Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,3,Mod(125,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.125");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.j (of order \(6\), degree \(2\), not 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: | \(5.88557371018\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 125.19 | ||
Character | \(\chi\) | \(=\) | 216.125 |
Dual form | 216.3.j.a.197.19 |
$q$-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 \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.87413 | − | 0.698310i | 0.937065 | − | 0.349155i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.02473 | − | 2.61745i | 0.756182 | − | 0.654362i | ||||
\(5\) | −3.98823 | + | 6.90782i | −0.797647 | + | 1.38156i | 0.123498 | + | 0.992345i | \(0.460589\pi\) |
−0.921145 | + | 0.389220i | \(0.872745\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.64852 | + | 9.78353i | 0.806932 | + | 1.39765i | 0.914979 | + | 0.403501i | \(0.132207\pi\) |
−0.108047 | + | 0.994146i | \(0.534460\pi\) | |||||||
\(8\) | 3.84094 | − | 7.01763i | 0.480117 | − | 0.877204i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.65067 | + | 15.7312i | −0.265067 | + | 1.57312i | ||||
\(11\) | 1.06057 | + | 1.83697i | 0.0964157 | + | 0.166997i | 0.910199 | − | 0.414172i | \(-0.135929\pi\) |
−0.813783 | + | 0.581169i | \(0.802596\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.03586 | + | 3.48480i | 0.464297 | + | 0.268062i | 0.713849 | − | 0.700299i | \(-0.246950\pi\) |
−0.249552 | + | 0.968361i | \(0.580284\pi\) | |||||||
\(14\) | 17.4180 | + | 14.3912i | 1.24414 | + | 1.02794i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.29794 | − | 15.8341i | 0.143621 | − | 0.989633i | ||||
\(17\) | − | 4.29594i | − | 0.252702i | −0.991986 | − | 0.126351i | \(-0.959673\pi\) | ||
0.991986 | − | 0.126351i | \(-0.0403266\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 11.2235i | − | 0.590711i | −0.955387 | − | 0.295356i | \(-0.904562\pi\) | ||
0.955387 | − | 0.295356i | \(-0.0954381\pi\) | |||||||
\(20\) | 6.01755 | + | 31.3333i | 0.300878 | + | 1.56666i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.27042 | + | 2.70210i | 0.148656 | + | 0.122823i | ||||
\(23\) | 3.40068 | + | 1.96338i | 0.147856 | + | 0.0853645i | 0.572103 | − | 0.820182i | \(-0.306128\pi\) |
−0.424247 | + | 0.905546i | \(0.639461\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −19.3120 | − | 33.4494i | −0.772480 | − | 1.33798i | ||||
\(26\) | 13.7455 | + | 2.31608i | 0.528671 | + | 0.0890798i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 42.6931 | + | 14.8078i | 1.52475 | + | 0.528849i | ||||
\(29\) | 0.512348 | + | 0.887412i | 0.0176672 | + | 0.0306004i | 0.874724 | − | 0.484622i | \(-0.161043\pi\) |
−0.857057 | + | 0.515222i | \(0.827709\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.18829 | − | 7.25434i | 0.135106 | − | 0.234011i | −0.790532 | − | 0.612421i | \(-0.790196\pi\) |
0.925638 | + | 0.378410i | \(0.123529\pi\) | |||||||
\(32\) | −6.75050 | − | 31.2799i | −0.210953 | − | 0.977496i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.99990 | − | 8.05114i | −0.0882322 | − | 0.236798i | ||||
\(35\) | −90.1105 | −2.57459 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 58.9714i | − | 1.59382i | −0.604097 | − | 0.796911i | \(-0.706466\pi\) | ||
0.604097 | − | 0.796911i | \(-0.293534\pi\) | |||||||
\(38\) | −7.83749 | − | 21.0343i | −0.206250 | − | 0.553535i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 33.1580 | + | 54.5205i | 0.828950 | + | 1.36301i | ||||
\(41\) | 48.6696 | + | 28.0994i | 1.18706 | + | 0.685351i | 0.957638 | − | 0.287975i | \(-0.0929821\pi\) |
0.229425 | + | 0.973326i | \(0.426315\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −49.8518 | + | 28.7820i | −1.15935 | + | 0.669348i | −0.951147 | − | 0.308738i | \(-0.900093\pi\) |
−0.208198 | + | 0.978087i | \(0.566760\pi\) | |||||||
\(44\) | 8.01611 | + | 2.78033i | 0.182184 | + | 0.0631892i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.74436 | + | 1.30491i | 0.168356 | + | 0.0283675i | ||||
\(47\) | −44.8348 | + | 25.8854i | −0.953931 | + | 0.550752i | −0.894300 | − | 0.447468i | \(-0.852326\pi\) |
−0.0596311 | + | 0.998220i | \(0.518992\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −39.3116 | + | 68.0897i | −0.802278 | + | 1.38959i | ||||
\(50\) | −59.5513 | − | 49.2027i | −1.19103 | − | 0.984054i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 27.3781 | − | 5.25796i | 0.526502 | − | 0.101115i | ||||
\(53\) | 42.6170 | 0.804094 | 0.402047 | − | 0.915619i | \(-0.368299\pi\) | ||||
0.402047 | + | 0.915619i | \(0.368299\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.9193 | −0.307623 | ||||||||
\(56\) | 90.3528 | − | 2.06132i | 1.61344 | − | 0.0368094i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.57990 | + | 1.30535i | 0.0272396 | + | 0.0225060i | ||||
\(59\) | 25.6501 | − | 44.4272i | 0.434747 | − | 0.753003i | −0.562528 | − | 0.826778i | \(-0.690171\pi\) |
0.997275 | + | 0.0737746i | \(0.0235046\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 42.9355 | − | 24.7888i | 0.703861 | − | 0.406374i | −0.104923 | − | 0.994480i | \(-0.533460\pi\) |
0.808784 | + | 0.588106i | \(0.200126\pi\) | |||||||
\(62\) | 2.78363 | − | 16.5203i | 0.0448973 | − | 0.266456i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −34.4944 | − | 53.9086i | −0.538975 | − | 0.842322i | ||||
\(65\) | −48.1448 | + | 27.7964i | −0.740689 | + | 0.427637i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −85.1906 | − | 49.1848i | −1.27150 | − | 0.734102i | −0.296231 | − | 0.955116i | \(-0.595730\pi\) |
−0.975271 | + | 0.221014i | \(0.929063\pi\) | |||||||
\(68\) | −11.2444 | − | 12.9940i | −0.165359 | − | 0.191089i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −168.879 | + | 62.9251i | −2.41255 | + | 0.898930i | ||||
\(71\) | − | 31.4710i | − | 0.443254i | −0.975132 | − | 0.221627i | \(-0.928863\pi\) | ||
0.975132 | − | 0.221627i | \(-0.0711367\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 85.4715 | 1.17084 | 0.585421 | − | 0.810729i | \(-0.300929\pi\) | ||||
0.585421 | + | 0.810729i | \(0.300929\pi\) | |||||||
\(74\) | −41.1803 | − | 110.520i | −0.556491 | − | 1.49351i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −29.3770 | − | 33.9480i | −0.386539 | − | 0.446685i | ||||
\(77\) | −11.9813 | + | 20.7523i | −0.155602 | + | 0.269510i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.61671 | − | 11.4605i | −0.0837558 | − | 0.145069i | 0.821105 | − | 0.570778i | \(-0.193358\pi\) |
−0.904860 | + | 0.425708i | \(0.860025\pi\) | |||||||
\(80\) | 100.215 | + | 79.0239i | 1.25268 | + | 0.987799i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 110.835 | + | 18.6755i | 1.35165 | + | 0.227750i | ||||
\(83\) | −41.8804 | − | 72.5390i | −0.504583 | − | 0.873964i | −0.999986 | − | 0.00530047i | \(-0.998313\pi\) |
0.495403 | − | 0.868663i | \(-0.335021\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 29.6756 | + | 17.1332i | 0.349124 | + | 0.201567i | ||||
\(86\) | −73.3301 | + | 88.7532i | −0.852675 | + | 1.03201i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 16.9648 | − | 0.387037i | 0.192781 | − | 0.00439814i | ||||
\(89\) | − | 105.027i | − | 1.18008i | −0.807374 | − | 0.590040i | \(-0.799112\pi\) | ||
0.807374 | − | 0.590040i | \(-0.200888\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 78.7360i | 0.865230i | ||||||||
\(92\) | 15.4252 | − | 2.96240i | 0.167665 | − | 0.0322000i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −65.9502 | + | 79.8211i | −0.701597 | + | 0.849161i | ||||
\(95\) | 77.5300 | + | 44.7620i | 0.816105 | + | 0.471179i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.54179 | − | 16.5269i | −0.0983690 | − | 0.170380i | 0.812641 | − | 0.582765i | \(-0.198029\pi\) |
−0.911010 | + | 0.412385i | \(0.864696\pi\) | |||||||
\(98\) | −26.1273 | + | 155.061i | −0.266605 | + | 1.58225i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −145.966 | − | 50.6270i | −1.45966 | − | 0.506270i | ||||
\(101\) | 53.0235 | + | 91.8395i | 0.524985 | + | 0.909302i | 0.999577 | + | 0.0290952i | \(0.00926259\pi\) |
−0.474591 | + | 0.880206i | \(0.657404\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −30.5290 | + | 52.8778i | −0.296398 | + | 0.513376i | −0.975309 | − | 0.220844i | \(-0.929119\pi\) |
0.678911 | + | 0.734220i | \(0.262452\pi\) | |||||||
\(104\) | 47.6384 | − | 28.9725i | 0.458062 | − | 0.278582i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 79.8697 | − | 29.7599i | 0.753488 | − | 0.280753i | ||||
\(107\) | 7.01531 | 0.0655636 | 0.0327818 | − | 0.999463i | \(-0.489563\pi\) | ||||
0.0327818 | + | 0.999463i | \(0.489563\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 38.1403i | 0.349911i | 0.984576 | + | 0.174956i | \(0.0559782\pi\) | ||||
−0.984576 | + | 0.174956i | \(0.944022\pi\) | |||||||
\(110\) | −31.7089 | + | 11.8149i | −0.288263 | + | 0.107408i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 167.894 | − | 66.9575i | 1.49905 | − | 0.597835i | ||||
