Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(37,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(24))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.bk (of order \(24\), degree \(8\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(368\) |
Relative dimension: | \(46\) over \(\Q(\zeta_{24})\) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{24}]$ |
Embedding invariants
Embedding label | 397.22 | ||
Character | \(\chi\) | \(=\) | 864.397 |
Dual form | 864.2.bk.a.37.22 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0671528 | − | 1.41262i | −0.0474842 | − | 0.998872i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.99098 | + | 0.189722i | −0.995491 | + | 0.0948612i | ||||
\(5\) | −3.52114 | − | 2.70187i | −1.57470 | − | 1.20831i | −0.862092 | − | 0.506751i | \(-0.830846\pi\) |
−0.712610 | − | 0.701560i | \(-0.752487\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.323768 | − | 1.20832i | −0.122373 | − | 0.456701i | 0.877360 | − | 0.479833i | \(-0.159303\pi\) |
−0.999732 | + | 0.0231321i | \(0.992636\pi\) | |||||||
\(8\) | 0.401705 | + | 2.79976i | 0.142024 | + | 0.989863i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.58025 | + | 5.15547i | −1.13218 | + | 1.63030i | ||||
\(11\) | −4.12219 | − | 0.542697i | −1.24289 | − | 0.163629i | −0.519741 | − | 0.854324i | \(-0.673972\pi\) |
−0.723147 | + | 0.690695i | \(0.757305\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0124827 | + | 0.0948153i | 0.00346207 | + | 0.0262970i | 0.993089 | − | 0.117366i | \(-0.0374451\pi\) |
−0.989627 | + | 0.143663i | \(0.954112\pi\) | |||||||
\(14\) | −1.68515 | + | 0.538502i | −0.450375 | + | 0.143921i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.92801 | − | 0.755467i | 0.982003 | − | 0.188867i | ||||
\(17\) | − | 2.57648i | − | 0.624888i | −0.949936 | − | 0.312444i | \(-0.898852\pi\) | ||
0.949936 | − | 0.312444i | \(-0.101148\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.07003 | + | 1.27165i | 0.704312 | + | 0.291736i | 0.705949 | − | 0.708263i | \(-0.250521\pi\) |
−0.00163643 | + | 0.999999i | \(0.500521\pi\) | |||||||
\(20\) | 7.52313 | + | 4.71133i | 1.68222 | + | 1.05348i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.489807 | + | 5.85953i | −0.104427 | + | 1.24926i | ||||
\(23\) | 0.135966 | − | 0.507432i | 0.0283509 | − | 0.105807i | −0.950301 | − | 0.311334i | \(-0.899224\pi\) |
0.978651 | + | 0.205527i | \(0.0658909\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.80426 | + | 14.1977i | 0.760851 | + | 2.83954i | ||||
\(26\) | 0.133100 | − | 0.0240004i | 0.0261030 | − | 0.00470686i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.873860 | + | 2.34431i | 0.165144 | + | 0.443033i | ||||
\(29\) | 3.35182 | + | 4.36818i | 0.622418 | + | 0.811151i | 0.993058 | − | 0.117626i | \(-0.0375283\pi\) |
−0.370640 | + | 0.928777i | \(0.620862\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.95771 | − | 3.39085i | −0.351615 | − | 0.609014i | 0.634918 | − | 0.772580i | \(-0.281034\pi\) |
−0.986533 | + | 0.163565i | \(0.947701\pi\) | |||||||
\(32\) | −1.33096 | − | 5.49805i | −0.235283 | − | 0.971927i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.63958 | + | 0.173018i | −0.624183 | + | 0.0296723i | ||||
\(35\) | −2.12468 | + | 5.12943i | −0.359137 | + | 0.867033i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.306228 | + | 0.126844i | −0.0503435 | + | 0.0208530i | −0.407713 | − | 0.913110i | \(-0.633674\pi\) |
0.357370 | + | 0.933963i | \(0.383674\pi\) | |||||||
\(38\) | 1.59019 | − | 4.42217i | 0.257963 | − | 0.717371i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.15011 | − | 10.9437i | 0.972417 | − | 1.73035i | ||||
\(41\) | −2.08827 | + | 7.79353i | −0.326133 | + | 1.21715i | 0.587035 | + | 0.809562i | \(0.300295\pi\) |
−0.913168 | + | 0.407584i | \(0.866371\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.26024 | − | 1.21913i | −1.41217 | − | 0.185916i | −0.614458 | − | 0.788950i | \(-0.710625\pi\) |
−0.797716 | + | 0.603033i | \(0.793959\pi\) | |||||||
\(44\) | 8.31017 | + | 0.298427i | 1.25280 | + | 0.0449895i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.725938 | − | 0.157993i | −0.107034 | − | 0.0232947i | ||||
\(47\) | 5.21248 | + | 3.00942i | 0.760318 | + | 0.438970i | 0.829410 | − | 0.558641i | \(-0.188677\pi\) |
−0.0690921 | + | 0.997610i | \(0.522010\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.70697 | − | 2.71757i | 0.672425 | − | 0.388224i | ||||
\(50\) | 19.8004 | − | 6.32738i | 2.80020 | − | 0.894826i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.0428413 | − | 0.186407i | −0.00594103 | − | 0.0258500i | ||||
\(53\) | −0.848306 | − | 2.04799i | −0.116524 | − | 0.281313i | 0.854848 | − | 0.518879i | \(-0.173650\pi\) |
−0.971371 | + | 0.237566i | \(0.923650\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.0485 | + | 13.0485i | 1.75946 | + | 1.75946i | ||||
\(56\) | 3.25294 | − | 1.39186i | 0.434692 | − | 0.185995i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.94549 | − | 5.02818i | 0.780681 | − | 0.660233i | ||||
\(59\) | 7.35945 | + | 5.64710i | 0.958119 | + | 0.735190i | 0.964306 | − | 0.264791i | \(-0.0853028\pi\) |
−0.00618735 | + | 0.999981i | \(0.501970\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.27002 | − | 10.7777i | −1.05887 | − | 1.37994i | −0.921032 | − | 0.389487i | \(-0.872652\pi\) |
−0.137835 | − | 0.990455i | \(-0.544014\pi\) | |||||||
\(62\) | −4.65851 | + | 2.99320i | −0.591631 | + | 0.380137i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.67727 | + | 2.24935i | −0.959658 | + | 0.281169i | ||||
\(65\) | 0.212225 | − | 0.367585i | 0.0263233 | − | 0.0455933i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.2722 | + | 1.61567i | −1.49929 | + | 0.197385i | −0.835066 | − | 0.550149i | \(-0.814571\pi\) |
−0.664223 | + | 0.747535i | \(0.731237\pi\) | |||||||
\(68\) | 0.488816 | + | 5.12972i | 0.0592776 | + | 0.622070i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.38861 | + | 2.65691i | 0.883108 | + | 0.317561i | ||||
\(71\) | −1.60783 | + | 1.60783i | −0.190815 | + | 0.190815i | −0.796048 | − | 0.605233i | \(-0.793080\pi\) |
0.605233 | + | 0.796048i | \(0.293080\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.47247 | + | 7.47247i | 0.874587 | + | 0.874587i | 0.992968 | − | 0.118381i | \(-0.0377706\pi\) |
−0.118381 | + | 0.992968i | \(0.537771\pi\) | |||||||
\(74\) | 0.199746 | + | 0.424065i | 0.0232200 | + | 0.0492965i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.35362 | − | 1.94937i | −0.728811 | − | 0.223608i | ||||
\(77\) | 0.678883 | + | 5.15662i | 0.0773658 | + | 0.587652i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.18365 | + | 0.683378i | 0.133171 | + | 0.0768861i | 0.565105 | − | 0.825019i | \(-0.308836\pi\) |
−0.431935 | + | 0.901905i | \(0.642169\pi\) | |||||||
\(80\) | −15.8723 | − | 7.95285i | −1.77457 | − | 0.889156i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11.1495 | + | 2.42657i | 1.23126 | + | 0.267970i | ||||
\(83\) | −9.75274 | + | 7.48354i | −1.07050 | + | 0.821425i | −0.984590 | − | 0.174878i | \(-0.944047\pi\) |
−0.0859118 | + | 0.996303i | \(0.527380\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.96130 | + | 9.07215i | −0.755059 | + | 0.984013i | ||||
\(86\) | −1.10032 | + | 13.1631i | −0.118651 | + | 1.41941i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.136487 | − | 11.7591i | −0.0145496 | − | 1.25353i | ||||
\(89\) | 1.96743 | − | 1.96743i | 0.208547 | − | 0.208547i | −0.595103 | − | 0.803650i | \(-0.702889\pi\) |
0.803650 | + | 0.595103i | \(0.202889\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.110526 | − | 0.0457812i | 0.0115862 | − | 0.00479917i | ||||
\(92\) | −0.174435 | + | 1.03608i | −0.0181861 | + | 0.108019i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.90114 | − | 7.56533i | 0.402371 | − | 0.780304i | ||||
\(95\) | −7.37418 | − | 12.7724i | −0.756575 | − | 1.31043i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.86403 | + | 10.1568i | −0.595402 | + | 1.03127i | 0.398088 | + | 0.917347i | \(0.369674\pi\) |
−0.993490 | + | 0.113919i | \(0.963660\pi\) | |||||||
\(98\) | −4.15498 | − | 6.46666i | −0.419716 | − | 0.653232i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −10.2678 | − | 27.5456i | −1.02678 | − | 2.75456i | ||||
\(101\) | 1.23206 | − | 9.35843i | 0.122595 | − | 0.931199i | −0.814020 | − | 0.580837i | \(-0.802725\pi\) |
0.936614 | − | 0.350362i | \(-0.113941\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.39206 | − | 1.44480i | −0.531296 | − | 0.142360i | −0.0168091 | − | 0.999859i | \(-0.505351\pi\) |
−0.514486 | + | 0.857499i | \(0.672017\pi\) | |||||||
\(104\) | −0.260445 | + | 0.0730362i | −0.0255388 | + | 0.00716179i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.83606 | + | 1.33586i | −0.275463 | + | 0.129750i | ||||
\(107\) | 2.57893 | + | 6.22609i | 0.249315 | + | 0.601899i | 0.998146 | − | 0.0608614i | \(-0.0193848\pi\) |
−0.748831 | + | 0.662760i | \(0.769385\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.85281 | − | 0.767459i | −0.177467 | − | 0.0735093i | 0.292181 | − | 0.956363i | \(-0.405619\pi\) |
