Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [156,3,Mod(103,156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(156, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("156.103");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 156 = 2^{2} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 156.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.25069212402\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 103.12 | ||
Character | \(\chi\) | \(=\) | 156.103 |
Dual form | 156.3.e.c.103.11 |
$q$-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 \(\left(\mathbb{Z}/156\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(79\) | \(145\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0830862 | + | 1.99827i | −0.0415431 | + | 0.999137i | ||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | −3.98619 | − | 0.332058i | −0.996548 | − | 0.0830145i | ||||
\(5\) | − | 0.451006i | − | 0.0902012i | −0.998982 | − | 0.0451006i | \(-0.985639\pi\) | ||
0.998982 | − | 0.0451006i | \(-0.0143608\pi\) | |||||||
\(6\) | 3.46111 | + | 0.143910i | 0.576852 | + | 0.0239849i | ||||
\(7\) | 9.24405 | 1.32058 | 0.660289 | − | 0.751011i | \(-0.270434\pi\) | ||||
0.660289 | + | 0.751011i | \(0.270434\pi\) | |||||||
\(8\) | 0.994741 | − | 7.93791i | 0.124343 | − | 0.992239i | ||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0.901234 | + | 0.0374724i | 0.0901234 | + | 0.00374724i | ||||
\(11\) | 11.2653 | 1.02412 | 0.512059 | − | 0.858951i | \(-0.328883\pi\) | ||||
0.512059 | + | 0.858951i | \(0.328883\pi\) | |||||||
\(12\) | −0.575141 | + | 6.90429i | −0.0479284 | + | 0.575357i | ||||
\(13\) | 8.66010 | + | 9.69550i | 0.666162 | + | 0.745807i | ||||
\(14\) | −0.768053 | + | 18.4721i | −0.0548609 | + | 1.31944i | ||||
\(15\) | −0.781166 | −0.0520777 | ||||||||
\(16\) | 15.7795 | + | 2.64730i | 0.986217 | + | 0.165456i | ||||
\(17\) | −5.48353 | −0.322561 | −0.161280 | − | 0.986909i | \(-0.551562\pi\) | ||||
−0.161280 | + | 0.986909i | \(0.551562\pi\) | |||||||
\(18\) | 0.249259 | − | 5.99482i | 0.0138477 | − | 0.333046i | ||||
\(19\) | 15.6424 | 0.823286 | 0.411643 | − | 0.911345i | \(-0.364955\pi\) | ||||
0.411643 | + | 0.911345i | \(0.364955\pi\) | |||||||
\(20\) | −0.149760 | + | 1.79780i | −0.00748801 | + | 0.0898899i | ||||
\(21\) | − | 16.0112i | − | 0.762436i | ||||||
\(22\) | −0.935990 | + | 22.5111i | −0.0425450 | + | 1.02323i | ||||
\(23\) | − | 15.8759i | − | 0.690255i | −0.938556 | − | 0.345128i | \(-0.887836\pi\) | ||
0.938556 | − | 0.345128i | \(-0.112164\pi\) | |||||||
\(24\) | −13.7489 | − | 1.72294i | −0.572870 | − | 0.0717892i | ||||
\(25\) | 24.7966 | 0.991864 | ||||||||
\(26\) | −20.0938 | + | 16.4997i | −0.772838 | + | 0.634603i | ||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | −36.8486 | − | 3.06956i | −1.31602 | − | 0.109627i | ||||
\(29\) | −41.4435 | −1.42908 | −0.714542 | − | 0.699592i | \(-0.753365\pi\) | ||||
−0.714542 | + | 0.699592i | \(0.753365\pi\) | |||||||
\(30\) | 0.0649041 | − | 1.56098i | 0.00216347 | − | 0.0520328i | ||||
\(31\) | −13.7377 | −0.443151 | −0.221575 | − | 0.975143i | \(-0.571120\pi\) | ||||
−0.221575 | + | 0.975143i | \(0.571120\pi\) | |||||||
\(32\) | −6.60108 | + | 31.3118i | −0.206284 | + | 0.978492i | ||||
\(33\) | − | 19.5121i | − | 0.591274i | ||||||
\(34\) | 0.455606 | − | 10.9576i | 0.0134002 | − | 0.322282i | ||||
\(35\) | − | 4.16912i | − | 0.119118i | ||||||
\(36\) | 11.9586 | + | 0.996174i | 0.332183 | + | 0.0276715i | ||||
\(37\) | 1.35152i | 0.0365275i | 0.999833 | + | 0.0182637i | \(0.00581385\pi\) | ||||
−0.999833 | + | 0.0182637i | \(0.994186\pi\) | |||||||
\(38\) | −1.29967 | + | 31.2579i | −0.0342019 | + | 0.822575i | ||||
\(39\) | 16.7931 | − | 14.9997i | 0.430592 | − | 0.384609i | ||||
\(40\) | −3.58005 | − | 0.448634i | −0.0895012 | − | 0.0112159i | ||||
\(41\) | 31.3221i | 0.763952i | 0.924172 | + | 0.381976i | \(0.124756\pi\) | ||||
−0.924172 | + | 0.381976i | \(0.875244\pi\) | |||||||
\(42\) | 31.9947 | + | 1.33031i | 0.761778 | + | 0.0316740i | ||||
\(43\) | − | 78.9583i | − | 1.83624i | −0.396304 | − | 0.918120i | \(-0.629707\pi\) | ||
0.396304 | − | 0.918120i | \(-0.370293\pi\) | |||||||
\(44\) | −44.9056 | − | 3.74073i | −1.02058 | − | 0.0850166i | ||||
\(45\) | 1.35302i | 0.0300671i | ||||||||
\(46\) | 31.7243 | + | 1.31907i | 0.689659 | + | 0.0286754i | ||||
\(47\) | 39.5689 | 0.841892 | 0.420946 | − | 0.907086i | \(-0.361698\pi\) | ||||
0.420946 | + | 0.907086i | \(0.361698\pi\) | |||||||
\(48\) | 4.58525 | − | 27.3309i | 0.0955260 | − | 0.569393i | ||||
\(49\) | 36.4524 | 0.743927 | ||||||||
\(50\) | −2.06026 | + | 49.5504i | −0.0412051 | + | 0.991007i | ||||
\(51\) | 9.49775i | 0.186230i | ||||||||
\(52\) | −31.3014 | − | 41.5238i | −0.601949 | − | 0.798534i | ||||
\(53\) | −67.3481 | −1.27072 | −0.635359 | − | 0.772217i | \(-0.719148\pi\) | ||||
−0.635359 | + | 0.772217i | \(0.719148\pi\) | |||||||
\(54\) | −10.3833 | − | 0.431729i | −0.192284 | − | 0.00799498i | ||||
\(55\) | − | 5.08071i | − | 0.0923766i | ||||||
\(56\) | 9.19543 | − | 73.3785i | 0.164204 | − | 1.31033i | ||||
\(57\) | − | 27.0935i | − | 0.475324i | ||||||
\(58\) | 3.44338 | − | 82.8153i | 0.0593686 | − | 1.42785i | ||||
\(59\) | −59.4363 | −1.00740 | −0.503698 | − | 0.863880i | \(-0.668027\pi\) | ||||
−0.503698 | + | 0.863880i | \(0.668027\pi\) | |||||||
\(60\) | 3.11388 | + | 0.259392i | 0.0518980 | + | 0.00432321i | ||||
\(61\) | 36.6282 | 0.600462 | 0.300231 | − | 0.953866i | \(-0.402936\pi\) | ||||
0.300231 | + | 0.953866i | \(0.402936\pi\) | |||||||
\(62\) | 1.14141 | − | 27.4516i | 0.0184099 | − | 0.442768i | ||||
\(63\) | −27.7321 | −0.440193 | ||||||||
\(64\) | −62.0210 | − | 15.7923i | −0.969078 | − | 0.246755i | ||||
\(65\) | 4.37273 | − | 3.90576i | 0.0672728 | − | 0.0600886i | ||||
\(66\) | 38.9904 | + | 1.62118i | 0.590764 | + | 0.0245634i | ||||
\(67\) | −66.2481 | −0.988777 | −0.494389 | − | 0.869241i | \(-0.664608\pi\) | ||||
−0.494389 | + | 0.869241i | \(0.664608\pi\) | |||||||
\(68\) | 21.8584 | + | 1.82085i | 0.321447 | + | 0.0267772i | ||||
\(69\) | −27.4978 | −0.398519 | ||||||||
\(70\) | 8.33105 | + | 0.346397i | 0.119015 | + | 0.00494853i | ||||
\(71\) | 66.8261 | 0.941212 | 0.470606 | − | 0.882343i | \(-0.344035\pi\) | ||||
0.470606 | + | 0.882343i | \(0.344035\pi\) | |||||||
\(72\) | −2.98422 | + | 23.8137i | −0.0414475 | + | 0.330746i | ||||
\(73\) | 82.4828i | 1.12990i | 0.825125 | + | 0.564950i | \(0.191105\pi\) | ||||
−0.825125 | + | 0.564950i | \(0.808895\pi\) | |||||||
\(74\) | −2.70070 | − | 0.112292i | −0.0364959 | − | 0.00151746i | ||||
\(75\) | − | 42.9490i | − | 0.572653i | ||||||
\(76\) | −62.3538 | − | 5.19420i | −0.820444 | − | 0.0683447i | ||||
\(77\) | 104.137 | 1.35243 | ||||||||
\(78\) | 28.5783 | + | 34.8035i | 0.366388 | + | 0.446198i | ||||
\(79\) | 91.4509i | 1.15761i | 0.815467 | + | 0.578803i | \(0.196480\pi\) | ||||
−0.815467 | + | 0.578803i | \(0.803520\pi\) | |||||||
\(80\) | 1.19395 | − | 7.11664i | 0.0149243 | − | 0.0889580i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −62.5900 | − | 2.60243i | −0.763293 | − | 0.0317370i | ||||
\(83\) | −121.470 | −1.46349 | −0.731746 | − | 0.681578i | \(-0.761294\pi\) | ||||
−0.731746 | + | 0.681578i | \(0.761294\pi\) | |||||||
\(84\) | −5.31663 | + | 63.8236i | −0.0632933 | + | 0.759805i | ||||
\(85\) | 2.47311i | 0.0290954i | ||||||||
\(86\) | 157.780 | + | 6.56035i | 1.83465 | + | 0.0762831i | ||||
\(87\) | 71.7822i | 0.825082i | ||||||||
\(88\) | 11.2060 | − | 89.4229i | 0.127341 | − | 1.01617i | ||||
\(89\) | − | 69.6007i | − | 0.782030i | −0.920384 | − | 0.391015i | \(-0.872124\pi\) | ||
0.920384 | − | 0.391015i | \(-0.127876\pi\) | |||||||
\(90\) | −2.70370 | − | 0.112417i | −0.0300411 | − | 0.00124908i | ||||
\(91\) | 80.0544 | + | 89.6256i | 0.879719 | + | 0.984897i | ||||
\(92\) | −5.27171 | + | 63.2843i | −0.0573012 | + | 0.687873i | ||||
\(93\) | 23.7943i | 0.255853i | ||||||||
\(94\) | −3.28763 | + | 79.0695i | −0.0349748 | + | 0.841165i | ||||
\(95\) | − | 7.05484i | − | 0.0742614i | ||||||
\(96\) | 54.2335 | + | 11.4334i | 0.564933 | + | 0.119098i | ||||
\(97\) | − | 92.5018i | − | 0.953627i | −0.879005 | − | 0.476813i | \(-0.841792\pi\) | ||
0.879005 | − | 0.476813i | \(-0.158208\pi\) | |||||||
\(98\) | −3.02870 | + | 72.8419i | −0.0309051 | + | 0.743285i | ||||
\(99\) | −33.7959 | −0.341372 | ||||||||
\(100\) | −98.8440 | − | 8.23391i | −0.988440 | − | 0.0823391i | ||||
\(101\) | −86.9141 | −0.860535 | −0.430268 | − | 0.902701i | \(-0.641581\pi\) | ||||
−0.430268 | + | 0.902701i | \(0.641581\pi\) | |||||||
\(102\) | −18.9791 | − | 0.789133i | −0.186070 | − | 0.00773659i | ||||
\(103\) | 110.505i | 1.07286i | 0.843944 | + | 0.536431i | \(0.180228\pi\) | ||||
−0.843944 | + | 0.536431i | \(0.819772\pi\) | |||||||
\(104\) | 85.5766 | − | 59.0986i | 0.822852 | − | 0.568256i | ||||
\(105\) | −7.22113 | −0.0687727 | ||||||||
\(106\) | 5.59570 | − | 134.580i | 0.0527896 | − | 1.26962i | ||||
\(107\) | 210.444i | 1.96677i | 0.181535 | + | 0.983384i | \(0.441893\pi\) | ||||
−0.181535 | + | 0.983384i | \(0.558107\pi\) | |||||||
\(108\) | 1.72542 | − | 20.7129i | 0.0159761 | − | 0.191786i | ||||
\(109\) | 178.380i | 1.63651i | 0.574852 | + | 0.818257i | \(0.305060\pi\) | ||||
−0.574852 | + | 0.818257i | \(0.694940\pi\) | |||||||
