Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(135,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("731.135");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.j (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(128\) |
Relative dimension: | \(64\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 135.6 | ||
Character | \(\chi\) | \(=\) | 731.135 |
Dual form | 731.2.j.a.509.6 |
$q$-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 \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.51145 | −1.77586 | −0.887931 | − | 0.459976i | \(-0.847858\pi\) | ||||
−0.887931 | + | 0.459976i | \(0.847858\pi\) | |||||||
\(3\) | 1.76122 | + | 1.01684i | 1.01684 | + | 0.587073i | 0.913187 | − | 0.407540i | \(-0.133613\pi\) |
0.103653 | + | 0.994614i | \(0.466947\pi\) | |||||||
\(4\) | 4.30737 | 2.15369 | ||||||||
\(5\) | −1.18626 | − | 0.684888i | −0.530512 | − | 0.306291i | 0.210713 | − | 0.977548i | \(-0.432421\pi\) |
−0.741225 | + | 0.671257i | \(0.765755\pi\) | |||||||
\(6\) | −4.42321 | − | 2.55374i | −1.80577 | − | 1.04256i | ||||
\(7\) | −3.84346 | + | 2.21902i | −1.45269 | + | 0.838711i | −0.998633 | − | 0.0522621i | \(-0.983357\pi\) |
−0.454056 | + | 0.890973i | \(0.650024\pi\) | |||||||
\(8\) | −5.79485 | −2.04879 | ||||||||
\(9\) | 0.567928 | + | 0.983681i | 0.189309 | + | 0.327894i | ||||
\(10\) | 2.97923 | + | 1.72006i | 0.942116 | + | 0.543931i | ||||
\(11\) | 5.71903i | 1.72435i | 0.506608 | + | 0.862176i | \(0.330899\pi\) | ||||
−0.506608 | + | 0.862176i | \(0.669101\pi\) | |||||||
\(12\) | 7.58623 | + | 4.37991i | 2.18996 | + | 1.26437i | ||||
\(13\) | −0.967741 | − | 1.67618i | −0.268403 | − | 0.464888i | 0.700047 | − | 0.714097i | \(-0.253163\pi\) |
−0.968450 | + | 0.249210i | \(0.919829\pi\) | |||||||
\(14\) | 9.65264 | − | 5.57296i | 2.57978 | − | 1.48944i | ||||
\(15\) | −1.39284 | − | 2.41247i | −0.359630 | − | 0.622898i | ||||
\(16\) | 5.93872 | 1.48468 | ||||||||
\(17\) | 1.23567 | + | 3.93359i | 0.299694 | + | 0.954035i | ||||
\(18\) | −1.42632 | − | 2.47046i | −0.336187 | − | 0.582294i | ||||
\(19\) | 3.28388 | − | 5.68786i | 0.753375 | − | 1.30488i | −0.192803 | − | 0.981237i | \(-0.561758\pi\) |
0.946178 | − | 0.323646i | \(-0.104909\pi\) | |||||||
\(20\) | −5.10967 | − | 2.95007i | −1.14256 | − | 0.659655i | ||||
\(21\) | −9.02556 | −1.96954 | ||||||||
\(22\) | − | 14.3631i | − | 3.06221i | ||||||
\(23\) | −3.56220 | − | 2.05664i | −0.742771 | − | 0.428839i | 0.0803052 | − | 0.996770i | \(-0.474410\pi\) |
−0.823076 | + | 0.567932i | \(0.807744\pi\) | |||||||
\(24\) | −10.2060 | − | 5.89244i | −2.08329 | − | 1.20279i | ||||
\(25\) | −1.56186 | − | 2.70522i | −0.312372 | − | 0.541043i | ||||
\(26\) | 2.43043 | + | 4.20963i | 0.476647 | + | 0.825577i | ||||
\(27\) | − | 3.79107i | − | 0.729592i | ||||||
\(28\) | −16.5552 | + | 9.55815i | −3.12864 | + | 1.80632i | ||||
\(29\) | 1.60279 | − | 0.925373i | 0.297631 | − | 0.171837i | −0.343747 | − | 0.939062i | \(-0.611696\pi\) |
0.641378 | + | 0.767225i | \(0.278363\pi\) | |||||||
\(30\) | 3.49805 | + | 6.05880i | 0.638654 | + | 1.10618i | ||||
\(31\) | −7.10692 | − | 4.10318i | −1.27644 | − | 0.736953i | −0.300248 | − | 0.953861i | \(-0.597070\pi\) |
−0.976192 | + | 0.216908i | \(0.930403\pi\) | |||||||
\(32\) | −3.32510 | −0.587800 | ||||||||
\(33\) | −5.81534 | + | 10.0725i | −1.01232 | + | 1.75339i | ||||
\(34\) | −3.10332 | − | 9.87901i | −0.532215 | − | 1.69424i | ||||
\(35\) | 6.07912 | 1.02756 | ||||||||
\(36\) | 2.44628 | + | 4.23708i | 0.407713 | + | 0.706180i | ||||
\(37\) | 0.467527 | + | 0.269927i | 0.0768610 | + | 0.0443757i | 0.537938 | − | 0.842984i | \(-0.319203\pi\) |
−0.461077 | + | 0.887360i | \(0.652537\pi\) | |||||||
\(38\) | −8.24731 | + | 14.2848i | −1.33789 | + | 2.31729i | ||||
\(39\) | − | 3.93615i | − | 0.630289i | ||||||
\(40\) | 6.87420 | + | 3.96882i | 1.08691 | + | 0.627526i | ||||
\(41\) | − | 3.51693i | − | 0.549253i | −0.961551 | − | 0.274626i | \(-0.911446\pi\) | ||
0.961551 | − | 0.274626i | \(-0.0885541\pi\) | |||||||
\(42\) | 22.6672 | 3.49763 | ||||||||
\(43\) | 4.98908 | − | 4.25548i | 0.760827 | − | 0.648955i | ||||
\(44\) | 24.6340i | 3.71372i | ||||||||
\(45\) | − | 1.55587i | − | 0.231935i | ||||||
\(46\) | 8.94629 | + | 5.16514i | 1.31906 | + | 0.761559i | ||||
\(47\) | −10.7488 | −1.56788 | −0.783939 | − | 0.620838i | \(-0.786793\pi\) | ||||
−0.783939 | + | 0.620838i | \(0.786793\pi\) | |||||||
\(48\) | 10.4594 | + | 6.03873i | 1.50968 | + | 0.871616i | ||||
\(49\) | 6.34810 | − | 10.9952i | 0.906872 | − | 1.57075i | ||||
\(50\) | 3.92253 | + | 6.79401i | 0.554729 | + | 0.960819i | ||||
\(51\) | −1.82355 | + | 8.18439i | −0.255348 | + | 1.14604i | ||||
\(52\) | −4.16842 | − | 7.21992i | −0.578056 | − | 1.00122i | ||||
\(53\) | −2.08650 | + | 3.61392i | −0.286603 | + | 0.496411i | −0.972997 | − | 0.230819i | \(-0.925859\pi\) |
0.686394 | + | 0.727230i | \(0.259193\pi\) | |||||||
\(54\) | 9.52108i | 1.29566i | ||||||||
\(55\) | 3.91689 | − | 6.78426i | 0.528154 | − | 0.914789i | ||||
\(56\) | 22.2723 | − | 12.8589i | 2.97626 | − | 1.71834i | ||||
\(57\) | 11.5673 | − | 6.67837i | 1.53212 | − | 0.884572i | ||||
\(58\) | −4.02533 | + | 2.32403i | −0.528552 | + | 0.305160i | ||||
\(59\) | −6.09785 | −0.793872 | −0.396936 | − | 0.917846i | \(-0.629927\pi\) | ||||
−0.396936 | + | 0.917846i | \(0.629927\pi\) | |||||||
\(60\) | −5.99949 | − | 10.3914i | −0.774531 | − | 1.34153i | ||||
\(61\) | 1.58893 | − | 0.917368i | 0.203441 | − | 0.117457i | −0.394818 | − | 0.918759i | \(-0.629192\pi\) |
0.598260 | + | 0.801302i | \(0.295859\pi\) | |||||||
\(62\) | 17.8487 | + | 10.3049i | 2.26678 | + | 1.30873i | ||||
\(63\) | −4.36561 | − | 2.52049i | −0.550016 | − | 0.317552i | ||||
\(64\) | −3.52664 | −0.440830 | ||||||||
\(65\) | 2.65118i | 0.328838i | ||||||||
\(66\) | 14.6049 | − | 25.2965i | 1.79774 | − | 3.11378i | ||||
\(67\) | −7.10904 | + | 12.3132i | −0.868508 | + | 1.50430i | −0.00498622 | + | 0.999988i | \(0.501587\pi\) |
−0.863522 | + | 0.504312i | \(0.831746\pi\) | |||||||
\(68\) | 5.32249 | + | 16.9434i | 0.645447 | + | 2.05469i | ||||
\(69\) | −4.18255 | − | 7.24438i | −0.503519 | − | 0.872121i | ||||
\(70\) | −15.2674 | −1.82480 | ||||||||
\(71\) | −4.83502 | + | 2.79150i | −0.573811 | + | 0.331290i | −0.758670 | − | 0.651475i | \(-0.774151\pi\) |
0.184859 | + | 0.982765i | \(0.440817\pi\) | |||||||
\(72\) | −3.29106 | − | 5.70028i | −0.387855 | − | 0.671785i | ||||
\(73\) | −5.46456 | + | 3.15496i | −0.639578 | + | 0.369261i | −0.784452 | − | 0.620190i | \(-0.787056\pi\) |
0.144874 | + | 0.989450i | \(0.453722\pi\) | |||||||
\(74\) | −1.17417 | − | 0.677908i | −0.136495 | − | 0.0788052i | ||||
\(75\) | − | 6.35264i | − | 0.733540i | ||||||
\(76\) | 14.1449 | − | 24.4997i | 1.62253 | − | 2.81031i | ||||
\(77\) | −12.6906 | − | 21.9808i | −1.44623 | − | 2.50495i | ||||
\(78\) | 9.88544i | 1.11931i | ||||||||
\(79\) | −11.6828 | + | 6.74508i | −1.31442 | + | 0.758880i | −0.982825 | − | 0.184541i | \(-0.940920\pi\) |
−0.331595 | + | 0.943422i | \(0.607587\pi\) | |||||||
\(80\) | −7.04487 | − | 4.06736i | −0.787641 | − | 0.454744i | ||||
\(81\) | 5.55870 | − | 9.62795i | 0.617633 | − | 1.06977i | ||||
\(82\) | 8.83259i | 0.975397i | ||||||||
\(83\) | −4.69845 | + | 8.13795i | −0.515722 | + | 0.893257i | 0.484112 | + | 0.875006i | \(0.339143\pi\) |
−0.999833 | + | 0.0182503i | \(0.994190\pi\) | |||||||
\(84\) | −38.8765 | −4.24177 | ||||||||
\(85\) | 1.22824 | − | 5.51255i | 0.133221 | − | 0.597920i | ||||
\(86\) | −12.5298 | + | 10.6874i | −1.35112 | + | 1.15245i | ||||
\(87\) | 3.76383 | 0.403525 | ||||||||
\(88\) | − | 33.1409i | − | 3.53284i | ||||||
\(89\) | 8.13518 | − | 14.0905i | 0.862327 | − | 1.49359i | −0.00734982 | − | 0.999973i | \(-0.502340\pi\) |
0.869677 | − | 0.493621i | \(-0.164327\pi\) | |||||||
\(90\) | 3.90748i | 0.411885i | ||||||||
\(91\) | 7.43894 | + | 4.29487i | 0.779813 | + | 0.450225i | ||||
\(92\) | −15.3437 | − | 8.85871i | −1.59970 | − | 0.923585i | ||||
\(93\) | −8.34456 | − | 14.4532i | −0.865291 | − | 1.49873i | ||||
\(94\) | 26.9951 | 2.78434 | ||||||||
\(95\) | −7.79108 | + | 4.49818i | −0.799348 | + | 0.461504i | ||||
\(96\) | −5.85622 | − | 3.38109i | −0.597698 | − | 0.345081i | ||||
\(97\) | − | 18.8175i | − | 1.91063i | −0.295585 | − | 0.955316i | \(-0.595515\pi\) | ||
0.295585 | − | 0.955316i | \(-0.404485\pi\) | |||||||
\(98\) | −15.9429 | + | 27.6140i | −1.61048 | + | 2.78943i | ||||
\(99\) | −5.62570 | + | 3.24800i | −0.565404 | + | 0.326436i | ||||
\(100\) | −6.72751 | − | 11.6524i | −0.672751 | − | 1.16524i | ||||
\(101\) | −0.223258 | − | 0.386694i | −0.0222150 | − | 0.0384775i | 0.854704 | − | 0.519115i | \(-0.173739\pi\) |
−0.876919 | + | 0.480638i | \(0.840405\pi\) | |||||||
\(102\) | 4.57974 | − | 20.5547i | 0.453462 | − | 2.03522i | ||||
\(103\) | −1.22446 | − | 2.12083i | −0.120650 | − | 0.208971i | 0.799374 | − | 0.600833i | \(-0.205164\pi\) |
−0.920024 | + | 0.391862i | \(0.871831\pi\) | |||||||
\(104\) | 5.60792 | + | 9.71319i | 0.549901 | + | 0.952457i | ||||
\(105\) | 10.7067 | + | 6.18149i | 1.04486 | + | 0.603252i | ||||
\(106\) | 5.24014 | − | 9.07619i | 0.508967 | − | 0.881557i | ||||
\(107\) | 4.76103i | 0.460266i | 0.973159 | + | 0.230133i | \(0.0739161\pi\) | ||||
−0.973159 | + | 0.230133i | \(0.926084\pi\) | |||||||
\(108\) | − | 16.3296i | − | 1.57131i | ||||||
\(109\) | 9.19461 | + | 5.30851i | 0.880684 | + | 0.508463i | 0.870884 | − | 0.491489i | \(-0.163547\pi\) |
0.00980034 | + | 0.999952i | \(0.496880\pi\) | |||||||
\(110\) | −9.83708 | + | 17.0383i | −0.937928 | + | 1.62454i | ||||
