Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(109,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.v (of order \(8\), degree \(4\), 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: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(128\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 109.10 | ||
Character | \(\chi\) | \(=\) | 864.109 |
Dual form | 864.2.v.a.325.10 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.934820 | + | 1.06118i | −0.661018 | + | 0.750370i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.252222 | − | 1.98403i | −0.126111 | − | 0.992016i | ||||
\(5\) | 0.930451 | − | 0.385405i | 0.416110 | − | 0.172359i | −0.164798 | − | 0.986327i | \(-0.552697\pi\) |
0.580909 | + | 0.813969i | \(0.302697\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.938500 | + | 0.938500i | −0.354720 | + | 0.354720i | −0.861862 | − | 0.507143i | \(-0.830702\pi\) |
0.507143 | + | 0.861862i | \(0.330702\pi\) | |||||||
\(8\) | 2.34121 | + | 1.58706i | 0.827741 | + | 0.561110i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.460818 | + | 1.34766i | −0.145724 | + | 0.426169i | ||||
\(11\) | −0.846222 | − | 2.04296i | −0.255145 | − | 0.615976i | 0.743459 | − | 0.668781i | \(-0.233184\pi\) |
−0.998605 | + | 0.0528055i | \(0.983184\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.64483 | − | 2.33816i | −1.56559 | − | 0.648490i | −0.579543 | − | 0.814941i | \(-0.696769\pi\) |
−0.986050 | + | 0.166451i | \(0.946769\pi\) | |||||||
\(14\) | −0.118592 | − | 1.87325i | −0.0316951 | − | 0.500647i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.87277 | + | 1.00083i | −0.968192 | + | 0.250209i | ||||
\(17\) | 7.71645i | 1.87151i | 0.352645 | + | 0.935757i | \(0.385282\pi\) | ||||
−0.352645 | + | 0.935757i | \(0.614718\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.36643 | − | 1.39442i | −0.772312 | − | 0.319902i | −0.0385035 | − | 0.999258i | \(-0.512259\pi\) |
−0.733809 | + | 0.679356i | \(0.762259\pi\) | |||||||
\(20\) | −0.999337 | − | 1.74884i | −0.223459 | − | 0.391052i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.95902 | + | 1.01180i | 0.630865 | + | 0.215717i | ||||
\(23\) | 5.65026 | + | 5.65026i | 1.17816 | + | 1.17816i | 0.980212 | + | 0.197948i | \(0.0634278\pi\) |
0.197948 | + | 0.980212i | \(0.436572\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.81833 | + | 2.81833i | −0.563666 | + | 0.563666i | ||||
\(26\) | 7.75812 | − | 3.80444i | 1.52149 | − | 0.746111i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.09872 | + | 1.62530i | 0.396622 | + | 0.307154i | ||||
\(29\) | −0.949070 | + | 2.29126i | −0.176238 | + | 0.425476i | −0.987172 | − | 0.159662i | \(-0.948960\pi\) |
0.810934 | + | 0.585138i | \(0.198960\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.39395 | 0.968782 | 0.484391 | − | 0.874852i | \(-0.339041\pi\) | ||||
0.484391 | + | 0.874852i | \(0.339041\pi\) | |||||||
\(32\) | 2.55827 | − | 5.04532i | 0.452243 | − | 0.891895i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.18857 | − | 7.21350i | −1.40433 | − | 1.23710i | ||||
\(35\) | −0.511525 | + | 1.23493i | −0.0864636 | + | 0.208741i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.01544 | + | 1.66325i | −0.660134 | + | 0.273436i | −0.687495 | − | 0.726189i | \(-0.741290\pi\) |
0.0273609 | + | 0.999626i | \(0.491290\pi\) | |||||||
\(38\) | 4.62674 | − | 2.26887i | 0.750557 | − | 0.368059i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.79004 | + | 0.574368i | 0.441144 | + | 0.0908155i | ||||
\(41\) | −6.02596 | − | 6.02596i | −0.941096 | − | 0.941096i | 0.0572629 | − | 0.998359i | \(-0.481763\pi\) |
−0.998359 | + | 0.0572629i | \(0.981763\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.38507 | + | 8.17229i | 0.516219 | + | 1.24626i | 0.940210 | + | 0.340596i | \(0.110629\pi\) |
−0.423991 | + | 0.905666i | \(0.639371\pi\) | |||||||
\(44\) | −3.83986 | + | 2.19421i | −0.578881 | + | 0.330790i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −11.2779 | + | 0.713987i | −1.66284 | + | 0.105272i | ||||
\(47\) | 6.68653i | 0.975331i | 0.873031 | + | 0.487666i | \(0.162151\pi\) | ||||
−0.873031 | + | 0.487666i | \(0.837849\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.23844i | 0.748348i | ||||||||
\(50\) | −0.356135 | − | 5.62540i | −0.0503650 | − | 0.795552i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.21524 | + | 11.7893i | −0.445874 | + | 1.63488i | ||||
\(53\) | 0.589451 | + | 1.42306i | 0.0809673 | + | 0.195472i | 0.959179 | − | 0.282800i | \(-0.0912632\pi\) |
−0.878212 | + | 0.478272i | \(0.841263\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.57474 | − | 1.57474i | −0.212337 | − | 0.212337i | ||||
\(56\) | −3.68668 | + | 0.707766i | −0.492653 | + | 0.0945792i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.54424 | − | 3.14905i | −0.202768 | − | 0.413491i | ||||
\(59\) | −7.21416 | + | 2.98820i | −0.939204 | + | 0.389031i | −0.799163 | − | 0.601115i | \(-0.794723\pi\) |
−0.140041 | + | 0.990146i | \(0.544723\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.05674 | + | 7.37963i | −0.391376 | + | 0.944865i | 0.598265 | + | 0.801298i | \(0.295857\pi\) |
−0.989641 | + | 0.143566i | \(0.954143\pi\) | |||||||
\(62\) | −5.04238 | + | 5.72397i | −0.640382 | + | 0.726946i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.96249 | + | 7.43126i | 0.370311 | + | 0.928908i | ||||
\(65\) | −6.15337 | −0.763232 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.77223 | − | 9.10696i | 0.460851 | − | 1.11259i | −0.507198 | − | 0.861830i | \(-0.669319\pi\) |
0.968049 | − | 0.250762i | \(-0.0806813\pi\) | |||||||
\(68\) | 15.3097 | − | 1.94626i | 1.85657 | − | 0.236019i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.832305 | − | 1.69726i | −0.0994795 | − | 0.202861i | ||||
\(71\) | −1.95353 | + | 1.95353i | −0.231842 | + | 0.231842i | −0.813461 | − | 0.581619i | \(-0.802419\pi\) |
0.581619 | + | 0.813461i | \(0.302419\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.58563 | − | 8.58563i | −1.00487 | − | 1.00487i | −0.999988 | − | 0.00488401i | \(-0.998445\pi\) |
−0.00488401 | − | 0.999988i | \(-0.501555\pi\) | |||||||
\(74\) | 1.98870 | − | 5.81596i | 0.231182 | − | 0.676091i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.91749 | + | 7.03081i | −0.219951 | + | 0.806489i | ||||
\(77\) | 2.71150 | + | 1.12314i | 0.309004 | + | 0.127994i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 11.7674i | − | 1.32394i | −0.749531 | − | 0.661969i | \(-0.769721\pi\) | ||
0.749531 | − | 0.661969i | \(-0.230279\pi\) | |||||||
\(80\) | −3.21769 | + | 2.42381i | −0.359749 | + | 0.270991i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 12.0278 | − | 0.761461i | 1.32825 | − | 0.0840894i | ||||
\(83\) | −6.05690 | − | 2.50885i | −0.664831 | − | 0.275382i | 0.0246390 | − | 0.999696i | \(-0.492156\pi\) |
−0.689470 | + | 0.724314i | \(0.742156\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.97396 | + | 7.17978i | 0.322571 | + | 0.778756i | ||||
\(86\) | −11.8367 | − | 4.04744i | −1.27639 | − | 0.436446i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.26112 | − | 6.12599i | 0.134436 | − | 0.653033i | ||||
\(89\) | −5.36845 | + | 5.36845i | −0.569055 | + | 0.569055i | −0.931864 | − | 0.362809i | \(-0.881818\pi\) |
0.362809 | + | 0.931864i | \(0.381818\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.49204 | − | 3.10330i | 0.785379 | − | 0.325315i | ||||
\(92\) | 9.78518 | − | 12.6354i | 1.02018 | − | 1.31733i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.09564 | − | 6.25071i | −0.731860 | − | 0.644711i | ||||
\(95\) | −3.66972 | −0.376505 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.31108 | −0.843862 | −0.421931 | − | 0.906628i | \(-0.638648\pi\) | ||||
−0.421931 | + | 0.906628i | \(0.638648\pi\) | |||||||
\(98\) | −5.55894 | − | 4.89700i | −0.561538 | − | 0.494671i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.30251 | + | 4.88082i | 0.630251 | + | 0.488082i | ||||
\(101\) | 3.21953 | − | 1.33357i | 0.320355 | − | 0.132695i | −0.216711 | − | 0.976236i | \(-0.569533\pi\) |
0.537066 | + | 0.843540i | \(0.319533\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.343343 | − | 0.343343i | 0.0338306 | − | 0.0338306i | −0.689989 | − | 0.723820i | \(-0.742385\pi\) |
0.723820 | + | 0.689989i | \(0.242385\pi\) | |||||||
\(104\) | −9.50489 | − | 14.4328i | −0.932032 | − | 1.41525i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.06116 | − | 0.704790i | −0.200198 | − | 0.0684553i | ||||
\(107\) | 1.86534 | + | 4.50334i | 0.180330 | + | 0.435354i | 0.988035 | − | 0.154233i | \(-0.0492906\pi\) |
−0.807705 | + | 0.589587i | \(0.799291\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.74343 | − | 2.79322i | −0.645904 | − | 0.267542i | 0.0355895 | − | 0.999366i | \(-0.488669\pi\) |
−0.681493 | + | 0.731824i | \(0.738669\pi\) | |||||||
