Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(47,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.l (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 47.7 | ||
Character | \(\chi\) | \(=\) | 966.47 |
Dual form | 966.2.l.d.185.7 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0.191760 | − | 1.72140i | 0.110712 | − | 0.993852i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −0.750837 | + | 1.30049i | −0.335785 | + | 0.581596i | −0.983635 | − | 0.180171i | \(-0.942335\pi\) |
0.647851 | + | 0.761767i | \(0.275668\pi\) | |||||||
\(6\) | −1.02677 | + | 1.39490i | −0.419177 | + | 0.569465i | ||||
\(7\) | −0.436788 | − | 2.60945i | −0.165090 | − | 0.986278i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −2.92646 | − | 0.660191i | −0.975486 | − | 0.220064i | ||||
\(10\) | 1.30049 | − | 0.750837i | 0.411251 | − | 0.237436i | ||||
\(11\) | −2.66629 | + | 1.53939i | −0.803918 | + | 0.464142i | −0.844839 | − | 0.535020i | \(-0.820304\pi\) |
0.0409215 | + | 0.999162i | \(0.486971\pi\) | |||||||
\(12\) | 1.58666 | − | 0.694633i | 0.458029 | − | 0.200523i | ||||
\(13\) | − | 4.82980i | − | 1.33954i | −0.742567 | − | 0.669772i | \(-0.766392\pi\) | ||
0.742567 | − | 0.669772i | \(-0.233608\pi\) | |||||||
\(14\) | −0.926454 | + | 2.47824i | −0.247605 | + | 0.662338i | ||||
\(15\) | 2.09468 | + | 1.54187i | 0.540845 | + | 0.398110i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.20803 | + | 2.09237i | 0.292991 | + | 0.507475i | 0.974515 | − | 0.224320i | \(-0.0720162\pi\) |
−0.681525 | + | 0.731795i | \(0.738683\pi\) | |||||||
\(18\) | 2.20429 | + | 2.03497i | 0.519556 | + | 0.479647i | ||||
\(19\) | −0.0226037 | − | 0.0130502i | −0.00518564 | − | 0.00299393i | 0.497405 | − | 0.867518i | \(-0.334286\pi\) |
−0.502591 | + | 0.864525i | \(0.667620\pi\) | |||||||
\(20\) | −1.50167 | −0.335785 | ||||||||
\(21\) | −4.57567 | + | 0.251502i | −0.998493 | + | 0.0548822i | ||||
\(22\) | 3.07877 | 0.656396 | ||||||||
\(23\) | −0.866025 | − | 0.500000i | −0.180579 | − | 0.104257i | ||||
\(24\) | −1.72140 | − | 0.191760i | −0.351380 | − | 0.0391428i | ||||
\(25\) | 1.37249 | + | 2.37722i | 0.274497 | + | 0.475443i | ||||
\(26\) | −2.41490 | + | 4.18273i | −0.473600 | + | 0.820300i | ||||
\(27\) | −1.69763 | + | 4.91101i | −0.326709 | + | 0.945125i | ||||
\(28\) | 2.04145 | − | 1.68299i | 0.385799 | − | 0.318056i | ||||
\(29\) | − | 3.75951i | − | 0.698123i | −0.937100 | − | 0.349061i | \(-0.886500\pi\) | ||
0.937100 | − | 0.349061i | \(-0.113500\pi\) | |||||||
\(30\) | −1.04311 | − | 2.38264i | −0.190445 | − | 0.435009i | ||||
\(31\) | −5.08651 | + | 2.93670i | −0.913564 | + | 0.527446i | −0.881576 | − | 0.472042i | \(-0.843517\pi\) |
−0.0319875 | + | 0.999488i | \(0.510184\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 2.13861 | + | 4.88496i | 0.372285 | + | 0.850362i | ||||
\(34\) | − | 2.41606i | − | 0.414351i | ||||||
\(35\) | 3.72151 | + | 1.39123i | 0.629050 | + | 0.235161i | ||||
\(36\) | −0.891486 | − | 2.86448i | −0.148581 | − | 0.477414i | ||||
\(37\) | −5.30627 | + | 9.19073i | −0.872346 | + | 1.51095i | −0.0127824 | + | 0.999918i | \(0.504069\pi\) |
−0.859563 | + | 0.511029i | \(0.829264\pi\) | |||||||
\(38\) | 0.0130502 | + | 0.0226037i | 0.00211703 | + | 0.00366680i | ||||
\(39\) | −8.31402 | − | 0.926160i | −1.33131 | − | 0.148304i | ||||
\(40\) | 1.30049 | + | 0.750837i | 0.205625 | + | 0.118718i | ||||
\(41\) | −1.28406 | −0.200536 | −0.100268 | − | 0.994960i | \(-0.531970\pi\) | ||||
−0.100268 | + | 0.994960i | \(0.531970\pi\) | |||||||
\(42\) | 4.08840 | + | 2.07003i | 0.630853 | + | 0.319412i | ||||
\(43\) | −2.89689 | −0.441772 | −0.220886 | − | 0.975300i | \(-0.570895\pi\) | ||||
−0.220886 | + | 0.975300i | \(0.570895\pi\) | |||||||
\(44\) | −2.66629 | − | 1.53939i | −0.401959 | − | 0.232071i | ||||
\(45\) | 3.05586 | − | 3.31013i | 0.455541 | − | 0.493445i | ||||
\(46\) | 0.500000 | + | 0.866025i | 0.0737210 | + | 0.127688i | ||||
\(47\) | 1.52890 | − | 2.64814i | 0.223013 | − | 0.386271i | −0.732708 | − | 0.680543i | \(-0.761744\pi\) |
0.955722 | + | 0.294272i | \(0.0950773\pi\) | |||||||
\(48\) | 1.39490 | + | 1.02677i | 0.201336 | + | 0.148202i | ||||
\(49\) | −6.61843 | + | 2.27955i | −0.945490 | + | 0.325650i | ||||
\(50\) | − | 2.74497i | − | 0.388198i | ||||||
\(51\) | 3.83347 | − | 1.67828i | 0.536793 | − | 0.235006i | ||||
\(52\) | 4.18273 | − | 2.41490i | 0.580040 | − | 0.334886i | ||||
\(53\) | −9.74877 | + | 5.62845i | −1.33910 | + | 0.773128i | −0.986673 | − | 0.162713i | \(-0.947975\pi\) |
−0.352423 | + | 0.935841i | \(0.614642\pi\) | |||||||
\(54\) | 3.92570 | − | 3.40425i | 0.534220 | − | 0.463259i | ||||
\(55\) | − | 4.62331i | − | 0.623407i | ||||||
\(56\) | −2.60945 | + | 0.436788i | −0.348702 | + | 0.0583683i | ||||
\(57\) | −0.0267992 | + | 0.0364076i | −0.00354964 | + | 0.00482230i | ||||
\(58\) | −1.87975 | + | 3.25583i | −0.246824 | + | 0.427511i | ||||
\(59\) | −3.71958 | − | 6.44250i | −0.484248 | − | 0.838742i | 0.515589 | − | 0.856836i | \(-0.327573\pi\) |
−0.999836 | + | 0.0180947i | \(0.994240\pi\) | |||||||
\(60\) | −0.287961 | + | 2.58499i | −0.0371755 | + | 0.333720i | ||||
\(61\) | −3.95328 | − | 2.28243i | −0.506165 | − | 0.292235i | 0.225091 | − | 0.974338i | \(-0.427732\pi\) |
−0.731256 | + | 0.682103i | \(0.761065\pi\) | |||||||
\(62\) | 5.87339 | 0.745922 | ||||||||
\(63\) | −0.444493 | + | 7.92480i | −0.0560008 | + | 0.998431i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 6.28109 | + | 3.62639i | 0.779074 | + | 0.449798i | ||||
\(66\) | 0.590384 | − | 5.29980i | 0.0726712 | − | 0.652361i | ||||
\(67\) | 2.16870 | + | 3.75630i | 0.264949 | + | 0.458905i | 0.967550 | − | 0.252679i | \(-0.0813116\pi\) |
−0.702601 | + | 0.711584i | \(0.747978\pi\) | |||||||
\(68\) | −1.20803 | + | 2.09237i | −0.146495 | + | 0.253737i | ||||
\(69\) | −1.02677 | + | 1.39490i | −0.123609 | + | 0.167926i | ||||
\(70\) | −2.52731 | − | 3.06560i | −0.302071 | − | 0.366409i | ||||
\(71\) | − | 1.04121i | − | 0.123569i | −0.998090 | − | 0.0617844i | \(-0.980321\pi\) | ||
0.998090 | − | 0.0617844i | \(-0.0196791\pi\) | |||||||
\(72\) | −0.660191 | + | 2.92646i | −0.0778043 | + | 0.344886i | ||||
\(73\) | −6.49916 | + | 3.75229i | −0.760670 | + | 0.439173i | −0.829536 | − | 0.558453i | \(-0.811395\pi\) |
0.0688665 | + | 0.997626i | \(0.478062\pi\) | |||||||
\(74\) | 9.19073 | − | 5.30627i | 1.06840 | − | 0.616842i | ||||
\(75\) | 4.35534 | − | 1.90675i | 0.502911 | − | 0.220172i | ||||
\(76\) | − | 0.0261005i | − | 0.00299393i | ||||||
\(77\) | 5.18155 | + | 6.28517i | 0.590492 | + | 0.716261i | ||||
\(78\) | 6.73708 | + | 4.95909i | 0.762824 | + | 0.561506i | ||||
\(79\) | 2.36902 | − | 4.10327i | 0.266536 | − | 0.461654i | −0.701429 | − | 0.712739i | \(-0.747454\pi\) |
0.967965 | + | 0.251086i | \(0.0807876\pi\) | |||||||
\(80\) | −0.750837 | − | 1.30049i | −0.0839462 | − | 0.145399i | ||||
\(81\) | 8.12830 | + | 3.86404i | 0.903144 | + | 0.429338i | ||||
\(82\) | 1.11202 | + | 0.642028i | 0.122803 | + | 0.0709001i | ||||
\(83\) | 13.2584 | 1.45530 | 0.727649 | − | 0.685949i | \(-0.240613\pi\) | ||||
0.727649 | + | 0.685949i | \(0.240613\pi\) | |||||||
\(84\) | −2.50564 | − | 3.83689i | −0.273388 | − | 0.418640i | ||||
\(85\) | −3.62814 | −0.393527 | ||||||||
\(86\) | 2.50878 | + | 1.44845i | 0.270529 | + | 0.156190i | ||||
\(87\) | −6.47162 | − | 0.720921i | −0.693831 | − | 0.0772909i | ||||
\(88\) | 1.53939 | + | 2.66629i | 0.164099 | + | 0.284228i | ||||
\(89\) | −6.74426 | + | 11.6814i | −0.714891 | + | 1.23823i | 0.248111 | + | 0.968732i | \(0.420190\pi\) |
−0.963002 | + | 0.269495i | \(0.913143\pi\) | |||||||
\(90\) | −4.30152 | + | 1.33872i | −0.453420 | + | 0.141114i | ||||
\(91\) | −12.6031 | + | 2.10960i | −1.32116 | + | 0.221146i | ||||
\(92\) | − | 1.00000i | − | 0.104257i | ||||||
\(93\) | 4.07985 | + | 9.31907i | 0.423061 | + | 0.966342i | ||||
\(94\) | −2.64814 | + | 1.52890i | −0.273135 | + | 0.157694i | ||||
\(95\) | 0.0339434 | − | 0.0195972i | 0.00348252 | − | 0.00201063i | ||||
\(96\) | −0.694633 | − | 1.58666i | −0.0708957 | − | 0.161938i | ||||
\(97\) | 9.55661i | 0.970327i | 0.874424 | + | 0.485163i | \(0.161240\pi\) | ||||
−0.874424 | + | 0.485163i | \(0.838760\pi\) | |||||||
\(98\) | 6.87151 | + | 1.33507i | 0.694127 | + | 0.134862i | ||||
\(99\) | 8.81908 | − | 2.74468i | 0.886351 | − | 0.275851i | ||||
\(100\) | −1.37249 | + | 2.37722i | −0.137249 | + | 0.237722i | ||||
\(101\) | 2.82588 | + | 4.89457i | 0.281185 | + | 0.487028i | 0.971677 | − | 0.236313i | \(-0.0759391\pi\) |
−0.690492 | + | 0.723340i | \(0.742606\pi\) | |||||||
\(102\) | −4.15902 | − | 0.463303i | −0.411804 | − | 0.0458739i | ||||
\(103\) | 11.0575 | + | 6.38405i | 1.08953 | + | 0.629039i | 0.933451 | − | 0.358706i | \(-0.116782\pi\) |
0.156077 | + | 0.987745i | \(0.450115\pi\) | |||||||
\(104\) | −4.82980 | −0.473600 | ||||||||
\(105\) | 3.10851 | − | 6.13944i | 0.303359 | − | 0.599148i | ||||
\(106\) | 11.2569 | 1.09337 | ||||||||
\(107\) | −3.67527 | − | 2.12192i | −0.355302 | − | 0.205134i | 0.311716 | − | 0.950175i | \(-0.399096\pi\) |
−0.667018 | + | 0.745042i | \(0.732430\pi\) | |||||||
\(108\) | −5.10188 | + | 0.985315i | −0.490928 | + | 0.0948120i | ||||
\(109\) | −8.32436 | − | 14.4182i | −0.797329 | − | 1.38102i | −0.921349 | − | 0.388735i | \(-0.872912\pi\) |
0.124020 | − | 0.992280i | \(-0.460421\pi\) | |||||||
\(110\) | −2.31166 | + | 4.00391i | −0.220408 | + | 0.381757i | ||||
\(111\) | 14.8034 | + | 10.8966i | 1.40508 | + | 1.03426i | ||||
\(112\) | 2.47824 | + | 0.926454i | 0.234172 | + | 0.0875417i | ||||
\(113\) | − | 16.7516i | − | 1.57586i | −0.615768 | − | 0.787928i | \(-0.711154\pi\) | ||
0.615768 | − | 0.787928i | \(-0.288846\pi\) | |||||||
\(114\) | 0.0414126 | − | 0.0181303i | 0.00387864 | − | 0.00169805i | ||||
\(115\) | 1.30049 | − | 0.750837i | 0.121271 | − | 0.0700159i | ||||
\(116\) | 3.25583 | − | 1.87975i | 0.302296 | − | 0.174531i | ||||
\(117\) | −3.18859 | + | 14.1342i | −0.294785 | + | 1.30671i | ||||
\(118\) | 7.43915i | 0.684830i | ||||||||