\(110\) | 10.1527 | + | 0.422137i | 0.0922969 | + | 0.00383761i | ||||
\(111\) | 2.34089 | 0.0210891 | ||||||||
\(112\) | 145.866 | + | 24.4717i | 1.30238 | + | 0.218498i | ||||
\(113\) | −8.85742 | −0.0783843 | −0.0391921 | − | 0.999232i | \(-0.512478\pi\) | ||||
−0.0391921 | + | 0.999232i | \(0.512478\pi\) | |||||||
\(114\) | 54.1402 | + | 2.25110i | 0.474914 | + | 0.0197465i | ||||
\(115\) | −7.16012 | −0.0622619 | ||||||||
\(116\) | 165.202 | + | 13.7616i | 1.42415 | + | 0.118635i | ||||
\(117\) | −25.9803 | − | 29.0865i | −0.222054 | − | 0.248602i | ||||
\(118\) | 4.93834 | − | 118.770i | 0.0418504 | − | 1.00653i | ||||
\(119\) | −50.6900 | −0.425967 | ||||||||
\(120\) | −0.777057 | + | 6.20083i | −0.00647548 | + | 0.0516736i | ||||
\(121\) | 5.90670 | 0.0488157 | ||||||||
\(122\) | −3.04330 | + | 73.1932i | −0.0249451 | + | 0.599944i | ||||
\(123\) | 54.2514 | 0.441068 | ||||||||
\(124\) | 54.7610 | + | 4.56170i | 0.441621 | + | 0.0367879i | ||||
\(125\) | − | 22.4586i | − | 0.179669i | ||||||
\(126\) | 2.30416 | − | 55.4164i | 0.0182870 | − | 0.439813i | ||||
\(127\) | 4.75632i | 0.0374514i | 0.999825 | + | 0.0187257i | \(0.00596092\pi\) | ||||
−0.999825 | + | 0.0187257i | \(0.994039\pi\) | |||||||
\(128\) | 36.7105 | − | 122.623i | 0.286801 | − | 0.957990i | ||||
\(129\) | −136.760 | −1.06015 | ||||||||
\(130\) | 7.44146 | + | 9.06242i | 0.0572420 | + | 0.0697109i | ||||
\(131\) | − | 136.014i | − | 1.03827i | −0.854691 | − | 0.519137i | \(-0.826254\pi\) | ||
0.854691 | − | 0.519137i | \(-0.173746\pi\) | |||||||
\(132\) | −6.47913 | + | 77.7788i | −0.0490843 | + | 0.589233i | ||||
\(133\) | 144.599 | 1.08721 | ||||||||
\(134\) | 5.50430 | − | 132.382i | 0.0410769 | − | 0.987924i | ||||
\(135\) | 2.34350 | 0.0173592 | ||||||||
\(136\) | −5.45469 | + | 43.5278i | −0.0401080 | + | 0.320057i | ||||
\(137\) | − | 140.844i | − | 1.02806i | −0.857772 | − | 0.514030i | \(-0.828152\pi\) | ||
0.857772 | − | 0.514030i | \(-0.171848\pi\) | |||||||
\(138\) | 2.28469 | − | 54.9482i | 0.0165557 | − | 0.398175i | ||||
\(139\) | − | 249.944i | − | 1.79816i | −0.437789 | − | 0.899078i | \(-0.644238\pi\) | ||
0.437789 | − | 0.899078i | \(-0.355762\pi\) | |||||||
\(140\) | −1.38439 | + | 16.6189i | −0.00988851 | + | 0.118707i | ||||
\(141\) | − | 68.5354i | − | 0.486067i | ||||||
\(142\) | −5.55233 | + | 133.537i | −0.0391009 | + | 0.940400i | ||||
\(143\) | 97.5585 | + | 109.223i | 0.682227 | + | 0.763794i | ||||
\(144\) | −47.3384 | − | 7.94189i | −0.328739 | − | 0.0551520i | ||||
\(145\) | 18.6913i | 0.128905i | ||||||||
\(146\) | −164.823 | − | 6.85318i | −1.12893 | − | 0.0469396i | ||||
\(147\) | − | 63.1375i | − | 0.429507i | ||||||
\(148\) | 0.448782 | − | 5.38741i | 0.00303231 | − | 0.0364014i | ||||
\(149\) | 42.7430i | 0.286866i | 0.989660 | + | 0.143433i | \(0.0458141\pi\) | ||||
−0.989660 | + | 0.143433i | \(0.954186\pi\) | |||||||
\(150\) | 85.8238 | + | 3.56847i | 0.572158 | + | 0.0237898i | ||||
\(151\) | −97.5689 | −0.646152 | −0.323076 | − | 0.946373i | \(-0.604717\pi\) | ||||
−0.323076 | + | 0.946373i | \(0.604717\pi\) | |||||||
\(152\) | 15.5602 | − | 124.168i | 0.102370 | − | 0.816897i | ||||
\(153\) | 16.4506 | 0.107520 | ||||||||
\(154\) | −8.65234 | + | 208.094i | −0.0561840 | + | 1.35126i | ||||
\(155\) | 6.19578i | 0.0399727i | ||||||||
\(156\) | −71.9213 | + | 54.2156i | −0.461034 | + | 0.347536i | ||||
\(157\) | 113.388 | 0.722218 | 0.361109 | − | 0.932524i | \(-0.382398\pi\) | ||||
0.361109 | + | 0.932524i | \(0.382398\pi\) | |||||||
\(158\) | −182.744 | − | 7.59831i | −1.15661 | − | 0.0480906i | ||||
\(159\) | 116.650i | 0.733650i | ||||||||
\(160\) | 14.1218 | + | 2.97713i | 0.0882612 | + | 0.0186070i | ||||
\(161\) | − | 146.757i | − | 0.911536i | ||||||
\(162\) | −0.747776 | + | 17.9845i | −0.00461590 | + | 0.111015i | ||||
\(163\) | −177.456 | −1.08868 | −0.544342 | − | 0.838863i | \(-0.683221\pi\) | ||||
−0.544342 | + | 0.838863i | \(0.683221\pi\) | |||||||
\(164\) | 10.4007 | − | 124.856i | 0.0634191 | − | 0.761316i | ||||
\(165\) | −8.80006 | −0.0533337 | ||||||||
\(166\) | 10.0925 | − | 242.730i | 0.0607980 | − | 1.46223i | ||||
\(167\) | 129.955 | 0.778171 | 0.389086 | − | 0.921202i | \(-0.372791\pi\) | ||||
0.389086 | + | 0.921202i | \(0.372791\pi\) | |||||||
\(168\) | −127.095 | − | 15.9270i | −0.756519 | − | 0.0948033i | ||||
\(169\) | −19.0053 | + | 167.928i | −0.112457 | + | 0.993657i | ||||
\(170\) | −4.94194 | − | 0.205481i | −0.0290702 | − | 0.00120871i | ||||
\(171\) | −46.9273 | −0.274429 | ||||||||
\(172\) | −26.2187 | + | 314.743i | −0.152434 | + | 1.82990i | ||||
\(173\) | 118.409 | 0.684443 | 0.342222 | − | 0.939619i | \(-0.388821\pi\) | ||||
0.342222 | + | 0.939619i | \(0.388821\pi\) | |||||||
\(174\) | −143.440 | − | 5.96411i | −0.824370 | − | 0.0342765i | ||||
\(175\) | 229.221 | 1.30983 | ||||||||
\(176\) | 177.760 | + | 29.8225i | 1.01000 | + | 0.169446i | ||||
\(177\) | 102.947i | 0.581620i | ||||||||
\(178\) | 139.081 | + | 5.78286i | 0.781355 | + | 0.0324880i | ||||
\(179\) | − | 260.347i | − | 1.45445i | −0.686398 | − | 0.727226i | \(-0.740809\pi\) | ||
0.686398 | − | 0.727226i | \(-0.259191\pi\) | |||||||
\(180\) | 0.449281 | − | 5.39339i | 0.00249600 | − | 0.0299633i | ||||
\(181\) | −269.411 | −1.48846 | −0.744229 | − | 0.667925i | \(-0.767183\pi\) | ||||
−0.744229 | + | 0.667925i | \(0.767183\pi\) | |||||||
\(182\) | −185.748 | + | 152.524i | −1.02059 | + | 0.838043i | ||||
\(183\) | − | 63.4419i | − | 0.346677i | ||||||
\(184\) | −126.021 | − | 15.7924i | −0.684898 | − | 0.0858281i | ||||
\(185\) | 0.609542 | 0.00329482 | ||||||||
\(186\) | −47.5476 | − | 1.97698i | −0.255632 | − | 0.0106289i | ||||
\(187\) | −61.7735 | −0.330340 | ||||||||
\(188\) | −157.729 | − | 13.1392i | −0.838986 | − | 0.0698892i | ||||
\(189\) | 48.0335i | 0.254145i | ||||||||
\(190\) | 14.0975 | + | 0.586160i | 0.0741973 | + | 0.00308505i | ||||
\(191\) | − | 70.8815i | − | 0.371107i | −0.982634 | − | 0.185554i | \(-0.940592\pi\) | ||
0.982634 | − | 0.185554i | \(-0.0594079\pi\) | |||||||
\(192\) | −27.3531 | + | 107.423i | −0.142464 | + | 0.559497i | ||||
\(193\) | 101.778i | 0.527347i | 0.964612 | + | 0.263674i | \(0.0849342\pi\) | ||||
−0.964612 | + | 0.263674i | \(0.915066\pi\) | |||||||
\(194\) | 184.844 | + | 7.68563i | 0.952803 | + | 0.0396166i | ||||
\(195\) | −6.76497 | − | 7.57379i | −0.0346922 | − | 0.0388399i | ||||
\(196\) | −145.306 | − | 12.1043i | −0.741359 | − | 0.0617567i | ||||
\(197\) | 110.548i | 0.561159i | 0.959831 | + | 0.280579i | \(0.0905266\pi\) | ||||
−0.959831 | + | 0.280579i | \(0.909473\pi\) | |||||||
\(198\) | 2.80797 | − | 67.5334i | 0.0141817 | − | 0.341078i | ||||
\(199\) | − | 172.019i | − | 0.864418i | −0.901773 | − | 0.432209i | \(-0.857734\pi\) | ||
0.901773 | − | 0.432209i | \(-0.142266\pi\) | |||||||
\(200\) | 24.6662 | − | 196.833i | 0.123331 | − | 0.984166i | ||||
\(201\) | 114.745i | 0.570871i | ||||||||
\(202\) | 7.22136 | − | 173.678i | 0.0357493 | − | 0.859792i | ||||
\(203\) | −383.105 | −1.88722 | ||||||||
\(204\) | 3.15381 | − | 37.8599i | 0.0154598 | − | 0.185588i | ||||
\(205\) | 14.1264 | 0.0689095 | ||||||||
\(206\) | −220.819 | − | 9.18143i | −1.07194 | − | 0.0445700i | ||||
\(207\) | 47.6276i | 0.230085i | ||||||||
\(208\) | 110.985 | + | 175.916i | 0.533582 | + | 0.845748i | ||||
\(209\) | 176.217 | 0.843141 | ||||||||
\(210\) | 0.599977 | − | 14.4298i | 0.00285703 | − | 0.0687133i | ||||
\(211\) | − | 16.2184i | − | 0.0768647i | −0.999261 | − | 0.0384323i | \(-0.987764\pi\) | ||
0.999261 | − | 0.0384323i | \(-0.0122364\pi\) | |||||||
\(212\) | 268.463 | + | 22.3635i | 1.26633 | + | 0.105488i | ||||
\(213\) | − | 115.746i | − | 0.543409i | ||||||
\(214\) | −420.525 | − | 17.4850i | −1.96507 | − | 0.0817057i | ||||
\(215\) | −35.6107 | −0.165631 | ||||||||
\(216\) | 41.2466 | + | 5.16882i | 0.190957 | + | 0.0239297i | ||||
\(217\) | −126.992 | −0.585215 | ||||||||
\(218\) | −356.452 | − | 14.8209i | −1.63510 | − | 0.0679859i | ||||
\(219\) | 142.864 | 0.652349 | ||||||||
\(220\) | −1.68709 | + | 20.2527i | −0.00766860 | + | 0.0920578i | ||||
\(221\) | −47.4879 | − | 53.1655i | −0.214877 | − | 0.240568i | ||||
\(222\) | −0.194496 | + | 4.67775i | −0.000876109 | + | 0.0210709i | ||||
\(223\) | 204.961 | 0.919107 | 0.459553 | − | 0.888150i | \(-0.348009\pi\) | ||||
0.459553 | + | 0.888150i | \(0.348009\pi\) | |||||||
\(224\) | −61.0207 | + | 289.447i | −0.272414 | + | 1.29218i | ||||
\(225\) | −74.3898 | −0.330621 | ||||||||
\(226\) | 0.735930 | − | 17.6996i | 0.00325633 | − | 0.0783166i | ||||
\(227\) | 247.892 | 1.09204 | 0.546018 | − | 0.837773i | \(-0.316143\pi\) | ||||
0.546018 | + | 0.837773i | \(0.316143\pi\) | |||||||
\(228\) | −8.99661 | + | 108.000i | −0.0394588 | + | 0.473684i | ||||
\(229\) | − | 341.405i | − | 1.49085i | −0.666589 | − | 0.745425i | \(-0.732246\pi\) | ||
0.666589 | − | 0.745425i | \(-0.267754\pi\) | |||||||
\(230\) | 0.594907 | − | 14.3079i | 0.00258655 | − | 0.0622081i | ||||
\(231\) | − | 180.370i | − | 0.780824i | ||||||
\(232\) | −41.2255 | + | 328.975i | −0.177696 | + | 1.41799i | ||||
\(233\) | 174.456 | 0.748739 | 0.374369 | − | 0.927280i | \(-0.377859\pi\) | ||||
0.374369 | + | 0.927280i | \(0.377859\pi\) | |||||||
\(234\) | 60.2814 | − | 49.4991i | 0.257613 | − | 0.211534i | ||||