\(110\) | 3.14318 | − | 0.198989i | 0.299690 | − | 0.0189729i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.69531 | − | 4.57388i | 0.254683 | − | 0.432191i | ||||
\(113\) | − | 2.17091i | − | 0.204222i | −0.994773 | − | 0.102111i | \(-0.967440\pi\) | ||
0.994773 | − | 0.102111i | \(-0.0325596\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.43493 | + | 3.07965i | 0.693311 | + | 0.287179i | ||||
\(116\) | 4.78531 | + | 1.30508i | 0.444304 | + | 0.121174i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.57291 | − | 10.4490i | 0.328913 | − | 0.961907i | ||||
\(119\) | −7.24189 | − | 7.24189i | −0.663863 | − | 0.663863i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.32058 | − | 4.32058i | 0.392780 | − | 0.392780i | ||||
\(122\) | −4.97364 | − | 10.1424i | −0.450292 | − | 0.918249i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.36047 | − | 10.7018i | −0.122174 | − | 0.961048i | ||||
\(125\) | −3.46315 | + | 8.36078i | −0.309753 | + | 0.747810i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.995355 | −0.0883235 | −0.0441617 | − | 0.999024i | \(-0.514062\pi\) | ||||
−0.0441617 | + | 0.999024i | \(0.514062\pi\) | |||||||
\(128\) | −10.6553 | − | 3.80315i | −0.941807 | − | 0.336154i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.75230 | − | 6.52986i | 0.504510 | − | 0.572707i | ||||
\(131\) | 4.10132 | − | 9.90147i | 0.358334 | − | 0.865096i | −0.637200 | − | 0.770698i | \(-0.719908\pi\) |
0.995535 | − | 0.0943974i | \(-0.0300924\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.46806 | − | 1.85073i | 0.387430 | − | 0.160479i | ||||
\(134\) | 6.13780 | + | 12.5164i | 0.530225 | + | 1.08125i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.2465 | + | 18.0658i | −1.05013 | + | 1.54913i | ||||
\(137\) | 12.7750 | + | 12.7750i | 1.09144 | + | 1.09144i | 0.995375 | + | 0.0960676i | \(0.0306265\pi\) |
0.0960676 | + | 0.995375i | \(0.469374\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.10035 | − | 2.65647i | −0.0933302 | − | 0.225319i | 0.870320 | − | 0.492487i | \(-0.163912\pi\) |
−0.963650 | + | 0.267168i | \(0.913912\pi\) | |||||||
\(140\) | 2.57916 | + | 0.703405i | 0.217979 | + | 0.0594486i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.246855 | − | 3.89926i | −0.0207156 | − | 0.327219i | ||||
\(143\) | 13.5108i | 1.12983i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.49768i | 0.207421i | ||||||||
\(146\) | 17.1370 | − | 1.08491i | 1.41826 | − | 0.0897879i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.31272 | + | 7.54725i | 0.354504 | + | 0.620380i | ||||
\(149\) | 0.247702 | + | 0.598004i | 0.0202925 | + | 0.0489904i | 0.933701 | − | 0.358054i | \(-0.116560\pi\) |
−0.913408 | + | 0.407044i | \(0.866560\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.5472 | + | 13.5472i | 1.10246 | + | 1.10246i | 0.994113 | + | 0.108344i | \(0.0345549\pi\) |
0.108344 | + | 0.994113i | \(0.465445\pi\) | |||||||
\(152\) | −5.66848 | − | 8.60735i | −0.459774 | − | 0.698148i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.72662 | + | 1.82746i | −0.300300 | + | 0.147261i | ||||
\(155\) | 5.01881 | − | 2.07886i | 0.403120 | − | 0.166978i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.17046 | − | 10.0684i | 0.332839 | − | 0.803544i | −0.665526 | − | 0.746375i | \(-0.731793\pi\) |
0.998365 | − | 0.0571689i | \(-0.0182074\pi\) | |||||||
\(158\) | 12.4874 | + | 11.0004i | 0.993444 | + | 0.875147i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.435854 | − | 5.68039i | 0.0344573 | − | 0.449075i | ||||
\(161\) | −10.6055 | −0.835834 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.29505 | + | 5.54074i | −0.179762 | + | 0.433985i | −0.987917 | − | 0.154986i | \(-0.950467\pi\) |
0.808154 | + | 0.588971i | \(0.200467\pi\) | |||||||
\(164\) | −10.4358 | + | 13.4756i | −0.814900 | + | 1.05227i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.32446 | − | 4.08216i | 0.646103 | − | 0.316837i | ||||
\(167\) | −6.22675 | + | 6.22675i | −0.481840 | + | 0.481840i | −0.905719 | − | 0.423879i | \(-0.860668\pi\) |
0.423879 | + | 0.905719i | \(0.360668\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.2047 | + | 17.2047i | 1.32344 | + | 1.32344i | ||||
\(170\) | −10.3992 | − | 3.55588i | −0.797581 | − | 0.272724i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 15.3603 | − | 8.77733i | 1.17121 | − | 0.669265i | ||||
\(173\) | −0.963826 | − | 0.399230i | −0.0732783 | − | 0.0303529i | 0.345743 | − | 0.938329i | \(-0.387627\pi\) |
−0.419022 | + | 0.907976i | \(0.637627\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 5.29001i | − | 0.399887i | ||||||
\(176\) | 5.32188 | + | 7.06498i | 0.401152 | + | 0.532543i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.678377 | − | 10.7154i | −0.0508465 | − | 0.803157i | ||||
\(179\) | −9.89224 | − | 4.09750i | −0.739381 | − | 0.306261i | −0.0189802 | − | 0.999820i | \(-0.506042\pi\) |
−0.720400 | + | 0.693558i | \(0.756042\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.31664 | + | 3.17865i | 0.0978651 | + | 0.236267i | 0.965228 | − | 0.261408i | \(-0.0841870\pi\) |
−0.867363 | + | 0.497676i | \(0.834187\pi\) | |||||||
\(182\) | −3.71053 | + | 10.8515i | −0.275043 | + | 0.804364i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.26112 | + | 22.1957i | 0.314134 | + | 1.63629i | ||||
\(185\) | −3.09514 | + | 3.09514i | −0.227559 | + | 0.227559i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.7644 | − | 6.52983i | 1.15281 | − | 0.477508i | ||||
\(188\) | 13.2663 | − | 1.68649i | 0.967544 | − | 0.123000i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.43052 | − | 3.89424i | 0.248876 | − | 0.282518i | ||||
\(191\) | 21.8507 | 1.58106 | 0.790531 | − | 0.612422i | \(-0.209805\pi\) | ||||
0.790531 | + | 0.612422i | \(0.209805\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.5286 | −1.04579 | −0.522897 | − | 0.852396i | \(-0.675149\pi\) | ||||
−0.522897 | + | 0.852396i | \(0.675149\pi\) | |||||||
\(194\) | 7.76936 | − | 8.81958i | 0.557808 | − | 0.633209i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.3932 | − | 1.32125i | 0.742373 | − | 0.0943750i | ||||
\(197\) | 15.9169 | − | 6.59300i | 1.13403 | − | 0.469732i | 0.264883 | − | 0.964280i | \(-0.414667\pi\) |
0.869150 | + | 0.494548i | \(0.164667\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.3938 | − | 12.3938i | 0.878574 | − | 0.878574i | −0.114813 | − | 0.993387i | \(-0.536627\pi\) |
0.993387 | + | 0.114813i | \(0.0366270\pi\) | |||||||
\(200\) | −11.0712 | + | 2.12543i | −0.782849 | + | 0.150291i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.59451 | + | 4.66316i | −0.112190 | + | 0.328099i | ||||
\(203\) | −1.25964 | − | 3.04105i | −0.0884096 | − | 0.213440i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.92929 | − | 3.28442i | −0.553806 | − | 0.229394i | ||||
\(206\) | 0.0433860 | + | 0.685313i | 0.00302285 | + | 0.0477480i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 24.2012 | + | 3.40563i | 1.67805 | + | 0.236138i | ||||
\(209\) | 8.05747i | 0.557347i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.6796 | − | 4.42362i | −0.735212 | − | 0.304535i | −0.0165202 | − | 0.999864i | \(-0.505259\pi\) |
−0.718692 | + | 0.695329i | \(0.755259\pi\) | |||||||
\(212\) | 2.67473 | − | 1.52842i | 0.183701 | − | 0.104972i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.52263 | − | 2.23034i | −0.445878 | − | 0.152463i | ||||
\(215\) | 6.29929 | + | 6.29929i | 0.429608 | + | 0.429608i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.06222 | + | 5.06222i | −0.343646 | + | 0.343646i | ||||
\(218\) | 9.26802 | − | 4.54486i | 0.627710 | − | 0.307817i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.72714 | + | 3.52151i | −0.183864 | + | 0.237420i | ||||
\(221\) | 18.0423 | − | 43.5580i | 1.21366 | − | 2.93003i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.0545 | 0.807226 | 0.403613 | − | 0.914930i | \(-0.367754\pi\) | ||||
0.403613 | + | 0.914930i | \(0.367754\pi\) | |||||||
\(224\) | 2.33409 | + | 7.13597i | 0.155953 | + | 0.476792i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.30373 | + | 2.02941i | 0.153242 | + | 0.134994i | ||||
\(227\) | 3.72637 | − | 8.99626i | 0.247328 | − | 0.597103i | −0.750647 | − | 0.660703i | \(-0.770258\pi\) |
0.997975 | + | 0.0636001i | \(0.0202582\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.6130 | + | 11.0235i | −1.75864 | + | 0.728452i | −0.761906 | + | 0.647688i | \(0.775736\pi\) |
−0.996733 | + | 0.0807641i | \(0.974264\pi\) | |||||||
\(230\) | −10.2184 | + | 5.01091i | −0.673781 | + | 0.330410i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.85833 | + | 3.85807i | −0.384618 | + | 0.253295i | ||||
\(233\) | −11.3815 | − | 11.3815i | −0.745628 | − | 0.745628i | 0.228027 | − | 0.973655i | \(-0.426773\pi\) |
−0.973655 | + | 0.228027i | \(0.926773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.57703 | + | 6.22149i | 0.168107 | + | 0.405845i | ||||
