Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,2,Mod(293,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("600.293");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.w (of order \(4\), 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: | \(4.79102412128\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 293.4 | ||
Character | \(\chi\) | \(=\) | 600.293 |
Dual form | 600.2.w.j.557.4 |
$q$-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 \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.11940 | − | 0.864261i | −0.791534 | − | 0.611125i | ||||
\(3\) | −0.170116 | − | 1.72368i | −0.0982164 | − | 0.995165i | ||||
\(4\) | 0.506107 | + | 1.93490i | 0.253054 | + | 0.967452i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.29928 | + | 2.07651i | −0.530428 | + | 0.847730i | ||||
\(7\) | −2.06963 | + | 2.06963i | −0.782246 | + | 0.782246i | −0.980209 | − | 0.197964i | \(-0.936567\pi\) |
0.197964 | + | 0.980209i | \(0.436567\pi\) | |||||||
\(8\) | 1.10573 | − | 2.60334i | 0.390933 | − | 0.920419i | ||||
\(9\) | −2.94212 | + | 0.586449i | −0.980707 | + | 0.195483i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.510276 | −0.153854 | −0.0769270 | − | 0.997037i | \(-0.524511\pi\) | ||||
−0.0769270 | + | 0.997037i | \(0.524511\pi\) | |||||||
\(12\) | 3.24905 | − | 1.20152i | 0.937921 | − | 0.346850i | ||||
\(13\) | −0.750647 | + | 0.750647i | −0.208192 | + | 0.208192i | −0.803499 | − | 0.595307i | \(-0.797031\pi\) |
0.595307 | + | 0.803499i | \(0.297031\pi\) | |||||||
\(14\) | 4.10544 | − | 0.528041i | 1.09722 | − | 0.141125i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.48771 | + | 1.95854i | −0.871928 | + | 0.489635i | ||||
\(17\) | 3.14698 | + | 3.14698i | 0.763254 | + | 0.763254i | 0.976909 | − | 0.213656i | \(-0.0685370\pi\) |
−0.213656 | + | 0.976909i | \(0.568537\pi\) | |||||||
\(18\) | 3.80025 | + | 1.88629i | 0.895728 | + | 0.444603i | ||||
\(19\) | 6.01198 | 1.37924 | 0.689622 | − | 0.724170i | \(-0.257777\pi\) | ||||
0.689622 | + | 0.724170i | \(0.257777\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.91945 | + | 3.21529i | 0.855293 | + | 0.701634i | ||||
\(22\) | 0.571203 | + | 0.441012i | 0.121781 | + | 0.0940240i | ||||
\(23\) | −2.54575 | + | 2.54575i | −0.530825 | + | 0.530825i | −0.920818 | − | 0.389993i | \(-0.872478\pi\) |
0.389993 | + | 0.920818i | \(0.372478\pi\) | |||||||
\(24\) | −4.67541 | − | 1.46305i | −0.954365 | − | 0.298643i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.48903 | − | 0.191519i | 0.292023 | − | 0.0375599i | ||||
\(27\) | 1.51135 | + | 4.97150i | 0.290859 | + | 0.956766i | ||||
\(28\) | −5.05199 | − | 2.95708i | −0.954736 | − | 0.558835i | ||||
\(29\) | 5.10739i | 0.948418i | 0.880412 | + | 0.474209i | \(0.157266\pi\) | ||||
−0.880412 | + | 0.474209i | \(0.842734\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.56672 | −0.820207 | −0.410104 | − | 0.912039i | \(-0.634507\pi\) | ||||
−0.410104 | + | 0.912039i | \(0.634507\pi\) | |||||||
\(32\) | 5.59683 | + | 0.821906i | 0.989389 | + | 0.145294i | ||||
\(33\) | 0.0868061 | + | 0.879551i | 0.0151110 | + | 0.153110i | ||||
\(34\) | −0.802913 | − | 6.24253i | −0.137699 | − | 1.07058i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.62375 | − | 5.39592i | −0.437292 | − | 0.899320i | ||||
\(37\) | 6.76263 | + | 6.76263i | 1.11177 | + | 1.11177i | 0.992911 | + | 0.118858i | \(0.0379234\pi\) |
0.118858 | + | 0.992911i | \(0.462077\pi\) | |||||||
\(38\) | −6.72981 | − | 5.19592i | −1.09172 | − | 0.842890i | ||||
\(39\) | 1.42157 | + | 1.16618i | 0.227633 | + | 0.186738i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.24355i | 0.662732i | 0.943502 | + | 0.331366i | \(0.107509\pi\) | ||||
−0.943502 | + | 0.331366i | \(0.892491\pi\) | |||||||
\(42\) | −1.60857 | − | 6.98662i | −0.248208 | − | 1.07806i | ||||
\(43\) | 5.95972 | − | 5.95972i | 0.908848 | − | 0.908848i | −0.0873310 | − | 0.996179i | \(-0.527834\pi\) |
0.996179 | + | 0.0873310i | \(0.0278338\pi\) | |||||||
\(44\) | −0.258254 | − | 0.987336i | −0.0389333 | − | 0.148846i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.04990 | − | 0.649518i | 0.744567 | − | 0.0957661i | ||||
\(47\) | −3.33849 | − | 3.33849i | −0.486969 | − | 0.486969i | 0.420379 | − | 0.907349i | \(-0.361897\pi\) |
−0.907349 | + | 0.420379i | \(0.861897\pi\) | |||||||
\(48\) | 3.96920 | + | 5.67851i | 0.572905 | + | 0.819622i | ||||
\(49\) | − | 1.56672i | − | 0.223817i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.88902 | − | 5.95972i | 0.684599 | − | 0.834527i | ||||
\(52\) | −1.83234 | − | 1.07252i | −0.254100 | − | 0.148732i | ||||
\(53\) | 5.75871 | + | 5.75871i | 0.791019 | + | 0.791019i | 0.981660 | − | 0.190641i | \(-0.0610565\pi\) |
−0.190641 | + | 0.981660i | \(0.561057\pi\) | |||||||
\(54\) | 2.60487 | − | 6.87129i | 0.354478 | − | 0.935064i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.09950 | + | 7.67638i | 0.414188 | + | 1.02580i | ||||
\(57\) | −1.02273 | − | 10.3627i | −0.135464 | − | 1.37257i | ||||
\(58\) | 4.41411 | − | 5.71720i | 0.579602 | − | 0.750706i | ||||
\(59\) | 1.16514i | 0.151689i | 0.997120 | + | 0.0758444i | \(0.0241652\pi\) | ||||
−0.997120 | + | 0.0758444i | \(0.975835\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.92929i | − | 0.631131i | −0.948904 | − | 0.315565i | \(-0.897806\pi\) | ||
0.948904 | − | 0.315565i | \(-0.102194\pi\) | |||||||
\(62\) | 5.11198 | + | 3.94684i | 0.649222 | + | 0.501249i | ||||
\(63\) | 4.87536 | − | 7.30283i | 0.614238 | − | 0.920070i | ||||
\(64\) | −5.55474 | − | 5.75716i | −0.694342 | − | 0.719645i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.662991 | − | 1.05959i | 0.0816085 | − | 0.130427i | ||||
\(67\) | −7.98415 | − | 7.98415i | −0.975419 | − | 0.975419i | 0.0242864 | − | 0.999705i | \(-0.492269\pi\) |
−0.999705 | + | 0.0242864i | \(0.992269\pi\) | |||||||
\(68\) | −4.49639 | + | 7.68180i | −0.545267 | + | 0.931555i | ||||
\(69\) | 4.82112 | + | 3.95497i | 0.580395 | + | 0.476123i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.09150i | 0.604250i | 0.953268 | + | 0.302125i | \(0.0976959\pi\) | ||||
−0.953268 | + | 0.302125i | \(0.902304\pi\) | |||||||
\(72\) | −1.72645 | + | 8.30779i | −0.203465 | + | 0.979082i | ||||
\(73\) | 3.20654 | + | 3.20654i | 0.375297 | + | 0.375297i | 0.869402 | − | 0.494105i | \(-0.164504\pi\) |
−0.494105 | + | 0.869402i | \(0.664504\pi\) | |||||||
\(74\) | −1.72540 | − | 13.4148i | −0.200574 | − | 1.55943i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.04271 | + | 11.6326i | 0.349023 | + | 1.33435i | ||||
\(77\) | 1.05608 | − | 1.05608i | 0.120352 | − | 0.120352i | ||||
\(78\) | −0.583424 | − | 2.53402i | −0.0660597 | − | 0.286922i | ||||
\(79\) | 7.31215i | 0.822682i | 0.911482 | + | 0.411341i | \(0.134939\pi\) | ||||
−0.911482 | + | 0.411341i | \(0.865061\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.31215 | − | 3.45081i | 0.923573 | − | 0.383423i | ||||
\(82\) | 3.66754 | − | 4.75023i | 0.405012 | − | 0.524575i | ||||
\(83\) | −4.77995 | − | 4.77995i | −0.524668 | − | 0.524668i | 0.394310 | − | 0.918978i | \(-0.370984\pi\) |
−0.918978 | + | 0.394310i | \(0.870984\pi\) | |||||||
\(84\) | −4.23762 | + | 9.21104i | −0.462363 | + | 1.00501i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11.8220 | + | 1.52055i | −1.27480 | + | 0.163965i | ||||
\(87\) | 8.80349 | − | 0.868848i | 0.943833 | − | 0.0931502i | ||||
\(88\) | −0.564226 | + | 1.32842i | −0.0601467 | + | 0.141610i | ||||
\(89\) | 12.6431 | 1.34017 | 0.670083 | − | 0.742286i | \(-0.266259\pi\) | ||||
0.670083 | + | 0.742286i | \(0.266259\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.10712i | − | 0.325715i | ||||||
\(92\) | −6.21420 | − | 3.63736i | −0.647875 | − | 0.379221i | ||||
\(93\) | 0.776871 | + | 7.87155i | 0.0805578 | + | 0.816241i | ||||
\(94\) | 0.851777 | + | 6.62243i | 0.0878541 | + | 0.683052i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.464592 | − | 9.78694i | 0.0474172 | − | 0.998875i | ||||
\(97\) | −10.8789 | + | 10.8789i | −1.10458 | + | 1.10458i | −0.110732 | + | 0.993850i | \(0.535320\pi\) |
−0.993850 | + | 0.110732i | \(0.964680\pi\) | |||||||
\(98\) | −1.35405 | + | 1.75378i | −0.136780 | + | 0.177159i | ||||
\(99\) | 1.50129 | − | 0.299251i | 0.150886 | − | 0.0300759i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.41002 | 0.637821 | 0.318911 | − | 0.947785i | \(-0.396683\pi\) | ||||
0.318911 | + | 0.947785i | \(0.396683\pi\) | |||||||
\(102\) | −10.6235 | + | 2.44592i | −1.05188 | + | 0.242182i | ||||
\(103\) | 1.86309 | + | 1.86309i | 0.183575 | + | 0.183575i | 0.792912 | − | 0.609336i | \(-0.208564\pi\) |
−0.609336 | + | 0.792912i | \(0.708564\pi\) | |||||||
\(104\) | 1.12418 | + | 2.78420i | 0.110235 | + | 0.273013i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.46927 | − | 11.4233i | −0.142708 | − | 1.10953i | ||||
\(107\) | −10.0319 | + | 10.0319i | −0.969824 | + | 0.969824i | −0.999558 | − | 0.0297341i | \(-0.990534\pi\) |
0.0297341 | + | 0.999558i | \(0.490534\pi\) | |||||||
\(108\) | −8.85447 | + | 5.44043i | −0.852022 | + | 0.523506i | ||||
\(109\) | −12.6448 | −1.21115 | −0.605577 | − | 0.795786i | \(-0.707058\pi\) | ||||
−0.605577 | + | 0.795786i | \(0.707058\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.5062 | − | 12.8070i | 0.997200 | − | 1.21559i | ||||
\(112\) | 3.16482 | − | 11.2717i | 0.299047 | − | 1.06508i | ||||
\(113\) | −1.88933 | + | 1.88933i | −0.177733 | + | 0.177733i | −0.790367 | − | 0.612634i | \(-0.790110\pi\) |
0.612634 | + | 0.790367i | \(0.290110\pi\) | |||||||