\(235\) | − | 17.8458i | − | 0.0759397i | ||||||
\(236\) | 236.925 | + | 19.7363i | 1.00392 | + | 0.0836285i | ||||
\(237\) | 158.398 | 0.668344 | ||||||||
\(238\) | 4.21164 | − | 101.293i | 0.0176960 | − | 0.425599i | ||||
\(239\) | 130.623 | 0.546540 | 0.273270 | − | 0.961937i | \(-0.411895\pi\) | ||||
0.273270 | + | 0.961937i | \(0.411895\pi\) | |||||||
\(240\) | −12.3264 | − | 2.06798i | −0.0513599 | − | 0.00861657i | ||||
\(241\) | − | 204.639i | − | 0.849124i | −0.905399 | − | 0.424562i | \(-0.860428\pi\) | ||
0.905399 | − | 0.424562i | \(-0.139572\pi\) | |||||||
\(242\) | −0.490766 | + | 11.8032i | −0.00202796 | + | 0.0487736i | ||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | −146.007 | − | 12.1627i | −0.598390 | − | 0.0498471i | ||||
\(245\) | − | 16.4403i | − | 0.0671031i | ||||||
\(246\) | −4.50754 | + | 108.409i | −0.0183233 | + | 0.440687i | ||||
\(247\) | 135.465 | + | 151.661i | 0.548442 | + | 0.614013i | ||||
\(248\) | −13.6654 | + | 109.048i | −0.0551025 | + | 0.439712i | ||||
\(249\) | 210.392i | 0.844947i | ||||||||
\(250\) | 44.8784 | + | 1.86600i | 0.179513 | + | 0.00746399i | ||||
\(251\) | − | 338.998i | − | 1.35059i | −0.737548 | − | 0.675295i | \(-0.764017\pi\) | ||
0.737548 | − | 0.675295i | \(-0.235983\pi\) | |||||||
\(252\) | 110.546 | + | 9.20868i | 0.438673 | + | 0.0365424i | ||||
\(253\) | − | 178.846i | − | 0.706902i | ||||||
\(254\) | −9.50444 | − | 0.395185i | −0.0374190 | − | 0.00155585i | ||||
\(255\) | 4.28355 | 0.0167982 | ||||||||
\(256\) | 241.984 | + | 83.5459i | 0.945249 | + | 0.326351i | ||||
\(257\) | −22.5409 | −0.0877078 | −0.0438539 | − | 0.999038i | \(-0.513964\pi\) | ||||
−0.0438539 | + | 0.999038i | \(0.513964\pi\) | |||||||
\(258\) | 11.3629 | − | 273.283i | 0.0440421 | − | 1.05924i | ||||
\(259\) | 12.4935i | 0.0482374i | ||||||||
\(260\) | −18.7275 | + | 14.1171i | −0.0720288 | + | 0.0542966i | ||||
\(261\) | 124.330 | 0.476362 | ||||||||
\(262\) | 271.793 | + | 11.3009i | 1.03738 | + | 0.0431331i | ||||
\(263\) | 164.263i | 0.624575i | 0.949988 | + | 0.312288i | \(0.101095\pi\) | ||||
−0.949988 | + | 0.312288i | \(0.898905\pi\) | |||||||
\(264\) | −154.885 | − | 19.4094i | −0.586686 | − | 0.0735206i | ||||
\(265\) | 30.3744i | 0.114620i | ||||||||
\(266\) | −12.0142 | + | 288.949i | −0.0451663 | + | 1.08628i | ||||
\(267\) | −120.552 | −0.451505 | ||||||||
\(268\) | 264.078 | + | 21.9982i | 0.985364 | + | 0.0820829i | ||||
\(269\) | −354.196 | −1.31671 | −0.658357 | − | 0.752706i | \(-0.728748\pi\) | ||||
−0.658357 | + | 0.752706i | \(0.728748\pi\) | |||||||
\(270\) | −0.194712 | + | 4.68295i | −0.000721157 | + | 0.0173443i | ||||
\(271\) | 460.038 | 1.69756 | 0.848779 | − | 0.528747i | \(-0.177338\pi\) | ||||
0.848779 | + | 0.528747i | \(0.177338\pi\) | |||||||
\(272\) | −86.5272 | − | 14.5165i | −0.318115 | − | 0.0533696i | ||||
\(273\) | 155.236 | − | 138.658i | 0.568631 | − | 0.507906i | ||||
\(274\) | 281.445 | + | 11.7022i | 1.02717 | + | 0.0427088i | ||||
\(275\) | 279.341 | 1.01578 | ||||||||
\(276\) | 109.612 | + | 9.13087i | 0.397144 | + | 0.0330829i | ||||
\(277\) | −320.964 | −1.15871 | −0.579357 | − | 0.815074i | \(-0.696696\pi\) | ||||
−0.579357 | + | 0.815074i | \(0.696696\pi\) | |||||||
\(278\) | 499.456 | + | 20.7669i | 1.79660 | + | 0.0747010i | ||||
\(279\) | 41.2130 | 0.147717 | ||||||||
\(280\) | −33.0941 | − | 4.14720i | −0.118193 | − | 0.0148114i | ||||
\(281\) | 392.202i | 1.39574i | 0.716226 | + | 0.697869i | \(0.245868\pi\) | ||||
−0.716226 | + | 0.697869i | \(0.754132\pi\) | |||||||
\(282\) | 136.952 | + | 5.69435i | 0.485647 | + | 0.0201927i | ||||
\(283\) | 98.5400i | 0.348198i | 0.984728 | + | 0.174099i | \(0.0557013\pi\) | ||||
−0.984728 | + | 0.174099i | \(0.944299\pi\) | |||||||
\(284\) | −266.382 | − | 22.1901i | −0.937964 | − | 0.0781343i | ||||
\(285\) | −12.2193 | −0.0428749 | ||||||||
\(286\) | −226.362 | + | 185.874i | −0.791477 | + | 0.649908i | ||||
\(287\) | 289.543i | 1.00886i | ||||||||
\(288\) | 19.8032 | − | 93.9353i | 0.0687612 | − | 0.326164i | ||||
\(289\) | −258.931 | −0.895955 | ||||||||
\(290\) | −37.3502 | − | 1.55299i | −0.128794 | − | 0.00535512i | ||||
\(291\) | −160.218 | −0.550577 | ||||||||
\(292\) | 27.3891 | − | 328.792i | 0.0937982 | − | 1.12600i | ||||
\(293\) | 480.251i | 1.63908i | 0.573021 | + | 0.819541i | \(0.305772\pi\) | ||||
−0.573021 | + | 0.819541i | \(0.694228\pi\) | |||||||
\(294\) | 126.166 | + | 5.24585i | 0.429136 | + | 0.0178430i | ||||
\(295\) | 26.8062i | 0.0908683i | ||||||||
\(296\) | 10.7282 | + | 1.34441i | 0.0362440 | + | 0.00454192i | ||||
\(297\) | 58.5362i | 0.197091i | ||||||||
\(298\) | −85.4122 | − | 3.55135i | −0.286618 | − | 0.0119173i | ||||
\(299\) | 153.924 | − | 137.487i | 0.514798 | − | 0.459822i | ||||
\(300\) | −14.2615 | + | 171.203i | −0.0475385 | + | 0.570676i | ||||
\(301\) | − | 729.894i | − | 2.42490i | ||||||
\(302\) | 8.10663 | − | 194.969i | 0.0268432 | − | 0.645594i | ||||
\(303\) | 150.540i | 0.496830i | ||||||||
\(304\) | 246.829 | + | 41.4101i | 0.811939 | + | 0.136218i | ||||
\(305\) | − | 16.5195i | − | 0.0541625i | ||||||
\(306\) | −1.36682 | + | 32.8728i | −0.00446672 | + | 0.107427i | ||||
\(307\) | −555.279 | −1.80873 | −0.904363 | − | 0.426764i | \(-0.859653\pi\) | ||||
−0.904363 | + | 0.426764i | \(0.859653\pi\) | |||||||
\(308\) | −415.110 | − | 34.5795i | −1.34776 | − | 0.112271i | ||||
\(309\) | 191.400 | 0.619417 | ||||||||
\(310\) | −12.3809 | − | 0.514784i | −0.0399382 | − | 0.00166059i | ||||
\(311\) | 290.366i | 0.933654i | 0.884349 | + | 0.466827i | \(0.154603\pi\) | ||||
−0.884349 | + | 0.466827i | \(0.845397\pi\) | |||||||
\(312\) | −102.362 | − | 148.223i | −0.328083 | − | 0.475074i | ||||
\(313\) | −239.279 | −0.764470 | −0.382235 | − | 0.924065i | \(-0.624845\pi\) | ||||
−0.382235 | + | 0.924065i | \(0.624845\pi\) | |||||||
\(314\) | −9.42100 | + | 226.581i | −0.0300032 | + | 0.721594i | ||||
\(315\) | 12.5074i | 0.0397059i | ||||||||
\(316\) | 30.3670 | − | 364.541i | 0.0960981 | − | 1.15361i | ||||
\(317\) | 171.315i | 0.540427i | 0.962800 | + | 0.270214i | \(0.0870943\pi\) | ||||
−0.962800 | + | 0.270214i | \(0.912906\pi\) | |||||||
\(318\) | −233.099 | − | 9.69204i | −0.733016 | − | 0.0304781i | ||||
\(319\) | −466.872 | −1.46355 | ||||||||
\(320\) | −7.12244 | + | 27.9718i | −0.0222576 | + | 0.0874120i | ||||
\(321\) | 364.500 | 1.13551 | ||||||||
\(322\) | 293.261 | + | 12.1935i | 0.910749 | + | 0.0378681i | ||||
\(323\) | −85.7758 | −0.265560 | ||||||||
\(324\) | −35.8757 | − | 2.98852i | −0.110728 | − | 0.00922383i | ||||
\(325\) | 214.741 | + | 240.415i | 0.660742 | + | 0.739739i | ||||
\(326\) | 14.7441 | − | 354.605i | 0.0452273 | − | 1.08774i | ||||
\(327\) | 308.963 | 0.944842 | ||||||||
\(328\) | 248.632 | + | 31.1573i | 0.758024 | + | 0.0949918i | ||||
\(329\) | 365.777 | 1.11178 | ||||||||
\(330\) | 0.731164 | − | 17.5849i | 0.00221565 | − | 0.0532876i | ||||
\(331\) | −21.8179 | −0.0659152 | −0.0329576 | − | 0.999457i | \(-0.510493\pi\) | ||||
−0.0329576 | + | 0.999457i | \(0.510493\pi\) | |||||||
\(332\) | 484.202 | + | 40.3350i | 1.45844 | + | 0.121491i | ||||
\(333\) | − | 4.05455i | − | 0.0121758i | ||||||
\(334\) | −10.7974 | + | 259.685i | −0.0323277 | + | 0.777499i | ||||
\(335\) | 29.8783i | 0.0891889i | ||||||||
\(336\) | 42.3863 | − | 252.648i | 0.126150 | − | 0.751928i | ||||
\(337\) | −58.7892 | −0.174449 | −0.0872243 | − | 0.996189i | \(-0.527800\pi\) | ||||
−0.0872243 | + | 0.996189i | \(0.527800\pi\) | |||||||
\(338\) | −333.987 | − | 51.9303i | −0.988127 | − | 0.153640i | ||||
\(339\) | 15.3415i | 0.0452552i | ||||||||
\(340\) | 0.821215 | − | 9.85828i | 0.00241534 | − | 0.0289949i | ||||
\(341\) | −154.759 | −0.453838 | ||||||||
\(342\) | 3.89901 | − | 93.7736i | 0.0114006 | − | 0.274192i | ||||
\(343\) | −115.990 | −0.338164 | ||||||||
\(344\) | −626.764 | − | 78.5430i | −1.82199 | − | 0.228323i | ||||
\(345\) | 12.4017i | 0.0359469i | ||||||||
\(346\) | −9.83813 | + | 236.613i | −0.0284339 | + | 0.683852i | ||||
\(347\) | 361.864i | 1.04284i | 0.853302 | + | 0.521418i | \(0.174597\pi\) | ||||
−0.853302 | + | 0.521418i | \(0.825403\pi\) | |||||||
\(348\) | 23.8358 | − | 286.138i | 0.0684938 | − | 0.822234i | ||||
\(349\) | − | 318.629i | − | 0.912977i | −0.889729 | − | 0.456489i | \(-0.849107\pi\) | ||
0.889729 | − | 0.456489i | \(-0.150893\pi\) | |||||||
\(350\) | −19.0451 | + | 458.046i | −0.0544146 | + | 1.30870i | ||||
\(351\) | −50.3793 | + | 44.9992i | −0.143531 | + | 0.128203i | ||||
\(352\) | −74.3630 | + | 352.736i | −0.211259 | + | 1.00209i | ||||
\(353\) | 162.240i | 0.459602i | 0.973238 | + | 0.229801i | \(0.0738076\pi\) | ||||
−0.973238 | + | 0.229801i | \(0.926192\pi\) | |||||||
\(354\) | −205.716 | − | 8.55346i | −0.581118 | − | 0.0241623i | ||||
\(355\) | − | 30.1390i | − | 0.0848985i | ||||||
\(356\) | −23.1115 | + | 277.442i | −0.0649198 | + | 0.779331i | ||||
\(357\) | 87.7977i | 0.245932i | ||||||||
\(358\) | 520.244 | + | 21.6312i | 1.45320 | + | 0.0604225i | ||||
\(359\) | −624.831 | −1.74048 | −0.870238 | − | 0.492632i | \(-0.836035\pi\) | ||||
−0.870238 | + | 0.492632i | \(0.836035\pi\) | |||||||
\(360\) | 10.7401 | + | 1.34590i | 0.0298337 | + | 0.00373862i | ||||
\(361\) | −116.314 | −0.322200 | ||||||||
\(362\) | 22.3843 | − | 538.356i | 0.0618352 | − | 1.48717i | ||||
