Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 170.17 | ||
Character | \(\chi\) | \(=\) | 1183.170 |
Dual form | 1183.2.e.l.508.17 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.593734 | − | 1.02838i | 0.419833 | − | 0.727172i | −0.576089 | − | 0.817387i | \(-0.695422\pi\) |
0.995922 | + | 0.0902146i | \(0.0287553\pi\) | |||||||
\(3\) | 1.46725 | + | 2.54136i | 0.847119 | + | 1.46725i | 0.883768 | + | 0.467925i | \(0.154998\pi\) |
−0.0366489 | + | 0.999328i | \(0.511668\pi\) | |||||||
\(4\) | 0.294961 | + | 0.510887i | 0.147480 | + | 0.255444i | ||||
\(5\) | −1.70195 | + | 2.94787i | −0.761136 | + | 1.31833i | 0.181129 | + | 0.983459i | \(0.442025\pi\) |
−0.942265 | + | 0.334867i | \(0.891308\pi\) | |||||||
\(6\) | 3.48463 | 1.42259 | ||||||||
\(7\) | −2.56390 | − | 0.653016i | −0.969062 | − | 0.246817i | ||||
\(8\) | 3.07545 | 1.08733 | ||||||||
\(9\) | −2.80567 | + | 4.85955i | −0.935222 | + | 1.61985i | ||||
\(10\) | 2.02101 | + | 3.50050i | 0.639100 | + | 1.10695i | ||||
\(11\) | −1.63377 | − | 2.82977i | −0.492600 | − | 0.853208i | 0.507364 | − | 0.861732i | \(-0.330620\pi\) |
−0.999964 | + | 0.00852407i | \(0.997287\pi\) | |||||||
\(12\) | −0.865565 | + | 1.49920i | −0.249867 | + | 0.432782i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.19382 | + | 2.24893i | −0.586323 | + | 0.601053i | ||||
\(15\) | −9.98878 | −2.57909 | ||||||||
\(16\) | 1.23607 | − | 2.14094i | 0.309019 | − | 0.535236i | ||||
\(17\) | 1.27943 | + | 2.21604i | 0.310307 | + | 0.537468i | 0.978429 | − | 0.206584i | \(-0.0662347\pi\) |
−0.668121 | + | 0.744052i | \(0.732901\pi\) | |||||||
\(18\) | 3.33164 | + | 5.77056i | 0.785274 | + | 1.36013i | ||||
\(19\) | −2.48424 | + | 4.30282i | −0.569923 | + | 0.987136i | 0.426650 | + | 0.904417i | \(0.359694\pi\) |
−0.996573 | + | 0.0827188i | \(0.973640\pi\) | |||||||
\(20\) | −2.00804 | −0.449011 | ||||||||
\(21\) | −2.10234 | − | 7.47392i | −0.458768 | − | 1.63094i | ||||
\(22\) | −3.88009 | −0.827239 | ||||||||
\(23\) | 0.938380 | − | 1.62532i | 0.195666 | − | 0.338903i | −0.751453 | − | 0.659787i | \(-0.770647\pi\) |
0.947119 | + | 0.320884i | \(0.103980\pi\) | |||||||
\(24\) | 4.51246 | + | 7.81581i | 0.921102 | + | 1.59540i | ||||
\(25\) | −3.29328 | − | 5.70414i | −0.658657 | − | 1.14083i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.66297 | −1.47474 | ||||||||
\(28\) | −0.422632 | − | 1.50248i | −0.0798699 | − | 0.283941i | ||||
\(29\) | 0.273228 | 0.0507371 | 0.0253686 | − | 0.999678i | \(-0.491924\pi\) | ||||
0.0253686 | + | 0.999678i | \(0.491924\pi\) | |||||||
\(30\) | −5.93068 | + | 10.2722i | −1.08279 | + | 1.87544i | ||||
\(31\) | 0.341474 | + | 0.591451i | 0.0613306 | + | 0.106228i | 0.895060 | − | 0.445945i | \(-0.147132\pi\) |
−0.833730 | + | 0.552173i | \(0.813799\pi\) | |||||||
\(32\) | 1.60765 | + | 2.78453i | 0.284195 | + | 0.492240i | ||||
\(33\) | 4.79431 | − | 8.30398i | 0.834581 | − | 1.44554i | ||||
\(34\) | 3.03856 | 0.521109 | ||||||||
\(35\) | 6.28864 | − | 6.44663i | 1.06297 | − | 1.08968i | ||||
\(36\) | −3.31025 | −0.551708 | ||||||||
\(37\) | 5.60742 | − | 9.71233i | 0.921854 | − | 1.59670i | 0.125309 | − | 0.992118i | \(-0.460008\pi\) |
0.796545 | − | 0.604579i | \(-0.206659\pi\) | |||||||
\(38\) | 2.94995 | + | 5.10946i | 0.478545 | + | 0.828864i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.23426 | + | 9.06601i | −0.827610 | + | 1.43346i | ||||
\(41\) | 1.85543 | 0.289769 | 0.144884 | − | 0.989449i | \(-0.453719\pi\) | ||||
0.144884 | + | 0.989449i | \(0.453719\pi\) | |||||||
\(42\) | −8.93424 | − | 2.27552i | −1.37858 | − | 0.351121i | ||||
\(43\) | −0.826020 | −0.125967 | −0.0629834 | − | 0.998015i | \(-0.520062\pi\) | ||||
−0.0629834 | + | 0.998015i | \(0.520062\pi\) | |||||||
\(44\) | 0.963796 | − | 1.66934i | 0.145298 | − | 0.251663i | ||||
\(45\) | −9.55022 | − | 16.5415i | −1.42366 | − | 2.46586i | ||||
\(46\) | −1.11430 | − | 1.93002i | −0.164294 | − | 0.284565i | ||||
\(47\) | −4.75484 | + | 8.23562i | −0.693564 | + | 1.20129i | 0.277098 | + | 0.960842i | \(0.410627\pi\) |
−0.970662 | + | 0.240447i | \(0.922706\pi\) | |||||||
\(48\) | 7.25454 | 1.04710 | ||||||||
\(49\) | 6.14714 | + | 3.34853i | 0.878163 | + | 0.478362i | ||||
\(50\) | −7.82133 | −1.10610 | ||||||||
\(51\) | −3.75450 | + | 6.50298i | −0.525735 | + | 0.910599i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.20948 | − | 3.82693i | −0.303495 | − | 0.525669i | 0.673430 | − | 0.739251i | \(-0.264820\pi\) |
−0.976925 | + | 0.213582i | \(0.931487\pi\) | |||||||
\(54\) | −4.54976 | + | 7.88042i | −0.619144 | + | 1.07239i | ||||
\(55\) | 11.1224 | 1.49974 | ||||||||
\(56\) | −7.88513 | − | 2.00832i | −1.05369 | − | 0.268373i | ||||
\(57\) | −14.5800 | −1.93117 | ||||||||
\(58\) | 0.162224 | − | 0.280981i | 0.0213011 | − | 0.0368946i | ||||
\(59\) | 1.96349 | + | 3.40086i | 0.255624 | + | 0.442754i | 0.965065 | − | 0.262011i | \(-0.0843857\pi\) |
−0.709441 | + | 0.704765i | \(0.751052\pi\) | |||||||
\(60\) | −2.94630 | − | 5.10314i | −0.380366 | − | 0.658813i | ||||
\(61\) | −3.60267 | + | 6.24000i | −0.461274 | + | 0.798950i | −0.999025 | − | 0.0441538i | \(-0.985941\pi\) |
0.537751 | + | 0.843104i | \(0.319274\pi\) | |||||||
\(62\) | 0.810979 | 0.102994 | ||||||||
\(63\) | 10.3668 | − | 10.6273i | 1.30609 | − | 1.33891i | ||||
\(64\) | 8.76236 | 1.09529 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.69308 | − | 9.86070i | −0.700770 | − | 1.21377i | ||||
\(67\) | 3.42338 | + | 5.92946i | 0.418232 | + | 0.724399i | 0.995762 | − | 0.0919708i | \(-0.0293166\pi\) |
−0.577530 | + | 0.816370i | \(0.695983\pi\) | |||||||
\(68\) | −0.754764 | + | 1.30729i | −0.0915286 | + | 0.158532i | ||||
\(69\) | 5.50736 | 0.663009 | ||||||||
\(70\) | −2.89579 | − | 10.2947i | −0.346113 | − | 1.23045i | ||||
\(71\) | 12.1910 | 1.44681 | 0.723404 | − | 0.690425i | \(-0.242576\pi\) | ||||
0.723404 | + | 0.690425i | \(0.242576\pi\) | |||||||
\(72\) | −8.62868 | + | 14.9453i | −1.01690 | + | 1.76132i | ||||
\(73\) | 1.43202 | + | 2.48034i | 0.167606 | + | 0.290302i | 0.937578 | − | 0.347776i | \(-0.113063\pi\) |
−0.769972 | + | 0.638078i | \(0.779730\pi\) | |||||||
\(74\) | −6.65862 | − | 11.5331i | −0.774049 | − | 1.34069i | ||||
\(75\) | 9.66417 | − | 16.7388i | 1.11592 | − | 1.93283i | ||||
\(76\) | −2.93101 | −0.336210 | ||||||||
\(77\) | 2.34093 | + | 8.32212i | 0.266774 | + | 0.948393i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.13249 | + | 14.0859i | −0.914977 | + | 1.58479i | −0.108041 | + | 0.994146i | \(0.534458\pi\) |
−0.806936 | + | 0.590640i | \(0.798876\pi\) | |||||||
\(80\) | 4.20748 | + | 7.28757i | 0.470411 | + | 0.814775i | ||||
\(81\) | −2.82652 | − | 4.89568i | −0.314058 | − | 0.543964i | ||||
\(82\) | 1.10163 | − | 1.90808i | 0.121654 | − | 0.210712i | ||||
\(83\) | −6.44277 | −0.707186 | −0.353593 | − | 0.935399i | \(-0.615040\pi\) | ||||
−0.353593 | + | 0.935399i | \(0.615040\pi\) | |||||||
\(84\) | 3.19822 | − | 3.27857i | 0.348955 | − | 0.357722i | ||||
\(85\) | −8.71012 | −0.944745 | ||||||||
\(86\) | −0.490436 | + | 0.849459i | −0.0528850 | + | 0.0915996i | ||||
\(87\) | 0.400894 | + | 0.694369i | 0.0429804 | + | 0.0744442i | ||||
\(88\) | −5.02457 | − | 8.70281i | −0.535621 | − | 0.927723i | ||||
\(89\) | −5.09689 | + | 8.82808i | −0.540270 | + | 0.935774i | 0.458619 | + | 0.888633i | \(0.348344\pi\) |
−0.998888 | + | 0.0471411i | \(0.984989\pi\) | |||||||
\(90\) | −22.6811 | −2.39080 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.10714 | 0.115427 | ||||||||
\(93\) | −1.00206 | + | 1.73562i | −0.103909 | + | 0.179975i | ||||
\(94\) | 5.64621 | + | 9.77953i | 0.582362 | + | 1.00868i | ||||
\(95\) | −8.45611 | − | 14.6464i | −0.867578 | − | 1.50269i | ||||
\(96\) | −4.71766 | + | 8.17122i | −0.481494 | + | 0.833972i | ||||
\(97\) | −1.21015 | −0.122872 | −0.0614361 | − | 0.998111i | \(-0.519568\pi\) | ||||
−0.0614361 | + | 0.998111i | \(0.519568\pi\) | |||||||
\(98\) | 7.09332 | − | 4.33344i | 0.716533 | − | 0.437743i | ||||
\(99\) | 18.3352 | 1.84276 | ||||||||
\(100\) | 1.94278 | − | 3.36499i | 0.194278 | − | 0.336499i | ||||
\(101\) | −8.49191 | − | 14.7084i | −0.844976 | − | 1.46354i | −0.885642 | − | 0.464369i | \(-0.846281\pi\) |
0.0406654 | − | 0.999173i | \(-0.487052\pi\) | |||||||
\(102\) | 4.45834 | + | 7.72208i | 0.441442 | + | 0.764599i | ||||
\(103\) | −1.52601 | + | 2.64312i | −0.150362 | + | 0.260434i | −0.931360 | − | 0.364098i | \(-0.881377\pi\) |
0.780999 | + | 0.624533i | \(0.214711\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 25.6102 | + | 6.52284i | 2.49930 | + | 0.636564i | ||||
\(106\) | −5.24736 | −0.509669 | ||||||||
\(107\) | −2.57076 | + | 4.45269i | −0.248525 | + | 0.430458i | −0.963117 | − | 0.269084i | \(-0.913279\pi\) |
0.714592 | + | 0.699542i | \(0.246612\pi\) | |||||||
\(108\) | −2.26028 | − | 3.91491i | −0.217495 | − | 0.376713i | ||||
\(109\) | 3.47153 | + | 6.01287i | 0.332512 | + | 0.575928i | 0.983004 | − | 0.183585i | \(-0.0587704\pi\) |
−0.650491 | + | 0.759514i | \(0.725437\pi\) | |||||||
\(110\) | 6.60373 | − | 11.4380i | 0.629641 | − | 1.09057i | ||||
\(111\) | 32.9100 | 3.12368 | ||||||||
\(112\) | −4.56724 | + | 4.68198i | −0.431564 | + | 0.442406i | ||||
\(113\) | −6.67849 | −0.628260 | −0.314130 | − | 0.949380i | \(-0.601713\pi\) | ||||
−0.314130 | + | 0.949380i | \(0.601713\pi\) | |||||||
\(114\) | −8.65665 | + | 14.9938i | −0.810769 | + | 1.40429i | ||||