−0.469648 | + | 0.882854i | \(0.655619\pi\) | |||||||
\(110\) | 17.5563 | − | 19.3088i | 1.67393 | − | 1.84102i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.18461 | − | 4.50169i | −0.206426 | − | 0.425370i | ||||
\(113\) | 0.627382 | − | 0.362219i | 0.0590191 | − | 0.0340747i | −0.470200 | − | 0.882560i | \(-0.655818\pi\) |
0.529219 | + | 0.848485i | \(0.322485\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.84977 | + | 1.41938i | −0.172492 | + | 0.132358i | ||||
\(116\) | −7.50216 | − | 8.06105i | −0.696558 | − | 0.748450i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.48299 | − | 10.7753i | 0.688865 | − | 0.991948i | ||||
\(119\) | −3.11321 | + | 0.834181i | −0.285387 | + | 0.0764692i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.07276 | + | 1.62719i | 0.552069 | + | 0.147926i | ||||
\(122\) | −14.6694 | + | 12.4061i | −1.32811 | + | 1.12320i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.54108 | + | 6.37969i | 0.407801 | + | 0.572913i | ||||
\(125\) | 16.4726 | − | 39.7684i | 1.47335 | − | 3.55699i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.41741 | −0.125775 | −0.0628875 | − | 0.998021i | \(-0.520031\pi\) | ||||
−0.0628875 | + | 0.998021i | \(0.520031\pi\) | |||||||
\(128\) | 3.69303 | + | 10.6940i | 0.326421 | + | 0.945225i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.533508 | − | 0.275109i | −0.0467918 | − | 0.0241286i | ||||
\(131\) | −18.4301 | + | 2.42637i | −1.61025 | + | 0.211993i | −0.881293 | − | 0.472570i | \(-0.843326\pi\) |
−0.728954 | + | 0.684563i | \(0.759993\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.542577 | − | 4.12128i | 0.0470474 | − | 0.357361i | ||||
\(134\) | 3.10643 | + | 17.2275i | 0.268355 | + | 1.48823i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.21351 | − | 1.03499i | 0.618554 | − | 0.0887492i | ||||
\(137\) | −3.55457 | + | 0.952444i | −0.303687 | + | 0.0813728i | −0.407445 | − | 0.913230i | \(-0.633580\pi\) |
0.103757 | + | 0.994603i | \(0.466913\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.34586 | + | 3.05719i | −0.198974 | + | 0.259307i | −0.882174 | − | 0.470923i | \(-0.843921\pi\) |
0.683201 | + | 0.730231i | \(0.260587\pi\) | |||||||
\(140\) | 3.25703 | − | 10.6157i | 0.275269 | − | 0.897191i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.37923 | + | 2.16329i | 0.199660 | + | 0.181539i | ||||
\(143\) | − | 0.397621i | − | 0.0332507i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 24.4372i | − | 2.02940i | ||||||
\(146\) | 10.0540 | − | 11.0575i | 0.832071 | − | 0.915129i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.585628 | − | 0.310641i | 0.0481383 | − | 0.0255346i | ||||
\(149\) | 1.07625 | − | 1.40260i | 0.0881698 | − | 0.114905i | −0.747185 | − | 0.664616i | \(-0.768595\pi\) |
0.835355 | + | 0.549711i | \(0.185262\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.89127 | + | 2.38241i | −0.723561 | + | 0.193878i | −0.601760 | − | 0.798677i | \(-0.705534\pi\) |
−0.121801 | + | 0.992555i | \(0.538867\pi\) | |||||||
\(152\) | −2.32705 | + | 9.10615i | −0.188749 | + | 0.738606i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.23875 | − | 1.30528i | 0.583315 | − | 0.105183i | ||||
\(155\) | −2.26826 | + | 17.2291i | −0.182191 | + | 1.38388i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.33732 | − | 0.702672i | 0.425965 | − | 0.0560793i | 0.0855034 | − | 0.996338i | \(-0.472750\pi\) |
0.340461 | + | 0.940259i | \(0.389417\pi\) | |||||||
\(158\) | 0.885868 | − | 1.71793i | 0.0704758 | − | 0.136671i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10.1685 | + | 22.9555i | −0.803889 | + | 1.81479i | ||||
\(161\) | −0.657161 | −0.0517915 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.49655 | + | 10.8556i | −0.352197 | + | 0.850279i | 0.644151 | + | 0.764898i | \(0.277211\pi\) |
−0.996348 | + | 0.0853808i | \(0.972789\pi\) | |||||||
\(164\) | 2.67910 | − | 15.9130i | 0.209203 | − | 1.24259i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.2263 | + | 13.2744i | 0.871330 | + | 1.03029i | ||||
\(167\) | 6.04195 | + | 1.61893i | 0.467540 | + | 0.125277i | 0.484895 | − | 0.874572i | \(-0.338858\pi\) |
−0.0173550 | + | 0.999849i | \(0.505525\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5482 | − | 3.36228i | 0.965246 | − | 0.258637i | ||||
\(170\) | 13.2830 | + | 9.22444i | 1.01876 | + | 0.707483i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 18.6683 | + | 0.670397i | 1.42344 | + | 0.0511173i | ||||
\(173\) | −4.59054 | + | 3.52245i | −0.349012 | + | 0.267807i | −0.768358 | − | 0.640020i | \(-0.778926\pi\) |
0.419346 | + | 0.907827i | \(0.362259\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.9236 | − | 9.19350i | 1.20371 | − | 0.694963i | ||||
\(176\) | −16.6020 | + | 0.982463i | −1.25142 | + | 0.0740559i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.91135 | − | 2.64711i | −0.218215 | − | 0.198409i | ||||
\(179\) | −11.1115 | − | 4.60252i | −0.830510 | − | 0.344009i | −0.0734055 | − | 0.997302i | \(-0.523387\pi\) |
−0.757105 | + | 0.653294i | \(0.773387\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.51362 | − | 15.7253i | −0.484153 | − | 1.16885i | −0.957619 | − | 0.288037i | \(-0.906997\pi\) |
0.473466 | − | 0.880812i | \(-0.343003\pi\) | |||||||
\(182\) | −0.0720934 | − | 0.153056i | −0.00534392 | − | 0.0113453i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.47530 | + | 0.176834i | 0.108761 | + | 0.0130363i | ||||
\(185\) | 1.42098 | + | 0.380752i | 0.104473 | + | 0.0279934i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.39825 | + | 10.6207i | −0.102250 | + | 0.776665i | ||||
\(188\) | −10.9489 | − | 5.00278i | −0.798530 | − | 0.364865i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −17.5474 | + | 11.2746i | −1.27302 | + | 0.817946i | ||||
\(191\) | −0.532783 | + | 0.922808i | −0.0385509 | + | 0.0667720i | −0.884657 | − | 0.466242i | \(-0.845607\pi\) |
0.846106 | + | 0.533014i | \(0.178941\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.00284 | − | 12.1293i | −0.504076 | − | 0.873084i | −0.999989 | − | 0.00471241i | \(-0.998500\pi\) |
0.495913 | − | 0.868372i | \(-0.334833\pi\) | |||||||
\(194\) | 14.7415 | + | 7.60157i | 1.05837 | + | 0.545761i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.85591 | + | 6.30365i | −0.632565 | + | 0.450261i | ||||
\(197\) | −6.33207 | + | 2.62283i | −0.451141 | + | 0.186869i | −0.596673 | − | 0.802485i | \(-0.703511\pi\) |
0.145531 | + | 0.989354i | \(0.453511\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.36707 | + | 6.36707i | −0.451350 | + | 0.451350i | −0.895802 | − | 0.444453i | \(-0.853398\pi\) |
0.444453 | + | 0.895802i | \(0.353398\pi\) | |||||||
\(200\) | −38.2219 | + | 16.3543i | −2.70269 | + | 1.15642i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.3026 | − | 1.11199i | −0.935970 | − | 0.0782392i | ||||
\(203\) | 4.19294 | − | 5.46434i | 0.294287 | − | 0.383522i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 28.4102 | − | 21.7999i | 1.98425 | − | 1.52257i | ||||
\(206\) | −1.67886 | + | 7.71395i | −0.116971 | + | 0.537456i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.120662 | + | 0.363005i | 0.00836640 | + | 0.0251699i | ||||
\(209\) | −11.9651 | − | 6.90806i | −0.827644 | − | 0.477841i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.477969 | + | 3.63053i | 0.0329047 | + | 0.249936i | 0.999990 | − | 0.00451706i | \(-0.00143783\pi\) |
−0.967085 | + | 0.254453i | \(0.918104\pi\) | |||||||
\(212\) | 2.07751 | + | 3.91657i | 0.142684 | + | 0.268991i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.62191 | − | 4.06115i | 0.589382 | − | 0.277614i | ||||
\(215\) | 29.3127 | + | 29.3127i | 1.99911 | + | 1.99911i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.46338 | + | 3.46338i | −0.235110 | + | 0.235110i | ||||
\(218\) | −0.959706 | + | 2.66885i | −0.0649995 | + | 0.180757i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −28.4550 | − | 23.5038i | −1.91843 | − | 1.58462i | ||||
\(221\) | 0.244290 | − | 0.0321613i | 0.0164327 | − | 0.00216341i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.22965 | + | 12.5221i | −0.484133 | + | 0.838543i | −0.999834 | − | 0.0182256i | \(-0.994198\pi\) |
0.515701 | + | 0.856769i | \(0.327532\pi\) | |||||||
\(224\) | −6.21247 | + | 3.38832i | −0.415088 | + | 0.226392i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.553808 | − | 0.861927i | −0.0368387 | − | 0.0573345i | ||||
\(227\) | −0.903483 | − | 1.17744i | −0.0599663 | − | 0.0781496i | 0.762407 | − | 0.647097i | \(-0.224017\pi\) |
−0.822374 | + | 0.568948i | \(0.807351\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.8674 | + | 9.87348i | 0.850300 | + | 0.652458i | 0.939120 | − | 0.343589i | \(-0.111643\pi\) |
−0.0888198 | + | 0.996048i | \(0.528310\pi\) | |||||||
\(230\) | 2.12926 | + | 2.51770i | 0.140399 | + | 0.166012i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.8834 | + | 11.1390i | −0.714530 | + | 0.731312i | ||||
\(233\) | −13.0471 | − | 13.0471i | −0.854741 | − | 0.854741i | 0.135972 | − | 0.990713i | \(-0.456584\pi\) |
−0.990713 | + | 0.135972i | \(0.956584\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.2228 | − | 24.6800i | −0.666862 | − | 1.60995i | ||||