\(363\) | − | 10.2307i | − | 0.0281838i | ||||||
\(364\) | −289.351 | − | 383.848i | −0.794921 | − | 1.05453i | ||||
\(365\) | 37.2002 | 0.101918 | ||||||||
\(366\) | 126.774 | + | 5.27115i | 0.346378 | + | 0.0144020i | ||||
\(367\) | 249.912i | 0.680958i | 0.940252 | + | 0.340479i | \(0.110589\pi\) | ||||
−0.940252 | + | 0.340479i | \(0.889411\pi\) | |||||||
\(368\) | 42.0281 | − | 250.513i | 0.114207 | − | 0.680742i | ||||
\(369\) | − | 93.9662i | − | 0.254651i | ||||||
\(370\) | −0.0506446 | + | 1.21803i | −0.000136877 | + | 0.00329198i | ||||
\(371\) | −622.569 | −1.67808 | ||||||||
\(372\) | 7.90110 | − | 94.8489i | 0.0212395 | − | 0.254970i | ||||
\(373\) | 511.549 | 1.37144 | 0.685722 | − | 0.727863i | \(-0.259486\pi\) | ||||
0.685722 | + | 0.727863i | \(0.259486\pi\) | |||||||
\(374\) | 5.13253 | − | 123.440i | 0.0137233 | − | 0.330055i | ||||
\(375\) | −38.8994 | −0.103732 | ||||||||
\(376\) | 39.3608 | − | 314.095i | 0.104683 | − | 0.835358i | ||||
\(377\) | −358.904 | − | 401.815i | −0.952001 | − | 1.06582i | ||||
\(378\) | −95.9840 | − | 3.99092i | −0.253926 | − | 0.0105580i | ||||
\(379\) | −28.7478 | −0.0758517 | −0.0379258 | − | 0.999281i | \(-0.512075\pi\) | ||||
−0.0379258 | + | 0.999281i | \(0.512075\pi\) | |||||||
\(380\) | −2.34261 | + | 28.1219i | −0.00616478 | + | 0.0740051i | ||||
\(381\) | 8.23820 | 0.0216226 | ||||||||
\(382\) | 141.641 | + | 5.88928i | 0.370787 | + | 0.0154170i | ||||
\(383\) | 259.475 | 0.677479 | 0.338740 | − | 0.940880i | \(-0.389999\pi\) | ||||
0.338740 | + | 0.940880i | \(0.389999\pi\) | |||||||
\(384\) | −212.389 | − | 63.5844i | −0.553096 | − | 0.165584i | ||||
\(385\) | − | 46.9664i | − | 0.121991i | ||||||
\(386\) | −203.380 | − | 8.45636i | −0.526892 | − | 0.0219077i | ||||
\(387\) | 236.875i | 0.612080i | ||||||||
\(388\) | −30.7160 | + | 368.730i | −0.0791648 | + | 0.950335i | ||||
\(389\) | 634.076 | 1.63002 | 0.815008 | − | 0.579450i | \(-0.196733\pi\) | ||||
0.815008 | + | 0.579450i | \(0.196733\pi\) | |||||||
\(390\) | 15.6966 | − | 12.8890i | 0.0402476 | − | 0.0330487i | ||||
\(391\) | 87.0558i | 0.222649i | ||||||||
\(392\) | 36.2607 | − | 289.356i | 0.0925018 | − | 0.738154i | ||||
\(393\) | −235.583 | −0.599447 | ||||||||
\(394\) | −220.906 | − | 9.18504i | −0.560674 | − | 0.0233123i | ||||
\(395\) | 41.2449 | 0.104418 | ||||||||
\(396\) | 134.717 | + | 11.2222i | 0.340194 | + | 0.0283389i | ||||
\(397\) | 458.005i | 1.15367i | 0.816862 | + | 0.576833i | \(0.195712\pi\) | ||||
−0.816862 | + | 0.576833i | \(0.804288\pi\) | |||||||
\(398\) | 343.742 | + | 14.2924i | 0.863672 | + | 0.0359106i | ||||
\(399\) | − | 250.454i | − | 0.627703i | ||||||
\(400\) | 391.277 | + | 65.6439i | 0.978193 | + | 0.164110i | ||||
\(401\) | 384.993i | 0.960083i | 0.877246 | + | 0.480042i | \(0.159378\pi\) | ||||
−0.877246 | + | 0.480042i | \(0.840622\pi\) | |||||||
\(402\) | −229.292 | − | 9.53373i | −0.570378 | − | 0.0237158i | ||||
\(403\) | −118.970 | − | 133.194i | −0.295210 | − | 0.330505i | ||||
\(404\) | 346.456 | + | 28.8605i | 0.857565 | + | 0.0714369i | ||||
\(405\) | − | 4.05906i | − | 0.0100224i | ||||||
\(406\) | 31.8308 | − | 765.549i | 0.0784009 | − | 1.88559i | ||||
\(407\) | 15.2252i | 0.0374084i | ||||||||
\(408\) | 75.3924 | + | 9.44780i | 0.184785 | + | 0.0231564i | ||||
\(409\) | − | 227.989i | − | 0.557431i | −0.960374 | − | 0.278716i | \(-0.910091\pi\) | ||
0.960374 | − | 0.278716i | \(-0.0899087\pi\) | |||||||
\(410\) | −1.17371 | + | 28.2285i | −0.00286271 | + | 0.0688500i | ||||
\(411\) | −243.949 | −0.593550 | ||||||||
\(412\) | 36.6940 | − | 440.493i | 0.0890631 | − | 1.06916i | ||||
\(413\) | −549.432 | −1.33034 | ||||||||
\(414\) | −95.1730 | − | 3.95720i | −0.229886 | − | 0.00955845i | ||||
\(415\) | 54.7836i | 0.132009i | ||||||||
\(416\) | −360.749 | + | 207.162i | −0.867185 | + | 0.497986i | ||||
\(417\) | −432.915 | −1.03817 | ||||||||
\(418\) | −14.6412 | + | 352.129i | −0.0350267 | + | 0.842413i | ||||
\(419\) | − | 698.831i | − | 1.66785i | −0.551875 | − | 0.833927i | \(-0.686087\pi\) | ||
0.551875 | − | 0.833927i | \(-0.313913\pi\) | |||||||
\(420\) | 28.7848 | + | 2.39784i | 0.0685353 | + | 0.00570913i | ||||
\(421\) | 559.647i | 1.32933i | 0.747142 | + | 0.664664i | \(0.231425\pi\) | ||||
−0.747142 | + | 0.664664i | \(0.768575\pi\) | |||||||
\(422\) | 32.4089 | + | 1.34753i | 0.0767983 | + | 0.00319320i | ||||
\(423\) | −118.707 | −0.280631 | ||||||||
\(424\) | −66.9939 | + | 534.603i | −0.158004 | + | 1.26086i | ||||
\(425\) | −135.973 | −0.319936 | ||||||||
\(426\) | 231.292 | + | 9.61691i | 0.542940 | + | 0.0225749i | ||||
\(427\) | 338.593 | 0.792958 | ||||||||
\(428\) | 69.8797 | − | 838.872i | 0.163270 | − | 1.95998i | ||||
\(429\) | 189.179 | − | 168.976i | 0.440977 | − | 0.393884i | ||||
\(430\) | 2.95876 | − | 71.1599i | 0.00688083 | − | 0.165488i | ||||
\(431\) | −134.369 | −0.311762 | −0.155881 | − | 0.987776i | \(-0.549822\pi\) | ||||
−0.155881 | + | 0.987776i | \(0.549822\pi\) | |||||||
\(432\) | −13.7557 | + | 81.9926i | −0.0318420 | + | 0.189798i | ||||
\(433\) | 58.1735 | 0.134350 | 0.0671749 | − | 0.997741i | \(-0.478601\pi\) | ||||
0.0671749 | + | 0.997741i | \(0.478601\pi\) | |||||||
\(434\) | 10.5513 | − | 253.764i | 0.0243117 | − | 0.584710i | ||||
\(435\) | 32.3742 | 0.0744235 | ||||||||
\(436\) | 59.2325 | − | 711.058i | 0.135854 | − | 1.63087i | ||||
\(437\) | − | 248.337i | − | 0.568278i | ||||||
\(438\) | −11.8701 | + | 285.482i | −0.0271006 | + | 0.651785i | ||||
\(439\) | − | 534.300i | − | 1.21709i | −0.793521 | − | 0.608543i | \(-0.791754\pi\) | ||
0.793521 | − | 0.608543i | \(-0.208246\pi\) | |||||||
\(440\) | −40.3303 | − | 5.05399i | −0.0916597 | − | 0.0114863i | ||||
\(441\) | −109.357 | −0.247976 | ||||||||
\(442\) | 110.185 | − | 90.4765i | 0.249287 | − | 0.204698i | ||||
\(443\) | 244.149i | 0.551127i | 0.961283 | + | 0.275563i | \(0.0888644\pi\) | ||||
−0.961283 | + | 0.275563i | \(0.911136\pi\) | |||||||
\(444\) | −9.33126 | − | 0.777313i | −0.0210164 | − | 0.00175070i | ||||
\(445\) | −31.3903 | −0.0705401 | ||||||||
\(446\) | −17.0294 | + | 409.568i | −0.0381826 | + | 0.918313i | ||||
\(447\) | 74.0330 | 0.165622 | ||||||||
\(448\) | −573.325 | − | 145.985i | −1.27974 | − | 0.325860i | ||||
\(449\) | − | 570.002i | − | 1.26949i | −0.772721 | − | 0.634746i | \(-0.781105\pi\) | ||
0.772721 | − | 0.634746i | \(-0.218895\pi\) | |||||||
\(450\) | 6.18077 | − | 148.651i | 0.0137350 | − | 0.330336i | ||||
\(451\) | 352.852i | 0.782377i | ||||||||
\(452\) | 35.3074 | + | 2.94118i | 0.0781137 | + | 0.00650703i | ||||
\(453\) | 168.994i | 0.373056i | ||||||||
\(454\) | −20.5964 | + | 495.356i | −0.0453666 | + | 1.09109i | ||||
\(455\) | 40.4217 | − | 36.1050i | 0.0888389 | − | 0.0793517i | ||||
\(456\) | −215.066 | − | 26.9510i | −0.471636 | − | 0.0591031i | ||||
\(457\) | − | 142.300i | − | 0.311379i | −0.987806 | − | 0.155690i | \(-0.950240\pi\) | ||
0.987806 | − | 0.155690i | \(-0.0497600\pi\) | |||||||
\(458\) | 682.220 | + | 28.3660i | 1.48956 | + | 0.0619346i | ||||
\(459\) | − | 28.4933i | − | 0.0620768i | ||||||
\(460\) | 28.5416 | + | 2.37757i | 0.0620470 | + | 0.00516864i | ||||
\(461\) | 687.268i | 1.49082i | 0.666607 | + | 0.745410i | \(0.267746\pi\) | ||||
−0.666607 | + | 0.745410i | \(0.732254\pi\) | |||||||
\(462\) | 360.429 | + | 14.9863i | 0.780150 | + | 0.0324379i | ||||
\(463\) | −675.771 | −1.45955 | −0.729774 | − | 0.683688i | \(-0.760375\pi\) | ||||
−0.729774 | + | 0.683688i | \(0.760375\pi\) | |||||||
\(464\) | −653.956 | − | 109.713i | −1.40939 | − | 0.236451i | ||||
\(465\) | 10.7314 | 0.0230783 | ||||||||
\(466\) | −14.4949 | + | 348.611i | −0.0311049 | + | 0.748093i | ||||
\(467\) | − | 374.263i | − | 0.801421i | −0.916205 | − | 0.400710i | \(-0.868763\pi\) | ||
0.916205 | − | 0.400710i | \(-0.131237\pi\) | |||||||
\(468\) | 93.9041 | + | 124.571i | 0.200650 | + | 0.266178i | ||||
\(469\) | −612.400 | −1.30576 | ||||||||
\(470\) | 35.6608 | + | 1.48274i | 0.0758741 | + | 0.00315477i | ||||
\(471\) | − | 196.394i | − | 0.416973i | ||||||
\(472\) | −59.1237 | + | 471.801i | −0.125262 | + | 0.999578i | ||||
\(473\) | − | 889.488i | − | 1.88052i | ||||||
\(474\) | −13.1607 | + | 316.522i | −0.0277651 | + | 0.667767i | ||||
\(475\) | 387.879 | 0.816588 | ||||||||
\(476\) | 202.060 | + | 16.8320i | 0.424496 | + | 0.0353614i | ||||
\(477\) | 202.044 | 0.423573 | ||||||||
\(478\) | −10.8530 | + | 261.020i | −0.0227050 | + | 0.546068i | ||||
\(479\) | 769.059 | 1.60555 | 0.802775 | − | 0.596282i | \(-0.203356\pi\) | ||||
0.802775 | + | 0.596282i | \(0.203356\pi\) | |||||||
\(480\) | 5.15653 | − | 24.4597i | 0.0107428 | − | 0.0509576i | ||||
\(481\) | −13.1036 | + | 11.7043i | −0.0272425 | + | 0.0243332i | ||||
\(482\) | 408.924 | + | 17.0027i | 0.848391 | + | 0.0352753i | ||||
\(483\) | −254.191 | −0.526276 | ||||||||
\(484\) | −23.5453 | − | 1.96137i | −0.0486472 | − | 0.00405241i | ||||
\(485\) | −41.7189 | −0.0860183 | ||||||||
\(486\) | 31.1500 | + | 1.29519i | 0.0640946 | + | 0.00266499i | ||||
\(487\) | 730.527 | 1.50006 | 0.750028 | − | 0.661406i | \(-0.230040\pi\) | ||||
0.750028 | + | 0.661406i | \(0.230040\pi\) | |||||||
\(488\) | 36.4356 | − | 290.752i | 0.0746630 | − | 0.595802i | ||||
\(489\) | 307.362i | 0.628552i | ||||||||
\(490\) | 32.8522 | + | 1.36596i | 0.0670452 | + | 0.00278767i | ||||