\(113\) | −120.801 | − | 69.7442i | −1.06903 | − | 0.617205i | −0.141115 | − | 0.989993i | \(-0.545069\pi\) |
−0.927917 | + | 0.372788i | \(0.878402\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −27.1254 | + | 15.6609i | −0.235873 | + | 0.136181i | ||||
\(116\) | 3.87247 | + | 1.34314i | 0.0333833 | + | 0.0115788i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.0476 | − | 101.174i | 0.144471 | − | 0.857407i | ||||
\(119\) | 42.0294 | − | 24.2657i | 0.353188 | − | 0.203913i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 58.2504 | − | 100.893i | 0.481408 | − | 0.833823i | ||||
\(122\) | 63.1564 | − | 76.4398i | 0.517676 | − | 0.626555i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.31941 | − | 32.9050i | −0.0509630 | − | 0.265363i | ||||
\(125\) | 108.672 | 0.869373 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.3165 | −0.0891066 | −0.0445533 | − | 0.999007i | \(-0.514186\pi\) | ||||
−0.0445533 | + | 0.999007i | \(0.514186\pi\) | |||||||
\(128\) | −102.292 | − | 76.9440i | −0.799155 | − | 0.601125i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −70.8191 | + | 85.7141i | −0.544762 | + | 0.659339i | ||||
\(131\) | −33.8613 | + | 58.6494i | −0.258483 | + | 0.447705i | −0.965836 | − | 0.259155i | \(-0.916556\pi\) |
0.707353 | + | 0.706861i | \(0.249889\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 109.806 | − | 63.3962i | 0.825605 | − | 0.476664i | ||||
\(134\) | −194.005 | − | 32.6893i | −1.44780 | − | 0.243950i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −30.1473 | − | 16.5004i | −0.221671 | − | 0.121327i | ||||
\(137\) | 12.4238 | − | 7.17291i | 0.0906850 | − | 0.0523570i | −0.453972 | − | 0.891016i | \(-0.649993\pi\) |
0.544657 | + | 0.838659i | \(0.316660\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 182.816 | + | 105.549i | 1.31522 | + | 0.759342i | 0.982955 | − | 0.183844i | \(-0.0588541\pi\) |
0.332264 | + | 0.943186i | \(0.392187\pi\) | |||||||
\(140\) | −272.560 | + | 235.860i | −1.94685 | + | 1.68471i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −21.9765 | − | 58.9808i | −0.154764 | − | 0.415358i | ||||
\(143\) | 14.7836i | 0.103382i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.17345 | −0.0563686 | ||||||||
\(146\) | 160.185 | − | 59.6856i | 1.09716 | − | 0.408806i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −154.355 | − | 178.372i | −1.04294 | − | 1.20522i | ||||
\(149\) | 91.6036 | − | 158.662i | 0.614789 | − | 1.06485i | −0.375632 | − | 0.926769i | \(-0.622574\pi\) |
0.990421 | − | 0.138077i | \(-0.0440922\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 78.9656 | + | 136.772i | 0.522951 | + | 0.905778i | 0.999643 | + | 0.0267076i | \(0.00850231\pi\) |
−0.476692 | + | 0.879070i | \(0.658164\pi\) | |||||||
\(152\) | −78.7625 | − | 43.1088i | −0.518174 | − | 0.283611i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.96306 | + | 47.2592i | −0.0517082 | + | 0.306878i | ||||
\(155\) | 33.4078 | + | 57.8640i | 0.215534 | + | 0.373316i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 137.812 | + | 79.5658i | 0.877784 | + | 0.506789i | 0.869927 | − | 0.493180i | \(-0.164166\pi\) |
0.00785670 | + | 0.999969i | \(0.497499\pi\) | |||||||
\(158\) | −20.4035 | − | 16.8579i | −0.129136 | − | 0.106696i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 242.998 | + | 78.1202i | 1.51874 | + | 0.488251i | ||||
\(161\) | 44.3608i | 0.275533i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 127.443i | 0.781861i | 0.920420 | + | 0.390930i | \(0.127847\pi\) | ||||
−0.920420 | + | 0.390930i | \(0.872153\pi\) | |||||||
\(164\) | 220.761 | − | 42.3971i | 1.34610 | − | 0.258519i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −129.144 | − | 106.702i | −0.777976 | − | 0.642783i | ||||
\(167\) | 14.9753 | + | 8.64602i | 0.0896727 | + | 0.0517726i | 0.544166 | − | 0.838978i | \(-0.316846\pi\) |
−0.454493 | + | 0.890750i | \(0.650180\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −60.2123 | − | 104.291i | −0.356286 | − | 0.617105i | ||||
\(170\) | 67.5802 | + | 11.3871i | 0.397530 | + | 0.0669829i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −75.4529 | + | 217.542i | −0.438679 | + | 1.26478i | ||||
\(173\) | 122.607 | + | 212.361i | 0.708709 | + | 1.22752i | 0.965336 | + | 0.261009i | \(0.0840554\pi\) |
−0.256627 | + | 0.966510i | \(0.582611\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 218.169 | − | 377.879i | 1.24668 | − | 2.15931i | ||||
\(176\) | 31.5239 | − | 12.5720i | 0.179113 | − | 0.0714319i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −73.3415 | − | 196.835i | −0.412031 | − | 1.10581i | ||||
\(179\) | 245.877 | 1.37361 | 0.686807 | − | 0.726840i | \(-0.259012\pi\) | ||||
0.686807 | + | 0.726840i | \(0.259012\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 53.7077i | 0.296728i | 0.988933 | + | 0.148364i | \(0.0474007\pi\) | ||||
−0.988933 | + | 0.148364i | \(0.952599\pi\) | |||||||
\(182\) | 54.9821 | + | 147.561i | 0.302100 | + | 0.810777i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 26.8401 | − | 16.3235i | 0.145870 | − | 0.0887146i | ||||
\(185\) | 407.364 | + | 235.192i | 2.20197 | + | 1.27131i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.89149 | − | 4.55615i | 0.0422005 | − | 0.0243645i | ||||
\(188\) | −67.8593 | + | 195.649i | −0.360954 | + | 1.04068i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 176.559 | + | 29.7498i | 0.929258 | + | 0.156578i | ||||
\(191\) | −208.549 | + | 120.406i | −1.09188 | + | 0.630396i | −0.934076 | − | 0.357075i | \(-0.883774\pi\) |
−0.157802 | + | 0.987471i | \(0.550441\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −124.900 | + | 216.333i | −0.647151 | + | 1.12090i | 0.336650 | + | 0.941630i | \(0.390706\pi\) |
−0.983800 | + | 0.179268i | \(0.942627\pi\) | |||||||
\(194\) | −29.4234 | − | 24.3104i | −0.151667 | − | 0.125311i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 59.3144 | + | 308.849i | 0.302624 | + | 1.57576i | ||||
\(197\) | −327.726 | −1.66359 | −0.831793 | − | 0.555086i | \(-0.812685\pi\) | ||||
−0.831793 | + | 0.555086i | \(0.812685\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −229.254 | −1.15203 | −0.576016 | − | 0.817439i | \(-0.695393\pi\) | ||||
−0.576016 | + | 0.817439i | \(0.695393\pi\) | |||||||
\(200\) | −308.912 | + | 7.04756i | −1.54456 | + | 0.0352378i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 163.505 | + | 135.092i | 0.809433 | + | 0.668773i | ||||
\(203\) | −5.78801 | + | 10.0251i | −0.0285124 | + | 0.0493849i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −388.211 | + | 224.134i | −1.89371 | + | 1.09334i | ||||
\(206\) | −20.2902 | + | 120.418i | −0.0984962 | + | 0.584556i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 69.0488 | − | 87.5647i | 0.331966 | − | 0.420984i | ||||
\(209\) | 20.6172 | − | 11.9034i | 0.0986469 | − | 0.0569538i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −135.544 | − | 78.2563i | −0.642388 | − | 0.370883i | 0.143146 | − | 0.989702i | \(-0.454278\pi\) |
−0.785534 | + | 0.618819i | \(0.787612\pi\) | |||||||
\(212\) | 128.905 | − | 111.548i | 0.608041 | − | 0.526168i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.1476 | − | 4.89886i | 0.0614374 | − | 0.0228919i | ||||
\(215\) | − | 459.157i | − | 2.13561i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 94.6307 | 0.436086 | ||||||||
\(218\) | 26.6338 | + | 71.4800i | 0.122173 | + | 0.327890i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −51.1761 | + | 44.2853i | −0.232619 | + | 0.201297i | ||||
\(221\) | 14.9705 | − | 25.9297i | 0.0677398 | − | 0.117329i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 120.451 | + | 208.628i | 0.540140 | + | 0.935550i | 0.998895 | + | 0.0469875i | \(0.0149621\pi\) |
−0.458755 | + | 0.888563i | \(0.651705\pi\) | |||||||
\(224\) | 267.897 | − | 242.729i | 1.19597 | − | 1.08361i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −275.099 | − | 46.3535i | −1.21725 | − | 0.205104i | ||||
\(227\) | 44.5553 | + | 77.1721i | 0.196279 | + | 0.339965i | 0.947319 | − | 0.320291i | \(-0.103781\pi\) |
−0.751040 | + | 0.660257i | \(0.770448\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −144.631 | − | 83.5027i | −0.631576 | − | 0.364641i | 0.149786 | − | 0.988718i | \(-0.452142\pi\) |
−0.781362 | + | 0.624078i | \(0.785475\pi\) | |||||||
\(230\) | −39.9004 | + | 48.2924i | −0.173480 | + | 0.209967i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.19543 | − | 0.186972i | 0.0353251 | − | 0.000805913i | ||||
\(233\) | − | 136.581i | − | 0.586185i | −0.956084 | − | 0.293092i | \(-0.905316\pi\) | ||
0.956084 | − | 0.293092i | \(-0.0946844\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 412.947i | − | 1.75722i | ||||||
\(236\) | −38.7015 | − | 201.518i | −0.163989 | − | 0.853889i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 61.8236 | − | 74.8266i | 0.259763 | − | 0.314398i | ||||
\(239\) | −133.564 | − | 77.1130i | −0.558844 | − | 0.322648i | 0.193838 | − | 0.981034i | \(-0.437906\pi\) |
