Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(478,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.478");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.bm (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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.2346760387617129.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 478.5 | ||
Root | \(0.874681 - 1.11128i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.478 |
Dual form | 819.2.bm.f.550.2 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.34523i | 0.951219i | 0.879657 | + | 0.475609i | \(0.157772\pi\) | ||||
−0.879657 | + | 0.475609i | \(0.842228\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.190366 | 0.0951832 | ||||||||
\(5\) | −3.08979 | − | 1.78389i | −1.38179 | − | 0.797779i | −0.389422 | − | 0.921059i | \(-0.627325\pi\) |
−0.992372 | + | 0.123280i | \(0.960659\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.44601 | − | 1.00849i | −0.924504 | − | 0.381172i | ||||
\(8\) | 2.94654i | 1.04176i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.39973 | − | 4.15646i | 0.758862 | − | 1.31439i | ||||
\(11\) | 1.10736 | + | 0.639336i | 0.333882 | + | 0.192767i | 0.657563 | − | 0.753399i | \(-0.271587\pi\) |
−0.323681 | + | 0.946166i | \(0.604920\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.57420 | − | 0.474474i | 0.991304 | − | 0.131595i | ||||
\(14\) | 1.35664 | − | 3.29043i | 0.362578 | − | 0.879406i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.58303 | −0.895757 | ||||||||
\(17\) | 7.73920 | 1.87703 | 0.938515 | − | 0.345238i | \(-0.112202\pi\) | ||||
0.938515 | + | 0.345238i | \(0.112202\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.817422 | − | 0.471939i | 0.187530 | − | 0.108270i | −0.403296 | − | 0.915070i | \(-0.632135\pi\) |
0.590826 | + | 0.806799i | \(0.298802\pi\) | |||||||
\(20\) | −0.588191 | − | 0.339592i | −0.131524 | − | 0.0759352i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.860052 | + | 1.48965i | −0.183364 | + | 0.317595i | ||||
\(23\) | 1.64727 | 0.343481 | 0.171740 | − | 0.985142i | \(-0.445061\pi\) | ||||
0.171740 | + | 0.985142i | \(0.445061\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.86451 | + | 6.69354i | 0.772903 | + | 1.33871i | ||||
\(26\) | 0.638275 | + | 4.80810i | 0.125176 | + | 0.942946i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.465638 | − | 0.191982i | −0.0879973 | − | 0.0362812i | ||||
\(29\) | 2.02242 | + | 3.50293i | 0.375554 | + | 0.650478i | 0.990410 | − | 0.138161i | \(-0.0441192\pi\) |
−0.614856 | + | 0.788639i | \(0.710786\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.46193 | − | 2.57610i | 0.801387 | − | 0.462681i | −0.0425691 | − | 0.999094i | \(-0.513554\pi\) |
0.843956 | + | 0.536413i | \(0.180221\pi\) | |||||||
\(32\) | 1.07309i | 0.189698i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.4110i | 1.78547i | ||||||||
\(35\) | 5.75861 | + | 7.47941i | 0.973383 | + | 1.26425i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.05608i | − | 0.173619i | −0.996225 | − | 0.0868094i | \(-0.972333\pi\) | ||
0.996225 | − | 0.0868094i | \(-0.0276671\pi\) | |||||||
\(38\) | 0.634865 | + | 1.09962i | 0.102989 | + | 0.178382i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.25629 | − | 9.10417i | 0.831093 | − | 1.43950i | ||||
\(41\) | 3.63629 | − | 2.09941i | 0.567893 | − | 0.327873i | −0.188415 | − | 0.982090i | \(-0.560335\pi\) |
0.756307 | + | 0.654217i | \(0.227002\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.91532 | − | 3.31744i | 0.292084 | − | 0.505904i | −0.682218 | − | 0.731148i | \(-0.738985\pi\) |
0.974302 | + | 0.225244i | \(0.0723180\pi\) | |||||||