\(114\) | −7.81124 | + | 12.4839i | −0.731590 | + | 1.16923i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.88231 | + | 2.58489i | −0.917549 | + | 0.240001i | ||||
\(117\) | 1.76828 | − | 2.64871i | 0.163477 | − | 0.244874i | ||||
\(118\) | 1.00699 | − | 1.30426i | 0.0927008 | − | 0.120067i | ||||
\(119\) | −13.0261 | −1.19410 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7396 | −0.976329 | ||||||||
\(122\) | −4.26019 | + | 5.51784i | −0.385700 | + | 0.499562i | ||||
\(123\) | 7.31452 | − | 0.721896i | 0.659528 | − | 0.0650912i | ||||
\(124\) | −2.31125 | − | 8.83617i | −0.207556 | − | 0.793511i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −11.7690 | + | 3.96119i | −1.04847 | + | 0.352891i | ||||
\(127\) | −0.964015 | + | 0.964015i | −0.0855425 | + | 0.0855425i | −0.748583 | − | 0.663041i | \(-0.769266\pi\) |
0.663041 | + | 0.748583i | \(0.269266\pi\) | |||||||
\(128\) | 1.24228 | + | 11.2453i | 0.109803 | + | 0.993953i | ||||
\(129\) | −11.2865 | − | 9.25878i | −0.993718 | − | 0.815190i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.59234 | −0.663346 | −0.331673 | − | 0.943395i | \(-0.607613\pi\) | ||||
−0.331673 | + | 0.943395i | \(0.607613\pi\) | |||||||
\(132\) | −1.65791 | + | 0.613109i | −0.144303 | + | 0.0533643i | ||||
\(133\) | −12.4426 | + | 12.4426i | −1.07891 | + | 1.07891i | ||||
\(134\) | 2.03706 | + | 15.8378i | 0.175975 | + | 1.36818i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.6723 | − | 4.71295i | 1.00089 | − | 0.404132i | ||||
\(137\) | −0.713542 | − | 0.713542i | −0.0609620 | − | 0.0609620i | 0.675968 | − | 0.736931i | \(-0.263726\pi\) |
−0.736931 | + | 0.675968i | \(0.763726\pi\) | |||||||
\(138\) | −1.97863 | − | 8.59390i | −0.168432 | − | 0.731561i | ||||
\(139\) | 9.01457 | 0.764606 | 0.382303 | − | 0.924037i | \(-0.375131\pi\) | ||||
0.382303 | + | 0.924037i | \(0.375131\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.18655 | + | 6.32241i | −0.436787 | + | 0.532443i | ||||
\(142\) | 4.40038 | − | 5.69942i | 0.369272 | − | 0.478284i | ||||
\(143\) | 0.383038 | − | 0.383038i | 0.0320312 | − | 0.0320312i | ||||
\(144\) | 9.11269 | − | 7.80762i | 0.759390 | − | 0.650635i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.818111 | − | 6.36069i | −0.0677073 | − | 0.526414i | ||||
\(147\) | −2.70052 | + | 0.266524i | −0.222735 | + | 0.0219825i | ||||
\(148\) | −9.66243 | + | 16.5077i | −0.794247 | + | 1.35692i | ||||
\(149\) | 13.1573i | 1.07789i | 0.842341 | + | 0.538944i | \(0.181177\pi\) | ||||
−0.842341 | + | 0.538944i | \(0.818823\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.75982 | 0.224591 | 0.112295 | − | 0.993675i | \(-0.464180\pi\) | ||||
0.112295 | + | 0.993675i | \(0.464180\pi\) | |||||||
\(152\) | 6.64761 | − | 15.6512i | 0.539192 | − | 1.26948i | ||||
\(153\) | −11.1043 | − | 7.41324i | −0.897731 | − | 0.599325i | ||||
\(154\) | −2.09491 | + | 0.269447i | −0.168812 | + | 0.0217126i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.53697 | + | 3.34081i | −0.123056 | + | 0.267479i | ||||
\(157\) | −4.38090 | − | 4.38090i | −0.349634 | − | 0.349634i | 0.510339 | − | 0.859973i | \(-0.329520\pi\) |
−0.859973 | + | 0.510339i | \(0.829520\pi\) | |||||||
\(158\) | 6.31961 | − | 8.18522i | 0.502761 | − | 0.651181i | ||||
\(159\) | 8.94650 | − | 10.9058i | 0.709504 | − | 0.864886i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 10.5375i | − | 0.830472i | ||||||
\(162\) | −12.2870 | − | 3.32104i | −0.965359 | − | 0.260925i | ||||
\(163\) | −0.470868 | + | 0.470868i | −0.0368812 | + | 0.0368812i | −0.725307 | − | 0.688426i | \(-0.758302\pi\) |
0.688426 | + | 0.725307i | \(0.258302\pi\) | |||||||
\(164\) | −8.21087 | + | 2.14769i | −0.641162 | + | 0.167707i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.21955 | + | 9.48180i | 0.0946553 | + | 0.735930i | ||||
\(167\) | 0.495354 | + | 0.495354i | 0.0383316 | + | 0.0383316i | 0.726013 | − | 0.687681i | \(-0.241371\pi\) |
−0.687681 | + | 0.726013i | \(0.741371\pi\) | |||||||
\(168\) | 12.7043 | − | 6.64841i | 0.980160 | − | 0.512936i | ||||
\(169\) | 11.8731i | 0.913312i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.6880 | + | 3.52572i | −1.35263 | + | 0.269619i | ||||
\(172\) | 14.5477 | + | 8.51523i | 1.10925 | + | 0.649280i | ||||
\(173\) | −2.32674 | − | 2.32674i | −0.176899 | − | 0.176899i | 0.613104 | − | 0.790002i | \(-0.289921\pi\) |
−0.790002 | + | 0.613104i | \(0.789921\pi\) | |||||||
\(174\) | −10.6055 | − | 6.63592i | −0.804002 | − | 0.503068i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.77970 | − | 0.999395i | 0.134150 | − | 0.0753323i | ||||
\(177\) | 2.00833 | − | 0.198209i | 0.150955 | − | 0.0148983i | ||||
\(178\) | −14.1527 | − | 10.9269i | −1.06079 | − | 0.819008i | ||||
\(179\) | − | 13.9141i | − | 1.03999i | −0.854169 | − | 0.519996i | \(-0.825934\pi\) | ||
0.854169 | − | 0.519996i | \(-0.174066\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.80972i | 0.431833i | 0.976412 | + | 0.215917i | \(0.0692740\pi\) | ||||
−0.976412 | + | 0.215917i | \(0.930726\pi\) | |||||||
\(182\) | −2.68536 | + | 3.47811i | −0.199052 | + | 0.257814i | ||||
\(183\) | −8.49650 | + | 0.838550i | −0.628079 | + | 0.0619874i | ||||
\(184\) | 3.81254 | + | 9.44235i | 0.281064 | + | 0.696099i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.93344 | − | 9.48282i | 0.435061 | − | 0.695314i | ||||
\(187\) | −1.60583 | − | 1.60583i | −0.117430 | − | 0.117430i | ||||
\(188\) | 4.77003 | − | 8.14930i | 0.347890 | − | 0.594349i | ||||
\(189\) | −13.4171 | − | 7.16122i | −0.975950 | − | 0.520902i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.8456i | 1.00183i | 0.865497 | + | 0.500914i | \(0.167003\pi\) | ||||
−0.865497 | + | 0.500914i | \(0.832997\pi\) | |||||||
\(192\) | −8.97853 | + | 10.5540i | −0.647969 | + | 0.761666i | ||||
\(193\) | −4.57254 | − | 4.57254i | −0.329138 | − | 0.329138i | 0.523120 | − | 0.852259i | \(-0.324768\pi\) |
−0.852259 | + | 0.523120i | \(0.824768\pi\) | |||||||
\(194\) | 21.5800 | − | 2.77562i | 1.54935 | − | 0.199278i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.03145 | − | 0.792928i | 0.216532 | − | 0.0566377i | ||||
\(197\) | −3.85757 | + | 3.85757i | −0.274840 | + | 0.274840i | −0.831045 | − | 0.556205i | \(-0.812257\pi\) |
0.556205 | + | 0.831045i | \(0.312257\pi\) | |||||||
\(198\) | −1.93918 | − | 0.962528i | −0.137811 | − | 0.0684039i | ||||
\(199\) | − | 5.91833i | − | 0.419540i | −0.977751 | − | 0.209770i | \(-0.932729\pi\) | ||
0.977751 | − | 0.209770i | \(-0.0672714\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.4039 | + | 15.1203i | −0.874900 | + | 1.06650i | ||||
\(202\) | −7.17537 | − | 5.53993i | −0.504858 | − | 0.389788i | ||||
\(203\) | −10.5704 | − | 10.5704i | −0.741896 | − | 0.741896i | ||||
\(204\) | 14.0058 | + | 6.44352i | 0.980606 | + | 0.451137i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.475344 | − | 3.69573i | −0.0331188 | − | 0.257494i | ||||
\(207\) | 5.99695 | − | 8.98285i | 0.416817 | − | 0.624351i | ||||
\(208\) | 1.14787 | − | 4.08821i | 0.0795904 | − | 0.283467i | ||||
\(209\) | −3.06777 | −0.212202 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 6.95372i | − | 0.478714i | −0.970932 | − | 0.239357i | \(-0.923063\pi\) | ||
0.970932 | − | 0.239357i | \(-0.0769366\pi\) | |||||||
\(212\) | −8.22802 | + | 14.0571i | −0.565103 | + | 0.965444i | ||||
\(213\) | 8.77609 | − | 0.866144i | 0.601328 | − | 0.0593472i | ||||
\(214\) | 19.8999 | − | 2.55953i | 1.36033 | − | 0.174966i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6136 | + | 1.56256i | 0.994332 | + | 0.106319i | ||||
\(217\) | 9.45141 | − | 9.45141i | 0.641604 | − | 0.641604i | ||||
\(218\) | 14.1546 | + | 10.9284i | 0.958671 | + | 0.740166i | ||||
\(219\) | 4.98156 | − | 6.07252i | 0.336622 | − | 0.410343i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.72454 | −0.317807 | ||||||||
\(222\) | −22.8292 | + | 5.25610i | −1.53219 | + | 0.352766i | ||||
\(223\) | 16.7218 | + | 16.7218i | 1.11977 | + | 1.11977i | 0.991774 | + | 0.127998i | \(0.0408550\pi\) |
0.127998 | + | 0.991774i | \(0.459145\pi\) | |||||||
\(224\) | −13.2844 | + | 9.88231i | −0.887601 | + | 0.660290i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.74778 | − | 0.482039i | 0.249298 | − | 0.0320647i | ||||
\(227\) | 12.4814 | − | 12.4814i | 0.828416 | − | 0.828416i | −0.158881 | − | 0.987298i | \(-0.550789\pi\) |
0.987298 | + | 0.158881i | \(0.0507887\pi\) | |||||||
\(228\) | 19.5332 | − | 7.22354i | 1.29362 | − | 0.478390i | ||||
\(229\) | −1.09678 | −0.0724770 | −0.0362385 | − | 0.999343i | \(-0.511538\pi\) | ||||
−0.0362385 | + | 0.999343i | \(0.511538\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.00000 | − | 1.64069i | −0.131590 | − | 0.107949i | ||||
\(232\) | 13.2963 | + | 5.64737i | 0.872942 | + | 0.370768i | ||||
\(233\) | 6.98082 | − | 6.98082i | 0.457329 | − | 0.457329i | −0.440449 | − | 0.897778i | \(-0.645181\pi\) |
0.897778 | + | 0.440449i | \(0.145181\pi\) | |||||||
\(234\) | −4.26859 | + | 1.43671i | −0.279046 | + | 0.0939207i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.25444 | + | 0.589688i | −0.146752 | + | 0.0383854i | ||||
\(237\) | 12.6038 | − | 1.24391i | 0.818704 | − | 0.0808008i | ||||
\(238\) | 14.5814 | + | 11.2580i | 0.945174 | + | 0.729746i | ||||
\(239\) | 12.3210 | 0.796976 | 0.398488 | − | 0.917173i | \(-0.369535\pi\) | ||||
0.398488 | + | 0.917173i | \(0.369535\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.03833 | −0.453379 | −0.226689 | − | 0.973967i | \(-0.572790\pi\) | ||||
−0.226689 | + | 0.973967i | \(0.572790\pi\) | |||||||
