Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(61,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.k (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.2 | ||
Character | \(\chi\) | \(=\) | 585.211 |
Dual form | 585.2.k.a.61.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.30568 | + | 2.26150i | −0.923253 | + | 1.59912i | −0.128906 | + | 0.991657i | \(0.541146\pi\) |
−0.794347 | + | 0.607464i | \(0.792187\pi\) | |||||||
\(3\) | 1.68776 | + | 0.389194i | 0.974428 | + | 0.224701i | ||||
\(4\) | −2.40958 | − | 4.17352i | −1.20479 | − | 2.08676i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | −3.08383 | + | 3.30870i | −1.25897 | + | 1.35077i | ||||
\(7\) | −1.51841 | −0.573905 | −0.286953 | − | 0.957945i | \(-0.592642\pi\) | ||||
−0.286953 | + | 0.957945i | \(0.592642\pi\) | |||||||
\(8\) | 7.36184 | 2.60280 | ||||||||
\(9\) | 2.69706 | + | 1.31373i | 0.899019 | + | 0.437910i | ||||
\(10\) | 1.30568 | + | 2.26150i | 0.412891 | + | 0.715149i | ||||
\(11\) | 1.10811 | − | 1.91931i | 0.334108 | − | 0.578693i | −0.649205 | − | 0.760614i | \(-0.724898\pi\) |
0.983313 | + | 0.181921i | \(0.0582315\pi\) | |||||||
\(12\) | −2.44248 | − | 7.98169i | −0.705085 | − | 2.30412i | ||||
\(13\) | 1.72140 | + | 3.16809i | 0.477431 | + | 0.878669i | ||||
\(14\) | 1.98255 | − | 3.43388i | 0.529860 | − | 0.917744i | ||||
\(15\) | 1.18093 | − | 1.26704i | 0.304915 | − | 0.327149i | ||||
\(16\) | −4.79302 | + | 8.30176i | −1.19826 | + | 2.07544i | ||||
\(17\) | 3.89453 | − | 6.74552i | 0.944562 | − | 1.63603i | 0.187937 | − | 0.982181i | \(-0.439820\pi\) |
0.756625 | − | 0.653849i | \(-0.226847\pi\) | |||||||
\(18\) | −6.49248 | + | 4.38408i | −1.53029 | + | 1.03334i | ||||
\(19\) | 1.35650 | − | 2.34953i | 0.311203 | − | 0.539019i | −0.667420 | − | 0.744681i | \(-0.732602\pi\) |
0.978623 | + | 0.205662i | \(0.0659348\pi\) | |||||||
\(20\) | −4.81917 | −1.07760 | ||||||||
\(21\) | −2.56271 | − | 0.590956i | −0.559229 | − | 0.128957i | ||||
\(22\) | 2.89367 | + | 5.01199i | 0.616933 | + | 1.06856i | ||||
\(23\) | 4.82428 | 1.00593 | 0.502966 | − | 0.864306i | \(-0.332242\pi\) | ||||
0.502966 | + | 0.864306i | \(0.332242\pi\) | |||||||
\(24\) | 12.4250 | + | 2.86519i | 2.53625 | + | 0.584854i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −9.41222 | − | 0.243552i | −1.84589 | − | 0.0477644i | ||||
\(27\) | 4.04068 | + | 3.26694i | 0.777630 | + | 0.628723i | ||||
\(28\) | 3.65874 | + | 6.33712i | 0.691436 | + | 1.19760i | ||||
\(29\) | −2.73933 | + | 4.74467i | −0.508682 | + | 0.881062i | 0.491268 | + | 0.871009i | \(0.336534\pi\) |
−0.999949 | + | 0.0100538i | \(0.996800\pi\) | |||||||
\(30\) | 1.32350 | + | 4.32502i | 0.241638 | + | 0.789638i | ||||
\(31\) | −3.21109 | + | 5.56177i | −0.576729 | + | 0.998924i | 0.419122 | + | 0.907930i | \(0.362338\pi\) |
−0.995851 | + | 0.0909942i | \(0.970996\pi\) | |||||||
\(32\) | −5.15443 | − | 8.92773i | −0.911183 | − | 1.57822i | ||||
\(33\) | 2.61721 | − | 2.80805i | 0.455597 | − | 0.488820i | ||||
\(34\) | 10.1700 | + | 17.6149i | 1.74414 | + | 3.02094i | ||||
\(35\) | −0.759205 | + | 1.31498i | −0.128329 | + | 0.222272i | ||||
\(36\) | −1.01590 | − | 14.4218i | −0.169316 | − | 2.40363i | ||||
\(37\) | 3.67149 | + | 6.35920i | 0.603589 | + | 1.04545i | 0.992273 | + | 0.124075i | \(0.0395965\pi\) |
−0.388684 | + | 0.921371i | \(0.627070\pi\) | |||||||
\(38\) | 3.54230 | + | 6.13545i | 0.574638 | + | 0.995302i | ||||
\(39\) | 1.67231 | + | 6.01692i | 0.267784 | + | 0.963479i | ||||
\(40\) | 3.68092 | − | 6.37554i | 0.582005 | − | 1.00806i | ||||
\(41\) | 0.650503 | 0.101591 | 0.0507957 | − | 0.998709i | \(-0.483824\pi\) | ||||
0.0507957 | + | 0.998709i | \(0.483824\pi\) | |||||||
\(42\) | 4.68252 | − | 5.02396i | 0.722528 | − | 0.775215i | ||||
\(43\) | 4.61852 | 0.704318 | 0.352159 | − | 0.935940i | \(-0.385448\pi\) | ||||
0.352159 | + | 0.935940i | \(0.385448\pi\) | |||||||
\(44\) | −10.6804 | −1.61012 | ||||||||
\(45\) | 2.48625 | − | 1.67885i | 0.370629 | − | 0.250269i | ||||
\(46\) | −6.29896 | + | 10.9101i | −0.928730 | + | 1.60861i | ||||
\(47\) | −5.92305 | − | 10.2590i | −0.863966 | − | 1.49643i | −0.868070 | − | 0.496441i | \(-0.834640\pi\) |
0.00410421 | − | 0.999992i | \(-0.498694\pi\) | |||||||
\(48\) | −11.3205 | + | 12.1459i | −1.63397 | + | 1.75312i | ||||
\(49\) | −4.69443 | −0.670633 | ||||||||
\(50\) | 2.61135 | 0.369301 | ||||||||
\(51\) | 9.19834 | − | 9.86908i | 1.28803 | − | 1.38195i | ||||
\(52\) | 9.07422 | − | 14.8181i | 1.25837 | − | 2.05490i | ||||
\(53\) | 10.3886 | 1.42699 | 0.713494 | − | 0.700661i | \(-0.247111\pi\) | ||||
0.713494 | + | 0.700661i | \(0.247111\pi\) | |||||||
\(54\) | −12.6640 | + | 4.87243i | −1.72335 | + | 0.663054i | ||||
\(55\) | −1.10811 | − | 1.91931i | −0.149418 | − | 0.258799i | ||||
\(56\) | −11.1783 | −1.49376 | ||||||||
\(57\) | 3.20387 | − | 3.43749i | 0.424363 | − | 0.455307i | ||||
\(58\) | −7.15337 | − | 12.3900i | −0.939284 | − | 1.62689i | ||||
\(59\) | 2.82979 | + | 4.90134i | 0.368407 | + | 0.638100i | 0.989317 | − | 0.145782i | \(-0.0465699\pi\) |
−0.620910 | + | 0.783882i | \(0.713237\pi\) | |||||||
\(60\) | −8.13359 | − | 1.87559i | −1.05004 | − | 0.242138i | ||||
\(61\) | 3.88662 | 0.497631 | 0.248815 | − | 0.968551i | \(-0.419959\pi\) | ||||
0.248815 | + | 0.968551i | \(0.419959\pi\) | |||||||
\(62\) | −8.38529 | − | 14.5238i | −1.06493 | − | 1.84452i | ||||
\(63\) | −4.09524 | − | 1.99478i | −0.515951 | − | 0.251319i | ||||
\(64\) | 7.74799 | 0.968499 | ||||||||
\(65\) | 3.60434 | + | 0.0932665i | 0.447064 | + | 0.0115683i | ||||
\(66\) | 2.93318 | + | 9.58522i | 0.361050 | + | 1.17986i | ||||
\(67\) | −8.97657 | −1.09666 | −0.548331 | − | 0.836261i | \(-0.684737\pi\) | ||||
−0.548331 | + | 0.836261i | \(0.684737\pi\) | |||||||
\(68\) | −37.5368 | −4.55200 | ||||||||
\(69\) | 8.14223 | + | 1.87758i | 0.980209 | + | 0.226034i | ||||
\(70\) | −1.98255 | − | 3.43388i | −0.236960 | − | 0.410427i | ||||
\(71\) | −4.14295 | + | 7.17580i | −0.491678 | + | 0.851611i | −0.999954 | − | 0.00958321i | \(-0.996950\pi\) |
0.508276 | + | 0.861194i | \(0.330283\pi\) | |||||||
\(72\) | 19.8553 | + | 9.67148i | 2.33997 | + | 1.13980i | ||||
\(73\) | −0.623359 | −0.0729586 | −0.0364793 | − | 0.999334i | \(-0.511614\pi\) | ||||
−0.0364793 | + | 0.999334i | \(0.511614\pi\) | |||||||
\(74\) | −19.1751 | −2.22906 | ||||||||
\(75\) | −0.506827 | − | 1.65624i | −0.0585234 | − | 0.191246i | ||||
\(76\) | −13.0744 | −1.49974 | ||||||||
\(77\) | −1.68257 | + | 2.91429i | −0.191746 | + | 0.332115i | ||||
\(78\) | −15.7908 | − | 4.07424i | −1.78795 | − | 0.461317i | ||||
\(79\) | −4.98663 | − | 8.63709i | −0.561039 | − | 0.971748i | −0.997406 | − | 0.0719796i | \(-0.977068\pi\) |
0.436367 | − | 0.899769i | \(-0.356265\pi\) | |||||||
\(80\) | 4.79302 | + | 8.30176i | 0.535876 | + | 0.928165i | ||||
\(81\) | 5.54822 | + | 7.08641i | 0.616469 | + | 0.787379i | ||||
\(82\) | −0.849347 | + | 1.47111i | −0.0937946 | + | 0.162457i | ||||
\(83\) | 3.10033 | + | 5.36992i | 0.340305 | + | 0.589426i | 0.984489 | − | 0.175445i | \(-0.0561363\pi\) |
−0.644184 | + | 0.764870i | \(0.722803\pi\) | |||||||
\(84\) | 3.70869 | + | 12.1195i | 0.404652 | + | 1.32234i | ||||
\(85\) | −3.89453 | − | 6.74552i | −0.422421 | − | 0.731655i | ||||
\(86\) | −6.03030 | + | 10.4448i | −0.650264 | + | 1.12629i | ||||
\(87\) | −6.46993 | + | 6.94172i | −0.693649 | + | 0.744230i | ||||
\(88\) | 8.15775 | − | 14.1296i | 0.869619 | − | 1.50622i | ||||
\(89\) | −4.35969 | − | 7.55120i | −0.462126 | − | 0.800426i | 0.536941 | − | 0.843620i | \(-0.319580\pi\) |
−0.999067 | + | 0.0431941i | \(0.986247\pi\) | |||||||
\(90\) | 0.550482 | + | 7.81470i | 0.0580259 | + | 0.823741i | ||||
\(91\) | −2.61379 | − | 4.81046i | −0.274000 | − | 0.504273i | ||||
\(92\) | −11.6245 | − | 20.1343i | −1.21194 | − | 2.09914i | ||||
\(93\) | −7.58416 | + | 8.13719i | −0.786440 | + | 0.843787i | ||||
\(94\) | 30.9344 | 3.19064 | ||||||||
\(95\) | −1.35650 | − | 2.34953i | −0.139174 | − | 0.241057i | ||||
\(96\) | −5.22481 | − | 17.0739i | −0.533255 | − | 1.74260i | ||||
\(97\) | 5.36548 | 0.544782 | 0.272391 | − | 0.962187i | \(-0.412186\pi\) | ||||
0.272391 | + | 0.962187i | \(0.412186\pi\) | |||||||
\(98\) | 6.12941 | − | 10.6164i | 0.619164 | − | 1.07242i | ||||
\(99\) | 5.51009 | − | 3.72072i | 0.553785 | − | 0.373946i | ||||
\(100\) | −2.40958 | + | 4.17352i | −0.240958 | + | 0.417352i | ||||
\(101\) | 8.61787 | − | 14.9266i | 0.857510 | − | 1.48525i | −0.0167863 | − | 0.999859i | \(-0.505344\pi\) |
0.874297 | − | 0.485392i | \(-0.161323\pi\) | |||||||
\(102\) | 10.3089 | + | 33.6879i | 1.02073 | + | 3.33560i | ||||
\(103\) | 0.886219 | − | 1.53498i | 0.0873218 | − | 0.151246i | −0.819056 | − | 0.573713i | \(-0.805503\pi\) |
0.906378 | + | 0.422467i | \(0.138836\pi\) | |||||||
\(104\) | 12.6727 | + | 23.3230i | 1.24266 | + | 2.28700i | ||||
\(105\) | −1.79314 | + | 1.92389i | −0.174992 | + | 0.187753i | ||||
\(106\) | −13.5642 | + | 23.4939i | −1.31747 | + | 2.28193i | ||||
\(107\) | −3.42653 | − | 5.93492i | −0.331255 | − | 0.573750i | 0.651503 | − | 0.758646i | \(-0.274139\pi\) |
−0.982758 | + | 0.184896i | \(0.940805\pi\) | |||||||
\(108\) | 3.89828 | − | 24.7358i | 0.375112 | − | 2.38021i | ||||
\(109\) | −10.0955 | −0.966972 | −0.483486 | − | 0.875352i | \(-0.660630\pi\) | ||||
−0.483486 | + | 0.875352i | \(0.660630\pi\) | |||||||
\(110\) | 5.78734 | 0.551802 | ||||||||
\(111\) | 3.72162 | + | 12.1617i | 0.353240 | + | 1.15434i | ||||
\(112\) | 7.27777 | − | 12.6055i | 0.687685 | − | 1.19110i | ||||
\(113\) | −0.450054 | − | 0.779517i | −0.0423376 | − | 0.0733308i | 0.844080 | − | 0.536217i | \(-0.180147\pi\) |
−0.886418 | + | 0.462886i | \(0.846814\pi\) | |||||||
\(114\) | 3.59067 | + | 11.7338i | 0.336297 | + | 1.09897i | ||||
\(115\) | 2.41214 | − | 4.17795i | 0.224933 | − | 0.389596i | ||||