\(44\) | 0.210805 | + | 0.121708i | 0.0317800 | + | 0.0183482i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.21596i | 0.326725i | ||||||||
\(47\) | −0.774415 | − | 0.447109i | −0.112960 | − | 0.0652175i | 0.442456 | − | 0.896790i | \(-0.354107\pi\) |
−0.555416 | + | 0.831573i | \(0.687441\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.96591 | + | 4.93353i | 0.709416 | + | 0.704790i | ||||
\(50\) | −9.00432 | + | 5.19865i | −1.27340 | + | 0.735200i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.680407 | − | 0.0903239i | 0.0943554 | − | 0.0125257i | ||||
\(53\) | −0.0399961 | − | 0.0692754i | −0.00549389 | − | 0.00951570i | 0.863265 | − | 0.504750i | \(-0.168415\pi\) |
−0.868759 | + | 0.495235i | \(0.835082\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.28101 | − | 3.95082i | −0.307571 | − | 0.532729i | ||||
\(56\) | 2.97154 | − | 7.20726i | 0.397089 | − | 0.963110i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.71224 | + | 2.72061i | −0.618747 | + | 0.357234i | ||||
\(59\) | − | 11.1847i | − | 1.45613i | −0.685509 | − | 0.728064i | \(-0.740420\pi\) | ||
0.685509 | − | 0.728064i | \(-0.259580\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.81196 | + | 6.60251i | 0.488072 | + | 0.845365i | 0.999906 | − | 0.0137195i | \(-0.00436719\pi\) |
−0.511834 | + | 0.859084i | \(0.671034\pi\) | |||||||
\(62\) | 3.46543 | + | 6.00231i | 0.440111 | + | 0.762294i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.60961 | −1.07620 | ||||||||
\(65\) | −11.8899 | − | 4.90994i | −1.47476 | − | 0.609003i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.47418 | + | 3.16052i | 0.668777 | + | 0.386119i | 0.795613 | − | 0.605805i | \(-0.207149\pi\) |
−0.126836 | + | 0.991924i | \(0.540482\pi\) | |||||||
\(68\) | 1.47328 | 0.178662 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −10.0615 | + | 7.74664i | −1.20258 | + | 0.925900i | ||||
\(71\) | −9.89346 | − | 5.71199i | −1.17414 | − | 0.677889i | −0.219487 | − | 0.975616i | \(-0.570438\pi\) |
−0.954651 | + | 0.297727i | \(0.903772\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.658617 | − | 0.380253i | 0.0770853 | − | 0.0445052i | −0.460962 | − | 0.887420i | \(-0.652496\pi\) |
0.538047 | + | 0.842915i | \(0.319162\pi\) | |||||||
\(74\) | 1.42067 | 0.165149 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.155610 | − | 0.0898413i | 0.0178497 | − | 0.0103055i | ||||
\(77\) | −2.06386 | − | 2.68058i | −0.235198 | − | 0.305481i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.42765 | − | 2.47277i | 0.160624 | − | 0.278208i | −0.774469 | − | 0.632612i | \(-0.781983\pi\) |
0.935093 | + | 0.354404i | \(0.115316\pi\) | |||||||
\(80\) | 11.0708 | + | 6.39172i | 1.23775 | + | 0.714616i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.82418 | + | 4.89163i | 0.311879 | + | 0.540190i | ||||
\(83\) | − | 2.32483i | − | 0.255183i | −0.991827 | − | 0.127591i | \(-0.959275\pi\) | ||
0.991827 | − | 0.127591i | \(-0.0407246\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −23.9125 | − | 13.8059i | −2.59367 | − | 1.49746i | ||||
\(86\) | 4.46270 | + | 2.57654i | 0.481226 | + | 0.277836i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.88383 | + | 3.26289i | −0.200817 | + | 0.347825i | ||||
\(89\) | 7.57626i | 0.803082i | 0.915841 | + | 0.401541i | \(0.131525\pi\) | ||||
−0.915841 | + | 0.401541i | \(0.868475\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.22101 | − | 2.44396i | −0.966625 | − | 0.256196i | ||||
\(92\) | 0.313586 | 0.0326936 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.601462 | − | 1.04176i | 0.0620361 | − | 0.107450i | ||||
\(95\) | −3.36755 | −0.345503 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.414443 | − | 0.239279i | −0.0420803 | − | 0.0242951i | 0.478812 | − | 0.877917i | \(-0.341067\pi\) |