\(115\) | 3.19416 | + | 5.53244i | 0.297856 | + | 0.515903i | ||||
\(116\) | 0.0805915 | + | 0.139589i | 0.00748273 | + | 0.0129605i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.66315 | 0.429278 | ||||||||
\(119\) | −1.83322 | − | 6.51718i | −0.168051 | − | 0.597429i | ||||
\(120\) | −30.7200 | −2.80434 | ||||||||
\(121\) | 0.161600 | − | 0.279900i | 0.0146909 | − | 0.0254454i | ||||
\(122\) | 4.27805 | + | 7.40980i | 0.387316 | + | 0.670851i | ||||
\(123\) | 2.72238 | + | 4.71530i | 0.245469 | + | 0.425164i | ||||
\(124\) | −0.201443 | + | 0.348910i | −0.0180901 | + | 0.0313330i | ||||
\(125\) | 5.40053 | 0.483038 | ||||||||
\(126\) | −4.77370 | − | 16.9707i | −0.425275 | − | 1.51187i | ||||
\(127\) | 4.96067 | 0.440189 | 0.220094 | − | 0.975479i | \(-0.429363\pi\) | ||||
0.220094 | + | 0.975479i | \(0.429363\pi\) | |||||||
\(128\) | 1.98721 | − | 3.44195i | 0.175646 | − | 0.304228i | ||||
\(129\) | −1.21198 | − | 2.09921i | −0.106709 | − | 0.184825i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.29574 | − | 16.1007i | 0.812173 | − | 1.40672i | −0.0991677 | − | 0.995071i | \(-0.531618\pi\) |
0.911340 | − | 0.411654i | \(-0.135049\pi\) | |||||||
\(132\) | 5.65653 | 0.492338 | ||||||||
\(133\) | 9.17914 | − | 9.40975i | 0.795933 | − | 0.815929i | ||||
\(134\) | 8.13029 | 0.702350 | ||||||||
\(135\) | 13.0420 | − | 22.5894i | 1.12248 | − | 1.94419i | ||||
\(136\) | 3.93482 | + | 6.81531i | 0.337408 | + | 0.584408i | ||||
\(137\) | 5.35355 | + | 9.27263i | 0.457385 | + | 0.792214i | 0.998822 | − | 0.0485274i | \(-0.0154528\pi\) |
−0.541437 | + | 0.840741i | \(0.682119\pi\) | |||||||
\(138\) | 3.26991 | − | 5.66364i | 0.278353 | − | 0.482121i | ||||
\(139\) | 15.3166 | 1.29914 | 0.649568 | − | 0.760303i | \(-0.274950\pi\) | ||||
0.649568 | + | 0.760303i | \(0.274950\pi\) | |||||||
\(140\) | 5.14840 | + | 1.31128i | 0.435119 | + | 0.110824i | ||||
\(141\) | −27.9062 | −2.35013 | ||||||||
\(142\) | 7.23822 | − | 12.5370i | 0.607418 | − | 1.05208i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.93602 | + | 12.0135i | 0.578002 | + | 1.00113i | ||||
\(145\) | −0.465021 | + | 0.805439i | −0.0386179 | + | 0.0668881i | ||||
\(146\) | 3.40096 | 0.281466 | ||||||||
\(147\) | 0.509588 | + | 20.5352i | 0.0420301 | + | 1.69372i | ||||
\(148\) | 6.61587 | 0.543821 | ||||||||
\(149\) | −0.925207 | + | 1.60251i | −0.0757959 | + | 0.131282i | −0.901432 | − | 0.432921i | \(-0.857483\pi\) |
0.825636 | + | 0.564203i | \(0.190816\pi\) | |||||||
\(150\) | −11.4759 | − | 19.8768i | −0.937002 | − | 1.62293i | ||||
\(151\) | −0.648755 | − | 1.12368i | −0.0527950 | − | 0.0914436i | 0.838420 | − | 0.545024i | \(-0.183480\pi\) |
−0.891215 | + | 0.453581i | \(0.850146\pi\) | |||||||
\(152\) | −7.64014 | + | 13.2331i | −0.619697 | + | 1.07335i | ||||
\(153\) | −14.3586 | −1.16083 | ||||||||
\(154\) | 9.94816 | + | 2.53376i | 0.801646 | + | 0.204177i | ||||
\(155\) | −2.32469 | −0.186724 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.95100 | − | 3.37923i | −0.155707 | − | 0.269692i | 0.777609 | − | 0.628748i | \(-0.216432\pi\) |
−0.933316 | + | 0.359056i | \(0.883099\pi\) | |||||||
\(158\) | 9.65707 | + | 16.7265i | 0.768275 | + | 1.33069i | ||||
\(159\) | 6.48372 | − | 11.2301i | 0.514193 | − | 0.890608i | ||||
\(160\) | −10.9446 | −0.865244 | ||||||||
\(161\) | −3.46727 | + | 3.55438i | −0.273259 | + | 0.280124i | ||||
\(162\) | −6.71280 | −0.527407 | ||||||||
\(163\) | −5.32843 | + | 9.22911i | −0.417355 | + | 0.722880i | −0.995672 | − | 0.0929320i | \(-0.970376\pi\) |
0.578318 | + | 0.815812i | \(0.303709\pi\) | |||||||
\(164\) | 0.547278 | + | 0.947913i | 0.0427352 | + | 0.0740196i | ||||
\(165\) | 16.3194 | + | 28.2660i | 1.27046 | + | 2.20050i | ||||
\(166\) | −3.82529 | + | 6.62559i | −0.296900 | + | 0.514246i | ||||
\(167\) | 12.2400 | 0.947156 | 0.473578 | − | 0.880752i | \(-0.342962\pi\) | ||||
0.473578 | + | 0.880752i | \(0.342962\pi\) | |||||||
\(168\) | −6.46563 | − | 22.9856i | −0.498834 | − | 1.77338i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −5.17149 | + | 8.95728i | −0.396635 | + | 0.686992i | ||||
\(171\) | −13.9399 | − | 24.1446i | −1.06601 | − | 1.84638i | ||||
\(172\) | −0.243643 | − | 0.422003i | −0.0185776 | − | 0.0321774i | ||||
\(173\) | 1.20055 | − | 2.07941i | 0.0912759 | − | 0.158095i | −0.816772 | − | 0.576960i | \(-0.804239\pi\) |
0.908048 | + | 0.418866i | \(0.137572\pi\) | |||||||
\(174\) | 0.952098 | 0.0721783 | ||||||||
\(175\) | 4.71875 | + | 16.7754i | 0.356704 | + | 1.26810i | ||||
\(176\) | −8.07784 | −0.608890 | ||||||||
\(177\) | −5.76187 | + | 9.97985i | −0.433088 | + | 0.750131i | ||||
\(178\) | 6.05239 | + | 10.4831i | 0.453646 | + | 0.785738i | ||||
\(179\) | 9.38644 | + | 16.2578i | 0.701576 | + | 1.21516i | 0.967913 | + | 0.251285i | \(0.0808531\pi\) |
−0.266337 | + | 0.963880i | \(0.585814\pi\) | |||||||
\(180\) | 5.63388 | − | 9.75817i | 0.419925 | − | 0.727331i | ||||
\(181\) | 19.9776 | 1.48492 | 0.742462 | − | 0.669889i | \(-0.233658\pi\) | ||||
0.742462 | + | 0.669889i | \(0.233658\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −21.1441 | −1.56302 | ||||||||
\(184\) | 2.88594 | − | 4.99859i | 0.212754 | − | 0.368501i | ||||
\(185\) | 19.0871 | + | 33.0598i | 1.40331 | + | 2.43061i | ||||
\(186\) | 1.18991 | + | 2.06099i | 0.0872486 | + | 0.151119i | ||||
\(187\) | 4.18059 | − | 7.24099i | 0.305715 | − | 0.529514i | ||||
\(188\) | −5.60996 | −0.409148 | ||||||||
\(189\) | 19.6471 | + | 5.00404i | 1.42911 | + | 0.363991i | ||||
\(190\) | −20.0827 | −1.45695 | ||||||||
\(191\) | 5.72727 | − | 9.91992i | 0.414411 | − | 0.717781i | −0.580956 | − | 0.813935i | \(-0.697321\pi\) |
0.995366 | + | 0.0961547i | \(0.0306543\pi\) | |||||||
\(192\) | 12.8566 | + | 22.2683i | 0.927845 | + | 1.60708i | ||||
\(193\) | −8.18572 | − | 14.1781i | −0.589221 | − | 1.02056i | −0.994335 | − | 0.106295i | \(-0.966101\pi\) |
0.405114 | − | 0.914266i | \(-0.367232\pi\) | |||||||
\(194\) | −0.718508 | + | 1.24449i | −0.0515858 | + | 0.0893493i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.102442 | + | 4.12818i | 0.00731729 | + | 0.294870i | ||||
\(197\) | 14.1479 | 1.00799 | 0.503997 | − | 0.863705i | \(-0.331862\pi\) | ||||
0.503997 | + | 0.863705i | \(0.331862\pi\) | |||||||
\(198\) | 10.8862 | − | 18.8555i | 0.773652 | − | 1.34000i | ||||
\(199\) | 1.09288 | + | 1.89293i | 0.0774725 | + | 0.134186i | 0.902159 | − | 0.431404i | \(-0.141982\pi\) |
−0.824686 | + | 0.565590i | \(0.808648\pi\) | |||||||
\(200\) | −10.1283 | − | 17.5428i | −0.716181 | − | 1.24046i | ||||
\(201\) | −10.0459 | + | 17.4000i | −0.708584 | + | 1.22730i | ||||
\(202\) | −20.1677 | −1.41900 | ||||||||
\(203\) | −0.700528 | − | 0.178422i | −0.0491674 | − | 0.0125228i | ||||
\(204\) | −4.42972 | −0.310142 | ||||||||
\(205\) | −3.15785 | + | 5.46955i | −0.220554 | + | 0.382010i | ||||
\(206\) | 1.81208 | + | 3.13862i | 0.126254 | + | 0.218678i | ||||
\(207\) | 5.26556 | + | 9.12021i | 0.365982 | + | 0.633899i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.2347 | 1.12298 | ||||||||
\(210\) | 21.9136 | − | 22.4641i | 1.51218 | − | 1.55017i | ||||
\(211\) | 3.72287 | 0.256293 | 0.128147 | − | 0.991755i | \(-0.459097\pi\) | ||||
0.128147 | + | 0.991755i | \(0.459097\pi\) | |||||||
\(212\) | 1.30342 | − | 2.25759i | 0.0895191 | − | 0.155052i | ||||
\(213\) | 17.8873 | + | 30.9817i | 1.22562 | + | 2.12283i | ||||
\(214\) | 3.05270 | + | 5.28743i | 0.208678 | + | 0.361441i | ||||
\(215\) | 1.40585 | − | 2.43500i | 0.0958779 | − | 0.166065i | ||||
\(216\) | −23.5671 | −1.60353 | ||||||||
\(217\) | −0.489278 | − | 1.73941i | −0.0332144 | − | 0.118079i | ||||
\(218\) | 8.24466 | 0.558399 | ||||||||
\(219\) | −4.20229 | + | 7.27857i | −0.283964 | + | 0.491840i | ||||
\(220\) | 3.28067 | + | 5.68228i | 0.221183 | + | 0.383100i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 19.5398 | − | 33.8439i | 1.31142 | − | 2.27145i | ||||
\(223\) | 25.6300 | 1.71631 | 0.858155 | − | 0.513390i | \(-0.171611\pi\) | ||||
0.858155 | + | 0.513390i | \(0.171611\pi\) | |||||||
\(224\) | −2.30350 | − | 8.18907i | −0.153909 | − | 0.547155i | ||||
\(225\) | 36.9594 | 2.46396 | ||||||||
\(226\) | −3.96524 | + | 6.86801i | −0.263764 | + | 0.456853i | ||||
\(227\) | −3.33904 | − | 5.78338i | −0.221620 | − | 0.383856i | 0.733680 | − | 0.679495i | \(-0.237801\pi\) |
−0.955300 | + | 0.295638i | \(0.904468\pi\) | |||||||
\(228\) | −4.30054 | − | 7.44875i | −0.284810 | − | 0.493305i | ||||
\(229\) | 11.4505 | − | 19.8329i | 0.756672 | − | 1.31059i | −0.187867 | − | 0.982195i | \(-0.560157\pi\) |
0.944539 | − | 0.328400i | \(-0.106509\pi\) | |||||||
\(230\) | 7.58591 | 0.500200 | ||||||||
\(231\) | −17.7147 | + | 18.1598i | −1.16554 | + | 1.19483i | ||||
\(232\) | 0.840297 | 0.0551682 | ||||||||
\(233\) | 4.04342 | − | 7.00341i | 0.264893 | − | 0.458809i | −0.702642 | − | 0.711543i | \(-0.747997\pi\) |
0.967536 | + | 0.252735i | \(0.0813299\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.1850 | − | 28.0333i | −1.05579 | − | 1.82869i | ||||
\(236\) | −1.15830 | + | 2.00624i | −0.0753992 | + | 0.130595i | ||||
\(237\) | −47.7297 | −3.10038 | ||||||||
\(238\) | −7.79056 | − | 1.98423i | −0.504987 | − | 0.128619i | ||||
\(239\) | −20.1517 | −1.30351 | −0.651753 | − | 0.758431i | \(-0.725966\pi\) | ||||
−0.651753 | + | 0.758431i | \(0.725966\pi\) | |||||||
