 | + | 23.8495i | −2.31647 | + | 1.33741i | ||||
\(319\) | −2.43920 | + | 1.40828i | −0.136569 | + | 0.0788483i | ||||
\(320\) | − | 27.5420i | − | 1.53965i | ||||||
\(321\) | −8.76951 | − | 15.1892i | −0.489466 | − | 0.847780i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.0608 | + | 9.85005i | 0.949288 | + | 0.548072i | ||||
\(324\) | 26.7477 | 1.48598 | ||||||||
\(325\) | 0.730493 | − | 0.180750i | 0.0405204 | − | 0.0100262i | ||||
\(326\) | 15.1652 | 0.839920 | ||||||||
\(327\) | 12.3131 | + | 7.10895i | 0.680914 | + | 0.393126i | ||||
\(328\) | −2.20871 | + | 3.82560i | −0.121956 | + | 0.211234i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 10.9445i | 0.602475i | ||||||||
\(331\) | 0.939205 | − | 0.542250i | 0.0516234 | − | 0.0298048i | −0.473966 | − | 0.880543i | \(-0.657178\pi\) |
0.525590 | + | 0.850738i | \(0.323845\pi\) | |||||||
\(332\) | −8.60436 | + | 4.96773i | −0.472225 | + | 0.272639i | ||||
\(333\) | − | 1.44600i | − | 0.0792403i | ||||||
\(334\) | 21.8521 | + | 37.8489i | 1.19569 | + | 2.07100i | ||||
\(335\) | 12.4782 | − | 21.6129i | 0.681758 | − | 1.18084i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.9564 | −0.705782 | −0.352891 | − | 0.935664i | \(-0.614801\pi\) | ||||
−0.352891 | + | 0.935664i | \(0.614801\pi\) | |||||||
\(338\) | 28.4347 | + | 1.09445i | 1.54664 | + | 0.0595303i | ||||
\(339\) | −2.53901 | −0.137900 | ||||||||
\(340\) | −15.8739 | − | 9.16478i | −0.860881 | − | 0.497030i | ||||
\(341\) | 5.52178 | − | 9.56400i | 0.299021 | − | 0.517920i | ||||
\(342\) | 1.50000 | + | 2.59808i | 0.0811107 | + | 0.140488i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.56080 | + | 3.78788i | −0.353734 | + | 0.204229i | ||||
\(345\) | 25.7477 | − | 14.8655i | 1.38621 | − | 0.800329i | ||||
\(346\) | 16.9590i | 0.911722i | ||||||||
\(347\) | 2.20871 | + | 3.82560i | 0.118570 | + | 0.205369i | 0.919201 | − | 0.393788i | \(-0.128836\pi\) |
−0.800631 | + | 0.599157i | \(0.795502\pi\) | |||||||
\(348\) | 5.52178 | − | 9.56400i | 0.295998 | − | 0.512684i | ||||
\(349\) | −9.24773 | − | 5.33918i | −0.495019 | − | 0.285800i | 0.231635 | − | 0.972803i | \(-0.425593\pi\) |
−0.726654 | + | 0.687003i | \(0.758926\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.5000 | − | 4.33013i | 0.934081 | − | 0.231125i | ||||
\(352\) | −9.41742 | −0.501950 | ||||||||
\(353\) | 23.2259 | + | 13.4095i | 1.23619 | + | 0.713716i | 0.968314 | − | 0.249737i | \(-0.0803441\pi\) |
0.267879 | + | 0.963453i | \(0.413677\pi\) | |||||||
\(354\) | −17.3521 | + | 30.0547i | −0.922253 | + | 1.59739i | ||||
\(355\) | 1.00000 | + | 1.73205i | 0.0530745 | + | 0.0919277i | ||||
\(356\) | − | 8.12795i | − | 0.430781i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.0608 | − | 9.85005i | 0.901691 | − | 0.520592i | ||||
\(359\) | 12.6766i | 0.669043i | 0.942388 | + | 0.334522i | \(0.108575\pi\) | ||||
−0.942388 | + | 0.334522i | \(0.891425\pi\) | |||||||
\(360\) | −0.395644 | − | 0.685275i | −0.0208523 | − | 0.0361172i | ||||
\(361\) | 12.0608 | − | 20.8899i | 0.634779 | − | 1.09947i | ||||
\(362\) | 17.3739 | + | 10.0308i | 0.913150 | + | 0.527207i | ||||
\(363\) | −16.7913 | −0.881314 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.58258 | −0.396890 | ||||||||
\(366\) | −43.2867 | − | 24.9916i | −2.26263 | − | 1.30633i | ||||
\(367\) | −9.00000 | + | 15.5885i | −0.469796 | + | 0.813711i | −0.999404 | − | 0.0345320i | \(-0.989006\pi\) |
0.529607 | + | 0.848243i | \(0.322339\pi\) | |||||||
\(368\) | 6.79129 | + | 11.7629i | 0.354020 | + | 0.613181i | ||||
\(369\) | − | 0.532300i | − | 0.0277104i | ||||||
\(370\) | 28.7477 | − | 16.5975i | 1.49452 | − | 0.862863i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 43.3013i | 2.24507i | ||||||||
\(373\) | −18.3956 | − | 31.8622i | −0.952490 | − | 1.64976i | −0.740009 | − | 0.672596i | \(-0.765179\pi\) |
−0.212481 | − | 0.977165i | \(-0.568154\pi\) | |||||||
\(374\) | −4.18693 | + | 7.25198i | −0.216501 | + | 0.374991i | ||||
\(375\) | −17.6869 | − | 10.2116i | −0.913349 | − | 0.527322i | ||||
\(376\) | 7.41742 | 0.382524 | ||||||||
\(377\) | 2.20871 | − | 7.65120i | 0.113754 | − | 0.394057i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.93920 | − | 2.27430i | −0.202343 | − | 0.116823i | 0.395405 | − | 0.918507i | \(-0.370604\pi\) |
−0.597748 | + | 0.801684i | \(0.703938\pi\) | |||||||
\(380\) | −20.0608 | + | 34.7463i | −1.02910 | + | 1.78245i | ||||
\(381\) | −14.2913 | − | 24.7532i | −0.732165 | − | 1.26815i | ||||
\(382\) | 1.37055i | 0.0701235i | ||||||||
\(383\) | −3.39564 | + | 1.96048i | −0.173509 | + | 0.100176i | −0.584240 | − | 0.811581i | \(-0.698607\pi\) |
0.410730 | + | 0.911757i | \(0.365274\pi\) | |||||||
\(384\) | 19.8131 | − | 11.4391i | 1.01108 | − | 0.583748i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.5826 | − | 23.5257i | −0.691335 | − | 1.19743i | ||||
\(387\) | 0.456439 | − | 0.790576i | 0.0232021 | − | 0.0401872i | ||||
\(388\) | −36.8085 | − | 21.2514i | −1.86867 | − | 1.07888i | ||||
\(389\) | 36.3303 | 1.84202 | 0.921010 | − | 0.389540i | \(-0.127366\pi\) | ||||
0.921010 | + | 0.389540i | \(0.127366\pi\) | |||||||
\(390\) | −21.4564 | − | 22.2982i | −1.08649 | − | 1.12911i | ||||
\(391\) | 22.7477 | 1.15040 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.24773 | + | 5.62523i | −0.163826 | + | 0.283755i | ||||
\(394\) | −11.9782 | − | 20.7469i | −0.603454 | − | 1.04521i | ||||
\(395\) | 13.1334i | 0.660813i | ||||||||
\(396\) | −0.643371 | + | 0.371450i | −0.0323306 | + | 0.0186661i | ||||
\(397\) | 13.1216 | − | 7.57575i | 0.658554 | − | 0.380216i | −0.133172 | − | 0.991093i | \(-0.542516\pi\) |
0.791726 | + | 0.610877i | \(0.209183\pi\) | |||||||
\(398\) | 24.0779i | 1.20692i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.186932 | − | 0.323775i | 0.00934659 | − | 0.0161888i | ||||
\(401\) | −25.5998 | − | 14.7801i | −1.27839 | − | 0.738081i | −0.301841 | − | 0.953358i | \(-0.597601\pi\) |
−0.976553 | + | 0.215278i | \(0.930934\pi\) | |||||||
\(402\) | 44.7042 | 2.22964 | ||||||||
\(403\) | 7.50000 | + | 30.3109i | 0.373602 | + | 1.50989i | ||||
\(404\) | −27.3303 | −1.35973 | ||||||||
\(405\) | −18.1652 | − | 10.4877i | −0.902634 | − | 0.521136i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.41742 | − | 7.65120i | −0.218964 | − | 0.379256i | ||||