\(111\) | 0.548945 | + | 0.950801i | 0.0521036 | + | 0.0902460i | ||||
\(112\) | −22.8252 | + | 13.1781i | −2.15678 | + | 1.24522i | ||||
\(113\) | 10.9962i | 1.03443i | 0.855854 | + | 0.517217i | \(0.173032\pi\) | ||||
−0.855854 | + | 0.517217i | \(0.826968\pi\) | |||||||
\(114\) | −29.0506 | + | 16.7724i | −2.72084 | + | 1.57088i | ||||
\(115\) | 2.81713 | + | 4.87942i | 0.262699 | + | 0.455008i | ||||
\(116\) | 6.90383 | − | 3.98593i | 0.641004 | − | 0.370084i | ||||
\(117\) | 1.09921 | − | 1.90390i | 0.101622 | − | 0.176015i | ||||
\(118\) | 15.3144 | 1.40981 | ||||||||
\(119\) | −13.4780 | − | 12.3766i | −1.23552 | − | 1.13456i | ||||
\(120\) | 8.07132 | + | 13.9799i | 0.736807 | + | 1.27619i | ||||
\(121\) | −21.7073 | −1.97339 | ||||||||
\(122\) | −3.99051 | + | 2.30392i | −0.361284 | + | 0.208587i | ||||
\(123\) | 3.57616 | − | 6.19409i | 0.322451 | − | 0.558502i | ||||
\(124\) | −30.6122 | − | 17.6739i | −2.74905 | − | 1.58717i | ||||
\(125\) | 11.1277i | 0.995289i | ||||||||
\(126\) | 10.9640 | + | 6.33008i | 0.976752 | + | 0.563928i | ||||
\(127\) | −4.14740 | −0.368022 | −0.184011 | − | 0.982924i | \(-0.558908\pi\) | ||||
−0.184011 | + | 0.982924i | \(0.558908\pi\) | |||||||
\(128\) | 15.5072 | 1.37065 | ||||||||
\(129\) | 13.1140 | − | 2.42174i | 1.15462 | − | 0.213222i | ||||
\(130\) | − | 6.65829i | − | 0.583971i | ||||||
\(131\) | − | 5.10448i | − | 0.445981i | −0.974821 | − | 0.222990i | \(-0.928418\pi\) | ||
0.974821 | − | 0.222990i | \(-0.0715819\pi\) | |||||||
\(132\) | −25.0489 | + | 43.3859i | −2.18022 | + | 3.77626i | ||||
\(133\) | 29.1480i | 2.52745i | ||||||||
\(134\) | 17.8540 | − | 30.9240i | 1.54235 | − | 2.67143i | ||||
\(135\) | −2.59646 | + | 4.49720i | −0.223468 | + | 0.387057i | ||||
\(136\) | −7.16052 | − | 22.7946i | −0.614010 | − | 1.95462i | ||||
\(137\) | −8.15290 | −0.696549 | −0.348275 | − | 0.937393i | \(-0.613232\pi\) | ||||
−0.348275 | + | 0.937393i | \(0.613232\pi\) | |||||||
\(138\) | 10.5042 | + | 18.1939i | 0.894181 | + | 1.54877i | ||||
\(139\) | 11.7337 | + | 6.77447i | 0.995242 | + | 0.574603i | 0.906837 | − | 0.421482i | \(-0.138490\pi\) |
0.0884048 | + | 0.996085i | \(0.471823\pi\) | |||||||
\(140\) | 26.1850 | 2.21304 | ||||||||
\(141\) | −18.9310 | − | 10.9298i | −1.59428 | − | 0.920459i | ||||
\(142\) | 12.1429 | − | 7.01071i | 1.01901 | − | 0.588325i | ||||
\(143\) | 9.58611 | − | 5.53454i | 0.801630 | − | 0.462822i | ||||
\(144\) | 3.37277 | + | 5.84181i | 0.281064 | + | 0.486817i | ||||
\(145\) | −2.53511 | −0.210529 | ||||||||
\(146\) | 13.7240 | − | 7.92353i | 1.13580 | − | 0.655756i | ||||
\(147\) | 22.3608 | − | 12.9100i | 1.84429 | − | 1.06480i | ||||
\(148\) | 2.01381 | + | 1.16268i | 0.165535 | + | 0.0955714i | ||||
\(149\) | 0.586861 | − | 1.01647i | 0.0480775 | − | 0.0832727i | −0.840985 | − | 0.541058i | \(-0.818024\pi\) |
0.889063 | + | 0.457785i | \(0.151357\pi\) | |||||||
\(150\) | 15.9543i | 1.30267i | ||||||||
\(151\) | 4.37075 | 0.355687 | 0.177843 | − | 0.984059i | \(-0.443088\pi\) | ||||
0.177843 | + | 0.984059i | \(0.443088\pi\) | |||||||
\(152\) | −19.0296 | + | 32.9603i | −1.54351 | + | 2.67343i | ||||
\(153\) | −3.16762 | + | 3.44950i | −0.256087 | + | 0.278876i | ||||
\(154\) | 31.8719 | + | 55.2038i | 2.56831 | + | 4.44845i | ||||
\(155\) | 5.62044 | + | 9.73488i | 0.451444 | + | 0.781924i | ||||
\(156\) | − | 16.9545i | − | 1.35744i | ||||||
\(157\) | 4.38370 | + | 7.59279i | 0.349857 | + | 0.605971i | 0.986224 | − | 0.165416i | \(-0.0528967\pi\) |
−0.636367 | + | 0.771387i | \(0.719563\pi\) | |||||||
\(158\) | 29.3408 | − | 16.9399i | 2.33423 | − | 1.34767i | ||||
\(159\) | −7.34957 | + | 4.24328i | −0.582859 | + | 0.336514i | ||||
\(160\) | 3.94443 | + | 2.27732i | 0.311835 | + | 0.180038i | ||||
\(161\) | 18.2549 | 1.43869 | ||||||||
\(162\) | −13.9604 | + | 24.1801i | −1.09683 | + | 1.89977i | ||||
\(163\) | −3.58760 | + | 2.07130i | −0.281003 | + | 0.162237i | −0.633877 | − | 0.773434i | \(-0.718538\pi\) |
0.352875 | + | 0.935671i | \(0.385204\pi\) | |||||||
\(164\) | − | 15.1487i | − | 1.18292i | ||||||
\(165\) | 13.7970 | − | 7.96571i | 1.07410 | − | 0.620130i | ||||
\(166\) | 11.7999 | − | 20.4381i | 0.915851 | − | 1.58630i | ||||
\(167\) | −2.80154 | − | 1.61747i | −0.216790 | − | 0.125164i | 0.387673 | − | 0.921797i | \(-0.373279\pi\) |
−0.604463 | + | 0.796633i | \(0.706612\pi\) | |||||||
\(168\) | 52.3018 | 4.03517 | ||||||||
\(169\) | 4.62696 | − | 8.01412i | 0.355920 | − | 0.616471i | ||||
\(170\) | −3.08466 | + | 13.8445i | −0.236583 | + | 1.06182i | ||||
\(171\) | 7.46004 | 0.570484 | ||||||||
\(172\) | 21.4898 | − | 18.3300i | 1.63858 | − | 1.39765i | ||||
\(173\) | − | 7.13873i | − | 0.542748i | −0.962474 | − | 0.271374i | \(-0.912522\pi\) | ||
0.962474 | − | 0.271374i | \(-0.0874780\pi\) | |||||||
\(174\) | −9.45266 | −0.716604 | ||||||||
\(175\) | 12.0059 | + | 6.93159i | 0.907558 | + | 0.523979i | ||||
\(176\) | 33.9637i | 2.56011i | ||||||||
\(177\) | −10.7396 | − | 6.20054i | −0.807241 | − | 0.466061i | ||||
\(178\) | −20.4311 | + | 35.3877i | −1.53137 | + | 2.65242i | ||||
\(179\) | 2.57082 | + | 4.45279i | 0.192152 | + | 0.332817i | 0.945963 | − | 0.324274i | \(-0.105120\pi\) |
−0.753811 | + | 0.657091i | \(0.771787\pi\) | |||||||
\(180\) | − | 6.70171i | − | 0.499516i | ||||||
\(181\) | 11.0474 | − | 6.37822i | 0.821147 | − | 0.474089i | −0.0296649 | − | 0.999560i | \(-0.509444\pi\) |
0.850812 | + | 0.525470i | \(0.176111\pi\) | |||||||
\(182\) | −18.6825 | − | 10.7864i | −1.38484 | − | 0.799538i | ||||
\(183\) | 3.73127 | 0.275823 | ||||||||
\(184\) | 20.6424 | + | 11.9179i | 1.52178 | + | 0.878600i | ||||
\(185\) | −0.369739 | − | 0.640407i | −0.0271838 | − | 0.0470837i | ||||
\(186\) | 20.9569 | + | 36.2985i | 1.53664 | + | 2.66153i | ||||
\(187\) | −22.4963 | + | 7.06683i | −1.64509 | + | 0.516778i | ||||
\(188\) | −46.2992 | −3.37672 | ||||||||
\(189\) | 8.41247 | + | 14.5708i | 0.611917 | + | 1.05987i | ||||
\(190\) | 19.5669 | − | 11.2970i | 1.41953 | − | 0.819567i | ||||
\(191\) | 2.78150 | − | 4.81770i | 0.201262 | − | 0.348597i | −0.747673 | − | 0.664067i | \(-0.768829\pi\) |
0.948935 | + | 0.315470i | \(0.102162\pi\) | |||||||
\(192\) | −6.21118 | − | 3.58603i | −0.448254 | − | 0.258799i | ||||
\(193\) | − | 0.578350i | − | 0.0416306i | −0.999783 | − | 0.0208153i | \(-0.993374\pi\) | ||
0.999783 | − | 0.0208153i | \(-0.00662619\pi\) | |||||||
\(194\) | 47.2593i | 3.39302i | ||||||||
\(195\) | −2.69582 | + | 4.66930i | −0.193052 | + | 0.334376i | ||||
\(196\) | 27.3437 | − | 47.3606i | 1.95312 | − | 3.38290i | ||||
\(197\) | −5.49896 | + | 3.17483i | −0.391785 | + | 0.226197i | −0.682933 | − | 0.730481i | \(-0.739296\pi\) |
0.291148 | + | 0.956678i | \(0.405963\pi\) | |||||||
\(198\) | 14.1287 | − | 8.15718i | 1.00408 | − | 0.579706i | ||||
\(199\) | − | 10.0023i | − | 0.709042i | −0.935048 | − | 0.354521i | \(-0.884644\pi\) | ||
0.935048 | − | 0.354521i | \(-0.115356\pi\) | |||||||
\(200\) | 9.05074 | + | 15.6763i | 0.639984 | + | 1.10848i | ||||
\(201\) | −25.0412 | + | 14.4575i | −1.76627 | + | 1.01975i | ||||
\(202\) | 0.560701 | + | 0.971163i | 0.0394508 | + | 0.0683308i | ||||
\(203\) | −4.10684 | + | 7.11326i | −0.288244 | + | 0.499253i | ||||
\(204\) | −7.85470 | + | 35.2532i | −0.549939 | + | 2.46822i | ||||
\(205\) | −2.40870 | + | 4.17200i | −0.168231 | + | 0.291385i | ||||
\(206\) | 3.07517 | + | 5.32635i | 0.214257 | + | 0.371104i | ||||
\(207\) | − | 4.67209i | − | 0.324733i | ||||||
\(208\) | −5.74715 | − | 9.95435i | −0.398493 | − | 0.690210i | ||||
\(209\) | 32.5290 | + | 18.7806i | 2.25008 | + | 1.29908i | ||||
\(210\) | −26.8892 | − | 15.5245i | −1.85553 | − | 1.07129i | ||||
\(211\) | 13.1262i | 0.903642i | 0.892109 | + | 0.451821i | \(0.149225\pi\) | ||||
−0.892109 | + | 0.451821i | \(0.850775\pi\) | |||||||
\(212\) | −8.98734 | + | 15.5665i | −0.617253 | + | 1.06911i | ||||
\(213\) | −11.3540 | −0.777966 | ||||||||
\(214\) | − | 11.9571i | − | 0.817369i | ||||||
\(215\) | −8.83287 | + | 1.63115i | −0.602397 | + | 0.111244i | ||||
\(216\) | 21.9687i | 1.49478i | ||||||||
\(217\) | 36.4202 | 2.47236 | ||||||||
\(218\) | −23.0918 | − | 13.3321i | −1.56397 | − | 0.902961i | ||||
\(219\) | −12.8324 | −0.867132 | ||||||||
\(220\) | 16.8715 | − | 29.2223i | 1.13748 | − | 1.97017i | ||||
\(221\) | 5.39758 | − | 5.87790i | 0.363081 | − | 0.395390i | ||||
\(222\) | −1.37865 | − | 2.38789i | −0.0925288 | − | 0.160265i | ||||
\(223\) | −13.2886 | −0.889872 | −0.444936 | − | 0.895562i | \(-0.646774\pi\) | ||||
−0.444936 | + | 0.895562i | \(0.646774\pi\) | |||||||
\(224\) | 12.7799 | − | 7.37846i | 0.853890 | − | 0.492994i | ||||
\(225\) | 1.77405 | − | 3.07274i | 0.118270 | − | 0.204849i | ||||
\(226\) | − | 27.6163i | − | 1.83701i | ||||||
\(227\) | 3.39154 | + | 1.95811i | 0.225105 | + | 0.129964i | 0.608312 | − | 0.793698i | \(-0.291847\pi\) |
−0.383207 | + | 0.923662i | \(0.625180\pi\) | |||||||
\(228\) | 49.8246 | − | 28.7662i | 3.29971 | − | 1.90509i | ||||
\(229\) | 2.79328 | + | 4.83811i | 0.184585 | + | 0.319711i | 0.943437 | − | 0.331553i | \(-0.107572\pi\) |
−0.758851 | + | 0.651264i | \(0.774239\pi\) | |||||||
\(230\) | −7.07508 | − | 12.2544i | −0.466517 | − | 0.808031i | ||||
\(231\) | − | 51.6174i | − | 3.39618i | ||||||
\(232\) | −9.28795 | + | 5.36240i | −0.609784 | + | 0.352059i | ||||
\(233\) | −9.70656 | + | 5.60409i | −0.635898 | + | 0.367136i | −0.783033 | − | 0.621981i | \(-0.786328\pi\) |
0.147135 | + | 0.989116i | \(0.452995\pi\) | |||||||
\(234\) | −2.76062 | + | 4.78154i | −0.180467 | + | 0.312579i | ||||
\(235\) | 12.7509 | + | 7.36174i | 0.831778 | + | 0.480227i | ||||
