Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [276,2,Mod(91,276)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(276, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("276.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 276 = 2^{2} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 276.e (of order \(2\), degree \(1\), 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: | \(2.20387109579\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.6 | ||
Character | \(\chi\) | \(=\) | 276.91 |
Dual form | 276.2.e.a.91.7 |
$q$-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 \(\left(\mathbb{Z}/276\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(139\) | \(185\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.588134 | − | 1.28612i | −0.415873 | − | 0.909422i | ||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.30820 | + | 1.51282i | −0.654099 | + | 0.756409i | ||||
\(5\) | 2.28672i | 1.02265i | 0.859387 | + | 0.511326i | \(0.170845\pi\) | ||||
−0.859387 | + | 0.511326i | \(0.829155\pi\) | |||||||
\(6\) | −1.28612 | + | 0.588134i | −0.525055 | + | 0.240105i | ||||
\(7\) | 3.41490 | 1.29071 | 0.645355 | − | 0.763882i | \(-0.276709\pi\) | ||||
0.645355 | + | 0.763882i | \(0.276709\pi\) | |||||||
\(8\) | 2.71506 | + | 0.792755i | 0.959918 | + | 0.280281i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.94099 | − | 1.34490i | 0.930023 | − | 0.425294i | ||||
\(11\) | 1.67149 | 0.503974 | 0.251987 | − | 0.967731i | \(-0.418916\pi\) | ||||
0.251987 | + | 0.967731i | \(0.418916\pi\) | |||||||
\(12\) | 1.51282 | + | 1.30820i | 0.436713 | + | 0.377644i | ||||
\(13\) | 0.215808 | 0.0598543 | 0.0299272 | − | 0.999552i | \(-0.490472\pi\) | ||||
0.0299272 | + | 0.999552i | \(0.490472\pi\) | |||||||
\(14\) | −2.00842 | − | 4.39196i | −0.536772 | − | 1.17380i | ||||
\(15\) | 2.28672 | 0.590428 | ||||||||
\(16\) | −0.577241 | − | 3.95813i | −0.144310 | − | 0.989533i | ||||
\(17\) | 0.222714i | 0.0540161i | 0.999635 | + | 0.0270081i | \(0.00859798\pi\) | ||||
−0.999635 | + | 0.0270081i | \(0.991402\pi\) | |||||||
\(18\) | 0.588134 | + | 1.28612i | 0.138624 | + | 0.303141i | ||||
\(19\) | 7.32186 | 1.67975 | 0.839875 | − | 0.542780i | \(-0.182628\pi\) | ||||
0.839875 | + | 0.542780i | \(0.182628\pi\) | |||||||
\(20\) | −3.45939 | − | 2.99148i | −0.773543 | − | 0.668915i | ||||
\(21\) | − | 3.41490i | − | 0.745192i | ||||||
\(22\) | −0.983061 | − | 2.14974i | −0.209589 | − | 0.458325i | ||||
\(23\) | −4.75380 | − | 0.633562i | −0.991235 | − | 0.132107i | ||||
\(24\) | 0.792755 | − | 2.71506i | 0.161821 | − | 0.554209i | ||||
\(25\) | −0.229084 | −0.0458167 | ||||||||
\(26\) | −0.126924 | − | 0.277554i | −0.0248918 | − | 0.0544329i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −4.46736 | + | 5.16612i | −0.844252 | + | 0.976306i | ||||
\(29\) | −6.15775 | −1.14346 | −0.571732 | − | 0.820440i | \(-0.693728\pi\) | ||||
−0.571732 | + | 0.820440i | \(0.693728\pi\) | |||||||
\(30\) | −1.34490 | − | 2.94099i | −0.245543 | − | 0.536949i | ||||
\(31\) | − | 3.33926i | − | 0.599749i | −0.953979 | − | 0.299874i | \(-0.903055\pi\) | ||
0.953979 | − | 0.299874i | \(-0.0969448\pi\) | |||||||
\(32\) | −4.75113 | + | 3.07031i | −0.839888 | + | 0.542759i | ||||
\(33\) | − | 1.67149i | − | 0.290969i | ||||||
\(34\) | 0.286437 | − | 0.130986i | 0.0491235 | − | 0.0224639i | ||||
\(35\) | 7.80892i | 1.31995i | ||||||||
\(36\) | 1.30820 | − | 1.51282i | 0.218033 | − | 0.252136i | ||||
\(37\) | 1.86514i | 0.306628i | 0.988178 | + | 0.153314i | \(0.0489945\pi\) | ||||
−0.988178 | + | 0.153314i | \(0.951005\pi\) | |||||||
\(38\) | −4.30623 | − | 9.41677i | −0.698563 | − | 1.52760i | ||||
\(39\) | − | 0.215808i | − | 0.0345569i | ||||||
\(40\) | −1.81281 | + | 6.20857i | −0.286630 | + | 0.981662i | ||||
\(41\) | 8.94190 | 1.39649 | 0.698245 | − | 0.715859i | \(-0.253965\pi\) | ||||
0.698245 | + | 0.715859i | \(0.253965\pi\) | |||||||
\(42\) | −4.39196 | + | 2.00842i | −0.677695 | + | 0.309906i | ||||
\(43\) | 2.67923 | 0.408579 | 0.204290 | − | 0.978911i | \(-0.434512\pi\) | ||||
0.204290 | + | 0.978911i | \(0.434512\pi\) | |||||||
\(44\) | −2.18664 | + | 2.52866i | −0.329649 | + | 0.381210i | ||||
\(45\) | − | 2.28672i | − | 0.340884i | ||||||
\(46\) | 1.98103 | + | 6.48656i | 0.292088 | + | 0.956392i | ||||
\(47\) | − | 6.03026i | − | 0.879603i | −0.898095 | − | 0.439802i | \(-0.855049\pi\) | ||
0.898095 | − | 0.439802i | \(-0.144951\pi\) | |||||||
\(48\) | −3.95813 | + | 0.577241i | −0.571307 | + | 0.0833175i | ||||
\(49\) | 4.66154 | 0.665934 | ||||||||
\(50\) | 0.134732 | + | 0.294628i | 0.0190539 | + | 0.0416667i | ||||
\(51\) | 0.222714 | 0.0311862 | ||||||||
\(52\) | −0.282319 | + | 0.326478i | −0.0391506 | + | 0.0452744i | ||||
\(53\) | 11.0574i | 1.51884i | 0.650598 | + | 0.759422i | \(0.274518\pi\) | ||||
−0.650598 | + | 0.759422i | \(0.725482\pi\) | |||||||
\(54\) | 1.28612 | − | 0.588134i | 0.175018 | − | 0.0800349i | ||||
\(55\) | 3.82223i | 0.515390i | ||||||||
\(56\) | 9.27165 | + | 2.70718i | 1.23898 | + | 0.361762i | ||||
\(57\) | − | 7.32186i | − | 0.969804i | ||||||
\(58\) | 3.62158 | + | 7.91959i | 0.475537 | + | 1.03989i | ||||
\(59\) | − | 3.93157i | − | 0.511847i | −0.966697 | − | 0.255923i | \(-0.917621\pi\) | ||
0.966697 | − | 0.255923i | \(-0.0823795\pi\) | |||||||
\(60\) | −2.99148 | + | 3.45939i | −0.386198 | + | 0.446605i | ||||
\(61\) | 9.89882i | 1.26741i | 0.773573 | + | 0.633707i | \(0.218467\pi\) | ||||
−0.773573 | + | 0.633707i | \(0.781533\pi\) | |||||||
\(62\) | −4.29468 | + | 1.96393i | −0.545425 | + | 0.249420i | ||||
\(63\) | −3.41490 | −0.430237 | ||||||||
\(64\) | 6.74308 | + | 4.30475i | 0.842885 | + | 0.538094i | ||||
\(65\) | 0.493492i | 0.0612101i | ||||||||
\(66\) | −2.14974 | + | 0.983061i | −0.264614 | + | 0.121006i | ||||
\(67\) | −1.94227 | −0.237286 | −0.118643 | − | 0.992937i | \(-0.537854\pi\) | ||||
−0.118643 | + | 0.992937i | \(0.537854\pi\) | |||||||
\(68\) | −0.336926 | − | 0.291354i | −0.0408583 | − | 0.0353319i | ||||
\(69\) | −0.633562 | + | 4.75380i | −0.0762719 | + | 0.572290i | ||||
\(70\) | 10.0432 | − | 4.59269i | 1.20039 | − | 0.548931i | ||||
\(71\) | − | 8.94968i | − | 1.06213i | −0.847331 | − | 0.531066i | \(-0.821792\pi\) | ||
0.847331 | − | 0.531066i | \(-0.178208\pi\) | |||||||
\(72\) | −2.71506 | − | 0.792755i | −0.319973 | − | 0.0934271i | ||||
\(73\) | −14.6311 | −1.71244 | −0.856221 | − | 0.516610i | \(-0.827194\pi\) | ||||
−0.856221 | + | 0.516610i | \(0.827194\pi\) | |||||||
\(74\) | 2.39879 | − | 1.09695i | 0.278854 | − | 0.127518i | ||||
\(75\) | 0.229084i | 0.0264523i | ||||||||
\(76\) | −9.57843 | + | 11.0766i | −1.09872 | + | 1.27058i | ||||
\(77\) | 5.70798 | 0.650484 | ||||||||
\(78\) | −0.277554 | + | 0.126924i | −0.0314268 | + | 0.0143713i | ||||
\(79\) | −4.15186 | −0.467121 | −0.233560 | − | 0.972342i | \(-0.575038\pi\) | ||||
−0.233560 | + | 0.972342i | \(0.575038\pi\) | |||||||
\(80\) | 9.05113 | − | 1.31999i | 1.01195 | − | 0.147579i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.25903 | − | 11.5003i | −0.580763 | − | 1.27000i | ||||
\(83\) | −15.1113 | −1.65868 | −0.829342 | − | 0.558741i | \(-0.811285\pi\) | ||||
−0.829342 | + | 0.558741i | \(0.811285\pi\) | |||||||
\(84\) | 5.16612 | + | 4.46736i | 0.563670 | + | 0.487429i | ||||
\(85\) | −0.509285 | −0.0552397 | ||||||||
\(86\) | −1.57575 | − | 3.44581i | −0.169917 | − | 0.371571i | ||||
\(87\) | 6.15775i | 0.660180i | ||||||||
\(88\) | 4.53820 | + | 1.32508i | 0.483773 | + | 0.141254i | ||||
\(89\) | 11.2497i | 1.19247i | 0.802811 | + | 0.596233i | \(0.203337\pi\) | ||||
−0.802811 | + | 0.596233i | \(0.796663\pi\) | |||||||
\(90\) | −2.94099 | + | 1.34490i | −0.310008 | + | 0.141765i | ||||
\(91\) | 0.736962 | 0.0772546 | ||||||||
\(92\) | 7.17737 | − | 6.36281i | 0.748292 | − | 0.663369i | ||||
\(93\) | −3.33926 | −0.346265 | ||||||||
\(94\) | −7.75562 | + | 3.54660i | −0.799931 | + | 0.365804i | ||||
\(95\) | 16.7430i | 1.71780i | ||||||||
\(96\) | 3.07031 | + | 4.75113i | 0.313362 | + | 0.484910i | ||||
\(97\) | − | 16.3374i | − | 1.65881i | −0.558647 | − | 0.829406i | \(-0.688679\pi\) | ||
0.558647 | − | 0.829406i | \(-0.311321\pi\) | |||||||
\(98\) | −2.74161 | − | 5.99529i | −0.276944 | − | 0.605616i | ||||
\(99\) | −1.67149 | −0.167991 | ||||||||
\(100\) | 0.299686 | − | 0.346562i | 0.0299686 | − | 0.0346562i | ||||
\(101\) | −2.59985 | −0.258695 | −0.129348 | − | 0.991599i | \(-0.541288\pi\) | ||||
−0.129348 | + | 0.991599i | \(0.541288\pi\) | |||||||
\(102\) | −0.130986 | − | 0.286437i | −0.0129695 | − | 0.0283615i | ||||
\(103\) | −16.7590 | −1.65131 | −0.825655 | − | 0.564175i | \(-0.809194\pi\) | ||||
−0.825655 | + | 0.564175i | \(0.809194\pi\) | |||||||
\(104\) | 0.585931 | + | 0.171083i | 0.0574552 | + | 0.0167761i | ||||
\(105\) | 7.80892 | 0.762072 | ||||||||
\(106\) | 14.2211 | − | 6.50320i | 1.38127 | − | 0.631647i | ||||
\(107\) | 4.71288 | 0.455611 | 0.227806 | − | 0.973707i | \(-0.426845\pi\) | ||||
0.227806 | + | 0.973707i | \(0.426845\pi\) | |||||||
\(108\) | −1.51282 | − | 1.30820i | −0.145571 | − | 0.125881i | ||||
\(109\) | − | 10.3442i | − | 0.990799i | −0.868665 | − | 0.495399i | \(-0.835022\pi\) | ||
0.868665 | − | 0.495399i | \(-0.164978\pi\) | |||||||
\(110\) | 4.91584 | − | 2.24798i | 0.468707 | − | 0.214337i | ||||
