Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(221,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.9 | ||
Character | \(\chi\) | \(=\) | 570.521 |
Dual form | 570.2.s.a.221.9 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 1.37489 | − | 1.05342i | 0.793790 | − | 0.608192i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.866025 | + | 0.500000i | 0.387298 | + | 0.223607i | ||||
\(6\) | 0.224845 | + | 1.71739i | 0.0917925 | + | 0.701123i | ||||
\(7\) | −1.74360 | −0.659019 | −0.329510 | − | 0.944152i | \(-0.606883\pi\) | ||||
−0.329510 | + | 0.944152i | \(0.606883\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.780619 | − | 2.89666i | 0.260206 | − | 0.965553i | ||||
\(10\) | −0.866025 | + | 0.500000i | −0.273861 | + | 0.158114i | ||||
\(11\) | 4.48400i | 1.35198i | 0.736913 | + | 0.675988i | \(0.236283\pi\) | ||||
−0.736913 | + | 0.675988i | \(0.763717\pi\) | |||||||
\(12\) | −1.59973 | − | 0.663976i | −0.461802 | − | 0.191673i | ||||
\(13\) | 3.14527 | − | 1.81592i | 0.872341 | − | 0.503646i | 0.00421545 | − | 0.999991i | \(-0.498658\pi\) |
0.868125 | + | 0.496345i | \(0.165325\pi\) | |||||||
\(14\) | 0.871800 | − | 1.51000i | 0.232998 | − | 0.403565i | ||||
\(15\) | 1.71739 | − | 0.224845i | 0.443429 | − | 0.0580546i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 5.72021 | + | 3.30257i | 1.38736 | + | 0.800990i | 0.993017 | − | 0.117975i | \(-0.0376402\pi\) |
0.394339 | + | 0.918965i | \(0.370974\pi\) | |||||||
\(18\) | 2.11827 | + | 2.12437i | 0.499281 | + | 0.500718i | ||||
\(19\) | 3.74911 | − | 2.22354i | 0.860106 | − | 0.510116i | ||||
\(20\) | − | 1.00000i | − | 0.223607i | ||||||
\(21\) | −2.39725 | + | 1.83674i | −0.523123 | + | 0.400810i | ||||
\(22\) | −3.88325 | − | 2.24200i | −0.827913 | − | 0.477996i | ||||
\(23\) | 1.69230 | − | 0.977053i | 0.352870 | − | 0.203730i | −0.313079 | − | 0.949727i | \(-0.601360\pi\) |
0.665949 | + | 0.745998i | \(0.268027\pi\) | |||||||
\(24\) | 1.37489 | − | 1.05342i | 0.280647 | − | 0.215028i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 3.63184i | 0.712263i | ||||||||
\(27\) | −1.97813 | − | 4.80489i | −0.380692 | − | 0.924702i | ||||
\(28\) | 0.871800 | + | 1.51000i | 0.164755 | + | 0.285364i | ||||
\(29\) | −0.271323 | − | 0.469946i | −0.0503835 | − | 0.0872668i | 0.839734 | − | 0.542998i | \(-0.182711\pi\) |
−0.890117 | + | 0.455732i | \(0.849378\pi\) | |||||||
\(30\) | −0.663976 | + | 1.59973i | −0.121225 | + | 0.292069i | ||||
\(31\) | − | 8.66957i | − | 1.55710i | −0.627583 | − | 0.778550i | \(-0.715956\pi\) | ||
0.627583 | − | 0.778550i | \(-0.284044\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 4.72353 | + | 6.16498i | 0.822260 | + | 1.07319i | ||||
\(34\) | −5.72021 | + | 3.30257i | −0.981009 | + | 0.566386i | ||||
\(35\) | −1.51000 | − | 0.871800i | −0.255237 | − | 0.147361i | ||||
\(36\) | −2.89889 | + | 0.772294i | −0.483148 | + | 0.128716i | ||||
\(37\) | 0.251265i | 0.0413078i | 0.999787 | + | 0.0206539i | \(0.00657480\pi\) | ||||
−0.999787 | + | 0.0206539i | \(0.993425\pi\) | |||||||
\(38\) | 0.0510884 | + | 4.35860i | 0.00828764 | + | 0.707058i | ||||
\(39\) | 2.41146 | − | 5.80997i | 0.386142 | − | 0.930340i | ||||
\(40\) | 0.866025 | + | 0.500000i | 0.136931 | + | 0.0790569i | ||||
\(41\) | 2.28336 | − | 3.95489i | 0.356600 | − | 0.617650i | −0.630790 | − | 0.775953i | \(-0.717269\pi\) |
0.987390 | + | 0.158304i | \(0.0506025\pi\) | |||||||
\(42\) | −0.392039 | − | 2.99445i | −0.0604930 | − | 0.462054i | ||||
\(43\) | −2.13741 | + | 3.70210i | −0.325952 | + | 0.564566i | −0.981705 | − | 0.190410i | \(-0.939018\pi\) |
0.655752 | + | 0.754976i | \(0.272351\pi\) | |||||||
\(44\) | 3.88325 | − | 2.24200i | 0.585423 | − | 0.337994i | ||||
\(45\) | 2.12437 | − | 2.11827i | 0.316682 | − | 0.315773i | ||||
\(46\) | 1.95411i | 0.288117i | ||||||||
\(47\) | 1.28818 | − | 0.743732i | 0.187901 | − | 0.108484i | −0.403099 | − | 0.915156i | \(-0.632067\pi\) |
0.590999 | + | 0.806672i | \(0.298734\pi\) | |||||||
\(48\) | 0.224845 | + | 1.71739i | 0.0324535 | + | 0.247885i | ||||
\(49\) | −3.95986 | −0.565694 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 11.3436 | − | 1.48513i | 1.58842 | − | 0.207960i | ||||
\(52\) | −3.14527 | − | 1.81592i | −0.436170 | − | 0.251823i | ||||
\(53\) | −0.0649443 | − | 0.112487i | −0.00892079 | − | 0.0154513i | 0.861531 | − | 0.507706i | \(-0.169506\pi\) |
−0.870451 | + | 0.492254i | \(0.836173\pi\) | |||||||
\(54\) | 5.15023 | + | 0.689332i | 0.700857 | + | 0.0938062i | ||||
\(55\) | −2.24200 | + | 3.88325i | −0.302311 | + | 0.523618i | ||||
\(56\) | −1.74360 | −0.232998 | ||||||||
\(57\) | 2.81228 | − | 7.00650i | 0.372495 | − | 0.928034i | ||||
\(58\) | 0.542647 | 0.0712530 | ||||||||
\(59\) | −3.22878 | + | 5.59241i | −0.420351 | + | 0.728069i | −0.995974 | − | 0.0896460i | \(-0.971426\pi\) |
0.575623 | + | 0.817715i | \(0.304760\pi\) | |||||||
\(60\) | −1.05342 | − | 1.37489i | −0.135996 | − | 0.177497i | ||||
\(61\) | 1.04215 | + | 1.80505i | 0.133433 | + | 0.231114i | 0.924998 | − | 0.379972i | \(-0.124066\pi\) |
−0.791564 | + | 0.611086i | \(0.790733\pi\) | |||||||
\(62\) | 7.50806 | + | 4.33478i | 0.953525 | + | 0.550518i | ||||
\(63\) | −1.36109 | + | 5.05062i | −0.171481 | + | 0.636318i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.63184 | 0.450475 | ||||||||
\(66\) | −7.70079 | + | 1.00820i | −0.947902 | + | 0.124101i | ||||
\(67\) | −7.40682 | + | 4.27633i | −0.904888 | + | 0.522437i | −0.878783 | − | 0.477222i | \(-0.841644\pi\) |
−0.0261048 | + | 0.999659i | \(0.508310\pi\) | |||||||
\(68\) | − | 6.60513i | − | 0.800990i | ||||||
\(69\) | 1.29748 | − | 3.12604i | 0.156198 | − | 0.376331i | ||||
\(70\) | 1.51000 | − | 0.871800i | 0.180480 | − | 0.104200i | ||||
\(71\) | −4.78907 | + | 8.29492i | −0.568358 | + | 0.984426i | 0.428370 | + | 0.903603i | \(0.359088\pi\) |
−0.996729 | + | 0.0808224i | \(0.974245\pi\) | |||||||
\(72\) | 0.780619 | − | 2.89666i | 0.0919968 | − | 0.341375i | ||||
\(73\) | −3.51522 | + | 6.08853i | −0.411425 | + | 0.712609i | −0.995046 | − | 0.0994174i | \(-0.968302\pi\) |
0.583621 | + | 0.812026i | \(0.301635\pi\) | |||||||
\(74\) | −0.217602 | − | 0.125633i | −0.0252957 | − | 0.0146045i | ||||
\(75\) | 1.59973 | + | 0.663976i | 0.184721 | + | 0.0766694i | ||||
\(76\) | −3.80020 | − | 2.13506i | −0.435913 | − | 0.244908i | ||||
\(77\) | − | 7.81830i | − | 0.890978i | ||||||
\(78\) | 3.82585 | + | 4.99337i | 0.433193 | + | 0.565388i | ||||
\(79\) | −5.04814 | − | 2.91454i | −0.567960 | − | 0.327912i | 0.188374 | − | 0.982097i | \(-0.439678\pi\) |
−0.756334 | + | 0.654186i | \(0.773012\pi\) | |||||||
\(80\) | −0.866025 | + | 0.500000i | −0.0968246 | + | 0.0559017i | ||||
\(81\) | −7.78127 | − | 4.52237i | −0.864586 | − | 0.502486i | ||||
\(82\) | 2.28336 | + | 3.95489i | 0.252154 | + | 0.436744i | ||||
\(83\) | 10.2566i | 1.12581i | 0.826523 | + | 0.562903i | \(0.190315\pi\) | ||||
−0.826523 | + | 0.562903i | \(0.809685\pi\) | |||||||
\(84\) | 2.78929 | + | 1.15771i | 0.304336 | + | 0.126316i | ||||
\(85\) | 3.30257 | + | 5.72021i | 0.358214 | + | 0.620444i | ||||
\(86\) | −2.13741 | − | 3.70210i | −0.230483 | − | 0.399208i | ||||
\(87\) | −0.868088 | − | 0.360305i | −0.0930688 | − | 0.0386287i | ||||
\(88\) | 4.48400i | 0.477996i | ||||||||
\(89\) | −2.10618 | − | 3.64801i | −0.223255 | − | 0.386689i | 0.732540 | − | 0.680724i | \(-0.238335\pi\) |
−0.955794 | + | 0.294036i | \(0.905002\pi\) | |||||||
\(90\) | 0.772294 | + | 2.89889i | 0.0814070 | + | 0.305570i | ||||
\(91\) | −5.48409 | + | 3.16624i | −0.574889 | + | 0.331912i | ||||
\(92\) | −1.69230 | − | 0.977053i | −0.176435 | − | 0.101865i | ||||
\(93\) | −9.13268 | − | 11.9197i | −0.947015 | − | 1.23601i | ||||
\(94\) | 1.48746i | 0.153420i | ||||||||
\(95\) | 4.35860 | − | 0.0510884i | 0.447183 | − | 0.00524156i | ||||
\(96\) | −1.59973 | − | 0.663976i | −0.163272 | − | 0.0677668i | ||||
\(97\) | 9.01717 | + | 5.20607i | 0.915555 | + | 0.528596i | 0.882214 | − | 0.470848i | \(-0.156052\pi\) |
0.0333409 | + | 0.999444i | \(0.489385\pi\) | |||||||
\(98\) | 1.97993 | − | 3.42934i | 0.200003 | − | 0.346415i | ||||
\(99\) | 12.9886 | + | 3.50029i | 1.30540 | + | 0.351792i | ||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | 9.94712 | − | 5.74297i | 0.989776 | − | 0.571447i | 0.0845686 | − | 0.996418i | \(-0.473049\pi\) |
0.905207 | + | 0.424970i | \(0.139715\pi\) | |||||||
\(102\) | −4.38565 | + | 10.5664i | −0.434244 | + | 1.04623i | ||||
\(103\) | 17.6607i | 1.74016i | 0.492909 | + | 0.870081i | \(0.335934\pi\) | ||||
−0.492909 | + | 0.870081i | \(0.664066\pi\) | |||||||
\(104\) | 3.14527 | − | 1.81592i | 0.308419 | − | 0.178066i | ||||
\(105\) | −2.99445 | + | 0.392039i | −0.292228 | + | 0.0382591i | ||||
\(106\) | 0.129889 | 0.0126159 | ||||||||
\(107\) | −20.1581 | −1.94875 | −0.974377 | − | 0.224920i | \(-0.927788\pi\) | ||||
−0.974377 | + | 0.224920i | \(0.927788\pi\) | |||||||
\(108\) | −3.17209 | + | 4.11556i | −0.305235 | + | 0.396020i | ||||
\(109\) | −5.41805 | − | 3.12812i | −0.518955 | − | 0.299619i | 0.217552 | − | 0.976049i | \(-0.430193\pi\) |
−0.736507 | + | 0.676430i | \(0.763526\pi\) | |||||||
\(110\) | −2.24200 | − | 3.88325i | −0.213766 | − | 0.370254i | ||||
\(111\) | 0.264688 | + | 0.345461i | 0.0251230 | + | 0.0327897i | ||||
\(112\) | 0.871800 | − | 1.51000i | 0.0823774 | − | 0.142682i | ||||
\(113\) | 6.35512 | 0.597840 | 0.298920 | − | 0.954278i | \(-0.403374\pi\) | ||||
0.298920 | + | 0.954278i | \(0.403374\pi\) | |||||||
\(114\) | 4.66167 | + | 5.93876i | 0.436605 | + | 0.556215i | ||||
\(115\) | 1.95411 | 0.182221 | ||||||||
\(116\) | −0.271323 | + | 0.469946i | −0.0251917 | + | 0.0436334i | ||||
\(117\) | −2.80485 | − | 10.5283i | −0.259309 | − | 0.973343i | ||||
\(118\) | −3.22878 | − | 5.59241i | −0.297233 | − | 0.514823i | ||||
\(119\) | −9.97377 | − | 5.75836i | −0.914294 | − | 0.527868i | ||||