−0.520893 | + | 0.853622i | \(0.674401\pi\) | |||||||
\(98\) | −6.63671 | + | 6.68028i | −0.670409 | + | 0.674810i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.735674 | + | 1.27422i | 0.0735674 | + | 0.127422i | ||||
\(101\) | −1.43918 | + | 2.49273i | −0.143204 | + | 0.248036i | −0.928701 | − | 0.370829i | \(-0.879074\pi\) |
0.785498 | + | 0.618865i | \(0.212407\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.66755 | + | 9.81649i | −0.558441 | + | 0.967248i | 0.439186 | + | 0.898396i | \(0.355267\pi\) |
−0.997627 | + | 0.0688516i | \(0.978066\pi\) | |||||||
\(104\) | 1.39806 | + | 10.5315i | 0.137091 | + | 1.03270i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.0931910 | − | 0.0538039i | 0.00905151 | − | 0.00522589i | ||||
\(107\) | 6.57206 | 0.635345 | 0.317673 | − | 0.948200i | \(-0.397099\pi\) | ||||
0.317673 | + | 0.948200i | \(0.397099\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.05684 | + | 2.91957i | −0.484358 | + | 0.279644i | −0.722231 | − | 0.691652i | \(-0.756883\pi\) |
0.237873 | + | 0.971296i | \(0.423550\pi\) | |||||||
\(110\) | 5.31475 | − | 3.06847i | 0.506741 | − | 0.292567i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.76412 | + | 3.61343i | 0.828131 | + | 0.341437i | ||||
\(113\) | 3.26617 | − | 5.65717i | 0.307255 | − | 0.532181i | −0.670506 | − | 0.741904i | \(-0.733923\pi\) |
0.977761 | + | 0.209723i | \(0.0672562\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.08973 | − | 2.93855i | −0.474619 | − | 0.274022i | ||||
\(116\) | 0.385001 | + | 0.666841i | 0.0357464 | + | 0.0619146i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.0460 | 1.38510 | ||||||||
\(119\) | −18.9301 | − | 7.80487i | −1.73532 | − | 0.715471i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.68250 | − | 8.11033i | −0.425682 | − | 0.737302i | ||||
\(122\) | −8.88187 | + | 5.12795i | −0.804127 | + | 0.464263i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.849402 | − | 0.490402i | 0.0762786 | − | 0.0440394i | ||||
\(125\) | − | 9.73656i | − | 0.870865i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.35818 | + | 12.7447i | 0.652932 | + | 1.13091i | 0.982408 | + | 0.186748i | \(0.0597948\pi\) |
−0.329475 | + | 0.944164i | \(0.606872\pi\) | |||||||
\(128\) | − | 9.43568i | − | 0.834005i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.60498 | − | 15.9946i | 0.579295 | − | 1.40282i | ||||
\(131\) | 5.59335 | − | 9.68796i | 0.488693 | − | 0.846441i | −0.511222 | − | 0.859448i | \(-0.670807\pi\) |
0.999915 | + | 0.0130074i | \(0.00414049\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.47537 | + | 0.330008i | −0.214641 | + | 0.0286153i | ||||
\(134\) | −4.25161 | + | 7.36400i | −0.367283 | + | 0.636153i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 22.8038i | 1.95541i | ||||||||
\(137\) | 17.6308i | 1.50630i | 0.657848 | + | 0.753151i | \(0.271467\pi\) | ||||
−0.657848 | + | 0.753151i | \(0.728533\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.92855 | − | 5.07240i | 0.248396 | − | 0.430235i | −0.714685 | − | 0.699447i | \(-0.753430\pi\) |
0.963081 | + | 0.269212i | \(0.0867631\pi\) | |||||||
\(140\) | 1.09625 | + | 1.42383i | 0.0926497 | + | 0.120335i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.68392 | − | 13.3089i | 0.644820 | − | 1.11686i | ||||
\(143\) | 4.26128 | + | 1.75970i | 0.356346 | + | 0.147153i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 14.4311i | − | 1.19844i | ||||||
\(146\) | 0.511526 | + | 0.885989i | 0.0423342 | + | 0.0733250i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 0.201043i | − | 0.0165256i | ||||||
\(149\) | −9.07505 | + | 5.23948i | −0.743457 | + | 0.429235i | −0.823325 | − | 0.567570i | \(-0.807884\pi\) |