\(119\) | 4.93228 | − | 4.06622i | 0.452141 | − | 0.372750i | ||||
\(120\) | 1.54187 | − | 2.09468i | 0.140753 | − | 0.191218i | ||||
\(121\) | −0.760587 | + | 1.31737i | −0.0691443 | + | 0.119761i | ||||
\(122\) | 2.28243 | + | 3.95328i | 0.206641 | + | 0.357913i | ||||
\(123\) | −0.246230 | + | 2.21038i | −0.0222018 | + | 0.199303i | ||||
\(124\) | −5.08651 | − | 2.93670i | −0.456782 | − | 0.263723i | ||||
\(125\) | −11.6304 | −1.04026 | ||||||||
\(126\) | 4.34734 | − | 6.64083i | 0.387292 | − | 0.591612i | ||||
\(127\) | 4.17322 | 0.370314 | 0.185157 | − | 0.982709i | \(-0.440721\pi\) | ||||
0.185157 | + | 0.982709i | \(0.440721\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −0.555507 | + | 4.98672i | −0.0489096 | + | 0.439056i | ||||
\(130\) | −3.62639 | − | 6.28109i | −0.318055 | − | 0.550888i | ||||
\(131\) | 4.64613 | − | 8.04733i | 0.405934 | − | 0.703098i | −0.588496 | − | 0.808500i | \(-0.700280\pi\) |
0.994430 | + | 0.105402i | \(0.0336130\pi\) | |||||||
\(132\) | −3.16119 | + | 4.29457i | −0.275146 | + | 0.373795i | ||||
\(133\) | −0.0241809 | + | 0.0646833i | −0.00209675 | + | 0.00560876i | ||||
\(134\) | − | 4.33740i | − | 0.374694i | ||||||
\(135\) | −5.11207 | − | 5.89512i | −0.439977 | − | 0.507371i | ||||
\(136\) | 2.09237 | − | 1.20803i | 0.179419 | − | 0.103588i | ||||
\(137\) | −9.67776 | + | 5.58745i | −0.826826 | + | 0.477368i | −0.852765 | − | 0.522295i | \(-0.825076\pi\) |
0.0259384 | + | 0.999664i | \(0.491743\pi\) | |||||||
\(138\) | 1.58666 | − | 0.694633i | 0.135065 | − | 0.0591311i | ||||
\(139\) | − | 16.3842i | − | 1.38969i | −0.719159 | − | 0.694845i | \(-0.755473\pi\) | ||
0.719159 | − | 0.694845i | \(-0.244527\pi\) | |||||||
\(140\) | 0.655914 | + | 3.91854i | 0.0554348 | + | 0.331177i | ||||
\(141\) | −4.26533 | − | 3.13967i | −0.359206 | − | 0.264407i | ||||
\(142\) | −0.520605 | + | 0.901714i | −0.0436882 | + | 0.0756701i | ||||
\(143\) | 7.43492 | + | 12.8777i | 0.621739 | + | 1.07688i | ||||
\(144\) | 2.03497 | − | 2.20429i | 0.169581 | − | 0.183691i | ||||
\(145\) | 4.88919 | + | 2.82278i | 0.406025 | + | 0.234419i | ||||
\(146\) | 7.50459 | 0.621084 | ||||||||
\(147\) | 2.65488 | + | 11.8301i | 0.218971 | + | 0.975731i | ||||
\(148\) | −10.6125 | −0.872346 | ||||||||
\(149\) | 0.939767 | + | 0.542574i | 0.0769887 | + | 0.0444494i | 0.538000 | − | 0.842945i | \(-0.319180\pi\) |
−0.461011 | + | 0.887394i | \(0.652513\pi\) | |||||||
\(150\) | −4.72521 | − | 0.526375i | −0.385811 | − | 0.0429783i | ||||
\(151\) | −8.61605 | − | 14.9234i | −0.701164 | − | 1.21445i | −0.968058 | − | 0.250726i | \(-0.919331\pi\) |
0.266894 | − | 0.963726i | \(-0.414003\pi\) | |||||||
\(152\) | −0.0130502 | + | 0.0226037i | −0.00105851 | + | 0.00183340i | ||||
\(153\) | −2.15389 | − | 6.92077i | −0.174131 | − | 0.559511i | ||||
\(154\) | −1.34477 | − | 8.03389i | −0.108365 | − | 0.647389i | ||||
\(155\) | − | 8.81992i | − | 0.708433i | ||||||
\(156\) | −3.35493 | − | 7.66324i | −0.268610 | − | 0.613550i | ||||
\(157\) | 9.16009 | − | 5.28858i | 0.731055 | − | 0.422075i | −0.0877532 | − | 0.996142i | \(-0.527969\pi\) |
0.818808 | + | 0.574068i | \(0.194635\pi\) | |||||||
\(158\) | −4.10327 | + | 2.36902i | −0.326438 | + | 0.188469i | ||||
\(159\) | 7.81942 | + | 17.8609i | 0.620120 | + | 1.41646i | ||||
\(160\) | 1.50167i | 0.118718i | ||||||||
\(161\) | −0.926454 | + | 2.47824i | −0.0730148 | + | 0.195313i | ||||
\(162\) | −5.10729 | − | 7.41051i | −0.401267 | − | 0.582224i | ||||
\(163\) | −1.13546 | + | 1.96667i | −0.0889357 | + | 0.154041i | −0.907062 | − | 0.420998i | \(-0.861680\pi\) |
0.818126 | + | 0.575039i | \(0.195013\pi\) | |||||||
\(164\) | −0.642028 | − | 1.11202i | −0.0501339 | − | 0.0868345i | ||||
\(165\) | −7.95858 | − | 0.886564i | −0.619575 | − | 0.0690189i | ||||
\(166\) | −11.4821 | − | 6.62920i | −0.891185 | − | 0.514526i | ||||
\(167\) | −7.09744 | −0.549216 | −0.274608 | − | 0.961556i | \(-0.588548\pi\) | ||||
−0.274608 | + | 0.961556i | \(0.588548\pi\) | |||||||
\(168\) | 0.251502 | + | 4.57567i | 0.0194038 | + | 0.353021i | ||||
\(169\) | −10.3269 | −0.794379 | ||||||||
\(170\) | 3.14206 | + | 1.81407i | 0.240985 | + | 0.139133i | ||||
\(171\) | 0.0575331 | + | 0.0531137i | 0.00439966 | + | 0.00406171i | ||||
\(172\) | −1.44845 | − | 2.50878i | −0.110443 | − | 0.191293i | ||||
\(173\) | −5.73569 | + | 9.93450i | −0.436076 | + | 0.755306i | −0.997383 | − | 0.0723017i | \(-0.976966\pi\) |
0.561307 | + | 0.827608i | \(0.310299\pi\) | |||||||
\(174\) | 5.24413 | + | 3.86015i | 0.397557 | + | 0.292637i | ||||
\(175\) | 5.60374 | − | 4.61977i | 0.423603 | − | 0.349222i | ||||
\(176\) | − | 3.07877i | − | 0.232071i | ||||||
\(177\) | −11.8034 | + | 5.16748i | −0.887198 | + | 0.388412i | ||||
\(178\) | 11.6814 | − | 6.74426i | 0.875559 | − | 0.505504i | ||||
\(179\) | 13.2886 | − | 7.67215i | 0.993233 | − | 0.573443i | 0.0869938 | − | 0.996209i | \(-0.472274\pi\) |
0.906239 | + | 0.422766i | \(0.138941\pi\) | |||||||
\(180\) | 4.39459 | + | 0.991392i | 0.327553 | + | 0.0738940i | ||||
\(181\) | − | 15.9378i | − | 1.18465i | −0.805699 | − | 0.592325i | \(-0.798210\pi\) | ||
0.805699 | − | 0.592325i | \(-0.201790\pi\) | |||||||
\(182\) | 11.9694 | + | 4.47458i | 0.887231 | + | 0.331678i | ||||
\(183\) | −4.68705 | + | 6.36751i | −0.346477 | + | 0.470700i | ||||
\(184\) | −0.500000 | + | 0.866025i | −0.0368605 | + | 0.0638442i | ||||
\(185\) | −7.96830 | − | 13.8015i | −0.585841 | − | 1.01471i | ||||
\(186\) | 1.12628 | − | 10.1105i | 0.0825828 | − | 0.741336i | ||||
\(187\) | −6.44193 | − | 3.71925i | −0.471081 | − | 0.271979i | ||||
\(188\) | 3.05781 | 0.223013 | ||||||||
\(189\) | 13.5565 | + | 2.28481i | 0.986093 | + | 0.166195i | ||||
\(190\) | −0.0391945 | −0.00284346 | ||||||||
\(191\) | 0.832944 | + | 0.480900i | 0.0602697 | + | 0.0347967i | 0.529832 | − | 0.848103i | \(-0.322255\pi\) |
−0.469562 | + | 0.882899i | \(0.655588\pi\) | |||||||
\(192\) | −0.191760 | + | 1.72140i | −0.0138391 | + | 0.124232i | ||||
\(193\) | −1.72865 | − | 2.99410i | −0.124431 | − | 0.215520i | 0.797080 | − | 0.603874i | \(-0.206377\pi\) |
−0.921510 | + | 0.388354i | \(0.873044\pi\) | |||||||
\(194\) | 4.77830 | − | 8.27627i | 0.343062 | − | 0.594201i | ||||
\(195\) | 7.44694 | − | 10.1169i | 0.533286 | − | 0.724486i | ||||
\(196\) | −5.28337 | − | 4.59196i | −0.377383 | − | 0.327997i | ||||
\(197\) | − | 12.2666i | − | 0.873961i | −0.899471 | − | 0.436980i | \(-0.856048\pi\) | ||
0.899471 | − | 0.436980i | \(-0.143952\pi\) | |||||||
\(198\) | −9.00989 | − | 2.03258i | −0.640305 | − | 0.144449i | ||||
\(199\) | −21.0587 | + | 12.1582i | −1.49281 | + | 0.861873i | −0.999966 | − | 0.00824502i | \(-0.997375\pi\) |
−0.492843 | + | 0.870118i | \(0.664042\pi\) | |||||||
\(200\) | 2.37722 | − | 1.37249i | 0.168095 | − | 0.0970495i | ||||
\(201\) | 6.88197 | − | 3.01290i | 0.485417 | − | 0.212513i | ||||
\(202\) | − | 5.65176i | − | 0.397656i | ||||||
\(203\) | −9.81023 | + | 1.64211i | −0.688543 | + | 0.115253i | ||||
\(204\) | 3.37016 | + | 2.48074i | 0.235959 | + | 0.173687i | ||||
\(205\) | 0.964117 | − | 1.66990i | 0.0673368 | − | 0.116631i | ||||
\(206\) | −6.38405 | − | 11.0575i | −0.444798 | − | 0.770412i | ||||
\(207\) | 2.20429 | + | 2.03497i | 0.153209 | + | 0.141440i | ||||
\(208\) | 4.18273 | + | 2.41490i | 0.290020 | + | 0.167443i | ||||
\(209\) | 0.0803574 | 0.00555844 | ||||||||
\(210\) | −5.76177 | + | 3.76266i | −0.397600 | + | 0.259648i | ||||
\(211\) | −24.4887 | −1.68587 | −0.842935 | − | 0.538016i | \(-0.819174\pi\) | ||||
−0.842935 | + | 0.538016i | \(0.819174\pi\) | |||||||
\(212\) | −9.74877 | − | 5.62845i | −0.669548 | − | 0.386564i | ||||
\(213\) | −1.79234 | − | 0.199662i | −0.122809 | − | 0.0136806i | ||||
\(214\) | 2.12192 | + | 3.67527i | 0.145052 | + | 0.251237i | ||||
\(215\) | 2.17509 | − | 3.76737i | 0.148340 | − | 0.256933i | ||||
\(216\) | 4.91101 | + | 1.69763i | 0.334152 | + | 0.115509i | ||||
\(217\) | 9.88488 | + | 11.9903i | 0.671029 | + | 0.813952i | ||||
\(218\) | 16.6487i | 1.12759i | ||||||||
\(219\) | 5.21293 | + | 11.9072i | 0.352257 | + | 0.804615i | ||||
\(220\) | 4.00391 | − | 2.31166i | 0.269943 | − | 0.155852i | ||||
\(221\) | 10.1057 | − | 5.83455i | 0.679785 | − | 0.392474i | ||||
\(222\) | −7.37182 | − | 16.8385i | −0.494764 | − | 1.13013i | ||||
\(223\) | − | 25.7452i | − | 1.72402i | −0.506888 | − | 0.862012i | \(-0.669204\pi\) | ||
0.506888 | − | 0.862012i | \(-0.330796\pi\) | |||||||
\(224\) | −1.68299 | − | 2.04145i | −0.112450 | − | 0.136400i | ||||
\(225\) | −2.44711 | − | 7.86292i | −0.163140 | − | 0.524195i | ||||
\(226\) | −8.37579 | + | 14.5073i | −0.557149 | + | 0.965010i | ||||
\(227\) | −3.81039 | − | 6.59979i | −0.252904 | − | 0.438043i | 0.711420 | − | 0.702767i | \(-0.248052\pi\) |
−0.964324 | + | 0.264724i | \(0.914719\pi\) | |||||||
\(228\) | −0.0449295 | − | 0.00500502i | −0.00297553 | − | 0.000331466i | ||||
\(229\) | −5.56463 | − | 3.21274i | −0.367721 | − | 0.212304i | 0.304741 | − | 0.952435i | \(-0.401430\pi\) |
−0.672462 | + | 0.740131i | \(0.734763\pi\) | |||||||
\(230\) | −1.50167 | −0.0990175 | ||||||||
\(231\) | 11.8129 | − | 7.71429i | 0.777233 | − | 0.507563i | ||||
\(232\) | −3.75951 | −0.246824 | ||||||||
\(233\) | −18.2981 | − | 10.5644i | −1.19875 | − | 0.692098i | −0.238472 | − | 0.971149i | \(-0.576647\pi\) |
−0.960276 | + | 0.279052i | \(0.909980\pi\) | |||||||
\(234\) | 9.82849 | − | 10.6463i | 0.642509 | − | 0.695968i | ||||
\(235\) | 2.29592 | + | 3.97664i | 0.149769 | + | 0.259408i | ||||
\(236\) | 3.71958 | − | 6.44250i | 0.242124 | − | 0.419371i | ||||
\(237\) | −6.60909 | − | 4.86488i | −0.429307 | − | 0.316008i | ||||
\(238\) | −6.30459 | + | 1.05531i | −0.408666 | + | 0.0684054i | ||||
\(239\) | − | 3.04481i | − | 0.196952i | −0.995139 | − | 0.0984762i | \(-0.968603\pi\) | ||
0.995139 | − | 0.0984762i | \(-0.0313968\pi\) | |||||||
\(240\) | −2.38264 | + | 1.04311i | −0.153799 | + | 0.0673326i | ||||
\(241\) | 17.9860 | − | 10.3842i | 1.15858 | − | 0.668906i | 0.207617 | − | 0.978210i | \(-0.433429\pi\) |