−0.752681 | + | 0.658385i | \(0.771240\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −31.9120 | − | 55.2732i | −0.132415 | − | 0.229350i | 0.792192 | − | 0.610272i | \(-0.208940\pi\) |
−0.924607 | + | 0.380922i | \(0.875606\pi\) | |||||||
\(242\) | 38.7144 | − | 229.763i | 0.159977 | − | 0.949432i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 64.9847 | − | 187.361i | 0.266331 | − | 0.767872i | ||||
\(245\) | −313.568 | − | 543.115i | −1.27987 | − | 2.21680i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 39.1117 | − | 67.7435i | 0.158347 | − | 0.274265i | ||||
\(248\) | −34.8213 | − | 57.2554i | −0.140409 | − | 0.230869i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 203.665 | − | 75.8864i | 0.814659 | − | 0.303546i | ||||
\(251\) | −99.6131 | −0.396865 | −0.198432 | − | 0.980115i | \(-0.563585\pi\) | ||||
−0.198432 | + | 0.980115i | \(0.563585\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.32924i | 0.0329219i | ||||||||
\(254\) | −21.2087 | + | 7.90245i | −0.0834986 | + | 0.0311120i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −245.439 | − | 72.7716i | −0.958746 | − | 0.284264i | ||||
\(257\) | −258.303 | − | 149.131i | −1.00507 | − | 0.580277i | −0.0953248 | − | 0.995446i | \(-0.530389\pi\) |
−0.909744 | + | 0.415169i | \(0.863722\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 576.948 | − | 333.101i | 2.22760 | − | 1.28611i | ||||
\(260\) | −72.8692 | + | 210.093i | −0.280266 | + | 0.808050i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −22.5049 | + | 133.562i | −0.0858966 | + | 0.509780i | ||||
\(263\) | −26.4361 | + | 15.2629i | −0.100518 | + | 0.0580338i | −0.549416 | − | 0.835549i | \(-0.685150\pi\) |
0.448899 | + | 0.893583i | \(0.351816\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −169.966 | + | 294.390i | −0.641383 | + | 1.11091i | ||||
\(266\) | 161.520 | − | 195.491i | 0.607216 | − | 0.734929i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −386.417 | + | 74.2114i | −1.44185 | + | 0.276908i | ||||
\(269\) | −218.092 | −0.810749 | −0.405375 | − | 0.914151i | \(-0.632859\pi\) | ||||
−0.405375 | + | 0.914151i | \(0.632859\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −343.470 | −1.26742 | −0.633709 | − | 0.773572i | \(-0.718468\pi\) | ||||
−0.633709 | + | 0.773572i | \(0.718468\pi\) | |||||||
\(272\) | −68.0224 | − | 9.87178i | −0.250082 | − | 0.0362933i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.2750 | − | 22.1187i | 0.0666970 | − | 0.0807250i | ||||
\(275\) | 40.9636 | − | 70.9510i | 0.148959 | − | 0.258004i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 110.463 | − | 63.7759i | 0.398784 | − | 0.230238i | −0.287175 | − | 0.957878i | \(-0.592716\pi\) |
0.685959 | + | 0.727640i | \(0.259383\pi\) | |||||||
\(278\) | 416.326 | + | 70.1499i | 1.49757 | + | 0.252338i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −346.109 | + | 632.362i | −1.23610 | + | 2.25844i | ||||
\(281\) | −336.249 | + | 194.134i | −1.19662 | + | 0.690867i | −0.959799 | − | 0.280687i | \(-0.909438\pi\) |
−0.236818 | + | 0.971554i | \(0.576104\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −215.980 | − | 124.696i | −0.763180 | − | 0.440622i | 0.0672566 | − | 0.997736i | \(-0.478575\pi\) |
−0.830436 | + | 0.557114i | \(0.811909\pi\) | |||||||
\(284\) | −82.3737 | − | 95.1912i | −0.290048 | − | 0.335180i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.3235 | + | 27.7063i | 0.0360962 | + | 0.0968752i | ||||
\(287\) | 634.880i | 2.21213i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 270.545 | 0.936142 | ||||||||
\(290\) | −15.3181 | + | 5.70760i | −0.0528211 | + | 0.0196814i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 258.528 | − | 223.717i | 0.885369 | − | 0.766155i | ||||
\(293\) | −56.0435 | + | 97.0701i | −0.191275 | + | 0.331297i | −0.945673 | − | 0.325120i | \(-0.894595\pi\) |
0.754398 | + | 0.656417i | \(0.227929\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 204.597 | + | 354.372i | 0.693549 | + | 1.20126i | ||||
\(296\) | −413.840 | − | 226.506i | −1.39811 | − | 0.765222i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 60.8817 | − | 361.321i | 0.204301 | − | 1.21249i | ||||
\(299\) | 13.6840 | + | 23.7014i | 0.0457659 | + | 0.0792689i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −563.179 | − | 325.151i | −1.87102 | − | 1.08024i | ||||
\(302\) | 243.501 | + | 201.187i | 0.806296 | + | 0.666182i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −177.714 | − | 25.7909i | −0.584587 | − | 0.0848385i | ||||
\(305\) | 395.454i | 1.29657i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 425.029i | 1.38446i | 0.721678 | + | 0.692229i | \(0.243371\pi\) | ||||
−0.721678 | + | 0.692229i | \(0.756629\pi\) | |||||||
\(308\) | 18.0778 | + | 94.1305i | 0.0586940 | + | 0.305619i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 103.018 | + | 85.1156i | 0.332315 | + | 0.274567i | ||||
\(311\) | 257.225 | + | 148.509i | 0.827089 | + | 0.477520i | 0.852855 | − | 0.522148i | \(-0.174869\pi\) |
−0.0257662 | + | 0.999668i | \(0.508203\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −101.171 | − | 175.234i | −0.323231 | − | 0.559852i | 0.657922 | − | 0.753086i | \(-0.271436\pi\) |
−0.981153 | + | 0.193234i | \(0.938102\pi\) | |||||||
\(314\) | 313.839 | + | 52.8811i | 0.999488 | + | 0.168411i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −50.0109 | − | 17.3459i | −0.158262 | − | 0.0548921i | ||||
\(317\) | −21.4220 | − | 37.1039i | −0.0675772 | − | 0.117047i | 0.830257 | − | 0.557381i | \(-0.188194\pi\) |
−0.897834 | + | 0.440333i | \(0.854860\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.08676 | + | 1.88233i | −0.00340678 | + | 0.00590072i | ||||
\(320\) | 509.963 | − | 23.2809i | 1.59363 | − | 0.0727527i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 30.9776 | + | 83.1380i | 0.0962038 | + | 0.258192i | ||||
\(323\) | −48.2155 | −0.149274 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 269.194i | − | 0.828290i | ||||||
\(326\) | 88.9950 | + | 238.845i | 0.272991 | + | 0.732655i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 384.128 | − | 233.617i | 1.17112 | − | 0.712248i | ||||
\(329\) | −506.500 | − | 292.428i | −1.53951 | − | 0.888839i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −184.989 | + | 106.804i | −0.558880 | + | 0.322669i | −0.752696 | − | 0.658369i | \(-0.771247\pi\) |
0.193816 | + | 0.981038i | \(0.437913\pi\) | |||||||
\(332\) | −316.544 | − | 109.791i | −0.953445 | − | 0.330695i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 34.1033 | + | 5.74633i | 0.102106 | + | 0.0172046i | ||||
\(335\) | 679.520 | − | 392.321i | 2.02842 | − | 1.17111i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 111.390 | − | 192.934i | 0.330535 | − | 0.572504i | −0.652082 | − | 0.758149i | \(-0.726104\pi\) |
0.982617 | + | 0.185645i | \(0.0594374\pi\) | |||||||
\(338\) | −185.673 | − | 153.408i | −0.549328 | − | 0.453868i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 134.606 | − | 25.8510i | 0.395899 | − | 0.0760324i | ||||
\(341\) | 17.7680 | 0.0521055 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −334.655 | −0.975670 | ||||||||
\(344\) | 10.5035 | + | 460.392i | 0.0305333 | + | 1.33835i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 378.075 | + | 312.375i | 1.09270 | + | 0.902817i | ||||
\(347\) | −72.3481 | + | 125.311i | −0.208496 | + | 0.361126i | −0.951241 | − | 0.308449i | \(-0.900190\pi\) |
0.742745 | + | 0.669574i | \(0.233523\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −191.412 | + | 110.512i | −0.548458 | + | 0.316652i | −0.748500 | − | 0.663135i | \(-0.769226\pi\) |
0.200042 | + | 0.979787i | \(0.435892\pi\) | |||||||
\(350\) | 145.000 | − | 860.544i | 0.414284 | − | 2.45870i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 50.3007 | − | 45.5750i | 0.142900 | − | 0.129475i | ||||
\(353\) | 600.193 | − | 346.521i | 1.70026 | − | 0.981647i | 0.754778 | − | 0.655981i | \(-0.227745\pi\) |
0.945485 | − | 0.325666i | \(-0.105589\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 217.396 | + | 125.514i | 0.612384 | + | 0.353560i | ||||
\(356\) | −274.903 | − | 317.678i | −0.772200 | − | 0.892355i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 460.805 | − | 171.698i | 1.28717 | − | 0.479604i | ||||
\(359\) | 287.752i | 0.801537i | 0.916179 | + | 0.400769i | \(0.131257\pi\) | ||||
−0.916179 | + | 0.400769i | \(0.868743\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 235.033 | 0.651060 | ||||||||
\(362\) | 37.5046 | + | 100.655i | 0.103604 | + | 0.278053i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 206.087 | + | 238.155i | 0.566174 | + | 0.654271i | ||||
\(365\) | −340.880 | + | 590.422i | −0.933919 | + | 1.61759i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −328.424 | − | 568.847i | −0.894888 | − | 1.54999i | −0.833943 | − | 0.551851i | \(-0.813922\pi\) |
−0.0609450 | − | 0.998141i | \(-0.519411\pi\) | |||||||
\(368\) | 38.9030 | − | 49.3350i | 0.105715 | − | 0.134063i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 927.690 | + | 156.313i | 2.50727 | + | 0.422469i | ||||