\(120\) | 1.71739 | − | 0.224845i | 0.156776 | − | 0.0205254i | ||||
\(121\) | −9.10622 | −0.827839 | ||||||||
\(122\) | −2.08430 | −0.188703 | ||||||||
\(123\) | −1.02680 | − | 7.84285i | −0.0925835 | − | 0.707166i | ||||
\(124\) | −7.50806 | + | 4.33478i | −0.674244 | + | 0.389275i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −3.69342 | − | 3.70404i | −0.329036 | − | 0.329982i | ||||
\(127\) | 10.3685 | − | 5.98626i | 0.920056 | − | 0.531195i | 0.0364032 | − | 0.999337i | \(-0.488410\pi\) |
0.883653 | + | 0.468142i | \(0.155077\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0.961171 | + | 7.34156i | 0.0846264 | + | 0.646388i | ||||
\(130\) | −1.81592 | + | 3.14527i | −0.159267 | + | 0.275858i | ||||
\(131\) | −7.92681 | − | 4.57655i | −0.692569 | − | 0.399855i | 0.112005 | − | 0.993708i | \(-0.464273\pi\) |
−0.804574 | + | 0.593853i | \(0.797606\pi\) | |||||||
\(132\) | 2.97727 | − | 7.17318i | 0.259138 | − | 0.624345i | ||||
\(133\) | −6.53696 | + | 3.87697i | −0.566826 | + | 0.336176i | ||||
\(134\) | − | 8.55266i | − | 0.738838i | ||||||
\(135\) | 0.689332 | − | 5.15023i | 0.0593282 | − | 0.443261i | ||||
\(136\) | 5.72021 | + | 3.30257i | 0.490504 | + | 0.283193i | ||||
\(137\) | −13.2938 | + | 7.67520i | −1.13577 | + | 0.655737i | −0.945380 | − | 0.325972i | \(-0.894309\pi\) |
−0.190390 | + | 0.981709i | \(0.560975\pi\) | |||||||
\(138\) | 2.05849 | + | 2.68667i | 0.175230 | + | 0.228705i | ||||
\(139\) | −7.91901 | − | 13.7161i | −0.671682 | − | 1.16339i | −0.977427 | − | 0.211273i | \(-0.932239\pi\) |
0.305745 | − | 0.952113i | \(-0.401094\pi\) | |||||||
\(140\) | 1.74360i | 0.147361i | ||||||||
\(141\) | 0.987641 | − | 2.37954i | 0.0831743 | − | 0.200393i | ||||
\(142\) | −4.78907 | − | 8.29492i | −0.401890 | − | 0.696094i | ||||
\(143\) | 8.14259 | + | 14.1034i | 0.680918 | + | 1.17938i | ||||
\(144\) | 2.11827 | + | 2.12437i | 0.176523 | + | 0.177030i | ||||
\(145\) | − | 0.542647i | − | 0.0450644i | ||||||
\(146\) | −3.51522 | − | 6.08853i | −0.290921 | − | 0.503891i | ||||
\(147\) | −5.44435 | + | 4.17139i | −0.449042 | + | 0.344050i | ||||
\(148\) | 0.217602 | − | 0.125633i | 0.0178868 | − | 0.0103269i | ||||
\(149\) | −17.1301 | − | 9.89007i | −1.40335 | − | 0.810226i | −0.408618 | − | 0.912706i | \(-0.633989\pi\) |
−0.994735 | + | 0.102480i | \(0.967322\pi\) | |||||||
\(150\) | −1.37489 | + | 1.05342i | −0.112259 | + | 0.0860113i | ||||
\(151\) | − | 21.5191i | − | 1.75120i | −0.483038 | − | 0.875599i | \(-0.660467\pi\) | ||
0.483038 | − | 0.875599i | \(-0.339533\pi\) | |||||||
\(152\) | 3.74911 | − | 2.22354i | 0.304093 | − | 0.180353i | ||||
\(153\) | 14.0317 | − | 13.9915i | 1.13440 | − | 1.13114i | ||||
\(154\) | 6.77084 | + | 3.90915i | 0.545610 | + | 0.315008i | ||||
\(155\) | 4.33478 | − | 7.50806i | 0.348178 | − | 0.603062i | ||||
\(156\) | −6.23731 | + | 0.816601i | −0.499385 | + | 0.0653804i | ||||
\(157\) | 6.77384 | − | 11.7326i | 0.540611 | − | 0.936366i | −0.458258 | − | 0.888819i | \(-0.651526\pi\) |
0.998869 | − | 0.0475464i | \(-0.0151402\pi\) | |||||||
\(158\) | 5.04814 | − | 2.91454i | 0.401608 | − | 0.231869i | ||||
\(159\) | −0.207787 | − | 0.0862430i | −0.0164786 | − | 0.00683951i | ||||
\(160\) | − | 1.00000i | − | 0.0790569i | ||||||
\(161\) | −2.95070 | + | 1.70359i | −0.232548 | + | 0.134262i | ||||
\(162\) | 7.80712 | − | 4.47759i | 0.613386 | − | 0.351793i | ||||
\(163\) | 7.90301 | 0.619011 | 0.309506 | − | 0.950898i | \(-0.399836\pi\) | ||||
0.309506 | + | 0.950898i | \(0.399836\pi\) | |||||||
\(164\) | −4.56671 | −0.356600 | ||||||||
\(165\) | 1.00820 | + | 7.70079i | 0.0784885 | + | 0.599506i | ||||
\(166\) | −8.88246 | − | 5.12829i | −0.689412 | − | 0.398032i | ||||
\(167\) | −4.08621 | − | 7.07753i | −0.316201 | − | 0.547676i | 0.663491 | − | 0.748184i | \(-0.269074\pi\) |
−0.979692 | + | 0.200508i | \(0.935741\pi\) | |||||||
\(168\) | −2.39725 | + | 1.83674i | −0.184952 | + | 0.141708i | ||||
\(169\) | 0.0951480 | − | 0.164801i | 0.00731908 | − | 0.0126770i | ||||
\(170\) | −6.60513 | −0.506591 | ||||||||
\(171\) | −3.51422 | − | 12.5956i | −0.268739 | − | 0.963213i | ||||
\(172\) | 4.27482 | 0.325952 | ||||||||
\(173\) | 8.82834 | − | 15.2911i | 0.671206 | − | 1.16256i | −0.306356 | − | 0.951917i | \(-0.599110\pi\) |
0.977562 | − | 0.210647i | \(-0.0675569\pi\) | |||||||
\(174\) | 0.746077 | − | 0.571634i | 0.0565600 | − | 0.0433355i | ||||
\(175\) | −0.871800 | − | 1.51000i | −0.0659019 | − | 0.114145i | ||||
\(176\) | −3.88325 | − | 2.24200i | −0.292711 | − | 0.168997i | ||||
\(177\) | 1.45195 | + | 11.0902i | 0.109135 | + | 0.833588i | ||||
\(178\) | 4.21236 | 0.315730 | ||||||||
\(179\) | −19.9723 | −1.49280 | −0.746402 | − | 0.665496i | \(-0.768220\pi\) | ||||
−0.746402 | + | 0.665496i | \(0.768220\pi\) | |||||||
\(180\) | −2.89666 | − | 0.780619i | −0.215904 | − | 0.0581839i | ||||
\(181\) | 2.87130 | − | 1.65774i | 0.213422 | − | 0.123219i | −0.389479 | − | 0.921035i | \(-0.627345\pi\) |
0.602901 | + | 0.797816i | \(0.294012\pi\) | |||||||
\(182\) | − | 6.33249i | − | 0.469395i | ||||||
\(183\) | 3.33431 | + | 1.38392i | 0.246480 | + | 0.102303i | ||||
\(184\) | 1.69230 | − | 0.977053i | 0.124758 | − | 0.0720293i | ||||
\(185\) | −0.125633 | + | 0.217602i | −0.00923670 | + | 0.0159984i | ||||
\(186\) | 14.8891 | − | 1.94931i | 1.09172 | − | 0.142930i | ||||
\(187\) | −14.8087 | + | 25.6494i | −1.08292 | + | 1.87567i | ||||
\(188\) | −1.28818 | − | 0.743732i | −0.0939503 | − | 0.0542422i | ||||
\(189\) | 3.44908 | + | 8.37781i | 0.250883 | + | 0.609396i | ||||
\(190\) | −2.13506 | + | 3.80020i | −0.154893 | + | 0.275696i | ||||
\(191\) | 9.19637i | 0.665426i | 0.943028 | + | 0.332713i | \(0.107964\pi\) | ||||
−0.943028 | + | 0.332713i | \(0.892036\pi\) | |||||||
\(192\) | 1.37489 | − | 1.05342i | 0.0992238 | − | 0.0760239i | ||||
\(193\) | 11.3952 | + | 6.57904i | 0.820247 | + | 0.473570i | 0.850502 | − | 0.525972i | \(-0.176298\pi\) |
−0.0302545 | + | 0.999542i | \(0.509632\pi\) | |||||||
\(194\) | −9.01717 | + | 5.20607i | −0.647395 | + | 0.373774i | ||||
\(195\) | 4.99337 | − | 3.82585i | 0.357583 | − | 0.273975i | ||||
\(196\) | 1.97993 | + | 3.42934i | 0.141423 | + | 0.244953i | ||||
\(197\) | 27.4692i | 1.95710i | 0.206016 | + | 0.978549i | \(0.433950\pi\) | ||||
−0.206016 | + | 0.978549i | \(0.566050\pi\) | |||||||
\(198\) | −9.52565 | + | 9.49832i | −0.676958 | + | 0.675016i | ||||
\(199\) | −4.51192 | − | 7.81487i | −0.319841 | − | 0.553981i | 0.660613 | − | 0.750726i | \(-0.270296\pi\) |
−0.980455 | + | 0.196745i | \(0.936963\pi\) | |||||||
\(200\) | 0.500000 | + | 0.866025i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | −5.67876 | + | 13.6820i | −0.400549 | + | 0.965050i | ||||
\(202\) | 11.4859i | 0.808149i | ||||||||
\(203\) | 0.473080 | + | 0.819398i | 0.0332037 | + | 0.0575105i | ||||
\(204\) | −6.95797 | − | 9.08130i | −0.487155 | − | 0.635818i | ||||
\(205\) | 3.95489 | − | 2.28336i | 0.276221 | − | 0.159476i | ||||
\(206\) | −15.2946 | − | 8.83036i | −1.06563 | − | 0.615240i | ||||
\(207\) | −1.50914 | − | 5.66474i | −0.104893 | − | 0.393726i | ||||
\(208\) | 3.63184i | 0.251823i | ||||||||
\(209\) | 9.97036 | + | 16.8110i | 0.689664 | + | 1.16284i | ||||
\(210\) | 1.15771 | − | 2.78929i | 0.0798895 | − | 0.192479i | ||||
\(211\) | −18.1457 | − | 10.4764i | −1.24920 | − | 0.721226i | −0.278251 | − | 0.960508i | \(-0.589755\pi\) |
−0.970950 | + | 0.239282i | \(0.923088\pi\) | |||||||
\(212\) | −0.0649443 | + | 0.112487i | −0.00446040 | + | 0.00772563i | ||||
\(213\) | 2.15360 | + | 16.4495i | 0.147562 | + | 1.12710i | ||||
\(214\) | 10.0790 | − | 17.4574i | 0.688989 | − | 1.19336i | ||||
\(215\) | −3.70210 | + | 2.13741i | −0.252481 | + | 0.145770i | ||||
\(216\) | −1.97813 | − | 4.80489i | −0.134595 | − | 0.326931i | ||||
\(217\) | 15.1163i | 1.02616i | ||||||||
\(218\) | 5.41805 | − | 3.12812i | 0.366957 | − | 0.211863i | ||||
\(219\) | 1.58076 | + | 12.0740i | 0.106818 | + | 0.815887i | ||||
\(220\) | 4.48400 | 0.302311 | ||||||||
\(221\) | 23.9888 | 1.61366 | ||||||||
\(222\) | −0.431522 | + | 0.0564957i | −0.0289618 | + | 0.00379174i | ||||
\(223\) | −11.2359 | − | 6.48704i | −0.752410 | − | 0.434404i | 0.0741541 | − | 0.997247i | \(-0.476374\pi\) |
−0.826564 | + | 0.562843i | \(0.809708\pi\) | |||||||
\(224\) | 0.871800 | + | 1.51000i | 0.0582496 | + | 0.100891i | ||||
\(225\) | 2.89889 | − | 0.772294i | 0.193259 | − | 0.0514863i | ||||
\(226\) | −3.17756 | + | 5.50370i | −0.211368 | + | 0.366100i | ||||
\(227\) | 21.2257 | 1.40880 | 0.704401 | − | 0.709803i | \(-0.251216\pi\) | ||||
0.704401 | + | 0.709803i | \(0.251216\pi\) | |||||||
\(228\) | −7.47395 | + | 1.06775i | −0.494974 | + | 0.0707133i | ||||
\(229\) | 9.69163 | 0.640441 | 0.320220 | − | 0.947343i | \(-0.396243\pi\) | ||||
0.320220 | + | 0.947343i | \(0.396243\pi\) | |||||||
\(230\) | −0.977053 | + | 1.69230i | −0.0644249 | + | 0.111587i | ||||
\(231\) | −8.23594 | − | 10.7493i | −0.541885 | − | 0.707250i | ||||
\(232\) | −0.271323 | − | 0.469946i | −0.0178133 | − | 0.0308535i | ||||
\(233\) | −14.0033 | − | 8.08481i | −0.917387 | − | 0.529654i | −0.0345867 | − | 0.999402i | \(-0.511011\pi\) |
−0.882801 | + | 0.469748i | \(0.844345\pi\) | |||||||
\(234\) | 10.5202 | + | 2.83509i | 0.687728 | + | 0.185335i | ||||
\(235\) | 1.48746 | 0.0970314 | ||||||||
\(236\) | 6.45756 | 0.420351 | ||||||||
\(237\) | −10.0108 | + | 1.31064i | −0.650274 | + | 0.0851352i | ||||
\(238\) | 9.97377 | − | 5.75836i | 0.646503 | − | 0.373259i | ||||
\(239\) | 21.3293i | 1.37968i | 0.723964 | + | 0.689838i | \(0.242318\pi\) | ||||
−0.723964 | + | 0.689838i | \(0.757682\pi\) | |||||||
\(240\) | −0.663976 | + | 1.59973i | −0.0428595 | + | 0.103262i | ||||
\(241\) | 3.63151 | − | 2.09666i | 0.233926 | − | 0.135057i | −0.378456 | − | 0.925619i | \(-0.623545\pi\) |
0.612382 | + | 0.790562i | \(0.290211\pi\) | |||||||
\(242\) | 4.55311 | − | 7.88622i | 0.292685 | − | 0.506946i | ||||