\(236\) | −15.7239 | − | 9.84702i | −1.02354 | − | 0.640987i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.38744 | + | 4.34175i | 0.0899343 | + | 0.281434i | ||||
\(239\) | −17.5726 | + | 10.1456i | −1.13668 | + | 0.656262i | −0.945606 | − | 0.325314i | \(-0.894530\pi\) |
−0.191073 | + | 0.981576i | \(0.561197\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.95525 | + | 4.01561i | 0.448027 | + | 0.258668i | 0.706997 | − | 0.707217i | \(-0.250050\pi\) |
−0.258970 | + | 0.965885i | \(0.583383\pi\) | |||||||
\(242\) | 1.89080 | − | 8.68776i | 0.121545 | − | 0.558470i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 18.5102 | + | 19.8892i | 1.18500 | + | 1.27327i | ||||
\(245\) | −23.9164 | − | 3.14866i | −1.52796 | − | 0.201160i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0822494 | + | 0.306959i | −0.00523340 | + | 0.0195313i | ||||
\(248\) | 8.70713 | − | 6.84322i | 0.552903 | − | 0.434545i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −57.2837 | − | 20.5989i | −3.62294 | − | 1.30279i | ||||
\(251\) | 6.63225 | − | 2.74717i | 0.418624 | − | 0.173400i | −0.163421 | − | 0.986556i | \(-0.552253\pi\) |
0.582045 | + | 0.813157i | \(0.302253\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.835860 | + | 2.01794i | −0.0525500 | + | 0.126867i | ||||
\(254\) | 0.0951831 | + | 2.00226i | 0.00597232 | + | 0.125633i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.8585 | − | 5.93497i | 0.928659 | − | 0.370936i | ||||
\(257\) | −12.6692 | − | 21.9436i | −0.790280 | − | 1.36881i | −0.925793 | − | 0.378030i | \(-0.876602\pi\) |
0.135513 | − | 0.990776i | \(-0.456732\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.252414 | + | 0.328952i | 0.0156842 | + | 0.0204401i | ||||
\(260\) | −0.352797 | + | 0.772118i | −0.0218795 | + | 0.0478847i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.66517 | + | 25.8718i | 0.288215 | + | 1.59836i | ||||
\(263\) | −4.97778 | − | 18.5773i | −0.306943 | − | 1.14553i | −0.931260 | − | 0.364356i | \(-0.881289\pi\) |
0.624317 | − | 0.781171i | \(-0.285378\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.54640 | + | 9.50328i | −0.156424 | + | 0.583782i | ||||
\(266\) | −5.85824 | − | 0.489699i | −0.359192 | − | 0.0300254i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 24.1272 | − | 5.54508i | 1.47380 | − | 0.338719i | ||||
\(269\) | 19.0648 | + | 7.89688i | 1.16240 | + | 0.481482i | 0.878673 | − | 0.477424i | \(-0.158429\pi\) |
0.283726 | + | 0.958905i | \(0.408429\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.3373i | 0.992423i | 0.868202 | + | 0.496211i | \(0.165276\pi\) | ||||
−0.868202 | + | 0.496211i | \(0.834724\pi\) | |||||||
\(272\) | −1.94645 | − | 10.1204i | −0.118021 | − | 0.613642i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.58414 | + | 4.95729i | 0.0957014 | + | 0.299481i | ||||
\(275\) | −7.97684 | − | 60.5901i | −0.481022 | − | 3.65372i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.9179 | − | 2.88554i | −1.31692 | − | 0.173376i | −0.560877 | − | 0.827899i | \(-0.689536\pi\) |
−0.756041 | + | 0.654524i | \(0.772869\pi\) | |||||||
\(278\) | 4.47617 | + | 3.10851i | 0.268463 | + | 0.186436i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −15.2147 | − | 3.88807i | −0.909250 | − | 0.232357i | ||||
\(281\) | 3.35403 | + | 12.5174i | 0.200085 | + | 0.746726i | 0.990892 | + | 0.134660i | \(0.0429943\pi\) |
−0.790807 | + | 0.612065i | \(0.790339\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.92178 | − | 6.07859i | −0.470901 | − | 0.361335i | 0.345884 | − | 0.938277i | \(-0.387579\pi\) |
−0.816785 | + | 0.576942i | \(0.804246\pi\) | |||||||
\(284\) | 2.89613 | − | 3.50621i | 0.171853 | − | 0.208055i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.561687 | + | 0.0267013i | −0.0332132 | + | 0.00157888i | ||||
\(287\) | 10.0932 | 0.595782 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.3618 | 0.609515 | ||||||||
\(290\) | −34.5204 | + | 1.64102i | −2.02711 | + | 0.0963642i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −16.2952 | − | 13.4599i | −0.953607 | − | 0.787678i | ||||
\(293\) | 11.0944 | + | 8.51304i | 0.648142 | + | 0.497337i | 0.879728 | − | 0.475478i | \(-0.157725\pi\) |
−0.231586 | + | 0.972815i | \(0.574391\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.6559 | − | 39.7685i | −0.620413 | − | 2.31541i | ||||
\(296\) | −0.478144 | − | 0.806409i | −0.0277916 | − | 0.0468715i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.05361 | − | 1.42614i | −0.118962 | − | 0.0826142i | ||||
\(299\) | 0.0498095 | + | 0.00655755i | 0.00288056 | + | 0.000379233i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.52507 | + | 11.5840i | 0.0879034 | + | 0.667693i | ||||
\(302\) | 3.96251 | + | 12.4000i | 0.228017 | + | 0.713539i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 13.0198 | + | 2.67574i | 0.746736 | + | 0.153464i | ||||
\(305\) | 60.2943i | 3.45244i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.3201 | + | 4.68895i | 0.646074 | + | 0.267613i | 0.681565 | − | 0.731757i | \(-0.261300\pi\) |
−0.0354914 | + | 0.999370i | \(0.511300\pi\) | |||||||
\(308\) | −2.32997 | − | 10.1379i | −0.132762 | − | 0.577663i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 24.4905 | + | 2.04720i | 1.39097 | + | 0.116273i | ||||
\(311\) | −6.51148 | + | 24.3012i | −0.369232 | + | 1.37799i | 0.492360 | + | 0.870392i | \(0.336134\pi\) |
−0.861592 | + | 0.507601i | \(0.830532\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.18723 | + | 4.43079i | 0.0671061 | + | 0.250443i | 0.991328 | − | 0.131413i | \(-0.0419515\pi\) |
−0.924222 | + | 0.381857i | \(0.875285\pi\) | |||||||
\(314\) | −1.35102 | − | 7.49241i | −0.0762426 | − | 0.422821i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.48627 | − | 1.13603i | −0.139864 | − | 0.0639066i | ||||
\(317\) | 15.3647 | + | 20.0237i | 0.862968 | + | 1.12464i | 0.991131 | + | 0.132889i | \(0.0424252\pi\) |
−0.128163 | + | 0.991753i | \(0.540908\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.4463 | − | 19.8255i | −0.640868 | − | 1.11002i | ||||
\(320\) | 33.1102 | + | 12.8227i | 1.85092 | + | 0.716808i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.0441301 | + | 0.928317i | 0.00245928 | + | 0.0517331i | ||||
\(323\) | 3.27637 | − | 7.90986i | 0.182302 | − | 0.440116i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.29867 | + | 0.537927i | −0.0720372 | + | 0.0298388i | ||||
\(326\) | 15.6368 | + | 5.62292i | 0.866043 | + | 0.311425i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −22.6589 | − | 2.71595i | −1.25113 | − | 0.149963i | ||||
\(329\) | 1.94871 | − | 7.27268i | 0.107436 | − | 0.400956i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.19754 | + | 1.21088i | 0.505542 | + | 0.0665559i | 0.378984 | − | 0.925403i | \(-0.376274\pi\) |
0.126558 | + | 0.991959i | \(0.459607\pi\) | |||||||
\(332\) | 17.9977 | − | 16.7499i | 0.987753 | − | 0.919270i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.88120 | − | 8.64368i | 0.102935 | − | 0.472961i | ||||
\(335\) | 47.5775 | + | 27.4689i | 2.59944 | + | 1.50079i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.87204 | − | 5.69962i | 0.537764 | − | 0.310478i | −0.206408 | − | 0.978466i | \(-0.566177\pi\) |
0.744172 | + | 0.667988i | \(0.232844\pi\) | |||||||
\(338\) | −5.59227 | − | 17.5000i | −0.304179 | − | 0.951876i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.1386 | − | 19.3832i | 0.658310 | − | 1.05120i | ||||
\(341\) | 6.22984 | + | 15.0402i | 0.337365 | + | 0.814471i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.9995 | − | 10.9995i | −0.593917 | − | 0.593917i | ||||
\(344\) | −0.306610 | − | 26.4162i | −0.0165313 | − | 1.42426i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.28414 | + | 6.24814i | 0.284077 | + | 0.335902i | ||||
\(347\) | 14.6438 | + | 11.2366i | 0.786123 | + | 0.603213i | 0.921856 | − | 0.387532i | \(-0.126672\pi\) |
−0.135733 | + | 0.990745i | \(0.543339\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.9141 | + | 16.8300i | 0.691278 | + | 0.900891i | 0.998715 | − | 0.0506774i | \(-0.0161380\pi\) |
−0.307437 | + | 0.951568i | \(0.599471\pi\) | |||||||
\(350\) | −14.0562 | − | 21.8766i | −0.751337 | − | 1.16935i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.50271 | + | 23.3863i | 0.133395 | + | 1.24649i | ||||
\(353\) | −1.81403 | + | 3.14198i | −0.0965508 | + | 0.167231i | −0.910255 | − | 0.414049i | \(-0.864114\pi\) |
0.813704 | + | 0.581280i | \(0.197448\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.0056 | − | 1.31726i | 0.531040 | − | 0.0699128i | ||||
\(356\) | −3.54385 | + | 4.29038i | −0.187824 | + | 0.227390i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.75544 | + | 16.0053i | −0.304184 | + | 0.845908i | ||||
\(359\) | −1.72433 | + | 1.72433i | −0.0910068 | + | 0.0910068i | −0.751145 | − | 0.660138i | \(-0.770498\pi\) |
0.660138 | + | 0.751145i | \(0.270498\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.62705 | − | 5.62705i | −0.296161 | − | 0.296161i | ||||
