Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(37,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(42))
chi = DirichletCharacter(H, H._module([0, 32]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.bb (of order \(21\), degree \(12\), 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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{21})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{21}]$ |
Embedding invariants
Embedding label | 100.1 | ||
Character | \(\chi\) | \(=\) | 441.100 |
Dual form | 441.2.bb.f.172.1 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{13}{21}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.49548 | − | 0.769754i | −1.76457 | − | 0.544298i | −0.769081 | − | 0.639151i | \(-0.779286\pi\) |
−0.995491 | + | 0.0948530i | \(0.969762\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.98243 | + | 2.71518i | 1.99122 | + | 1.35759i | ||||
\(5\) | −1.69843 | + | 0.255997i | −0.759562 | + | 0.114486i | −0.517392 | − | 0.855748i | \(-0.673097\pi\) |
−0.242170 | + | 0.970234i | \(0.577859\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.62887 | − | 0.298395i | −0.993620 | − | 0.112783i | ||||
\(8\) | −4.59158 | − | 5.75765i | −1.62337 | − | 2.03564i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.43546 | + | 0.668538i | 1.40262 | + | 0.211410i | ||||
\(11\) | 2.79059 | − | 2.58929i | 0.841395 | − | 0.780701i | −0.136314 | − | 0.990666i | \(-0.543525\pi\) |
0.977709 | + | 0.209965i | \(0.0673350\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.351587 | − | 1.54041i | −0.0975128 | − | 0.427231i | 0.902481 | − | 0.430729i | \(-0.141744\pi\) |
−0.999994 | + | 0.00349800i | \(0.998887\pi\) | |||||||
\(14\) | 6.33061 | + | 2.76822i | 1.69193 | + | 0.739839i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.50436 | + | 8.92897i | 0.876091 | + | 2.23224i | ||||
\(17\) | 0.385913 | + | 5.14966i | 0.0935977 | + | 1.24898i | 0.824250 | + | 0.566226i | \(0.191597\pi\) |
−0.730653 | + | 0.682749i | \(0.760784\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.59925 | − | 2.76998i | 0.366893 | − | 0.635477i | −0.622185 | − | 0.782870i | \(-0.713755\pi\) |
0.989078 | + | 0.147393i | \(0.0470882\pi\) | |||||||
\(20\) | −7.45897 | − | 3.59205i | −1.66788 | − | 0.803207i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.95699 | + | 4.31346i | −1.90964 | + | 0.919633i | ||||
\(23\) | −0.388520 | + | 5.18444i | −0.0810120 | + | 1.08103i | 0.797503 | + | 0.603315i | \(0.206154\pi\) |
−0.878515 | + | 0.477715i | \(0.841465\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.95873 | + | 0.604187i | −0.391745 | + | 0.120837i | ||||
\(26\) | −0.308353 | + | 4.11469i | −0.0604731 | + | 0.806957i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −9.65910 | − | 8.32618i | −1.82540 | − | 1.57350i | ||||
\(29\) | −3.72828 | − | 1.79544i | −0.692324 | − | 0.333406i | 0.0544193 | − | 0.998518i | \(-0.482669\pi\) |
−0.746743 | + | 0.665113i | \(0.768384\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.21402 | + | 9.03095i | 0.936466 | + | 1.62201i | 0.771999 | + | 0.635624i | \(0.219257\pi\) |
0.164467 | + | 0.986383i | \(0.447409\pi\) | |||||||
\(32\) | −0.771289 | − | 10.2921i | −0.136346 | − | 1.81941i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.00093 | − | 13.1479i | 0.514655 | − | 2.25485i | ||||
\(35\) | 4.54135 | − | 0.166180i | 0.767628 | − | 0.0280895i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.68787 | + | 1.15077i | −0.277484 | + | 0.189185i | −0.694063 | − | 0.719914i | \(-0.744181\pi\) |
0.416579 | + | 0.909099i | \(0.363229\pi\) | |||||||
\(38\) | −6.12310 | + | 5.68141i | −0.993299 | + | 0.921646i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 9.27242 | + | 8.60355i | 1.46610 | + | 1.36034i | ||||
\(41\) | 4.23617 | + | 5.31199i | 0.661578 | + | 0.829593i | 0.993514 | − | 0.113709i | \(-0.0362732\pi\) |
−0.331936 | + | 0.943302i | \(0.607702\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.22334 | + | 9.05779i | −1.10155 | + | 1.38130i | −0.184355 | + | 0.982860i | \(0.559020\pi\) |
−0.917195 | + | 0.398440i | \(0.869552\pi\) | |||||||
\(44\) | 18.1437 | − | 2.73473i | 2.73527 | − | 0.412276i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.96028 | − | 12.6386i | 0.731354 | − | 1.86346i | ||||
\(47\) | 11.8376 | + | 3.65142i | 1.72669 | + | 0.532614i | 0.989684 | − | 0.143269i | \(-0.0457616\pi\) |
0.737009 | + | 0.675883i | \(0.236238\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.82192 | + | 1.56889i | 0.974560 | + | 0.224127i | ||||
\(50\) | 5.35304 | 0.757034 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.78230 | − | 7.08918i | 0.385835 | − | 0.983092i | ||||
\(53\) | 1.50059 | + | 1.02308i | 0.206121 | + | 0.140531i | 0.661981 | − | 0.749520i | \(-0.269716\pi\) |
−0.455860 | + | 0.890052i | \(0.650668\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.07678 | + | 5.11212i | −0.549713 | + | 0.689318i | ||||
\(56\) | 10.3526 | + | 16.5062i | 1.38342 | + | 2.20574i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.92180 | + | 7.35036i | 1.04018 | + | 0.965149i | ||||
\(59\) | −1.27898 | − | 0.192775i | −0.166509 | − | 0.0250972i | 0.0652585 | − | 0.997868i | \(-0.479213\pi\) |
−0.231768 | + | 0.972771i | \(0.574451\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.03671 | − | 4.79755i | 0.900958 | − | 0.614263i | −0.0217495 | − | 0.999763i | \(-0.506924\pi\) |
0.922708 | + | 0.385501i | \(0.125971\pi\) | |||||||
\(62\) | −6.05989 | − | 26.5501i | −0.769606 | − | 3.37186i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.72882 | + | 7.57447i | −0.216103 | + | 0.946808i | ||||
\(65\) | 0.991487 | + | 2.52627i | 0.122979 | + | 0.313345i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.93580 | + | 6.81700i | 0.480834 | + | 0.832829i | 0.999758 | − | 0.0219914i | \(-0.00700065\pi\) |
−0.518924 | + | 0.854820i | \(0.673667\pi\) | |||||||
\(68\) | −12.4453 | + | 21.5560i | −1.50922 | + | 2.61405i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −11.4608 | − | 3.08102i | −1.36982 | − | 0.368253i | ||||
\(71\) | −10.8760 | + | 5.23762i | −1.29075 | + | 0.621591i | −0.948130 | − | 0.317883i | \(-0.897028\pi\) |
−0.342618 | + | 0.939475i | \(0.611314\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.74013 | − | 0.845219i | 0.320708 | − | 0.0989254i | −0.130221 | − | 0.991485i | \(-0.541569\pi\) |
0.450929 | + | 0.892560i | \(0.351093\pi\) | |||||||
\(74\) | 5.09786 | − | 1.57248i | 0.592614 | − | 0.182797i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 13.8899 | − | 6.68902i | 1.59328 | − | 0.767283i | ||||
\(77\) | −8.10874 | + | 5.97421i | −0.924077 | + | 0.680825i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.483737 | + | 0.837858i | −0.0544247 | + | 0.0942664i | −0.891954 | − | 0.452126i | \(-0.850666\pi\) |
0.837529 | + | 0.546392i | \(0.183999\pi\) | |||||||
\(80\) | −8.23772 | − | 14.2681i | −0.921005 | − | 1.59523i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.48236 | − | 16.5168i | −0.715857 | − | 1.82397i | ||||
\(83\) | 2.28170 | − | 9.99677i | 0.250449 | − | 1.09729i | −0.680675 | − | 0.732585i | \(-0.738313\pi\) |
0.931124 | − | 0.364703i | \(-0.118829\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.97375 | − | 8.64755i | −0.214083 | − | 0.937959i | ||||
\(86\) | 24.9980 | − | 17.0433i | 2.69560 | − | 1.83783i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −27.7215 | − | 4.17834i | −2.95512 | − | 0.445412i | ||||
\(89\) | −0.289929 | − | 0.269015i | −0.0307325 | − | 0.0285155i | 0.664657 | − | 0.747149i | \(-0.268578\pi\) |
−0.695390 | + | 0.718633i | \(0.744768\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.464628 | + | 4.15444i | 0.0487062 | + | 0.435503i | ||||
\(92\) | −15.6239 | + | 19.5918i | −1.62890 | + | 2.04258i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −26.7298 | − | 18.2241i | −2.75697 | − | 1.87967i | ||||
\(95\) | −2.00711 | + | 5.11403i | −0.205925 | + | 0.524688i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.55821 | 0.767420 | 0.383710 | − | 0.923454i | \(-0.374646\pi\) | ||||
0.383710 | + | 0.923454i | \(0.374646\pi\) | |||||||
\(98\) | −15.8163 | − | 9.16633i | −1.59769 | − | 0.925939i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.44097 | − | 2.91215i | −0.944097 | − | 0.291215i | ||||
\(101\) | −2.24733 | + | 5.72611i | −0.223618 | + | 0.569769i | −0.998018 | − | 0.0629268i | \(-0.979957\pi\) |
0.774400 | + | 0.632696i | \(0.218052\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.8434 | + | 2.84019i | −1.85670 | + | 0.279852i | −0.979675 | − | 0.200594i | \(-0.935713\pi\) |
−0.877024 | + | 0.480446i | \(0.840475\pi\) | |||||||
\(104\) | −7.25478 | + | 9.09720i | −0.711389 | + | 0.892054i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.95716 | − | 3.70817i | −0.287225 | − | 0.360169i | ||||
\(107\) | −6.36556 | − | 5.90638i | −0.615382 | − | 0.570991i | 0.309664 | − | 0.950846i | \(-0.399783\pi\) |
−0.925046 | + | 0.379855i | \(0.875974\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.12935 | + | 7.54293i | −0.778650 | + | 0.722482i | −0.965641 | − | 0.259880i | \(-0.916317\pi\) |