\(236\) | 7.74826 | + | 13.5594i | 0.504369 | + | 0.882644i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 14.4548 | − | 0.915111i | 0.936968 | − | 0.0593179i | ||||
\(239\) | 12.1171i | 0.783790i | 0.920010 | + | 0.391895i | \(0.128180\pi\) | ||||
−0.920010 | + | 0.391895i | \(0.871820\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.31602i | 0.0847721i | 0.999101 | + | 0.0423860i | \(0.0134959\pi\) | ||||
−0.999101 | + | 0.0423860i | \(0.986504\pi\) | |||||||
\(242\) | 0.545964 | + | 8.62390i | 0.0350959 | + | 0.554365i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 15.4124 | + | 4.20337i | 0.986678 | + | 0.269093i | ||||
\(245\) | 2.01892 | + | 4.87411i | 0.128984 | + | 0.311395i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.7425 | + | 15.7425i | 1.00167 | + | 1.00167i | ||||
\(248\) | 12.6283 | + | 8.56052i | 0.801901 | + | 0.543594i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.63490 | − | 11.4909i | −0.356382 | − | 0.726746i | ||||
\(251\) | −9.63552 | + | 3.99117i | −0.608189 | + | 0.251920i | −0.665454 | − | 0.746439i | \(-0.731762\pi\) |
0.0572650 | + | 0.998359i | \(0.481762\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.76188 | − | 16.3246i | 0.425116 | − | 1.02632i | ||||
\(254\) | 0.930478 | − | 1.05625i | 0.0583834 | − | 0.0662753i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.9967 | − | 7.75200i | 0.874791 | − | 0.484500i | ||||
\(257\) | −8.53035 | −0.532109 | −0.266054 | − | 0.963958i | \(-0.585720\pi\) | ||||
−0.266054 | + | 0.963958i | \(0.585720\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.20753 | − | 5.32945i | 0.137169 | − | 0.331156i | ||||
\(260\) | 1.55202 | + | 12.2085i | 0.0962521 | + | 0.757139i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.67328 | + | 13.6084i | 0.412277 | + | 0.840727i | ||||
\(263\) | −6.53095 | + | 6.53095i | −0.402715 | + | 0.402715i | −0.879189 | − | 0.476473i | \(-0.841915\pi\) |
0.476473 | + | 0.879189i | \(0.341915\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.09691 | + | 1.09691i | 0.0673827 | + | 0.0673827i | ||||
\(266\) | −2.21287 | + | 6.47153i | −0.135680 | + | 0.396795i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −19.0199 | − | 5.18724i | −1.16183 | − | 0.316861i | ||||
\(269\) | 22.7725 | + | 9.43267i | 1.38846 | + | 0.575120i | 0.946731 | − | 0.322027i | \(-0.104364\pi\) |
0.441732 | + | 0.897147i | \(0.354364\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 30.4157i | − | 1.84762i | −0.382847 | − | 0.923812i | \(-0.625056\pi\) | ||
0.382847 | − | 0.923812i | \(-0.374944\pi\) | |||||||
\(272\) | −7.72289 | − | 29.8840i | −0.468269 | − | 1.81199i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −25.4990 | + | 1.61430i | −1.54045 | + | 0.0975232i | ||||
\(275\) | 8.14267 | + | 3.37281i | 0.491022 | + | 0.203388i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.9512 | + | 28.8527i | 0.718077 | + | 1.73359i | 0.678755 | + | 0.734365i | \(0.262520\pi\) |
0.0393221 | + | 0.999227i | \(0.487480\pi\) | |||||||
\(278\) | 3.84763 | + | 1.31565i | 0.230766 | + | 0.0789077i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.15749 | + | 2.07941i | −0.188696 | + | 0.124268i | ||||
\(281\) | −23.3117 | + | 23.3117i | −1.39066 | + | 1.39066i | −0.566816 | + | 0.823844i | \(0.691825\pi\) |
−0.823844 | + | 0.566816i | \(0.808175\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.7460 | − | 9.42171i | 1.35211 | − | 0.560063i | 0.415232 | − | 0.909716i | \(-0.363701\pi\) |
0.936879 | + | 0.349653i | \(0.113701\pi\) | |||||||
\(284\) | 4.36860 | + | 3.38315i | 0.259228 | + | 0.200753i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.3374 | − | 12.6301i | −0.847788 | − | 0.746835i | ||||
\(287\) | 11.3107 | 0.667651 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −42.5436 | −2.50257 | ||||||||
\(290\) | −2.65050 | − | 2.33488i | −0.155643 | − | 0.137109i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.8687 | + | 19.1997i | −0.870124 | + | 1.12357i | ||||
\(293\) | 10.6254 | − | 4.40120i | 0.620744 | − | 0.257121i | −0.0500704 | − | 0.998746i | \(-0.515945\pi\) |
0.670815 | + | 0.741625i | \(0.265945\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.56075 | + | 5.56075i | −0.323759 | + | 0.323759i | ||||
\(296\) | −12.0406 | − | 2.47873i | −0.699848 | − | 0.144073i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.866149 | − | 0.296170i | −0.0501747 | − | 0.0171567i | ||||
\(299\) | −18.6835 | − | 45.1060i | −1.08050 | − | 2.60855i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.8466 | − | 4.49280i | −0.625187 | − | 0.258961i | ||||
\(302\) | −27.0403 | + | 1.71188i | −1.55600 | + | 0.0985074i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.4330 | + | 2.03103i | 0.827789 | + | 0.116488i | ||||
\(305\) | 8.04447i | 0.460625i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.33416 | − | 1.38105i | −0.190290 | − | 0.0788209i | 0.285504 | − | 0.958378i | \(-0.407839\pi\) |
−0.475794 | + | 0.879557i | \(0.657839\pi\) | |||||||
\(308\) | 1.54444 | − | 5.66298i | 0.0880028 | − | 0.322678i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.48563 | + | 7.26924i | −0.141174 | + | 0.412865i | ||||
\(311\) | 15.7937 | + | 15.7937i | 0.895577 | + | 0.895577i | 0.995041 | − | 0.0994642i | \(-0.0317129\pi\) |
−0.0994642 | + | 0.995041i | \(0.531713\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.6900 | − | 22.6900i | 1.28251 | − | 1.28251i | 0.343279 | − | 0.939234i | \(-0.388462\pi\) |
0.939234 | − | 0.343279i | \(-0.111538\pi\) | |||||||
\(314\) | 6.78577 | + | 13.8377i | 0.382943 | + | 0.780909i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −23.3469 | + | 2.96801i | −1.31337 | + | 0.166963i | ||||
\(317\) | −0.135667 | + | 0.327529i | −0.00761982 | + | 0.0183959i | −0.927644 | − | 0.373467i | \(-0.878169\pi\) |
0.920024 | + | 0.391862i | \(0.128169\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.48407 | 0.307049 | ||||||||
\(320\) | 5.62050 | + | 5.77267i | 0.314195 | + | 0.322702i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.91427 | − | 11.2544i | 0.552501 | − | 0.627185i | ||||
\(323\) | 10.7600 | − | 25.9769i | 0.598701 | − | 1.44539i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.4987 | − | 9.31927i | 1.24800 | − | 0.516940i | ||||
\(326\) | −3.73429 | − | 7.61507i | −0.206823 | − | 0.421760i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.54445 | − | 23.6716i | −0.250925 | − | 1.30704i | ||||
\(329\) | −6.27531 | − | 6.27531i | −0.345969 | − | 0.345969i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.599578 | − | 1.44751i | −0.0329558 | − | 0.0795622i | 0.906545 | − | 0.422110i | \(-0.138710\pi\) |
−0.939501 | + | 0.342547i | \(0.888710\pi\) | |||||||
\(332\) | −3.44995 | + | 12.6499i | −0.189341 | + | 0.694252i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.786835 | − | 12.4286i | −0.0430537 | − | 0.680064i | ||||
\(335\) | − | 9.92741i | − | 0.542393i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.16524i | 0.499262i | 0.968341 | + | 0.249631i | \(0.0803094\pi\) | ||||
−0.968341 | + | 0.249631i | \(0.919691\pi\) | |||||||
\(338\) | −34.3406 | + | 2.17404i | −1.86788 | + | 0.118252i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 13.4948 | − | 7.71134i | 0.731859 | − | 0.418206i | ||||
\(341\) | −4.56448 | − | 11.0196i | −0.247180 | − | 0.596746i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.4858 | − | 11.4858i | −0.620173 | − | 0.620173i | ||||
\(344\) | −5.04476 | + | 24.5053i | −0.271995 | + | 1.32124i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.32466 | − | 0.649588i | 0.0712141 | − | 0.0349221i | ||||
\(347\) | 0.809488 | − | 0.335301i | 0.0434556 | − | 0.0179999i | −0.360850 | − | 0.932624i | \(-0.617513\pi\) |
0.404305 | + | 0.914624i | \(0.367513\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.88249 | − | 4.54472i | 0.100767 | − | 0.243273i | −0.865454 | − | 0.500989i | \(-0.832970\pi\) |
0.966221 | + | 0.257716i | \(0.0829697\pi\) | |||||||
\(350\) | 5.61367 | + | 4.94521i | 0.300063 | + | 0.264333i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12.4722 | − | 0.956990i | −0.664773 | − | 0.0510078i | ||||
\(353\) | 6.05956 | 0.322518 | 0.161259 | − | 0.986912i | \(-0.448445\pi\) | ||||
0.161259 | + | 0.986912i | \(0.448445\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.06476 | + | 2.57057i | −0.0565118 | + | 0.136432i | ||||
\(356\) | 12.0052 | + | 9.29714i | 0.636275 | + | 0.492747i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.5957 | − | 6.66706i | 0.718553 | − | 0.352365i | ||||
\(359\) | 11.1337 | − | 11.1337i | 0.587616 | − | 0.587616i | −0.349369 | − | 0.936985i | \(-0.613604\pi\) |
0.936985 | + | 0.349369i | \(0.113604\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.04659 | − | 4.04659i | −0.212978 | − | 0.212978i | ||||