\(243\) | −15.4623 | + | 1.97919i | −0.991907 | + | 0.126965i | ||||
\(244\) | 1.04215 | − | 1.80505i | 0.0667167 | − | 0.115557i | ||||
\(245\) | −3.42934 | − | 1.97993i | −0.219092 | − | 0.126493i | ||||
\(246\) | 7.30551 | + | 3.03219i | 0.465782 | + | 0.193325i | ||||
\(247\) | 7.75419 | − | 13.8017i | 0.493387 | − | 0.878184i | ||||
\(248\) | − | 8.66957i | − | 0.550518i | ||||||
\(249\) | 10.8045 | + | 14.1016i | 0.684705 | + | 0.893654i | ||||
\(250\) | −0.866025 | − | 0.500000i | −0.0547723 | − | 0.0316228i | ||||
\(251\) | 20.8600 | − | 12.0435i | 1.31667 | − | 0.760179i | 0.333478 | − | 0.942758i | \(-0.391778\pi\) |
0.983191 | + | 0.182579i | \(0.0584444\pi\) | |||||||
\(252\) | 5.05451 | − | 1.34657i | 0.318404 | − | 0.0848261i | ||||
\(253\) | 4.38110 | + | 7.58829i | 0.275437 | + | 0.477072i | ||||
\(254\) | 11.9725i | 0.751223i | ||||||||
\(255\) | 10.5664 | + | 4.38565i | 0.661696 | + | 0.274640i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −5.58082 | − | 9.66626i | −0.348122 | − | 0.602965i | 0.637794 | − | 0.770207i | \(-0.279847\pi\) |
−0.985916 | + | 0.167242i | \(0.946514\pi\) | |||||||
\(258\) | −6.83856 | − | 2.83838i | −0.425750 | − | 0.176710i | ||||
\(259\) | − | 0.438106i | − | 0.0272226i | ||||||
\(260\) | −1.81592 | − | 3.14527i | −0.112619 | − | 0.195061i | ||||
\(261\) | −1.57307 | + | 0.419083i | −0.0973708 | + | 0.0259406i | ||||
\(262\) | 7.92681 | − | 4.57655i | 0.489720 | − | 0.282740i | ||||
\(263\) | 12.8454 | + | 7.41629i | 0.792081 | + | 0.457308i | 0.840695 | − | 0.541510i | \(-0.182147\pi\) |
−0.0486138 | + | 0.998818i | \(0.515480\pi\) | |||||||
\(264\) | 4.72353 | + | 6.16498i | 0.290713 | + | 0.379428i | ||||
\(265\) | − | 0.129889i | − | 0.00797900i | ||||||
\(266\) | −0.0890778 | − | 7.59966i | −0.00546171 | − | 0.465965i | ||||
\(267\) | −6.73865 | − | 2.79691i | −0.412398 | − | 0.171168i | ||||
\(268\) | 7.40682 | + | 4.27633i | 0.452444 | + | 0.261219i | ||||
\(269\) | −3.20285 | + | 5.54749i | −0.195281 | + | 0.338237i | −0.946993 | − | 0.321255i | \(-0.895895\pi\) |
0.751712 | + | 0.659492i | \(0.229229\pi\) | |||||||
\(270\) | 4.11556 | + | 3.17209i | 0.250465 | + | 0.193047i | ||||
\(271\) | 8.80426 | − | 15.2494i | 0.534820 | − | 0.926336i | −0.464352 | − | 0.885651i | \(-0.653713\pi\) |
0.999172 | − | 0.0406852i | \(-0.0129541\pi\) | |||||||
\(272\) | −5.72021 | + | 3.30257i | −0.346839 | + | 0.200248i | ||||
\(273\) | −4.20462 | + | 10.1303i | −0.254475 | + | 0.613112i | ||||
\(274\) | − | 15.3504i | − | 0.927352i | ||||||
\(275\) | −3.88325 | + | 2.24200i | −0.234169 | + | 0.135198i | ||||
\(276\) | −3.35597 | + | 0.439370i | −0.202006 | + | 0.0264470i | ||||
\(277\) | −27.5243 | −1.65377 | −0.826887 | − | 0.562369i | \(-0.809890\pi\) | ||||
−0.826887 | + | 0.562369i | \(0.809890\pi\) | |||||||
\(278\) | 15.8380 | 0.949901 | ||||||||
\(279\) | −25.1128 | − | 6.76762i | −1.50346 | − | 0.405167i | ||||
\(280\) | −1.51000 | − | 0.871800i | −0.0902399 | − | 0.0521000i | ||||
\(281\) | 2.25447 | + | 3.90486i | 0.134490 | + | 0.232944i | 0.925403 | − | 0.378985i | \(-0.123727\pi\) |
−0.790912 | + | 0.611930i | \(0.790394\pi\) | |||||||
\(282\) | 1.56692 | + | 2.04509i | 0.0933089 | + | 0.121783i | ||||
\(283\) | −14.2001 | + | 24.5953i | −0.844109 | + | 1.46204i | 0.0422840 | + | 0.999106i | \(0.486537\pi\) |
−0.886393 | + | 0.462934i | \(0.846797\pi\) | |||||||
\(284\) | 9.57815 | 0.568358 | ||||||||
\(285\) | 5.93876 | − | 4.66167i | 0.351782 | − | 0.276134i | ||||
\(286\) | −16.2852 | −0.962963 | ||||||||
\(287\) | −3.98126 | + | 6.89574i | −0.235006 | + | 0.407043i | ||||
\(288\) | −2.89889 | + | 0.772294i | −0.170819 | + | 0.0455079i | ||||
\(289\) | 13.3139 | + | 23.0603i | 0.783170 | + | 1.35649i | ||||
\(290\) | 0.469946 | + | 0.271323i | 0.0275962 | + | 0.0159327i | ||||
\(291\) | 17.8817 | − | 2.34111i | 1.04825 | − | 0.137238i | ||||
\(292\) | 7.03043 | 0.411425 | ||||||||
\(293\) | 14.9955 | 0.876047 | 0.438024 | − | 0.898963i | \(-0.355679\pi\) | ||||
0.438024 | + | 0.898963i | \(0.355679\pi\) | |||||||
\(294\) | −0.890353 | − | 6.80064i | −0.0519264 | − | 0.396621i | ||||
\(295\) | −5.59241 | + | 3.22878i | −0.325603 | + | 0.187987i | ||||
\(296\) | 0.251265i | 0.0146045i | ||||||||
\(297\) | 21.5451 | − | 8.86995i | 1.25017 | − | 0.514686i | ||||
\(298\) | 17.1301 | − | 9.89007i | 0.992320 | − | 0.572916i | ||||
\(299\) | 3.54850 | − | 6.14619i | 0.205215 | − | 0.355443i | ||||
\(300\) | −0.224845 | − | 1.71739i | −0.0129814 | − | 0.0991538i | ||||
\(301\) | 3.72679 | − | 6.45499i | 0.214809 | − | 0.372060i | ||||
\(302\) | 18.6361 | + | 10.7595i | 1.07239 | + | 0.619142i | ||||
\(303\) | 7.62640 | − | 18.3744i | 0.438125 | − | 1.05558i | ||||
\(304\) | 0.0510884 | + | 4.35860i | 0.00293012 | + | 0.249983i | ||||
\(305\) | 2.08430i | 0.119347i | ||||||||
\(306\) | 5.10111 | + | 19.1476i | 0.291611 | + | 1.09459i | ||||
\(307\) | 17.6339 | + | 10.1810i | 1.00642 | + | 0.581058i | 0.910142 | − | 0.414296i | \(-0.135972\pi\) |
0.0962802 | + | 0.995354i | \(0.469306\pi\) | |||||||
\(308\) | −6.77084 | + | 3.90915i | −0.385805 | + | 0.222744i | ||||
\(309\) | 18.6041 | + | 24.2815i | 1.05835 | + | 1.38132i | ||||
\(310\) | 4.33478 | + | 7.50806i | 0.246199 | + | 0.426429i | ||||
\(311\) | 12.1717i | 0.690194i | 0.938567 | + | 0.345097i | \(0.112154\pi\) | ||||
−0.938567 | + | 0.345097i | \(0.887846\pi\) | |||||||
\(312\) | 2.41146 | − | 5.80997i | 0.136522 | − | 0.328925i | ||||
\(313\) | −6.57209 | − | 11.3832i | −0.371476 | − | 0.643416i | 0.618317 | − | 0.785929i | \(-0.287815\pi\) |
−0.989793 | + | 0.142513i | \(0.954482\pi\) | |||||||
\(314\) | 6.77384 | + | 11.7326i | 0.382270 | + | 0.662110i | ||||
\(315\) | −3.70404 | + | 3.69342i | −0.208699 | + | 0.208101i | ||||
\(316\) | 5.82909i | 0.327912i | ||||||||
\(317\) | 3.43470 | + | 5.94907i | 0.192912 | + | 0.334133i | 0.946214 | − | 0.323542i | \(-0.104874\pi\) |
−0.753302 | + | 0.657675i | \(0.771540\pi\) | |||||||
\(318\) | 0.178582 | − | 0.136827i | 0.0100144 | − | 0.00767288i | ||||
\(319\) | 2.10724 | − | 1.21661i | 0.117983 | − | 0.0681173i | ||||
\(320\) | 0.866025 | + | 0.500000i | 0.0484123 | + | 0.0279508i | ||||
\(321\) | −27.7150 | + | 21.2349i | −1.54690 | + | 1.18522i | ||||
\(322\) | − | 3.40718i | − | 0.189875i | ||||||
\(323\) | 28.7891 | − | 0.337446i | 1.60187 | − | 0.0187760i | ||||
\(324\) | −0.0258539 | + | 8.99996i | −0.00143633 | + | 0.499998i | ||||
\(325\) | 3.14527 | + | 1.81592i | 0.174468 | + | 0.100729i | ||||
\(326\) | −3.95150 | + | 6.84420i | −0.218854 | + | 0.379065i | ||||
\(327\) | −10.7444 | + | 1.40668i | −0.594168 | + | 0.0777896i | ||||
\(328\) | 2.28336 | − | 3.95489i | 0.126077 | − | 0.218372i | ||||
\(329\) | −2.24607 | + | 1.29677i | −0.123830 | + | 0.0714933i | ||||
\(330\) | −7.17318 | − | 2.97727i | −0.394871 | − | 0.163893i | ||||
\(331\) | 7.78853i | 0.428096i | 0.976823 | + | 0.214048i | \(0.0686649\pi\) | ||||
−0.976823 | + | 0.214048i | \(0.931335\pi\) | |||||||
\(332\) | 8.88246 | − | 5.12829i | 0.487488 | − | 0.281451i | ||||
\(333\) | 0.727830 | + | 0.196142i | 0.0398848 | + | 0.0107485i | ||||
\(334\) | 8.17243 | 0.447175 | ||||||||
\(335\) | −8.55266 | −0.467282 | ||||||||
\(336\) | −0.392039 | − | 2.99445i | −0.0213875 | − | 0.163361i | ||||
\(337\) | 23.2844 | + | 13.4433i | 1.26838 | + | 0.732301i | 0.974682 | − | 0.223597i | \(-0.0717799\pi\) |
0.293700 | + | 0.955898i | \(0.405113\pi\) | |||||||
\(338\) | 0.0951480 | + | 0.164801i | 0.00517537 | + | 0.00896401i | ||||
\(339\) | 8.73756 | − | 6.69460i | 0.474559 | − | 0.363601i | ||||
\(340\) | 3.30257 | − | 5.72021i | 0.179107 | − | 0.310222i | ||||
\(341\) | 38.8743 | 2.10516 | ||||||||
\(342\) | 12.6653 | + | 3.25442i | 0.684859 | + | 0.175979i | ||||
\(343\) | 19.1096 | 1.03182 | ||||||||
\(344\) | −2.13741 | + | 3.70210i | −0.115241 | + | 0.199604i | ||||
\(345\) | 2.68667 | − | 2.05849i | 0.144645 | − | 0.110825i | ||||
\(346\) | 8.82834 | + | 15.2911i | 0.474615 | + | 0.822057i | ||||
\(347\) | −24.5180 | − | 14.1555i | −1.31620 | − | 0.759906i | −0.333081 | − | 0.942898i | \(-0.608088\pi\) |
−0.983114 | + | 0.182992i | \(0.941422\pi\) | |||||||
\(348\) | 0.122011 | + | 0.931939i | 0.00654049 | + | 0.0499572i | ||||
\(349\) | 4.70839 | 0.252034 | 0.126017 | − | 0.992028i | \(-0.459781\pi\) | ||||
0.126017 | + | 0.992028i | \(0.459781\pi\) | |||||||
\(350\) | 1.74360 | 0.0931994 | ||||||||
\(351\) | −14.9471 | − | 11.5205i | −0.797816 | − | 0.614921i | ||||
\(352\) | 3.88325 | − | 2.24200i | 0.206978 | − | 0.119499i | ||||
\(353\) | − | 16.8453i | − | 0.896587i | −0.893886 | − | 0.448293i | \(-0.852032\pi\) | ||
0.893886 | − | 0.448293i | \(-0.147968\pi\) | |||||||
\(354\) | −10.3303 | − | 4.28766i | −0.549052 | − | 0.227887i | ||||
\(355\) | −8.29492 | + | 4.78907i | −0.440249 | + | 0.254178i | ||||
\(356\) | −2.10618 | + | 3.64801i | −0.111627 | + | 0.193344i | ||||
\(357\) | −19.7787 | + | 2.58947i | −1.04680 | + | 0.137049i | ||||
\(358\) | 9.98617 | − | 17.2966i | 0.527786 | − | 0.914152i | ||||
\(359\) | −27.5785 | − | 15.9225i | −1.45554 | − | 0.840356i | −0.456752 | − | 0.889594i | \(-0.650987\pi\) |
−0.998787 | + | 0.0492381i | \(0.984321\pi\) | |||||||
\(360\) | 2.12437 | − | 2.11827i | 0.111964 | − | 0.111643i | ||||
\(361\) | 9.11171 | − | 16.6726i | 0.479564 | − | 0.877507i | ||||
\(362\) | 3.31549i | 0.174258i | ||||||||
\(363\) | −12.5200 | + | 9.59267i | −0.657130 | + | 0.503484i | ||||
\(364\) | 5.48409 | + | 3.16624i | 0.287445 | + | 0.165956i | ||||
\(365\) | −6.08853 | + | 3.51522i | −0.318688 | + | 0.183995i | ||||
\(366\) | −2.86567 | + | 2.19564i | −0.149791 | + | 0.114768i | ||||
\(367\) | −15.1447 | − | 26.2313i | −0.790545 | − | 1.36926i | −0.925630 | − | 0.378430i | \(-0.876464\pi\) |
0.135085 | − | 0.990834i | \(-0.456869\pi\) | |||||||
\(368\) | 1.95411i | 0.101865i | ||||||||
\(369\) | −9.67353 | − | 9.70136i | −0.503584 | − | 0.505033i | ||||
