Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [798,2,Mod(569,798)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(798, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("798.569");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 798.bf (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.37206208130\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Relative dimension: | \(26\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 569.10 | ||
Character | \(\chi\) | \(=\) | 798.569 |
Dual form | 798.2.bf.a.683.10 |
$q$-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 \(\left(\mathbb{Z}/798\mathbb{Z}\right)^\times\).
\(n\) | \(115\) | \(211\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.819227 | + | 1.52606i | −0.472981 | + | 0.881073i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.45289 | + | 0.838824i | 0.649751 | + | 0.375134i | 0.788361 | − | 0.615213i | \(-0.210930\pi\) |
−0.138610 | + | 0.990347i | \(0.544263\pi\) | |||||||
\(6\) | −0.911995 | − | 1.47250i | −0.372320 | − | 0.601147i | ||||
\(7\) | −2.58974 | + | 0.541515i | −0.978830 | + | 0.204673i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.65773 | − | 2.50038i | −0.552578 | − | 0.833461i | ||||
\(10\) | −1.45289 | + | 0.838824i | −0.459443 | + | 0.265260i | ||||
\(11\) | 1.63083 | − | 0.941562i | 0.491715 | − | 0.283892i | −0.233571 | − | 0.972340i | \(-0.575041\pi\) |
0.725286 | + | 0.688448i | \(0.241708\pi\) | |||||||
\(12\) | 1.73122 | − | 0.0535596i | 0.499761 | − | 0.0154613i | ||||
\(13\) | 6.20177i | 1.72006i | 0.510242 | + | 0.860031i | \(0.329556\pi\) | ||||
−0.510242 | + | 0.860031i | \(0.670444\pi\) | |||||||
\(14\) | 0.825905 | − | 2.51354i | 0.220732 | − | 0.671772i | ||||
\(15\) | −2.47034 | + | 1.53001i | −0.637840 | + | 0.395046i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −5.02644 | + | 2.90202i | −1.21909 | + | 0.703842i | −0.964723 | − | 0.263265i | \(-0.915201\pi\) |
−0.254367 | + | 0.967108i | \(0.581867\pi\) | |||||||
\(18\) | 2.99426 | − | 0.185447i | 0.705754 | − | 0.0437103i | ||||
\(19\) | 0.991378 | − | 4.24466i | 0.227438 | − | 0.973793i | ||||
\(20\) | − | 1.67765i | − | 0.375134i | ||||||
\(21\) | 1.29520 | − | 4.39573i | 0.282636 | − | 0.959227i | ||||
\(22\) | 1.88312i | 0.401483i | ||||||||
\(23\) | −4.73869 | − | 2.73588i | −0.988085 | − | 0.570471i | −0.0833836 | − | 0.996518i | \(-0.526573\pi\) |
−0.904701 | + | 0.426046i | \(0.859906\pi\) | |||||||
\(24\) | −0.819227 | + | 1.52606i | −0.167224 | + | 0.311506i | ||||
\(25\) | −1.09275 | − | 1.89269i | −0.218549 | − | 0.378539i | ||||
\(26\) | −5.37089 | − | 3.10089i | −1.05332 | − | 0.608134i | ||||
\(27\) | 5.17380 | − | 0.481422i | 0.995699 | − | 0.0926497i | ||||
\(28\) | 1.76384 | + | 1.97202i | 0.333334 | + | 0.372678i | ||||
\(29\) | −6.90040 | −1.28137 | −0.640686 | − | 0.767803i | \(-0.721350\pi\) | ||||
−0.640686 | + | 0.767803i | \(0.721350\pi\) | |||||||
\(30\) | −0.0898542 | − | 2.90438i | −0.0164051 | − | 0.530265i | ||||
\(31\) | −6.28440 | + | 3.62830i | −1.12871 | + | 0.651662i | −0.943611 | − | 0.331058i | \(-0.892595\pi\) |
−0.185101 | + | 0.982720i | \(0.559261\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0.100859 | + | 3.26011i | 0.0175574 | + | 0.567512i | ||||
\(34\) | − | 5.80403i | − | 0.995383i | ||||||
\(35\) | −4.21684 | − | 1.38558i | −0.712775 | − | 0.234206i | ||||
\(36\) | −1.33653 | + | 2.68583i | −0.222755 | + | 0.447639i | ||||
\(37\) | 3.04066 | + | 1.75553i | 0.499882 | + | 0.288607i | 0.728665 | − | 0.684871i | \(-0.240141\pi\) |
−0.228783 | + | 0.973477i | \(0.573475\pi\) | |||||||
\(38\) | 3.18030 | + | 2.98089i | 0.515912 | + | 0.483564i | ||||
\(39\) | −9.46429 | − | 5.08066i | −1.51550 | − | 0.813557i | ||||
\(40\) | 1.45289 | + | 0.838824i | 0.229722 | + | 0.132630i | ||||
\(41\) | 2.11947 | 0.331005 | 0.165503 | − | 0.986209i | \(-0.447075\pi\) | ||||
0.165503 | + | 0.986209i | \(0.447075\pi\) | |||||||
\(42\) | 3.15921 | + | 3.31954i | 0.487477 | + | 0.512217i | ||||
\(43\) | 7.03656 | 1.07306 | 0.536532 | − | 0.843880i | \(-0.319734\pi\) | ||||
0.536532 | + | 0.843880i | \(0.319734\pi\) | |||||||
\(44\) | −1.63083 | − | 0.941562i | −0.245857 | − | 0.141946i | ||||
\(45\) | −0.311115 | − | 5.02332i | −0.0463783 | − | 0.748832i | ||||
\(46\) | 4.73869 | − | 2.73588i | 0.698681 | − | 0.403384i | ||||
\(47\) | 3.23065 | + | 1.86522i | 0.471238 | + | 0.272070i | 0.716758 | − | 0.697322i | \(-0.245625\pi\) |
−0.245520 | + | 0.969392i | \(0.578959\pi\) | |||||||
\(48\) | −0.911995 | − | 1.47250i | −0.131635 | − | 0.212537i | ||||
\(49\) | 6.41352 | − | 2.80477i | 0.916218 | − | 0.400681i | ||||
\(50\) | 2.18549 | 0.309076 | ||||||||
\(51\) | −0.310862 | − | 10.0481i | −0.0435293 | − | 1.40701i | ||||
\(52\) | 5.37089 | − | 3.10089i | 0.744809 | − | 0.430016i | ||||
\(53\) | −5.47641 | − | 9.48541i | −0.752242 | − | 1.30292i | −0.946734 | − | 0.322017i | \(-0.895639\pi\) |
0.194492 | − | 0.980904i | \(-0.437694\pi\) | |||||||
\(54\) | −2.16998 | + | 4.72136i | −0.295297 | + | 0.642495i | ||||
\(55\) | 3.15922 | 0.425989 | ||||||||
\(56\) | −2.58974 | + | 0.541515i | −0.346069 | + | 0.0723630i | ||||
\(57\) | 5.66546 | + | 4.99025i | 0.750408 | + | 0.660975i | ||||
\(58\) | 3.45020 | − | 5.97592i | 0.453034 | − | 0.784677i | ||||
\(59\) | −6.63269 | − | 11.4882i | −0.863503 | − | 1.49563i | −0.868526 | − | 0.495643i | \(-0.834932\pi\) |
0.00502360 | − | 0.999987i | \(-0.498401\pi\) | |||||||
\(60\) | 2.56020 | + | 1.37438i | 0.330520 | + | 0.177431i | ||||
\(61\) | −6.54347 | + | 11.3336i | −0.837806 | + | 1.45112i | 0.0539192 | + | 0.998545i | \(0.482829\pi\) |
−0.891725 | + | 0.452577i | \(0.850505\pi\) | |||||||
\(62\) | − | 7.25660i | − | 0.921589i | ||||||
\(63\) | 5.64710 | + | 5.57766i | 0.711467 | + | 0.702719i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.20220 | + | 9.01047i | −0.645253 | + | 1.11761i | ||||
\(66\) | −2.87376 | − | 1.54271i | −0.353736 | − | 0.189894i | ||||
\(67\) | 5.36441 | − | 3.09715i | 0.655367 | − | 0.378377i | −0.135142 | − | 0.990826i | \(-0.543149\pi\) |
0.790510 | + | 0.612450i | \(0.209816\pi\) | |||||||
\(68\) | 5.02644 | + | 2.90202i | 0.609545 | + | 0.351921i | ||||
\(69\) | 8.05719 | − | 4.99022i | 0.969972 | − | 0.600752i | ||||
\(70\) | 3.30836 | − | 2.95910i | 0.395425 | − | 0.353680i | ||||
\(71\) | −2.69469 | −0.319800 | −0.159900 | − | 0.987133i | \(-0.551117\pi\) | ||||
−0.159900 | + | 0.987133i | \(0.551117\pi\) | |||||||
\(72\) | −1.65773 | − | 2.50038i | −0.195366 | − | 0.294673i | ||||
\(73\) | 1.42570 | + | 2.46938i | 0.166865 | + | 0.289019i | 0.937316 | − | 0.348480i | \(-0.113302\pi\) |
−0.770451 | + | 0.637500i | \(0.779969\pi\) | |||||||
\(74\) | −3.04066 | + | 1.75553i | −0.353470 | + | 0.204076i | ||||
\(75\) | 3.78358 | − | 0.117054i | 0.436890 | − | 0.0135163i | ||||
\(76\) | −4.17168 | + | 1.26377i | −0.478524 | + | 0.144965i | ||||
\(77\) | −3.71357 | + | 3.32152i | −0.423200 | + | 0.378523i | ||||
\(78\) | 9.13213 | − | 5.65599i | 1.03401 | − | 0.640414i | ||||
\(79\) | −4.30342 | − | 2.48458i | −0.484172 | − | 0.279537i | 0.237981 | − | 0.971270i | \(-0.423514\pi\) |
−0.722153 | + | 0.691733i | \(0.756848\pi\) | |||||||
\(80\) | −1.45289 | + | 0.838824i | −0.162438 | + | 0.0937834i | ||||
\(81\) | −3.50384 | + | 8.28994i | −0.389316 | + | 0.921104i | ||||
\(82\) | −1.05973 | + | 1.83551i | −0.117028 | + | 0.202698i | ||||
\(83\) | − | 10.7064i | − | 1.17518i | −0.809158 | − | 0.587591i | \(-0.800076\pi\) | ||
0.809158 | − | 0.587591i | \(-0.199924\pi\) | |||||||
\(84\) | −4.45442 | + | 1.07619i | −0.486017 | + | 0.117422i | ||||
\(85\) | −9.73713 | −1.05614 | ||||||||
\(86\) | −3.51828 | + | 6.09384i | −0.379386 | + | 0.657115i | ||||
\(87\) | 5.65300 | − | 10.5304i | 0.606065 | − | 1.12898i | ||||
\(88\) | 1.63083 | − | 0.941562i | 0.173847 | − | 0.100371i | ||||
\(89\) | −3.30170 | + | 5.71872i | −0.349980 | + | 0.606183i | −0.986245 | − | 0.165287i | \(-0.947145\pi\) |
0.636266 | + | 0.771470i | \(0.280478\pi\) | |||||||
\(90\) | 4.50588 | + | 2.24223i | 0.474962 | + | 0.236351i | ||||
\(91\) | −3.35835 | − | 16.0610i | −0.352051 | − | 1.68365i | ||||
\(92\) | 5.47177i | 0.570471i | ||||||||
\(93\) | −0.388661 | − | 12.5628i | −0.0403022 | − | 1.30270i | ||||
\(94\) | −3.23065 | + | 1.86522i | −0.333216 | + | 0.192382i | ||||
\(95\) | 5.00089 | − | 5.33542i | 0.513080 | − | 0.547403i | ||||
\(96\) | 1.73122 | − | 0.0535596i | 0.176692 | − | 0.00546640i | ||||
\(97\) | 11.3610i | 1.15353i | 0.816909 | + | 0.576766i | \(0.195686\pi\) | ||||
−0.816909 | + | 0.576766i | \(0.804314\pi\) | |||||||
\(98\) | −0.777761 | + | 6.95666i | −0.0785658 | + | 0.702729i | ||||
\(99\) | −5.05775 | − | 2.51685i | −0.508323 | − | 0.252953i | ||||
\(100\) | −1.09275 | + | 1.89269i | −0.109275 | + | 0.189269i | ||||
\(101\) | −2.15201 | + | 1.24246i | −0.214133 | + | 0.123629i | −0.603230 | − | 0.797567i | \(-0.706120\pi\) |
0.389098 | + | 0.921196i | \(0.372787\pi\) | |||||||
\(102\) | 8.85732 | + | 4.75482i | 0.877005 | + | 0.470798i | ||||
\(103\) | −11.9593 | − | 6.90469i | −1.17838 | − | 0.680339i | −0.222742 | − | 0.974877i | \(-0.571501\pi\) |
−0.955640 | + | 0.294538i | \(0.904834\pi\) | |||||||
\(104\) | 6.20177i | 0.608134i | ||||||||
\(105\) | 5.56903 | − | 5.30005i | 0.543481 | − | 0.517232i | ||||
\(106\) | 10.9528 | 1.06383 | ||||||||
\(107\) | −3.37596 | + | 5.84734i | −0.326366 | + | 0.565283i | −0.981788 | − | 0.189980i | \(-0.939158\pi\) |
0.655421 | + | 0.755263i | \(0.272491\pi\) | |||||||
\(108\) | −3.00382 | − | 4.23993i | −0.289043 | − | 0.407988i | ||||
\(109\) | 1.19227 | − | 0.688355i | 0.114198 | − | 0.0659325i | −0.441813 | − | 0.897107i | \(-0.645664\pi\) |
0.556011 | + | 0.831175i | \(0.312331\pi\) | |||||||
\(110\) | −1.57961 | + | 2.73597i | −0.150610 | + | 0.260864i | ||||
\(111\) | −5.17004 | + | 3.20207i | −0.490718 | + | 0.303927i | ||||
\(112\) | 0.825905 | − | 2.51354i | 0.0780407 | − | 0.237507i | ||||
\(113\) | 11.0633 | 1.04075 | 0.520373 | − | 0.853939i | \(-0.325793\pi\) | ||||
0.520373 | + | 0.853939i | \(0.325793\pi\) | |||||||