\(111\) | 1.86514 | 0.177032 | ||||||||
\(112\) | −1.97122 | − | 13.5166i | −0.186263 | − | 1.27720i | ||||
\(113\) | − | 15.1580i | − | 1.42594i | −0.701194 | − | 0.712971i | \(-0.747349\pi\) | ||
0.701194 | − | 0.712971i | \(-0.252651\pi\) | |||||||
\(114\) | −9.41677 | + | 4.30623i | −0.881961 | + | 0.403316i | ||||
\(115\) | 1.44878 | − | 10.8706i | 0.135099 | − | 1.01369i | ||||
\(116\) | 8.05555 | − | 9.31555i | 0.747939 | − | 0.864927i | ||||
\(117\) | −0.215808 | −0.0199514 | ||||||||
\(118\) | −5.05646 | + | 2.31229i | −0.465485 | + | 0.212863i | ||||
\(119\) | 0.760547i | 0.0697192i | ||||||||
\(120\) | 6.20857 | + | 1.81281i | 0.566763 | + | 0.165486i | ||||
\(121\) | −8.20611 | −0.746010 | ||||||||
\(122\) | 12.7310 | − | 5.82183i | 1.15261 | − | 0.527084i | ||||
\(123\) | − | 8.94190i | − | 0.806264i | ||||||
\(124\) | 5.05169 | + | 4.36841i | 0.453656 | + | 0.392295i | ||||
\(125\) | 10.9097i | 0.975797i | ||||||||
\(126\) | 2.00842 | + | 4.39196i | 0.178924 | + | 0.391267i | ||||
\(127\) | 19.6957i | 1.74771i | 0.486189 | + | 0.873853i | \(0.338387\pi\) | ||||
−0.486189 | + | 0.873853i | \(0.661613\pi\) | |||||||
\(128\) | 1.57059 | − | 11.2042i | 0.138822 | − | 0.990317i | ||||
\(129\) | − | 2.67923i | − | 0.235893i | ||||||
\(130\) | 0.634689 | − | 0.290239i | 0.0556659 | − | 0.0254557i | ||||
\(131\) | 15.1167i | 1.32075i | 0.750936 | + | 0.660375i | \(0.229602\pi\) | ||||
−0.750936 | + | 0.660375i | \(0.770398\pi\) | |||||||
\(132\) | 2.52866 | + | 2.18664i | 0.220092 | + | 0.190323i | ||||
\(133\) | 25.0034 | 2.16807 | ||||||||
\(134\) | 1.14231 | + | 2.49799i | 0.0986809 | + | 0.215793i | ||||
\(135\) | −2.28672 | −0.196809 | ||||||||
\(136\) | −0.176558 | + | 0.604682i | −0.0151397 | + | 0.0518511i | ||||
\(137\) | − | 8.64369i | − | 0.738480i | −0.929334 | − | 0.369240i | \(-0.879618\pi\) | ||
0.929334 | − | 0.369240i | \(-0.120382\pi\) | |||||||
\(138\) | 6.48656 | − | 1.98103i | 0.552173 | − | 0.168637i | ||||
\(139\) | − | 12.0852i | − | 1.02506i | −0.858670 | − | 0.512528i | \(-0.828709\pi\) | ||
0.858670 | − | 0.512528i | \(-0.171291\pi\) | |||||||
\(140\) | −11.8135 | − | 10.2156i | −0.998421 | − | 0.863376i | ||||
\(141\) | −6.03026 | −0.507839 | ||||||||
\(142\) | −11.5103 | + | 5.26361i | −0.965927 | + | 0.441712i | ||||
\(143\) | 0.360721 | 0.0301650 | ||||||||
\(144\) | 0.577241 | + | 3.95813i | 0.0481034 | + | 0.329844i | ||||
\(145\) | − | 14.0810i | − | 1.16937i | ||||||
\(146\) | 8.60505 | + | 18.8173i | 0.712159 | + | 1.55733i | ||||
\(147\) | − | 4.66154i | − | 0.384477i | ||||||
\(148\) | −2.82162 | − | 2.43997i | −0.231936 | − | 0.200565i | ||||
\(149\) | 6.26416i | 0.513180i | 0.966520 | + | 0.256590i | \(0.0825990\pi\) | ||||
−0.966520 | + | 0.256590i | \(0.917401\pi\) | |||||||
\(150\) | 0.294628 | − | 0.134732i | 0.0240563 | − | 0.0110008i | ||||
\(151\) | − | 7.96308i | − | 0.648026i | −0.946053 | − | 0.324013i | \(-0.894968\pi\) | ||
0.946053 | − | 0.324013i | \(-0.105032\pi\) | |||||||
\(152\) | 19.8793 | + | 5.80444i | 1.61242 | + | 0.470802i | ||||
\(153\) | − | 0.222714i | − | 0.0180054i | ||||||
\(154\) | −3.35705 | − | 7.34113i | −0.270519 | − | 0.591565i | ||||
\(155\) | 7.63595 | 0.613334 | ||||||||
\(156\) | 0.326478 | + | 0.282319i | 0.0261392 | + | 0.0226036i | ||||
\(157\) | − | 14.6161i | − | 1.16649i | −0.812296 | − | 0.583245i | \(-0.801783\pi\) | ||
0.812296 | − | 0.583245i | \(-0.198217\pi\) | |||||||
\(158\) | 2.44185 | + | 5.33978i | 0.194263 | + | 0.424810i | ||||
\(159\) | 11.0574 | 0.876905 | ||||||||
\(160\) | −7.02094 | − | 10.8645i | −0.555054 | − | 0.858913i | ||||
\(161\) | −16.2337 | − | 2.16355i | −1.27940 | − | 0.170512i | ||||
\(162\) | −0.588134 | − | 1.28612i | −0.0462082 | − | 0.101047i | ||||
\(163\) | 6.24865i | 0.489432i | 0.969595 | + | 0.244716i | \(0.0786947\pi\) | ||||
−0.969595 | + | 0.244716i | \(0.921305\pi\) | |||||||
\(164\) | −11.6978 | + | 13.5275i | −0.913442 | + | 1.05632i | ||||
\(165\) | 3.82223 | 0.297560 | ||||||||
\(166\) | 8.88749 | + | 19.4350i | 0.689803 | + | 1.50844i | ||||
\(167\) | − | 20.4559i | − | 1.58293i | −0.611216 | − | 0.791463i | \(-0.709320\pi\) | ||
0.611216 | − | 0.791463i | \(-0.290680\pi\) | |||||||
\(168\) | 2.70718 | − | 9.27165i | 0.208863 | − | 0.715323i | ||||
\(169\) | −12.9534 | −0.996417 | ||||||||
\(170\) | 0.299528 | + | 0.655000i | 0.0229727 | + | 0.0502362i | ||||
\(171\) | −7.32186 | −0.559916 | ||||||||
\(172\) | −3.50496 | + | 4.05319i | −0.267251 | + | 0.309053i | ||||
\(173\) | −12.6233 | −0.959733 | −0.479867 | − | 0.877341i | \(-0.659315\pi\) | ||||
−0.479867 | + | 0.877341i | \(0.659315\pi\) | |||||||
\(174\) | 7.91959 | − | 3.62158i | 0.600382 | − | 0.274551i | ||||
\(175\) | −0.782297 | −0.0591361 | ||||||||
\(176\) | −0.964853 | − | 6.61598i | −0.0727285 | − | 0.498698i | ||||
\(177\) | −3.93157 | −0.295515 | ||||||||
\(178\) | 14.4685 | − | 6.61634i | 1.08446 | − | 0.495915i | ||||
\(179\) | − | 10.9656i | − | 0.819609i | −0.912173 | − | 0.409805i | \(-0.865597\pi\) | ||
0.912173 | − | 0.409805i | \(-0.134403\pi\) | |||||||
\(180\) | 3.45939 | + | 2.99148i | 0.257848 | + | 0.222972i | ||||
\(181\) | − | 0.836647i | − | 0.0621875i | −0.999516 | − | 0.0310937i | \(-0.990101\pi\) | ||
0.999516 | − | 0.0310937i | \(-0.00989904\pi\) | |||||||
\(182\) | −0.433432 | − | 0.947820i | −0.0321281 | − | 0.0702571i | ||||
\(183\) | 9.89882 | 0.731741 | ||||||||
\(184\) | −12.4046 | − | 5.48876i | −0.914478 | − | 0.404636i | ||||
\(185\) | −4.26506 | −0.313573 | ||||||||
\(186\) | 1.96393 | + | 4.29468i | 0.144002 | + | 0.314901i | ||||
\(187\) | 0.372265i | 0.0272227i | ||||||||
\(188\) | 9.12268 | + | 7.88876i | 0.665340 | + | 0.575347i | ||||
\(189\) | 3.41490i | 0.248397i | ||||||||
\(190\) | 21.5335 | − | 9.84714i | 1.56220 | − | 0.714387i | ||||
\(191\) | 2.31708 | 0.167658 | 0.0838289 | − | 0.996480i | \(-0.473285\pi\) | ||||
0.0838289 | + | 0.996480i | \(0.473285\pi\) | |||||||
\(192\) | 4.30475 | − | 6.74308i | 0.310669 | − | 0.486640i | ||||
\(193\) | 17.7641 | 1.27869 | 0.639344 | − | 0.768921i | \(-0.279206\pi\) | ||||
0.639344 | + | 0.768921i | \(0.279206\pi\) | |||||||
\(194\) | −21.0118 | + | 9.60858i | −1.50856 | + | 0.689856i | ||||
\(195\) | 0.493492 | 0.0353397 | ||||||||
\(196\) | −6.09821 | + | 7.05206i | −0.435587 | + | 0.503719i | ||||
\(197\) | 22.6018 | 1.61031 | 0.805157 | − | 0.593061i | \(-0.202081\pi\) | ||||
0.805157 | + | 0.593061i | \(0.202081\pi\) | |||||||
\(198\) | 0.983061 | + | 2.14974i | 0.0698631 | + | 0.152775i | ||||
\(199\) | −8.34906 | −0.591849 | −0.295925 | − | 0.955211i | \(-0.595628\pi\) | ||||
−0.295925 | + | 0.955211i | \(0.595628\pi\) | |||||||
\(200\) | −0.621975 | − | 0.181607i | −0.0439803 | − | 0.0128416i | ||||
\(201\) | 1.94227i | 0.136997i | ||||||||
\(202\) | 1.52906 | + | 3.34372i | 0.107584 | + | 0.235263i | ||||
\(203\) | −21.0281 | −1.47588 | ||||||||
\(204\) | −0.291354 | + | 0.336926i | −0.0203989 | + | 0.0235896i | ||||
\(205\) | 20.4476i | 1.42812i | ||||||||
\(206\) | 9.85652 | + | 21.5540i | 0.686736 | + | 1.50174i | ||||
\(207\) | 4.75380 | + | 0.633562i | 0.330412 | + | 0.0440356i | ||||
\(208\) | −0.124573 | − | 0.854196i | −0.00863759 | − | 0.0592278i | ||||
\(209\) | 12.2384 | 0.846550 | ||||||||
\(210\) | −4.59269 | − | 10.0432i | −0.316926 | − | 0.693046i | ||||
\(211\) | 13.6444i | 0.939318i | 0.882848 | + | 0.469659i | \(0.155623\pi\) | ||||
−0.882848 | + | 0.469659i | \(0.844377\pi\) | |||||||
\(212\) | −16.7278 | − | 14.4652i | −1.14887 | − | 0.993474i | ||||
\(213\) | −8.94968 | −0.613222 | ||||||||
\(214\) | −2.77180 | − | 6.06132i | −0.189477 | − | 0.414343i | ||||
\(215\) | 6.12665i | 0.417834i | ||||||||
\(216\) | −0.792755 | + | 2.71506i | −0.0539402 | + | 0.184736i | ||||
\(217\) | − | 11.4032i | − | 0.774102i | ||||||
\(218\) | −13.3039 | + | 6.08380i | −0.901055 | + | 0.412047i | ||||
\(219\) | 14.6311i | 0.988679i | ||||||||
\(220\) | −5.78234 | − | 5.00023i | −0.389846 | − | 0.337116i | ||||
\(221\) | 0.0480635i | 0.00323310i | ||||||||
\(222\) | −1.09695 | − | 2.39879i | −0.0736227 | − | 0.160996i | ||||
\(223\) | 11.6016i | 0.776904i | 0.921469 | + | 0.388452i | \(0.126990\pi\) | ||||
−0.921469 | + | 0.388452i | \(0.873010\pi\) | |||||||
\(224\) | −16.2246 | + | 10.4848i | −1.08405 | + | 0.700545i | ||||
\(225\) | 0.229084 | 0.0152722 | ||||||||
\(226\) | −19.4949 | + | 8.91491i | −1.29678 | + | 0.593011i | ||||
\(227\) | 8.50129 | 0.564251 | 0.282125 | − | 0.959378i | \(-0.408961\pi\) | ||||
0.282125 | + | 0.959378i | \(0.408961\pi\) | |||||||
\(228\) | 11.0766 | + | 9.57843i | 0.733569 | + | 0.634347i | ||||
\(229\) | 24.5691i | 1.62357i | 0.583955 | + | 0.811786i | \(0.301505\pi\) | ||||
−0.583955 | + | 0.811786i | \(0.698495\pi\) | |||||||
\(230\) | −14.8329 | + | 4.53007i | −0.978056 | + | 0.298704i | ||||
\(231\) | − | 5.70798i | − | 0.375557i | ||||||
\(232\) | −16.7186 | − | 4.88159i | −1.09763 | − | 0.320492i | ||||
\(233\) | 1.51528 | 0.0992694 | 0.0496347 | − | 0.998767i | \(-0.484194\pi\) | ||||
0.0496347 | + | 0.998767i | \(0.484194\pi\) | |||||||
\(234\) | 0.126924 | + | 0.277554i | 0.00829728 | + | 0.0181443i | ||||
\(235\) | 13.7895 | 0.899528 | ||||||||
\(236\) | 5.94775 | + | 5.14327i | 0.387166 | + | 0.334798i | ||||