0.950963 | + | 0.309304i | \(0.100096\pi\) | |||||||
\(242\) | 1.31737 | − | 0.760587i | 0.0846841 | − | 0.0488924i | ||||
\(243\) | 8.21025 | − | 13.2511i | 0.526688 | − | 0.850059i | ||||
\(244\) | − | 4.56485i | − | 0.292235i | ||||||
\(245\) | 2.00484 | − | 10.3188i | 0.128084 | − | 0.659242i | ||||
\(246\) | 1.31843 | − | 1.79113i | 0.0840600 | − | 0.114198i | ||||
\(247\) | −0.0630300 | + | 0.109171i | −0.00401050 | + | 0.00694640i | ||||
\(248\) | 2.93670 | + | 5.08651i | 0.186480 | + | 0.322993i | ||||
\(249\) | 2.54243 | − | 22.8231i | 0.161120 | − | 1.44635i | ||||
\(250\) | 10.0722 | + | 5.81521i | 0.637025 | + | 0.367786i | ||||
\(251\) | −5.91219 | −0.373174 | −0.186587 | − | 0.982438i | \(-0.559743\pi\) | ||||
−0.186587 | + | 0.982438i | \(0.559743\pi\) | |||||||
\(252\) | −7.08532 | + | 3.57746i | −0.446333 | + | 0.225359i | ||||
\(253\) | 3.07877 | 0.193561 | ||||||||
\(254\) | −3.61412 | − | 2.08661i | −0.226770 | − | 0.130926i | ||||
\(255\) | −0.695731 | + | 6.24549i | −0.0435684 | + | 0.391108i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 0.453399 | − | 0.785311i | 0.0282823 | − | 0.0489863i | −0.851538 | − | 0.524293i | \(-0.824330\pi\) |
0.879820 | + | 0.475307i | \(0.157663\pi\) | |||||||
\(258\) | 2.97444 | − | 4.04087i | 0.185181 | − | 0.251574i | ||||
\(259\) | 26.3005 | + | 9.83204i | 1.63423 | + | 0.610933i | ||||
\(260\) | 7.25278i | 0.449798i | ||||||||
\(261\) | −2.48199 | + | 11.0020i | −0.153631 | + | 0.681009i | ||||
\(262\) | −8.04733 | + | 4.64613i | −0.497166 | + | 0.287039i | ||||
\(263\) | 25.1424 | − | 14.5160i | 1.55035 | − | 0.895094i | 0.552236 | − | 0.833688i | \(-0.313775\pi\) |
0.998113 | − | 0.0614061i | \(-0.0195585\pi\) | |||||||
\(264\) | 4.88496 | − | 2.13861i | 0.300648 | − | 0.131623i | ||||
\(265\) | − | 16.9042i | − | 1.03842i | ||||||
\(266\) | 0.0532830 | − | 0.0439270i | 0.00326699 | − | 0.00269333i | ||||
\(267\) | 18.8151 | + | 13.8496i | 1.15147 | + | 0.847583i | ||||
\(268\) | −2.16870 | + | 3.75630i | −0.132474 | + | 0.229452i | ||||
\(269\) | 14.2990 | + | 24.7666i | 0.871827 | + | 1.51005i | 0.860105 | + | 0.510117i | \(0.170398\pi\) |
0.0117223 | + | 0.999931i | \(0.496269\pi\) | |||||||
\(270\) | 1.47962 | + | 7.66136i | 0.0900470 | + | 0.466256i | ||||
\(271\) | 14.1438 | + | 8.16593i | 0.859175 | + | 0.496045i | 0.863736 | − | 0.503945i | \(-0.168118\pi\) |
−0.00456084 | + | 0.999990i | \(0.501452\pi\) | |||||||
\(272\) | −2.41606 | −0.146495 | ||||||||
\(273\) | 1.21470 | + | 22.0995i | 0.0735171 | + | 1.33753i | ||||
\(274\) | 11.1749 | 0.675101 | ||||||||
\(275\) | −7.31890 | − | 4.22557i | −0.441347 | − | 0.254812i | ||||
\(276\) | −1.72140 | − | 0.191760i | −0.103616 | − | 0.0115426i | ||||
\(277\) | −7.29593 | − | 12.6369i | −0.438370 | − | 0.759279i | 0.559194 | − | 0.829037i | \(-0.311111\pi\) |
−0.997564 | + | 0.0697581i | \(0.977777\pi\) | |||||||
\(278\) | −8.19210 | + | 14.1891i | −0.491330 | + | 0.851008i | ||||
\(279\) | 16.8242 | − | 5.23605i | 1.00724 | − | 0.313474i | ||||
\(280\) | 1.39123 | − | 3.72151i | 0.0831421 | − | 0.222403i | ||||
\(281\) | 8.03415i | 0.479277i | 0.970862 | + | 0.239639i | \(0.0770290\pi\) | ||||
−0.970862 | + | 0.239639i | \(0.922971\pi\) | |||||||
\(282\) | 2.12405 | + | 4.85170i | 0.126486 | + | 0.288914i | ||||
\(283\) | −1.32163 | + | 0.763045i | −0.0785630 | + | 0.0453583i | −0.538767 | − | 0.842455i | \(-0.681110\pi\) |
0.460204 | + | 0.887813i | \(0.347776\pi\) | |||||||
\(284\) | 0.901714 | − | 0.520605i | 0.0535069 | − | 0.0308922i | ||||
\(285\) | −0.0272258 | − | 0.0621882i | −0.00161271 | − | 0.00368371i | ||||
\(286\) | − | 14.8698i | − | 0.879271i | ||||||
\(287\) | 0.560860 | + | 3.35067i | 0.0331065 | + | 0.197784i | ||||
\(288\) | −2.86448 | + | 0.891486i | −0.168791 | + | 0.0525313i | ||||
\(289\) | 5.58132 | − | 9.66713i | 0.328313 | − | 0.568655i | ||||
\(290\) | −2.82278 | − | 4.88919i | −0.165759 | − | 0.287103i | ||||
\(291\) | 16.4508 | + | 1.83257i | 0.964362 | + | 0.107427i | ||||
\(292\) | −6.49916 | − | 3.75229i | −0.380335 | − | 0.219586i | ||||
\(293\) | 21.3633 | 1.24806 | 0.624028 | − | 0.781402i | \(-0.285495\pi\) | ||||
0.624028 | + | 0.781402i | \(0.285495\pi\) | |||||||
\(294\) | 3.61587 | − | 11.5726i | 0.210882 | − | 0.674929i | ||||
\(295\) | 11.1712 | 0.650412 | ||||||||
\(296\) | 9.19073 | + | 5.30627i | 0.534201 | + | 0.308421i | ||||
\(297\) | −3.03356 | − | 15.7075i | −0.176025 | − | 0.911442i | ||||
\(298\) | −0.542574 | − | 0.939767i | −0.0314305 | − | 0.0544392i | ||||
\(299\) | −2.41490 | + | 4.18273i | −0.139657 | + | 0.241893i | ||||
\(300\) | 3.82896 | + | 2.81846i | 0.221065 | + | 0.162724i | ||||
\(301\) | 1.26533 | + | 7.55928i | 0.0729323 | + | 0.435710i | ||||
\(302\) | 17.2321i | 0.991596i | ||||||||
\(303\) | 8.96741 | − | 3.92590i | 0.515164 | − | 0.225537i | ||||
\(304\) | 0.0226037 | − | 0.0130502i | 0.00129641 | − | 0.000748483i | ||||
\(305\) | 5.93654 | − | 3.42746i | 0.339925 | − | 0.196256i | ||||
\(306\) | −1.59506 | + | 7.07050i | −0.0911837 | + | 0.404194i | ||||
\(307\) | 18.9288i | 1.08032i | 0.841562 | + | 0.540161i | \(0.181637\pi\) | ||||
−0.841562 | + | 0.540161i | \(0.818363\pi\) | |||||||
\(308\) | −2.85234 | + | 7.62994i | −0.162527 | + | 0.434756i | ||||
\(309\) | 13.1099 | − | 17.8102i | 0.745796 | − | 1.01319i | ||||
\(310\) | −4.40996 | + | 7.63828i | −0.250469 | + | 0.433825i | ||||
\(311\) | −1.10821 | − | 1.91947i | −0.0628408 | − | 0.108843i | 0.832893 | − | 0.553433i | \(-0.186683\pi\) |
−0.895734 | + | 0.444590i | \(0.853349\pi\) | |||||||
\(312\) | −0.926160 | + | 8.31402i | −0.0524335 | + | 0.470689i | ||||
\(313\) | 5.13701 | + | 2.96585i | 0.290361 | + | 0.167640i | 0.638105 | − | 0.769950i | \(-0.279719\pi\) |
−0.347744 | + | 0.937590i | \(0.613052\pi\) | |||||||
\(314\) | −10.5772 | −0.596904 | ||||||||
\(315\) | −9.97237 | − | 6.52829i | −0.561879 | − | 0.367828i | ||||
\(316\) | 4.73805 | 0.266536 | ||||||||
\(317\) | −24.0968 | − | 13.9123i | −1.35341 | − | 0.781391i | −0.364684 | − | 0.931131i | \(-0.618823\pi\) |
−0.988725 | + | 0.149740i | \(0.952156\pi\) | |||||||
\(318\) | 2.15862 | − | 19.3777i | 0.121049 | − | 1.08665i | ||||
\(319\) | 5.78733 | + | 10.0239i | 0.324028 | + | 0.561233i | ||||
\(320\) | 0.750837 | − | 1.30049i | 0.0419731 | − | 0.0726995i | ||||
\(321\) | −4.35745 | + | 5.91973i | −0.243209 | + | 0.330407i | ||||
\(322\) | 2.04145 | − | 1.68299i | 0.113766 | − | 0.0937895i | ||||
\(323\) | − | 0.0630604i | − | 0.00350878i | ||||||
\(324\) | 0.717790 | + | 8.97133i | 0.0398772 | + | 0.498407i | ||||
\(325\) | 11.4815 | − | 6.62883i | 0.636877 | − | 0.367701i | ||||
\(326\) | 1.96667 | − | 1.13546i | 0.108924 | − | 0.0628871i | ||||
\(327\) | −26.4158 | + | 11.5648i | −1.46080 | + | 0.639532i | ||||
\(328\) | 1.28406i | 0.0709001i | ||||||||
\(329\) | −7.57799 | − | 2.83292i | −0.417788 | − | 0.156184i | ||||
\(330\) | 6.44905 | + | 4.74708i | 0.355009 | + | 0.261318i | ||||
\(331\) | −10.0924 | + | 17.4805i | −0.554727 | + | 0.960815i | 0.443198 | + | 0.896424i | \(0.353844\pi\) |
−0.997925 | + | 0.0643914i | \(0.979489\pi\) | |||||||
\(332\) | 6.62920 | + | 11.4821i | 0.363825 | + | 0.630163i | ||||
\(333\) | 21.5962 | − | 23.3931i | 1.18347 | − | 1.28194i | ||||
\(334\) | 6.14656 | + | 3.54872i | 0.336325 | + | 0.194177i | ||||
\(335\) | −6.51336 | −0.355863 | ||||||||
\(336\) | 2.07003 | − | 4.08840i | 0.112929 | − | 0.223040i | ||||
\(337\) | −34.4475 | −1.87648 | −0.938238 | − | 0.345991i | \(-0.887543\pi\) | ||||
−0.938238 | + | 0.345991i | \(0.887543\pi\) | |||||||
\(338\) | 8.94338 | + | 5.16346i | 0.486456 | + | 0.280855i | ||||
\(339\) | −28.8362 | − | 3.21227i | −1.56617 | − | 0.174467i | ||||
\(340\) | −1.81407 | − | 3.14206i | −0.0983818 | − | 0.170402i | ||||
\(341\) | 9.04141 | − | 15.6602i | 0.489620 | − | 0.848047i | ||||
\(342\) | −0.0232682 | − | 0.0747644i | −0.00125820 | − | 0.00404279i | ||||
\(343\) | 8.83922 | + | 16.2748i | 0.477273 | + | 0.878755i | ||||
\(344\) | 2.89689i | 0.156190i | ||||||||
\(345\) | −1.04311 | − | 2.38264i | −0.0561593 | − | 0.128277i | ||||
\(346\) | 9.93450 | − | 5.73569i | 0.534082 | − | 0.308353i | ||||
\(347\) | 16.5783 | − | 9.57147i | 0.889968 | − | 0.513823i | 0.0160361 | − | 0.999871i | \(-0.494895\pi\) |
0.873932 | + | 0.486048i | \(0.161562\pi\) | |||||||
\(348\) | −2.61148 | − | 5.96505i | −0.139990 | − | 0.319760i | ||||
\(349\) | − | 21.1015i | − | 1.12953i | −0.825250 | − | 0.564767i | \(-0.808966\pi\) | ||
0.825250 | − | 0.564767i | \(-0.191034\pi\) | |||||||
\(350\) | −7.16286 | + | 1.19897i | −0.382871 | + | 0.0640877i | ||||
\(351\) | 23.7192 | + | 8.19921i | 1.26604 | + | 0.437641i | ||||
\(352\) | −1.53939 | + | 2.66629i | −0.0820495 | + | 0.142114i | ||||
\(353\) | 9.13391 | + | 15.8204i | 0.486149 | + | 0.842034i | 0.999873 | − | 0.0159209i | \(-0.00506800\pi\) |
−0.513725 | + | 0.857955i | \(0.671735\pi\) | |||||||
\(354\) | 12.8058 | + | 1.42653i | 0.680620 | + | 0.0758192i | ||||
\(355\) | 1.35408 | + | 0.781779i | 0.0718672 | + | 0.0414925i | ||||
\(356\) | −13.4885 | −0.714891 | ||||||||
\(357\) | −6.05379 | − | 9.27018i | −0.320400 | − | 0.490630i | ||||
\(358\) | −15.3443 | −0.810971 | ||||||||
\(359\) | −20.9162 | − | 12.0760i | −1.10392 | − | 0.637346i | −0.166669 | − | 0.986013i | \(-0.553301\pi\) |
−0.937247 | + | 0.348667i | \(0.886634\pi\) | |||||||
\(360\) | −3.31013 | − | 3.05586i | −0.174459 | − | 0.161058i | ||||
\(361\) | −9.49966 | − | 16.4539i | −0.499982 | − | 0.865994i | ||||
\(362\) | −7.96892 | + | 13.8026i | −0.418837 | + | 0.725447i | ||||
\(363\) | 2.12188 | + | 1.56190i | 0.111370 | + | 0.0819783i | ||||
\(364\) | −8.12851 | − | 9.85980i | −0.426050 | − | 0.516794i | ||||
\(365\) | − | 11.2694i | − | 0.589870i | ||||||
\(366\) | 7.24286 | − | 3.17090i | 0.378590 | − | 0.165745i | ||||
\(367\) | −0.414105 | + | 0.239083i | −0.0216161 | + | 0.0124801i | −0.510769 | − | 0.859718i | \(-0.670639\pi\) |
0.489153 | + | 0.872198i | \(0.337306\pi\) | |||||||