\(491\) | 700.539i | 1.42676i | 0.700777 | + | 0.713380i | \(0.252837\pi\) | ||||
−0.700777 | + | 0.713380i | \(0.747163\pi\) | |||||||
\(492\) | −216.257 | − | 18.0146i | −0.439546 | − | 0.0366151i | ||||
\(493\) | 227.256 | 0.460966 | ||||||||
\(494\) | −314.316 | + | 258.095i | −0.636267 | + | 0.522460i | ||||
\(495\) | 15.2421i | 0.0307922i | ||||||||
\(496\) | −216.773 | − | 36.3677i | −0.437043 | − | 0.0733219i | ||||
\(497\) | 617.743 | 1.24294 | ||||||||
\(498\) | −420.420 | − | 17.4807i | −0.844218 | − | 0.0351017i | ||||
\(499\) | 86.4734 | 0.173293 | 0.0866466 | − | 0.996239i | \(-0.472385\pi\) | ||||
0.0866466 | + | 0.996239i | \(0.472385\pi\) | |||||||
\(500\) | −7.45755 | + | 89.5242i | −0.0149151 | + | 0.179048i | ||||
\(501\) | − | 225.088i | − | 0.449277i | ||||||
\(502\) | 677.410 | + | 28.1661i | 1.34942 | + | 0.0561077i | ||||
\(503\) | − | 157.257i | − | 0.312637i | −0.987707 | − | 0.156319i | \(-0.950037\pi\) | ||
0.987707 | − | 0.156319i | \(-0.0499627\pi\) | |||||||
\(504\) | −27.5863 | + | 220.135i | −0.0547347 | + | 0.436777i | ||||
\(505\) | 39.1988i | 0.0776214i | ||||||||
\(506\) | 357.384 | + | 14.8597i | 0.706292 | + | 0.0293669i | ||||
\(507\) | 290.860 | + | 32.9181i | 0.573688 | + | 0.0649273i | ||||
\(508\) | 1.57938 | − | 18.9596i | 0.00310901 | − | 0.0373221i | ||||
\(509\) | − | 260.990i | − | 0.512751i | −0.966577 | − | 0.256375i | \(-0.917472\pi\) | ||
0.966577 | − | 0.256375i | \(-0.0825283\pi\) | |||||||
\(510\) | −0.355904 | + | 8.55970i | −0.000697850 | + | 0.0167837i | ||||
\(511\) | 762.475i | 1.49212i | ||||||||
\(512\) | −187.053 | + | 476.608i | −0.365338 | + | 0.930875i | ||||
\(513\) | 81.2805i | 0.158441i | ||||||||
\(514\) | 1.87284 | − | 45.0429i | 0.00364365 | − | 0.0876320i | ||||
\(515\) | 49.8383 | 0.0967735 | ||||||||
\(516\) | 545.151 | + | 45.4122i | 1.05649 | + | 0.0880081i | ||||
\(517\) | 445.755 | 0.862196 | ||||||||
\(518\) | −24.9654 | − | 1.03804i | −0.0481957 | − | 0.00200393i | ||||
\(519\) | − | 205.090i | − | 0.395163i | ||||||
\(520\) | −26.6539 | − | 38.5956i | −0.0512574 | − | 0.0742222i | ||||
\(521\) | 328.800 | 0.631095 | 0.315547 | − | 0.948910i | \(-0.397812\pi\) | ||||
0.315547 | + | 0.948910i | \(0.397812\pi\) | |||||||
\(522\) | −10.3301 | + | 248.446i | −0.0197895 | + | 0.475950i | ||||
\(523\) | 235.465i | 0.450220i | 0.974333 | + | 0.225110i | \(0.0722742\pi\) | ||||
−0.974333 | + | 0.225110i | \(0.927726\pi\) | |||||||
\(524\) | −45.1645 | + | 542.177i | −0.0861918 | + | 1.03469i | ||||
\(525\) | − | 397.022i | − | 0.756233i | ||||||
\(526\) | −328.243 | − | 13.6480i | −0.624036 | − | 0.0259468i | ||||
\(527\) | 75.3309 | 0.142943 | ||||||||
\(528\) | 51.6542 | − | 307.890i | 0.0978298 | − | 0.583125i | ||||
\(529\) | 276.957 | 0.523548 | ||||||||
\(530\) | −60.6964 | − | 2.52370i | −0.114521 | − | 0.00476169i | ||||
\(531\) | 178.309 | 0.335799 | ||||||||
\(532\) | −576.401 | − | 48.0154i | −1.08346 | − | 0.0902545i | ||||
\(533\) | −303.683 | + | 271.252i | −0.569761 | + | 0.508916i | ||||
\(534\) | 10.0162 | − | 240.896i | 0.0187569 | − | 0.451115i | ||||
\(535\) | 94.9117 | 0.177405 | ||||||||
\(536\) | −65.8997 | + | 525.872i | −0.122947 | + | 0.981104i | ||||
\(537\) | −450.934 | −0.839728 | ||||||||
\(538\) | 29.4288 | − | 707.780i | 0.0547004 | − | 1.31558i | ||||
\(539\) | 410.647 | 0.761868 | ||||||||
\(540\) | −9.34163 | − | 0.778177i | −0.0172993 | − | 0.00144107i | ||||
\(541\) | − | 497.494i | − | 0.919582i | −0.888027 | − | 0.459791i | \(-0.847924\pi\) | ||
0.888027 | − | 0.459791i | \(-0.152076\pi\) | |||||||
\(542\) | −38.2229 | + | 919.283i | −0.0705219 | + | 1.69609i | ||||
\(543\) | 466.633i | 0.859361i | ||||||||
\(544\) | 36.1972 | − | 171.699i | 0.0665390 | − | 0.315623i | ||||
\(545\) | 80.4505 | 0.147616 | ||||||||
\(546\) | 264.179 | + | 321.725i | 0.483845 | + | 0.589240i | ||||
\(547\) | − | 759.042i | − | 1.38764i | −0.720146 | − | 0.693822i | \(-0.755925\pi\) | ||
0.720146 | − | 0.693822i | \(-0.244075\pi\) | |||||||
\(548\) | −46.7684 | + | 561.432i | −0.0853438 | + | 1.02451i | ||||
\(549\) | −109.885 | −0.200154 | ||||||||
\(550\) | −23.2094 | + | 558.199i | −0.0421989 | + | 1.01491i | ||||
\(551\) | −648.277 | −1.17655 | ||||||||
\(552\) | −27.3532 | + | 218.275i | −0.0495529 | + | 0.395426i | ||||
\(553\) | 845.377i | 1.52871i | ||||||||
\(554\) | 26.6677 | − | 641.374i | 0.0481366 | − | 1.15771i | ||||
\(555\) | − | 1.05576i | − | 0.00190227i | ||||||
\(556\) | −82.9958 | + | 996.324i | −0.149273 | + | 1.79195i | ||||
\(557\) | 135.121i | 0.242586i | 0.992617 | + | 0.121293i | \(0.0387041\pi\) | ||||
−0.992617 | + | 0.121293i | \(0.961296\pi\) | |||||||
\(558\) | −3.42423 | + | 82.3549i | −0.00613662 | + | 0.147589i | ||||
\(559\) | 765.540 | − | 683.787i | 1.36948 | − | 1.22323i | ||||
\(560\) | 11.0369 | − | 65.7866i | 0.0197087 | − | 0.117476i | ||||
\(561\) | 106.995i | 0.190722i | ||||||||
\(562\) | −783.727 | − | 32.5866i | −1.39453 | − | 0.0579833i | ||||
\(563\) | 352.278i | 0.625715i | 0.949800 | + | 0.312858i | \(0.101286\pi\) | ||||
−0.949800 | + | 0.312858i | \(0.898714\pi\) | |||||||
\(564\) | −22.7577 | + | 273.195i | −0.0403506 | + | 0.484389i | ||||
\(565\) | 3.99475i | 0.00707036i | ||||||||
\(566\) | −196.910 | − | 8.18732i | −0.347897 | − | 0.0144652i | ||||
\(567\) | 83.1964 | 0.146731 | ||||||||
\(568\) | 66.4746 | − | 530.460i | 0.117033 | − | 0.933908i | ||||
\(569\) | 646.281 | 1.13582 | 0.567909 | − | 0.823091i | \(-0.307753\pi\) | ||||
0.567909 | + | 0.823091i | \(0.307753\pi\) | |||||||
\(570\) | 1.01526 | − | 24.4176i | 0.00178116 | − | 0.0428378i | ||||
\(571\) | − | 497.031i | − | 0.870456i | −0.900320 | − | 0.435228i | \(-0.856668\pi\) | ||
0.900320 | − | 0.435228i | \(-0.143332\pi\) | |||||||
\(572\) | −352.619 | − | 467.777i | −0.616467 | − | 0.817793i | ||||
\(573\) | −122.770 | −0.214259 | ||||||||
\(574\) | −578.585 | − | 24.0570i | −1.00799 | − | 0.0419112i | ||||
\(575\) | − | 393.668i | − | 0.684639i | ||||||
\(576\) | 186.063 | + | 47.3770i | 0.323026 | + | 0.0822517i | ||||
\(577\) | 916.695i | 1.58873i | 0.607443 | + | 0.794363i | \(0.292195\pi\) | ||||
−0.607443 | + | 0.794363i | \(0.707805\pi\) | |||||||
\(578\) | 21.5136 | − | 517.415i | 0.0372208 | − | 0.895181i | ||||
\(579\) | 176.285 | 0.304464 | ||||||||
\(580\) | 6.20658 | − | 74.5070i | 0.0107010 | − | 0.128460i | ||||
\(581\) | −1122.87 | −1.93266 | ||||||||
\(582\) | 13.3119 | − | 320.159i | 0.0228727 | − | 0.550101i | ||||
\(583\) | −758.696 | −1.30136 | ||||||||
\(584\) | 654.741 | + | 82.0489i | 1.12113 | + | 0.140495i | ||||
\(585\) | −13.1182 | + | 11.7173i | −0.0224243 | + | 0.0200295i | ||||
\(586\) | −959.673 | − | 39.9022i | −1.63767 | − | 0.0680926i | ||||
\(587\) | 507.493 | 0.864554 | 0.432277 | − | 0.901741i | \(-0.357710\pi\) | ||||
0.432277 | + | 0.901741i | \(0.357710\pi\) | |||||||
\(588\) | −20.9653 | + | 251.678i | −0.0356553 | + | 0.428024i | ||||
\(589\) | −214.891 | −0.364840 | ||||||||
\(590\) | −53.5660 | − | 2.22722i | −0.0907899 | − | 0.00377495i | ||||
\(591\) | 191.475 | 0.323985 | ||||||||
\(592\) | −3.57786 | + | 21.3262i | −0.00604369 | + | 0.0360240i | ||||
\(593\) | − | 480.305i | − | 0.809959i | −0.914326 | − | 0.404979i | \(-0.867279\pi\) | ||
0.914326 | − | 0.404979i | \(-0.132721\pi\) | |||||||
\(594\) | −116.971 | − | 4.86355i | −0.196921 | − | 0.00818779i | ||||
\(595\) | 22.8615i | 0.0384227i | ||||||||
\(596\) | 14.1932 | − | 170.382i | 0.0238140 | − | 0.285876i | ||||
\(597\) | −297.946 | −0.499072 | ||||||||
\(598\) | 261.947 | + | 319.006i | 0.438038 | + | 0.533456i | ||||
\(599\) | − | 825.195i | − | 1.37762i | −0.724941 | − | 0.688810i | \(-0.758133\pi\) | ||
0.724941 | − | 0.688810i | \(-0.241867\pi\) | |||||||
\(600\) | −340.925 | − | 42.7231i | −0.568209 | − | 0.0712051i | ||||
\(601\) | −80.2976 | −0.133607 | −0.0668033 | − | 0.997766i | \(-0.521280\pi\) | ||||
−0.0668033 | + | 0.997766i | \(0.521280\pi\) | |||||||
\(602\) | 1458.53 | + | 60.6442i | 2.42280 | + | 0.100738i | ||||
\(603\) | 198.744 | 0.329592 | ||||||||
\(604\) | 388.929 | + | 32.3985i | 0.643921 | + | 0.0536400i | ||||
\(605\) | − | 2.66396i | − | 0.00440324i | ||||||
\(606\) | −300.819 | − | 12.5078i | −0.496401 | − | 0.0206399i | ||||
\(607\) | 59.4403i | 0.0979247i | 0.998801 | + | 0.0489623i | \(0.0155914\pi\) | ||||
−0.998801 | + | 0.0489623i | \(0.984409\pi\) | |||||||
\(608\) | −103.257 | + | 489.792i | −0.169830 | + | 0.805579i | ||||
\(609\) | 663.558i | 1.08959i | ||||||||
\(610\) | 33.0106 | + | 1.37255i | 0.0541157 | + | 0.00225008i | ||||
\(611\) | 342.671 | + | 383.640i | 0.560836 | + | 0.627889i | ||||
\(612\) | −65.5752 | − | 5.46255i | −0.107149 | − | 0.00892574i | ||||
\(613\) | 269.847i | 0.440207i | 0.975476 | + | 0.220104i | \(0.0706396\pi\) | ||||
−0.975476 | + | 0.220104i | \(0.929360\pi\) | |||||||
\(614\) | 46.1360 | − | 1109.60i | 0.0751401 | − | 1.80716i | ||||
\(615\) | − | 24.4677i | − | 0.0397849i | ||||||
\(616\) | 103.589 | − | 826.630i | 0.168164 | − | 1.34193i | ||||
\(617\) | − | 759.186i | − | 1.23045i | −0.788352 | − | 0.615224i | \(-0.789066\pi\) | ||
0.788352 | − | 0.615224i | \(-0.210934\pi\) | |||||||
\(618\) | −15.9027 | + | 382.469i | −0.0257325 | + | 0.618882i | ||||