\(240\) | −12.3469 | + | 21.3854i | −0.796988 | + | 1.38042i | ||||
\(241\) | 2.81203 | + | 4.87058i | 0.181139 | + | 0.313741i | 0.942269 | − | 0.334858i | \(-0.108688\pi\) |
−0.761130 | + | 0.648600i | \(0.775355\pi\) | |||||||
\(242\) | −0.191895 | − | 0.332372i | −0.0123355 | − | 0.0213657i | ||||
\(243\) | −3.20001 | + | 5.54258i | −0.205281 | + | 0.355557i | ||||
\(244\) | −4.25058 | −0.272116 | ||||||||
\(245\) | −20.3332 | + | 12.4219i | −1.29904 | + | 0.793607i | ||||
\(246\) | 6.46547 | 0.412223 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.05019 | + | 1.81898i | 0.0666869 | + | 0.115505i | ||||
\(249\) | −9.45317 | − | 16.3734i | −0.599071 | − | 1.03762i | ||||
\(250\) | 3.20648 | − | 5.55378i | 0.202795 | − | 0.351252i | ||||
\(251\) | 0.651130 | 0.0410990 | 0.0205495 | − | 0.999789i | \(-0.493458\pi\) | ||||
0.0205495 | + | 0.999789i | \(0.493458\pi\) | |||||||
\(252\) | 8.48713 | + | 2.16164i | 0.534639 | + | 0.136171i | ||||
\(253\) | −6.13238 | −0.385539 | ||||||||
\(254\) | 2.94532 | − | 5.10144i | 0.184806 | − | 0.320093i | ||||
\(255\) | −12.7800 | − | 22.1355i | −0.800312 | − | 1.38618i | ||||
\(256\) | 6.40261 | + | 11.0897i | 0.400163 | + | 0.693103i | ||||
\(257\) | 8.47855 | − | 14.6853i | 0.528877 | − | 0.916042i | −0.470556 | − | 0.882370i | \(-0.655947\pi\) |
0.999433 | − | 0.0336719i | \(-0.0107201\pi\) | |||||||
\(258\) | −2.87837 | −0.179200 | ||||||||
\(259\) | −20.7192 | + | 21.2397i | −1.28743 | + | 1.31977i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.766586 | + | 1.32777i | −0.0474505 | + | 0.0821866i | ||||
\(262\) | −11.0384 | − | 19.1190i | −0.681954 | − | 1.18118i | ||||
\(263\) | −4.67384 | − | 8.09533i | −0.288201 | − | 0.499179i | 0.685179 | − | 0.728375i | \(-0.259724\pi\) |
−0.973380 | + | 0.229195i | \(0.926391\pi\) | |||||||
\(264\) | 14.7446 | − | 25.5385i | 0.907469 | − | 1.57178i | ||||
\(265\) | 15.0417 | 0.924004 | ||||||||
\(266\) | −4.22681 | − | 15.0265i | −0.259162 | − | 0.921334i | ||||
\(267\) | −29.9137 | −1.83069 | ||||||||
\(268\) | −2.01952 | + | 3.49792i | −0.123362 | + | 0.213669i | ||||
\(269\) | −14.3611 | − | 24.8741i | −0.875609 | − | 1.51660i | −0.856112 | − | 0.516790i | \(-0.827127\pi\) |
−0.0194968 | − | 0.999810i | \(-0.506206\pi\) | |||||||
\(270\) | −15.4870 | − | 26.8242i | −0.942506 | − | 1.63247i | ||||
\(271\) | 4.21074 | − | 7.29322i | 0.255784 | − | 0.443031i | −0.709324 | − | 0.704883i | \(-0.751000\pi\) |
0.965108 | + | 0.261851i | \(0.0843330\pi\) | |||||||
\(272\) | 6.32589 | 0.383563 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.7143 | 0.768101 | ||||||||
\(275\) | −10.7609 | + | 18.6385i | −0.648909 | + | 1.12394i | ||||
\(276\) | 1.62446 | + | 2.81364i | 0.0977808 | + | 0.169361i | ||||
\(277\) | 11.0091 | + | 19.0683i | 0.661473 | + | 1.14571i | 0.980229 | + | 0.197868i | \(0.0634018\pi\) |
−0.318756 | + | 0.947837i | \(0.603265\pi\) | |||||||
\(278\) | 9.09398 | − | 15.7512i | 0.545420 | − | 0.944696i | ||||
\(279\) | −3.83225 | −0.229431 | ||||||||
\(280\) | 19.3404 | − | 19.8263i | 1.15581 | − | 1.18485i | ||||
\(281\) | −13.7819 | −0.822156 | −0.411078 | − | 0.911600i | \(-0.634848\pi\) | ||||
−0.411078 | + | 0.911600i | \(0.634848\pi\) | |||||||
\(282\) | −16.5688 | + | 28.6981i | −0.986660 | + | 1.70895i | ||||
\(283\) | 11.1163 | + | 19.2540i | 0.660797 | + | 1.14453i | 0.980407 | + | 0.196985i | \(0.0631149\pi\) |
−0.319610 | + | 0.947549i | \(0.603552\pi\) | |||||||
\(284\) | 3.59587 | + | 6.22824i | 0.213376 | + | 0.369578i | ||||
\(285\) | 24.8145 | − | 42.9800i | 1.46988 | − | 2.54591i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.75712 | − | 1.21162i | −0.280804 | − | 0.0715199i | ||||
\(288\) | −18.0421 | −1.06314 | ||||||||
\(289\) | 5.22612 | − | 9.05190i | 0.307419 | − | 0.532465i | ||||
\(290\) | 0.552197 | + | 0.956433i | 0.0324261 | + | 0.0561637i | ||||
\(291\) | −1.77560 | − | 3.07543i | −0.104087 | − | 0.180285i | ||||
\(292\) | −0.844782 | + | 1.46321i | −0.0494372 | + | 0.0856277i | ||||
\(293\) | −17.1666 | −1.00288 | −0.501441 | − | 0.865192i | \(-0.667197\pi\) | ||||
−0.501441 | + | 0.865192i | \(0.667197\pi\) | |||||||
\(294\) | 21.4205 | + | 11.6684i | 1.24927 | + | 0.680515i | ||||
\(295\) | −13.3670 | −0.778260 | ||||||||
\(296\) | 17.2453 | − | 29.8698i | 1.00236 | − | 1.73614i | ||||
\(297\) | 12.5195 | + | 21.6844i | 0.726456 | + | 1.25826i | ||||
\(298\) | 1.09865 | + | 1.90292i | 0.0636432 | + | 0.110233i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 11.4022 | 0.658306 | ||||||||
\(301\) | 2.11783 | + | 0.539404i | 0.122070 | + | 0.0310908i | ||||
\(302\) | −1.54075 | −0.0886603 | ||||||||
\(303\) | 24.9196 | − | 43.1619i | 1.43159 | − | 2.47959i | ||||
\(304\) | 6.14140 | + | 10.6372i | 0.352234 | + | 0.610087i | ||||
\(305\) | −12.2631 | − | 21.2404i | −0.702185 | − | 1.21622i | ||||
\(306\) | −8.52519 | + | 14.7661i | −0.487353 | + | 0.844120i | ||||
\(307\) | 25.4565 | 1.45288 | 0.726438 | − | 0.687232i | \(-0.241174\pi\) | ||||
0.726438 | + | 0.687232i | \(0.241174\pi\) | |||||||
\(308\) | −3.56118 | + | 3.65065i | −0.202917 | + | 0.208015i | ||||
\(309\) | −8.95615 | −0.509497 | ||||||||
\(310\) | −1.38025 | + | 2.39066i | −0.0783928 | + | 0.135780i | ||||
\(311\) | −4.87615 | − | 8.44574i | −0.276501 | − | 0.478914i | 0.694012 | − | 0.719964i | \(-0.255842\pi\) |
−0.970513 | + | 0.241050i | \(0.922508\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.48061 | + | 9.49270i | −0.309783 | + | 0.536559i | −0.978315 | − | 0.207124i | \(-0.933590\pi\) |
0.668532 | + | 0.743683i | \(0.266923\pi\) | |||||||
\(314\) | −4.63349 | −0.261483 | ||||||||
\(315\) | 13.6839 | + | 48.6471i | 0.771002 | + | 2.74095i | ||||
\(316\) | −9.59506 | −0.539765 | ||||||||
\(317\) | 13.9907 | − | 24.2326i | 0.785796 | − | 1.36104i | −0.142726 | − | 0.989762i | \(-0.545587\pi\) |
0.928522 | − | 0.371277i | \(-0.121080\pi\) | |||||||
\(318\) | −7.69921 | − | 13.3354i | −0.431750 | − | 0.747813i | ||||
\(319\) | −0.446391 | − | 0.773172i | −0.0249931 | − | 0.0432893i | ||||
\(320\) | −14.9131 | + | 25.8303i | −0.833669 | + | 1.44396i | ||||
\(321\) | −15.0878 | −0.842121 | ||||||||
\(322\) | 1.59661 | + | 5.67601i | 0.0889754 | + | 0.316312i | ||||
\(323\) | −12.7136 | −0.707406 | ||||||||
\(324\) | 1.66743 | − | 2.88807i | 0.0926347 | − | 0.160448i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.32733 | + | 10.9593i | 0.350439 | + | 0.606978i | ||||
\(327\) | −10.1872 | + | 17.6448i | −0.563355 | + | 0.975760i | ||||
\(328\) | 5.70626 | 0.315076 | ||||||||
\(329\) | 17.5689 | − | 18.0103i | 0.968605 | − | 0.992940i | ||||
\(330\) | 38.7574 | 2.13353 | ||||||||
\(331\) | −11.7979 | + | 20.4346i | −0.648471 | + | 1.12319i | 0.335017 | + | 0.942212i | \(0.391258\pi\) |
−0.983488 | + | 0.180973i | \(0.942075\pi\) | |||||||
\(332\) | −1.90036 | − | 3.29153i | −0.104296 | − | 0.180646i | ||||
\(333\) | 31.4651 | + | 54.4991i | 1.72428 | + | 2.98653i | ||||
\(334\) | 7.26727 | − | 12.5873i | 0.397647 | − | 0.688746i | ||||
\(335\) | −23.3057 | −1.27333 | ||||||||
\(336\) | −18.5999 | − | 4.73733i | −1.01471 | − | 0.258443i | ||||
\(337\) | −1.84324 | −0.100408 | −0.0502038 | − | 0.998739i | \(-0.515987\pi\) | ||||
−0.0502038 | + | 0.998739i | \(0.515987\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.79904 | − | 16.9724i | −0.532211 | − | 0.921816i | ||||
\(340\) | −2.56914 | − | 4.44989i | −0.139331 | − | 0.241329i | ||||
\(341\) | 1.11578 | − | 1.93259i | 0.0604229 | − | 0.104656i | ||||
\(342\) | −33.1063 | −1.79018 | ||||||||
\(343\) | −13.5740 | − | 12.5995i | −0.732926 | − | 0.680308i | ||||
\(344\) | −2.54038 | −0.136968 | ||||||||
\(345\) | −9.37327 | + | 16.2350i | −0.504640 | + | 0.874062i | ||||
\(346\) | −1.42561 | − | 2.46923i | −0.0766413 | − | 0.132747i | ||||
\(347\) | −4.11186 | − | 7.12195i | −0.220736 | − | 0.382326i | 0.734296 | − | 0.678830i | \(-0.237513\pi\) |
−0.955032 | + | 0.296504i | \(0.904179\pi\) | |||||||
\(348\) | −0.236496 | + | 0.409624i | −0.0126775 | + | 0.0219581i | ||||
\(349\) | −17.8420 | −0.955062 | −0.477531 | − | 0.878615i | \(-0.658468\pi\) | ||||
−0.477531 | + | 0.878615i | \(0.658468\pi\) | |||||||
\(350\) | 20.0531 | + | 5.10746i | 1.07188 | + | 0.273005i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.25305 | − | 9.09855i | 0.279989 | − | 0.484955i | ||||
\(353\) | −5.80919 | − | 10.0618i | −0.309192 | − | 0.535537i | 0.668994 | − | 0.743268i | \(-0.266725\pi\) |
−0.978186 | + | 0.207731i | \(0.933392\pi\) | |||||||
\(354\) | 6.84203 | + | 11.8507i | 0.363650 | + | 0.629860i | ||||
\(355\) | −20.7485 | + | 35.9375i | −1.10122 | + | 1.90737i | ||||
\(356\) | −6.01353 | −0.318717 | ||||||||
\(357\) | 13.8727 | − | 14.2212i | 0.734221 | − | 0.752667i | ||||
\(358\) | 22.2922 | 1.17818 | ||||||||
\(359\) | 11.8364 | − | 20.5013i | 0.624704 | − | 1.08202i | −0.363895 | − | 0.931440i | \(-0.618553\pi\) |
0.988598 | − | 0.150578i | \(-0.0481135\pi\) | |||||||
\(360\) | −29.3712 | − | 50.8724i | −1.54800 | − | 2.68121i | ||||
\(361\) | −2.84287 | − | 4.92399i | −0.149625 | − | 0.259157i | ||||
\(362\) | 11.8614 | − | 20.5445i | 0.623420 | − | 1.07979i | ||||
\(363\) | 0.948433 | 0.0497798 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.74895 | −0.510283 | ||||||||
\(366\) | −12.5540 | + | 21.7441i | −0.656206 | + | 1.13658i | ||||
\(367\) | −4.89825 | − | 8.48402i | −0.255687 | − | 0.442862i | 0.709395 | − | 0.704811i | \(-0.248968\pi\) |