\(370\) | −0.125633 | − | 0.217602i | −0.00653133 | − | 0.0113126i | ||||
\(371\) | 0.113237 | + | 0.196132i | 0.00587897 | + | 0.0101827i | ||||
\(372\) | −5.75639 | + | 13.8690i | −0.298455 | + | 0.719072i | ||||
\(373\) | − | 37.2564i | − | 1.92906i | −0.263966 | − | 0.964532i | \(-0.585031\pi\) | ||
0.263966 | − | 0.964532i | \(-0.414969\pi\) | |||||||
\(374\) | −14.8087 | − | 25.6494i | −0.765740 | − | 1.32630i | ||||
\(375\) | 1.05342 | + | 1.37489i | 0.0543983 | + | 0.0709988i | ||||
\(376\) | 1.28818 | − | 0.743732i | 0.0664329 | − | 0.0383550i | ||||
\(377\) | −1.70677 | − | 0.985405i | −0.0879032 | − | 0.0507509i | ||||
\(378\) | −8.97994 | − | 1.20192i | −0.461878 | − | 0.0618200i | ||||
\(379\) | 33.6356i | 1.72775i | 0.503709 | + | 0.863873i | \(0.331968\pi\) | ||||
−0.503709 | + | 0.863873i | \(0.668032\pi\) | |||||||
\(380\) | −2.22354 | − | 3.74911i | −0.114065 | − | 0.192325i | ||||
\(381\) | 7.94947 | − | 19.1528i | 0.407264 | − | 0.981228i | ||||
\(382\) | −7.96429 | − | 4.59818i | −0.407488 | − | 0.235264i | ||||
\(383\) | −4.65017 | + | 8.05432i | −0.237612 | + | 0.411557i | −0.960029 | − | 0.279902i | \(-0.909698\pi\) |
0.722416 | + | 0.691458i | \(0.243031\pi\) | |||||||
\(384\) | 0.224845 | + | 1.71739i | 0.0114741 | + | 0.0876404i | ||||
\(385\) | 3.90915 | − | 6.77084i | 0.199229 | − | 0.345074i | ||||
\(386\) | −11.3952 | + | 6.57904i | −0.580002 | + | 0.334865i | ||||
\(387\) | 9.05523 | + | 9.08128i | 0.460303 | + | 0.461628i | ||||
\(388\) | − | 10.4121i | − | 0.528596i | ||||||
\(389\) | 7.08705 | − | 4.09171i | 0.359328 | − | 0.207458i | −0.309458 | − | 0.950913i | \(-0.600148\pi\) |
0.668786 | + | 0.743455i | \(0.266814\pi\) | |||||||
\(390\) | 0.816601 | + | 6.23731i | 0.0413502 | + | 0.315839i | ||||
\(391\) | 12.9071 | 0.652741 | ||||||||
\(392\) | −3.95986 | −0.200003 | ||||||||
\(393\) | −15.7195 | + | 2.05802i | −0.792943 | + | 0.103814i | ||||
\(394\) | −23.7890 | − | 13.7346i | −1.19847 | − | 0.691938i | ||||
\(395\) | −2.91454 | − | 5.04814i | −0.146647 | − | 0.253999i | ||||
\(396\) | −3.46296 | − | 12.9986i | −0.174021 | − | 0.653205i | ||||
\(397\) | 2.72560 | − | 4.72088i | 0.136794 | − | 0.236934i | −0.789487 | − | 0.613767i | \(-0.789653\pi\) |
0.926281 | + | 0.376833i | \(0.122987\pi\) | |||||||
\(398\) | 9.02384 | 0.452324 | ||||||||
\(399\) | −4.90349 | + | 12.2165i | −0.245482 | + | 0.611592i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | −14.4054 | + | 24.9508i | −0.719369 | + | 1.24598i | 0.241881 | + | 0.970306i | \(0.422236\pi\) |
−0.961250 | + | 0.275678i | \(0.911098\pi\) | |||||||
\(402\) | −9.00953 | − | 11.7589i | −0.449355 | − | 0.586482i | ||||
\(403\) | −15.7433 | − | 27.2681i | −0.784228 | − | 1.35832i | ||||
\(404\) | −9.94712 | − | 5.74297i | −0.494888 | − | 0.285724i | ||||
\(405\) | −4.47759 | − | 7.80712i | −0.222493 | − | 0.387939i | ||||
\(406\) | −0.946159 | −0.0469571 | ||||||||
\(407\) | −1.12667 | −0.0558471 | ||||||||
\(408\) | 11.3436 | − | 1.48513i | 0.561593 | − | 0.0735249i | ||||
\(409\) | 25.3296 | − | 14.6240i | 1.25247 | − | 0.723113i | 0.280869 | − | 0.959746i | \(-0.409377\pi\) |
0.971599 | + | 0.236633i | \(0.0760440\pi\) | |||||||
\(410\) | 4.56671i | 0.225534i | ||||||||
\(411\) | −10.1923 | + | 24.5565i | −0.502749 | + | 1.21128i | ||||
\(412\) | 15.2946 | − | 8.83036i | 0.753512 | − | 0.435040i | ||||
\(413\) | 5.62970 | − | 9.75092i | 0.277019 | − | 0.479812i | ||||
\(414\) | 5.66038 | + | 1.52541i | 0.278192 | + | 0.0749698i | ||||
\(415\) | −5.12829 | + | 8.88246i | −0.251738 | + | 0.436023i | ||||
\(416\) | −3.14527 | − | 1.81592i | −0.154210 | − | 0.0890329i | ||||
\(417\) | −25.3365 | − | 10.5161i | −1.24074 | − | 0.514974i | ||||
\(418\) | −19.5439 | + | 0.229080i | −0.955926 | + | 0.0112047i | ||||
\(419\) | 1.11183i | 0.0543167i | 0.999631 | + | 0.0271583i | \(0.00864583\pi\) | ||||
−0.999631 | + | 0.0271583i | \(0.991354\pi\) | |||||||
\(420\) | 1.83674 | + | 2.39725i | 0.0896238 | + | 0.116974i | ||||
\(421\) | 17.1508 | + | 9.90200i | 0.835877 | + | 0.482594i | 0.855861 | − | 0.517206i | \(-0.173028\pi\) |
−0.0199835 | + | 0.999800i | \(0.506361\pi\) | |||||||
\(422\) | 18.1457 | − | 10.4764i | 0.883318 | − | 0.509984i | ||||
\(423\) | −1.14876 | − | 4.31199i | −0.0558546 | − | 0.209656i | ||||
\(424\) | −0.0649443 | − | 0.112487i | −0.00315398 | − | 0.00546285i | ||||
\(425\) | 6.60513i | 0.320396i | ||||||||
\(426\) | −15.3224 | − | 6.35966i | −0.742375 | − | 0.308127i | ||||
\(427\) | −1.81709 | − | 3.14729i | −0.0879352 | − | 0.152308i | ||||
\(428\) | 10.0790 | + | 17.4574i | 0.487189 | + | 0.843835i | ||||
\(429\) | 26.0519 | + | 10.8130i | 1.25780 | + | 0.522055i | ||||
\(430\) | − | 4.27482i | − | 0.206150i | ||||||
\(431\) | −3.16146 | − | 5.47581i | −0.152282 | − | 0.263760i | 0.779784 | − | 0.626049i | \(-0.215329\pi\) |
−0.932066 | + | 0.362288i | \(0.881996\pi\) | |||||||
\(432\) | 5.15023 | + | 0.689332i | 0.247790 | + | 0.0331655i | ||||
\(433\) | −24.2858 | + | 14.0214i | −1.16710 | + | 0.673827i | −0.952996 | − | 0.302983i | \(-0.902017\pi\) |
−0.214107 | + | 0.976810i | \(0.568684\pi\) | |||||||
\(434\) | −13.0911 | − | 7.55813i | −0.628391 | − | 0.362802i | ||||
\(435\) | −0.571634 | − | 0.746077i | −0.0274078 | − | 0.0357717i | ||||
\(436\) | 6.25623i | 0.299619i | ||||||||
\(437\) | 4.17212 | − | 7.42600i | 0.199580 | − | 0.355234i | ||||
\(438\) | −11.2468 | − | 4.66804i | −0.537393 | − | 0.223048i | ||||
\(439\) | −8.39710 | − | 4.84807i | −0.400772 | − | 0.231386i | 0.286045 | − | 0.958216i | \(-0.407659\pi\) |
−0.686817 | + | 0.726830i | \(0.740993\pi\) | |||||||
\(440\) | −2.24200 | + | 3.88325i | −0.106883 | + | 0.185127i | ||||
\(441\) | −3.09114 | + | 11.4704i | −0.147197 | + | 0.546208i | ||||
\(442\) | −11.9944 | + | 20.7749i | −0.570516 | + | 0.988163i | ||||
\(443\) | −8.85438 | + | 5.11208i | −0.420684 | + | 0.242882i | −0.695370 | − | 0.718652i | \(-0.744760\pi\) |
0.274686 | + | 0.961534i | \(0.411426\pi\) | |||||||
\(444\) | 0.166834 | − | 0.401957i | 0.00791760 | − | 0.0190760i | ||||
\(445\) | − | 4.21236i | − | 0.199685i | ||||||
\(446\) | 11.2359 | − | 6.48704i | 0.532034 | − | 0.307170i | ||||
\(447\) | −33.9703 | + | 4.44746i | −1.60674 | + | 0.210358i | ||||
\(448\) | −1.74360 | −0.0823774 | ||||||||
\(449\) | 6.66710 | 0.314640 | 0.157320 | − | 0.987548i | \(-0.449715\pi\) | ||||
0.157320 | + | 0.987548i | \(0.449715\pi\) | |||||||
\(450\) | −0.780619 | + | 2.89666i | −0.0367987 | + | 0.136550i | ||||
\(451\) | 17.7337 | + | 10.2386i | 0.835048 | + | 0.482115i | ||||
\(452\) | −3.17756 | − | 5.50370i | −0.149460 | − | 0.258872i | ||||
\(453\) | −22.6686 | − | 29.5863i | −1.06506 | − | 1.39008i | ||||
\(454\) | −10.6129 | + | 18.3820i | −0.498086 | + | 0.862711i | ||||
\(455\) | −6.33249 | −0.296872 | ||||||||
\(456\) | 2.81228 | − | 7.00650i | 0.131697 | − | 0.328110i | ||||
\(457\) | −12.8650 | −0.601800 | −0.300900 | − | 0.953656i | \(-0.597287\pi\) | ||||
−0.300900 | + | 0.953656i | \(0.597287\pi\) | |||||||
\(458\) | −4.84581 | + | 8.39319i | −0.226430 | + | 0.392188i | ||||
\(459\) | 4.55313 | − | 34.0179i | 0.212522 | − | 1.58782i | ||||
\(460\) | −0.977053 | − | 1.69230i | −0.0455553 | − | 0.0789041i | ||||
\(461\) | 4.75855 | + | 2.74735i | 0.221628 | + | 0.127957i | 0.606704 | − | 0.794928i | \(-0.292491\pi\) |
−0.385076 | + | 0.922885i | \(0.625825\pi\) | |||||||
\(462\) | 13.4271 | − | 1.75790i | 0.624685 | − | 0.0817850i | ||||
\(463\) | 9.12169 | 0.423921 | 0.211960 | − | 0.977278i | \(-0.432015\pi\) | ||||
0.211960 | + | 0.977278i | \(0.432015\pi\) | |||||||
\(464\) | 0.542647 | 0.0251917 | ||||||||
\(465\) | −1.94931 | − | 14.8891i | −0.0903969 | − | 0.690464i | ||||
\(466\) | 14.0033 | − | 8.08481i | 0.648691 | − | 0.374522i | ||||
\(467\) | 31.0365i | 1.43620i | 0.695940 | + | 0.718100i | \(0.254988\pi\) | ||||
−0.695940 | + | 0.718100i | \(0.745012\pi\) | |||||||
\(468\) | −7.71536 | + | 7.69323i | −0.356643 | + | 0.355620i | ||||
\(469\) | 12.9145 | − | 7.45621i | 0.596338 | − | 0.344296i | ||||
\(470\) | −0.743732 | + | 1.28818i | −0.0343058 | + | 0.0594194i | ||||
\(471\) | −3.04612 | − | 23.2667i | −0.140358 | − | 1.07207i | ||||
\(472\) | −3.22878 | + | 5.59241i | −0.148617 | + | 0.257411i | ||||
\(473\) | −16.6002 | − | 9.58414i | −0.763279 | − | 0.440679i | ||||
\(474\) | 3.87037 | − | 9.32496i | 0.177772 | − | 0.428310i | ||||
\(475\) | 3.80020 | + | 2.13506i | 0.174365 | + | 0.0979631i | ||||
\(476\) | 11.5167i | 0.527868i | ||||||||
\(477\) | −0.376533 | + | 0.100312i | −0.0172403 | + | 0.00459298i | ||||
\(478\) | −18.4717 | − | 10.6646i | −0.844876 | − | 0.487789i | ||||
\(479\) | −5.77360 | + | 3.33339i | −0.263802 | + | 0.152306i | −0.626068 | − | 0.779769i | \(-0.715337\pi\) |
0.362265 | + | 0.932075i | \(0.382003\pi\) | |||||||
\(480\) | −1.05342 | − | 1.37489i | −0.0480818 | − | 0.0627546i | ||||
\(481\) | 0.456278 | + | 0.790297i | 0.0208045 | + | 0.0360345i | ||||
\(482\) | 4.19331i | 0.191000i | ||||||||
\(483\) | −2.26229 | + | 5.45057i | −0.102938 | + | 0.248009i | ||||
\(484\) | 4.55311 | + | 7.88622i | 0.206960 | + | 0.358465i | ||||
\(485\) | 5.20607 | + | 9.01717i | 0.236395 | + | 0.409449i | ||||
\(486\) | 6.01712 | − | 14.3803i | 0.272942 | − | 0.652306i | ||||
\(487\) | − | 21.6443i | − | 0.980797i | −0.871498 | − | 0.490399i | \(-0.836851\pi\) | ||
0.871498 | − | 0.490399i | \(-0.163149\pi\) | |||||||
\(488\) | 1.04215 | + | 1.80505i | 0.0471759 | + | 0.0817110i | ||||
\(489\) | 10.8657 | − | 8.32517i | 0.491365 | − | 0.376477i | ||||
\(490\) | 3.42934 | − | 1.97993i | 0.154922 | − | 0.0894441i | ||||
\(491\) | 2.23804 | + | 1.29214i | 0.101002 | + | 0.0583132i | 0.549650 | − | 0.835395i | \(-0.314761\pi\) |
−0.448648 | + | 0.893708i | \(0.648094\pi\) | |||||||
\(492\) | −6.27870 | + | 4.81066i | −0.283066 | + | 0.216881i | ||||
\(493\) | − | 3.58426i | − | 0.161427i | ||||||