\(371\) | 240.723 | + | 416.944i | 0.648849 | + | 1.12384i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 320.900 | + | 185.272i | 0.860322 | + | 0.496707i | 0.864120 | − | 0.503286i | \(-0.167876\pi\) |
−0.00379823 | + | 0.999993i | \(0.501209\pi\) | |||||||
\(374\) | 11.6081 | − | 14.0495i | 0.0310376 | − | 0.0375656i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.44638 | + | 414.058i | 0.0251234 | + | 1.10122i | ||||
\(377\) | 7.14173i | 0.0189436i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 603.632i | − | 1.59270i | −0.604839 | − | 0.796348i | \(-0.706762\pi\) | ||
0.604839 | − | 0.796348i | \(-0.293238\pi\) | |||||||
\(380\) | 351.669 | − | 67.5381i | 0.925445 | − | 0.177732i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −306.767 | + | 371.287i | −0.803054 | + | 0.971956i | ||||
\(383\) | −285.312 | − | 164.725i | −0.744939 | − | 0.430091i | 0.0789230 | − | 0.996881i | \(-0.474852\pi\) |
−0.823862 | + | 0.566790i | \(0.808185\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −95.5688 | − | 165.530i | −0.248231 | − | 0.429948i | ||||
\(386\) | −83.0113 | + | 492.656i | −0.215055 | + | 1.27631i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −72.1195 | − | 25.0141i | −0.185875 | − | 0.0644693i | ||||
\(389\) | −298.296 | − | 516.663i | −0.766827 | − | 1.32818i | −0.939275 | − | 0.343164i | \(-0.888501\pi\) |
0.172449 | − | 0.985019i | \(-0.444832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.43457 | − | 14.6091i | 0.0215718 | − | 0.0373634i | ||||
\(392\) | 326.835 | + | 537.403i | 0.833763 | + | 1.37093i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −614.202 | + | 228.855i | −1.55889 | + | 0.580849i | ||||
\(395\) | 105.556 | 0.267230 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 777.319i | 1.95798i | 0.203902 | + | 0.978991i | \(0.434637\pi\) | ||||
−0.203902 | + | 0.978991i | \(0.565363\pi\) | |||||||
\(398\) | −429.652 | + | 160.091i | −1.07953 | + | 0.402238i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −574.019 | + | 228.924i | −1.43505 | + | 0.572311i | ||||
\(401\) | 433.690 | + | 250.391i | 1.08152 | + | 0.624417i | 0.931307 | − | 0.364236i | \(-0.118670\pi\) |
0.150215 | + | 0.988653i | \(0.452003\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 50.5599 | − | 29.1908i | 0.125459 | − | 0.0724337i | ||||
\(404\) | 400.767 | + | 139.003i | 0.991997 | + | 0.344066i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.84684 | + | 22.8302i | −0.00947497 | + | 0.0562321i | ||||
\(407\) | 108.328 | − | 62.5435i | 0.266163 | − | 0.153669i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −210.054 | + | 363.824i | −0.513579 | + | 0.889546i | 0.486297 | + | 0.873794i | \(0.338347\pi\) |
−0.999876 | + | 0.0157518i | \(0.994986\pi\) | |||||||
\(410\) | −571.043 | + | 691.148i | −1.39279 | + | 1.68573i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 46.0629 | + | 239.849i | 0.111803 | + | 0.582157i | ||||
\(413\) | 579.540 | 1.40324 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 668.115 | 1.60992 | ||||||||
\(416\) | 68.2592 | − | 212.325i | 0.164085 | − | 0.510397i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 30.3271 | − | 36.7056i | 0.0725529 | − | 0.0878125i | ||||
\(419\) | 103.906 | − | 179.970i | 0.247985 | − | 0.429523i | −0.714981 | − | 0.699143i | \(-0.753565\pi\) |
0.962967 | + | 0.269620i | \(0.0868982\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −82.2587 | + | 47.4921i | −0.195389 | + | 0.112808i | −0.594503 | − | 0.804094i | \(-0.702651\pi\) |
0.399114 | + | 0.916901i | \(0.369318\pi\) | |||||||
\(422\) | −308.674 | − | 52.0108i | −0.731455 | − | 0.123248i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 163.689 | − | 299.070i | 0.386059 | − | 0.705354i | ||||
\(425\) | −143.696 | + | 82.9632i | −0.338109 | + | 0.195207i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 485.044 | + | 280.040i | 1.13594 | + | 0.655832i | ||||
\(428\) | 21.2194 | − | 18.3622i | 0.0495780 | − | 0.0429023i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −320.634 | − | 860.520i | −0.745660 | − | 2.00121i | ||||
\(431\) | − | 239.645i | − | 0.556021i | −0.960578 | − | 0.278010i | \(-0.910325\pi\) | ||
0.960578 | − | 0.278010i | \(-0.0896750\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 41.9180 | 0.0968083 | 0.0484042 | − | 0.998828i | \(-0.484586\pi\) | ||||
0.0484042 | + | 0.998828i | \(0.484586\pi\) | |||||||
\(434\) | 177.350 | − | 66.0816i | 0.408641 | − | 0.152262i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 99.8303 | + | 115.364i | 0.228969 | + | 0.264597i | ||||
\(437\) | 22.0360 | − | 38.1676i | 0.0504257 | − | 0.0873399i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −265.485 | − | 459.834i | −0.604749 | − | 1.04746i | −0.992091 | − | 0.125521i | \(-0.959940\pi\) |
0.387342 | − | 0.921936i | \(-0.373393\pi\) | |||||||
\(440\) | −64.9858 | + | 118.733i | −0.147695 | + | 0.269848i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.94971 | − | 59.0496i | 0.0225107 | − | 0.133596i | ||||
\(443\) | −146.570 | − | 253.866i | −0.330857 | − | 0.573061i | 0.651823 | − | 0.758371i | \(-0.274004\pi\) |
−0.982680 | + | 0.185310i | \(0.940671\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 725.509 | + | 418.873i | 1.63036 | + | 0.941287i | ||||
\(446\) | 371.428 | + | 306.883i | 0.832798 | + | 0.688079i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 332.574 | − | 641.981i | 0.742353 | − | 1.43299i | ||||
\(449\) | 268.273i | 0.597491i | 0.954333 | + | 0.298746i | \(0.0965682\pi\) | ||||
−0.954333 | + | 0.298746i | \(0.903432\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 119.206i | 0.264315i | ||||||||
\(452\) | −547.940 | + | 105.232i | −1.21226 | + | 0.232814i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 137.393 | + | 113.517i | 0.302627 | + | 0.250038i | ||||
\(455\) | −543.894 | − | 314.017i | −1.19537 | − | 0.690148i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 372.941 | + | 645.954i | 0.816064 | + | 1.41347i | 0.908561 | + | 0.417752i | \(0.137182\pi\) |
−0.0924966 | + | 0.995713i | \(0.529485\pi\) | |||||||
\(458\) | −329.368 | − | 55.4977i | −0.719144 | − | 0.121174i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −41.0554 | + | 118.369i | −0.0892509 | + | 0.257324i | ||||
\(461\) | 331.542 | + | 574.248i | 0.719180 | + | 1.24566i | 0.961325 | + | 0.275416i | \(0.0888157\pi\) |
−0.242145 | + | 0.970240i | \(0.577851\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −142.342 | + | 246.544i | −0.307435 | + | 0.532493i | −0.977800 | − | 0.209538i | \(-0.932804\pi\) |
0.670366 | + | 0.742031i | \(0.266137\pi\) | |||||||
\(464\) | 15.2287 | − | 6.07336i | 0.0328206 | − | 0.0130891i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −95.3759 | − | 255.971i | −0.204669 | − | 0.549293i | ||||
\(467\) | 174.804 | 0.374313 | 0.187157 | − | 0.982330i | \(-0.440073\pi\) | ||||
0.187157 | + | 0.982330i | \(0.440073\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1111.29i | − | 2.36948i | ||||||
\(470\) | −288.365 | − | 773.917i | −0.613543 | − | 1.64663i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −213.254 | − | 350.645i | −0.451808 | − | 0.742892i | ||||
\(473\) | −105.743 | − | 61.0508i | −0.223558 | − | 0.129071i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −375.420 | + | 216.749i | −0.790357 | + | 0.456313i | ||||
\(476\) | 63.6133 | − | 183.407i | 0.133641 | − | 0.385309i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −304.164 | − | 51.2509i | −0.636327 | − | 0.107220i | ||||
\(479\) | −621.273 | + | 358.692i | −1.29702 | + | 0.748836i | −0.979889 | − | 0.199545i | \(-0.936054\pi\) |
−0.317133 | + | 0.948381i | \(0.602720\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 205.504 | − | 355.943i | 0.427243 | − | 0.740006i | ||||
\(482\) | −98.4051 | − | 81.3047i | −0.204160 | − | 0.168682i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −87.8897 | − | 457.640i | −0.181590 | − | 0.945537i | ||||
\(485\) | 152.220 | 0.313855 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 668.869 | 1.37345 | 0.686724 | − | 0.726919i | \(-0.259048\pi\) | ||||
0.686724 | + | 0.726919i | \(0.259048\pi\) | |||||||
\(488\) | −9.04622 | − | 396.518i | −0.0185373 | − | 0.812537i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −966.930 | − | 798.901i | −1.97333 | − | 1.63041i | ||||
\(491\) | −87.6907 | + | 151.885i | −0.178596 | + | 0.309337i | −0.941400 | − | 0.337293i | \(-0.890489\pi\) |
0.762804 | + | 0.646630i | \(0.223822\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.81227 | − | 2.20101i | 0.00773279 | − | 0.00446453i | ||||
\(494\) | 25.9945 | − | 154.272i | 0.0526204 | − | 0.312292i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −105.242 | − | 82.9880i | −0.212181 | − | 0.167314i | ||||
\(497\) | 307.898 | − | 177.765i | 0.619512 | − | 0.357676i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −455.645 | − | 263.067i | −0.913116 | − | 0.527188i | −0.0316835 | − | 0.999498i | \(-0.510087\pi\) |
−0.881432 | + | 0.472310i | \(0.843420\pi\) | |||||||