\(237\) | 4.15186i | 0.269692i | ||||||||
\(238\) | 0.978153 | − | 0.447303i | 0.0634042 | − | 0.0289944i | ||||
\(239\) | − | 0.931528i | − | 0.0602555i | −0.999546 | − | 0.0301278i | \(-0.990409\pi\) | ||
0.999546 | − | 0.0301278i | \(-0.00959141\pi\) | |||||||
\(240\) | −1.31999 | − | 9.05113i | −0.0852048 | − | 0.584248i | ||||
\(241\) | 8.72544i | 0.562055i | 0.959700 | + | 0.281027i | \(0.0906752\pi\) | ||||
−0.959700 | + | 0.281027i | \(0.909325\pi\) | |||||||
\(242\) | 4.82629 | + | 10.5540i | 0.310246 | + | 0.678439i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −14.9751 | − | 12.9496i | −0.958683 | − | 0.829013i | ||||
\(245\) | 10.6596i | 0.681019i | ||||||||
\(246\) | −11.5003 | + | 5.25903i | −0.733234 | + | 0.335304i | ||||
\(247\) | 1.58011 | 0.100540 | ||||||||
\(248\) | 2.64722 | − | 9.06628i | 0.168098 | − | 0.575710i | ||||
\(249\) | 15.1113i | 0.957642i | ||||||||
\(250\) | 14.0312 | − | 6.41639i | 0.887412 | − | 0.405808i | ||||
\(251\) | 3.46463 | 0.218685 | 0.109343 | − | 0.994004i | \(-0.465125\pi\) | ||||
0.109343 | + | 0.994004i | \(0.465125\pi\) | |||||||
\(252\) | 4.46736 | − | 5.16612i | 0.281417 | − | 0.325435i | ||||
\(253\) | −7.94594 | − | 1.05899i | −0.499557 | − | 0.0665783i | ||||
\(254\) | 25.3309 | − | 11.5837i | 1.58940 | − | 0.726825i | ||||
\(255\) | 0.509285i | 0.0318927i | ||||||||
\(256\) | −15.3336 | + | 4.56959i | −0.958349 | + | 0.285599i | ||||
\(257\) | −2.26338 | −0.141186 | −0.0705928 | − | 0.997505i | \(-0.522489\pi\) | ||||
−0.0705928 | + | 0.997505i | \(0.522489\pi\) | |||||||
\(258\) | −3.44581 | + | 1.57575i | −0.214527 | + | 0.0981017i | ||||
\(259\) | 6.36928i | 0.395768i | ||||||||
\(260\) | −0.746564 | − | 0.645585i | −0.0462999 | − | 0.0400375i | ||||
\(261\) | 6.15775 | 0.381155 | ||||||||
\(262\) | 19.4418 | − | 8.89062i | 1.20112 | − | 0.549265i | ||||
\(263\) | −1.20387 | −0.0742340 | −0.0371170 | − | 0.999311i | \(-0.511817\pi\) | ||||
−0.0371170 | + | 0.999311i | \(0.511817\pi\) | |||||||
\(264\) | 1.32508 | − | 4.53820i | 0.0815533 | − | 0.279307i | ||||
\(265\) | −25.2851 | −1.55325 | ||||||||
\(266\) | −14.7054 | − | 32.1573i | −0.901643 | − | 1.97169i | ||||
\(267\) | 11.2497 | 0.688471 | ||||||||
\(268\) | 2.54087 | − | 2.93830i | 0.155208 | − | 0.179485i | ||||
\(269\) | 16.0520 | 0.978710 | 0.489355 | − | 0.872085i | \(-0.337232\pi\) | ||||
0.489355 | + | 0.872085i | \(0.337232\pi\) | |||||||
\(270\) | 1.34490 | + | 2.94099i | 0.0818478 | + | 0.178983i | ||||
\(271\) | − | 19.4504i | − | 1.18152i | −0.806846 | − | 0.590762i | \(-0.798827\pi\) | ||
0.806846 | − | 0.590762i | \(-0.201173\pi\) | |||||||
\(272\) | 0.881532 | − | 0.128560i | 0.0534507 | − | 0.00779508i | ||||
\(273\) | − | 0.736962i | − | 0.0446030i | ||||||
\(274\) | −11.1168 | + | 5.08365i | −0.671590 | + | 0.307114i | ||||
\(275\) | −0.382911 | −0.0230904 | ||||||||
\(276\) | −6.36281 | − | 7.17737i | −0.382996 | − | 0.432027i | ||||
\(277\) | −10.4753 | −0.629402 | −0.314701 | − | 0.949191i | \(-0.601904\pi\) | ||||
−0.314701 | + | 0.949191i | \(0.601904\pi\) | |||||||
\(278\) | −15.5430 | + | 7.10774i | −0.932209 | + | 0.426294i | ||||
\(279\) | 3.33926i | 0.199916i | ||||||||
\(280\) | −6.19056 | + | 21.2017i | −0.369957 | + | 1.26704i | ||||
\(281\) | − | 5.01591i | − | 0.299224i | −0.988745 | − | 0.149612i | \(-0.952198\pi\) | ||
0.988745 | − | 0.149612i | \(-0.0478025\pi\) | |||||||
\(282\) | 3.54660 | + | 7.75562i | 0.211197 | + | 0.461840i | ||||
\(283\) | −5.75726 | −0.342234 | −0.171117 | − | 0.985251i | \(-0.554738\pi\) | ||||
−0.171117 | + | 0.985251i | \(0.554738\pi\) | |||||||
\(284\) | 13.5392 | + | 11.7079i | 0.803406 | + | 0.694739i | ||||
\(285\) | 16.7430 | 0.991771 | ||||||||
\(286\) | −0.212152 | − | 0.463930i | −0.0125448 | − | 0.0274327i | ||||
\(287\) | 30.5357 | 1.80246 | ||||||||
\(288\) | 4.75113 | − | 3.07031i | 0.279963 | − | 0.180920i | ||||
\(289\) | 16.9504 | 0.997082 | ||||||||
\(290\) | −18.1099 | + | 8.28153i | −1.06345 | + | 0.486308i | ||||
\(291\) | −16.3374 | −0.957715 | ||||||||
\(292\) | 19.1404 | − | 22.1342i | 1.12011 | − | 1.29531i | ||||
\(293\) | 1.86241i | 0.108803i | 0.998519 | + | 0.0544017i | \(0.0173252\pi\) | ||||
−0.998519 | + | 0.0544017i | \(0.982675\pi\) | |||||||
\(294\) | −5.99529 | + | 2.74161i | −0.349652 | + | 0.159894i | ||||
\(295\) | 8.99039 | 0.523441 | ||||||||
\(296\) | −1.47860 | + | 5.06397i | −0.0859420 | + | 0.294337i | ||||
\(297\) | 1.67149i | 0.0969898i | ||||||||
\(298\) | 8.05644 | − | 3.68416i | 0.466697 | − | 0.213418i | ||||
\(299\) | −1.02591 | − | 0.136728i | −0.0593297 | − | 0.00790716i | ||||
\(300\) | −0.346562 | − | 0.299686i | −0.0200088 | − | 0.0173024i | ||||
\(301\) | 9.14931 | 0.527357 | ||||||||
\(302\) | −10.2415 | + | 4.68336i | −0.589330 | + | 0.269497i | ||||
\(303\) | 2.59985i | 0.149358i | ||||||||
\(304\) | −4.22647 | − | 28.9809i | −0.242405 | − | 1.66217i | ||||
\(305\) | −22.6358 | −1.29612 | ||||||||
\(306\) | −0.286437 | + | 0.130986i | −0.0163745 | + | 0.00748796i | ||||
\(307\) | − | 29.6535i | − | 1.69242i | −0.532852 | − | 0.846208i | \(-0.678880\pi\) | ||
0.532852 | − | 0.846208i | \(-0.321120\pi\) | |||||||
\(308\) | −7.46716 | + | 8.63513i | −0.425481 | + | 0.492032i | ||||
\(309\) | 16.7590i | 0.953385i | ||||||||
\(310\) | −4.49096 | − | 9.82073i | −0.255069 | − | 0.557780i | ||||
\(311\) | − | 1.49246i | − | 0.0846297i | −0.999104 | − | 0.0423149i | \(-0.986527\pi\) | ||
0.999104 | − | 0.0423149i | \(-0.0134733\pi\) | |||||||
\(312\) | 0.171083 | − | 0.585931i | 0.00968566 | − | 0.0331718i | ||||
\(313\) | 26.6881i | 1.50850i | 0.656586 | + | 0.754252i | \(0.272000\pi\) | ||||
−0.656586 | + | 0.754252i | \(0.728000\pi\) | |||||||
\(314\) | −18.7980 | + | 8.59621i | −1.06083 | + | 0.485112i | ||||
\(315\) | − | 7.80892i | − | 0.439983i | ||||||
\(316\) | 5.43145 | − | 6.28101i | 0.305543 | − | 0.353335i | ||||
\(317\) | −10.1157 | −0.568155 | −0.284077 | − | 0.958801i | \(-0.591687\pi\) | ||||
−0.284077 | + | 0.958801i | \(0.591687\pi\) | |||||||
\(318\) | −6.50320 | − | 14.2211i | −0.364682 | − | 0.797477i | ||||
\(319\) | −10.2926 | −0.576276 | ||||||||
\(320\) | −9.84376 | + | 15.4195i | −0.550283 | + | 0.861978i | ||||
\(321\) | − | 4.71288i | − | 0.263047i | ||||||
\(322\) | 6.76504 | + | 22.1510i | 0.377001 | + | 1.23442i | ||||
\(323\) | 1.63068i | 0.0907336i | ||||||||
\(324\) | −1.30820 | + | 1.51282i | −0.0726776 | + | 0.0840455i | ||||
\(325\) | −0.0494380 | −0.00274233 | ||||||||
\(326\) | 8.03650 | − | 3.67504i | 0.445101 | − | 0.203542i | ||||
\(327\) | −10.3442 | −0.572038 | ||||||||
\(328\) | 24.2778 | + | 7.08874i | 1.34052 | + | 0.391410i | ||||
\(329\) | − | 20.5927i | − | 1.13531i | ||||||
\(330\) | −2.24798 | − | 4.91584i | −0.123747 | − | 0.270608i | ||||
\(331\) | 7.15217i | 0.393119i | 0.980492 | + | 0.196559i | \(0.0629769\pi\) | ||||
−0.980492 | + | 0.196559i | \(0.937023\pi\) | |||||||
\(332\) | 19.7686 | − | 22.8607i | 1.08494 | − | 1.25464i | ||||
\(333\) | − | 1.86514i | − | 0.102209i | ||||||
\(334\) | −26.3087 | + | 12.0308i | −1.43955 | + | 0.658297i | ||||
\(335\) | − | 4.44142i | − | 0.242661i | ||||||
\(336\) | −13.5166 | + | 1.97122i | −0.737392 | + | 0.107539i | ||||
\(337\) | − | 24.7318i | − | 1.34723i | −0.739084 | − | 0.673613i | \(-0.764741\pi\) | ||
0.739084 | − | 0.673613i | \(-0.235259\pi\) | |||||||
\(338\) | 7.61835 | + | 16.6596i | 0.414384 | + | 0.906164i | ||||
\(339\) | −15.1580 | −0.823267 | ||||||||
\(340\) | 0.666245 | − | 0.770456i | 0.0361322 | − | 0.0417838i | ||||
\(341\) | − | 5.58155i | − | 0.302258i | ||||||
\(342\) | 4.30623 | + | 9.41677i | 0.232854 | + | 0.509201i | ||||
\(343\) | −7.98561 | −0.431182 | ||||||||
\(344\) | 7.27427 | + | 2.12398i | 0.392202 | + | 0.114517i | ||||
\(345\) | −10.8706 | − | 1.44878i | −0.585253 | − | 0.0779996i | ||||
\(346\) | 7.42420 | + | 16.2351i | 0.399128 | + | 0.872803i | ||||
\(347\) | − | 2.97378i | − | 0.159641i | −0.996809 | − | 0.0798205i | \(-0.974565\pi\) | ||
0.996809 | − | 0.0798205i | \(-0.0254347\pi\) | |||||||
\(348\) | −9.31555 | − | 8.05555i | −0.499366 | − | 0.431823i | ||||
\(349\) | −26.6834 | −1.42833 | −0.714164 | − | 0.699978i | \(-0.753193\pi\) | ||||
−0.714164 | + | 0.699978i | \(0.753193\pi\) | |||||||
\(350\) | 0.460095 | + | 1.00613i | 0.0245931 | + | 0.0537797i | ||||
\(351\) | 0.215808i | 0.0115190i | ||||||||
\(352\) | −7.94147 | + | 5.13200i | −0.423282 | + | 0.273536i | ||||
\(353\) | 13.4160 | 0.714059 | 0.357030 | − | 0.934093i | \(-0.383790\pi\) | ||||
0.357030 | + | 0.934093i | \(0.383790\pi\) | |||||||
\(354\) | 2.31229 | + | 5.05646i | 0.122897 | + | 0.268748i | ||||
\(355\) | 20.4654 | 1.08619 | ||||||||
\(356\) | −17.0188 | − | 14.7168i | −0.901993 | − | 0.779991i | ||||
\(357\) | 0.760547 | 0.0402524 | ||||||||
\(358\) | −14.1031 | + | 6.44925i | −0.745371 | + | 0.340854i | ||||
\(359\) | 31.0658 | 1.63959 | 0.819796 | − | 0.572656i | \(-0.194087\pi\) | ||||
0.819796 | + | 0.572656i | \(0.194087\pi\) | |||||||
\(360\) | 1.81281 | − | 6.20857i | 0.0955434 | − | 0.327221i | ||||
\(361\) | 34.6096 | 1.82156 | ||||||||
\(362\) | −1.07603 | + | 0.492060i | −0.0565547 | + | 0.0258621i | ||||
\(363\) | 8.20611i | 0.430709i | ||||||||
\(364\) | −0.964092 | + | 1.11489i | −0.0505321 | + | 0.0584361i | ||||