\(408\) | − | 9.30780i | − | 0.460805i | ||||||
\(409\) | −0.313068 | + | 0.180750i | −0.0154802 | + | 0.00893751i | −0.507720 | − | 0.861522i | \(-0.669512\pi\) |
0.492240 | + | 0.870460i | \(0.336178\pi\) | |||||||
\(410\) | 10.5826 | − | 6.10985i | 0.522636 | − | 0.301744i | ||||
\(411\) | 30.7201i | 1.51531i | ||||||||
\(412\) | −6.39564 | − | 11.0776i | −0.315091 | − | 0.545753i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.00000 | + | 1.73205i | 0.147442 | + | 0.0851257i | ||||
\(415\) | 7.79129 | 0.382459 | ||||||||
\(416\) | 19.1869 | − | 18.4626i | 0.940717 | − | 0.905205i | ||||
\(417\) | 1.41742 | 0.0694116 | ||||||||
\(418\) | 15.8739 | + | 9.16478i | 0.776416 | + | 0.448264i | ||||
\(419\) | 12.8739 | − | 22.2982i | 0.628929 | − | 1.08934i | −0.358838 | − | 0.933400i | \(-0.616827\pi\) |
0.987767 | − | 0.155938i | \(-0.0498399\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0616i | 0.977743i | 0.872356 | + | 0.488872i | \(0.162591\pi\) | ||||
−0.872356 | + | 0.488872i | \(0.837409\pi\) | |||||||
\(422\) | −2.68693 | + | 1.55130i | −0.130798 | + | 0.0755161i | ||||
\(423\) | −0.774053 | + | 0.446900i | −0.0376358 | + | 0.0217290i | ||||
\(424\) | − | 21.0707i | − | 1.02328i | ||||||
\(425\) | −0.313068 | − | 0.542250i | −0.0151860 | − | 0.0263030i | ||||
\(426\) | −1.79129 | + | 3.10260i | −0.0867882 | + | 0.150322i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 27.3303 | 1.32106 | ||||||||
\(429\) | −5.93466 | + | 5.71063i | −0.286528 | + | 0.275712i | ||||
\(430\) | 20.9564 | 1.01061 | ||||||||
\(431\) | −13.5172 | − | 7.80418i | −0.651102 | − | 0.375914i | 0.137776 | − | 0.990463i | \(-0.456005\pi\) |
−0.788878 | + | 0.614549i | \(0.789338\pi\) | |||||||
\(432\) | 4.47822 | − | 7.75650i | 0.215458 | − | 0.373185i | ||||
\(433\) | 11.2477 | + | 19.4816i | 0.540531 | + | 0.936228i | 0.998874 | + | 0.0474518i | \(0.0151101\pi\) |
−0.458342 | + | 0.888776i | \(0.651557\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.50000 | + | 4.33013i | −0.359597 | + | 0.207614i | ||||
\(436\) | −19.1869 | + | 11.0776i | −0.918887 | + | 0.530520i | ||||
\(437\) | − | 49.7925i | − | 2.38190i | ||||||
\(438\) | −6.79129 | − | 11.7629i | −0.324500 | − | 0.562051i | ||||
\(439\) | 5.76951 | − | 9.99308i | 0.275364 | − | 0.476944i | −0.694863 | − | 0.719142i | \(-0.744535\pi\) |
0.970227 | + | 0.242198i | \(0.0778684\pi\) | |||||||
\(440\) | −4.18693 | − | 2.41733i | −0.199604 | − | 0.115242i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.68693 | − | 22.9835i | −0.270500 | − | 1.09321i | ||||
\(443\) | 3.16515 | 0.150381 | 0.0751904 | − | 0.997169i | \(-0.476044\pi\) | ||||
0.0751904 | + | 0.997169i | \(0.476044\pi\) | |||||||
\(444\) | 30.0000 | + | 17.3205i | 1.42374 | + | 0.821995i | ||||
\(445\) | −3.18693 | + | 5.51993i | −0.151075 | + | 0.261670i | ||||
\(446\) | −22.6652 | − | 39.2572i | −1.07323 | − | 1.85888i | ||||
\(447\) | − | 3.92095i | − | 0.185455i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.2087 | + | 9.93545i | −0.812129 | + | 0.468883i | −0.847695 | − | 0.530484i | \(-0.822010\pi\) |
0.0355654 | + | 0.999367i | \(0.488677\pi\) | |||||||
\(450\) | − | 0.0953502i | − | 0.00449485i | ||||||
\(451\) | −1.62614 | − | 2.81655i | −0.0765718 | − | 0.132626i | ||||
\(452\) | 1.97822 | − | 3.42638i | 0.0930476 | − | 0.161163i | ||||
\(453\) | −18.8085 | − | 10.8591i | −0.883701 | − | 0.510205i | ||||
\(454\) | 26.9564 | 1.26513 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −20.3739 | −0.954094 | ||||||||
\(457\) | −7.74773 | − | 4.47315i | −0.362423 | − | 0.209245i | 0.307720 | − | 0.951477i | \(-0.400434\pi\) |
−0.670143 | + | 0.742232i | \(0.733767\pi\) | |||||||
\(458\) | 7.58258 | − | 13.1334i | 0.354310 | − | 0.613684i | ||||
\(459\) | −7.50000 | − | 12.9904i | −0.350070 | − | 0.606339i | ||||
\(460\) | 46.3284i | 2.16007i | ||||||||
\(461\) | −15.4782 | + | 8.93635i | −0.720893 | + | 0.416208i | −0.815081 | − | 0.579347i | \(-0.803308\pi\) |
0.0941885 | + | 0.995554i | \(0.469974\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 7.93725i | − | 0.368875i | −0.982844 | − | 0.184438i | \(-0.940954\pi\) | ||
0.982844 | − | 0.184438i | \(-0.0590464\pi\) | |||||||
\(464\) | −1.97822 | − | 3.42638i | −0.0918365 | − | 0.159066i | ||||
\(465\) | 16.9782 | − | 29.4071i | 0.787346 | − | 1.36372i | ||||
\(466\) | −13.1869 | − | 7.61348i | −0.610873 | − | 0.352688i | ||||
\(467\) | −11.8348 | −0.547651 | −0.273826 | − | 0.961779i | \(-0.588289\pi\) | ||||
−0.273826 | + | 0.961779i | \(0.588289\pi\) | |||||||
\(468\) | 0.582576 | − | 2.01810i | 0.0269296 | − | 0.0932868i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −17.7695 | − | 10.2592i | −0.819646 | − | 0.473223i | ||||
\(471\) | 19.6652 | − | 34.0610i | 0.906122 | − | 1.56945i | ||||
\(472\) | −7.66515 | − | 13.2764i | −0.352817 | − | 0.611097i | ||||
\(473\) | − | 5.57755i | − | 0.256456i | ||||||
\(474\) | −20.3739 | + | 11.7629i | −0.935803 | + | 0.540286i | ||||
\(475\) | −1.18693 | + | 0.685275i | −0.0544602 | + | 0.0314426i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.26951 | + | 2.19885i | 0.0581268 | + | 0.100678i | ||||
\(478\) | 14.4782 | − | 25.0770i | 0.662218 | − | 1.14700i | ||||
\(479\) | −8.85208 | − | 5.11075i | −0.404462 | − | 0.233516i | 0.283945 | − | 0.958840i | \(-0.408357\pi\) |
−0.688407 | + | 0.725324i | \(0.741690\pi\) | |||||||
\(480\) | −28.9564 | −1.32167 | ||||||||
\(481\) | 24.0000 | + | 6.92820i | 1.09431 | + | 0.315899i | ||||
\(482\) | −9.00000 | −0.409939 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13.0826 | − | 22.6597i | 0.594663 | − | 1.02999i | ||||
\(485\) | 16.6652 | + | 28.8649i | 0.756726 | + | 1.31069i | ||||
\(486\) | − | 4.73930i | − | 0.214979i | ||||||
\(487\) | −8.93466 | + | 5.15843i | −0.404868 | + | 0.233751i | −0.688582 | − | 0.725158i | \(-0.741767\pi\) |
0.283714 | + | 0.958909i | \(0.408433\pi\) | |||||||
\(488\) | 19.1216 | − | 11.0399i | 0.865594 | − | 0.499751i | ||||
\(489\) | − | 12.4104i | − | 0.561218i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.5608 | + | 32.1482i | −0.837637 | + | 1.45083i | 0.0542283 | + | 0.998529i | \(0.482730\pi\) |