\(114\) | −7.15441 | + | 2.41131i | −0.670072 | + | 0.225840i | ||||
\(115\) | −4.58985 | − | 7.94985i | −0.428006 | − | 0.741328i | ||||
\(116\) | 3.45020 | + | 5.97592i | 0.320343 | + | 0.554851i | ||||
\(117\) | 15.5068 | − | 10.2809i | 1.43361 | − | 0.950468i | ||||
\(118\) | 13.2654 | 1.22118 | ||||||||
\(119\) | 11.4457 | − | 10.2374i | 1.04923 | − | 0.938458i | ||||
\(120\) | −2.47034 | + | 1.53001i | −0.225510 | + | 0.139670i | ||||
\(121\) | −3.72692 | + | 6.45522i | −0.338811 | + | 0.586838i | ||||
\(122\) | −6.54347 | − | 11.3336i | −0.592418 | − | 1.02610i | ||||
\(123\) | −1.73632 | + | 3.23444i | −0.156559 | + | 0.291639i | ||||
\(124\) | 6.28440 | + | 3.62830i | 0.564356 | + | 0.325831i | ||||
\(125\) | − | 12.0547i | − | 1.07821i | ||||||
\(126\) | −7.65394 | + | 2.10170i | −0.681868 | + | 0.187234i | ||||
\(127\) | 13.4785i | 1.19602i | 0.801489 | + | 0.598010i | \(0.204042\pi\) | ||||
−0.801489 | + | 0.598010i | \(0.795958\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −5.76454 | + | 10.7382i | −0.507539 | + | 0.945448i | ||||
\(130\) | −5.20220 | − | 9.01047i | −0.456263 | − | 0.790271i | ||||
\(131\) | 10.8979 | + | 6.29193i | 0.952158 | + | 0.549728i | 0.893751 | − | 0.448564i | \(-0.148065\pi\) |
0.0584071 | + | 0.998293i | \(0.481398\pi\) | |||||||
\(132\) | 2.77291 | − | 1.71740i | 0.241350 | − | 0.149480i | ||||
\(133\) | −0.268863 | + | 11.5294i | −0.0233134 | + | 0.999728i | ||||
\(134\) | 6.19429i | 0.535105i | ||||||||
\(135\) | 7.92078 | + | 3.64046i | 0.681712 | + | 0.313321i | ||||
\(136\) | −5.02644 | + | 2.90202i | −0.431014 | + | 0.248846i | ||||
\(137\) | −15.1944 | + | 8.77249i | −1.29815 | + | 0.749485i | −0.980084 | − | 0.198585i | \(-0.936365\pi\) |
−0.318062 | + | 0.948070i | \(0.603032\pi\) | |||||||
\(138\) | 0.293066 | + | 9.47284i | 0.0249474 | + | 0.806382i | ||||
\(139\) | 13.6779 | 1.16015 | 0.580073 | − | 0.814564i | \(-0.303024\pi\) | ||||
0.580073 | + | 0.814564i | \(0.303024\pi\) | |||||||
\(140\) | 0.908472 | + | 4.34468i | 0.0767799 | + | 0.367192i | ||||
\(141\) | −5.49307 | + | 3.40213i | −0.462600 | + | 0.286511i | ||||
\(142\) | 1.34734 | − | 2.33367i | 0.113067 | − | 0.195837i | ||||
\(143\) | 5.83935 | + | 10.1141i | 0.488311 | + | 0.845780i | ||||
\(144\) | 2.99426 | − | 0.185447i | 0.249522 | − | 0.0154539i | ||||
\(145\) | −10.0255 | − | 5.78822i | −0.832572 | − | 0.480686i | ||||
\(146\) | −2.85140 | −0.235983 | ||||||||
\(147\) | −0.973882 | + | 12.0852i | −0.0803244 | + | 0.996769i | ||||
\(148\) | − | 3.51106i | − | 0.288607i | ||||||
\(149\) | 3.17968 | + | 1.83579i | 0.260490 | + | 0.150394i | 0.624558 | − | 0.780978i | \(-0.285279\pi\) |
−0.364068 | + | 0.931372i | \(0.618613\pi\) | |||||||
\(150\) | −1.79042 | + | 3.33520i | −0.146187 | + | 0.272318i | ||||
\(151\) | −11.0293 | + | 6.36774i | −0.897548 | + | 0.518199i | −0.876404 | − | 0.481577i | \(-0.840064\pi\) |
−0.0211439 | + | 0.999776i | \(0.506731\pi\) | |||||||
\(152\) | 0.991378 | − | 4.24466i | 0.0804114 | − | 0.344288i | ||||
\(153\) | 15.5887 | + | 7.75726i | 1.26027 | + | 0.627137i | ||||
\(154\) | −1.01974 | − | 4.87680i | −0.0821730 | − | 0.392984i | ||||
\(155\) | −12.1740 | −0.977841 | ||||||||
\(156\) | 0.332165 | + | 10.7366i | 0.0265944 | + | 0.859620i | ||||
\(157\) | 8.82182 | + | 15.2798i | 0.704058 | + | 1.21946i | 0.967031 | + | 0.254660i | \(0.0819636\pi\) |
−0.262973 | + | 0.964803i | \(0.584703\pi\) | |||||||
\(158\) | 4.30342 | − | 2.48458i | 0.342361 | − | 0.197662i | ||||
\(159\) | 18.9618 | − | 0.586628i | 1.50376 | − | 0.0465226i | ||||
\(160\) | − | 1.67765i | − | 0.132630i | ||||||
\(161\) | 13.7535 | + | 4.51916i | 1.08393 | + | 0.356160i | ||||
\(162\) | −5.42738 | − | 7.17938i | −0.426415 | − | 0.564066i | ||||
\(163\) | −9.12550 | + | 15.8058i | −0.714764 | + | 1.23801i | 0.248286 | + | 0.968687i | \(0.420133\pi\) |
−0.963050 | + | 0.269321i | \(0.913201\pi\) | |||||||
\(164\) | −1.05973 | − | 1.83551i | −0.0827513 | − | 0.143329i | ||||
\(165\) | −2.58812 | + | 4.82117i | −0.201485 | + | 0.375327i | ||||
\(166\) | 9.27203 | + | 5.35321i | 0.719649 | + | 0.415490i | ||||
\(167\) | −9.66632 | −0.748002 | −0.374001 | − | 0.927428i | \(-0.622014\pi\) | ||||
−0.374001 | + | 0.927428i | \(0.622014\pi\) | |||||||
\(168\) | 1.29520 | − | 4.39573i | 0.0999269 | − | 0.339138i | ||||
\(169\) | −25.4620 | −1.95861 | ||||||||
\(170\) | 4.86856 | − | 8.43260i | 0.373402 | − | 0.646751i | ||||
\(171\) | −12.2567 | + | 4.55770i | −0.937296 | + | 0.348536i | ||||
\(172\) | −3.51828 | − | 6.09384i | −0.268266 | − | 0.464651i | ||||
\(173\) | −12.8259 | + | 22.2151i | −0.975134 | + | 1.68898i | −0.295641 | + | 0.955299i | \(0.595533\pi\) |
−0.679493 | + | 0.733682i | \(0.737800\pi\) | |||||||
\(174\) | 6.29313 | + | 10.1609i | 0.477081 | + | 0.770293i | ||||
\(175\) | 3.85486 | + | 4.30985i | 0.291400 | + | 0.325794i | ||||
\(176\) | 1.88312i | 0.141946i | ||||||||
\(177\) | 22.9653 | − | 0.710489i | 1.72618 | − | 0.0534036i | ||||
\(178\) | −3.30170 | − | 5.71872i | −0.247473 | − | 0.428636i | ||||
\(179\) | 4.86204 | + | 8.42131i | 0.363406 | + | 0.629438i | 0.988519 | − | 0.151096i | \(-0.0482804\pi\) |
−0.625113 | + | 0.780534i | \(0.714947\pi\) | |||||||
\(180\) | −4.19477 | + | 2.78109i | −0.312659 | + | 0.207291i | ||||
\(181\) | − | 1.01843i | − | 0.0756996i | −0.999283 | − | 0.0378498i | \(-0.987949\pi\) | ||
0.999283 | − | 0.0378498i | \(-0.0120508\pi\) | |||||||
\(182\) | 15.5884 | + | 5.12208i | 1.15549 | + | 0.379674i | ||||
\(183\) | −11.9352 | − | 19.2706i | −0.882278 | − | 1.42452i | ||||
\(184\) | −4.73869 | − | 2.73588i | −0.349341 | − | 0.201692i | ||||
\(185\) | 2.94516 | + | 5.10116i | 0.216532 | + | 0.375045i | ||||
\(186\) | 11.0740 | + | 5.94480i | 0.811987 | + | 0.435894i | ||||
\(187\) | −5.46486 | + | 9.46541i | −0.399630 | + | 0.692179i | ||||
\(188\) | − | 3.73043i | − | 0.272070i | ||||||
\(189\) | −13.1381 | + | 4.04845i | −0.955657 | + | 0.294481i | ||||
\(190\) | 2.12017 | + | 6.99861i | 0.153813 | + | 0.507732i | ||||
\(191\) | −6.78720 | − | 3.91859i | −0.491105 | − | 0.283539i | 0.233928 | − | 0.972254i | \(-0.424842\pi\) |
−0.725033 | + | 0.688715i | \(0.758175\pi\) | |||||||
\(192\) | −0.819227 | + | 1.52606i | −0.0591226 | + | 0.110134i | ||||
\(193\) | 10.8570 | − | 6.26830i | 0.781505 | − | 0.451202i | −0.0554587 | − | 0.998461i | \(-0.517662\pi\) |
0.836963 | + | 0.547259i | \(0.184329\pi\) | |||||||
\(194\) | −9.83890 | − | 5.68049i | −0.706392 | − | 0.407835i | ||||
\(195\) | −9.48876 | − | 15.3205i | −0.679504 | − | 1.09712i | ||||
\(196\) | −5.63576 | − | 4.15189i | −0.402554 | − | 0.296564i | ||||
\(197\) | − | 1.84349i | − | 0.131343i | −0.997841 | − | 0.0656716i | \(-0.979081\pi\) | ||
0.997841 | − | 0.0656716i | \(-0.0209190\pi\) | |||||||
\(198\) | 4.70853 | − | 3.12172i | 0.334621 | − | 0.221851i | ||||
\(199\) | −8.23827 | − | 14.2691i | −0.583996 | − | 1.01151i | −0.995000 | − | 0.0998768i | \(-0.968155\pi\) |
0.411004 | − | 0.911633i | \(-0.365178\pi\) | |||||||
\(200\) | −1.09275 | − | 1.89269i | −0.0772689 | − | 0.133834i | ||||
\(201\) | 0.331764 | + | 10.7237i | 0.0234008 | + | 0.756391i | ||||
\(202\) | − | 2.48492i | − | 0.174838i | ||||||
\(203\) | 17.8703 | − | 3.73667i | 1.25425 | − | 0.262263i | ||||
\(204\) | −8.54645 | + | 5.29325i | −0.598372 | + | 0.370602i | ||||
\(205\) | 3.07934 | + | 1.77786i | 0.215071 | + | 0.124171i | ||||
\(206\) | 11.9593 | − | 6.90469i | 0.833242 | − | 0.481072i | ||||
\(207\) | 1.01472 | + | 16.3839i | 0.0705282 | + | 1.13876i | ||||
\(208\) | −5.37089 | − | 3.10089i | −0.372404 | − | 0.215008i | ||||
\(209\) | −2.37984 | − | 7.85578i | −0.164617 | − | 0.543396i | ||||
\(210\) | 1.80547 | + | 7.47294i | 0.124589 | + | 0.515682i | ||||
\(211\) | 12.9088i | 0.888677i | 0.895859 | + | 0.444338i | \(0.146561\pi\) | ||||
−0.895859 | + | 0.444338i | \(0.853439\pi\) | |||||||
\(212\) | −5.47641 | + | 9.48541i | −0.376121 | + | 0.651461i | ||||
\(213\) | 2.20756 | − | 4.11226i | 0.151260 | − | 0.281767i | ||||
\(214\) | −3.37596 | − | 5.84734i | −0.230776 | − | 0.399716i | ||||
\(215\) | 10.2233 | + | 5.90243i | 0.697224 | + | 0.402543i | ||||
\(216\) | 5.17380 | − | 0.481422i | 0.352033 | − | 0.0327566i | ||||
\(217\) | 14.3102 | − | 12.7995i | 0.971439 | − | 0.868884i | ||||
\(218\) | 1.37671i | 0.0932426i | ||||||||
\(219\) | −4.93640 | + | 0.152720i | −0.333571 | + | 0.0103198i | ||||
\(220\) | −1.57961 | − | 2.73597i | −0.106497 | − | 0.184459i | ||||
\(221\) | −17.9976 | − | 31.1728i | −1.21065 | − | 2.09691i | ||||
\(222\) | −0.188051 | − | 6.07842i | −0.0126211 | − | 0.407957i | ||||
\(223\) | 15.0341i | 1.00676i | 0.864065 | + | 0.503381i | \(0.167911\pi\) | ||||
−0.864065 | + | 0.503381i | \(0.832089\pi\) | |||||||
\(224\) | 1.76384 | + | 1.97202i | 0.117851 | + | 0.131761i | ||||
\(225\) | −2.92098 | + | 5.86987i | −0.194732 | + | 0.391325i | ||||
\(226\) | −5.53164 | + | 9.58108i | −0.367959 | + | 0.637324i | ||||
\(227\) | −4.44013 | − | 7.69054i | −0.294702 | − | 0.510439i | 0.680213 | − | 0.733014i | \(-0.261887\pi\) |
−0.974916 | + | 0.222575i | \(0.928554\pi\) | |||||||
\(228\) | 1.48895 | − | 7.40156i | 0.0986083 | − | 0.490180i | ||||
\(229\) | 1.73528 | − | 3.00559i | 0.114671 | − | 0.198615i | −0.802977 | − | 0.596009i | \(-0.796752\pi\) |
0.917648 | + | 0.397394i | \(0.130085\pi\) | |||||||
\(230\) | 9.17970 | 0.605292 | ||||||||
\(231\) | −2.02660 | − | 8.38822i | −0.133340 | − | 0.551904i | ||||
\(232\) | −6.90040 | −0.453034 | ||||||||
\(233\) | 0.752525 | + | 0.434470i | 0.0492995 | + | 0.0284631i | 0.524447 | − | 0.851443i | \(-0.324272\pi\) |
−0.475148 | + | 0.879906i | \(0.657605\pi\) | |||||||
\(234\) | 1.15010 | + | 18.5697i | 0.0751845 | + | 1.21394i | ||||
\(235\) | 3.12918 | + | 5.41989i | 0.204125 | + | 0.353555i | ||||
\(236\) | −6.63269 | + | 11.4882i | −0.431751 | + | 0.747815i | ||||
\(237\) | 7.31710 | − | 4.53185i | 0.475296 | − | 0.294375i | ||||
\(238\) | 3.14297 | + | 15.0309i | 0.203729 | + | 0.974311i | ||||
\(239\) | − | 11.5353i | − | 0.746155i | −0.927800 | − | 0.373078i | \(-0.878303\pi\) | ||
0.927800 | − | 0.373078i | \(-0.121697\pi\) | |||||||