\(236\) | −26.2657 | −1.70975 | ||||||||
\(237\) | −27.4347 | −1.78207 | ||||||||
\(238\) | 33.8492 | + | 31.0832i | 2.19412 | + | 2.01482i | ||||
\(239\) | −13.4872 | + | 23.3605i | −0.872413 | + | 1.51106i | −0.0129202 | + | 0.999917i | \(0.504113\pi\) |
−0.859493 | + | 0.511148i | \(0.829221\pi\) | |||||||
\(240\) | −8.27171 | − | 14.3270i | −0.533936 | − | 0.924805i | ||||
\(241\) | 5.97009 | − | 3.44683i | 0.384567 | − | 0.222030i | −0.295236 | − | 0.955424i | \(-0.595398\pi\) |
0.679804 | + | 0.733394i | \(0.262065\pi\) | |||||||
\(242\) | 54.5168 | 3.50447 | ||||||||
\(243\) | 9.73068 | − | 5.61801i | 0.624223 | − | 0.360396i | ||||
\(244\) | 6.84411 | − | 3.95145i | 0.438149 | − | 0.252965i | ||||
\(245\) | −15.0610 | + | 8.69547i | −0.962212 | + | 0.555533i | ||||
\(246\) | −8.98134 | + | 15.5561i | −0.572629 | + | 0.991823i | ||||
\(247\) | −12.7118 | −0.808832 | ||||||||
\(248\) | 41.1835 | + | 23.7773i | 2.61516 | + | 1.50986i | ||||
\(249\) | −16.5500 | + | 9.55515i | −1.04881 | + | 0.605533i | ||||
\(250\) | − | 27.9466i | − | 1.76750i | ||||||
\(251\) | −12.1298 | − | 21.0095i | −0.765629 | − | 1.32611i | −0.939913 | − | 0.341413i | \(-0.889094\pi\) |
0.174284 | − | 0.984695i | \(-0.444239\pi\) | |||||||
\(252\) | −18.8043 | − | 10.8567i | −1.18456 | − | 0.683907i | ||||
\(253\) | 11.7620 | − | 20.3723i | 0.739469 | − | 1.28080i | ||||
\(254\) | 10.4160 | 0.653556 | ||||||||
\(255\) | 7.76859 | − | 8.45989i | 0.486488 | − | 0.529779i | ||||
\(256\) | −31.8922 | −1.99326 | ||||||||
\(257\) | 1.53014 | 0.0954475 | 0.0477237 | − | 0.998861i | \(-0.484803\pi\) | ||||
0.0477237 | + | 0.998861i | \(0.484803\pi\) | |||||||
\(258\) | −32.9351 | + | 6.08208i | −2.05045 | + | 0.378654i | ||||
\(259\) | −2.39589 | −0.148874 | ||||||||
\(260\) | 11.4196i | 0.708214i | ||||||||
\(261\) | 1.82054 | + | 1.05109i | 0.112689 | + | 0.0650609i | ||||
\(262\) | 12.8196i | 0.792001i | ||||||||
\(263\) | 6.75217 | − | 11.6951i | 0.416357 | − | 0.721151i | −0.579213 | − | 0.815176i | \(-0.696640\pi\) |
0.995570 | + | 0.0940254i | \(0.0299735\pi\) | |||||||
\(264\) | 33.6990 | − | 58.3684i | 2.07403 | − | 3.59233i | ||||
\(265\) | 4.95026 | − | 2.85804i | 0.304092 | − | 0.175568i | ||||
\(266\) | − | 73.2038i | − | 4.48841i | ||||||
\(267\) | 28.6557 | − | 16.5444i | 1.75370 | − | 1.01250i | ||||
\(268\) | −30.6213 | + | 53.0377i | −1.87049 | + | 3.23979i | ||||
\(269\) | 9.71634i | 0.592416i | 0.955124 | + | 0.296208i | \(0.0957221\pi\) | ||||
−0.955124 | + | 0.296208i | \(0.904278\pi\) | |||||||
\(270\) | 6.52087 | − | 11.2945i | 0.396848 | − | 0.687360i | ||||
\(271\) | 14.0264 | + | 24.2944i | 0.852042 | + | 1.47578i | 0.879363 | + | 0.476153i | \(0.157969\pi\) |
−0.0273211 | + | 0.999627i | \(0.508698\pi\) | |||||||
\(272\) | 7.33830 | + | 23.3605i | 0.444950 | + | 1.41644i | ||||
\(273\) | 8.73440 | + | 15.1284i | 0.528630 | + | 0.915614i | ||||
\(274\) | 20.4756 | 1.23698 | ||||||||
\(275\) | 15.4712 | − | 8.93231i | 0.932950 | − | 0.538639i | ||||
\(276\) | −18.0158 | − | 31.2043i | −1.08442 | − | 1.87828i | ||||
\(277\) | −19.5223 | − | 11.2712i | −1.17298 | − | 0.677222i | −0.218601 | − | 0.975814i | \(-0.570149\pi\) |
−0.954381 | + | 0.298593i | \(0.903483\pi\) | |||||||
\(278\) | −29.4687 | − | 17.0137i | −1.76741 | − | 1.02042i | ||||
\(279\) | − | 9.32125i | − | 0.558049i | ||||||
\(280\) | −35.2276 | −2.10525 | ||||||||
\(281\) | −7.71795 | + | 13.3679i | −0.460414 | + | 0.797461i | −0.998981 | − | 0.0451218i | \(-0.985632\pi\) |
0.538567 | + | 0.842582i | \(0.318966\pi\) | |||||||
\(282\) | 47.5444 | + | 27.4497i | 2.83123 | + | 1.63461i | ||||
\(283\) | −25.7997 | + | 14.8955i | −1.53364 | + | 0.885445i | −0.534446 | + | 0.845203i | \(0.679480\pi\) |
−0.999190 | + | 0.0402423i | \(0.987187\pi\) | |||||||
\(284\) | −20.8262 | + | 12.0240i | −1.23581 | + | 0.713495i | ||||
\(285\) | −18.2957 | −1.08375 | ||||||||
\(286\) | −24.0750 | + | 13.8997i | −1.42359 | + | 0.821907i | ||||
\(287\) | 7.80414 | + | 13.5172i | 0.460664 | + | 0.797894i | ||||
\(288\) | −1.88842 | − | 3.27083i | −0.111276 | − | 0.192736i | ||||
\(289\) | −13.9462 | + | 9.72123i | −0.820367 | + | 0.571837i | ||||
\(290\) | 6.36679 | 0.373871 | ||||||||
\(291\) | 19.1344 | − | 33.1418i | 1.12168 | − | 1.94281i | ||||
\(292\) | −23.5379 | + | 13.5896i | −1.37745 | + | 0.795272i | ||||
\(293\) | −14.1121 | −0.824440 | −0.412220 | − | 0.911084i | \(-0.635247\pi\) | ||||
−0.412220 | + | 0.911084i | \(0.635247\pi\) | |||||||
\(294\) | −56.1580 | + | 32.4228i | −3.27520 | + | 1.89094i | ||||
\(295\) | 7.23363 | + | 4.17634i | 0.421158 | + | 0.243156i | ||||
\(296\) | −2.70925 | − | 1.56419i | −0.157472 | − | 0.0909165i | ||||
\(297\) | 21.6813 | 1.25807 | ||||||||
\(298\) | −1.47387 | + | 2.55282i | −0.0853791 | + | 0.147881i | ||||
\(299\) | 7.96117i | 0.460407i | ||||||||
\(300\) | − | 27.3632i | − | 1.57982i | ||||||
\(301\) | −9.73229 | + | 27.4266i | −0.560960 | + | 1.58084i | ||||
\(302\) | −10.9769 | −0.631650 | ||||||||
\(303\) | − | 0.908071i | − | 0.0521673i | ||||||
\(304\) | 19.5021 | − | 33.7786i | 1.11852 | − | 1.93734i | ||||
\(305\) | −2.51318 | −0.143904 | ||||||||
\(306\) | 7.95532 | − | 8.66324i | 0.454776 | − | 0.495245i | ||||
\(307\) | 8.07909 | − | 13.9934i | 0.461098 | − | 0.798646i | −0.537918 | − | 0.842997i | \(-0.680789\pi\) |
0.999016 | + | 0.0443517i | \(0.0141222\pi\) | |||||||
\(308\) | −54.6634 | − | 94.6797i | −3.11473 | − | 5.39488i | ||||
\(309\) | − | 4.98032i | − | 0.283320i | ||||||
\(310\) | −14.1154 | − | 24.4487i | −0.801703 | − | 1.38859i | ||||
\(311\) | −15.8950 | − | 9.17695i | −0.901320 | − | 0.520377i | −0.0236918 | − | 0.999719i | \(-0.507542\pi\) |
−0.877628 | + | 0.479342i | \(0.840875\pi\) | |||||||
\(312\) | 22.8094i | 1.29133i | ||||||||
\(313\) | 2.33614 | + | 1.34877i | 0.132046 | + | 0.0762370i | 0.564568 | − | 0.825387i | \(-0.309043\pi\) |
−0.432522 | + | 0.901624i | \(0.642376\pi\) | |||||||
\(314\) | −11.0094 | − | 19.0689i | −0.621298 | − | 1.07612i | ||||
\(315\) | 3.45250 | + | 5.97991i | 0.194527 | + | 0.336930i | ||||
\(316\) | −50.3223 | + | 29.0536i | −2.83085 | + | 1.63439i | ||||
\(317\) | 14.9707i | 0.840835i | 0.907331 | + | 0.420418i | \(0.138116\pi\) | ||||
−0.907331 | + | 0.420418i | \(0.861884\pi\) | |||||||
\(318\) | 18.4581 | − | 10.6568i | 1.03508 | − | 0.597602i | ||||
\(319\) | 5.29224 | + | 9.16642i | 0.296308 | + | 0.513221i | ||||
\(320\) | 4.18351 | + | 2.41535i | 0.233865 | + | 0.135022i | ||||
\(321\) | −4.84121 | + | 8.38521i | −0.270210 | + | 0.468017i | ||||
\(322\) | −45.8462 | −2.55491 | ||||||||
\(323\) | 26.4315 | + | 5.88914i | 1.47069 | + | 0.327681i | ||||
\(324\) | 23.9434 | − | 41.4712i | 1.33019 | − | 2.30395i | ||||
\(325\) | −3.02295 | + | 5.23590i | −0.167683 | + | 0.290435i | ||||
\(326\) | 9.01007 | − | 5.20197i | 0.499022 | − | 0.288110i | ||||
\(327\) | 10.7958 | + | 18.6989i | 0.597010 | + | 1.03405i | ||||
\(328\) | 20.3801i | 1.12530i | ||||||||
\(329\) | 41.3127 | − | 23.8519i | 2.27764 | − | 1.31500i | ||||
\(330\) | −34.6505 | + | 20.0055i | −1.90745 | + | 1.10126i | ||||
\(331\) | 2.62803 | + | 4.55188i | 0.144449 | + | 0.250194i | 0.929167 | − | 0.369659i | \(-0.120526\pi\) |
−0.784718 | + | 0.619853i | \(0.787192\pi\) | |||||||
\(332\) | −20.2380 | + | 35.0532i | −1.11070 | + | 1.92380i | ||||
\(333\) | 0.613196i | 0.0336030i | ||||||||
\(334\) | 7.03593 | + | 4.06219i | 0.384989 | + | 0.222273i | ||||
\(335\) | 16.8663 | − | 9.73779i | 0.921507 | − | 0.532032i | ||||
\(336\) | −53.6003 | −2.92414 | ||||||||
\(337\) | 19.8729 | − | 11.4736i | 1.08255 | − | 0.625008i | 0.150964 | − | 0.988539i | \(-0.451762\pi\) |
0.931582 | + | 0.363531i | \(0.118429\pi\) | |||||||
\(338\) | −11.6204 | + | 20.1271i | −0.632064 | + | 1.09477i | ||||
\(339\) | −11.1814 | + | 19.3667i | −0.607288 | + | 1.05185i | ||||
\(340\) | 5.29049 | − | 23.7446i | 0.286917 | − | 1.28773i | ||||
\(341\) | 23.4662 | − | 40.6447i | 1.27077 | − | 2.20103i | ||||
\(342\) | −18.7355 | −1.01310 | ||||||||
\(343\) | 25.2800i | 1.36499i | ||||||||
\(344\) | −28.9110 | + | 24.6599i | −1.55877 | + | 1.32957i | ||||
\(345\) | 11.4583i | 0.616894i | ||||||||
\(346\) | 17.9286i | 0.963846i | ||||||||
\(347\) | 12.0411 | + | 6.95194i | 0.646401 | + | 0.373200i | 0.787076 | − | 0.616856i | \(-0.211594\pi\) |
−0.140675 | + | 0.990056i | \(0.544927\pi\) | |||||||
\(348\) | 16.2122 | 0.869066 | ||||||||
\(349\) | −14.8500 | + | 25.7210i | −0.794905 | + | 1.37682i | 0.127995 | + | 0.991775i | \(0.459146\pi\) |
−0.922900 | + | 0.385041i | \(0.874187\pi\) | |||||||
\(350\) | −30.1521 | − | 17.4083i | −1.61170 | − | 0.930514i | ||||
\(351\) | −6.35451 | + | 3.66878i | −0.339178 | + | 0.195825i | ||||
\(352\) | − | 19.0163i | − | 1.01357i | ||||||
\(353\) | 2.32936 | + | 4.03456i | 0.123979 | + | 0.214738i | 0.921333 | − | 0.388773i | \(-0.127101\pi\) |
−0.797354 | + | 0.603511i | \(0.793768\pi\) | |||||||
\(354\) | 26.9721 | + | 15.5723i | 1.43355 | + | 0.827660i | ||||
\(355\) | 7.64745 | 0.405885 | ||||||||
\(356\) | 35.0413 | − | 60.6932i | 1.85718 | − | 3.21673i | ||||
\(357\) | −11.1526 | − | 35.5028i | −0.590259 | − | 1.87901i | ||||
\(358\) | −6.45649 | − | 11.1830i | −0.341236 | − | 0.591038i | ||||
\(359\) | 1.62902 | + | 2.82155i | 0.0859766 | + | 0.148916i | 0.905807 | − | 0.423691i | \(-0.139266\pi\) |
−0.819830 | + | 0.572606i | \(0.805932\pi\) | |||||||
\(360\) | 9.01603i | 0.475186i | ||||||||
\(361\) | −12.0678 | − | 20.9020i | −0.635147 | − | 1.10011i | ||||
\(362\) | −27.7450 | + | 16.0186i | −1.45824 | + | 0.841918i | ||||