0.186991 | + | 0.982362i | \(0.440127\pi\) | |||||||
\(110\) | 14.1086 | − | 9.61909i | 1.34520 | − | 0.917144i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.54815 | − | 24.5188i | −0.618742 | − | 2.31681i | ||||
\(113\) | 0.649444 | − | 2.84540i | 0.0610945 | − | 0.267673i | −0.935151 | − | 0.354251i | \(-0.884736\pi\) |
0.996245 | + | 0.0865779i | \(0.0275931\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.667328 | − | 8.90487i | −0.0622286 | − | 0.830384i | ||||
\(116\) | −9.97266 | − | 17.2732i | −0.925939 | − | 1.60377i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.04328 | + | 1.46557i | 0.280157 | + | 0.134917i | ||||
\(119\) | 0.522118 | − | 13.6529i | 0.0478625 | − | 1.25156i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.260945 | − | 3.48208i | 0.0237223 | − | 0.316552i | ||||
\(122\) | −21.2529 | + | 6.55565i | −1.92415 | + | 0.593521i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.75613 | + | 50.1221i | −0.337311 | + | 4.50110i | ||||
\(125\) | 10.9097 | − | 5.25383i | 0.975792 | − | 0.469917i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.0092 | + | 6.26488i | 1.15438 | + | 0.555919i | 0.910346 | − | 0.413849i | \(-0.135816\pi\) |
0.244031 | + | 0.969767i | \(0.421530\pi\) | |||||||
\(128\) | −0.176272 | + | 0.305312i | −0.0155804 | + | 0.0269860i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.529633 | − | 7.06746i | −0.0464519 | − | 0.619857i | ||||
\(131\) | 5.93545 | + | 15.1233i | 0.518583 | + | 1.32133i | 0.915073 | + | 0.403289i | \(0.132133\pi\) |
−0.396490 | + | 0.918039i | \(0.629772\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.03077 | + | 6.80471i | −0.436223 | + | 0.590044i | ||||
\(134\) | −4.57429 | − | 20.0413i | −0.395159 | − | 1.73130i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 27.8780 | − | 25.8670i | 2.39052 | − | 2.21808i | ||||
\(137\) | 15.0611 | + | 2.27009i | 1.28676 | + | 0.193947i | 0.756558 | − | 0.653927i | \(-0.226880\pi\) |
0.530198 | + | 0.847874i | \(0.322118\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.45552 | + | 3.07913i | 0.208275 | + | 0.261168i | 0.874986 | − | 0.484148i | \(-0.160870\pi\) |
−0.666712 | + | 0.745316i | \(0.732299\pi\) | |||||||
\(140\) | 18.5368 | + | 11.6688i | 1.56665 | + | 0.986190i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 31.1726 | − | 4.69852i | 2.61595 | − | 0.394291i | ||||
\(143\) | −4.96970 | − | 3.38828i | −0.415587 | − | 0.283342i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.79186 | + | 2.09501i | 0.564033 | + | 0.173981i | ||||
\(146\) | −7.48856 | −0.619758 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.84637 | −0.809367 | ||||||||
\(149\) | −13.8941 | − | 4.28577i | −1.13825 | − | 0.351104i | −0.332352 | − | 0.943156i | \(-0.607842\pi\) |
−0.805900 | + | 0.592051i | \(0.798318\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.01797 | + | 0.694042i | 0.0828415 | + | 0.0564804i | 0.604032 | − | 0.796960i | \(-0.293560\pi\) |
−0.521191 | + | 0.853440i | \(0.674512\pi\) | |||||||
\(152\) | −23.2917 | + | 3.51065i | −1.88920 | + | 0.284752i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 24.8339 | − | 8.66680i | 2.00117 | − | 0.698391i | ||||
\(155\) | −11.1676 | − | 14.0037i | −0.897000 | − | 1.12480i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.10689 | − | 0.468288i | −0.247957 | − | 0.0373735i | 0.0238878 | − | 0.999715i | \(-0.492396\pi\) |
−0.271845 | + | 0.962341i | \(0.587634\pi\) | |||||||
\(158\) | 1.85210 | − | 1.71850i | 0.147345 | − | 0.136717i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.94474 | + | 17.2831i | 0.311859 | + | 1.36635i | ||||
\(161\) | 2.56838 | − | 13.5133i | 0.202417 | − | 1.06500i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.66250 | − | 6.78395i | −0.208543 | − | 0.531360i | 0.787883 | − | 0.615825i | \(-0.211177\pi\) |
−0.996426 | + | 0.0844649i | \(0.973082\pi\) | |||||||
\(164\) | 2.44727 | + | 32.6566i | 0.191100 | + | 2.55005i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.3890 | + | 23.1904i | −1.03919 | + | 1.79993i | ||||
\(167\) | −11.8835 | − | 5.72280i | −0.919574 | − | 0.442843i | −0.0866547 | − | 0.996238i | \(-0.527618\pi\) |
−0.832919 | + | 0.553395i | \(0.813332\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.46336 | − | 4.55731i | 0.727951 | − | 0.350563i | ||||
\(170\) | −1.73104 | + | 23.0991i | −0.132765 | + | 1.77162i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −53.3599 | + | 16.4594i | −4.06866 | + | 1.25501i | ||||
\(173\) | 1.44410 | − | 19.2702i | 0.109793 | − | 1.46508i | −0.621711 | − | 0.783247i | \(-0.713562\pi\) |
0.731503 | − | 0.681838i | \(-0.238819\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.32952 | − | 1.00385i | 0.402874 | − | 0.0758843i | ||||
\(176\) | 32.8990 | + | 15.8433i | 2.47985 | + | 1.19423i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.516438 | + | 0.894497i | 0.0387087 | + | 0.0670454i | ||||
\(179\) | −0.108159 | − | 1.44328i | −0.00808418 | − | 0.107876i | 0.991702 | − | 0.128559i | \(-0.0410351\pi\) |
−0.999786 | + | 0.0206827i | \(0.993416\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.38463 | + | 14.8290i | −0.251578 | + | 1.10223i | 0.678422 | + | 0.734672i | \(0.262664\pi\) |
−0.930000 | + | 0.367561i | \(0.880193\pi\) | |||||||
\(182\) | 2.03843 | − | 10.7250i | 0.151098 | − | 0.794988i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 31.6341 | − | 21.5678i | 2.33210 | − | 1.59000i | ||||
\(185\) | 2.57214 | − | 2.38660i | 0.189107 | − | 0.175466i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.4109 | + | 13.3714i | 1.05383 | + | 0.977810i | ||||
\(188\) | 37.2282 | + | 46.6827i | 2.71515 | + | 3.40469i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.94525 | − | 11.2170i | 0.648957 | − | 0.813766i | ||||
\(191\) | −8.47349 | + | 1.27717i | −0.613120 | + | 0.0924130i | −0.448259 | − | 0.893904i | \(-0.647956\pi\) |
−0.164861 | + | 0.986317i | \(0.552718\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.33106 | − | 21.2272i | 0.599683 | − | 1.52797i | −0.231999 | − | 0.972716i | \(-0.574527\pi\) |
0.831682 | − | 0.555252i | \(-0.187378\pi\) | |||||||
\(194\) | −18.8614 | − | 5.81796i | −1.35417 | − | 0.417705i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 22.9080 | + | 24.7707i | 1.63629 | + | 1.76934i | ||||
\(197\) | −3.97035 | −0.282876 | −0.141438 | − | 0.989947i | \(-0.545173\pi\) | ||||
−0.141438 | + | 0.989947i | \(0.545173\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.82262 | + | 14.8358i | −0.412755 | + | 1.05168i | 0.561748 | + | 0.827308i | \(0.310129\pi\) |
−0.974503 | + | 0.224374i | \(0.927966\pi\) | |||||||
\(200\) | 12.4723 | + | 8.50350i | 0.881928 | + | 0.601288i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.0159 | − | 12.5595i | 0.704715 | − | 0.883684i | ||||
\(203\) | 9.26541 | + | 5.83249i | 0.650304 | + | 0.409361i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.55470 | − | 7.93760i | −0.597486 | − | 0.554386i | ||||
\(206\) | 49.2097 | + | 7.41717i | 3.42860 | + | 0.516779i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 12.5221 | − | 8.53745i | 0.868254 | − | 0.591966i | ||||
\(209\) | −2.70944 | − | 11.8708i | −0.187416 | − | 0.821121i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.450809 | − | 1.97512i | 0.0310350 | − | 0.135973i | −0.957037 | − | 0.289966i | \(-0.906356\pi\) |
0.988072 | + | 0.153993i | \(0.0492132\pi\) | |||||||
\(212\) | 3.19813 | + | 8.14871i | 0.219649 | + | 0.559656i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.3387 | + | 19.6392i | 0.775096 | + | 1.34251i | ||||
\(215\) | 9.94959 | − | 17.2332i | 0.678556 | − | 1.17529i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.0122 | − | 25.2970i | −0.747556 | − | 1.71728i | ||||
\(218\) | 26.0928 | − | 12.5657i | 1.76723 | − | 0.851053i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −30.1158 | + | 9.28950i | −2.03041 | + | 0.626298i | ||||
\(221\) | 7.79687 | − | 2.40502i | 0.524475 | − | 0.161779i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.1422 | + | 9.69996i | −1.34882 | + | 0.649557i | −0.962114 | − | 0.272646i | \(-0.912101\pi\) |
−0.386705 | + | 0.922203i | \(0.626387\pi\) | |||||||
\(224\) | −1.04351 | + | 27.2868i | −0.0697223 | + | 1.82318i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.81093 | + | 6.60073i | −0.253500 | + | 0.439074i | ||||
\(227\) | 5.82472 | + | 10.0887i | 0.386600 | + | 0.669611i | 0.991990 | − | 0.126318i | \(-0.0403160\pi\) |
−0.605390 | + | 0.795929i | \(0.706983\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.52259 | − | 3.87949i | −0.100616 | − | 0.256364i | 0.871698 | − | 0.490043i | \(-0.163019\pi\) |
−0.972314 | + | 0.233679i | \(0.924924\pi\) | |||||||
\(230\) | −5.18926 | + | 22.7356i | −0.342170 | + | 1.49914i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.78112 | + | 29.7100i | 0.445203 | + | 1.95056i | ||||
\(233\) | −13.3178 | + | 9.07991i | −0.872477 | + | 0.594844i | −0.914641 | − | 0.404266i | \(-0.867527\pi\) |