\(500\) | 328.702 | − | 284.442i | 0.657403 | − | 0.568884i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −186.688 | + | 69.5608i | −0.371888 | + | 0.138567i | ||||
\(503\) | − | 94.2248i | − | 0.187326i | −0.995604 | − | 0.0936629i | \(-0.970142\pi\) | ||
0.995604 | − | 0.0936629i | \(-0.0298576\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −845.881 | −1.67501 | ||||||||
\(506\) | 5.81639 | + | 15.6101i | 0.0114949 | + | 0.0308500i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −34.2294 | + | 29.6204i | −0.0673807 | + | 0.0583080i | ||||
\(509\) | 321.839 | − | 557.442i | 0.632297 | − | 1.09517i | −0.354784 | − | 0.934948i | \(-0.615445\pi\) |
0.987081 | − | 0.160223i | \(-0.0512212\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 482.788 | + | 836.213i | 0.944790 | + | 1.63642i | ||||
\(512\) | −510.802 | + | 35.0091i | −0.997660 | + | 0.0683772i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −588.233 | − | 99.1157i | −1.14442 | − | 0.192832i | ||||
\(515\) | −243.513 | − | 421.778i | −0.472842 | − | 0.818986i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −95.1011 | − | 54.9066i | −0.183948 | − | 0.106202i | ||||
\(518\) | 848.668 | − | 1027.16i | 1.63836 | − | 1.98294i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.1438 | + | 444.627i | 0.0195073 | + | 0.855052i | ||||
\(521\) | − | 124.089i | − | 0.238174i | −0.992884 | − | 0.119087i | \(-0.962003\pi\) | ||
0.992884 | − | 0.119087i | \(-0.0379967\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 570.827i | 1.09145i | 0.837965 | + | 0.545724i | \(0.183745\pi\) | ||||
−0.837965 | + | 0.545724i | \(0.816255\pi\) | |||||||
\(524\) | 51.0908 | + | 266.028i | 0.0975014 | + | 0.507688i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −38.8865 | + | 47.0653i | −0.0739287 | + | 0.0894777i | ||||
\(527\) | −31.1642 | − | 17.9926i | −0.0591351 | − | 0.0341417i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −256.790 | − | 444.774i | −0.485426 | − | 0.840782i | ||||
\(530\) | −112.963 | + | 670.415i | −0.213138 | + | 1.26493i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 166.195 | − | 479.167i | 0.312397 | − | 0.900689i | ||||
\(533\) | 195.842 | + | 339.208i | 0.367433 | + | 0.636413i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27.9787 | + | 48.4605i | −0.0522966 | + | 0.0905804i | ||||
\(536\) | −672.373 | + | 408.921i | −1.25443 | + | 0.762912i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −408.732 | + | 152.296i | −0.759725 | + | 0.283077i | ||||
\(539\) | −166.771 | −0.309409 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 380.160i | 0.702699i | 0.936244 | + | 0.351350i | \(0.114277\pi\) | ||||
−0.936244 | + | 0.351350i | \(0.885723\pi\) | |||||||
\(542\) | −643.708 | + | 239.849i | −1.18765 | + | 0.442525i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −134.376 | + | 28.9997i | −0.247015 | + | 0.0533083i | ||||
\(545\) | −263.467 | − | 152.113i | −0.483425 | − | 0.279106i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −610.683 | + | 352.578i | −1.11642 | + | 0.644567i | −0.940485 | − | 0.339835i | \(-0.889629\pi\) |
−0.175937 | + | 0.984401i | \(0.556296\pi\) | |||||||
\(548\) | 18.8040 | − | 54.2149i | 0.0343139 | − | 0.0989322i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 27.2253 | − | 161.577i | 0.0495005 | − | 0.293776i | ||||
\(551\) | 9.95988 | − | 5.75034i | 0.0180760 | − | 0.0104362i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 74.7493 | − | 129.470i | 0.135170 | − | 0.234122i | ||||
\(554\) | 162.487 | − | 196.662i | 0.293298 | − | 0.354985i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 829.235 | − | 159.255i | 1.49143 | − | 0.286429i | ||||
\(557\) | 450.847 | 0.809420 | 0.404710 | − | 0.914445i | \(-0.367372\pi\) | ||||
0.404710 | + | 0.914445i | \(0.367372\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −401.198 | −0.717707 | ||||||||
\(560\) | −207.068 | + | 1426.82i | −0.369764 | + | 2.54789i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −494.610 | + | 598.638i | −0.880088 | + | 1.06519i | ||||
\(563\) | 50.2105 | − | 86.9671i | 0.0891838 | − | 0.154471i | −0.817983 | − | 0.575243i | \(-0.804907\pi\) |
0.907166 | + | 0.420772i | \(0.138241\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 963.561 | − | 556.312i | 1.70542 | − | 0.984624i | ||||
\(566\) | −491.851 | − | 82.8756i | −0.868994 | − | 0.146423i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −220.852 | − | 120.878i | −0.388824 | − | 0.212814i | ||||
\(569\) | 149.043 | − | 86.0498i | 0.261938 | − | 0.151230i | −0.363280 | − | 0.931680i | \(-0.618343\pi\) |
0.625218 | + | 0.780450i | \(0.285010\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 406.657 | + | 234.784i | 0.712184 | + | 0.411180i | 0.811869 | − | 0.583839i | \(-0.198450\pi\) |
−0.0996851 | + | 0.995019i | \(0.531784\pi\) | |||||||
\(572\) | 38.6952 | + | 44.7162i | 0.0676489 | + | 0.0781752i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 443.343 | + | 1189.85i | 0.772375 | + | 2.07291i | ||||
\(575\) | − | 151.667i | − | 0.263770i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 402.048 | 0.696791 | 0.348395 | − | 0.937348i | \(-0.386727\pi\) | ||||
0.348395 | + | 0.937348i | \(0.386727\pi\) | |||||||
\(578\) | 507.036 | − | 188.924i | 0.877226 | − | 0.326859i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −24.7224 | + | 21.3936i | −0.0426249 | + | 0.0368855i | ||||
\(581\) | 473.125 | − | 819.476i | 0.814329 | − | 1.41046i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 45.1984 | + | 78.2859i | 0.0775273 | + | 0.134281i | ||||
\(584\) | 328.291 | − | 599.808i | 0.562142 | − | 1.02707i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −37.2477 | + | 221.058i | −0.0635626 | + | 0.377232i | ||||
\(587\) | −159.999 | − | 277.126i | −0.272570 | − | 0.472105i | 0.696949 | − | 0.717121i | \(-0.254540\pi\) |
−0.969519 | + | 0.245015i | \(0.921207\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −81.4192 | − | 47.0074i | −0.138233 | − | 0.0798088i | ||||
\(590\) | 630.903 | + | 521.267i | 1.06933 | + | 0.883504i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −933.760 | − | 135.512i | −1.57730 | − | 0.228906i | ||||
\(593\) | − | 700.450i | − | 1.18120i | −0.806965 | − | 0.590599i | \(-0.798892\pi\) | ||
0.806965 | − | 0.590599i | \(-0.201108\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 387.109i | 0.650603i | ||||||||
\(596\) | −138.214 | − | 719.677i | −0.231902 | − | 1.20751i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 42.1965 | + | 34.8638i | 0.0705628 | + | 0.0583007i | ||||
\(599\) | 461.232 | + | 266.292i | 0.770003 | + | 0.444561i | 0.832876 | − | 0.553460i | \(-0.186693\pi\) |
−0.0628729 | + | 0.998022i | \(0.520026\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −440.321 | − | 762.658i | −0.732647 | − | 1.26898i | −0.955748 | − | 0.294187i | \(-0.904951\pi\) |
0.223101 | − | 0.974795i | \(-0.428382\pi\) | |||||||
\(602\) | −1282.53 | − | 216.102i | −2.13044 | − | 0.358974i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 596.844 | + | 207.011i | 0.988153 | + | 0.342733i | ||||
\(605\) | 464.632 | + | 804.766i | 0.767987 | + | 1.33019i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −180.816 | + | 313.182i | −0.297884 | + | 0.515951i | −0.975652 | − | 0.219326i | \(-0.929614\pi\) |
0.677767 | + | 0.735276i | \(0.262948\pi\) | |||||||
\(608\) | −351.070 | + | 75.7643i | −0.577418 | + | 0.124612i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 276.150 | + | 741.133i | 0.452705 | + | 1.21497i | ||||
\(611\) | −360.822 | −0.590543 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 237.930i | 0.388140i | 0.980988 | + | 0.194070i | \(0.0621689\pi\) | ||||
−0.980988 | + | 0.194070i | \(0.937831\pi\) | |||||||
\(614\) | 296.802 | + | 796.559i | 0.483390 | + | 1.29733i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 99.6124 | + | 163.789i | 0.161708 | + | 0.265891i | ||||
\(617\) | −182.219 | − | 105.204i | −0.295331 | − | 0.170510i | 0.345012 | − | 0.938598i | \(-0.387875\pi\) |
−0.640344 | + | 0.768089i | \(0.721208\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −117.749 | + | 67.9823i | −0.190224 | + | 0.109826i | −0.592088 | − | 0.805874i | \(-0.701696\pi\) |
0.401863 | + | 0.915700i | \(0.368363\pi\) | |||||||
\(620\) | 252.505 | + | 87.5796i | 0.407267 | + | 0.141257i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 585.777 | + | 98.7020i | 0.941764 | + | 0.158685i | ||||
\(623\) | 1027.54 | − | 593.248i | 1.64934 | − | 0.952244i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 49.3927 | − | 85.5507i | 0.0790284 | − | 0.136881i | ||||
\(626\) | −311.975 | − | 257.762i | −0.498363 | − | 0.411760i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 625.103 | − | 120.051i | 0.995387 | − | 0.191164i | ||||
\(629\) | −253.337 | −0.402762 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 368.187 | 0.583498 | 0.291749 | − | 0.956495i | \(-0.405763\pi\) | ||||
0.291749 | + | 0.956495i | \(0.405763\pi\) | |||||||