\(242\) | 12.0219 | + | 9.28183i | 0.772798 | + | 0.596659i | ||||
\(243\) | −7.36211 | − | 13.7404i | −0.472279 | − | 0.881449i | ||||
\(244\) | 9.53771 | − | 2.49475i | 0.610589 | − | 0.159710i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.81177 | − | 5.51356i | −0.561818 | − | 0.351532i | ||||
\(247\) | −4.51288 | + | 4.51288i | −0.287148 | + | 0.287148i | ||||
\(248\) | −5.04954 | + | 11.8887i | −0.320646 | + | 0.754934i | ||||
\(249\) | −7.42595 | + | 9.05224i | −0.470600 | + | 0.573662i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.92262 | 0.626311 | 0.313155 | − | 0.949702i | \(-0.398614\pi\) | ||||
0.313155 | + | 0.949702i | \(0.398614\pi\) | |||||||
\(252\) | 16.5977 | + | 5.73735i | 1.04556 | + | 0.361419i | ||||
\(253\) | 1.29904 | − | 1.29904i | 0.0816696 | − | 0.0816696i | ||||
\(254\) | 1.91228 | − | 0.245957i | 0.119987 | − | 0.0154327i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.32826 | − | 13.6616i | 0.520516 | − | 0.853852i | ||||
\(257\) | 14.5324 | + | 14.5324i | 0.906508 | + | 0.906508i | 0.995989 | − | 0.0894809i | \(-0.0285208\pi\) |
−0.0894809 | + | 0.995989i | \(0.528521\pi\) | |||||||
\(258\) | 4.63206 | + | 20.1187i | 0.288379 | + | 1.25254i | ||||
\(259\) | −27.9923 | −1.73935 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.99522 | − | 15.0266i | −0.185400 | − | 0.930120i | ||||
\(262\) | 8.49885 | + | 6.56176i | 0.525061 | + | 0.405387i | ||||
\(263\) | −10.8634 | + | 10.8634i | −0.669867 | + | 0.669867i | −0.957685 | − | 0.287818i | \(-0.907070\pi\) |
0.287818 | + | 0.957685i | \(0.407070\pi\) | |||||||
\(264\) | 2.38575 | + | 0.746557i | 0.146833 | + | 0.0459474i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 24.6818 | − | 3.17457i | 1.51334 | − | 0.194646i | ||||
\(267\) | −2.15079 | − | 21.7926i | −0.131626 | − | 1.33369i | ||||
\(268\) | 11.4077 | − | 19.4894i | 0.696838 | − | 1.19050i | ||||
\(269\) | − | 32.3280i | − | 1.97108i | −0.169455 | − | 0.985538i | \(-0.554201\pi\) | ||
0.169455 | − | 0.985538i | \(-0.445799\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.306338 | 0.0186087 | 0.00930434 | − | 0.999957i | \(-0.497038\pi\) | ||||
0.00930434 | + | 0.999957i | \(0.497038\pi\) | |||||||
\(272\) | −17.1392 | − | 4.81227i | −1.03922 | − | 0.291787i | ||||
\(273\) | −5.35567 | + | 0.528571i | −0.324140 | + | 0.0319905i | ||||
\(274\) | 0.182052 | + | 1.41543i | 0.0109982 | + | 0.0855090i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.21250 | + | 11.3300i | −0.313755 | + | 0.681989i | ||||
\(277\) | −6.97897 | − | 6.97897i | −0.419326 | − | 0.419326i | 0.465645 | − | 0.884971i | \(-0.345822\pi\) |
−0.884971 | + | 0.465645i | \(0.845822\pi\) | |||||||
\(278\) | −10.0909 | − | 7.79094i | −0.605212 | − | 0.467270i | ||||
\(279\) | 13.4358 | − | 2.67815i | 0.804383 | − | 0.160337i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 15.4596i | − | 0.922240i | −0.887338 | − | 0.461120i | \(-0.847448\pi\) | ||
0.887338 | − | 0.461120i | \(-0.152552\pi\) | |||||||
\(282\) | 11.2700 | − | 2.59477i | 0.671121 | − | 0.154516i | ||||
\(283\) | −8.86458 | + | 8.86458i | −0.526945 | + | 0.526945i | −0.919660 | − | 0.392715i | \(-0.871536\pi\) |
0.392715 | + | 0.919660i | \(0.371536\pi\) | |||||||
\(284\) | −9.85156 | + | 2.57684i | −0.584583 | + | 0.152908i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.759816 | + | 0.0977275i | −0.0449289 | + | 0.00577875i | ||||
\(287\) | −8.78258 | − | 8.78258i | −0.518419 | − | 0.518419i | ||||
\(288\) | −16.9485 | + | 0.864107i | −0.998703 | + | 0.0509180i | ||||
\(289\) | 2.80690i | 0.165112i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20.6023 | + | 16.9010i | 1.20773 | + | 0.990754i | ||||
\(292\) | −4.58150 | + | 7.82720i | −0.268112 | + | 0.458053i | ||||
\(293\) | −1.49638 | − | 1.49638i | −0.0874192 | − | 0.0874192i | 0.662045 | − | 0.749464i | \(-0.269689\pi\) |
−0.749464 | + | 0.662045i | \(0.769689\pi\) | |||||||
\(294\) | 3.25330 | + | 2.03560i | 0.189736 | + | 0.118719i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 25.0830 | − | 10.1278i | 1.45792 | − | 0.588666i | ||||
\(297\) | −0.771206 | − | 2.53684i | −0.0447499 | − | 0.147202i | ||||
\(298\) | 11.3713 | − | 14.7283i | 0.658724 | − | 0.853186i | ||||
\(299\) | − | 3.82192i | − | 0.221027i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.6688i | 1.42189i | ||||||||
\(302\) | −3.08933 | − | 2.38520i | −0.177771 | − | 0.137253i | ||||
\(303\) | −1.09045 | − | 11.0488i | −0.0626445 | − | 0.634738i | ||||
\(304\) | −20.9681 | + | 11.7747i | −1.20260 | + | 0.675325i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.02319 | + | 17.8954i | 0.344323 | + | 1.02301i | ||||
\(307\) | 12.4948 | + | 12.4948i | 0.713118 | + | 0.713118i | 0.967186 | − | 0.254068i | \(-0.0817688\pi\) |
−0.254068 | + | 0.967186i | \(0.581769\pi\) | |||||||
\(308\) | 2.57791 | + | 1.50893i | 0.146890 | + | 0.0859791i | ||||
\(309\) | 2.89442 | − | 3.52830i | 0.164658 | − | 0.200718i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 0.224632i | − | 0.0127377i | −0.999980 | − | 0.00636886i | \(-0.997973\pi\) | ||
0.999980 | − | 0.00636886i | \(-0.00202728\pi\) | |||||||
\(312\) | 4.60782 | − | 2.41136i | 0.260866 | − | 0.136516i | ||||
\(313\) | 12.0383 | + | 12.0383i | 0.680447 | + | 0.680447i | 0.960101 | − | 0.279654i | \(-0.0902198\pi\) |
−0.279654 | + | 0.960101i | \(0.590220\pi\) | |||||||
\(314\) | 1.11774 | + | 8.69022i | 0.0630775 | + | 0.490417i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.1483 | + | 3.70073i | −0.795905 | + | 0.208183i | ||||
\(317\) | 20.2257 | − | 20.2257i | 1.13599 | − | 1.13599i | 0.146829 | − | 0.989162i | \(-0.453093\pi\) |
0.989162 | − | 0.146829i | \(-0.0469068\pi\) | |||||||
\(318\) | −19.4401 | + | 4.47582i | −1.09015 | + | 0.250992i | ||||
\(319\) | − | 2.60618i | − | 0.145918i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.9984 | + | 15.5852i | 1.06039 | + | 0.869882i | ||||
\(322\) | −9.10715 | + | 11.7957i | −0.507522 | + | 0.657347i | ||||
\(323\) | 18.9196 | + | 18.9196i | 1.05271 | + | 1.05271i | ||||
\(324\) | 10.8838 | + | 14.3367i | 0.604657 | + | 0.796486i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.934042 | − | 0.120136i | 0.0517318 | − | 0.00665374i | ||||
\(327\) | 2.15109 | + | 21.7956i | 0.118955 | + | 1.20530i | ||||
\(328\) | 11.0474 | + | 4.69221i | 0.609991 | + | 0.259084i | ||||
\(329\) | 13.8189 | 0.761860 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.3308i | 0.677760i | 0.940830 | + | 0.338880i | \(0.110048\pi\) | ||||
−0.940830 | + | 0.338880i | \(0.889952\pi\) | |||||||
\(332\) | 6.82959 | − | 11.6679i | 0.374822 | − | 0.640361i | ||||
\(333\) | −23.8624 | − | 15.9305i | −1.30765 | − | 0.872988i | ||||
\(334\) | −0.126384 | − | 0.982613i | −0.00691540 | − | 0.0537662i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −19.9672 | − | 3.53763i | −1.08930 | − | 0.192993i | ||||
\(337\) | −10.6723 | + | 10.6723i | −0.581359 | + | 0.581359i | −0.935277 | − | 0.353918i | \(-0.884849\pi\) |
0.353918 | + | 0.935277i | \(0.384849\pi\) | |||||||
\(338\) | 10.2614 | − | 13.2907i | 0.558147 | − | 0.722918i | ||||
\(339\) | 3.57799 | + | 2.93518i | 0.194330 | + | 0.159417i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.33029 | 0.126192 | ||||||||
\(342\) | 22.8470 | + | 11.3403i | 1.23543 | + | 0.613215i | ||||
\(343\) | −11.2449 | − | 11.2449i | −0.607166 | − | 0.607166i | ||||
\(344\) | −8.92534 | − | 22.1050i | −0.481222 | − | 1.19182i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.593640 | + | 4.61546i | 0.0319143 | + | 0.248129i | ||||
\(347\) | 8.00457 | − | 8.00457i | 0.429708 | − | 0.429708i | −0.458821 | − | 0.888529i | \(-0.651728\pi\) |
0.888529 | + | 0.458821i | \(0.151728\pi\) | |||||||
\(348\) | 6.13664 | + | 16.5942i | 0.328959 | + | 0.889541i | ||||
\(349\) | 13.9579 | 0.747152 | 0.373576 | − | 0.927600i | \(-0.378132\pi\) | ||||
0.373576 | + | 0.927600i | \(0.378132\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.86633 | − | 2.59735i | −0.259746 | − | 0.138636i | ||||
\(352\) | −2.85593 | − | 0.419399i | −0.152221 | − | 0.0223541i | ||||
\(353\) | 11.8744 | − | 11.8744i | 0.632008 | − | 0.632008i | −0.316563 | − | 0.948571i | \(-0.602529\pi\) |
0.948571 | + | 0.316563i | \(0.102529\pi\) | |||||||
\(354\) | −2.41943 | − | 1.51385i | −0.128591 | − | 0.0804600i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.39876 | + | 24.4632i | 0.339134 | + | 1.29655i | ||||
\(357\) | 2.21595 | + | 22.4528i | 0.117281 | + | 1.18833i | ||||
\(358\) | −12.0254 | + | 15.5755i | −0.635564 | + | 0.823189i | ||||
\(359\) | −33.8765 | −1.78793 | −0.893967 | − | 0.448133i | \(-0.852089\pi\) | ||||
−0.893967 | + | 0.448133i | \(0.852089\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.1439 | 0.902313 | ||||||||
\(362\) | 5.02112 | − | 6.50340i | 0.263904 | − | 0.341811i | ||||
\(363\) | 1.82698 | + | 18.5116i | 0.0958915 | + | 0.971608i | ||||
\(364\) | 6.01198 | − | 1.57254i | 0.315114 | − | 0.0824233i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.2357 | + | 6.40452i | 0.535029 | + | 0.334770i | ||||
\(367\) | −10.7900 | + | 10.7900i | −0.563233 | + | 0.563233i | −0.930224 | − | 0.366992i | \(-0.880388\pi\) |
0.366992 | + | 0.930224i | \(0.380388\pi\) | |||||||
\(368\) | 3.89289 | − | 13.8648i | 0.202931 | − | 0.722752i | ||||
\(369\) | −2.48863 | − | 12.4851i | −0.129553 | − | 0.649946i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −23.8368 | −1.23754 | ||||||||
\(372\) | −14.8375 | + | 5.48702i | −0.769289 | + | 0.284489i | ||||