0.0421648 | + | 0.999111i | \(0.486575\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.0401 | − | 3.17129i | −1.37251 | − | 0.206872i | ||||
\(236\) | −4.57003 | − | 4.24037i | −0.297484 | − | 0.276025i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −11.8123 | + | 33.6687i | −0.765680 | + | 2.18242i | ||||
\(239\) | −7.73805 | + | 9.70321i | −0.500533 | + | 0.627648i | −0.966349 | − | 0.257233i | \(-0.917189\pi\) |
0.465817 | + | 0.884881i | \(0.345761\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.48357 | + | 2.37506i | 0.224397 | + | 0.152991i | 0.670300 | − | 0.742090i | \(-0.266165\pi\) |
−0.445904 | + | 0.895081i | \(0.647118\pi\) | |||||||
\(242\) | −3.33153 | + | 8.48859i | −0.214159 | + | 0.545667i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 41.0494 | 2.62792 | ||||||||
\(245\) | −11.9882 | − | 0.918253i | −0.765898 | − | 0.0586650i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.82917 | − | 1.48960i | −0.307273 | − | 0.0947811i | ||||
\(248\) | 28.0565 | − | 71.4868i | 1.78159 | − | 4.53942i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −31.2691 | + | 4.71306i | −1.97763 | + | 0.298080i | ||||
\(251\) | 5.32606 | − | 6.67867i | 0.336178 | − | 0.421554i | −0.584795 | − | 0.811181i | \(-0.698825\pi\) |
0.920972 | + | 0.389628i | \(0.127396\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.3398 | + | 15.4736i | 0.775797 | + | 0.972819i | ||||
\(254\) | −27.6417 | − | 25.6478i | −1.73440 | − | 1.60928i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.0654 | − | 11.1951i | 0.754090 | − | 0.699693i | ||||
\(257\) | 1.35475 | − | 0.923655i | 0.0845072 | − | 0.0576160i | −0.520329 | − | 0.853966i | \(-0.674191\pi\) |
0.604837 | + | 0.796350i | \(0.293238\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.78058 | − | 2.52157i | 0.297051 | − | 0.156683i | ||||
\(260\) | −2.91073 | + | 12.7528i | −0.180516 | + | 0.790892i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.17060 | − | 42.3087i | −0.195880 | − | 2.61384i | ||||
\(263\) | 11.1172 | + | 19.2555i | 0.685513 | + | 1.18734i | 0.973275 | + | 0.229642i | \(0.0737555\pi\) |
−0.287762 | + | 0.957702i | \(0.592911\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.81055 | − | 1.35349i | −0.172651 | − | 0.0831442i | ||||
\(266\) | 17.7922 | − | 13.1086i | 1.09091 | − | 0.803739i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.83531 | + | 37.8346i | −0.173194 | + | 2.31112i | ||||
\(269\) | −18.9224 | + | 5.83678i | −1.15372 | + | 0.355875i | −0.811846 | − | 0.583872i | \(-0.801537\pi\) |
−0.341872 | + | 0.939747i | \(0.611061\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.803367 | − | 10.7202i | 0.0488011 | − | 0.651205i | −0.918148 | − | 0.396237i | \(-0.870316\pi\) |
0.966949 | − | 0.254968i | \(-0.0820650\pi\) | |||||||
\(272\) | −44.6287 | + | 21.4921i | −2.70602 | + | 1.30315i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −35.8373 | − | 17.2583i | −2.16501 | − | 1.04261i | ||||
\(275\) | −3.90159 | + | 6.75775i | −0.235275 | + | 0.407508i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.102015 | + | 1.36129i | 0.00612948 | + | 0.0817922i | 0.999430 | − | 0.0337711i | \(-0.0107517\pi\) |
−0.993300 | + | 0.115563i | \(0.963133\pi\) | |||||||
\(278\) | −3.75754 | − | 9.57406i | −0.225362 | − | 0.574214i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −21.8087 | − | 25.3845i | −1.30332 | − | 1.51701i | ||||
\(281\) | −3.34721 | − | 14.6651i | −0.199678 | − | 0.874847i | −0.971128 | − | 0.238557i | \(-0.923326\pi\) |
0.771450 | − | 0.636289i | \(-0.219532\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.4476 | − | 16.1890i | 1.03715 | − | 0.962339i | 0.0378373 | − | 0.999284i | \(-0.487953\pi\) |
0.999317 | + | 0.0369450i | \(0.0117626\pi\) | |||||||
\(284\) | −57.5341 | − | 8.67187i | −3.41402 | − | 0.514581i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.79364 | + | 12.2808i | 0.579110 | + | 0.726181i | ||||
\(287\) | −9.55126 | − | 15.2286i | −0.563793 | − | 0.898915i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.55991 | + | 1.44092i | −0.562348 | + | 0.0847602i | ||||
\(290\) | −15.3363 | − | 10.4561i | −0.900579 | − | 0.614005i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.2073 | + | 4.07391i | 0.772899 | + | 0.238408i | ||||
\(293\) | 31.1663 | 1.82075 | 0.910377 | − | 0.413780i | \(-0.135792\pi\) | ||||
0.910377 | + | 0.413780i | \(0.135792\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.22161 | 0.129347 | ||||||||
\(296\) | 14.3757 | + | 4.43432i | 0.835572 | + | 0.257740i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 31.3736 | + | 21.3901i | 1.81742 | + | 1.23910i | ||||
\(299\) | 8.12273 | − | 1.22430i | 0.469750 | − | 0.0708033i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.6920 | − | 21.6563i | 1.25031 | − | 1.24825i | ||||
\(302\) | −2.00609 | − | 2.51556i | −0.115438 | − | 0.144754i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 30.3374 | + | 4.57263i | 1.73997 | + | 0.262258i | ||||
\(305\) | −10.7232 | + | 9.94969i | −0.614009 | + | 0.569717i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.121847 | + | 0.533847i | 0.00695418 | + | 0.0304682i | 0.978286 | − | 0.207260i | \(-0.0664545\pi\) |
−0.971332 | + | 0.237728i | \(0.923597\pi\) | |||||||
\(308\) | −48.5135 | + | 1.77524i | −2.76432 | + | 0.101153i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 17.0891 | + | 43.5422i | 0.970593 | + | 2.47303i | ||||
\(311\) | 1.56398 | + | 20.8699i | 0.0886853 | + | 1.18342i | 0.847021 | + | 0.531559i | \(0.178394\pi\) |
−0.758336 | + | 0.651864i | \(0.773987\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.6552 | − | 20.1873i | 0.658789 | − | 1.14106i | −0.322141 | − | 0.946692i | \(-0.604402\pi\) |
0.980929 | − | 0.194364i | \(-0.0622643\pi\) | |||||||
\(314\) | 7.39272 | + | 3.56015i | 0.417195 | + | 0.200911i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.20138 | + | 2.02328i | −0.236346 | + | 0.113818i | ||||
\(317\) | 0.397685 | − | 5.30674i | 0.0223362 | − | 0.298056i | −0.974837 | − | 0.222919i | \(-0.928441\pi\) |
0.997173 | − | 0.0751373i | \(-0.0239395\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.0530 | + | 4.64325i | −0.842808 | + | 0.259972i | ||||
\(320\) | 0.997244 | − | 13.3073i | 0.0557476 | − | 0.743900i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −16.8112 | + | 31.7451i | −0.936854 | + | 1.76909i | ||||
\(323\) | 14.8816 | + | 7.16661i | 0.828036 | + | 0.398761i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.61936 | + | 2.80481i | 0.0898257 | + | 0.155583i | ||||
\(326\) | 1.42226 | + | 18.9787i | 0.0787715 | + | 1.05113i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.1339 | − | 48.7808i | 0.614766 | − | 2.69347i | ||||
\(329\) | −30.0300 | − | 13.1314i | −1.65561 | − | 0.723957i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.3887 | + | 7.08286i | −0.571012 | + | 0.389309i | −0.814126 | − | 0.580688i | \(-0.802783\pi\) |
0.243114 | + | 0.969998i | \(0.421831\pi\) | |||||||
\(332\) | 36.2297 | − | 33.6162i | 1.98836 | − | 1.84493i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 25.2499 | + | 23.4285i | 1.38162 | + | 1.28195i | ||||
\(335\) | −8.42982 | − | 10.5707i | −0.460570 | − | 0.577537i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.44269 | + | 9.33284i | −0.405429 | + | 0.508392i | −0.942069 | − | 0.335419i | \(-0.891122\pi\) |
0.536640 | + | 0.843812i | \(0.319693\pi\) | |||||||
\(338\) | −27.1237 | + | 4.08823i | −1.47533 | + | 0.222371i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 15.6193 | − | 39.7973i | 0.847076 | − | 2.15831i | ||||
\(341\) | 37.9340 | + | 11.7011i | 2.05424 | + | 0.633649i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.4658 | − | 6.16003i | −0.943064 | − | 0.332610i | ||||
\(344\) | 85.3181 | 4.60004 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.4370 | + | 46.9768i | −0.991181 | + | 2.52549i | ||||
\(347\) | −3.29079 | − | 2.24362i | −0.176659 | − | 0.120444i | 0.471762 | − | 0.881726i | \(-0.343618\pi\) |
−0.648421 | + | 0.761282i | \(0.724570\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.55174 | − | 9.46958i | 0.404235 | − | 0.506895i | −0.537494 | − | 0.843268i | \(-0.680629\pi\) |
0.941729 | + | 0.336373i | \(0.109200\pi\) | |||||||
\(350\) | −14.0725 | − | 1.59732i | −0.752204 | − | 0.0853805i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −28.8017 | − | 26.7241i | −1.53514 | − | 1.42440i | ||||
\(353\) | 4.39316 | + | 0.662162i | 0.233824 | + | 0.0352433i | 0.264909 | − | 0.964273i | \(-0.414658\pi\) |
−0.0310848 | + | 0.999517i | \(0.509896\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.1314 | − | 11.6800i | 0.909240 | − | 0.619909i | ||||
\(356\) | −0.424200 | − | 1.85854i | −0.0224826 | − | 0.0985026i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.841063 | + | 3.68494i | −0.0444516 | + | 0.194755i | ||||
\(359\) | −0.213363 | − | 0.543640i | −0.0112609 | − | 0.0286922i | 0.925133 | − | 0.379644i | \(-0.123953\pi\) |