\(116\) | 26.4026 | 2.45142 | ||||||||
\(117\) | 0.480700 | + | 10.8060i | 0.0444407 | + | 0.999012i | ||||
\(118\) | −14.7792 | −1.36053 | ||||||||
\(119\) | −5.91349 | + | 10.2425i | −0.542089 | + | 0.938926i | ||||
\(120\) | 8.69383 | − | 9.32778i | 0.793635 | − | 0.851506i | ||||
\(121\) | 3.04418 | + | 5.27267i | 0.276743 | + | 0.479333i | ||||
\(122\) | −5.07467 | + | 8.78959i | −0.459439 | + | 0.795772i | ||||
\(123\) | 1.09789 | + | 0.253172i | 0.0989936 | + | 0.0228277i | ||||
\(124\) | 30.9496 | 2.77935 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 9.85825 | − | 6.65683i | 0.878243 | − | 0.593038i | ||||
\(127\) | 0.852752 | + | 1.47701i | 0.0756695 | + | 0.131063i | 0.901377 | − | 0.433035i | \(-0.142557\pi\) |
−0.825708 | + | 0.564098i | \(0.809224\pi\) | |||||||
\(128\) | 0.192485 | − | 0.333394i | 0.0170135 | − | 0.0294682i | ||||
\(129\) | 7.79495 | + | 1.79750i | 0.686307 | + | 0.158261i | ||||
\(130\) | −4.91703 | + | 8.02944i | −0.431252 | + | 0.704229i | ||||
\(131\) | 8.45193 | − | 14.6392i | 0.738448 | − | 1.27903i | −0.214746 | − | 0.976670i | \(-0.568892\pi\) |
0.953194 | − | 0.302360i | \(-0.0977745\pi\) | |||||||
\(132\) | −18.0259 | − | 4.15673i | −1.56895 | − | 0.361797i | ||||
\(133\) | −2.05973 | + | 3.56755i | −0.178601 | + | 0.309346i | ||||
\(134\) | 11.7205 | − | 20.3005i | 1.01250 | − | 1.75370i | ||||
\(135\) | 4.84959 | − | 1.86586i | 0.417387 | − | 0.160588i | ||||
\(136\) | 28.6709 | − | 49.6595i | 2.45851 | − | 4.25827i | ||||
\(137\) | −12.7126 | −1.08611 | −0.543054 | − | 0.839698i | \(-0.682732\pi\) | ||||
−0.543054 | + | 0.839698i | \(0.682732\pi\) | |||||||
\(138\) | −14.8773 | + | 15.9621i | −1.26644 | + | 1.35879i | ||||
\(139\) | −3.96645 | − | 6.87009i | −0.336430 | − | 0.582714i | 0.647329 | − | 0.762211i | \(-0.275886\pi\) |
−0.983758 | + | 0.179497i | \(0.942553\pi\) | |||||||
\(140\) | 7.31747 | 0.618439 | ||||||||
\(141\) | −6.00393 | − | 19.6200i | −0.505622 | − | 1.65230i | ||||
\(142\) | −10.8187 | − | 18.7386i | −0.907886 | − | 1.57250i | ||||
\(143\) | 7.98804 | + | 0.206699i | 0.667993 | + | 0.0172851i | ||||
\(144\) | −23.8333 | + | 16.0936i | −1.98611 | + | 1.34113i | ||||
\(145\) | 2.73933 | + | 4.74467i | 0.227489 | + | 0.394023i | ||||
\(146\) | 0.813905 | − | 1.40972i | 0.0673593 | − | 0.116670i | ||||
\(147\) | −7.92306 | − | 1.82705i | −0.653483 | − | 0.150692i | ||||
\(148\) | 17.6935 | − | 30.6461i | 1.45440 | − | 2.51909i | ||||
\(149\) | 4.82098 | + | 8.35019i | 0.394950 | + | 0.684074i | 0.993095 | − | 0.117314i | \(-0.0374284\pi\) |
−0.598144 | + | 0.801388i | \(0.704095\pi\) | |||||||
\(150\) | 4.40733 | + | 1.01632i | 0.359857 | + | 0.0829825i | ||||
\(151\) | −0.0663036 | − | 0.114841i | −0.00539571 | − | 0.00934565i | 0.863315 | − | 0.504666i | \(-0.168384\pi\) |
−0.868711 | + | 0.495320i | \(0.835051\pi\) | |||||||
\(152\) | 9.98635 | − | 17.2969i | 0.810000 | − | 1.40296i | ||||
\(153\) | 19.3656 | − | 13.0767i | 1.56561 | − | 1.05719i | ||||
\(154\) | −4.39378 | − | 7.61025i | −0.354061 | − | 0.613252i | ||||
\(155\) | 3.21109 | + | 5.56177i | 0.257921 | + | 0.446732i | ||||
\(156\) | 21.0822 | − | 21.4777i | 1.68793 | − | 1.71959i | ||||
\(157\) | −7.97470 | + | 13.8126i | −0.636450 | + | 1.10236i | 0.349756 | + | 0.936841i | \(0.386265\pi\) |
−0.986206 | + | 0.165523i | \(0.947069\pi\) | |||||||
\(158\) | 26.0437 | 2.07192 | ||||||||
\(159\) | 17.5335 | + | 4.04320i | 1.39050 | + | 0.320646i | ||||
\(160\) | −10.3089 | −0.814987 | ||||||||
\(161\) | −7.32524 | −0.577310 | ||||||||
\(162\) | −23.2701 | + | 3.29473i | −1.82827 | + | 0.258858i | ||||
\(163\) | 6.42632 | − | 11.1307i | 0.503348 | − | 0.871824i | −0.496645 | − | 0.867954i | \(-0.665435\pi\) |
0.999993 | − | 0.00387008i | \(-0.00123189\pi\) | |||||||
\(164\) | −1.56744 | − | 2.71489i | −0.122397 | − | 0.211997i | ||||
\(165\) | −1.12324 | − | 3.67060i | −0.0874443 | − | 0.285756i | ||||
\(166\) | −16.1921 | −1.25675 | ||||||||
\(167\) | 10.5438 | 0.815900 | 0.407950 | − | 0.913004i | \(-0.366244\pi\) | ||||
0.407950 | + | 0.913004i | \(0.366244\pi\) | |||||||
\(168\) | −18.8663 | − | 4.35053i | −1.45556 | − | 0.335651i | ||||
\(169\) | −7.07356 | + | 10.9071i | −0.544120 | + | 0.839008i | ||||
\(170\) | 20.3400 | 1.56001 | ||||||||
\(171\) | 6.74521 | − | 4.55473i | 0.515819 | − | 0.348309i | ||||
\(172\) | −11.1287 | − | 19.2755i | −0.848557 | − | 1.46974i | ||||
\(173\) | −16.2583 | −1.23609 | −0.618047 | − | 0.786141i | \(-0.712076\pi\) | ||||
−0.618047 | + | 0.786141i | \(0.712076\pi\) | |||||||
\(174\) | −7.25104 | − | 23.6954i | −0.549700 | − | 1.79634i | ||||
\(175\) | 0.759205 | + | 1.31498i | 0.0573905 | + | 0.0994033i | ||||
\(176\) | 10.6224 | + | 18.3986i | 0.800694 | + | 1.38684i | ||||
\(177\) | 2.86843 | + | 9.37361i | 0.215604 | + | 0.704564i | ||||
\(178\) | 22.7694 | 1.70664 | ||||||||
\(179\) | 3.44039 | + | 5.95893i | 0.257147 | + | 0.445391i | 0.965476 | − | 0.260490i | \(-0.0838843\pi\) |
−0.708330 | + | 0.705882i | \(0.750551\pi\) | |||||||
\(180\) | −12.9976 | − | 6.33109i | −0.968781 | − | 0.471892i | ||||
\(181\) | 1.95012 | 0.144951 | 0.0724757 | − | 0.997370i | \(-0.476910\pi\) | ||||
0.0724757 | + | 0.997370i | \(0.476910\pi\) | |||||||
\(182\) | 14.2916 | + | 0.369811i | 1.05936 | + | 0.0274123i | ||||
\(183\) | 6.55968 | + | 1.51265i | 0.484905 | + | 0.111818i | ||||
\(184\) | 35.5156 | 2.61825 | ||||||||
\(185\) | 7.34298 | 0.539866 | ||||||||
\(186\) | −8.49979 | − | 27.7761i | −0.623235 | − | 2.03664i | ||||
\(187\) | −8.63115 | − | 14.9496i | −0.631172 | − | 1.09322i | ||||
\(188\) | −28.5442 | + | 49.4400i | −2.08180 | + | 3.60578i | ||||
\(189\) | −6.13541 | − | 4.96055i | −0.446286 | − | 0.360827i | ||||
\(190\) | 7.08461 | 0.513972 | ||||||||
\(191\) | −21.5402 | −1.55859 | −0.779297 | − | 0.626655i | \(-0.784424\pi\) | ||||
−0.779297 | + | 0.626655i | \(0.784424\pi\) | |||||||
\(192\) | 13.0767 | + | 3.01547i | 0.943732 | + | 0.217623i | ||||
\(193\) | −5.00867 | −0.360532 | −0.180266 | − | 0.983618i | \(-0.557696\pi\) | ||||
−0.180266 | + | 0.983618i | \(0.557696\pi\) | |||||||
\(194\) | −7.00559 | + | 12.1340i | −0.502972 | + | 0.871173i | ||||
\(195\) | 6.04696 | + | 1.56020i | 0.433032 | + | 0.111728i | ||||
\(196\) | 11.3116 | + | 19.5923i | 0.807973 | + | 1.39945i | ||||
\(197\) | 12.6479 | + | 21.9068i | 0.901127 | + | 1.56080i | 0.826034 | + | 0.563621i | \(0.190592\pi\) |
0.0750929 | + | 0.997177i | \(0.476075\pi\) | |||||||
\(198\) | 1.21999 | + | 17.3191i | 0.0867010 | + | 1.23082i | ||||
\(199\) | −7.83148 | + | 13.5645i | −0.555159 | + | 0.961563i | 0.442732 | + | 0.896654i | \(0.354009\pi\) |
−0.997891 | + | 0.0649096i | \(0.979324\pi\) | |||||||
\(200\) | −3.68092 | − | 6.37554i | −0.260280 | − | 0.450819i | ||||
\(201\) | −15.1503 | − | 3.49363i | −1.06862 | − | 0.246422i | ||||
\(202\) | 22.5043 | + | 38.9786i | 1.58340 | + | 2.74253i | ||||
\(203\) | 4.15943 | − | 7.20435i | 0.291935 | − | 0.505646i | ||||
\(204\) | −63.3530 | − | 14.6091i | −4.43560 | − | 1.02284i | ||||
\(205\) | 0.325251 | − | 0.563352i | 0.0227165 | − | 0.0393462i | ||||
\(206\) | 2.31423 | + | 4.00837i | 0.161240 | + | 0.279276i | ||||
\(207\) | 13.0114 | + | 6.33781i | 0.904352 | + | 0.440508i | ||||
\(208\) | −34.5514 | − | 0.894057i | −2.39571 | − | 0.0619917i | ||||
\(209\) | −3.00631 | − | 5.20708i | −0.207951 | − | 0.360181i | ||||
\(210\) | −2.00962 | − | 6.56716i | −0.138677 | − | 0.453177i | ||||
\(211\) | −16.2810 | −1.12083 | −0.560414 | − | 0.828212i | \(-0.689358\pi\) | ||||
−0.560414 | + | 0.828212i | \(0.689358\pi\) | |||||||
\(212\) | −25.0323 | − | 43.3572i | −1.71922 | − | 2.97778i | ||||
\(213\) | −9.78508 | + | 10.4986i | −0.670462 | + | 0.719353i | ||||
\(214\) | 17.8957 | 1.22333 | ||||||||
\(215\) | 2.30926 | − | 3.99976i | 0.157490 | − | 0.272781i | ||||
\(216\) | 29.7469 | + | 24.0507i | 2.02402 | + | 1.63644i | ||||
\(217\) | 4.87575 | − | 8.44505i | 0.330988 | − | 0.573287i | ||||
\(218\) | 13.1814 | − | 22.8309i | 0.892760 | − | 1.54631i | ||||
\(219\) | −1.05208 | − | 0.242608i | −0.0710929 | − | 0.0163939i | ||||
\(220\) | −5.34018 | + | 9.24946i | −0.360035 | + | 0.623598i | ||||
\(221\) | 28.0745 | + | 0.726458i | 1.88849 | + | 0.0488669i | ||||
\(222\) | −32.3629 | − | 7.46284i | −2.17206 | − | 0.500873i | ||||
\(223\) | 2.20096 | − | 3.81217i | 0.147387 | − | 0.255282i | −0.782874 | − | 0.622180i | \(-0.786247\pi\) |
0.930261 | + | 0.366898i | \(0.119580\pi\) | |||||||
\(224\) | 7.82654 | + | 13.5560i | 0.522933 | + | 0.905746i | ||||
\(225\) | −0.210803 | − | 2.99258i | −0.0140536 | − | 0.199506i | ||||
\(226\) | 2.35050 | 0.156353 | ||||||||
\(227\) | −11.1168 | −0.737847 | −0.368923 | − | 0.929460i | \(-0.620274\pi\) | ||||
−0.368923 | + | 0.929460i | \(0.620274\pi\) | |||||||
\(228\) | −22.0665 | − | 5.08849i | −1.46139 | − | 0.336993i | ||||
\(229\) | −9.46002 | + | 16.3852i | −0.625136 | + | 1.08277i | 0.363379 | + | 0.931641i | \(0.381623\pi\) |
−0.988515 | + | 0.151125i | \(0.951710\pi\) | |||||||
\(230\) | 6.29896 | + | 10.9101i | 0.415341 | + | 0.719392i | ||||
\(231\) | −3.97399 | + | 4.26378i | −0.261470 | + | 0.280536i | ||||
\(232\) | −20.1666 | + | 34.9295i | −1.32400 | + | 2.29323i | ||||
\(233\) | −8.68243 | −0.568805 | −0.284402 | − | 0.958705i | \(-0.591795\pi\) | ||||
−0.284402 | + | 0.958705i | \(0.591795\pi\) | |||||||
\(234\) | −25.0653 | − | 13.0220i | −1.63857 | − | 0.851275i | ||||
\(235\) | −11.8461 | −0.772755 | ||||||||
\(236\) | 13.6372 | − | 23.6204i | 0.887708 | − | 1.53755i | ||||
\(237\) | −5.05471 | − | 16.5181i | −0.328339 | − | 1.07296i | ||||
\(238\) | −15.4422 | − | 26.7467i | −1.00097 | − | 1.73373i | ||||
\(239\) | 12.3481 | − | 21.3875i | 0.798730 | − | 1.38344i | −0.121713 | − | 0.992565i | \(-0.538839\pi\) |
0.920443 | − | 0.390876i | \(-0.127828\pi\) | |||||||