\(494\) | 8.07557 | + | 13.6162i | 0.363337 | + | 0.612622i | ||||
\(495\) | 9.49832 | + | 9.52565i | 0.426918 | + | 0.428146i | ||||
\(496\) | 7.50806 | + | 4.33478i | 0.337122 | + | 0.194638i | ||||
\(497\) | 8.35023 | − | 14.4630i | 0.374559 | − | 0.648755i | ||||
\(498\) | −17.6146 | + | 2.30614i | −0.789329 | + | 0.103340i | ||||
\(499\) | −9.18058 | + | 15.9012i | −0.410979 | + | 0.711837i | −0.994997 | − | 0.0999040i | \(-0.968146\pi\) |
0.584018 | + | 0.811741i | \(0.301480\pi\) | |||||||
\(500\) | 0.866025 | − | 0.500000i | 0.0387298 | − | 0.0223607i | ||||
\(501\) | −13.0737 | − | 5.42630i | −0.584089 | − | 0.242429i | ||||
\(502\) | 24.0870i | 1.07506i | ||||||||
\(503\) | −26.6006 | + | 15.3579i | −1.18606 | + | 0.684774i | −0.957409 | − | 0.288734i | \(-0.906766\pi\) |
−0.228654 | + | 0.973508i | \(0.573432\pi\) | |||||||
\(504\) | −1.36109 | + | 5.05062i | −0.0606276 | + | 0.224972i | ||||
\(505\) | 11.4859 | 0.511118 | ||||||||
\(506\) | −8.76220 | −0.389527 | ||||||||
\(507\) | −0.0427871 | − | 0.326814i | −0.00190024 | − | 0.0145143i | ||||
\(508\) | −10.3685 | − | 5.98626i | −0.460028 | − | 0.265597i | ||||
\(509\) | 1.76397 | + | 3.05529i | 0.0781868 | + | 0.135424i | 0.902468 | − | 0.430758i | \(-0.141754\pi\) |
−0.824281 | + | 0.566181i | \(0.808420\pi\) | |||||||
\(510\) | −9.08130 | + | 6.95797i | −0.402127 | + | 0.308104i | ||||
\(511\) | 6.12913 | − | 10.6160i | 0.271137 | − | 0.469623i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −18.1001 | − | 13.6156i | −0.799141 | − | 0.601144i | ||||
\(514\) | 11.1616 | 0.492319 | ||||||||
\(515\) | −8.83036 | + | 15.2946i | −0.389112 | + | 0.673962i | ||||
\(516\) | 5.87739 | − | 4.50318i | 0.258738 | − | 0.198241i | ||||
\(517\) | 3.33489 | + | 5.77620i | 0.146668 | + | 0.254037i | ||||
\(518\) | 0.379411 | + | 0.219053i | 0.0166704 | + | 0.00962465i | ||||
\(519\) | −3.97001 | − | 30.3235i | −0.174264 | − | 1.33105i | ||||
\(520\) | 3.63184 | 0.159267 | ||||||||
\(521\) | 10.7293 | 0.470059 | 0.235030 | − | 0.971988i | \(-0.424481\pi\) | ||||
0.235030 | + | 0.971988i | \(0.424481\pi\) | |||||||
\(522\) | 0.423600 | − | 1.57186i | 0.0185405 | − | 0.0687986i | ||||
\(523\) | 16.2359 | − | 9.37381i | 0.709947 | − | 0.409888i | −0.101094 | − | 0.994877i | \(-0.532234\pi\) |
0.811042 | + | 0.584989i | \(0.198901\pi\) | |||||||
\(524\) | 9.15309i | 0.399855i | ||||||||
\(525\) | −2.78929 | − | 1.15771i | −0.121735 | − | 0.0505266i | ||||
\(526\) | −12.8454 | + | 7.41629i | −0.560086 | + | 0.323366i | ||||
\(527\) | 28.6318 | − | 49.5918i | 1.24722 | − | 2.16025i | ||||
\(528\) | −7.70079 | + | 1.00820i | −0.335134 | + | 0.0438764i | ||||
\(529\) | −9.59074 | + | 16.6116i | −0.416989 | + | 0.722245i | ||||
\(530\) | 0.112487 | + | 0.0649443i | 0.00488612 | + | 0.00282100i | ||||
\(531\) | 13.6789 | + | 13.7182i | 0.593612 | + | 0.595319i | ||||
\(532\) | 6.62603 | + | 3.72268i | 0.287275 | + | 0.161399i | ||||
\(533\) | − | 16.5856i | − | 0.718402i | ||||||
\(534\) | 5.79152 | − | 4.43738i | 0.250623 | − | 0.192024i | ||||
\(535\) | −17.4574 | − | 10.0790i | −0.754749 | − | 0.435755i | ||||
\(536\) | −7.40682 | + | 4.27633i | −0.319926 | + | 0.184709i | ||||
\(537\) | −27.4597 | + | 21.0392i | −1.18497 | + | 0.907910i | ||||
\(538\) | −3.20285 | − | 5.54749i | −0.138084 | − | 0.239169i | ||||
\(539\) | − | 17.7560i | − | 0.764805i | ||||||
\(540\) | −4.80489 | + | 1.97813i | −0.206770 | + | 0.0851253i | ||||
\(541\) | 18.9536 | + | 32.8286i | 0.814878 | + | 1.41141i | 0.909415 | + | 0.415889i | \(0.136529\pi\) |
−0.0945373 | + | 0.995521i | \(0.530137\pi\) | |||||||
\(542\) | 8.80426 | + | 15.2494i | 0.378175 | + | 0.655019i | ||||
\(543\) | 2.20141 | − | 5.30389i | 0.0944714 | − | 0.227612i | ||||
\(544\) | − | 6.60513i | − | 0.283193i | ||||||
\(545\) | −3.12812 | − | 5.41805i | −0.133994 | − | 0.232084i | ||||
\(546\) | −6.67076 | − | 8.70644i | −0.285482 | − | 0.372601i | ||||
\(547\) | 14.2392 | − | 8.22099i | 0.608823 | − | 0.351504i | −0.163682 | − | 0.986513i | \(-0.552337\pi\) |
0.772505 | + | 0.635009i | \(0.219004\pi\) | |||||||
\(548\) | 13.2938 | + | 7.67520i | 0.567885 | + | 0.327868i | ||||
\(549\) | 6.04215 | − | 1.60969i | 0.257873 | − | 0.0686999i | ||||
\(550\) | − | 4.48400i | − | 0.191198i | ||||||
\(551\) | −2.06217 | − | 1.15858i | −0.0878513 | − | 0.0493572i | ||||
\(552\) | 1.29748 | − | 3.12604i | 0.0552244 | − | 0.133053i | ||||
\(553\) | 8.80193 | + | 5.08180i | 0.374296 | + | 0.216100i | ||||
\(554\) | 13.7621 | − | 23.8367i | 0.584697 | − | 1.01273i | ||||
\(555\) | 0.0564957 | + | 0.431522i | 0.00239811 | + | 0.0183171i | ||||
\(556\) | −7.91901 | + | 13.7161i | −0.335841 | + | 0.581693i | ||||
\(557\) | −10.7408 | + | 6.20119i | −0.455101 | + | 0.262753i | −0.709982 | − | 0.704220i | \(-0.751297\pi\) |
0.254881 | + | 0.966972i | \(0.417964\pi\) | |||||||
\(558\) | 18.4173 | − | 18.3645i | 0.779667 | − | 0.777431i | ||||
\(559\) | 15.5255i | 0.656658i | ||||||||
\(560\) | 1.51000 | − | 0.871800i | 0.0638092 | − | 0.0368403i | ||||
\(561\) | 6.65931 | + | 50.8648i | 0.281156 | + | 2.14751i | ||||
\(562\) | −4.50894 | −0.190198 | ||||||||
\(563\) | 10.1274 | 0.426819 | 0.213410 | − | 0.976963i | \(-0.431543\pi\) | ||||
0.213410 | + | 0.976963i | \(0.431543\pi\) | |||||||
\(564\) | −2.55456 | + | 0.334448i | −0.107566 | + | 0.0140828i | ||||
\(565\) | 5.50370 | + | 3.17756i | 0.231542 | + | 0.133681i | ||||
\(566\) | −14.2001 | − | 24.5953i | −0.596875 | − | 1.03382i | ||||
\(567\) | 13.5674 | + | 7.88521i | 0.569778 | + | 0.331148i | ||||
\(568\) | −4.78907 | + | 8.29492i | −0.200945 | + | 0.348047i | ||||
\(569\) | −19.0157 | −0.797180 | −0.398590 | − | 0.917129i | \(-0.630500\pi\) | ||||
−0.398590 | + | 0.917129i | \(0.630500\pi\) | |||||||
\(570\) | 1.06775 | + | 7.47395i | 0.0447230 | + | 0.313049i | ||||
\(571\) | 0.0688168 | 0.00287989 | 0.00143995 | − | 0.999999i | \(-0.499542\pi\) | ||||
0.00143995 | + | 0.999999i | \(0.499542\pi\) | |||||||
\(572\) | 8.14259 | − | 14.1034i | 0.340459 | − | 0.589692i | ||||
\(573\) | 9.68763 | + | 12.6440i | 0.404706 | + | 0.528209i | ||||
\(574\) | −3.98126 | − | 6.89574i | −0.166175 | − | 0.287823i | ||||
\(575\) | 1.69230 | + | 0.977053i | 0.0705740 | + | 0.0407459i | ||||
\(576\) | 0.780619 | − | 2.89666i | 0.0325258 | − | 0.120694i | ||||
\(577\) | 20.4867 | 0.852872 | 0.426436 | − | 0.904518i | \(-0.359769\pi\) | ||||
0.426436 | + | 0.904518i | \(0.359769\pi\) | |||||||
\(578\) | −26.6278 | −1.10757 | ||||||||
\(579\) | 22.5976 | − | 2.95853i | 0.939126 | − | 0.122952i | ||||
\(580\) | −0.469946 | + | 0.271323i | −0.0195134 | + | 0.0112661i | ||||
\(581\) | − | 17.8834i | − | 0.741927i | ||||||
\(582\) | −6.91341 | + | 16.6566i | −0.286570 | + | 0.690438i | ||||
\(583\) | 0.504391 | − | 0.291210i | 0.0208897 | − | 0.0120607i | ||||
\(584\) | −3.51522 | + | 6.08853i | −0.145461 | + | 0.251945i | ||||
\(585\) | 2.83509 | − | 10.5202i | 0.117216 | − | 0.434957i | ||||
\(586\) | −7.49776 | + | 12.9865i | −0.309730 | + | 0.536467i | ||||
\(587\) | −18.2857 | − | 10.5573i | −0.754733 | − | 0.435745i | 0.0726687 | − | 0.997356i | \(-0.476848\pi\) |
−0.827401 | + | 0.561611i | \(0.810182\pi\) | |||||||
\(588\) | 6.33470 | + | 2.62925i | 0.261239 | + | 0.108428i | ||||
\(589\) | −19.2772 | − | 32.5032i | −0.794302 | − | 1.33927i | ||||
\(590\) | − | 6.45756i | − | 0.265853i | ||||||
\(591\) | 28.9365 | + | 37.7670i | 1.19029 | + | 1.55352i | ||||
\(592\) | −0.217602 | − | 0.125633i | −0.00894340 | − | 0.00516347i | ||||
\(593\) | 5.51015 | − | 3.18129i | 0.226275 | − | 0.130640i | −0.382578 | − | 0.923923i | \(-0.624964\pi\) |
0.608852 | + | 0.793284i | \(0.291630\pi\) | |||||||
\(594\) | −3.09096 | + | 23.0936i | −0.126824 | + | 0.947542i | ||||
\(595\) | −5.75836 | − | 9.97377i | −0.236070 | − | 0.408885i | ||||
\(596\) | 19.7801i | 0.810226i | ||||||||
\(597\) | −14.4357 | − | 5.99161i | −0.590814 | − | 0.245220i | ||||
\(598\) | 3.54850 | + | 6.14619i | 0.145109 | + | 0.251336i | ||||
\(599\) | −21.4869 | − | 37.2163i | −0.877929 | − | 1.52062i | −0.853610 | − | 0.520913i | \(-0.825591\pi\) |
−0.0243194 | − | 0.999704i | \(-0.507742\pi\) | |||||||
\(600\) | 1.59973 | + | 0.663976i | 0.0653087 | + | 0.0271067i | ||||
\(601\) | 15.3531i | 0.626264i | 0.949710 | + | 0.313132i | \(0.101378\pi\) | ||||
−0.949710 | + | 0.313132i | \(0.898622\pi\) | |||||||
\(602\) | 3.72679 | + | 6.45499i | 0.151893 | + | 0.263086i | ||||
\(603\) | 6.60517 | + | 24.7932i | 0.268983 | + | 1.00966i | ||||
\(604\) | −18.6361 | + | 10.7595i | −0.758291 | + | 0.437800i | ||||
\(605\) | −7.88622 | − | 4.55311i | −0.320621 | − | 0.185110i | ||||
\(606\) | 12.0995 | + | 15.7919i | 0.491509 | + | 0.641501i | ||||
\(607\) | − | 8.61899i | − | 0.349834i | −0.984583 | − | 0.174917i | \(-0.944034\pi\) | ||
0.984583 | − | 0.174917i | \(-0.0559657\pi\) | |||||||
\(608\) | −3.80020 | − | 2.13506i | −0.154119 | − | 0.0865879i | ||||
\(609\) | 1.51360 | + | 0.628227i | 0.0613341 | + | 0.0254571i | ||||
\(610\) | −1.80505 | − | 1.04215i | −0.0730845 | − | 0.0421954i | ||||
\(611\) | 2.70112 | − | 4.67848i | 0.109276 | − | 0.189271i | ||||
\(612\) | −19.1328 | − | 5.15609i | −0.773399 | − | 0.208423i | ||||
\(613\) | −15.0671 | + | 26.0970i | −0.608555 | + | 1.05405i | 0.382924 | + | 0.923780i | \(0.374917\pi\) |
−0.991479 | + | 0.130268i | \(0.958416\pi\) | |||||||
\(614\) | −17.6339 | + | 10.1810i | −0.711648 | + | 0.410870i | ||||
\(615\) | 3.03219 | − | 7.30551i | 0.122270 | − | 0.294586i | ||||
\(616\) | − | 7.81830i | − | 0.315008i | ||||||
\(617\) | 23.8215 | − | 13.7533i | 0.959017 | − | 0.553688i | 0.0631463 | − | 0.998004i | \(-0.479887\pi\) |
0.895870 | + | 0.444316i | \(0.146553\pi\) | |||||||
\(618\) | −30.3304 | + | 3.97092i | −1.22007 | + | 0.159734i | ||||
\(619\) | 16.8953 | 0.679078 | 0.339539 | − | 0.940592i | \(-0.389729\pi\) | ||||
0.339539 | + | 0.940592i | \(0.389729\pi\) | |||||||