\(365\) | − | 33.4572i | − | 1.75123i | ||||||
\(366\) | −5.82183 | − | 12.7310i | −0.304312 | − | 0.665462i | ||||
\(367\) | −12.2462 | −0.639249 | −0.319625 | − | 0.947544i | \(-0.603557\pi\) | ||||
−0.319625 | + | 0.947544i | \(0.603557\pi\) | |||||||
\(368\) | 0.236366 | + | 19.1819i | 0.0123214 | + | 0.999924i | ||||
\(369\) | −8.94190 | −0.465497 | ||||||||
\(370\) | 2.50842 | + | 5.48537i | 0.130407 | + | 0.285171i | ||||
\(371\) | 37.7598i | 1.96039i | ||||||||
\(372\) | 4.36841 | − | 5.05169i | 0.226492 | − | 0.261918i | ||||
\(373\) | 26.3387i | 1.36377i | 0.731461 | + | 0.681884i | \(0.238839\pi\) | ||||
−0.731461 | + | 0.681884i | \(0.761161\pi\) | |||||||
\(374\) | 0.478777 | − | 0.218942i | 0.0247569 | − | 0.0113212i | ||||
\(375\) | 10.9097 | 0.563377 | ||||||||
\(376\) | 4.78052 | − | 16.3725i | 0.246536 | − | 0.844347i | ||||
\(377\) | −1.32889 | −0.0684413 | ||||||||
\(378\) | 4.39196 | − | 2.00842i | 0.225898 | − | 0.103302i | ||||
\(379\) | 27.3785 | 1.40634 | 0.703169 | − | 0.711023i | \(-0.251768\pi\) | ||||
0.703169 | + | 0.711023i | \(0.251768\pi\) | |||||||
\(380\) | −25.3292 | − | 21.9032i | −1.29936 | − | 1.12361i | ||||
\(381\) | 19.6957 | 1.00904 | ||||||||
\(382\) | −1.36275 | − | 2.98003i | −0.0697244 | − | 0.152472i | ||||
\(383\) | 7.27236 | 0.371600 | 0.185800 | − | 0.982588i | \(-0.440512\pi\) | ||||
0.185800 | + | 0.982588i | \(0.440512\pi\) | |||||||
\(384\) | −11.2042 | − | 1.57059i | −0.571760 | − | 0.0801487i | ||||
\(385\) | 13.0525i | 0.665219i | ||||||||
\(386\) | −10.4477 | − | 22.8467i | −0.531772 | − | 1.16287i | ||||
\(387\) | −2.67923 | −0.136193 | ||||||||
\(388\) | 24.7155 | + | 21.3725i | 1.25474 | + | 1.08503i | ||||
\(389\) | − | 2.95190i | − | 0.149668i | −0.997196 | − | 0.0748338i | \(-0.976157\pi\) | ||
0.997196 | − | 0.0748338i | \(-0.0238426\pi\) | |||||||
\(390\) | −0.290239 | − | 0.634689i | −0.0146968 | − | 0.0321387i | ||||
\(391\) | 0.141103 | − | 1.05874i | 0.00713590 | − | 0.0535427i | ||||
\(392\) | 12.6563 | + | 3.69546i | 0.639242 | + | 0.186649i | ||||
\(393\) | 15.1167 | 0.762535 | ||||||||
\(394\) | −13.2929 | − | 29.0686i | −0.669687 | − | 1.46446i | ||||
\(395\) | − | 9.49414i | − | 0.477702i | ||||||
\(396\) | 2.18664 | − | 2.52866i | 0.109883 | − | 0.127070i | ||||
\(397\) | −6.45977 | −0.324206 | −0.162103 | − | 0.986774i | \(-0.551828\pi\) | ||||
−0.162103 | + | 0.986774i | \(0.551828\pi\) | |||||||
\(398\) | 4.91036 | + | 10.7379i | 0.246134 | + | 0.538241i | ||||
\(399\) | − | 25.0034i | − | 1.25174i | ||||||
\(400\) | 0.132236 | + | 0.906742i | 0.00661182 | + | 0.0453371i | ||||
\(401\) | − | 26.1702i | − | 1.30688i | −0.756979 | − | 0.653439i | \(-0.773326\pi\) | ||
0.756979 | − | 0.653439i | \(-0.226674\pi\) | |||||||
\(402\) | 2.49799 | − | 1.14231i | 0.124588 | − | 0.0569735i | ||||
\(403\) | − | 0.720639i | − | 0.0358976i | ||||||
\(404\) | 3.40112 | − | 3.93311i | 0.169212 | − | 0.195679i | ||||
\(405\) | 2.28672i | 0.113628i | ||||||||
\(406\) | 12.3673 | + | 27.0446i | 0.613780 | + | 1.34220i | ||||
\(407\) | 3.11757i | 0.154532i | ||||||||
\(408\) | 0.604682 | + | 0.176558i | 0.0299362 | + | 0.00874092i | ||||
\(409\) | 31.4425 | 1.55473 | 0.777366 | − | 0.629048i | \(-0.216555\pi\) | ||||
0.777366 | + | 0.629048i | \(0.216555\pi\) | |||||||
\(410\) | 26.2980 | − | 12.0259i | 1.29877 | − | 0.593918i | ||||
\(411\) | −8.64369 | −0.426362 | ||||||||
\(412\) | 21.9240 | − | 25.3533i | 1.08012 | − | 1.24907i | ||||
\(413\) | − | 13.4259i | − | 0.660646i | ||||||
\(414\) | −1.98103 | − | 6.48656i | −0.0973626 | − | 0.318797i | ||||
\(415\) | − | 34.5554i | − | 1.69626i | ||||||
\(416\) | −1.02533 | + | 0.662597i | −0.0502710 | + | 0.0324865i | ||||
\(417\) | −12.0852 | −0.591817 | ||||||||
\(418\) | −7.19783 | − | 15.7401i | −0.352057 | − | 0.769871i | ||||
\(419\) | 8.80834 | 0.430316 | 0.215158 | − | 0.976579i | \(-0.430973\pi\) | ||||
0.215158 | + | 0.976579i | \(0.430973\pi\) | |||||||
\(420\) | −10.2156 | + | 11.8135i | −0.498470 | + | 0.576438i | ||||
\(421\) | 20.1534i | 0.982218i | 0.871098 | + | 0.491109i | \(0.163408\pi\) | ||||
−0.871098 | + | 0.491109i | \(0.836592\pi\) | |||||||
\(422\) | 17.5483 | − | 8.02472i | 0.854237 | − | 0.390637i | ||||
\(423\) | 6.03026i | 0.293201i | ||||||||
\(424\) | −8.76578 | + | 30.0214i | −0.425704 | + | 1.45797i | ||||
\(425\) | − | 0.0510202i | − | 0.00247484i | ||||||
\(426\) | 5.26361 | + | 11.5103i | 0.255023 | + | 0.557678i | ||||
\(427\) | 33.8035i | 1.63586i | ||||||||
\(428\) | −6.16537 | + | 7.12973i | −0.298015 | + | 0.344629i | ||||
\(429\) | − | 0.360721i | − | 0.0174158i | ||||||
\(430\) | 7.87959 | − | 3.60329i | 0.379988 | − | 0.173766i | ||||
\(431\) | 23.3895 | 1.12663 | 0.563317 | − | 0.826241i | \(-0.309525\pi\) | ||||
0.563317 | + | 0.826241i | \(0.309525\pi\) | |||||||
\(432\) | 3.95813 | − | 0.577241i | 0.190436 | − | 0.0277725i | ||||
\(433\) | − | 13.5765i | − | 0.652444i | −0.945293 | − | 0.326222i | \(-0.894224\pi\) | ||
0.945293 | − | 0.326222i | \(-0.105776\pi\) | |||||||
\(434\) | −14.6659 | + | 6.70663i | −0.703986 | + | 0.321929i | ||||
\(435\) | −14.0810 | −0.675134 | ||||||||
\(436\) | 15.6490 | + | 13.5323i | 0.749450 | + | 0.648080i | ||||
\(437\) | −34.8066 | − | 4.63885i | −1.66503 | − | 0.221906i | ||||
\(438\) | 18.8173 | − | 8.60505i | 0.899127 | − | 0.411165i | ||||
\(439\) | 41.3682i | 1.97440i | 0.159500 | + | 0.987198i | \(0.449012\pi\) | ||||
−0.159500 | + | 0.987198i | \(0.550988\pi\) | |||||||
\(440\) | −3.03010 | + | 10.3776i | −0.144454 | + | 0.494732i | ||||
\(441\) | −4.66154 | −0.221978 | ||||||||
\(442\) | 0.0618153 | − | 0.0282678i | 0.00294025 | − | 0.00134456i | ||||
\(443\) | − | 14.5889i | − | 0.693138i | −0.938024 | − | 0.346569i | \(-0.887347\pi\) | ||
0.938024 | − | 0.346569i | \(-0.112653\pi\) | |||||||
\(444\) | −2.43997 | + | 2.82162i | −0.115796 | + | 0.133908i | ||||
\(445\) | −25.7249 | −1.21948 | ||||||||
\(446\) | 14.9211 | − | 6.82332i | 0.706534 | − | 0.323094i | ||||
\(447\) | 6.26416 | 0.296285 | ||||||||
\(448\) | 23.0269 | + | 14.7003i | 1.08792 | + | 0.694524i | ||||
\(449\) | −26.5707 | −1.25395 | −0.626975 | − | 0.779040i | \(-0.715707\pi\) | ||||
−0.626975 | + | 0.779040i | \(0.715707\pi\) | |||||||
\(450\) | −0.134732 | − | 0.294628i | −0.00635132 | − | 0.0138889i | ||||
\(451\) | 14.9463 | 0.703794 | ||||||||
\(452\) | 22.9312 | + | 19.8296i | 1.07860 | + | 0.932706i | ||||
\(453\) | −7.96308 | −0.374138 | ||||||||
\(454\) | −4.99990 | − | 10.9337i | −0.234657 | − | 0.513142i | ||||
\(455\) | 1.68523i | 0.0790046i | ||||||||
\(456\) | 5.80444 | − | 19.8793i | 0.271818 | − | 0.930932i | ||||
\(457\) | 25.5083i | 1.19323i | 0.802529 | + | 0.596613i | \(0.203487\pi\) | ||||
−0.802529 | + | 0.596613i | \(0.796513\pi\) | |||||||
\(458\) | 31.5988 | − | 14.4499i | 1.47651 | − | 0.675201i | ||||
\(459\) | −0.222714 | −0.0103954 | ||||||||
\(460\) | 14.5500 | + | 16.4126i | 0.678395 | + | 0.765243i | ||||
\(461\) | 4.44751 | 0.207141 | 0.103570 | − | 0.994622i | \(-0.466973\pi\) | ||||
0.103570 | + | 0.994622i | \(0.466973\pi\) | |||||||
\(462\) | −7.34113 | + | 3.35705i | −0.341540 | + | 0.156184i | ||||
\(463\) | − | 26.1370i | − | 1.21469i | −0.794438 | − | 0.607345i | \(-0.792234\pi\) | ||
0.794438 | − | 0.607345i | \(-0.207766\pi\) | |||||||
\(464\) | 3.55450 | + | 24.3732i | 0.165014 | + | 1.13150i | ||||
\(465\) | − | 7.63595i | − | 0.354109i | ||||||
\(466\) | −0.891188 | − | 1.94883i | −0.0412835 | − | 0.0902778i | ||||
\(467\) | −36.8413 | −1.70481 | −0.852407 | − | 0.522879i | \(-0.824858\pi\) | ||||
−0.852407 | + | 0.522879i | \(0.824858\pi\) | |||||||
\(468\) | 0.282319 | − | 0.326478i | 0.0130502 | − | 0.0150915i | ||||
\(469\) | −6.63266 | −0.306268 | ||||||||
\(470\) | −8.11007 | − | 17.7349i | −0.374090 | − | 0.818051i | ||||
\(471\) | −14.6161 | −0.673474 | ||||||||
\(472\) | 3.11677 | − | 10.6744i | 0.143461 | − | 0.491331i | ||||
\(473\) | 4.47831 | 0.205913 | ||||||||
\(474\) | 5.33978 | − | 2.44185i | 0.245264 | − | 0.112158i | ||||
\(475\) | −1.67732 | −0.0769606 | ||||||||
\(476\) | −1.15057 | − | 0.994945i | −0.0527363 | − | 0.0456032i | ||||
\(477\) | − | 11.0574i | − | 0.506281i | ||||||
\(478\) | −1.19805 | + | 0.547863i | −0.0547977 | + | 0.0250587i | ||||
\(479\) | −3.16502 | −0.144613 | −0.0723067 | − | 0.997382i | \(-0.523036\pi\) | ||||
−0.0723067 | + | 0.997382i | \(0.523036\pi\) | |||||||
\(480\) | −10.8645 | + | 7.02094i | −0.495894 | + | 0.320460i | ||||
\(481\) | 0.402513i | 0.0183530i | ||||||||
\(482\) | 11.2219 | − | 5.13173i | 0.511145 | − | 0.233744i | ||||
\(483\) | −2.16355 | + | 16.2337i | −0.0984449 | + | 0.738661i | ||||
\(484\) | 10.7352 | − | 12.4144i | 0.487964 | − | 0.564289i | ||||
\(485\) | 37.3590 | 1.69639 | ||||||||
\(486\) | −1.28612 | + | 0.588134i | −0.0583395 | + | 0.0266783i | ||||
\(487\) | 7.18055i | 0.325382i | 0.986677 | + | 0.162691i | \(0.0520173\pi\) | ||||
−0.986677 | + | 0.162691i | \(0.947983\pi\) | |||||||
\(488\) | −7.84734 | + | 26.8759i | −0.355232 | + | 1.21661i | ||||
\(489\) | 6.24865 | 0.282574 | ||||||||
\(490\) | 13.7095 | − | 6.26929i | 0.619334 | − | 0.283218i | ||||
\(491\) | − | 6.31534i | − | 0.285007i | −0.989794 | − | 0.142504i | \(-0.954485\pi\) | ||
0.989794 | − | 0.142504i | \(-0.0455152\pi\) | |||||||