\(363\) | −38.2313 | − | 22.0729i | −2.00662 | − | 1.15853i | ||||
\(364\) | 32.0423 | + | 18.4996i | 1.67947 | + | 0.969644i | ||||
\(365\) | 8.64318 | 0.452405 | ||||||||
\(366\) | −9.37088 | −0.489824 | ||||||||
\(367\) | −20.2158 | − | 11.6716i | −1.05526 | − | 0.609253i | −0.131141 | − | 0.991364i | \(-0.541864\pi\) |
−0.924117 | + | 0.382111i | \(0.875197\pi\) | |||||||
\(368\) | −21.1549 | − | 12.2138i | −1.10278 | − | 0.636689i | ||||
\(369\) | 3.45954 | − | 1.99737i | 0.180096 | − | 0.103979i | ||||
\(370\) | 0.928581 | + | 1.60835i | 0.0482746 | + | 0.0836141i | ||||
\(371\) | − | 18.5199i | − | 0.961508i | ||||||
\(372\) | −35.9431 | − | 62.2554i | −1.86357 | − | 3.22779i | ||||
\(373\) | −1.92466 | − | 3.33361i | −0.0996550 | − | 0.172608i | 0.811887 | − | 0.583815i | \(-0.198441\pi\) |
−0.911542 | + | 0.411207i | \(0.865107\pi\) | |||||||
\(374\) | 56.4983 | − | 17.7480i | 2.92146 | − | 0.917727i | ||||
\(375\) | −11.3151 | + | 19.5983i | −0.584307 | + | 1.01205i | ||||
\(376\) | 62.2879 | 3.21225 | ||||||||
\(377\) | −3.10218 | − | 1.79104i | −0.159770 | − | 0.0922434i | ||||
\(378\) | −21.1275 | − | 36.5939i | −1.08668 | − | 1.88219i | ||||
\(379\) | 0.0120364i | 0.000618270i | 1.00000 | 0.000309135i | \(9.84007e-5\pi\) | |||||
−1.00000 | 0.000309135i | \(0.999902\pi\) | ||||||||
\(380\) | −33.5591 | + | 19.3754i | −1.72155 | + | 0.993935i | ||||
\(381\) | −7.30447 | − | 4.21724i | −0.374220 | − | 0.216056i | ||||
\(382\) | −6.98560 | + | 12.0994i | −0.357414 | + | 0.619060i | ||||
\(383\) | 34.3781 | 1.75664 | 0.878320 | − | 0.478073i | \(-0.158665\pi\) | ||||
0.878320 | + | 0.478073i | \(0.158665\pi\) | |||||||
\(384\) | 27.3115 | + | 15.7683i | 1.39373 | + | 0.804673i | ||||
\(385\) | 34.7667i | 1.77187i | ||||||||
\(386\) | 1.45250i | 0.0739302i | ||||||||
\(387\) | 7.01947 | + | 2.49085i | 0.356820 | + | 0.126617i | ||||
\(388\) | − | 81.0542i | − | 4.11490i | ||||||
\(389\) | 22.0169 | 1.11630 | 0.558150 | − | 0.829740i | \(-0.311512\pi\) | ||||
0.558150 | + | 0.829740i | \(0.311512\pi\) | |||||||
\(390\) | 6.77042 | − | 11.7267i | 0.342833 | − | 0.593805i | ||||
\(391\) | 3.68826 | − | 16.5536i | 0.186524 | − | 0.837150i | ||||
\(392\) | −36.7863 | + | 63.7158i | −1.85799 | + | 3.21813i | ||||
\(393\) | 5.19044 | − | 8.99011i | 0.261823 | − | 0.453491i | ||||
\(394\) | 13.8104 | − | 7.97341i | 0.695756 | − | 0.401695i | ||||
\(395\) | 18.4785 | 0.929753 | ||||||||
\(396\) | −24.2320 | + | 13.9903i | −1.21770 | + | 0.703042i | ||||
\(397\) | 17.7075 | + | 10.2234i | 0.888715 | + | 0.513100i | 0.873522 | − | 0.486785i | \(-0.161830\pi\) |
0.0151930 | + | 0.999885i | \(0.495164\pi\) | |||||||
\(398\) | 25.1202i | 1.25916i | ||||||||
\(399\) | −29.6389 | + | 51.3361i | −1.48380 | + | 2.57002i | ||||
\(400\) | −9.27544 | − | 16.0655i | −0.463772 | − | 0.803277i | ||||
\(401\) | −1.42805 | + | 0.824485i | −0.0713134 | + | 0.0411728i | −0.535233 | − | 0.844705i | \(-0.679776\pi\) |
0.463919 | + | 0.885877i | \(0.346443\pi\) | |||||||
\(402\) | 62.8896 | − | 36.3093i | 3.13665 | − | 1.81094i | ||||
\(403\) | 15.8833i | 0.791202i | ||||||||
\(404\) | −0.961656 | − | 1.66564i | −0.0478442 | − | 0.0828686i | ||||
\(405\) | −13.1881 | + | 7.61417i | −0.655323 | + | 0.378351i | ||||
\(406\) | 10.3141 | − | 17.8646i | 0.511881 | − | 0.886605i | ||||
\(407\) | −1.54372 | + | 2.67380i | −0.0765194 | + | 0.132535i | ||||
\(408\) | 10.5672 | − | 47.4273i | 0.523153 | − | 2.34800i | ||||
\(409\) | −30.2220 | −1.49438 | −0.747191 | − | 0.664609i | \(-0.768598\pi\) | ||||
−0.747191 | + | 0.664609i | \(0.768598\pi\) | |||||||
\(410\) | 6.04933 | − | 10.4778i | 0.298755 | − | 0.517459i | ||||
\(411\) | −14.3590 | − | 8.29020i | −0.708280 | − | 0.408925i | ||||
\(412\) | −5.27421 | − | 9.13519i | −0.259841 | − | 0.450059i | ||||
\(413\) | 23.4368 | − | 13.5312i | 1.15325 | − | 0.665829i | ||||
\(414\) | 11.7337i | 0.576681i | ||||||||
\(415\) | 11.1472 | − | 6.43582i | 0.547193 | − | 0.315922i | ||||
\(416\) | 3.21783 | + | 5.57345i | 0.157767 | + | 0.273261i | ||||
\(417\) | 13.7771 | + | 23.8627i | 0.674668 | + | 1.16856i | ||||
\(418\) | −81.6950 | − | 47.1666i | −3.99583 | − | 2.30699i | ||||
\(419\) | − | 4.37648i | − | 0.213805i | −0.994270 | − | 0.106902i | \(-0.965907\pi\) | ||
0.994270 | − | 0.106902i | \(-0.0340933\pi\) | |||||||
\(420\) | 46.1176 | + | 26.6260i | 2.25031 | + | 1.29922i | ||||
\(421\) | 4.11951 | + | 7.13520i | 0.200773 | + | 0.347749i | 0.948778 | − | 0.315945i | \(-0.102321\pi\) |
−0.748005 | + | 0.663693i | \(0.768988\pi\) | |||||||
\(422\) | − | 32.9657i | − | 1.60474i | ||||||
\(423\) | −6.10457 | − | 10.5734i | −0.296814 | − | 0.514097i | ||||
\(424\) | 12.0910 | − | 20.9422i | 0.587189 | − | 1.01704i | ||||
\(425\) | 8.71127 | − | 9.48646i | 0.422559 | − | 0.460161i | ||||
\(426\) | 28.5151 | 1.38156 | ||||||||
\(427\) | −4.07132 | + | 7.05173i | −0.197025 | + | 0.341257i | ||||
\(428\) | 20.5075i | 0.991269i | ||||||||
\(429\) | 22.5110 | 1.08684 | ||||||||
\(430\) | 22.1833 | − | 4.09655i | 1.06977 | − | 0.197553i | ||||
\(431\) | − | 15.6456i | − | 0.753621i | −0.926290 | − | 0.376810i | \(-0.877021\pi\) | ||
0.926290 | − | 0.376810i | \(-0.122979\pi\) | |||||||
\(432\) | − | 22.5141i | − | 1.08321i | ||||||
\(433\) | −14.9478 | + | 25.8904i | −0.718347 | + | 1.24421i | 0.243307 | + | 0.969949i | \(0.421768\pi\) |
−0.961654 | + | 0.274265i | \(0.911566\pi\) | |||||||
\(434\) | −91.4674 | −4.39058 | ||||||||
\(435\) | −4.46488 | − | 2.57780i | −0.214074 | − | 0.123596i | ||||
\(436\) | 39.6046 | + | 22.8658i | 1.89672 | + | 1.09507i | ||||
\(437\) | −23.3957 | + | 13.5075i | −1.11917 | + | 0.646153i | ||||
\(438\) | 32.2279 | 1.53991 | ||||||||
\(439\) | 8.11746 | − | 4.68662i | 0.387425 | − | 0.223680i | −0.293619 | − | 0.955923i | \(-0.594860\pi\) |
0.681044 | + | 0.732242i | \(0.261526\pi\) | |||||||
\(440\) | −22.6978 | + | 39.3138i | −1.08208 | + | 1.87421i | ||||
\(441\) | 14.4211 | 0.686718 | ||||||||
\(442\) | −13.5557 | + | 14.7620i | −0.644781 | + | 0.702158i | ||||
\(443\) | 0.638830 | + | 1.10649i | 0.0303517 | + | 0.0525707i | 0.880802 | − | 0.473484i | \(-0.157004\pi\) |
−0.850451 | + | 0.526055i | \(0.823671\pi\) | |||||||
\(444\) | 2.36451 | + | 4.09545i | 0.112215 | + | 0.194362i | ||||
\(445\) | −19.3009 | + | 11.1434i | −0.914949 | + | 0.528246i | ||||
\(446\) | 33.3737 | 1.58029 | ||||||||
\(447\) | 2.06718 | − | 1.19349i | 0.0977743 | − | 0.0564500i | ||||
\(448\) | 13.5545 | − | 7.82568i | 0.640389 | − | 0.369729i | ||||
\(449\) | −18.8811 | − | 10.9010i | −0.891057 | − | 0.514452i | −0.0167686 | − | 0.999859i | \(-0.505338\pi\) |
−0.874288 | + | 0.485408i | \(0.838671\pi\) | |||||||
\(450\) | −4.45543 | + | 7.71703i | −0.210031 | + | 0.363784i | ||||
\(451\) | 20.1134 | 0.947105 | ||||||||
\(452\) | 47.3647i | 2.22785i | ||||||||
\(453\) | 7.69785 | + | 4.44436i | 0.361676 | + | 0.208814i | ||||
\(454\) | −8.51768 | − | 4.91769i | −0.399755 | − | 0.230798i | ||||
\(455\) | −5.88301 | − | 10.1897i | −0.275800 | − | 0.477699i | ||||
\(456\) | −67.0307 | + | 38.7002i | −3.13900 | + | 1.81230i | ||||
\(457\) | −27.1570 | −1.27035 | −0.635175 | − | 0.772368i | \(-0.719072\pi\) | ||||
−0.635175 | + | 0.772368i | \(0.719072\pi\) | |||||||
\(458\) | −7.01519 | − | 12.1507i | −0.327798 | − | 0.567763i | ||||
\(459\) | 14.9125 | − | 4.68451i | 0.696057 | − | 0.218654i | ||||
\(460\) | 12.1344 | + | 21.0175i | 0.565771 | + | 0.979945i | ||||
\(461\) | −0.901498 | + | 1.56144i | −0.0419869 | + | 0.0727235i | −0.886255 | − | 0.463197i | \(-0.846702\pi\) |
0.844268 | + | 0.535921i | \(0.180035\pi\) | |||||||
\(462\) | 129.635i | 6.03115i | ||||||||
\(463\) | −14.8320 | + | 25.6897i | −0.689301 | + | 1.19390i | 0.282764 | + | 0.959190i | \(0.408749\pi\) |
−0.972064 | + | 0.234714i | \(0.924585\pi\) | |||||||
\(464\) | 9.51855 | − | 5.49553i | 0.441887 | − | 0.255124i | ||||
\(465\) | 22.8603i | 1.06012i | ||||||||
\(466\) | 24.3775 | − | 14.0744i | 1.12927 | − | 0.651983i | ||||
\(467\) | −10.2978 | + | 17.8363i | −0.476524 | + | 0.825363i | −0.999638 | − | 0.0268992i | \(-0.991437\pi\) |
0.523114 | + | 0.852262i | \(0.324770\pi\) | |||||||
\(468\) | 4.73473 | − | 8.20079i | 0.218863 | − | 0.379082i | ||||
\(469\) | − | 63.1004i | − | 2.91371i | ||||||
\(470\) | −32.0233 | − | 18.4886i | −1.47712 | − | 0.852817i | ||||
\(471\) | 17.8301i | 0.821567i | ||||||||
\(472\) | 35.3361 | 1.62648 | ||||||||
\(473\) | 24.3372 | + | 28.5327i | 1.11903 | + | 1.31193i | ||||
\(474\) | 68.9008 | 3.16472 | ||||||||
\(475\) | −20.5158 | −0.941332 | ||||||||
\(476\) | −58.0546 | − | 53.3106i | −2.66093 | − | 2.44349i | ||||
\(477\) | −4.73993 | −0.217027 | ||||||||
\(478\) | 33.8724 | − | 58.6687i | 1.54929 | − | 2.68344i | ||||
\(479\) | −19.3025 | − | 11.1443i | −0.881952 | − | 0.509195i | −0.0106505 | − | 0.999943i | \(-0.503390\pi\) |
−0.871302 | + | 0.490748i | \(0.836724\pi\) | |||||||
\(480\) | 4.63134 | + | 8.02171i | 0.211391 | + | 0.366139i | ||||
\(481\) | − | 1.04488i | − | 0.0476423i | ||||||
\(482\) | −14.9936 | + | 8.65654i | −0.682939 | + | 0.394295i | ||||
\(483\) | 32.1509 | + | 18.5623i | 1.46291 | + | 0.844614i | ||||
\(484\) | −93.5015 | −4.25007 | ||||||||
\(485\) | −12.8879 | + | 22.3225i | −0.585210 | + | 1.01361i | ||||
\(486\) | −24.4381 | + | 14.1093i | −1.10853 | + | 0.640013i | ||||
\(487\) | 19.8836 | − | 11.4798i | 0.901010 | − | 0.520198i | 0.0234821 | − | 0.999724i | \(-0.492525\pi\) |
0.877528 | + | 0.479526i | \(0.159191\pi\) | |||||||
\(488\) | −9.20760 | + | 5.31601i | −0.416808 | + | 0.240644i | ||||
\(489\) | −8.42473 | −0.380980 | ||||||||