−0.936394 | + | 0.350952i | \(0.885858\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.38480 | + | 7.59470i | 0.230779 | + | 0.399721i | ||||
\(362\) | 19.8610 | − | 34.4002i | 1.04387 | − | 1.80804i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.42968 | + | 17.8063i | −0.494249 | + | 0.933304i | ||||
\(365\) | −4.43756 | + | 2.13701i | −0.232272 | + | 0.111856i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.72093 | + | 0.530838i | −0.0898320 | + | 0.0277095i | −0.339345 | − | 0.940662i | \(-0.610206\pi\) |
0.249513 | + | 0.968371i | \(0.419729\pi\) | |||||||
\(368\) | −47.6532 | + | 14.6991i | −2.48409 | + | 0.766241i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.25582 | + | 3.97579i | −0.429200 | + | 0.206692i | ||||
\(371\) | −3.63956 | − | 3.13732i | −0.188957 | − | 0.162881i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.2267 | − | 17.7131i | 0.529516 | − | 0.917149i | −0.469891 | − | 0.882724i | \(-0.655707\pi\) |
0.999407 | − | 0.0344248i | \(-0.0109599\pi\) | |||||||
\(374\) | −25.6695 | − | 44.4608i | −1.32734 | − | 2.29901i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −33.3297 | − | 84.9226i | −1.71885 | − | 4.37955i | ||||
\(377\) | −1.45490 | + | 6.37431i | −0.0749309 | + | 0.328294i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.46660 | + | 19.5694i | 0.229434 | + | 1.00521i | 0.950103 | + | 0.311936i | \(0.100977\pi\) |
−0.720670 | + | 0.693279i | \(0.756165\pi\) | |||||||
\(380\) | −21.8787 | + | 14.9166i | −1.12235 | + | 0.765206i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 22.1285 | + | 3.33534i | 1.13219 | + | 0.170651i | ||||
\(383\) | −10.1445 | − | 9.41270i | −0.518359 | − | 0.480967i | 0.377062 | − | 0.926188i | \(-0.376934\pi\) |
−0.895420 | + | 0.445221i | \(0.853125\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.2428 | − | 12.2226i | 0.623949 | − | 0.622922i | ||||
\(386\) | −37.1297 | + | 46.5592i | −1.88985 | + | 2.36980i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 30.1000 | + | 20.5219i | 1.52810 | + | 1.04184i | ||||
\(389\) | −8.90724 | + | 22.6953i | −0.451615 | + | 1.15070i | 0.505971 | + | 0.862550i | \(0.331134\pi\) |
−0.957586 | + | 0.288146i | \(0.906961\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.8480 | −1.35776 | ||||||||
\(392\) | −22.2903 | − | 46.4819i | −1.12583 | − | 2.34769i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.90794 | + | 3.05620i | 0.499155 | + | 0.153969i | ||||
\(395\) | 0.607106 | − | 1.54688i | 0.0305468 | − | 0.0778320i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.72395 | − | 1.01347i | 0.337465 | − | 0.0508647i | 0.0218763 | − | 0.999761i | \(-0.493036\pi\) |
0.315589 | + | 0.948896i | \(0.397798\pi\) | |||||||
\(398\) | 25.9502 | − | 32.5405i | 1.30076 | − | 1.63111i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.2589 | − | 15.3721i | −0.612943 | − | 0.768606i | ||||
\(401\) | 23.6232 | + | 21.9191i | 1.17969 | + | 1.09459i | 0.993704 | + | 0.112035i | \(0.0357368\pi\) |
0.185981 | + | 0.982553i | \(0.440454\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0781 | − | 11.2069i | 0.601655 | − | 0.558254i | ||||
\(404\) | −24.4972 | + | 16.7019i | −1.21878 | + | 0.830952i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.6321 | − | 21.6870i | −0.924694 | − | 1.07631i | ||||
\(407\) | −1.73048 | + | 7.58172i | −0.0857766 | + | 0.375812i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.451630 | + | 6.02658i | 0.0223316 | + | 0.297995i | 0.997176 | + | 0.0751063i | \(0.0239296\pi\) |
−0.974844 | + | 0.222889i | \(0.928451\pi\) | |||||||
\(410\) | 15.2381 | + | 26.3932i | 0.752556 | + | 1.30347i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −82.7543 | − | 39.8524i | −4.07701 | − | 1.96339i | ||||
\(413\) | 3.30475 | + | 0.888424i | 0.162616 | + | 0.0437165i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.31616 | + | 17.5629i | −0.0646078 | + | 0.862131i | ||||
\(416\) | −15.5829 | + | 4.80668i | −0.764014 | + | 0.235667i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.37626 | + | 31.7090i | −0.116227 | + | 1.55094i | ||||
\(419\) | −9.19292 | + | 4.42708i | −0.449103 | + | 0.216277i | −0.644744 | − | 0.764399i | \(-0.723036\pi\) |
0.195640 | + | 0.980676i | \(0.437322\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.1814 | − | 11.1636i | −1.12979 | − | 0.544080i | −0.226889 | − | 0.973921i | \(-0.572855\pi\) |
−0.902905 | + | 0.429841i | \(0.858570\pi\) | |||||||
\(422\) | −2.64534 | + | 4.58187i | −0.128773 | + | 0.223042i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.999501 | − | 13.3374i | −0.0485401 | − | 0.647722i | ||||
\(425\) | −3.86725 | − | 9.85360i | −0.187589 | − | 0.477970i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.9302 | + | 10.5124i | −0.964488 | + | 0.508731i | ||||
\(428\) | −9.31355 | − | 40.8053i | −0.450188 | − | 1.97240i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −38.0943 | + | 35.3464i | −1.83707 | + | 1.70455i | ||||
\(431\) | 6.66968 | + | 1.00529i | 0.321267 | + | 0.0484232i | 0.307696 | − | 0.951485i | \(-0.400442\pi\) |
0.0135710 | + | 0.999908i | \(0.495680\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.2693 | − | 12.8773i | −0.493511 | − | 0.618843i | 0.471241 | − | 0.882005i | \(-0.343806\pi\) |
−0.964752 | + | 0.263161i | \(0.915235\pi\) | |||||||
\(434\) | 8.00823 | + | 71.6050i | 0.384407 | + | 3.43715i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −52.8550 | + | 7.96660i | −2.53129 | + | 0.381531i | ||||
\(437\) | 13.7394 | + | 9.36740i | 0.657247 | + | 0.448103i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.65409 | − | 2.66943i | −0.413037 | − | 0.127405i | 0.0812706 | − | 0.996692i | \(-0.474102\pi\) |
−0.494308 | + | 0.869287i | \(0.664578\pi\) | |||||||
\(440\) | 48.1527 | 2.29559 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −21.3082 | −1.01353 | ||||||||
\(443\) | 4.52712 | + | 1.39643i | 0.215090 | + | 0.0663464i | 0.400427 | − | 0.916328i | \(-0.368862\pi\) |
−0.185338 | + | 0.982675i | \(0.559338\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.561293 | + | 0.382683i | 0.0266078 | + | 0.0181409i | ||||
\(446\) | 57.7310 | − | 8.70155i | 2.73364 | − | 0.412030i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.80504 | − | 19.3964i | 0.321508 | − | 0.916395i | ||||
\(449\) | −6.74742 | − | 8.46100i | −0.318430 | − | 0.399299i | 0.596695 | − | 0.802468i | \(-0.296480\pi\) |
−0.915126 | + | 0.403169i | \(0.867909\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.5757 | + | 3.85492i | 1.20431 | + | 0.181521i | ||||
\(452\) | 10.3121 | − | 9.56825i | 0.485042 | − | 0.450053i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.76966 | − | 29.6598i | −0.317716 | − | 1.39200i | ||||
\(455\) | −1.85266 | − | 6.93709i | −0.0868543 | − | 0.325216i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.51500 | − | 19.1479i | −0.351537 | − | 0.895701i | −0.991830 | − | 0.127570i | \(-0.959282\pi\) |
0.640293 | − | 0.768131i | \(-0.278813\pi\) | |||||||
\(458\) | 0.813337 | + | 10.8532i | 0.0380047 | + | 0.507138i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 21.5207 | − | 37.2750i | 1.00341 | − | 1.73795i | ||||
\(461\) | 6.28012 | + | 3.02435i | 0.292495 | + | 0.140858i | 0.574377 | − | 0.818591i | \(-0.305244\pi\) |
−0.281882 | + | 0.959449i | \(0.590959\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.06099 | + | 2.43725i | −0.235204 | + | 0.113268i | −0.547774 | − | 0.836626i | \(-0.684525\pi\) |
0.312570 | + | 0.949895i | \(0.398810\pi\) | |||||||
\(464\) | 2.96623 | − | 39.5816i | 0.137704 | − | 1.83753i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 40.2236 | − | 12.4073i | 1.86332 | − | 0.574758i | ||||
\(467\) | −2.93227 | + | 39.1284i | −0.135689 | + | 1.81065i | 0.350253 | + | 0.936655i | \(0.386096\pi\) |
−0.485942 | + | 0.873991i | \(0.661523\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.31254 | − | 19.0954i | −0.383837 | − | 0.881745i | ||||
\(470\) | 50.0641 | + | 24.1096i | 2.30929 | + | 1.11209i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.76260 | + | 8.24907i | 0.219217 | + | 0.379694i | ||||
\(473\) | 3.29584 | + | 43.9799i | 0.151543 | + | 2.02220i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.45891 | + | 6.39188i | −0.0669392 | + | 0.293280i | ||||
\(476\) | 39.1494 | − | 52.9542i | 1.79441 | − | 2.42715i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 26.7793 | − | 18.2578i | 1.22485 | − | 0.835092i | ||||
\(479\) | 3.80819 | − | 3.53348i | 0.174001 | − | 0.161449i | −0.588365 | − | 0.808595i | \(-0.700228\pi\) |
0.762366 | + | 0.647146i | \(0.224038\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.36609 | + | 2.19541i | 0.107884 | + | 0.100102i | ||||
\(482\) | −6.86498 | − | 8.60841i | −0.312691 | − | 0.392102i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.4936 | − | 13.1586i | 0.476984 | − | 0.598119i | ||||
\(485\) | −12.8371 | + | 1.93488i | −0.582903 | + | 0.0878585i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.32620 | + | 21.2148i | −0.377296 | + | 0.961335i | 0.608525 | + | 0.793535i | \(0.291762\pi\) |