\(240\) | −0.0898542 | − | 2.90438i | −0.00580006 | − | 0.187477i | ||||
\(241\) | −1.96067 | + | 1.13200i | −0.126298 | + | 0.0729182i | −0.561818 | − | 0.827261i | \(-0.689898\pi\) |
0.435520 | + | 0.900179i | \(0.356565\pi\) | |||||||
\(242\) | −3.72692 | − | 6.45522i | −0.239576 | − | 0.414957i | ||||
\(243\) | −9.78052 | − | 12.1384i | −0.627421 | − | 0.778680i | ||||
\(244\) | 13.0869 | 0.837806 | ||||||||
\(245\) | 11.6708 | + | 1.30481i | 0.745622 | + | 0.0833613i | ||||
\(246\) | −1.93294 | − | 3.12092i | −0.123240 | − | 0.198983i | ||||
\(247\) | 26.3244 | + | 6.14830i | 1.67498 | + | 0.391207i | ||||
\(248\) | −6.28440 | + | 3.62830i | −0.399060 | + | 0.230397i | ||||
\(249\) | 16.3387 | + | 8.77099i | 1.03542 | + | 0.555839i | ||||
\(250\) | 10.4397 | + | 6.02737i | 0.660265 | + | 0.381204i | ||||
\(251\) | 21.5897i | 1.36273i | 0.731945 | + | 0.681364i | \(0.238613\pi\) | ||||
−0.731945 | + | 0.681364i | \(0.761387\pi\) | |||||||
\(252\) | 2.00685 | − | 7.67936i | 0.126420 | − | 0.483754i | ||||
\(253\) | −10.3040 | −0.647808 | ||||||||
\(254\) | −11.6727 | − | 6.73923i | −0.732409 | − | 0.422857i | ||||
\(255\) | 7.97692 | − | 14.8595i | 0.499534 | − | 0.930536i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −0.182046 | + | 0.315313i | −0.0113557 | + | 0.0196687i | −0.871647 | − | 0.490133i | \(-0.836948\pi\) |
0.860292 | + | 0.509802i | \(0.170281\pi\) | |||||||
\(258\) | −6.41731 | − | 10.3613i | −0.399524 | − | 0.645069i | ||||
\(259\) | −8.82518 | − | 2.89980i | −0.548370 | − | 0.180185i | ||||
\(260\) | 10.4044 | 0.645253 | ||||||||
\(261\) | 11.4390 | + | 17.2537i | 0.708058 | + | 1.06797i | ||||
\(262\) | −10.8979 | + | 6.29193i | −0.673277 | + | 0.388717i | ||||
\(263\) | −19.3153 | + | 11.1517i | −1.19103 | + | 0.687643i | −0.958541 | − | 0.284956i | \(-0.908021\pi\) |
−0.232491 | + | 0.972598i | \(0.574688\pi\) | |||||||
\(264\) | 0.100859 | + | 3.26011i | 0.00620747 | + | 0.200646i | ||||
\(265\) | − | 18.3750i | − | 1.12877i | ||||||
\(266\) | −9.85035 | − | 5.99756i | −0.603963 | − | 0.367734i | ||||
\(267\) | −6.02227 | − | 9.72353i | −0.368557 | − | 0.595071i | ||||
\(268\) | −5.36441 | − | 3.09715i | −0.327684 | − | 0.189188i | ||||
\(269\) | 7.98963 | + | 13.8384i | 0.487136 | + | 0.843745i | 0.999891 | − | 0.0147907i | \(-0.00470819\pi\) |
−0.512754 | + | 0.858535i | \(0.671375\pi\) | |||||||
\(270\) | −7.11312 | + | 5.03936i | −0.432891 | + | 0.306686i | ||||
\(271\) | 8.33777 | − | 14.4414i | 0.506483 | − | 0.877255i | −0.493488 | − | 0.869752i | \(-0.664278\pi\) |
0.999972 | − | 0.00750263i | \(-0.00238818\pi\) | |||||||
\(272\) | − | 5.80403i | − | 0.351921i | ||||||
\(273\) | 27.2613 | + | 8.03254i | 1.64993 | + | 0.486152i | ||||
\(274\) | − | 17.5450i | − | 1.05993i | ||||||
\(275\) | −3.56418 | − | 2.05778i | −0.214928 | − | 0.124089i | ||||
\(276\) | −8.35026 | − | 4.48262i | −0.502626 | − | 0.269822i | ||||
\(277\) | −0.482345 | − | 0.835445i | −0.0289813 | − | 0.0501970i | 0.851171 | − | 0.524888i | \(-0.175893\pi\) |
−0.880152 | + | 0.474691i | \(0.842560\pi\) | |||||||
\(278\) | −6.83897 | + | 11.8454i | −0.410174 | + | 0.710442i | ||||
\(279\) | 19.4900 | + | 9.69866i | 1.16684 | + | 0.580644i | ||||
\(280\) | −4.21684 | − | 1.38558i | −0.252004 | − | 0.0828042i | ||||
\(281\) | 11.5077 | 0.686493 | 0.343246 | − | 0.939245i | \(-0.388473\pi\) | ||||
0.343246 | + | 0.939245i | \(0.388473\pi\) | |||||||
\(282\) | −0.199800 | − | 6.45820i | −0.0118979 | − | 0.384580i | ||||
\(283\) | 13.0864 | + | 22.6663i | 0.777905 | + | 1.34737i | 0.933147 | + | 0.359495i | \(0.117051\pi\) |
−0.155242 | + | 0.987877i | \(0.549616\pi\) | |||||||
\(284\) | 1.34734 | + | 2.33367i | 0.0799501 | + | 0.138478i | ||||
\(285\) | 4.04533 | + | 12.0026i | 0.239624 | + | 0.710972i | ||||
\(286\) | −11.6787 | −0.690576 | ||||||||
\(287\) | −5.48887 | + | 1.14772i | −0.323998 | + | 0.0677479i | ||||
\(288\) | −1.33653 | + | 2.68583i | −0.0787557 | + | 0.158264i | ||||
\(289\) | 8.34340 | − | 14.4512i | 0.490788 | − | 0.850070i | ||||
\(290\) | 10.0255 | − | 5.78822i | 0.588718 | − | 0.339896i | ||||
\(291\) | −17.3376 | − | 9.30722i | −1.01635 | − | 0.545599i | ||||
\(292\) | 1.42570 | − | 2.46938i | 0.0834327 | − | 0.144510i | ||||
\(293\) | −9.71891 | −0.567785 | −0.283892 | − | 0.958856i | \(-0.591626\pi\) | ||||
−0.283892 | + | 0.958856i | \(0.591626\pi\) | |||||||
\(294\) | −9.97913 | − | 6.88600i | −0.581995 | − | 0.401599i | ||||
\(295\) | − | 22.2546i | − | 1.29572i | ||||||
\(296\) | 3.04066 | + | 1.75553i | 0.176735 | + | 0.102038i | ||||
\(297\) | 7.98432 | − | 5.65657i | 0.463297 | − | 0.328228i | ||||
\(298\) | −3.17968 | + | 1.83579i | −0.184194 | + | 0.106344i | ||||
\(299\) | 16.9673 | − | 29.3883i | 0.981246 | − | 1.69957i | ||||
\(300\) | −1.99316 | − | 3.21815i | −0.115075 | − | 0.185800i | ||||
\(301\) | −18.2229 | + | 3.81040i | −1.05035 | + | 0.219628i | ||||
\(302\) | − | 12.7355i | − | 0.732845i | ||||||
\(303\) | −0.133091 | − | 4.30195i | −0.00764590 | − | 0.247141i | ||||
\(304\) | 3.18030 | + | 2.98089i | 0.182403 | + | 0.170966i | ||||
\(305\) | −19.0138 | + | 10.9777i | −1.08873 | + | 0.628578i | ||||
\(306\) | −14.5123 | + | 9.62154i | −0.829614 | + | 0.550027i | ||||
\(307\) | − | 19.3583i | − | 1.10484i | −0.833567 | − | 0.552418i | \(-0.813705\pi\) | ||
0.833567 | − | 0.552418i | \(-0.186295\pi\) | |||||||
\(308\) | 4.73331 | + | 1.55528i | 0.269705 | + | 0.0886204i | ||||
\(309\) | 20.3343 | − | 12.5941i | 1.15678 | − | 0.716452i | ||||
\(310\) | 6.08701 | − | 10.5430i | 0.345719 | − | 0.598803i | ||||
\(311\) | 22.8171 | − | 13.1735i | 1.29384 | − | 0.746999i | 0.314508 | − | 0.949255i | \(-0.398161\pi\) |
0.979333 | + | 0.202256i | \(0.0648273\pi\) | |||||||
\(312\) | −9.46429 | − | 5.08066i | −0.535810 | − | 0.287636i | ||||
\(313\) | 5.38324 | − | 9.32405i | 0.304279 | − | 0.527026i | −0.672822 | − | 0.739805i | \(-0.734918\pi\) |
0.977100 | + | 0.212778i | \(0.0682512\pi\) | |||||||
\(314\) | −17.6436 | −0.995688 | ||||||||
\(315\) | 3.52591 | + | 12.8406i | 0.198663 | + | 0.723488i | ||||
\(316\) | 4.96916i | 0.279537i | ||||||||
\(317\) | 0.403484 | − | 0.698855i | 0.0226619 | − | 0.0392516i | −0.854472 | − | 0.519497i | \(-0.826119\pi\) |
0.877134 | + | 0.480246i | \(0.159453\pi\) | |||||||
\(318\) | −8.97284 | + | 16.7147i | −0.503172 | + | 0.937312i | ||||
\(319\) | −11.2534 | + | 6.49716i | −0.630070 | + | 0.363771i | ||||
\(320\) | 1.45289 | + | 0.838824i | 0.0812188 | + | 0.0468917i | ||||
\(321\) | −6.15772 | − | 9.94223i | −0.343690 | − | 0.554921i | ||||
\(322\) | −10.7905 | + | 9.65130i | −0.601329 | + | 0.537846i | ||||
\(323\) | 7.33498 | + | 24.2125i | 0.408129 | + | 1.34722i | ||||
\(324\) | 8.93122 | − | 1.11056i | 0.496179 | − | 0.0616975i | ||||
\(325\) | 11.7381 | − | 6.77697i | 0.651110 | − | 0.375919i | ||||
\(326\) | −9.12550 | − | 15.8058i | −0.505415 | − | 0.875404i | ||||
\(327\) | 0.0737361 | + | 2.38339i | 0.00407761 | + | 0.131802i | ||||
\(328\) | 2.11947 | 0.117028 | ||||||||
\(329\) | −9.37658 | − | 3.08098i | −0.516948 | − | 0.169860i | ||||
\(330\) | −2.88119 | − | 4.65196i | −0.158605 | − | 0.256082i | ||||
\(331\) | −9.13676 | − | 5.27511i | −0.502202 | − | 0.289946i | 0.227421 | − | 0.973797i | \(-0.426971\pi\) |
−0.729622 | + | 0.683850i | \(0.760304\pi\) | |||||||
\(332\) | −9.27203 | + | 5.35321i | −0.508869 | + | 0.293796i | ||||
\(333\) | −0.651115 | − | 10.5130i | −0.0356809 | − | 0.576110i | ||||
\(334\) | 4.83316 | − | 8.37128i | 0.264459 | − | 0.458056i | ||||
\(335\) | 10.3918 | 0.567767 | ||||||||
\(336\) | 3.15921 | + | 3.31954i | 0.172349 | + | 0.181096i | ||||
\(337\) | 3.52393i | 0.191961i | 0.995383 | + | 0.0959804i | \(0.0305986\pi\) | ||||
−0.995383 | + | 0.0959804i | \(0.969401\pi\) | |||||||
\(338\) | 12.7310 | − | 22.0507i | 0.692475 | − | 1.19940i | ||||
\(339\) | −9.06334 | + | 16.8833i | −0.492253 | + | 0.916973i | ||||
\(340\) | 4.86856 | + | 8.43260i | 0.264035 | + | 0.457322i | ||||
\(341\) | −6.83254 | + | 11.8343i | −0.370003 | + | 0.640863i | ||||
\(342\) | 2.18128 | − | 12.8935i | 0.117950 | − | 0.697200i | ||||
\(343\) | −15.0905 | + | 10.7366i | −0.814813 | + | 0.579724i | ||||
\(344\) | 7.03656 | 0.379386 | ||||||||
\(345\) | 15.8921 | − | 0.491661i | 0.855602 | − | 0.0264701i | ||||
\(346\) | −12.8259 | − | 22.2151i | −0.689524 | − | 1.19429i | ||||
\(347\) | 11.0411 | − | 6.37460i | 0.592719 | − | 0.342207i | −0.173453 | − | 0.984842i | \(-0.555492\pi\) |
0.766172 | + | 0.642636i | \(0.222159\pi\) | |||||||
\(348\) | −11.9461 | + | 0.369583i | −0.640380 | + | 0.0198117i | ||||
\(349\) | 23.6648 | 1.26675 | 0.633373 | − | 0.773847i | \(-0.281670\pi\) | ||||
0.633373 | + | 0.773847i | \(0.281670\pi\) | |||||||
\(350\) | −5.65987 | + | 1.18348i | −0.302533 | + | 0.0632596i | ||||
\(351\) | 2.98567 | + | 32.0867i | 0.159363 | + | 1.71266i | ||||
\(352\) | −1.63083 | − | 0.941562i | −0.0869237 | − | 0.0501854i | ||||
\(353\) | −7.10645 | + | 4.10291i | −0.378238 | + | 0.218376i | −0.677051 | − | 0.735936i | \(-0.736743\pi\) |
0.298813 | + | 0.954312i | \(0.403409\pi\) | |||||||
\(354\) | −10.8674 | + | 20.2438i | −0.577594 | + | 1.07595i | ||||
\(355\) | −3.91507 | − | 2.26037i | −0.207790 | − | 0.119968i | ||||
\(356\) | 6.60341 | 0.349980 | ||||||||
\(357\) | 6.24623 | + | 25.8536i | 0.330586 | + | 1.36832i | ||||
\(358\) | −9.72409 | −0.513934 | ||||||||
\(359\) | 4.39323 | + | 2.53643i | 0.231866 | + | 0.133868i | 0.611433 | − | 0.791297i | \(-0.290594\pi\) |
−0.379567 | + | 0.925164i | \(0.623927\pi\) | |||||||
\(360\) | −0.311115 | − | 5.02332i | −0.0163972 | − | 0.264752i | ||||
\(361\) | −17.0343 | − | 8.41613i | −0.896544 | − | 0.442954i | ||||
\(362\) | 0.881990 | + | 0.509217i | 0.0463563 | + | 0.0267638i | ||||
\(363\) | −6.79787 | − | 10.9758i | −0.356796 | − | 0.576080i | ||||
\(364\) | −12.2300 | + | 10.9389i | −0.641029 | + | 0.573355i | ||||
\(365\) | 4.78364i | 0.250387i | ||||||||
\(366\) | 22.6564 | − | 0.700932i | 1.18427 | − | 0.0366383i | ||||
\(367\) | 12.6569 | + | 21.9224i | 0.660685 | + | 1.14434i | 0.980436 | + | 0.196838i | \(0.0630674\pi\) |