\(240\) | 4.85847 | + | 15.8768i | 0.313613 | + | 1.02484i | ||||
\(241\) | −21.5308 | −1.38692 | −0.693461 | − | 0.720494i | \(-0.743915\pi\) | ||||
−0.693461 | + | 0.720494i | \(0.743915\pi\) | |||||||
\(242\) | −15.8988 | −1.02202 | ||||||||
\(243\) | 6.60606 | + | 14.1195i | 0.423779 | + | 0.905766i | ||||
\(244\) | −9.36514 | − | 16.2209i | −0.599542 | − | 1.03844i | ||||
\(245\) | −2.34722 | + | 4.06550i | −0.149958 | + | 0.259735i | ||||
\(246\) | −2.00604 | + | 2.15232i | −0.127900 | + | 0.137227i | ||||
\(247\) | 9.77860 | + | 0.253032i | 0.622197 | + | 0.0161001i | ||||
\(248\) | −23.6396 | + | 40.9449i | −1.50111 | + | 2.60000i | ||||
\(249\) | 3.14266 | + | 10.2698i | 0.199158 | + | 0.650820i | ||||
\(250\) | 1.30568 | − | 2.26150i | 0.0825783 | − | 0.143030i | ||||
\(251\) | −11.8610 | + | 20.5439i | −0.748660 | + | 1.29672i | 0.199805 | + | 0.979836i | \(0.435969\pi\) |
−0.948465 | + | 0.316881i | \(0.897364\pi\) | |||||||
\(252\) | 1.54255 | + | 21.8982i | 0.0971713 | + | 1.37945i | ||||
\(253\) | 5.34585 | − | 9.25928i | 0.336091 | − | 0.582126i | ||||
\(254\) | −4.45367 | −0.279448 | ||||||||
\(255\) | −3.94771 | − | 12.9005i | −0.247215 | − | 0.807863i | ||||
\(256\) | 8.25064 | + | 14.2905i | 0.515665 | + | 0.893158i | ||||
\(257\) | −14.7553 | −0.920407 | −0.460204 | − | 0.887813i | \(-0.652224\pi\) | ||||
−0.460204 | + | 0.887813i | \(0.652224\pi\) | |||||||
\(258\) | −14.2427 | + | 15.2813i | −0.886714 | + | 0.951373i | ||||
\(259\) | −5.57482 | − | 9.65588i | −0.346403 | − | 0.599987i | ||||
\(260\) | −8.29572 | − | 15.2675i | −0.514479 | − | 0.946853i | ||||
\(261\) | −13.6214 | + | 9.19788i | −0.843141 | + | 0.569335i | ||||
\(262\) | 22.0710 | + | 38.2280i | 1.36355 | + | 2.36174i | ||||
\(263\) | 1.15065 | − | 1.99299i | 0.0709524 | − | 0.122893i | −0.828367 | − | 0.560186i | \(-0.810729\pi\) |
0.899319 | + | 0.437293i | \(0.144063\pi\) | |||||||
\(264\) | 19.2675 | − | 20.6725i | 1.18583 | − | 1.27230i | ||||
\(265\) | 5.19432 | − | 8.99682i | 0.319084 | − | 0.552670i | ||||
\(266\) | −5.37867 | − | 9.31613i | −0.329787 | − | 0.571209i | ||||
\(267\) | −4.41922 | − | 14.4414i | −0.270452 | − | 0.883798i | ||||
\(268\) | 21.6298 | + | 37.4639i | 1.32125 | + | 2.28847i | ||||
\(269\) | 11.3541 | − | 19.6658i | 0.692269 | − | 1.19905i | −0.278823 | − | 0.960342i | \(-0.589944\pi\) |
0.971093 | − | 0.238703i | \(-0.0767223\pi\) | |||||||
\(270\) | −2.11235 | + | 13.4036i | −0.128554 | + | 0.815715i | ||||
\(271\) | −7.18044 | − | 12.4369i | −0.436181 | − | 0.755487i | 0.561210 | − | 0.827673i | \(-0.310336\pi\) |
−0.997391 | + | 0.0721858i | \(0.977003\pi\) | |||||||
\(272\) | 37.3331 | + | 64.6629i | 2.26365 | + | 3.92076i | ||||
\(273\) | −2.53925 | − | 9.13616i | −0.153682 | − | 0.552945i | ||||
\(274\) | 16.5985 | − | 28.7495i | 1.00275 | − | 1.73682i | ||||
\(275\) | −2.21622 | −0.133643 | ||||||||
\(276\) | −11.7832 | − | 38.5060i | −0.709268 | − | 2.31779i | ||||
\(277\) | 4.95002 | 0.297418 | 0.148709 | − | 0.988881i | \(-0.452488\pi\) | ||||
0.148709 | + | 0.988881i | \(0.452488\pi\) | |||||||
\(278\) | 20.7156 | 1.24244 | ||||||||
\(279\) | −15.9672 | + | 10.7819i | −0.955929 | + | 0.645496i | ||||
\(280\) | −5.58915 | + | 9.68069i | −0.334016 | + | 0.578532i | ||||
\(281\) | −2.56975 | − | 4.45094i | −0.153298 | − | 0.265521i | 0.779140 | − | 0.626850i | \(-0.215656\pi\) |
−0.932438 | + | 0.361330i | \(0.882323\pi\) | |||||||
\(282\) | 52.2097 | + | 12.0395i | 3.10904 | + | 0.716940i | ||||
\(283\) | 7.93360 | 0.471603 | 0.235802 | − | 0.971801i | \(-0.424228\pi\) | ||||
0.235802 | + | 0.971801i | \(0.424228\pi\) | |||||||
\(284\) | 39.9311 | 2.36948 | ||||||||
\(285\) | −1.37502 | − | 4.49338i | −0.0814494 | − | 0.266165i | ||||
\(286\) | −10.8972 | + | 17.7950i | −0.644368 | + | 1.05224i | ||||
\(287\) | −0.987730 | −0.0583039 | ||||||||
\(288\) | −2.17314 | − | 30.8501i | −0.128054 | − | 1.81786i | ||||
\(289\) | −21.8347 | − | 37.8189i | −1.28440 | − | 2.22464i | ||||
\(290\) | −14.3067 | −0.840121 | ||||||||
\(291\) | 9.05564 | + | 2.08821i | 0.530851 | + | 0.122413i | ||||
\(292\) | 1.50204 | + | 2.60160i | 0.0879000 | + | 0.152247i | ||||
\(293\) | −4.61817 | − | 7.99890i | −0.269796 | − | 0.467301i | 0.699013 | − | 0.715109i | \(-0.253623\pi\) |
−0.968809 | + | 0.247808i | \(0.920290\pi\) | |||||||
\(294\) | 14.4768 | − | 15.5325i | 0.844305 | − | 0.905872i | ||||
\(295\) | 5.65958 | 0.329513 | ||||||||
\(296\) | 27.0289 | + | 46.8155i | 1.57102 | + | 2.72109i | ||||
\(297\) | 10.7478 | − | 4.13517i | 0.623650 | − | 0.239947i | ||||
\(298\) | −25.1786 | −1.45856 | ||||||||
\(299\) | 8.30453 | + | 15.2838i | 0.480263 | + | 0.883882i | ||||
\(300\) | −5.69111 | + | 6.10610i | −0.328576 | + | 0.352536i | ||||
\(301\) | −7.01281 | −0.404212 | ||||||||
\(302\) | 0.346285 | 0.0199264 | ||||||||
\(303\) | 20.3542 | − | 21.8385i | 1.16932 | − | 1.25459i | ||||
\(304\) | 13.0035 | + | 22.5227i | 0.745801 | + | 1.29176i | ||||
\(305\) | 1.94331 | − | 3.36591i | 0.111274 | − | 0.192732i | ||||
\(306\) | 4.28774 | + | 60.8691i | 0.245114 | + | 3.47966i | ||||
\(307\) | −17.4742 | −0.997307 | −0.498653 | − | 0.866801i | \(-0.666172\pi\) | ||||
−0.498653 | + | 0.866801i | \(0.666172\pi\) | |||||||
\(308\) | 16.2172 | 0.924058 | ||||||||
\(309\) | 2.09313 | − | 2.24576i | 0.119074 | − | 0.127757i | ||||
\(310\) | −16.7706 | −0.952505 | ||||||||
\(311\) | −7.40231 | + | 12.8212i | −0.419746 | + | 0.727022i | −0.995914 | − | 0.0903097i | \(-0.971214\pi\) |
0.576167 | + | 0.817332i | \(0.304548\pi\) | |||||||
\(312\) | 12.3113 | + | 44.2957i | 0.696989 | + | 2.50775i | ||||
\(313\) | 9.56555 | + | 16.5680i | 0.540677 | + | 0.936480i | 0.998865 | + | 0.0476246i | \(0.0151651\pi\) |
−0.458189 | + | 0.888855i | \(0.651502\pi\) | |||||||
\(314\) | −20.8248 | − | 36.0695i | −1.17521 | − | 2.03552i | ||||
\(315\) | −3.77515 | + | 2.54919i | −0.212706 | + | 0.143630i | ||||
\(316\) | −24.0314 | + | 41.6236i | −1.35187 | + | 2.34151i | ||||
\(317\) | 14.2923 | + | 24.7550i | 0.802737 | + | 1.39038i | 0.917808 | + | 0.397025i | \(0.129957\pi\) |
−0.115071 | + | 0.993357i | \(0.536709\pi\) | |||||||
\(318\) | −32.0368 | + | 34.3729i | −1.79653 | + | 1.92754i | ||||
\(319\) | 6.07098 | + | 10.5152i | 0.339910 | + | 0.588741i | ||||
\(320\) | 3.87400 | − | 6.70996i | 0.216563 | − | 0.375098i | ||||
\(321\) | −3.47331 | − | 11.3503i | −0.193861 | − | 0.633511i | ||||
\(322\) | 9.56440 | − | 16.5660i | 0.533003 | − | 0.923188i | ||||
\(323\) | −10.5659 | − | 18.3006i | −0.587901 | − | 1.01827i | ||||
\(324\) | 16.2064 | − | 40.2309i | 0.900355 | − | 2.23505i | ||||
\(325\) | 1.88294 | − | 3.07482i | 0.104447 | − | 0.170560i | ||||
\(326\) | 16.7814 | + | 29.0662i | 0.929435 | + | 1.60983i | ||||
\(327\) | −17.0387 | − | 3.92910i | −0.942244 | − | 0.217280i | ||||
\(328\) | 4.78890 | 0.264423 | ||||||||
\(329\) | 8.99362 | + | 15.5774i | 0.495834 | + | 0.858810i | ||||
\(330\) | 9.76764 | + | 2.25240i | 0.537691 | + | 0.123991i | ||||
\(331\) | −27.4292 | −1.50764 | −0.753822 | − | 0.657078i | \(-0.771792\pi\) | ||||
−0.753822 | + | 0.657078i | \(0.771792\pi\) | |||||||
\(332\) | 14.9410 | − | 25.8786i | 0.819994 | − | 1.42027i | ||||
\(333\) | 1.54792 | + | 21.9745i | 0.0848257 | + | 1.20419i | ||||
\(334\) | −13.7667 | + | 23.8447i | −0.753282 | + | 1.30472i | ||||
\(335\) | −4.48829 | + | 7.77394i | −0.245221 | + | 0.424736i | ||||
\(336\) | 17.1891 | − | 18.4425i | 0.937742 | − | 1.00612i | ||||
\(337\) | 1.34610 | − | 2.33152i | 0.0733268 | − | 0.127006i | −0.827031 | − | 0.562157i | \(-0.809972\pi\) |
0.900357 | + | 0.435151i | \(0.143305\pi\) | |||||||
\(338\) | −15.4306 | − | 30.2380i | −0.839315 | − | 1.64473i | ||||
\(339\) | −0.456200 | − | 1.49080i | −0.0247774 | − | 0.0809689i | ||||
\(340\) | −18.7684 | + | 32.5078i | −1.01786 | + | 1.76298i | ||||
\(341\) | 7.11650 | + | 12.3261i | 0.385380 | + | 0.667498i | ||||
\(342\) | 1.49346 | + | 21.2013i | 0.0807570 | + | 1.14643i | ||||
\(343\) | 17.7569 | 0.958785 | ||||||||
\(344\) | 34.0008 | 1.83320 | ||||||||
\(345\) | 5.69715 | − | 6.11258i | 0.306724 | − | 0.329090i | ||||
\(346\) | 21.2281 | − | 36.7681i | 1.14123 | − | 1.97666i | ||||
\(347\) | −3.77332 | − | 6.53558i | −0.202562 | − | 0.350848i | 0.746791 | − | 0.665059i | \(-0.231594\pi\) |
−0.949353 | + | 0.314211i | \(0.898260\pi\) | |||||||
\(348\) | 44.5612 | + | 10.2757i | 2.38873 | + | 0.550838i | ||||
\(349\) | 1.30705 | − | 2.26388i | 0.0699648 | − | 0.121183i | −0.828921 | − | 0.559366i | \(-0.811045\pi\) |
0.898886 | + | 0.438183i | \(0.144378\pi\) | |||||||
\(350\) | −3.96511 | −0.211944 | ||||||||
\(351\) | −3.39431 | + | 18.4249i | −0.181175 | + | 0.983451i | ||||
\(352\) | −22.8467 | −1.21774 | ||||||||
\(353\) | 5.51962 | − | 9.56026i | 0.293780 | − | 0.508841i | −0.680921 | − | 0.732357i | \(-0.738420\pi\) |
0.974700 | + | 0.223516i | \(0.0717535\pi\) | |||||||
\(354\) | −24.9436 | − | 5.75196i | −1.32574 | − | 0.305713i | ||||
\(355\) | 4.14295 | + | 7.17580i | 0.219885 | + | 0.380852i | ||||
\(356\) | −21.0101 | + | 36.3905i | −1.11353 | + | 1.92869i | ||||
\(357\) | −13.9669 | + | 14.9853i | −0.739204 | + | 0.793107i | ||||
\(358\) | −17.9682 | −0.949646 | ||||||||
\(359\) | −20.8092 | −1.09827 | −0.549134 | − | 0.835734i | \(-0.685042\pi\) | ||||
−0.549134 | + | 0.835734i | \(0.685042\pi\) | |||||||
\(360\) | 18.3034 | − | 12.3595i | 0.964674 | − | 0.651401i | ||||
\(361\) | 5.81981 | + | 10.0802i | 0.306306 | + | 0.530537i | ||||
\(362\) | −2.54623 | + | 4.41019i | −0.133827 | + | 0.231795i | ||||
\(363\) | 3.08574 | + | 10.0838i | 0.161959 | + | 0.529260i | ||||
\(364\) | −13.7784 | + | 22.4999i | −0.722184 | + | 1.17932i | ||||
\(365\) | −0.311679 | + | 0.539844i | −0.0163140 | + | 0.0282568i | ||||
\(366\) | −11.9857 | + | 12.8597i | −0.626501 | + | 0.672186i | ||||