\(368\) | 0.866025 | − | 0.500000i | 0.0451447 | − | 0.0260643i | ||||
\(369\) | 3.75773 | + | 0.847722i | 0.195620 | + | 0.0441306i | ||||
\(370\) | 15.9366i | 0.828504i | ||||||||
\(371\) | 18.9453 | + | 22.9805i | 0.983591 | + | 1.19309i | ||||
\(372\) | −6.03062 | + | 8.19279i | −0.312673 | + | 0.424776i | ||||
\(373\) | 1.00479 | − | 1.74035i | 0.0520260 | − | 0.0901117i | −0.838840 | − | 0.544379i | \(-0.816765\pi\) |
0.890866 | + | 0.454267i | \(0.150099\pi\) | |||||||
\(374\) | 3.71925 | + | 6.44193i | 0.192318 | + | 0.333104i | ||||
\(375\) | −2.23025 | + | 20.0207i | −0.115169 | + | 1.03386i | ||||
\(376\) | −2.64814 | − | 1.52890i | −0.136567 | − | 0.0788472i | ||||
\(377\) | −18.1576 | −0.935166 | ||||||||
\(378\) | −10.5979 | − | 8.75697i | −0.545097 | − | 0.450410i | ||||
\(379\) | −19.9262 | −1.02354 | −0.511770 | − | 0.859123i | \(-0.671010\pi\) | ||||
−0.511770 | + | 0.859123i | \(0.671010\pi\) | |||||||
\(380\) | 0.0339434 | + | 0.0195972i | 0.00174126 | + | 0.00100532i | ||||
\(381\) | 0.800256 | − | 7.18380i | 0.0409983 | − | 0.368037i | ||||
\(382\) | −0.480900 | − | 0.832944i | −0.0246050 | − | 0.0426171i | ||||
\(383\) | −10.0209 | + | 17.3567i | −0.512043 | + | 0.886885i | 0.487859 | + | 0.872922i | \(0.337778\pi\) |
−0.999903 | + | 0.0139629i | \(0.995555\pi\) | |||||||
\(384\) | 1.02677 | − | 1.39490i | 0.0523971 | − | 0.0711831i | ||||
\(385\) | −12.0643 | + | 2.01941i | −0.614853 | + | 0.102919i | ||||
\(386\) | 3.45729i | 0.175972i | ||||||||
\(387\) | 8.47763 | + | 1.91250i | 0.430942 | + | 0.0972179i | ||||
\(388\) | −8.27627 | + | 4.77830i | −0.420164 | + | 0.242582i | ||||
\(389\) | −14.8957 | + | 8.60002i | −0.755240 | + | 0.436038i | −0.827584 | − | 0.561342i | \(-0.810285\pi\) |
0.0723439 | + | 0.997380i | \(0.476952\pi\) | |||||||
\(390\) | −11.5077 | + | 5.03802i | −0.582714 | + | 0.255110i | ||||
\(391\) | − | 2.41606i | − | 0.122186i | ||||||
\(392\) | 2.27955 | + | 6.61843i | 0.115135 | + | 0.334281i | ||||
\(393\) | −12.9618 | − | 9.54101i | −0.653834 | − | 0.481280i | ||||
\(394\) | −6.13331 | + | 10.6232i | −0.308992 | + | 0.535190i | ||||
\(395\) | 3.55750 | + | 6.16177i | 0.178997 | + | 0.310032i | ||||
\(396\) | 6.78650 | + | 6.26521i | 0.341035 | + | 0.314838i | ||||
\(397\) | 17.6264 | + | 10.1766i | 0.884645 | + | 0.510750i | 0.872187 | − | 0.489173i | \(-0.162701\pi\) |
0.0124576 | + | 0.999922i | \(0.496035\pi\) | |||||||
\(398\) | 24.3164 | 1.21887 | ||||||||
\(399\) | 0.106709 | + | 0.0540288i | 0.00534214 | + | 0.00270482i | ||||
\(400\) | −2.74497 | −0.137249 | ||||||||
\(401\) | 1.52201 | + | 0.878732i | 0.0760054 | + | 0.0438818i | 0.537521 | − | 0.843250i | \(-0.319361\pi\) |
−0.461516 | + | 0.887132i | \(0.652694\pi\) | |||||||
\(402\) | −7.46641 | − | 0.831738i | −0.372391 | − | 0.0414833i | ||||
\(403\) | 14.1836 | + | 24.5668i | 0.706537 | + | 1.22376i | ||||
\(404\) | −2.82588 | + | 4.89457i | −0.140593 | + | 0.243514i | ||||
\(405\) | −11.1282 | + | 7.66949i | −0.552963 | + | 0.381100i | ||||
\(406\) | 9.31697 | + | 3.48301i | 0.462393 | + | 0.172859i | ||||
\(407\) | − | 32.6736i | − | 1.61957i | ||||||
\(408\) | −1.67828 | − | 3.83347i | −0.0830871 | − | 0.189785i | ||||
\(409\) | −17.4826 | + | 10.0936i | −0.864458 | + | 0.499095i | −0.865503 | − | 0.500905i | \(-0.833001\pi\) |
0.00104483 | + | 0.999999i | \(0.499667\pi\) | |||||||
\(410\) | −1.66990 | + | 0.964117i | −0.0824704 | + | 0.0476143i | ||||
\(411\) | 7.76246 | + | 17.7308i | 0.382894 | + | 0.874594i | ||||
\(412\) | 12.7681i | 0.629039i | ||||||||
\(413\) | −15.1867 | + | 12.5200i | −0.747288 | + | 0.616071i | ||||
\(414\) | −0.891486 | − | 2.86448i | −0.0438141 | − | 0.140782i | ||||
\(415\) | −9.95490 | + | 17.2424i | −0.488667 | + | 0.846396i | ||||
\(416\) | −2.41490 | − | 4.18273i | −0.118400 | − | 0.205075i | ||||
\(417\) | −28.2038 | − | 3.14183i | −1.38115 | − | 0.153856i | ||||
\(418\) | −0.0695916 | − | 0.0401787i | −0.00340384 | − | 0.00196521i | ||||
\(419\) | −28.8533 | −1.40957 | −0.704787 | − | 0.709419i | \(-0.748958\pi\) | ||||
−0.704787 | + | 0.709419i | \(0.748958\pi\) | |||||||
\(420\) | 6.87117 | − | 0.377674i | 0.335279 | − | 0.0184286i | ||||
\(421\) | 9.07695 | 0.442384 | 0.221192 | − | 0.975230i | \(-0.429005\pi\) | ||||
0.221192 | + | 0.975230i | \(0.429005\pi\) | |||||||
\(422\) | 21.2078 | + | 12.2443i | 1.03238 | + | 0.596045i | ||||
\(423\) | −6.22255 | + | 6.74029i | −0.302551 | + | 0.327724i | ||||
\(424\) | 5.62845 | + | 9.74877i | 0.273342 | + | 0.473442i | ||||
\(425\) | −3.31601 | + | 5.74351i | −0.160850 | + | 0.278601i | ||||
\(426\) | 1.45238 | + | 1.06908i | 0.0703681 | + | 0.0517972i | ||||
\(427\) | −4.22913 | + | 11.3128i | −0.204662 | + | 0.547465i | ||||
\(428\) | − | 4.24384i | − | 0.205134i | ||||||
\(429\) | 23.5933 | − | 10.3291i | 1.13910 | − | 0.498692i | ||||
\(430\) | −3.76737 | + | 2.17509i | −0.181679 | + | 0.104892i | ||||
\(431\) | 8.70617 | − | 5.02651i | 0.419361 | − | 0.242118i | −0.275443 | − | 0.961317i | \(-0.588824\pi\) |
0.694804 | + | 0.719199i | \(0.255491\pi\) | |||||||
\(432\) | −3.40425 | − | 3.92570i | −0.163787 | − | 0.188875i | ||||
\(433\) | − | 7.21858i | − | 0.346903i | −0.984842 | − | 0.173451i | \(-0.944508\pi\) | ||
0.984842 | − | 0.173451i | \(-0.0554919\pi\) | |||||||
\(434\) | −2.56543 | − | 15.3263i | −0.123144 | − | 0.735686i | ||||
\(435\) | 5.79669 | − | 7.87498i | 0.277930 | − | 0.377576i | ||||
\(436\) | 8.32436 | − | 14.4182i | 0.398665 | − | 0.690508i | ||||
\(437\) | 0.0130502 | + | 0.0226037i | 0.000624278 | + | 0.00108128i | ||||
\(438\) | 1.43908 | − | 12.9184i | 0.0687617 | − | 0.617266i | ||||
\(439\) | 8.66524 | + | 5.00288i | 0.413569 | + | 0.238774i | 0.692322 | − | 0.721589i | \(-0.256588\pi\) |
−0.278753 | + | 0.960363i | \(0.589921\pi\) | |||||||
\(440\) | −4.62331 | −0.220408 | ||||||||
\(441\) | 20.8735 | − | 2.30158i | 0.993976 | − | 0.109599i | ||||
\(442\) | −11.6691 | −0.555042 | ||||||||
\(443\) | −32.1174 | − | 18.5430i | −1.52594 | − | 0.881003i | −0.999526 | − | 0.0307766i | \(-0.990202\pi\) |
−0.526416 | − | 0.850227i | \(-0.676465\pi\) | |||||||
\(444\) | −2.03506 | + | 18.2685i | −0.0965795 | + | 0.866983i | ||||
\(445\) | −10.1277 | − | 17.5417i | −0.480099 | − | 0.831555i | ||||
\(446\) | −12.8726 | + | 22.2960i | −0.609534 | + | 1.05574i | ||||
\(447\) | 1.11420 | − | 1.51367i | 0.0526998 | − | 0.0715943i | ||||
\(448\) | 0.436788 | + | 2.60945i | 0.0206363 | + | 0.123285i | ||||
\(449\) | 37.6371i | 1.77620i | 0.459646 | + | 0.888102i | \(0.347976\pi\) | ||||
−0.459646 | + | 0.888102i | \(0.652024\pi\) | |||||||
\(450\) | −1.81221 | + | 8.03304i | −0.0854282 | + | 0.378681i | ||||
\(451\) | 3.42367 | − | 1.97666i | 0.161214 | − | 0.0930771i | ||||
\(452\) | 14.5073 | − | 8.37579i | 0.682365 | − | 0.393964i | ||||
\(453\) | −27.3415 | + | 11.9700i | −1.28461 | + | 0.562399i | ||||
\(454\) | 7.62078i | 0.357661i | ||||||||
\(455\) | 6.71937 | − | 17.9741i | 0.315009 | − | 0.842641i | ||||
\(456\) | 0.0364076 | + | 0.0267992i | 0.00170494 | + | 0.00125499i | ||||
\(457\) | 1.93541 | − | 3.35223i | 0.0905348 | − | 0.156811i | −0.817202 | − | 0.576352i | \(-0.804476\pi\) |
0.907736 | + | 0.419541i | \(0.137809\pi\) | |||||||
\(458\) | 3.21274 | + | 5.56463i | 0.150121 | + | 0.260018i | ||||
\(459\) | −12.3265 | + | 2.38058i | −0.575350 | + | 0.111116i | ||||
\(460\) | 1.30049 | + | 0.750837i | 0.0606356 | + | 0.0350080i | ||||
\(461\) | −19.0584 | −0.887640 | −0.443820 | − | 0.896116i | \(-0.646377\pi\) | ||||
−0.443820 | + | 0.896116i | \(0.646377\pi\) | |||||||
\(462\) | −14.0874 | + | 0.774316i | −0.655407 | + | 0.0360244i | ||||
\(463\) | 16.7280 | 0.777414 | 0.388707 | − | 0.921361i | \(-0.372922\pi\) | ||||
0.388707 | + | 0.921361i | \(0.372922\pi\) | |||||||
\(464\) | 3.25583 | + | 1.87975i | 0.151148 | + | 0.0872653i | ||||
\(465\) | −15.1826 | − | 1.69130i | −0.704078 | − | 0.0784324i | ||||
\(466\) | 10.5644 | + | 18.2981i | 0.489387 | + | 0.847643i | ||||
\(467\) | 1.86844 | − | 3.23624i | 0.0864612 | − | 0.149755i | −0.819552 | − | 0.573005i | \(-0.805777\pi\) |
0.906013 | + | 0.423250i | \(0.139111\pi\) | |||||||
\(468\) | −13.8349 | + | 4.30569i | −0.639517 | + | 0.199031i | ||||
\(469\) | 8.85460 | − | 7.29981i | 0.408867 | − | 0.337074i | ||||
\(470\) | − | 4.59183i | − | 0.211805i | ||||||
\(471\) | −7.34724 | − | 16.7823i | −0.338543 | − | 0.773289i | ||||
\(472\) | −6.44250 | + | 3.71958i | −0.296540 | + | 0.171207i | ||||
\(473\) | 7.72396 | − | 4.45943i | 0.355148 | − | 0.205045i | ||||
\(474\) | 3.29120 | + | 7.51766i | 0.151170 | + | 0.345298i | ||||
\(475\) | − | 0.0716452i | − | 0.00328731i | ||||||
\(476\) | 5.98759 | + | 2.23837i | 0.274441 | + | 0.102596i | ||||
\(477\) | 32.2452 | − | 10.0354i | 1.47641 | − | 0.459488i | ||||
\(478\) | −1.52240 | + | 2.63688i | −0.0696332 | + | 0.120608i | ||||
\(479\) | −13.7953 | − | 23.8941i | −0.630322 | − | 1.09175i | −0.987486 | − | 0.157708i | \(-0.949589\pi\) |
0.357163 | − | 0.934042i | \(-0.383744\pi\) | |||||||
\(480\) | 2.58499 | + | 0.287961i | 0.117988 | + | 0.0131435i | ||||
\(481\) | 44.3894 | + | 25.6282i | 2.02398 | + | 1.16855i | ||||
\(482\) | −20.7684 | −0.945976 | ||||||||
\(483\) | 4.08840 | + | 2.07003i | 0.186028 | + | 0.0941895i | ||||
\(484\) | −1.52117 | −0.0691443 | ||||||||
\(485\) | −12.4283 | − | 7.17546i | −0.564338 | − | 0.325821i | ||||
\(486\) | −13.7358 | + | 7.37067i | −0.623070 | + | 0.334340i | ||||
\(487\) | 5.25709 | + | 9.10554i | 0.238221 | + | 0.412611i | 0.960204 | − | 0.279300i | \(-0.0901023\pi\) |
−0.721983 | + | 0.691911i | \(0.756769\pi\) | |||||||
\(488\) | −2.28243 | + | 3.95328i | −0.103321 | + | 0.178956i | ||||
\(489\) | 3.16769 | + | 2.33170i | 0.143248 | + | 0.105443i | ||||
\(490\) | −6.89562 | + | 7.93390i | −0.311512 | + | 0.358417i | ||||
\(491\) | − | 4.88347i | − | 0.220388i | −0.993910 | − | 0.110194i | \(-0.964853\pi\) | ||
0.993910 | − | 0.110194i | \(-0.0351472\pi\) | |||||||
\(492\) | −2.03736 | + | 0.891947i | −0.0918512 | + | 0.0402121i | ||||