−0.319751 | + | 0.947502i | \(0.603599\pi\) | |||||||
\(368\) | 4.73869 | − | 2.73588i | 0.247021 | − | 0.142618i | ||||
\(369\) | −3.51351 | − | 5.29948i | −0.182906 | − | 0.275880i | ||||
\(370\) | −5.89032 | −0.306223 | ||||||||
\(371\) | 19.3190 | + | 21.5992i | 1.00299 | + | 1.12138i | ||||
\(372\) | −10.6854 | + | 6.61798i | −0.554010 | + | 0.343127i | ||||
\(373\) | 4.95651 | + | 2.86164i | 0.256639 | + | 0.148170i | 0.622800 | − | 0.782381i | \(-0.285995\pi\) |
−0.366162 | + | 0.930551i | \(0.619328\pi\) | |||||||
\(374\) | −5.46486 | − | 9.46541i | −0.282581 | − | 0.489445i | ||||
\(375\) | 18.3963 | + | 9.87557i | 0.949980 | + | 0.509972i | ||||
\(376\) | 3.23065 | + | 1.86522i | 0.166608 | + | 0.0961911i | ||||
\(377\) | − | 42.7947i | − | 2.20404i | ||||||
\(378\) | 3.06300 | − | 13.4022i | 0.157544 | − | 0.689333i | ||||
\(379\) | 11.9156i | 0.612062i | 0.952022 | + | 0.306031i | \(0.0990012\pi\) | ||||
−0.952022 | + | 0.306031i | \(0.900999\pi\) | |||||||
\(380\) | −7.12105 | − | 1.66318i | −0.365302 | − | 0.0853195i | ||||
\(381\) | −20.5690 | − | 11.0419i | −1.05378 | − | 0.565694i | ||||
\(382\) | 6.78720 | − | 3.91859i | 0.347263 | − | 0.200493i | ||||
\(383\) | 2.20238 | − | 3.81464i | 0.112536 | − | 0.194919i | −0.804256 | − | 0.594283i | \(-0.797436\pi\) |
0.916792 | + | 0.399364i | \(0.130769\pi\) | |||||||
\(384\) | −0.911995 | − | 1.47250i | −0.0465401 | − | 0.0751433i | ||||
\(385\) | −8.18156 | + | 1.71077i | −0.416971 | + | 0.0871887i | ||||
\(386\) | 12.5366i | 0.638096i | ||||||||
\(387\) | −11.6647 | − | 17.5941i | −0.592952 | − | 0.894358i | ||||
\(388\) | 9.83890 | − | 5.68049i | 0.499494 | − | 0.288383i | ||||
\(389\) | −22.3267 | + | 12.8903i | −1.13201 | + | 0.653565i | −0.944439 | − | 0.328686i | \(-0.893394\pi\) |
−0.187569 | + | 0.982251i | \(0.560061\pi\) | |||||||
\(390\) | 18.0123 | − | 0.557255i | 0.912090 | − | 0.0282177i | ||||
\(391\) | 31.7583 | 1.60609 | ||||||||
\(392\) | 6.41352 | − | 2.80477i | 0.323932 | − | 0.141662i | ||||
\(393\) | −18.5298 | + | 11.4764i | −0.934703 | + | 0.578909i | ||||
\(394\) | 1.59651 | + | 0.921744i | 0.0804309 | + | 0.0464368i | ||||
\(395\) | −4.16825 | − | 7.21962i | −0.209727 | − | 0.363258i | ||||
\(396\) | 0.349220 | + | 5.63857i | 0.0175490 | + | 0.283349i | ||||
\(397\) | −0.832842 | + | 1.44252i | −0.0417991 | + | 0.0723982i | −0.886168 | − | 0.463364i | \(-0.846642\pi\) |
0.844369 | + | 0.535762i | \(0.179976\pi\) | |||||||
\(398\) | 16.4765 | 0.825895 | ||||||||
\(399\) | −17.3744 | − | 9.85552i | −0.869806 | − | 0.493393i | ||||
\(400\) | 2.18549 | 0.109275 | ||||||||
\(401\) | 7.42121 | − | 12.8539i | 0.370597 | − | 0.641894i | −0.619060 | − | 0.785344i | \(-0.712486\pi\) |
0.989658 | + | 0.143450i | \(0.0458196\pi\) | |||||||
\(402\) | −9.45287 | − | 5.07453i | −0.471467 | − | 0.253095i | ||||
\(403\) | −22.5019 | − | 38.9744i | −1.12090 | − | 1.94145i | ||||
\(404\) | 2.15201 | + | 1.24246i | 0.107066 | + | 0.0618147i | ||||
\(405\) | −12.0445 | + | 9.10523i | −0.598495 | + | 0.452443i | ||||
\(406\) | −5.69908 | + | 17.3444i | −0.282840 | + | 0.860790i | ||||
\(407\) | 6.61175 | 0.327732 | ||||||||
\(408\) | −0.310862 | − | 10.0481i | −0.0153899 | − | 0.497454i | ||||
\(409\) | 28.8596 | − | 16.6621i | 1.42702 | − | 0.823888i | 0.430132 | − | 0.902766i | \(-0.358467\pi\) |
0.996884 | + | 0.0788776i | \(0.0251336\pi\) | |||||||
\(410\) | −3.07934 | + | 1.77786i | −0.152078 | + | 0.0878022i | ||||
\(411\) | −0.939702 | − | 30.3743i | −0.0463521 | − | 1.49825i | ||||
\(412\) | 13.8094i | 0.680339i | ||||||||
\(413\) | 23.3980 | + | 26.1597i | 1.15134 | + | 1.28723i | ||||
\(414\) | −14.6962 | − | 7.31318i | −0.722281 | − | 0.359423i | ||||
\(415\) | 8.98081 | − | 15.5552i | 0.440850 | − | 0.763575i | ||||
\(416\) | 5.37089 | − | 3.10089i | 0.263330 | − | 0.152033i | ||||
\(417\) | −11.2053 | + | 20.8734i | −0.548728 | + | 1.02217i | ||||
\(418\) | 7.99323 | + | 1.86689i | 0.390962 | + | 0.0913124i | ||||
\(419\) | − | 3.21593i | − | 0.157109i | −0.996910 | − | 0.0785543i | \(-0.974970\pi\) | ||
0.996910 | − | 0.0785543i | \(-0.0250304\pi\) | |||||||
\(420\) | −7.37449 | − | 2.17289i | −0.359838 | − | 0.106026i | ||||
\(421\) | − | 2.71489i | − | 0.132316i | −0.997809 | − | 0.0661579i | \(-0.978926\pi\) | ||
0.997809 | − | 0.0661579i | \(-0.0210741\pi\) | |||||||
\(422\) | −11.1793 | − | 6.45439i | −0.544201 | − | 0.314195i | ||||
\(423\) | −0.691798 | − | 11.1699i | −0.0336364 | − | 0.543099i | ||||
\(424\) | −5.47641 | − | 9.48541i | −0.265958 | − | 0.460652i | ||||
\(425\) | 10.9853 | + | 6.34234i | 0.532863 | + | 0.307649i | ||||
\(426\) | 2.45754 | + | 3.96793i | 0.119068 | + | 0.192247i | ||||
\(427\) | 10.8086 | − | 32.8946i | 0.523064 | − | 1.59188i | ||||
\(428\) | 6.75192 | 0.326366 | ||||||||
\(429\) | −20.2184 | + | 0.625507i | −0.976156 | + | 0.0301998i | ||||
\(430\) | −10.2233 | + | 5.90243i | −0.493012 | + | 0.284641i | ||||
\(431\) | −0.353770 | − | 0.612748i | −0.0170405 | − | 0.0295150i | 0.857379 | − | 0.514685i | \(-0.172091\pi\) |
−0.874420 | + | 0.485170i | \(0.838758\pi\) | |||||||
\(432\) | −2.16998 | + | 4.72136i | −0.104403 | + | 0.227156i | ||||
\(433\) | − | 15.7336i | − | 0.756109i | −0.925783 | − | 0.378054i | \(-0.876593\pi\) | ||
0.925783 | − | 0.378054i | \(-0.123407\pi\) | |||||||
\(434\) | 3.92956 | + | 18.7927i | 0.188625 | + | 0.902079i | ||||
\(435\) | 17.0464 | − | 10.5577i | 0.817310 | − | 0.506201i | ||||
\(436\) | −1.19227 | − | 0.688355i | −0.0570992 | − | 0.0329662i | ||||
\(437\) | −16.3107 | + | 17.4018i | −0.780248 | + | 0.832443i | ||||
\(438\) | 2.33594 | − | 4.35141i | 0.111616 | − | 0.207918i | ||||
\(439\) | −0.395316 | − | 0.228236i | −0.0188674 | − | 0.0108931i | 0.490537 | − | 0.871421i | \(-0.336801\pi\) |
−0.509404 | + | 0.860527i | \(0.670134\pi\) | |||||||
\(440\) | 3.15922 | 0.150610 | ||||||||
\(441\) | −17.6449 | − | 11.3867i | −0.840234 | − | 0.542224i | ||||
\(442\) | 35.9953 | 1.71212 | ||||||||
\(443\) | −28.8295 | − | 16.6447i | −1.36973 | − | 0.790814i | −0.378836 | − | 0.925464i | \(-0.623676\pi\) |
−0.990893 | + | 0.134650i | \(0.957009\pi\) | |||||||
\(444\) | 5.35809 | + | 2.87635i | 0.254284 | + | 0.136506i | ||||
\(445\) | −9.59400 | + | 5.53910i | −0.454799 | + | 0.262578i | ||||
\(446\) | −13.0200 | − | 7.51707i | −0.616513 | − | 0.355944i | ||||
\(447\) | −5.40641 | + | 3.34846i | −0.255715 | + | 0.158377i | ||||
\(448\) | −2.58974 | + | 0.541515i | −0.122354 | + | 0.0255842i | ||||
\(449\) | 24.7667 | 1.16881 | 0.584407 | − | 0.811461i | \(-0.301327\pi\) | ||||
0.584407 | + | 0.811461i | \(0.301327\pi\) | |||||||
\(450\) | −3.62297 | − | 5.46458i | −0.170788 | − | 0.257603i | ||||
\(451\) | 3.45650 | − | 1.99561i | 0.162760 | − | 0.0939695i | ||||
\(452\) | −5.53164 | − | 9.58108i | −0.260187 | − | 0.450656i | ||||
\(453\) | −0.682107 | − | 22.0480i | −0.0320482 | − | 1.03590i | ||||
\(454\) | 8.88027 | 0.416772 | ||||||||
\(455\) | 8.59304 | − | 26.1519i | 0.402848 | − | 1.22602i | ||||
\(456\) | 5.66546 | + | 4.99025i | 0.265309 | + | 0.233690i | ||||
\(457\) | −15.4070 | + | 26.6857i | −0.720709 | + | 1.24830i | 0.240007 | + | 0.970771i | \(0.422850\pi\) |
−0.960716 | + | 0.277533i | \(0.910483\pi\) | |||||||
\(458\) | 1.73528 | + | 3.00559i | 0.0810844 | + | 0.140442i | ||||
\(459\) | −24.6087 | + | 17.4343i | −1.14864 | + | 0.813763i | ||||
\(460\) | −4.58985 | + | 7.94985i | −0.214003 | + | 0.370664i | ||||
\(461\) | − | 22.3737i | − | 1.04205i | −0.853542 | − | 0.521024i | \(-0.825550\pi\) | ||
0.853542 | − | 0.521024i | \(-0.174450\pi\) | |||||||
\(462\) | 8.27771 | + | 2.43902i | 0.385114 | + | 0.113474i | ||||
\(463\) | 6.23559 | 0.289792 | 0.144896 | − | 0.989447i | \(-0.453715\pi\) | ||||
0.144896 | + | 0.989447i | \(0.453715\pi\) | |||||||
\(464\) | 3.45020 | − | 5.97592i | 0.160172 | − | 0.277425i | ||||
\(465\) | 9.97329 | − | 18.5783i | 0.462500 | − | 0.861549i | ||||
\(466\) | −0.752525 | + | 0.434470i | −0.0348600 | + | 0.0201265i | ||||
\(467\) | −20.4308 | − | 11.7957i | −0.945425 | − | 0.545842i | −0.0537685 | − | 0.998553i | \(-0.517123\pi\) |
−0.891657 | + | 0.452712i | \(0.850457\pi\) | |||||||
\(468\) | −16.6569 | − | 8.28885i | −0.769966 | − | 0.383152i | ||||
\(469\) | −12.2153 | + | 10.9257i | −0.564050 | + | 0.504503i | ||||
\(470\) | −6.25835 | −0.288676 | ||||||||
\(471\) | −30.5451 | + | 0.944986i | −1.40744 | + | 0.0435427i | ||||
\(472\) | −6.63269 | − | 11.4882i | −0.305294 | − | 0.528785i | ||||
\(473\) | 11.4754 | − | 6.62535i | 0.527642 | − | 0.304634i | ||||
\(474\) | 0.266146 | + | 8.60271i | 0.0122245 | + | 0.395136i | ||||
\(475\) | −9.11718 | + | 2.76197i | −0.418325 | + | 0.126728i | ||||
\(476\) | −14.5887 | − | 4.79358i | −0.668670 | − | 0.219713i | ||||
\(477\) | −14.6388 | + | 29.4174i | −0.670262 | + | 1.34693i | ||||
\(478\) | 9.98985 | + | 5.76764i | 0.456925 | + | 0.263806i | ||||
\(479\) | −16.7018 | + | 9.64280i | −0.763126 | + | 0.440591i | −0.830417 | − | 0.557142i | \(-0.811898\pi\) |
0.0672910 | + | 0.997733i | \(0.478564\pi\) | |||||||
\(480\) | 2.56020 | + | 1.37438i | 0.116856 | + | 0.0627314i | ||||
\(481\) | −10.8874 | + | 18.8575i | −0.496422 | + | 0.859828i | ||||
\(482\) | − | 2.26399i | − | 0.103122i | ||||||
\(483\) | −18.1638 | + | 17.2865i | −0.826480 | + | 0.786562i | ||||
\(484\) | 7.45384 | 0.338811 | ||||||||
\(485\) | −9.52987 | + | 16.5062i | −0.432729 | + | 0.749509i | ||||
\(486\) | 15.4024 | − | 2.40097i | 0.698669 | − | 0.108910i | ||||
\(487\) | 13.2005 | − | 7.62129i | 0.598170 | − | 0.345354i | −0.170151 | − | 0.985418i | \(-0.554426\pi\) |
0.768321 | + | 0.640064i | \(0.221092\pi\) | |||||||
\(488\) | −6.54347 | + | 11.3336i | −0.296209 | + | 0.513049i | ||||
\(489\) | −16.6448 | − | 26.8746i | −0.752705 | − | 1.21531i | ||||
\(490\) | −6.96541 | + | 9.45483i | −0.314665 | + | 0.427126i | ||||
\(491\) | 31.8405i | 1.43694i | 0.695557 | + | 0.718471i | \(0.255158\pi\) | ||||
−0.695557 | + | 0.718471i | \(0.744842\pi\) | |||||||
\(492\) | 3.66927 | − | 0.113518i | 0.165423 | − | 0.00511778i | ||||