\(373\) | 25.8380 | − | 25.8380i | 1.33784 | − | 1.33784i | 0.439697 | − | 0.898146i | \(-0.355086\pi\) |
0.898146 | − | 0.439697i | \(-0.144914\pi\) | |||||||
\(374\) | 0.409708 | + | 3.18541i | 0.0211855 | + | 0.164714i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.3827 | + | 4.99977i | −0.638588 | + | 0.257843i | ||||
\(377\) | −3.83385 | − | 3.83385i | −0.197453 | − | 0.197453i | ||||
\(378\) | 8.82991 | + | 19.6121i | 0.454162 | + | 1.00874i | ||||
\(379\) | −12.2262 | −0.628019 | −0.314010 | − | 0.949420i | \(-0.601672\pi\) | ||||
−0.314010 | + | 0.949420i | \(0.601672\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.82564 | + | 1.49766i | 0.0935306 | + | 0.0767272i | ||||
\(382\) | 11.9662 | − | 15.4987i | 0.612242 | − | 0.792982i | ||||
\(383\) | 21.6256 | − | 21.6256i | 1.10501 | − | 1.10501i | 0.111219 | − | 0.993796i | \(-0.464525\pi\) |
0.993796 | − | 0.111219i | \(-0.0354754\pi\) | |||||||
\(384\) | 19.1719 | − | 4.05430i | 0.978363 | − | 0.206895i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.16663 | + | 9.07035i | 0.0593798 | + | 0.461669i | ||||
\(387\) | −14.0391 | + | 21.0293i | −0.713649 | + | 1.06898i | ||||
\(388\) | −26.5555 | − | 15.5437i | −1.34815 | − | 0.789112i | ||||
\(389\) | 6.63941i | 0.336632i | 0.985733 | + | 0.168316i | \(0.0538328\pi\) | ||||
−0.985733 | + | 0.168316i | \(0.946167\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0228 | −0.810309 | ||||||||
\(392\) | −4.07870 | − | 1.73236i | −0.206006 | − | 0.0874975i | ||||
\(393\) | 1.29158 | + | 13.0867i | 0.0651514 | + | 0.660138i | ||||
\(394\) | 7.65210 | − | 0.984213i | 0.385507 | − | 0.0495839i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.33884 | + | 2.75341i | 0.0672792 | + | 0.138364i | ||||
\(397\) | −14.0596 | − | 14.0596i | −0.705629 | − | 0.705629i | 0.259984 | − | 0.965613i | \(-0.416283\pi\) |
−0.965613 | + | 0.259984i | \(0.916283\pi\) | |||||||
\(398\) | −5.11498 | + | 6.62498i | −0.256391 | + | 0.332080i | ||||
\(399\) | 23.5636 | + | 19.3303i | 1.17966 | + | 0.967725i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 18.1176i | − | 0.904751i | −0.891827 | − | 0.452376i | \(-0.850577\pi\) | ||
0.891827 | − | 0.452376i | \(-0.149423\pi\) | |||||||
\(402\) | 26.9528 | − | 6.20550i | 1.34428 | − | 0.309502i | ||||
\(403\) | 3.42800 | − | 3.42800i | 0.170761 | − | 0.170761i | ||||
\(404\) | 3.24416 | + | 12.4028i | 0.161403 | + | 0.617062i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.69691 | + | 20.9681i | 0.133845 | + | 1.04063i | ||||
\(407\) | −3.45081 | − | 3.45081i | −0.171050 | − | 0.171050i | ||||
\(408\) | −10.1092 | − | 19.3176i | −0.500482 | − | 0.956363i | ||||
\(409\) | − | 26.3245i | − | 1.30166i | −0.759223 | − | 0.650831i | \(-0.774421\pi\) | ||
0.759223 | − | 0.650831i | \(-0.225579\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.10853 | + | 1.35130i | −0.0546798 | + | 0.0666548i | ||||
\(412\) | −2.66197 | + | 4.54782i | −0.131146 | + | 0.224055i | ||||
\(413\) | −2.41142 | − | 2.41142i | −0.118658 | − | 0.118658i | ||||
\(414\) | −14.4765 | + | 4.87247i | −0.711481 | + | 0.239469i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.81820 | + | 3.58428i | −0.236232 | + | 0.175734i | ||||
\(417\) | −1.53352 | − | 15.5382i | −0.0750969 | − | 0.760909i | ||||
\(418\) | 3.43406 | + | 2.65135i | 0.167965 | + | 0.129682i | ||||
\(419\) | 12.7809i | 0.624385i | 0.950019 | + | 0.312193i | \(0.101063\pi\) | ||||
−0.950019 | + | 0.312193i | \(0.898937\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 26.3792i | − | 1.28564i | −0.766017 | − | 0.642821i | \(-0.777764\pi\) | ||
0.766017 | − | 0.642821i | \(-0.222236\pi\) | |||||||
\(422\) | −6.00983 | + | 7.78398i | −0.292554 | + | 0.378918i | ||||
\(423\) | 11.7801 | + | 7.86440i | 0.572769 | + | 0.382380i | ||||
\(424\) | 21.3594 | − | 8.62431i | 1.03730 | − | 0.418833i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10.5725 | − | 6.61527i | −0.512240 | − | 0.320511i | ||||
\(427\) | 10.2018 | + | 10.2018i | 0.493700 | + | 0.493700i | ||||
\(428\) | −24.4881 | − | 14.3336i | −1.18368 | − | 0.692841i | ||||
\(429\) | −0.725393 | − | 0.595072i | −0.0350223 | − | 0.0287303i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 28.6818i | − | 1.38155i | −0.723068 | − | 0.690777i | \(-0.757269\pi\) | ||
0.723068 | − | 0.690777i | \(-0.242731\pi\) | |||||||
\(432\) | −15.0080 | − | 14.3791i | −0.722074 | − | 0.691816i | ||||
\(433\) | 2.25457 | + | 2.25457i | 0.108347 | + | 0.108347i | 0.759202 | − | 0.650855i | \(-0.225589\pi\) |
−0.650855 | + | 0.759202i | \(0.725589\pi\) | |||||||
\(434\) | −18.7484 | + | 2.41142i | −0.899951 | + | 0.115752i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.39964 | − | 24.4665i | −0.306487 | − | 1.17173i | ||||
\(437\) | −15.3050 | + | 15.3050i | −0.732137 | + | 0.732137i | ||||
\(438\) | −10.8246 | + | 2.49221i | −0.517219 | + | 0.119082i | ||||
\(439\) | 11.8510i | 0.565620i | 0.959176 | + | 0.282810i | \(0.0912665\pi\) | ||||
−0.959176 | + | 0.282810i | \(0.908733\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.918802 | + | 4.60948i | 0.0437525 | + | 0.219499i | ||||
\(442\) | 5.28864 | + | 4.08323i | 0.251555 | + | 0.194219i | ||||
\(443\) | −1.66807 | − | 1.66807i | −0.0792526 | − | 0.0792526i | 0.666369 | − | 0.745622i | \(-0.267847\pi\) |
−0.745622 | + | 0.666369i | \(0.767847\pi\) | |||||||
\(444\) | 30.0976 | + | 13.8467i | 1.42837 | + | 0.657135i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.26636 | − | 33.1703i | −0.202018 | − | 1.57066i | ||||
\(447\) | 22.6789 | − | 2.23827i | 1.07268 | − | 0.105866i | ||||
\(448\) | 23.4114 | + | 0.418930i | 1.10609 | + | 0.0197926i | ||||
\(449\) | 34.3414 | 1.62067 | 0.810336 | − | 0.585966i | \(-0.199285\pi\) | ||||
0.810336 | + | 0.585966i | \(0.199285\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.16539i | − | 0.101964i | ||||||
\(452\) | −4.61186 | − | 2.69946i | −0.216924 | − | 0.126972i | ||||
\(453\) | −0.469488 | − | 4.75703i | −0.0220585 | − | 0.223505i | ||||
\(454\) | −24.7588 | + | 3.18447i | −1.16199 | + | 0.149455i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −28.1085 | − | 8.79580i | −1.31630 | − | 0.411901i | ||||
\(457\) | 4.61474 | − | 4.61474i | 0.215869 | − | 0.215869i | −0.590886 | − | 0.806755i | \(-0.701222\pi\) |
0.806755 | + | 0.590886i | \(0.201222\pi\) | |||||||
\(458\) | 1.22773 | + | 0.947900i | 0.0573680 | + | 0.0442925i | ||||
\(459\) | −10.8890 | + | 20.4014i | −0.508255 | + | 0.952254i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.6452 | −0.961543 | −0.480772 | − | 0.876846i | \(-0.659643\pi\) | ||||
−0.480772 | + | 0.876846i | \(0.659643\pi\) | |||||||
\(462\) | 0.820816 | + | 3.56510i | 0.0381878 | + | 0.165864i | ||||
\(463\) | −27.1817 | − | 27.1817i | −1.26324 | − | 1.26324i | −0.949512 | − | 0.313730i | \(-0.898421\pi\) |
−0.313730 | − | 0.949512i | \(-0.601579\pi\) | |||||||
\(464\) | −10.0030 | − | 17.8131i | −0.464378 | − | 0.826952i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.8476 | + | 1.78107i | −0.641476 | + | 0.0825067i | ||||
\(467\) | 6.39901 | − | 6.39901i | 0.296111 | − | 0.296111i | −0.543378 | − | 0.839488i | \(-0.682855\pi\) |
0.839488 | + | 0.543378i | \(0.182855\pi\) | |||||||
\(468\) | 6.01994 | + | 2.08092i | 0.278272 | + | 0.0961905i | ||||
\(469\) | 33.0484 | 1.52603 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.80600 | + | 8.29652i | −0.313604 | + | 0.382283i | ||||
\(472\) | 3.03326 | + | 1.28833i | 0.139617 | + | 0.0593002i | ||||
\(473\) | −3.04110 | + | 3.04110i | −0.139830 | + | 0.139830i | ||||
\(474\) | −15.1837 | − | 9.50052i | −0.697412 | − | 0.436373i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.59262 | − | 25.2043i | −0.302172 | − | 1.15524i | ||||
\(477\) | −20.3200 | − | 13.5656i | −0.930389 | − | 0.621127i | ||||
\(478\) | −13.7921 | − | 10.6485i | −0.630834 | − | 0.487052i | ||||
\(479\) | −35.9113 | −1.64083 | −0.820414 | − | 0.571770i | \(-0.806257\pi\) | ||||
−0.820414 | + | 0.571770i | \(0.806257\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.1527 | −0.462923 | ||||||||
\(482\) | 7.87870 | + | 6.08295i | 0.358865 | + | 0.277071i | ||||
\(483\) | −18.1632 | + | 1.79260i | −0.826456 | + | 0.0815660i | ||||
\(484\) | −5.43540 | − | 20.7801i | −0.247064 | − | 0.944552i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.63418 | + | 21.7438i | −0.164850 | + | 0.986319i | ||||
\(487\) | 23.9090 | − | 23.9090i | 1.08342 | − | 1.08342i | 0.0872343 | − | 0.996188i | \(-0.472197\pi\) |
0.996188 | − | 0.0872343i | \(-0.0278029\pi\) | |||||||
\(488\) | −12.8326 | − | 5.45044i | −0.580905 | − | 0.246730i | ||||
\(489\) | 0.891726 | + | 0.731522i | 0.0403252 | + | 0.0330806i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.9507 | 1.39678 | 0.698392 | − | 0.715715i | \(-0.253899\pi\) | ||||
0.698392 | + | 0.715715i | \(0.253899\pi\) | |||||||
\(492\) | 5.09873 | + | 13.7875i | 0.229868 | + | 0.621590i | ||||
\(493\) | −16.0728 | + | 16.0728i | −0.723884 | + | 0.723884i | ||||
\(494\) | 8.95201 | − | 1.15141i | 0.402770 | − | 0.0518043i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15.9274 | − | 8.94409i | 0.715161 | − | 0.401602i | ||||
\(497\) | −10.5375 | − | 10.5375i | −0.472672 | − | 0.472672i | ||||
\(498\) | 16.1361 | − | 3.71511i | 0.723076 | − | 0.166478i | ||||
\(499\) | 19.9194 | 0.891716 | 0.445858 | − | 0.895104i | \(-0.352899\pi\) | ||||
0.445858 | + | 0.895104i | \(0.352899\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.769562 | − | 0.938097i | 0.0343815 | − | 0.0419111i | ||||