−0.891865 | + | 0.452301i | \(0.850603\pi\) | |||||||
\(492\) | 11.0436 | + | 6.37600i | 0.497882 | + | 0.287452i | ||||
\(493\) | −6.62614 | −0.298426 | ||||||||
\(494\) | −50.3085 | + | 12.4481i | −2.26349 | + | 0.560068i | ||||
\(495\) | 0.582576 | 0.0261848 | ||||||||
\(496\) | 13.4347 | + | 7.75650i | 0.603234 | + | 0.348277i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6.97822 | + | 12.0866i | 0.312701 | + | 0.541615i | ||||
\(499\) | 42.2168i | 1.88988i | 0.327240 | + | 0.944941i | \(0.393881\pi\) | ||||
−0.327240 | + | 0.944941i | \(0.606119\pi\) | |||||||
\(500\) | 27.5608 | − | 15.9122i | 1.23256 | − | 0.711617i | ||||
\(501\) | 30.9737 | − | 17.8827i | 1.38380 | − | 0.798938i | ||||
\(502\) | − | 46.3284i | − | 2.06774i | ||||||
\(503\) | −11.0608 | − | 19.1579i | −0.493176 | − | 0.854207i | 0.506793 | − | 0.862068i | \(-0.330831\pi\) |
−0.999969 | + | 0.00786127i | \(0.997498\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.5608 | + | 10.7161i | 0.825945 | + | 0.476859i | ||||
\(506\) | 21.1652 | 0.940906 | ||||||||
\(507\) | 0.895644 | − | 23.2695i | 0.0397769 | − | 1.03344i | ||||
\(508\) | 44.5390 | 1.97610 | ||||||||
\(509\) | −19.0390 | − | 10.9922i | −0.843890 | − | 0.487220i | 0.0146949 | − | 0.999892i | \(-0.495322\pi\) |
−0.858584 | + | 0.512672i | \(0.828656\pi\) | |||||||
\(510\) | −12.8739 | + | 22.2982i | −0.570064 | + | 0.987380i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 19.4340i | − | 0.858868i | ||||||
\(513\) | −28.4347 | + | 16.4168i | −1.25542 | + | 0.724818i | ||||
\(514\) | 52.9955 | − | 30.5969i | 2.33753 | − | 1.34957i | ||||
\(515\) | 10.0308i | 0.442010i | ||||||||
\(516\) | 10.9347 | + | 18.9394i | 0.481372 | + | 0.833760i | ||||
\(517\) | −2.73049 | + | 4.72935i | −0.120087 | + | 0.207997i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.8784 | 0.609195 | ||||||||
\(520\) | 13.2695 | − | 3.28335i | 0.581906 | − | 0.143984i | ||||
\(521\) | −25.5826 | −1.12079 | −0.560396 | − | 0.828224i | \(-0.689351\pi\) | ||||
−0.560396 | + | 0.828224i | \(0.689351\pi\) | |||||||
\(522\) | −0.873864 | − | 0.504525i | −0.0382480 | − | 0.0220825i | ||||
\(523\) | −6.16515 | + | 10.6784i | −0.269583 | + | 0.466932i | −0.968754 | − | 0.248023i | \(-0.920219\pi\) |
0.699171 | + | 0.714954i | \(0.253553\pi\) | |||||||
\(524\) | −5.06080 | − | 8.76555i | −0.221082 | − | 0.382925i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 51.8085 | − | 29.9117i | 2.25896 | − | 1.30421i | ||||
\(527\) | 22.5000 | − | 12.9904i | 0.980115 | − | 0.565870i | ||||
\(528\) | 4.09175i | 0.178071i | ||||||||
\(529\) | −17.2477 | − | 29.8739i | −0.749901 | − | 1.29887i | ||||
\(530\) | −29.1434 | + | 50.4778i | −1.26591 | + | 2.19262i | ||||
\(531\) | 1.59981 | + | 0.923651i | 0.0694259 | + | 0.0400830i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.83485 | + | 2.55040i | 0.382680 | + | 0.110470i | ||||
\(534\) | −11.4174 | −0.494080 | ||||||||
\(535\) | −18.5608 | − | 10.7161i | −0.802453 | − | 0.463297i | ||||
\(536\) | −9.87386 | + | 17.1020i | −0.426486 | + | 0.738695i | ||||
\(537\) | −8.06080 | − | 13.9617i | −0.347849 | − | 0.602492i | ||||
\(538\) | − | 24.5348i | − | 1.05777i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 26.4564 | − | 15.2746i | 1.13850 | − | 0.657316i | ||||
\(541\) | 30.0924i | 1.29377i | 0.762586 | + | 0.646887i | \(0.223929\pi\) | ||||
−0.762586 | + | 0.646887i | \(0.776071\pi\) | |||||||
\(542\) | 31.4347 | + | 54.4464i | 1.35023 | + | 2.33867i | ||||
\(543\) | 8.20871 | − | 14.2179i | 0.352270 | − | 0.610149i | ||||
\(544\) | −19.1869 | − | 11.0776i | −0.822633 | − | 0.474947i | ||||
\(545\) | 17.3739 | 0.744215 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.7477 | 0.673324 | 0.336662 | − | 0.941626i | \(-0.390702\pi\) | ||||
0.336662 | + | 0.941626i | \(0.390702\pi\) | |||||||
\(548\) | −41.4564 | − | 23.9349i | −1.77093 | − | 1.02245i | ||||
\(549\) | −1.33030 | + | 2.30415i | −0.0567759 | + | 0.0983388i | ||||
\(550\) | −0.291288 | − | 0.504525i | −0.0124206 | − | 0.0215130i | ||||
\(551\) | 14.5040i | 0.617889i | ||||||||
\(552\) | −20.3739 | + | 11.7629i | −0.867169 | + | 0.500660i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 34.4702i | 1.46450i | ||||||||
\(555\) | −13.5826 | − | 23.5257i | −0.576548 | − | 0.998611i | ||||
\(556\) | −1.10436 | + | 1.91280i | −0.0468351 | + | 0.0811208i | ||||
\(557\) | 24.0998 | + | 13.9140i | 1.02114 | + | 0.589556i | 0.914434 | − | 0.404734i | \(-0.132636\pi\) |
0.106707 | + | 0.994290i | \(0.465969\pi\) | |||||||
\(558\) | 3.95644 | 0.167489 | ||||||||
\(559\) | 10.9347 | + | 11.3636i | 0.462487 | + | 0.480630i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.93466 | + | 3.42638i | 0.250561 | + | 0.144662i | ||||
\(562\) | 7.00000 | − | 12.1244i | 0.295277 | − | 0.511435i | ||||
\(563\) | −0.165151 | − | 0.286051i | −0.00696030 | − | 0.0120556i | 0.862524 | − | 0.506016i | \(-0.168882\pi\) |
−0.869485 | + | 0.493960i | \(0.835549\pi\) | |||||||
\(564\) | − | 21.4123i | − | 0.901619i | ||||||
\(565\) | −2.68693 | + | 1.55130i | −0.113040 | + | 0.0652637i | ||||
\(566\) | −46.9129 | + | 27.0852i | −1.97190 | + | 1.13847i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.791288 | − | 1.37055i | −0.0332017 | − | 0.0575070i | ||||
\(569\) | 5.37386 | − | 9.30780i | 0.225284 | − | 0.390203i | −0.731121 | − | 0.682248i | \(-0.761002\pi\) |
0.956405 | + | 0.292045i | \(0.0943356\pi\) | |||||||
\(570\) | 48.8085 | + | 28.1796i | 2.04436 | + | 1.18031i | ||||
\(571\) | −24.9564 | −1.04439 | −0.522197 | − | 0.852825i | \(-0.674888\pi\) | ||||
−0.522197 | + | 0.852825i | \(0.674888\pi\) | |||||||
\(572\) | −3.08258 | − | 12.4581i | −0.128889 | − | 0.520899i | ||||
\(573\) | 1.12159 | 0.0468551 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.791288 | + | 1.37055i | −0.0329990 | + | 0.0571559i | ||||
\(576\) | −1.31307 | − | 2.27430i | −0.0547112 | − | 0.0947625i | ||||
\(577\) | − | 19.7756i | − | 0.823267i | −0.911349 | − | 0.411634i | \(-0.864958\pi\) | ||
0.911349 | − | 0.411634i | \(-0.135042\pi\) | |||||||
\(578\) | 15.1652 | − | 8.75560i | 0.630787 | − | 0.364185i | ||||
\(579\) | −19.2523 | + | 11.1153i | −0.800097 | + | 0.461936i | ||||