−0.985821 | + | 0.167800i | \(0.946334\pi\) | |||||||
\(488\) | −59.9322 | − | 18.4866i | −2.71300 | − | 0.836850i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 29.2095 | + | 11.5195i | 1.31955 | + | 0.520396i | ||||
\(491\) | 13.6563 | 0.616302 | 0.308151 | − | 0.951337i | \(-0.400290\pi\) | ||||
0.308151 | + | 0.951337i | \(0.400290\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.80713 | − | 19.8922i | 0.351615 | − | 0.895901i | ||||
\(494\) | 10.9045 | + | 7.43455i | 0.490616 | + | 0.334496i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −62.3653 | + | 78.2036i | −2.80028 | + | 3.51144i | ||||
\(497\) | 30.1546 | − | 10.5237i | 1.35262 | − | 0.472051i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.4777 | + | 15.2890i | 0.737642 | + | 0.684432i | 0.956633 | − | 0.291295i | \(-0.0940862\pi\) |
−0.218991 | + | 0.975727i | \(0.570277\pi\) | |||||||
\(500\) | 57.7122 | + | 8.69871i | 2.58097 | + | 0.389018i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.4320 | + | 12.5667i | −0.822661 | + | 0.560881i | ||||
\(503\) | 6.22443 | + | 27.2710i | 0.277534 | + | 1.21595i | 0.900901 | + | 0.434025i | \(0.142907\pi\) |
−0.623367 | + | 0.781929i | \(0.714236\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.35107 | − | 10.3007i | 0.104621 | − | 0.458376i | ||||
\(506\) | −18.8829 | − | 48.1128i | −0.839447 | − | 2.13888i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 34.7978 | + | 60.2716i | 1.54390 | + | 2.67412i | ||||
\(509\) | 4.45457 | − | 7.71554i | 0.197445 | − | 0.341985i | −0.750254 | − | 0.661150i | \(-0.770069\pi\) |
0.947699 | + | 0.319164i | \(0.103402\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.45566 | + | 1.40433i | −0.329819 | + | 0.0621238i | ||||
\(512\) | −38.0913 | + | 18.3438i | −1.68341 | + | 0.810689i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.09175 | + | 1.26214i | −0.180479 | + | 0.0556705i | ||||
\(515\) | 31.2772 | − | 9.64774i | 1.37824 | − | 0.425130i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 42.4885 | − | 20.4614i | 1.86864 | − | 0.899891i | ||||
\(518\) | −13.8708 | + | 2.61267i | −0.609449 | + | 0.114794i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.99289 | − | 17.3082i | 0.438217 | − | 0.759014i | ||||
\(521\) | 12.8583 | + | 22.2713i | 0.563333 | + | 0.975721i | 0.997203 | + | 0.0747457i | \(0.0238145\pi\) |
−0.433870 | + | 0.900976i | \(0.642852\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.34565 | − | 16.1684i | −0.277476 | − | 0.706997i | −0.999879 | − | 0.0155252i | \(-0.995058\pi\) |
0.722404 | − | 0.691472i | \(-0.243037\pi\) | |||||||
\(524\) | −17.4248 | + | 76.3432i | −0.761208 | + | 3.33507i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.9207 | − | 56.6092i | −0.563368 | − | 2.46828i | ||||
\(527\) | −44.4941 | + | 30.3356i | −1.93819 | + | 1.32144i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.98431 | − | 0.600538i | −0.173231 | − | 0.0261104i | ||||
\(530\) | 5.97182 | + | 5.54104i | 0.259399 | + | 0.240688i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −38.5107 | + | 13.4399i | −1.66965 | + | 0.582693i | ||||
\(533\) | 6.69323 | − | 8.39304i | 0.289916 | − | 0.363543i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.3235 | + | 8.40201i | 0.532791 | + | 0.363251i | ||||
\(536\) | 21.1784 | − | 53.9617i | 0.914768 | − | 2.33079i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 51.7133 | 2.22952 | ||||||||
\(539\) | 23.0995 | − | 13.2858i | 0.994966 | − | 0.572261i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.1194 | − | 8.05678i | −1.12296 | − | 0.346388i | −0.322976 | − | 0.946407i | \(-0.604683\pi\) |
−0.799986 | + | 0.600019i | \(0.795160\pi\) | |||||||
\(542\) | −10.2567 | + | 26.1336i | −0.440563 | + | 1.12254i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 52.7033 | − | 7.94375i | 2.25964 | − | 0.340585i | ||||
\(545\) | 11.8762 | − | 14.8923i | 0.508720 | − | 0.637914i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.44712 | + | 1.81463i | 0.0618742 | + | 0.0775878i | 0.811806 | − | 0.583928i | \(-0.198485\pi\) |
−0.749931 | + | 0.661516i | \(0.769913\pi\) | |||||||
\(548\) | 53.8160 | + | 49.9340i | 2.29891 | + | 2.13307i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 14.9382 | − | 13.8606i | 0.636965 | − | 0.591017i | ||||
\(551\) | −10.9358 | + | 7.45590i | −0.465880 | + | 0.317632i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.52170 | − | 2.05827i | 0.0647091 | − | 0.0875267i | ||||
\(554\) | 0.793285 | − | 3.47561i | 0.0337035 | − | 0.147665i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.41858 | + | 18.9296i | 0.0601610 | + | 0.802793i | ||||
\(557\) | −21.0582 | − | 36.4738i | −0.892264 | − | 1.54545i | −0.837155 | − | 0.546966i | \(-0.815783\pi\) |
−0.0551086 | − | 0.998480i | \(-0.517550\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.4923 | + | 7.94227i | 0.697550 | + | 0.335922i | ||||
\(560\) | 17.3983 | + | 39.9672i | 0.735214 | + | 1.68892i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.93561 | + | 39.1730i | −0.123831 | + | 1.65241i | ||||
\(563\) | −27.5244 | + | 8.49015i | −1.16002 | + | 0.357817i | −0.814256 | − | 0.580506i | \(-0.802855\pi\) |
−0.345759 | + | 0.938323i | \(0.612379\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.374621 | + | 4.99898i | −0.0157604 | + | 0.210308i | ||||
\(566\) | −56.0019 | + | 26.9691i | −2.35393 | + | 1.13359i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 80.0945 | + | 38.5715i | 3.36069 | + | 1.61842i | ||||
\(569\) | 11.2218 | − | 19.4367i | 0.470442 | − | 0.814830i | −0.528986 | − | 0.848630i | \(-0.677428\pi\) |
0.999429 | + | 0.0338006i | \(0.0107611\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.51796 | − | 20.2558i | −0.0635248 | − | 0.847679i | −0.934412 | − | 0.356195i | \(-0.884074\pi\) |
0.870887 | − | 0.491484i | \(-0.163545\pi\) | |||||||
\(572\) | −10.5917 | − | 26.9872i | −0.442861 | − | 1.12839i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.1127 | + | 45.3548i | 0.505576 | + | 1.89307i | ||||
\(575\) | −2.37136 | − | 10.3896i | −0.0988927 | − | 0.433277i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.425690 | − | 0.394982i | 0.0177217 | − | 0.0164433i | −0.671262 | − | 0.741220i | \(-0.734248\pi\) |
0.688984 | + | 0.724777i | \(0.258057\pi\) | |||||||
\(578\) | 24.9657 | + | 3.76298i | 1.03844 | + | 0.156519i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 21.3598 | + | 26.7843i | 0.886917 | + | 1.11216i | ||||
\(581\) | −8.98128 | + | 25.5994i | −0.372606 | + | 1.06204i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.83658 | − | 1.03045i | 0.283142 | − | 0.0426768i | ||||
\(584\) | −17.4480 | − | 11.8958i | −0.722003 | − | 0.492254i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −77.7749 | − | 23.9904i | −3.21285 | − | 0.991034i | ||||
\(587\) | 4.76773 | 0.196785 | 0.0983926 | − | 0.995148i | \(-0.468630\pi\) | ||||
0.0983926 | + | 0.995148i | \(0.468630\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.3541 | 1.37433 | ||||||||
\(590\) | −5.54399 | − | 1.71010i | −0.228243 | − | 0.0704035i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16.1901 | − | 11.0382i | −0.665409 | − | 0.453668i | ||||
\(593\) | −7.56007 | + | 1.13950i | −0.310455 | + | 0.0467935i | −0.302422 | − | 0.953174i | \(-0.597795\pi\) |
−0.00803305 | + | 0.999968i | \(0.502557\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.60834 | + | 23.3222i | 0.106931 | + | 0.956119i | ||||
\(596\) | −43.6958 | − | 54.7928i | −1.78985 | − | 2.24440i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −21.2125 | − | 3.19728i | −0.867445 | − | 0.130746i | ||||
\(599\) | 25.0128 | − | 23.2085i | 1.02199 | − | 0.948272i | 0.0233186 | − | 0.999728i | \(-0.492577\pi\) |
0.998675 | + | 0.0514564i | \(0.0163863\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.93938 | + | 43.5473i | 0.405436 | + | 1.77633i | 0.604772 | + | 0.796399i | \(0.293264\pi\) |
−0.199336 | + | 0.979931i | \(0.563878\pi\) | |||||||
\(602\) | −70.8021 | + | 37.3454i | −2.88568 | + | 1.52209i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.16956 | + | 5.52795i | 0.0882782 | + | 0.224929i | ||||
\(605\) | 0.448204 | + | 5.98087i | 0.0182221 | + | 0.243157i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.40654 | + | 5.90030i | −0.138267 | + | 0.239486i | −0.926841 | − | 0.375455i | \(-0.877487\pi\) |
0.788574 | + | 0.614940i | \(0.210820\pi\) | |||||||
\(608\) | −29.7425 | − | 14.3232i | −1.20622 | − | 0.580884i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 34.4184 | − | 16.5750i | 1.39356 | − | 0.671103i | ||||
\(611\) | 1.46271 | − | 19.5185i | 0.0591749 | − | 0.789634i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.6691 | + | 8.22633i | −1.07716 | + | 0.332258i | −0.782056 | − | 0.623208i | \(-0.785829\pi\) |
−0.295099 | + | 0.955467i | \(0.595353\pi\) | |||||||
\(614\) | 0.106864 | − | 1.42600i | 0.00431267 | − | 0.0575486i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 71.6293 | + | 19.2563i | 2.88603 | + | 0.775857i | ||||