\(619\) | 890.555 | 1.43870 | 0.719350 | − | 0.694648i | \(-0.244440\pi\) | ||||
0.719350 | + | 0.694648i | \(0.244440\pi\) | |||||||
\(620\) | 2.05736 | − | 24.6976i | 0.00331832 | − | 0.0398348i | ||||
\(621\) | 82.4935 | 0.132840 | ||||||||
\(622\) | −580.231 | − | 24.1255i | −0.932848 | − | 0.0387869i | ||||
\(623\) | − | 643.392i | − | 1.03273i | ||||||
\(624\) | 304.695 | − | 192.232i | 0.488293 | − | 0.308064i | ||||
\(625\) | 609.786 | 0.975657 | ||||||||
\(626\) | 19.8808 | − | 478.145i | 0.0317585 | − | 0.763810i | ||||
\(627\) | − | 305.216i | − | 0.486788i | ||||||
\(628\) | −451.987 | − | 37.6515i | −0.719725 | − | 0.0599545i | ||||
\(629\) | − | 7.41108i | − | 0.0117823i | ||||||
\(630\) | −24.9931 | − | 1.03919i | −0.0396717 | − | 0.00164951i | ||||
\(631\) | −915.214 | −1.45042 | −0.725209 | − | 0.688528i | \(-0.758257\pi\) | ||||
−0.725209 | + | 0.688528i | \(0.758257\pi\) | |||||||
\(632\) | 725.929 | + | 90.9699i | 1.14862 | + | 0.143940i | ||||
\(633\) | −28.0912 | −0.0443778 | ||||||||
\(634\) | −342.335 | − | 14.2339i | −0.539960 | − | 0.0224510i | ||||
\(635\) | 2.14513 | 0.00337816 | ||||||||
\(636\) | 38.7347 | − | 464.991i | 0.0609036 | − | 0.731117i | ||||
\(637\) | 315.682 | + | 353.424i | 0.495576 | + | 0.554826i | ||||
\(638\) | 38.7907 | − | 932.939i | 0.0608004 | − | 1.46229i | ||||
\(639\) | −200.478 | −0.313737 | ||||||||
\(640\) | −55.3036 | − | 16.5567i | −0.0864119 | − | 0.0258698i | ||||
\(641\) | 1079.76 | 1.68449 | 0.842243 | − | 0.539099i | \(-0.181235\pi\) | ||||
0.842243 | + | 0.539099i | \(0.181235\pi\) | |||||||
\(642\) | −30.2849 | + | 728.371i | −0.0471728 | + | 1.13453i | ||||
\(643\) | 8.94154 | 0.0139060 | 0.00695299 | − | 0.999976i | \(-0.497787\pi\) | ||||
0.00695299 | + | 0.999976i | \(0.497787\pi\) | |||||||
\(644\) | −48.7319 | + | 585.003i | −0.0756707 | + | 0.908390i | ||||
\(645\) | 61.6795i | 0.0956271i | ||||||||
\(646\) | 7.12679 | − | 171.403i | 0.0110322 | − | 0.265330i | ||||
\(647\) | 128.346i | 0.198372i | 0.995069 | + | 0.0991858i | \(0.0316238\pi\) | ||||
−0.995069 | + | 0.0991858i | \(0.968376\pi\) | |||||||
\(648\) | 8.95267 | − | 71.4412i | 0.0138158 | − | 0.110249i | ||||
\(649\) | −669.567 | −1.03169 | ||||||||
\(650\) | −498.257 | + | 409.136i | −0.766550 | + | 0.629440i | ||||
\(651\) | 219.956i | 0.337874i | ||||||||
\(652\) | 707.372 | + | 58.9255i | 1.08493 | + | 0.0903766i | ||||
\(653\) | −218.498 | −0.334607 | −0.167304 | − | 0.985905i | \(-0.553506\pi\) | ||||
−0.167304 | + | 0.985905i | \(0.553506\pi\) | |||||||
\(654\) | −25.6706 | + | 617.393i | −0.0392517 | + | 0.944026i | ||||
\(655\) | −61.3431 | −0.0936535 | ||||||||
\(656\) | −82.9187 | + | 494.246i | −0.126400 | + | 0.753423i | ||||
\(657\) | − | 247.448i | − | 0.376634i | ||||||
\(658\) | −30.3910 | + | 730.922i | −0.0461870 | + | 1.11082i | ||||
\(659\) | − | 445.749i | − | 0.676402i | −0.941074 | − | 0.338201i | \(-0.890182\pi\) | ||
0.941074 | − | 0.338201i | \(-0.109818\pi\) | |||||||
\(660\) | 35.0787 | + | 2.92213i | 0.0531496 | + | 0.00442747i | ||||
\(661\) | − | 1213.03i | − | 1.83515i | −0.397567 | − | 0.917573i | \(-0.630145\pi\) | ||
0.397567 | − | 0.917573i | \(-0.369855\pi\) | |||||||
\(662\) | 1.81277 | − | 43.5982i | 0.00273832 | − | 0.0658583i | ||||
\(663\) | −92.0854 | + | 82.2515i | −0.138892 | + | 0.124060i | ||||
\(664\) | −120.831 | + | 964.217i | −0.181974 | + | 1.45213i | ||||
\(665\) | − | 65.2152i | − | 0.0980680i | ||||||
\(666\) | 8.10210 | + | 0.336877i | 0.0121653 | + | 0.000505822i | ||||
\(667\) | 657.951i | 0.986433i | ||||||||
\(668\) | −518.024 | − | 43.1525i | −0.775485 | − | 0.0645995i | ||||
\(669\) | − | 355.003i | − | 0.530647i | ||||||
\(670\) | −59.7050 | − | 2.48248i | −0.0891120 | − | 0.00370519i | ||||
\(671\) | 412.627 | 0.614944 | ||||||||
\(672\) | 501.338 | + | 105.691i | 0.746038 | + | 0.157278i | ||||
\(673\) | 414.657 | 0.616132 | 0.308066 | − | 0.951365i | \(-0.400318\pi\) | ||||
0.308066 | + | 0.951365i | \(0.400318\pi\) | |||||||
\(674\) | 4.88457 | − | 117.477i | 0.00724714 | − | 0.174298i | ||||
\(675\) | 128.847i | 0.190884i | ||||||||
\(676\) | 131.521 | − | 663.082i | 0.194557 | − | 0.980891i | ||||
\(677\) | 784.713 | 1.15910 | 0.579552 | − | 0.814935i | \(-0.303228\pi\) | ||||
0.579552 | + | 0.814935i | \(0.303228\pi\) | |||||||
\(678\) | −30.6565 | − | 1.27467i | −0.0452161 | − | 0.00188004i | ||||
\(679\) | − | 855.091i | − | 1.25934i | ||||||
\(680\) | 19.6313 | + | 2.46010i | 0.0288696 | + | 0.00361779i | ||||
\(681\) | − | 429.362i | − | 0.630487i | ||||||
\(682\) | 12.8583 | − | 309.250i | 0.0188539 | − | 0.453446i | ||||
\(683\) | −340.606 | −0.498691 | −0.249346 | − | 0.968415i | \(-0.580216\pi\) | ||||
−0.249346 | + | 0.968415i | \(0.580216\pi\) | |||||||
\(684\) | 187.061 | + | 15.5826i | 0.273481 | + | 0.0227816i | ||||
\(685\) | −63.5216 | −0.0927322 | ||||||||
\(686\) | 9.63720 | − | 231.780i | 0.0140484 | − | 0.337872i | ||||
\(687\) | −591.331 | −0.860743 | ||||||||
\(688\) | 209.026 | − | 1245.92i | 0.303817 | − | 1.81093i | ||||
\(689\) | −583.241 | − | 652.973i | −0.846504 | − | 0.947711i | ||||
\(690\) | −24.7820 | − | 1.03041i | −0.0359159 | − | 0.00149335i | ||||
\(691\) | −604.139 | −0.874297 | −0.437148 | − | 0.899389i | \(-0.644012\pi\) | ||||
−0.437148 | + | 0.899389i | \(0.644012\pi\) | |||||||
\(692\) | −472.000 | − | 39.3186i | −0.682081 | − | 0.0568187i | ||||
\(693\) | −312.411 | −0.450809 | ||||||||
\(694\) | −723.103 | − | 30.0659i | −1.04194 | − | 0.0433226i | ||||
\(695\) | −112.726 | −0.162196 | ||||||||
\(696\) | 569.801 | + | 71.4046i | 0.818679 | + | 0.102593i | ||||
\(697\) | − | 171.755i | − | 0.246421i | ||||||
\(698\) | 636.708 | + | 26.4737i | 0.912189 | + | 0.0379279i | ||||
\(699\) | − | 302.167i | − | 0.432285i | ||||||
\(700\) | −913.719 | − | 76.1146i | −1.30531 | − | 0.108735i | ||||
\(701\) | −546.639 | −0.779799 | −0.389900 | − | 0.920857i | \(-0.627490\pi\) | ||||
−0.389900 | + | 0.920857i | \(0.627490\pi\) | |||||||
\(702\) | −85.7349 | − | 104.410i | −0.122129 | − | 0.148733i | ||||
\(703\) | 21.1410i | 0.0300726i | ||||||||
\(704\) | −698.684 | − | 177.905i | −0.992449 | − | 0.252706i | ||||
\(705\) | −30.9099 | −0.0438438 | ||||||||
\(706\) | −324.199 | − | 13.4799i | −0.459205 | − | 0.0190933i | ||||
\(707\) | −803.438 | −1.13640 | ||||||||
\(708\) | 34.1843 | − | 410.366i | 0.0482829 | − | 0.579613i | ||||
\(709\) | 467.889i | 0.659928i | 0.943993 | + | 0.329964i | \(0.107037\pi\) | ||||
−0.943993 | + | 0.329964i | \(0.892963\pi\) | |||||||
\(710\) | 60.2259 | + | 2.50413i | 0.0848252 | + | 0.00352695i | ||||
\(711\) | − | 274.353i | − | 0.385869i | ||||||
\(712\) | −552.484 | − | 69.2346i | −0.775961 | − | 0.0972396i | ||||
\(713\) | 218.098i | 0.305887i | ||||||||
\(714\) | −175.444 | − | 7.29478i | −0.245720 | − | 0.0102168i | ||||
\(715\) | 49.2601 | − | 43.9995i | 0.0688952 | − | 0.0615378i | ||||
\(716\) | −86.4503 | + | 1037.79i | −0.120741 | + | 1.44943i | ||||
\(717\) | − | 226.246i | − | 0.315545i | ||||||
\(718\) | 51.9148 | − | 1248.58i | 0.0723048 | − | 1.73897i | ||||
\(719\) | 1115.45i | 1.55139i | 0.631106 | + | 0.775697i | \(0.282601\pi\) | ||||
−0.631106 | + | 0.775697i | \(0.717399\pi\) | |||||||
\(720\) | −3.58184 | + | 21.3499i | −0.00497478 | + | 0.0296527i | ||||
\(721\) | 1021.51i | 1.41680i | ||||||||
\(722\) | 9.66411 | − | 232.428i | 0.0133852 | − | 0.321922i | ||||
\(723\) | −354.445 | −0.490242 | ||||||||
\(724\) | 1073.92 | + | 89.4600i | 1.48332 | + | 0.123564i | ||||
\(725\) | −1027.66 | −1.41746 | ||||||||
\(726\) | 20.4437 | + | 0.850031i | 0.0281594 | + | 0.00117084i | ||||
\(727\) | − | 279.653i | − | 0.384666i | −0.981330 | − | 0.192333i | \(-0.938395\pi\) | ||
0.981330 | − | 0.192333i | \(-0.0616054\pi\) | |||||||
\(728\) | 791.074 | − | 546.311i | 1.08664 | − | 0.750427i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | −3.09083 | + | 74.3362i | −0.00423401 | + | 0.101830i | ||||
\(731\) | 432.970i | 0.592298i | ||||||||
\(732\) | −21.0664 | + | 252.892i | −0.0287792 | + | 0.345481i | ||||
\(733\) | 468.555i | 0.639229i | 0.947548 | + | 0.319614i | \(0.103553\pi\) | ||||
−0.947548 | + | 0.319614i | \(0.896447\pi\) | |||||||
\(734\) | −499.392 | − | 20.7642i | −0.680370 | − | 0.0282891i | ||||
\(735\) | −28.4754 | −0.0387420 | ||||||||
\(736\) | 497.101 | + | 104.798i | 0.675409 | + | 0.142388i | ||||
\(737\) | −746.304 | −1.01262 | ||||||||
\(738\) | 187.770 | + | 7.80729i | 0.254431 | + | 0.0105790i | ||||
\(739\) | 108.879 | 0.147333 | 0.0736666 | − | 0.997283i | \(-0.476530\pi\) | ||||
0.0736666 | + | 0.997283i | \(0.476530\pi\) | |||||||
\(740\) | −2.42975 | − | 0.202403i | −0.00328345 | − | 0.000273518i | ||||
\(741\) | 262.685 | − | 234.632i | 0.354500 | − | 0.316643i | ||||
\(742\) | 51.7269 | − | 1244.06i | 0.0697128 | − | 1.67663i | ||||
\(743\) | −1383.12 | −1.86153 | −0.930765 | − | 0.365619i | \(-0.880857\pi\) | ||||
−0.930765 | + | 0.365619i | \(0.880857\pi\) | |||||||
\(744\) | 188.877 | + | 23.6692i | 0.253868 | + | 0.0318134i | ||||
\(745\) | 19.2774 | 0.0258756 | ||||||||
\(746\) | −42.5027 | + | 1022.21i | −0.0569741 | + | 1.37026i | ||||
\(747\) | 364.409 | 0.487831 | ||||||||
\(748\) | 246.241 | + | 20.5124i | 0.329200 | + | 0.0274230i | ||||
\(749\) | 1945.36i | 2.59727i | ||||||||
\(750\) | 3.23200 | − | 77.7316i | 0.00430934 | − | 0.103642i | ||||