\(367\) | −13.9798 | + | 24.2138i | −0.729741 | + | 1.26395i | 0.227252 | + | 0.973836i | \(0.427026\pi\) |
−0.956993 | + | 0.290112i | \(0.906308\pi\) | |||||||
\(368\) | −23.1229 | + | 40.0500i | −1.20536 | + | 2.08775i | ||||
\(369\) | 1.75444 | + | 0.854586i | 0.0913326 | + | 0.0444880i | ||||
\(370\) | −9.58755 | + | 16.6061i | −0.498433 | + | 0.863312i | ||||
\(371\) | −15.7742 | −0.818956 | ||||||||
\(372\) | 52.2354 | + | 12.0454i | 2.70828 | + | 0.624525i | ||||
\(373\) | 6.18601 | + | 10.7145i | 0.320299 | + | 0.554775i | 0.980550 | − | 0.196271i | \(-0.0628832\pi\) |
−0.660250 | + | 0.751045i | \(0.729550\pi\) | |||||||
\(374\) | 45.0780 | 2.33093 | ||||||||
\(375\) | −1.68776 | − | 0.389194i | −0.0871555 | − | 0.0200979i | ||||
\(376\) | −43.6046 | − | 75.5254i | −2.24874 | − | 3.89492i | ||||
\(377\) | −19.7470 | − | 0.510976i | −1.01702 | − | 0.0263166i | ||||
\(378\) | 19.2291 | − | 7.39835i | 0.989041 | − | 0.380530i | ||||
\(379\) | 5.29558 | + | 9.17221i | 0.272016 | + | 0.471145i | 0.969378 | − | 0.245574i | \(-0.0789764\pi\) |
−0.697362 | + | 0.716719i | \(0.745643\pi\) | |||||||
\(380\) | −6.53721 | + | 11.3228i | −0.335352 | + | 0.580846i | ||||
\(381\) | 0.864396 | + | 2.82472i | 0.0442843 | + | 0.144715i | ||||
\(382\) | 28.1245 | − | 48.7131i | 1.43898 | − | 2.49238i | ||||
\(383\) | −9.93697 | − | 17.2113i | −0.507755 | − | 0.879458i | −0.999960 | − | 0.00897845i | \(-0.997142\pi\) |
0.492204 | − | 0.870480i | \(-0.336191\pi\) | |||||||
\(384\) | 0.454624 | − | 0.487775i | 0.0231999 | − | 0.0248917i | ||||
\(385\) | 1.68257 | + | 2.91429i | 0.0857516 | + | 0.148526i | ||||
\(386\) | 6.53970 | − | 11.3271i | 0.332862 | − | 0.576534i | ||||
\(387\) | 12.4564 | + | 6.06750i | 0.633195 | + | 0.308428i | ||||
\(388\) | −12.9286 | − | 22.3930i | −0.656349 | − | 1.13683i | ||||
\(389\) | 13.5377 | + | 23.4481i | 0.686391 | + | 1.18886i | 0.972997 | + | 0.230816i | \(0.0741395\pi\) |
−0.286606 | + | 0.958048i | \(0.592527\pi\) | |||||||
\(390\) | −11.4238 | + | 11.6381i | −0.578465 | + | 0.589317i | ||||
\(391\) | 18.7883 | − | 32.5423i | 0.950166 | − | 1.64574i | ||||
\(392\) | −34.5597 | −1.74553 | ||||||||
\(393\) | 19.9623 | − | 21.4179i | 1.00696 | − | 1.08039i | ||||
\(394\) | −66.0564 | −3.32787 | ||||||||
\(395\) | −9.97325 | −0.501809 | ||||||||
\(396\) | −28.8055 | − | 14.0311i | −1.44753 | − | 0.705090i | ||||
\(397\) | 19.0723 | − | 33.0342i | 0.957211 | − | 1.65794i | 0.227986 | − | 0.973664i | \(-0.426786\pi\) |
0.729225 | − | 0.684274i | \(-0.239881\pi\) | |||||||
\(398\) | −20.4508 | − | 35.4218i | −1.02510 | − | 1.77553i | ||||
\(399\) | −4.86479 | + | 5.21953i | −0.243544 | + | 0.261303i | ||||
\(400\) | 9.58604 | 0.479302 | ||||||||
\(401\) | 31.1625 | 1.55618 | 0.778092 | − | 0.628151i | \(-0.216188\pi\) | ||||
0.778092 | + | 0.628151i | \(0.216188\pi\) | |||||||
\(402\) | 27.6822 | − | 29.7008i | 1.38066 | − | 1.48134i | ||||
\(403\) | −23.1478 | − | 0.598974i | −1.15307 | − | 0.0298370i | ||||
\(404\) | −83.0619 | −4.13249 | ||||||||
\(405\) | 8.91112 | − | 1.26169i | 0.442797 | − | 0.0626940i | ||||
\(406\) | 10.8617 | + | 18.8131i | 0.539060 | + | 0.933679i | ||||
\(407\) | 16.2737 | 0.806656 | ||||||||
\(408\) | 67.7168 | − | 72.6547i | 3.35248 | − | 3.59694i | ||||
\(409\) | 0.413863 | + | 0.716831i | 0.0204642 | + | 0.0354450i | 0.876076 | − | 0.482173i | \(-0.160152\pi\) |
−0.855612 | + | 0.517618i | \(0.826819\pi\) | |||||||
\(410\) | 0.849347 | + | 1.47111i | 0.0419462 | + | 0.0726530i | ||||
\(411\) | −21.4557 | − | 4.94766i | −1.05833 | − | 0.244050i | ||||
\(412\) | −8.54168 | −0.420818 | ||||||||
\(413\) | −4.29678 | − | 7.44224i | −0.211431 | − | 0.366209i | ||||
\(414\) | −31.3216 | + | 21.1500i | −1.53937 | + | 1.03947i | ||||
\(415\) | 6.20065 | 0.304378 | ||||||||
\(416\) | 19.4110 | − | 31.6979i | 0.951703 | − | 1.55412i | ||||
\(417\) | −4.02061 | − | 13.1388i | −0.196890 | − | 0.643409i | ||||
\(418\) | 15.7011 | 0.767965 | ||||||||
\(419\) | −33.6746 | −1.64511 | −0.822556 | − | 0.568685i | \(-0.807452\pi\) | ||||
−0.822556 | + | 0.568685i | \(0.807452\pi\) | |||||||
\(420\) | 12.3501 | + | 2.84792i | 0.602624 | + | 0.138964i | ||||
\(421\) | 4.75864 | + | 8.24220i | 0.231922 | + | 0.401700i | 0.958374 | − | 0.285517i | \(-0.0921653\pi\) |
−0.726452 | + | 0.687217i | \(0.758832\pi\) | |||||||
\(422\) | 21.2577 | − | 36.8194i | 1.03481 | − | 1.79234i | ||||
\(423\) | −2.49720 | − | 35.4505i | −0.121418 | − | 1.72366i | ||||
\(424\) | 76.4795 | 3.71417 | ||||||||
\(425\) | −7.78906 | −0.377825 | ||||||||
\(426\) | −10.9664 | − | 35.8367i | −0.531325 | − | 1.73629i | ||||
\(427\) | −5.90148 | −0.285593 | ||||||||
\(428\) | −16.5130 | + | 28.6014i | −0.798186 | + | 1.38250i | ||||
\(429\) | 13.4014 | + | 3.45776i | 0.647027 | + | 0.166942i | ||||
\(430\) | 6.03030 | + | 10.4448i | 0.290807 | + | 0.503692i | ||||
\(431\) | −12.3943 | − | 21.4675i | −0.597012 | − | 1.03406i | −0.993260 | − | 0.115912i | \(-0.963021\pi\) |
0.396247 | − | 0.918144i | \(-0.370312\pi\) | |||||||
\(432\) | −46.4884 | + | 17.8862i | −2.23667 | + | 0.860552i | ||||
\(433\) | −2.02166 | + | 3.50162i | −0.0971548 | + | 0.168277i | −0.910506 | − | 0.413496i | \(-0.864308\pi\) |
0.813351 | + | 0.581773i | \(0.197641\pi\) | |||||||
\(434\) | 12.7323 | + | 22.0530i | 0.611171 | + | 1.05858i | ||||
\(435\) | 2.77674 | + | 9.07398i | 0.133134 | + | 0.435064i | ||||
\(436\) | 24.3259 | + | 42.1337i | 1.16500 | + | 2.01784i | ||||
\(437\) | 6.54415 | − | 11.3348i | 0.313049 | − | 0.542217i | ||||
\(438\) | 1.92233 | − | 2.06251i | 0.0918526 | − | 0.0985504i | ||||
\(439\) | 16.6737 | − | 28.8797i | 0.795792 | − | 1.37835i | −0.126543 | − | 0.991961i | \(-0.540388\pi\) |
0.922335 | − | 0.386391i | \(-0.126279\pi\) | |||||||
\(440\) | −8.15775 | − | 14.1296i | −0.388905 | − | 0.673604i | ||||
\(441\) | −12.6611 | − | 6.16722i | −0.602912 | − | 0.293677i | ||||
\(442\) | −38.2991 | + | 62.5418i | −1.82170 | + | 2.97481i | ||||
\(443\) | −8.45494 | − | 14.6444i | −0.401706 | − | 0.695776i | 0.592226 | − | 0.805772i | \(-0.298249\pi\) |
−0.993932 | + | 0.109996i | \(0.964916\pi\) | |||||||
\(444\) | 41.7896 | − | 44.8369i | 1.98325 | − | 2.12787i | ||||
\(445\) | −8.71938 | −0.413338 | ||||||||
\(446\) | 5.74749 | + | 9.95494i | 0.272151 | + | 0.471380i | ||||
\(447\) | 4.88681 | + | 15.9694i | 0.231138 | + | 0.755327i | ||||
\(448\) | −11.7646 | −0.555827 | ||||||||
\(449\) | −6.57032 | + | 11.3801i | −0.310072 | + | 0.537061i | −0.978378 | − | 0.206826i | \(-0.933687\pi\) |
0.668305 | + | 0.743887i | \(0.267020\pi\) | |||||||
\(450\) | 7.04297 | + | 3.43062i | 0.332009 | + | 0.161721i | ||||
\(451\) | 0.720830 | − | 1.24851i | 0.0339426 | − | 0.0587903i | ||||
\(452\) | −2.16889 | + | 3.75662i | −0.102016 | + | 0.176697i | ||||
\(453\) | −0.0672090 | − | 0.219629i | −0.00315775 | − | 0.0103191i | ||||
\(454\) | 14.5149 | − | 25.1406i | 0.681219 | − | 1.17991i | ||||
\(455\) | −5.47287 | − | 0.141617i | −0.256572 | − | 0.00663910i | ||||
\(456\) | 23.5864 | − | 25.3063i | 1.10453 | − | 1.18508i | ||||
\(457\) | 5.11881 | − | 8.86604i | 0.239448 | − | 0.414736i | −0.721108 | − | 0.692823i | \(-0.756367\pi\) |
0.960556 | + | 0.278087i | \(0.0897003\pi\) | |||||||
\(458\) | −24.7035 | − | 42.7876i | −1.15432 | − | 1.99933i | ||||
\(459\) | 37.7738 | − | 14.5333i | 1.76313 | − | 0.678357i | ||||
\(460\) | −23.2490 | −1.08399 | ||||||||
\(461\) | −24.8222 | −1.15608 | −0.578042 | − | 0.816007i | \(-0.696183\pi\) | ||||
−0.578042 | + | 0.816007i | \(0.696183\pi\) | |||||||
\(462\) | −4.45377 | − | 14.5543i | −0.207208 | − | 0.677127i | ||||
\(463\) | −1.66549 | + | 2.88471i | −0.0774018 | + | 0.134064i | −0.902128 | − | 0.431468i | \(-0.857996\pi\) |
0.824726 | + | 0.565532i | \(0.191329\pi\) | |||||||
\(464\) | −26.2594 | − | 45.4826i | −1.21906 | − | 2.11148i | ||||
\(465\) | 3.25494 | + | 10.6367i | 0.150944 | + | 0.493264i | ||||
\(466\) | 11.3364 | − | 19.6353i | 0.525151 | − | 0.909588i | ||||
\(467\) | 9.81015 | 0.453959 | 0.226980 | − | 0.973899i | \(-0.427115\pi\) | ||||
0.226980 | + | 0.973899i | \(0.427115\pi\) | |||||||
\(468\) | 43.9407 | − | 28.0441i | 2.03116 | − | 1.29634i | ||||
\(469\) | 13.6301 | 0.629380 | ||||||||
\(470\) | 15.4672 | − | 26.7899i | 0.713448 | − | 1.23573i | ||||
\(471\) | −18.8351 | + | 20.2086i | −0.867877 | + | 0.931163i | ||||
\(472\) | 20.8325 | + | 36.0829i | 0.958892 | + | 1.66085i | ||||
\(473\) | 5.11784 | − | 8.86436i | 0.235319 | − | 0.407584i | ||||
\(474\) | 43.9554 | + | 10.1361i | 2.01894 | + | 0.465564i | ||||
\(475\) | −2.71300 | −0.124481 | ||||||||
\(476\) | 56.9962 | 2.61242 | ||||||||
\(477\) | 28.0187 | + | 13.6479i | 1.28289 | + | 0.624893i | ||||
\(478\) | 32.2452 | + | 55.8503i | 1.47486 | + | 2.55453i | ||||
\(479\) | −10.4517 | + | 18.1028i | −0.477549 | + | 0.827139i | −0.999669 | − | 0.0257329i | \(-0.991808\pi\) |
0.522120 | + | 0.852872i | \(0.325141\pi\) | |||||||
\(480\) | −17.3989 | − | 4.01215i | −0.794146 | − | 0.183129i | ||||
\(481\) | −13.8264 | + | 22.5783i | −0.630430 | + | 1.02948i | ||||
\(482\) | 28.1123 | − | 48.6919i | 1.28048 | − | 2.21786i | ||||
\(483\) | −12.3632 | − | 2.85094i | −0.562547 | − | 0.129722i | ||||
\(484\) | 14.6704 | − | 25.4099i | 0.666836 | − | 1.15499i | ||||
\(485\) | 2.68274 | − | 4.64664i | 0.121817 | − | 0.210993i | ||||
\(486\) | −40.5566 | − | 3.49588i | −1.83968 | − | 0.158576i | ||||
\(487\) | 7.91472 | − | 13.7087i | 0.358650 | − | 0.621200i | −0.629086 | − | 0.777336i | \(-0.716570\pi\) |
0.987736 | + | 0.156136i | \(0.0499038\pi\) | |||||||
\(488\) | 28.6127 | 1.29524 | ||||||||
\(489\) | 15.1781 | − | 16.2849i | 0.686376 | − | 0.736427i | ||||
\(490\) | −6.12941 | − | 10.6164i | −0.276899 | − | 0.479602i | ||||
\(491\) | −28.8861 | −1.30361 | −0.651805 | − | 0.758386i | \(-0.725988\pi\) | ||||