\(493\) | 34.6845 | − | 20.0251i | 1.56211 | − | 0.901884i | ||||
\(494\) | −18.4868 | + | 19.7235i | −0.831761 | + | 0.887402i | ||||
\(495\) | −5.23714 | − | 7.89926i | −0.235392 | − | 0.355046i | ||||
\(496\) | − | 7.25660i | − | 0.325831i | ||||||
\(497\) | 6.97854 | − | 1.45921i | 0.313030 | − | 0.0654546i | ||||
\(498\) | −15.7652 | + | 9.76421i | −0.706457 | + | 0.437545i | ||||
\(499\) | −10.9039 | + | 18.8860i | −0.488124 | + | 0.845455i | −0.999907 | − | 0.0136598i | \(-0.995652\pi\) |
0.511783 | + | 0.859115i | \(0.328985\pi\) | |||||||
\(500\) | −10.4397 | + | 6.02737i | −0.466878 | + | 0.269552i | ||||
\(501\) | 7.91891 | − | 14.7514i | 0.353791 | − | 0.659044i | ||||
\(502\) | −18.6972 | − | 10.7948i | −0.834497 | − | 0.481797i | ||||
\(503\) | 17.8945i | 0.797875i | 0.916978 | + | 0.398938i | \(0.130621\pi\) | ||||
−0.916978 | + | 0.398938i | \(0.869379\pi\) | |||||||
\(504\) | 5.64710 | + | 5.57766i | 0.251542 | + | 0.248449i | ||||
\(505\) | −4.16883 | −0.185510 | ||||||||
\(506\) | 5.15201 | − | 8.92354i | 0.229035 | − | 0.396700i | ||||
\(507\) | 20.8592 | − | 38.8566i | 0.926388 | − | 1.72568i | ||||
\(508\) | 11.6727 | − | 6.73923i | 0.517891 | − | 0.299005i | ||||
\(509\) | 16.5121 | − | 28.5998i | 0.731887 | − | 1.26767i | −0.224189 | − | 0.974546i | \(-0.571973\pi\) |
0.956076 | − | 0.293120i | \(-0.0946935\pi\) | |||||||
\(510\) | 8.88021 | + | 14.3379i | 0.393223 | + | 0.634895i | ||||
\(511\) | −5.02940 | − | 5.62303i | −0.222488 | − | 0.248748i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.08572 | − | 22.4383i | 0.136238 | − | 0.990676i | ||||
\(514\) | −0.182046 | − | 0.315313i | −0.00802971 | − | 0.0139079i | ||||
\(515\) | −11.5836 | − | 20.0634i | −0.510436 | − | 0.884101i | ||||
\(516\) | 12.1818 | − | 0.376875i | 0.536276 | − | 0.0165910i | ||||
\(517\) | 7.02486 | 0.308953 | ||||||||
\(518\) | 6.92389 | − | 6.19293i | 0.304218 | − | 0.272102i | ||||
\(519\) | −23.3943 | − | 37.7723i | −1.02690 | − | 1.65802i | ||||
\(520\) | −5.20220 | + | 9.01047i | −0.228131 | + | 0.395135i | ||||
\(521\) | 5.23770 | + | 9.07197i | 0.229468 | + | 0.397450i | 0.957651 | − | 0.287933i | \(-0.0929681\pi\) |
−0.728183 | + | 0.685383i | \(0.759635\pi\) | |||||||
\(522\) | −20.6616 | + | 1.27966i | −0.904334 | + | 0.0560092i | ||||
\(523\) | −5.30741 | − | 3.06423i | −0.232077 | − | 0.133989i | 0.379453 | − | 0.925211i | \(-0.376112\pi\) |
−0.611530 | + | 0.791221i | \(0.709446\pi\) | |||||||
\(524\) | − | 12.5839i | − | 0.549728i | ||||||
\(525\) | −9.73510 | + | 2.35200i | −0.424875 | + | 0.102650i | ||||
\(526\) | − | 22.3034i | − | 0.972474i | ||||||
\(527\) | 21.0588 | − | 36.4749i | 0.917335 | − | 1.58887i | ||||
\(528\) | −2.87376 | − | 1.54271i | −0.125065 | − | 0.0671377i | ||||
\(529\) | 3.47011 | + | 6.01041i | 0.150874 | + | 0.261322i | ||||
\(530\) | 15.9132 | + | 9.18748i | 0.691225 | + | 0.399079i | ||||
\(531\) | −17.7296 | + | 35.6286i | −0.769398 | + | 1.54615i | ||||
\(532\) | 10.1192 | − | 5.53187i | 0.438723 | − | 0.239837i | ||||
\(533\) | 13.1444i | 0.569349i | ||||||||
\(534\) | 11.4320 | − | 0.353676i | 0.494710 | − | 0.0153050i | ||||
\(535\) | −9.80978 | + | 5.66368i | −0.424114 | + | 0.244862i | ||||
\(536\) | 5.36441 | − | 3.09715i | 0.231707 | − | 0.133776i | ||||
\(537\) | −16.8346 | + | 0.520818i | −0.726465 | + | 0.0224750i | ||||
\(538\) | −15.9793 | −0.688915 | ||||||||
\(539\) | 7.81852 | − | 10.6128i | 0.336768 | − | 0.457127i | ||||
\(540\) | −0.807657 | − | 8.67982i | −0.0347560 | − | 0.373520i | ||||
\(541\) | −7.06541 | + | 12.2377i | −0.303766 | + | 0.526138i | −0.976986 | − | 0.213305i | \(-0.931577\pi\) |
0.673220 | + | 0.739442i | \(0.264911\pi\) | |||||||
\(542\) | 8.33777 | + | 14.4414i | 0.358138 | + | 0.620313i | ||||
\(543\) | 1.55419 | + | 0.834329i | 0.0666968 | + | 0.0358045i | ||||
\(544\) | 5.02644 | + | 2.90202i | 0.215507 | + | 0.124423i | ||||
\(545\) | 2.30964 | 0.0989339 | ||||||||
\(546\) | −20.5871 | + | 19.5927i | −0.881044 | + | 0.838491i | ||||
\(547\) | − | 26.1503i | − | 1.11811i | −0.829132 | − | 0.559053i | \(-0.811165\pi\) | ||
0.829132 | − | 0.559053i | \(-0.188835\pi\) | |||||||
\(548\) | 15.1944 | + | 8.77249i | 0.649073 | + | 0.374742i | ||||
\(549\) | 39.1858 | − | 2.42694i | 1.67241 | − | 0.103579i | ||||
\(550\) | 3.56418 | − | 2.05778i | 0.151977 | − | 0.0877440i | ||||
\(551\) | −6.84090 | + | 29.2899i | −0.291432 | + | 1.24779i | ||||
\(552\) | 8.05719 | − | 4.99022i | 0.342937 | − | 0.212398i | ||||
\(553\) | 12.4902 | + | 4.10405i | 0.531136 | + | 0.174522i | ||||
\(554\) | 0.964689 | 0.0409857 | ||||||||
\(555\) | −10.1974 | + | 0.315483i | −0.432858 | + | 0.0133915i | ||||
\(556\) | −6.83897 | − | 11.8454i | −0.290037 | − | 0.502358i | ||||
\(557\) | 38.2625 | − | 22.0909i | 1.62123 | − | 0.936020i | 0.634644 | − | 0.772805i | \(-0.281147\pi\) |
0.986590 | − | 0.163216i | \(-0.0521866\pi\) | |||||||
\(558\) | −18.1443 | + | 12.0295i | −0.768109 | + | 0.509250i | ||||
\(559\) | 43.6391i | 1.84574i | ||||||||
\(560\) | 3.30836 | − | 2.95910i | 0.139804 | − | 0.125045i | ||||
\(561\) | −9.96785 | − | 16.0940i | −0.420843 | − | 0.679491i | ||||
\(562\) | −5.75386 | + | 9.96598i | −0.242712 | + | 0.420389i | ||||
\(563\) | 14.6974 | + | 25.4567i | 0.619423 | + | 1.07287i | 0.989591 | + | 0.143907i | \(0.0459665\pi\) |
−0.370169 | + | 0.928965i | \(0.620700\pi\) | |||||||
\(564\) | 5.69287 | + | 3.05607i | 0.239713 | + | 0.128684i | ||||
\(565\) | 16.0737 | + | 9.28015i | 0.676225 | + | 0.390419i | ||||
\(566\) | −26.1728 | −1.10012 | ||||||||
\(567\) | 4.58491 | − | 23.3662i | 0.192548 | − | 0.981287i | ||||
\(568\) | −2.69469 | −0.113067 | ||||||||
\(569\) | −5.07313 | + | 8.78693i | −0.212677 | + | 0.368367i | −0.952551 | − | 0.304378i | \(-0.901551\pi\) |
0.739875 | + | 0.672745i | \(0.234885\pi\) | |||||||
\(570\) | −12.4172 | − | 2.49794i | −0.520100 | − | 0.104627i | ||||
\(571\) | −2.20025 | − | 3.81095i | −0.0920777 | − | 0.159483i | 0.816308 | − | 0.577618i | \(-0.196017\pi\) |
−0.908385 | + | 0.418134i | \(0.862684\pi\) | |||||||
\(572\) | 5.83935 | − | 10.1141i | 0.244156 | − | 0.422890i | ||||
\(573\) | 11.5403 | − | 7.14747i | 0.482102 | − | 0.298590i | ||||
\(574\) | 1.75048 | − | 5.32736i | 0.0730635 | − | 0.222360i | ||||
\(575\) | 11.9585i | 0.498705i | ||||||||
\(576\) | −1.65773 | − | 2.50038i | −0.0690722 | − | 0.104183i | ||||
\(577\) | −0.987047 | − | 1.70962i | −0.0410913 | − | 0.0711722i | 0.844748 | − | 0.535164i | \(-0.179750\pi\) |
−0.885840 | + | 0.463992i | \(0.846417\pi\) | |||||||
\(578\) | 8.34340 | + | 14.4512i | 0.347040 | + | 0.601090i | ||||
\(579\) | 0.671455 | + | 21.7036i | 0.0279047 | + | 0.901972i | ||||
\(580\) | 11.5764i | 0.480686i | ||||||||
\(581\) | 5.79769 | + | 27.7269i | 0.240529 | + | 1.15030i | ||||
\(582\) | 16.7291 | − | 10.3612i | 0.693442 | − | 0.429484i | ||||
\(583\) | −17.8622 | − | 10.3128i | −0.739777 | − | 0.427110i | ||||
\(584\) | 1.42570 | + | 2.46938i | 0.0589958 | + | 0.102184i | ||||
\(585\) | 31.1535 | − | 1.92947i | 1.28804 | − | 0.0797736i | ||||
\(586\) | 4.85946 | − | 8.41682i | 0.200742 | − | 0.347696i | ||||
\(587\) | − | 24.6473i | − | 1.01730i | −0.860972 | − | 0.508652i | \(-0.830144\pi\) | ||
0.860972 | − | 0.508652i | \(-0.169856\pi\) | |||||||
\(588\) | 10.9530 | − | 5.19918i | 0.451695 | − | 0.214411i | ||||
\(589\) | 9.17070 | + | 30.2722i | 0.377872 | + | 1.24734i | ||||
\(590\) | 19.2731 | + | 11.1273i | 0.793461 | + | 0.458105i | ||||
\(591\) | 2.81328 | + | 1.51024i | 0.115723 | + | 0.0621228i | ||||
\(592\) | −3.04066 | + | 1.75553i | −0.124970 | + | 0.0721517i | ||||
\(593\) | 0.825213 | + | 0.476437i | 0.0338875 | + | 0.0195649i | 0.516848 | − | 0.856077i | \(-0.327105\pi\) |
−0.482961 | + | 0.875642i | \(0.660439\pi\) | |||||||
\(594\) | 0.906577 | + | 9.74291i | 0.0371973 | + | 0.399756i | ||||
\(595\) | 25.2166 | − | 5.27280i | 1.03378 | − | 0.216164i | ||||
\(596\) | − | 3.67158i | − | 0.150394i | ||||||
\(597\) | 28.5246 | − | 0.882477i | 1.16743 | − | 0.0361174i | ||||
\(598\) | 16.9673 | + | 29.3883i | 0.693846 | + | 1.20178i | ||||
\(599\) | −3.89609 | − | 6.74823i | −0.159190 | − | 0.275725i | 0.775387 | − | 0.631487i | \(-0.217555\pi\) |
−0.934577 | + | 0.355761i | \(0.884222\pi\) | |||||||
\(600\) | 3.78358 | − | 0.117054i | 0.154464 | − | 0.00477872i | ||||
\(601\) | 8.21500i | 0.335097i | 0.985864 | + | 0.167548i | \(0.0535851\pi\) | ||||
−0.985864 | + | 0.167548i | \(0.946415\pi\) | |||||||
\(602\) | 5.81153 | − | 17.6867i | 0.236860 | − | 0.720855i | ||||
\(603\) | −16.6368 | − | 8.27885i | −0.677504 | − | 0.337141i | ||||
\(604\) | 11.0293 | + | 6.36774i | 0.448774 | + | 0.259100i | ||||
\(605\) | −10.8296 | + | 6.25247i | −0.440285 | + | 0.254199i | ||||
\(606\) | 3.79215 | + | 2.03572i | 0.154045 | + | 0.0826953i | ||||
\(607\) | −29.1674 | − | 16.8398i | −1.18387 | − | 0.683507i | −0.226963 | − | 0.973903i | \(-0.572880\pi\) |
−0.956907 | + | 0.290396i | \(0.906213\pi\) | |||||||
\(608\) | −4.17168 | + | 1.26377i | −0.169184 | + | 0.0512528i | ||||
\(609\) | −8.93741 | + | 30.3323i | −0.362162 | + | 1.22913i | ||||
\(610\) | − | 21.9553i | − | 0.888944i | ||||||
\(611\) | −11.5676 | + | 20.0357i | −0.467977 | + | 0.810559i | ||||
\(612\) | −1.07634 | − | 17.3788i | −0.0435085 | − | 0.702496i | ||||
\(613\) | 10.0732 | + | 17.4474i | 0.406854 | + | 0.704693i | 0.994535 | − | 0.104400i | \(-0.0332923\pi\) |
−0.587681 | + | 0.809093i | \(0.699959\pi\) | |||||||
\(614\) | 16.7648 | + | 9.67915i | 0.676572 | + | 0.390619i | ||||
\(615\) | −5.23581 | + | 3.24280i | −0.211128 | + | 0.130762i | ||||
\(616\) | −3.71357 | + | 3.32152i | −0.149624 | + | 0.133828i | ||||
\(617\) | − | 7.95233i | − | 0.320149i | −0.987105 | − | 0.160074i | \(-0.948827\pi\) | ||
0.987105 | − | 0.160074i | \(-0.0511734\pi\) | |||||||
\(618\) | 0.739625 | + | 23.9071i | 0.0297521 | + | 0.961684i | ||||
\(619\) | 9.72833 | + | 16.8500i | 0.391014 | + | 0.677257i | 0.992584 | − | 0.121564i | \(-0.0387909\pi\) |
−0.601569 | + | 0.798821i | \(0.705458\pi\) | |||||||
\(620\) | 6.08701 | + | 10.5430i | 0.244460 | + | 0.423418i | ||||