\(502\) | −11.1074 | − | 8.57573i | −0.495746 | − | 0.382754i | ||||
\(503\) | −14.6687 | + | 14.6687i | −0.654047 | + | 0.654047i | −0.953965 | − | 0.299918i | \(-0.903041\pi\) |
0.299918 | + | 0.953965i | \(0.403041\pi\) | |||||||
\(504\) | −13.6209 | − | 20.7671i | −0.606724 | − | 0.925042i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.57684 | + | 0.331433i | −0.114555 | + | 0.0147340i | ||||
\(507\) | 20.4653 | − | 2.01979i | 0.908896 | − | 0.0897022i | ||||
\(508\) | −2.35317 | − | 1.37738i | −0.104405 | − | 0.0611114i | ||||
\(509\) | − | 4.85493i | − | 0.215191i | −0.994195 | − | 0.107595i | \(-0.965685\pi\) | ||
0.994195 | − | 0.107595i | \(-0.0343151\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.2727 | −0.587149 | ||||||||
\(512\) | −21.1298 | + | 8.09503i | −0.933816 | + | 0.357753i | ||||
\(513\) | 9.08621 | + | 29.8886i | 0.401166 | + | 1.31961i | ||||
\(514\) | −3.70778 | − | 28.8274i | −0.163543 | − | 1.27152i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 12.2027 | − | 26.5242i | 0.537194 | − | 1.16766i | ||||
\(517\) | 1.70355 | + | 1.70355i | 0.0749222 | + | 0.0749222i | ||||
\(518\) | 31.3345 | + | 24.1926i | 1.37676 | + | 1.06296i | ||||
\(519\) | −3.61473 | + | 4.40636i | −0.158669 | + | 0.193418i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.0499i | 0.659346i | 0.944095 | + | 0.329673i | \(0.106939\pi\) | ||||
−0.944095 | + | 0.329673i | \(0.893061\pi\) | |||||||
\(522\) | −9.63401 | + | 19.4094i | −0.421669 | + | 0.849525i | ||||
\(523\) | −15.6997 | + | 15.6997i | −0.686499 | + | 0.686499i | −0.961456 | − | 0.274957i | \(-0.911336\pi\) |
0.274957 | + | 0.961456i | \(0.411336\pi\) | |||||||
\(524\) | −3.84254 | − | 14.6904i | −0.167862 | − | 0.641755i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.5493 | − | 2.77167i | 0.939596 | − | 0.120851i | ||||
\(527\) | −14.3714 | − | 14.3714i | −0.626026 | − | 0.626026i | ||||
\(528\) | −2.02539 | − | 2.89761i | −0.0881437 | − | 0.126102i | ||||
\(529\) | 10.0383i | 0.436449i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.683298 | − | 3.42800i | −0.0296526 | − | 0.148762i | ||||
\(532\) | −30.3725 | − | 17.7779i | −1.31681 | − | 0.770770i | ||||
\(533\) | −3.18541 | − | 3.18541i | −0.137976 | − | 0.137976i | ||||
\(534\) | −16.4269 | + | 26.2535i | −0.710862 | + | 1.13610i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −29.6137 | + | 11.9572i | −1.27912 | + | 0.516470i | ||||
\(537\) | −23.9835 | + | 2.36701i | −1.03496 | + | 0.102144i | ||||
\(538\) | −27.9399 | + | 36.1880i | −1.20457 | + | 1.56017i | ||||
\(539\) | 0.799460i | 0.0344352i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.45079i | 0.0623742i | 0.999514 | + | 0.0311871i | \(0.00992877\pi\) | ||||
−0.999514 | + | 0.0311871i | \(0.990071\pi\) | |||||||
\(542\) | −0.342914 | − | 0.264756i | −0.0147294 | − | 0.0113722i | ||||
\(543\) | 10.0141 | − | 0.988326i | 0.429745 | − | 0.0424131i | ||||
\(544\) | 15.0266 | + | 20.1996i | 0.644258 | + | 0.866050i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.45196 | + | 4.03702i | 0.276118 | + | 0.172768i | ||||
\(547\) | 1.86763 | + | 1.86763i | 0.0798541 | + | 0.0798541i | 0.745906 | − | 0.666052i | \(-0.232017\pi\) |
−0.666052 | + | 0.745906i | \(0.732017\pi\) | |||||||
\(548\) | 1.01951 | − | 1.74177i | 0.0435512 | − | 0.0744045i | ||||
\(549\) | 2.89078 | + | 14.5026i | 0.123375 | + | 0.618955i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.7055i | 1.30810i | ||||||||
\(552\) | 15.6270 | − | 8.17788i | 0.665128 | − | 0.348074i | ||||
\(553\) | −15.1334 | − | 15.1334i | −0.643539 | − | 0.643539i | ||||
\(554\) | 1.78060 | + | 13.8439i | 0.0756505 | + | 0.588171i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.56234 | + | 17.4423i | 0.193486 | + | 0.739720i | ||||
\(557\) | −22.6188 | + | 22.6188i | −0.958389 | + | 0.958389i | −0.999168 | − | 0.0407789i | \(-0.987016\pi\) |
0.0407789 | + | 0.999168i | \(0.487016\pi\) | |||||||
\(558\) | −17.3547 | − | 8.61415i | −0.734682 | − | 0.364666i | ||||
\(559\) | 8.94729i | 0.378430i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.49475 | + | 3.04110i | −0.105328 | + | 0.128395i | ||||
\(562\) | −13.3611 | + | 17.3054i | −0.563604 | + | 0.729985i | ||||
\(563\) | 26.6638 | + | 26.6638i | 1.12375 | + | 1.12375i | 0.991173 | + | 0.132574i | \(0.0423241\pi\) |
0.132574 | + | 0.991173i | \(0.457676\pi\) | |||||||
\(564\) | −14.8582 | − | 6.83567i | −0.625644 | − | 0.287833i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 17.5843 | − | 2.26169i | 0.739123 | − | 0.0950660i | ||||
\(567\) | −10.0612 | + | 24.3450i | −0.422530 | + | 1.02239i | ||||
\(568\) | 13.2549 | + | 5.62980i | 0.556163 | + | 0.236221i | ||||
\(569\) | −29.3180 | −1.22907 | −0.614537 | − | 0.788888i | \(-0.710657\pi\) | ||||
−0.614537 | + | 0.788888i | \(0.710657\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 28.4036i | − | 1.18865i | −0.804224 | − | 0.594326i | \(-0.797419\pi\) | ||
0.804224 | − | 0.594326i | \(-0.202581\pi\) | |||||||
\(572\) | 0.934999 | + | 0.547283i | 0.0390943 | + | 0.0228831i | ||||
\(573\) | 23.8652 | − | 2.35535i | 0.996985 | − | 0.0983960i | ||||
\(574\) | 2.24077 | + | 17.4216i | 0.0935280 | + | 0.727165i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 19.7190 | + | 13.6807i | 0.821625 | + | 0.570028i | ||||
\(577\) | 18.9787 | − | 18.9787i | 0.790092 | − | 0.790092i | −0.191417 | − | 0.981509i | \(-0.561308\pi\) |
0.981509 | + | 0.191417i | \(0.0613081\pi\) | |||||||
\(578\) | 2.42590 | − | 3.14204i | 0.100904 | − | 0.130692i | ||||
\(579\) | −7.10371 | + | 8.65943i | −0.295220 | + | 0.359874i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.7855 | 0.820839 | ||||||||
\(582\) | −8.45536 | − | 36.7247i | −0.350486 | − | 1.52229i | ||||
\(583\) | −2.93853 | − | 2.93853i | −0.121702 | − | 0.121702i | ||||
\(584\) | 11.8933 | − | 4.80216i | 0.492147 | − | 0.198715i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.381782 | + | 2.96830i | 0.0157713 | + | 0.122619i | ||||
\(587\) | −11.2326 | + | 11.2326i | −0.463619 | + | 0.463619i | −0.899840 | − | 0.436220i | \(-0.856317\pi\) |
0.436220 | + | 0.899840i | \(0.356317\pi\) | |||||||
\(588\) | −1.88245 | − | 5.09035i | −0.0776309 | − | 0.209923i | ||||
\(589\) | −27.4550 | −1.13127 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.30543 | + | 5.99297i | 0.300505 | + | 0.246518i | ||||
\(592\) | −36.8310 | − | 10.3412i | −1.51374 | − | 0.425022i | ||||
\(593\) | −0.161070 | + | 0.161070i | −0.00661435 | + | 0.00661435i | −0.710406 | − | 0.703792i | \(-0.751489\pi\) |
0.703792 | + | 0.710406i | \(0.251489\pi\) | |||||||
\(594\) | −1.32920 | + | 3.50626i | −0.0545378 | + | 0.143863i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −25.4581 | + | 6.65901i | −1.04281 | + | 0.272764i | ||||
\(597\) | −10.2013 | + | 1.00680i | −0.417511 | + | 0.0412057i | ||||
\(598\) | −3.30313 | + | 4.27825i | −0.135075 | + | 0.174951i | ||||
\(599\) | 15.6557 | 0.639673 | 0.319837 | − | 0.947473i | \(-0.396372\pi\) | ||||
0.319837 | + | 0.947473i | \(0.396372\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.1506 | 1.18908 | 0.594540 | − | 0.804066i | \(-0.297334\pi\) | ||||
0.594540 | + | 0.804066i | \(0.297334\pi\) | |||||||
\(602\) | 21.3203 | − | 27.6142i | 0.868949 | − | 1.12547i | ||||
\(603\) | 28.1726 | + | 18.8080i | 1.14728 | + | 0.765922i | ||||
\(604\) | 1.39676 | + | 5.33998i | 0.0568335 | + | 0.217281i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.32841 | + | 13.3105i | −0.338318 | + | 0.540700i | ||||
\(607\) | −18.7872 | + | 18.7872i | −0.762550 | + | 0.762550i | −0.976783 | − | 0.214232i | \(-0.931275\pi\) |
0.214232 | + | 0.976783i | \(0.431275\pi\) | |||||||
\(608\) | 33.6480 | + | 4.94129i | 1.36461 | + | 0.200396i | ||||
\(609\) | −16.4217 | + | 20.0181i | −0.665443 | + | 0.811176i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.01206 | 0.202766 | ||||||||
\(612\) | 8.72394 | − | 25.2377i | 0.352644 | − | 1.02017i | ||||
\(613\) | 29.5115 | − | 29.5115i | 1.19196 | − | 1.19196i | 0.215443 | − | 0.976516i | \(-0.430880\pi\) |
0.976516 | − | 0.215443i | \(-0.0691195\pi\) | |||||||
\(614\) | −3.18791 | − | 24.7855i | −0.128654 | − | 1.00026i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.58160 | − | 3.91708i | −0.0637245 | − | 0.157823i | ||||
\(617\) | 29.7517 | + | 29.7517i | 1.19776 | + | 1.19776i | 0.974836 | + | 0.222923i | \(0.0715598\pi\) |
0.222923 | + | 0.974836i | \(0.428440\pi\) | |||||||
\(618\) | −6.28938 | + | 1.44804i | −0.252996 | + | 0.0582488i | ||||
\(619\) | −12.4498 | −0.500402 | −0.250201 | − | 0.968194i | \(-0.580497\pi\) | ||||
−0.250201 | + | 0.968194i | \(0.580497\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.5037 | − | 8.80867i | −0.662271 | − | 0.353480i | ||||
\(622\) | −0.194141 | + | 0.251453i | −0.00778433 | + | 0.0100823i | ||||
\(623\) | −26.1665 | + | 26.1665i | −1.04834 | + | 1.04834i | ||||
\(624\) | −7.24203 | − | 1.28309i | −0.289913 | − | 0.0513646i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.07144 | − | 23.8799i | −0.122759 | − | 0.954434i | ||||
\(627\) | 0.521877 | + | 5.28785i | 0.0208417 | + | 0.211176i | ||||
\(628\) | 6.25942 | − | 10.6938i | 0.249778 | − | 0.426730i | ||||
\(629\) | 42.5637i | 1.69712i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.7481 | 1.74158 | 0.870791 | − | 0.491653i | \(-0.163607\pi\) | ||||
0.870791 | + | 0.491653i | \(0.163607\pi\) | |||||||
\(632\) | 19.0360 | + | 8.08524i | 0.757212 | + | 0.321614i | ||||
\(633\) | −11.9860 | + | 1.18294i | −0.476399 | + | 0.0470176i | ||||