−0.965082 | + | 0.261949i | \(0.915635\pi\) | |||||||
\(368\) | −2.31981 | − | 4.01804i | −0.120929 | − | 0.209455i | ||||
\(369\) | −5.20570 | + | 9.01654i | −0.270998 | + | 0.469382i | ||||
\(370\) | 45.3306 | 2.35663 | ||||||||
\(371\) | 3.16583 | + | 11.2547i | 0.164361 | + | 0.584313i | ||||
\(372\) | −1.18227 | −0.0612980 | ||||||||
\(373\) | 16.9903 | − | 29.4281i | 0.879724 | − | 1.52373i | 0.0280810 | − | 0.999606i | \(-0.491060\pi\) |
0.851643 | − | 0.524122i | \(-0.175606\pi\) | |||||||
\(374\) | −4.96431 | − | 8.59844i | −0.256698 | − | 0.444615i | ||||
\(375\) | 7.92395 | + | 13.7247i | 0.409191 | + | 0.708739i | ||||
\(376\) | −14.6232 | + | 25.3282i | −0.754136 | + | 1.30620i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 16.8112 | − | 17.2335i | 0.864673 | − | 0.886396i | ||||
\(379\) | 20.6390 | 1.06016 | 0.530078 | − | 0.847949i | \(-0.322163\pi\) | ||||
0.530078 | + | 0.847949i | \(0.322163\pi\) | |||||||
\(380\) | 4.98844 | − | 8.64023i | 0.255902 | − | 0.443235i | ||||
\(381\) | 7.27856 | + | 12.6068i | 0.372892 | + | 0.645868i | ||||
\(382\) | −6.80095 | − | 11.7796i | −0.347967 | − | 0.602696i | ||||
\(383\) | 7.01089 | − | 12.1432i | 0.358240 | − | 0.620489i | −0.629427 | − | 0.777059i | \(-0.716710\pi\) |
0.987667 | + | 0.156570i | \(0.0500438\pi\) | |||||||
\(384\) | 11.6630 | 0.595173 | ||||||||
\(385\) | −28.5167 | − | 7.26310i | −1.45334 | − | 0.370162i | ||||
\(386\) | −19.4406 | −0.989498 | ||||||||
\(387\) | 2.31753 | − | 4.01409i | 0.117807 | − | 0.204048i | ||||
\(388\) | −0.356947 | − | 0.618251i | −0.0181213 | − | 0.0313869i | ||||
\(389\) | 6.74508 | + | 11.6828i | 0.341989 | + | 0.592342i | 0.984802 | − | 0.173681i | \(-0.0555661\pi\) |
−0.642813 | + | 0.766023i | \(0.722233\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.80237 | 0.242866 | ||||||||
\(392\) | 18.9052 | + | 10.2982i | 0.954857 | + | 0.520140i | ||||
\(393\) | 54.5568 | 2.75203 | ||||||||
\(394\) | 8.40007 | − | 14.5493i | 0.423189 | − | 0.732985i | ||||
\(395\) | −27.6822 | − | 47.9470i | −1.39284 | − | 2.41248i | ||||
\(396\) | 5.40818 | + | 9.36723i | 0.271771 | + | 0.470721i | ||||
\(397\) | −2.17798 | + | 3.77237i | −0.109309 | + | 0.189330i | −0.915491 | − | 0.402339i | \(-0.868197\pi\) |
0.806181 | + | 0.591669i | \(0.201531\pi\) | |||||||
\(398\) | 2.59553 | 0.130102 | ||||||||
\(399\) | 37.3817 | + | 9.52099i | 1.87142 | + | 0.476646i | ||||
\(400\) | −16.2830 | −0.814149 | ||||||||
\(401\) | −12.8948 | + | 22.3344i | −0.643935 | + | 1.11533i | 0.340611 | + | 0.940204i | \(0.389366\pi\) |
−0.984546 | + | 0.175124i | \(0.943967\pi\) | |||||||
\(402\) | 11.9292 | + | 20.6620i | 0.594974 | + | 1.03053i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5.00956 | − | 8.67681i | 0.249235 | − | 0.431688i | ||||
\(405\) | 19.2424 | 0.956163 | ||||||||
\(406\) | −0.599412 | + | 0.614471i | −0.0297483 | + | 0.0304957i | ||||
\(407\) | −36.6449 | −1.81642 | ||||||||
\(408\) | −11.5468 | + | 19.9996i | −0.571650 | + | 0.990126i | ||||
\(409\) | −13.6128 | − | 23.5780i | −0.673108 | − | 1.16586i | −0.977018 | − | 0.213156i | \(-0.931626\pi\) |
0.303910 | − | 0.952701i | \(-0.401708\pi\) | |||||||
\(410\) | 3.74984 | + | 6.49491i | 0.185191 | + | 0.320761i | ||||
\(411\) | −15.7100 | + | 27.2106i | −0.774919 | + | 1.34220i | ||||
\(412\) | −1.80045 | −0.0887017 | ||||||||
\(413\) | −2.81336 | − | 10.0016i | −0.138437 | − | 0.492149i | ||||
\(414\) | 12.5054 | 0.614605 | ||||||||
\(415\) | 10.9653 | − | 18.9924i | 0.538265 | − | 0.932302i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.4733 | + | 38.9249i | 1.10052 | + | 1.90616i | ||||
\(418\) | 9.63907 | − | 16.6954i | 0.471462 | − | 0.816597i | ||||
\(419\) | 12.1220 | 0.592199 | 0.296100 | − | 0.955157i | \(-0.404314\pi\) | ||||
0.296100 | + | 0.955157i | \(0.404314\pi\) | |||||||
\(420\) | 4.22157 | + | 15.0079i | 0.205992 | + | 0.732311i | ||||
\(421\) | 33.7008 | 1.64248 | 0.821238 | − | 0.570585i | \(-0.193284\pi\) | ||||
0.821238 | + | 0.570585i | \(0.193284\pi\) | |||||||
\(422\) | 2.21040 | − | 3.82852i | 0.107600 | − | 0.186369i | ||||
\(423\) | −26.6810 | − | 46.2128i | −1.29727 | − | 2.24694i | ||||
\(424\) | −6.79513 | − | 11.7695i | −0.330001 | − | 0.571578i | ||||
\(425\) | 8.42706 | − | 14.5961i | 0.408772 | − | 0.708014i | ||||
\(426\) | 42.4812 | 2.05822 | ||||||||
\(427\) | 13.3117 | − | 13.6461i | 0.644198 | − | 0.660382i | ||||
\(428\) | −3.03310 | −0.146610 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.66940 | − | 2.89148i | −0.0805054 | − | 0.139439i | ||||
\(431\) | 3.59780 | + | 6.23158i | 0.173300 | + | 0.300165i | 0.939572 | − | 0.342352i | \(-0.111224\pi\) |
−0.766272 | + | 0.642517i | \(0.777890\pi\) | |||||||
\(432\) | −9.47200 | + | 16.4060i | −0.455722 | + | 0.789333i | ||||
\(433\) | 13.2177 | 0.635204 | 0.317602 | − | 0.948224i | \(-0.397122\pi\) | ||||
0.317602 | + | 0.948224i | \(0.397122\pi\) | |||||||
\(434\) | −2.07927 | − | 0.529583i | −0.0998080 | − | 0.0254208i | ||||
\(435\) | −2.72921 | −0.130856 | ||||||||
\(436\) | −2.04793 | + | 3.54712i | −0.0980781 | + | 0.169876i | ||||
\(437\) | 4.66231 | + | 8.07537i | 0.223029 | + | 0.386297i | ||||
\(438\) | 4.99008 | + | 8.64307i | 0.238435 | + | 0.412982i | ||||
\(439\) | −12.0196 | + | 20.8185i | −0.573663 | + | 0.993613i | 0.422523 | + | 0.906352i | \(0.361145\pi\) |
−0.996186 | + | 0.0872606i | \(0.972189\pi\) | |||||||
\(440\) | 34.2063 | 1.63072 | ||||||||
\(441\) | −33.5192 | + | 20.4775i | −1.59615 | + | 0.975119i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.0445 | + | 20.8616i | −0.572250 | + | 0.991166i | 0.424085 | + | 0.905623i | \(0.360596\pi\) |
−0.996334 | + | 0.0855431i | \(0.972737\pi\) | |||||||
\(444\) | 9.70716 | + | 16.8133i | 0.460682 | + | 0.797924i | ||||
\(445\) | −17.3493 | − | 30.0499i | −0.822437 | − | 1.42450i | ||||
\(446\) | 15.2174 | − | 26.3573i | 0.720564 | − | 1.24805i | ||||
\(447\) | −5.43005 | −0.256833 | ||||||||
\(448\) | −22.4658 | − | 5.72196i | −1.06141 | − | 0.270337i | ||||
\(449\) | −20.8235 | −0.982723 | −0.491362 | − | 0.870956i | \(-0.663501\pi\) | ||||
−0.491362 | + | 0.870956i | \(0.663501\pi\) | |||||||
\(450\) | 21.9440 | − | 38.0082i | 1.03445 | − | 1.79172i | ||||
\(451\) | −3.03134 | − | 5.25043i | −0.142740 | − | 0.247233i | ||||
\(452\) | −1.96989 | − | 3.41196i | −0.0926560 | − | 0.160485i | ||||
\(453\) | 1.90378 | − | 3.29744i | 0.0894473 | − | 0.154927i | ||||
\(454\) | −7.92999 | −0.372173 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −44.8401 | −2.09983 | ||||||||
\(457\) | 8.01041 | − | 13.8744i | 0.374711 | − | 0.649019i | −0.615573 | − | 0.788080i | \(-0.711075\pi\) |
0.990284 | + | 0.139061i | \(0.0444086\pi\) | |||||||
\(458\) | −13.5971 | − | 23.5509i | −0.635352 | − | 1.10046i | ||||
\(459\) | −9.80423 | − | 16.9814i | −0.457622 | − | 0.792625i | ||||
\(460\) | −1.88430 | + | 3.26371i | −0.0878560 | + | 0.152171i | ||||
\(461\) | 1.76847 | 0.0823657 | 0.0411829 | − | 0.999152i | \(-0.486887\pi\) | ||||
0.0411829 | + | 0.999152i | \(0.486887\pi\) | |||||||
\(462\) | 8.15727 | + | 28.9995i | 0.379511 | + | 1.34918i | ||||
\(463\) | 6.86187 | 0.318898 | 0.159449 | − | 0.987206i | \(-0.449028\pi\) | ||||
0.159449 | + | 0.987206i | \(0.449028\pi\) | |||||||
\(464\) | 0.337730 | − | 0.584965i | 0.0156787 | − | 0.0271563i | ||||
\(465\) | −3.41091 | − | 5.90788i | −0.158177 | − | 0.273971i | ||||
\(466\) | −4.80143 | − | 8.31632i | −0.222422 | − | 0.385246i | ||||
\(467\) | −3.95352 | + | 6.84770i | −0.182947 | + | 0.316874i | −0.942883 | − | 0.333125i | \(-0.891897\pi\) |
0.759936 | + | 0.649998i | \(0.225230\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.90515 | − | 17.4380i | −0.226499 | − | 0.805214i | ||||
\(470\) | −38.4383 | −1.77303 | ||||||||
\(471\) | 5.72522 | − | 9.91637i | 0.263804 | − | 0.456922i | ||||
\(472\) | 6.03860 | + | 10.4592i | 0.277949 | + | 0.481422i | ||||
\(473\) | 1.34952 | + | 2.33745i | 0.0620512 | + | 0.107476i | ||||
\(474\) | −28.3387 | + | 49.0841i | −1.30164 | + | 2.25451i | ||||
\(475\) | 32.7252 | 1.50154 | ||||||||
\(476\) | 2.78882 | − | 2.85888i | 0.127825 | − | 0.131037i | ||||
\(477\) | 24.7962 | 1.13534 | ||||||||
\(478\) | −11.9648 | + | 20.7236i | −0.547255 | + | 0.947874i | ||||
\(479\) | −19.8204 | − | 34.3300i | −0.905618 | − | 1.56858i | −0.820086 | − | 0.572241i | \(-0.806074\pi\) |
−0.0855323 | − | 0.996335i | \(-0.527259\pi\) | |||||||
\(480\) | −16.0585 | − | 27.8141i | −0.732965 | − | 1.26953i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 6.67838 | 0.304192 | ||||||||
\(483\) | −14.1203 | − | 3.59640i | −0.642496 | − | 0.163642i | ||||
\(484\) | 0.190663 | 0.00866649 | ||||||||
\(485\) | 2.05962 | − | 3.56737i | 0.0935225 | − | 0.161986i | ||||
\(486\) | 3.79991 | + | 6.58163i | 0.172367 | + | 0.298549i | ||||
\(487\) | 9.78376 | + | 16.9460i | 0.443344 | + | 0.767895i | 0.997935 | − | 0.0642282i | \(-0.0204586\pi\) |
−0.554591 | + | 0.832123i | \(0.687125\pi\) | |||||||
\(488\) | −11.0798 | + | 19.1908i | −0.501559 | + | 0.868726i | ||||
\(489\) | −31.2726 | −1.41420 | ||||||||
\(490\) | 0.701913 | + | 28.2855i | 0.0317092 | + | 1.27781i | ||||
\(491\) | −37.9284 | −1.71168 | −0.855841 | − | 0.517239i | \(-0.826960\pi\) | ||||
−0.855841 | + | 0.517239i | \(0.826960\pi\) | |||||||
\(492\) | −1.60599 | + | 2.78166i | −0.0724036 | + | 0.125407i | ||||