\(632\) | −105.840 | + | 2.41465i | −0.167468 | + | 0.00382064i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −66.0576 | − | 54.5784i | −0.104192 | − | 0.0860858i | ||||
\(635\) | 45.1330 | − | 78.1726i | 0.0710756 | − | 0.123106i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −474.559 | + | 273.986i | −0.744990 | + | 0.430120i | ||||
\(638\) | −0.722287 | + | 4.28663i | −0.00113211 | + | 0.00671886i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 939.479 | − | 399.743i | 1.46794 | − | 0.624599i | ||||
\(641\) | −212.362 | + | 122.607i | −0.331297 | + | 0.191275i | −0.656417 | − | 0.754398i | \(-0.727929\pi\) |
0.325120 | + | 0.945673i | \(0.394595\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1052.52 | − | 607.675i | −1.63690 | − | 0.945062i | −0.981893 | − | 0.189435i | \(-0.939334\pi\) |
−0.655002 | − | 0.755627i | \(-0.727332\pi\) | |||||||
\(644\) | 116.112 | + | 134.179i | 0.180298 | + | 0.208353i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −90.3621 | + | 33.6694i | −0.139879 | + | 0.0521198i | ||||
\(647\) | 887.961i | 1.37243i | 0.727399 | + | 0.686214i | \(0.240729\pi\) | ||||
−0.727399 | + | 0.686214i | \(0.759271\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 108.815 | 0.167666 | ||||||||
\(650\) | −187.981 | − | 504.505i | −0.289202 | − | 0.776162i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 333.576 | + | 385.481i | 0.511620 | + | 0.591229i | ||||
\(653\) | −467.477 | + | 809.694i | −0.715891 | + | 1.23996i | 0.246723 | + | 0.969086i | \(0.420646\pi\) |
−0.962615 | + | 0.270874i | \(0.912687\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −270.093 | − | 467.815i | −0.412356 | − | 0.714221i | ||||
\(656\) | 556.769 | − | 706.070i | 0.848733 | − | 1.07633i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1153.45 | − | 194.354i | −1.75297 | − | 0.295371i | ||||
\(659\) | −449.326 | − | 778.255i | −0.681830 | − | 1.18096i | −0.974422 | − | 0.224727i | \(-0.927851\pi\) |
0.292592 | − | 0.956237i | \(-0.405482\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −169.415 | − | 97.8116i | −0.256301 | − | 0.147975i | 0.366345 | − | 0.930479i | \(-0.380609\pi\) |
−0.622646 | + | 0.782504i | \(0.713942\pi\) | |||||||
\(662\) | −272.112 | + | 329.344i | −0.411045 | + | 0.497498i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −669.912 | + | 15.2835i | −1.00890 | + | 0.0230173i | ||||
\(665\) | 1011.36i | 1.52084i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.02374i | 0.00603259i | ||||||||
\(668\) | 67.9268 | − | 13.0453i | 0.101687 | − | 0.0195290i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 999.547 | − | 1209.78i | 1.49186 | − | 1.80564i | ||||
\(671\) | 91.0725 | + | 52.5807i | 0.135726 | + | 0.0783617i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 417.087 | + | 722.416i | 0.619743 | + | 1.07343i | 0.989532 | + | 0.144311i | \(0.0460967\pi\) |
−0.369789 | + | 0.929116i | \(0.620570\pi\) | |||||||
\(674\) | 74.0324 | − | 439.368i | 0.109840 | − | 0.651882i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −455.101 | − | 157.848i | −0.673227 | − | 0.233504i | ||||
\(677\) | 61.6931 | + | 106.856i | 0.0911272 | + | 0.157837i | 0.907986 | − | 0.419001i | \(-0.137620\pi\) |
−0.816859 | + | 0.576838i | \(0.804286\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 107.794 | − | 186.705i | 0.158754 | − | 0.274970i | ||||
\(680\) | 234.217 | − | 142.445i | 0.344436 | − | 0.209478i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 33.2995 | − | 12.4076i | 0.0488262 | − | 0.0181929i | ||||
\(683\) | 799.370 | 1.17038 | 0.585191 | − | 0.810896i | \(-0.301020\pi\) | ||||
0.585191 | + | 0.810896i | \(0.301020\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 114.429i | 0.167050i | ||||||||
\(686\) | −627.187 | + | 233.693i | −0.914266 | + | 0.340660i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 341.181 | + | 855.499i | 0.495903 | + | 1.24346i | ||||
\(689\) | 257.230 | + | 148.512i | 0.373338 | + | 0.215547i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 581.995 | − | 336.015i | 0.842250 | − | 0.486273i | −0.0157784 | − | 0.999876i | \(-0.505023\pi\) |
0.858028 | + | 0.513602i | \(0.171689\pi\) | |||||||
\(692\) | 926.695 | + | 321.417i | 1.33915 | + | 0.464476i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −48.0841 | + | 285.370i | −0.0692854 | + | 0.411196i | ||||
\(695\) | −1458.22 | + | 841.905i | −2.09816 | + | 1.21137i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 120.713 | − | 209.081i | 0.173190 | − | 0.299973i | ||||
\(698\) | −281.559 | + | 340.778i | −0.403380 | + | 0.488221i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −329.179 | − | 1714.03i | −0.470255 | − | 2.44861i | ||||
\(701\) | −345.561 | −0.492954 | −0.246477 | − | 0.969149i | \(-0.579273\pi\) | ||||
−0.246477 | + | 0.969149i | \(0.579273\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −661.866 | −0.941488 | ||||||||
\(704\) | 62.4445 | − | 120.539i | 0.0886996 | − | 0.171220i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 882.860 | − | 1068.55i | 1.25051 | − | 1.51352i | ||||
\(707\) | −599.009 | + | 1037.51i | −0.847255 | + | 1.46749i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1200.93 | − | 693.354i | 1.69383 | − | 0.977933i | 0.742455 | − | 0.669896i | \(-0.233661\pi\) |
0.951374 | − | 0.308037i | \(-0.0996721\pi\) | |||||||
\(710\) | 495.076 | + | 83.4191i | 0.697290 | + | 0.117492i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −737.042 | − | 403.403i | −1.03517 | − | 0.566577i | ||||
\(713\) | 28.4861 | − | 16.4465i | 0.0399524 | − | 0.0230665i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −102.122 | − | 58.9603i | −0.142828 | − | 0.0824619i | ||||
\(716\) | 743.710 | − | 643.570i | 1.03870 | − | 0.898841i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 200.940 | + | 539.285i | 0.279861 | + | 0.751093i | ||||
\(719\) | − | 226.454i | − | 0.314956i | −0.987522 | − | 0.157478i | \(-0.949664\pi\) | ||
0.987522 | − | 0.157478i | \(-0.0503364\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −689.775 | −0.956692 | ||||||||
\(722\) | 440.482 | − | 164.126i | 0.610086 | − | 0.227321i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 140.577 | + | 162.451i | 0.194167 | + | 0.224380i | ||||
\(725\) | 19.7889 | − | 34.2754i | 0.0272951 | − | 0.0472765i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −348.940 | − | 604.381i | −0.479972 | − | 0.831336i | 0.519764 | − | 0.854310i | \(-0.326020\pi\) |
−0.999736 | + | 0.0229740i | \(0.992687\pi\) | |||||||
\(728\) | 552.540 | + | 302.420i | 0.758984 | + | 0.415412i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −226.556 | + | 1344.57i | −0.310351 | + | 1.84187i | ||||
\(731\) | 123.646 | + | 214.160i | 0.169146 | + | 0.292969i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 174.486 | + | 100.740i | 0.238044 | + | 0.137435i | 0.614278 | − | 0.789090i | \(-0.289448\pi\) |
−0.376233 | + | 0.926525i | \(0.622781\pi\) | |||||||
\(734\) | −1012.74 | − | 836.751i | −1.37976 | − | 1.13999i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 38.4581 | − | 119.627i | 0.0522528 | − | 0.162536i | ||||
\(737\) | − | 208.656i | − | 0.283116i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 914.779i | − | 1.23786i | −0.785446 | − | 0.618930i | \(-0.787566\pi\) | ||
0.785446 | − | 0.618930i | \(-0.212434\pi\) | |||||||
\(740\) | 1847.77 | − | 354.863i | 2.49698 | − | 0.479545i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 742.302 | + | 613.309i | 1.00041 | + | 0.826561i | ||||
\(743\) | 727.202 | + | 419.850i | 0.978738 | + | 0.565074i | 0.901889 | − | 0.431968i | \(-0.142181\pi\) |
0.0768489 | + | 0.997043i | \(0.475514\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 730.673 | + | 1265.56i | 0.980769 | + | 1.69874i | ||||
\(746\) | 730.785 | + | 123.136i | 0.979605 | + | 0.165061i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.9441 | − | 34.4367i | 0.0159681 | − | 0.0460384i | ||||
\(749\) | 39.6261 | + | 68.6344i | 0.0529054 | + | 0.0916348i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −92.3794 | + | 160.006i | −0.123008 | + | 0.213057i | −0.920953 | − | 0.389674i | \(-0.872588\pi\) |
0.797944 | + | 0.602731i | \(0.205921\pi\) | |||||||
\(752\) | 306.845 | + | 769.402i | 0.408038 | + | 1.02314i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.98714 | + | 13.3845i | 0.00661424 | + | 0.0177514i | ||||
\(755\) | −1259.73 | −1.66852 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 549.800i | − | 0.726288i | −0.931733 | − | 0.363144i | \(-0.881703\pi\) | ||
0.931733 | − | 0.363144i | \(-0.118297\pi\) | |||||||
\(758\) | −421.522 | − | 1131.28i | −0.556098 | − | 1.49246i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 611.911 | − | 372.149i | 0.805146 | − | 0.489670i | ||||
\(761\) | 454.835 | + | 262.599i | 0.597680 | + | 0.345071i | 0.768128 | − | 0.640296i | \(-0.221188\pi\) |
−0.170448 | + | 0.985367i | \(0.554522\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −373.147 | + | 215.437i | −0.489053 | + | 0.282355i | ||||