\(580\) | − | 13.4949i | − | 0.560345i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −29.8521 | + | 51.7053i | −1.23741 | + | 2.14325i | ||||
\(583\) | 13.4347 | + | 7.75650i | 0.556407 | + | 0.321242i | ||||
\(584\) | 6.00000 | 0.248282 | ||||||||
\(585\) | −1.18693 | + | 1.14213i | −0.0490736 | + | 0.0472211i | ||||
\(586\) | −17.1652 | −0.709086 | ||||||||
\(587\) | −30.7259 | − | 17.7396i | −1.26820 | − | 0.732193i | −0.293549 | − | 0.955944i | \(-0.594836\pi\) |
−0.974646 | + | 0.223751i | \(0.928170\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.4347 | − | 49.2503i | −1.17163 | − | 2.02932i | ||||
\(590\) | 42.4075i | 1.74589i | ||||||||
\(591\) | −16.9782 | + | 9.80238i | −0.698391 | + | 0.403216i | ||||
\(592\) | 10.7477 | − | 6.20520i | 0.441729 | − | 0.255032i | ||||
\(593\) | − | 19.6048i | − | 0.805071i | −0.915404 | − | 0.402535i | \(-0.868129\pi\) | ||
0.915404 | − | 0.402535i | \(-0.131871\pi\) | |||||||
\(594\) | −6.97822 | − | 12.0866i | −0.286320 | − | 0.495920i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.29129 | + | 3.05493i | 0.216740 | + | 0.125135i | ||||
\(597\) | 19.7042 | 0.806438 | ||||||||
\(598\) | −43.1216 | + | 41.4938i | −1.76337 | + | 1.69681i | ||||
\(599\) | −20.3739 | −0.832453 | −0.416227 | − | 0.909261i | \(-0.636648\pi\) | ||||
−0.416227 | + | 0.909261i | \(0.636648\pi\) | |||||||
\(600\) | 0.560795 | + | 0.323775i | 0.0228944 | + | 0.0132181i | ||||
\(601\) | 0.686932 | − | 1.18980i | 0.0280205 | − | 0.0485330i | −0.851675 | − | 0.524070i | \(-0.824413\pi\) |
0.879696 | + | 0.475537i | \(0.157746\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 2.37960i | − | 0.0969049i | ||||||
\(604\) | 29.3085 | − | 16.9213i | 1.19255 | − | 0.688517i | ||||
\(605\) | −17.7695 | + | 10.2592i | −0.722433 | + | 0.417097i | ||||
\(606\) | 38.3912i | 1.55953i | ||||||||
\(607\) | 3.87386 | + | 6.70973i | 0.157235 | + | 0.272339i | 0.933871 | − | 0.357611i | \(-0.116409\pi\) |
−0.776635 | + | 0.629950i | \(0.783075\pi\) | |||||||
\(608\) | −24.2477 | + | 41.9983i | −0.983375 | + | 1.70326i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −61.0780 | −2.47298 | ||||||||
\(611\) | −3.70871 | − | 14.9886i | −0.150038 | − | 0.606373i | ||||
\(612\) | −1.74773 | −0.0706477 | ||||||||
\(613\) | 32.3085 | + | 18.6533i | 1.30493 | + | 0.753401i | 0.981245 | − | 0.192764i | \(-0.0617453\pi\) |
0.323684 | + | 0.946165i | \(0.395079\pi\) | |||||||
\(614\) | −26.4564 | + | 45.8239i | −1.06769 | + | 1.84930i | ||||
\(615\) | −5.00000 | − | 8.66025i | −0.201619 | − | 0.349215i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.0826 | + | 13.9041i | −0.969528 | + | 0.559757i | −0.899092 | − | 0.437759i | \(-0.855772\pi\) |
−0.0704357 | + | 0.997516i | \(0.522439\pi\) | |||||||
\(618\) | −15.5608 | + | 8.98403i | −0.625947 | + | 0.361391i | ||||
\(619\) | 12.4104i | 0.498816i | 0.968398 | + | 0.249408i | \(0.0802361\pi\) | ||||
−0.968398 | + | 0.249408i | \(0.919764\pi\) | |||||||
\(620\) | 26.4564 | + | 45.8239i | 1.06252 | + | 1.84033i | ||||
\(621\) | −18.9564 | + | 32.8335i | −0.760696 | + | 1.31756i | ||||
\(622\) | 10.5000 | + | 6.06218i | 0.421012 | + | 0.243071i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −8.02178 | − | 8.33648i | −0.321128 | − | 0.333726i | ||||
\(625\) | −23.9129 | −0.956515 | ||||||||
\(626\) | −39.3303 | − | 22.7074i | −1.57196 | − | 0.907569i | ||||
\(627\) | 7.50000 | − | 12.9904i | 0.299521 | − | 0.518786i | ||||
\(628\) | 30.6434 | + | 53.0759i | 1.22280 | + | 2.11796i | ||||
\(629\) | − | 20.7846i | − | 0.828737i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.4347 | + | 6.02445i | −0.415397 | + | 0.239830i | −0.693106 | − | 0.720836i | \(-0.743758\pi\) |
0.277709 | + | 0.960665i | \(0.410425\pi\) | |||||||
\(632\) | − | 10.3923i | − | 0.413384i | ||||||
\(633\) | 1.26951 | + | 2.19885i | 0.0504584 | + | 0.0873965i | ||||
\(634\) | −20.2695 | + | 35.1078i | −0.805005 | + | 1.39431i | ||||
\(635\) | −30.2477 | − | 17.4635i | −1.20034 | − | 0.693019i | ||||
\(636\) | −60.8258 | −2.41190 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.16515 | −0.244081 | ||||||||
\(639\) | 0.165151 | + | 0.0953502i | 0.00653329 | + | 0.00377200i | ||||
\(640\) | 13.9782 | − | 24.2110i | 0.552538 | − | 0.957023i | ||||
\(641\) | −7.81307 | − | 13.5326i | −0.308598 | − | 0.534507i | 0.669458 | − | 0.742850i | \(-0.266526\pi\) |
−0.978056 | + | 0.208343i | \(0.933193\pi\) | |||||||
\(642\) | − | 38.3912i | − | 1.51518i | ||||||
\(643\) | −11.7523 | + | 6.78518i | −0.463464 | + | 0.267581i | −0.713500 | − | 0.700655i | \(-0.752891\pi\) |
0.250035 | + | 0.968237i | \(0.419558\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 17.1497i | − | 0.675269i | ||||||
\(646\) | 21.5608 | + | 37.3444i | 0.848298 | + | 1.46930i | ||||
\(647\) | −14.5390 | + | 25.1823i | −0.571588 | + | 0.990019i | 0.424816 | + | 0.905280i | \(0.360339\pi\) |
−0.996403 | + | 0.0847389i | \(0.972994\pi\) | |||||||
\(648\) | 14.3739 | + | 8.29875i | 0.564659 | + | 0.326006i | ||||
\(649\) | 11.2867 | 0.443043 | ||||||||
\(650\) | 1.58258 | + | 0.456850i | 0.0620737 | + | 0.0179191i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.7477 | + | 9.66930i | 0.655892 | + | 0.378679i | ||||
\(653\) | −5.60436 | + | 9.70703i | −0.219315 | + | 0.379865i | −0.954599 | − | 0.297894i | \(-0.903716\pi\) |
0.735283 | + | 0.677760i | \(0.237049\pi\) | |||||||
\(654\) | 15.5608 | + | 26.9521i | 0.608475 | + | 1.05391i | ||||
\(655\) | 7.93725i | 0.310134i | ||||||||
\(656\) | 3.95644 | − | 2.28425i | 0.154473 | − | 0.0891850i | ||||
\(657\) | −0.626136 | + | 0.361500i | −0.0244279 | + | 0.0141035i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.00000 | − | 5.19615i | −0.116863 | − | 0.202413i | 0.801660 | − | 0.597781i | \(-0.203951\pi\) |
−0.918523 | + | 0.395367i | \(0.870617\pi\) | |||||||
\(660\) | −6.97822 | + | 12.0866i | −0.271627 | + | 0.470471i | ||||
\(661\) | 16.2523 | + | 9.38325i | 0.632140 | + | 0.364966i | 0.781580 | − | 0.623804i | \(-0.214414\pi\) |
−0.149440 | + | 0.988771i | \(0.547747\pi\) | |||||||
\(662\) | 2.37386 | 0.0922628 | ||||||||
\(663\) | −18.8085 | + | 4.65390i | −0.730462 | + | 0.180743i | ||||