\(362\) | −21.7764 | + | 10.2573i | −1.14454 | + | 0.539109i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.211368 | + | 0.112119i | −0.0110787 | + | 0.00587661i | ||||
\(365\) | −6.12201 | − | 46.5013i | −0.320440 | − | 2.43399i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.658261 | − | 0.380047i | −0.0343610 | − | 0.0198383i | 0.482721 | − | 0.875774i | \(-0.339648\pi\) |
−0.517082 | + | 0.855936i | \(0.672982\pi\) | |||||||
\(368\) | 0.150728 | − | 2.09592i | 0.00785722 | − | 0.109257i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.442434 | − | 2.03288i | 0.0230010 | − | 0.105684i | ||||
\(371\) | −2.19997 | + | 1.68810i | −0.114217 | + | 0.0876416i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.43765 | − | 10.9962i | 0.436885 | − | 0.569360i | −0.522075 | − | 0.852899i | \(-0.674842\pi\) |
0.958961 | + | 0.283539i | \(0.0915087\pi\) | |||||||
\(374\) | 15.0969 | + | 1.26198i | 0.780645 | + | 0.0652553i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.33177 | + | 15.8026i | −0.326536 | + | 0.814955i | ||||
\(377\) | −0.372331 | + | 0.372331i | −0.0191760 | + | 0.0191760i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.3658 | + | 7.19316i | −0.892023 | + | 0.369488i | −0.781148 | − | 0.624346i | \(-0.785365\pi\) |
−0.110875 | + | 0.993834i | \(0.535365\pi\) | |||||||
\(380\) | 17.1051 | + | 24.0307i | 0.877471 | + | 1.23275i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.33935 | + | 0.690651i | 0.0685273 | + | 0.0353368i | ||||
\(383\) | 8.70697 | + | 15.0809i | 0.444905 | + | 0.770599i | 0.998046 | − | 0.0624894i | \(-0.0199040\pi\) |
−0.553140 | + | 0.833088i | \(0.686571\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.5421 | − | 19.9915i | 0.588238 | − | 1.01886i | ||||
\(386\) | −16.6638 | + | 10.7069i | −0.848164 | + | 0.544965i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.74819 | − | 21.3345i | 0.494890 | − | 1.08310i | ||||
\(389\) | −2.11221 | + | 16.0439i | −0.107094 | + | 0.813456i | 0.850630 | + | 0.525765i | \(0.176221\pi\) |
−0.957723 | + | 0.287691i | \(0.907112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.30739 | − | 0.350314i | −0.0661175 | − | 0.0177161i | ||||
\(392\) | 9.49935 | + | 12.0867i | 0.479790 | + | 0.610471i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.13027 | + | 8.76867i | 0.208080 | + | 0.441759i | ||||
\(395\) | −2.32139 | − | 5.60433i | −0.116802 | − | 0.281984i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.8435 | − | 12.7758i | −1.54799 | − | 0.641198i | −0.565038 | − | 0.825065i | \(-0.691138\pi\) |
−0.982951 | + | 0.183867i | \(0.941138\pi\) | |||||||
\(398\) | 9.42181 | + | 8.56668i | 0.472273 | + | 0.429409i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 25.6691 | + | 52.8947i | 1.28345 | + | 2.64473i | ||||
\(401\) | −9.16260 | + | 5.29003i | −0.457558 | + | 0.264171i | −0.711017 | − | 0.703175i | \(-0.751765\pi\) |
0.253459 | + | 0.967346i | \(0.418432\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.297067 | − | 0.227947i | 0.0147980 | − | 0.0113549i | ||||
\(404\) | −0.677506 | + | 18.8662i | −0.0337072 | + | 0.938629i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.00060 | − | 5.55608i | −0.397063 | − | 0.275743i | ||||
\(407\) | 1.33117 | − | 0.356685i | 0.0659835 | − | 0.0176802i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.9225 | + | 6.94590i | 1.28178 | + | 0.343453i | 0.834534 | − | 0.550957i | \(-0.185737\pi\) |
0.447249 | + | 0.894409i | \(0.352404\pi\) | |||||||
\(410\) | −32.7028 | − | 38.6688i | −1.61507 | − | 1.90972i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.0096 | + | 1.85357i | 0.542404 | + | 0.0913189i | ||||
\(413\) | 4.44074 | − | 10.7209i | 0.218515 | − | 0.527541i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 54.5603 | 2.67826 | ||||||||
\(416\) | 0.504685 | − | 0.194826i | 0.0247442 | − | 0.00955213i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.95497 | + | 17.3660i | −0.438002 | + | 0.849401i | ||||
\(419\) | 17.9185 | − | 2.35902i | 0.875378 | − | 0.115246i | 0.320571 | − | 0.947225i | \(-0.396125\pi\) |
0.554807 | + | 0.831979i | \(0.312792\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.02970 | + | 7.82137i | −0.0501846 | + | 0.381190i | 0.947860 | + | 0.318687i | \(0.103242\pi\) |
−0.998045 | + | 0.0625034i | \(0.980092\pi\) | |||||||
\(422\) | 5.09646 | − | 0.918988i | 0.248092 | − | 0.0447356i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.39311 | − | 3.19774i | 0.261912 | − | 0.155296i | ||||
\(425\) | 36.5800 | − | 9.80159i | 1.77439 | − | 0.475447i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.3453 | + | 13.4823i | −0.500645 | + | 0.652453i | ||||
\(428\) | −6.31583 | − | 11.9068i | −0.305287 | − | 0.575535i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 39.4392 | − | 43.3761i | 1.90193 | − | 2.09178i | ||||
\(431\) | − | 38.9561i | − | 1.87645i | −0.346025 | − | 0.938225i | \(-0.612469\pi\) | ||
0.346025 | − | 0.938225i | \(-0.387531\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.62134i | 0.270145i | 0.990836 | + | 0.135072i | \(0.0431267\pi\) | ||||
−0.990836 | + | 0.135072i | \(0.956873\pi\) | |||||||
\(434\) | 5.12501 | + | 4.65986i | 0.246008 | + | 0.223680i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.83452 | + | 1.17648i | 0.183640 | + | 0.0563430i | ||||
\(437\) | 1.06269 | − | 1.38493i | 0.0508355 | − | 0.0662501i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.4146 | − | 2.79058i | 0.497062 | − | 0.133187i | −0.00157424 | − | 0.999999i | \(-0.500501\pi\) |
0.498636 | + | 0.866811i | \(0.333834\pi\) | |||||||
\(440\) | −31.2910 | + | 41.7743i | −1.49174 | + | 1.99151i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.0618364 | − | 0.342928i | −0.00294126 | − | 0.0163114i | ||||
\(443\) | 5.18080 | − | 39.3521i | 0.246147 | − | 1.86967i | −0.207145 | − | 0.978310i | \(-0.566417\pi\) |
0.453292 | − | 0.891362i | \(-0.350249\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.2433 | + | 1.61186i | −0.580389 | + | 0.0764097i | ||||
\(446\) | 18.1745 | + | 9.37184i | 0.860586 | + | 0.443769i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.20358 | + | 8.54831i | 0.245846 | + | 0.403870i | ||||
\(449\) | −23.0258 | −1.08665 | −0.543327 | − | 0.839521i | \(-0.682836\pi\) | ||||
−0.543327 | + | 0.839521i | \(0.682836\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.8378 | − | 30.9931i | 0.604507 | − | 1.45941i | ||||
\(452\) | −1.18038 | + | 0.840200i | −0.0555206 | + | 0.0395197i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.60260 | + | 1.35534i | −0.0752140 | + | 0.0636095i | ||||
\(455\) | −0.512871 | − | 0.137423i | −0.0240437 | − | 0.00644250i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.66319 | + | 2.05335i | −0.358469 | + | 0.0960515i | −0.433559 | − | 0.901125i | \(-0.642742\pi\) |
0.0750898 | + | 0.997177i | \(0.476076\pi\) | |||||||
\(458\) | 13.0834 | − | 18.8397i | 0.611346 | − | 0.880322i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.41357 | − | 3.17690i | 0.159158 | − | 0.148124i | ||||
\(461\) | 1.96944 | − | 1.51121i | 0.0917261 | − | 0.0703839i | −0.561880 | − | 0.827219i | \(-0.689922\pi\) |
0.653606 | + | 0.756835i | \(0.273255\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.1636 | − | 10.4867i | 0.844133 | − | 0.487360i | −0.0145342 | − | 0.999894i | \(-0.504627\pi\) |
0.858667 | + | 0.512534i | \(0.171293\pi\) | |||||||
\(464\) | 16.4660 | + | 14.6261i | 0.764416 | + | 0.678998i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.5544 | + | 19.3067i | −0.813190 | + | 0.894363i | ||||
\(467\) | 2.29510 | + | 0.950660i | 0.106204 | + | 0.0439913i | 0.435153 | − | 0.900357i | \(-0.356694\pi\) |
−0.328949 | + | 0.944348i | \(0.606694\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.92559 | + | 14.3056i | 0.273618 | + | 0.660573i | ||||
\(470\) | −34.1770 | + | 16.0982i | −1.57647 | + | 0.742557i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.8542 | + | 22.8731i | −0.591662 | + | 1.05282i | ||||
\(473\) | 37.5109 | + | 10.0510i | 1.72475 | + | 0.462146i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.37526 | + | 48.4249i | −0.292517 | + | 2.22189i | ||||
\(476\) | 6.04007 | − | 2.25148i | 0.276846 | − | 0.103197i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.5119 | + | 24.1421i | 0.709496 | + | 1.10424i | ||||
\(479\) | 9.96920 | − | 17.2672i | 0.455504 | − | 0.788957i | −0.543213 | − | 0.839595i | \(-0.682792\pi\) |
0.998717 | + | 0.0506384i | \(0.0161256\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0158492 | − | 0.0274517i | −0.000722664 | − | 0.00125169i | ||||
\(482\) | 5.20547 | − | 10.0948i | 0.237102 | − | 0.459804i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.3995 | − | 2.08757i | −0.563612 | − | 0.0948894i | ||||
\(485\) | 48.0904 | − | 19.9197i | 2.18367 | − | 0.904506i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.1033 | + | 21.1033i | −0.956283 | + | 0.956283i | −0.999084 | − | 0.0428006i | \(-0.986372\pi\) |
0.0428006 | + | 0.999084i | \(0.486372\pi\) | |||||||
\(488\) | 26.8528 | − | 27.4835i | 1.21557 | − | 1.24412i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.84180 | + | 33.9962i | −0.128379 | + | 1.53579i | ||||