\(634\) | −40.1210 | + | 5.16036i | −1.59341 | + | 0.204944i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 25.6296 | + | 11.7911i | 1.01628 | + | 0.467548i | ||||
\(637\) | 1.17605 | + | 1.17605i | 0.0465969 | + | 0.0465969i | ||||
\(638\) | −2.25242 | + | 2.91735i | −0.0891741 | + | 0.115499i | ||||
\(639\) | −2.98590 | − | 14.9798i | −0.118121 | − | 0.592592i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.3935i | 0.529013i | 0.964384 | + | 0.264506i | \(0.0852090\pi\) | ||||
−0.964384 | + | 0.264506i | \(0.914791\pi\) | |||||||
\(642\) | −7.79709 | − | 33.8656i | −0.307727 | − | 1.33657i | ||||
\(643\) | −12.4335 | + | 12.4335i | −0.490331 | + | 0.490331i | −0.908410 | − | 0.418080i | \(-0.862703\pi\) |
0.418080 | + | 0.908410i | \(0.362703\pi\) | |||||||
\(644\) | 20.3891 | − | 5.33311i | 0.803442 | − | 0.210154i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.82710 | − | 37.5300i | −0.189920 | − | 1.47660i | ||||
\(647\) | −0.352589 | − | 0.352589i | −0.0138617 | − | 0.0138617i | 0.700142 | − | 0.714004i | \(-0.253120\pi\) |
−0.714004 | + | 0.700142i | \(0.753120\pi\) | |||||||
\(648\) | 0.207341 | − | 25.4550i | 0.00814512 | − | 0.999967i | ||||
\(649\) | − | 0.594545i | − | 0.0233380i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.8990 | − | 14.6833i | −0.701517 | − | 0.575485i | ||||
\(652\) | −1.14939 | − | 0.672775i | −0.0450138 | − | 0.0263479i | ||||
\(653\) | −10.5497 | − | 10.5497i | −0.412841 | − | 0.412841i | 0.469886 | − | 0.882727i | \(-0.344295\pi\) |
−0.882727 | + | 0.469886i | \(0.844295\pi\) | |||||||
\(654\) | 16.4291 | − | 26.2571i | 0.642431 | − | 1.02673i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.31116 | − | 14.8003i | −0.324496 | − | 0.577854i | ||||
\(657\) | −11.3145 | − | 7.55356i | −0.441421 | − | 0.294692i | ||||
\(658\) | −15.4688 | − | 11.9431i | −0.603038 | − | 0.465591i | ||||
\(659\) | 30.8600i | 1.20213i | 0.799199 | + | 0.601067i | \(0.205258\pi\) | ||||
−0.799199 | + | 0.601067i | \(0.794742\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 44.1992i | − | 1.71915i | −0.511009 | − | 0.859575i | \(-0.670728\pi\) | ||
0.511009 | − | 0.859575i | \(-0.329272\pi\) | |||||||
\(662\) | 10.6570 | − | 13.8030i | 0.414196 | − | 0.536470i | ||||
\(663\) | 0.803718 | + | 8.14357i | 0.0312138 | + | 0.316270i | ||||
\(664\) | −17.7292 | + | 7.15852i | −0.688025 | + | 0.277804i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.9434 | + | 38.4560i | 0.501547 | + | 1.49014i | ||||
\(667\) | −13.0021 | − | 13.0021i | −0.503444 | − | 0.503444i | ||||
\(668\) | −0.707760 | + | 1.20916i | −0.0273841 | + | 0.0467840i | ||||
\(669\) | 25.9783 | − | 31.6675i | 1.00438 | − | 1.22434i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.51530i | 0.0971021i | ||||||||
\(672\) | 19.2938 | + | 21.2169i | 0.744274 | + | 0.818458i | ||||
\(673\) | −13.1276 | − | 13.1276i | −0.506033 | − | 0.506033i | 0.407274 | − | 0.913306i | \(-0.366480\pi\) |
−0.913306 | + | 0.407274i | \(0.866480\pi\) | |||||||
\(674\) | 21.1703 | − | 2.72292i | 0.815448 | − | 0.104883i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.9732 | + | 6.00904i | −0.883586 | + | 0.231117i | ||||
\(677\) | −23.1658 | + | 23.1658i | −0.890334 | + | 0.890334i | −0.994554 | − | 0.104220i | \(-0.966765\pi\) |
0.104220 | + | 0.994554i | \(0.466765\pi\) | |||||||
\(678\) | −1.46844 | − | 6.37795i | −0.0563949 | − | 0.244944i | ||||
\(679\) | − | 45.0304i | − | 1.72811i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.6371 | − | 19.3905i | −0.905775 | − | 0.743047i | ||||
\(682\) | −2.60852 | − | 2.01398i | −0.0998855 | − | 0.0771192i | ||||
\(683\) | −14.8655 | − | 14.8655i | −0.568814 | − | 0.568814i | 0.362982 | − | 0.931796i | \(-0.381759\pi\) |
−0.931796 | + | 0.362982i | \(0.881759\pi\) | |||||||
\(684\) | −15.7740 | − | 32.4402i | −0.603132 | − | 1.24038i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.86899 | + | 22.3060i | 0.109539 | + | 0.851647i | ||||
\(687\) | 0.186579 | + | 1.89049i | 0.00711843 | + | 0.0721266i | ||||
\(688\) | −9.11344 | + | 32.4581i | −0.347447 | + | 1.23745i | ||||
\(689\) | −8.64552 | −0.329368 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.2699i | 1.79823i | 0.437710 | + | 0.899116i | \(0.355790\pi\) | ||||
−0.437710 | + | 0.899116i | \(0.644210\pi\) | |||||||
\(692\) | 3.32444 | − | 5.67960i | 0.126376 | − | 0.215906i | ||||
\(693\) | −2.48778 | + | 3.72646i | −0.0945031 | + | 0.141557i | ||||
\(694\) | −15.8783 | + | 2.04227i | −0.602733 | + | 0.0775235i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.47234 | − | 23.8792i | 0.283238 | − | 0.905137i | ||||
\(697\) | −13.3544 | + | 13.3544i | −0.505833 | + | 0.505833i | ||||
\(698\) | −15.6245 | − | 12.0633i | −0.591396 | − | 0.456603i | ||||
\(699\) | −13.2202 | − | 10.8451i | −0.500035 | − | 0.410201i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.65973 | 0.289304 | 0.144652 | − | 0.989483i | \(-0.453794\pi\) | ||||
0.144652 | + | 0.989483i | \(0.453794\pi\) | |||||||
\(702\) | 3.20258 | + | 7.11325i | 0.120874 | + | 0.268473i | ||||
\(703\) | 40.6568 | + | 40.6568i | 1.53340 | + | 1.53340i | ||||
\(704\) | 2.83445 | + | 2.93774i | 0.106827 | + | 0.110720i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.5547 | + | 3.02960i | −0.886492 | + | 0.114021i | ||||
\(707\) | −13.2664 | + | 13.2664i | −0.498933 | + | 0.498933i | ||||
\(708\) | 1.39995 | + | 3.78562i | 0.0526133 | + | 0.142272i | ||||
\(709\) | 43.9829 | 1.65181 | 0.825906 | − | 0.563808i | \(-0.190664\pi\) | ||||
0.825906 | + | 0.563808i | \(0.190664\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.28821 | − | 21.5132i | −0.160820 | − | 0.806810i | ||||
\(712\) | 13.9798 | − | 32.9143i | 0.523915 | − | 1.23351i | ||||
\(713\) | 11.6257 | − | 11.6257i | 0.435387 | − | 0.435387i | ||||
\(714\) | 16.9246 | − | 27.0488i | 0.633386 | − | 1.01228i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 26.9225 | − | 7.04204i | 1.00614 | − | 0.263174i | ||||
\(717\) | −2.09599 | − | 21.2373i | −0.0782762 | − | 0.793123i | ||||
\(718\) | 37.9213 | + | 29.2781i | 1.41521 | + | 1.09265i | ||||
\(719\) | 14.6227 | 0.545333 | 0.272666 | − | 0.962109i | \(-0.412094\pi\) | ||||
0.272666 | + | 0.962109i | \(0.412094\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.71179 | −0.287202 | ||||||||
\(722\) | −19.1909 | − | 14.8168i | −0.714212 | − | 0.551425i | ||||
\(723\) | 1.19733 | + | 12.1318i | 0.0445292 | + | 0.451186i | ||||
\(724\) | −11.2413 | + | 2.94034i | −0.417778 | + | 0.109277i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 13.9538 | − | 22.3009i | 0.517872 | − | 0.827663i | ||||
\(727\) | 22.1109 | − | 22.1109i | 0.820048 | − | 0.820048i | −0.166067 | − | 0.986115i | \(-0.553107\pi\) |
0.986115 | + | 0.166067i | \(0.0531067\pi\) | |||||||
\(728\) | −8.08889 | − | 3.43563i | −0.299794 | − | 0.127333i | ||||
\(729\) | −22.4316 | + | 15.0274i | −0.830802 | + | 0.556569i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.5102 | 1.38736 | ||||||||
\(732\) | −5.92266 | − | 16.0155i | −0.218908 | − | 0.591951i | ||||
\(733\) | 8.64610 | − | 8.64610i | 0.319351 | − | 0.319351i | −0.529167 | − | 0.848518i | \(-0.677495\pi\) |
0.848518 | + | 0.529167i | \(0.177495\pi\) | |||||||
\(734\) | 21.4037 | − | 2.75294i | 0.790023 | − | 0.101613i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.3405 | + | 12.1557i | −0.602318 | + | 0.448067i | ||||
\(737\) | 4.07412 | + | 4.07412i | 0.150072 | + | 0.150072i | ||||
\(738\) | −8.00457 | + | 16.1266i | −0.294652 | + | 0.593628i | ||||
\(739\) | 29.8509 | 1.09808 | 0.549041 | − | 0.835796i | \(-0.314993\pi\) | ||||
0.549041 | + | 0.835796i | \(0.314993\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.54646 | + | 7.01103i | 0.313962 | + | 0.257557i | ||||
\(742\) | 26.6828 | + | 20.6012i | 0.979558 | + | 0.756293i | ||||
\(743\) | 6.78930 | − | 6.78930i | 0.249075 | − | 0.249075i | −0.571516 | − | 0.820591i | \(-0.693644\pi\) |
0.820591 | + | 0.571516i | \(0.193644\pi\) | |||||||
\(744\) | 21.3513 | + | 6.68132i | 0.782777 | + | 0.244949i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −51.2539 | + | 6.59227i | −1.87654 | + | 0.241360i | ||||
\(747\) | 16.8664 | + | 11.2600i | 0.617110 | + | 0.411982i | ||||
\(748\) | 2.29440 | − | 3.91984i | 0.0838916 | − | 0.143324i | ||||
\(749\) | − | 41.5247i | − | 1.51728i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.5357 | 0.822339 | 0.411170 | − | 0.911559i | \(-0.365120\pi\) | ||||
0.411170 | + | 0.911559i | \(0.365120\pi\) | |||||||
\(752\) | 18.1823 | + | 5.10513i | 0.663039 | + | 0.186165i | ||||
\(753\) | −1.68800 | − | 17.1034i | −0.0615140 | − | 0.623282i | ||||
\(754\) | 0.978161 | + | 7.60505i | 0.0356225 | + | 0.276959i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 7.06580 | − | 29.5851i | 0.256981 | − | 1.07600i | ||||
\(757\) | 33.9790 | + | 33.9790i | 1.23499 | + | 1.23499i | 0.962025 | + | 0.272963i | \(0.0880035\pi\) |
0.272963 | + | 0.962025i | \(0.411996\pi\) | |||||||
\(758\) | 13.6860 | + | 10.5666i | 0.497099 | + | 0.383798i | ||||
\(759\) | −2.46010 | − | 2.01813i | −0.0892961 | − | 0.0732535i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 34.4290i | − | 1.24805i | −0.781404 | − | 0.624025i | \(-0.785496\pi\) | ||
0.781404 | − | 0.624025i | \(-0.214504\pi\) | |||||||
\(762\) | −0.749259 | − | 3.25431i | −0.0271428 | − | 0.117891i | ||||
\(763\) | 26.1701 | − | 26.1701i | 0.947421 | − | 0.947421i | ||||
\(764\) | −26.7898 | + | 7.00733i | −0.969222 | + | 0.253516i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −42.8977 | + | 5.51751i | −1.54996 | + | 0.199356i | ||||