\(620\) | −8.66957 | −0.348178 | ||||||||
\(621\) | −8.04224 | − | 6.19860i | −0.322724 | − | 0.248741i | ||||
\(622\) | −10.5410 | − | 6.08585i | −0.422656 | − | 0.244020i | ||||
\(623\) | 3.67234 | + | 6.36068i | 0.147129 | + | 0.254835i | ||||
\(624\) | 3.82585 | + | 4.99337i | 0.153157 | + | 0.199895i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 13.1442 | 0.525347 | ||||||||
\(627\) | 31.4171 | + | 12.6102i | 1.25468 | + | 0.503605i | ||||
\(628\) | −13.5477 | −0.540611 | ||||||||
\(629\) | −0.829821 | + | 1.43729i | −0.0330871 | + | 0.0573086i | ||||
\(630\) | −1.34657 | − | 5.05451i | −0.0536487 | − | 0.201376i | ||||
\(631\) | 19.8257 | + | 34.3391i | 0.789247 | + | 1.36702i | 0.926429 | + | 0.376470i | \(0.122862\pi\) |
−0.137182 | + | 0.990546i | \(0.543804\pi\) | |||||||
\(632\) | −5.04814 | − | 2.91454i | −0.200804 | − | 0.115934i | ||||
\(633\) | −35.9843 | + | 4.71113i | −1.43025 | + | 0.187251i | ||||
\(634\) | −6.86939 | −0.272818 | ||||||||
\(635\) | 11.9725 | 0.475115 | ||||||||
\(636\) | 0.0292048 | + | 0.223070i | 0.00115804 | + | 0.00884531i | ||||
\(637\) | −12.4548 | + | 7.19079i | −0.493478 | + | 0.284910i | ||||
\(638\) | 2.43323i | 0.0963324i | ||||||||
\(639\) | 20.2891 | + | 20.3475i | 0.802625 | + | 0.804934i | ||||
\(640\) | −0.866025 | + | 0.500000i | −0.0342327 | + | 0.0197642i | ||||
\(641\) | 14.2303 | − | 24.6475i | 0.562062 | − | 0.973520i | −0.435255 | − | 0.900307i | \(-0.643342\pi\) |
0.997316 | − | 0.0732121i | \(-0.0233250\pi\) | |||||||
\(642\) | −4.53244 | − | 34.6194i | −0.178881 | − | 1.36632i | ||||
\(643\) | −1.54529 | + | 2.67653i | −0.0609405 | + | 0.105552i | −0.894886 | − | 0.446295i | \(-0.852743\pi\) |
0.833946 | + | 0.551847i | \(0.186077\pi\) | |||||||
\(644\) | 2.95070 | + | 1.70359i | 0.116274 | + | 0.0671308i | ||||
\(645\) | −2.83838 | + | 6.83856i | −0.111761 | + | 0.269268i | ||||
\(646\) | −14.1023 | + | 25.1008i | −0.554849 | + | 0.987580i | ||||
\(647\) | 7.89351i | 0.310326i | 0.987889 | + | 0.155163i | \(0.0495903\pi\) | ||||
−0.987889 | + | 0.155163i | \(0.950410\pi\) | |||||||
\(648\) | −7.78127 | − | 4.52237i | −0.305677 | − | 0.177656i | ||||
\(649\) | −25.0763 | − | 14.4778i | −0.984332 | − | 0.568305i | ||||
\(650\) | −3.14527 | + | 1.81592i | −0.123368 | + | 0.0712263i | ||||
\(651\) | 15.9237 | + | 20.7831i | 0.624101 | + | 0.814555i | ||||
\(652\) | −3.95150 | − | 6.84420i | −0.154753 | − | 0.268040i | ||||
\(653\) | 18.1037i | 0.708453i | 0.935160 | + | 0.354227i | \(0.115256\pi\) | ||||
−0.935160 | + | 0.354227i | \(0.884744\pi\) | |||||||
\(654\) | 4.15399 | − | 10.0083i | 0.162434 | − | 0.391355i | ||||
\(655\) | −4.57655 | − | 7.92681i | −0.178820 | − | 0.309726i | ||||
\(656\) | 2.28336 | + | 3.95489i | 0.0891501 | + | 0.154412i | ||||
\(657\) | 14.8924 | + | 14.9352i | 0.581006 | + | 0.582678i | ||||
\(658\) | − | 2.59354i | − | 0.101107i | ||||||
\(659\) | 8.56885 | + | 14.8417i | 0.333795 | + | 0.578150i | 0.983253 | − | 0.182248i | \(-0.0583373\pi\) |
−0.649457 | + | 0.760398i | \(0.725004\pi\) | |||||||
\(660\) | 6.16498 | − | 4.72353i | 0.239972 | − | 0.183863i | ||||
\(661\) | −31.8623 | + | 18.3957i | −1.23930 | + | 0.715510i | −0.968951 | − | 0.247253i | \(-0.920472\pi\) |
−0.270348 | + | 0.962763i | \(0.587139\pi\) | |||||||
\(662\) | −6.74506 | − | 3.89426i | −0.262154 | − | 0.151355i | ||||
\(663\) | 32.9819 | − | 25.2703i | 1.28091 | − | 0.981416i | ||||
\(664\) | 10.2566i | 0.398032i | ||||||||
\(665\) | −7.59966 | + | 0.0890778i | −0.294702 | + | 0.00345429i | ||||
\(666\) | −0.533779 | + | 0.532248i | −0.0206835 | + | 0.0206242i | ||||
\(667\) | −0.918324 | − | 0.530195i | −0.0355576 | − | 0.0205292i | ||||
\(668\) | −4.08621 | + | 7.07753i | −0.158100 | + | 0.273838i | ||||
\(669\) | −22.2816 | + | 2.91715i | −0.861457 | + | 0.112784i | ||||
\(670\) | 4.27633 | − | 7.40682i | 0.165209 | − | 0.286151i | ||||
\(671\) | −8.09386 | + | 4.67299i | −0.312460 | + | 0.180399i | ||||
\(672\) | 2.78929 | + | 1.15771i | 0.107599 | + | 0.0446596i | ||||
\(673\) | − | 19.1641i | − | 0.738723i | −0.929286 | − | 0.369361i | \(-0.879576\pi\) | ||
0.929286 | − | 0.369361i | \(-0.120424\pi\) | |||||||
\(674\) | −23.2844 | + | 13.4433i | −0.896881 | + | 0.517815i | ||||
\(675\) | 3.17209 | − | 4.11556i | 0.122094 | − | 0.158408i | ||||
\(676\) | −0.190296 | −0.00731908 | ||||||||
\(677\) | 45.3076 | 1.74131 | 0.870656 | − | 0.491892i | \(-0.163694\pi\) | ||||
0.870656 | + | 0.491892i | \(0.163694\pi\) | |||||||
\(678\) | 1.42892 | + | 10.9143i | 0.0548772 | + | 0.419159i | ||||
\(679\) | −15.7223 | − | 9.07730i | −0.603368 | − | 0.348355i | ||||
\(680\) | 3.30257 | + | 5.72021i | 0.126648 | + | 0.219360i | ||||
\(681\) | 29.1829 | − | 22.3596i | 1.11829 | − | 0.856821i | ||||
\(682\) | −19.4372 | + | 33.6661i | −0.744287 | + | 1.28914i | ||||
\(683\) | 38.3931 | 1.46907 | 0.734535 | − | 0.678571i | \(-0.237400\pi\) | ||||
0.734535 | + | 0.678571i | \(0.237400\pi\) | |||||||
\(684\) | −9.15104 | + | 9.34123i | −0.349899 | + | 0.357171i | ||||
\(685\) | −15.3504 | −0.586509 | ||||||||
\(686\) | −9.55481 | + | 16.5494i | −0.364804 | + | 0.631859i | ||||
\(687\) | 13.3249 | − | 10.2093i | 0.508376 | − | 0.389511i | ||||
\(688\) | −2.13741 | − | 3.70210i | −0.0814880 | − | 0.141141i | ||||
\(689\) | −0.408535 | − | 0.235868i | −0.0155639 | − | 0.00898585i | ||||
\(690\) | 0.439370 | + | 3.35597i | 0.0167265 | + | 0.127760i | ||||
\(691\) | 25.7083 | 0.977988 | 0.488994 | − | 0.872287i | \(-0.337364\pi\) | ||||
0.488994 | + | 0.872287i | \(0.337364\pi\) | |||||||
\(692\) | −17.6567 | −0.671206 | ||||||||
\(693\) | −22.6469 | − | 6.10311i | −0.860286 | − | 0.231838i | ||||
\(694\) | 24.5180 | − | 14.1555i | 0.930691 | − | 0.537335i | ||||
\(695\) | − | 15.8380i | − | 0.600770i | ||||||
\(696\) | −0.868088 | − | 0.360305i | −0.0329048 | − | 0.0136573i | ||||
\(697\) | 26.1226 | − | 15.0819i | 0.989463 | − | 0.571267i | ||||
\(698\) | −2.35419 | + | 4.07758i | −0.0891075 | + | 0.154339i | ||||
\(699\) | −27.7696 | + | 3.63566i | −1.05034 | + | 0.137513i | ||||
\(700\) | −0.871800 | + | 1.51000i | −0.0329510 | + | 0.0570727i | ||||
\(701\) | −35.5687 | − | 20.5356i | −1.34341 | − | 0.775619i | −0.356106 | − | 0.934446i | \(-0.615896\pi\) |
−0.987307 | + | 0.158826i | \(0.949229\pi\) | |||||||
\(702\) | 17.4506 | − | 7.18428i | 0.658631 | − | 0.271153i | ||||
\(703\) | 0.558700 | + | 0.942022i | 0.0210718 | + | 0.0355290i | ||||
\(704\) | 4.48400i | 0.168997i | ||||||||
\(705\) | 2.04509 | − | 1.56692i | 0.0770226 | − | 0.0590137i | ||||
\(706\) | 14.5885 | + | 8.42267i | 0.549045 | + | 0.316991i | ||||
\(707\) | −17.3438 | + | 10.0135i | −0.652281 | + | 0.376595i | ||||
\(708\) | 8.87840 | − | 6.80251i | 0.333671 | − | 0.255654i | ||||
\(709\) | −4.57770 | − | 7.92881i | −0.171919 | − | 0.297773i | 0.767172 | − | 0.641442i | \(-0.221663\pi\) |
−0.939091 | + | 0.343669i | \(0.888330\pi\) | |||||||
\(710\) | − | 9.57815i | − | 0.359461i | ||||||
\(711\) | −12.3831 | + | 12.3476i | −0.464403 | + | 0.463071i | ||||
\(712\) | −2.10618 | − | 3.64801i | −0.0789325 | − | 0.136715i | ||||
\(713\) | −8.47062 | − | 14.6715i | −0.317227 | − | 0.549454i | ||||
\(714\) | 7.64682 | − | 18.4236i | 0.286175 | − | 0.689487i | ||||
\(715\) | 16.2852i | 0.609031i | ||||||||
\(716\) | 9.98617 | + | 17.2966i | 0.373201 | + | 0.646403i | ||||
\(717\) | 22.4687 | + | 29.3253i | 0.839107 | + | 1.09517i | ||||
\(718\) | 27.5785 | − | 15.9225i | 1.02922 | − | 0.594221i | ||||
\(719\) | −40.8433 | − | 23.5809i | −1.52320 | − | 0.879420i | −0.999623 | − | 0.0274407i | \(-0.991264\pi\) |
−0.523576 | − | 0.851979i | \(-0.675402\pi\) | |||||||
\(720\) | 0.772294 | + | 2.89889i | 0.0287817 | + | 0.108035i | ||||
\(721\) | − | 30.7932i | − | 1.14680i | ||||||
\(722\) | 9.88307 | + | 16.2273i | 0.367810 | + | 0.603917i | ||||
\(723\) | 2.78426 | − | 6.70817i | 0.103548 | − | 0.249479i | ||||
\(724\) | −2.87130 | − | 1.65774i | −0.106711 | − | 0.0616096i | ||||
\(725\) | 0.271323 | − | 0.469946i | 0.0100767 | − | 0.0174534i | ||||
\(726\) | −2.04749 | − | 15.6390i | −0.0759893 | − | 0.580417i | ||||
\(727\) | 0.839710 | − | 1.45442i | 0.0311431 | − | 0.0539414i | −0.850034 | − | 0.526728i | \(-0.823419\pi\) |
0.881177 | + | 0.472787i | \(0.156752\pi\) | |||||||
\(728\) | −5.48409 | + | 3.16624i | −0.203254 | + | 0.117349i | ||||
\(729\) | −19.1740 | + | 19.0094i | −0.710147 | + | 0.704053i | ||||
\(730\) | − | 7.03043i | − | 0.260208i | ||||||
\(731\) | −24.4529 | + | 14.1179i | −0.904423 | + | 0.522169i | ||||
\(732\) | −0.468643 | − | 3.57956i | −0.0173216 | − | 0.132304i | ||||
\(733\) | −50.5483 | −1.86704 | −0.933522 | − | 0.358519i | \(-0.883282\pi\) | ||||
−0.933522 | + | 0.358519i | \(0.883282\pi\) | |||||||
\(734\) | 30.2893 | 1.11800 | ||||||||
\(735\) | −6.80064 | + | 0.890353i | −0.250845 | + | 0.0328412i | ||||
\(736\) | −1.69230 | − | 0.977053i | −0.0623792 | − | 0.0360146i | ||||
\(737\) | −19.1751 | − | 33.2122i | −0.706322 | − | 1.22339i | ||||
\(738\) | 13.2384 | − | 3.52684i | 0.487312 | − | 0.129825i | ||||
\(739\) | 23.1698 | − | 40.1313i | 0.852316 | − | 1.47626i | −0.0267963 | − | 0.999641i | \(-0.508531\pi\) |
0.879113 | − | 0.476614i | \(-0.158136\pi\) | |||||||
\(740\) | 0.251265 | 0.00923670 | ||||||||
\(741\) | −3.87789 | − | 27.1442i | −0.142458 | − | 0.997168i | ||||
\(742\) | −0.226474 | −0.00831412 | ||||||||
\(743\) | −8.82641 | + | 15.2878i | −0.323810 | + | 0.560855i | −0.981271 | − | 0.192634i | \(-0.938297\pi\) |
0.657461 | + | 0.753488i | \(0.271630\pi\) | |||||||
\(744\) | −9.13268 | − | 11.9197i | −0.334820 | − | 0.436996i | ||||
\(745\) | −9.89007 | − | 17.1301i | −0.362344 | − | 0.627598i | ||||
\(746\) | 32.2650 | + | 18.6282i | 1.18131 | + | 0.682027i | ||||
\(747\) | 29.7098 | + | 8.00647i | 1.08703 | + | 0.292942i | ||||
\(748\) | 29.6174 | 1.08292 | ||||||||
\(749\) | 35.1476 | 1.28427 | ||||||||