\(764\) | −315.647 | + | 910.059i | −0.413151 | + | 1.19118i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −649.740 | − | 109.480i | −0.848225 | − | 0.142924i | ||||
\(767\) | 309.640 | − | 178.771i | 0.403703 | − | 0.233078i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 70.7173 | − | 122.486i | 0.0919601 | − | 0.159280i | −0.816376 | − | 0.577521i | \(-0.804020\pi\) |
0.908336 | + | 0.418242i | \(0.137353\pi\) | |||||||
\(770\) | −294.700 | − | 243.488i | −0.382727 | − | 0.316218i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 188.453 | + | 981.268i | 0.244110 | + | 1.27107i | ||||
\(773\) | −746.557 | −0.965792 | −0.482896 | − | 0.875678i | \(-0.660415\pi\) | ||||
−0.482896 | + | 0.875678i | \(0.660415\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −323.538 | −0.417468 | ||||||||
\(776\) | −152.629 | + | 3.48210i | −0.196687 | + | 0.00448724i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −919.836 | − | 759.991i | −1.18231 | − | 0.976852i | ||||
\(779\) | 315.374 | − | 546.244i | 0.404845 | − | 0.701211i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 57.8112 | − | 33.3773i | 0.0740220 | − | 0.0427366i | ||||
\(782\) | 5.60579 | − | 33.2693i | 0.00716853 | − | 0.0425439i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 987.805 | + | 778.931i | 1.25996 | + | 0.993534i | ||||
\(785\) | −1099.25 | + | 634.654i | −1.40032 | + | 0.808477i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 515.762 | + | 297.776i | 0.655352 | + | 0.378368i | 0.790504 | − | 0.612457i | \(-0.209819\pi\) |
−0.135151 | + | 0.990825i | \(0.543152\pi\) | |||||||
\(788\) | −991.282 | + | 857.807i | −1.25797 | + | 1.08859i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 197.825 | − | 73.7108i | 0.250412 | − | 0.0933048i | ||||
\(791\) | − | 1575.81i | − | 1.99217i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 345.537 | 0.435734 | ||||||||
\(794\) | 542.810 | + | 1456.80i | 0.683639 | + | 1.83476i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −693.431 | + | 600.061i | −0.871145 | + | 0.753845i | ||||
\(797\) | −329.698 | + | 571.054i | −0.413674 | + | 0.716504i | −0.995288 | − | 0.0969605i | \(-0.969088\pi\) |
0.581614 | + | 0.813465i | \(0.302421\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 111.202 | + | 192.607i | 0.139176 | + | 0.241060i | ||||
\(800\) | −915.927 | + | 829.877i | −1.14491 | + | 1.03735i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 987.643 | + | 166.415i | 1.23147 | + | 0.207500i | ||||
\(803\) | 90.6488 | + | 157.008i | 0.112888 | + | 0.195527i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −306.437 | − | 176.921i | −0.380667 | − | 0.219778i | ||||
\(806\) | 74.3716 | − | 90.0138i | 0.0922725 | − | 0.111680i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 848.156 | − | 19.3500i | 1.04970 | − | 0.0239480i | ||||
\(809\) | − | 1442.15i | − | 1.78263i | −0.453382 | − | 0.891317i | \(-0.649783\pi\) | ||
0.453382 | − | 0.891317i | \(-0.350217\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 907.692i | 1.11923i | 0.828754 | + | 0.559613i | \(0.189050\pi\) | ||||
−0.828754 | + | 0.559613i | \(0.810950\pi\) | |||||||
\(812\) | 8.73311 | + | 45.4731i | 0.0107551 | + | 0.0560014i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 159.347 | − | 192.861i | 0.195758 | − | 0.236931i | ||||
\(815\) | −880.356 | − | 508.274i | −1.08019 | − | 0.623649i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 323.035 | + | 559.513i | 0.395391 | + | 0.684838i | ||||
\(818\) | −139.606 | + | 828.537i | −0.170668 | + | 1.01288i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −587.574 | + | 1694.07i | −0.716554 | + | 2.06593i | ||||
\(821\) | −775.205 | − | 1342.69i | −0.944221 | − | 1.63544i | −0.757304 | − | 0.653063i | \(-0.773484\pi\) |
−0.186917 | − | 0.982376i | \(-0.559850\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 332.778 | − | 576.389i | 0.404348 | − | 0.700351i | −0.589898 | − | 0.807478i | \(-0.700832\pi\) |
0.994245 | + | 0.107127i | \(0.0341652\pi\) | |||||||
\(824\) | 253.817 | + | 417.342i | 0.308030 | + | 0.506482i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1086.13 | − | 404.698i | 1.31493 | − | 0.489950i | ||||
\(827\) | −911.934 | −1.10270 | −0.551351 | − | 0.834274i | \(-0.685887\pi\) | ||||
−0.551351 | + | 0.834274i | \(0.685887\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 463.817i | − | 0.559489i | −0.960074 | − | 0.279745i | \(-0.909750\pi\) | ||
0.960074 | − | 0.279745i | \(-0.0902498\pi\) | |||||||
\(830\) | 1252.14 | − | 466.552i | 1.50860 | − | 0.562111i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20.3421 | − | 445.591i | −0.0244497 | − | 0.535566i | ||||
\(833\) | 292.509 | + | 168.880i | 0.351151 | + | 0.202737i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −119.450 | + | 68.9647i | −0.143054 | + | 0.0825924i | ||||
\(836\) | 31.2050 | − | 89.9689i | 0.0373266 | − | 0.107618i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 69.0580 | − | 409.846i | 0.0824082 | − | 0.489076i | ||||
\(839\) | −54.8140 | + | 31.6469i | −0.0653326 | + | 0.0377198i | −0.532310 | − | 0.846549i | \(-0.678676\pi\) |
0.466978 | + | 0.884269i | \(0.345343\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 419.975 | − | 727.418i | 0.499376 | − | 0.864944i | ||||
\(842\) | −120.999 | + | 146.448i | −0.143705 | + | 0.173929i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −614.815 | + | 118.075i | −0.728454 | + | 0.139899i | ||||
\(845\) | 960.563 | 1.13676 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1316.11 | 1.55385 | ||||||||
\(848\) | 97.9310 | − | 674.802i | 0.115485 | − | 0.795758i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −211.372 | + | 255.828i | −0.248673 | + | 0.300975i | ||||
\(851\) | 115.783 | − | 200.543i | 0.136056 | − | 0.235655i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −396.697 | + | 229.033i | −0.465061 | + | 0.268503i | −0.714170 | − | 0.699972i | \(-0.753196\pi\) |
0.249109 | + | 0.968475i | \(0.419862\pi\) | |||||||
\(854\) | 1104.59 | + | 186.121i | 1.29343 | + | 0.217940i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 26.9454 | − | 49.2308i | 0.0314782 | − | 0.0575127i | ||||
\(857\) | 1107.08 | − | 639.171i | 1.29181 | − | 0.745824i | 0.312831 | − | 0.949809i | \(-0.398723\pi\) |
0.978974 | + | 0.203984i | \(0.0653892\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −363.697 | − | 209.981i | −0.423396 | − | 0.244448i | 0.273133 | − | 0.961976i | \(-0.411940\pi\) |
−0.696529 | + | 0.717528i | \(0.745273\pi\) | |||||||
\(860\) | −1201.82 | − | 1388.82i | −1.39746 | − | 1.61491i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −167.346 | − | 449.126i | −0.194137 | − | 0.521028i | ||||
\(863\) | 918.683i | 1.06452i | 0.846580 | + | 0.532261i | \(0.178658\pi\) | ||||
−0.846580 | + | 0.532261i | \(0.821342\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1955.94 | −2.26120 | ||||||||
\(866\) | 78.5598 | − | 29.2718i | 0.0907157 | − | 0.0338011i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 286.232 | − | 247.691i | 0.329760 | − | 0.285358i | ||||
\(869\) | 14.0350 | − | 24.3093i | 0.0161508 | − | 0.0279739i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −342.799 | − | 593.745i | −0.393570 | − | 0.681682i | ||||
\(872\) | 267.655 | + | 146.495i | 0.306944 | + | 0.167999i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 14.6456 | − | 86.9189i | 0.0167570 | − | 0.0994496i | ||||
\(875\) | 613.834 | + | 1063.19i | 0.701524 | + | 1.21508i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1104.62 | − | 637.754i | −1.25955 | − | 0.727200i | −0.286561 | − | 0.958062i | \(-0.592512\pi\) |
−0.972986 | + | 0.230862i | \(0.925845\pi\) | |||||||
\(878\) | −818.660 | − | 676.397i | −0.932414 | − | 0.770384i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −38.8793 | + | 267.902i | −0.0441811 | + | 0.304434i | ||||
\(881\) | 211.510i | 0.240079i | 0.992769 | + | 0.120039i | \(0.0383021\pi\) | ||||
−0.992769 | + | 0.120039i | \(0.961698\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 613.635i | − | 0.694943i | −0.937690 | − | 0.347472i | \(-0.887040\pi\) | ||
0.937690 | − | 0.347472i | \(-0.112960\pi\) | |||||||
\(884\) | −22.5879 | − | 117.615i | −0.0255519 | − | 0.133048i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −451.968 | − | 373.427i | −0.510122 | − | 0.421475i | ||||
\(887\) | 978.062 | + | 564.684i | 1.10266 | + | 0.636623i | 0.936919 | − | 0.349546i | \(-0.113664\pi\) |
0.165744 | + | 0.986169i | \(0.446997\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −63.9217 | − | 110.716i | −0.0719029 | − | 0.124540i | ||||
\(890\) | 1652.20 | + | 278.392i | 1.85641 | + | 0.312800i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 910.404 | + | 315.767i | 1.02063 | + | 0.353999i | ||||
\(893\) | 290.525 | + | 503.203i | 0.325335 | + | 0.563498i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −980.615 | + | 1698.47i | −1.09566 | + | 1.89774i | ||||
\(896\) | 174.986 | − | 1435.39i | 0.195297 | − | 1.60200i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 187.338 | + | 502.779i | 0.208617 | + | 0.559888i | ||||