\(493\) | 0.349576 | + | 0.605483i | 0.0157441 | + | 0.0272696i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −31.2057 | + | 54.0498i | −1.40259 | + | 2.42936i | ||||
\(496\) | 1.68835 | 0.0758092 | ||||||||
\(497\) | −31.2565 | − | 7.96094i | −1.40205 | − | 0.357097i | ||||
\(498\) | −22.4507 | −1.00604 | ||||||||
\(499\) | −21.8463 | + | 37.8389i | −0.977975 | + | 1.69390i | −0.308230 | + | 0.951312i | \(0.599737\pi\) |
−0.669745 | + | 0.742591i | \(0.733597\pi\) | |||||||
\(500\) | 1.59295 | + | 2.75906i | 0.0712387 | + | 0.123389i | ||||
\(501\) | 17.9591 | + | 31.1061i | 0.802354 | + | 1.38972i | ||||
\(502\) | 0.386598 | − | 0.669607i | 0.0172547 | − | 0.0298860i | ||||
\(503\) | 10.9162 | 0.486728 | 0.243364 | − | 0.969935i | \(-0.421749\pi\) | ||||
0.243364 | + | 0.969935i | \(0.421749\pi\) | |||||||
\(504\) | 31.8826 | − | 32.6836i | 1.42016 | − | 1.45584i | ||||
\(505\) | 57.8113 | 2.57257 | ||||||||
\(506\) | −3.64100 | + | 6.30640i | −0.161862 | + | 0.280354i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.46320 | + | 2.53434i | 0.0649192 | + | 0.112443i | ||||
\(509\) | −12.0920 | + | 20.9440i | −0.535968 | + | 0.928324i | 0.463147 | + | 0.886281i | \(0.346720\pi\) |
−0.999116 | + | 0.0420432i | \(0.986613\pi\) | |||||||
\(510\) | −30.3516 | −1.34399 | ||||||||
\(511\) | −2.05186 | − | 7.29447i | −0.0907690 | − | 0.322688i | ||||
\(512\) | 23.1546 | 1.02330 | ||||||||
\(513\) | 19.0366 | − | 32.9724i | 0.840488 | − | 1.45577i | ||||
\(514\) | −10.0680 | − | 17.4383i | −0.444080 | − | 0.769169i | ||||
\(515\) | −5.19438 | − | 8.99693i | −0.228892 | − | 0.396452i | ||||
\(516\) | 0.714973 | − | 1.23837i | 0.0314749 | − | 0.0545162i | ||||
\(517\) | 31.0732 | 1.36660 | ||||||||
\(518\) | 9.54074 | + | 33.9178i | 0.419196 | + | 1.49026i | ||||
\(519\) | 7.04603 | 0.309286 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.1573 | − | 19.3251i | −0.488812 | − | 0.846647i | 0.511105 | − | 0.859518i | \(-0.329236\pi\) |
−0.999917 | + | 0.0128710i | \(0.995903\pi\) | |||||||
\(522\) | 0.910295 | + | 1.57668i | 0.0398425 | + | 0.0690093i | ||||
\(523\) | −21.4951 | + | 37.2306i | −0.939916 | + | 1.62798i | −0.174292 | + | 0.984694i | \(0.555764\pi\) |
−0.765624 | + | 0.643289i | \(0.777570\pi\) | |||||||
\(524\) | 10.9675 | 0.479118 | ||||||||
\(525\) | −35.7087 | + | 36.6058i | −1.55845 | + | 1.59761i | ||||
\(526\) | −11.1001 | −0.483986 | ||||||||
\(527\) | −0.873785 | + | 1.51344i | −0.0380627 | + | 0.0659265i | ||||
\(528\) | −11.8522 | − | 20.5287i | −0.515802 | − | 0.893396i | ||||
\(529\) | 9.73889 | + | 16.8682i | 0.423430 | + | 0.733402i | ||||
\(530\) | 8.93076 | − | 15.4685i | 0.387927 | − | 0.671910i | ||||
\(531\) | −22.0356 | −0.956262 | ||||||||
\(532\) | 7.51481 | + | 1.91400i | 0.325808 | + | 0.0829823i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −17.7608 | + | 30.7626i | −0.768584 | + | 1.33123i | ||||
\(535\) | −8.75063 | − | 15.1565i | −0.378323 | − | 0.655274i | ||||
\(536\) | 10.5284 | + | 18.2357i | 0.454758 | + | 0.787664i | ||||
\(537\) | −27.5446 | + | 47.7086i | −1.18864 | + | 2.05878i | ||||
\(538\) | −34.1066 | −1.47044 | ||||||||
\(539\) | −0.567420 | − | 22.8657i | −0.0244405 | − | 0.984896i | ||||
\(540\) | 15.3875 | 0.662174 | ||||||||
\(541\) | 10.4901 | − | 18.1693i | 0.451004 | − | 0.781161i | −0.547445 | − | 0.836842i | \(-0.684399\pi\) |
0.998449 | + | 0.0556804i | \(0.0177328\pi\) | |||||||
\(542\) | −5.00012 | − | 8.66045i | −0.214773 | − | 0.371998i | ||||
\(543\) | 29.3122 | + | 50.7702i | 1.25791 | + | 2.17876i | ||||
\(544\) | −4.11375 | + | 7.12522i | −0.176376 | + | 0.305491i | ||||
\(545\) | −23.6335 | −1.01235 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.9017 | 1.27850 | 0.639251 | − | 0.768998i | \(-0.279244\pi\) | ||||
0.639251 | + | 0.768998i | \(0.279244\pi\) | |||||||
\(548\) | −3.15818 | + | 5.47012i | −0.134911 | + | 0.233672i | ||||
\(549\) | −20.2157 | − | 35.0147i | −0.862787 | − | 1.49439i | ||||
\(550\) | 12.7783 | + | 22.1326i | 0.544866 | + | 0.943736i | ||||
\(551\) | −0.678762 | + | 1.17565i | −0.0289163 | + | 0.0500844i | ||||
\(552\) | 16.9376 | 0.720912 | ||||||||
\(553\) | 30.0492 | − | 30.8041i | 1.27782 | − | 1.30992i | ||||
\(554\) | 26.1459 | 1.11083 | ||||||||
\(555\) | −56.0113 | + | 97.0143i | −2.37755 | + | 4.11803i | ||||
\(556\) | 4.51779 | + | 7.82505i | 0.191597 | + | 0.331856i | ||||
\(557\) | −5.24796 | − | 9.08973i | −0.222363 | − | 0.385144i | 0.733162 | − | 0.680054i | \(-0.238044\pi\) |
−0.955525 | + | 0.294910i | \(0.904710\pi\) | |||||||
\(558\) | −2.27534 | + | 3.94100i | −0.0963227 | + | 0.166836i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −6.02864 | − | 21.4321i | −0.254757 | − | 0.905673i | ||||
\(561\) | 24.5359 | 1.03591 | ||||||||
\(562\) | −8.18275 | + | 14.1729i | −0.345168 | + | 0.597849i | ||||
\(563\) | 0.133223 | + | 0.230748i | 0.00561466 | + | 0.00972488i | 0.868819 | − | 0.495130i | \(-0.164879\pi\) |
−0.863204 | + | 0.504855i | \(0.831546\pi\) | |||||||
\(564\) | −8.23124 | − | 14.2569i | −0.346598 | − | 0.600325i | ||||
\(565\) | 11.3665 | − | 19.6873i | 0.478191 | − | 0.828251i | ||||
\(566\) | 26.4005 | 1.10970 | ||||||||
\(567\) | 4.04995 | + | 14.3978i | 0.170082 | + | 0.604650i | ||||
\(568\) | 37.4928 | 1.57316 | ||||||||
\(569\) | 3.78338 | − | 6.55300i | 0.158607 | − | 0.274716i | −0.775759 | − | 0.631029i | \(-0.782633\pi\) |
0.934367 | + | 0.356313i | \(0.115966\pi\) | |||||||
\(570\) | −29.4664 | − | 51.0373i | −1.23421 | − | 2.13772i | ||||
\(571\) | −21.0515 | − | 36.4623i | −0.880978 | − | 1.52590i | −0.850255 | − | 0.526371i | \(-0.823552\pi\) |
−0.0307235 | − | 0.999528i | \(-0.509781\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.6134 | 1.40422 | ||||||||
\(574\) | −4.07047 | + | 4.17273i | −0.169898 | + | 0.174166i | ||||
\(575\) | −12.3614 | −0.515506 | ||||||||
\(576\) | −24.5842 | + | 42.5812i | −1.02434 | + | 1.77422i | ||||
\(577\) | −8.74752 | − | 15.1512i | −0.364164 | − | 0.630751i | 0.624478 | − | 0.781043i | \(-0.285312\pi\) |
−0.988642 | + | 0.150292i | \(0.951979\pi\) | |||||||
\(578\) | −6.20584 | − | 10.7488i | −0.258129 | − | 0.447092i | ||||
\(579\) | 24.0211 | − | 41.6057i | 0.998281 | − | 1.72907i | ||||
\(580\) | −0.548651 | −0.0227815 | ||||||||
\(581\) | 16.5186 | + | 4.20723i | 0.685307 | + | 0.174545i | ||||
\(582\) | −4.21693 | −0.174797 | ||||||||
\(583\) | −7.21955 | + | 12.5046i | −0.299003 | + | 0.517888i | ||||
\(584\) | 4.40412 | + | 7.62815i | 0.182244 | + | 0.315655i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.1924 | + | 17.6537i | −0.421043 | + | 0.729268i | ||||
\(587\) | −15.3011 | −0.631545 | −0.315773 | − | 0.948835i | \(-0.602264\pi\) | ||||
−0.315773 | + | 0.948835i | \(0.602264\pi\) | |||||||
\(588\) | −10.3409 | + | 6.31743i | −0.426450 | + | 0.260526i | ||||
\(589\) | −3.39321 | −0.139815 | ||||||||
\(590\) | −7.93647 | + | 13.7464i | −0.326739 | + | 0.565929i | ||||
\(591\) | 20.7585 | + | 35.9548i | 0.853891 | + | 1.47898i | ||||
\(592\) | −13.8624 | − | 24.0103i | −0.569740 | − | 0.986818i | ||||
\(593\) | 13.4352 | − | 23.2705i | 0.551718 | − | 0.955604i | −0.446433 | − | 0.894817i | \(-0.647306\pi\) |
0.998151 | − | 0.0607866i | \(-0.0193609\pi\) | |||||||
\(594\) | 29.7330 | 1.21996 | ||||||||
\(595\) | 22.3319 | + | 5.68785i | 0.915517 | + | 0.233179i | ||||
\(596\) | −1.09160 | −0.0447136 | ||||||||
\(597\) | −3.20708 | + | 5.55482i | −0.131257 | + | 0.227344i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.96301 | − | 13.7923i | −0.325360 | − | 0.563540i | 0.656225 | − | 0.754565i | \(-0.272152\pi\) |
−0.981585 | + | 0.191025i | \(0.938819\pi\) | |||||||
\(600\) | 29.7216 | − | 51.4794i | 1.21338 | − | 2.10164i | ||||
\(601\) | −12.4393 | −0.507408 | −0.253704 | − | 0.967282i | \(-0.581649\pi\) | ||||
−0.253704 | + | 0.967282i | \(0.581649\pi\) | |||||||
\(602\) | 1.81214 | − | 1.85766i | 0.0738572 | − | 0.0757127i | ||||
\(603\) | −38.4194 | −1.56456 | ||||||||
\(604\) | 0.382715 | − | 0.662882i | 0.0155724 | − | 0.0269723i | ||||
\(605\) | 0.550071 | + | 0.952752i | 0.0223636 | + | 0.0387349i | ||||
\(606\) | −29.5912 | − | 51.2534i | −1.20206 | − | 2.08203i | ||||
\(607\) | −2.96829 | + | 5.14123i | −0.120479 | + | 0.208676i | −0.919957 | − | 0.392020i | \(-0.871776\pi\) |
0.799477 | + | 0.600696i | \(0.205110\pi\) | |||||||
\(608\) | −15.9751 | −0.647877 | ||||||||
\(609\) | −0.574417 | − | 2.04208i | −0.0232766 | − | 0.0827494i | ||||
\(610\) | −29.1241 | −1.17920 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −4.23523 | − | 7.33563i | −0.171199 | − | 0.296525i | ||||
\(613\) | 8.79919 | + | 15.2406i | 0.355396 | + | 0.615564i | 0.987186 | − | 0.159576i | \(-0.0510127\pi\) |
−0.631790 | + | 0.775140i | \(0.717679\pi\) | |||||||
\(614\) | 15.1144 | − | 26.1788i | 0.609966 | − | 1.05649i | ||||
\(615\) | −18.5334 | −0.747340 | ||||||||
\(616\) | 7.19940 | + | 25.5942i | 0.290072 | + | 1.03122i | ||||
\(617\) | 2.96426 | 0.119337 | 0.0596684 | − | 0.998218i | \(-0.480996\pi\) | ||||
0.0596684 | + | 0.998218i | \(0.480996\pi\) | |||||||
\(618\) | −5.31757 | + | 9.21029i | −0.213904 | + | 0.370492i | ||||
\(619\) | 22.0915 | + | 38.2636i | 0.887932 | + | 1.53794i | 0.842316 | + | 0.538984i | \(0.181192\pi\) |
0.0456153 | + | 0.998959i | \(0.485475\pi\) | |||||||
\(620\) | −0.685693 | − | 1.18766i | −0.0275381 | − | 0.0476974i | ||||