\(750\) | −1.71739 | + | 0.224845i | −0.0627104 | + | 0.00821017i | ||||
\(751\) | 21.4154 | − | 12.3642i | 0.781459 | − | 0.451176i | −0.0554880 | − | 0.998459i | \(-0.517671\pi\) |
0.836947 | + | 0.547284i | \(0.184338\pi\) | |||||||
\(752\) | 1.48746i | 0.0542422i | ||||||||
\(753\) | 15.9932 | − | 38.5327i | 0.582825 | − | 1.40421i | ||||
\(754\) | 1.70677 | − | 0.985405i | 0.0621569 | − | 0.0358863i | ||||
\(755\) | 10.7595 | − | 18.6361i | 0.391580 | − | 0.678236i | ||||
\(756\) | 5.53086 | − | 7.17589i | 0.201155 | − | 0.260985i | ||||
\(757\) | −11.0903 | + | 19.2089i | −0.403084 | + | 0.698161i | −0.994096 | − | 0.108501i | \(-0.965395\pi\) |
0.591013 | + | 0.806662i | \(0.298728\pi\) | |||||||
\(758\) | −29.1293 | − | 16.8178i | −1.05802 | − | 0.610851i | ||||
\(759\) | 14.0172 | + | 5.81789i | 0.508790 | + | 0.211176i | ||||
\(760\) | 4.35860 | − | 0.0510884i | 0.158103 | − | 0.00185317i | ||||
\(761\) | 1.21908i | 0.0441915i | 0.999756 | + | 0.0220957i | \(0.00703386\pi\) | ||||
−0.999756 | + | 0.0220957i | \(0.992966\pi\) | |||||||
\(762\) | 12.6121 | + | 16.4608i | 0.456887 | + | 0.596313i | ||||
\(763\) | 9.44692 | + | 5.45418i | 0.342002 | + | 0.197455i | ||||
\(764\) | 7.96429 | − | 4.59818i | 0.288138 | − | 0.166356i | ||||
\(765\) | 19.1476 | − | 5.10111i | 0.692281 | − | 0.184431i | ||||
\(766\) | −4.65017 | − | 8.05432i | −0.168017 | − | 0.291015i | ||||
\(767\) | 23.4528i | 0.846833i | ||||||||
\(768\) | −1.59973 | − | 0.663976i | −0.0577253 | − | 0.0239592i | ||||
\(769\) | −3.96820 | − | 6.87313i | −0.143097 | − | 0.247851i | 0.785564 | − | 0.618780i | \(-0.212373\pi\) |
−0.928661 | + | 0.370929i | \(0.879039\pi\) | |||||||
\(770\) | 3.90915 | + | 6.77084i | 0.140876 | + | 0.244004i | ||||
\(771\) | −17.8556 | − | 7.41106i | −0.643054 | − | 0.266903i | ||||
\(772\) | − | 13.1581i | − | 0.473570i | ||||||
\(773\) | 24.0038 | + | 41.5758i | 0.863357 | + | 1.49538i | 0.868669 | + | 0.495393i | \(0.164976\pi\) |
−0.00531153 | + | 0.999986i | \(0.501691\pi\) | |||||||
\(774\) | −12.3922 | + | 3.30142i | −0.445430 | + | 0.118667i | ||||
\(775\) | 7.50806 | − | 4.33478i | 0.269698 | − | 0.155710i | ||||
\(776\) | 9.01717 | + | 5.20607i | 0.323698 | + | 0.186887i | ||||
\(777\) | −0.461509 | − | 0.602346i | −0.0165566 | − | 0.0216090i | ||||
\(778\) | 8.18343i | 0.293390i | ||||||||
\(779\) | −0.233306 | − | 19.9045i | −0.00835906 | − | 0.713152i | ||||
\(780\) | −5.80997 | − | 2.41146i | −0.208030 | − | 0.0863441i | ||||
\(781\) | −37.1944 | − | 21.4742i | −1.33092 | − | 0.768407i | ||||
\(782\) | −6.45356 | + | 11.1779i | −0.230779 | + | 0.399721i | ||||
\(783\) | −1.72133 | + | 2.23330i | −0.0615152 | + | 0.0798115i | ||||
\(784\) | 1.97993 | − | 3.42934i | 0.0707117 | − | 0.122476i | ||||
\(785\) | 11.7326 | − | 6.77384i | 0.418755 | − | 0.241769i | ||||
\(786\) | 6.07744 | − | 14.6425i | 0.216775 | − | 0.522280i | ||||
\(787\) | 17.2022i | 0.613193i | 0.951840 | + | 0.306597i | \(0.0991902\pi\) | ||||
−0.951840 | + | 0.306597i | \(0.900810\pi\) | |||||||
\(788\) | 23.7890 | − | 13.7346i | 0.847448 | − | 0.489274i | ||||
\(789\) | 25.4734 | − | 3.33503i | 0.906877 | − | 0.118730i | ||||
\(790\) | 5.82909 | 0.207390 | ||||||||
\(791\) | −11.0808 | −0.393988 | ||||||||
\(792\) | 12.9886 | + | 3.50029i | 0.461530 | + | 0.124377i | ||||
\(793\) | 6.55568 | + | 3.78492i | 0.232799 | + | 0.134407i | ||||
\(794\) | 2.72560 | + | 4.72088i | 0.0967281 | + | 0.167538i | ||||
\(795\) | −0.136827 | − | 0.178582i | −0.00485276 | − | 0.00633365i | ||||
\(796\) | −4.51192 | + | 7.81487i | −0.159921 | + | 0.276991i | ||||
\(797\) | −13.6397 | −0.483142 | −0.241571 | − | 0.970383i | \(-0.577663\pi\) | ||||
−0.241571 | + | 0.970383i | \(0.577663\pi\) | |||||||
\(798\) | −8.12809 | − | 10.3548i | −0.287731 | − | 0.366557i | ||||
\(799\) | 9.82490 | 0.347580 | ||||||||
\(800\) | 0.500000 | − | 0.866025i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | −12.2112 | + | 3.25318i | −0.431461 | + | 0.114946i | ||||
\(802\) | −14.4054 | − | 24.9508i | −0.508671 | − | 0.881044i | ||||
\(803\) | −27.3010 | − | 15.7622i | −0.963430 | − | 0.556237i | ||||
\(804\) | 14.6883 | − | 1.92302i | 0.518016 | − | 0.0678197i | ||||
\(805\) | −3.40718 | −0.120087 | ||||||||
\(806\) | 31.4865 | 1.10907 | ||||||||
\(807\) | 1.44029 | + | 11.0011i | 0.0507005 | + | 0.387257i | ||||
\(808\) | 9.94712 | − | 5.74297i | 0.349939 | − | 0.202037i | ||||
\(809\) | 48.0047i | 1.68776i | 0.536535 | + | 0.843878i | \(0.319733\pi\) | ||||
−0.536535 | + | 0.843878i | \(0.680267\pi\) | |||||||
\(810\) | 8.99996 | + | 0.0258539i | 0.316226 | + | 0.000908415i | ||||
\(811\) | −16.9494 | + | 9.78575i | −0.595175 | + | 0.343624i | −0.767141 | − | 0.641479i | \(-0.778321\pi\) |
0.171966 | + | 0.985103i | \(0.444988\pi\) | |||||||
\(812\) | 0.473080 | − | 0.819398i | 0.0166018 | − | 0.0287552i | ||||
\(813\) | −3.95918 | − | 30.2408i | −0.138855 | − | 1.06059i | ||||
\(814\) | 0.563337 | − | 0.975727i | 0.0197449 | − | 0.0341992i | ||||
\(815\) | 6.84420 | + | 3.95150i | 0.239742 | + | 0.138415i | ||||
\(816\) | −4.38565 | + | 10.5664i | −0.153529 | + | 0.369899i | ||||
\(817\) | 0.218394 | + | 18.6322i | 0.00764064 | + | 0.651859i | ||||
\(818\) | 29.2481i | 1.02264i | ||||||||
\(819\) | 4.89054 | + | 18.3572i | 0.170889 | + | 0.641452i | ||||
\(820\) | −3.95489 | − | 2.28336i | −0.138111 | − | 0.0797382i | ||||
\(821\) | −19.8535 | + | 11.4624i | −0.692892 | + | 0.400041i | −0.804694 | − | 0.593689i | \(-0.797671\pi\) |
0.111803 | + | 0.993730i | \(0.464338\pi\) | |||||||
\(822\) | −16.1704 | − | 21.1050i | −0.564008 | − | 0.736123i | ||||
\(823\) | −16.1127 | − | 27.9080i | −0.561653 | − | 0.972811i | −0.997352 | − | 0.0727192i | \(-0.976832\pi\) |
0.435700 | − | 0.900092i | \(-0.356501\pi\) | |||||||
\(824\) | 17.6607i | 0.615240i | ||||||||
\(825\) | −2.97727 | + | 7.17318i | −0.103655 | + | 0.249738i | ||||
\(826\) | 5.62970 | + | 9.75092i | 0.195882 | + | 0.339278i | ||||
\(827\) | 20.0676 | + | 34.7581i | 0.697819 | + | 1.20866i | 0.969221 | + | 0.246192i | \(0.0791795\pi\) |
−0.271402 | + | 0.962466i | \(0.587487\pi\) | |||||||
\(828\) | −4.15123 | + | 4.13932i | −0.144265 | + | 0.143851i | ||||
\(829\) | 43.1212i | 1.49766i | 0.662762 | + | 0.748830i | \(0.269384\pi\) | ||||
−0.662762 | + | 0.748830i | \(0.730616\pi\) | |||||||
\(830\) | −5.12829 | − | 8.88246i | −0.178005 | − | 0.308315i | ||||
\(831\) | −37.8427 | + | 28.9946i | −1.31275 | + | 1.00581i | ||||
\(832\) | 3.14527 | − | 1.81592i | 0.109043 | − | 0.0629558i | ||||
\(833\) | −22.6512 | − | 13.0777i | −0.784819 | − | 0.453115i | ||||
\(834\) | 21.7755 | − | 16.6841i | 0.754022 | − | 0.577722i | ||||
\(835\) | − | 8.17243i | − | 0.282819i | ||||||
\(836\) | 9.57358 | − | 17.0401i | 0.331109 | − | 0.589344i | ||||
\(837\) | −41.6563 | + | 17.1496i | −1.43985 | + | 0.592776i | ||||
\(838\) | −0.962877 | − | 0.555917i | −0.0332620 | − | 0.0192038i | ||||
\(839\) | 16.9630 | − | 29.3808i | 0.585628 | − | 1.01434i | −0.409169 | − | 0.912459i | \(-0.634181\pi\) |
0.994797 | − | 0.101879i | \(-0.0324854\pi\) | |||||||
\(840\) | −2.99445 | + | 0.392039i | −0.103318 | + | 0.0135266i | ||||
\(841\) | 14.3528 | − | 24.8597i | 0.494923 | − | 0.857232i | ||||
\(842\) | −17.1508 | + | 9.90200i | −0.591054 | + | 0.341245i | ||||
\(843\) | 7.21309 | + | 2.99383i | 0.248432 | + | 0.103113i | ||||
\(844\) | 20.9528i | 0.721226i | ||||||||
\(845\) | 0.164801 | − | 0.0951480i | 0.00566934 | − | 0.00327319i | ||||
\(846\) | 4.30868 | + | 1.16114i | 0.148135 | + | 0.0399209i | ||||
\(847\) | 15.8776 | 0.545561 | ||||||||
\(848\) | 0.129889 | 0.00446040 | ||||||||
\(849\) | 6.38564 | + | 48.7744i | 0.219155 | + | 1.67393i | ||||
\(850\) | −5.72021 | − | 3.30257i | −0.196202 | − | 0.113277i | ||||
\(851\) | 0.245499 | + | 0.425218i | 0.00841561 | + | 0.0145763i | ||||
\(852\) | 13.1689 | − | 10.0898i | 0.451157 | − | 0.345671i | ||||
\(853\) | 3.13675 | − | 5.43302i | 0.107400 | − | 0.186023i | −0.807316 | − | 0.590119i | \(-0.799081\pi\) |
0.914716 | + | 0.404096i | \(0.132414\pi\) | |||||||
\(854\) | 3.63418 | 0.124359 | ||||||||
\(855\) | 3.25442 | − | 12.6653i | 0.111299 | − | 0.433143i | ||||
\(856\) | −20.1581 | −0.688989 | ||||||||
\(857\) | 5.57983 | − | 9.66455i | 0.190603 | − | 0.330135i | −0.754847 | − | 0.655901i | \(-0.772289\pi\) |
0.945450 | + | 0.325766i | \(0.105622\pi\) | |||||||
\(858\) | −22.3903 | + | 17.1551i | −0.764391 | + | 0.585666i | ||||
\(859\) | 26.7797 | + | 46.3839i | 0.913713 | + | 1.58260i | 0.808775 | + | 0.588118i | \(0.200131\pi\) |
0.104937 | + | 0.994479i | \(0.466536\pi\) | |||||||
\(860\) | 3.70210 | + | 2.13741i | 0.126241 | + | 0.0728851i | ||||
\(861\) | 1.79033 | + | 13.6748i | 0.0610143 | + | 0.466036i | ||||
\(862\) | 6.32292 | 0.215359 | ||||||||
\(863\) | −12.4085 | −0.422390 | −0.211195 | − | 0.977444i | \(-0.567736\pi\) | ||||
−0.211195 | + | 0.977444i | \(0.567736\pi\) | |||||||
\(864\) | −3.17209 | + | 4.11556i | −0.107917 | + | 0.140014i | ||||
\(865\) | 15.2911 | − | 8.82834i | 0.519914 | − | 0.300173i | ||||
\(866\) | − | 28.0429i | − | 0.952935i | ||||||
\(867\) | 42.5973 | + | 17.6802i | 1.44668 | + | 0.600452i | ||||
\(868\) | 13.0911 | − | 7.55813i | 0.444340 | − | 0.256540i | ||||
\(869\) | 13.0688 | − | 22.6358i | 0.443329 | − | 0.767868i | ||||
\(870\) | 0.931939 | − | 0.122011i | 0.0315957 | − | 0.00413657i | ||||
\(871\) | −15.5310 | + | 26.9004i | −0.526247 | + | 0.911486i | ||||
\(872\) | −5.41805 | − | 3.12812i | −0.183478 | − | 0.105931i | ||||
\(873\) | 22.1192 | − | 22.0557i | 0.748621 | − | 0.746473i | ||||
\(874\) | 4.34504 | + | 7.32616i | 0.146973 | + | 0.247811i | ||||
\(875\) | − | 1.74360i | − | 0.0589445i | ||||||
\(876\) | 9.66604 | − | 7.40599i | 0.326585 | − | 0.250225i | ||||
\(877\) | −21.0398 | − | 12.1473i | −0.710463 | − | 0.410186i | 0.100770 | − | 0.994910i | \(-0.467869\pi\) |