0.0798677 | + | 0.996805i | \(0.474550\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.08249 | + | 2.35703i | −0.332229 | + | 0.191812i | −0.656830 | − | 0.754039i | \(-0.728103\pi\) |
0.324602 | + | 0.945851i | \(0.394770\pi\) | |||||||
\(152\) | 1.39059 | + | 2.40857i | 0.112791 | + | 0.195361i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.60599 | − | 2.77635i | 0.290579 | − | 0.223725i | ||||
\(155\) | −18.3819 | −1.47647 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.50105 | − | 7.79604i | −0.359223 | − | 0.622192i | 0.628608 | − | 0.777722i | \(-0.283625\pi\) |
−0.987831 | + | 0.155530i | \(0.950291\pi\) | |||||||
\(158\) | 3.32643 | + | 1.92052i | 0.264637 | + | 0.152788i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.91428 | − | 3.31563i | 0.151337 | − | 0.262123i | ||||
\(161\) | −4.02925 | − | 1.66125i | −0.317549 | − | 0.130925i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.4203 | − | 6.01619i | 0.816185 | − | 0.471224i | −0.0329144 | − | 0.999458i | \(-0.510479\pi\) |
0.849099 | + | 0.528234i | \(0.177146\pi\) | |||||||
\(164\) | 0.692227 | − | 0.399657i | 0.0540538 | − | 0.0312080i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.12742 | 0.242735 | ||||||||
\(167\) | 16.8199 | − | 9.71099i | 1.30157 | − | 0.751459i | 0.320893 | − | 0.947116i | \(-0.396017\pi\) |
0.980672 | + | 0.195657i | \(0.0626838\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5497 | − | 3.39173i | 0.965365 | − | 0.260902i | ||||
\(170\) | 18.5720 | − | 32.1677i | 1.42441 | − | 2.46715i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.364613 | − | 0.631528i | 0.0278015 | − | 0.0481536i | ||||
\(173\) | −7.18976 | − | 12.4530i | −0.546627 | − | 0.946786i | −0.998503 | − | 0.0547049i | \(-0.982578\pi\) |
0.451875 | − | 0.892081i | \(-0.350755\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.70230 | − | 20.2697i | −0.204275 | − | 1.53225i | ||||
\(176\) | −3.96771 | − | 2.29076i | −0.299077 | − | 0.172672i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.1918 | −0.763907 | ||||||||
\(179\) | −2.71303 | + | 4.69911i | −0.202781 | + | 0.351228i | −0.949424 | − | 0.313998i | \(-0.898331\pi\) |
0.746642 | + | 0.665226i | \(0.231665\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.4902 | −1.15138 | −0.575688 | − | 0.817669i | \(-0.695266\pi\) | ||||
−0.575688 | + | 0.817669i | \(0.695266\pi\) | |||||||
\(182\) | 3.28768 | − | 12.4043i | 0.243699 | − | 0.919471i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.85376i | 0.357824i | ||||||||
\(185\) | −1.88393 | + | 3.26307i | −0.138509 | + | 0.239905i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.57010 | + | 4.94795i | 0.626707 | + | 0.361830i | ||||
\(188\) | −0.147423 | − | 0.0851144i | −0.0107519 | − | 0.00620761i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 4.53011i | − | 0.328649i | ||||||
\(191\) | 2.37311 | + | 4.11035i | 0.171712 | + | 0.297414i | 0.939019 | − | 0.343866i | \(-0.111737\pi\) |
−0.767306 | + | 0.641281i | \(0.778403\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.2204 | + | 10.5196i | 1.31154 | + | 0.757215i | 0.982350 | − | 0.187050i | \(-0.0598928\pi\) |
0.329185 | + | 0.944266i | \(0.393226\pi\) | |||||||
\(194\) | 0.321884 | − | 0.557519i | 0.0231099 | − | 0.0400276i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.945343 | + | 0.939178i | 0.0675245 | + | 0.0670842i | ||||
\(197\) | −5.03342 | + | 2.90604i | −0.358616 | + | 0.207047i | −0.668474 | − | 0.743736i | \(-0.733052\pi\) |
0.309857 | + | 0.950783i | \(0.399719\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.6182 | −0.752703 | −0.376352 | − | 0.926477i | \(-0.622821\pi\) | ||||
−0.376352 | + | 0.926477i | \(0.622821\pi\) | |||||||