\(664\) | −6.16515 | −0.239254 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.58258 | − | 2.74110i | 0.0613236 | − | 0.106216i | ||||
\(667\) | 8.37386 | + | 14.5040i | 0.324237 | + | 0.561595i | ||||
\(668\) | 55.7316i | 2.15632i | ||||||||
\(669\) | −32.1261 | + | 18.5480i | −1.24207 | + | 0.717108i | ||||
\(670\) | 47.3085 | − | 27.3136i | 1.82769 | − | 1.05522i | ||||
\(671\) | 16.2559i | 0.627552i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.2477 | − | 24.6778i | 0.549210 | − | 0.951259i | −0.449119 | − | 0.893472i | \(-0.648262\pi\) |
0.998329 | − | 0.0577870i | \(-0.0184044\pi\) | |||||||
\(674\) | −24.5608 | − | 14.1802i | −0.946046 | − | 0.546200i | ||||
\(675\) | 1.04356 | 0.0401667 | ||||||||
\(676\) | 30.7042 | + | 19.3386i | 1.18093 | + | 0.743793i | ||||
\(677\) | 33.7913 | 1.29870 | 0.649352 | − | 0.760488i | \(-0.275040\pi\) | ||||
0.649352 | + | 0.760488i | \(0.275040\pi\) | |||||||
\(678\) | −4.81307 | − | 2.77883i | −0.184845 | − | 0.106720i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5.68693 | − | 9.85005i | −0.218084 | − | 0.377732i | ||||
\(681\) | − | 22.0598i | − | 0.845334i | ||||||
\(682\) | 20.9347 | − | 12.0866i | 0.801630 | − | 0.462821i | ||||
\(683\) | 21.7087 | − | 12.5335i | 0.830661 | − | 0.479582i | −0.0234181 | − | 0.999726i | \(-0.507455\pi\) |
0.854079 | + | 0.520144i | \(0.174122\pi\) | |||||||
\(684\) | 3.82560i | 0.146276i | ||||||||
\(685\) | 18.7695 | + | 32.5097i | 0.717146 | + | 1.24213i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.7477 | − | 6.20520i | −0.410051 | − | 0.236743i | ||||
\(688\) | 7.83485 | 0.298701 | ||||||||
\(689\) | −42.5780 | + | 10.5353i | −1.62209 | + | 0.401364i | ||||
\(690\) | 65.0780 | 2.47748 | ||||||||
\(691\) | −25.4347 | − | 14.6847i | −0.967580 | − | 0.558633i | −0.0690824 | − | 0.997611i | \(-0.522007\pi\) |
−0.898498 | + | 0.438978i | \(0.855340\pi\) | |||||||
\(692\) | −10.8131 | + | 18.7288i | −0.411051 | + | 0.711962i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.66930i | 0.367042i | ||||||||
\(695\) | 1.50000 | − | 0.866025i | 0.0568982 | − | 0.0328502i | ||||
\(696\) | 5.93466 | − | 3.42638i | 0.224953 | − | 0.129876i | ||||
\(697\) | − | 7.65120i | − | 0.289810i | ||||||
\(698\) | −11.6869 | − | 20.2424i | −0.442357 | − | 0.766185i | ||||
\(699\) | −6.23049 | + | 10.7915i | −0.235659 | + | 0.408173i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.9129 | 1.20533 | 0.602666 | − | 0.797993i | \(-0.294105\pi\) | ||||
0.602666 | + | 0.797993i | \(0.294105\pi\) | |||||||
\(702\) | 37.9129 | + | 10.9445i | 1.43093 | + | 0.413074i | ||||
\(703\) | −45.4955 | −1.71589 | ||||||||
\(704\) | −13.8956 | − | 8.02265i | −0.523712 | − | 0.302365i | ||||
\(705\) | −8.39564 | + | 14.5417i | −0.316198 | + | 0.547671i | ||||
\(706\) | 29.3521 | + | 50.8393i | 1.10468 | + | 1.91336i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −38.3258 | + | 22.1274i | −1.44037 | + | 0.831598i | ||||
\(709\) | −6.31307 | + | 3.64485i | −0.237092 | + | 0.136885i | −0.613840 | − | 0.789431i | \(-0.710376\pi\) |
0.376747 | + | 0.926316i | \(0.377043\pi\) | |||||||
\(710\) | 4.37780i | 0.164296i | ||||||||
\(711\) | 0.626136 | + | 1.08450i | 0.0234820 | + | 0.0406719i | ||||
\(712\) | 2.52178 | − | 4.36785i | 0.0945077 | − | 0.163692i | ||||
\(713\) | −56.8693 | − | 32.8335i | −2.12977 | − | 1.22962i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.79129 | + | 9.66930i | −0.104388 | + | 0.361611i | ||||
\(716\) | 25.1216 | 0.938838 | ||||||||
\(717\) | −20.5218 | − | 11.8483i | −0.766400 | − | 0.442481i | ||||
\(718\) | −13.8739 | + | 24.0302i | −0.517768 | + | 0.896800i | ||||
\(719\) | 2.91742 | + | 5.05313i | 0.108802 | + | 0.188450i | 0.915285 | − | 0.402807i | \(-0.131965\pi\) |
−0.806483 | + | 0.591257i | \(0.798632\pi\) | |||||||
\(720\) | 0.818350i | 0.0304981i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 45.7259 | − | 26.3999i | 1.70174 | − | 0.982502i | ||||
\(723\) | 7.36515i | 0.273913i | ||||||||
\(724\) | 12.7913 | + | 22.1552i | 0.475384 | + | 0.823390i | ||||
\(725\) | 0.230493 | − | 0.399225i | 0.00856028 | − | 0.0148268i | ||||
\(726\) | −31.8303 | − | 18.3772i | −1.18133 | − | 0.682043i | ||||
\(727\) | 27.7477 | 1.02911 | 0.514553 | − | 0.857459i | \(-0.327958\pi\) | ||||
0.514553 | + | 0.857459i | \(0.327958\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.8693 | 0.921086 | ||||||||
\(730\) | −14.3739 | − | 8.29875i | −0.532001 | − | 0.307151i | ||||
\(731\) | 6.56080 | − | 11.3636i | 0.242660 | − | 0.420299i | ||||
\(732\) | −31.8693 | − | 55.1993i | −1.17792 | − | 2.04022i | ||||
\(733\) | − | 9.02175i | − | 0.333226i | −0.986022 | − | 0.166613i | \(-0.946717\pi\) | ||
0.986022 | − | 0.166613i | \(-0.0532831\pi\) | |||||||
\(734\) | −34.1216 | + | 19.7001i | −1.25945 | + | 0.727144i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 55.9977i | 2.06410i | ||||||||
\(737\) | −7.26951 | − | 12.5912i | −0.267776 | − | 0.463801i | ||||
\(738\) | 0.582576 | − | 1.00905i | 0.0214449 | − | 0.0371437i | ||||
\(739\) | −10.7477 | − | 6.20520i | −0.395362 | − | 0.228262i | 0.289119 | − | 0.957293i | \(-0.406638\pi\) |
−0.684481 | + | 0.729031i | \(0.739971\pi\) | |||||||
\(740\) | 42.3303 | 1.55609 | ||||||||
\(741\) | 10.1869 | + | 41.1700i | 0.374226 | + | 1.51242i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.64792 | + | 2.68348i | 0.170516 | + | 0.0984472i | 0.582829 | − | 0.812595i | \(-0.301946\pi\) |
−0.412313 | + | 0.911042i | \(0.635279\pi\) | |||||||
\(744\) | −13.4347 | + | 23.2695i | −0.492538 | + | 0.853102i | ||||
\(745\) | −2.39564 | − | 4.14938i | −0.0877696 | − | 0.152021i | ||||
\(746\) | − | 80.5325i | − | 2.94850i | ||||||
\(747\) | 0.643371 | − | 0.371450i | 0.0235397 | − | 0.0135907i | ||||
\(748\) | −9.24773 | + | 5.33918i | −0.338130 | + | 0.195220i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −22.3521 | − | 38.7149i | −0.816183 | − | 1.41367i | ||||
\(751\) | 1.87386 | − | 3.24563i | 0.0683783 | − | 0.118435i | −0.829809 | − | 0.558047i | \(-0.811551\pi\) |
0.898188 | + | 0.439612i | \(0.144884\pi\) | |||||||
\(752\) | −6.64337 | − | 3.83555i | −0.242259 | − | 0.139868i | ||||
\(753\) | −37.9129 | −1.38162 | ||||||||
\(754\) | 12.5608 | − | 12.0866i | 0.457437 | − | 0.440169i | ||||