\(490\) | 37.8249 | − | 21.8382i | 1.70876 | − | 0.986551i | ||||
\(491\) | −3.40750 | − | 5.90197i | −0.153778 | − | 0.266352i | 0.778835 | − | 0.627229i | \(-0.215811\pi\) |
−0.932614 | + | 0.360877i | \(0.882478\pi\) | |||||||
\(492\) | 15.4039 | − | 26.6803i | 0.694459 | − | 1.20284i | ||||
\(493\) | 5.62056 | + | 5.16127i | 0.253137 | + | 0.232452i | ||||
\(494\) | 31.9250 | 1.43637 | ||||||||
\(495\) | 8.89806 | 0.399938 | ||||||||
\(496\) | −42.2060 | − | 24.3677i | −1.89511 | − | 1.09414i | ||||
\(497\) | 12.3888 | − | 21.4580i | 0.555713 | − | 0.962523i | ||||
\(498\) | 41.5645 | − | 23.9973i | 1.86255 | − | 1.07534i | ||||
\(499\) | −5.83929 | + | 3.37132i | −0.261403 | + | 0.150921i | −0.624974 | − | 0.780645i | \(-0.714891\pi\) |
0.363572 | + | 0.931566i | \(0.381557\pi\) | |||||||
\(500\) | 47.9310i | 2.14354i | ||||||||
\(501\) | −3.28942 | − | 5.69744i | −0.146960 | − | 0.254543i | ||||
\(502\) | 30.4635 | + | 52.7643i | 1.35965 | + | 2.35499i | ||||
\(503\) | −13.2162 | + | 7.63037i | −0.589281 | + | 0.340221i | −0.764813 | − | 0.644252i | \(-0.777169\pi\) |
0.175532 | + | 0.984474i | \(0.443835\pi\) | |||||||
\(504\) | 25.2981 | + | 14.6059i | 1.12687 | + | 0.650597i | ||||
\(505\) | 0.611627i | 0.0272170i | ||||||||
\(506\) | −29.5396 | + | 51.1641i | −1.31320 | + | 2.27452i | ||||
\(507\) | 16.2982 | − | 9.40975i | 0.723827 | − | 0.417902i | ||||
\(508\) | −17.8644 | −0.792604 | ||||||||
\(509\) | −5.14392 | − | 8.90953i | −0.228000 | − | 0.394908i | 0.729215 | − | 0.684285i | \(-0.239885\pi\) |
−0.957215 | + | 0.289376i | \(0.906552\pi\) | |||||||
\(510\) | −19.5104 | + | 21.2466i | −0.863935 | + | 0.940814i | ||||
\(511\) | 14.0019 | − | 24.2519i | 0.619406 | − | 1.07284i | ||||
\(512\) | 49.0812 | 2.16910 | ||||||||
\(513\) | −21.5631 | − | 12.4494i | −0.952033 | − | 0.549656i | ||||
\(514\) | −3.84287 | −0.169502 | ||||||||
\(515\) | 3.35447i | 0.147816i | ||||||||
\(516\) | 56.4869 | − | 10.4313i | 2.48670 | − | 0.459214i | ||||
\(517\) | − | 61.4729i | − | 2.70358i | ||||||
\(518\) | 6.01716 | 0.264379 | ||||||||
\(519\) | 7.25895 | − | 12.5729i | 0.318633 | − | 0.551888i | ||||
\(520\) | − | 15.3632i | − | 0.673719i | ||||||
\(521\) | −18.6103 | − | 10.7447i | −0.815334 | − | 0.470733i | 0.0334709 | − | 0.999440i | \(-0.489344\pi\) |
−0.848805 | + | 0.528707i | \(0.822677\pi\) | |||||||
\(522\) | −4.57220 | − | 2.63976i | −0.200120 | − | 0.115539i | ||||
\(523\) | 14.3812 | + | 24.9090i | 0.628846 | + | 1.08919i | 0.987784 | + | 0.155832i | \(0.0498058\pi\) |
−0.358937 | + | 0.933362i | \(0.616861\pi\) | |||||||
\(524\) | − | 21.9869i | − | 0.960503i | ||||||
\(525\) | 14.0966 | + | 24.4161i | 0.615228 | + | 1.06561i | ||||
\(526\) | −16.9577 | + | 29.3716i | −0.739392 | + | 1.28066i | ||||
\(527\) | 7.35842 | − | 33.0259i | 0.320538 | − | 1.43863i | ||||
\(528\) | −34.5357 | + | 59.8176i | −1.50297 | + | 2.60323i | ||||
\(529\) | −3.04048 | − | 5.26626i | −0.132195 | − | 0.228968i | ||||
\(530\) | −12.4323 | + | 7.17781i | −0.540026 | + | 0.311784i | ||||
\(531\) | −3.46314 | − | 5.99833i | −0.150287 | − | 0.260306i | ||||
\(532\) | 125.551i | 5.44335i | ||||||||
\(533\) | −5.89500 | + | 3.40348i | −0.255341 | + | 0.147421i | ||||
\(534\) | −71.9672 | + | 41.5503i | −3.11433 | + | 1.79806i | ||||
\(535\) | 3.26077 | − | 5.64782i | 0.140975 | − | 0.244176i | ||||
\(536\) | 41.1958 | − | 71.3533i | 1.77939 | − | 3.08199i | ||||
\(537\) | 10.4565i | 0.451230i | ||||||||
\(538\) | − | 24.4021i | − | 1.05205i | ||||||
\(539\) | 62.8821 | + | 36.3050i | 2.70852 | + | 1.56377i | ||||
\(540\) | −11.1839 | + | 19.3711i | −0.481279 | + | 0.833600i | ||||
\(541\) | 4.91450 | − | 2.83739i | 0.211291 | − | 0.121989i | −0.390620 | − | 0.920552i | \(-0.627739\pi\) |
0.601911 | + | 0.798563i | \(0.294406\pi\) | |||||||
\(542\) | −35.2265 | − | 61.0141i | −1.51311 | − | 2.62078i | ||||
\(543\) | 25.9425 | 1.11330 | ||||||||
\(544\) | −4.10872 | − | 13.0796i | −0.176160 | − | 0.560782i | ||||
\(545\) | −7.27147 | − | 12.5946i | −0.311476 | − | 0.539491i | ||||
\(546\) | −21.9360 | − | 37.9943i | −0.938774 | − | 1.62600i | ||||
\(547\) | 23.2117 | + | 13.4013i | 0.992460 | + | 0.572997i | 0.906009 | − | 0.423259i | \(-0.139114\pi\) |
0.0864512 | + | 0.996256i | \(0.472447\pi\) | |||||||
\(548\) | −35.1176 | −1.50015 | ||||||||
\(549\) | 1.80479 | + | 1.04200i | 0.0770267 | + | 0.0444714i | ||||
\(550\) | −38.8552 | + | 22.4330i | −1.65679 | + | 0.956548i | ||||
\(551\) | − | 12.1553i | − | 0.517832i | ||||||
\(552\) | 24.2372 | + | 41.9801i | 1.03161 | + | 1.78679i | ||||
\(553\) | 29.9349 | − | 51.8488i | 1.27296 | − | 2.20484i | ||||
\(554\) | 49.0293 | + | 28.3071i | 2.08305 | + | 1.20265i | ||||
\(555\) | − | 1.50386i | − | 0.0638354i | ||||||
\(556\) | 50.5416 | + | 29.1802i | 2.14344 | + | 1.23752i | ||||
\(557\) | −4.61019 | −0.195340 | −0.0976699 | − | 0.995219i | \(-0.531139\pi\) | ||||
−0.0976699 | + | 0.995219i | \(0.531139\pi\) | |||||||
\(558\) | 23.4098i | 0.991018i | ||||||||
\(559\) | −11.9611 | − | 4.24437i | −0.505899 | − | 0.179518i | ||||
\(560\) | 36.1022 | 1.52560 | ||||||||
\(561\) | −46.8068 | − | 10.4289i | −1.97618 | − | 0.440309i | ||||
\(562\) | 19.3832 | − | 33.5727i | 0.817632 | − | 1.41618i | ||||
\(563\) | 22.1779 | 0.934688 | 0.467344 | − | 0.884076i | \(-0.345211\pi\) | ||||
0.467344 | + | 0.884076i | \(0.345211\pi\) | |||||||
\(564\) | −81.5431 | − | 47.0789i | −3.43358 | − | 1.98238i | ||||
\(565\) | 7.53115 | − | 13.0443i | 0.316838 | − | 0.548779i | ||||
\(566\) | 64.7947 | − | 37.4093i | 2.72353 | − | 1.57243i | ||||
\(567\) | 49.3395i | 2.07206i | ||||||||
\(568\) | 28.0182 | − | 16.1763i | 1.17562 | − | 0.678744i | ||||
\(569\) | −20.3358 | + | 35.2226i | −0.852519 | + | 1.47661i | 0.0264086 | + | 0.999651i | \(0.491593\pi\) |
−0.878928 | + | 0.476955i | \(0.841740\pi\) | |||||||
\(570\) | 45.9488 | 1.92458 | ||||||||
\(571\) | −39.4525 | − | 22.7779i | −1.65103 | − | 0.953225i | −0.976648 | − | 0.214846i | \(-0.931075\pi\) |
−0.674386 | − | 0.738379i | \(-0.735592\pi\) | |||||||
\(572\) | 41.2909 | − | 23.8393i | 1.72646 | − | 0.996773i | ||||
\(573\) | 9.79767 | − | 5.65669i | 0.409303 | − | 0.236311i | ||||
\(574\) | −19.5997 | − | 33.9477i | −0.818076 | − | 1.41695i | ||||
\(575\) | 12.8487i | 0.535828i | ||||||||
\(576\) | −2.00288 | − | 3.46909i | −0.0834532 | − | 0.144545i | ||||
\(577\) | −8.81635 | − | 15.2704i | −0.367030 | − | 0.635714i | 0.622070 | − | 0.782962i | \(-0.286292\pi\) |
−0.989100 | + | 0.147248i | \(0.952959\pi\) | |||||||
\(578\) | 35.0253 | − | 24.4144i | 1.45686 | − | 1.01550i | ||||
\(579\) | 0.588090 | − | 1.01860i | 0.0244402 | − | 0.0423316i | ||||
\(580\) | −10.9196 | −0.453414 | ||||||||
\(581\) | − | 41.7038i | − | 1.73017i | ||||||
\(582\) | −48.0552 | + | 83.2340i | −1.99195 | + | 3.45016i | ||||
\(583\) | −20.6681 | − | 11.9328i | −0.855987 | − | 0.494204i | ||||
\(584\) | 31.6663 | − | 18.2825i | 1.31036 | − | 0.756537i | ||||
\(585\) | −2.60791 | + | 1.50568i | −0.107824 | + | 0.0622521i | ||||
\(586\) | 35.4419 | 1.46409 | ||||||||
\(587\) | −15.6017 | − | 27.0230i | −0.643953 | − | 1.11536i | −0.984542 | − | 0.175147i | \(-0.943960\pi\) |
0.340590 | − | 0.940212i | \(-0.389373\pi\) | |||||||
\(588\) | 96.3163 | − | 55.6083i | 3.97202 | − | 2.29325i | ||||
\(589\) | −46.6766 | + | 26.9487i | −1.92328 | + | 1.11040i | ||||
\(590\) | −18.1669 | − | 10.4887i | −0.747919 | − | 0.431811i | ||||
\(591\) | −12.9132 | −0.531177 | ||||||||
\(592\) | 2.77651 | + | 1.60302i | 0.114114 | + | 0.0658838i | ||||
\(593\) | −11.3200 | − | 19.6068i | −0.464855 | − | 0.805153i | 0.534340 | − | 0.845270i | \(-0.320560\pi\) |
−0.999195 | + | 0.0401168i | \(0.987227\pi\) | |||||||
\(594\) | −54.4514 | −2.23417 | ||||||||
\(595\) | 7.51178 | + | 23.9127i | 0.307953 | + | 0.980327i | ||||
\(596\) | 2.52783 | − | 4.37833i | 0.103544 | − | 0.179343i | ||||
\(597\) | 10.1707 | − | 17.6162i | 0.416259 | − | 0.720982i | ||||
\(598\) | − | 19.9941i | − | 0.817619i | ||||||
\(599\) | 0.0513591 | − | 0.0889565i | 0.00209848 | − | 0.00363467i | −0.864974 | − | 0.501816i | \(-0.832665\pi\) |
0.867073 | + | 0.498182i | \(0.165999\pi\) | |||||||
\(600\) | 36.8126i | 1.50287i | ||||||||
\(601\) | 16.2904i | 0.664500i | 0.943191 | + | 0.332250i | \(0.107808\pi\) | ||||
−0.943191 | + | 0.332250i | \(0.892192\pi\) | |||||||
\(602\) | 24.4422 | − | 68.8805i | 0.996188 | − | 2.80736i | ||||
\(603\) | −16.1497 | −0.657667 | ||||||||
\(604\) | 18.8265 | 0.766038 | ||||||||
\(605\) | 25.7505 | + | 14.8671i | 1.04691 | + | 0.604432i | ||||
\(606\) | 2.28057i | 0.0926420i | ||||||||
\(607\) | −31.4586 | − | 18.1626i | −1.27686 | − | 0.737198i | −0.300594 | − | 0.953752i | \(-0.597185\pi\) |
−0.976271 | + | 0.216554i | \(0.930518\pi\) | |||||||
\(608\) | −10.9192 | + | 18.9127i | −0.442833 | + | 0.767010i | ||||
\(609\) | −14.4661 | + | 8.35201i | −0.586196 | + | 0.338440i | ||||
\(610\) | 6.31171 | 0.255554 | ||||||||
\(611\) | 10.4021 | + | 18.0169i | 0.420823 | + | 0.728887i | ||||
\(612\) | −13.6441 | + | 14.8583i | −0.551532 | + | 0.600611i | ||||
\(613\) | 28.5802 | 1.15434 | 0.577171 | − | 0.816623i | \(-0.304156\pi\) | ||||
0.577171 | + | 0.816623i | \(0.304156\pi\) | |||||||
\(614\) | −20.2902 | + | 35.1437i | −0.818847 | + | 1.41828i | ||||
\(615\) | −8.48451 | + | 4.89853i | −0.342128 | + | 0.197528i | ||||
\(616\) | 73.5404 | + | 127.376i | 2.96303 | + | 5.13211i | ||||
\(617\) | −6.79067 | + | 3.92060i | −0.273382 | + | 0.157837i | −0.630424 | − | 0.776251i | \(-0.717119\pi\) |
0.357042 | + | 0.934089i | \(0.383785\pi\) | |||||||