\(200\) | −19.7228 | + | 11.3869i | −1.39461 | + | 0.805178i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.35329 | − | 1.93602i | −0.235936 | − | 0.136218i | ||||
\(203\) | −1.41420 | − | 10.6078i | −0.0992571 | − | 0.744520i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.9805 | −1.04628 | ||||||||
\(206\) | −13.2054 | − | 7.62414i | −0.920064 | − | 0.531199i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.8064 | + | 1.70005i | −0.887967 | + | 0.117877i | ||||
\(209\) | 1.20691 | 0.0834837 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.33275 | + | 4.04043i | 0.160593 | + | 0.278155i | 0.935081 | − | 0.354433i | \(-0.115326\pi\) |
−0.774489 | + | 0.632588i | \(0.781993\pi\) | |||||||
\(212\) | −0.00761392 | − | 0.0131877i | −0.000522926 | − | 0.000905735i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.84091i | 0.604352i | ||||||||
\(215\) | −11.8359 | + | 6.83344i | −0.807200 | + | 0.466037i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.5119 | + | 1.80136i | −0.917246 | + | 0.122284i | ||||
\(218\) | −3.92748 | − | 6.80260i | −0.266003 | − | 0.460730i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.434227 | − | 0.752104i | −0.0292756 | − | 0.0507068i | ||||
\(221\) | 27.6614 | − | 3.67205i | 1.86071 | − | 0.247009i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.9798 | − | 12.1127i | 1.40491 | − | 0.811126i | 0.410020 | − | 0.912076i | \(-0.365522\pi\) |
0.994891 | + | 0.100950i | \(0.0321883\pi\) | |||||||
\(224\) | 1.08220 | − | 2.62480i | 0.0723075 | − | 0.175377i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.61017 | + | 4.39373i | 0.506221 | + | 0.292267i | ||||
\(227\) | 15.3753i | 1.02049i | 0.860028 | + | 0.510247i | \(0.170446\pi\) | ||||
−0.860028 | + | 0.510247i | \(0.829554\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.1608 | − | 8.17573i | −0.935771 | − | 0.540268i | −0.0471389 | − | 0.998888i | \(-0.515010\pi\) |
−0.888632 | + | 0.458621i | \(0.848344\pi\) | |||||||
\(230\) | 3.95302 | − | 6.84683i | 0.260654 | − | 0.451467i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.3215 | + | 5.95913i | −0.677641 | + | 0.391236i | ||||
\(233\) | 14.5554 | − | 25.2106i | 0.953554 | − | 1.65160i | 0.215911 | − | 0.976413i | \(-0.430728\pi\) |
0.737643 | − | 0.675191i | \(-0.235939\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.59518 | + | 2.76294i | 0.104058 | + | 0.180234i | ||||
\(236\) | − | 2.12920i | − | 0.138599i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.4993 | − | 25.4653i | 0.680570 | − | 1.65067i | ||||
\(239\) | 8.65409i | 0.559787i | 0.960031 | + | 0.279893i | \(0.0902991\pi\) | ||||
−0.960031 | + | 0.279893i | \(0.909701\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.1982i | 1.17225i | 0.810222 | + | 0.586124i | \(0.199347\pi\) | ||||
−0.810222 | + | 0.586124i | \(0.800653\pi\) | |||||||
\(242\) | 10.9102 | − | 6.29902i | 0.701336 | − | 0.404916i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.725669 | + | 1.25690i | 0.0464562 | + | 0.0804645i | ||||
\(245\) | −6.54274 | − | 24.1022i | −0.418000 | − | 1.53983i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.69770 | − | 2.07465i | 0.171651 | − | 0.132007i | ||||
\(248\) | 7.59057 | + | 13.1473i | 0.482002 | + | 0.834851i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.0979 | 0.828383 | ||||||||
\(251\) | −7.93598 | + | 13.7455i | −0.500915 | + | 0.867610i | 0.499085 | + | 0.866553i | \(0.333670\pi\) |
−0.999999 | + | 0.00105678i | \(0.999664\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.82413 | + | 1.05316i | 0.114682 | + | 0.0662117i | ||||
\(254\) | −17.1446 | + | 9.89841i | −1.07574 | + | 0.621082i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.52609 | −0.282880 | ||||||||