−0.651805 | + | 0.758386i | \(0.725988\pi\) | |||||||
\(492\) | −1.58884 | − | 5.19211i | −0.0716306 | − | 0.234079i | ||||
\(493\) | 21.3368 | + | 36.9565i | 0.960963 | + | 1.66444i | ||||
\(494\) | −13.3399 | + | 21.7839i | −0.600191 | + | 0.980104i | ||||
\(495\) | −0.467187 | − | 6.63224i | −0.0209985 | − | 0.298097i | ||||
\(496\) | −30.7817 | − | 53.3154i | −1.38214 | − | 2.39393i | ||||
\(497\) | 6.29070 | − | 10.8958i | 0.282176 | − | 0.488744i | ||||
\(498\) | −27.3284 | − | 6.30187i | −1.22461 | − | 0.282394i | ||||
\(499\) | 3.64275 | − | 6.30943i | 0.163072 | − | 0.282449i | −0.772897 | − | 0.634531i | \(-0.781193\pi\) |
0.935969 | + | 0.352083i | \(0.114526\pi\) | |||||||
\(500\) | 2.40958 | + | 4.17352i | 0.107760 | + | 0.186646i | ||||
\(501\) | 17.7953 | + | 4.10357i | 0.795036 | + | 0.183334i | ||||
\(502\) | −30.9733 | − | 53.6473i | −1.38241 | − | 2.39440i | ||||
\(503\) | −15.7003 | + | 27.1938i | −0.700044 | + | 1.21251i | 0.268407 | + | 0.963306i | \(0.413503\pi\) |
−0.968451 | + | 0.249205i | \(0.919831\pi\) | |||||||
\(504\) | −30.1485 | − | 14.6853i | −1.34292 | − | 0.654134i | ||||
\(505\) | −8.61787 | − | 14.9266i | −0.383490 | − | 0.664225i | ||||
\(506\) | 13.9599 | + | 24.1793i | 0.620593 | + | 1.07490i | ||||
\(507\) | −16.1834 | + | 15.6556i | −0.718731 | + | 0.695288i | ||||
\(508\) | 4.10956 | − | 7.11796i | 0.182332 | − | 0.315808i | ||||
\(509\) | −23.5807 | −1.04520 | −0.522599 | − | 0.852579i | \(-0.675037\pi\) | ||||
−0.522599 | + | 0.852579i | \(0.675037\pi\) | |||||||
\(510\) | 34.3290 | + | 7.91620i | 1.52011 | + | 0.350535i | ||||
\(511\) | 0.946514 | 0.0418713 | ||||||||
\(512\) | −42.3207 | −1.87033 | ||||||||
\(513\) | 13.1570 | − | 5.06209i | 0.580894 | − | 0.223497i | ||||
\(514\) | 19.2656 | − | 33.3690i | 0.849769 | − | 1.47184i | ||||
\(515\) | −0.886219 | − | 1.53498i | −0.0390515 | − | 0.0676391i | ||||
\(516\) | −11.2807 | − | 36.8636i | −0.496604 | − | 1.62283i | ||||
\(517\) | −26.2536 | −1.15463 | ||||||||
\(518\) | 29.1157 | 1.27927 | ||||||||
\(519\) | −27.4400 | − | 6.32763i | −1.20448 | − | 0.277752i | ||||
\(520\) | 26.5346 | + | 0.686613i | 1.16362 | + | 0.0301100i | ||||
\(521\) | 30.9740 | 1.35699 | 0.678497 | − | 0.734603i | \(-0.262632\pi\) | ||||
0.678497 | + | 0.734603i | \(0.262632\pi\) | |||||||
\(522\) | −3.01591 | − | 42.8141i | −0.132003 | − | 1.87392i | ||||
\(523\) | −5.43961 | − | 9.42167i | −0.237857 | − | 0.411981i | 0.722242 | − | 0.691641i | \(-0.243112\pi\) |
−0.960099 | + | 0.279660i | \(0.909778\pi\) | |||||||
\(524\) | −81.4625 | −3.55871 | ||||||||
\(525\) | 0.769571 | + | 2.51485i | 0.0335868 | + | 0.109757i | ||||
\(526\) | 3.00477 | + | 5.20441i | 0.131014 | + | 0.226923i | ||||
\(527\) | 25.0114 | + | 43.3210i | 1.08951 | + | 1.88709i | ||||
\(528\) | 10.7675 | + | 35.1865i | 0.468593 | + | 1.53130i | ||||
\(529\) | 0.273722 | 0.0119010 | ||||||||
\(530\) | 13.5642 | + | 23.4939i | 0.589191 | + | 1.02051i | ||||
\(531\) | 1.19306 | + | 16.9368i | 0.0517743 | + | 0.734993i | ||||
\(532\) | 19.8523 | 0.860707 | ||||||||
\(533\) | 1.11978 | + | 2.06085i | 0.0485029 | + | 0.0892653i | ||||
\(534\) | 38.4292 | + | 8.86171i | 1.66299 | + | 0.383484i | ||||
\(535\) | −6.85305 | −0.296283 | ||||||||
\(536\) | −66.0841 | −2.85440 | ||||||||
\(537\) | 3.48737 | + | 11.3962i | 0.150491 | + | 0.491783i | ||||
\(538\) | 29.6495 | + | 51.3544i | 1.27828 | + | 2.21404i | ||||
\(539\) | −5.20196 | + | 9.01005i | −0.224064 | + | 0.388090i | ||||
\(540\) | −19.4727 | − | 15.7439i | −0.837973 | − | 0.677511i | ||||
\(541\) | −16.6842 | −0.717308 | −0.358654 | − | 0.933471i | \(-0.616764\pi\) | ||||
−0.358654 | + | 0.933471i | \(0.616764\pi\) | |||||||
\(542\) | 37.5014 | 1.61082 | ||||||||
\(543\) | 3.29133 | + | 0.758975i | 0.141245 | + | 0.0325708i | ||||
\(544\) | −80.2963 | −3.44268 | ||||||||
\(545\) | −5.04774 | + | 8.74295i | −0.216222 | + | 0.374507i | ||||
\(546\) | 23.9768 | + | 6.18636i | 1.02611 | + | 0.264752i | ||||
\(547\) | 19.3482 | + | 33.5121i | 0.827271 | + | 1.43287i | 0.900171 | + | 0.435536i | \(0.143441\pi\) |
−0.0729008 | + | 0.997339i | \(0.523226\pi\) | |||||||
\(548\) | 30.6320 | + | 53.0562i | 1.30853 | + | 2.26645i | ||||
\(549\) | 10.4824 | + | 5.10598i | 0.447379 | + | 0.217918i | ||||
\(550\) | 2.89367 | − | 5.01199i | 0.123387 | − | 0.213712i | ||||
\(551\) | 7.43182 | + | 12.8723i | 0.316606 | + | 0.548378i | ||||
\(552\) | 59.9418 | + | 13.8225i | 2.55129 | + | 0.588324i | ||||
\(553\) | 7.57174 | + | 13.1146i | 0.321983 | + | 0.557691i | ||||
\(554\) | −6.46313 | + | 11.1945i | −0.274592 | + | 0.475608i | ||||
\(555\) | 12.3932 | + | 2.85784i | 0.526061 | + | 0.121309i | ||||
\(556\) | −19.1150 | + | 33.1081i | −0.810656 | + | 1.40410i | ||||
\(557\) | −4.33443 | − | 7.50745i | −0.183656 | − | 0.318101i | 0.759467 | − | 0.650546i | \(-0.225460\pi\) |
−0.943123 | + | 0.332445i | \(0.892126\pi\) | |||||||
\(558\) | −3.53530 | − | 50.1874i | −0.149661 | − | 2.12460i | ||||
\(559\) | 7.95033 | + | 14.6319i | 0.336263 | + | 0.618863i | ||||
\(560\) | −7.27777 | − | 12.6055i | −0.307542 | − | 0.532678i | ||||
\(561\) | −8.74900 | − | 28.5905i | −0.369383 | − | 1.20709i | ||||
\(562\) | 13.4211 | 0.566133 | ||||||||
\(563\) | 8.34729 | + | 14.4579i | 0.351796 | + | 0.609329i | 0.986564 | − | 0.163374i | \(-0.0522376\pi\) |
−0.634768 | + | 0.772703i | \(0.718904\pi\) | |||||||
\(564\) | −67.4174 | + | 72.3335i | −2.83879 | + | 3.04579i | ||||
\(565\) | −0.900109 | −0.0378679 | ||||||||
\(566\) | −10.3587 | + | 17.9418i | −0.435409 | + | 0.754151i | ||||
\(567\) | −8.42447 | − | 10.7601i | −0.353795 | − | 0.451881i | ||||
\(568\) | −30.4998 | + | 52.8271i | −1.27974 | + | 2.21658i | ||||
\(569\) | 0.118747 | − | 0.205676i | 0.00497815 | − | 0.00862240i | −0.863526 | − | 0.504305i | \(-0.831749\pi\) |
0.868504 | + | 0.495683i | \(0.165082\pi\) | |||||||
\(570\) | 11.9571 | + | 2.75729i | 0.500828 | + | 0.115490i | ||||
\(571\) | 7.10342 | − | 12.3035i | 0.297269 | − | 0.514885i | −0.678241 | − | 0.734839i | \(-0.737258\pi\) |
0.975510 | + | 0.219954i | \(0.0705909\pi\) | |||||||
\(572\) | −18.3852 | − | 33.8363i | −0.768723 | − | 1.41477i | ||||
\(573\) | −36.3547 | − | 8.38332i | −1.51874 | − | 0.350218i | ||||
\(574\) | 1.28966 | − | 2.23375i | 0.0538292 | − | 0.0932349i | ||||
\(575\) | −2.41214 | − | 4.17795i | −0.100593 | − | 0.174233i | ||||
\(576\) | 20.8968 | + | 10.1788i | 0.870699 | + | 0.424116i | ||||
\(577\) | −8.91083 | −0.370963 | −0.185481 | − | 0.982648i | \(-0.559384\pi\) | ||||
−0.185481 | + | 0.982648i | \(0.559384\pi\) | |||||||
\(578\) | 114.036 | 4.74329 | ||||||||
\(579\) | −8.45342 | − | 1.94934i | −0.351312 | − | 0.0810120i | ||||
\(580\) | 13.2013 | − | 22.8653i | 0.548155 | − | 0.949432i | ||||
\(581\) | −4.70757 | − | 8.15375i | −0.195303 | − | 0.338274i | ||||
\(582\) | −16.5462 | + | 17.7528i | −0.685863 | + | 0.735876i | ||||
\(583\) | 11.5118 | − | 19.9390i | 0.476769 | − | 0.825788i | ||||
\(584\) | −4.58907 | −0.189897 | ||||||||
\(585\) | 9.59859 | + | 4.98669i | 0.396853 | + | 0.206174i | ||||
\(586\) | 24.1193 | 0.996360 | ||||||||
\(587\) | −6.91359 | + | 11.9747i | −0.285354 | + | 0.494248i | −0.972695 | − | 0.232087i | \(-0.925445\pi\) |
0.687341 | + | 0.726335i | \(0.258778\pi\) | |||||||
\(588\) | 11.4661 | + | 37.4695i | 0.472853 | + | 1.54522i | ||||
\(589\) | 8.71170 | + | 15.0891i | 0.358959 | + | 0.621736i | ||||
\(590\) | −7.38958 | + | 12.7991i | −0.304224 | + | 0.526932i | ||||
\(591\) | 12.8206 | + | 41.8959i | 0.527370 | + | 1.72337i | ||||
\(592\) | −70.3901 | −2.89301 | ||||||||
\(593\) | 26.8894 | 1.10422 | 0.552108 | − | 0.833773i | \(-0.313824\pi\) | ||||
0.552108 | + | 0.833773i | \(0.313824\pi\) | |||||||
\(594\) | −4.68145 | + | 29.7053i | −0.192082 | + | 1.21882i | ||||
\(595\) | 5.91349 | + | 10.2425i | 0.242430 | + | 0.419900i | ||||
\(596\) | 23.2331 | − | 40.2410i | 0.951666 | − | 1.64833i | ||||
\(597\) | −18.4969 | + | 19.8457i | −0.757027 | + | 0.812229i | ||||
\(598\) | −45.4072 | − | 1.17496i | −1.85684 | − | 0.0480478i | ||||
\(599\) | −14.1910 | + | 24.5795i | −0.579828 | + | 1.00429i | 0.415670 | + | 0.909515i | \(0.363547\pi\) |
−0.995499 | + | 0.0947765i | \(0.969786\pi\) | |||||||
\(600\) | −3.73118 | − | 12.1930i | −0.152325 | − | 0.497776i | ||||
\(601\) | 10.8784 | − | 18.8419i | 0.443738 | − | 0.768576i | −0.554226 | − | 0.832366i | \(-0.686986\pi\) |
0.997963 | + | 0.0637904i | \(0.0203189\pi\) | |||||||
\(602\) | 9.15646 | − | 15.8595i | 0.373190 | − | 0.646383i | ||||
\(603\) | −24.2103 | − | 11.7928i | −0.985920 | − | 0.480240i | ||||
\(604\) | −0.319528 | + | 0.553439i | −0.0130014 | + | 0.0225191i | ||||
\(605\) | 6.08835 | 0.247527 | ||||||||
\(606\) | 22.8116 | + | 74.5450i | 0.926657 | + | 3.02818i | ||||
\(607\) | 0.0344775 | + | 0.0597168i | 0.00139940 | + | 0.00242383i | 0.866724 | − | 0.498788i | \(-0.166221\pi\) |
−0.865325 | + | 0.501211i | \(0.832888\pi\) | |||||||
\(608\) | −27.9680 | −1.13425 | ||||||||
\(609\) | 9.82401 | − | 10.5404i | 0.398089 | − | 0.427117i | ||||
\(610\) | 5.07467 | + | 8.78959i | 0.205467 | + | 0.355880i | ||||
\(611\) | 22.3055 | − | 36.4247i | 0.902386 | − | 1.47358i | ||||
\(612\) | −101.239 | − | 49.3132i | −4.09234 | − | 1.99337i | ||||
\(613\) | 19.4119 | + | 33.6224i | 0.784039 | + | 1.35800i | 0.929571 | + | 0.368642i | \(0.120177\pi\) |
−0.145532 | + | 0.989353i | \(0.546490\pi\) | |||||||
\(614\) | 22.8157 | − | 39.5179i | 0.920767 | − | 1.59481i | ||||
\(615\) | 0.768199 | − | 0.824216i | 0.0309768 | − | 0.0332356i | ||||
\(616\) | −12.3868 | + | 21.4546i | −0.499079 | + | 0.864430i | ||||
\(617\) | 8.57087 | + | 14.8452i | 0.345050 | + | 0.597645i | 0.985363 | − | 0.170470i | \(-0.0545285\pi\) |
−0.640313 | + | 0.768114i | \(0.721195\pi\) | |||||||