\(617\) | −35.3753 | − | 17.0358i | −1.42416 | − | 0.685837i | −0.446255 | − | 0.894906i | \(-0.647243\pi\) |
−0.977901 | + | 0.209069i | \(0.932957\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.51094 | − | 6.08112i | −0.141116 | − | 0.244421i | 0.786801 | − | 0.617207i | \(-0.211736\pi\) |
−0.927917 | + | 0.372786i | \(0.878403\pi\) | |||||||
\(620\) | −6.45160 | − | 86.0906i | −0.259102 | − | 3.45748i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.1618 | − | 53.2843i | 0.487644 | − | 2.13651i | ||||
\(623\) | 0.681914 | + | 0.793720i | 0.0273203 | + | 0.0317997i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.71631 | + | 5.94268i | −0.348652 | + | 0.237707i | ||||
\(626\) | −44.6245 | + | 41.4055i | −1.78356 | + | 1.65490i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.1015 | − | 10.3007i | −0.442998 | − | 0.411042i | ||||
\(629\) | −6.57744 | − | 8.24785i | −0.262260 | − | 0.328863i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.0954 | + | 18.9290i | −0.600937 | + | 0.753551i | −0.985524 | − | 0.169538i | \(-0.945772\pi\) |
0.384587 | + | 0.923089i | \(0.374344\pi\) | |||||||
\(632\) | 7.04521 | − | 1.06189i | 0.280243 | − | 0.0422399i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.07730 | + | 12.9368i | −0.201646 | + | 0.513784i | ||||
\(635\) | −23.6990 | − | 7.31017i | −0.940465 | − | 0.290095i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0182190 | − | 11.0601i | 0.000721862 | − | 0.438218i | ||||
\(638\) | 41.1387 | 1.62870 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.221227 | − | 0.563677i | 0.00874477 | − | 0.0222813i | ||||
\(641\) | −30.0872 | − | 20.5131i | −1.18837 | − | 0.810218i | −0.202757 | − | 0.979229i | \(-0.564990\pi\) |
−0.985614 | + | 0.169011i | \(0.945943\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.6589 | + | 23.3976i | −0.735837 | + | 0.922710i | −0.999117 | − | 0.0420095i | \(-0.986624\pi\) |
0.263281 | + | 0.964719i | \(0.415195\pi\) | |||||||
\(644\) | 46.9193 | − | 46.8421i | 1.84888 | − | 1.84584i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −31.6203 | − | 29.3393i | −1.24408 | − | 1.15434i | ||||
\(647\) | 43.1638 | + | 6.50590i | 1.69695 | + | 0.255773i | 0.925014 | − | 0.379933i | \(-0.124053\pi\) |
0.771931 | + | 0.635706i | \(0.219291\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.06827 | + | 2.77370i | −0.159693 | + | 0.108877i | ||||
\(650\) | −1.88206 | − | 8.24585i | −0.0738205 | − | 0.323429i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.81638 | − | 34.2458i | 0.306113 | − | 1.34117i | ||||
\(653\) | 8.97306 | + | 22.8630i | 0.351143 | + | 0.894697i | 0.991908 | + | 0.126960i | \(0.0405221\pi\) |
−0.640765 | + | 0.767737i | \(0.721383\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.9525 | − | 24.1664i | −0.545169 | − | 0.944260i | ||||
\(656\) | −32.5855 | + | 56.4398i | −1.27225 | + | 2.20360i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 64.8313 | + | 55.8848i | 2.52739 | + | 2.17862i | ||||
\(659\) | 5.89632 | − | 2.83952i | 0.229688 | − | 0.110612i | −0.315500 | − | 0.948925i | \(-0.602172\pi\) |
0.545189 | + | 0.838313i | \(0.316458\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.3186 | + | 4.41672i | −0.556931 | + | 0.171790i | −0.560427 | − | 0.828204i | \(-0.689363\pi\) |
0.00349685 | + | 0.999994i | \(0.498887\pi\) | |||||||
\(662\) | 31.3768 | − | 9.67845i | 1.21949 | − | 0.376164i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −68.0345 | + | 32.7637i | −2.64025 | + | 1.27148i | ||||
\(665\) | 6.80243 | − | 12.8452i | 0.263787 | − | 0.498116i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.7569 | − | 18.6314i | 0.416508 | − | 0.721413i | ||||
\(668\) | −31.7869 | − | 55.0565i | −1.22987 | − | 2.13020i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.8996 | + | 32.8678i | 0.498357 | + | 1.26979i | ||||
\(671\) | 7.21434 | − | 31.6081i | 0.278506 | − | 1.22022i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.09355 | − | 17.9350i | −0.157795 | − | 0.691344i | −0.990487 | − | 0.137607i | \(-0.956059\pi\) |
0.832692 | − | 0.553736i | \(-0.186798\pi\) | |||||||
\(674\) | 25.7571 | − | 17.5609i | 0.992126 | − | 0.676420i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 50.0611 | + | 7.54550i | 1.92543 | + | 0.290211i | ||||
\(677\) | −8.98052 | − | 8.33270i | −0.345149 | − | 0.320252i | 0.488481 | − | 0.872574i | \(-0.337551\pi\) |
−0.833630 | + | 0.552323i | \(0.813742\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.8695 | − | 2.25533i | −0.762523 | − | 0.0865518i | ||||
\(680\) | −40.7270 | + | 51.0700i | −1.56181 | + | 1.95845i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −85.6566 | − | 58.3997i | −3.27996 | − | 2.23624i | ||||
\(683\) | −12.5728 | + | 32.0349i | −0.481083 | + | 1.22578i | 0.460095 | + | 0.887870i | \(0.347815\pi\) |
−0.941178 | + | 0.337911i | \(0.890280\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.1614 | −0.999575 | ||||||||
\(686\) | 38.8439 | + | 28.8166i | 1.48307 | + | 1.10022i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −106.190 | − | 32.7552i | −4.04845 | − | 1.24878i | ||||
\(689\) | 1.04837 | − | 2.67121i | 0.0399399 | − | 0.101765i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.81770 | − | 1.17833i | 0.297399 | − | 0.0448257i | 0.00135224 | − | 0.999999i | \(-0.499570\pi\) |
0.296047 | + | 0.955173i | \(0.404331\pi\) | |||||||
\(692\) | 58.0730 | − | 72.8212i | 2.20760 | − | 2.76825i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.48507 | + | 8.13202i | 0.246170 | + | 0.308687i | ||||
\(695\) | −4.95879 | − | 4.60108i | −0.188098 | − | 0.174529i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.7201 | + | 23.8648i | −0.974219 | + | 0.903943i | ||||
\(698\) | −26.1345 | + | 17.8182i | −0.989204 | + | 0.674428i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 23.9501 | + | 10.4728i | 0.905229 | + | 0.395835i | ||||
\(701\) | −4.10883 | + | 18.0020i | −0.155188 | + | 0.679925i | 0.836140 | + | 0.548516i | \(0.184807\pi\) |
−0.991328 | + | 0.131409i | \(0.958050\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.488287 | + | 6.51574i | 0.0184161 | + | 0.245746i | ||||
\(704\) | 14.7881 | + | 25.6137i | 0.557346 | + | 0.965352i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.4533 | − | 5.03406i | −0.393417 | − | 0.189459i | ||||
\(707\) | 7.61659 | − | 14.3826i | 0.286451 | − | 0.540914i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.78550 | − | 37.1700i | 0.104612 | − | 1.39595i | −0.659908 | − | 0.751346i | \(-0.729405\pi\) |
0.764520 | − | 0.644600i | \(-0.222976\pi\) | |||||||
\(710\) | −51.7418 | + | 15.9602i | −1.94183 | + | 0.598977i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.217663 | + | 2.90452i | −0.00815728 | + | 0.108851i | ||||
\(713\) | −48.8461 | + | 23.5231i | −1.82930 | + | 0.880945i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.30808 | + | 4.48254i | 0.348103 | + | 0.167637i | ||||
\(716\) | 3.48803 | − | 6.04144i | 0.130354 | − | 0.225779i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.113974 | + | 1.52088i | 0.00425348 | + | 0.0567588i | ||||
\(719\) | −1.39031 | − | 3.54246i | −0.0518499 | − | 0.132111i | 0.902602 | − | 0.430476i | \(-0.141654\pi\) |
−0.954452 | + | 0.298364i | \(0.903559\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 50.3845 | − | 1.84370i | 1.87642 | − | 0.0686629i | ||||
\(722\) | −5.09614 | − | 22.3277i | −0.189659 | − | 0.830949i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −53.7425 | + | 49.8657i | −1.99732 | + | 1.85325i | ||||
\(725\) | 8.38746 | + | 1.26421i | 0.311502 | + | 0.0469514i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.48721 | + | 4.37282i | 0.129333 | + | 0.162179i | 0.842282 | − | 0.539038i | \(-0.181212\pi\) |
−0.712948 | + | 0.701217i | \(0.752641\pi\) | |||||||
\(728\) | 21.7864 | − | 21.7506i | 0.807459 | − | 0.806130i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.7188 | − | 1.91705i | 0.470744 | − | 0.0709533i | ||||
\(731\) | −49.4321 | − | 33.7022i | −1.82831 | − | 1.24652i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.9583 | + | 11.4001i | 1.36509 | + | 0.421074i | 0.888832 | − | 0.458233i | \(-0.151518\pi\) |
0.476255 | + | 0.879307i | \(0.341994\pi\) | |||||||
\(734\) | 4.70317 | 0.173597 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 53.6586 | 1.97788 | ||||||||
\(737\) | 28.6344 | + | 8.83254i | 1.05476 | + | 0.325351i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.27473 | − | 2.23267i | −0.120463 | − | 0.0821301i | 0.501590 | − | 0.865106i | \(-0.332749\pi\) |
−0.622053 | + | 0.782975i | \(0.713701\pi\) | |||||||
\(740\) | 16.7234 | − | 2.52065i | 0.614764 | − | 0.0926608i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.66750 | + | 10.6307i | 0.244772 | + | 0.390265i | ||||
\(743\) | −1.00788 | − | 1.26384i | −0.0369754 | − | 0.0463657i | 0.763000 | − | 0.646398i | \(-0.223726\pi\) |
−0.799975 | + | 0.600033i | \(0.795154\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.6954 | + | 3.72223i | 0.904769 | + | 0.136372i | ||||