\(767\) | −0.874612 | − | 0.874612i | −0.0315804 | − | 0.0315804i | ||||
\(768\) | −24.9650 | − | 12.0312i | −0.900847 | − | 0.434137i | ||||
\(769\) | 14.8941i | 0.537094i | 0.963267 | + | 0.268547i | \(0.0865434\pi\) | ||||
−0.963267 | + | 0.268547i | \(0.913457\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.5770 | − | 27.5214i | 0.813091 | − | 0.991159i | ||||
\(772\) | 6.53323 | − | 11.1616i | 0.235136 | − | 0.401715i | ||||
\(773\) | 7.32969 | + | 7.32969i | 0.263631 | + | 0.263631i | 0.826527 | − | 0.562897i | \(-0.190313\pi\) |
−0.562897 | + | 0.826527i | \(0.690313\pi\) | |||||||
\(774\) | 33.8902 | − | 11.4067i | 1.21816 | − | 0.410005i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 16.2923 | + | 40.3504i | 0.584861 | + | 1.44850i | ||||
\(777\) | 4.76193 | + | 48.2496i | 0.170833 | + | 1.73094i | ||||
\(778\) | 5.73818 | − | 7.43215i | 0.205724 | − | 0.266455i | ||||
\(779\) | 25.5122i | 0.914069i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 2.59807i | − | 0.0929663i | ||||||
\(782\) | 17.9359 | + | 13.8479i | 0.641387 | + | 0.495199i | ||||
\(783\) | −25.3914 | + | 7.71905i | −0.907414 | + | 0.275856i | ||||
\(784\) | 3.06848 | + | 5.46427i | 0.109589 | + | 0.195152i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.86456 | − | 15.7655i | 0.351857 | − | 0.562338i | ||||
\(787\) | 4.66068 | + | 4.66068i | 0.166135 | + | 0.166135i | 0.785278 | − | 0.619143i | \(-0.212520\pi\) |
−0.619143 | + | 0.785278i | \(0.712520\pi\) | |||||||
\(788\) | −9.41637 | − | 5.51168i | −0.335444 | − | 0.196346i | ||||
\(789\) | 20.5731 | + | 16.8770i | 0.732421 | + | 0.600837i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 7.82040i | − | 0.278061i | ||||||
\(792\) | 0.880969 | − | 4.23927i | 0.0313039 | − | 0.150636i | ||||
\(793\) | 3.70016 | + | 3.70016i | 0.131396 | + | 0.131396i | ||||
\(794\) | 3.58713 | + | 27.8894i | 0.127303 | + | 0.989757i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.4514 | − | 2.99531i | 0.405884 | − | 0.106166i | ||||
\(797\) | 27.8720 | − | 27.8720i | 0.987276 | − | 0.987276i | −0.0126440 | − | 0.999920i | \(-0.504025\pi\) |
0.999920 | + | 0.0126440i | \(0.00402483\pi\) | |||||||
\(798\) | −9.67071 | − | 42.0034i | −0.342339 | − | 1.48691i | ||||
\(799\) | − | 21.0123i | − | 0.743362i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −37.1975 | + | 7.41454i | −1.31431 | + | 0.261980i | ||||
\(802\) | −15.6584 | + | 20.2809i | −0.552916 | + | 0.716142i | ||||
\(803\) | −1.63622 | − | 1.63622i | −0.0577410 | − | 0.0577410i | ||||
\(804\) | −35.5340 | − | 16.3478i | −1.25319 | − | 0.576542i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.79998 | + | 0.874612i | −0.239519 | + | 0.0308069i | ||||
\(807\) | −55.7231 | + | 5.49951i | −1.96155 | + | 0.193592i | ||||
\(808\) | 7.08773 | − | 16.6875i | 0.249346 | − | 0.587063i | ||||
\(809\) | 18.8285 | 0.661975 | 0.330988 | − | 0.943635i | \(-0.392618\pi\) | ||||
0.330988 | + | 0.943635i | \(0.392618\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.4113i | 1.31369i | 0.754026 | + | 0.656845i | \(0.228109\pi\) | ||||
−0.754026 | + | 0.656845i | \(0.771891\pi\) | |||||||
\(812\) | 15.1030 | − | 25.8025i | 0.530010 | − | 0.905489i | ||||
\(813\) | −0.0521129 | − | 0.528027i | −0.00182768 | − | 0.0185187i | ||||
\(814\) | 0.880433 | + | 6.84523i | 0.0308592 | + | 0.239925i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −5.37914 | + | 30.3611i | −0.188308 | + | 1.06285i | ||||
\(817\) | 35.8297 | − | 35.8297i | 1.25352 | − | 1.25352i | ||||
\(818\) | −22.7512 | + | 29.4676i | −0.795477 | + | 1.03031i | ||||
\(819\) | 1.82217 | + | 9.14153i | 0.0636717 | + | 0.319431i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.3129 | 0.499523 | 0.249761 | − | 0.968307i | \(-0.419648\pi\) | ||||
0.249761 | + | 0.968307i | \(0.419648\pi\) | |||||||
\(822\) | 2.40877 | − | 0.554585i | 0.0840153 | − | 0.0193434i | ||||
\(823\) | −10.8660 | − | 10.8660i | −0.378766 | − | 0.378766i | 0.491891 | − | 0.870657i | \(-0.336306\pi\) |
−0.870657 | + | 0.491891i | \(0.836306\pi\) | |||||||
\(824\) | 6.91031 | − | 2.79018i | 0.240732 | − | 0.0972006i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.615244 | + | 4.78343i | 0.0214071 | + | 0.166437i | ||||
\(827\) | 2.49596 | − | 2.49596i | 0.0867932 | − | 0.0867932i | −0.662377 | − | 0.749170i | \(-0.730452\pi\) |
0.749170 | + | 0.662377i | \(0.230452\pi\) | |||||||
\(828\) | 20.4161 | + | 7.05724i | 0.709507 | + | 0.245256i | ||||
\(829\) | −49.1212 | −1.70605 | −0.853026 | − | 0.521869i | \(-0.825235\pi\) | ||||
−0.853026 | + | 0.521869i | \(0.825235\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.8423 | + | 13.2167i | −0.376114 | + | 0.458483i | ||||
\(832\) | 8.49125 | + | 0.151945i | 0.294381 | + | 0.00526773i | ||||
\(833\) | 4.93043 | − | 4.93043i | 0.170829 | − | 0.170829i | ||||
\(834\) | −11.7124 | + | 18.7188i | −0.405569 | + | 0.648179i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.55262 | − | 5.93585i | −0.0536985 | − | 0.205296i | ||||
\(837\) | −6.90191 | − | 22.7034i | −0.238565 | − | 0.784746i | ||||
\(838\) | 11.0460 | − | 14.3069i | 0.381577 | − | 0.494223i | ||||
\(839\) | 26.9749 | 0.931277 | 0.465638 | − | 0.884975i | \(-0.345825\pi\) | ||||
0.465638 | + | 0.884975i | \(0.345825\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.91458 | 0.100503 | ||||||||
\(842\) | −22.7985 | + | 29.5288i | −0.785687 | + | 1.01763i | ||||
\(843\) | −26.6473 | + | 2.62992i | −0.917782 | + | 0.0905792i | ||||
\(844\) | 13.4548 | − | 3.51933i | 0.463133 | − | 0.121140i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.38975 | − | 18.9845i | −0.219684 | − | 0.652700i | ||||
\(847\) | 22.2270 | − | 22.2270i | 0.763729 | − | 0.763729i | ||||
\(848\) | −31.3634 | − | 8.80606i | −1.07702 | − | 0.302401i | ||||
\(849\) | 16.7877 | + | 13.7717i | 0.576151 | + | 0.472642i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.4319 | −1.18031 | ||||||||
\(852\) | 6.11755 | + | 16.5425i | 0.209584 | + | 0.566738i | ||||
\(853\) | −16.4190 | + | 16.4190i | −0.562174 | + | 0.562174i | −0.929925 | − | 0.367750i | \(-0.880128\pi\) |
0.367750 | + | 0.929925i | \(0.380128\pi\) | |||||||
\(854\) | −2.60287 | − | 20.2369i | −0.0890683 | − | 0.692492i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.0239 | + | 37.2091i | 0.513508 | + | 1.27178i | ||||
\(857\) | −24.4641 | − | 24.4641i | −0.835678 | − | 0.835678i | 0.152608 | − | 0.988287i | \(-0.451233\pi\) |
−0.988287 | + | 0.152608i | \(0.951233\pi\) | |||||||
\(858\) | 0.297707 | + | 1.29305i | 0.0101636 | + | 0.0441441i | ||||
\(859\) | 1.68121 | 0.0573622 | 0.0286811 | − | 0.999589i | \(-0.490869\pi\) | ||||
0.0286811 | + | 0.999589i | \(0.490869\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.6443 | + | 16.6324i | −0.464995 | + | 0.566830i | ||||
\(862\) | −24.7886 | + | 32.1064i | −0.844302 | + | 1.09355i | ||||
\(863\) | 23.0950 | − | 23.0950i | 0.786161 | − | 0.786161i | −0.194701 | − | 0.980863i | \(-0.562374\pi\) |
0.980863 | + | 0.194701i | \(0.0623737\pi\) | |||||||
\(864\) | 4.37266 | + | 29.0668i | 0.148761 | + | 0.988873i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.575226 | − | 4.47229i | −0.0195470 | − | 0.151975i | ||||
\(867\) | 4.83819 | − | 0.477499i | 0.164314 | − | 0.0162167i | ||||
\(868\) | 23.0710 | + | 13.5042i | 0.783081 | + | 0.458361i | ||||
\(869\) | − | 3.73122i | − | 0.126573i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.9866 | 0.406149 | ||||||||
\(872\) | −13.9817 | + | 32.9188i | −0.473481 | + | 1.11477i | ||||
\(873\) | 25.6271 | − | 38.3869i | 0.867345 | − | 1.29920i | ||||
\(874\) | 30.3599 | − | 3.90489i | 1.02694 | − | 0.132085i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.2710 | + | 6.56549i | 0.482171 | + | 0.221827i | ||||
\(877\) | 14.2900 | + | 14.2900i | 0.482539 | + | 0.482539i | 0.905942 | − | 0.423403i | \(-0.139164\pi\) |
−0.423403 | + | 0.905942i | \(0.639164\pi\) | |||||||
\(878\) | 10.2424 | − | 13.2660i | 0.345664 | − | 0.447707i | ||||
\(879\) | −2.32471 | + | 2.83382i | −0.0784105 | + | 0.0955825i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.2886i | 1.52581i | 0.646509 | + | 0.762906i | \(0.276228\pi\) | ||||
−0.646509 | + | 0.762906i | \(0.723772\pi\) | |||||||
\(882\) | 2.95529 | − | 5.95393i | 0.0995096 | − | 0.200479i | ||||
\(883\) | −3.68252 | + | 3.68252i | −0.123927 | + | 0.123927i | −0.766350 | − | 0.642423i | \(-0.777929\pi\) |
0.642423 | + | 0.766350i | \(0.277929\pi\) | |||||||
\(884\) | −2.39112 | − | 9.14153i | −0.0804221 | − | 0.307463i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.425589 | + | 3.30889i | 0.0142980 | + | 0.111164i | ||||
\(887\) | 14.7506 | + | 14.7506i | 0.495277 | + | 0.495277i | 0.909964 | − | 0.414687i | \(-0.136109\pi\) |
−0.414687 | + | 0.909964i | \(0.636109\pi\) | |||||||
\(888\) | −21.7241 | − | 41.5121i | −0.729012 | − | 1.39306i | ||||
\(889\) | − | 3.99030i | − | 0.133830i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.24150 | + | 1.76087i | −0.142095 | + | 0.0589912i | ||||
\(892\) | −23.8920 | + | 40.8180i | −0.799964 | + | 1.36669i | ||||
\(893\) | −20.0710 | − | 20.0710i | −0.671649 | − | 0.671649i | ||||
\(894\) | −27.3212 | − | 17.0950i | −0.913758 | − | 0.571742i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −25.8446 | − | 20.7025i | −0.863409 | − | 0.691623i | ||||
\(897\) | −6.58775 | + | 0.650169i | −0.219959 | + | 0.0217085i | ||||
\(898\) | −38.4417 | − | 29.6799i | −1.28282 | − | 0.990432i | ||||