\(621\) | −25.8342 | − | 11.8736i | −1.03669 | − | 0.476472i | ||||
\(622\) | 26.3469i | 1.05642i | ||||||||
\(623\) | 5.45379 | − | 16.5979i | 0.218501 | − | 0.664982i | ||||
\(624\) | 9.13213 | − | 5.65599i | 0.365578 | − | 0.226421i | ||||
\(625\) | 4.64807 | − | 8.05069i | 0.185923 | − | 0.322028i | ||||
\(626\) | 5.38324 | + | 9.32405i | 0.215158 | + | 0.372664i | ||||
\(627\) | 13.9380 | + | 2.80388i | 0.556632 | + | 0.111976i | ||||
\(628\) | 8.82182 | − | 15.2798i | 0.352029 | − | 0.609732i | ||||
\(629\) | −20.3783 | −0.812535 | ||||||||
\(630\) | −12.8833 | − | 3.36679i | −0.513282 | − | 0.134136i | ||||
\(631\) | 12.3930 | 0.493359 | 0.246680 | − | 0.969097i | \(-0.420660\pi\) | ||||
0.246680 | + | 0.969097i | \(0.420660\pi\) | |||||||
\(632\) | −4.30342 | − | 2.48458i | −0.171181 | − | 0.0988312i | ||||
\(633\) | −19.6996 | − | 10.5752i | −0.782989 | − | 0.420327i | ||||
\(634\) | 0.403484 | + | 0.698855i | 0.0160244 | + | 0.0277551i | ||||
\(635\) | −11.3061 | + | 19.5827i | −0.448667 | + | 0.777114i | ||||
\(636\) | −9.98891 | − | 16.1280i | −0.396086 | − | 0.639519i | ||||
\(637\) | 17.3945 | + | 39.7752i | 0.689197 | + | 1.57595i | ||||
\(638\) | − | 12.9943i | − | 0.514450i | ||||||
\(639\) | 4.46707 | + | 6.73775i | 0.176715 | + | 0.266541i | ||||
\(640\) | −1.45289 | + | 0.838824i | −0.0574304 | + | 0.0331574i | ||||
\(641\) | −18.0642 | − | 31.2882i | −0.713495 | − | 1.23581i | −0.963537 | − | 0.267574i | \(-0.913778\pi\) |
0.250042 | − | 0.968235i | \(-0.419555\pi\) | |||||||
\(642\) | 11.6891 | − | 0.361630i | 0.461331 | − | 0.0142724i | ||||
\(643\) | 20.5963 | 0.812237 | 0.406119 | − | 0.913820i | \(-0.366882\pi\) | ||||
0.406119 | + | 0.913820i | \(0.366882\pi\) | |||||||
\(644\) | −2.96304 | − | 14.1705i | −0.116760 | − | 0.558394i | ||||
\(645\) | −17.3827 | + | 10.7660i | −0.684443 | + | 0.423910i | ||||
\(646\) | −24.6362 | − | 5.75399i | −0.969297 | − | 0.226388i | ||||
\(647\) | −25.6124 | + | 14.7873i | −1.00693 | + | 0.581350i | −0.910291 | − | 0.413970i | \(-0.864142\pi\) |
−0.0966369 | + | 0.995320i | \(0.530809\pi\) | |||||||
\(648\) | −3.50384 | + | 8.28994i | −0.137644 | + | 0.325660i | ||||
\(649\) | −21.6336 | − | 12.4902i | −0.849194 | − | 0.490282i | ||||
\(650\) | 13.5539i | 0.531629i | ||||||||
\(651\) | 7.80947 | + | 32.3239i | 0.306077 | + | 1.26687i | ||||
\(652\) | 18.2510 | 0.714764 | ||||||||
\(653\) | 30.9910 | + | 17.8927i | 1.21277 | + | 0.700195i | 0.963362 | − | 0.268203i | \(-0.0864297\pi\) |
0.249411 | + | 0.968398i | \(0.419763\pi\) | |||||||
\(654\) | −2.10095 | − | 1.12784i | −0.0821535 | − | 0.0441020i | ||||
\(655\) | 10.5556 | + | 18.2829i | 0.412443 | + | 0.714373i | ||||
\(656\) | −1.05973 | + | 1.83551i | −0.0413756 | + | 0.0716647i | ||||
\(657\) | 3.81098 | − | 7.65837i | 0.148680 | − | 0.298782i | ||||
\(658\) | 7.35650 | − | 6.57987i | 0.286786 | − | 0.256510i | ||||
\(659\) | −7.97290 | −0.310580 | −0.155290 | − | 0.987869i | \(-0.549631\pi\) | ||||
−0.155290 | + | 0.987869i | \(0.549631\pi\) | |||||||
\(660\) | 5.46931 | − | 0.169207i | 0.212893 | − | 0.00658636i | ||||
\(661\) | −36.4070 | + | 21.0196i | −1.41607 | + | 0.817566i | −0.995950 | − | 0.0899038i | \(-0.971344\pi\) |
−0.420116 | + | 0.907470i | \(0.638011\pi\) | |||||||
\(662\) | 9.13676 | − | 5.27511i | 0.355110 | − | 0.205023i | ||||
\(663\) | 62.3159 | − | 1.92789i | 2.42015 | − | 0.0748732i | ||||
\(664\) | − | 10.7064i | − | 0.415490i | ||||||
\(665\) | −10.0618 | + | 16.5254i | −0.390180 | + | 0.640828i | ||||
\(666\) | 9.43010 | + | 4.69263i | 0.365409 | + | 0.181836i | ||||
\(667\) | 32.6989 | + | 18.8787i | 1.26610 | + | 0.730986i | ||||
\(668\) | 4.83316 | + | 8.37128i | 0.187001 | + | 0.323894i | ||||
\(669\) | −22.9431 | − | 12.3164i | −0.887030 | − | 0.476179i | ||||
\(670\) | −5.19592 | + | 8.99960i | −0.200736 | + | 0.347685i | ||||
\(671\) | 24.6443i | 0.951384i | ||||||||
\(672\) | −4.45442 | + | 1.07619i | −0.171833 | + | 0.0415149i | ||||
\(673\) | − | 6.77033i | − | 0.260977i | −0.991450 | − | 0.130488i | \(-0.958345\pi\) | ||
0.991450 | − | 0.130488i | \(-0.0416546\pi\) | |||||||
\(674\) | −3.05182 | − | 1.76197i | −0.117552 | − | 0.0678684i | ||||
\(675\) | −6.56484 | − | 9.26635i | −0.252681 | − | 0.356662i | ||||
\(676\) | 12.7310 | + | 22.0507i | 0.489654 | + | 0.848105i | ||||
\(677\) | −9.66590 | + | 16.7418i | −0.371491 | + | 0.643441i | −0.989795 | − | 0.142498i | \(-0.954487\pi\) |
0.618304 | + | 0.785939i | \(0.287820\pi\) | |||||||
\(678\) | −10.0897 | − | 16.2907i | −0.387491 | − | 0.625641i | ||||
\(679\) | −6.15214 | − | 29.4220i | −0.236098 | − | 1.12911i | ||||
\(680\) | −9.73713 | −0.373402 | ||||||||
\(681\) | 15.3737 | − | 0.475624i | 0.589122 | − | 0.0182259i | ||||
\(682\) | −6.83254 | − | 11.8343i | −0.261631 | − | 0.453159i | ||||
\(683\) | −4.84130 | − | 8.38537i | −0.185247 | − | 0.320857i | 0.758413 | − | 0.651775i | \(-0.225975\pi\) |
−0.943660 | + | 0.330917i | \(0.892642\pi\) | |||||||
\(684\) | 10.0754 | + | 8.33579i | 0.385244 | + | 0.318727i | ||||
\(685\) | −29.4343 | −1.12463 | ||||||||
\(686\) | −1.75293 | − | 18.4371i | −0.0669273 | − | 0.703932i | ||||
\(687\) | 3.16514 | + | 5.11041i | 0.120757 | + | 0.194974i | ||||
\(688\) | −3.51828 | + | 6.09384i | −0.134133 | + | 0.232325i | ||||
\(689\) | 58.8264 | − | 33.9634i | 2.24111 | − | 1.29390i | ||||
\(690\) | −7.52026 | + | 14.0088i | −0.286291 | + | 0.533306i | ||||
\(691\) | −20.3764 | + | 35.2930i | −0.775157 | + | 1.34261i | 0.159550 | + | 0.987190i | \(0.448996\pi\) |
−0.934706 | + | 0.355421i | \(0.884338\pi\) | |||||||
\(692\) | 25.6518 | 0.975134 | ||||||||
\(693\) | 14.4612 | + | 3.77914i | 0.549335 | + | 0.143558i | ||||
\(694\) | 12.7492i | 0.483953i | ||||||||
\(695\) | 19.8725 | + | 11.4734i | 0.753806 | + | 0.435210i | ||||
\(696\) | 5.65300 | − | 10.5304i | 0.214276 | − | 0.399155i | ||||
\(697\) | −10.6534 | + | 6.15073i | −0.403525 | + | 0.232975i | ||||
\(698\) | −11.8324 | + | 20.4943i | −0.447862 | + | 0.775720i | ||||
\(699\) | −1.27952 | + | 0.792470i | −0.0483958 | + | 0.0299740i | ||||
\(700\) | 1.80501 | − | 5.49333i | 0.0682230 | − | 0.207628i | ||||
\(701\) | − | 35.1465i | − | 1.32746i | −0.747971 | − | 0.663732i | \(-0.768972\pi\) | ||
0.747971 | − | 0.663732i | \(-0.231028\pi\) | |||||||
\(702\) | −29.2808 | − | 13.4577i | −1.10513 | − | 0.507928i | ||||
\(703\) | 10.4661 | − | 11.1662i | 0.394735 | − | 0.421141i | ||||
\(704\) | 1.63083 | − | 0.941562i | 0.0614643 | − | 0.0354865i | ||||
\(705\) | −10.8346 | + | 0.335195i | −0.408055 | + | 0.0126242i | ||||
\(706\) | − | 8.20582i | − | 0.308830i | ||||||
\(707\) | 4.90033 | − | 4.38300i | 0.184296 | − | 0.164840i | ||||
\(708\) | −12.0980 | − | 19.5333i | −0.454669 | − | 0.734107i | ||||
\(709\) | 19.4394 | − | 33.6700i | 0.730061 | − | 1.26450i | −0.226795 | − | 0.973942i | \(-0.572825\pi\) |
0.956857 | − | 0.290561i | \(-0.0938418\pi\) | |||||||
\(710\) | 3.91507 | − | 2.26037i | 0.146930 | − | 0.0848301i | ||||
\(711\) | 0.921516 | + | 14.8790i | 0.0345595 | + | 0.558005i | ||||
\(712\) | −3.30170 | + | 5.71872i | −0.123737 | + | 0.214318i | ||||
\(713\) | 39.7064 | 1.48702 | ||||||||
\(714\) | −25.5130 | − | 7.51739i | −0.954799 | − | 0.281331i | ||||
\(715\) | 19.5928i | 0.732728i | ||||||||
\(716\) | 4.86204 | − | 8.42131i | 0.181703 | − | 0.314719i | ||||
\(717\) | 17.6036 | + | 9.45002i | 0.657417 | + | 0.352917i | ||||
\(718\) | −4.39323 | + | 2.53643i | −0.163954 | + | 0.0946588i | ||||
\(719\) | −32.0990 | − | 18.5323i | −1.19709 | − | 0.691140i | −0.237184 | − | 0.971465i | \(-0.576225\pi\) |
−0.959905 | + | 0.280325i | \(0.909558\pi\) | |||||||
\(720\) | 4.50588 | + | 2.24223i | 0.167924 | + | 0.0835629i | ||||
\(721\) | 34.7104 | + | 11.4052i | 1.29268 | + | 0.424753i | ||||
\(722\) | 15.8058 | − | 10.5441i | 0.588229 | − | 0.392411i | ||||
\(723\) | −0.121258 | − | 3.91947i | −0.00450965 | − | 0.145767i | ||||
\(724\) | −0.881990 | + | 0.509217i | −0.0327789 | + | 0.0189249i | ||||
\(725\) | 7.54040 | + | 13.0603i | 0.280043 | + | 0.485049i | ||||
\(726\) | 12.9043 | − | 0.399225i | 0.478922 | − | 0.0148166i | ||||
\(727\) | 8.11741 | 0.301058 | 0.150529 | − | 0.988606i | \(-0.451902\pi\) | ||||
0.150529 | + | 0.988606i | \(0.451902\pi\) | |||||||
\(728\) | −3.35835 | − | 16.0610i | −0.124469 | − | 0.595260i | ||||
\(729\) | 26.5365 | − | 4.98156i | 0.982832 | − | 0.184502i | ||||
\(730\) | −4.14276 | − | 2.39182i | −0.153330 | − | 0.0885253i | ||||
\(731\) | −35.3688 | + | 20.4202i | −1.30816 | + | 0.755268i | ||||
\(732\) | −10.7212 | + | 19.9715i | −0.396266 | + | 0.738168i | ||||
\(733\) | 0.922882 | − | 1.59848i | 0.0340874 | − | 0.0590412i | −0.848478 | − | 0.529230i | \(-0.822481\pi\) |
0.882566 | + | 0.470189i | \(0.155814\pi\) | |||||||
\(734\) | −25.3138 | −0.934350 | ||||||||
\(735\) | −11.5523 | + | 16.7415i | −0.426112 | + | 0.617519i | ||||
\(736\) | 5.47177i | 0.201692i | ||||||||
\(737\) | 5.83231 | − | 10.1019i | 0.214836 | − | 0.372107i | ||||
\(738\) | 6.34624 | − | 0.393049i | 0.233608 | − | 0.0144683i | ||||
\(739\) | −9.74739 | − | 16.8830i | −0.358563 | − | 0.621050i | 0.629158 | − | 0.777278i | \(-0.283400\pi\) |
−0.987721 | + | 0.156228i | \(0.950067\pi\) | |||||||
\(740\) | 2.94516 | − | 5.10116i | 0.108266 | − | 0.187523i | ||||
\(741\) | −30.9484 | + | 35.1359i | −1.13692 | + | 1.29075i | ||||
\(742\) | −28.3650 | + | 5.93111i | −1.04131 | + | 0.217738i | ||||
\(743\) | 23.9925 | 0.880200 | 0.440100 | − | 0.897949i | \(-0.354943\pi\) | ||||
0.440100 | + | 0.897949i | \(0.354943\pi\) | |||||||
\(744\) | −0.388661 | − | 12.5628i | −0.0142490 | − | 0.460574i | ||||
\(745\) | 3.07981 | + | 5.33439i | 0.112836 | + | 0.195437i | ||||
\(746\) | −4.95651 | + | 2.86164i | −0.181471 | + | 0.104772i | ||||
\(747\) | −26.7702 | + | 17.7484i | −0.979469 | + | 0.649380i | ||||
\(748\) | 10.9297 | 0.399630 | ||||||||
\(749\) | 5.57645 | − | 16.9712i | 0.203759 | − | 0.620115i | ||||
\(750\) | −17.7506 | + | 10.9939i | −0.648161 | + | 0.401439i | ||||
\(751\) | −14.6805 | − | 8.47581i | −0.535700 | − | 0.309287i | 0.207634 | − | 0.978207i | \(-0.433424\pi\) |