\(751\) | 884.139i | 1.17728i | 0.808394 | + | 0.588641i | \(0.200337\pi\) | ||||
−0.808394 | + | 0.588641i | \(0.799663\pi\) | |||||||
\(752\) | 624.377 | + | 104.751i | 0.830288 | + | 0.139296i | ||||
\(753\) | −587.162 | −0.779763 | ||||||||
\(754\) | 832.756 | − | 683.804i | 1.10445 | − | 0.906902i | ||||
\(755\) | 44.0042i | 0.0582837i | ||||||||
\(756\) | 15.9499 | − | 191.471i | 0.0210978 | − | 0.253268i | ||||
\(757\) | 1396.91 | 1.84532 | 0.922661 | − | 0.385613i | \(-0.126010\pi\) | ||||
0.922661 | + | 0.385613i | \(0.126010\pi\) | |||||||
\(758\) | 2.38855 | − | 57.4459i | 0.00315111 | − | 0.0757862i | ||||
\(759\) | −309.771 | −0.408130 | ||||||||
\(760\) | −56.0007 | − | 7.01773i | −0.0736851 | − | 0.00923386i | ||||
\(761\) | − | 138.688i | − | 0.182244i | −0.995840 | − | 0.0911220i | \(-0.970955\pi\) | ||
0.995840 | − | 0.0911220i | \(-0.0290453\pi\) | |||||||
\(762\) | −0.684481 | + | 16.4622i | −0.000898269 | + | 0.0216039i | ||||
\(763\) | 1648.95i | 2.16115i | ||||||||
\(764\) | −23.5368 | + | 282.547i | −0.0308073 | + | 0.369826i | ||||
\(765\) | − | 7.41932i | − | 0.00969846i | ||||||
\(766\) | −21.5588 | + | 518.501i | −0.0281446 | + | 0.676895i | ||||
\(767\) | −514.725 | − | 576.265i | −0.671088 | − | 0.751323i | ||||
\(768\) | 144.706 | − | 419.128i | 0.188419 | − | 0.545740i | ||||
\(769\) | 250.681i | 0.325983i | 0.986627 | + | 0.162992i | \(0.0521143\pi\) | ||||
−0.986627 | + | 0.162992i | \(0.947886\pi\) | |||||||
\(770\) | 93.8517 | + | 3.90226i | 0.121885 | + | 0.00506787i | ||||
\(771\) | 39.0420i | 0.0506381i | ||||||||
\(772\) | 33.7962 | − | 405.707i | 0.0437775 | − | 0.525527i | ||||
\(773\) | − | 885.091i | − | 1.14501i | −0.819902 | − | 0.572504i | \(-0.805972\pi\) | ||
0.819902 | − | 0.572504i | \(-0.194028\pi\) | |||||||
\(774\) | −473.341 | − | 19.6810i | −0.611551 | − | 0.0254277i | ||||
\(775\) | −340.647 | −0.439545 | ||||||||
\(776\) | −734.271 | − | 92.0153i | −0.946226 | − | 0.118576i | ||||
\(777\) | 21.6393 | 0.0278499 | ||||||||
\(778\) | −52.6830 | + | 1267.06i | −0.0677159 | + | 1.62861i | ||||
\(779\) | 489.953i | 0.628951i | ||||||||
\(780\) | 24.4516 | + | 32.4370i | 0.0313481 | + | 0.0415858i | ||||
\(781\) | 752.815 | 0.963912 | ||||||||
\(782\) | −173.961 | − | 7.23314i | −0.222457 | − | 0.00924954i | ||||
\(783\) | − | 215.346i | − | 0.275027i | ||||||
\(784\) | 575.200 | + | 96.5003i | 0.733674 | + | 0.123087i | ||||
\(785\) | − | 51.1388i | − | 0.0651449i | ||||||
\(786\) | 19.5737 | − | 470.759i | 0.0249029 | − | 0.598930i | ||||
\(787\) | 753.982 | 0.958046 | 0.479023 | − | 0.877802i | \(-0.340991\pi\) | ||||
0.479023 | + | 0.877802i | \(0.340991\pi\) | |||||||
\(788\) | 36.7084 | − | 440.667i | 0.0465843 | − | 0.559222i | ||||
\(789\) | 284.512 | 0.360599 | ||||||||
\(790\) | −3.42689 | + | 82.4186i | −0.00433783 | + | 0.104327i | ||||
\(791\) | −81.8784 | −0.103513 | ||||||||
\(792\) | −33.6181 | + | 268.269i | −0.0424471 | + | 0.338723i | ||||
\(793\) | 317.204 | + | 355.129i | 0.400005 | + | 0.447829i | ||||
\(794\) | −915.220 | − | 38.0539i | −1.15267 | − | 0.0479269i | ||||
\(795\) | 52.6100 | 0.0661761 | ||||||||
\(796\) | −57.1204 | + | 685.702i | −0.0717593 | + | 0.861435i | ||||
\(797\) | −354.297 | −0.444538 | −0.222269 | − | 0.974985i | \(-0.571346\pi\) | ||||
−0.222269 | + | 0.974985i | \(0.571346\pi\) | |||||||
\(798\) | 500.475 | + | 20.8092i | 0.627161 | + | 0.0260767i | ||||
\(799\) | −216.977 | −0.271561 | ||||||||
\(800\) | −163.684 | + | 776.425i | −0.204605 | + | 0.970531i | ||||
\(801\) | 208.802i | 0.260677i | ||||||||
\(802\) | −769.322 | − | 31.9876i | −0.959254 | − | 0.0398848i | ||||
\(803\) | 929.192i | 1.15715i | ||||||||
\(804\) | 38.1020 | − | 457.396i | 0.0473906 | − | 0.568900i | ||||
\(805\) | −66.1885 | −0.0822217 | ||||||||
\(806\) | 276.042 | − | 226.667i | 0.342484 | − | 0.281225i | ||||
\(807\) | 613.485i | 0.760205i | ||||||||
\(808\) | −86.4570 | + | 689.917i | −0.107001 | + | 0.853857i | ||||
\(809\) | −770.844 | −0.952836 | −0.476418 | − | 0.879219i | \(-0.658065\pi\) | ||||
−0.476418 | + | 0.879219i | \(0.658065\pi\) | |||||||
\(810\) | 8.11110 | + | 0.337252i | 0.0100137 | + | 0.000416360i | ||||
\(811\) | −288.795 | −0.356098 | −0.178049 | − | 0.984022i | \(-0.556979\pi\) | ||||
−0.178049 | + | 0.984022i | \(0.556979\pi\) | |||||||
\(812\) | 1527.13 | + | 127.213i | 1.88070 | + | 0.156666i | ||||
\(813\) | − | 796.810i | − | 0.980086i | ||||||
\(814\) | −30.4242 | − | 1.26501i | −0.0373761 | − | 0.00155406i | ||||
\(815\) | 80.0336i | 0.0982007i | ||||||||
\(816\) | −25.1434 | + | 149.870i | −0.0308129 | + | 0.183664i | ||||
\(817\) | − | 1235.10i | − | 1.51175i | ||||||
\(818\) | 455.585 | + | 18.9428i | 0.556950 | + | 0.0231574i | ||||
\(819\) | −240.163 | − | 268.877i | −0.293240 | − | 0.328299i | ||||
\(820\) | −56.3107 | − | 4.69080i | −0.0686716 | − | 0.00572049i | ||||
\(821\) | 809.780i | 0.986334i | 0.869935 | + | 0.493167i | \(0.164161\pi\) | ||||
−0.869935 | + | 0.493167i | \(0.835839\pi\) | |||||||
\(822\) | 20.2688 | − | 487.477i | 0.0246579 | − | 0.593038i | ||||
\(823\) | − | 194.010i | − | 0.235735i | −0.993029 | − | 0.117868i | \(-0.962394\pi\) | ||
0.993029 | − | 0.117868i | \(-0.0376058\pi\) | |||||||
\(824\) | 877.178 | + | 109.924i | 1.06454 | + | 0.133402i | ||||
\(825\) | − | 483.832i | − | 0.586463i | ||||||
\(826\) | 45.6503 | − | 1097.92i | 0.0552667 | − | 1.32920i | ||||
\(827\) | 663.097 | 0.801810 | 0.400905 | − | 0.916120i | \(-0.368696\pi\) | ||||
0.400905 | + | 0.916120i | \(0.368696\pi\) | |||||||
\(828\) | 15.8151 | − | 189.853i | 0.0191004 | − | 0.229291i | ||||
\(829\) | −88.1628 | −0.106348 | −0.0531742 | − | 0.998585i | \(-0.516934\pi\) | ||||
−0.0531742 | + | 0.998585i | \(0.516934\pi\) | |||||||
\(830\) | −109.473 | − | 4.55177i | −0.131895 | − | 0.00548406i | ||||
\(831\) | 555.926i | 0.668984i | ||||||||
\(832\) | −383.993 | − | 738.087i | −0.461531 | − | 0.887124i | ||||
\(833\) | −199.888 | −0.239962 | ||||||||
\(834\) | 35.9693 | − | 865.083i | 0.0431286 | − | 1.03727i | ||||
\(835\) | − | 58.6103i | − | 0.0701920i | ||||||
\(836\) | −702.433 | − | 58.5141i | −0.840231 | − | 0.0699930i | ||||
\(837\) | − | 71.3830i | − | 0.0852844i | ||||||
\(838\) | 1396.46 | + | 58.0632i | 1.66641 | + | 0.0692879i | ||||
\(839\) | 719.761 | 0.857879 | 0.428940 | − | 0.903333i | \(-0.358887\pi\) | ||||
0.428940 | + | 0.903333i | \(0.358887\pi\) | |||||||
\(840\) | −7.18315 | + | 57.3207i | −0.00855137 | + | 0.0682390i | ||||
\(841\) | 876.560 | 1.04228 | ||||||||
\(842\) | −1118.33 | − | 46.4990i | −1.32818 | − | 0.0552244i | ||||
\(843\) | 679.314 | 0.805830 | ||||||||
\(844\) | −5.38547 | + | 64.6499i | −0.00638088 | + | 0.0765994i | ||||
\(845\) | 75.7366 | + | 8.57151i | 0.0896291 | + | 0.0101438i | ||||
\(846\) | 9.86290 | − | 237.209i | 0.0116583 | − | 0.280388i | ||||
\(847\) | 54.6018 | 0.0644650 | ||||||||
\(848\) | −1062.72 | − | 178.290i | −1.25320 | − | 0.210248i | ||||
\(849\) | 170.676 | 0.201032 | ||||||||
\(850\) | 11.2975 | − | 271.711i | 0.0132911 | − | 0.319660i | ||||
\(851\) | 21.4565 | 0.0252133 | ||||||||
\(852\) | −38.4344 | + | 461.387i | −0.0451108 | + | 0.541533i | ||||
\(853\) | − | 1206.29i | − | 1.41417i | −0.707129 | − | 0.707085i | \(-0.750010\pi\) | ||
0.707129 | − | 0.707085i | \(-0.249990\pi\) | |||||||
\(854\) | −28.1324 | + | 676.601i | −0.0329419 | + | 0.792273i | ||||
\(855\) | 21.1645i | 0.0247538i | ||||||||
\(856\) | 1670.49 | + | 209.337i | 1.95151 | + | 0.244553i | ||||
\(857\) | 1229.54 | 1.43470 | 0.717352 | − | 0.696711i | \(-0.245354\pi\) | ||||
0.717352 | + | 0.696711i | \(0.245354\pi\) | |||||||
\(858\) | 321.943 | + | 392.071i | 0.375225 | + | 0.456959i | ||||
\(859\) | 754.293i | 0.878106i | 0.898461 | + | 0.439053i | \(0.144686\pi\) | ||||
−0.898461 | + | 0.439053i | \(0.855314\pi\) | |||||||
\(860\) | 141.951 | + | 11.8248i | 0.165059 | + | 0.0137498i | ||||
\(861\) | 501.502 | 0.582465 | ||||||||
\(862\) | 11.1642 | − | 268.506i | 0.0129515 | − | 0.311492i | ||||
\(863\) | 698.704 | 0.809622 | 0.404811 | − | 0.914400i | \(-0.367337\pi\) | ||||
0.404811 | + | 0.914400i | \(0.367337\pi\) | |||||||
\(864\) | −162.701 | − | 34.3002i | −0.188311 | − | 0.0396993i | ||||
\(865\) | − | 53.4030i | − | 0.0617376i | ||||||
\(866\) | −4.83341 | + | 116.246i | −0.00558131 | + | 0.134234i | ||||
\(867\) | 448.481i | 0.517280i | ||||||||
\(868\) | 506.213 | + | 42.1686i | 0.583195 | + | 0.0485814i | ||||
\(869\) | 1030.22i | 1.18552i | ||||||||
\(870\) | −2.68985 | + | 64.6925i | −0.00309178 | + | 0.0743592i | ||||
\(871\) | −573.715 | − | 642.308i | −0.658686 | − | 0.737438i | ||||
\(872\) | 1415.97 | + | 177.442i | 1.62381 | + | 0.203488i | ||||
\(873\) | 277.505i | 0.317876i | ||||||||
\(874\) | 496.246 | + | 20.6334i | 0.567787 | + | 0.0236080i | ||||
\(875\) | − | 207.608i | − | 0.237266i | ||||||
\(876\) | −569.485 | − | 47.4392i | −0.650097 | − | 0.0541544i | ||||
\(877\) | 883.451i | 1.00736i | 0.863892 | + | 0.503678i | \(0.168020\pi\) | ||||
−0.863892 | + | 0.503678i | \(0.831980\pi\) | |||||||
\(878\) | 1067.68 | + | 44.3930i | 1.21603 | + | 0.0505615i | ||||
\(879\) | 831.819 | 0.946324 | ||||||||
\(880\) | 13.4502 | − | 80.1710i | 0.0152843 | − | 0.0911034i | ||||