\(492\) | 13.5275 | + | 11.6978i | 0.609865 | + | 0.527376i | ||||
\(493\) | − | 1.37142i | − | 0.0617655i | ||||||
\(494\) | −0.929319 | − | 2.03221i | −0.0418120 | − | 0.0914336i | ||||
\(495\) | − | 3.82223i | − | 0.171797i | ||||||
\(496\) | −13.2172 | + | 1.92756i | −0.593471 | + | 0.0865498i | ||||
\(497\) | − | 30.5623i | − | 1.37090i | ||||||
\(498\) | 19.4350 | − | 8.88749i | 0.870901 | − | 0.398258i | ||||
\(499\) | 15.5187i | 0.694713i | 0.937733 | + | 0.347356i | \(0.112921\pi\) | ||||
−0.937733 | + | 0.347356i | \(0.887079\pi\) | |||||||
\(500\) | −16.5045 | − | 14.2721i | −0.738102 | − | 0.638268i | ||||
\(501\) | −20.4559 | −0.913903 | ||||||||
\(502\) | −2.03766 | − | 4.45592i | −0.0909454 | − | 0.198877i | ||||
\(503\) | −25.7887 | −1.14986 | −0.574931 | − | 0.818202i | \(-0.694971\pi\) | ||||
−0.574931 | + | 0.818202i | \(0.694971\pi\) | |||||||
\(504\) | −9.27165 | − | 2.70718i | −0.412992 | − | 0.120587i | ||||
\(505\) | − | 5.94513i | − | 0.264555i | ||||||
\(506\) | 3.31128 | + | 10.8422i | 0.147205 | + | 0.481996i | ||||
\(507\) | 12.9534i | 0.575282i | ||||||||
\(508\) | −29.7960 | − | 25.7658i | −1.32198 | − | 1.14317i | ||||
\(509\) | 15.2413 | 0.675560 | 0.337780 | − | 0.941225i | \(-0.390324\pi\) | ||||
0.337780 | + | 0.941225i | \(0.390324\pi\) | |||||||
\(510\) | 0.655000 | − | 0.299528i | 0.0290039 | − | 0.0132633i | ||||
\(511\) | −49.9638 | −2.21027 | ||||||||
\(512\) | 14.8952 | + | 17.0333i | 0.658282 | + | 0.752771i | ||||
\(513\) | 7.32186i | 0.323268i | ||||||||
\(514\) | 1.33117 | + | 2.91097i | 0.0587154 | + | 0.128397i | ||||
\(515\) | − | 38.3231i | − | 1.68872i | ||||||
\(516\) | 4.05319 | + | 3.50496i | 0.178432 | + | 0.154297i | ||||
\(517\) | − | 10.0795i | − | 0.443297i | ||||||
\(518\) | 8.19164 | − | 3.74599i | 0.359920 | − | 0.164589i | ||||
\(519\) | 12.6233i | 0.554102i | ||||||||
\(520\) | −0.391218 | + | 1.33986i | −0.0171561 | + | 0.0587567i | ||||
\(521\) | − | 16.0695i | − | 0.704017i | −0.935997 | − | 0.352008i | \(-0.885499\pi\) | ||
0.935997 | − | 0.352008i | \(-0.114501\pi\) | |||||||
\(522\) | −3.62158 | − | 7.91959i | −0.158512 | − | 0.346631i | ||||
\(523\) | −23.1547 | −1.01248 | −0.506242 | − | 0.862391i | \(-0.668966\pi\) | ||||
−0.506242 | + | 0.862391i | \(0.668966\pi\) | |||||||
\(524\) | −22.8688 | − | 19.7756i | −0.999027 | − | 0.863900i | ||||
\(525\) | 0.782297i | 0.0341422i | ||||||||
\(526\) | 0.708039 | + | 1.54832i | 0.0308720 | + | 0.0675101i | ||||
\(527\) | 0.743701 | 0.0323961 | ||||||||
\(528\) | −6.61598 | + | 0.964853i | −0.287924 | + | 0.0419898i | ||||
\(529\) | 22.1972 | + | 6.02365i | 0.965096 | + | 0.261898i | ||||
\(530\) | 14.8710 | + | 32.5196i | 0.645955 | + | 1.41256i | ||||
\(531\) | 3.93157i | 0.170616i | ||||||||
\(532\) | −32.7094 | + | 37.8256i | −1.41813 | + | 1.63995i | ||||
\(533\) | 1.92973 | 0.0835860 | ||||||||
\(534\) | −6.61634 | − | 14.4685i | −0.286317 | − | 0.626111i | ||||
\(535\) | 10.7770i | 0.465932i | ||||||||
\(536\) | −5.27337 | − | 1.53974i | −0.227775 | − | 0.0665068i | ||||
\(537\) | −10.9656 | −0.473202 | ||||||||
\(538\) | −9.44074 | − | 20.6448i | −0.407019 | − | 0.890061i | ||||
\(539\) | 7.79172 | 0.335613 | ||||||||
\(540\) | 2.99148 | − | 3.45939i | 0.128733 | − | 0.148868i | ||||
\(541\) | −4.33392 | −0.186330 | −0.0931650 | − | 0.995651i | \(-0.529698\pi\) | ||||
−0.0931650 | + | 0.995651i | \(0.529698\pi\) | |||||||
\(542\) | −25.0154 | + | 11.4394i | −1.07451 | + | 0.491365i | ||||
\(543\) | −0.836647 | −0.0359040 | ||||||||
\(544\) | −0.683802 | − | 1.05814i | −0.0293178 | − | 0.0453675i | ||||
\(545\) | 23.6544 | 1.01324 | ||||||||
\(546\) | −0.947820 | + | 0.433432i | −0.0405630 | + | 0.0185492i | ||||
\(547\) | − | 38.0780i | − | 1.62810i | −0.580797 | − | 0.814049i | \(-0.697259\pi\) | ||
0.580797 | − | 0.814049i | \(-0.302741\pi\) | |||||||
\(548\) | 13.0763 | + | 11.3076i | 0.558593 | + | 0.483039i | ||||
\(549\) | − | 9.89882i | − | 0.422471i | ||||||
\(550\) | 0.225203 | + | 0.492469i | 0.00960269 | + | 0.0209989i | ||||
\(551\) | −45.0861 | −1.92073 | ||||||||
\(552\) | −5.48876 | + | 12.4046i | −0.233617 | + | 0.527974i | ||||
\(553\) | −14.1782 | −0.602918 | ||||||||
\(554\) | 6.16090 | + | 13.4725i | 0.261751 | + | 0.572392i | ||||
\(555\) | 4.26506i | 0.181042i | ||||||||
\(556\) | 18.2828 | + | 15.8099i | 0.775362 | + | 0.670488i | ||||
\(557\) | 27.4879i | 1.16470i | 0.812938 | + | 0.582350i | \(0.197867\pi\) | ||||
−0.812938 | + | 0.582350i | \(0.802133\pi\) | |||||||
\(558\) | 4.29468 | − | 1.96393i | 0.181808 | − | 0.0831399i | ||||
\(559\) | 0.578199 | 0.0244552 | ||||||||
\(560\) | 30.9087 | − | 4.50762i | 1.30613 | − | 0.190482i | ||||
\(561\) | 0.372265 | 0.0157170 | ||||||||
\(562\) | −6.45105 | + | 2.95003i | −0.272121 | + | 0.124439i | ||||
\(563\) | −36.8387 | −1.55257 | −0.776284 | − | 0.630384i | \(-0.782898\pi\) | ||||
−0.776284 | + | 0.630384i | \(0.782898\pi\) | |||||||
\(564\) | 7.88876 | − | 9.12268i | 0.332177 | − | 0.384134i | ||||
\(565\) | 34.6620 | 1.45824 | ||||||||
\(566\) | 3.38604 | + | 7.40452i | 0.142326 | + | 0.311235i | ||||
\(567\) | 3.41490 | 0.143412 | ||||||||
\(568\) | 7.09491 | − | 24.2989i | 0.297696 | − | 1.01956i | ||||
\(569\) | 29.8461i | 1.25121i | 0.780139 | + | 0.625606i | \(0.215148\pi\) | ||||
−0.780139 | + | 0.625606i | \(0.784852\pi\) | |||||||
\(570\) | −9.84714 | − | 21.5335i | −0.412451 | − | 0.901939i | ||||
\(571\) | 4.27041 | 0.178711 | 0.0893555 | − | 0.996000i | \(-0.471519\pi\) | ||||
0.0893555 | + | 0.996000i | \(0.471519\pi\) | |||||||
\(572\) | −0.471894 | + | 0.545706i | −0.0197309 | + | 0.0228171i | ||||
\(573\) | − | 2.31708i | − | 0.0967973i | ||||||
\(574\) | −17.9591 | − | 39.2725i | −0.749597 | − | 1.63920i | ||||
\(575\) | 1.08902 | + | 0.145139i | 0.0454151 | + | 0.00605270i | ||||
\(576\) | −6.74308 | − | 4.30475i | −0.280962 | − | 0.179365i | ||||
\(577\) | −5.65262 | −0.235322 | −0.117661 | − | 0.993054i | \(-0.537540\pi\) | ||||
−0.117661 | + | 0.993054i | \(0.537540\pi\) | |||||||
\(578\) | −9.96910 | − | 21.8002i | −0.414660 | − | 0.906769i | ||||
\(579\) | − | 17.7641i | − | 0.738250i | ||||||
\(580\) | 21.3021 | + | 18.4208i | 0.884520 | + | 0.764881i | ||||
\(581\) | −51.6037 | −2.14088 | ||||||||
\(582\) | 9.60858 | + | 21.0118i | 0.398288 | + | 0.870968i | ||||
\(583\) | 18.4823i | 0.765458i | ||||||||
\(584\) | −39.7243 | − | 11.5989i | −1.64380 | − | 0.479965i | ||||
\(585\) | − | 0.493492i | − | 0.0204034i | ||||||
\(586\) | 2.39528 | − | 1.09535i | 0.0989483 | − | 0.0452484i | ||||
\(587\) | − | 18.3560i | − | 0.757632i | −0.925472 | − | 0.378816i | \(-0.876331\pi\) | ||
0.925472 | − | 0.378816i | \(-0.123669\pi\) | |||||||
\(588\) | 7.05206 | + | 6.09821i | 0.290822 | + | 0.251486i | ||||
\(589\) | − | 24.4496i | − | 1.00743i | ||||||
\(590\) | −5.28755 | − | 11.5627i | −0.217685 | − | 0.476029i | ||||
\(591\) | − | 22.6018i | − | 0.929716i | ||||||
\(592\) | 7.38248 | − | 1.07664i | 0.303418 | − | 0.0442495i | ||||
\(593\) | 6.20287 | 0.254721 | 0.127361 | − | 0.991856i | \(-0.459349\pi\) | ||||
0.127361 | + | 0.991856i | \(0.459349\pi\) | |||||||
\(594\) | 2.14974 | − | 0.983061i | 0.0882047 | − | 0.0403355i | ||||
\(595\) | −1.73916 | −0.0712985 | ||||||||
\(596\) | −9.47654 | − | 8.19475i | −0.388174 | − | 0.335670i | ||||
\(597\) | 8.34906i | 0.341704i | ||||||||
\(598\) | 0.427523 | + | 1.39985i | 0.0174827 | + | 0.0572442i | ||||
\(599\) | 10.1258i | 0.413730i | 0.978370 | + | 0.206865i | \(0.0663260\pi\) | ||||
−0.978370 | + | 0.206865i | \(0.933674\pi\) | |||||||
\(600\) | −0.181607 | + | 0.621975i | −0.00741408 | + | 0.0253920i | ||||
\(601\) | 25.2858 | 1.03143 | 0.515714 | − | 0.856761i | \(-0.327527\pi\) | ||||
0.515714 | + | 0.856761i | \(0.327527\pi\) | |||||||
\(602\) | −5.38102 | − | 11.7671i | −0.219314 | − | 0.479591i | ||||
\(603\) | 1.94227 | 0.0790953 | ||||||||
\(604\) | 12.0467 | + | 10.4173i | 0.490173 | + | 0.423873i | ||||
\(605\) | − | 18.7651i | − | 0.762909i | ||||||
\(606\) | 3.34372 | − | 1.52906i | 0.135829 | − | 0.0621139i | ||||
\(607\) | 23.2916i | 0.945379i | 0.881229 | + | 0.472689i | \(0.156717\pi\) | ||||
−0.881229 | + | 0.472689i | \(0.843283\pi\) | |||||||
\(608\) | −34.7871 | + | 22.4804i | −1.41080 | + | 0.911699i | ||||
\(609\) | 21.0281i | 0.852101i | ||||||||
\(610\) | 13.3129 | + | 29.1123i | 0.539023 | + | 1.17872i | ||||
\(611\) | − | 1.30138i | − | 0.0526481i | ||||||
\(612\) | 0.336926 | + | 0.291354i | 0.0136194 | + | 0.0117773i | ||||
\(613\) | − | 34.8237i | − | 1.40652i | −0.710934 | − | 0.703259i | \(-0.751728\pi\) | ||
0.710934 | − | 0.703259i | \(-0.248272\pi\) | |||||||
\(614\) | −38.1379 | + | 17.4403i | −1.53912 | + | 0.703831i | ||||
\(615\) | 20.4476 | 0.824527 | ||||||||
\(616\) | 15.4975 | + | 4.52503i | 0.624412 | + | 0.182319i | ||||
\(617\) | 38.6296i | 1.55517i | 0.628778 | + | 0.777585i | \(0.283556\pi\) | ||||
−0.628778 | + | 0.777585i | \(0.716444\pi\) | |||||||
\(618\) | 21.5540 | − | 9.85652i | 0.867029 | − | 0.396487i | ||||
\(619\) | −1.81828 | −0.0730829 | −0.0365414 | − | 0.999332i | \(-0.511634\pi\) | ||||
−0.0365414 | + | 0.999332i | \(0.511634\pi\) | |||||||
\(620\) | −9.98933 | + | 11.5518i | −0.401181 | + | 0.463932i | ||||