\(618\) | 2.34583 | + | 7.66584i | 0.0943631 | + | 0.308365i | ||||
\(619\) | −9.48341 | − | 16.4258i | −0.381171 | − | 0.660207i | 0.610059 | − | 0.792356i | \(-0.291146\pi\) |
−0.991230 | + | 0.132149i | \(0.957812\pi\) | |||||||
\(620\) | 15.4748 | − | 26.8031i | 0.621482 | − | 1.07644i | ||||
\(621\) | 19.4934 | + | 15.7606i | 0.782243 | + | 0.632453i | ||||
\(622\) | −19.3300 | − | 33.4806i | −0.775064 | − | 1.34245i | ||||
\(623\) | 6.61980 | + | 11.4658i | 0.265217 | + | 0.459368i | ||||
\(624\) | −57.9665 | − | 14.9562i | −2.32052 | − | 0.598725i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −49.9581 | −1.99673 | ||||||||
\(627\) | −3.04736 | − | 9.95834i | −0.121700 | − | 0.397698i | ||||
\(628\) | 76.8628 | 3.06716 | ||||||||
\(629\) | 57.1949 | 2.28051 | ||||||||
\(630\) | −0.835857 | − | 11.8659i | −0.0333013 | − | 0.472749i | ||||
\(631\) | 0.0473814 | − | 0.0820669i | 0.00188622 | − | 0.00326703i | −0.865081 | − | 0.501633i | \(-0.832733\pi\) |
0.866967 | + | 0.498366i | \(0.166066\pi\) | |||||||
\(632\) | −36.7108 | − | 63.5849i | −1.46028 | − | 2.52927i | ||||
\(633\) | −27.4783 | − | 6.33646i | −1.09217 | − | 0.251852i | ||||
\(634\) | −74.6447 | −2.96452 | ||||||||
\(635\) | 1.70550 | 0.0676809 | ||||||||
\(636\) | −25.3741 | − | 82.9189i | −1.00615 | − | 3.28795i | ||||
\(637\) | −8.08100 | − | 14.8724i | −0.320181 | − | 0.589265i | ||||
\(638\) | −31.7069 | −1.25529 | ||||||||
\(639\) | −20.6008 | + | 13.9108i | −0.814957 | + | 0.550303i | ||||
\(640\) | −0.192485 | − | 0.333394i | −0.00760865 | − | 0.0131786i | ||||
\(641\) | 27.3779 | 1.08136 | 0.540680 | − | 0.841228i | \(-0.318167\pi\) | ||||
0.540680 | + | 0.841228i | \(0.318167\pi\) | |||||||
\(642\) | 30.2037 | + | 6.96492i | 1.19204 | + | 0.274883i | ||||
\(643\) | 0.729225 | + | 1.26305i | 0.0287578 | + | 0.0498100i | 0.880046 | − | 0.474888i | \(-0.157512\pi\) |
−0.851288 | + | 0.524698i | \(0.824178\pi\) | |||||||
\(644\) | 17.6508 | + | 30.5721i | 0.695538 | + | 1.20471i | ||||
\(645\) | 5.45416 | − | 5.85187i | 0.214757 | − | 0.230417i | ||||
\(646\) | 55.1824 | 2.17112 | ||||||||
\(647\) | −2.87909 | − | 4.98673i | −0.113189 | − | 0.196049i | 0.803866 | − | 0.594811i | \(-0.202773\pi\) |
−0.917054 | + | 0.398762i | \(0.869440\pi\) | |||||||
\(648\) | 40.8451 | + | 52.1691i | 1.60455 | + | 2.04939i | ||||
\(649\) | 12.5429 | 0.492352 | ||||||||
\(650\) | 4.49519 | + | 8.27300i | 0.176316 | + | 0.324494i | ||||
\(651\) | 11.5159 | − | 12.3556i | 0.451342 | − | 0.484254i | ||||
\(652\) | −61.9390 | −2.42572 | ||||||||
\(653\) | −9.29890 | −0.363894 | −0.181947 | − | 0.983308i | \(-0.558240\pi\) | ||||
−0.181947 | + | 0.983308i | \(0.558240\pi\) | |||||||
\(654\) | 31.1327 | − | 33.4029i | 1.21739 | − | 1.30616i | ||||
\(655\) | −8.45193 | − | 14.6392i | −0.330244 | − | 0.572000i | ||||
\(656\) | −3.11787 | + | 5.40032i | −0.121733 | + | 0.210847i | ||||
\(657\) | −1.68123 | − | 0.818926i | −0.0655912 | − | 0.0319493i | ||||
\(658\) | −46.9711 | −1.83112 | ||||||||
\(659\) | −7.54198 | −0.293794 | −0.146897 | − | 0.989152i | \(-0.546929\pi\) | ||||
−0.146897 | + | 0.989152i | \(0.546929\pi\) | |||||||
\(660\) | −12.6128 | + | 13.5325i | −0.490951 | + | 0.526751i | ||||
\(661\) | 37.4941 | 1.45835 | 0.729175 | − | 0.684327i | \(-0.239904\pi\) | ||||
0.729175 | + | 0.684327i | \(0.239904\pi\) | |||||||
\(662\) | 35.8137 | − | 62.0311i | 1.39194 | − | 2.41091i | ||||
\(663\) | 47.1002 | + | 12.1525i | 1.82922 | + | 0.471964i | ||||
\(664\) | 22.8241 | + | 39.5325i | 0.885748 | + | 1.53416i | ||||
\(665\) | 2.05973 | + | 3.56755i | 0.0798727 | + | 0.138344i | ||||
\(666\) | −51.7163 | − | 25.1909i | −2.00397 | − | 0.976129i | ||||
\(667\) | −13.2153 | + | 22.8896i | −0.511700 | + | 0.886290i | ||||
\(668\) | −25.4061 | − | 44.0046i | −0.982990 | − | 1.70259i | ||||
\(669\) | 5.19836 | − | 5.57743i | 0.200980 | − | 0.215636i | ||||
\(670\) | −11.7205 | − | 20.3005i | −0.452802 | − | 0.784277i | ||||
\(671\) | 4.30681 | − | 7.45962i | 0.166263 | − | 0.287975i | ||||
\(672\) | 7.93340 | + | 25.9252i | 0.306038 | + | 1.00009i | ||||
\(673\) | −24.0003 | + | 41.5698i | −0.925145 | + | 1.60240i | −0.133817 | + | 0.991006i | \(0.542723\pi\) |
−0.791328 | + | 0.611392i | \(0.790610\pi\) | |||||||
\(674\) | 3.51515 | + | 6.08842i | 0.135398 | + | 0.234517i | ||||
\(675\) | 0.808911 | − | 5.13280i | 0.0311350 | − | 0.197562i | ||||
\(676\) | 62.5653 | + | 3.24007i | 2.40636 | + | 0.124618i | ||||
\(677\) | 10.7632 | + | 18.6425i | 0.413665 | + | 0.716488i | 0.995287 | − | 0.0969704i | \(-0.0309152\pi\) |
−0.581622 | + | 0.813459i | \(0.697582\pi\) | |||||||
\(678\) | 3.96708 | + | 0.914802i | 0.152355 | + | 0.0351328i | ||||
\(679\) | −8.14700 | −0.312653 | ||||||||
\(680\) | −28.6709 | − | 49.6595i | −1.09948 | − | 1.90435i | ||||
\(681\) | −18.7624 | − | 4.32659i | −0.718978 | − | 0.165795i | ||||
\(682\) | −37.1674 | −1.42321 | ||||||||
\(683\) | 18.2668 | − | 31.6390i | 0.698960 | − | 1.21063i | −0.269868 | − | 0.962897i | \(-0.586980\pi\) |
0.968827 | − | 0.247736i | \(-0.0796867\pi\) | |||||||
\(684\) | −35.2624 | − | 17.1763i | −1.34829 | − | 0.656751i | ||||
\(685\) | −6.35628 | + | 11.0094i | −0.242861 | + | 0.420648i | ||||
\(686\) | −23.1848 | + | 40.1573i | −0.885201 | + | 1.53321i | ||||
\(687\) | −22.3433 | + | 23.9725i | −0.852449 | + | 0.914609i | ||||
\(688\) | −22.1367 | + | 38.3418i | −0.843953 | + | 1.46177i | ||||
\(689\) | 17.8830 | + | 32.9121i | 0.681289 | + | 1.25385i | ||||
\(690\) | 6.38496 | + | 20.8652i | 0.243071 | + | 0.794323i | ||||
\(691\) | 11.0869 | − | 19.2031i | 0.421765 | − | 0.730519i | −0.574347 | − | 0.818612i | \(-0.694744\pi\) |
0.996112 | + | 0.0880929i | \(0.0280772\pi\) | |||||||
\(692\) | 39.1757 | + | 67.8543i | 1.48924 | + | 2.57943i | ||||
\(693\) | −8.36658 | + | 5.64957i | −0.317820 | + | 0.214609i | ||||
\(694\) | 19.7069 | 0.748065 | ||||||||
\(695\) | −7.93290 | −0.300912 | ||||||||
\(696\) | −47.6306 | + | 51.1038i | −1.80543 | + | 1.93709i | ||||
\(697\) | 2.53340 | − | 4.38798i | 0.0959595 | − | 0.166207i | ||||
\(698\) | 3.41317 | + | 5.91178i | 0.129190 | + | 0.223764i | ||||
\(699\) | −14.6538 | − | 3.37915i | −0.554259 | − | 0.127811i | ||||
\(700\) | 3.65874 | − | 6.33712i | 0.138287 | − | 0.239521i | ||||
\(701\) | −14.9607 | −0.565058 | −0.282529 | − | 0.959259i | \(-0.591173\pi\) | ||||
−0.282529 | + | 0.959259i | \(0.591173\pi\) | |||||||
\(702\) | −37.2361 | − | 31.7333i | −1.40539 | − | 1.19769i | ||||
\(703\) | 19.9215 | 0.751354 | ||||||||
\(704\) | 8.58564 | − | 14.8708i | 0.323584 | − | 0.560463i | ||||
\(705\) | −19.9934 | − | 4.61043i | −0.752994 | − | 0.173639i | ||||
\(706\) | 14.4137 | + | 24.9652i | 0.542466 | + | 0.939578i | ||||
\(707\) | −13.0855 | + | 22.6647i | −0.492129 | + | 0.852393i | ||||
\(708\) | 32.2092 | − | 34.5579i | 1.21050 | − | 1.29877i | ||||
\(709\) | 14.6803 | 0.551329 | 0.275664 | − | 0.961254i | \(-0.411102\pi\) | ||||
0.275664 | + | 0.961254i | \(0.411102\pi\) | |||||||
\(710\) | −21.6374 | −0.812038 | ||||||||
\(711\) | −2.10239 | − | 29.8458i | −0.0788459 | − | 1.11930i | ||||
\(712\) | −32.0954 | − | 55.5908i | −1.20282 | − | 2.08335i | ||||
\(713\) | −15.4912 | + | 26.8316i | −0.580151 | + | 1.00485i | ||||
\(714\) | −15.6531 | − | 51.1520i | −0.585802 | − | 1.91432i | ||||
\(715\) | 4.17302 | − | 6.81449i | 0.156062 | − | 0.254848i | ||||
\(716\) | 16.5798 | − | 28.7171i | 0.619617 | − | 1.07321i | ||||
\(717\) | 29.1644 | − | 31.2911i | 1.08917 | − | 1.16859i | ||||
\(718\) | 27.1701 | − | 47.0600i | 1.01398 | − | 1.75626i | ||||
\(719\) | −5.45911 | + | 9.45545i | −0.203590 | + | 0.352629i | −0.949683 | − | 0.313214i | \(-0.898594\pi\) |
0.746092 | + | 0.665842i | \(0.231928\pi\) | |||||||
\(720\) | 2.02077 | + | 28.6870i | 0.0753096 | + | 1.06910i | ||||
\(721\) | −1.34564 | + | 2.33072i | −0.0501144 | + | 0.0868007i | ||||
\(722\) | −30.3952 | −1.13119 | ||||||||
\(723\) | −36.3388 | − | 8.37967i | −1.35146 | − | 0.311643i | ||||
\(724\) | −4.69898 | − | 8.13887i | −0.174636 | − | 0.302479i | ||||
\(725\) | 5.47867 | 0.203473 | ||||||||
\(726\) | −26.8334 | − | 6.18773i | −0.995881 | − | 0.229648i | ||||
\(727\) | 14.8068 | + | 25.6461i | 0.549153 | + | 0.951161i | 0.998333 | + | 0.0577195i | \(0.0183829\pi\) |
−0.449180 | + | 0.893441i | \(0.648284\pi\) | |||||||
\(728\) | −19.2423 | − | 35.4138i | −0.713168 | − | 1.31252i | ||||
\(729\) | 5.65422 | + | 26.4013i | 0.209415 | + | 0.977827i | ||||
\(730\) | −0.813905 | − | 1.40972i | −0.0301240 | − | 0.0521763i | ||||
\(731\) | 17.9870 | − | 31.1543i | 0.665272 | − | 1.15229i | ||||
\(732\) | −9.49301 | − | 31.0218i | −0.350872 | − | 1.14660i | ||||
\(733\) | 3.48671 | − | 6.03916i | 0.128785 | − | 0.223061i | −0.794421 | − | 0.607367i | \(-0.792226\pi\) |
0.923206 | + | 0.384306i | \(0.125559\pi\) | |||||||
\(734\) | −36.5062 | − | 63.2307i | −1.34747 | − | 2.33389i | ||||
\(735\) | −5.54380 | + | 5.94805i | −0.204486 | + | 0.219397i | ||||
\(736\) | −24.8664 | − | 43.0699i | −0.916589 | − | 1.58758i | ||||
\(737\) | −9.94705 | + | 17.2288i | −0.366404 | + | 0.634631i | ||||
\(738\) | −4.22338 | + | 2.85186i | −0.155465 | + | 0.104978i | ||||
\(739\) | −22.7924 | − | 39.4776i | −0.838433 | − | 1.45221i | −0.891204 | − | 0.453602i | \(-0.850139\pi\) |
0.0527713 | − | 0.998607i | \(-0.483195\pi\) | |||||||
\(740\) | −17.6935 | − | 30.6461i | −0.650427 | − | 1.12657i | ||||
\(741\) | 16.4054 | + | 4.23283i | 0.602668 | + | 0.155497i | ||||
\(742\) | 20.5960 | − | 35.6734i | 0.756104 | − | 1.30961i | ||||
\(743\) | 38.5886 | 1.41568 | 0.707839 | − | 0.706374i | \(-0.249670\pi\) | ||||
0.707839 | + | 0.706374i | \(0.249670\pi\) | |||||||
\(744\) | −55.8334 | + | 59.9047i | −2.04695 | + | 2.19621i | ||||
\(745\) | 9.64197 | 0.353254 | ||||||||
\(746\) | −32.3077 | −1.18287 | ||||||||