−0.743335 | + | 0.668920i | \(0.766757\pi\) | |||||||
\(752\) | −3.23065 | + | 1.86522i | −0.117810 | + | 0.0680174i | ||||
\(753\) | −32.9472 | − | 17.6868i | −1.20066 | − | 0.644544i | ||||
\(754\) | 37.0613 | + | 21.3974i | 1.34969 | + | 0.779246i | ||||
\(755\) | −21.3657 | −0.777576 | ||||||||
\(756\) | 10.0751 | + | 9.35372i | 0.366428 | + | 0.340191i | ||||
\(757\) | −34.7601 | −1.26338 | −0.631689 | − | 0.775222i | \(-0.717638\pi\) | ||||
−0.631689 | + | 0.775222i | \(0.717638\pi\) | |||||||
\(758\) | −10.3192 | − | 5.95779i | −0.374810 | − | 0.216397i | ||||
\(759\) | 8.44133 | − | 15.7246i | 0.306401 | − | 0.570766i | ||||
\(760\) | 5.00089 | − | 5.33542i | 0.181401 | − | 0.193536i | ||||
\(761\) | 13.4406 | + | 7.75991i | 0.487220 | + | 0.281297i | 0.723420 | − | 0.690408i | \(-0.242569\pi\) |
−0.236200 | + | 0.971704i | \(0.575902\pi\) | |||||||
\(762\) | 19.8471 | − | 12.2923i | 0.718983 | − | 0.445302i | ||||
\(763\) | −2.71491 | + | 2.42829i | −0.0982862 | + | 0.0879101i | ||||
\(764\) | 7.83718i | 0.283539i | ||||||||
\(765\) | 16.1416 | + | 24.3466i | 0.583599 | + | 0.880252i | ||||
\(766\) | 2.20238 | + | 3.81464i | 0.0795753 | + | 0.137828i | ||||
\(767\) | 71.2469 | − | 41.1344i | 2.57258 | − | 1.48528i | ||||
\(768\) | 1.73122 | − | 0.0535596i | 0.0624701 | − | 0.00193267i | ||||
\(769\) | −53.7765 | −1.93923 | −0.969615 | − | 0.244636i | \(-0.921332\pi\) | ||||
−0.969615 | + | 0.244636i | \(0.921332\pi\) | |||||||
\(770\) | 2.60922 | − | 7.94083i | 0.0940296 | − | 0.286167i | ||||
\(771\) | −0.332050 | − | 0.536127i | −0.0119585 | − | 0.0193081i | ||||
\(772\) | −10.8570 | − | 6.26830i | −0.390752 | − | 0.225601i | ||||
\(773\) | 5.30069 | + | 9.18107i | 0.190653 | + | 0.330220i | 0.945467 | − | 0.325719i | \(-0.105606\pi\) |
−0.754814 | + | 0.655939i | \(0.772273\pi\) | |||||||
\(774\) | 21.0693 | − | 1.30491i | 0.757320 | − | 0.0469040i | ||||
\(775\) | 13.7345 | + | 7.92963i | 0.493359 | + | 0.284841i | ||||
\(776\) | 11.3610i | 0.407835i | ||||||||
\(777\) | 11.6551 | − | 11.0922i | 0.418124 | − | 0.397930i | ||||
\(778\) | − | 25.7806i | − | 0.924281i | ||||||
\(779\) | 2.10119 | − | 8.99642i | 0.0752830 | − | 0.322330i | ||||
\(780\) | −8.52357 | + | 15.8778i | −0.305193 | + | 0.568515i | ||||
\(781\) | −4.39458 | + | 2.53721i | −0.157251 | + | 0.0907886i | ||||
\(782\) | −15.8792 | + | 27.5035i | −0.567837 | + | 0.983523i | ||||
\(783\) | −35.7013 | + | 3.32200i | −1.27586 | + | 0.118719i | ||||
\(784\) | −0.777761 | + | 6.95666i | −0.0277772 | + | 0.248452i | ||||
\(785\) | 29.5998i | 1.05646i | ||||||||
\(786\) | −0.673987 | − | 21.7855i | −0.0240403 | − | 0.777062i | ||||
\(787\) | −26.4523 | + | 15.2722i | −0.942922 | + | 0.544397i | −0.890875 | − | 0.454248i | \(-0.849908\pi\) |
−0.0520472 | + | 0.998645i | \(0.516575\pi\) | |||||||
\(788\) | −1.59651 | + | 0.921744i | −0.0568732 | + | 0.0328358i | ||||
\(789\) | −1.19456 | − | 38.6121i | −0.0425275 | − | 1.37463i | ||||
\(790\) | 8.33650 | 0.296599 | ||||||||
\(791\) | −28.6510 | + | 5.99093i | −1.01871 | + | 0.213013i | ||||
\(792\) | −5.05775 | − | 2.51685i | −0.179719 | − | 0.0894324i | ||||
\(793\) | −70.2886 | − | 40.5811i | −2.49602 | − | 1.44108i | ||||
\(794\) | −0.832842 | − | 1.44252i | −0.0295565 | − | 0.0511933i | ||||
\(795\) | 28.0414 | + | 15.0533i | 0.994524 | + | 0.533885i | ||||
\(796\) | −8.23827 | + | 14.2691i | −0.291998 | + | 0.505755i | ||||
\(797\) | 9.20729 | 0.326139 | 0.163069 | − | 0.986615i | \(-0.447861\pi\) | ||||
0.163069 | + | 0.986615i | \(0.447861\pi\) | |||||||
\(798\) | 17.2223 | − | 10.1189i | 0.609663 | − | 0.358205i | ||||
\(799\) | −21.6515 | −0.765976 | ||||||||
\(800\) | −1.09275 | + | 1.89269i | −0.0386345 | + | 0.0669168i | ||||
\(801\) | 19.7723 | − | 1.22458i | 0.698621 | − | 0.0432685i | ||||
\(802\) | 7.42121 | + | 12.8539i | 0.262052 | + | 0.453887i | ||||
\(803\) | 4.65015 | + | 2.68477i | 0.164100 | + | 0.0947434i | ||||
\(804\) | 9.12111 | − | 5.64916i | 0.321677 | − | 0.199231i | ||||
\(805\) | 16.1915 | + | 18.1026i | 0.570675 | + | 0.638033i | ||||
\(806\) | 45.0038 | 1.58519 | ||||||||
\(807\) | −27.6636 | + | 0.855843i | −0.973806 | + | 0.0301271i | ||||
\(808\) | −2.15201 | + | 1.24246i | −0.0757073 | + | 0.0437096i | ||||
\(809\) | 37.5452 | − | 21.6767i | 1.32002 | − | 0.762113i | 0.336288 | − | 0.941759i | \(-0.390829\pi\) |
0.983731 | + | 0.179646i | \(0.0574952\pi\) | |||||||
\(810\) | −1.86312 | − | 14.9834i | −0.0654634 | − | 0.526465i | ||||
\(811\) | − | 2.37812i | − | 0.0835070i | −0.999128 | − | 0.0417535i | \(-0.986706\pi\) | ||
0.999128 | − | 0.0417535i | \(-0.0132944\pi\) | |||||||
\(812\) | −12.1712 | − | 13.6078i | −0.427125 | − | 0.477539i | ||||
\(813\) | 15.2080 | + | 24.5548i | 0.533368 | + | 0.861174i | ||||
\(814\) | −3.30588 | + | 5.72595i | −0.115871 | + | 0.200694i | ||||
\(815\) | −26.5166 | + | 15.3094i | −0.928837 | + | 0.536264i | ||||
\(816\) | 8.85732 | + | 4.75482i | 0.310068 | + | 0.166452i | ||||
\(817\) | 6.97589 | − | 29.8678i | 0.244055 | − | 1.04494i | ||||
\(818\) | 33.3242i | 1.16515i | ||||||||
\(819\) | −34.5914 | + | 35.0220i | −1.20872 | + | 1.22377i | ||||
\(820\) | − | 3.55572i | − | 0.124171i | ||||||
\(821\) | 45.5218 | + | 26.2820i | 1.58872 | + | 0.917248i | 0.993518 | + | 0.113672i | \(0.0362613\pi\) |
0.595202 | + | 0.803576i | \(0.297072\pi\) | |||||||
\(822\) | 26.7747 | + | 14.3733i | 0.933876 | + | 0.501327i | ||||
\(823\) | 3.54044 | + | 6.13222i | 0.123412 | + | 0.213756i | 0.921111 | − | 0.389300i | \(-0.127283\pi\) |
−0.797699 | + | 0.603056i | \(0.793950\pi\) | |||||||
\(824\) | −11.9593 | − | 6.90469i | −0.416621 | − | 0.240536i | ||||
\(825\) | 6.06017 | − | 3.75337i | 0.210988 | − | 0.130676i | ||||
\(826\) | −34.3539 | + | 7.18340i | −1.19533 | + | 0.249943i | ||||
\(827\) | −3.77750 | −0.131357 | −0.0656784 | − | 0.997841i | \(-0.520921\pi\) | ||||
−0.0656784 | + | 0.997841i | \(0.520921\pi\) | |||||||
\(828\) | 13.6815 | − | 9.07073i | 0.475466 | − | 0.315230i | ||||
\(829\) | −35.0687 | + | 20.2469i | −1.21799 | + | 0.703205i | −0.964487 | − | 0.264131i | \(-0.914915\pi\) |
−0.253499 | + | 0.967336i | \(0.581582\pi\) | |||||||
\(830\) | 8.98081 | + | 15.5552i | 0.311728 | + | 0.539929i | ||||
\(831\) | 1.67009 | − | 0.0516684i | 0.0579348 | − | 0.00179236i | ||||
\(832\) | 6.20177i | 0.215008i | ||||||||
\(833\) | −24.0977 | + | 32.7101i | −0.834936 | + | 1.13334i | ||||
\(834\) | −12.4742 | − | 20.1408i | −0.431946 | − | 0.697419i | ||||
\(835\) | −14.0441 | − | 8.10834i | −0.486015 | − | 0.280601i | ||||
\(836\) | −5.61339 | + | 5.98889i | −0.194143 | + | 0.207130i | ||||
\(837\) | −30.7675 | + | 21.7976i | −1.06348 | + | 0.753434i | ||||
\(838\) | 2.78508 | + | 1.60797i | 0.0962090 | + | 0.0555463i | ||||
\(839\) | −17.2654 | −0.596069 | −0.298034 | − | 0.954555i | \(-0.596331\pi\) | ||||
−0.298034 | + | 0.954555i | \(0.596331\pi\) | |||||||
\(840\) | 5.56903 | − | 5.30005i | 0.192150 | − | 0.182869i | ||||
\(841\) | 18.6155 | 0.641915 | ||||||||
\(842\) | 2.35117 | + | 1.35745i | 0.0810265 | + | 0.0467807i | ||||
\(843\) | −9.42744 | + | 17.5615i | −0.324698 | + | 0.604850i | ||||
\(844\) | 11.1793 | − | 6.45439i | 0.384808 | − | 0.222169i | ||||
\(845\) | −36.9934 | − | 21.3581i | −1.27261 | − | 0.734742i | ||||
\(846\) | 10.0193 | + | 4.98583i | 0.344471 | + | 0.171416i | ||||
\(847\) | 6.15617 | − | 18.7355i | 0.211528 | − | 0.643760i | ||||
\(848\) | 10.9528 | 0.376121 | ||||||||
\(849\) | −45.3109 | + | 1.40180i | −1.55507 | + | 0.0481098i | ||||
\(850\) | −10.9853 | + | 6.34234i | −0.376791 | + | 0.217541i | ||||
\(851\) | −9.60584 | − | 16.6378i | −0.329284 | − | 0.570336i | ||||
\(852\) | −4.66510 | + | 0.144326i | −0.159824 | + | 0.00494454i | ||||
\(853\) | −28.6752 | −0.981821 | −0.490911 | − | 0.871210i | \(-0.663336\pi\) | ||||
−0.490911 | + | 0.871210i | \(0.663336\pi\) | |||||||
\(854\) | 23.0832 | + | 25.8078i | 0.789892 | + | 0.883124i | ||||
\(855\) | −21.6307 | − | 3.65943i | −0.739756 | − | 0.125150i | ||||
\(856\) | −3.37596 | + | 5.84734i | −0.115388 | + | 0.199858i | ||||
\(857\) | 5.27762 | + | 9.14110i | 0.180280 | + | 0.312254i | 0.941976 | − | 0.335681i | \(-0.108966\pi\) |
−0.761696 | + | 0.647935i | \(0.775633\pi\) | |||||||
\(858\) | 9.56752 | − | 17.8224i | 0.326630 | − | 0.608448i | ||||
\(859\) | 10.6346 | − | 18.4196i | 0.362847 | − | 0.628470i | −0.625581 | − | 0.780159i | \(-0.715138\pi\) |
0.988428 | + | 0.151689i | \(0.0484714\pi\) | |||||||
\(860\) | − | 11.8049i | − | 0.402543i | ||||||
\(861\) | 2.74514 | − | 9.31660i | 0.0935540 | − | 0.317509i | ||||
\(862\) | 0.707540 | 0.0240989 | ||||||||
\(863\) | −16.6074 | + | 28.7649i | −0.565323 | + | 0.979167i | 0.431697 | + | 0.902019i | \(0.357915\pi\) |
−0.997020 | + | 0.0771487i | \(0.975418\pi\) | |||||||
\(864\) | −3.00382 | − | 4.23993i | −0.102192 | − | 0.144245i | ||||
\(865\) | −37.2691 | + | 21.5173i | −1.26719 | + | 0.731611i | ||||
\(866\) | 13.6257 | + | 7.86680i | 0.463020 | + | 0.267325i | ||||
\(867\) | 15.2183 | + | 24.5714i | 0.516840 | + | 0.834487i | ||||
\(868\) | −18.2398 | − | 5.99326i | −0.619097 | − | 0.203425i | ||||
\(869\) | −9.35754 | −0.317433 | ||||||||
\(870\) | 0.620030 | + | 20.0414i | 0.0210210 | + | 0.679467i | ||||
\(871\) | 19.2078 | + | 33.2689i | 0.650831 | + | 1.12727i | ||||
\(872\) | 1.19227 | − | 0.688355i | 0.0403752 | − | 0.0233106i | ||||
\(873\) | 28.4068 | − | 18.8335i | 0.961425 | − | 0.637417i | ||||
\(874\) | −6.91507 | − | 22.8264i | −0.233906 | − | 0.772116i | ||||
\(875\) | 6.52782 | + | 31.2187i | 0.220681 | + | 1.05538i | ||||
\(876\) | 2.60046 | + | 4.19869i | 0.0878614 | + | 0.141861i | ||||
\(877\) | −4.44865 | − | 2.56843i | −0.150220 | − | 0.0867297i | 0.423006 | − | 0.906127i | \(-0.360975\pi\) |
−0.573226 | + | 0.819397i | \(0.694308\pi\) | |||||||
\(878\) | 0.395316 | − | 0.228236i | 0.0133413 | − | 0.00770258i | ||||
\(879\) | 7.96200 | − | 14.8317i | 0.268552 | − | 0.500260i | ||||
\(880\) | −1.57961 | + | 2.73597i | −0.0532486 | + | 0.0922294i | ||||
\(881\) | 50.3341i | 1.69580i | 0.530157 | + | 0.847900i | \(0.322133\pi\) | ||||