\(362\) | −4.60395 | − | 1.57427i | −0.241978 | − | 0.0827418i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.04671 | − | 14.0817i | −0.421762 | − | 0.738083i | ||||
\(365\) | −11.2975 | − | 4.67956i | −0.591336 | − | 0.244939i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.7822i | 1.76341i | 0.471797 | + | 0.881707i | \(0.343606\pi\) | ||||
−0.471797 | + | 0.881707i | \(0.656394\pi\) | |||||||
\(368\) | −27.5371 | − | 16.2272i | −1.43547 | − | 0.845900i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.391113 | − | 6.17792i | −0.0203330 | − | 0.321175i | ||||
\(371\) | −1.88874 | − | 0.782343i | −0.0980586 | − | 0.0406172i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.132294 | + | 0.319386i | 0.00684991 | + | 0.0165372i | 0.927267 | − | 0.374400i | \(-0.122151\pi\) |
−0.920418 | + | 0.390937i | \(0.872151\pi\) | |||||||
\(374\) | −7.80753 | + | 22.8331i | −0.403718 | + | 1.18067i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.6119 | + | 15.6545i | −0.547268 | + | 0.807322i | ||||
\(377\) | 10.7147 | − | 10.7147i | 0.551834 | − | 0.551834i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.705525 | − | 0.292238i | 0.0362404 | − | 0.0150112i | −0.364490 | − | 0.931207i | \(-0.618757\pi\) |
0.400730 | + | 0.916196i | \(0.368757\pi\) | |||||||
\(380\) | 0.925584 | + | 7.28083i | 0.0474815 | + | 0.373499i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −20.4265 | + | 23.1876i | −1.04511 | + | 1.18638i | ||||
\(383\) | 0.0618011 | 0.00315789 | 0.00157894 | − | 0.999999i | \(-0.499497\pi\) | ||||
0.00157894 | + | 0.999999i | \(0.499497\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.95578 | 0.150640 | ||||||||
\(386\) | 13.5817 | − | 15.4176i | 0.691289 | − | 0.784733i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.09624 | + | 16.4894i | 0.106420 | + | 0.837125i | ||||
\(389\) | 22.0157 | − | 9.11918i | 1.11624 | − | 0.462361i | 0.253156 | − | 0.967425i | \(-0.418531\pi\) |
0.863082 | + | 0.505064i | \(0.168531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −43.6000 | + | 43.6000i | −2.20494 | + | 2.20494i | ||||
\(392\) | −8.31371 | + | 12.2643i | −0.419906 | + | 0.619438i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.88307 | + | 23.0541i | −0.397143 | + | 1.16145i | ||||
\(395\) | −4.53523 | − | 10.9490i | −0.228192 | − | 0.550904i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.50388 | + | 1.03714i | 0.125666 | + | 0.0520525i | 0.444630 | − | 0.895714i | \(-0.353335\pi\) |
−0.318964 | + | 0.947767i | \(0.603335\pi\) | |||||||
\(398\) | 1.56613 | + | 24.7381i | 0.0785028 | + | 1.24001i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.09406 | − | 13.7354i | 0.404703 | − | 0.686771i | ||||
\(401\) | − | 14.8862i | − | 0.743380i | −0.928357 | − | 0.371690i | \(-0.878778\pi\) | ||
0.928357 | − | 0.371690i | \(-0.121222\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −30.4479 | − | 12.6119i | −1.51672 | − | 0.628246i | ||||
\(404\) | −3.45789 | − | 6.05129i | −0.172036 | − | 0.301063i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.40465 | + | 1.50612i | 0.218599 | + | 0.0747475i | ||||
\(407\) | 6.79590 | + | 6.79590i | 0.336860 | + | 0.336860i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.5375 | − | 12.5375i | 0.619938 | − | 0.619938i | −0.325578 | − | 0.945515i | \(-0.605559\pi\) |
0.945515 | + | 0.325578i | \(0.105559\pi\) | |||||||
\(410\) | 10.8978 | − | 5.34409i | 0.538206 | − | 0.263926i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.767802 | − | 0.594604i | −0.0378269 | − | 0.0292941i | ||||
\(413\) | 3.96606 | − | 9.57492i | 0.195157 | − | 0.471151i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.60257 | −0.324107 | ||||||||
\(416\) | −26.2378 | + | 22.4983i | −1.28641 | + | 1.10307i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.55046 | − | 7.53229i | −0.418217 | − | 0.368416i | ||||
\(419\) | −15.1946 | + | 36.6829i | −0.742303 | + | 1.79208i | −0.146060 | + | 0.989276i | \(0.546659\pi\) |
−0.596244 | + | 0.802803i | \(0.703341\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.0470 | + | 4.57581i | −0.538397 | + | 0.223011i | −0.635276 | − | 0.772285i | \(-0.719114\pi\) |
0.0968796 | + | 0.995296i | \(0.469114\pi\) | |||||||
\(422\) | 14.6778 | − | 7.19770i | 0.714502 | − | 0.350378i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.878456 | + | 4.26717i | −0.0426616 | + | 0.207232i | ||||
\(425\) | −21.7475 | − | 21.7475i | −1.05491 | − | 1.05491i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.05703 | − | 9.79454i | −0.196333 | − | 0.473991i | ||||
\(428\) | 8.46428 | − | 4.83674i | 0.409137 | − | 0.233793i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.5734 | + | 0.796001i | −0.606343 | + | 0.0383866i | ||||
\(431\) | − | 27.7654i | − | 1.33741i | −0.743527 | − | 0.668706i | \(-0.766848\pi\) | ||
0.743527 | − | 0.668706i | \(-0.233152\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.43486i | 0.261183i | 0.991436 | + | 0.130591i | \(0.0416876\pi\) | ||||
−0.991436 | + | 0.130591i | \(0.958312\pi\) | |||||||
\(434\) | −0.639681 | − | 10.1042i | −0.0307057 | − | 0.485018i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.84100 | + | 14.0837i | −0.183950 | + | 0.674487i | ||||
\(437\) | −11.1424 | − | 26.9001i | −0.533012 | − | 1.28680i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.46141 | − | 7.46141i | −0.356114 | − | 0.356114i | 0.506265 | − | 0.862378i | \(-0.331026\pi\) |
−0.862378 | + | 0.506265i | \(0.831026\pi\) | |||||||
\(440\) | −1.18758 | − | 6.18598i | −0.0566157 | − | 0.294905i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 29.3567 | + | 59.8652i | 1.39636 | + | 2.84749i | ||||
\(443\) | 33.3044 | − | 13.7951i | 1.58234 | − | 0.655427i | 0.593558 | − | 0.804791i | \(-0.297723\pi\) |
0.988782 | + | 0.149365i | \(0.0477229\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.92605 | + | 7.06411i | −0.138708 | + | 0.334871i | ||||
\(446\) | −11.2687 | + | 12.7920i | −0.533591 | + | 0.605718i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9.75453 | − | 4.19395i | −0.460858 | − | 0.198145i | ||||
\(449\) | −7.32090 | −0.345494 | −0.172747 | − | 0.984966i | \(-0.555264\pi\) | ||||
−0.172747 | + | 0.984966i | \(0.555264\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.21149 | + | 17.4101i | −0.339576 | + | 0.819809i | ||||
\(452\) | −4.30715 | + | 0.547551i | −0.202591 | + | 0.0257546i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.06320 | + | 12.3643i | 0.284560 | + | 0.580283i | ||||
\(455\) | 5.77494 | − | 5.77494i | 0.270733 | − | 0.270733i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.2198 | − | 13.2198i | −0.618398 | − | 0.618398i | 0.326723 | − | 0.945120i | \(-0.394056\pi\) |
−0.945120 | + | 0.326723i | \(0.894056\pi\) | |||||||
\(458\) | 13.1805 | − | 38.5463i | 0.615883 | − | 1.80115i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.23487 | − | 15.5279i | 0.197452 | − | 0.723992i | ||||
\(461\) | −3.91240 | − | 1.62057i | −0.182219 | − | 0.0754774i | 0.289709 | − | 0.957115i | \(-0.406442\pi\) |
−0.471927 | + | 0.881637i | \(0.656442\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 19.9447i | − | 0.926910i | −0.886121 | − | 0.463455i | \(-0.846610\pi\) | ||
0.886121 | − | 0.463455i | \(-0.153390\pi\) | |||||||
\(464\) | 1.38236 | − | 9.82337i | 0.0641744 | − | 0.456038i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22.7176 | − | 1.43821i | 1.05237 | − | 0.0666238i | ||||
\(467\) | −23.4125 | − | 9.69779i | −1.08340 | − | 0.448760i | −0.231701 | − | 0.972787i | \(-0.574429\pi\) |
−0.851702 | + | 0.524027i | \(0.824429\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.00665 | + | 12.0871i | 0.231185 | + | 0.558131i | ||||
\(470\) | −9.01120 | − | 3.08128i | −0.415656 | − | 0.142129i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −21.6323 | − | 4.45330i | −0.995707 | − | 0.204980i | ||||
\(473\) | 13.8311 | − | 13.8311i | 0.635956 | − | 0.635956i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.4177 | − | 5.55778i | 0.615645 | − | 0.255008i | ||||
\(476\) | −12.5416 | + | 16.1947i | −0.574842 | + | 0.742283i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.8585 | − | 11.3273i | −0.588133 | − | 0.518099i | ||||
\(479\) | −15.7464 | −0.719470 | −0.359735 | − | 0.933054i | \(-0.617133\pi\) | ||||
−0.359735 | + | 0.933054i | \(0.617133\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.5554 | 1.21082 | ||||||||
\(482\) | −1.39654 | − | 1.23024i | −0.0636104 | − | 0.0560358i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.66192 | − | 7.48243i | −0.439178 | − | 0.340110i | ||||
\(485\) | −7.73305 | + | 3.20313i | −0.351140 | + | 0.145447i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.8941 | + | 21.8941i | −0.992116 | + | 0.992116i | −0.999969 | − | 0.00785353i | \(-0.997500\pi\) |
0.00785353 | + | 0.999969i | \(0.497500\pi\) | |||||||