\(747\) | 1.30712 | + | 18.5560i | 0.0478250 | + | 0.678928i | ||||
\(748\) | −41.5950 | + | 72.0446i | −1.52086 | + | 2.63421i | ||||
\(749\) | 5.20287 | + | 9.01164i | 0.190109 | + | 0.329278i | ||||
\(750\) | 3.08383 | − | 3.30870i | 0.112606 | − | 0.120817i | ||||
\(751\) | −31.7736 | −1.15944 | −0.579718 | − | 0.814817i | \(-0.696837\pi\) | ||||
−0.579718 | + | 0.814817i | \(0.696837\pi\) | |||||||
\(752\) | 113.557 | 4.14101 | ||||||||
\(753\) | −28.0141 | + | 30.0568i | −1.02089 | + | 1.09533i | ||||
\(754\) | 26.9388 | − | 43.9907i | 0.981053 | − | 1.60205i | ||||
\(755\) | −0.132607 | −0.00482607 | ||||||||
\(756\) | −5.91919 | + | 37.5591i | −0.215279 | + | 1.36601i | ||||
\(757\) | 21.8063 | + | 37.7697i | 0.792564 | + | 1.37276i | 0.924374 | + | 0.381486i | \(0.124588\pi\) |
−0.131810 | + | 0.991275i | \(0.542079\pi\) | |||||||
\(758\) | −27.6573 | −1.00456 | ||||||||
\(759\) | 12.6262 | − | 13.5469i | 0.458300 | − | 0.491720i | ||||
\(760\) | −9.98635 | − | 17.2969i | −0.362243 | − | 0.627423i | ||||
\(761\) | 3.52276 | + | 6.10159i | 0.127700 | + | 0.221183i | 0.922785 | − | 0.385315i | \(-0.125907\pi\) |
−0.795085 | + | 0.606498i | \(0.792574\pi\) | |||||||
\(762\) | −7.51673 | − | 1.73334i | −0.272302 | − | 0.0627924i | ||||
\(763\) | 15.3291 | 0.554950 | ||||||||
\(764\) | 51.9029 | + | 89.8985i | 1.87778 | + | 3.25241i | ||||
\(765\) | −1.64196 | − | 23.3094i | −0.0593652 | − | 0.842754i | ||||
\(766\) | 51.8979 | 1.87515 | ||||||||
\(767\) | −10.6567 | + | 17.4022i | −0.384790 | + | 0.628356i | ||||
\(768\) | 8.36330 | + | 27.3301i | 0.301784 | + | 0.986188i | ||||
\(769\) | 18.2259 | 0.657243 | 0.328622 | − | 0.944462i | \(-0.393416\pi\) | ||||
0.328622 | + | 0.944462i | \(0.393416\pi\) | |||||||
\(770\) | −8.78756 | −0.316682 | ||||||||
\(771\) | −24.9033 | − | 5.74266i | −0.896870 | − | 0.206817i | ||||
\(772\) | 12.0688 | + | 20.9038i | 0.434366 | + | 0.752344i | ||||
\(773\) | −24.8841 | + | 43.1005i | −0.895018 | + | 1.55022i | −0.0612350 | + | 0.998123i | \(0.519504\pi\) |
−0.833783 | + | 0.552093i | \(0.813829\pi\) | |||||||
\(774\) | −29.9857 | + | 20.2480i | −1.07781 | + | 0.727798i | ||||
\(775\) | 6.42218 | 0.230692 | ||||||||
\(776\) | 39.4998 | 1.41796 | ||||||||
\(777\) | −5.65094 | − | 18.4665i | −0.202726 | − | 0.662481i | ||||
\(778\) | −70.7037 | −2.53485 | ||||||||
\(779\) | 0.882408 | − | 1.52838i | 0.0316156 | − | 0.0547597i | ||||
\(780\) | −8.05913 | − | 28.9966i | −0.288563 | − | 1.03824i | ||||
\(781\) | 9.18171 | + | 15.9032i | 0.328547 | + | 0.569061i | ||||
\(782\) | 49.0629 | + | 84.9795i | 1.75449 | + | 3.03886i | ||||
\(783\) | −26.5693 | + | 10.2224i | −0.949510 | + | 0.365320i | ||||
\(784\) | 22.5005 | − | 38.9720i | 0.803590 | − | 1.39186i | ||||
\(785\) | 7.97470 | + | 13.8126i | 0.284629 | + | 0.492992i | ||||
\(786\) | 22.3723 | + | 73.1096i | 0.797995 | + | 2.60773i | ||||
\(787\) | −8.32284 | − | 14.4156i | −0.296677 | − | 0.513860i | 0.678696 | − | 0.734419i | \(-0.262545\pi\) |
−0.975374 | + | 0.220559i | \(0.929212\pi\) | |||||||
\(788\) | 60.9524 | − | 105.573i | 2.17134 | − | 3.76087i | ||||
\(789\) | 2.71769 | − | 2.91586i | 0.0967523 | − | 0.103807i | ||||
\(790\) | 13.0218 | − | 22.5545i | 0.463296 | − | 0.802453i | ||||
\(791\) | 0.683367 | + | 1.18363i | 0.0242977 | + | 0.0420849i | ||||
\(792\) | 40.5644 | − | 27.3913i | 1.44139 | − | 0.973308i | ||||
\(793\) | 6.69043 | + | 12.3132i | 0.237584 | + | 0.437253i | ||||
\(794\) | 49.8045 | + | 86.2639i | 1.76750 | + | 3.06139i | ||||
\(795\) | 12.2683 | − | 13.1629i | 0.435111 | − | 0.466839i | ||||
\(796\) | 75.4824 | 2.67540 | ||||||||
\(797\) | −15.9465 | − | 27.6202i | −0.564854 | − | 0.978356i | −0.997063 | − | 0.0765828i | \(-0.975599\pi\) |
0.432209 | − | 0.901773i | \(-0.357734\pi\) | |||||||
\(798\) | −5.45211 | − | 17.8167i | −0.193003 | − | 0.630705i | ||||
\(799\) | −92.2700 | −3.26428 | ||||||||
\(800\) | −5.15443 | + | 8.92773i | −0.182237 | + | 0.315643i | ||||
\(801\) | −1.83807 | − | 26.0935i | −0.0649451 | − | 0.921968i | ||||
\(802\) | −40.6882 | + | 70.4740i | −1.43675 | + | 2.48853i | ||||
\(803\) | −0.690751 | + | 1.19642i | −0.0243761 | + | 0.0422206i | ||||
\(804\) | 21.9251 | + | 71.6482i | 0.773240 | + | 2.52684i | ||||
\(805\) | −3.66262 | + | 6.34385i | −0.129090 | + | 0.223591i | ||||
\(806\) | 31.5781 | − | 51.5666i | 1.11229 | − | 1.81635i | ||||
\(807\) | 26.8167 | − | 28.7722i | 0.943993 | − | 1.01283i | ||||
\(808\) | 63.4434 | − | 109.887i | 2.23193 | − | 3.86582i | ||||
\(809\) | −10.2607 | − | 17.7721i | −0.360747 | − | 0.624833i | 0.627337 | − | 0.778748i | \(-0.284145\pi\) |
−0.988084 | + | 0.153915i | \(0.950812\pi\) | |||||||
\(810\) | −8.78173 | + | 21.7999i | −0.308559 | + | 0.765969i | ||||
\(811\) | 17.8609 | 0.627181 | 0.313590 | − | 0.949558i | \(-0.398468\pi\) | ||||
0.313590 | + | 0.949558i | \(0.398468\pi\) | |||||||
\(812\) | −40.0900 | −1.40688 | ||||||||
\(813\) | −7.27849 | − | 23.7851i | −0.255268 | − | 0.834178i | ||||
\(814\) | −21.2482 | + | 36.8029i | −0.744748 | + | 1.28994i | ||||
\(815\) | −6.42632 | − | 11.1307i | −0.225104 | − | 0.389892i | ||||
\(816\) | 37.8429 | + | 123.665i | 1.32477 | + | 4.32915i | ||||
\(817\) | 6.26503 | − | 10.8514i | 0.219186 | − | 0.379641i | ||||
\(818\) | −2.16148 | −0.0755745 | ||||||||
\(819\) | −0.729899 | − | 16.4079i | −0.0255047 | − | 0.573338i | ||||
\(820\) | −3.13488 | −0.109475 | ||||||||
\(821\) | −0.367023 | + | 0.635703i | −0.0128092 | + | 0.0221862i | −0.872359 | − | 0.488866i | \(-0.837411\pi\) |
0.859550 | + | 0.511052i | \(0.170744\pi\) | |||||||
\(822\) | 39.2034 | − | 42.0621i | 1.36738 | − | 1.46708i | ||||
\(823\) | −14.4636 | − | 25.0517i | −0.504170 | − | 0.873248i | −0.999988 | − | 0.00482168i | \(-0.998465\pi\) |
0.495818 | − | 0.868426i | \(-0.334868\pi\) | |||||||
\(824\) | 6.52421 | − | 11.3003i | 0.227282 | − | 0.393663i | ||||
\(825\) | −3.74045 | − | 0.862541i | −0.130226 | − | 0.0300298i | ||||
\(826\) | 22.4408 | 0.780816 | ||||||||
\(827\) | −17.4090 | −0.605370 | −0.302685 | − | 0.953091i | \(-0.597883\pi\) | ||||
−0.302685 | + | 0.953091i | \(0.597883\pi\) | |||||||
\(828\) | −4.90097 | − | 69.5747i | −0.170321 | − | 2.41789i | ||||
\(829\) | −25.3663 | − | 43.9358i | −0.881010 | − | 1.52595i | −0.850220 | − | 0.526428i | \(-0.823531\pi\) |
−0.0307899 | − | 0.999526i | \(-0.509802\pi\) | |||||||
\(830\) | −8.09605 | + | 14.0228i | −0.281018 | + | 0.486738i | ||||
\(831\) | 8.35444 | + | 1.92652i | 0.289812 | + | 0.0668303i | ||||
\(832\) | 13.3374 | + | 24.5463i | 0.462391 | + | 0.850990i | ||||
\(833\) | −18.2826 | + | 31.6664i | −0.633455 | + | 1.09718i | ||||
\(834\) | 34.9629 | + | 8.06239i | 1.21067 | + | 0.279178i | ||||
\(835\) | 5.27188 | − | 9.13116i | 0.182441 | − | 0.315997i | ||||
\(836\) | −14.4879 | + | 25.0938i | −0.501075 | + | 0.867888i | ||||
\(837\) | −31.1450 | + | 11.9829i | −1.07653 | + | 0.414190i | ||||
\(838\) | 43.9681 | − | 76.1550i | 1.51885 | − | 2.63073i | ||||
\(839\) | −3.15817 | −0.109032 | −0.0545161 | − | 0.998513i | \(-0.517362\pi\) | ||||
−0.0545161 | + | 0.998513i | \(0.517362\pi\) | |||||||
\(840\) | −13.2008 | + | 14.1634i | −0.455471 | + | 0.488684i | ||||
\(841\) | −0.507905 | − | 0.879717i | −0.0175140 | − | 0.0303351i | ||||
\(842\) | −24.8530 | −0.856490 | ||||||||
\(843\) | −2.60484 | − | 8.51224i | −0.0897154 | − | 0.293177i | ||||
\(844\) | 39.2304 | + | 67.9490i | 1.35037 | + | 2.33890i | ||||
\(845\) | 5.90905 | + | 11.5794i | 0.203277 | + | 0.398344i | ||||
\(846\) | 83.4317 | + | 40.6394i | 2.86844 | + | 1.39721i | ||||
\(847\) | −4.62231 | − | 8.00607i | −0.158824 | − | 0.275092i | ||||
\(848\) | −49.7930 | + | 86.2439i | −1.70990 | + | 2.96163i | ||||
\(849\) | 13.3900 | + | 3.08771i | 0.459543 | + | 0.105970i | ||||
\(850\) | 10.1700 | − | 17.6149i | 0.348828 | − | 0.604188i | ||||
\(851\) | 17.7123 | + | 30.6786i | 0.607170 | + | 1.05165i | ||||
\(852\) | 67.3941 | + | 15.5410i | 2.30888 | + | 0.532425i | ||||
\(853\) | −4.05291 | − | 7.01985i | −0.138769 | − | 0.240355i | 0.788262 | − | 0.615340i | \(-0.210981\pi\) |
−0.927031 | + | 0.374985i | \(0.877648\pi\) | |||||||
\(854\) | 7.70543 | − | 13.3462i | 0.263674 | − | 0.456697i | ||||
\(855\) | −0.571910 | − | 8.11889i | −0.0195589 | − | 0.277660i | ||||
\(856\) | −25.2256 | − | 43.6919i | −0.862192 | − | 1.49336i | ||||
\(857\) | −1.99817 | − | 3.46093i | −0.0682562 | − | 0.118223i | 0.829878 | − | 0.557946i | \(-0.188410\pi\) |
−0.898134 | + | 0.439722i | \(0.855077\pi\) | |||||||
\(858\) | −25.3176 | + | 25.7926i | −0.864330 | + | 0.880545i | ||||
\(859\) | −13.4957 | + | 23.3752i | −0.460467 | + | 0.797552i | −0.998984 | − | 0.0450627i | \(-0.985651\pi\) |
0.538518 | + | 0.842614i | \(0.318985\pi\) | |||||||
\(860\) | −22.2574 | −0.758972 | ||||||||
\(861\) | −1.66705 | − | 0.384419i | −0.0568129 | − | 0.0131010i | ||||
\(862\) | 64.7318 | 2.20477 | ||||||||
\(863\) | −26.2622 | −0.893976 | −0.446988 | − | 0.894540i | \(-0.647503\pi\) | ||||
−0.446988 | + | 0.894540i | \(0.647503\pi\) | |||||||
\(864\) | 8.33895 | − | 52.9133i | 0.283697 | − | 1.80015i | ||||
\(865\) | −8.12914 | + | 14.0801i | −0.276399 | + | 0.478737i | ||||
\(866\) | −5.27927 | − | 9.14396i | −0.179397 | − | 0.310724i | ||||
\(867\) | −22.1329 | − | 72.3270i | −0.751671 | − | 2.45635i | ||||
\(868\) | −46.9941 | −1.59509 | ||||||||
\(869\) | −22.1030 | −0.749792 | ||||||||
\(870\) | −24.1463 | − | 5.56810i | −0.818637 | − | 0.188776i | ||||
\(871\) | −15.4523 | − | 28.4386i | −0.523581 | − | 0.963604i | ||||
\(872\) | −74.3214 | −2.51684 | ||||||||
\(873\) | 14.4710 | + | 7.04880i | 0.489769 | + | 0.238566i | ||||
\(874\) | 17.0891 | + | 29.5992i | 0.578047 | + | 1.00121i | ||||
\(875\) | 1.51841 | 0.0513316 | ||||||||
\(876\) | 1.52254 | + | 4.97546i | 0.0514420 | + | 0.168105i | ||||