\(618\) | 12.5078i | 0.503138i | ||||||||
\(619\) | −31.9910 | + | 18.4700i | −1.28583 | + | 0.742372i | −0.977907 | − | 0.209041i | \(-0.932966\pi\) |
−0.307919 | + | 0.951413i | \(0.599633\pi\) | |||||||
\(620\) | 24.2093 | + | 41.9318i | 0.972270 | + | 1.68402i | ||||
\(621\) | −7.79687 | + | 13.5046i | −0.312877 | + | 0.541920i | ||||
\(622\) | 39.9194 | + | 23.0474i | 1.60062 | + | 0.924119i | ||||
\(623\) | 72.2085i | 2.89297i | ||||||||
\(624\) | − | 23.3757i | − | 0.935778i | ||||||
\(625\) | −0.188091 | + | 0.325782i | −0.00752362 | + | 0.0130313i | ||||
\(626\) | −5.86710 | − | 3.38737i | −0.234496 | − | 0.135386i | ||||
\(627\) | 38.1938 | + | 66.1536i | 1.52531 | + | 2.64192i | ||||
\(628\) | 18.8822 | + | 32.7050i | 0.753483 | + | 1.30507i | ||||
\(629\) | −0.484072 | + | 2.17260i | −0.0193012 | + | 0.0866272i | ||||
\(630\) | −8.67078 | − | 15.0182i | −0.345452 | − | 0.598341i | ||||
\(631\) | −3.32085 | − | 5.75188i | −0.132201 | − | 0.228979i | 0.792324 | − | 0.610101i | \(-0.208871\pi\) |
−0.924525 | + | 0.381122i | \(0.875538\pi\) | |||||||
\(632\) | 67.7002 | − | 39.0867i | 2.69297 | − | 1.55479i | ||||
\(633\) | −13.3472 | + | 23.1180i | −0.530504 | + | 0.918859i | ||||
\(634\) | − | 37.5980i | − | 1.49321i | ||||||
\(635\) | 4.91989 | + | 2.84050i | 0.195240 | + | 0.112722i | ||||
\(636\) | −31.6573 | + | 18.2774i | −1.25530 | + | 0.724745i | ||||
\(637\) | −24.5733 | −0.973629 | ||||||||
\(638\) | −13.2912 | − | 23.0210i | −0.526203 | − | 0.911410i | ||||
\(639\) | −5.49189 | − | 3.17074i | −0.217256 | − | 0.125433i | ||||
\(640\) | −18.3955 | − | 10.6207i | −0.727147 | − | 0.419819i | ||||
\(641\) | 25.1134i | 0.991919i | 0.868346 | + | 0.495960i | \(0.165184\pi\) | ||||
−0.868346 | + | 0.495960i | \(0.834816\pi\) | |||||||
\(642\) | 12.1584 | − | 21.0590i | 0.479855 | − | 0.831134i | ||||
\(643\) | − | 3.42114i | − | 0.134916i | −0.997722 | − | 0.0674582i | \(-0.978511\pi\) | ||
0.997722 | − | 0.0674582i | \(-0.0214889\pi\) | |||||||
\(644\) | 78.6306 | 3.09848 | ||||||||
\(645\) | −17.2152 | − | 6.10880i | −0.677849 | − | 0.240534i | ||||
\(646\) | −66.3813 | − | 14.7903i | −2.61174 | − | 0.581916i | ||||
\(647\) | −13.7238 | −0.539537 | −0.269769 | − | 0.962925i | \(-0.586947\pi\) | ||||
−0.269769 | + | 0.962925i | \(0.586947\pi\) | |||||||
\(648\) | −32.2118 | + | 55.7925i | −1.26540 | + | 2.19174i | ||||
\(649\) | − | 34.8738i | − | 1.36892i | ||||||
\(650\) | 7.59198 | − | 13.1497i | 0.297782 | − | 0.515773i | ||||
\(651\) | 64.1439 | + | 37.0335i | 2.51400 | + | 1.45146i | ||||
\(652\) | −15.4531 | + | 8.92187i | −0.605192 | + | 0.349408i | ||||
\(653\) | 20.9825i | 0.821110i | 0.911836 | + | 0.410555i | \(0.134665\pi\) | ||||
−0.911836 | + | 0.410555i | \(0.865335\pi\) | |||||||
\(654\) | −27.1131 | − | 46.9613i | −1.06021 | − | 1.83633i | ||||
\(655\) | −3.49600 | + | 6.05525i | −0.136600 | + | 0.236598i | ||||
\(656\) | − | 20.8861i | − | 0.815465i | ||||||
\(657\) | −6.20695 | − | 3.58359i | −0.242156 | − | 0.139809i | ||||
\(658\) | −103.755 | + | 59.9028i | −4.04478 | + | 2.33525i | ||||
\(659\) | −7.21480 | − | 12.4964i | −0.281049 | − | 0.486790i | 0.690595 | − | 0.723242i | \(-0.257349\pi\) |
−0.971643 | + | 0.236452i | \(0.924016\pi\) | |||||||
\(660\) | 59.4289 | − | 34.3113i | 2.31327 | − | 1.33557i | ||||
\(661\) | 37.9604 | 1.47649 | 0.738245 | − | 0.674533i | \(-0.235655\pi\) | ||||
0.738245 | + | 0.674533i | \(0.235655\pi\) | |||||||
\(662\) | −6.60016 | − | 11.4318i | −0.256522 | − | 0.444310i | ||||
\(663\) | 15.4832 | − | 4.86378i | 0.601318 | − | 0.188894i | ||||
\(664\) | 27.2268 | − | 47.1582i | 1.05661 | − | 1.83009i | ||||
\(665\) | 19.9631 | − | 34.5771i | 0.774137 | − | 1.34084i | ||||
\(666\) | − | 1.54001i | − | 0.0596742i | ||||||
\(667\) | −7.61263 | −0.294762 | ||||||||
\(668\) | −12.0673 | − | 6.96705i | −0.466897 | − | 0.269563i | ||||
\(669\) | −23.4042 | − | 13.5124i | −0.904857 | − | 0.522420i | ||||
\(670\) | −42.3590 | + | 24.4560i | −1.63647 | + | 0.944816i | ||||
\(671\) | 5.24646 | + | 9.08713i | 0.202537 | + | 0.350805i | ||||
\(672\) | 30.0108 | 1.15769 | ||||||||
\(673\) | 15.4260 | − | 8.90621i | 0.594629 | − | 0.343309i | −0.172297 | − | 0.985045i | \(-0.555119\pi\) |
0.766926 | + | 0.641736i | \(0.221785\pi\) | |||||||
\(674\) | −49.9098 | + | 28.8154i | −1.92245 | + | 1.10993i | ||||
\(675\) | −10.2557 | + | 5.92112i | −0.394741 | + | 0.227904i | ||||
\(676\) | 19.9300 | − | 34.5198i | 0.766539 | − | 1.32769i | ||||
\(677\) | − | 16.4685i | − | 0.632936i | −0.948603 | − | 0.316468i | \(-0.897503\pi\) | ||
0.948603 | − | 0.316468i | \(-0.102497\pi\) | |||||||
\(678\) | 28.0814 | − | 48.6384i | 1.07846 | − | 1.86795i | ||||
\(679\) | 41.7565 | + | 72.3244i | 1.60247 | + | 2.77556i | ||||
\(680\) | −7.11747 | + | 31.9444i | −0.272943 | + | 1.22501i | ||||
\(681\) | 3.98217 | + | 6.89731i | 0.152597 | + | 0.264306i | ||||
\(682\) | −58.9342 | + | 102.077i | −2.25671 | + | 3.90873i | ||||
\(683\) | 9.20879 | + | 5.31670i | 0.352365 | + | 0.203438i | 0.665726 | − | 0.746196i | \(-0.268122\pi\) |
−0.313362 | + | 0.949634i | \(0.601455\pi\) | |||||||
\(684\) | 32.1332 | 1.22864 | ||||||||
\(685\) | 9.67146 | + | 5.58382i | 0.369528 | + | 0.213347i | ||||
\(686\) | − | 63.4894i | − | 2.42404i | ||||||
\(687\) | 11.3613i | 0.433460i | ||||||||
\(688\) | 29.6287 | − | 25.2721i | 1.12959 | − | 0.963491i | ||||
\(689\) | 8.07677 | 0.307700 | ||||||||
\(690\) | − | 28.7769i | − | 1.09552i | ||||||
\(691\) | 8.97676 | + | 5.18273i | 0.341492 | + | 0.197160i | 0.660932 | − | 0.750446i | \(-0.270161\pi\) |
−0.319440 | + | 0.947607i | \(0.603495\pi\) | |||||||
\(692\) | − | 30.7492i | − | 1.16891i | ||||||
\(693\) | 14.4148 | − | 24.9671i | 0.547571 | − | 0.948421i | ||||
\(694\) | −30.2407 | − | 17.4594i | −1.14792 | − | 0.662752i | ||||
\(695\) | −9.27950 | − | 16.0726i | −0.351992 | − | 0.609667i | ||||
\(696\) | −21.8108 | −0.826737 | ||||||||
\(697\) | 13.8342 | − | 4.34577i | 0.524006 | − | 0.164608i | ||||
\(698\) | 37.2951 | − | 64.5971i | 1.41164 | − | 2.44503i | ||||
\(699\) | −22.7938 | −0.862142 | ||||||||
\(700\) | 51.7138 | + | 29.8569i | 1.95460 | + | 1.12849i | ||||
\(701\) | 10.6373 | + | 18.4243i | 0.401765 | + | 0.695877i | 0.993939 | − | 0.109933i | \(-0.0350636\pi\) |
−0.592174 | + | 0.805810i | \(0.701730\pi\) | |||||||
\(702\) | 15.9590 | − | 9.21394i | 0.602334 | − | 0.347758i | ||||
\(703\) | 3.07061 | − | 1.77282i | 0.115810 | − | 0.0668631i | ||||
\(704\) | − | 20.1690i | − | 0.760146i | ||||||
\(705\) | 14.9714 | + | 25.9313i | 0.563857 | + | 0.976629i | ||||
\(706\) | −5.85006 | − | 10.1326i | −0.220170 | − | 0.381345i | ||||
\(707\) | 1.71617 | + | 0.990828i | 0.0645430 | + | 0.0372639i | ||||
\(708\) | −46.2597 | − | 26.7080i | −1.73854 | − | 1.00375i | ||||
\(709\) | − | 45.3238i | − | 1.70217i | −0.525027 | − | 0.851086i | \(-0.675945\pi\) | ||
0.525027 | − | 0.851086i | \(-0.324055\pi\) | |||||||
\(710\) | −19.2062 | −0.720795 | ||||||||
\(711\) | −13.2700 | − | 7.66144i | −0.497664 | − | 0.287326i | ||||
\(712\) | −47.1421 | + | 81.6526i | −1.76673 | + | 3.06006i | ||||
\(713\) | 16.8775 | + | 29.2327i | 0.632068 | + | 1.09477i | ||||
\(714\) | 28.0092 | + | 89.1635i | 1.04822 | + | 3.33686i | ||||
\(715\) | −15.1622 | −0.567032 | ||||||||
\(716\) | 11.0735 | + | 19.1798i | 0.413836 | + | 0.716785i | ||||
\(717\) | −47.5078 | + | 27.4286i | −1.77421 | + | 1.02434i | ||||
\(718\) | −4.09121 | − | 7.08618i | −0.152683 | − | 0.264454i | ||||
\(719\) | −20.7953 | − | 12.0062i | −0.775534 | − | 0.447755i | 0.0593112 | − | 0.998240i | \(-0.481110\pi\) |
−0.834845 | + | 0.550485i | \(0.814443\pi\) | |||||||
\(720\) | − | 9.23987i | − | 0.344350i | ||||||
\(721\) | 9.41231 | + | 5.43420i | 0.350533 | + | 0.202380i | ||||
\(722\) | 30.3077 | + | 52.4944i | 1.12793 | + | 1.95364i | ||||
\(723\) | 14.0195 | 0.521391 | ||||||||
\(724\) | 47.5853 | − | 27.4734i | 1.76849 | − | 1.02104i | ||||
\(725\) | −5.00667 | − | 2.89060i | −0.185943 | − | 0.107354i | ||||
\(726\) | 96.0160 | + | 55.4349i | 3.56349 | + | 2.05738i | ||||
\(727\) | 25.2064 | 0.934853 | 0.467426 | − | 0.884032i | \(-0.345181\pi\) | ||||
0.467426 | + | 0.884032i | \(0.345181\pi\) | |||||||
\(728\) | −43.1075 | − | 24.8882i | −1.59767 | − | 0.922416i | ||||
\(729\) | −10.5017 | −0.388953 | ||||||||
\(730\) | −21.7069 | −0.803409 | ||||||||
\(731\) | 22.9042 | + | 14.3666i | 0.847141 | + | 0.531368i | ||||
\(732\) | 16.0720 | 0.594037 | ||||||||
\(733\) | 17.5659 | 0.648813 | 0.324406 | − | 0.945918i | \(-0.394835\pi\) | ||||
0.324406 | + | 0.945918i | \(0.394835\pi\) | |||||||
\(734\) | 50.7710 | + | 29.3126i | 1.87399 | + | 1.08195i | ||||
\(735\) | −35.3676 | −1.30455 | ||||||||
\(736\) | 11.8447 | + | 6.83852i | 0.436600 | + | 0.252071i | ||||
\(737\) | −70.4197 | − | 40.6568i | −2.59394 | − | 1.49761i | ||||
\(738\) | −8.68845 | + | 5.01628i | −0.319826 | + | 0.184652i | ||||
\(739\) | 31.7737 | 1.16882 | 0.584408 | − | 0.811460i | \(-0.301327\pi\) | ||||
0.584408 | + | 0.811460i | \(0.301327\pi\) | |||||||
\(740\) | −1.59260 | − | 2.75847i | −0.0585453 | − | 0.101403i | ||||
\(741\) | −22.3883 | − | 12.9259i | −0.822453 | − | 0.474844i | ||||
\(742\) | 46.5119i | 1.70751i | ||||||||
\(743\) | −5.91820 | − | 3.41688i | −0.217118 | − | 0.125353i | 0.387497 | − | 0.921871i | \(-0.373340\pi\) |
−0.604615 | + | 0.796518i | \(0.706673\pi\) | |||||||
\(744\) | 48.3555 | + | 83.7542i | 1.77280 | + | 3.07058i | ||||
\(745\) | −1.39234 | + | 0.803867i | −0.0510114 | + | 0.0294514i | ||||
\(746\) | 4.83368 | + | 8.37218i | 0.176974 | + | 0.306527i | ||||