−0.811232 | + | 0.584724i | \(0.801203\pi\) | |||||||
\(878\) | 8.39710 | − | 4.84807i | 0.283388 | − | 0.163614i | ||||
\(879\) | 20.6171 | − | 15.7966i | 0.695398 | − | 0.532805i | ||||
\(880\) | −2.24200 | − | 3.88325i | −0.0755777 | − | 0.130904i | ||||
\(881\) | − | 45.6855i | − | 1.53918i | −0.638536 | − | 0.769592i | \(-0.720460\pi\) | ||
0.638536 | − | 0.769592i | \(-0.279540\pi\) | |||||||
\(882\) | −8.38805 | − | 8.41218i | −0.282440 | − | 0.283253i | ||||
\(883\) | 15.2288 | + | 26.3771i | 0.512491 | + | 0.887660i | 0.999895 | + | 0.0144835i | \(0.00461041\pi\) |
−0.487404 | + | 0.873176i | \(0.662056\pi\) | |||||||
\(884\) | −11.9944 | − | 20.7749i | −0.403416 | − | 0.698736i | ||||
\(885\) | −4.28766 | + | 10.3303i | −0.144128 | + | 0.347251i | ||||
\(886\) | − | 10.2242i | − | 0.343487i | ||||||
\(887\) | −7.35088 | − | 12.7321i | −0.246818 | − | 0.427502i | 0.715823 | − | 0.698282i | \(-0.246052\pi\) |
−0.962641 | + | 0.270780i | \(0.912718\pi\) | |||||||
\(888\) | 0.264688 | + | 0.345461i | 0.00888233 | + | 0.0115929i | ||||
\(889\) | −18.0785 | + | 10.4376i | −0.606335 | + | 0.350067i | ||||
\(890\) | 3.64801 | + | 2.10618i | 0.122282 | + | 0.0705994i | ||||
\(891\) | 20.2783 | − | 34.8912i | 0.679349 | − | 1.16890i | ||||
\(892\) | 12.9741i | 0.434404i | ||||||||
\(893\) | 3.17582 | − | 5.65266i | 0.106275 | − | 0.189159i | ||||
\(894\) | 13.1335 | − | 31.6429i | 0.439251 | − | 1.05830i | ||||
\(895\) | −17.2966 | − | 9.98617i | −0.578160 | − | 0.333801i | ||||
\(896\) | 0.871800 | − | 1.51000i | 0.0291248 | − | 0.0504456i | ||||
\(897\) | −1.59572 | − | 12.1884i | −0.0532797 | − | 0.406958i | ||||
\(898\) | −3.33355 | + | 5.77387i | −0.111242 | + | 0.192677i | ||||
\(899\) | −4.07423 | + | 2.35226i | −0.135883 | + | 0.0784521i | ||||
\(900\) | −2.11827 | − | 2.12437i | −0.0706090 | − | 0.0708122i | ||||
\(901\) | − | 0.857932i | − | 0.0285819i | ||||||
\(902\) | −17.7337 | + | 10.2386i | −0.590468 | + | 0.340907i | ||||
\(903\) | −1.67590 | − | 12.8007i | −0.0557704 | − | 0.425982i | ||||
\(904\) | 6.35512 | 0.211368 | ||||||||
\(905\) | 3.31549 | 0.110211 | ||||||||
\(906\) | 36.9568 | − | 4.83845i | 1.22781 | − | 0.160747i | ||||
\(907\) | 5.41439 | + | 3.12600i | 0.179782 | + | 0.103797i | 0.587190 | − | 0.809449i | \(-0.300234\pi\) |
−0.407408 | + | 0.913246i | \(0.633567\pi\) | |||||||
\(908\) | −10.6129 | − | 18.3820i | −0.352200 | − | 0.610029i | ||||
\(909\) | −8.87053 | − | 33.2965i | −0.294217 | − | 1.10438i | ||||
\(910\) | 3.16624 | − | 5.48409i | 0.104960 | − | 0.181796i | ||||
\(911\) | 49.4685 | 1.63896 | 0.819481 | − | 0.573106i | \(-0.194262\pi\) | ||||
0.819481 | + | 0.573106i | \(0.194262\pi\) | |||||||
\(912\) | 4.66167 | + | 5.93876i | 0.154363 | + | 0.196652i | ||||
\(913\) | −45.9905 | −1.52206 | ||||||||
\(914\) | 6.43251 | − | 11.1414i | 0.212768 | − | 0.368526i | ||||
\(915\) | 2.19564 | + | 2.86567i | 0.0725855 | + | 0.0947361i | ||||
\(916\) | −4.84581 | − | 8.39319i | −0.160110 | − | 0.277319i | ||||
\(917\) | 13.8212 | + | 7.97967i | 0.456416 | + | 0.263512i | ||||
\(918\) | 27.1838 | + | 20.9521i | 0.897200 | + | 0.691522i | ||||
\(919\) | 27.8719 | 0.919409 | 0.459705 | − | 0.888072i | \(-0.347955\pi\) | ||||
0.459705 | + | 0.888072i | \(0.347955\pi\) | |||||||
\(920\) | 1.95411 | 0.0644249 | ||||||||
\(921\) | 34.9695 | − | 4.57827i | 1.15228 | − | 0.150859i | ||||
\(922\) | −4.75855 | + | 2.74735i | −0.156715 | + | 0.0904792i | ||||
\(923\) | 34.7863i | 1.14501i | ||||||||
\(924\) | −5.19116 | + | 12.5072i | −0.170777 | + | 0.411456i | ||||
\(925\) | −0.217602 | + | 0.125633i | −0.00715472 | + | 0.00413078i | ||||
\(926\) | −4.56084 | + | 7.89961i | −0.149879 | + | 0.259597i | ||||
\(927\) | 51.1571 | + | 13.7863i | 1.68022 | + | 0.452801i | ||||
\(928\) | −0.271323 | + | 0.469946i | −0.00890663 | + | 0.0154267i | ||||
\(929\) | 38.9043 | + | 22.4614i | 1.27641 | + | 0.736934i | 0.976186 | − | 0.216935i | \(-0.0696060\pi\) |
0.300222 | + | 0.953869i | \(0.402939\pi\) | |||||||
\(930\) | 13.8690 | + | 5.75639i | 0.454781 | + | 0.188759i | ||||
\(931\) | −14.8460 | + | 8.80492i | −0.486557 | + | 0.288569i | ||||
\(932\) | 16.1696i | 0.529654i | ||||||||
\(933\) | 12.8219 | + | 16.7347i | 0.419770 | + | 0.547869i | ||||
\(934\) | −26.8784 | − | 15.5183i | −0.879489 | − | 0.507773i | ||||
\(935\) | −25.6494 | + | 14.8087i | −0.838826 | + | 0.484296i | ||||
\(936\) | −2.80485 | − | 10.5283i | −0.0916795 | − | 0.344129i | ||||
\(937\) | 5.70404 | + | 9.87968i | 0.186343 | + | 0.322755i | 0.944028 | − | 0.329865i | \(-0.107003\pi\) |
−0.757685 | + | 0.652620i | \(0.773670\pi\) | |||||||
\(938\) | 14.9124i | 0.486908i | ||||||||
\(939\) | −21.0271 | − | 8.72742i | −0.686195 | − | 0.284809i | ||||
\(940\) | −0.743732 | − | 1.28818i | −0.0242579 | − | 0.0420158i | ||||
\(941\) | 9.04539 | + | 15.6671i | 0.294871 | + | 0.510732i | 0.974955 | − | 0.222403i | \(-0.0713899\pi\) |
−0.680084 | + | 0.733134i | \(0.738057\pi\) | |||||||
\(942\) | 21.6726 | + | 8.99533i | 0.706132 | + | 0.293084i | ||||
\(943\) | − | 8.92384i | − | 0.290600i | ||||||
\(944\) | −3.22878 | − | 5.59241i | −0.105088 | − | 0.182017i | ||||
\(945\) | −1.20192 | + | 8.97994i | −0.0390984 | + | 0.292117i | ||||
\(946\) | 16.6002 | − | 9.58414i | 0.539720 | − | 0.311607i | ||||
\(947\) | 18.9963 | + | 10.9675i | 0.617296 | + | 0.356396i | 0.775815 | − | 0.630960i | \(-0.217339\pi\) |
−0.158520 | + | 0.987356i | \(0.550672\pi\) | |||||||
\(948\) | 6.14047 | + | 8.01432i | 0.199433 | + | 0.260293i | ||||
\(949\) | 25.5334i | 0.828850i | ||||||||
\(950\) | −3.74911 | + | 2.22354i | −0.121637 | + | 0.0721413i | ||||
\(951\) | 10.9892 | + | 4.56111i | 0.356348 | + | 0.147904i | ||||
\(952\) | −9.97377 | − | 5.75836i | −0.323252 | − | 0.186629i | ||||
\(953\) | 17.8637 | − | 30.9409i | 0.578663 | − | 1.00227i | −0.416969 | − | 0.908920i | \(-0.636908\pi\) |
0.995633 | − | 0.0933541i | \(-0.0297589\pi\) | |||||||
\(954\) | 0.101393 | − | 0.376243i | 0.00328274 | − | 0.0121813i | ||||
\(955\) | −4.59818 | + | 7.96429i | −0.148794 | + | 0.257718i | ||||
\(956\) | 18.4717 | − | 10.6646i | 0.597417 | − | 0.344919i | ||||
\(957\) | 1.61560 | − | 3.89251i | 0.0522251 | − | 0.125827i | ||||
\(958\) | − | 6.66678i | − | 0.215394i | ||||||
\(959\) | 23.1792 | − | 13.3825i | 0.748494 | − | 0.432143i | ||||
\(960\) | 1.71739 | − | 0.224845i | 0.0554287 | − | 0.00725683i | ||||
\(961\) | −44.1614 | −1.42456 | ||||||||
\(962\) | −0.912557 | −0.0294220 | ||||||||
\(963\) | −15.7358 | + | 58.3911i | −0.507078 | + | 1.88163i | ||||
\(964\) | −3.63151 | − | 2.09666i | −0.116963 | − | 0.0675287i | ||||
\(965\) | 6.57904 | + | 11.3952i | 0.211787 | + | 0.366826i | ||||
\(966\) | −3.58919 | − | 4.68448i | −0.115480 | − | 0.150721i | ||||
\(967\) | −3.90937 | + | 6.77123i | −0.125717 | + | 0.217748i | −0.922013 | − | 0.387159i | \(-0.873456\pi\) |
0.796296 | + | 0.604907i | \(0.206790\pi\) | |||||||
\(968\) | −9.10622 | −0.292685 | ||||||||
\(969\) | 39.2263 | − | 30.7910i | 1.26013 | − | 0.989148i | ||||
\(970\) | −10.4121 | −0.334314 | ||||||||
\(971\) | 3.20611 | − | 5.55314i | 0.102889 | − | 0.178209i | −0.809985 | − | 0.586451i | \(-0.800525\pi\) |
0.912874 | + | 0.408242i | \(0.133858\pi\) | |||||||
\(972\) | 9.44518 | + | 12.4012i | 0.302954 | + | 0.397767i | ||||
\(973\) | 13.8076 | + | 23.9154i | 0.442651 | + | 0.766694i | ||||
\(974\) | 18.7445 | + | 10.8222i | 0.600613 | + | 0.346764i | ||||
\(975\) | 6.23731 | − | 0.816601i | 0.199754 | − | 0.0261522i | ||||
\(976\) | −2.08430 | −0.0667167 | ||||||||
\(977\) | −10.1495 | −0.324713 | −0.162356 | − | 0.986732i | \(-0.551909\pi\) | ||||
−0.162356 | + | 0.986732i | \(0.551909\pi\) | |||||||
\(978\) | 1.77695 | + | 13.5726i | 0.0568206 | + | 0.434003i | ||||
\(979\) | 16.3577 | − | 9.44411i | 0.522794 | − | 0.301835i | ||||
\(980\) | 3.95986i | 0.126493i | ||||||||
\(981\) | −13.2905 | + | 13.2524i | −0.424334 | + | 0.423116i | ||||
\(982\) | −2.23804 | + | 1.29214i | −0.0714188 | + | 0.0412337i | ||||
\(983\) | −9.71885 | + | 16.8335i | −0.309983 | + | 0.536907i | −0.978358 | − | 0.206918i | \(-0.933657\pi\) |
0.668375 | + | 0.743824i | \(0.266990\pi\) | |||||||
\(984\) | −1.02680 | − | 7.84285i | −0.0327332 | − | 0.250021i | ||||
\(985\) | −13.7346 | + | 23.7890i | −0.437620 | + | 0.757981i | ||||
\(986\) | 3.10406 | + | 1.79213i | 0.0988533 | + | 0.0570730i | ||||
\(987\) | −1.72205 | + | 4.14897i | −0.0548135 | + | 0.132063i | ||||
\(988\) | −15.8298 | + | 0.185545i | −0.503612 | + | 0.00590298i | ||||
\(989\) | 8.35345i | 0.265624i | ||||||||
\(990\) | −12.9986 | + | 3.46296i | −0.413123 | + | 0.110060i | ||||
\(991\) | −10.1730 | − | 5.87340i | −0.323157 | − | 0.186575i | 0.329642 | − | 0.944106i | \(-0.393072\pi\) |
−0.652799 | + | 0.757531i | \(0.726405\pi\) | |||||||
\(992\) | −7.50806 | + | 4.33478i | −0.238381 | + | 0.137630i | ||||
\(993\) | 8.20458 | + | 10.7083i | 0.260364 | + | 0.339819i | ||||
\(994\) | 8.35023 | + | 14.4630i | 0.264853 | + | 0.458739i | ||||
\(995\) | − | 9.02384i | − | 0.286075i | ||||||
\(996\) | 6.81012 | − | 16.4078i | 0.215787 | − | 0.519900i | ||||
\(997\) | −26.3056 | − | 45.5626i | −0.833105 | − | 1.44298i | −0.895564 | − | 0.444933i | \(-0.853228\pi\) |
0.0624587 | − | 0.998048i | \(-0.480106\pi\) | |||||||
\(998\) | −9.18058 | − | 15.9012i | −0.290606 | − | 0.503345i | ||||
\(999\) | 1.20730 | − | 0.497037i | 0.0381974 | − | 0.0157255i |
(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 | 570.2.s.a.521.9 | yes | 24 | |
3.2 | odd | 2 | 570.2.s.b.521.5 | yes | 24 | ||
19.12 | odd | 6 | 570.2.s.b.221.5 | yes | 24 | ||
57.50 | even | 6 | inner | 570.2.s.a.221.9 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.s.a.221.9 | ✓ | 24 | 57.50 | even | 6 | inner | |
570.2.s.a.521.9 | yes | 24 | 1.1 | even | 1 | trivial | |
570.2.s.b.221.5 | yes | 24 | 19.12 | odd | 6 | ||
570.2.s.b.521.5 | yes | 24 | 3.2 | odd | 2 |