\(877\) | 19.4001 | + | 33.6020i | 0.655096 | + | 1.13466i | 0.981870 | + | 0.189557i | \(0.0607053\pi\) |
−0.326773 | + | 0.945103i | \(0.605961\pi\) | |||||||
\(878\) | 43.5409 | + | 75.4151i | 1.46943 | + | 2.54514i | ||||
\(879\) | −4.68122 | − | 15.2976i | −0.157894 | − | 0.515974i | ||||
\(880\) | 21.2448 | 0.716163 | ||||||||
\(881\) | −14.5303 | − | 25.1672i | −0.489538 | − | 0.847904i | 0.510390 | − | 0.859943i | \(-0.329501\pi\) |
−0.999928 | + | 0.0120389i | \(0.996168\pi\) | |||||||
\(882\) | 30.4785 | − | 20.5808i | 1.02627 | − | 0.692990i | ||||
\(883\) | 29.1018 | 0.979355 | 0.489677 | − | 0.871904i | \(-0.337115\pi\) | ||||
0.489677 | + | 0.871904i | \(0.337115\pi\) | |||||||
\(884\) | −64.6159 | − | 118.920i | −2.17327 | − | 3.99971i | ||||
\(885\) | 9.55200 | + | 2.20267i | 0.321087 | + | 0.0740421i | ||||
\(886\) | 44.1577 | 1.48351 | ||||||||
\(887\) | 9.27217 | 0.311329 | 0.155664 | − | 0.987810i | \(-0.450248\pi\) | ||||
0.155664 | + | 0.987810i | \(0.450248\pi\) | |||||||
\(888\) | 27.3980 | + | 89.5327i | 0.919416 | + | 3.00452i | ||||
\(889\) | −1.29483 | − | 2.24271i | −0.0434271 | − | 0.0752180i | ||||
\(890\) | 11.3847 | − | 19.7189i | 0.381616 | − | 0.660978i | ||||
\(891\) | 19.7490 | − | 2.79619i | 0.661618 | − | 0.0936761i | ||||
\(892\) | −21.2136 | −0.710284 | ||||||||
\(893\) | −32.1385 | −1.07547 | ||||||||
\(894\) | −42.4954 | − | 9.79936i | −1.42126 | − | 0.327740i | ||||
\(895\) | 6.88078 | 0.229999 | ||||||||
\(896\) | −0.292272 | + | 0.506229i | −0.00976411 | + | 0.0169119i | ||||
\(897\) | 8.06769 | + | 29.0274i | 0.269372 | + | 0.969195i | ||||
\(898\) | −17.1574 | − | 29.7175i | −0.572550 | − | 0.991687i | ||||
\(899\) | −17.5925 | − | 30.4711i | −0.586743 | − | 1.01627i | ||||
\(900\) | −11.9817 | + | 8.09068i | −0.399389 | + | 0.269689i | ||||
\(901\) | 40.4589 | − | 70.0768i | 1.34788 | − | 2.33460i | ||||
\(902\) | 1.88234 | + | 3.26031i | 0.0626752 | + | 0.108557i | ||||
\(903\) | −11.8359 | − | 2.72934i | −0.393875 | − | 0.0908269i | ||||
\(904\) | −3.31323 | − | 5.73868i | −0.110196 | − | 0.190866i | ||||
\(905\) | 0.975060 | − | 1.68885i | 0.0324121 | − | 0.0561394i | ||||
\(906\) | 0.584445 | + | 0.134772i | 0.0194169 | + | 0.00447750i | ||||
\(907\) | 18.7827 | − | 32.5326i | 0.623669 | − | 1.08023i | −0.365127 | − | 0.930958i | \(-0.618975\pi\) |
0.988797 | − | 0.149269i | \(-0.0476921\pi\) | |||||||
\(908\) | 26.7868 | + | 46.3961i | 0.888952 | + | 1.53971i | ||||
\(909\) | 42.8524 | − | 28.9363i | 1.42132 | − | 0.959756i | ||||
\(910\) | 7.46607 | − | 12.1920i | 0.247498 | − | 0.404161i | ||||
\(911\) | 12.0750 | + | 20.9146i | 0.400064 | + | 0.692931i | 0.993733 | − | 0.111778i | \(-0.0356546\pi\) |
−0.593669 | + | 0.804709i | \(0.702321\pi\) | |||||||
\(912\) | 13.1810 | + | 43.0737i | 0.436468 | + | 1.42631i | ||||
\(913\) | 13.7420 | 0.454795 | ||||||||
\(914\) | 13.3670 | + | 23.1524i | 0.442142 | + | 0.765812i | ||||
\(915\) | 4.58983 | − | 4.92452i | 0.151735 | − | 0.162800i | ||||
\(916\) | 91.1788 | 3.01263 | ||||||||
\(917\) | −12.8335 | + | 22.2283i | −0.423799 | + | 0.734042i | ||||
\(918\) | −16.4532 | + | 104.401i | −0.543038 | + | 3.44575i | ||||
\(919\) | −7.35962 | + | 12.7472i | −0.242771 | + | 0.420492i | −0.961503 | − | 0.274796i | \(-0.911390\pi\) |
0.718731 | + | 0.695288i | \(0.244723\pi\) | |||||||
\(920\) | 17.7578 | − | 30.7574i | 0.585458 | − | 1.01404i | ||||
\(921\) | −29.4923 | − | 6.80087i | −0.971803 | − | 0.224096i | ||||
\(922\) | 32.4098 | − | 56.1354i | 1.06736 | − | 1.84872i | ||||
\(923\) | −29.8652 | − | 0.772797i | −0.983026 | − | 0.0254369i | ||||
\(924\) | 27.3706 | + | 6.31162i | 0.900428 | + | 0.207637i | ||||
\(925\) | 3.67149 | − | 6.35920i | 0.120718 | − | 0.209089i | ||||
\(926\) | −4.34918 | − | 7.53300i | −0.142923 | − | 0.247550i | ||||
\(927\) | 4.40673 | − | 2.97566i | 0.144736 | − | 0.0977336i | ||||
\(928\) | 56.4788 | 1.85401 | ||||||||
\(929\) | 25.8981 | 0.849688 | 0.424844 | − | 0.905267i | \(-0.360329\pi\) | ||||
0.424844 | + | 0.905267i | \(0.360329\pi\) | |||||||
\(930\) | −28.3047 | − | 6.52702i | −0.928148 | − | 0.214029i | ||||
\(931\) | −6.36800 | + | 11.0297i | −0.208703 | + | 0.361484i | ||||
\(932\) | 20.9210 | + | 36.2363i | 0.685292 | + | 1.18696i | ||||
\(933\) | −17.4832 | + | 18.7581i | −0.572375 | + | 0.614113i | ||||
\(934\) | −12.8089 | + | 22.1856i | −0.419119 | + | 0.725936i | ||||
\(935\) | −17.2623 | −0.564538 | ||||||||
\(936\) | 3.53884 | + | 79.5518i | 0.115671 | + | 2.60023i | ||||
\(937\) | 21.1191 | 0.689931 | 0.344965 | − | 0.938615i | \(-0.387891\pi\) | ||||
0.344965 | + | 0.938615i | \(0.387891\pi\) | |||||||
\(938\) | −17.7965 | + | 30.8245i | −0.581077 | + | 1.00646i | ||||
\(939\) | 9.69616 | + | 31.6857i | 0.316422 | + | 1.03402i | ||||
\(940\) | 28.5442 | + | 49.4400i | 0.931009 | + | 1.61255i | ||||
\(941\) | 8.40481 | − | 14.5576i | 0.273989 | − | 0.474563i | −0.695891 | − | 0.718148i | \(-0.744990\pi\) |
0.969880 | + | 0.243585i | \(0.0783235\pi\) | |||||||
\(942\) | −21.1091 | − | 68.9815i | −0.687772 | − | 2.24754i | ||||
\(943\) | 3.13821 | 0.102194 | ||||||||
\(944\) | −54.2529 | −1.76578 | ||||||||
\(945\) | −7.36367 | + | 2.83315i | −0.239540 | + | 0.0921622i | ||||
\(946\) | 13.3645 | + | 23.1480i | 0.434517 | + | 0.752606i | ||||
\(947\) | −6.80091 | + | 11.7795i | −0.221000 | + | 0.382783i | −0.955112 | − | 0.296245i | \(-0.904265\pi\) |
0.734112 | + | 0.679028i | \(0.237599\pi\) | |||||||
\(948\) | −56.7588 | + | 60.8977i | −1.84344 | + | 1.97786i | ||||
\(949\) | −1.07305 | − | 1.97485i | −0.0348327 | − | 0.0641065i | ||||
\(950\) | 3.54230 | − | 6.13545i | 0.114928 | − | 0.199060i | ||||
\(951\) | 14.4875 | + | 47.3430i | 0.469789 | + | 1.53520i | ||||
\(952\) | −43.5342 | + | 75.4035i | −1.41095 | + | 2.44384i | ||||
\(953\) | 16.7114 | − | 28.9450i | 0.541335 | − | 0.937619i | −0.457493 | − | 0.889213i | \(-0.651253\pi\) |
0.998828 | − | 0.0484061i | \(-0.0154142\pi\) | |||||||
\(954\) | −67.4481 | + | 45.5446i | −2.18371 | + | 1.47456i | ||||
\(955\) | −10.7701 | + | 18.6544i | −0.348512 | + | 0.603641i | ||||
\(956\) | −119.015 | −3.84922 | ||||||||
\(957\) | 6.15387 | + | 20.1100i | 0.198926 | + | 0.650063i | ||||
\(958\) | −27.2930 | − | 47.2729i | −0.881797 | − | 1.52732i | ||||
\(959\) | 19.3029 | 0.623323 | ||||||||
\(960\) | 9.14985 | − | 9.81705i | 0.295310 | − | 0.316844i | ||||
\(961\) | −5.12221 | − | 8.87193i | −0.165233 | − | 0.286191i | ||||
\(962\) | −33.0081 | − | 60.7484i | −1.06422 | − | 1.95861i | ||||
\(963\) | −1.44465 | − | 20.5083i | −0.0465531 | − | 0.660872i | ||||
\(964\) | 51.8803 | + | 89.8594i | 1.67095 | + | 2.89418i | ||||
\(965\) | −2.50433 | + | 4.33763i | −0.0806174 | + | 0.139633i | ||||
\(966\) | 22.5898 | − | 24.2370i | 0.726815 | − | 0.779814i | ||||
\(967\) | 15.9169 | − | 27.5689i | 0.511854 | − | 0.886557i | −0.488052 | − | 0.872815i | \(-0.662292\pi\) |
0.999906 | − | 0.0137423i | \(-0.00437446\pi\) | |||||||
\(968\) | 22.4107 | + | 38.8165i | 0.720309 | + | 1.24761i | ||||
\(969\) | −10.7101 | − | 34.9992i | −0.344059 | − | 1.12434i | ||||
\(970\) | 7.00559 | + | 12.1340i | 0.224936 | + | 0.389600i | ||||
\(971\) | 4.17466 | − | 7.23072i | 0.133971 | − | 0.232045i | −0.791233 | − | 0.611515i | \(-0.790560\pi\) |
0.925204 | + | 0.379470i | \(0.123894\pi\) | |||||||
\(972\) | 43.0101 | − | 61.5926i | 1.37955 | − | 1.97558i | ||||
\(973\) | 6.02270 | + | 10.4316i | 0.193079 | + | 0.334422i | ||||
\(974\) | 20.6681 | + | 35.7982i | 0.662249 | + | 1.14705i | ||||
\(975\) | 4.37466 | − | 4.45672i | 0.140101 | − | 0.142729i | ||||
\(976\) | −18.6287 | + | 32.2658i | −0.596289 | + | 1.03280i | ||||
\(977\) | 28.0990 | 0.898967 | 0.449484 | − | 0.893289i | \(-0.351608\pi\) | ||||
0.449484 | + | 0.893289i | \(0.351608\pi\) | |||||||
\(978\) | 17.0105 | + | 55.5879i | 0.543936 | + | 1.77751i | ||||
\(979\) | −19.3241 | −0.617601 | ||||||||
\(980\) | 22.6233 | 0.722673 | ||||||||
\(981\) | −27.2281 | − | 13.2628i | −0.869326 | − | 0.423447i | ||||
\(982\) | 37.7159 | − | 65.3258i | 1.20356 | − | 2.08463i | ||||
\(983\) | −12.2726 | − | 21.2567i | −0.391434 | − | 0.677984i | 0.601205 | − | 0.799095i | \(-0.294688\pi\) |
−0.992639 | + | 0.121111i | \(0.961354\pi\) | |||||||
\(984\) | 8.08251 | + | 1.86381i | 0.257661 | + | 0.0594162i | ||||
\(985\) | 25.2958 | 0.805992 | ||||||||
\(986\) | −111.436 | −3.54885 | ||||||||
\(987\) | 9.11642 | + | 29.7912i | 0.290179 | + | 0.948263i | ||||
\(988\) | −22.5063 | − | 41.4209i | −0.716021 | − | 1.31777i | ||||
\(989\) | 22.2811 | 0.708497 | ||||||||
\(990\) | 15.6088 | + | 7.60302i | 0.496080 | + | 0.241640i | ||||
\(991\) | 14.1676 | + | 24.5389i | 0.450047 | + | 0.779505i | 0.998388 | − | 0.0567498i | \(-0.0180737\pi\) |
−0.548341 | + | 0.836255i | \(0.684740\pi\) | |||||||
\(992\) | 66.2054 | 2.10202 | ||||||||
\(993\) | −46.2939 | − | 10.6753i | −1.46909 | − | 0.338770i | ||||
\(994\) | 16.4272 | + | 28.4528i | 0.521040 | + | 0.902468i | ||||
\(995\) | 7.83148 | + | 13.5645i | 0.248275 | + | 0.430024i | ||||
\(996\) | 35.2886 | − | 37.8618i | 1.11816 | − | 1.19970i | ||||
\(997\) | −10.4067 | −0.329583 | −0.164792 | − | 0.986328i | \(-0.552695\pi\) | ||||
−0.164792 | + | 0.986328i | \(0.552695\pi\) | |||||||
\(998\) | 9.51250 | + | 16.4761i | 0.301113 | + | 0.521543i | ||||
\(999\) | −5.93982 | + | 37.6900i | −0.187927 | + | 1.19246i |
(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 | 585.2.k.a.211.2 | yes | 56 | |
9.7 | even | 3 | 585.2.l.a.16.27 | yes | 56 | ||
13.9 | even | 3 | 585.2.l.a.256.27 | yes | 56 | ||
117.61 | even | 3 | inner | 585.2.k.a.61.2 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.k.a.61.2 | ✓ | 56 | 117.61 | even | 3 | inner | |
585.2.k.a.211.2 | yes | 56 | 1.1 | even | 1 | trivial | |
585.2.l.a.16.27 | yes | 56 | 9.7 | even | 3 | ||
585.2.l.a.256.27 | yes | 56 | 13.9 | even | 3 |