\(755\) | −26.5390 | −0.965854 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.00000 | + | 5.19615i | −0.109037 | + | 0.188857i | −0.915380 | − | 0.402590i | \(-0.868110\pi\) |
0.806343 | + | 0.591448i | \(0.201443\pi\) | |||||||
\(758\) | −4.97822 | − | 8.62253i | −0.180817 | − | 0.313184i | ||||
\(759\) | − | 17.3205i | − | 0.628695i | ||||||
\(760\) | −21.5608 | + | 12.4481i | −0.782092 | + | 0.451541i | ||||
\(761\) | 27.7259 | − | 16.0076i | 1.00506 | − | 0.580274i | 0.0953219 | − | 0.995447i | \(-0.469612\pi\) |
0.909743 | + | 0.415172i | \(0.136279\pi\) | |||||||
\(762\) | − | 62.5644i | − | 2.26647i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.873864 | + | 1.51358i | −0.0316153 | + | 0.0547593i | ||||
\(765\) | 1.18693 | + | 0.685275i | 0.0429136 | + | 0.0247762i | ||||
\(766\) | −8.58258 | −0.310101 | ||||||||
\(767\) | −22.9955 | + | 22.1274i | −0.830318 | + | 0.798974i | ||||
\(768\) | 5.00000 | 0.180422 | ||||||||
\(769\) | 21.8739 | + | 12.6289i | 0.788792 | + | 0.455409i | 0.839537 | − | 0.543303i | \(-0.182826\pi\) |
−0.0507453 | + | 0.998712i | \(0.516160\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.0390 | − | 43.3688i | −0.901758 | − | 1.56189i | ||||
\(772\) | − | 34.6410i | − | 1.24676i | ||||||
\(773\) | 19.8303 | − | 11.4490i | 0.713246 | − | 0.411793i | −0.0990155 | − | 0.995086i | \(-0.531569\pi\) |
0.812262 | + | 0.583293i | \(0.198236\pi\) | |||||||
\(774\) | 1.73049 | − | 0.999100i | 0.0622013 | − | 0.0359119i | ||||
\(775\) | 1.80750i | 0.0649273i | ||||||||
\(776\) | −13.1869 | − | 22.8404i | −0.473383 | − | 0.819924i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 68.8693 | + | 39.7617i | 2.46908 | + | 1.42553i | ||||
\(779\) | −16.7477 | −0.600050 | ||||||||
\(780\) | −9.47822 | − | 38.3058i | −0.339375 | − | 1.37157i | ||||
\(781\) | 1.16515 | 0.0416924 | ||||||||
\(782\) | 43.1216 | + | 24.8963i | 1.54202 | + | 0.890289i | ||||
\(783\) | 5.52178 | − | 9.56400i | 0.197332 | − | 0.341790i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 48.0605i | − | 1.71535i | ||||||
\(786\) | −12.3131 | + | 7.10895i | −0.439193 | + | 0.253568i | ||||
\(787\) | 4.74773 | − | 2.74110i | 0.169238 | − | 0.0977097i | −0.412988 | − | 0.910736i | \(-0.635515\pi\) |
0.582227 | + | 0.813027i | \(0.302182\pi\) | |||||||
\(788\) | − | 30.5493i | − | 1.08827i | ||||||
\(789\) | −24.4782 | − | 42.3975i | −0.871448 | − | 1.50939i | ||||
\(790\) | −14.3739 | + | 24.8963i | −0.511399 | + | 0.885769i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.460985 | −0.0163804 | ||||||||
\(793\) | −31.8693 | − | 33.1196i | −1.13171 | − | 1.17611i | ||||
\(794\) | 33.1652 | 1.17699 | ||||||||
\(795\) | 41.3085 | + | 23.8495i | 1.46506 | + | 0.845854i | ||||
\(796\) | −15.3521 | + | 26.5906i | −0.544140 | + | 0.942478i | ||||
\(797\) | −6.00000 | − | 10.3923i | −0.212531 | − | 0.368114i | 0.739975 | − | 0.672634i | \(-0.234837\pi\) |
−0.952506 | + | 0.304520i | \(0.901504\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.1261 | + | 6.42368i | −0.393614 | + | 0.227253i | ||||
\(800\) | 1.33485 | − | 0.770675i | 0.0471940 | − | 0.0272475i | ||||
\(801\) | 0.607749i | 0.0214738i | ||||||||
\(802\) | −32.3521 | − | 56.0355i | −1.14239 | − | 1.97868i | ||||
\(803\) | −2.20871 | + | 3.82560i | −0.0779438 | + | 0.135003i | ||||
\(804\) | 49.3693 | + | 28.5034i | 1.74112 | + | 1.00524i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −18.9564 | + | 65.6670i | −0.667712 | + | 2.31302i | ||||
\(807\) | −20.0780 | −0.706780 | ||||||||
\(808\) | −14.6869 | − | 8.47950i | −0.516684 | − | 0.298308i | ||||
\(809\) | 14.6216 | − | 25.3253i | 0.514068 | − | 0.890391i | −0.485799 | − | 0.874071i | \(-0.661471\pi\) |
0.999867 | − | 0.0163209i | \(-0.00519535\pi\) | |||||||
\(810\) | −22.9564 | − | 39.7617i | −0.806607 | − | 1.39708i | ||||
\(811\) | 12.0489i | 0.423094i | 0.977368 | + | 0.211547i | \(0.0678502\pi\) | ||||
−0.977368 | + | 0.211547i | \(0.932150\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 44.5562 | − | 25.7246i | 1.56266 | − | 0.902200i | ||||
\(814\) | − | 19.3386i | − | 0.677818i | ||||||
\(815\) | −7.58258 | − | 13.1334i | −0.265606 | − | 0.460043i | ||||
\(816\) | −4.81307 | + | 8.33648i | −0.168491 | + | 0.291835i | ||||
\(817\) | −24.8739 | − | 14.3609i | −0.870226 | − | 0.502425i | ||||
\(818\) | −0.791288 | −0.0276667 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.5826 | 0.544167 | ||||||||
\(821\) | 43.0390 | + | 24.8486i | 1.50207 | + | 0.867222i | 0.999997 | + | 0.00239749i | \(0.000763146\pi\) |
0.502075 | + | 0.864824i | \(0.332570\pi\) | |||||||
\(822\) | −33.6216 | + | 58.2343i | −1.17269 | + | 2.03115i | ||||
\(823\) | −16.2477 | − | 28.1419i | −0.566360 | − | 0.980965i | −0.996922 | − | 0.0784034i | \(-0.975018\pi\) |
0.430562 | − | 0.902561i | \(-0.358316\pi\) | |||||||
\(824\) | − | 7.93725i | − | 0.276507i | ||||||
\(825\) | −0.412878 | + | 0.238375i | −0.0143746 | + | 0.00829917i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 0.989150i | − | 0.0343961i | −0.999852 | − | 0.0171981i | \(-0.994525\pi\) | ||
0.999852 | − | 0.0171981i | \(-0.00547458\pi\) | |||||||
\(828\) | 2.20871 | + | 3.82560i | 0.0767581 | + | 0.132949i | ||||
\(829\) | 10.3131 | − | 17.8628i | 0.358188 | − | 0.620399i | −0.629470 | − | 0.777024i | \(-0.716728\pi\) |
0.987658 | + | 0.156625i | \(0.0500615\pi\) | |||||||
\(830\) | 14.7695 | + | 8.52718i | 0.512657 | + | 0.295983i | ||||
\(831\) | 28.2087 | 0.978549 | ||||||||
\(832\) | 44.0390 | − | 10.8968i | 1.52678 | − | 0.377780i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.68693 | + | 1.55130i | 0.0930408 | + | 0.0537172i | ||||
\(835\) | 21.8521 | − | 37.8489i | 0.756223 | − | 1.30982i | ||||
\(836\) | 11.6869 | + | 20.2424i | 0.404201 | + | 0.700097i | ||||
\(837\) | 43.3013i | 1.49671i | ||||||||
\(838\) | 48.8085 | − | 28.1796i | 1.68606 | − | 0.973449i | ||||
\(839\) | 40.2695 | − | 23.2496i | 1.39026 | − | 0.802666i | 0.396914 | − | 0.917856i | \(-0.370081\pi\) |
0.993343 | + | 0.115190i | \(0.0367477\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.0608 | + | 20.8899i | 0.415889 | + | 0.720342i | ||||
\(842\) | −21.9564 | + | 38.0297i | −0.756669 | + | 1.31059i | ||||