\(746\) | −39.1552 | + | 36.3307i | −1.43357 | + | 1.33016i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 21.0848 | + | 92.3786i | 0.770937 | + | 3.37770i | ||||
\(749\) | 14.9718 | + | 17.4265i | 0.547057 | + | 0.636752i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.34928 | − | 23.8216i | −0.341160 | − | 0.869262i | −0.993758 | − | 0.111557i | \(-0.964416\pi\) |
0.652598 | − | 0.757705i | \(-0.273679\pi\) | |||||||
\(752\) | 8.87986 | + | 118.494i | 0.323815 | + | 4.32101i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.53732 | − | 14.7871i | 0.310911 | − | 0.538513i | ||||
\(755\) | −1.90663 | − | 0.918185i | −0.0693894 | − | 0.0334162i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0801 | + | 4.85434i | −0.366369 | + | 0.176434i | −0.608005 | − | 0.793933i | \(-0.708030\pi\) |
0.241637 | + | 0.970367i | \(0.422316\pi\) | |||||||
\(758\) | 3.91735 | − | 52.2734i | 0.142284 | − | 1.89865i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 38.6606 | − | 11.9252i | 1.40237 | − | 0.432573i | ||||
\(761\) | −1.23188 | + | 16.4383i | −0.0446555 | + | 0.595886i | 0.929326 | + | 0.369260i | \(0.120389\pi\) |
−0.973982 | + | 0.226626i | \(0.927230\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.6218 | − | 17.4036i | 0.855166 | − | 0.630054i | ||||
\(764\) | −37.2128 | − | 17.9207i | −1.34631 | − | 0.648350i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.0699 | + | 31.2980i | 0.652892 | + | 1.13084i | ||||
\(767\) | 0.152721 | + | 2.03793i | 0.00551445 | + | 0.0735852i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.08770 | − | 4.76553i | 0.0392235 | − | 0.171849i | −0.951522 | − | 0.307580i | \(-0.900481\pi\) |
0.990746 | + | 0.135730i | \(0.0433381\pi\) | |||||||
\(770\) | −39.9600 | + | 21.0774i | −1.44006 | + | 0.759576i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 90.8135 | − | 61.9156i | 3.26845 | − | 2.22839i | ||||
\(773\) | 23.4654 | − | 21.7727i | 0.843990 | − | 0.783108i | −0.134171 | − | 0.990958i | \(-0.542837\pi\) |
0.978161 | + | 0.207850i | \(0.0666465\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.6692 | − | 14.5389i | −0.562855 | − | 0.522253i | ||||
\(776\) | −34.7041 | − | 43.5175i | −1.24580 | − | 1.56219i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 39.6976 | − | 49.7793i | 1.42323 | − | 1.78467i | ||||
\(779\) | 21.4888 | − | 3.23892i | 0.769916 | − | 0.116046i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.7889 | + | 42.7773i | −0.600752 | + | 1.53069i | ||||
\(782\) | 66.9987 | + | 20.6664i | 2.39587 | + | 0.739027i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.89794 | + | 66.4107i | 0.353498 | + | 2.37181i | ||||
\(785\) | 5.39672 | 0.192617 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.41670 | − | 3.60970i | 0.0505000 | − | 0.128672i | −0.903398 | − | 0.428803i | \(-0.858935\pi\) |
0.953898 | + | 0.300131i | \(0.0970305\pi\) | |||||||
\(788\) | −15.8117 | − | 10.7802i | −0.563267 | − | 0.384029i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.70574 | + | 3.39289i | −0.0962659 | + | 0.120714i | ||||
\(791\) | −2.55636 | + | 7.28640i | −0.0908936 | + | 0.259074i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.86418 | − | 9.15262i | −0.350287 | − | 0.325019i | ||||
\(794\) | −17.5596 | − | 2.64669i | −0.623168 | − | 0.0939274i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −63.4700 | + | 43.2731i | −2.24963 | + | 1.53377i | ||||
\(797\) | −9.11843 | − | 39.9504i | −0.322991 | − | 1.41512i | −0.832201 | − | 0.554475i | \(-0.812919\pi\) |
0.509209 | − | 0.860643i | \(-0.329938\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.2353 | + | 62.3687i | −0.503607 | + | 2.20645i | ||||
\(800\) | 7.72912 | + | 19.6935i | 0.273266 | + | 0.696270i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −42.0789 | − | 72.8828i | −1.48586 | − | 2.57358i | ||||
\(803\) | 5.45807 | − | 9.45366i | 0.192611 | − | 0.333613i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.902855 | + | 23.6089i | −0.0318215 | + | 0.832104i | ||||
\(806\) | −38.7673 | + | 18.6694i | −1.36552 | + | 0.657600i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 43.2878 | − | 13.3525i | 1.52286 | − | 0.469739i | ||||
\(809\) | −16.4538 | + | 5.07532i | −0.578485 | + | 0.178439i | −0.570170 | − | 0.821527i | \(-0.693123\pi\) |
−0.00831439 | + | 0.999965i | \(0.502647\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.68918 | + | 1.29504i | −0.0944298 | + | 0.0454750i | −0.480502 | − | 0.876993i | \(-0.659546\pi\) |
0.386073 | + | 0.922468i | \(0.373831\pi\) | |||||||
\(812\) | 21.0626 | + | 48.3847i | 0.739153 | + | 1.69797i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.1544 | − | 17.5880i | 0.355913 | − | 0.616459i | ||||
\(815\) | 6.25876 | + | 10.8405i | 0.219235 | + | 0.379726i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.5380 | + | 34.4942i | 0.473634 | + | 1.20680i | ||||
\(818\) | 3.51195 | − | 15.3869i | 0.122792 | − | 0.537989i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.5165 | − | 54.8385i | −0.437096 | − | 1.91504i | ||||
\(821\) | 18.7449 | − | 12.7801i | 0.654203 | − | 0.446028i | −0.190194 | − | 0.981747i | \(-0.560912\pi\) |
0.844396 | + | 0.535719i | \(0.179959\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.7230 | − | 1.91768i | −0.443495 | − | 0.0668461i | −0.0765011 | − | 0.997069i | \(-0.524375\pi\) |
−0.366994 | + | 0.930223i | \(0.619613\pi\) | |||||||
\(824\) | 102.874 | + | 95.4530i | 3.58378 | + | 3.32526i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.56308 | − | 4.76089i | −0.263153 | − | 0.165653i | ||||
\(827\) | −14.3930 | + | 18.0482i | −0.500492 | + | 0.627598i | −0.966340 | − | 0.257267i | \(-0.917178\pi\) |
0.465848 | + | 0.884865i | \(0.345749\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.7871 | + | 10.0817i | 0.513576 | + | 0.350151i | 0.792212 | − | 0.610247i | \(-0.208930\pi\) |
−0.278635 | + | 0.960397i | \(0.589882\pi\) | |||||||
\(830\) | 16.8036 | − | 42.8149i | 0.583262 | − | 1.48613i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 12.2756 | 0.425579 | ||||||||
\(833\) | −5.44655 | + | 35.7360i | −0.188712 | + | 1.23818i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.6484 | + | 6.67763i | 0.749172 | + | 0.231089i | ||||
\(836\) | 21.4412 | − | 54.6313i | 0.741560 | − | 1.88946i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 26.3485 | − | 3.97140i | 0.910195 | − | 0.137190i | ||||
\(839\) | 15.0875 | − | 18.9191i | 0.520878 | − | 0.653160i | −0.449917 | − | 0.893070i | \(-0.648547\pi\) |
0.970795 | + | 0.239910i | \(0.0771180\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.40477 | − | 9.28529i | −0.255337 | − | 0.320182i | ||||
\(842\) | 49.2556 | + | 45.7025i | 1.69746 | + | 1.57501i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.15812 | − | 6.64177i | 0.246393 | − | 0.228619i | ||||
\(845\) | −14.9062 | + | 10.1629i | −0.512789 | + | 0.349614i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.72503 | + | 9.07606i | −0.0592726 | + | 0.311857i | ||||
\(848\) | −3.87647 | + | 16.9839i | −0.133119 | + | 0.583231i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.06581 | + | 27.5663i | 0.0708567 | + | 0.945517i | ||||
\(851\) | −5.31032 | − | 9.19775i | −0.182036 | − | 0.315295i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.8247 | + | 10.5102i | 0.747263 | + | 0.359863i | 0.768448 | − | 0.639913i | \(-0.221029\pi\) |
−0.0211846 | + | 0.999776i | \(0.506744\pi\) | |||||||
\(854\) | 57.8273 | − | 10.8922i | 1.97881 | − | 0.372723i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.77892 | + | 63.7702i | −0.163340 | + | 2.17962i | ||||
\(857\) | −26.4497 | + | 8.15867i | −0.903506 | + | 0.278695i | −0.711489 | − | 0.702697i | \(-0.751979\pi\) |
−0.192017 | + | 0.981392i | \(0.561503\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.79189 | − | 50.5993i | 0.129378 | − | 1.72643i | −0.434589 | − | 0.900629i | \(-0.643106\pi\) |
0.563967 | − | 0.825797i | \(-0.309275\pi\) | |||||||
\(860\) | 86.4147 | − | 41.6151i | 2.94672 | − | 1.41906i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.8702 | − | 7.64270i | −0.540542 | − | 0.260311i | ||||
\(863\) | 12.0287 | − | 20.8344i | 0.409463 | − | 0.709211i | −0.585367 | − | 0.810769i | \(-0.699049\pi\) |
0.994830 | + | 0.101558i | \(0.0323827\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.48041 | + | 33.0988i | 0.0843365 | + | 1.12539i | ||||
\(866\) | 15.7145 | + | 40.0399i | 0.534000 | + | 1.36061i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 24.8306 | − | 130.644i | 0.842806 | − | 4.43434i | ||||
\(869\) | 0.819544 | + | 3.59066i | 0.0278011 | + | 0.121805i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.11716 | − | 8.45949i | 0.308923 | − | 0.286639i | ||||
\(872\) | 80.7561 | + | 12.1720i | 2.73475 | + | 0.412197i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −27.0760 | − | 33.9522i | −0.915858 | − | 1.14845i | ||||