\(621\) | −7.19077 | + | 12.4548i | −0.288556 | + | 0.499793i | ||||
\(622\) | −11.5805 | −0.464337 | ||||||||
\(623\) | 18.8328 | − | 19.3059i | 0.754520 | − | 0.773476i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.27498 | − | 12.6006i | 0.290999 | − | 0.504025i | ||||
\(626\) | 6.50805 | + | 11.2723i | 0.260114 | + | 0.450531i | ||||
\(627\) | 23.8204 | + | 41.2581i | 0.951294 | + | 1.64769i | ||||
\(628\) | 1.15094 | − | 1.99348i | 0.0459274 | − | 0.0795485i | ||||
\(629\) | 28.6972 | 1.14423 | ||||||||
\(630\) | 58.1521 | + | 14.8112i | 2.31684 | + | 0.590091i | ||||
\(631\) | −3.13417 | −0.124769 | −0.0623847 | − | 0.998052i | \(-0.519871\pi\) | ||||
−0.0623847 | + | 0.998052i | \(0.519871\pi\) | |||||||
\(632\) | −25.0110 | + | 43.3204i | −0.994886 | + | 1.72319i | ||||
\(633\) | 5.46240 | + | 9.46115i | 0.217111 | + | 0.376047i | ||||
\(634\) | −16.6135 | − | 28.7754i | −0.659806 | − | 1.14282i | ||||
\(635\) | −8.44283 | + | 14.6234i | −0.335043 | + | 0.580312i | ||||
\(636\) | 7.64978 | 0.303333 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.06015 | −0.0419717 | ||||||||
\(639\) | −34.2039 | + | 59.2429i | −1.35309 | + | 2.34361i | ||||
\(640\) | 6.76427 | + | 11.7161i | 0.267381 | + | 0.463118i | ||||
\(641\) | 14.5674 | + | 25.2315i | 0.575379 | + | 0.996585i | 0.996000 | + | 0.0893491i | \(0.0284787\pi\) |
−0.420622 | + | 0.907236i | \(0.638188\pi\) | |||||||
\(642\) | −8.95816 | + | 15.5160i | −0.353550 | + | 0.612367i | ||||
\(643\) | 14.1646 | 0.558598 | 0.279299 | − | 0.960204i | \(-0.409898\pi\) | ||||
0.279299 | + | 0.960204i | \(0.409898\pi\) | |||||||
\(644\) | −2.83860 | − | 0.722981i | −0.111856 | − | 0.0284895i | ||||
\(645\) | 8.25093 | 0.324880 | ||||||||
\(646\) | −7.54851 | + | 13.0744i | −0.296992 | + | 0.514406i | ||||
\(647\) | −8.37607 | − | 14.5078i | −0.329297 | − | 0.570360i | 0.653075 | − | 0.757293i | \(-0.273478\pi\) |
−0.982373 | + | 0.186933i | \(0.940145\pi\) | |||||||
\(648\) | −8.69281 | − | 15.0564i | −0.341486 | − | 0.591471i | ||||
\(649\) | 6.41577 | − | 11.1124i | 0.251841 | − | 0.436201i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.70256 | − | 3.79558i | 0.145115 | − | 0.148761i | ||||
\(652\) | −6.28671 | −0.246207 | ||||||||
\(653\) | −13.6044 | + | 23.5635i | −0.532381 | + | 0.922111i | 0.466904 | + | 0.884308i | \(0.345369\pi\) |
−0.999285 | + | 0.0378028i | \(0.987964\pi\) | |||||||
\(654\) | 12.0970 | + | 20.9526i | 0.473030 | + | 0.819312i | ||||
\(655\) | 31.6418 | + | 54.8052i | 1.23635 | + | 2.14142i | ||||
\(656\) | 2.29344 | − | 3.97236i | 0.0895439 | − | 0.155095i | ||||
\(657\) | −16.0711 | −0.626994 | ||||||||
\(658\) | −8.09012 | − | 28.7608i | −0.315386 | − | 1.12121i | ||||
\(659\) | 4.44470 | 0.173141 | 0.0865705 | − | 0.996246i | \(-0.472409\pi\) | ||||
0.0865705 | + | 0.996246i | \(0.472409\pi\) | |||||||
\(660\) | −9.62714 | + | 16.6747i | −0.374736 | + | 0.649062i | ||||
\(661\) | 4.16609 | + | 7.21588i | 0.162042 | + | 0.280665i | 0.935601 | − | 0.353059i | \(-0.114859\pi\) |
−0.773559 | + | 0.633725i | \(0.781525\pi\) | |||||||
\(662\) | 14.0096 | + | 24.2654i | 0.544499 | + | 0.943101i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −19.8144 | −0.768948 | ||||||||
\(665\) | 12.1162 | + | 43.0739i | 0.469848 | + | 1.67033i | ||||
\(666\) | 74.7275 | 2.89563 | ||||||||
\(667\) | 0.256391 | − | 0.444083i | 0.00992751 | − | 0.0171950i | ||||
\(668\) | 3.61031 | + | 6.25324i | 0.139687 | + | 0.241945i | ||||
\(669\) | 37.6057 | + | 65.1349i | 1.45392 | + | 2.51826i | ||||
\(670\) | −13.8374 | + | 23.9670i | −0.534584 | + | 0.925927i | ||||
\(671\) | 23.5437 | 0.908894 | ||||||||
\(672\) | 17.4315 | − | 17.8695i | 0.672436 | − | 0.689330i | ||||
\(673\) | 43.4054 | 1.67316 | 0.836578 | − | 0.547847i | \(-0.184553\pi\) | ||||
0.836578 | + | 0.547847i | \(0.184553\pi\) | |||||||
\(674\) | −1.09439 | + | 1.89555i | −0.0421545 | + | 0.0730137i | ||||
\(675\) | 25.2363 | + | 43.7106i | 0.971347 | + | 1.68242i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.9474 | + | 24.1576i | −0.536043 | + | 0.928453i | 0.463069 | + | 0.886322i | \(0.346748\pi\) |
−0.999112 | + | 0.0421311i | \(0.986585\pi\) | |||||||
\(678\) | −23.2721 | −0.893759 | ||||||||
\(679\) | 3.10270 | + | 0.790249i | 0.119071 | + | 0.0303270i | ||||
\(680\) | −26.7875 | −1.02725 | ||||||||
\(681\) | 9.79842 | − | 16.9714i | 0.375476 | − | 0.650344i | ||||
\(682\) | −1.32495 | − | 2.29488i | −0.0507351 | − | 0.0878757i | ||||
\(683\) | 16.6346 | + | 28.8120i | 0.636506 | + | 1.10246i | 0.986194 | + | 0.165594i | \(0.0529542\pi\) |
−0.349688 | + | 0.936866i | \(0.613713\pi\) | |||||||
\(684\) | 8.22343 | − | 14.2434i | 0.314431 | − | 0.544610i | ||||
\(685\) | −36.4460 | −1.39253 | ||||||||
\(686\) | −21.0163 | + | 6.47844i | −0.802408 | + | 0.247348i | ||||
\(687\) | 67.2033 | 2.56397 | ||||||||
\(688\) | −1.02102 | + | 1.76846i | −0.0389261 | + | 0.0674220i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 11.1305 | + | 19.2785i | 0.423729 | + | 0.733920i | ||||
\(691\) | −8.24422 | + | 14.2794i | −0.313625 | + | 0.543215i | −0.979144 | − | 0.203166i | \(-0.934877\pi\) |
0.665519 | + | 0.746381i | \(0.268210\pi\) | |||||||
\(692\) | 1.41646 | 0.0538456 | ||||||||
\(693\) | −47.0097 | − | 11.9732i | −1.78575 | − | 0.454825i | ||||
\(694\) | −9.76539 | −0.370689 | ||||||||
\(695\) | −26.0681 | + | 45.1513i | −0.988820 | + | 1.71269i | ||||
\(696\) | 1.23293 | + | 2.13550i | 0.0467341 | + | 0.0809458i | ||||
\(697\) | 2.37389 | + | 4.11169i | 0.0899174 | + | 0.155742i | ||||
\(698\) | −10.5934 | + | 18.3483i | −0.400967 | + | 0.694494i | ||||
\(699\) | 23.7309 | 0.897585 | ||||||||
\(700\) | −7.17848 | + | 7.35883i | −0.271321 | + | 0.278138i | ||||
\(701\) | −19.6850 | −0.743490 | −0.371745 | − | 0.928335i | \(-0.621240\pi\) | ||||
−0.371745 | + | 0.928335i | \(0.621240\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.8603 | + | 48.2555i | 1.05077 | + | 1.81999i | ||||
\(704\) | −14.3157 | − | 24.7955i | −0.539542 | − | 0.934514i | ||||
\(705\) | 47.4950 | − | 82.2638i | 1.78877 | − | 3.09823i | ||||
\(706\) | −13.7965 | −0.519236 | ||||||||
\(707\) | 12.1675 | + | 43.2562i | 0.457607 | + | 1.62682i | ||||
\(708\) | −6.79810 | −0.255488 | ||||||||
\(709\) | 4.23199 | − | 7.33002i | 0.158936 | − | 0.275285i | −0.775550 | − | 0.631287i | \(-0.782527\pi\) |
0.934485 | + | 0.356002i | \(0.115860\pi\) | |||||||
\(710\) | 24.6382 | + | 42.6746i | 0.924655 | + | 1.60155i | ||||
\(711\) | −45.6341 | − | 79.0406i | −1.71141 | − | 2.96425i | ||||
\(712\) | −15.6752 | + | 27.1503i | −0.587454 | + | 1.01750i | ||||
\(713\) | 1.28173 | 0.0480012 | ||||||||
\(714\) | −6.38809 | − | 22.7100i | −0.239068 | − | 0.849900i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.53727 | + | 9.59083i | −0.206937 | + | 0.358426i | ||||
\(717\) | −29.5677 | − | 51.2127i | −1.10423 | − | 1.91257i | ||||
\(718\) | −14.0554 | − | 24.3446i | −0.524542 | − | 0.908534i | ||||
\(719\) | 2.44667 | − | 4.23776i | 0.0912454 | − | 0.158042i | −0.816790 | − | 0.576935i | \(-0.804249\pi\) |
0.908035 | + | 0.418893i | \(0.137582\pi\) | |||||||
\(720\) | −47.2191 | −1.75975 | ||||||||
\(721\) | 5.63852 | − | 5.78018i | 0.209990 | − | 0.215265i | ||||
\(722\) | −6.75162 | −0.251269 | ||||||||
\(723\) | −8.25192 | + | 14.2927i | −0.306892 | + | 0.531553i | ||||
\(724\) | 5.89261 | + | 10.2063i | 0.218997 | + | 0.379314i | ||||
\(725\) | −0.899817 | − | 1.55853i | −0.0334184 | − | 0.0578823i | ||||
\(726\) | 0.563117 | − | 0.975347i | 0.0208992 | − | 0.0361985i | ||||
\(727\) | −47.2542 | −1.75256 | −0.876281 | − | 0.481800i | \(-0.839983\pi\) | ||||
−0.876281 | + | 0.481800i | \(0.839983\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −35.7400 | −1.32370 | ||||||||
\(730\) | −5.78828 | + | 10.0256i | −0.214234 | + | 0.371064i | ||||
\(731\) | −1.05683 | − | 1.83049i | −0.0390884 | − | 0.0677032i | ||||
\(732\) | −6.23668 | − | 10.8022i | −0.230514 | − | 0.399263i | ||||
\(733\) | 15.1872 | − | 26.3049i | 0.560951 | − | 0.971595i | −0.436463 | − | 0.899722i | \(-0.643769\pi\) |
0.997414 | − | 0.0718731i | \(-0.0228977\pi\) | |||||||
\(734\) | −11.6330 | −0.429383 | ||||||||
\(735\) | −61.4024 | − | 33.4478i | −2.26486 | − | 1.23374i | ||||
\(736\) | 6.03434 | 0.222429 | ||||||||
\(737\) | 11.1860 | − | 19.3747i | 0.412042 | − | 0.713677i | ||||
\(738\) | 6.18160 | + | 10.7068i | 0.227548 | + | 0.394124i | ||||
\(739\) | −6.10330 | − | 10.5712i | −0.224513 | − | 0.388869i | 0.731660 | − | 0.681670i | \(-0.238746\pi\) |
−0.956173 | + | 0.292801i | \(0.905413\pi\) | |||||||
\(740\) | −11.2599 | + | 19.5027i | −0.413922 | + | 0.716934i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.4537 | + | 3.42661i | 0.493901 | + | 0.125795i | ||||
\(743\) | 13.0307 | 0.478051 | 0.239025 | − | 0.971013i | \(-0.423172\pi\) | ||||
0.239025 | + | 0.971013i | \(0.423172\pi\) | |||||||
\(744\) | −3.08178 | + | 5.33780i | −0.112984 | + | 0.195693i | ||||
\(745\) | −3.14932 | − | 5.45477i | −0.115382 | − | 0.199847i | ||||
\(746\) | −20.1754 | − | 34.9449i | −0.738675 | − | 1.27942i | ||||
\(747\) | 18.0763 | − | 31.3090i | 0.661376 | − | 1.14554i | ||||
\(748\) | 4.93244 | 0.180348 | ||||||||
\(749\) | 9.49885 | − | 9.73749i | 0.347081 | − | 0.355800i | ||||
\(750\) | 18.8189 | 0.687167 | ||||||||
\(751\) | 22.9275 | − | 39.7116i | 0.836636 | − | 1.44910i | −0.0560561 | − | 0.998428i | \(-0.517853\pi\) |