\(843\) | −9.92197 | − | 5.72845i | −0.341731 | − | 0.197298i | ||||
\(844\) | −3.95644 | −0.136186 | ||||||||
\(845\) | −13.2695 | − | 25.1724i | −0.456485 | − | 0.865956i | ||||
\(846\) | −1.95644 | −0.0672638 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10.8956 | + | 18.8718i | −0.374158 | + | 0.648061i | ||||
\(849\) | 22.1652 | + | 38.3912i | 0.760706 | + | 1.31758i | ||||
\(850\) | − | 1.37055i | − | 0.0470095i | ||||||
\(851\) | −45.4955 | + | 26.2668i | −1.55956 | + | 0.900415i | ||||
\(852\) | −3.95644 | + | 2.28425i | −0.135545 | + | 0.0782572i | ||||
\(853\) | − | 17.6066i | − | 0.602837i | −0.953492 | − | 0.301419i | \(-0.902540\pi\) | ||
0.953492 | − | 0.301419i | \(-0.0974601\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.50000 | − | 2.59808i | 0.0512989 | − | 0.0888523i | ||||
\(856\) | 14.6869 | + | 8.47950i | 0.501989 | + | 0.289823i | ||||
\(857\) | −47.5390 | −1.62390 | −0.811951 | − | 0.583726i | \(-0.801594\pi\) | ||||
−0.811951 | + | 0.583726i | \(0.801594\pi\) | |||||||
\(858\) | −17.5000 | + | 4.33013i | −0.597440 | + | 0.147828i | ||||
\(859\) | 14.0000 | 0.477674 | 0.238837 | − | 0.971060i | \(-0.423234\pi\) | ||||
0.238837 | + | 0.971060i | \(0.423234\pi\) | |||||||
\(860\) | 23.1434 | + | 13.3618i | 0.789182 | + | 0.455635i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −17.0826 | − | 29.5879i | −0.581835 | − | 1.00777i | ||||
\(863\) | 3.08270i | 0.104936i | 0.998623 | + | 0.0524682i | \(0.0167088\pi\) | ||||
−0.998623 | + | 0.0524682i | \(0.983291\pi\) | |||||||
\(864\) | 31.9782 | − | 18.4626i | 1.08792 | − | 0.628112i | ||||
\(865\) | 14.6869 | − | 8.47950i | 0.499371 | − | 0.288312i | ||||
\(866\) | 49.2403i | 1.67325i | ||||||||
\(867\) | −7.16515 | − | 12.4104i | −0.243341 | − | 0.421479i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.62614 | + | 3.82560i | 0.224776 | + | 0.129775i | ||||
\(870\) | −18.9564 | −0.642683 | ||||||||
\(871\) | 39.4955 | + | 11.4014i | 1.33825 | + | 0.386320i | ||||
\(872\) | −13.7477 | −0.465557 | ||||||||
\(873\) | 2.75227 | + | 1.58903i | 0.0931503 | + | 0.0537804i | ||||
\(874\) | 54.4955 | − | 94.3889i | 1.84334 | − | 3.19275i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 17.3205i | − | 0.585206i | ||||||
\(877\) | 30.2477 | − | 17.4635i | 1.02139 | − | 0.589702i | 0.106886 | − | 0.994271i | \(-0.465912\pi\) |
0.914507 | + | 0.404570i | \(0.132579\pi\) | |||||||
\(878\) | 21.8739 | − | 12.6289i | 0.738207 | − | 0.426204i | ||||
\(879\) | 14.0471i | 0.473797i | ||||||||
\(880\) | 2.50000 | + | 4.33013i | 0.0842750 | + | 0.145969i | ||||
\(881\) | 3.70871 | − | 6.42368i | 0.124950 | − | 0.216419i | −0.796764 | − | 0.604291i | \(-0.793456\pi\) |
0.921713 | + | 0.387872i | \(0.126790\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −53.2432 | −1.79178 | −0.895888 | − | 0.444280i | \(-0.853459\pi\) | ||||
−0.895888 | + | 0.444280i | \(0.853459\pi\) | |||||||
\(884\) | 8.37386 | − | 29.0079i | 0.281644 | − | 0.975642i | ||||
\(885\) | 34.7042 | 1.16657 | ||||||||
\(886\) | 6.00000 | + | 3.46410i | 0.201574 | + | 0.116379i | ||||
\(887\) | 15.7913 | − | 27.3513i | 0.530220 | − | 0.918367i | −0.469159 | − | 0.883114i | \(-0.655443\pi\) |
0.999378 | − | 0.0352534i | \(-0.0112238\pi\) | |||||||
\(888\) | 10.7477 | + | 18.6156i | 0.360670 | + | 0.624699i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12.0826 | + | 6.97588i | −0.405009 | + | 0.233832i | ||||
\(891\) | −10.5826 | + | 6.10985i | −0.354530 | + | 0.204688i | ||||
\(892\) | − | 57.8052i | − | 1.93546i | ||||||
\(893\) | 14.0608 | + | 24.3540i | 0.470527 | + | 0.814976i | ||||
\(894\) | 4.29129 | − | 7.43273i | 0.143522 | − | 0.248588i | ||||
\(895\) | −17.0608 | − | 9.85005i | −0.570279 | − | 0.329251i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 33.9564 | + | 35.2886i | 1.13377 | + | 1.17825i | ||||
\(898\) | −43.4955 | −1.45146 | ||||||||
\(899\) | 16.5653 | + | 9.56400i | 0.552485 | + | 0.318977i | ||||
\(900\) | 0.0607953 | − | 0.105301i | 0.00202651 | − | 0.00351002i | ||||
\(901\) | 18.2477 | + | 31.6060i | 0.607920 | + | 1.05295i | ||||
\(902\) | − | 7.11890i | − | 0.237034i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.12614 | − | 1.22753i | 0.0707142 | − | 0.0408269i | ||||
\(905\) | − | 20.0616i | − | 0.666870i | ||||||
\(906\) | −23.7695 | − | 41.1700i | −0.789689 | − | 1.36778i | ||||
\(907\) | −11.5390 | + | 19.9862i | −0.383147 | + | 0.663630i | −0.991510 | − | 0.130029i | \(-0.958493\pi\) |
0.608363 | + | 0.793659i | \(0.291826\pi\) | |||||||
\(908\) | 29.7695 | + | 17.1874i | 0.987936 | + | 0.570385i | ||||
\(909\) | 2.04356 | 0.0677806 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.87841 | −0.0622345 | −0.0311172 | − | 0.999516i | \(-0.509907\pi\) | ||||
−0.0311172 | + | 0.999516i | \(0.509907\pi\) | |||||||
\(912\) | 18.2477 | + | 10.5353i | 0.604243 | + | 0.348860i | ||||
\(913\) | 2.26951 | − | 3.93090i | 0.0751097 | − | 0.130094i | ||||
\(914\) | −9.79129 | − | 16.9590i | −0.323867 | − | 0.560954i | ||||
\(915\) | 49.9832i | 1.65239i | ||||||||
\(916\) | 16.7477 | − | 9.66930i | 0.553360 | − | 0.319483i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 32.8335i | − | 1.08367i | ||||||
\(919\) | 9.95644 | + | 17.2451i | 0.328433 | + | 0.568862i | 0.982201 | − | 0.187833i | \(-0.0601463\pi\) |
−0.653768 | + | 0.756695i | \(0.726813\pi\) | |||||||
\(920\) | −14.3739 | + | 24.8963i | −0.473892 | + | 0.820805i | ||||
\(921\) | 37.5000 | + | 21.6506i | 1.23567 | + | 0.713413i | ||||
\(922\) | −39.1216 | −1.28840 | ||||||||
\(923\) | −2.37386 | + | 2.28425i | −0.0781367 | + | 0.0751870i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.25227 | + | 0.723000i | 0.0411745 | + | 0.0237721i | ||||
\(926\) | 8.68693 | − | 15.0462i | 0.285470 | − | 0.494449i | ||||
\(927\) | 0.478220 | + | 0.828301i | 0.0157068 | + | 0.0272050i | ||||
\(928\) | − | 16.3115i | − | 0.535450i | ||||||
\(929\) | −23.1606 | + | 13.3718i | −0.759875 | + | 0.438714i | −0.829251 | − | 0.558877i | \(-0.811233\pi\) |
0.0693760 | + | 0.997591i | \(0.477899\pi\) | |||||||
\(930\) | 64.3693 | − | 37.1636i | 2.11075 | − | 1.21864i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −9.70871 | − | 16.8160i | −0.318019 | − | 0.550826i | ||||