\(488\) | −18.8684 | + | 12.4260i | −0.854131 | + | 0.562498i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7.05965 | − | 2.41397i | −0.318923 | − | 0.109052i | ||||
\(491\) | 3.16126 | + | 7.63197i | 0.142666 | + | 0.344426i | 0.979020 | − | 0.203763i | \(-0.0653173\pi\) |
−0.836354 | + | 0.548189i | \(0.815317\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.6804 | − | 7.32345i | −0.796284 | − | 0.329832i | ||||
\(494\) | −31.4222 | + | 1.98928i | −1.41375 | + | 0.0895021i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −20.8895 | + | 5.39845i | −0.937967 | + | 0.242398i | ||||
\(497\) | − | 3.66678i | − | 0.164478i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.1527 | − | 9.59016i | −1.03646 | − | 0.429314i | −0.201418 | − | 0.979505i | \(-0.564555\pi\) |
−0.835039 | + | 0.550191i | \(0.814555\pi\) | |||||||
\(500\) | 17.4615 | + | 4.76222i | 0.780903 | + | 0.212973i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.77212 | − | 13.9561i | 0.212990 | − | 0.622891i | ||||
\(503\) | 5.59362 | + | 5.59362i | 0.249407 | + | 0.249407i | 0.820727 | − | 0.571320i | \(-0.193569\pi\) |
−0.571320 | + | 0.820727i | \(0.693569\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.48165 | − | 2.48165i | 0.110432 | − | 0.110432i | ||||
\(506\) | 11.0023 | + | 22.4362i | 0.489111 | + | 0.997410i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.251051 | + | 1.97482i | 0.0111386 | + | 0.0876183i | ||||
\(509\) | −13.2327 | + | 31.9466i | −0.586530 | + | 1.41601i | 0.300270 | + | 0.953854i | \(0.402923\pi\) |
−0.886800 | + | 0.462154i | \(0.847077\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.1152 | 0.712896 | ||||||||
\(512\) | −4.85807 | + | 22.0998i | −0.214698 | + | 0.976680i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.97435 | − | 9.05227i | 0.351733 | − | 0.399279i | ||||
\(515\) | 0.187137 | − | 0.451790i | 0.00824626 | − | 0.0199082i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.6603 | − | 5.65829i | 0.600780 | − | 0.248851i | ||||
\(518\) | 3.59188 | + | 7.32467i | 0.157818 | + | 0.321828i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −14.4063 | − | 9.76577i | −0.631759 | − | 0.428257i | ||||
\(521\) | 15.3045 | + | 15.3045i | 0.670500 | + | 0.670500i | 0.957831 | − | 0.287331i | \(-0.0927680\pi\) |
−0.287331 | + | 0.957831i | \(0.592768\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.5084 | + | 27.7838i | 0.503229 | + | 1.21490i | 0.947716 | + | 0.319116i | \(0.103386\pi\) |
−0.444487 | + | 0.895785i | \(0.646614\pi\) | |||||||
\(524\) | −20.6793 | − | 5.63979i | −0.903379 | − | 0.246375i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.825274 | − | 13.0358i | −0.0359837 | − | 0.568388i | ||||
\(527\) | 41.6222i | 1.81309i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 40.8509i | 1.77613i | ||||||||
\(530\) | −2.18944 | + | 0.138610i | −0.0951031 | + | 0.00602081i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.79885 | − | 8.39798i | −0.208057 | − | 0.364099i | ||||
\(533\) | 19.9258 | + | 48.1051i | 0.863082 | + | 2.08367i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.47122 | + | 3.47122i | 0.150074 | + | 0.150074i | ||||
\(536\) | 23.2848 | − | 15.3345i | 1.00575 | − | 0.662350i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −31.2980 | + | 15.3479i | −1.34935 | + | 0.661697i | ||||
\(539\) | 10.7019 | − | 4.43288i | 0.460964 | − | 0.190938i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.65267 | + | 8.81833i | −0.157041 | + | 0.379130i | −0.982743 | − | 0.184976i | \(-0.940779\pi\) |
0.825702 | + | 0.564106i | \(0.190779\pi\) | |||||||
\(542\) | 32.2767 | + | 28.4332i | 1.38640 | + | 1.22131i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 38.9320 | + | 19.7408i | 1.66919 | + | 0.846379i | ||||
\(545\) | −7.35096 | −0.314880 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.85086 | + | 16.5394i | −0.292921 | + | 0.707175i | 0.707079 | + | 0.707135i | \(0.250013\pi\) |
−1.00000 | 3.99033e-5i | \(0.999987\pi\) | ||||||||
\(548\) | 22.1239 | − | 28.5682i | 0.945085 | − | 1.22037i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −11.1911 | + | 5.48791i | −0.477190 | + | 0.234005i | ||||
\(551\) | 6.38996 | − | 6.38996i | 0.272221 | − | 0.272221i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.0437 | + | 11.0437i | 0.469627 | + | 0.469627i | ||||
\(554\) | −41.7902 | − | 14.2897i | −1.77550 | − | 0.607111i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.99300 | + | 2.85315i | −0.211750 | + | 0.121000i | ||||
\(557\) | 3.33392 | + | 1.38096i | 0.141263 | + | 0.0585130i | 0.452195 | − | 0.891919i | \(-0.350641\pi\) |
−0.310932 | + | 0.950432i | \(0.600641\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 54.0460i | − | 2.28590i | ||||||
\(560\) | 0.745057 | − | 5.29455i | 0.0314844 | − | 0.223736i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.94575 | − | 46.5303i | −0.124259 | − | 1.96276i | ||||
\(563\) | −15.8181 | − | 6.55208i | −0.666654 | − | 0.276137i | 0.0235814 | − | 0.999722i | \(-0.492493\pi\) |
−0.690236 | + | 0.723585i | \(0.742493\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.836679 | − | 2.01992i | −0.0351993 | − | 0.0849787i | ||||
\(566\) | −11.2653 | + | 32.9453i | −0.473515 | + | 1.38480i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.67399 | + | 1.47325i | −0.321994 | + | 0.0618161i | ||||
\(569\) | −14.2778 | + | 14.2778i | −0.598558 | + | 0.598558i | −0.939929 | − | 0.341371i | \(-0.889109\pi\) |
0.341371 | + | 0.939929i | \(0.389109\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.4753 | + | 8.48116i | −0.856866 | + | 0.354926i | −0.767481 | − | 0.641071i | \(-0.778490\pi\) |
−0.0893852 | + | 0.995997i | \(0.528490\pi\) | |||||||
\(572\) | 26.8058 | − | 3.40771i | 1.12081 | − | 0.142484i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.5735 | + | 12.0028i | −0.441329 | + | 0.500985i | ||||
\(575\) | −31.8486 | −1.32818 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.9749 | −1.37276 | −0.686382 | − | 0.727241i | \(-0.740802\pi\) | ||||
−0.686382 | + | 0.727241i | \(0.740802\pi\) | |||||||
\(578\) | 39.7706 | − | 45.1466i | 1.65424 | − | 1.87785i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.95548 | − | 0.629970i | 0.205765 | − | 0.0261581i | ||||
\(581\) | 8.03895 | − | 3.32984i | 0.333512 | − | 0.138145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.40845 | − | 2.40845i | 0.0997478 | − | 0.0997478i | ||||
\(584\) | −6.47482 | − | 33.7266i | −0.267930 | − | 1.39562i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.26239 | + | 15.3899i | −0.217387 | + | 0.635749i | ||||
\(587\) | −6.25478 | − | 15.1004i | −0.258162 | − | 0.623259i | 0.740655 | − | 0.671886i | \(-0.234516\pi\) |
−0.998817 | + | 0.0486267i | \(0.984516\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.1584 | − | 7.52144i | −0.748202 | − | 0.309916i | ||||
\(590\) | −0.702677 | − | 11.0993i | −0.0289287 | − | 0.456950i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 13.8862 | − | 10.4602i | 0.570720 | − | 0.429910i | ||||
\(593\) | 2.82225i | 0.115896i | 0.998320 | + | 0.0579479i | \(0.0184557\pi\) | ||||
−0.998320 | + | 0.0579479i | \(0.981544\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.52929 | − | 3.94716i | −0.390663 | − | 0.161818i | ||||
\(596\) | 1.12398 | − | 0.642278i | 0.0460402 | − | 0.0263087i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 65.3314 | + | 22.3393i | 2.67160 | + | 0.913524i | ||||
\(599\) | 4.80895 | + | 4.80895i | 0.196488 | + | 0.196488i | 0.798493 | − | 0.602004i | \(-0.205631\pi\) |
−0.602004 | + | 0.798493i | \(0.705631\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.97562 | − | 1.97562i | 0.0805873 | − | 0.0805873i | −0.665664 | − | 0.746251i | \(-0.731852\pi\) |
0.746251 | + | 0.665664i | \(0.231852\pi\) | |||||||
\(602\) | 14.9073 | − | 7.31026i | 0.607576 | − | 0.297944i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 23.4612 | − | 30.2950i | 0.954624 | − | 1.23269i | ||||
\(605\) | 2.35491 | − | 5.68526i | 0.0957408 | − | 0.231139i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.25264 | −0.0914320 | −0.0457160 | − | 0.998954i | \(-0.514557\pi\) | ||||
−0.0457160 | + | 0.998954i | \(0.514557\pi\) | |||||||
\(608\) | −15.6475 | + | 13.4174i | −0.634592 | + | 0.544148i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.53666 | − | 7.52013i | −0.345639 | − | 0.304481i | ||||
\(611\) | 15.6342 | − | 37.7443i | 0.632492 | − | 1.52697i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.1764 | − | 15.8132i | 1.54193 | − | 0.638688i | 0.560095 | − | 0.828428i | \(-0.310764\pi\) |
0.981834 | + | 0.189740i | \(0.0607644\pi\) | |||||||
\(614\) | 4.58239 | − | 2.24712i | 0.184930 | − | 0.0906863i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.56568 | + | 6.93281i | 0.183957 | + | 0.279331i | ||||