\(621\) | 0.633562 | − | 4.75380i | 0.0254240 | − | 0.190763i | ||||
\(622\) | −1.91948 | + | 0.877767i | −0.0769642 | + | 0.0351952i | ||||
\(623\) | 38.4166i | 1.53913i | ||||||||
\(624\) | −0.854196 | + | 0.124573i | −0.0341952 | + | 0.00498691i | ||||
\(625\) | −26.0929 | −1.04372 | ||||||||
\(626\) | 34.3241 | − | 15.6962i | 1.37187 | − | 0.627346i | ||||
\(627\) | − | 12.2384i | − | 0.488756i | ||||||
\(628\) | 22.1115 | + | 19.1207i | 0.882344 | + | 0.763000i | ||||
\(629\) | −0.415394 | −0.0165628 | ||||||||
\(630\) | −10.0432 | + | 4.59269i | −0.400130 | + | 0.182977i | ||||
\(631\) | 9.23992 | 0.367835 | 0.183918 | − | 0.982942i | \(-0.441122\pi\) | ||||
0.183918 | + | 0.982942i | \(0.441122\pi\) | |||||||
\(632\) | −11.2725 | − | 3.29141i | −0.448398 | − | 0.130925i | ||||
\(633\) | 13.6444 | 0.542316 | ||||||||
\(634\) | 5.94939 | + | 13.0100i | 0.236281 | + | 0.516693i | ||||
\(635\) | −45.0384 | −1.78730 | ||||||||
\(636\) | −14.4652 | + | 16.7278i | −0.573582 | + | 0.663299i | ||||
\(637\) | 1.00600 | 0.0398590 | ||||||||
\(638\) | 6.05344 | + | 13.2375i | 0.239658 | + | 0.524079i | ||||
\(639\) | 8.94968i | 0.354044i | ||||||||
\(640\) | 25.6208 | + | 3.59149i | 1.01275 | + | 0.141966i | ||||
\(641\) | 1.91640i | 0.0756931i | 0.999284 | + | 0.0378465i | \(0.0120498\pi\) | ||||
−0.999284 | + | 0.0378465i | \(0.987950\pi\) | |||||||
\(642\) | −6.06132 | + | 2.77180i | −0.239221 | + | 0.109394i | ||||
\(643\) | 25.7633 | 1.01601 | 0.508003 | − | 0.861355i | \(-0.330384\pi\) | ||||
0.508003 | + | 0.861355i | \(0.330384\pi\) | |||||||
\(644\) | 24.5100 | − | 21.7284i | 0.965829 | − | 0.856217i | ||||
\(645\) | 6.12665 | 0.241237 | ||||||||
\(646\) | 2.09725 | − | 0.959059i | 0.0825151 | − | 0.0377337i | ||||
\(647\) | 44.3852i | 1.74496i | 0.488649 | + | 0.872481i | \(0.337490\pi\) | ||||
−0.488649 | + | 0.872481i | \(0.662510\pi\) | |||||||
\(648\) | 2.71506 | + | 0.792755i | 0.106658 | + | 0.0311424i | ||||
\(649\) | − | 6.57158i | − | 0.257957i | ||||||
\(650\) | 0.0290762 | + | 0.0635831i | 0.00114046 | + | 0.00249393i | ||||
\(651\) | −11.4032 | −0.446928 | ||||||||
\(652\) | −9.45307 | − | 8.17447i | −0.370211 | − | 0.320137i | ||||
\(653\) | −1.40588 | −0.0550162 | −0.0275081 | − | 0.999622i | \(-0.508757\pi\) | ||||
−0.0275081 | + | 0.999622i | \(0.508757\pi\) | |||||||
\(654\) | 6.08380 | + | 13.3039i | 0.237895 | + | 0.520224i | ||||
\(655\) | −34.5676 | −1.35067 | ||||||||
\(656\) | −5.16163 | − | 35.3932i | −0.201528 | − | 1.38187i | ||||
\(657\) | 14.6311 | 0.570814 | ||||||||
\(658\) | −26.4847 | + | 12.1113i | −1.03248 | + | 0.472147i | ||||
\(659\) | 23.4125 | 0.912020 | 0.456010 | − | 0.889975i | \(-0.349278\pi\) | ||||
0.456010 | + | 0.889975i | \(0.349278\pi\) | |||||||
\(660\) | −5.00023 | + | 5.78234i | −0.194634 | + | 0.225077i | ||||
\(661\) | 16.2832i | 0.633343i | 0.948535 | + | 0.316671i | \(0.102565\pi\) | ||||
−0.948535 | + | 0.316671i | \(0.897435\pi\) | |||||||
\(662\) | 9.19854 | − | 4.20643i | 0.357511 | − | 0.163488i | ||||
\(663\) | 0.0480635 | 0.00186663 | ||||||||
\(664\) | −41.0281 | − | 11.9796i | −1.59220 | − | 0.464898i | ||||
\(665\) | 57.1758i | 2.21718i | ||||||||
\(666\) | −2.39879 | + | 1.09695i | −0.0929513 | + | 0.0425061i | ||||
\(667\) | 29.2727 | + | 3.90131i | 1.13344 | + | 0.151059i | ||||
\(668\) | 30.9461 | + | 26.7604i | 1.19734 | + | 1.03539i | ||||
\(669\) | 11.6016 | 0.448546 | ||||||||
\(670\) | −5.71219 | + | 2.61215i | −0.220681 | + | 0.100916i | ||||
\(671\) | 16.5458i | 0.638743i | ||||||||
\(672\) | 10.4848 | + | 16.2246i | 0.404460 | + | 0.625878i | ||||
\(673\) | −30.6829 | −1.18274 | −0.591369 | − | 0.806401i | \(-0.701412\pi\) | ||||
−0.591369 | + | 0.806401i | \(0.701412\pi\) | |||||||
\(674\) | −31.8080 | + | 14.5456i | −1.22520 | + | 0.560276i | ||||
\(675\) | − | 0.229084i | − | 0.00881743i | ||||||
\(676\) | 16.9456 | − | 19.5962i | 0.651755 | − | 0.753699i | ||||
\(677\) | 27.1779i | 1.04453i | 0.852783 | + | 0.522265i | \(0.174913\pi\) | ||||
−0.852783 | + | 0.522265i | \(0.825087\pi\) | |||||||
\(678\) | 8.91491 | + | 19.4949i | 0.342375 | + | 0.748698i | ||||
\(679\) | − | 55.7906i | − | 2.14105i | ||||||
\(680\) | −1.38274 | − | 0.403738i | −0.0530256 | − | 0.0154827i | ||||
\(681\) | − | 8.50129i | − | 0.325770i | ||||||
\(682\) | −7.17852 | + | 3.28270i | −0.274880 | + | 0.125701i | ||||
\(683\) | 7.03091i | 0.269030i | 0.990912 | + | 0.134515i | \(0.0429477\pi\) | ||||
−0.990912 | + | 0.134515i | \(0.957052\pi\) | |||||||
\(684\) | 9.57843 | − | 11.0766i | 0.366241 | − | 0.423526i | ||||
\(685\) | 19.7657 | 0.755208 | ||||||||
\(686\) | 4.69661 | + | 10.2704i | 0.179317 | + | 0.392127i | ||||
\(687\) | 24.5691 | 0.937370 | ||||||||
\(688\) | −1.54656 | − | 10.6047i | −0.0589621 | − | 0.404302i | ||||
\(689\) | 2.38626i | 0.0909094i | ||||||||
\(690\) | 4.53007 | + | 14.8329i | 0.172457 | + | 0.564681i | ||||
\(691\) | − | 14.4883i | − | 0.551161i | −0.961278 | − | 0.275581i | \(-0.911130\pi\) | ||
0.961278 | − | 0.275581i | \(-0.0888701\pi\) | |||||||
\(692\) | 16.5138 | − | 19.0968i | 0.627760 | − | 0.725951i | ||||
\(693\) | −5.70798 | −0.216828 | ||||||||
\(694\) | −3.82463 | + | 1.74898i | −0.145181 | + | 0.0663904i | ||||
\(695\) | 27.6355 | 1.04828 | ||||||||
\(696\) | −4.88159 | + | 16.7186i | −0.185036 | + | 0.633718i | ||||
\(697\) | 1.99149i | 0.0754330i | ||||||||
\(698\) | 15.6934 | + | 34.3180i | 0.594004 | + | 1.29895i | ||||
\(699\) | − | 1.51528i | − | 0.0573132i | ||||||
\(700\) | 1.02340 | − | 1.18347i | 0.0386808 | − | 0.0447311i | ||||
\(701\) | − | 30.6833i | − | 1.15889i | −0.815011 | − | 0.579446i | \(-0.803269\pi\) | ||
0.815011 | − | 0.579446i | \(-0.196731\pi\) | |||||||
\(702\) | 0.277554 | − | 0.126924i | 0.0104756 | − | 0.00479043i | ||||
\(703\) | 13.6563i | 0.515057i | ||||||||
\(704\) | 11.2710 | + | 7.19536i | 0.424792 | + | 0.271185i | ||||
\(705\) | − | 13.7895i | − | 0.519343i | ||||||
\(706\) | −7.89038 | − | 17.2545i | −0.296958 | − | 0.649381i | ||||
\(707\) | −8.87824 | −0.333901 | ||||||||
\(708\) | 5.14327 | − | 5.94775i | 0.193296 | − | 0.223530i | ||||
\(709\) | 40.3842i | 1.51666i | 0.651872 | + | 0.758329i | \(0.273984\pi\) | ||||
−0.651872 | + | 0.758329i | \(0.726016\pi\) | |||||||
\(710\) | −12.0364 | − | 26.3209i | −0.451718 | − | 0.987806i | ||||
\(711\) | 4.15186 | 0.155707 | ||||||||
\(712\) | −8.91827 | + | 30.5436i | −0.334226 | + | 1.14467i | ||||
\(713\) | −2.11563 | + | 15.8742i | −0.0792309 | + | 0.594492i | ||||
\(714\) | −0.447303 | − | 0.978153i | −0.0167399 | − | 0.0366064i | ||||
\(715\) | 0.824868i | 0.0308483i | ||||||||
\(716\) | 16.5890 | + | 14.3452i | 0.619960 | + | 0.536105i | ||||
\(717\) | −0.931528 | −0.0347885 | ||||||||
\(718\) | −18.2709 | − | 39.9543i | −0.681862 | − | 1.49108i | ||||
\(719\) | − | 10.1289i | − | 0.377743i | −0.982002 | − | 0.188871i | \(-0.939517\pi\) | ||
0.982002 | − | 0.188871i | \(-0.0604829\pi\) | |||||||
\(720\) | −9.05113 | + | 1.31999i | −0.337316 | + | 0.0491930i | ||||
\(721\) | −57.2302 | −2.13136 | ||||||||
\(722\) | −20.3551 | − | 44.5120i | −0.757537 | − | 1.65657i | ||||
\(723\) | 8.72544 | 0.324503 | ||||||||
\(724\) | 1.26570 | + | 1.09450i | 0.0470392 | + | 0.0406767i | ||||
\(725\) | 1.41064 | 0.0523898 | ||||||||
\(726\) | 10.5540 | − | 4.82629i | 0.391697 | − | 0.179121i | ||||
\(727\) | −19.6637 | −0.729287 | −0.364643 | − | 0.931147i | \(-0.618809\pi\) | ||||
−0.364643 | + | 0.931147i | \(0.618809\pi\) | |||||||
\(728\) | 2.00089 | + | 0.584231i | 0.0741581 | + | 0.0216530i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −43.0299 | + | 19.6773i | −1.59261 | + | 0.728291i | ||||
\(731\) | 0.596703i | 0.0220699i | ||||||||
\(732\) | −12.9496 | + | 14.9751i | −0.478631 | + | 0.553496i | ||||
\(733\) | − | 43.7893i | − | 1.61740i | −0.588225 | − | 0.808698i | \(-0.700173\pi\) | ||
0.588225 | − | 0.808698i | \(-0.299827\pi\) | |||||||
\(734\) | 7.20243 | + | 15.7501i | 0.265847 | + | 0.581347i | ||||
\(735\) | 10.6596 | 0.393186 | ||||||||
\(736\) | 24.5311 | − | 11.5855i | 0.904229 | − | 0.427047i | ||||
\(737\) | −3.24649 | −0.119586 | ||||||||
\(738\) | 5.25903 | + | 11.5003i | 0.193588 | + | 0.423333i | ||||
\(739\) | − | 5.01539i | − | 0.184494i | −0.995736 | − | 0.0922471i | \(-0.970595\pi\) | ||
0.995736 | − | 0.0922471i | \(-0.0294050\pi\) | |||||||
\(740\) | 5.57954 | − | 6.45226i | 0.205108 | − | 0.237190i | ||||
\(741\) | − | 1.58011i | − | 0.0580470i | ||||||
\(742\) | 48.5635 | − | 22.2078i | 1.78282 | − | 0.815274i | ||||
\(743\) | 25.6622 | 0.941456 | 0.470728 | − | 0.882278i | \(-0.343991\pi\) | ||||
0.470728 | + | 0.882278i | \(0.343991\pi\) | |||||||
\(744\) | −9.06628 | − | 2.64722i | −0.332386 | − | 0.0970517i | ||||
\(745\) | −14.3244 | −0.524804 | ||||||||
\(746\) | 33.8747 | − | 15.4907i | 1.24024 | − | 0.567155i | ||||
\(747\) | 15.1113 | 0.552895 | ||||||||
\(748\) | −0.563169 | − | 0.486996i | −0.0205915 | − | 0.0178063i | ||||
\(749\) | 16.0940 | 0.588062 | ||||||||
\(750\) | −6.41639 | − | 14.0312i | −0.234293 | − | 0.512348i | ||||
\(751\) | 2.55682 | 0.0932995 | 0.0466498 | − | 0.998911i | \(-0.485146\pi\) | ||||
0.0466498 | + | 0.998911i | \(0.485146\pi\) | |||||||
\(752\) | −23.8685 | + | 3.48091i | −0.870396 | + | 0.126936i | ||||
\(753\) | − | 3.46463i | − | 0.126258i | ||||||