\(491\) | −7.97841 | + | 10.3977i | −0.360061 | + | 0.469240i | −0.937898 | − | 0.346912i | \(-0.887230\pi\) |
0.577837 | + | 0.816152i | \(0.303897\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.2545 | − | 8.63590i | 0.506879 | − | 0.388942i | ||||
\(494\) | 0.439139 | + | 0.0955739i | 0.0197578 | + | 0.00430007i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.2516 | − | 11.8403i | −0.460309 | − | 0.531645i | ||||
\(497\) | 2.46334 | + | 1.42221i | 0.110496 | + | 0.0637948i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.80424 | − | 21.3003i | −0.125535 | − | 0.953532i | −0.932053 | − | 0.362322i | \(-0.881984\pi\) |
0.806518 | − | 0.591209i | \(-0.201349\pi\) | |||||||
\(500\) | −25.2517 | + | 82.3033i | −1.12929 | + | 3.68071i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.32608 | − | 9.18436i | −0.193082 | − | 0.409918i | ||||
\(503\) | −29.1393 | − | 29.1393i | −1.29926 | − | 1.29926i | −0.928882 | − | 0.370377i | \(-0.879229\pi\) |
−0.370377 | − | 0.928882i | \(-0.620771\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.6235 | + | 29.6235i | −1.31823 | + | 1.31823i | ||||
\(506\) | 2.90671 | + | 1.04524i | 0.129219 | + | 0.0464666i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.82204 | − | 0.268915i | 0.125208 | − | 0.0119312i | ||||
\(509\) | −19.4327 | + | 2.55836i | −0.861340 | + | 0.113398i | −0.548238 | − | 0.836322i | \(-0.684701\pi\) |
−0.313101 | + | 0.949720i | \(0.601368\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.60977 | − | 11.4485i | 0.292399 | − | 0.506450i | ||||
\(512\) | −9.38164 | − | 20.5909i | −0.414614 | − | 0.909998i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −30.1472 | + | 19.3703i | −1.32974 | + | 0.854385i | ||||
\(515\) | 15.0826 | + | 19.6560i | 0.664617 | + | 0.866145i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.8536 | − | 15.2342i | −0.873161 | − | 0.670000i | ||||
\(518\) | 0.447734 | − | 0.378655i | 0.0196723 | − | 0.0166371i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.11440 | + | 0.446518i | 0.0488696 | + | 0.0195811i | ||||
\(521\) | 2.53175 | + | 2.53175i | 0.110918 | + | 0.110918i | 0.760388 | − | 0.649469i | \(-0.225009\pi\) |
−0.649469 | + | 0.760388i | \(0.725009\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.0621 | + | 24.2921i | 0.439986 | + | 1.06222i | 0.975953 | + | 0.217982i | \(0.0699473\pi\) |
−0.535967 | + | 0.844239i | \(0.680053\pi\) | |||||||
\(524\) | 36.2337 | − | 8.32746i | 1.58288 | − | 0.363787i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −25.9084 | + | 8.27922i | −1.12966 | + | 0.360991i | ||||
\(527\) | −8.73645 | + | 5.04399i | −0.380566 | + | 0.219720i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.6796 | + | 11.3620i | 0.855634 | + | 0.494001i | ||||
\(530\) | 13.5955 | + | 2.95891i | 0.590551 | + | 0.128527i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.298361 | + | 8.30834i | −0.0129356 | + | 0.360212i | ||||
\(533\) | −0.765013 | − | 0.100716i | −0.0331364 | − | 0.00436249i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.74129 | − | 28.8909i | 0.334685 | − | 1.24906i | ||||
\(536\) | −9.45328 | − | 33.7102i | −0.408320 | − | 1.45606i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.87503 | − | 27.4615i | 0.425743 | − | 1.18395i | ||||
\(539\) | −20.8779 | + | 8.64789i | −0.899273 | + | 0.372491i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.84101 | − | 11.6872i | 0.208131 | − | 0.502473i | −0.784998 | − | 0.619499i | \(-0.787336\pi\) |
0.993129 | + | 0.117025i | \(0.0373359\pi\) | |||||||
\(542\) | 23.0784 | − | 1.09710i | 0.991303 | − | 0.0471244i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −14.1656 | + | 3.42920i | −0.607345 | + | 0.147026i | ||||
\(545\) | 4.45044 | + | 7.70838i | 0.190636 | + | 0.330191i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.7870 | − | 28.3933i | −0.931544 | − | 1.21401i | −0.976608 | − | 0.215027i | \(-0.931016\pi\) |
0.0450643 | − | 0.998984i | \(-0.485651\pi\) | |||||||
\(548\) | 6.89638 | − | 2.57068i | 0.294599 | − | 0.109814i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −85.0550 | + | 15.3370i | −3.62676 | + | 0.653973i | ||||
\(551\) | 4.73540 | + | 17.6728i | 0.201735 | + | 0.752885i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.442512 | − | 1.65148i | 0.0188175 | − | 0.0702279i | ||||
\(554\) | −2.60433 | + | 31.1554i | −0.110647 | + | 1.32366i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.09055 | − | 6.53187i | 0.173478 | − | 0.277013i | ||||
\(557\) | −8.33216 | − | 3.45129i | −0.353045 | − | 0.146236i | 0.199111 | − | 0.979977i | \(-0.436195\pi\) |
−0.552156 | + | 0.833741i | \(0.686195\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.893231i | − | 0.0377796i | ||||||
\(560\) | −4.47065 | + | 21.7536i | −0.188919 | + | 0.919258i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17.4571 | − | 5.57854i | 0.736382 | − | 0.235316i | ||||
\(563\) | −2.21051 | − | 16.7905i | −0.0931620 | − | 0.707636i | −0.972743 | − | 0.231886i | \(-0.925510\pi\) |
0.879581 | − | 0.475749i | \(-0.157823\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.18777 | − | 0.419678i | −0.134110 | − | 0.0176560i | ||||
\(566\) | −8.05477 | + | 11.5986i | −0.338567 | + | 0.487527i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.14742 | − | 3.85567i | −0.215981 | − | 0.161780i | ||||
\(569\) | −2.22261 | − | 8.29489i | −0.0931766 | − | 0.347740i | 0.903560 | − | 0.428461i | \(-0.140944\pi\) |
−0.996737 | + | 0.0807216i | \(0.974278\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.8168 | + | 24.4139i | 1.33149 | + | 1.02169i | 0.996847 | + | 0.0793466i | \(0.0252834\pi\) |
0.334646 | + | 0.942344i | \(0.391383\pi\) | |||||||
\(572\) | 0.0754376 | + | 0.791656i | 0.00315421 | + | 0.0331008i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.677785 | − | 14.2578i | −0.0282902 | − | 0.595109i | ||||
\(575\) | 7.72161 | 0.322013 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.1637 | −1.04758 | −0.523790 | − | 0.851847i | \(-0.675482\pi\) | ||||
−0.523790 | + | 0.851847i | \(0.675482\pi\) | |||||||
\(578\) | −0.695820 | − | 14.6372i | −0.0289423 | − | 0.608828i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.63628 | + | 48.6539i | 0.192511 | + | 2.02024i | ||||
\(581\) | 12.2001 | + | 9.36148i | 0.506146 | + | 0.388379i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.38544 | + | 8.90259i | 0.0987949 | + | 0.368707i | ||||
\(584\) | −17.9194 | + | 23.9228i | −0.741509 | + | 0.989934i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.2807 | − | 16.2438i | 0.465999 | − | 0.671027i | ||||
\(587\) | −12.4858 | − | 1.64378i | −0.515343 | − | 0.0678462i | −0.131631 | − | 0.991299i | \(-0.542021\pi\) |
−0.383713 | + | 0.923453i | \(0.625355\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.69825 | − | 12.8995i | −0.0699753 | − | 0.531515i | ||||
\(590\) | −55.4621 | + | 17.7233i | −2.28334 | + | 0.729658i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.10704 | + | 0.729588i | −0.0454990 | + | 0.0299859i | ||||
\(593\) | 2.54265i | 0.104414i | 0.998636 | + | 0.0522070i | \(0.0166255\pi\) | ||||
−0.998636 | + | 0.0522070i | \(0.983374\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.2159 | + | 5.47420i | 0.541798 | + | 0.224420i | ||||
\(596\) | −1.87669 | + | 2.99673i | −0.0768722 | + | 0.122751i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.00591847 | − | 0.0708022i | 0.000242024 | − | 0.00289532i | ||||
\(599\) | 1.63697 | − | 6.10924i | 0.0668846 | − | 0.249617i | −0.924386 | − | 0.381458i | \(-0.875422\pi\) |
0.991271 | + | 0.131841i | \(0.0420888\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.899964 | + | 3.35871i | 0.0367103 | + | 0.137005i | 0.981849 | − | 0.189665i | \(-0.0607402\pi\) |
−0.945139 | + | 0.326670i | \(0.894074\pi\) | |||||||
\(602\) | 16.2614 | − | 2.93224i | 0.662765 | − | 0.119509i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.2503 | − | 6.43020i | 0.701907 | − | 0.261641i | ||||
\(605\) | −16.9866 | − | 22.1374i | −0.690603 | − | 0.900011i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.8432 | − | 25.7092i | −0.602468 | − | 1.04351i | −0.992446 | − | 0.122681i | \(-0.960851\pi\) |
0.389978 | − | 0.920824i | \(-0.372483\pi\) | |||||||
\(608\) | 2.90548 | − | 18.5717i | 0.117833 | − | 0.753181i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 85.1728 | − | 4.04893i | 3.44855 | − | 0.163936i | ||||
\(611\) | −0.220274 | + | 0.531788i | −0.00891132 | + | 0.0215138i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.6841 | − | 13.9524i | 1.36049 | − | 0.563533i | 0.421297 | − | 0.906923i | \(-0.361575\pi\) |
0.939193 | + | 0.343390i | \(0.111575\pi\) | |||||||
\(614\) | 5.86352 | − | 16.3059i | 0.236632 | − | 0.658052i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.1646 | + | 3.97215i | −0.570707 | + | 0.160042i | ||||
\(617\) | 3.98938 | − | 14.8886i | 0.160606 | − | 0.599391i | −0.837953 | − | 0.545742i | \(-0.816248\pi\) |
0.998560 | − | 0.0536496i | \(-0.0170854\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.3309 | − | 4.25644i | −1.29949 | − | 0.171081i | −0.551154 | − | 0.834404i | \(-0.685812\pi\) |