\(493\) | 7.86629 | − | 4.54160i | 0.354280 | − | 0.204543i | ||||
\(494\) | 0.109171 | − | 0.0630300i | 0.00491185 | − | 0.00283586i | ||||
\(495\) | −3.05227 | + | 13.5299i | −0.137189 | + | 0.608125i | ||||
\(496\) | − | 5.87339i | − | 0.263723i | ||||||
\(497\) | −2.71698 | + | 0.454788i | −0.121873 | + | 0.0204000i | ||||
\(498\) | −13.6133 | + | 18.4941i | −0.610028 | + | 0.828742i | ||||
\(499\) | −1.16452 | + | 2.01701i | −0.0521310 | + | 0.0902936i | −0.890913 | − | 0.454173i | \(-0.849935\pi\) |
0.838782 | + | 0.544467i | \(0.183268\pi\) | |||||||
\(500\) | −5.81521 | − | 10.0722i | −0.260064 | − | 0.450445i | ||||
\(501\) | −1.36100 | + | 12.2176i | −0.0608051 | + | 0.545840i | ||||
\(502\) | 5.12011 | + | 2.95610i | 0.228522 | + | 0.131937i | ||||
\(503\) | 22.7572 | 1.01469 | 0.507346 | − | 0.861742i | \(-0.330627\pi\) | ||||
0.507346 | + | 0.861742i | \(0.330627\pi\) | |||||||
\(504\) | 7.92480 | + | 0.444493i | 0.352999 | + | 0.0197993i | ||||
\(505\) | −8.48710 | −0.377671 | ||||||||
\(506\) | −2.66629 | − | 1.53939i | −0.118531 | − | 0.0684340i | ||||
\(507\) | −1.98029 | + | 17.7768i | −0.0879476 | + | 0.789495i | ||||
\(508\) | 2.08661 | + | 3.61412i | 0.0925785 | + | 0.160351i | ||||
\(509\) | −0.500517 | + | 0.866921i | −0.0221850 | + | 0.0384256i | −0.876905 | − | 0.480664i | \(-0.840396\pi\) |
0.854720 | + | 0.519090i | \(0.173729\pi\) | |||||||
\(510\) | 3.72527 | − | 5.06089i | 0.164958 | − | 0.224100i | ||||
\(511\) | 12.6302 | + | 15.3203i | 0.558726 | + | 0.677729i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0.102463 | − | 0.0888525i | 0.00452384 | − | 0.00392293i | ||||
\(514\) | −0.785311 | + | 0.453399i | −0.0346386 | + | 0.0199986i | ||||
\(515\) | −16.6048 | + | 9.58676i | −0.731693 | + | 0.422443i | ||||
\(516\) | −4.59638 | + | 2.01228i | −0.202344 | + | 0.0885855i | ||||
\(517\) | 9.41429i | 0.414040i | ||||||||
\(518\) | −17.8608 | − | 21.6650i | −0.784760 | − | 0.951906i | ||||
\(519\) | 16.0014 | + | 11.7785i | 0.702384 | + | 0.517017i | ||||
\(520\) | 3.62639 | − | 6.28109i | 0.159028 | − | 0.275444i | ||||
\(521\) | 8.70230 | + | 15.0728i | 0.381255 | + | 0.660353i | 0.991242 | − | 0.132059i | \(-0.0421587\pi\) |
−0.609987 | + | 0.792411i | \(0.708825\pi\) | |||||||
\(522\) | 7.65048 | − | 8.28704i | 0.334853 | − | 0.362714i | ||||
\(523\) | 23.8522 | + | 13.7710i | 1.04298 | + | 0.602166i | 0.920676 | − | 0.390327i | \(-0.127638\pi\) |
0.122305 | + | 0.992493i | \(0.460971\pi\) | |||||||
\(524\) | 9.29225 | 0.405934 | ||||||||
\(525\) | −6.87792 | − | 10.5322i | −0.300177 | − | 0.459662i | ||||
\(526\) | −29.0320 | −1.26585 | ||||||||
\(527\) | −12.2893 | − | 7.09524i | −0.535331 | − | 0.309074i | ||||
\(528\) | −5.29980 | − | 0.590384i | −0.230644 | − | 0.0256932i | ||||
\(529\) | 0.500000 | + | 0.866025i | 0.0217391 | + | 0.0376533i | ||||
\(530\) | −8.45211 | + | 14.6395i | −0.367136 | + | 0.635898i | ||||
\(531\) | 6.63190 | + | 21.3093i | 0.287800 | + | 0.924746i | ||||
\(532\) | −0.0681079 | + | 0.0114004i | −0.00295285 | + | 0.000494269i | ||||
\(533\) | 6.20172i | 0.268626i | ||||||||
\(534\) | −9.36957 | − | 21.4017i | −0.405461 | − | 0.926142i | ||||
\(535\) | 5.51907 | − | 3.18643i | 0.238610 | − | 0.137762i | ||||
\(536\) | 3.75630 | − | 2.16870i | 0.162247 | − | 0.0936735i | ||||
\(537\) | −10.6587 | − | 24.3462i | −0.459955 | − | 1.05061i | ||||
\(538\) | − | 28.5981i | − | 1.23295i | ||||||
\(539\) | 14.1376 | − | 16.2663i | 0.608948 | − | 0.700638i | ||||
\(540\) | 2.54929 | − | 7.37474i | 0.109704 | − | 0.317358i | ||||
\(541\) | 0.142989 | − | 0.247665i | 0.00614759 | − | 0.0106479i | −0.862935 | − | 0.505315i | \(-0.831376\pi\) |
0.869083 | + | 0.494667i | \(0.164710\pi\) | |||||||
\(542\) | −8.16593 | − | 14.1438i | −0.350757 | − | 0.607529i | ||||
\(543\) | −27.4355 | − | 3.05623i | −1.17737 | − | 0.131156i | ||||
\(544\) | 2.09237 | + | 1.20803i | 0.0897097 | + | 0.0517939i | ||||
\(545\) | 25.0010 | 1.07092 | ||||||||
\(546\) | 9.99781 | − | 19.7461i | 0.427867 | − | 0.845056i | ||||
\(547\) | 15.1321 | 0.647000 | 0.323500 | − | 0.946228i | \(-0.395140\pi\) | ||||
0.323500 | + | 0.946228i | \(0.395140\pi\) | |||||||
\(548\) | −9.67776 | − | 5.58745i | −0.413413 | − | 0.238684i | ||||
\(549\) | 10.0623 | + | 9.28934i | 0.429447 | + | 0.396459i | ||||
\(550\) | 4.22557 | + | 7.31890i | 0.180179 | + | 0.312079i | ||||
\(551\) | −0.0490625 | + | 0.0849787i | −0.00209013 | + | 0.00362022i | ||||
\(552\) | 1.39490 | + | 1.02677i | 0.0593708 | + | 0.0437022i | ||||
\(553\) | −11.7420 | − | 4.38958i | −0.499322 | − | 0.186664i | ||||
\(554\) | 14.5919i | 0.619948i | ||||||||
\(555\) | −25.2859 | + | 11.0701i | −1.07333 | + | 0.469899i | ||||
\(556\) | 14.1891 | − | 8.19210i | 0.601754 | − | 0.347423i | ||||
\(557\) | −11.3641 | + | 6.56106i | −0.481512 | + | 0.278001i | −0.721046 | − | 0.692887i | \(-0.756339\pi\) |
0.239535 | + | 0.970888i | \(0.423005\pi\) | |||||||
\(558\) | −17.1882 | − | 3.87756i | −0.727636 | − | 0.164150i | ||||
\(559\) | 13.9914i | 0.591773i | ||||||||
\(560\) | −3.06560 | + | 2.52731i | −0.129545 | + | 0.106798i | ||||
\(561\) | −7.63763 | + | 10.3760i | −0.322461 | + | 0.438073i | ||||
\(562\) | 4.01708 | − | 6.95778i | 0.169450 | − | 0.293496i | ||||
\(563\) | 22.3405 | + | 38.6949i | 0.941541 | + | 1.63080i | 0.762532 | + | 0.646950i | \(0.223956\pi\) |
0.179009 | + | 0.983847i | \(0.442711\pi\) | |||||||
\(564\) | 0.586364 | − | 5.26372i | 0.0246904 | − | 0.221643i | ||||
\(565\) | 21.7852 | + | 12.5777i | 0.916511 | + | 0.529148i | ||||
\(566\) | 1.52609 | 0.0641464 | ||||||||
\(567\) | 6.53267 | − | 22.8981i | 0.274346 | − | 0.961631i | ||||
\(568\) | −1.04121 | −0.0436882 | ||||||||
\(569\) | 5.55223 | + | 3.20558i | 0.232762 | + | 0.134385i | 0.611845 | − | 0.790977i | \(-0.290427\pi\) |
−0.379084 | + | 0.925362i | \(0.623761\pi\) | |||||||
\(570\) | −0.00751591 | + | 0.0674695i | −0.000314807 | + | 0.00282598i | ||||
\(571\) | 9.50704 | + | 16.4667i | 0.397857 | + | 0.689109i | 0.993461 | − | 0.114169i | \(-0.0364206\pi\) |
−0.595604 | + | 0.803278i | \(0.703087\pi\) | |||||||
\(572\) | −7.43492 | + | 12.8777i | −0.310869 | + | 0.538442i | ||||
\(573\) | 0.987548 | − | 1.34161i | 0.0412554 | − | 0.0560468i | ||||
\(574\) | 1.18962 | − | 3.18220i | 0.0496537 | − | 0.132822i | ||||
\(575\) | − | 2.74497i | − | 0.114473i | ||||||
\(576\) | 2.92646 | + | 0.660191i | 0.121936 | + | 0.0275080i | ||||
\(577\) | −22.8071 | + | 13.1677i | −0.949472 | + | 0.548178i | −0.892917 | − | 0.450222i | \(-0.851345\pi\) |
−0.0565550 | + | 0.998399i | \(0.518012\pi\) | |||||||
\(578\) | −9.66713 | + | 5.58132i | −0.402100 | + | 0.232152i | ||||
\(579\) | −5.48554 | + | 2.40155i | −0.227971 | + | 0.0998050i | ||||
\(580\) | 5.64555i | 0.234419i | ||||||||
\(581\) | −5.79111 | − | 34.5971i | −0.240256 | − | 1.43533i | ||||
\(582\) | −13.3305 | − | 9.81244i | −0.552567 | − | 0.406739i | ||||
\(583\) | 17.3287 | − | 30.0142i | 0.717682 | − | 1.24306i | ||||
\(584\) | 3.75229 | + | 6.49916i | 0.155271 | + | 0.268937i | ||||
\(585\) | −15.9872 | − | 14.7592i | −0.660991 | − | 0.610218i | ||||
\(586\) | −18.5011 | − | 10.6816i | −0.764275 | − | 0.441254i | ||||
\(587\) | −16.7095 | −0.689675 | −0.344838 | − | 0.938662i | \(-0.612066\pi\) | ||||
−0.344838 | + | 0.938662i | \(0.612066\pi\) | |||||||
\(588\) | −8.91774 | + | 8.21425i | −0.367761 | + | 0.338750i | ||||
\(589\) | 0.153298 | 0.00631655 | ||||||||
\(590\) | −9.67453 | − | 5.58559i | −0.398294 | − | 0.229955i | ||||
\(591\) | −21.1158 | − | 2.35224i | −0.868588 | − | 0.0967584i | ||||
\(592\) | −5.30627 | − | 9.19073i | −0.218086 | − | 0.377737i | ||||
\(593\) | −19.7393 | + | 34.1895i | −0.810596 | + | 1.40399i | 0.101852 | + | 0.994800i | \(0.467523\pi\) |
−0.912448 | + | 0.409193i | \(0.865810\pi\) | |||||||
\(594\) | −5.22662 | + | 15.1199i | −0.214451 | + | 0.620376i | ||||
\(595\) | 1.58473 | + | 9.46744i | 0.0649675 | + | 0.388127i | ||||
\(596\) | 1.08515i | 0.0444494i | ||||||||
\(597\) | 16.8910 | + | 38.5819i | 0.691303 | + | 1.57905i | ||||
\(598\) | 4.18273 | − | 2.41490i | 0.171044 | − | 0.0987525i | ||||
\(599\) | 35.6684 | − | 20.5931i | 1.45737 | − | 0.841413i | 0.458488 | − | 0.888700i | \(-0.348391\pi\) |
0.998881 | + | 0.0472876i | \(0.0150577\pi\) | |||||||
\(600\) | −1.90675 | − | 4.35534i | −0.0778427 | − | 0.177806i | ||||
\(601\) | 35.7074i | 1.45654i | 0.685292 | + | 0.728269i | \(0.259675\pi\) | ||||
−0.685292 | + | 0.728269i | \(0.740325\pi\) | |||||||
\(602\) | 2.68384 | − | 7.17920i | 0.109385 | − | 0.292602i | ||||
\(603\) | −3.86673 | − | 12.4244i | −0.157465 | − | 0.505960i | ||||
\(604\) | 8.61605 | − | 14.9234i | 0.350582 | − | 0.607226i | ||||
\(605\) | −1.14215 | − | 1.97827i | −0.0464352 | − | 0.0804281i | ||||
\(606\) | −9.72895 | − | 1.08378i | −0.395212 | − | 0.0440255i | ||||
\(607\) | −29.6896 | − | 17.1413i | −1.20507 | − | 0.695745i | −0.243388 | − | 0.969929i | \(-0.578259\pi\) |
−0.961677 | + | 0.274184i | \(0.911592\pi\) | |||||||
\(608\) | −0.0261005 | −0.00105851 | ||||||||
\(609\) | 0.945522 | + | 17.2023i | 0.0383145 | + | 0.697071i | ||||
\(610\) | −6.85492 | −0.277548 | ||||||||
\(611\) | −12.7900 | − | 7.38429i | −0.517427 | − | 0.298736i | ||||
\(612\) | 4.91662 | − | 5.32570i | 0.198742 | − | 0.215279i | ||||
\(613\) | −12.7418 | − | 22.0694i | −0.514636 | − | 0.891376i | −0.999856 | − | 0.0169837i | \(-0.994594\pi\) |
0.485220 | − | 0.874392i | \(-0.338740\pi\) | |||||||
\(614\) | 9.46438 | − | 16.3928i | 0.381951 | − | 0.661559i | ||||
\(615\) | −2.68969 | − | 1.97985i | −0.108459 | − | 0.0798354i | ||||
\(616\) | 6.28517 | − | 5.18155i | 0.253237 | − | 0.208771i | ||||
\(617\) | 22.0558i | 0.887932i | 0.896044 | + | 0.443966i | \(0.146429\pi\) | ||||
−0.896044 | + | 0.443966i | \(0.853571\pi\) | |||||||
\(618\) | −20.2586 | + | 8.86914i | −0.814921 | + | 0.356769i | ||||
\(619\) | 23.6169 | − | 13.6352i | 0.949244 | − | 0.548046i | 0.0563982 | − | 0.998408i | \(-0.482038\pi\) |