\(747\) | −10.6735 | −0.390524 | ||||||||
\(748\) | −96.9001 | + | 30.4395i | −3.54302 | + | 1.11298i | ||||
\(749\) | −10.5648 | − | 18.2988i | −0.386030 | − | 0.668624i | ||||
\(750\) | 28.4172 | − | 49.2200i | 1.03765 | − | 1.79726i | ||||
\(751\) | 24.3491 | + | 14.0579i | 0.888510 | + | 0.512982i | 0.873455 | − | 0.486905i | \(-0.161874\pi\) |
0.0150554 | + | 0.999887i | \(0.495208\pi\) | |||||||
\(752\) | −63.8343 | −2.32780 | ||||||||
\(753\) | − | 49.3365i | − | 1.79792i | ||||||
\(754\) | 7.79096 | + | 4.49811i | 0.283730 | + | 0.163812i | ||||
\(755\) | −5.18485 | − | 2.99347i | −0.188696 | − | 0.108944i | ||||
\(756\) | 36.2356 | + | 62.7620i | 1.31788 | + | 2.28263i | ||||
\(757\) | −20.6236 | − | 35.7212i | −0.749579 | − | 1.29831i | −0.948025 | − | 0.318197i | \(-0.896923\pi\) |
0.198446 | − | 0.980112i | \(-0.436411\pi\) | |||||||
\(758\) | − | 0.0302289i | − | 0.00109796i | ||||||
\(759\) | 41.4308 | − | 23.9201i | 1.50384 | − | 0.868245i | ||||
\(760\) | 45.1482 | − | 26.0663i | 1.63770 | − | 0.945524i | ||||
\(761\) | −26.9871 | − | 46.7431i | −0.978282 | − | 1.69443i | −0.668648 | − | 0.743579i | \(-0.733127\pi\) |
−0.309635 | − | 0.950856i | \(-0.600207\pi\) | |||||||
\(762\) | 18.3448 | + | 10.5914i | 0.664562 | + | 0.383685i | ||||
\(763\) | −47.1188 | −1.70581 | ||||||||
\(764\) | 11.9810 | − | 20.7516i | 0.433456 | − | 0.750768i | ||||
\(765\) | 6.12015 | − | 1.92254i | 0.221274 | − | 0.0695096i | ||||
\(766\) | −86.3389 | −3.11955 | ||||||||
\(767\) | 5.90114 | + | 10.2211i | 0.213078 | + | 0.369061i | ||||
\(768\) | −56.1691 | − | 32.4292i | −2.02683 | − | 1.17019i | ||||
\(769\) | −6.70884 | + | 11.6201i | −0.241927 | + | 0.419030i | −0.961263 | − | 0.275632i | \(-0.911113\pi\) |
0.719336 | + | 0.694662i | \(0.244446\pi\) | |||||||
\(770\) | − | 87.3147i | − | 3.14660i | ||||||
\(771\) | 2.69491 | + | 1.55591i | 0.0970548 | + | 0.0560346i | ||||
\(772\) | − | 2.49117i | − | 0.0896592i | ||||||
\(773\) | −24.1643 | −0.869128 | −0.434564 | − | 0.900641i | \(-0.643097\pi\) | ||||
−0.434564 | + | 0.900641i | \(0.643097\pi\) | |||||||
\(774\) | −17.6290 | − | 6.25564i | −0.633663 | − | 0.224854i | ||||
\(775\) | 25.6343i | 0.920813i | ||||||||
\(776\) | 109.045i | 3.91448i | ||||||||
\(777\) | −4.21969 | − | 2.43624i | −0.151381 | − | 0.0873996i | ||||
\(778\) | −55.2942 | −1.98239 | ||||||||
\(779\) | −20.0038 | − | 11.5492i | −0.716711 | − | 0.413793i | ||||
\(780\) | −11.6119 | + | 20.1124i | −0.415773 | + | 0.720140i | ||||
\(781\) | −15.9647 | − | 27.6516i | −0.571261 | − | 0.989453i | ||||
\(782\) | −9.26288 | + | 41.5734i | −0.331240 | + | 1.48666i | ||||
\(783\) | −3.50816 | − | 6.07630i | −0.125371 | − | 0.217149i | ||||
\(784\) | 37.6996 | − | 65.2977i | 1.34642 | − | 2.33206i | ||||
\(785\) | − | 12.0094i | − | 0.428633i | ||||||
\(786\) | −13.0355 | + | 22.5782i | −0.464962 | + | 0.805338i | ||||
\(787\) | −0.936636 | + | 0.540767i | −0.0333875 | + | 0.0192763i | −0.516601 | − | 0.856226i | \(-0.672803\pi\) |
0.483213 | + | 0.875503i | \(0.339470\pi\) | |||||||
\(788\) | −23.6861 | + | 13.6752i | −0.843782 | + | 0.487158i | ||||
\(789\) | 23.7841 | − | 13.7318i | 0.846736 | − | 0.488863i | ||||
\(790\) | −46.4078 | −1.65111 | ||||||||
\(791\) | −24.4007 | − | 42.2633i | −0.867591 | − | 1.50271i | ||||
\(792\) | 32.6001 | − | 18.8217i | 1.15839 | − | 0.668799i | ||||
\(793\) | −3.07534 | − | 1.77555i | −0.109209 | − | 0.0630516i | ||||
\(794\) | −44.4715 | − | 25.6756i | −1.57824 | − | 0.911195i | ||||
\(795\) | 11.6247 | 0.412284 | ||||||||
\(796\) | − | 43.0835i | − | 1.52705i | ||||||
\(797\) | −2.35135 | + | 4.07266i | −0.0832892 | + | 0.144261i | −0.904661 | − | 0.426132i | \(-0.859876\pi\) |
0.821372 | + | 0.570393i | \(0.193209\pi\) | |||||||
\(798\) | 74.4365 | − | 128.928i | 2.63503 | − | 4.56400i | ||||
\(799\) | −13.2820 | − | 42.2815i | −0.469884 | − | 1.49581i | ||||
\(800\) | 5.19333 | + | 8.99511i | 0.183612 | + | 0.318025i | ||||
\(801\) | 18.4808 | 0.652987 | ||||||||
\(802\) | 3.58647 | − | 2.07065i | 0.126643 | − | 0.0731172i | ||||
\(803\) | −18.0433 | − | 31.2520i | −0.636736 | − | 1.10286i | ||||
\(804\) | −107.862 | + | 62.2740i | −3.80399 | + | 2.19623i | ||||
\(805\) | −21.6550 | − | 12.5025i | −0.763240 | − | 0.440657i | ||||
\(806\) | − | 39.8900i | − | 1.40507i | ||||||
\(807\) | −9.87996 | + | 17.1126i | −0.347791 | + | 0.602392i | ||||
\(808\) | 1.29375 | + | 2.24084i | 0.0455139 | + | 0.0788323i | ||||
\(809\) | − | 10.9139i | − | 0.383713i | −0.981423 | − | 0.191857i | \(-0.938549\pi\) | ||
0.981423 | − | 0.191857i | \(-0.0614509\pi\) | |||||||
\(810\) | 33.1213 | − | 19.1226i | 1.16376 | − | 0.671899i | ||||
\(811\) | 1.01339 | + | 0.585080i | 0.0355849 | + | 0.0205449i | 0.517687 | − | 0.855570i | \(-0.326793\pi\) |
−0.482102 | + | 0.876115i | \(0.660127\pi\) | |||||||
\(812\) | −17.6897 | + | 30.6395i | −0.620787 | + | 1.07523i | ||||
\(813\) | 57.0503i | 2.00084i | ||||||||
\(814\) | 3.87697 | − | 6.71512i | 0.135888 | − | 0.235365i | ||||
\(815\) | 5.67444 | 0.198767 | ||||||||
\(816\) | −10.8295 | + | 48.6048i | −0.379110 | + | 1.70151i | ||||
\(817\) | −7.82101 | − | 42.3516i | −0.273623 | − | 1.48170i | ||||
\(818\) | 75.9010 | 2.65382 | ||||||||
\(819\) | 9.75672i | 0.340927i | ||||||||
\(820\) | −10.3752 | + | 17.9703i | −0.362317 | + | 0.627552i | ||||
\(821\) | 43.2389i | 1.50905i | 0.656272 | + | 0.754524i | \(0.272132\pi\) | ||||
−0.656272 | + | 0.754524i | \(0.727868\pi\) | |||||||
\(822\) | 36.0620 | + | 20.8204i | 1.25781 | + | 0.726195i | ||||
\(823\) | 1.20177 | + | 0.693840i | 0.0418909 | + | 0.0241857i | 0.520799 | − | 0.853679i | \(-0.325634\pi\) |
−0.478908 | + | 0.877865i | \(0.658967\pi\) | |||||||
\(824\) | 7.09556 | + | 12.2899i | 0.247186 | + | 0.428138i | ||||
\(825\) | 36.3309 | 1.26488 | ||||||||
\(826\) | −58.8603 | + | 33.9830i | −2.04801 | + | 1.18242i | ||||
\(827\) | −1.72267 | − | 0.994583i | −0.0599030 | − | 0.0345850i | 0.469749 | − | 0.882800i | \(-0.344344\pi\) |
−0.529652 | + | 0.848215i | \(0.677678\pi\) | |||||||
\(828\) | − | 20.1245i | − | 0.699373i | ||||||
\(829\) | 8.47665 | − | 14.6820i | 0.294406 | − | 0.509927i | −0.680440 | − | 0.732804i | \(-0.738211\pi\) |
0.974847 | + | 0.222877i | \(0.0715448\pi\) | |||||||
\(830\) | −27.9955 | + | 16.1632i | −0.971739 | + | 0.561034i | ||||
\(831\) | −22.9220 | − | 39.7021i | −0.795157 | − | 1.37725i | ||||
\(832\) | 3.41287 | + | 5.91127i | 0.118320 | + | 0.204936i | ||||
\(833\) | 51.0949 | + | 11.3843i | 1.77033 | + | 0.394444i | ||||
\(834\) | −34.6005 | − | 59.9298i | −1.19812 | − | 2.07520i | ||||
\(835\) | 2.21557 | + | 3.83748i | 0.0766730 | + | 0.132802i | ||||
\(836\) | 140.115 | + | 80.8952i | 4.84597 | + | 2.79782i | ||||
\(837\) | −15.5555 | + | 26.9428i | −0.537675 | + | 0.931281i | ||||
\(838\) | 10.9913i | 0.379688i | ||||||||
\(839\) | − | 12.4160i | − | 0.428648i | −0.976763 | − | 0.214324i | \(-0.931245\pi\) | ||
0.976763 | − | 0.214324i | \(-0.0687549\pi\) | |||||||
\(840\) | −62.0435 | − | 35.8208i | −2.14070 | − | 1.23594i | ||||
\(841\) | −12.7874 | + | 22.1484i | −0.440944 | + | 0.763737i | ||||
\(842\) | −10.3459 | − | 17.9197i | −0.356545 | − | 0.617554i | ||||
\(843\) | −27.1860 | + | 15.6958i | −0.936335 | + | 0.540593i | ||||
\(844\) | 56.5393i | 1.94616i | ||||||||
\(845\) | −10.9775 | + | 6.33789i | −0.377639 | + | 0.218030i | ||||
\(846\) | 15.3313 | + | 26.5546i | 0.527101 | + | 0.912966i | ||||
\(847\) | 83.4311 | − | 48.1690i | 2.86673 | − | 1.65511i | ||||
\(848\) | −12.3911 | + | 21.4621i | −0.425514 | + | 0.737012i | ||||
\(849\) | −60.5853 | −2.07928 | ||||||||
\(850\) | −21.8779 | + | 23.8248i | −0.750406 | + | 0.817183i | ||||
\(851\) | −1.11028 | − | 1.92307i | −0.0380600 | − | 0.0659219i | ||||
\(852\) | −48.9061 | −1.67549 | ||||||||
\(853\) | 24.8955 | − | 14.3734i | 0.852404 | − | 0.492136i | −0.00905718 | − | 0.999959i | \(-0.502883\pi\) |
0.861461 | + | 0.507823i | \(0.169550\pi\) | |||||||
\(854\) | 10.2249 | − | 17.7100i | 0.349889 | − | 0.606025i | ||||
\(855\) | −8.84955 | − | 5.10929i | −0.302648 | − | 0.174734i | ||||
\(856\) | − | 27.5895i | − | 0.942988i | ||||||
\(857\) | −16.0963 | − | 9.29320i | −0.549839 | − | 0.317450i | 0.199218 | − | 0.979955i | \(-0.436160\pi\) |
−0.749057 | + | 0.662505i | \(0.769493\pi\) | |||||||
\(858\) | −56.5352 | −1.93008 | ||||||||
\(859\) | 36.4400 | 1.24332 | 0.621659 | − | 0.783288i | \(-0.286459\pi\) | ||||
0.621659 | + | 0.783288i | \(0.286459\pi\) | |||||||
\(860\) | −38.0465 | + | 7.02598i | −1.29737 | + | 0.239584i | ||||
\(861\) | 31.7423i | 1.08177i | ||||||||
\(862\) | 39.2930i | 1.33833i | ||||||||
\(863\) | 24.2347 | − | 41.9758i | 0.824960 | − | 1.42887i | −0.0769892 | − | 0.997032i | \(-0.524531\pi\) |
0.901950 | − | 0.431841i | \(-0.142136\pi\) | |||||||
\(864\) | 12.6057i | 0.428854i | ||||||||
\(865\) | −4.88923 | + | 8.46840i | −0.166239 | + | 0.287934i | ||||
\(866\) | 37.5407 | − | 65.0225i | 1.27569 | − | 2.20955i | ||||
\(867\) | −34.4473 | + | 2.94012i | −1.16989 | + | 0.0998519i | ||||
\(868\) | 156.875 | 5.32470 | ||||||||
\(869\) | −38.5753 | − | 66.8144i | −1.30858 | − | 2.26652i | ||||
\(870\) | 11.2133 | + | 6.47401i | 0.380167 | + | 0.219489i | ||||
\(871\) | 27.5188 | 0.932440 | ||||||||
\(872\) | −53.2814 | − | 30.7620i | −1.80434 | − | 1.04173i | ||||
\(873\) | 18.5105 | − | 10.6870i | 0.626484 | − | 0.361701i | ||||
\(874\) | 58.7572 | − | 33.9235i | 1.98749 | − | 1.14748i | ||||
\(875\) | −24.6925 | − | 42.7687i | −0.834759 | − | 1.44585i | ||||
\(876\) | −55.2739 | −1.86753 | ||||||||