−0.748333 | + | 0.663323i | \(0.769146\pi\) | |||||||
\(620\) | 1.24731 | − | 34.7332i | 0.0500930 | − | 1.39492i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 34.7655 | + | 7.56634i | 1.39397 | + | 0.303383i | ||||
\(623\) | −3.01427 | − | 1.74029i | −0.120764 | − | 0.0697232i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −101.805 | + | 58.7770i | −4.07219 | + | 2.35108i | ||||
\(626\) | 6.17929 | − | 1.97464i | 0.246974 | − | 0.0789225i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.4932 | + | 2.41162i | −0.418724 | + | 0.0962339i | ||||
\(629\) | 0.326810 | + | 0.788989i | 0.0130308 | + | 0.0314590i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.7370 | − | 12.7370i | −0.507050 | − | 0.507050i | 0.406569 | − | 0.913620i | \(-0.366725\pi\) |
−0.913620 | + | 0.406569i | \(0.866725\pi\) | |||||||
\(632\) | −1.43782 | + | 3.58844i | −0.0571932 | + | 0.142740i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 27.2540 | − | 23.0491i | 1.08240 | − | 0.915397i | ||||
\(635\) | 4.99091 | + | 3.82966i | 0.198058 | + | 0.151975i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.316423 | + | 0.412370i | 0.0125371 | + | 0.0163387i | ||||
\(638\) | −27.2372 | + | 17.5005i | −1.07833 | + | 0.692853i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 15.8901 | − | 47.6331i | 0.628111 | − | 1.88287i | ||||
\(641\) | −9.54719 | + | 16.5362i | −0.377091 | + | 0.653141i | −0.990638 | − | 0.136518i | \(-0.956409\pi\) |
0.613546 | + | 0.789659i | \(0.289742\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.4855 | − | 3.22358i | 0.965615 | − | 0.127126i | 0.368804 | − | 0.929507i | \(-0.379767\pi\) |
0.596811 | + | 0.802382i | \(0.296434\pi\) | |||||||
\(644\) | 1.30839 | − | 0.124678i | 0.0515580 | − | 0.00491300i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.3936 | − | 4.09709i | −0.448276 | − | 0.161198i | ||||
\(647\) | −23.5792 | + | 23.5792i | −0.926995 | + | 0.926995i | −0.997511 | − | 0.0705153i | \(-0.977536\pi\) |
0.0705153 | + | 0.997511i | \(0.477536\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.2724 | − | 27.2724i | −1.07053 | − | 1.07053i | ||||
\(650\) | 0.847094 | + | 1.79840i | 0.0332258 | + | 0.0705391i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.89299 | − | 22.4665i | 0.269950 | − | 0.879854i | ||||
\(653\) | −4.96094 | − | 37.6821i | −0.194137 | − | 1.47461i | −0.759897 | − | 0.650044i | \(-0.774750\pi\) |
0.565760 | − | 0.824570i | \(-0.308583\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 71.4508 | + | 41.2521i | 2.79181 | + | 1.61185i | ||||
\(656\) | −2.31499 | + | 32.1907i | −0.0903852 | + | 1.25684i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.4044 | − | 2.26440i | −0.405605 | − | 0.0882756i | ||||
\(659\) | −28.1403 | + | 21.5928i | −1.09619 | + | 0.841136i | −0.988223 | − | 0.153018i | \(-0.951101\pi\) |
−0.107967 | + | 0.994155i | \(0.534434\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.4498 | + | 35.7732i | −1.06767 | + | 1.39142i | −0.152525 | + | 0.988300i | \(0.548740\pi\) |
−0.915148 | + | 0.403118i | \(0.867926\pi\) | |||||||
\(662\) | 1.09287 | − | 13.0739i | 0.0424756 | − | 0.508133i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −24.8698 | − | 24.2991i | −0.965136 | − | 0.942988i | ||||
\(665\) | −13.0457 | + | 13.0457i | −0.505889 | + | 0.505889i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.67229 | − | 1.10690i | 0.103471 | − | 0.0428593i | ||||
\(668\) | −12.3365 | − | 2.07698i | −0.477315 | − | 0.0803606i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 35.6081 | − | 69.0535i | 1.37566 | − | 2.66777i | ||||
\(671\) | 28.2416 | + | 48.9158i | 1.09025 | + | 1.88837i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.1138 | − | 17.5177i | 0.389859 | − | 0.675256i | −0.602571 | − | 0.798065i | \(-0.705857\pi\) |
0.992430 | + | 0.122809i | \(0.0391903\pi\) | |||||||
\(674\) | −8.71433 | − | 13.5627i | −0.335663 | − | 0.522415i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −24.3453 | + | 9.07491i | −0.936359 | + | 0.349035i | ||||
\(677\) | 3.22554 | − | 24.5004i | 0.123967 | − | 0.941626i | −0.810540 | − | 0.585683i | \(-0.800826\pi\) |
0.934508 | − | 0.355943i | \(-0.115840\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.1712 | + | 3.79716i | 0.543841 | + | 0.145722i | ||||
\(680\) | −28.1962 | − | 15.8456i | −1.08127 | − | 0.607652i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 20.8277 | − | 9.81038i | 0.797533 | − | 0.375659i | ||||
\(683\) | −1.02439 | − | 2.47310i | −0.0391973 | − | 0.0946307i | 0.903068 | − | 0.429497i | \(-0.141309\pi\) |
−0.942266 | + | 0.334866i | \(0.891309\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.0895 | + | 6.25029i | 0.576541 | + | 0.238811i | ||||
\(686\) | −14.7995 | + | 16.2767i | −0.565046 | + | 0.621449i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −37.2954 | + | 2.20704i | −1.42187 | + | 0.0841426i | ||||
\(689\) | 0.183592 | − | 0.105997i | 0.00699429 | − | 0.00403815i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.20272 | + | 3.22486i | −0.159879 | + | 0.122679i | −0.685603 | − | 0.727976i | \(-0.740461\pi\) |
0.525724 | + | 0.850655i | \(0.323795\pi\) | |||||||
\(692\) | 8.47139 | − | 7.88405i | 0.322034 | − | 0.299707i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.8897 | − | 21.4407i | 0.565204 | − | 0.813879i | ||||
\(695\) | 16.5202 | − | 4.42658i | 0.626648 | − | 0.167910i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.0799 | + | 5.38039i | 0.760580 | + | 0.203797i | ||||
\(698\) | 22.9072 | − | 19.3729i | 0.867050 | − | 0.733276i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −29.9594 | + | 21.3252i | −1.13236 | + | 0.806015i | ||||
\(701\) | −12.4676 | + | 30.0995i | −0.470895 | + | 1.13684i | 0.492873 | + | 0.870101i | \(0.335947\pi\) |
−0.963768 | + | 0.266740i | \(0.914053\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.10143 | −0.0415411 | ||||||||
\(704\) | 32.8679 | − | 5.10584i | 1.23875 | − | 0.192433i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.56024 | + | 2.35153i | 0.171627 | + | 0.0885011i | ||||
\(707\) | −11.7069 | + | 1.54124i | −0.440282 | + | 0.0579642i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.21164 | − | 16.7991i | 0.0830598 | − | 0.630902i | −0.898392 | − | 0.439194i | \(-0.855264\pi\) |
0.981452 | − | 0.191708i | \(-0.0614026\pi\) | |||||||
\(710\) | −2.53268 | − | 14.0456i | −0.0950499 | − | 0.527122i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.29865 | + | 4.71800i | 0.236052 | + | 0.176814i | ||||
\(713\) | −1.98681 | + | 0.532363i | −0.0744065 | + | 0.0199372i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.07432 | + | 1.40008i | −0.0401773 | + | 0.0523600i | ||||
\(716\) | 22.9959 | + | 7.05544i | 0.859398 | + | 0.263674i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.55162 | + | 2.32003i | 0.0952255 | + | 0.0865827i | ||||
\(719\) | − | 33.2500i | − | 1.24002i | −0.784596 | − | 0.620008i | \(-0.787129\pi\) | ||
0.784596 | − | 0.620008i | \(-0.212871\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.98310i | 0.260064i | ||||||||
\(722\) | −7.57101 | + | 8.32675i | −0.281764 | + | 0.309890i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15.9519 | + | 30.0729i | 0.592849 | + | 1.11765i | ||||
\(725\) | −49.2669 | + | 64.2058i | −1.82973 | + | 2.38454i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.8441 | + | 5.85311i | −0.810153 | + | 0.217080i | −0.640037 | − | 0.768344i | \(-0.721081\pi\) |
−0.170116 | + | 0.985424i | \(0.554414\pi\) | |||||||
\(728\) | 0.172575 | + | 0.291054i | 0.00639605 | + | 0.0107872i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −65.2774 | + | 11.7707i | −2.41603 | + | 0.435655i | ||||
\(731\) | −3.14107 | + | 23.8588i | −0.116177 | + | 0.882451i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.9125 | + | 3.01649i | −0.846293 | + | 0.111417i | −0.541188 | − | 0.840902i | \(-0.682025\pi\) |
−0.305106 | + | 0.952319i | \(0.598692\pi\) | |||||||
\(734\) | −0.492658 | + | 0.955393i | −0.0181843 | + | 0.0352642i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.97085 | − | 0.0721739i | −0.109507 | − | 0.00266037i | ||||
\(737\) | 51.4652 | 1.89575 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.7055 | + | 25.8453i | −0.393807 | + | 0.950734i | 0.595296 | + | 0.803507i | \(0.297035\pi\) |
−0.989103 | + | 0.147227i | \(0.952965\pi\) | |||||||
\(740\) | −2.90139 | − | 0.488477i | −0.106657 | − | 0.0179568i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.53237 | + | 2.99436i | 0.0929662 | + | 0.109926i | ||||
\(743\) | −47.9896 | − | 12.8588i | −1.76057 | − | 0.471742i | −0.773737 | − | 0.633507i | \(-0.781615\pi\) |
−0.986829 | + | 0.161765i | \(0.948281\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.57925 | + | 2.03086i | −0.277682 | + | 0.0744048i | ||||
\(746\) | −16.1000 | − | 11.1808i | −0.589463 | − | 0.409357i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.768891 | − | 21.4110i | 0.0281134 | − | 0.782863i | ||||
\(749\) | 6.68812 | − | 5.13198i | 0.244379 | − | 0.187518i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.98357 | + | 4.03197i | −0.254834 | + | 0.147129i | −0.621976 | − | 0.783036i | \(-0.713670\pi\) |