0.892846 | + | 0.450362i | \(0.148705\pi\) | |||||||
\(620\) | 7.63828 | − | 4.40996i | 0.306761 | − | 0.177108i | ||||
\(621\) | 3.92570 | − | 3.40425i | 0.157533 | − | 0.136608i | ||||
\(622\) | 2.21642i | 0.0888702i | ||||||||
\(623\) | 33.4278 | + | 12.4965i | 1.33926 | + | 0.500662i | ||||
\(624\) | 4.95909 | − | 6.73708i | 0.198522 | − | 0.269699i | ||||
\(625\) | 1.87013 | − | 3.23916i | 0.0748051 | − | 0.129566i | ||||
\(626\) | −2.96585 | − | 5.13701i | −0.118539 | − | 0.205316i | ||||
\(627\) | 0.0154093 | − | 0.138328i | 0.000615389 | − | 0.00552427i | ||||
\(628\) | 9.16009 | + | 5.28858i | 0.365527 | + | 0.211037i | ||||
\(629\) | −25.6406 | −1.02236 | ||||||||
\(630\) | 5.37218 | + | 10.6398i | 0.214033 | + | 0.423902i | ||||
\(631\) | 27.3740 | 1.08974 | 0.544871 | − | 0.838520i | \(-0.316579\pi\) | ||||
0.544871 | + | 0.838520i | \(0.316579\pi\) | |||||||
\(632\) | −4.10327 | − | 2.36902i | −0.163219 | − | 0.0942347i | ||||
\(633\) | −4.69594 | + | 42.1549i | −0.186647 | + | 1.67551i | ||||
\(634\) | 13.9123 | + | 24.0968i | 0.552527 | + | 0.957005i | ||||
\(635\) | −3.13341 | + | 5.42723i | −0.124346 | + | 0.215373i | ||||
\(636\) | −11.5583 | + | 15.7022i | −0.458315 | + | 0.622635i | ||||
\(637\) | 11.0098 | + | 31.9657i | 0.436223 | + | 1.26653i | ||||
\(638\) | − | 11.5747i | − | 0.458245i | ||||||
\(639\) | −0.687397 | + | 3.04705i | −0.0271930 | + | 0.120540i | ||||
\(640\) | −1.30049 | + | 0.750837i | −0.0514063 | + | 0.0296795i | ||||
\(641\) | 14.5096 | − | 8.37714i | 0.573096 | − | 0.330877i | −0.185289 | − | 0.982684i | \(-0.559322\pi\) |
0.758385 | + | 0.651807i | \(0.225989\pi\) | |||||||
\(642\) | 6.73353 | − | 2.94791i | 0.265751 | − | 0.116345i | ||||
\(643\) | 5.70826i | 0.225112i | 0.993645 | + | 0.112556i | \(0.0359038\pi\) | ||||
−0.993645 | + | 0.112556i | \(0.964096\pi\) | |||||||
\(644\) | −2.60945 | + | 0.436788i | −0.102827 | + | 0.0172119i | ||||
\(645\) | −6.06807 | − | 4.46664i | −0.238930 | − | 0.175874i | ||||
\(646\) | −0.0315302 | + | 0.0546120i | −0.00124054 | + | 0.00214868i | ||||
\(647\) | −11.3024 | − | 19.5763i | −0.444344 | − | 0.769626i | 0.553663 | − | 0.832741i | \(-0.313230\pi\) |
−0.998006 | + | 0.0631154i | \(0.979896\pi\) | |||||||
\(648\) | 3.86404 | − | 8.12830i | 0.151794 | − | 0.319310i | ||||
\(649\) | 19.8350 | + | 11.4517i | 0.778591 | + | 0.449519i | ||||
\(650\) | −13.2577 | −0.520008 | ||||||||
\(651\) | 22.5356 | − | 14.7166i | 0.883239 | − | 0.576790i | ||||
\(652\) | −2.27091 | −0.0889357 | ||||||||
\(653\) | −20.3703 | − | 11.7608i | −0.797152 | − | 0.460236i | 0.0453224 | − | 0.998972i | \(-0.485568\pi\) |
−0.842474 | + | 0.538737i | \(0.818902\pi\) | |||||||
\(654\) | 28.6592 | + | 3.19255i | 1.12066 | + | 0.124839i | ||||
\(655\) | 6.97697 | + | 12.0845i | 0.272613 | + | 0.472179i | ||||
\(656\) | 0.642028 | − | 1.11202i | 0.0250670 | − | 0.0434173i | ||||
\(657\) | 21.4968 | − | 6.69023i | 0.838668 | − | 0.261011i | ||||
\(658\) | 5.14627 | + | 6.24237i | 0.200622 | + | 0.243353i | ||||
\(659\) | − | 17.1234i | − | 0.667035i | −0.942744 | − | 0.333517i | \(-0.891764\pi\) | ||
0.942744 | − | 0.333517i | \(-0.108236\pi\) | |||||||
\(660\) | −3.21150 | − | 7.33562i | −0.125008 | − | 0.285538i | ||||
\(661\) | 2.75291 | − | 1.58939i | 0.107076 | − | 0.0618202i | −0.445506 | − | 0.895279i | \(-0.646976\pi\) |
0.552581 | + | 0.833459i | \(0.313643\pi\) | |||||||
\(662\) | 17.4805 | − | 10.0924i | 0.679399 | − | 0.392251i | ||||
\(663\) | −8.10573 | − | 18.5149i | −0.314801 | − | 0.719058i | ||||
\(664\) | − | 13.2584i | − | 0.514526i | ||||||
\(665\) | −0.0659640 | − | 0.0800137i | −0.00255797 | − | 0.00310280i | ||||
\(666\) | −30.3994 | + | 9.46094i | −1.17795 | + | 0.366604i | ||||
\(667\) | −1.87975 | + | 3.25583i | −0.0727843 | + | 0.126066i | ||||
\(668\) | −3.54872 | − | 6.14656i | −0.137304 | − | 0.237818i | ||||
\(669\) | −44.3178 | − | 4.93688i | −1.71342 | − | 0.190871i | ||||
\(670\) | 5.64073 | + | 3.25668i | 0.217921 | + | 0.125817i | ||||
\(671\) | 14.0541 | 0.542554 | ||||||||
\(672\) | −3.83689 | + | 2.50564i | −0.148011 | + | 0.0966572i | ||||
\(673\) | 43.2475 | 1.66707 | 0.833534 | − | 0.552468i | \(-0.186314\pi\) | ||||
0.833534 | + | 0.552468i | \(0.186314\pi\) | |||||||
\(674\) | 29.8324 | + | 17.2238i | 1.14910 | + | 0.663434i | ||||
\(675\) | −14.0045 | + | 2.70466i | −0.539034 | + | 0.104103i | ||||
\(676\) | −5.16346 | − | 8.94338i | −0.198595 | − | 0.343976i | ||||
\(677\) | 15.1682 | − | 26.2721i | 0.582961 | − | 1.00972i | −0.412166 | − | 0.911109i | \(-0.635228\pi\) |
0.995126 | − | 0.0986085i | \(-0.0314392\pi\) | |||||||
\(678\) | 23.3668 | + | 17.2000i | 0.897395 | + | 0.660563i | ||||
\(679\) | 24.9375 | − | 4.17421i | 0.957012 | − | 0.160192i | ||||
\(680\) | 3.62814i | 0.139133i | ||||||||
\(681\) | −12.0916 | + | 5.29364i | −0.463350 | + | 0.202853i | ||||
\(682\) | −15.6602 | + | 9.04141i | −0.599659 | + | 0.346214i | ||||
\(683\) | 25.9506 | − | 14.9826i | 0.992972 | − | 0.573293i | 0.0868107 | − | 0.996225i | \(-0.472332\pi\) |
0.906161 | + | 0.422932i | \(0.138999\pi\) | |||||||
\(684\) | −0.0172313 | + | 0.0763820i | −0.000658856 | + | 0.00292054i | ||||
\(685\) | − | 16.7811i | − | 0.641172i | ||||||
\(686\) | 0.482396 | − | 18.5140i | 0.0184180 | − | 0.706867i | ||||
\(687\) | −6.59749 | + | 8.96289i | −0.251710 | + | 0.341956i | ||||
\(688\) | 1.44845 | − | 2.50878i | 0.0552215 | − | 0.0956464i | ||||
\(689\) | 27.1843 | + | 47.0846i | 1.03564 | + | 1.79378i | ||||
\(690\) | −0.287961 | + | 2.58499i | −0.0109625 | + | 0.0984088i | ||||
\(691\) | 3.94753 | + | 2.27911i | 0.150171 | + | 0.0867014i | 0.573203 | − | 0.819414i | \(-0.305701\pi\) |
−0.423032 | + | 0.906115i | \(0.639034\pi\) | |||||||
\(692\) | −11.4714 | −0.436076 | ||||||||
\(693\) | −11.0142 | − | 21.8141i | −0.418394 | − | 0.828648i | ||||
\(694\) | −19.1429 | −0.726656 | ||||||||
\(695\) | 21.3075 | + | 12.3019i | 0.808238 | + | 0.466637i | ||||
\(696\) | −0.720921 | + | 6.47162i | −0.0273265 | + | 0.245306i | ||||
\(697\) | −1.55118 | − | 2.68672i | −0.0587551 | − | 0.101767i | ||||
\(698\) | −10.5507 | + | 18.2744i | −0.399351 | + | 0.691696i | ||||
\(699\) | −21.6945 | + | 29.4726i | −0.820559 | + | 1.11476i | ||||
\(700\) | 6.80271 | + | 2.54309i | 0.257118 | + | 0.0961198i | ||||
\(701\) | − | 16.6012i | − | 0.627017i | −0.949585 | − | 0.313508i | \(-0.898496\pi\) | ||
0.949585 | − | 0.313508i | \(-0.101504\pi\) | |||||||
\(702\) | −16.4418 | − | 18.9603i | −0.620556 | − | 0.715611i | ||||
\(703\) | 0.239883 | − | 0.138496i | 0.00904735 | − | 0.00522349i | ||||
\(704\) | 2.66629 | − | 1.53939i | 0.100490 | − | 0.0580178i | ||||
\(705\) | 7.28567 | − | 3.18964i | 0.274394 | − | 0.120129i | ||||
\(706\) | − | 18.2678i | − | 0.687518i | ||||||
\(707\) | 11.5378 | − | 9.51187i | 0.433924 | − | 0.357731i | ||||
\(708\) | −10.3769 | − | 7.63830i | −0.389987 | − | 0.287065i | ||||
\(709\) | 23.8810 | − | 41.3630i | 0.896868 | − | 1.55342i | 0.0653929 | − | 0.997860i | \(-0.479170\pi\) |
0.831475 | − | 0.555562i | \(-0.187497\pi\) | |||||||
\(710\) | −0.781779 | − | 1.35408i | −0.0293396 | − | 0.0508177i | ||||
\(711\) | −9.64178 | + | 10.4440i | −0.361595 | + | 0.391682i | ||||
\(712\) | 11.6814 | + | 6.74426i | 0.437779 | + | 0.252752i | ||||
\(713\) | 5.87339 | 0.219960 | ||||||||
\(714\) | 0.607644 | + | 11.0551i | 0.0227405 | + | 0.413727i | ||||
\(715\) | −22.3296 | −0.835081 | ||||||||
\(716\) | 13.2886 | + | 7.67215i | 0.496616 | + | 0.286722i | ||||
\(717\) | −5.24134 | − | 0.583871i | −0.195742 | − | 0.0218051i | ||||
\(718\) | 12.0760 | + | 20.9162i | 0.450672 | + | 0.780586i | ||||
\(719\) | 9.60627 | − | 16.6385i | 0.358253 | − | 0.620513i | −0.629416 | − | 0.777069i | \(-0.716706\pi\) |
0.987669 | + | 0.156556i | \(0.0500390\pi\) | |||||||
\(720\) | 1.33872 | + | 4.30152i | 0.0498912 | + | 0.160308i | ||||
\(721\) | 11.8291 | − | 31.6424i | 0.440537 | − | 1.17843i | ||||
\(722\) | 18.9993i | 0.707081i | ||||||||
\(723\) | −14.4264 | − | 32.9524i | −0.536525 | − | 1.22551i | ||||
\(724\) | 13.8026 | − | 7.96892i | 0.512969 | − | 0.296163i | ||||
\(725\) | 8.93716 | − | 5.15987i | 0.331918 | − | 0.191633i | ||||
\(726\) | −1.05666 | − | 2.41358i | −0.0392162 | − | 0.0895765i | ||||
\(727\) | 35.8705i | 1.33036i | 0.746682 | + | 0.665181i | \(0.231646\pi\) | ||||
−0.746682 | + | 0.665181i | \(0.768354\pi\) | |||||||
\(728\) | 2.10960 | + | 12.6031i | 0.0781869 | + | 0.467102i | ||||
\(729\) | −21.2361 | − | 16.6742i | −0.786522 | − | 0.617562i | ||||
\(730\) | −5.63472 | + | 9.75963i | −0.208551 | + | 0.361220i | ||||
\(731\) | −3.49954 | − | 6.06137i | −0.129435 | − | 0.224188i | ||||
\(732\) | −7.85795 | − | 0.875354i | −0.290438 | − | 0.0323540i | ||||
\(733\) | 7.73979 | + | 4.46857i | 0.285876 | + | 0.165050i | 0.636080 | − | 0.771623i | \(-0.280555\pi\) |
−0.350205 | + | 0.936673i | \(0.613888\pi\) | |||||||
\(734\) | 0.478167 | 0.0176495 | ||||||||
\(735\) | −17.3783 | − | 5.42985i | −0.641009 | − | 0.200283i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −11.5648 | − | 6.67693i | −0.425994 | − | 0.245948i | ||||
\(738\) | −2.83043 | − | 2.61301i | −0.104190 | − | 0.0961864i | ||||
\(739\) | −27.1059 | − | 46.9488i | −0.997106 | − | 1.72704i | −0.564394 | − | 0.825506i | \(-0.690890\pi\) |
−0.432712 | − | 0.901532i | \(-0.642443\pi\) | |||||||
\(740\) | 7.96830 | − | 13.8015i | 0.292920 | − | 0.507353i | ||||
\(741\) | 0.175841 | + | 0.129435i | 0.00645968 | + | 0.00475490i | ||||
\(742\) | −4.91688 | − | 29.3743i | −0.180504 | − | 1.07836i | ||||
\(743\) | 19.6002i | 0.719060i | 0.933134 | + | 0.359530i | \(0.117063\pi\) | ||||
−0.933134 | + | 0.359530i | \(0.882937\pi\) | |||||||
\(744\) | 9.31907 | − | 4.07985i | 0.341654 | − | 0.149575i | ||||
\(745\) | −1.41122 | + | 0.814770i | −0.0517032 | + | 0.0298509i | ||||
\(746\) | −1.74035 | + | 1.00479i | −0.0637186 | + | 0.0367880i | ||||
\(747\) | −38.8001 | − | 8.75308i | −1.41962 | − | 0.320258i | ||||
\(748\) | − | 7.43850i | − | 0.271979i | ||||||