\(877\) | 25.3430 | − | 14.6318i | 0.855772 | − | 0.494080i | −0.00682189 | − | 0.999977i | \(-0.502171\pi\) |
0.862594 | + | 0.505896i | \(0.168838\pi\) | |||||||
\(878\) | −20.3866 | + | 11.7702i | −0.688014 | + | 0.397225i | ||||
\(879\) | −24.8546 | − | 14.3498i | −0.838324 | − | 0.484007i | ||||
\(880\) | 23.2613 | − | 40.2898i | 0.784140 | − | 1.35817i | ||||
\(881\) | 52.8264i | 1.77977i | 0.456187 | + | 0.889884i | \(0.349215\pi\) | ||||
−0.456187 | + | 0.889884i | \(0.650785\pi\) | |||||||
\(882\) | −36.2178 | −1.21952 | ||||||||
\(883\) | −8.43591 | + | 14.6114i | −0.283891 | + | 0.491713i | −0.972340 | − | 0.233572i | \(-0.924959\pi\) |
0.688449 | + | 0.725285i | \(0.258292\pi\) | |||||||
\(884\) | 23.2494 | − | 25.3183i | 0.781962 | − | 0.851546i | ||||
\(885\) | 8.49334 | + | 14.7109i | 0.285501 | + | 0.494501i | ||||
\(886\) | −1.60439 | − | 2.77888i | −0.0539005 | − | 0.0933584i | ||||
\(887\) | − | 48.0721i | − | 1.61410i | −0.590480 | − | 0.807052i | \(-0.701062\pi\) | ||
0.590480 | − | 0.807052i | \(-0.298938\pi\) | |||||||
\(888\) | −3.18106 | − | 5.50975i | −0.106749 | − | 0.184895i | ||||
\(889\) | 15.9403 | − | 9.20316i | 0.534622 | − | 0.308664i | ||||
\(890\) | 48.4732 | − | 27.9860i | 1.62482 | − | 0.938092i | ||||
\(891\) | 55.0625 | + | 31.7904i | 1.84466 | + | 1.06502i | ||||
\(892\) | −57.2390 | −1.91650 | ||||||||
\(893\) | −35.2979 | + | 61.1378i | −1.18120 | + | 2.04590i | ||||
\(894\) | −5.19162 | + | 2.99738i | −0.173634 | + | 0.100247i | ||||
\(895\) | − | 7.04290i | − | 0.235418i | ||||||
\(896\) | −59.6011 | + | 34.4107i | −1.99113 | + | 1.14958i | ||||
\(897\) | −8.09524 | + | 14.0214i | −0.270292 | + | 0.468160i | ||||
\(898\) | 47.4190 | + | 27.3774i | 1.58239 | + | 0.913595i | ||||
\(899\) | −15.1879 | −0.506545 | ||||||||
\(900\) | 7.64148 | − | 13.2354i | 0.254716 | − | 0.441181i | ||||
\(901\) | −16.7939 | − | 3.74182i | −0.559487 | − | 0.124658i | ||||
\(902\) | −50.5139 | −1.68193 | ||||||||
\(903\) | −45.0292 | + | 38.4081i | −1.49848 | + | 1.27814i | ||||
\(904\) | − | 63.7212i | − | 2.11934i | ||||||
\(905\) | −17.4735 | −0.580837 | ||||||||
\(906\) | −19.3328 | − | 11.1618i | −0.642288 | − | 0.370825i | ||||
\(907\) | 39.7575i | 1.32013i | 0.751211 | + | 0.660063i | \(0.229470\pi\) | ||||
−0.751211 | + | 0.660063i | \(0.770530\pi\) | |||||||
\(908\) | 14.6086 | + | 8.43430i | 0.484805 | + | 0.279902i | ||||
\(909\) | 0.253589 | − | 0.439229i | 0.00841102 | − | 0.0145683i | ||||
\(910\) | 14.7749 | + | 25.5908i | 0.489783 | + | 0.848328i | ||||
\(911\) | 9.10274i | 0.301587i | 0.988565 | + | 0.150794i | \(0.0481829\pi\) | ||||
−0.988565 | + | 0.150794i | \(0.951817\pi\) | |||||||
\(912\) | 68.6949 | − | 39.6610i | 2.27471 | − | 1.31331i | ||||
\(913\) | −46.5412 | − | 26.8706i | −1.54029 | − | 0.889287i | ||||
\(914\) | 68.2033 | 2.25597 | ||||||||
\(915\) | −4.42625 | − | 2.55550i | −0.146327 | − | 0.0844822i | ||||
\(916\) | 12.0317 | + | 20.8395i | 0.397539 | + | 0.688558i | ||||
\(917\) | 11.3270 | + | 19.6189i | 0.374049 | + | 0.647872i | ||||
\(918\) | −37.4520 | + | 11.7649i | −1.23610 | + | 0.388300i | ||||
\(919\) | 46.8822 | 1.54650 | 0.773251 | − | 0.634100i | \(-0.218629\pi\) | ||||
0.773251 | + | 0.634100i | \(0.218629\pi\) | |||||||
\(920\) | −16.3249 | − | 28.2755i | −0.538215 | − | 0.932215i | ||||
\(921\) | 28.4581 | − | 16.4303i | 0.937727 | − | 0.541397i | ||||
\(922\) | 2.26407 | − | 3.92148i | 0.0745630 | − | 0.129147i | ||||
\(923\) | 9.35809 | + | 5.40290i | 0.308025 | + | 0.177839i | ||||
\(924\) | − | 222.336i | − | 7.31431i | ||||||
\(925\) | − | 1.68635i | − | 0.0554468i | ||||||
\(926\) | 37.2498 | − | 64.5185i | 1.22410 | − | 2.12021i | ||||
\(927\) | 1.39081 | − | 2.40895i | 0.0456802 | − | 0.0791205i | ||||
\(928\) | −5.32944 | + | 3.07695i | −0.174947 | + | 0.101006i | ||||
\(929\) | 45.7157 | − | 26.3940i | 1.49988 | − | 0.865958i | 0.499884 | − | 0.866093i | \(-0.333376\pi\) |
1.00000 | 0.000134320i | \(4.27555e-5\pi\) | ||||||||
\(930\) | − | 57.4126i | − | 1.88263i | ||||||
\(931\) | −41.6929 | − | 72.2142i | −1.36643 | − | 2.36672i | ||||
\(932\) | −41.8098 | + | 24.1389i | −1.36953 | + | 0.790696i | ||||
\(933\) | −18.6630 | − | 32.3253i | −0.610999 | − | 1.05828i | ||||
\(934\) | 25.8623 | − | 44.7948i | 0.846240 | − | 1.46573i | ||||
\(935\) | 31.5265 | + | 7.02434i | 1.03103 | + | 0.229721i | ||||
\(936\) | −6.36979 | + | 11.0328i | −0.208203 | + | 0.360618i | ||||
\(937\) | 12.1415 | + | 21.0297i | 0.396645 | + | 0.687009i | 0.993310 | − | 0.115481i | \(-0.0368410\pi\) |
−0.596665 | + | 0.802491i | \(0.703508\pi\) | |||||||
\(938\) | 158.474i | 5.17434i | ||||||||
\(939\) | 2.74297 | + | 4.75096i | 0.0895134 | + | 0.155042i | ||||
\(940\) | 54.9229 | + | 31.7098i | 1.79139 | + | 1.03426i | ||||
\(941\) | −11.7112 | − | 6.76145i | −0.381774 | − | 0.220417i | 0.296816 | − | 0.954935i | \(-0.404075\pi\) |
−0.678590 | + | 0.734518i | \(0.737409\pi\) | |||||||
\(942\) | − | 44.7794i | − | 1.45899i | ||||||
\(943\) | −7.23306 | + | 12.5280i | −0.235541 | + | 0.407969i | ||||
\(944\) | −36.2134 | −1.17865 | ||||||||
\(945\) | − | 23.0464i | − | 0.749699i | ||||||
\(946\) | −61.1217 | − | 71.6584i | −1.98724 | − | 2.32981i | ||||
\(947\) | 33.5617i | 1.09061i | 0.838238 | + | 0.545304i | \(0.183586\pi\) | ||||
−0.838238 | + | 0.545304i | \(0.816414\pi\) | |||||||
\(948\) | −118.171 | −3.83803 | ||||||||
\(949\) | 10.5766 | + | 6.10638i | 0.343329 | + | 0.198221i | ||||
\(950\) | 51.5245 | 1.67168 | ||||||||
\(951\) | −15.2228 | + | 26.3666i | −0.493632 | + | 0.854995i | ||||
\(952\) | 78.1028 | + | 71.7206i | 2.53132 | + | 2.32448i | ||||
\(953\) | 9.75277 | + | 16.8923i | 0.315923 | + | 0.547195i | 0.979633 | − | 0.200795i | \(-0.0643525\pi\) |
−0.663710 | + | 0.747990i | \(0.731019\pi\) | |||||||
\(954\) | 11.9041 | 0.385409 | ||||||||
\(955\) | −6.59917 | + | 3.81003i | −0.213544 | + | 0.123290i | ||||
\(956\) | −58.0943 | + | 100.622i | −1.87891 | + | 3.25436i | ||||
\(957\) | 21.5254i | 0.695819i | ||||||||
\(958\) | 48.4771 | + | 27.9883i | 1.56623 | + | 0.904261i | ||||
\(959\) | 31.3353 | − | 18.0915i | 1.01187 | − | 0.584204i | ||||
\(960\) | 4.91205 | + | 8.50792i | 0.158536 | + | 0.274592i | ||||
\(961\) | 18.1722 | + | 31.4752i | 0.586200 | + | 1.01533i | ||||
\(962\) | 2.62416i | 0.0846062i | ||||||||
\(963\) | −4.68333 | + | 2.70392i | −0.150918 | + | 0.0871327i | ||||
\(964\) | 25.7154 | − | 14.8468i | 0.828238 | − | 0.478183i | ||||
\(965\) | −0.396105 | + | 0.686074i | −0.0127511 | + | 0.0220855i | ||||
\(966\) | −80.7452 | − | 46.6183i | −2.59794 | − | 1.49992i | ||||
\(967\) | 16.0624 | 0.516532 | 0.258266 | − | 0.966074i | \(-0.416849\pi\) | ||||
0.258266 | + | 0.966074i | \(0.416849\pi\) | |||||||
\(968\) | 125.791 | 4.04307 | ||||||||
\(969\) | 40.5633 | + | 37.2487i | 1.30308 | + | 1.19660i | ||||
\(970\) | 32.3673 | − | 56.0618i | 1.03925 | − | 1.80004i | ||||
\(971\) | 21.9395 | + | 38.0003i | 0.704071 | + | 1.21949i | 0.967026 | + | 0.254678i | \(0.0819696\pi\) |
−0.262955 | + | 0.964808i | \(0.584697\pi\) | |||||||
\(972\) | 41.9137 | − | 24.1989i | 1.34438 | − | 0.776179i | ||||
\(973\) | −60.1308 | −1.92770 | ||||||||
\(974\) | −49.9365 | + | 28.8309i | −1.60007 | + | 0.923800i | ||||
\(975\) | −10.6481 | + | 6.14771i | −0.341014 | + | 0.196884i | ||||
\(976\) | 9.43620 | − | 5.44799i | 0.302045 | − | 0.174386i | ||||
\(977\) | 3.21030 | − | 5.56040i | 0.102707 | − | 0.177893i | −0.810092 | − | 0.586302i | \(-0.800583\pi\) |
0.912799 | + | 0.408409i | \(0.133916\pi\) | |||||||
\(978\) | 21.1583 | 0.676567 | ||||||||
\(979\) | 80.5842 | + | 46.5253i | 2.57548 | + | 1.48696i | ||||
\(980\) | −64.8734 | + | 37.4547i | −2.07230 | + | 1.19645i | ||||
\(981\) | 12.0594i | 0.385028i | ||||||||
\(982\) | 8.55777 | + | 14.8225i | 0.273089 | + | 0.473005i | ||||
\(983\) | −3.55603 | − | 2.05307i | −0.113420 | − | 0.0654828i | 0.442217 | − | 0.896908i | \(-0.354192\pi\) |
−0.555637 | + | 0.831425i | \(0.687525\pi\) | |||||||
\(984\) | −20.7233 | + | 35.8938i | −0.660635 | + | 1.14425i | ||||
\(985\) | 8.69760 | 0.277129 | ||||||||
\(986\) | −14.1157 | − | 12.9623i | −0.449537 | − | 0.412803i | ||||
\(987\) | 97.0142 | 3.08800 | ||||||||
\(988\) | −54.7545 | −1.74197 | ||||||||
\(989\) | −26.5241 | + | 4.89816i | −0.843417 | + | 0.155752i | ||||
\(990\) | −22.3470 | −0.710235 | ||||||||
\(991\) | 61.9572i | 1.96814i | 0.177794 | + | 0.984068i | \(0.443104\pi\) | ||||
−0.177794 | + | 0.984068i | \(0.556896\pi\) | |||||||
\(992\) | 23.6312 | + | 13.6435i | 0.750291 | + | 0.433181i | ||||
\(993\) | 10.6891i | 0.339210i | ||||||||
\(994\) | −31.1138 | + | 53.8907i | −0.986870 | + | 1.70931i | ||||
\(995\) | −6.85043 | + | 11.8653i | −0.217173 | + | 0.376155i | ||||
\(996\) | −71.2870 | + | 41.1576i | −2.25882 | + | 1.30413i | ||||
\(997\) | − | 13.1965i | − | 0.417936i | −0.977922 | − | 0.208968i | \(-0.932990\pi\) | ||
0.977922 | − | 0.208968i | \(-0.0670104\pi\) | |||||||
\(998\) | 14.6651 | − | 8.46689i | 0.464215 | − | 0.268015i | ||||
\(999\) | 1.02331 | − | 1.77243i | 0.0323762 | − | 0.0560772i |
(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 | 731.2.j.a.135.6 | yes | 128 | |
17.16 | even | 2 | inner | 731.2.j.a.135.5 | ✓ | 128 | |
43.36 | even | 3 | inner | 731.2.j.a.509.5 | yes | 128 | |
731.509 | even | 6 | inner | 731.2.j.a.509.6 | yes | 128 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.j.a.135.5 | ✓ | 128 | 17.16 | even | 2 | inner | |
731.2.j.a.135.6 | yes | 128 | 1.1 | even | 1 | trivial | |
731.2.j.a.509.5 | yes | 128 | 43.36 | even | 3 | inner | |
731.2.j.a.509.6 | yes | 128 | 731.509 | even | 6 | inner |