−0.530157 | + | 0.847900i | \(0.677867\pi\) | |||||||
\(882\) | 18.6836 | − | 9.58758i | 0.629111 | − | 0.322831i | ||||
\(883\) | 0.790125 | 0.0265898 | 0.0132949 | − | 0.999912i | \(-0.495768\pi\) | ||||
0.0132949 | + | 0.999912i | \(0.495768\pi\) | |||||||
\(884\) | −17.9976 | + | 31.1728i | −0.605326 | + | 1.04846i | ||||
\(885\) | 33.9620 | + | 18.2316i | 1.14162 | + | 0.612849i | ||||
\(886\) | 28.8295 | − | 16.6447i | 0.968545 | − | 0.559190i | ||||
\(887\) | 10.7878 | − | 18.6850i | 0.362219 | − | 0.627382i | −0.626107 | − | 0.779737i | \(-0.715353\pi\) |
0.988326 | + | 0.152356i | \(0.0486859\pi\) | |||||||
\(888\) | −5.17004 | + | 3.20207i | −0.173495 | + | 0.107454i | ||||
\(889\) | −7.29878 | − | 34.9057i | −0.244793 | − | 1.17070i | ||||
\(890\) | − | 11.0782i | − | 0.371342i | ||||||
\(891\) | 2.09131 | + | 16.8186i | 0.0700616 | + | 0.563444i | ||||
\(892\) | 13.0200 | − | 7.51707i | 0.435940 | − | 0.251690i | ||||
\(893\) | 11.1200 | − | 11.8639i | 0.372117 | − | 0.397010i | ||||
\(894\) | −0.196648 | − | 6.35632i | −0.00657691 | − | 0.212587i | ||||
\(895\) | 16.3136i | 0.545304i | ||||||||
\(896\) | 0.825905 | − | 2.51354i | 0.0275916 | − | 0.0839715i | ||||
\(897\) | 30.9482 | + | 49.9689i | 1.03333 | + | 1.66841i | ||||
\(898\) | −12.3834 | + | 21.4486i | −0.413238 | + | 0.715750i | ||||
\(899\) | 43.3649 | − | 25.0367i | 1.44630 | − | 0.835022i | ||||
\(900\) | 6.54395 | − | 0.405294i | 0.218132 | − | 0.0135098i | ||||
\(901\) | 55.0536 | + | 31.7852i | 1.83410 | + | 1.05892i | ||||
\(902\) | 3.99122i | 0.132893i | ||||||||
\(903\) | 9.11376 | − | 30.9308i | 0.303287 | − | 1.02931i | ||||
\(904\) | 11.0633 | 0.367959 | ||||||||
\(905\) | 0.854287 | − | 1.47967i | 0.0283975 | − | 0.0491859i | ||||
\(906\) | 19.4351 | + | 10.4333i | 0.645689 | + | 0.346622i | ||||
\(907\) | 18.6722 | − | 10.7804i | 0.619999 | − | 0.357957i | −0.156869 | − | 0.987619i | \(-0.550140\pi\) |
0.776869 | + | 0.629663i | \(0.216807\pi\) | |||||||
\(908\) | −4.44013 | + | 7.69054i | −0.147351 | + | 0.255219i | ||||
\(909\) | 6.67408 | + | 3.32117i | 0.221365 | + | 0.110156i | ||||
\(910\) | 18.3517 | + | 20.5177i | 0.608351 | + | 0.680156i | ||||
\(911\) | −1.77715 | −0.0588797 | −0.0294398 | − | 0.999567i | \(-0.509372\pi\) | ||||
−0.0294398 | + | 0.999567i | \(0.509372\pi\) | |||||||
\(912\) | −7.15441 | + | 2.41131i | −0.236906 | + | 0.0798463i | ||||
\(913\) | −10.0808 | − | 17.4604i | −0.333624 | − | 0.577854i | ||||
\(914\) | −15.4070 | − | 26.6857i | −0.509618 | − | 0.882685i | ||||
\(915\) | −1.17592 | − | 38.0095i | −0.0388746 | − | 1.25656i | ||||
\(916\) | −3.47056 | −0.114671 | ||||||||
\(917\) | −31.6300 | − | 10.3931i | −1.04452 | − | 0.343209i | ||||
\(918\) | −2.79419 | − | 30.0289i | −0.0922220 | − | 0.991102i | ||||
\(919\) | 17.3122 | − | 29.9856i | 0.571077 | − | 0.989134i | −0.425379 | − | 0.905015i | \(-0.639859\pi\) |
0.996456 | − | 0.0841185i | \(-0.0268074\pi\) | |||||||
\(920\) | −4.58985 | − | 7.94985i | −0.151323 | − | 0.262099i | ||||
\(921\) | 29.5420 | + | 15.8588i | 0.973441 | + | 0.522567i | ||||
\(922\) | 19.3762 | + | 11.1869i | 0.638122 | + | 0.368420i | ||||
\(923\) | − | 16.7118i | − | 0.550077i | ||||||
\(924\) | −6.25111 | + | 5.94919i | −0.205646 | + | 0.195714i | ||||
\(925\) | − | 7.67339i | − | 0.252300i | ||||||
\(926\) | −3.11779 | + | 5.40018i | −0.102457 | + | 0.177461i | ||||
\(927\) | 2.56091 | + | 41.3489i | 0.0841113 | + | 1.35808i | ||||
\(928\) | 3.45020 | + | 5.97592i | 0.113258 | + | 0.196169i | ||||
\(929\) | 1.97501 | + | 1.14027i | 0.0647980 | + | 0.0374112i | 0.532049 | − | 0.846714i | \(-0.321422\pi\) |
−0.467251 | + | 0.884125i | \(0.654756\pi\) | |||||||
\(930\) | 11.1027 | + | 17.9263i | 0.364070 | + | 0.587826i | ||||
\(931\) | −5.54707 | − | 30.0038i | −0.181798 | − | 0.983336i | ||||
\(932\) | − | 0.868941i | − | 0.0284631i | ||||||
\(933\) | 1.41113 | + | 45.6124i | 0.0461984 | + | 1.49328i | ||||
\(934\) | 20.4308 | − | 11.7957i | 0.668517 | − | 0.385968i | ||||
\(935\) | −15.8796 | + | 9.16811i | −0.519319 | + | 0.299829i | ||||
\(936\) | 15.5068 | − | 10.2809i | 0.506856 | − | 0.336041i | ||||
\(937\) | 53.3235 | 1.74200 | 0.871001 | − | 0.491281i | \(-0.163471\pi\) | ||||
0.871001 | + | 0.491281i | \(0.163471\pi\) | |||||||
\(938\) | −3.35430 | − | 16.0416i | −0.109522 | − | 0.523777i | ||||
\(939\) | 9.81898 | + | 15.8537i | 0.320430 | + | 0.517365i | ||||
\(940\) | 3.12918 | − | 5.41989i | 0.102062 | − | 0.176777i | ||||
\(941\) | −25.9239 | − | 44.9016i | −0.845096 | − | 1.46375i | −0.885537 | − | 0.464568i | \(-0.846210\pi\) |
0.0404409 | − | 0.999182i | \(-0.487124\pi\) | |||||||
\(942\) | 14.4541 | − | 26.9253i | 0.470941 | − | 0.877273i | ||||
\(943\) | −10.0435 | − | 5.79861i | −0.327061 | − | 0.188829i | ||||
\(944\) | 13.2654 | 0.431751 | ||||||||
\(945\) | −22.4841 | − | 5.13863i | −0.731409 | − | 0.167160i | ||||
\(946\) | 13.2507i | 0.430818i | ||||||||
\(947\) | 10.0954 | + | 5.82859i | 0.328057 | + | 0.189404i | 0.654978 | − | 0.755648i | \(-0.272678\pi\) |
−0.326921 | + | 0.945052i | \(0.606011\pi\) | |||||||
\(948\) | −7.58324 | − | 4.07087i | −0.246292 | − | 0.132216i | ||||
\(949\) | −15.3146 | + | 8.84186i | −0.497131 | + | 0.287019i | ||||
\(950\) | 2.16665 | − | 9.27669i | 0.0702954 | − | 0.300976i | ||||
\(951\) | 0.735951 | + | 1.18826i | 0.0238648 | + | 0.0385321i | ||||
\(952\) | 11.4457 | − | 10.2374i | 0.370957 | − | 0.331795i | ||||
\(953\) | −10.3944 | −0.336707 | −0.168354 | − | 0.985727i | \(-0.553845\pi\) | ||||
−0.168354 | + | 0.985727i | \(0.553845\pi\) | |||||||
\(954\) | −18.1568 | − | 27.3862i | −0.587849 | − | 0.886662i | ||||
\(955\) | −6.57402 | − | 11.3865i | −0.212730 | − | 0.368460i | ||||
\(956\) | −9.98985 | + | 5.76764i | −0.323095 | + | 0.186539i | ||||
\(957\) | −0.695970 | − | 22.4960i | −0.0224975 | − | 0.727194i | ||||
\(958\) | − | 19.2856i | − | 0.623090i | ||||||
\(959\) | 34.5991 | − | 30.9465i | 1.11726 | − | 0.999314i | ||||
\(960\) | −2.47034 | + | 1.53001i | −0.0797300 | + | 0.0493808i | ||||
\(961\) | 10.8291 | − | 18.7566i | 0.349327 | − | 0.605051i | ||||
\(962\) | −10.8874 | − | 18.8575i | −0.351023 | − | 0.607990i | ||||
\(963\) | 20.2170 | − | 1.25213i | 0.651485 | − | 0.0403492i | ||||
\(964\) | 1.96067 | + | 1.13200i | 0.0631490 | + | 0.0364591i | ||||
\(965\) | 21.0320 | 0.677044 | ||||||||
\(966\) | −5.88865 | − | 24.3735i | −0.189464 | − | 0.784205i | ||||
\(967\) | 15.5191 | 0.499060 | 0.249530 | − | 0.968367i | \(-0.419724\pi\) | ||||
0.249530 | + | 0.968367i | \(0.419724\pi\) | |||||||
\(968\) | −3.72692 | + | 6.45522i | −0.119788 | + | 0.207479i | ||||
\(969\) | −42.9589 | − | 8.64193i | −1.38004 | − | 0.277619i | ||||
\(970\) | −9.52987 | − | 16.5062i | −0.305986 | − | 0.529983i | ||||
\(971\) | 26.5466 | − | 45.9801i | 0.851922 | − | 1.47557i | −0.0275491 | − | 0.999620i | \(-0.508770\pi\) |
0.879471 | − | 0.475952i | \(-0.157896\pi\) | |||||||
\(972\) | −5.62192 | + | 14.5394i | −0.180323 | + | 0.466351i | ||||
\(973\) | −35.4223 | + | 7.40680i | −1.13559 | + | 0.237451i | ||||
\(974\) | 15.2426i | 0.488404i | ||||||||
\(975\) | 0.725944 | + | 23.4649i | 0.0232488 | + | 0.751478i | ||||
\(976\) | −6.54347 | − | 11.3336i | −0.209452 | − | 0.362781i | ||||
\(977\) | −12.2250 | − | 21.1743i | −0.391112 | − | 0.677426i | 0.601484 | − | 0.798884i | \(-0.294576\pi\) |
−0.992596 | + | 0.121459i | \(0.961243\pi\) | |||||||
\(978\) | 31.5965 | − | 0.977516i | 1.01035 | − | 0.0312575i | ||||
\(979\) | 12.4350i | 0.397425i | ||||||||
\(980\) | −4.70542 | − | 10.7596i | −0.150309 | − | 0.343704i | ||||
\(981\) | −3.69761 | − | 1.84001i | −0.118056 | − | 0.0587471i | ||||
\(982\) | −27.5747 | − | 15.9203i | −0.879944 | − | 0.508036i | ||||
\(983\) | 25.1696 | + | 43.5949i | 0.802784 | + | 1.39046i | 0.917777 | + | 0.397096i | \(0.129982\pi\) |
−0.114993 | + | 0.993366i | \(0.536685\pi\) | |||||||
\(984\) | −1.73632 | + | 3.23444i | −0.0553520 | + | 0.103110i | ||||
\(985\) | 1.54636 | − | 2.67838i | 0.0492712 | − | 0.0853403i | ||||
\(986\) | 40.0502i | 1.27546i | ||||||||
\(987\) | 12.3833 | − | 11.7852i | 0.394165 | − | 0.375128i | ||||
\(988\) | −7.83764 | − | 25.8718i | −0.249348 | − | 0.823091i | ||||
\(989\) | −33.3440 | − | 19.2512i | −1.06028 | − | 0.612152i | ||||
\(990\) | 9.45954 | − | 0.585869i | 0.300644 | − | 0.0186201i | ||||
\(991\) | 34.8170 | − | 20.1016i | 1.10600 | − | 0.638549i | 0.168208 | − | 0.985751i | \(-0.446202\pi\) |
0.937790 | + | 0.347203i | \(0.112868\pi\) | |||||||
\(992\) | 6.28440 | + | 3.62830i | 0.199530 | + | 0.115199i | ||||
\(993\) | 15.5352 | − | 9.62175i | 0.492996 | − | 0.305337i | ||||
\(994\) | −2.22555 | + | 6.77320i | −0.0705903 | + | 0.214833i | ||||
\(995\) | − | 27.6419i | − | 0.876306i | ||||||
\(996\) | −0.573432 | − | 18.5352i | −0.0181699 | − | 0.587310i | ||||
\(997\) | −7.71246 | − | 13.3584i | −0.244256 | − | 0.423064i | 0.717666 | − | 0.696387i | \(-0.245210\pi\) |
−0.961922 | + | 0.273323i | \(0.911877\pi\) | |||||||
\(998\) | −10.9039 | − | 18.8860i | −0.345155 | − | 0.597827i | ||||
\(999\) | 16.5769 | + | 7.61891i | 0.524471 | + | 0.241052i |
(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 | 798.2.bf.a.569.10 | ✓ | 52 | |
3.2 | odd | 2 | 798.2.bf.b.569.1 | yes | 52 | ||
7.4 | even | 3 | inner | 798.2.bf.a.683.26 | yes | 52 | |
19.18 | odd | 2 | 798.2.bf.b.569.17 | yes | 52 | ||
21.11 | odd | 6 | 798.2.bf.b.683.17 | yes | 52 | ||
57.56 | even | 2 | inner | 798.2.bf.a.569.26 | yes | 52 | |
133.18 | odd | 6 | 798.2.bf.b.683.1 | yes | 52 | ||
399.284 | even | 6 | inner | 798.2.bf.a.683.10 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
798.2.bf.a.569.10 | ✓ | 52 | 1.1 | even | 1 | trivial | |
798.2.bf.a.569.26 | yes | 52 | 57.56 | even | 2 | inner | |
798.2.bf.a.683.10 | yes | 52 | 399.284 | even | 6 | inner | |
798.2.bf.a.683.26 | yes | 52 | 7.4 | even | 3 | inner | |
798.2.bf.b.569.1 | yes | 52 | 3.2 | odd | 2 | ||
798.2.bf.b.569.17 | yes | 52 | 19.18 | odd | 2 | ||
798.2.bf.b.683.1 | yes | 52 | 133.18 | odd | 6 | ||
798.2.bf.b.683.17 | yes | 52 | 21.11 | odd | 6 |