0.367142 | + | 0.930165i | \(0.380336\pi\) | |||||||
\(752\) | 22.7482 | + | 7.88319i | 0.829541 | + | 0.287471i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.550964 | + | 0.500958i | 0.0200649 | + | 0.0182438i | ||||
\(755\) | 37.7444 | + | 15.6342i | 1.37366 | + | 0.568988i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.1892 | − | 41.4984i | −0.624752 | − | 1.50828i | −0.846064 | − | 0.533081i | \(-0.821034\pi\) |
0.221312 | − | 0.975203i | \(-0.428966\pi\) | |||||||
\(758\) | 11.3274 | + | 24.0482i | 0.411428 | + | 0.873472i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 32.7975 | − | 25.7767i | 1.18969 | − | 0.935017i | ||||
\(761\) | 42.8027 | + | 11.4690i | 1.55160 | + | 0.415749i | 0.929991 | − | 0.367581i | \(-0.119814\pi\) |
0.621606 | + | 0.783330i | \(0.286481\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.327454 | + | 2.48726i | −0.0118546 | + | 0.0900450i | ||||
\(764\) | 0.885684 | − | 1.93837i | 0.0320429 | − | 0.0701279i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.7189 | − | 13.3123i | 0.748604 | − | 0.480995i | ||||
\(767\) | −0.443566 | + | 0.768279i | −0.0160162 | + | 0.0277410i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.6506 | + | 27.1076i | 0.564374 | + | 0.977524i | 0.997108 | + | 0.0760022i | \(0.0242156\pi\) |
−0.432734 | + | 0.901522i | \(0.642451\pi\) | |||||||
\(770\) | −29.0154 | − | 14.9621i | −1.04564 | − | 0.539195i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 16.2437 | + | 22.8206i | 0.584624 | + | 0.821330i | ||||
\(773\) | −32.9033 | + | 13.6290i | −1.18345 | + | 0.490200i | −0.885616 | − | 0.464418i | \(-0.846263\pi\) |
−0.297832 | + | 0.954618i | \(0.596263\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40.6946 | − | 40.6946i | 1.46179 | − | 1.46179i | ||||
\(776\) | −30.7921 | − | 12.3378i | −1.10537 | − | 0.442901i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.8057 | + | 1.90636i | 0.817624 | + | 0.0683464i | ||||
\(779\) | −16.3217 | + | 21.2708i | −0.584784 | + | 0.762106i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.50037 | − | 5.75523i | 0.268384 | − | 0.205938i | ||||
\(782\) | −0.407065 | + | 1.87036i | −0.0145566 | + | 0.0668841i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 16.4360 | − | 14.2306i | 0.587000 | − | 0.508236i | ||||
\(785\) | −20.6920 | − | 11.9465i | −0.738529 | − | 0.426390i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.192434 | − | 1.46168i | −0.00685953 | − | 0.0521033i | 0.987673 | − | 0.156533i | \(-0.0500317\pi\) |
−0.994532 | + | 0.104429i | \(0.966698\pi\) | |||||||
\(788\) | 12.1094 | − | 6.42334i | 0.431380 | − | 0.228822i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.76088 | + | 3.65558i | −0.276120 | + | 0.130060i | ||||
\(791\) | −0.640802 | − | 0.640802i | −0.0227843 | − | 0.0227843i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.918658 | − | 0.918658i | 0.0326225 | − | 0.0326225i | ||||
\(794\) | −15.9761 | + | 44.4280i | −0.566970 | + | 1.57669i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.4687 | − | 13.8847i | 0.406499 | − | 0.492130i | ||||
\(797\) | −34.2921 | + | 4.51465i | −1.21469 | + | 0.159917i | −0.710513 | − | 0.703684i | \(-0.751537\pi\) |
−0.504177 | + | 0.863601i | \(0.668204\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.75372 | − | 13.4298i | 0.274307 | − | 0.475113i | ||||
\(800\) | 72.9962 | − | 39.8126i | 2.58081 | − | 1.40759i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.08808 | + | 12.5880i | 0.285600 | + | 0.444498i | ||||
\(803\) | −26.7477 | − | 34.8582i | −0.943905 | − | 1.23012i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.31396 | + | 1.77556i | 0.0815562 | + | 0.0625803i | ||||
\(806\) | −0.341952 | − | 0.404335i | −0.0120447 | − | 0.0142421i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 26.6962 | − | 0.309861i | 0.939171 | − | 0.0109009i | ||||
\(809\) | 1.44428 | + | 1.44428i | 0.0507784 | + | 0.0507784i | 0.732040 | − | 0.681262i | \(-0.238568\pi\) |
−0.681262 | + | 0.732040i | \(0.738568\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.0225622 | + | 0.0544699i | 0.000792266 | + | 0.00191270i | 0.924275 | − | 0.381727i | \(-0.124671\pi\) |
−0.923483 | + | 0.383640i | \(0.874671\pi\) | |||||||
\(812\) | −7.31135 | + | 11.6749i | −0.256578 | + | 0.409709i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.593251 | − | 1.85648i | −0.0207934 | − | 0.0650695i | ||||
\(815\) | 45.1635 | − | 26.0751i | 1.58201 | − | 0.913372i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.8789 | − | 15.5185i | −0.940373 | − | 0.542925i | ||||
\(818\) | 8.07114 | − | 37.0850i | 0.282201 | − | 1.29665i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −52.4282 | + | 48.7932i | −1.83087 | + | 1.70393i | ||||
\(821\) | 6.98686 | + | 0.919838i | 0.243843 | + | 0.0321026i | 0.251457 | − | 0.967868i | \(-0.419090\pi\) |
−0.00761391 | + | 0.999971i | \(0.502424\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.4669 | + | 39.0630i | −0.364853 | + | 1.36165i | 0.502766 | + | 0.864422i | \(0.332316\pi\) |
−0.867620 | + | 0.497229i | \(0.834351\pi\) | |||||||
\(824\) | 1.87906 | − | 15.6768i | 0.0654603 | − | 0.546128i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.4428 | − | 5.55314i | −0.537322 | − | 0.193218i | ||||
\(827\) | −2.55963 | + | 1.06023i | −0.0890070 | + | 0.0368679i | −0.426743 | − | 0.904373i | \(-0.640339\pi\) |
0.337736 | + | 0.941241i | \(0.390339\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.2938 | + | 48.9935i | −0.704832 | + | 1.70161i | 0.00769626 | + | 0.999970i | \(0.497550\pi\) |
−0.712528 | + | 0.701644i | \(0.752450\pi\) | |||||||
\(830\) | −3.66387 | − | 77.0729i | −0.127175 | − | 2.67524i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.309106 | − | 0.699844i | −0.0107163 | − | 0.0242627i | ||||
\(833\) | −7.00177 | − | 12.1274i | −0.242597 | − | 0.420190i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.9004 | − | 22.0250i | −0.584862 | − | 0.762208i | ||||
\(836\) | 25.1329 | + | 11.4838i | 0.869241 | + | 0.397175i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.53567 | − | 25.1536i | −0.156682 | − | 0.868918i | ||||
\(839\) | −8.93815 | − | 33.3576i | −0.308579 | − | 1.15163i | −0.929820 | − | 0.368014i | \(-0.880038\pi\) |
0.621241 | − | 0.783620i | \(-0.286629\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.340538 | + | 1.27091i | −0.0117427 | + | 0.0438244i | ||||
\(842\) | 11.1178 | + | 0.929350i | 0.383143 | + | 0.0320275i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.64042 | − | 7.13764i | −0.0564656 | − | 0.245688i | ||||
\(845\) | −53.2684 | − | 22.0645i | −1.83249 | − | 0.759042i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.86465i | − | 0.270233i | ||||||
\(848\) | −4.87935 | − | 7.40366i | −0.167557 | − | 0.254243i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −16.3024 | − | 51.0154i | −0.559166 | − | 1.74981i | ||||
\(851\) | 0.0227280 | + | 0.172636i | 0.000779105 | + | 0.00591789i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.2308 | − | 4.63822i | −1.20628 | − | 0.158810i | −0.499545 | − | 0.866288i | \(-0.666499\pi\) |
−0.706735 | + | 0.707478i | \(0.749833\pi\) | |||||||
\(854\) | 19.7400 | + | 13.7086i | 0.675490 | + | 0.469099i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.3956 | + | 9.72143i | −0.560389 | + | 0.332272i | ||||
\(857\) | 5.29457 | + | 19.7596i | 0.180859 | + | 0.674976i | 0.995479 | + | 0.0949805i | \(0.0302789\pi\) |
−0.814620 | + | 0.579995i | \(0.803054\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.1488 | + | 13.9261i | 0.619229 | + | 0.475151i | 0.870104 | − | 0.492869i | \(-0.164052\pi\) |
−0.250875 | + | 0.968019i | \(0.580718\pi\) | |||||||
\(860\) | −63.9223 | − | 52.7997i | −2.17973 | − | 1.80046i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −55.0301 | + | 2.61601i | −1.87433 | + | 0.0891017i | ||||
\(863\) | −37.7370 | −1.28458 | −0.642290 | − | 0.766461i | \(-0.722016\pi\) | ||||
−0.642290 | + | 0.766461i | \(0.722016\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.6811 | 0.873185 | ||||||||
\(866\) | 7.94081 | − | 0.377489i | 0.269840 | − | 0.0128276i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.23844 | − | 7.55260i | 0.211747 | − | 0.256352i | ||||
\(869\) | −4.50835 | − | 3.45938i | −0.152935 | − | 0.117351i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.306380 | − | 1.14343i | −0.0103813 | − | 0.0387435i | ||||
\(872\) | 1.40442 | − | 5.49571i | 0.0475595 | − | 0.186108i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.02774 | − | 1.40818i | −0.0685893 | − | 0.0476323i | ||||
\(875\) | −53.3861 | − | 7.02841i | −1.80478 | − | 0.237604i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.64843 | − | 12.5211i | −0.0556635 | − | 0.422806i | −0.996476 | − | 0.0838787i | \(-0.973269\pi\) |
0.940812 | − | 0.338928i | \(-0.110064\pi\) | |||||||
\(878\) | −4.64140 | − | 14.5245i | −0.156640 | − | 0.490177i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 61.1125 | + | 41.3970i | 2.06010 | + | 1.39549i | ||||