\(899\) | − | 23.3240i | − | 0.777899i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.2450i | 1.20750i | ||||||||
\(902\) | −1.87146 | + | 2.42393i | −0.0623127 | + | 0.0807080i | ||||
\(903\) | 42.5210 | − | 4.19655i | 1.41501 | − | 0.139653i | ||||
\(904\) | 2.82948 | + | 7.00763i | 0.0941070 | + | 0.233070i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.58577 | + | 5.73077i | −0.119129 | + | 0.190392i | ||||
\(907\) | 8.08868 | + | 8.08868i | 0.268580 | + | 0.268580i | 0.828528 | − | 0.559948i | \(-0.189179\pi\) |
−0.559948 | + | 0.828528i | \(0.689179\pi\) | |||||||
\(908\) | 30.4671 | + | 17.8333i | 1.01109 | + | 0.591820i | ||||
\(909\) | −18.8591 | + | 3.75915i | −0.625516 | + | 0.124683i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.7011i | 1.28222i | 0.767448 | + | 0.641112i | \(0.221527\pi\) | ||||
−0.767448 | + | 0.641112i | \(0.778473\pi\) | |||||||
\(912\) | 23.8628 | + | 34.1391i | 0.790175 | + | 1.13046i | ||||
\(913\) | 2.43910 | + | 2.43910i | 0.0807223 | + | 0.0807223i | ||||
\(914\) | −9.15408 | + | 1.17740i | −0.302790 | + | 0.0389448i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.555086 | − | 2.12216i | −0.0183406 | − | 0.0701180i | ||||
\(917\) | 15.7133 | − | 15.7133i | 0.518899 | − | 0.518899i | ||||
\(918\) | 29.8212 | − | 13.4263i | 0.984248 | − | 0.443135i | ||||
\(919\) | 39.9611i | 1.31819i | 0.752058 | + | 0.659097i | \(0.229061\pi\) | ||||
−0.752058 | + | 0.659097i | \(0.770939\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.4115 | − | 23.6626i | 0.639630 | − | 0.779710i | ||||
\(922\) | 23.1102 | + | 17.8428i | 0.761094 | + | 0.587623i | ||||
\(923\) | −3.82192 | − | 3.82192i | −0.125800 | − | 0.125800i | ||||
\(924\) | 2.16236 | − | 4.70017i | 0.0711364 | − | 0.154624i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.93510 | + | 53.9193i | 0.227901 | + | 1.77190i | ||||
\(927\) | −6.57403 | − | 4.38882i | −0.215920 | − | 0.144148i | ||||
\(928\) | −4.19779 | + | 28.5852i | −0.137799 | + | 0.938354i | ||||
\(929\) | −0.568113 | −0.0186392 | −0.00931959 | − | 0.999957i | \(-0.502967\pi\) | ||||
−0.00931959 | + | 0.999957i | \(0.502967\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 9.41909i | − | 0.308698i | ||||||
\(932\) | 17.0403 | + | 9.97418i | 0.558173 | + | 0.326715i | ||||
\(933\) | −0.387193 | + | 0.0382135i | −0.0126761 | + | 0.00125105i | ||||
\(934\) | −12.6935 | + | 1.63263i | −0.415343 | + | 0.0534213i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.94026 | − | 7.53218i | −0.161477 | − | 0.246197i | ||||
\(937\) | −18.2630 | + | 18.2630i | −0.596626 | + | 0.596626i | −0.939413 | − | 0.342787i | \(-0.888629\pi\) |
0.342787 | + | 0.939413i | \(0.388629\pi\) | |||||||
\(938\) | −36.9944 | − | 28.5624i | −1.20791 | − | 0.932597i | ||||
\(939\) | 18.7023 | − | 22.7981i | 0.610326 | − | 0.743988i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.3971 | −0.730125 | −0.365063 | − | 0.930983i | \(-0.618952\pi\) | ||||
−0.365063 | + | 0.930983i | \(0.618952\pi\) | |||||||
\(942\) | 14.7890 | − | 3.40496i | 0.481851 | − | 0.110940i | ||||
\(943\) | −10.8030 | − | 10.8030i | −0.351795 | − | 0.351795i | ||||
\(944\) | −2.28198 | − | 4.06369i | −0.0742721 | − | 0.132262i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.03251 | − | 0.775901i | 0.196134 | − | 0.0252267i | ||||
\(947\) | 15.7486 | − | 15.7486i | 0.511761 | − | 0.511761i | −0.403305 | − | 0.915066i | \(-0.632139\pi\) |
0.915066 | + | 0.403305i | \(0.132139\pi\) | |||||||
\(948\) | 8.78572 | + | 23.7576i | 0.285347 | + | 0.771610i | ||||
\(949\) | −4.81396 | −0.156268 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −38.3034 | − | 31.4219i | −1.24207 | − | 1.01893i | ||||
\(952\) | −14.4033 | + | 33.9114i | −0.466815 | + | 1.09908i | ||||
\(953\) | −33.3609 | + | 33.3609i | −1.08067 | + | 1.08067i | −0.0842194 | + | 0.996447i | \(0.526840\pi\) |
−0.996447 | + | 0.0842194i | \(0.973160\pi\) | |||||||
\(954\) | 11.0220 | + | 32.7471i | 0.356849 | + | 1.06023i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.23572 | + | 23.8399i | 0.201678 | + | 0.771037i | ||||
\(957\) | −4.49221 | + | 0.443352i | −0.145213 | + | 0.0143315i | ||||
\(958\) | 40.1990 | + | 31.0367i | 1.29877 | + | 1.00275i | ||||
\(959\) | 2.95353 | 0.0953746 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.1451 | −0.327260 | ||||||||
\(962\) | 11.3649 | + | 8.77458i | 0.366420 | + | 0.282904i | ||||
\(963\) | 23.6319 | − | 35.3984i | 0.761529 | − | 1.14070i | ||||
\(964\) | −3.56215 | − | 13.6185i | −0.114729 | − | 0.438622i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 21.8812 | + | 13.6912i | 0.704016 | + | 0.440506i | ||||
\(967\) | 8.01398 | − | 8.01398i | 0.257712 | − | 0.257712i | −0.566411 | − | 0.824123i | \(-0.691668\pi\) |
0.824123 | + | 0.566411i | \(0.191668\pi\) | |||||||
\(968\) | −11.8751 | + | 27.9589i | −0.381679 | + | 0.898632i | ||||
\(969\) | 29.3927 | − | 35.8297i | 0.944229 | − | 1.15102i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43.4981 | −1.39592 | −0.697961 | − | 0.716136i | \(-0.745909\pi\) | ||||
−0.697961 | + | 0.716136i | \(0.745909\pi\) | |||||||
\(972\) | 22.8604 | − | 21.1991i | 0.733248 | − | 0.679962i | ||||
\(973\) | −18.6568 | + | 18.6568i | −0.598110 | + | 0.598110i | ||||
\(974\) | −47.4274 | + | 6.10011i | −1.51967 | + | 0.195460i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.65420 | + | 17.1919i | 0.309024 | + | 0.550301i | ||||
\(977\) | −39.7367 | − | 39.7367i | −1.27129 | − | 1.27129i | −0.945411 | − | 0.325880i | \(-0.894339\pi\) |
−0.325880 | − | 0.945411i | \(-0.605661\pi\) | |||||||
\(978\) | −0.365972 | − | 1.58955i | −0.0117025 | − | 0.0508282i | ||||
\(979\) | −6.45147 | −0.206190 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37.2026 | − | 7.41555i | 1.18779 | − | 0.236760i | ||||
\(982\) | −34.6462 | − | 26.7495i | −1.10560 | − | 0.853609i | ||||
\(983\) | 9.14087 | − | 9.14087i | 0.291548 | − | 0.291548i | −0.546143 | − | 0.837692i | \(-0.683905\pi\) |
0.837692 | + | 0.546143i | \(0.183905\pi\) | |||||||
\(984\) | 6.20851 | − | 19.8404i | 0.197920 | − | 0.632488i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 31.8830 | − | 4.10079i | 1.01536 | − | 0.130596i | ||||
\(987\) | −2.35081 | − | 23.8193i | −0.0748271 | − | 0.758176i | ||||
\(988\) | −11.0160 | − | 6.44799i | −0.350465 | − | 0.205138i | ||||
\(989\) | 30.3439i | 0.964879i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.1823 | −0.736409 | −0.368205 | − | 0.929745i | \(-0.620027\pi\) | ||||
−0.368205 | + | 0.929745i | \(0.620027\pi\) | |||||||
\(992\) | −25.5591 | − | 3.75342i | −0.811503 | − | 0.119171i | ||||
\(993\) | 21.2542 | − | 2.09766i | 0.674483 | − | 0.0665671i | ||||
\(994\) | 2.68852 | + | 20.9028i | 0.0852747 | + | 0.662997i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −21.2735 | − | 9.78710i | −0.674078 | − | 0.310116i | ||||
\(997\) | 3.70273 | + | 3.70273i | 0.117267 | + | 0.117267i | 0.763305 | − | 0.646038i | \(-0.223575\pi\) |
−0.646038 | + | 0.763305i | \(0.723575\pi\) | |||||||
\(998\) | −22.2978 | − | 17.2156i | −0.705824 | − | 0.544949i | ||||
\(999\) | −23.3997 | + | 43.8411i | −0.740334 | + | 1.38707i |
(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 | 600.2.w.j.293.4 | 32 | ||
3.2 | odd | 2 | inner | 600.2.w.j.293.13 | 32 | ||
5.2 | odd | 4 | inner | 600.2.w.j.557.12 | 32 | ||
5.3 | odd | 4 | 120.2.w.c.77.5 | yes | 32 | ||
5.4 | even | 2 | 120.2.w.c.53.13 | yes | 32 | ||
8.5 | even | 2 | inner | 600.2.w.j.293.5 | 32 | ||
15.2 | even | 4 | inner | 600.2.w.j.557.5 | 32 | ||
15.8 | even | 4 | 120.2.w.c.77.12 | yes | 32 | ||
15.14 | odd | 2 | 120.2.w.c.53.4 | ✓ | 32 | ||
20.3 | even | 4 | 480.2.bi.c.17.1 | 32 | |||
20.19 | odd | 2 | 480.2.bi.c.113.8 | 32 | |||
24.5 | odd | 2 | inner | 600.2.w.j.293.12 | 32 | ||
40.3 | even | 4 | 480.2.bi.c.17.16 | 32 | |||
40.13 | odd | 4 | 120.2.w.c.77.4 | yes | 32 | ||
40.19 | odd | 2 | 480.2.bi.c.113.9 | 32 | |||
40.29 | even | 2 | 120.2.w.c.53.12 | yes | 32 | ||
40.37 | odd | 4 | inner | 600.2.w.j.557.13 | 32 | ||
60.23 | odd | 4 | 480.2.bi.c.17.9 | 32 | |||
60.59 | even | 2 | 480.2.bi.c.113.16 | 32 | |||
120.29 | odd | 2 | 120.2.w.c.53.5 | yes | 32 | ||
120.53 | even | 4 | 120.2.w.c.77.13 | yes | 32 | ||
120.59 | even | 2 | 480.2.bi.c.113.1 | 32 | |||
120.77 | even | 4 | inner | 600.2.w.j.557.4 | 32 | ||
120.83 | odd | 4 | 480.2.bi.c.17.8 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.2.w.c.53.4 | ✓ | 32 | 15.14 | odd | 2 | ||
120.2.w.c.53.5 | yes | 32 | 120.29 | odd | 2 | ||
120.2.w.c.53.12 | yes | 32 | 40.29 | even | 2 | ||
120.2.w.c.53.13 | yes | 32 | 5.4 | even | 2 | ||
120.2.w.c.77.4 | yes | 32 | 40.13 | odd | 4 | ||
120.2.w.c.77.5 | yes | 32 | 5.3 | odd | 4 | ||
120.2.w.c.77.12 | yes | 32 | 15.8 | even | 4 | ||
120.2.w.c.77.13 | yes | 32 | 120.53 | even | 4 | ||
480.2.bi.c.17.1 | 32 | 20.3 | even | 4 | |||
480.2.bi.c.17.8 | 32 | 120.83 | odd | 4 | |||
480.2.bi.c.17.9 | 32 | 60.23 | odd | 4 | |||
480.2.bi.c.17.16 | 32 | 40.3 | even | 4 | |||
480.2.bi.c.113.1 | 32 | 120.59 | even | 2 | |||
480.2.bi.c.113.8 | 32 | 20.19 | odd | 2 | |||
480.2.bi.c.113.9 | 32 | 40.19 | odd | 2 | |||
480.2.bi.c.113.16 | 32 | 60.59 | even | 2 | |||
600.2.w.j.293.4 | 32 | 1.1 | even | 1 | trivial | ||
600.2.w.j.293.5 | 32 | 8.5 | even | 2 | inner | ||
600.2.w.j.293.12 | 32 | 24.5 | odd | 2 | inner | ||
600.2.w.j.293.13 | 32 | 3.2 | odd | 2 | inner | ||
600.2.w.j.557.4 | 32 | 120.77 | even | 4 | inner | ||
600.2.w.j.557.5 | 32 | 15.2 | even | 4 | inner | ||
600.2.w.j.557.12 | 32 | 5.2 | odd | 4 | inner | ||
600.2.w.j.557.13 | 32 | 40.37 | odd | 4 | inner |