\(749\) | −3.93173 | + | 10.5173i | −0.143662 | + | 0.384293i | ||||
\(750\) | 11.9418 | − | 16.2233i | 0.436052 | − | 0.592390i | ||||
\(751\) | 12.4601 | − | 21.5814i | 0.454674 | − | 0.787518i | −0.543996 | − | 0.839088i | \(-0.683089\pi\) |
0.998669 | + | 0.0515700i | \(0.0164225\pi\) | |||||||
\(752\) | 1.52890 | + | 2.64814i | 0.0557534 | + | 0.0965677i | ||||
\(753\) | −1.13372 | + | 10.1773i | −0.0413150 | + | 0.370880i | ||||
\(754\) | 15.7250 | + | 9.07882i | 0.572670 | + | 0.330631i | ||||
\(755\) | 25.8770 | 0.941761 | ||||||||
\(756\) | 4.79957 | + | 12.8827i | 0.174559 | + | 0.468540i | ||||
\(757\) | −40.1278 | −1.45847 | −0.729235 | − | 0.684263i | \(-0.760124\pi\) | ||||
−0.729235 | + | 0.684263i | \(0.760124\pi\) | |||||||
\(758\) | 17.2566 | + | 9.96310i | 0.626788 | + | 0.361876i | ||||
\(759\) | 0.590384 | − | 5.29980i | 0.0214296 | − | 0.192371i | ||||
\(760\) | −0.0195972 | − | 0.0339434i | −0.000710866 | − | 0.00123126i | ||||
\(761\) | −22.1654 | + | 38.3916i | −0.803494 | + | 1.39169i | 0.113809 | + | 0.993503i | \(0.463695\pi\) |
−0.917303 | + | 0.398190i | \(0.869638\pi\) | |||||||
\(762\) | −4.28494 | + | 5.82123i | −0.155227 | + | 0.210881i | ||||
\(763\) | −33.9876 | + | 28.0197i | −1.23043 | + | 1.01438i | ||||
\(764\) | 0.961801i | 0.0347967i | ||||||||
\(765\) | 10.6176 | + | 2.39527i | 0.383880 | + | 0.0866010i | ||||
\(766\) | 17.3567 | − | 10.0209i | 0.627123 | − | 0.362069i | ||||
\(767\) | −31.1159 | + | 17.9648i | −1.12353 | + | 0.648671i | ||||
\(768\) | −1.58666 | + | 0.694633i | −0.0572536 | + | 0.0250654i | ||||
\(769\) | 35.6919i | 1.28708i | 0.765411 | + | 0.643542i | \(0.222536\pi\) | ||||
−0.765411 | + | 0.643542i | \(0.777464\pi\) | |||||||
\(770\) | 11.4577 | + | 4.28329i | 0.412906 | + | 0.154359i | ||||
\(771\) | −1.26489 | − | 0.931074i | −0.0455540 | − | 0.0335318i | ||||
\(772\) | 1.72865 | − | 2.99410i | 0.0622153 | − | 0.107760i | ||||
\(773\) | 8.81138 | + | 15.2618i | 0.316923 | + | 0.548927i | 0.979844 | − | 0.199762i | \(-0.0640169\pi\) |
−0.662921 | + | 0.748689i | \(0.730684\pi\) | |||||||
\(774\) | −6.38559 | − | 5.89509i | −0.229525 | − | 0.211895i | ||||
\(775\) | −13.9623 | − | 8.06115i | −0.501542 | − | 0.289565i | ||||
\(776\) | 9.55661 | 0.343062 | ||||||||
\(777\) | 21.9683 | − | 43.3883i | 0.788107 | − | 1.55655i | ||||
\(778\) | 17.2000 | 0.616651 | ||||||||
\(779\) | 0.0290244 | + | 0.0167572i | 0.00103991 | + | 0.000600390i | ||||
\(780\) | 12.4850 | + | 1.39079i | 0.447033 | + | 0.0497983i | ||||
\(781\) | 1.60282 | + | 2.77617i | 0.0573535 | + | 0.0993392i | ||||
\(782\) | −1.20803 | + | 2.09237i | −0.0431991 | + | 0.0748231i | ||||
\(783\) | 18.4630 | + | 6.38225i | 0.659813 | + | 0.228083i | ||||
\(784\) | 1.33507 | − | 6.87151i | 0.0476810 | − | 0.245411i | ||||
\(785\) | 15.8835i | 0.566905i | ||||||||
\(786\) | 6.45470 | + | 14.7436i | 0.230232 | + | 0.525888i | ||||
\(787\) | −16.1818 | + | 9.34255i | −0.576818 | + | 0.333026i | −0.759868 | − | 0.650078i | \(-0.774736\pi\) |
0.183050 | + | 0.983104i | \(0.441403\pi\) | |||||||
\(788\) | 10.6232 | − | 6.13331i | 0.378436 | − | 0.218490i | ||||
\(789\) | −20.1666 | − | 46.0638i | −0.717949 | − | 1.63992i | ||||
\(790\) | − | 7.11500i | − | 0.253140i | ||||||
\(791\) | −43.7123 | + | 7.31689i | −1.55423 | + | 0.260159i | ||||
\(792\) | −2.74468 | − | 8.81908i | −0.0975280 | − | 0.313372i | ||||
\(793\) | −11.0236 | + | 19.0935i | −0.391461 | + | 0.678031i | ||||
\(794\) | −10.1766 | − | 17.6264i | −0.361155 | − | 0.625538i | ||||
\(795\) | −29.0990 | − | 3.24154i | −1.03203 | − | 0.114966i | ||||
\(796\) | −21.0587 | − | 12.1582i | −0.746404 | − | 0.430937i | ||||
\(797\) | 29.7695 | 1.05449 | 0.527245 | − | 0.849714i | \(-0.323225\pi\) | ||||
0.527245 | + | 0.849714i | \(0.323225\pi\) | |||||||
\(798\) | −0.0653985 | − | 0.100145i | −0.00231508 | − | 0.00354509i | ||||
\(799\) | 7.38785 | 0.261364 | ||||||||
\(800\) | 2.37722 | + | 1.37249i | 0.0840473 | + | 0.0485247i | ||||
\(801\) | 27.4488 | − | 29.7326i | 0.969854 | − | 1.05055i | ||||
\(802\) | −0.878732 | − | 1.52201i | −0.0310291 | − | 0.0537440i | ||||
\(803\) | 11.5525 | − | 20.0094i | 0.407677 | − | 0.706117i | ||||
\(804\) | 6.05023 | + | 4.45351i | 0.213375 | + | 0.157063i | ||||
\(805\) | −2.52731 | − | 3.06560i | −0.0890759 | − | 0.108048i | ||||
\(806\) | − | 28.3673i | − | 0.999195i | ||||||
\(807\) | 45.3753 | − | 19.8651i | 1.59729 | − | 0.699286i | ||||
\(808\) | 4.89457 | − | 2.82588i | 0.172190 | − | 0.0994141i | ||||
\(809\) | −33.7407 | + | 19.4802i | −1.18626 | + | 0.684888i | −0.957455 | − | 0.288584i | \(-0.906816\pi\) |
−0.228806 | + | 0.973472i | \(0.573482\pi\) | |||||||
\(810\) | 13.4720 | − | 1.07789i | 0.473359 | − | 0.0378731i | ||||
\(811\) | − | 37.3800i | − | 1.31259i | −0.754505 | − | 0.656295i | \(-0.772123\pi\) | ||
0.754505 | − | 0.656295i | \(-0.227877\pi\) | |||||||
\(812\) | −6.32722 | − | 7.67486i | −0.222042 | − | 0.269335i | ||||
\(813\) | 16.7691 | − | 22.7813i | 0.588117 | − | 0.798975i | ||||
\(814\) | −16.3368 | + | 28.2962i | −0.572604 | + | 0.991780i | ||||
\(815\) | −1.70508 | − | 2.95329i | −0.0597265 | − | 0.103449i | ||||
\(816\) | −0.463303 | + | 4.15902i | −0.0162189 | + | 0.145595i | ||||
\(817\) | 0.0654804 | + | 0.0378051i | 0.00229087 | + | 0.00132263i | ||||
\(818\) | 20.1871 | 0.705827 | ||||||||
\(819\) | 38.2752 | + | 2.14681i | 1.33744 | + | 0.0750156i | ||||
\(820\) | 1.92823 | 0.0673368 | ||||||||
\(821\) | −18.2842 | − | 10.5564i | −0.638123 | − | 0.368420i | 0.145768 | − | 0.989319i | \(-0.453435\pi\) |
−0.783891 | + | 0.620899i | \(0.786768\pi\) | |||||||
\(822\) | 2.14290 | − | 19.2365i | 0.0747421 | − | 0.670951i | ||||
\(823\) | 22.7409 | + | 39.3883i | 0.792696 | + | 1.37299i | 0.924292 | + | 0.381687i | \(0.124657\pi\) |
−0.131596 | + | 0.991303i | \(0.542010\pi\) | |||||||
\(824\) | 6.38405 | − | 11.0575i | 0.222399 | − | 0.385206i | ||||
\(825\) | −8.67738 | + | 11.7885i | −0.302108 | + | 0.410423i | ||||
\(826\) | 19.4121 | − | 3.24933i | 0.675433 | − | 0.113059i | ||||
\(827\) | 44.9883i | 1.56440i | 0.623029 | + | 0.782199i | \(0.285902\pi\) | ||||
−0.623029 | + | 0.782199i | \(0.714098\pi\) | |||||||
\(828\) | −0.660191 | + | 2.92646i | −0.0229432 | + | 0.101701i | ||||
\(829\) | 26.5770 | − | 15.3442i | 0.923056 | − | 0.532927i | 0.0384475 | − | 0.999261i | \(-0.487759\pi\) |
0.884609 | + | 0.466334i | \(0.154425\pi\) | |||||||
\(830\) | 17.2424 | − | 9.95490i | 0.598492 | − | 0.345540i | ||||
\(831\) | −23.1523 | + | 10.1360i | −0.803144 | + | 0.351613i | ||||
\(832\) | 4.82980i | 0.167443i | ||||||||
\(833\) | −12.7649 | − | 11.0945i | −0.442279 | − | 0.384400i | ||||
\(834\) | 22.8543 | + | 16.8228i | 0.791380 | + | 0.582526i | ||||
\(835\) | 5.32902 | − | 9.23014i | 0.184418 | − | 0.319422i | ||||
\(836\) | 0.0401787 | + | 0.0695916i | 0.00138961 | + | 0.00240688i | ||||
\(837\) | −5.78714 | − | 29.9653i | −0.200033 | − | 1.03575i | ||||
\(838\) | 24.9877 | + | 14.4266i | 0.863185 | + | 0.498360i | ||||
\(839\) | 42.5498 | 1.46898 | 0.734492 | − | 0.678618i | \(-0.237421\pi\) | ||||
0.734492 | + | 0.678618i | \(0.237421\pi\) | |||||||
\(840\) | −6.13944 | − | 3.10851i | −0.211831 | − | 0.107254i | ||||
\(841\) | 14.8661 | 0.512625 | ||||||||
\(842\) | −7.86087 | − | 4.53848i | −0.270904 | − | 0.156406i | ||||
\(843\) | 13.8300 | + | 1.54063i | 0.476331 | + | 0.0530620i | ||||
\(844\) | −12.2443 | − | 21.2078i | −0.421467 | − | 0.730003i | ||||
\(845\) | 7.75384 | − | 13.4300i | 0.266740 | − | 0.462008i | ||||
\(846\) | 8.75903 | − | 2.72599i | 0.301142 | − | 0.0937215i | ||||
\(847\) | 3.76984 | + | 1.40930i | 0.129533 | + | 0.0484240i | ||||
\(848\) | − | 11.2569i | − | 0.386564i | ||||||
\(849\) | 1.06007 | + | 2.42138i | 0.0363816 | + | 0.0831017i | ||||
\(850\) | 5.74351 | − | 3.31601i | 0.197001 | − | 0.113738i | ||||
\(851\) | 9.19073 | − | 5.30627i | 0.315054 | − | 0.181897i | ||||
\(852\) | −0.723258 | − | 1.65204i | −0.0247784 | − | 0.0565981i | ||||
\(853\) | − | 47.6026i | − | 1.62988i | −0.579543 | − | 0.814942i | \(-0.696769\pi\) | ||
0.579543 | − | 0.814942i | \(-0.303231\pi\) | |||||||
\(854\) | 9.31893 | − | 7.68261i | 0.318887 | − | 0.262894i | ||||
\(855\) | −0.112272 | + | 0.0349413i | −0.00383961 | + | 0.00119497i | ||||
\(856\) | −2.12192 | + | 3.67527i | −0.0725258 | + | 0.125618i | ||||
\(857\) | −13.6167 | − | 23.5848i | −0.465137 | − | 0.805640i | 0.534071 | − | 0.845440i | \(-0.320662\pi\) |
−0.999208 | + | 0.0397992i | \(0.987328\pi\) | |||||||
\(858\) | −25.5970 | − | 2.85143i | −0.873866 | − | 0.0973463i | ||||
\(859\) | −38.4110 | − | 22.1766i | −1.31057 | − | 0.756656i | −0.328377 | − | 0.944547i | \(-0.606502\pi\) |
−0.982190 | + | 0.187891i | \(0.939835\pi\) | |||||||
\(860\) | 4.35019 | 0.148340 | ||||||||
\(861\) | 5.87541 | − | 0.322942i | 0.200234 | − | 0.0110058i | ||||
\(862\) | −10.0530 | −0.342407 | ||||||||
\(863\) | 38.1437 | + | 22.0223i | 1.29843 | + | 0.749647i | 0.980132 | − | 0.198345i | \(-0.0635567\pi\) |
0.318294 | + | 0.947992i | \(0.396890\pi\) | |||||||
\(864\) | 0.985315 | + | 5.10188i | 0.0335211 | + | 0.173569i | ||||
\(865\) | −8.61314 | − | 14.9184i | −0.292855 | − | 0.507241i | ||||
\(866\) | −3.60929 | + | 6.25147i | −0.122649 | + | 0.212434i | ||||
\(867\) | −15.5708 | − | 11.4615i | −0.528810 | − | 0.389252i | ||||
\(868\) | −5.44143 | + | 14.5557i | −0.184694 | + | 0.494052i | ||||
\(869\) | 14.5874i | 0.494842i | ||||||||
\(870\) | −8.95757 | + | 3.92159i | −0.303690 | + | 0.132954i | ||||
\(871\) | 18.1421 | − | 10.4744i | 0.614723 | − | 0.354911i | ||||
\(872\) | −14.4182 | + | 8.32436i | −0.488263 | + | 0.281899i | ||||
\(873\) | 6.30919 | − | 27.9670i | 0.213534 | − | 0.946540i | ||||
\(874\) | − | 0.0261005i | − | 0.000882862i | ||||||
\(875\) | 5.08003 | + | 30.3490i | 0.171736 | + | 1.02598i | ||||
\(876\) | −7.70549 | + | 10.4681i | −0.260344 | + | 0.353686i | ||||
\(877\) | −6.48935 | + | 11.2399i | −0.219130 | + | 0.379544i | −0.954542 | − | 0.298076i | \(-0.903655\pi\) |