\(933\) | 4.96099 | − | 8.59268i | 0.162415 | − | 0.281312i | ||||
\(934\) | −22.4347 | − | 12.9527i | −0.734084 | − | 0.423824i | ||||
\(935\) | 8.37386 | 0.273855 | ||||||||
\(936\) | 0.939205 | − | 0.903750i | 0.0306989 | − | 0.0295400i | ||||
\(937\) | 34.4955 | 1.12692 | 0.563459 | − | 0.826144i | \(-0.309470\pi\) | ||||
0.563459 | + | 0.826144i | \(0.309470\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.5826 | + | 32.1860i | −0.606419 | + | 1.05035i | ||||
\(940\) | −13.0826 | − | 22.6597i | −0.426707 | − | 0.739077i | ||||
\(941\) | 2.26435i | 0.0738157i | 0.999319 | + | 0.0369079i | \(0.0117508\pi\) | ||||
−0.999319 | + | 0.0369079i | \(0.988249\pi\) | |||||||
\(942\) | 74.5562 | − | 43.0451i | 2.42917 | − | 1.40248i | ||||
\(943\) | −16.7477 | + | 9.66930i | −0.545381 | + | 0.314876i | ||||
\(944\) | 15.8546i | 0.516024i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.10436 | − | 10.5731i | 0.198470 | − | 0.343760i | ||||
\(947\) | −49.2695 | − | 28.4458i | −1.60104 | − | 0.924363i | −0.991279 | − | 0.131781i | \(-0.957930\pi\) |
−0.609765 | − | 0.792582i | \(-0.708736\pi\) | |||||||
\(948\) | −30.0000 | −0.974355 | ||||||||
\(949\) | −3.00000 | − | 12.1244i | −0.0973841 | − | 0.393573i | ||||
\(950\) | −3.00000 | −0.0973329 | ||||||||
\(951\) | 28.7305 | + | 16.5876i | 0.931650 | + | 0.537888i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.50000 | + | 12.9904i | 0.242949 | + | 0.420800i | 0.961553 | − | 0.274620i | \(-0.0885520\pi\) |
−0.718604 | + | 0.695419i | \(0.755219\pi\) | |||||||
\(954\) | 5.55765i | 0.179936i | ||||||||
\(955\) | 1.18693 | − | 0.685275i | 0.0384082 | − | 0.0221750i | ||||
\(956\) | 31.9782 | − | 18.4626i | 1.03425 | − | 0.597124i | ||||
\(957\) | 5.04525i | 0.163090i | ||||||||
\(958\) | −11.1869 | − | 19.3763i | −0.361433 | − | 0.626021i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −42.7259 | − | 24.6678i | −1.37897 | − | 0.796151i | ||||
\(961\) | −44.0000 | −1.41935 | ||||||||
\(962\) | 37.9129 | + | 39.4002i | 1.22236 | + | 1.27031i | ||||
\(963\) | −2.04356 | −0.0658528 | ||||||||
\(964\) | −9.93920 | − | 5.73840i | −0.320120 | − | 0.184821i | ||||
\(965\) | −13.5826 | + | 23.5257i | −0.437239 | + | 0.757319i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.8118i | 0.765735i | 0.923803 | + | 0.382867i | \(0.125063\pi\) | ||||
−0.923803 | + | 0.382867i | \(0.874937\pi\) | |||||||
\(968\) | 14.0608 | − | 8.11800i | 0.451931 | − | 0.260923i | ||||
\(969\) | 30.5608 | − | 17.6443i | 0.981754 | − | 0.566816i | ||||
\(970\) | 72.9567i | 2.34250i | ||||||||
\(971\) | 24.8739 | + | 43.0828i | 0.798240 | + | 1.38259i | 0.920761 | + | 0.390127i | \(0.127569\pi\) |
−0.122521 | + | 0.992466i | \(0.539098\pi\) | |||||||
\(972\) | 3.02178 | − | 5.23388i | 0.0969237 | − | 0.167877i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −22.5826 | −0.723592 | ||||||||
\(975\) | 0.373864 | − | 1.29510i | 0.0119732 | − | 0.0414764i | ||||
\(976\) | −22.8348 | −0.730926 | ||||||||
\(977\) | 49.2042 | + | 28.4080i | 1.57418 | + | 0.908854i | 0.995648 | + | 0.0931946i | \(0.0297079\pi\) |
0.578533 | + | 0.815659i | \(0.303625\pi\) | |||||||
\(978\) | 13.5826 | − | 23.5257i | 0.434323 | − | 0.752269i | ||||
\(979\) | 1.85663 | + | 3.21578i | 0.0593381 | + | 0.102777i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.43466 | − | 0.828301i | 0.0458051 | − | 0.0264456i | ||||
\(982\) | −70.3693 | + | 40.6277i | −2.24558 | + | 1.29648i | ||||
\(983\) | 25.0870i | 0.800150i | 0.916482 | + | 0.400075i | \(0.131016\pi\) | ||||
−0.916482 | + | 0.400075i | \(0.868984\pi\) | |||||||
\(984\) | 3.95644 | + | 6.85275i | 0.126127 | + | 0.218458i | ||||
\(985\) | −11.9782 | + | 20.7469i | −0.381658 | + | 0.661051i | ||||
\(986\) | −12.5608 | − | 7.25198i | −0.400017 | − | 0.230950i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −63.4955 | − | 18.3296i | −2.02006 | − | 0.583141i | ||||
\(989\) | −33.1652 | −1.05459 | ||||||||
\(990\) | 1.10436 | + | 0.637600i | 0.0350987 | + | 0.0202643i | ||||
\(991\) | 13.3131 | − | 23.0589i | 0.422904 | − | 0.732490i | −0.573319 | − | 0.819333i | \(-0.694344\pi\) |
0.996222 | + | 0.0868421i | \(0.0276776\pi\) | |||||||
\(992\) | 31.9782 | + | 55.3879i | 1.01531 | + | 1.75857i | ||||
\(993\) | − | 1.94265i | − | 0.0616482i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.8521 | − | 12.0390i | 0.661055 | − | 0.381661i | ||||
\(996\) | 17.7973i | 0.563928i | ||||||||
\(997\) | 25.0390 | + | 43.3688i | 0.792994 | + | 1.37351i | 0.924105 | + | 0.382138i | \(0.124812\pi\) |
−0.131112 | + | 0.991368i | \(0.541855\pi\) | |||||||
\(998\) | −46.2042 | + | 80.0280i | −1.46257 | + | 2.53324i | ||||
\(999\) | 30.0000 | + | 17.3205i | 0.949158 | + | 0.547997i |
(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 | 637.2.q.e.589.2 | yes | 4 | |
7.2 | even | 3 | 637.2.k.d.459.1 | 4 | |||
7.3 | odd | 6 | 637.2.u.d.30.1 | 4 | |||
7.4 | even | 3 | 637.2.u.e.30.1 | 4 | |||
7.5 | odd | 6 | 637.2.k.f.459.1 | 4 | |||
7.6 | odd | 2 | 637.2.q.f.589.2 | yes | 4 | ||
13.6 | odd | 12 | 8281.2.a.bs.1.1 | 4 | |||
13.7 | odd | 12 | 8281.2.a.bs.1.4 | 4 | |||
13.10 | even | 6 | inner | 637.2.q.e.491.2 | ✓ | 4 | |
91.6 | even | 12 | 8281.2.a.bq.1.1 | 4 | |||
91.10 | odd | 6 | 637.2.k.f.569.2 | 4 | |||
91.20 | even | 12 | 8281.2.a.bq.1.4 | 4 | |||
91.23 | even | 6 | 637.2.u.e.361.1 | 4 | |||
91.62 | odd | 6 | 637.2.q.f.491.2 | yes | 4 | ||
91.75 | odd | 6 | 637.2.u.d.361.1 | 4 | |||
91.88 | even | 6 | 637.2.k.d.569.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.k.d.459.1 | 4 | 7.2 | even | 3 | |||
637.2.k.d.569.2 | 4 | 91.88 | even | 6 | |||
637.2.k.f.459.1 | 4 | 7.5 | odd | 6 | |||
637.2.k.f.569.2 | 4 | 91.10 | odd | 6 | |||
637.2.q.e.491.2 | ✓ | 4 | 13.10 | even | 6 | inner | |
637.2.q.e.589.2 | yes | 4 | 1.1 | even | 1 | trivial | |
637.2.q.f.491.2 | yes | 4 | 91.62 | odd | 6 | ||
637.2.q.f.589.2 | yes | 4 | 7.6 | odd | 2 | ||
637.2.u.d.30.1 | 4 | 7.3 | odd | 6 | |||
637.2.u.d.361.1 | 4 | 91.75 | odd | 6 | |||
637.2.u.e.30.1 | 4 | 7.4 | even | 3 | |||
637.2.u.e.361.1 | 4 | 91.23 | even | 6 | |||
8281.2.a.bq.1.1 | 4 | 91.6 | even | 12 | |||
8281.2.a.bq.1.4 | 4 | 91.20 | even | 12 | |||
8281.2.a.bs.1.1 | 4 | 13.6 | odd | 12 | |||
8281.2.a.bs.1.4 | 4 | 13.7 | odd | 12 |