\(754\) | 0.781565 | + | 1.70911i | 0.0284629 | + | 0.0622421i | ||||
\(755\) | 18.2093 | 0.662705 | ||||||||
\(756\) | −5.16612 | − | 4.46736i | −0.187890 | − | 0.162476i | ||||
\(757\) | − | 38.7648i | − | 1.40893i | −0.709738 | − | 0.704465i | \(-0.751187\pi\) | ||
0.709738 | − | 0.704465i | \(-0.248813\pi\) | |||||||
\(758\) | −16.1022 | − | 35.2119i | −0.584859 | − | 1.27896i | ||||
\(759\) | −1.05899 | + | 7.94594i | −0.0384390 | + | 0.288419i | ||||
\(760\) | −13.2731 | + | 45.4583i | −0.481467 | + | 1.64895i | ||||
\(761\) | 8.24722 | 0.298961 | 0.149481 | − | 0.988765i | \(-0.452240\pi\) | ||||
0.149481 | + | 0.988765i | \(0.452240\pi\) | |||||||
\(762\) | −11.5837 | − | 25.3309i | −0.419633 | − | 0.917643i | ||||
\(763\) | − | 35.3246i | − | 1.27883i | ||||||
\(764\) | −3.03119 | + | 3.50532i | −0.109665 | + | 0.126818i | ||||
\(765\) | 0.509285 | 0.0184132 | ||||||||
\(766\) | −4.27712 | − | 9.35311i | −0.154539 | − | 0.337942i | ||||
\(767\) | − | 0.848463i | − | 0.0306362i | ||||||
\(768\) | 4.56959 | + | 15.3336i | 0.164891 | + | 0.553303i | ||||
\(769\) | 3.32777i | 0.120003i | 0.998198 | + | 0.0600013i | \(0.0191105\pi\) | ||||
−0.998198 | + | 0.0600013i | \(0.980890\pi\) | |||||||
\(770\) | 16.7871 | − | 7.67664i | 0.604965 | − | 0.276647i | ||||
\(771\) | 2.26338i | 0.0815136i | ||||||||
\(772\) | −23.2389 | + | 26.8738i | −0.836387 | + | 0.967211i | ||||
\(773\) | 7.05843i | 0.253874i | 0.991911 | + | 0.126937i | \(0.0405146\pi\) | ||||
−0.991911 | + | 0.126937i | \(0.959485\pi\) | |||||||
\(774\) | 1.57575 | + | 3.44581i | 0.0566391 | + | 0.123857i | ||||
\(775\) | 0.764969i | 0.0274785i | ||||||||
\(776\) | 12.9516 | − | 44.3570i | 0.464934 | − | 1.59232i | ||||
\(777\) | 6.36928 | 0.228496 | ||||||||
\(778\) | −3.79650 | + | 1.73612i | −0.136111 | + | 0.0622427i | ||||
\(779\) | 65.4713 | 2.34575 | ||||||||
\(780\) | −0.645585 | + | 0.746564i | −0.0231156 | + | 0.0267313i | ||||
\(781\) | − | 14.9593i | − | 0.535287i | ||||||
\(782\) | −1.44465 | + | 0.441205i | −0.0516606 | + | 0.0157774i | ||||
\(783\) | − | 6.15775i | − | 0.220060i | ||||||
\(784\) | −2.69083 | − | 18.4510i | −0.0961011 | − | 0.658964i | ||||
\(785\) | 33.4229 | 1.19291 | ||||||||
\(786\) | −8.89062 | − | 19.4418i | −0.317118 | − | 0.693466i | ||||
\(787\) | 36.6452 | 1.30626 | 0.653130 | − | 0.757246i | \(-0.273455\pi\) | ||||
0.653130 | + | 0.757246i | \(0.273455\pi\) | |||||||
\(788\) | −29.5677 | + | 34.1925i | −1.05330 | + | 1.21806i | ||||
\(789\) | 1.20387i | 0.0428590i | ||||||||
\(790\) | −12.2106 | + | 5.58383i | −0.434433 | + | 0.198664i | ||||
\(791\) | − | 51.7629i | − | 1.84048i | ||||||
\(792\) | −4.53820 | − | 1.32508i | −0.161258 | − | 0.0470848i | ||||
\(793\) | 2.13624i | 0.0758602i | ||||||||
\(794\) | 3.79921 | + | 8.30802i | 0.134829 | + | 0.294841i | ||||
\(795\) | 25.2851i | 0.896769i | ||||||||
\(796\) | 10.9222 | − | 12.6306i | 0.387128 | − | 0.447680i | ||||
\(797\) | 37.8542i | 1.34086i | 0.741971 | + | 0.670432i | \(0.233891\pi\) | ||||
−0.741971 | + | 0.670432i | \(0.766109\pi\) | |||||||
\(798\) | −32.1573 | + | 14.7054i | −1.13836 | + | 0.520564i | ||||
\(799\) | 1.34302 | 0.0475128 | ||||||||
\(800\) | 1.08840 | − | 0.703357i | 0.0384809 | − | 0.0248674i | ||||
\(801\) | − | 11.2497i | − | 0.397489i | ||||||
\(802\) | −33.6580 | + | 15.3916i | −1.18850 | + | 0.543496i | ||||
\(803\) | −24.4558 | −0.863026 | ||||||||
\(804\) | −2.93830 | − | 2.54087i | −0.103626 | − | 0.0896096i | ||||
\(805\) | 4.94743 | − | 37.1220i | 0.174374 | − | 1.30838i | ||||
\(806\) | −0.926826 | + | 0.423832i | −0.0326461 | + | 0.0149288i | ||||
\(807\) | − | 16.0520i | − | 0.565058i | ||||||
\(808\) | −7.05875 | − | 2.06105i | −0.248326 | − | 0.0725074i | ||||
\(809\) | −16.8995 | −0.594153 | −0.297077 | − | 0.954854i | \(-0.596012\pi\) | ||||
−0.297077 | + | 0.954854i | \(0.596012\pi\) | |||||||
\(810\) | 2.94099 | − | 1.34490i | 0.103336 | − | 0.0472549i | ||||
\(811\) | 33.7625i | 1.18556i | 0.805364 | + | 0.592781i | \(0.201970\pi\) | ||||
−0.805364 | + | 0.592781i | \(0.798030\pi\) | |||||||
\(812\) | 27.5089 | − | 31.8117i | 0.965372 | − | 1.11637i | ||||
\(813\) | −19.4504 | −0.682154 | ||||||||
\(814\) | 4.00956 | − | 1.83355i | 0.140535 | − | 0.0642659i | ||||
\(815\) | −14.2889 | −0.500519 | ||||||||
\(816\) | −0.128560 | − | 0.881532i | −0.00450049 | − | 0.0308598i | ||||
\(817\) | 19.6170 | 0.686310 | ||||||||
\(818\) | −18.4924 | − | 40.4388i | −0.646572 | − | 1.41391i | ||||
\(819\) | −0.736962 | −0.0257515 | ||||||||
\(820\) | −30.9335 | − | 26.7495i | −1.08025 | − | 0.934133i | ||||
\(821\) | 6.08599 | 0.212403 | 0.106201 | − | 0.994345i | \(-0.466131\pi\) | ||||
0.106201 | + | 0.994345i | \(0.466131\pi\) | |||||||
\(822\) | 5.08365 | + | 11.1168i | 0.177313 | + | 0.387743i | ||||
\(823\) | 9.97406i | 0.347674i | 0.984774 | + | 0.173837i | \(0.0556166\pi\) | ||||
−0.984774 | + | 0.173837i | \(0.944383\pi\) | |||||||
\(824\) | −45.5016 | − | 13.2858i | −1.58512 | − | 0.462832i | ||||
\(825\) | 0.382911i | 0.0133313i | ||||||||
\(826\) | −17.2673 | + | 7.89623i | −0.600806 | + | 0.274745i | ||||
\(827\) | 20.5116 | 0.713258 | 0.356629 | − | 0.934246i | \(-0.383926\pi\) | ||||
0.356629 | + | 0.934246i | \(0.383926\pi\) | |||||||
\(828\) | −7.17737 | + | 6.36281i | −0.249431 | + | 0.221123i | ||||
\(829\) | −7.44995 | −0.258748 | −0.129374 | − | 0.991596i | \(-0.541297\pi\) | ||||
−0.129374 | + | 0.991596i | \(0.541297\pi\) | |||||||
\(830\) | −44.4423 | + | 20.3232i | −1.54261 | + | 0.705428i | ||||
\(831\) | 10.4753i | 0.363385i | ||||||||
\(832\) | 1.45521 | + | 0.929000i | 0.0504503 | + | 0.0322073i | ||||
\(833\) | 1.03819i | 0.0359712i | ||||||||
\(834\) | 7.10774 | + | 15.5430i | 0.246121 | + | 0.538211i | ||||
\(835\) | 46.7770 | 1.61878 | ||||||||
\(836\) | −16.0103 | + | 18.5145i | −0.553727 | + | 0.640338i | ||||
\(837\) | 3.33926 | 0.115422 | ||||||||
\(838\) | −5.18049 | − | 11.3286i | −0.178957 | − | 0.391339i | ||||
\(839\) | 14.4632 | 0.499324 | 0.249662 | − | 0.968333i | \(-0.419681\pi\) | ||||
0.249662 | + | 0.968333i | \(0.419681\pi\) | |||||||
\(840\) | 21.2017 | + | 6.19056i | 0.731527 | + | 0.213595i | ||||
\(841\) | 8.91784 | 0.307512 | ||||||||
\(842\) | 25.9197 | − | 11.8529i | 0.893252 | − | 0.408479i | ||||
\(843\) | −5.01591 | −0.172757 | ||||||||
\(844\) | −20.6415 | − | 17.8495i | −0.710509 | − | 0.614407i | ||||
\(845\) | − | 29.6208i | − | 1.01899i | ||||||
\(846\) | 7.75562 | − | 3.54660i | 0.266644 | − | 0.121935i | ||||
\(847\) | −28.0231 | −0.962884 | ||||||||
\(848\) | 43.7664 | − | 6.38275i | 1.50295 | − | 0.219185i | ||||
\(849\) | 5.75726i | 0.197589i | ||||||||
\(850\) | −0.0656179 | + | 0.0300067i | −0.00225068 | + | 0.00102922i | ||||
\(851\) | 1.18168 | − | 8.86651i | 0.0405076 | − | 0.303940i | ||||
\(852\) | 11.7079 | − | 13.5392i | 0.401108 | − | 0.463847i | ||||
\(853\) | 2.97482 | 0.101856 | 0.0509279 | − | 0.998702i | \(-0.483782\pi\) | ||||
0.0509279 | + | 0.998702i | \(0.483782\pi\) | |||||||
\(854\) | 43.4752 | − | 19.8810i | 1.48769 | − | 0.680312i | ||||
\(855\) | − | 16.7430i | − | 0.572600i | ||||||
\(856\) | 12.7957 | + | 3.73616i | 0.437349 | + | 0.127699i | ||||
\(857\) | 36.9443 | 1.26199 | 0.630997 | − | 0.775786i | \(-0.282646\pi\) | ||||
0.630997 | + | 0.775786i | \(0.282646\pi\) | |||||||
\(858\) | −0.463930 | + | 0.212152i | −0.0158383 | + | 0.00724276i | ||||
\(859\) | 16.5018i | 0.563034i | 0.959556 | + | 0.281517i | \(0.0908376\pi\) | ||||
−0.959556 | + | 0.281517i | \(0.909162\pi\) | |||||||
\(860\) | −9.26851 | − | 8.01487i | −0.316054 | − | 0.273305i | ||||
\(861\) | − | 30.5357i | − | 1.04065i | ||||||
\(862\) | −13.7562 | − | 30.0817i | −0.468537 | − | 1.02459i | ||||
\(863\) | − | 45.7125i | − | 1.55607i | −0.628219 | − | 0.778037i | \(-0.716216\pi\) | ||
0.628219 | − | 0.778037i | \(-0.283784\pi\) | |||||||
\(864\) | −3.07031 | − | 4.75113i | −0.104454 | − | 0.161637i | ||||
\(865\) | − | 28.8660i | − | 0.981473i | ||||||
\(866\) | −17.4610 | + | 7.98479i | −0.593347 | + | 0.271334i | ||||
\(867\) | − | 16.9504i | − | 0.575666i | ||||||
\(868\) | 17.2510 | + | 14.9177i | 0.585538 | + | 0.506339i | ||||
\(869\) | −6.93980 | −0.235417 | ||||||||
\(870\) | 8.28153 | + | 18.1099i | 0.280770 | + | 0.613982i | ||||
\(871\) | −0.419157 | −0.0142026 | ||||||||
\(872\) | 8.20046 | − | 28.0852i | 0.277702 | − | 0.951086i | ||||
\(873\) | 16.3374i | 0.552937i | ||||||||
\(874\) | 14.5049 | + | 47.4937i | 0.490634 | + | 1.60650i | ||||
\(875\) | 37.2557i | 1.25947i | ||||||||
\(876\) | −22.1342 | − | 19.1404i | −0.747846 | − | 0.646693i | ||||
\(877\) | 45.1046 | 1.52307 | 0.761537 | − | 0.648121i | \(-0.224445\pi\) | ||||
0.761537 | + | 0.648121i | \(0.224445\pi\) | |||||||
\(878\) | 53.2044 | − | 24.3300i | 1.79556 | − | 0.821099i | ||||
\(879\) | 1.86241 | 0.0628177 | ||||||||
\(880\) | 15.1289 | − | 2.20635i | 0.509995 | − | 0.0743760i | ||||
\(881\) | 43.8083i | 1.47594i | 0.674833 | + | 0.737970i | \(0.264216\pi\) | ||||
−0.674833 | + | 0.737970i | \(0.735784\pi\) | |||||||
\(882\) | 2.74161 | + | 5.99529i | 0.0923148 | + | 0.201872i | ||||
\(883\) | 17.2830i | 0.581618i | 0.956781 | + | 0.290809i | \(0.0939244\pi\) | ||||
−0.956781 | + | 0.290809i | \(0.906076\pi\) | |||||||