\(617\) | 11.7568 | + | 11.7568i | 0.473312 | + | 0.473312i | 0.902985 | − | 0.429673i | \(-0.141371\pi\) |
−0.429673 | + | 0.902985i | \(0.641371\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.6215 | + | 35.2995i | 0.587689 | + | 1.41881i | 0.885706 | + | 0.464247i | \(0.153675\pi\) |
−0.298017 | + | 0.954561i | \(0.596325\pi\) | |||||||
\(620\) | −5.39038 | − | 9.43314i | −0.216483 | − | 0.378844i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −31.5242 | + | 1.99575i | −1.26401 | + | 0.0800221i | ||||
\(623\) | − | 10.0766i | − | 0.403710i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 10.8146i | − | 0.432584i | ||||||
\(626\) | 2.86719 | + | 45.2893i | 0.114596 | + | 1.81012i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −21.0279 | − | 5.73485i | −0.839103 | − | 0.228846i | ||||
\(629\) | −12.8344 | − | 30.9849i | −0.511740 | − | 1.23545i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.538322 | + | 0.538322i | 0.0214302 | + | 0.0214302i | 0.717741 | − | 0.696310i | \(-0.245176\pi\) |
−0.696310 | + | 0.717741i | \(0.745176\pi\) | |||||||
\(632\) | 18.6756 | − | 27.5499i | 0.742875 | − | 1.09588i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.220744 | − | 0.450149i | −0.00876688 | − | 0.0178777i | ||||
\(635\) | −0.926129 | + | 0.383615i | −0.0367523 | + | 0.0152233i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.2483 | − | 29.5701i | 0.485296 | − | 1.17161i | ||||
\(638\) | −5.12662 | + | 5.81961i | −0.202965 | + | 0.230400i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.3800 | + | 0.567973i | −0.449835 | + | 0.0224511i | ||||
\(641\) | 13.2510 | 0.523384 | 0.261692 | − | 0.965151i | \(-0.415719\pi\) | ||||
0.261692 | + | 0.965151i | \(0.415719\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.36388 | − | 10.5353i | 0.172095 | − | 0.415473i | −0.814174 | − | 0.580621i | \(-0.802810\pi\) |
0.986269 | + | 0.165147i | \(0.0528100\pi\) | |||||||
\(644\) | 2.67495 | + | 21.0417i | 0.105408 | + | 0.829160i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.5076 | + | 35.7020i | 0.688828 | + | 1.40468i | ||||
\(647\) | 0.948610 | − | 0.948610i | 0.0372937 | − | 0.0372937i | −0.688214 | − | 0.725508i | \(-0.741605\pi\) |
0.725508 | + | 0.688214i | \(0.241605\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.2096 | + | 12.2096i | 0.479267 | + | 0.479267i | ||||
\(650\) | −11.1428 | + | 32.5871i | −0.437056 | + | 1.27817i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.5719 | + | 3.15596i | 0.453190 | + | 0.123597i | ||||
\(653\) | 42.6127 | + | 17.6508i | 1.66756 | + | 0.690727i | 0.998617 | − | 0.0525829i | \(-0.0167454\pi\) |
0.668947 | + | 0.743310i | \(0.266745\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 10.7935i | − | 0.421737i | ||||||
\(656\) | 29.3681 | + | 17.3061i | 1.14663 | + | 0.675691i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.5255 | − | 0.792971i | 0.488297 | − | 0.0309132i | ||||
\(659\) | 7.85964 | + | 3.25557i | 0.306168 | + | 0.126819i | 0.530477 | − | 0.847699i | \(-0.322013\pi\) |
−0.224310 | + | 0.974518i | \(0.572013\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.31440 | − | 10.4159i | −0.167811 | − | 0.405131i | 0.817494 | − | 0.575937i | \(-0.195363\pi\) |
−0.985305 | + | 0.170806i | \(0.945363\pi\) | |||||||
\(662\) | 2.09657 | + | 0.716898i | 0.0814855 | + | 0.0278630i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.1987 | − | 15.4864i | −0.395788 | − | 0.600988i | ||||
\(665\) | 3.44403 | − | 3.44403i | 0.133554 | − | 0.133554i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.3087 | + | 7.58371i | −0.708915 | + | 0.293642i | ||||
\(668\) | 13.9246 | + | 10.7835i | 0.538759 | + | 0.417228i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.5348 | + | 9.28035i | 0.406995 | + | 0.358531i | ||||
\(671\) | 17.6630 | 0.681871 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.74887 | −0.260150 | −0.130075 | − | 0.991504i | \(-0.541522\pi\) | ||||
−0.130075 | + | 0.991504i | \(0.541522\pi\) | |||||||
\(674\) | −9.72601 | − | 8.56785i | −0.374632 | − | 0.330021i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 29.7952 | − | 38.4740i | 1.14597 | − | 1.47977i | ||||
\(677\) | −11.8633 | + | 4.91394i | −0.455944 | + | 0.188858i | −0.598822 | − | 0.800882i | \(-0.704364\pi\) |
0.142878 | + | 0.989740i | \(0.454364\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.79995 | − | 7.79995i | 0.299334 | − | 0.299334i | ||||
\(680\) | −4.43208 | + | 21.5292i | −0.169963 | + | 0.825607i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 15.9608 | + | 5.45762i | 0.611171 | + | 0.208983i | ||||
\(683\) | 14.3773 | + | 34.7099i | 0.550132 | + | 1.32814i | 0.917379 | + | 0.398014i | \(0.130300\pi\) |
−0.367247 | + | 0.930123i | \(0.619700\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.8101 | + | 6.96296i | 0.642280 | + | 0.266041i | ||||
\(686\) | 22.9256 | − | 1.45138i | 0.875305 | − | 0.0554141i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −21.2887 | − | 28.2615i | −0.811624 | − | 1.07746i | ||||
\(689\) | − | 9.41116i | − | 0.358537i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.7721 | − | 18.9594i | −1.74125 | − | 0.721250i | −0.998673 | − | 0.0514917i | \(-0.983602\pi\) |
−0.742579 | − | 0.669759i | \(-0.766398\pi\) | |||||||
\(692\) | −0.548986 | + | 2.01296i | −0.0208693 | + | 0.0765211i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.400910 | + | 1.17246i | −0.0152183 | + | 0.0445060i | ||||
\(695\) | −2.04764 | − | 2.04764i | −0.0776713 | − | 0.0776713i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 46.4990 | − | 46.4990i | 1.76128 | − | 1.76128i | ||||
\(698\) | 3.06300 | + | 6.24616i | 0.115936 | + | 0.236421i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −10.4956 | + | 1.33426i | −0.396695 | + | 0.0504302i | ||||
\(701\) | 13.2680 | − | 32.0317i | 0.501124 | − | 1.20982i | −0.447748 | − | 0.894160i | \(-0.647774\pi\) |
0.948872 | − | 0.315661i | \(-0.102226\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.8370 | 0.597302 | ||||||||
\(704\) | 12.6749 | − | 12.3407i | 0.477702 | − | 0.465109i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.66459 | + | 6.43030i | −0.213190 | + | 0.242008i | ||||
\(707\) | −1.76997 | + | 4.27309i | −0.0665666 | + | 0.160706i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.1634 | − | 9.18039i | 0.832365 | − | 0.344777i | 0.0745263 | − | 0.997219i | \(-0.476256\pi\) |
0.757838 | + | 0.652442i | \(0.226256\pi\) | |||||||
\(710\) | −1.73248 | − | 3.53293i | −0.0650189 | − | 0.132588i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −21.0887 | + | 4.04860i | −0.790332 | + | 0.151728i | ||||
\(713\) | 30.4772 | + | 30.4772i | 1.14138 | + | 1.14138i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.20712 | + | 12.5711i | 0.194735 | + | 0.470132i | ||||
\(716\) | −5.63453 | + | 20.6600i | −0.210572 | + | 0.772101i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.40690 | + | 22.2230i | 0.0525050 | + | 0.829354i | ||||
\(719\) | 30.9298i | 1.15349i | 0.816925 | + | 0.576744i | \(0.195677\pi\) | ||||
−0.816925 | + | 0.576744i | \(0.804323\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.644454i | 0.0240007i | ||||||||
\(722\) | 8.07700 | − | 0.511341i | 0.300595 | − | 0.0190301i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.97446 | − | 3.41398i | 0.222039 | − | 0.126880i | ||||
\(725\) | −3.78273 | − | 9.13232i | −0.140487 | − | 0.339166i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.17119 | − | 1.17119i | −0.0434369 | − | 0.0434369i | 0.685055 | − | 0.728492i | \(-0.259778\pi\) |
−0.728492 | + | 0.685055i | \(0.759778\pi\) | |||||||
\(728\) | 22.4655 | + | 4.62484i | 0.832628 | + | 0.171408i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 15.5270 | − | 7.61413i | 0.574679 | − | 0.281812i | ||||
\(731\) | −63.0611 | + | 26.1207i | −2.33240 | + | 0.966111i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.77936 | − | 6.70998i | 0.102658 | − | 0.247839i | −0.864202 | − | 0.503145i | \(-0.832176\pi\) |
0.966860 | + | 0.255306i | \(0.0821762\pi\) | |||||||
\(734\) | −35.8491 | − | 31.5803i | −1.32321 | − | 1.16565i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 42.9623 | − | 14.0525i | 1.58361 | − | 0.517980i | ||||
\(737\) | −21.7973 | −0.802913 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.42163 | − | 3.43212i | 0.0522956 | − | 0.126253i | −0.895573 | − | 0.444915i | \(-0.853234\pi\) |
0.947868 | + | 0.318663i | \(0.103234\pi\) | |||||||
\(740\) | 6.92153 | + | 5.36020i | 0.254440 | + | 0.197045i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.59584 | − | 1.27295i | 0.0952964 | − | 0.0467316i | ||||
\(743\) | −15.7962 | + | 15.7962i | −0.579505 | + | 0.579505i | −0.934767 | − | 0.355262i | \(-0.884392\pi\) |
0.355262 | + | 0.934767i | \(0.384392\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.460948 | + | 0.460948i | 0.0168878 | + | 0.0168878i | ||||