0.735412 | + | 0.677620i | \(0.236988\pi\) | |||||||
\(878\) | −5.00288 | − | 8.66524i | −0.168839 | − | 0.292438i | ||||
\(879\) | 4.09661 | − | 36.7748i | 0.138175 | − | 1.24038i | ||||
\(880\) | 4.00391 | + | 2.31166i | 0.134972 | + | 0.0779259i | ||||
\(881\) | −10.5523 | −0.355515 | −0.177757 | − | 0.984074i | \(-0.556884\pi\) | ||||
−0.177757 | + | 0.984074i | \(0.556884\pi\) | |||||||
\(882\) | −19.2278 | − | 8.44352i | −0.647433 | − | 0.284308i | ||||
\(883\) | −31.6948 | −1.06661 | −0.533307 | − | 0.845922i | \(-0.679051\pi\) | ||||
−0.533307 | + | 0.845922i | \(0.679051\pi\) | |||||||
\(884\) | 10.1057 | + | 5.83455i | 0.339892 | + | 0.196237i | ||||
\(885\) | 2.14218 | − | 19.2301i | 0.0720087 | − | 0.646413i | ||||
\(886\) | 18.5430 | + | 32.1174i | 0.622964 | + | 1.07900i | ||||
\(887\) | 11.4688 | − | 19.8646i | 0.385086 | − | 0.666989i | −0.606695 | − | 0.794935i | \(-0.707505\pi\) |
0.991781 | + | 0.127946i | \(0.0408384\pi\) | |||||||
\(888\) | 10.8966 | − | 14.8034i | 0.365667 | − | 0.496771i | ||||
\(889\) | −1.82281 | − | 10.8898i | −0.0611352 | − | 0.365233i | ||||
\(890\) | 20.2554i | 0.678962i | ||||||||
\(891\) | −27.6207 | + | 2.20991i | −0.925327 | + | 0.0740348i | ||||
\(892\) | 22.2960 | − | 12.8726i | 0.746524 | − | 0.431006i | ||||
\(893\) | −0.0691177 | + | 0.0399051i | −0.00231294 | + | 0.00133537i | ||||
\(894\) | −1.72176 | + | 0.753780i | −0.0575843 | + | 0.0252102i | ||||
\(895\) | 23.0421i | 0.770214i | ||||||||
\(896\) | 0.926454 | − | 2.47824i | 0.0309507 | − | 0.0827922i | ||||
\(897\) | 6.73708 | + | 4.95909i | 0.224944 | + | 0.165579i | ||||
\(898\) | 18.8185 | − | 32.5947i | 0.627983 | − | 1.08770i | ||||
\(899\) | 11.0405 | + | 19.1228i | 0.368222 | + | 0.637779i | ||||
\(900\) | 5.58594 | − | 6.05072i | 0.186198 | − | 0.201691i | ||||
\(901\) | −23.5536 | − | 13.5987i | −0.784686 | − | 0.453038i | ||||
\(902\) | −3.95331 | −0.131631 | ||||||||
\(903\) | 13.2552 | − | 0.728573i | 0.441106 | − | 0.0242454i | ||||
\(904\) | −16.7516 | −0.557149 | ||||||||
\(905\) | 20.7270 | + | 11.9667i | 0.688988 | + | 0.397787i | ||||
\(906\) | 29.6634 | + | 3.30442i | 0.985500 | + | 0.109782i | ||||
\(907\) | 7.39782 | + | 12.8134i | 0.245641 | + | 0.425462i | 0.962312 | − | 0.271949i | \(-0.0876683\pi\) |
−0.716671 | + | 0.697412i | \(0.754335\pi\) | |||||||
\(908\) | 3.81039 | − | 6.59979i | 0.126452 | − | 0.219022i | ||||
\(909\) | −5.03846 | − | 16.1894i | −0.167115 | − | 0.536967i | ||||
\(910\) | −14.8062 | + | 12.2064i | −0.490821 | + | 0.404638i | ||||
\(911\) | 46.0986i | 1.52731i | 0.645623 | + | 0.763657i | \(0.276598\pi\) | ||||
−0.645623 | + | 0.763657i | \(0.723402\pi\) | |||||||
\(912\) | −0.0181303 | − | 0.0414126i | −0.000600353 | − | 0.00137131i | ||||
\(913\) | −35.3508 | + | 20.4098i | −1.16994 | + | 0.675465i | ||||
\(914\) | −3.35223 | + | 1.93541i | −0.110882 | + | 0.0640178i | ||||
\(915\) | −4.76165 | − | 10.8764i | −0.157415 | − | 0.359563i | ||||
\(916\) | − | 6.42548i | − | 0.212304i | ||||||
\(917\) | −23.0284 | − | 8.60885i | −0.760466 | − | 0.284289i | ||||
\(918\) | 11.8653 | + | 4.10158i | 0.391614 | + | 0.135372i | ||||
\(919\) | −23.9909 | + | 41.5534i | −0.791385 | + | 1.37072i | 0.133724 | + | 0.991019i | \(0.457306\pi\) |
−0.925109 | + | 0.379701i | \(0.876027\pi\) | |||||||
\(920\) | −0.750837 | − | 1.30049i | −0.0247544 | − | 0.0428758i | ||||
\(921\) | 32.5840 | + | 3.62977i | 1.07368 | + | 0.119605i | ||||
\(922\) | 16.5051 | + | 9.52922i | 0.543566 | + | 0.313828i | ||||
\(923\) | −5.02883 | −0.165526 | ||||||||
\(924\) | 12.5872 | + | 6.37314i | 0.414090 | + | 0.209661i | ||||
\(925\) | −29.1312 | −0.957826 | ||||||||
\(926\) | −14.4868 | − | 8.36398i | −0.476067 | − | 0.274857i | ||||
\(927\) | −28.1446 | − | 25.9827i | −0.924389 | − | 0.853384i | ||||
\(928\) | −1.87975 | − | 3.25583i | −0.0617059 | − | 0.106878i | ||||
\(929\) | 15.5228 | − | 26.8863i | 0.509288 | − | 0.882112i | −0.490655 | − | 0.871354i | \(-0.663242\pi\) |
0.999942 | − | 0.0107577i | \(-0.00342435\pi\) | |||||||
\(930\) | 12.3029 | + | 9.05603i | 0.403428 | + | 0.296959i | ||||
\(931\) | 0.179350 | + | 0.0348459i | 0.00587795 | + | 0.00114203i | ||||
\(932\) | − | 21.1288i | − | 0.692098i | ||||||
\(933\) | −3.51670 | + | 1.53960i | −0.115132 | + | 0.0504041i | ||||
\(934\) | −3.23624 | + | 1.86844i | −0.105893 | + | 0.0611373i | ||||
\(935\) | 9.67369 | − | 5.58511i | 0.316363 | − | 0.182652i | ||||
\(936\) | 14.1342 | + | 3.18859i | 0.461990 | + | 0.104222i | ||||
\(937\) | − | 24.2243i | − | 0.791373i | −0.918386 | − | 0.395686i | \(-0.870507\pi\) | ||
0.918386 | − | 0.395686i | \(-0.129493\pi\) | |||||||
\(938\) | −11.3182 | + | 1.89452i | −0.369553 | + | 0.0618584i | ||||
\(939\) | 6.09050 | − | 8.27413i | 0.198756 | − | 0.270016i | ||||
\(940\) | −2.29592 | + | 3.97664i | −0.0748845 | + | 0.129704i | ||||
\(941\) | −15.3714 | − | 26.6240i | −0.501092 | − | 0.867918i | −0.999999 | − | 0.00126196i | \(-0.999598\pi\) |
0.498907 | − | 0.866656i | \(-0.333735\pi\) | |||||||
\(942\) | −2.02827 | + | 18.2076i | −0.0660847 | + | 0.593234i | ||||
\(943\) | 1.11202 | + | 0.642028i | 0.0362125 | + | 0.0209073i | ||||
\(944\) | 7.43915 | 0.242124 | ||||||||
\(945\) | −13.1501 | + | 15.9146i | −0.427773 | + | 0.517702i | ||||
\(946\) | −8.91886 | −0.289977 | ||||||||
\(947\) | −32.5458 | − | 18.7904i | −1.05760 | − | 0.610604i | −0.132831 | − | 0.991139i | \(-0.542407\pi\) |
−0.924767 | + | 0.380534i | \(0.875740\pi\) | |||||||
\(948\) | 0.908566 | − | 8.15609i | 0.0295088 | − | 0.264897i | ||||
\(949\) | 18.1228 | + | 31.3896i | 0.588291 | + | 1.01895i | ||||
\(950\) | −0.0358226 | + | 0.0620465i | −0.00116224 | + | 0.00201306i | ||||
\(951\) | −28.5694 | + | 38.8124i | −0.926427 | + | 1.25858i | ||||
\(952\) | −4.06622 | − | 4.93228i | −0.131787 | − | 0.159856i | ||||
\(953\) | − | 6.29718i | − | 0.203986i | −0.994785 | − | 0.101993i | \(-0.967478\pi\) | ||
0.994785 | − | 0.101993i | \(-0.0325219\pi\) | |||||||
\(954\) | −32.9429 | − | 7.43171i | −1.06656 | − | 0.240610i | ||||
\(955\) | −1.25081 | + | 0.722156i | −0.0404753 | + | 0.0233684i | ||||
\(956\) | 2.63688 | − | 1.52240i | 0.0852828 | − | 0.0492381i | ||||
\(957\) | 18.3650 | − | 8.04014i | 0.593657 | − | 0.259901i | ||||
\(958\) | 27.5906i | 0.891410i | ||||||||
\(959\) | 18.8073 | + | 22.8131i | 0.607319 | + | 0.736672i | ||||
\(960\) | −2.09468 | − | 1.54187i | −0.0676056 | − | 0.0497638i | ||||
\(961\) | 1.74837 | − | 3.02826i | 0.0563989 | − | 0.0976858i | ||||
\(962\) | −25.6282 | − | 44.3894i | −0.826287 | − | 1.43117i | ||||
\(963\) | 9.35466 | + | 8.63609i | 0.301450 | + | 0.278294i | ||||
\(964\) | 17.9860 | + | 10.3842i | 0.579290 | + | 0.334453i | ||||
\(965\) | 5.19173 | 0.167128 | ||||||||
\(966\) | −2.50564 | − | 3.83689i | −0.0806177 | − | 0.123450i | ||||
\(967\) | −21.0343 | −0.676418 | −0.338209 | − | 0.941071i | \(-0.609821\pi\) | ||||
−0.338209 | + | 0.941071i | \(0.609821\pi\) | |||||||
\(968\) | 1.31737 | + | 0.760587i | 0.0423420 | + | 0.0244462i | ||||
\(969\) | −0.108552 | − | 0.0120924i | −0.00348721 | − | 0.000388465i | ||||
\(970\) | 7.17546 | + | 12.4283i | 0.230390 | + | 0.399047i | ||||
\(971\) | 7.70782 | − | 13.3503i | 0.247356 | − | 0.428432i | −0.715436 | − | 0.698679i | \(-0.753772\pi\) |
0.962791 | + | 0.270246i | \(0.0871051\pi\) | |||||||
\(972\) | 15.5809 | + | 0.484733i | 0.499758 | + | 0.0155478i | ||||
\(973\) | −42.7537 | + | 7.15643i | −1.37062 | + | 0.229424i | ||||
\(974\) | − | 10.5142i | − | 0.336896i | ||||||
\(975\) | −9.20920 | − | 21.0354i | −0.294931 | − | 0.673671i | ||||
\(976\) | 3.95328 | − | 2.28243i | 0.126541 | − | 0.0730587i | ||||
\(977\) | −5.33224 | + | 3.07857i | −0.170593 | + | 0.0984922i | −0.582866 | − | 0.812569i | \(-0.698069\pi\) |
0.412272 | + | 0.911061i | \(0.364735\pi\) | |||||||
\(978\) | −1.57745 | − | 3.60316i | −0.0504413 | − | 0.115216i | ||||
\(979\) | − | 41.5281i | − | 1.32724i | ||||||
\(980\) | 9.93873 | − | 3.42314i | 0.317481 | − | 0.109348i | ||||
\(981\) | 14.8421 | + | 47.6900i | 0.473872 | + | 1.52262i | ||||
\(982\) | −2.44174 | + | 4.22921i | −0.0779189 | + | 0.134960i | ||||
\(983\) | 24.7464 | + | 42.8619i | 0.789286 | + | 1.36708i | 0.926405 | + | 0.376529i | \(0.122882\pi\) |
−0.137119 | + | 0.990555i | \(0.543784\pi\) | |||||||
\(984\) | 2.21038 | + | 0.246230i | 0.0704642 | + | 0.00784952i | ||||
\(985\) | 15.9526 | + | 9.21024i | 0.508292 | + | 0.293463i | ||||
\(986\) | −9.08320 | −0.289268 | ||||||||
\(987\) | −6.32975 | + | 12.5015i | −0.201478 | + | 0.397928i | ||||
\(988\) | −0.126060 | −0.00401050 | ||||||||
\(989\) | 2.50878 | + | 1.44845i | 0.0797746 | + | 0.0460579i | ||||
\(990\) | 9.40830 | − | 10.1911i | 0.299015 | − | 0.323895i | ||||
\(991\) | −14.1368 | − | 24.4857i | −0.449070 | − | 0.777813i | 0.549255 | − | 0.835654i | \(-0.314911\pi\) |
−0.998326 | + | 0.0578420i | \(0.981578\pi\) | |||||||
\(992\) | −2.93670 | + | 5.08651i | −0.0932402 | + | 0.161497i | ||||
\(993\) | 28.1557 | + | 20.7251i | 0.893493 | + | 0.657691i | ||||
\(994\) | 2.58037 | + | 0.964633i | 0.0818443 | + | 0.0305963i | ||||
\(995\) | − | 36.5154i | − | 1.15762i | ||||||
\(996\) | 21.0366 | − | 9.20972i | 0.666569 | − | 0.291821i | ||||
\(997\) | −35.2487 | + | 20.3508i | −1.11634 | + | 0.644518i | −0.940463 | − | 0.339895i | \(-0.889608\pi\) |
−0.175874 | + | 0.984413i | \(0.556275\pi\) | |||||||
\(998\) | 2.01701 | − | 1.16452i | 0.0638472 | − | 0.0368622i | ||||
\(999\) | −36.1277 | − | 41.6616i | −1.14303 | − | 1.31812i |
(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 | 966.2.l.d.47.7 | ✓ | 56 | |
3.2 | odd | 2 | inner | 966.2.l.d.47.27 | yes | 56 | |
7.3 | odd | 6 | inner | 966.2.l.d.185.27 | yes | 56 | |
21.17 | even | 6 | inner | 966.2.l.d.185.7 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.l.d.47.7 | ✓ | 56 | 1.1 | even | 1 | trivial | |
966.2.l.d.47.27 | yes | 56 | 3.2 | odd | 2 | inner | |
966.2.l.d.185.7 | yes | 56 | 21.17 | even | 6 | inner | |
966.2.l.d.185.27 | yes | 56 | 7.3 | odd | 6 | inner |