\(884\) | −0.0727113 | − | 0.0628765i | −0.00244555 | − | 0.00211477i | ||||
\(885\) | − | 8.99039i | − | 0.302209i | ||||||
\(886\) | −18.7630 | + | 8.58021i | −0.630355 | + | 0.288258i | ||||
\(887\) | − | 23.4906i | − | 0.788737i | −0.918952 | − | 0.394368i | \(-0.870963\pi\) | ||
0.918952 | − | 0.394368i | \(-0.129037\pi\) | |||||||
\(888\) | 5.06397 | + | 1.47860i | 0.169936 | + | 0.0496186i | ||||
\(889\) | 67.2587i | 2.25578i | ||||||||
\(890\) | 15.1297 | + | 33.0853i | 0.507149 | + | 1.10902i | ||||
\(891\) | 1.67149 | 0.0559971 | ||||||||
\(892\) | −17.5512 | − | 15.1772i | −0.587657 | − | 0.508172i | ||||
\(893\) | − | 44.1527i | − | 1.47751i | ||||||
\(894\) | −3.68416 | − | 8.05644i | −0.123217 | − | 0.269448i | ||||
\(895\) | 25.0753 | 0.838175 | ||||||||
\(896\) | 5.36340 | − | 38.2611i | 0.179179 | − | 1.27821i | ||||
\(897\) | −0.136728 | + | 1.02591i | −0.00456520 | + | 0.0342540i | ||||
\(898\) | 15.6271 | + | 34.1731i | 0.521484 | + | 1.14037i | ||||
\(899\) | 20.5623i | 0.685792i | ||||||||
\(900\) | −0.299686 | + | 0.346562i | −0.00998955 | + | 0.0115521i | ||||
\(901\) | −2.46263 | −0.0820421 | ||||||||
\(902\) | −8.79043 | − | 19.2227i | −0.292689 | − | 0.640046i | ||||
\(903\) | − | 9.14931i | − | 0.304470i | ||||||
\(904\) | 12.0166 | − | 41.1547i | 0.399665 | − | 1.36879i | ||||
\(905\) | 1.91318 | 0.0635961 | ||||||||
\(906\) | 4.68336 | + | 10.2415i | 0.155594 | + | 0.340250i | ||||
\(907\) | −48.6715 | −1.61611 | −0.808056 | − | 0.589106i | \(-0.799480\pi\) | ||||
−0.808056 | + | 0.589106i | \(0.799480\pi\) | |||||||
\(908\) | −11.1214 | + | 12.8609i | −0.369075 | + | 0.426804i | ||||
\(909\) | 2.59985 | 0.0862317 | ||||||||
\(910\) | 2.16740 | − | 0.991138i | 0.0718485 | − | 0.0328559i | ||||
\(911\) | 41.6954 | 1.38143 | 0.690716 | − | 0.723126i | \(-0.257296\pi\) | ||||
0.690716 | + | 0.723126i | \(0.257296\pi\) | |||||||
\(912\) | −28.9809 | + | 4.22647i | −0.959652 | + | 0.139953i | ||||
\(913\) | −25.2585 | −0.835933 | ||||||||
\(914\) | 32.8066 | − | 15.0023i | 1.08515 | − | 0.496231i | ||||
\(915\) | 22.6358i | 0.748317i | ||||||||
\(916\) | −37.1686 | − | 32.1412i | −1.22809 | − | 1.06198i | ||||
\(917\) | 51.6219i | 1.70471i | ||||||||
\(918\) | 0.130986 | + | 0.286437i | 0.00432318 | + | 0.00945382i | ||||
\(919\) | 17.1500 | 0.565725 | 0.282862 | − | 0.959160i | \(-0.408716\pi\) | ||||
0.282862 | + | 0.959160i | \(0.408716\pi\) | |||||||
\(920\) | 12.5512 | − | 28.3658i | 0.413802 | − | 0.935192i | ||||
\(921\) | −29.6535 | −0.977117 | ||||||||
\(922\) | −2.61573 | − | 5.72001i | −0.0861444 | − | 0.188379i | ||||
\(923\) | − | 1.93141i | − | 0.0635732i | ||||||
\(924\) | 8.63513 | + | 7.46716i | 0.284075 | + | 0.245651i | ||||
\(925\) | − | 0.427273i | − | 0.0140487i | ||||||
\(926\) | −33.6153 | + | 15.3721i | −1.10467 | + | 0.505158i | ||||
\(927\) | 16.7590 | 0.550437 | ||||||||
\(928\) | 29.2562 | − | 18.9062i | 0.960383 | − | 0.620626i | ||||
\(929\) | −50.4355 | −1.65474 | −0.827368 | − | 0.561660i | \(-0.810163\pi\) | ||||
−0.827368 | + | 0.561660i | \(0.810163\pi\) | |||||||
\(930\) | −9.82073 | + | 4.49096i | −0.322034 | + | 0.147264i | ||||
\(931\) | 34.1311 | 1.11860 | ||||||||
\(932\) | −1.98229 | + | 2.29235i | −0.0649320 | + | 0.0750883i | ||||
\(933\) | −1.49246 | −0.0488610 | ||||||||
\(934\) | 21.6676 | + | 47.3823i | 0.708987 | + | 1.55040i | ||||
\(935\) | −0.851265 | −0.0278394 | ||||||||
\(936\) | −0.585931 | − | 0.171083i | −0.0191517 | − | 0.00559202i | ||||
\(937\) | − | 34.3371i | − | 1.12174i | −0.827902 | − | 0.560872i | \(-0.810466\pi\) | ||
0.827902 | − | 0.560872i | \(-0.189534\pi\) | |||||||
\(938\) | 3.90089 | + | 8.53038i | 0.127369 | + | 0.278527i | ||||
\(939\) | 26.6881 | 0.870935 | ||||||||
\(940\) | −18.0394 | + | 20.8610i | −0.588380 | + | 0.680411i | ||||
\(941\) | − | 21.1847i | − | 0.690600i | −0.938492 | − | 0.345300i | \(-0.887777\pi\) | ||
0.938492 | − | 0.345300i | \(-0.112223\pi\) | |||||||
\(942\) | 8.59621 | + | 18.7980i | 0.280080 | + | 0.612472i | ||||
\(943\) | −42.5080 | − | 5.66524i | −1.38425 | − | 0.184486i | ||||
\(944\) | −15.5617 | + | 2.26946i | −0.506489 | + | 0.0738647i | ||||
\(945\) | −7.80892 | −0.254024 | ||||||||
\(946\) | −2.63385 | − | 5.75964i | −0.0856338 | − | 0.187262i | ||||
\(947\) | − | 1.66910i | − | 0.0542384i | −0.999632 | − | 0.0271192i | \(-0.991367\pi\) | ||
0.999632 | − | 0.0271192i | \(-0.00863336\pi\) | |||||||
\(948\) | −6.28101 | − | 5.43145i | −0.203998 | − | 0.176405i | ||||
\(949\) | −3.15751 | −0.102497 | ||||||||
\(950\) | 0.986487 | + | 2.15723i | 0.0320059 | + | 0.0699897i | ||||
\(951\) | 10.1157i | 0.328024i | ||||||||
\(952\) | −0.602928 | + | 2.06493i | −0.0195410 | + | 0.0669247i | ||||
\(953\) | 2.48553i | 0.0805144i | 0.999189 | + | 0.0402572i | \(0.0128177\pi\) | ||||
−0.999189 | + | 0.0402572i | \(0.987182\pi\) | |||||||
\(954\) | −14.2211 | + | 6.50320i | −0.460424 | + | 0.210549i | ||||
\(955\) | 5.29850i | 0.171456i | ||||||||
\(956\) | 1.40923 | + | 1.21862i | 0.0455778 | + | 0.0394130i | ||||
\(957\) | 10.2926i | 0.332713i | ||||||||
\(958\) | 1.86145 | + | 4.07058i | 0.0601409 | + | 0.131515i | ||||
\(959\) | − | 29.5173i | − | 0.953164i | ||||||
\(960\) | 15.4195 | + | 9.84376i | 0.497663 | + | 0.317706i | ||||
\(961\) | 19.8493 | 0.640301 | ||||||||
\(962\) | 0.517678 | − | 0.236731i | 0.0166906 | − | 0.00763252i | ||||
\(963\) | −4.71288 | −0.151870 | ||||||||
\(964\) | −13.2000 | − | 11.4146i | −0.425144 | − | 0.367639i | ||||
\(965\) | 40.6215i | 1.30765i | ||||||||
\(966\) | 22.1510 | − | 6.76504i | 0.712696 | − | 0.217661i | ||||
\(967\) | − | 34.4514i | − | 1.10788i | −0.832556 | − | 0.553941i | \(-0.813123\pi\) | ||
0.832556 | − | 0.553941i | \(-0.186877\pi\) | |||||||
\(968\) | −22.2801 | − | 6.50544i | −0.716109 | − | 0.209093i | ||||
\(969\) | 1.63068 | 0.0523850 | ||||||||
\(970\) | −21.9721 | − | 48.0481i | −0.705482 | − | 1.54273i | ||||
\(971\) | −42.1631 | −1.35308 | −0.676539 | − | 0.736407i | \(-0.736521\pi\) | ||||
−0.676539 | + | 0.736407i | \(0.736521\pi\) | |||||||
\(972\) | 1.51282 | + | 1.30820i | 0.0485237 | + | 0.0419604i | ||||
\(973\) | − | 41.2699i | − | 1.32305i | ||||||
\(974\) | 9.23503 | − | 4.22313i | 0.295910 | − | 0.135318i | ||||
\(975\) | 0.0494380i | 0.00158328i | ||||||||
\(976\) | 39.1808 | − | 5.71400i | 1.25415 | − | 0.182901i | ||||
\(977\) | 56.9040i | 1.82052i | 0.414037 | + | 0.910260i | \(0.364118\pi\) | ||||
−0.414037 | + | 0.910260i | \(0.635882\pi\) | |||||||
\(978\) | −3.67504 | − | 8.03650i | −0.117515 | − | 0.256979i | ||||
\(979\) | 18.8038i | 0.600972i | ||||||||
\(980\) | −16.1261 | − | 13.9449i | −0.515129 | − | 0.445453i | ||||
\(981\) | 10.3442i | 0.330266i | ||||||||
\(982\) | −8.12226 | + | 3.71426i | −0.259192 | + | 0.118527i | ||||
\(983\) | −28.7573 | −0.917215 | −0.458608 | − | 0.888639i | \(-0.651652\pi\) | ||||
−0.458608 | + | 0.888639i | \(0.651652\pi\) | |||||||
\(984\) | 7.08874 | − | 24.2778i | 0.225981 | − | 0.773947i | ||||
\(985\) | 51.6841i | 1.64679i | ||||||||
\(986\) | −1.76380 | + | 0.806577i | −0.0561710 | + | 0.0256867i | ||||
\(987\) | −20.5927 | −0.655473 | ||||||||
\(988\) | −2.06710 | + | 2.39043i | −0.0657632 | + | 0.0760496i | ||||
\(989\) | −12.7365 | − | 1.69746i | −0.404998 | − | 0.0539760i | ||||
\(990\) | −4.91584 | + | 2.24798i | −0.156236 | + | 0.0714456i | ||||
\(991\) | 46.2858i | 1.47032i | 0.677895 | + | 0.735159i | \(0.262892\pi\) | ||||
−0.677895 | + | 0.735159i | \(0.737108\pi\) | |||||||
\(992\) | 10.2526 | + | 15.8652i | 0.325519 | + | 0.503722i | ||||
\(993\) | 7.15217 | 0.226967 | ||||||||
\(994\) | −39.3067 | + | 17.9747i | −1.24673 | + | 0.570123i | ||||
\(995\) | − | 19.0920i | − | 0.605256i | ||||||
\(996\) | −22.8607 | − | 19.7686i | −0.724369 | − | 0.626392i | ||||
\(997\) | −8.77812 | −0.278006 | −0.139003 | − | 0.990292i | \(-0.544390\pi\) | ||||
−0.139003 | + | 0.990292i | \(0.544390\pi\) | |||||||
\(998\) | 19.9589 | − | 9.12708i | 0.631787 | − | 0.288913i | ||||
\(999\) | −1.86514 | −0.0590105 |
(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 | 276.2.e.a.91.6 | yes | 24 | |
3.2 | odd | 2 | 828.2.e.f.91.19 | 24 | |||
4.3 | odd | 2 | inner | 276.2.e.a.91.8 | yes | 24 | |
8.3 | odd | 2 | 4416.2.i.d.1471.13 | 24 | |||
8.5 | even | 2 | 4416.2.i.d.1471.16 | 24 | |||
12.11 | even | 2 | 828.2.e.f.91.17 | 24 | |||
23.22 | odd | 2 | inner | 276.2.e.a.91.5 | ✓ | 24 | |
69.68 | even | 2 | 828.2.e.f.91.20 | 24 | |||
92.91 | even | 2 | inner | 276.2.e.a.91.7 | yes | 24 | |
184.45 | odd | 2 | 4416.2.i.d.1471.15 | 24 | |||
184.91 | even | 2 | 4416.2.i.d.1471.14 | 24 | |||
276.275 | odd | 2 | 828.2.e.f.91.18 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.e.a.91.5 | ✓ | 24 | 23.22 | odd | 2 | inner | |
276.2.e.a.91.6 | yes | 24 | 1.1 | even | 1 | trivial | |
276.2.e.a.91.7 | yes | 24 | 92.91 | even | 2 | inner | |
276.2.e.a.91.8 | yes | 24 | 4.3 | odd | 2 | inner | |
828.2.e.f.91.17 | 24 | 12.11 | even | 2 | |||
828.2.e.f.91.18 | 24 | 276.275 | odd | 2 | |||
828.2.e.f.91.19 | 24 | 3.2 | odd | 2 | |||
828.2.e.f.91.20 | 24 | 69.68 | even | 2 | |||
4416.2.i.d.1471.13 | 24 | 8.3 | odd | 2 | |||
4416.2.i.d.1471.14 | 24 | 184.91 | even | 2 | |||
4416.2.i.d.1471.15 | 24 | 184.45 | odd | 2 | |||
4416.2.i.d.1471.16 | 24 | 8.5 | even | 2 |