\(746\) | −0.462598 | − | 0.158180i | −0.0169369 | − | 0.00579138i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −16.9315 | − | 29.6301i | −0.619078 | − | 1.08338i | ||||
\(749\) | −5.97701 | − | 2.47576i | −0.218395 | − | 0.0904622i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.5578i | 0.494731i | 0.968922 | + | 0.247366i | \(0.0795649\pi\) | ||||
−0.968922 | + | 0.247366i | \(0.920435\pi\) | |||||||
\(752\) | −6.69211 | − | 25.8954i | −0.244036 | − | 0.944308i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.35394 | + | 21.3865i | 0.0493077 | + | 0.778851i | ||||
\(755\) | 17.8262 | + | 7.38386i | 0.648762 | + | 0.268726i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.6598 | + | 40.2204i | 0.605512 | + | 1.46184i | 0.867834 | + | 0.496855i | \(0.165512\pi\) |
−0.262322 | + | 0.964980i | \(0.584488\pi\) | |||||||
\(758\) | −0.349421 | + | 1.02188i | −0.0126915 | + | 0.0371164i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.59156 | − | 5.82406i | −0.311649 | − | 0.211261i | ||||
\(761\) | −4.92005 | + | 4.92005i | −0.178352 | + | 0.178352i | −0.790637 | − | 0.612285i | \(-0.790250\pi\) |
0.612285 | + | 0.790637i | \(0.290250\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.95015 | − | 3.70727i | 0.324017 | − | 0.134212i | ||||
\(764\) | −5.51123 | − | 43.3525i | −0.199389 | − | 1.56844i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.0577729 | + | 0.0655823i | −0.00208742 | + | 0.00236958i | ||||
\(767\) | 47.7096 | 1.72269 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.1958 | 1.08889 | 0.544444 | − | 0.838797i | \(-0.316741\pi\) | ||||
0.544444 | + | 0.838797i | \(0.316741\pi\) | |||||||
\(770\) | −2.76312 | + | 3.13662i | −0.0995760 | + | 0.113036i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.66445 | + | 28.8253i | 0.131886 | + | 1.03744i | ||||
\(773\) | −28.5054 | + | 11.8073i | −1.02527 | + | 0.424679i | −0.831002 | − | 0.556270i | \(-0.812232\pi\) |
−0.194265 | + | 0.980949i | \(0.562232\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.2019 | + | 15.2019i | −0.546070 | + | 0.546070i | ||||
\(776\) | −19.4579 | − | 13.1902i | −0.698499 | − | 0.473500i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.9035 | + | 31.8875i | −0.390911 | + | 1.14322i | ||||
\(779\) | 11.8832 | + | 28.6887i | 0.425761 | + | 1.02788i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.64411 | + | 2.33787i | 0.201962 | + | 0.0836554i | ||||
\(782\) | −5.50945 | − | 87.0257i | −0.197017 | − | 3.11203i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.24281 | − | 20.2872i | −0.187243 | − | 0.724544i | ||||
\(785\) | − | 10.9754i | − | 0.391730i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.1718 | + | 5.04174i | 0.433879 | + | 0.179719i | 0.588923 | − | 0.808189i | \(-0.299552\pi\) |
−0.155044 | + | 0.987908i | \(0.549552\pi\) | |||||||
\(788\) | −17.0953 | − | 29.9168i | −0.608996 | − | 1.06574i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 15.8585 | + | 5.42264i | 0.564221 | + | 0.192929i | ||||
\(791\) | 2.03740 | + | 2.03740i | 0.0724414 | + | 0.0724414i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 34.5096 | − | 34.5096i | 1.22547 | − | 1.22547i | ||||
\(794\) | −3.44127 | + | 1.68753i | −0.122126 | + | 0.0598883i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −27.7157 | − | 21.4637i | −0.982357 | − | 0.760761i | ||||
\(797\) | −1.91098 | + | 4.61351i | −0.0676903 | + | 0.163419i | −0.954104 | − | 0.299474i | \(-0.903189\pi\) |
0.886414 | + | 0.462893i | \(0.153189\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −51.5963 | −1.82535 | ||||||||
\(800\) | 7.00932 | + | 21.4294i | 0.247817 | + | 0.757645i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15.7970 | + | 13.9159i | 0.557810 | + | 0.491387i | ||||
\(803\) | −10.2748 | + | 24.8054i | −0.362588 | + | 0.875365i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.86793 | + | 4.08743i | −0.347799 | + | 0.144063i | ||||
\(806\) | 41.8469 | − | 20.5209i | 1.47400 | − | 0.722819i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.65404 | + | 1.98742i | 0.339628 | + | 0.0699170i | ||||
\(809\) | −18.3954 | − | 18.3954i | −0.646746 | − | 0.646746i | 0.305459 | − | 0.952205i | \(-0.401190\pi\) |
−0.952205 | + | 0.305459i | \(0.901190\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.3184 | + | 41.8102i | 0.608130 | + | 1.46816i | 0.865031 | + | 0.501718i | \(0.167299\pi\) |
−0.256901 | + | 0.966438i | \(0.582701\pi\) | |||||||
\(812\) | −5.71583 | + | 3.26619i | −0.200586 | + | 0.114621i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −13.5646 | + | 0.858755i | −0.475441 | + | 0.0300993i | ||||
\(815\) | 6.03992i | 0.211569i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 32.2317i | − | 1.12764i | ||||||
\(818\) | 1.58428 | + | 25.0248i | 0.0553930 | + | 0.874973i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.51645 | + | 16.5604i | −0.157721 | + | 0.578313i | ||||
\(821\) | 8.21305 | + | 19.8281i | 0.286638 | + | 0.692004i | 0.999961 | − | 0.00883070i | \(-0.00281093\pi\) |
−0.713323 | + | 0.700835i | \(0.752811\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.0587 | + | 22.0587i | 0.768918 | + | 0.768918i | 0.977916 | − | 0.208998i | \(-0.0670202\pi\) |
−0.208998 | + | 0.977916i | \(0.567020\pi\) | |||||||
\(824\) | 1.34874 | − | 0.258931i | 0.0469856 | − | 0.00902027i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.45319 | + | 13.1595i | 0.224535 | + | 0.457879i | ||||
\(827\) | −5.61721 | + | 2.32672i | −0.195329 | + | 0.0809081i | −0.478204 | − | 0.878249i | \(-0.658712\pi\) |
0.282875 | + | 0.959157i | \(0.408712\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.9329 | − | 38.4654i | 0.553373 | − | 1.33596i | −0.361558 | − | 0.932349i | \(-0.617755\pi\) |
0.914931 | − | 0.403610i | \(-0.132245\pi\) | |||||||
\(830\) | 6.17221 | − | 7.00654i | 0.214241 | − | 0.243201i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.652794 | − | 48.8750i | 0.0226315 | − | 1.69443i | ||||
\(833\) | −40.4221 | −1.40054 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.39386 | + | 8.19351i | −0.117449 | + | 0.283548i | ||||
\(836\) | 15.9863 | − | 2.03227i | 0.552897 | − | 0.0702877i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −24.7232 | − | 50.4162i | −0.854047 | − | 1.74160i | ||||
\(839\) | −19.8239 | + | 19.8239i | −0.684399 | + | 0.684399i | −0.960988 | − | 0.276590i | \(-0.910796\pi\) |
0.276590 | + | 0.960988i | \(0.410796\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.1570 | + | 16.1570i | 0.557137 | + | 0.557137i | ||||
\(842\) | 5.47116 | − | 16.0004i | 0.188549 | − | 0.551411i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.08299 | + | 22.3044i | −0.209385 | + | 0.767747i | ||||
\(845\) | 22.6389 | + | 9.37733i | 0.778801 | + | 0.322590i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.10973i | 0.278654i | ||||||||
\(848\) | −3.70705 | − | 4.92124i | −0.127301 | − | 0.168996i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 43.4081 | − | 2.74810i | 1.48889 | − | 0.0942589i | ||||
\(851\) | −32.0861 | − | 13.2905i | −1.09990 | − | 0.455592i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.282320 | − | 0.681580i | −0.00966645 | − | 0.0233369i | 0.918973 | − | 0.394321i | \(-0.129020\pi\) |
−0.928639 | + | 0.370984i | \(0.879020\pi\) | |||||||
\(854\) | 14.1864 | + | 4.85088i | 0.485449 | + | 0.165994i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.77991 | + | 13.5036i | −0.0950154 | + | 0.461545i | ||||
\(857\) | −28.6025 | + | 28.6025i | −0.977043 | + | 0.977043i | −0.999742 | − | 0.0226993i | \(-0.992774\pi\) |
0.0226993 | + | 0.999742i | \(0.492774\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.1822 | − | 16.6440i | 1.37100 | − | 0.567886i | 0.428939 | − | 0.903333i | \(-0.358887\pi\) |
0.942059 | + | 0.335447i | \(0.108887\pi\) | |||||||
\(860\) | 10.9092 | − | 14.0868i | 0.372000 | − | 0.480356i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 29.4642 | + | 25.9557i | 1.00355 | + | 0.884053i | ||||
\(863\) | −24.3873 | −0.830152 | −0.415076 | − | 0.909787i | \(-0.636245\pi\) | ||||
−0.415076 | + | 0.909787i | \(0.636245\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.05066 | −0.0357234 | ||||||||
\(866\) | −5.76738 | − | 5.08062i | −0.195984 | − | 0.172646i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11.3204 | + | 8.76681i | 0.384240 | + | 0.297565i | ||||
\(869\) | −24.0404 | + | 9.95785i | −0.815514 | + | 0.337797i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −42.5871 | + | 42.5871i | −1.44301 | + | 1.44301i | ||||
\(872\) | −11.3548 | − | 17.2417i | −0.384521 | − | 0.583879i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 38.9620 | + | 13.3226i | 1.31791 | + | 0.450644i | ||||
\(875\) | −4.59642 | − | 11.0968i | −0.155388 | − | 0.375139i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.2085 | − | 11.2701i | −0.918765 | − | 0.380565i | −0.127360 | − | 0.991857i | \(-0.540650\pi\) |