\(881\) | −736.089 | −0.835515 | −0.417757 | − | 0.908559i | \(-0.637184\pi\) | ||||
−0.417757 | + | 0.908559i | \(0.637184\pi\) | |||||||
\(882\) | 9.08609 | − | 218.526i | 0.0103017 | − | 0.247762i | ||||
\(883\) | − | 161.432i | − | 0.182822i | −0.995813 | − | 0.0914112i | \(-0.970862\pi\) | ||
0.995813 | − | 0.0914112i | \(-0.0291378\pi\) | |||||||
\(884\) | 171.642 | + | 227.697i | 0.194165 | + | 0.257576i | ||||
\(885\) | 46.4296 | 0.0524629 | ||||||||
\(886\) | −487.877 | − | 20.2854i | −0.550651 | − | 0.0228955i | ||||
\(887\) | − | 691.631i | − | 0.779741i | −0.920870 | − | 0.389871i | \(-0.872520\pi\) | ||
0.920870 | − | 0.389871i | \(-0.127480\pi\) | |||||||
\(888\) | 2.32858 | − | 18.5818i | 0.00262228 | − | 0.0209255i | ||||
\(889\) | 43.9677i | 0.0494575i | ||||||||
\(890\) | 2.60810 | − | 62.7265i | 0.00293045 | − | 0.0704792i | ||||
\(891\) | 101.388 | 0.113791 | ||||||||
\(892\) | −817.014 | − | 68.0589i | −0.915934 | − | 0.0762992i | ||||
\(893\) | 618.954 | 0.693118 | ||||||||
\(894\) | −6.15113 | + | 147.938i | −0.00688045 | + | 0.165479i | ||||
\(895\) | −117.418 | −0.131193 | ||||||||
\(896\) | 339.354 | − | 1133.53i | 0.378743 | − | 1.26510i | ||||
\(897\) | −238.134 | − | 266.605i | −0.265478 | − | 0.297218i | ||||
\(898\) | 1139.02 | + | 47.3593i | 1.26840 | + | 0.0527387i | ||||
\(899\) | 569.337 | 0.633300 | ||||||||
\(900\) | 296.532 | + | 24.7017i | 0.329480 | + | 0.0274464i | ||||
\(901\) | 369.305 | 0.409884 | ||||||||
\(902\) | −705.095 | − | 29.3171i | −0.781701 | − | 0.0325024i | ||||
\(903\) | −1264.21 | −1.40002 | ||||||||
\(904\) | −8.81084 | + | 70.3095i | −0.00974650 | + | 0.0777760i | ||||
\(905\) | 121.506i | 0.134261i | ||||||||
\(906\) | −337.697 | − | 14.0411i | −0.372734 | − | 0.0154979i | ||||
\(907\) | 82.2700i | 0.0907056i | 0.998971 | + | 0.0453528i | \(0.0144412\pi\) | ||||
−0.998971 | + | 0.0453528i | \(0.985559\pi\) | |||||||
\(908\) | −988.146 | − | 82.3146i | −1.08827 | − | 0.0906548i | ||||
\(909\) | 260.742 | 0.286845 | ||||||||
\(910\) | 68.7892 | + | 83.7735i | 0.0755926 | + | 0.0920588i | ||||
\(911\) | 659.385i | 0.723804i | 0.932216 | + | 0.361902i | \(0.117872\pi\) | ||||
−0.932216 | + | 0.361902i | \(0.882128\pi\) | |||||||
\(912\) | 71.7245 | − | 427.521i | 0.0786453 | − | 0.468773i | ||||
\(913\) | −1368.39 | −1.49879 | ||||||||
\(914\) | 284.355 | + | 11.8232i | 0.311110 | + | 0.0129357i | ||||
\(915\) | −28.6127 | −0.0312707 | ||||||||
\(916\) | −113.366 | + | 1360.91i | −0.123762 | + | 1.48570i | ||||
\(917\) | − | 1257.32i | − | 1.37112i | ||||||
\(918\) | 56.9373 | + | 2.36740i | 0.0620232 | + | 0.00257886i | ||||
\(919\) | − | 742.422i | − | 0.807859i | −0.914790 | − | 0.403929i | \(-0.867644\pi\) | ||
0.914790 | − | 0.403929i | \(-0.132356\pi\) | |||||||
\(920\) | −7.12246 | + | 56.8364i | −0.00774180 | + | 0.0617787i | ||||
\(921\) | 961.771i | 1.04427i | ||||||||
\(922\) | −1373.35 | − | 57.1025i | −1.48953 | − | 0.0619333i | ||||
\(923\) | 578.721 | + | 647.912i | 0.626999 | + | 0.701963i | ||||
\(924\) | −59.8934 | + | 718.991i | −0.0648197 | + | 0.778129i | ||||
\(925\) | 33.5130i | 0.0362303i | ||||||||
\(926\) | 56.1473 | − | 1350.38i | 0.0606342 | − | 1.45829i | ||||
\(927\) | − | 331.514i | − | 0.357621i | ||||||
\(928\) | 273.571 | − | 1297.67i | 0.294797 | − | 1.39835i | ||||
\(929\) | 161.647i | 0.174001i | 0.996208 | + | 0.0870003i | \(0.0277281\pi\) | ||||
−0.996208 | + | 0.0870003i | \(0.972272\pi\) | |||||||
\(930\) | −0.891631 | + | 21.4443i | −0.000958744 | + | 0.0230584i | ||||
\(931\) | 570.205 | 0.612465 | ||||||||
\(932\) | −695.416 | − | 57.9296i | −0.746155 | − | 0.0621562i | ||||
\(933\) | 502.929 | 0.539045 | ||||||||
\(934\) | 747.881 | + | 31.0961i | 0.800729 | + | 0.0332935i | ||||
\(935\) | 27.8603i | 0.0297971i | ||||||||
\(936\) | −256.730 | + | 177.296i | −0.274284 | + | 0.189419i | ||||
\(937\) | −1303.54 | −1.39118 | −0.695590 | − | 0.718439i | \(-0.744857\pi\) | ||||
−0.695590 | + | 0.718439i | \(0.744857\pi\) | |||||||
\(938\) | 50.8821 | − | 1223.74i | 0.0542453 | − | 1.30463i | ||||
\(939\) | 414.443i | 0.441367i | ||||||||
\(940\) | −5.92585 | + | 71.1369i | −0.00630410 | + | 0.0756776i | ||||
\(941\) | 483.653i | 0.513978i | 0.966414 | + | 0.256989i | \(0.0827304\pi\) | ||||
−0.966414 | + | 0.256989i | \(0.917270\pi\) | |||||||
\(942\) | 392.449 | + | 16.3176i | 0.416613 | + | 0.0173223i | ||||
\(943\) | 497.265 | 0.527322 | ||||||||
\(944\) | −937.874 | − | 157.346i | −0.993511 | − | 0.166680i | ||||
\(945\) | 21.6634 | 0.0229242 | ||||||||
\(946\) | 1777.44 | + | 73.9042i | 1.87890 | + | 0.0781228i | ||||
\(947\) | −1203.23 | −1.27057 | −0.635286 | − | 0.772277i | \(-0.719118\pi\) | ||||
−0.635286 | + | 0.772277i | \(0.719118\pi\) | |||||||
\(948\) | −631.404 | − | 52.5972i | −0.666037 | − | 0.0554823i | ||||
\(949\) | −799.711 | + | 714.309i | −0.842688 | + | 0.752697i | ||||
\(950\) | −32.2274 | + | 775.089i | −0.0339236 | + | 0.815883i | ||||
\(951\) | 296.727 | 0.312016 | ||||||||
\(952\) | −50.4234 | + | 402.373i | −0.0529658 | + | 0.422661i | ||||
\(953\) | 409.611 | 0.429812 | 0.214906 | − | 0.976635i | \(-0.431056\pi\) | ||||
0.214906 | + | 0.976635i | \(0.431056\pi\) | |||||||
\(954\) | −16.7871 | + | 403.740i | −0.0175965 | + | 0.423207i | ||||
\(955\) | −31.9680 | −0.0334743 | ||||||||
\(956\) | −520.688 | − | 43.3744i | −0.544653 | − | 0.0453707i | ||||
\(957\) | 808.647i | 0.844981i | ||||||||
\(958\) | −63.8982 | + | 1536.79i | −0.0666996 | + | 1.60416i | ||||
\(959\) | − | 1301.97i | − | 1.35763i | ||||||
\(960\) | 48.4487 | + | 12.3364i | 0.0504674 | + | 0.0128504i | ||||
\(961\) | −772.276 | −0.803617 | ||||||||
\(962\) | −22.2996 | − | 27.1571i | −0.0231805 | − | 0.0282298i | ||||
\(963\) | − | 631.333i | − | 0.655590i | ||||||
\(964\) | −67.9520 | + | 815.730i | −0.0704896 | + | 0.846193i | ||||
\(965\) | 45.9025 | 0.0475674 | ||||||||
\(966\) | 21.1198 | − | 507.943i | 0.0218631 | − | 0.525821i | ||||
\(967\) | −493.084 | −0.509911 | −0.254956 | − | 0.966953i | \(-0.582061\pi\) | ||||
−0.254956 | + | 0.966953i | \(0.582061\pi\) | |||||||
\(968\) | 5.87563 | − | 46.8869i | 0.00606987 | − | 0.0484369i | ||||
\(969\) | 148.568i | 0.153321i | ||||||||
\(970\) | 3.46626 | − | 83.3657i | 0.00357347 | − | 0.0859440i | ||||
\(971\) | 749.707i | 0.772097i | 0.922478 | + | 0.386049i | \(0.126160\pi\) | ||||
−0.922478 | + | 0.386049i | \(0.873840\pi\) | |||||||
\(972\) | −5.17627 | + | 62.1386i | −0.00532538 | + | 0.0639286i | ||||
\(973\) | − | 2310.49i | − | 2.37461i | ||||||
\(974\) | −60.6967 | + | 1459.79i | −0.0623170 | + | 1.49876i | ||||
\(975\) | 416.411 | − | 371.942i | 0.427089 | − | 0.381479i | ||||
\(976\) | 577.974 | + | 96.9657i | 0.592186 | + | 0.0993501i | ||||
\(977\) | − | 442.080i | − | 0.452487i | −0.974071 | − | 0.226243i | \(-0.927356\pi\) | ||
0.974071 | − | 0.226243i | \(-0.0726445\pi\) | |||||||
\(978\) | −614.193 | − | 25.5376i | −0.628010 | − | 0.0261120i | ||||
\(979\) | − | 784.071i | − | 0.800890i | ||||||
\(980\) | −5.45912 | + | 65.5341i | −0.00557054 | + | 0.0668715i | ||||
\(981\) | − | 535.140i | − | 0.545505i | ||||||
\(982\) | −1399.87 | − | 58.2052i | −1.42553 | − | 0.0592721i | ||||
\(983\) | −179.850 | −0.182960 | −0.0914801 | − | 0.995807i | \(-0.529160\pi\) | ||||
−0.0914801 | + | 0.995807i | \(0.529160\pi\) | |||||||
\(984\) | 53.9661 | − | 430.643i | 0.0548436 | − | 0.437645i | ||||
\(985\) | 49.8580 | 0.0506172 | ||||||||
\(986\) | −18.8819 | + | 454.120i | −0.0191500 | + | 0.460568i | ||||
\(987\) | − | 633.544i | − | 0.641889i | ||||||
\(988\) | −489.630 | − | 649.533i | −0.495577 | − | 0.657422i | ||||
\(989\) | −1253.53 | −1.26747 | ||||||||
\(990\) | −30.4580 | − | 1.26641i | −0.0307656 | − | 0.00127920i | ||||
\(991\) | − | 652.511i | − | 0.658437i | −0.944254 | − | 0.329219i | \(-0.893215\pi\) | ||
0.944254 | − | 0.329219i | \(-0.106785\pi\) | |||||||
\(992\) | 90.6834 | − | 430.151i | 0.0914147 | − | 0.433620i | ||||
\(993\) | 37.7898i | 0.0380562i | ||||||||
\(994\) | −51.3260 | + | 1234.42i | −0.0516358 | + | 1.24187i | ||||
\(995\) | −77.5818 | −0.0779716 | ||||||||
\(996\) | 69.8623 | − | 838.663i | 0.0701429 | − | 0.842031i | ||||
\(997\) | −435.535 | −0.436845 | −0.218423 | − | 0.975854i | \(-0.570091\pi\) | ||||
−0.218423 | + | 0.975854i | \(0.570091\pi\) | |||||||
\(998\) | −7.18475 | + | 172.797i | −0.00719914 | + | 0.173144i | ||||
\(999\) | −7.02268 | −0.00702971 |
(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 | 156.3.e.c.103.12 | yes | 24 | |
3.2 | odd | 2 | 468.3.e.m.415.13 | 24 | |||
4.3 | odd | 2 | inner | 156.3.e.c.103.14 | yes | 24 | |
12.11 | even | 2 | 468.3.e.m.415.11 | 24 | |||
13.12 | even | 2 | inner | 156.3.e.c.103.13 | yes | 24 | |
39.38 | odd | 2 | 468.3.e.m.415.12 | 24 | |||
52.51 | odd | 2 | inner | 156.3.e.c.103.11 | ✓ | 24 | |
156.155 | even | 2 | 468.3.e.m.415.14 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
156.3.e.c.103.11 | ✓ | 24 | 52.51 | odd | 2 | inner | |
156.3.e.c.103.12 | yes | 24 | 1.1 | even | 1 | trivial | |
156.3.e.c.103.13 | yes | 24 | 13.12 | even | 2 | inner | |
156.3.e.c.103.14 | yes | 24 | 4.3 | odd | 2 | inner | |
468.3.e.m.415.11 | 24 | 12.11 | even | 2 | |||
468.3.e.m.415.12 | 24 | 39.38 | odd | 2 | |||
468.3.e.m.415.13 | 24 | 3.2 | odd | 2 | |||
468.3.e.m.415.14 | 24 | 156.155 | even | 2 |