0.892692 | − | 0.450668i | \(-0.148814\pi\) | |||||||
\(752\) | 11.7547 | + | 20.3597i | 0.428648 | + | 0.742441i | ||||
\(753\) | 0.955373 | + | 1.65476i | 0.0348157 | + | 0.0603026i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.41660 | 0.160737 | ||||||||
\(756\) | 3.23861 | + | 11.5134i | 0.117787 | + | 0.418739i | ||||
\(757\) | 6.79168 | 0.246848 | 0.123424 | − | 0.992354i | \(-0.460613\pi\) | ||||
0.123424 | + | 0.992354i | \(0.460613\pi\) | |||||||
\(758\) | 12.2541 | − | 21.2247i | 0.445089 | − | 0.770916i | ||||
\(759\) | −8.99776 | − | 15.5846i | −0.326598 | − | 0.565684i | ||||
\(760\) | −26.0063 | − | 45.0442i | −0.943348 | − | 1.63393i | ||||
\(761\) | −3.04905 | + | 5.28111i | −0.110528 | + | 0.191440i | −0.915983 | − | 0.401216i | \(-0.868588\pi\) |
0.805455 | + | 0.592657i | \(0.201921\pi\) | |||||||
\(762\) | 17.2861 | 0.626210 | ||||||||
\(763\) | −4.97415 | − | 17.6833i | −0.180076 | − | 0.640180i | ||||
\(764\) | 6.75728 | 0.244470 | ||||||||
\(765\) | 24.4377 | − | 42.3273i | 0.883546 | − | 1.53035i | ||||
\(766\) | −8.32520 | − | 14.4197i | −0.300802 | − | 0.521004i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −18.7885 | + | 32.5427i | −0.677972 | + | 1.17428i | ||||
\(769\) | −31.7262 | −1.14408 | −0.572038 | − | 0.820227i | \(-0.693847\pi\) | ||||
−0.572038 | + | 0.820227i | \(0.693847\pi\) | |||||||
\(770\) | −24.4005 | + | 25.0135i | −0.879333 | + | 0.901425i | ||||
\(771\) | 49.7607 | 1.79209 | ||||||||
\(772\) | 4.82893 | − | 8.36396i | 0.173797 | − | 0.301026i | ||||
\(773\) | −16.5081 | − | 28.5928i | −0.593754 | − | 1.02841i | −0.993721 | − | 0.111883i | \(-0.964312\pi\) |
0.399967 | − | 0.916529i | \(-0.369021\pi\) | |||||||
\(774\) | −2.75200 | − | 4.76660i | −0.0989185 | − | 0.171332i | ||||
\(775\) | 2.24914 | − | 3.89563i | 0.0807917 | − | 0.139935i | ||||
\(776\) | −3.72176 | −0.133603 | ||||||||
\(777\) | −84.3779 | − | 21.4908i | −3.02704 | − | 0.770977i | ||||
\(778\) | 16.0191 | 0.574313 | ||||||||
\(779\) | −4.60932 | + | 7.98357i | −0.165146 | + | 0.286041i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.9173 | − | 34.4978i | −0.712697 | − | 1.23443i | ||||
\(782\) | 2.85133 | − | 4.93864i | 0.101963 | − | 0.176605i | ||||
\(783\) | −2.09374 | −0.0748240 | ||||||||
\(784\) | 14.7673 | − | 9.02164i | 0.527405 | − | 0.322201i | ||||
\(785\) | 13.2820 | 0.474056 | ||||||||
\(786\) | 32.3922 | − | 56.1050i | 1.15539 | − | 2.00120i | ||||
\(787\) | 6.34805 | + | 10.9951i | 0.226283 | + | 0.391935i | 0.956704 | − | 0.291063i | \(-0.0940091\pi\) |
−0.730420 | + | 0.682998i | \(0.760676\pi\) | |||||||
\(788\) | 4.17307 | + | 7.22797i | 0.148659 | + | 0.257486i | ||||
\(789\) | 13.7154 | − | 23.7558i | 0.488282 | − | 0.845729i | ||||
\(790\) | −65.7435 | −2.33905 | ||||||||
\(791\) | 17.1230 | + | 4.36116i | 0.608823 | + | 0.155065i | ||||
\(792\) | 56.3890 | 2.00370 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 2.58628 | + | 4.47956i | 0.0917835 | + | 0.158974i | ||||
\(795\) | 22.0700 | + | 38.2263i | 0.782742 | + | 1.35575i | ||||
\(796\) | −0.644716 | + | 1.11668i | −0.0228513 | + | 0.0395797i | ||||
\(797\) | −17.4478 | −0.618033 | −0.309016 | − | 0.951057i | \(-0.600000\pi\) | ||||
−0.309016 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(798\) | 31.9859 | − | 32.7895i | 1.13229 | − | 1.16074i | ||||
\(799\) | −24.3339 | −0.860873 | ||||||||
\(800\) | 10.5889 | − | 18.3405i | 0.374374 | − | 0.648435i | ||||
\(801\) | −28.6003 | − | 49.5373i | −1.01054 | − | 1.75031i | ||||
\(802\) | 15.3121 | + | 26.5214i | 0.540691 | + | 0.936504i | ||||
\(803\) | 4.67919 | − | 8.10460i | 0.165125 | − | 0.286005i | ||||
\(804\) | −11.8526 | −0.418009 | ||||||||
\(805\) | −4.57671 | − | 16.2704i | −0.161308 | − | 0.573458i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 42.1426 | − | 72.9932i | 1.48349 | − | 2.56948i | ||||
\(808\) | −26.1164 | − | 45.2350i | −0.918772 | − | 1.59136i | ||||
\(809\) | −20.4458 | − | 35.4132i | −0.718837 | − | 1.24506i | −0.961461 | − | 0.274942i | \(-0.911341\pi\) |
0.242623 | − | 0.970121i | \(-0.421992\pi\) | |||||||
\(810\) | 11.4249 | − | 19.7884i | 0.401429 | − | 0.695295i | ||||
\(811\) | 36.1160 | 1.26821 | 0.634103 | − | 0.773249i | \(-0.281370\pi\) | ||||
0.634103 | + | 0.773249i | \(0.281370\pi\) | |||||||
\(812\) | −0.115475 | − | 0.410518i | −0.00405237 | − | 0.0144064i | ||||
\(813\) | 24.7129 | 0.866719 | ||||||||
\(814\) | −21.7573 | + | 37.6847i | −0.762593 | + | 1.32085i | ||||
\(815\) | −18.1375 | − | 31.4150i | −0.635328 | − | 1.10042i | ||||
\(816\) | 9.28168 | + | 16.0763i | 0.324924 | + | 0.562784i | ||||
\(817\) | 2.05203 | − | 3.55422i | 0.0717914 | − | 0.124346i | ||||
\(818\) | −32.3294 | −1.13037 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.72576 | −0.130109 | ||||||||
\(821\) | 19.4762 | − | 33.7338i | 0.679725 | − | 1.17732i | −0.295339 | − | 0.955392i | \(-0.595433\pi\) |
0.975064 | − | 0.221925i | \(-0.0712340\pi\) | |||||||
\(822\) | 18.6552 | + | 32.3117i | 0.650673 | + | 1.12700i | ||||
\(823\) | −21.6825 | − | 37.5552i | −0.755805 | − | 1.30909i | −0.944973 | − | 0.327148i | \(-0.893912\pi\) |
0.189168 | − | 0.981945i | \(-0.439421\pi\) | |||||||
\(824\) | −4.69315 | + | 8.12877i | −0.163494 | + | 0.283179i | ||||
\(825\) | −63.1560 | −2.19881 | ||||||||
\(826\) | −11.9558 | − | 3.04512i | −0.415997 | − | 0.105953i | ||||
\(827\) | −27.1617 | −0.944506 | −0.472253 | − | 0.881463i | \(-0.656559\pi\) | ||||
−0.472253 | + | 0.881463i | \(0.656559\pi\) | |||||||
\(828\) | −3.10627 | + | 5.38021i | −0.107950 | + | 0.186975i | ||||
\(829\) | −15.0681 | − | 26.0986i | −0.523335 | − | 0.906443i | −0.999631 | − | 0.0271583i | \(-0.991354\pi\) |
0.476296 | − | 0.879285i | \(-0.341979\pi\) | |||||||
\(830\) | −13.0209 | − | 22.5529i | −0.451963 | − | 0.782822i | ||||
\(831\) | −32.3063 | + | 55.9562i | −1.12069 | + | 1.94110i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.444356 | + | 17.9065i | 0.0153960 | + | 0.620424i | ||||
\(834\) | 53.3727 | 1.84814 | ||||||||
\(835\) | −20.8318 | + | 36.0818i | −0.720915 | + | 1.24866i | ||||
\(836\) | 4.78859 | + | 8.29409i | 0.165617 | + | 0.286857i | ||||
\(837\) | −2.61671 | − | 4.53227i | −0.0904466 | − | 0.156658i | ||||
\(838\) | 7.19725 | − | 12.4660i | 0.248625 | − | 0.430631i | ||||
\(839\) | 31.7497 | 1.09612 | 0.548060 | − | 0.836439i | \(-0.315366\pi\) | ||||
0.548060 | + | 0.836439i | \(0.315366\pi\) | |||||||
\(840\) | 78.7629 | + | 20.0606i | 2.71758 | + | 0.692158i | ||||
\(841\) | −28.9253 | −0.997426 | ||||||||
\(842\) | 20.0093 | − | 34.6571i | 0.689566 | − | 1.19436i | ||||
\(843\) | −20.2215 | − | 35.0246i | −0.696464 | − | 1.20631i | ||||
\(844\) | 1.09810 | + | 1.90197i | 0.0377982 | + | 0.0654684i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −63.3655 | −2.17855 | ||||||||
\(847\) | −0.597105 | + | 0.612106i | −0.0205168 | + | 0.0210322i | ||||
\(848\) | −10.9243 | −0.375142 | ||||||||
\(849\) | −32.6209 | + | 56.5011i | −1.11955 | + | 1.93911i | ||||
\(850\) | −10.0069 | − | 17.3324i | −0.343232 | − | 0.594496i | ||||
\(851\) | −10.5238 | − | 18.2277i | −0.360750 | − | 0.624838i | ||||
\(852\) | −10.5521 | + | 18.2768i | −0.361510 | + | 0.626153i | ||||
\(853\) | −8.74842 | −0.299540 | −0.149770 | − | 0.988721i | \(-0.547853\pi\) | ||||
−0.149770 | + | 0.988721i | \(0.547853\pi\) | |||||||
\(854\) | −6.12976 | − | 21.7916i | −0.209756 | − | 0.745693i | ||||
\(855\) | 94.9000 | 3.24551 | ||||||||
\(856\) | −7.90624 | + | 13.6940i | −0.270230 | + | 0.468052i | ||||
\(857\) | −3.57567 | − | 6.19324i | −0.122143 | − | 0.211557i | 0.798470 | − | 0.602035i | \(-0.205643\pi\) |
−0.920612 | + | 0.390478i | \(0.872310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.2643 | − | 17.7782i | 0.350212 | − | 0.606586i | −0.636074 | − | 0.771628i | \(-0.719443\pi\) |
0.986286 | + | 0.165042i | \(0.0527761\pi\) | |||||||
\(860\) | 1.65868 | 0.0565605 | ||||||||
\(861\) | −3.90073 | − | 13.8673i | −0.132937 | − | 0.472596i | ||||
\(862\) | 8.54455 | 0.291028 | ||||||||
\(863\) | 4.21313 | − | 7.29735i | 0.143417 | − | 0.248405i | −0.785365 | − | 0.619034i | \(-0.787524\pi\) |
0.928781 | + | 0.370629i | \(0.120858\pi\) | |||||||
\(864\) | −12.3194 | − | 21.3378i | −0.419113 | − | 0.725925i | ||||
\(865\) | 4.08655 | + | 7.07811i | 0.138947 | + | 0.240663i | ||||
\(866\) | 7.84781 | − | 13.5928i | 0.266680 | − | 0.461903i | ||||
\(867\) | 30.6721 | 1.04168 | ||||||||
\(868\) | 0.744323 | − | 0.763023i | 0.0252640 | − | 0.0258987i | ||||
\(869\) | 53.1464 | 1.80287 | ||||||||
\(870\) | −1.62043 | + | 2.80666i | −0.0549376 | + | 0.0951546i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 10.6765 | + | 18.4923i | 0.361552 | + | 0.626227i | ||||
\(873\) | 3.39528 | − | 5.88080i | 0.114913 | − | 0.199035i | ||||
\(874\) | 11.0727 | 0.374539 | ||||||||
\(875\) | −13.8464 | − | 3.52664i | −0.468094 | − | 0.119222i | ||||
\(876\) | −4.95804 | −0.167517 | ||||||||
\(877\) | −17.0044 | + | 29.4524i | −0.574196 | + | 0.994537i | 0.421932 | + | 0.906627i | \(0.361352\pi\) |
−0.996128 | + | 0.0879097i | \(0.971981\pi\) | |||||||
\(878\) | 14.2728 | + | 24.7213i | 0.481685 | + | 0.834303i | ||||
\(879\) | −25.1877 | − | 43.6264i | −0.849561 | − | 1.47148i | ||||
\(880\) | 13.7481 | − | 23.8124i | 0.463448 | − | 0.802716i | ||||
\(881\) | 16.4339 | 0.553671 | 0.276836 | − | 0.960917i | \(-0.410714\pi\) | ||||