−0.791405 | + | 0.611292i | \(0.790650\pi\) | |||||||
\(878\) | 14.8930 | − | 0.942851i | 0.502615 | − | 0.0318197i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.67463 | + | 4.52254i | 0.258712 | + | 0.152455i | ||||
\(881\) | 39.5282i | 1.33174i | 0.746069 | + | 0.665869i | \(0.231939\pi\) | ||||
−0.746069 | + | 0.665869i | \(0.768061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.08879 | − | 1.69363i | −0.137599 | − | 0.0569952i | 0.312822 | − | 0.949812i | \(-0.398726\pi\) |
−0.450420 | + | 0.892817i | \(0.648726\pi\) | |||||||
\(884\) | −90.9712 | − | 24.8103i | −3.05969 | − | 0.834459i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.4945 | + | 48.2381i | −0.554142 | + | 1.62059i | ||||
\(887\) | −8.25045 | − | 8.25045i | −0.277023 | − | 0.277023i | 0.554896 | − | 0.831919i | \(-0.312758\pi\) |
−0.831919 | + | 0.554896i | \(0.812758\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.934141 | − | 0.934141i | 0.0313301 | − | 0.0313301i | ||||
\(890\) | −4.76099 | − | 9.70875i | −0.159589 | − | 0.325438i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.04040 | − | 23.9164i | −0.101800 | − | 0.800781i | ||||
\(893\) | 9.32384 | − | 22.5097i | 0.312011 | − | 0.753260i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.7834 | −0.360451 | ||||||||
\(896\) | 13.5693 | − | 6.43077i | 0.453318 | − | 0.214837i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.84372 | − | 7.76882i | 0.228378 | − | 0.259249i | ||||
\(899\) | −5.11924 | + | 12.3589i | −0.170736 | + | 0.412193i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.9810 | + | 4.54847i | −0.365829 | + | 0.151532i | ||||
\(902\) | −11.7338 | − | 23.9280i | −0.390694 | − | 0.796716i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.44536 | − | 5.08254i | 0.114591 | − | 0.169043i | ||||
\(905\) | 2.45014 | + | 2.45014i | 0.0814453 | + | 0.0814453i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.7593 | − | 47.7031i | −0.656096 | − | 1.58396i | −0.803784 | − | 0.594921i | \(-0.797183\pi\) |
0.147688 | − | 0.989034i | \(-0.452817\pi\) | |||||||
\(908\) | −18.7888 | − | 5.12419i | −0.623527 | − | 0.170052i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.729743 | + | 11.5268i | 0.0241907 | + | 0.382110i | ||||
\(911\) | − | 51.4196i | − | 1.70361i | −0.523862 | − | 0.851803i | \(-0.675509\pi\) | ||
0.523862 | − | 0.851803i | \(-0.324491\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.4970i | 0.479782i | ||||||||
\(914\) | 26.3868 | − | 1.67051i | 0.872799 | − | 0.0552554i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 28.5833 | + | 50.0208i | 0.944420 | + | 1.65273i | ||||
\(917\) | 5.44344 | + | 13.1416i | 0.179758 | + | 0.433975i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.9328 | + | 15.9328i | 0.525575 | + | 0.525575i | 0.919250 | − | 0.393675i | \(-0.128796\pi\) |
−0.393675 | + | 0.919250i | \(0.628796\pi\) | |||||||
\(920\) | 12.5191 | + | 19.0098i | 0.412743 | + | 0.626733i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.37711 | − | 2.63683i | 0.177086 | − | 0.0868395i | ||||
\(923\) | 15.5950 | − | 6.45967i | 0.513317 | − | 0.212623i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.62925 | − | 16.0044i | 0.217968 | − | 0.526222i | ||||
\(926\) | 21.1650 | + | 18.6447i | 0.695526 | + | 0.612704i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.13214 | + | 10.6500i | 0.299777 | + | 0.349604i | ||||
\(929\) | 25.5885 | 0.839532 | 0.419766 | − | 0.907632i | \(-0.362112\pi\) | ||||
0.419766 | + | 0.907632i | \(0.362112\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.30458 | − | 17.6348i | 0.239398 | − | 0.577958i | ||||
\(932\) | −19.7106 | + | 25.4520i | −0.645643 | + | 0.833707i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 32.1776 | − | 15.7793i | 1.05288 | − | 0.516315i | ||||
\(935\) | 12.1514 | − | 12.1514i | 0.397392 | − | 0.397392i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.19246 | + | 6.19246i | 0.202299 | + | 0.202299i | 0.800984 | − | 0.598685i | \(-0.204310\pi\) |
−0.598685 | + | 0.800984i | \(0.704310\pi\) | |||||||
\(938\) | −17.5070 | − | 5.98631i | −0.571623 | − | 0.195460i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.6937 | − | 6.68210i | 0.381405 | − | 0.217946i | ||||
\(941\) | −22.7706 | − | 9.43189i | −0.742300 | − | 0.307471i | −0.0207048 | − | 0.999786i | \(-0.506591\pi\) |
−0.721596 | + | 0.692315i | \(0.756591\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 68.0964i | − | 2.21753i | ||||||
\(944\) | 24.9481 | − | 18.7928i | 0.811990 | − | 0.611653i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.74775 | + | 27.6070i | 0.0568243 | + | 0.897581i | ||||
\(947\) | 35.7353 | + | 14.8021i | 1.16124 | + | 0.481002i | 0.878288 | − | 0.478131i | \(-0.158686\pi\) |
0.282954 | + | 0.959134i | \(0.408686\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.3898 | + | 68.5390i | 0.921571 | + | 2.22487i | ||||
\(950\) | −6.64528 | + | 19.4341i | −0.215601 | + | 0.630526i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.46144 | − | 28.4481i | −0.177006 | − | 0.922007i | ||||
\(953\) | 2.65738 | − | 2.65738i | 0.0860809 | − | 0.0860809i | −0.662755 | − | 0.748836i | \(-0.730613\pi\) |
0.748836 | + | 0.662755i | \(0.230613\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.3310 | − | 8.42138i | 0.657896 | − | 0.272509i | ||||
\(956\) | 24.0407 | − | 3.05620i | 0.777532 | − | 0.0988447i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.7200 | − | 16.7098i | 0.475583 | − | 0.539869i | ||||
\(959\) | −23.9787 | −0.774312 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.90528 | −0.0614607 | ||||||||
\(962\) | −24.8245 | + | 28.1802i | −0.800375 | + | 0.908565i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.61102 | − | 0.331929i | 0.0840952 | − | 0.0106907i | ||||
\(965\) | −13.5182 | + | 5.59942i | −0.435166 | + | 0.180252i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.32503 | + | 5.32503i | −0.171241 | + | 0.171241i | −0.787525 | − | 0.616283i | \(-0.788638\pi\) |
0.616283 | + | 0.787525i | \(0.288638\pi\) | |||||||
\(968\) | 16.9724 | − | 3.25835i | 0.545513 | − | 0.104727i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.82990 | − | 11.2005i | 0.122971 | − | 0.359628i | ||||
\(971\) | −9.21695 | − | 22.2517i | −0.295786 | − | 0.714090i | −0.999992 | − | 0.00409432i | \(-0.998697\pi\) |
0.704206 | − | 0.709996i | \(-0.251303\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.52578 | + | 1.46042i | 0.113031 | + | 0.0468190i | ||||
\(974\) | −2.76662 | − | 43.7007i | −0.0886481 | − | 1.40026i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.45227 | − | 31.6389i | 0.142514 | − | 1.01274i | ||||
\(977\) | 21.7322i | 0.695274i | 0.937629 | + | 0.347637i | \(0.113016\pi\) | ||||
−0.937629 | + | 0.347637i | \(0.886984\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.5104 | + | 6.42463i | 0.495715 | + | 0.205332i | ||||
\(980\) | 9.16117 | − | 5.23496i | 0.292643 | − | 0.167225i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −11.0541 | − | 3.77984i | −0.352752 | − | 0.120619i | ||||
\(983\) | −30.7394 | − | 30.7394i | −0.980436 | − | 0.980436i | 0.0193762 | − | 0.999812i | \(-0.493832\pi\) |
−0.999812 | + | 0.0193762i | \(0.993832\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.2689 | − | 12.2689i | 0.390921 | − | 0.390921i | ||||
\(986\) | 24.2995 | − | 11.9160i | 0.773854 | − | 0.379483i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 27.2631 | − | 35.2043i | 0.867354 | − | 1.12000i | ||||
\(989\) | −27.0490 | + | 65.3021i | −0.860109 | + | 2.07649i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.5981 | 0.400192 | 0.200096 | − | 0.979776i | \(-0.435875\pi\) | ||||
0.200096 | + | 0.979776i | \(0.435875\pi\) | |||||||
\(992\) | 13.7992 | − | 27.2142i | 0.438125 | − | 0.864052i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.89113 | + | 3.42778i | 0.123419 | + | 0.108723i | ||||
\(995\) | 6.75519 | − | 16.3085i | 0.214154 | − | 0.517013i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.0205884 | − | 0.00852802i | 0.000652043 | − | 0.000270085i | −0.382357 | − | 0.924015i | \(-0.624888\pi\) |
0.383009 | + | 0.923744i | \(0.374888\pi\) | |||||||
\(998\) | 31.8205 | − | 15.6042i | 1.00726 | − | 0.493942i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 864.2.v.a.109.10 | ✓ | 128 | |
3.2 | odd | 2 | inner | 864.2.v.a.109.23 | yes | 128 | |
32.5 | even | 8 | inner | 864.2.v.a.325.10 | yes | 128 | |
96.5 | odd | 8 | inner | 864.2.v.a.325.23 | yes | 128 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.2.v.a.109.10 | ✓ | 128 | 1.1 | even | 1 | trivial | |
864.2.v.a.109.23 | yes | 128 | 3.2 | odd | 2 | inner | |
864.2.v.a.325.10 | yes | 128 | 32.5 | even | 8 | inner | |
864.2.v.a.325.23 | yes | 128 | 96.5 | odd | 8 | inner |