\(875\) | −30.2479 | + | 10.5562i | −1.02256 | + | 0.356866i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.04456 | − | 0.609620i | 0.136575 | − | 0.0205854i | −0.0803989 | − | 0.996763i | \(-0.525619\pi\) |
0.216974 | + | 0.976177i | \(0.430381\pi\) | |||||||
\(878\) | 19.5413 | + | 13.3230i | 0.659487 | + | 0.449631i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −59.9325 | − | 18.4867i | −2.02032 | − | 0.623187i | ||||
\(881\) | −16.5619 | −0.557983 | −0.278992 | − | 0.960294i | \(-0.590000\pi\) | ||||
−0.278992 | + | 0.960294i | \(0.590000\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.5572 | 1.02833 | 0.514166 | − | 0.857690i | \(-0.328101\pi\) | ||||
0.514166 | + | 0.857690i | \(0.328101\pi\) | |||||||
\(884\) | 37.5806 | + | 11.5921i | 1.26397 | + | 0.389883i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.2224 | − | 6.96953i | −0.343429 | − | 0.234146i | ||||
\(887\) | 9.01759 | − | 1.35918i | 0.302781 | − | 0.0456369i | 0.00410539 | − | 0.999992i | \(-0.498693\pi\) |
0.298676 | + | 0.954355i | \(0.403455\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.3300 | − | 20.3514i | −1.08431 | − | 0.682566i | ||||
\(890\) | −1.10612 | − | 1.38704i | −0.0370774 | − | 0.0464935i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −106.552 | − | 16.0601i | −3.56762 | − | 0.537732i | ||||
\(893\) | 29.0456 | − | 26.9504i | 0.971975 | − | 0.901861i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.553177 | + | 2.42363i | 0.0184907 | + | 0.0810129i | ||||
\(896\) | 0.554500 | − | 0.750027i | 0.0185246 | − | 0.0250567i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.3252 | + | 26.3081i | 0.344556 | + | 0.877913i | ||||
\(899\) | −3.22476 | − | 43.0314i | −0.107552 | − | 1.43518i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.68943 | + | 8.12232i | −0.156227 | + | 0.270594i | ||||
\(902\) | −60.8564 | − | 29.3069i | −2.02630 | − | 0.975812i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.3648 | + | 9.32559i | −0.644064 | + | 0.310165i | ||||
\(905\) | 1.95237 | − | 26.0526i | 0.0648990 | − | 0.866017i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.6163 | − | 6.35929i | 0.684553 | − | 0.211157i | 0.0670789 | − | 0.997748i | \(-0.478632\pi\) |
0.617474 | + | 0.786591i | \(0.288156\pi\) | |||||||
\(908\) | −4.19608 | + | 55.9927i | −0.139252 | + | 1.85818i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.716562 | + | 18.7375i | −0.0237538 | + | 0.621141i | ||||
\(911\) | 43.1242 | + | 20.7675i | 1.42877 | + | 0.688059i | 0.978768 | − | 0.204969i | \(-0.0657095\pi\) |
0.450001 | + | 0.893028i | \(0.351424\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.5173 | − | 33.8049i | −0.645927 | − | 1.11878i | ||||
\(914\) | 4.01436 | + | 53.5680i | 0.132783 | + | 1.77187i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.46990 | − | 19.5839i | 0.147690 | − | 0.647071i | ||||
\(917\) | −11.0908 | − | 41.5283i | −0.366251 | − | 1.37138i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.42115 | + | 5.74144i | −0.277788 | + | 0.189393i | −0.694198 | − | 0.719784i | \(-0.744241\pi\) |
0.416410 | + | 0.909177i | \(0.363288\pi\) | |||||||
\(920\) | −48.2071 | + | 44.7296i | −1.58934 | + | 1.47469i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13.3439 | − | 12.3814i | −0.439459 | − | 0.407758i | ||||
\(923\) | 11.8919 | + | 14.9120i | 0.391428 | + | 0.490835i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.61080 | − | 3.27383i | 0.0858424 | − | 0.107643i | ||||
\(926\) | 14.5057 | − | 2.18638i | 0.476687 | − | 0.0718490i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −15.6034 | + | 39.7568i | −0.512206 | + | 1.30508i | ||||
\(929\) | 8.54408 | + | 2.63550i | 0.280322 | + | 0.0864679i | 0.431728 | − | 0.902004i | \(-0.357904\pi\) |
−0.151406 | + | 0.988472i | \(0.548380\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.2557 | − | 16.3876i | 0.499987 | − | 0.537080i | ||||
\(932\) | −77.6907 | −2.54484 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 37.4367 | − | 95.3871i | 1.22497 | − | 3.12116i | ||||
\(935\) | −27.8990 | − | 19.0212i | −0.912393 | − | 0.622059i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.2362 | + | 15.3438i | −0.399741 | + | 0.501259i | −0.940441 | − | 0.339956i | \(-0.889588\pi\) |
0.540701 | + | 0.841215i | \(0.318159\pi\) | |||||||
\(938\) | 6.04500 | + | 54.0509i | 0.197376 | + | 1.76482i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −75.1802 | − | 69.7571i | −2.45211 | − | 2.27522i | ||||
\(941\) | −15.9280 | − | 2.40076i | −0.519239 | − | 0.0782627i | −0.115806 | − | 0.993272i | \(-0.536945\pi\) |
−0.403433 | + | 0.915009i | \(0.632183\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29.1855 | + | 19.8983i | −0.950410 | + | 0.647979i | ||||
\(944\) | −2.76073 | − | 12.0955i | −0.0898540 | − | 0.393676i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25.6290 | − | 112.288i | 0.833272 | − | 3.65080i | ||||
\(947\) | 0.772015 | + | 1.96706i | 0.0250871 | + | 0.0639209i | 0.942868 | − | 0.333165i | \(-0.108117\pi\) |
−0.917781 | + | 0.397086i | \(0.870021\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.26538 | − | 3.92375i | −0.0735372 | − | 0.127370i | ||||
\(950\) | 8.56085 | − | 14.8278i | 0.277751 | − | 0.481078i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −81.0062 | + | 59.6823i | −2.62543 | + | 1.93431i | ||||
\(953\) | 14.3178 | − | 6.89510i | 0.463799 | − | 0.223354i | −0.187366 | − | 0.982290i | \(-0.559995\pi\) |
0.651165 | + | 0.758936i | \(0.274281\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.0647 | − | 4.33838i | 0.455123 | − | 0.140387i | ||||
\(956\) | −57.1622 | + | 17.6322i | −1.84876 | + | 0.570266i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.2232 | + | 5.88638i | −0.394913 | + | 0.190180i | ||||
\(959\) | −38.9163 | − | 10.4619i | −1.25667 | − | 0.337834i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −38.8721 | + | 67.3284i | −1.25394 | + | 2.17188i | ||||
\(962\) | −4.21460 | − | 7.29990i | −0.135884 | − | 0.235358i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.42438 | + | 18.9170i | 0.239123 | + | 0.609276i | ||||
\(965\) | −8.71564 | + | 38.1857i | −0.280566 | + | 1.22924i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.70518 | + | 42.5212i | 0.312098 | + | 1.36739i | 0.851064 | + | 0.525062i | \(0.175958\pi\) |
−0.538967 | + | 0.842327i | \(0.681185\pi\) | |||||||
\(968\) | −21.2467 | + | 14.4858i | −0.682896 | + | 0.465591i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 33.5241 | + | 5.05295i | 1.07640 | + | 0.162240i | ||||
\(971\) | −34.1207 | − | 31.6594i | −1.09499 | − | 1.01600i | −0.999789 | − | 0.0205407i | \(-0.993461\pi\) |
−0.0951976 | − | 0.995458i | \(-0.530348\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.53645 | − | 8.82734i | −0.177491 | − | 0.282992i | ||||
\(974\) | 37.1081 | − | 46.5321i | 1.18902 | − | 1.49098i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 67.4963 | + | 46.0182i | 2.16050 | + | 1.47301i | ||||
\(977\) | 3.83768 | − | 9.77825i | 0.122778 | − | 0.312834i | −0.856249 | − | 0.516563i | \(-0.827211\pi\) |
0.979027 | + | 0.203729i | \(0.0653063\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.50563 | −0.0481203 | ||||||||
\(980\) | −45.2490 | − | 36.2069i | −1.44543 | − | 1.15659i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −34.0791 | − | 10.5120i | −1.08751 | − | 0.335452i | ||||
\(983\) | −1.40490 | + | 3.57963i | −0.0448094 | + | 0.114173i | −0.951526 | − | 0.307567i | \(-0.900485\pi\) |
0.906717 | + | 0.421740i | \(0.138580\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.74337 | − | 1.01640i | 0.214862 | − | 0.0323852i | ||||
\(986\) | −34.7947 | + | 43.6311i | −1.10809 | + | 1.38950i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15.1873 | − | 19.0443i | −0.483173 | − | 0.605879i | ||||
\(989\) | −44.1531 | − | 40.9681i | −1.40399 | − | 1.30271i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.60080 | − | 7.05251i | 0.241447 | − | 0.224030i | −0.550162 | − | 0.835058i | \(-0.685434\pi\) |
0.791609 | + | 0.611028i | \(0.209244\pi\) | |||||||
\(992\) | 88.9263 | − | 60.6289i | 2.82341 | − | 1.92497i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −83.3508 | + | 3.05002i | −2.64373 | + | 0.0967409i | ||||
\(995\) | 6.09140 | − | 26.6882i | 0.193110 | − | 0.846072i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.54087 | + | 60.5937i | 0.143811 | + | 1.91902i | 0.343484 | + | 0.939158i | \(0.388393\pi\) |
−0.199674 | + | 0.979862i | \(0.563988\pi\) | |||||||
\(998\) | −29.3509 | − | 50.8373i | −0.929087 | − | 1.60923i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.2.bb.f.100.1 | ✓ | 72 | |
3.2 | odd | 2 | inner | 441.2.bb.f.100.6 | yes | 72 | |
49.25 | even | 21 | inner | 441.2.bb.f.172.1 | yes | 72 | |
147.74 | odd | 42 | inner | 441.2.bb.f.172.6 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.bb.f.100.1 | ✓ | 72 | 1.1 | even | 1 | trivial | |
441.2.bb.f.100.6 | yes | 72 | 3.2 | odd | 2 | inner | |
441.2.bb.f.172.1 | yes | 72 | 49.25 | even | 21 | inner | |
441.2.bb.f.172.6 | yes | 72 | 147.74 | odd | 42 | inner |