0.276836 | + | 0.960917i | \(0.410714\pi\) | |||||||
\(882\) | 1.15710 | + | 46.6285i | 0.0389616 | + | 1.57006i | ||||
\(883\) | 40.7500 | 1.37135 | 0.685674 | − | 0.727909i | \(-0.259508\pi\) | ||||
0.685674 | + | 0.727909i | \(0.259508\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19.6128 | − | 33.9705i | −0.659279 | − | 1.14190i | ||||
\(886\) | 14.3024 | + | 24.7725i | 0.480499 | + | 0.832248i | ||||
\(887\) | −13.4071 | + | 23.2219i | −0.450168 | + | 0.779714i | −0.998396 | − | 0.0566150i | \(-0.981969\pi\) |
0.548228 | + | 0.836329i | \(0.315303\pi\) | |||||||
\(888\) | 101.213 | 3.39648 | ||||||||
\(889\) | −12.7187 | − | 3.23940i | −0.426570 | − | 0.108646i | ||||
\(890\) | −41.2035 | −1.38115 | ||||||||
\(891\) | −9.23576 | + | 15.9968i | −0.309410 | + | 0.535913i | ||||
\(892\) | 7.55984 | + | 13.0940i | 0.253122 | + | 0.438421i | ||||
\(893\) | −23.6243 | − | 40.9185i | −0.790556 | − | 1.36928i | ||||
\(894\) | −3.22400 | + | 5.58414i | −0.107827 | + | 0.186762i | ||||
\(895\) | −63.9011 | −2.13598 | ||||||||
\(896\) | −7.34265 | + | 7.52712i | −0.245301 | + | 0.251463i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.3636 | + | 21.4144i | −0.412580 | + | 0.714609i | ||||
\(899\) | 0.0933003 | + | 0.161601i | 0.00311174 | + | 0.00538969i | ||||
\(900\) | 10.9016 | + | 18.8821i | 0.363386 | + | 0.629403i | ||||
\(901\) | 5.65374 | − | 9.79257i | 0.188353 | − | 0.326238i | ||||
\(902\) | −7.19922 | −0.239708 | ||||||||
\(903\) | 1.73657 | + | 6.17360i | 0.0577895 | + | 0.205445i | ||||
\(904\) | −20.5393 | −0.683128 | ||||||||
\(905\) | −34.0009 | + | 58.8913i | −1.13023 | + | 1.95761i | ||||
\(906\) | −2.26067 | − | 3.91560i | −0.0751058 | − | 0.130087i | ||||
\(907\) | −11.4592 | − | 19.8479i | −0.380497 | − | 0.659040i | 0.610636 | − | 0.791911i | \(-0.290914\pi\) |
−0.991133 | + | 0.132871i | \(0.957580\pi\) | |||||||
\(908\) | 1.96977 | − | 3.41174i | 0.0653691 | − | 0.113223i | ||||
\(909\) | 95.3018 | 3.16096 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.7375 | 0.355750 | 0.177875 | − | 0.984053i | \(-0.443078\pi\) | ||||
0.177875 | + | 0.984053i | \(0.443078\pi\) | |||||||
\(912\) | −18.0220 | + | 31.2150i | −0.596768 | + | 1.03363i | ||||
\(913\) | 10.5260 | + | 18.2316i | 0.348360 | + | 0.603376i | ||||
\(914\) | −9.51210 | − | 16.4754i | −0.314632 | − | 0.544959i | ||||
\(915\) | 35.9862 | − | 62.3300i | 1.18967 | − | 2.06057i | ||||
\(916\) | 13.5098 | 0.446377 | ||||||||
\(917\) | −34.3473 | + | 35.2103i | −1.13425 | + | 1.16275i | ||||
\(918\) | −23.2844 | −0.768500 | ||||||||
\(919\) | −8.90924 | + | 15.4313i | −0.293889 | + | 0.509030i | −0.974726 | − | 0.223405i | \(-0.928283\pi\) |
0.680837 | + | 0.732435i | \(0.261616\pi\) | |||||||
\(920\) | 9.82345 | + | 17.0147i | 0.323870 | + | 0.560959i | ||||
\(921\) | 37.3511 | + | 64.6940i | 1.23076 | + | 2.13174i | ||||
\(922\) | 1.05000 | − | 1.81865i | 0.0345799 | − | 0.0598941i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −14.5028 | − | 3.69381i | −0.477106 | − | 0.121517i | ||||
\(925\) | −73.8673 | −2.42874 | ||||||||
\(926\) | 4.07412 | − | 7.05658i | 0.133884 | − | 0.231894i | ||||
\(927\) | −8.56292 | − | 14.8314i | −0.281243 | − | 0.487128i | ||||
\(928\) | 0.439254 | + | 0.760811i | 0.0144192 | + | 0.0249748i | ||||
\(929\) | 11.6619 | − | 20.1990i | 0.382614 | − | 0.662707i | −0.608821 | − | 0.793308i | \(-0.708357\pi\) |
0.991435 | + | 0.130600i | \(0.0416905\pi\) | |||||||
\(930\) | −8.10070 | −0.265632 | ||||||||
\(931\) | −29.6791 | + | 18.1315i | −0.972693 | + | 0.594236i | ||||
\(932\) | 4.77060 | 0.156266 | ||||||||
\(933\) | 14.3091 | − | 24.7841i | 0.468459 | − | 0.811395i | ||||
\(934\) | 4.69467 | + | 8.13141i | 0.153614 | + | 0.266068i | ||||
\(935\) | 14.2303 | + | 24.6476i | 0.465381 | + | 0.806064i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.9789 | −0.685351 | −0.342676 | − | 0.939454i | \(-0.611333\pi\) | ||||
−0.342676 | + | 0.939454i | \(0.611333\pi\) | |||||||
\(938\) | −20.8452 | − | 5.30921i | −0.680621 | − | 0.173352i | ||||
\(939\) | −32.1658 | −1.04969 | ||||||||
\(940\) | 9.54789 | − | 16.5374i | 0.311418 | − | 0.539391i | ||||
\(941\) | 25.0373 | + | 43.3660i | 0.816194 | + | 1.41369i | 0.908467 | + | 0.417956i | \(0.137253\pi\) |
−0.0922732 | + | 0.995734i | \(0.529413\pi\) | |||||||
\(942\) | −6.79851 | − | 11.7754i | −0.221507 | − | 0.383662i | ||||
\(943\) | 1.74109 | − | 3.01566i | 0.0566978 | − | 0.0982035i | ||||
\(944\) | 9.70807 | 0.315971 | ||||||||
\(945\) | −48.1896 | + | 49.4003i | −1.56761 | + | 1.60699i | ||||
\(946\) | 3.20503 | 0.104205 | ||||||||
\(947\) | 1.66126 | − | 2.87740i | 0.0539839 | − | 0.0935028i | −0.837771 | − | 0.546022i | \(-0.816141\pi\) |
0.891755 | + | 0.452520i | \(0.149475\pi\) | |||||||
\(948\) | −14.0784 | − | 24.3845i | −0.457245 | − | 0.791971i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 19.4300 | − | 33.6538i | 0.630394 | − | 1.09187i | ||||
\(951\) | 82.1116 | 2.66265 | ||||||||
\(952\) | −5.63797 | − | 20.0433i | −0.182728 | − | 0.649606i | ||||
\(953\) | 13.8176 | 0.447595 | 0.223797 | − | 0.974636i | \(-0.428155\pi\) | ||||
0.223797 | + | 0.974636i | \(0.428155\pi\) | |||||||
\(954\) | 14.7223 | − | 25.4998i | 0.476653 | − | 0.825588i | ||||
\(955\) | 19.4951 | + | 33.7665i | 0.630846 | + | 1.09266i | ||||
\(956\) | −5.94397 | − | 10.2953i | −0.192242 | − | 0.332972i | ||||
\(957\) | 1.30994 | − | 2.26888i | 0.0423443 | − | 0.0733424i | ||||
\(958\) | −47.0722 | −1.52083 | ||||||||
\(959\) | −7.67078 | − | 27.2700i | −0.247703 | − | 0.880595i | ||||
\(960\) | −87.5253 | −2.82487 | ||||||||
\(961\) | 15.2668 | − | 26.4429i | 0.492477 | − | 0.852995i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.4254 | − | 24.9855i | −0.464852 | − | 0.805147i | ||||
\(964\) | −1.65888 | + | 2.87326i | −0.0534288 | + | 0.0925414i | ||||
\(965\) | 55.7268 | 1.79391 | ||||||||
\(966\) | −12.0822 | + | 12.3857i | −0.388737 | + | 0.398503i | ||||
\(967\) | −16.7893 | −0.539906 | −0.269953 | − | 0.962873i | \(-0.587008\pi\) | ||||
−0.269953 | + | 0.962873i | \(0.587008\pi\) | |||||||
\(968\) | 0.496993 | − | 0.860816i | 0.0159739 | − | 0.0276677i | ||||
\(969\) | −18.6541 | − | 32.3099i | −0.599257 | − | 1.03794i | ||||
\(970\) | −2.44573 | − | 4.23613i | −0.0785277 | − | 0.136014i | ||||
\(971\) | −7.35394 | + | 12.7374i | −0.235999 | + | 0.408762i | −0.959563 | − | 0.281495i | \(-0.909170\pi\) |
0.723563 | + | 0.690258i | \(0.242503\pi\) | |||||||
\(972\) | −3.77551 | −0.121100 | ||||||||
\(973\) | −39.2702 | − | 10.0020i | −1.25894 | − | 0.320649i | ||||
\(974\) | 23.2358 | 0.744522 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.90633 | + | 15.4262i | 0.285085 | + | 0.493781i | ||||
\(977\) | −22.4065 | − | 38.8091i | −0.716847 | − | 1.24161i | −0.962243 | − | 0.272192i | \(-0.912251\pi\) |
0.245397 | − | 0.969423i | \(-0.421082\pi\) | |||||||
\(978\) | −18.5676 | + | 32.1600i | −0.593727 | + | 1.02836i | ||||
\(979\) | 33.3086 | 1.06455 | ||||||||
\(980\) | −12.3437 | − | 6.72398i | −0.394305 | − | 0.214790i | ||||
\(981\) | −38.9598 | −1.24389 | ||||||||
\(982\) | −22.5193 | + | 39.0046i | −0.718621 | + | 1.24469i | ||||
\(983\) | −11.8635 | − | 20.5481i | −0.378386 | − | 0.655383i | 0.612442 | − | 0.790516i | \(-0.290187\pi\) |
−0.990828 | + | 0.135133i | \(0.956854\pi\) | |||||||
\(984\) | 8.37253 | + | 14.5017i | 0.266907 | + | 0.462296i | ||||
\(985\) | −24.0790 | + | 41.7061i | −0.767221 | + | 1.32887i | ||||
\(986\) | 0.830220 | 0.0264396 | ||||||||
\(987\) | 71.5486 | + | 18.2232i | 2.27742 | + | 0.580051i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.775120 | + | 1.34255i | −0.0246474 | + | 0.0426905i | ||||
\(990\) | 37.0557 | + | 64.1824i | 1.17771 | + | 2.03985i | ||||
\(991\) | −10.1338 | − | 17.5523i | −0.321912 | − | 0.557568i | 0.658970 | − | 0.752169i | \(-0.270992\pi\) |
−0.980883 | + | 0.194600i | \(0.937659\pi\) | |||||||
\(992\) | −1.09794 | + | 1.90169i | −0.0348597 | + | 0.0603788i | ||||
\(993\) | −69.2421 | −2.19733 | ||||||||
\(994\) | −26.7449 | + | 27.4168i | −0.848296 | + | 0.869608i | ||||
\(995\) | −7.44015 | −0.235868 | ||||||||
\(996\) | 5.57663 | − | 9.65901i | 0.176702 | − | 0.306057i | ||||
\(997\) | 20.1215 | + | 34.8515i | 0.637255 | + | 1.10376i | 0.986033 | + | 0.166552i | \(0.0532634\pi\) |
−0.348778 | + | 0.937205i | \(0.613403\pi\) | |||||||
\(998\) | 25.9418 | + | 44.9325i | 0.821173 | + | 1.42231i | ||||
\(999\) | −42.9694 | + | 74.4253i | −1.35949 | + | 2.35471i |
(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 | 1183.2.e.l.170.17 | yes | 48 | |
7.2 | even | 3 | 8281.2.a.cu.1.8 | 24 | |||
7.4 | even | 3 | inner | 1183.2.e.l.508.17 | yes | 48 | |
7.5 | odd | 6 | 8281.2.a.ct.1.8 | 24 | |||
13.12 | even | 2 | 1183.2.e.k.170.8 | ✓ | 48 | ||
91.12 | odd | 6 | 8281.2.a.cw.1.17 | 24 | |||
91.25 | even | 6 | 1183.2.e.k.508.8 | yes | 48 | ||
91.51 | even | 6 | 8281.2.a.cv.1.17 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1183.2.e.k.170.8 | ✓ | 48 | 13.12 | even | 2 | ||
1183.2.e.k.508.8 | yes | 48 | 91.25 | even | 6 | ||
1183.2.e.l.170.17 | yes | 48 | 1.1 | even | 1 | trivial | |
1183.2.e.l.508.17 | yes | 48 | 7.4 | even | 3 | inner | |
8281.2.a.ct.1.8 | 24 | 7.5 | odd | 6 | |||
8281.2.a.cu.1.8 | 24 | 7.2 | even | 3 | |||
8281.2.a.cv.1.17 | 24 | 91.51 | even | 6 | |||
8281.2.a.cw.1.17 | 24 | 91.12 | odd | 6 |