\(899\) | 8.58345 | 0.00954778 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 183.080i | − | 0.203196i | ||||||
\(902\) | 83.2427 | + | 223.407i | 0.0922868 | + | 0.247680i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −953.427 | + | 579.851i | −1.05468 | + | 0.641428i | ||||
\(905\) | −371.003 | − | 214.199i | −0.409948 | − | 0.236684i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 515.588 | − | 297.675i | 0.568454 | − | 0.328197i | −0.188078 | − | 0.982154i | \(-0.560226\pi\) |
0.756532 | + | 0.653957i | \(0.226892\pi\) | |||||||
\(908\) | 336.762 | + | 116.803i | 0.370883 | + | 0.128638i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1238.61 | − | 208.703i | −1.36111 | − | 0.229344i | ||||
\(911\) | 316.089 | − | 182.494i | 0.346969 | − | 0.200323i | −0.316381 | − | 0.948632i | \(-0.602468\pi\) |
0.663349 | + | 0.748310i | \(0.269134\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 88.8345 | − | 153.866i | 0.0972995 | − | 0.168528i | ||||
\(914\) | 1150.02 | + | 950.172i | 1.25822 | + | 1.03958i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −656.033 | + | 125.991i | −0.716193 | + | 0.137545i | ||||
\(917\) | −765.064 | −0.834312 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 317.896 | 0.345915 | 0.172957 | − | 0.984929i | \(-0.444668\pi\) | ||||
0.172957 | + | 0.984929i | \(0.444668\pi\) | |||||||
\(920\) | 5.71514 | + | 250.509i | 0.00621211 | + | 0.272292i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1022.36 | + | 844.695i | 1.10885 | + | 0.916156i | ||||
\(923\) | 109.670 | − | 189.955i | 0.118819 | − | 0.205801i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1972.56 | + | 1138.86i | −2.13249 | + | 1.23120i | ||||
\(926\) | −94.6038 | + | 561.455i | −0.102164 | + | 0.606323i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 24.2995 | − | 22.0166i | 0.0261849 | − | 0.0237248i | ||||
\(929\) | −1405.17 | + | 811.273i | −1.51256 | + | 0.873276i | −0.512666 | + | 0.858588i | \(0.671342\pi\) |
−0.999892 | + | 0.0146874i | \(0.995325\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 764.205 | + | 441.214i | 0.820844 | + | 0.473914i | ||||
\(932\) | −357.494 | − | 413.120i | −0.383577 | − | 0.443262i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 327.606 | − | 122.068i | 0.350756 | − | 0.130693i | ||||
\(935\) | 72.6840i | 0.0777369i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −935.489 | −0.998387 | −0.499194 | − | 0.866490i | \(-0.666370\pi\) | ||||
−0.499194 | + | 0.866490i | \(0.666370\pi\) | |||||||
\(938\) | −776.023 | − | 2082.70i | −0.827316 | − | 2.22036i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1080.87 | − | 1249.05i | −1.14986 | − | 1.32878i | ||||
\(941\) | 344.673 | − | 596.990i | 0.366283 | − | 0.634421i | −0.622698 | − | 0.782462i | \(-0.713963\pi\) |
0.988981 | + | 0.148041i | \(0.0472968\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 110.340 | + | 191.114i | 0.117009 | + | 0.202666i | ||||
\(944\) | −644.524 | − | 508.237i | −0.682758 | − | 0.538387i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −240.809 | − | 40.5757i | −0.254555 | − | 0.0428918i | ||||
\(947\) | 571.731 | + | 990.266i | 0.603728 | + | 1.04569i | 0.992251 | + | 0.124249i | \(0.0396521\pi\) |
−0.388523 | + | 0.921439i | \(0.627015\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 515.894 | + | 297.851i | 0.543618 | + | 0.313858i | ||||
\(950\) | −552.227 | + | 668.374i | −0.581292 | + | 0.703552i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.85532 | − | 388.150i | −0.00930180 | − | 0.407721i | ||||
\(953\) | 1635.29i | 1.71594i | 0.513697 | + | 0.857972i | \(0.328276\pi\) | ||||
−0.513697 | + | 0.857972i | \(0.671724\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1920.82i | − | 2.01133i | ||||||
\(956\) | −605.833 | + | 116.350i | −0.633716 | + | 0.121705i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −913.869 | + | 1106.08i | −0.953934 | + | 1.15457i | ||||
\(959\) | 140.353 | + | 81.0327i | 0.146353 | + | 0.0844971i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 445.416 | + | 771.484i | 0.463493 | + | 0.802793i | ||||
\(962\) | 136.582 | − | 810.589i | 0.141977 | − | 0.842608i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −241.200 | − | 83.6584i | −0.250207 | − | 0.0867825i | ||||
\(965\) | −996.261 | − | 1725.58i | −1.03240 | − | 1.78816i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −524.608 | + | 908.647i | −0.542510 | + | 0.939656i | 0.456249 | + | 0.889852i | \(0.349193\pi\) |
−0.998759 | + | 0.0498033i | \(0.984141\pi\) | |||||||
\(968\) | −484.291 | − | 796.302i | −0.500301 | − | 0.822626i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 285.279 | − | 106.296i | 0.294102 | − | 0.109584i | ||||
\(971\) | 1469.41 | 1.51329 | 0.756646 | − | 0.653824i | \(-0.226836\pi\) | ||||
0.756646 | + | 0.653824i | \(0.226836\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2384.77i | 2.45095i | ||||||||
\(974\) | 1253.55 | − | 467.078i | 1.28701 | − | 0.479546i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −293.846 | − | 736.809i | −0.301072 | − | 0.754927i | ||||
\(977\) | 517.184 | + | 298.596i | 0.529359 | + | 0.305626i | 0.740756 | − | 0.671775i | \(-0.234468\pi\) |
−0.211396 | + | 0.977400i | \(0.567801\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 192.931 | − | 111.389i | 0.197070 | − | 0.113778i | ||||
\(980\) | −2370.03 | − | 822.028i | −2.41840 | − | 0.838804i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −58.2811 | + | 345.887i | −0.0593494 | + | 0.352227i | ||||
\(983\) | −1503.96 | + | 868.311i | −1.52997 | + | 0.883328i | −0.530606 | + | 0.847619i | \(0.678036\pi\) |
−0.999362 | + | 0.0357088i | \(0.988631\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1307.05 | − | 2263.88i | 1.32695 | − | 2.29835i | ||||
\(986\) | 5.60769 | − | 6.78713i | 0.00568732 | − | 0.00688350i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −59.0128 | − | 307.278i | −0.0597296 | − | 0.311011i | ||||
\(989\) | −226.040 | −0.228554 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 506.650 | 0.511251 | 0.255626 | − | 0.966776i | \(-0.417719\pi\) | ||||
0.255626 | + | 0.966776i | \(0.417719\pi\) | |||||||
\(992\) | −255.188 | − | 82.0389i | −0.257246 | − | 0.0827005i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 452.905 | − | 548.162i | 0.455639 | − | 0.551471i | ||||
\(995\) | 914.319 | − | 1583.65i | 0.918914 | − | 1.59161i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −420.474 | + | 242.761i | −0.421739 | + | 0.243491i | −0.695821 | − | 0.718215i | \(-0.744959\pi\) |
0.274082 | + | 0.961706i | \(0.411626\pi\) | |||||||
\(998\) | −1037.64 | − | 174.840i | −1.03972 | − | 0.175190i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 216.3.j.a.125.19 | 44 | ||
3.2 | odd | 2 | 72.3.j.a.5.4 | ✓ | 44 | ||
4.3 | odd | 2 | 864.3.n.a.17.2 | 44 | |||
8.3 | odd | 2 | 864.3.n.a.17.21 | 44 | |||
8.5 | even | 2 | inner | 216.3.j.a.125.17 | 44 | ||
9.2 | odd | 6 | inner | 216.3.j.a.197.17 | 44 | ||
9.4 | even | 3 | 648.3.h.a.485.20 | 44 | |||
9.5 | odd | 6 | 648.3.h.a.485.25 | 44 | |||
9.7 | even | 3 | 72.3.j.a.29.6 | yes | 44 | ||
12.11 | even | 2 | 288.3.n.a.113.9 | 44 | |||
24.5 | odd | 2 | 72.3.j.a.5.6 | yes | 44 | ||
24.11 | even | 2 | 288.3.n.a.113.14 | 44 | |||
36.7 | odd | 6 | 288.3.n.a.209.14 | 44 | |||
36.11 | even | 6 | 864.3.n.a.305.21 | 44 | |||
36.23 | even | 6 | 2592.3.h.a.1457.4 | 44 | |||
36.31 | odd | 6 | 2592.3.h.a.1457.42 | 44 | |||
72.5 | odd | 6 | 648.3.h.a.485.19 | 44 | |||
72.11 | even | 6 | 864.3.n.a.305.2 | 44 | |||
72.13 | even | 6 | 648.3.h.a.485.26 | 44 | |||
72.29 | odd | 6 | inner | 216.3.j.a.197.19 | 44 | ||
72.43 | odd | 6 | 288.3.n.a.209.9 | 44 | |||
72.59 | even | 6 | 2592.3.h.a.1457.41 | 44 | |||
72.61 | even | 6 | 72.3.j.a.29.4 | yes | 44 | ||
72.67 | odd | 6 | 2592.3.h.a.1457.3 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.3.j.a.5.4 | ✓ | 44 | 3.2 | odd | 2 | ||
72.3.j.a.5.6 | yes | 44 | 24.5 | odd | 2 | ||
72.3.j.a.29.4 | yes | 44 | 72.61 | even | 6 | ||
72.3.j.a.29.6 | yes | 44 | 9.7 | even | 3 | ||
216.3.j.a.125.17 | 44 | 8.5 | even | 2 | inner | ||
216.3.j.a.125.19 | 44 | 1.1 | even | 1 | trivial | ||
216.3.j.a.197.17 | 44 | 9.2 | odd | 6 | inner | ||
216.3.j.a.197.19 | 44 | 72.29 | odd | 6 | inner | ||
288.3.n.a.113.9 | 44 | 12.11 | even | 2 | |||
288.3.n.a.113.14 | 44 | 24.11 | even | 2 | |||
288.3.n.a.209.9 | 44 | 72.43 | odd | 6 | |||
288.3.n.a.209.14 | 44 | 36.7 | odd | 6 | |||
648.3.h.a.485.19 | 44 | 72.5 | odd | 6 | |||
648.3.h.a.485.20 | 44 | 9.4 | even | 3 | |||
648.3.h.a.485.25 | 44 | 9.5 | odd | 6 | |||
648.3.h.a.485.26 | 44 | 72.13 | even | 6 | |||
864.3.n.a.17.2 | 44 | 4.3 | odd | 2 | |||
864.3.n.a.17.21 | 44 | 8.3 | odd | 2 | |||
864.3.n.a.305.2 | 44 | 72.11 | even | 6 | |||
864.3.n.a.305.21 | 44 | 36.11 | even | 6 | |||
2592.3.h.a.1457.3 | 44 | 72.67 | odd | 6 | |||
2592.3.h.a.1457.4 | 44 | 36.23 | even | 6 | |||
2592.3.h.a.1457.41 | 44 | 72.59 | even | 6 | |||
2592.3.h.a.1457.42 | 44 | 36.31 | odd | 6 |