\(881\) | − | 13.4697i | − | 0.453805i | −0.973917 | − | 0.226903i | \(-0.927140\pi\) | ||
0.973917 | − | 0.226903i | \(-0.0728599\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.92492 | + | 1.62576i | 0.132084 | + | 0.0547111i | 0.447747 | − | 0.894161i | \(-0.352227\pi\) |
−0.315662 | + | 0.948872i | \(0.602227\pi\) | |||||||
\(884\) | −0.480274 | + | 0.110380i | −0.0161534 | + | 0.00371248i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −55.9373 | − | 4.67589i | −1.87925 | − | 0.157090i | ||||
\(887\) | 2.27256 | − | 8.48131i | 0.0763051 | − | 0.284775i | −0.917221 | − | 0.398379i | \(-0.869573\pi\) |
0.993526 | + | 0.113604i | \(0.0362396\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.458912 | + | 1.71268i | 0.0153914 | + | 0.0574416i | ||||
\(890\) | 3.09912 | + | 17.1869i | 0.103883 | + | 0.576107i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.0184 | − | 26.3029i | 0.402405 | − | 0.880687i | ||||
\(893\) | 12.1755 | + | 15.8674i | 0.407438 | + | 0.530983i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26.6897 | + | 46.2278i | 0.892137 | + | 1.54523i | ||||
\(896\) | 11.7261 | − | 7.92472i | 0.391740 | − | 0.264746i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.54625 | + | 32.5267i | 0.0515989 | + | 1.08543i | ||||
\(899\) | 8.24995 | − | 19.9171i | 0.275151 | − | 0.664274i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.27661 | + | 2.18564i | −0.175789 | + | 0.0728143i | ||||
\(902\) | −44.6436 | − | 16.0536i | −1.48647 | − | 0.534527i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.26615 | + | 1.61101i | 0.0421114 | + | 0.0535814i | ||||
\(905\) | −19.5522 | + | 72.9698i | −0.649937 | + | 2.42560i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.8882 | − | 1.69677i | −0.427946 | − | 0.0563402i | −0.0865229 | − | 0.996250i | \(-0.527576\pi\) |
−0.341423 | + | 0.939910i | \(0.610909\pi\) | |||||||
\(908\) | 2.02220 | + | 2.17285i | 0.0671092 | + | 0.0721087i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.159686 | + | 0.733719i | −0.00529354 | + | 0.0243225i | ||||
\(911\) | −40.1326 | − | 23.1706i | −1.32965 | − | 0.767675i | −0.344407 | − | 0.938821i | \(-0.611920\pi\) |
−0.985246 | + | 0.171145i | \(0.945253\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44.2639 | − | 25.5558i | 1.46492 | − | 0.845773i | ||||
\(914\) | 3.41520 | + | 10.6873i | 0.112965 | + | 0.353504i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −27.4919 | − | 17.2167i | −0.908359 | − | 0.568855i | ||||
\(917\) | 8.89890 | + | 21.4839i | 0.293868 | + | 0.709459i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.2252 | − | 15.2252i | −0.502234 | − | 0.502234i | 0.409898 | − | 0.912131i | \(-0.365564\pi\) |
−0.912131 | + | 0.409898i | \(0.865564\pi\) | |||||||
\(920\) | −4.71697 | − | 4.60873i | −0.155514 | − | 0.151945i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.26701 | − | 2.68059i | −0.0746600 | − | 0.0882805i | ||||
\(923\) | −0.172517 | − | 0.132377i | −0.00567848 | − | 0.00435725i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.96585 | − | 3.86518i | −0.0975167 | − | 0.127086i | ||||
\(926\) | −16.0335 | − | 24.9540i | −0.526893 | − | 0.820039i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 19.5553 | − | 24.2424i | 0.641935 | − | 0.795795i | ||||
\(929\) | 28.1355 | − | 48.7321i | 0.923096 | − | 1.59885i | 0.128501 | − | 0.991709i | \(-0.458983\pi\) |
0.794595 | − | 0.607140i | \(-0.207683\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.9063 | − | 2.35741i | 0.586856 | − | 0.0772610i | ||||
\(932\) | 28.4518 | + | 23.5011i | 0.931968 | + | 0.769805i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.18880 | − | 3.30593i | 0.0388986 | − | 0.108173i | ||||
\(935\) | 33.6192 | − | 33.6192i | 1.09947 | − | 1.09947i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.58034 | − | 6.58034i | −0.214970 | − | 0.214970i | 0.591405 | − | 0.806375i | \(-0.298574\pi\) |
−0.806375 | + | 0.591405i | \(0.798574\pi\) | |||||||
\(938\) | 19.8105 | − | 9.33125i | 0.646835 | − | 0.304676i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 25.0358 | + | 47.1980i | 0.816576 | + | 1.53943i | ||||
\(941\) | 2.70922 | + | 20.5785i | 0.0883180 | + | 0.670841i | 0.977141 | + | 0.212591i | \(0.0681903\pi\) |
−0.888823 | + | 0.458250i | \(0.848476\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.67075 | + | 2.11931i | 0.119536 | + | 0.0690143i | ||||
\(944\) | 33.1742 | + | 16.6221i | 1.07973 | + | 0.541002i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.6793 | − | 53.6635i | 0.379726 | − | 1.74475i | ||||
\(947\) | 15.2792 | − | 11.7242i | 0.496508 | − | 0.380984i | −0.329936 | − | 0.944003i | \(-0.607027\pi\) |
0.826444 | + | 0.563019i | \(0.190360\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.615228 | + | 0.801781i | −0.0199712 | + | 0.0260269i | ||||
\(950\) | 68.8340 | + | 5.75394i | 2.23327 | + | 0.186683i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.58609 | − | 8.38112i | −0.116226 | − | 0.271634i | ||||
\(953\) | −21.2848 | + | 21.2848i | −0.689482 | + | 0.689482i | −0.962117 | − | 0.272635i | \(-0.912105\pi\) |
0.272635 | + | 0.962117i | \(0.412105\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.36931 | − | 1.80983i | 0.141388 | − | 0.0585646i | ||||
\(956\) | 33.0619 | − | 23.5336i | 1.06930 | − | 0.761130i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −25.0614 | − | 12.9231i | −0.809696 | − | 0.417528i | ||||
\(959\) | 2.30171 | + | 3.98668i | 0.0743261 | + | 0.128737i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.83476 | − | 13.5702i | 0.252734 | − | 0.437749i | ||||
\(962\) | −0.0377145 | + | 0.0242324i | −0.00121596 | + | 0.000781284i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.6096 | − | 6.67544i | −0.470544 | − | 0.215002i | ||||
\(965\) | −8.11370 | + | 61.6296i | −0.261189 | + | 1.98393i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.4432 | + | 7.08544i | 0.850357 | + | 0.227852i | 0.657575 | − | 0.753389i | \(-0.271582\pi\) |
0.192782 | + | 0.981242i | \(0.438249\pi\) | |||||||
\(968\) | −2.11628 | + | 17.6559i | −0.0680197 | + | 0.567482i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −31.3683 | − | 66.5957i | −1.00718 | − | 2.13826i | ||||
\(971\) | 6.85568 | + | 16.5511i | 0.220009 | + | 0.531149i | 0.994891 | − | 0.100957i | \(-0.0321905\pi\) |
−0.774882 | + | 0.632107i | \(0.782191\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.45357 | + | 1.84473i | 0.142775 | + | 0.0591393i | ||||
\(974\) | 31.2281 | + | 28.3938i | 1.00061 | + | 0.909796i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −40.6269 | − | 36.0872i | −1.30044 | − | 1.15512i | ||||
\(977\) | −8.31807 | + | 4.80244i | −0.266119 | + | 0.153644i | −0.627122 | − | 0.778921i | \(-0.715767\pi\) |
0.361004 | + | 0.932564i | \(0.382434\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.17784 | + | 7.04240i | −0.293325 | + | 0.225076i | ||||
\(980\) | 48.2145 | + | 1.73143i | 1.54016 | + | 0.0553087i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.2237 | + | 10.5722i | 0.485808 | + | 0.337373i | ||||
\(983\) | −13.9877 | + | 3.74798i | −0.446137 | + | 0.119542i | −0.474891 | − | 0.880044i | \(-0.657513\pi\) |
0.0287541 | + | 0.999587i | \(0.490846\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.3827 | + | 7.87306i | 0.936209 | + | 0.250857i | ||||
\(986\) | −12.9550 | − | 15.3184i | −0.412572 | − | 0.487838i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.105520 | − | 0.626754i | 0.00335704 | − | 0.0199397i | ||||
\(989\) | −1.87771 | + | 4.53318i | −0.0597076 | + | 0.144147i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.4755 | −0.618661 | −0.309330 | − | 0.950955i | \(-0.600105\pi\) | ||||
−0.309330 | + | 0.950955i | \(0.600105\pi\) | |||||||
\(992\) | −16.0374 | + | 15.2767i | −0.509188 | + | 0.485035i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.84362 | − | 3.57526i | 0.0584761 | − | 0.113400i | ||||
\(995\) | 39.6223 | − | 5.21638i | 1.25611 | − | 0.165370i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.48752 | + | 34.0861i | −0.142121 | + | 1.07952i | 0.760578 | + | 0.649246i | \(0.224916\pi\) |
−0.902699 | + | 0.430272i | \(0.858418\pi\) | |||||||
\(998\) | −29.9009 | + | 5.39169i | −0.946495 | + | 0.170671i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 864.2.bk.a.397.22 | 368 | ||
3.2 | odd | 2 | 288.2.bc.a.205.25 | yes | 368 | ||
9.4 | even | 3 | inner | 864.2.bk.a.685.39 | 368 | ||
9.5 | odd | 6 | 288.2.bc.a.13.8 | ✓ | 368 | ||
32.5 | even | 8 | inner | 864.2.bk.a.613.39 | 368 | ||
96.5 | odd | 8 | 288.2.bc.a.133.8 | yes | 368 | ||
288.5 | odd | 24 | 288.2.bc.a.229.25 | yes | 368 | ||
288.229 | even | 24 | inner | 864.2.bk.a.37.22 | 368 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.bc.a.13.8 | ✓ | 368 | 9.5 | odd | 6 | ||
288.2.bc.a.133.8 | yes | 368 | 96.5 | odd | 8 | ||
288.2.bc.a.205.25 | yes | 368 | 3.2 | odd | 2 | ||
288.2.bc.a.229.25 | yes | 368 | 288.5 | odd | 24 | ||
864.2.bk.a.37.22 | 368 | 288.229 | even | 24 | inner | ||
864.2.bk.a.397.22 | 368 | 1.1 | even | 1 | trivial | ||
864.2.bk.a.613.39 | 368 | 32.5 | even | 8 | inner | ||
864.2.bk.a.685.39 | 368 | 9.4 | even | 3 | inner |