\(257\) | −24.3267 | −1.51746 | −0.758730 | − | 0.651406i | \(-0.774180\pi\) | ||||
−0.758730 | + | 0.651406i | \(0.774180\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.06504 | + | 2.58319i | −0.0661786 | + | 0.160511i | ||||
\(260\) | −2.26344 | − | 0.934688i | −0.140372 | − | 0.0579669i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.0325 | + | 7.52432i | 0.805150 | + | 0.464854i | ||||
\(263\) | 7.71727 | − | 13.3667i | 0.475867 | − | 0.824226i | −0.523751 | − | 0.851872i | \(-0.675468\pi\) |
0.999618 | + | 0.0276456i | \(0.00880099\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.285395i | 0.0175317i | ||||||||
\(266\) | −0.443935 | − | 3.32993i | −0.0272194 | − | 0.204171i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.04210 | + | 0.601656i | 0.0636563 | + | 0.0367520i | ||||
\(269\) | 13.0407 | 0.795106 | 0.397553 | − | 0.917579i | \(-0.369859\pi\) | ||||
0.397553 | + | 0.917579i | \(0.369859\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 26.9706i | − | 1.63835i | −0.573544 | − | 0.819174i | \(-0.694432\pi\) | ||
0.573544 | − | 0.819174i | \(-0.305568\pi\) | |||||||
\(272\) | −27.7298 | −1.68136 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −23.7174 | −1.43282 | ||||||||
\(275\) | 9.88289i | 0.595961i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.7015 | −0.763156 | −0.381578 | − | 0.924337i | \(-0.624619\pi\) | ||||
−0.381578 | + | 0.924337i | \(0.624619\pi\) | |||||||
\(278\) | 6.82352 | + | 3.93956i | 0.409248 | + | 0.236279i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −22.0384 | + | 16.9680i | −1.31704 | + | 1.01403i | ||||
\(281\) | 26.7216i | 1.59408i | 0.603930 | + | 0.797038i | \(0.293601\pi\) | ||||
−0.603930 | + | 0.797038i | \(0.706399\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.37113 | − | 12.7672i | 0.438168 | − | 0.758929i | −0.559380 | − | 0.828911i | \(-0.688961\pi\) |
0.997548 | + | 0.0699819i | \(0.0222941\pi\) | |||||||
\(284\) | −1.88338 | − | 1.08737i | −0.111758 | − | 0.0645236i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.36719 | + | 5.73238i | −0.139975 | + | 0.338963i | ||||
\(287\) | −11.0116 | + | 1.46803i | −0.649995 | + | 0.0866553i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 42.8952 | 2.52324 | ||||||||
\(290\) | 19.4131 | 1.13997 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.125379 | − | 0.0723874i | 0.00733723 | − | 0.00423615i | ||||
\(293\) | 10.0312 | + | 5.79153i | 0.586030 | + | 0.338345i | 0.763526 | − | 0.645777i | \(-0.223466\pi\) |
−0.177496 | + | 0.984121i | \(0.556800\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.9523 | + | 34.5584i | −1.16167 | + | 2.01207i | ||||
\(296\) | 3.11179 | 0.180869 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.04829 | − | 12.2080i | −0.408297 | − | 0.707190i | ||||
\(299\) | 5.88768 | − | 0.781589i | 0.340493 | − | 0.0452005i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.03048 | + | 6.18290i | −0.462869 | + | 0.356376i | ||||
\(302\) | −3.17074 | − | 5.49188i | −0.182455 | − | 0.316022i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.92885 | + | 1.69097i | −0.167981 | + | 0.0969838i | ||||
\(305\) | − | 27.2004i | − | 1.55749i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 29.3335i | − | 1.67415i | −0.547086 | − | 0.837076i | \(-0.684263\pi\) | ||
0.547086 | − | 0.837076i | \(-0.315737\pi\) | |||||||
\(308\) | −0.392889 | − | 0.510293i | −0.0223869 | − | 0.0290766i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 24.7278i | − | 1.40444i | ||||||
\(311\) | 0.0753271 | + | 0.130470i | 0.00427141 | + | 0.00739830i | 0.868153 | − | 0.496296i | \(-0.165307\pi\) |
−0.863882 | + | 0.503695i | \(0.831974\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.26057 | − | 9.11157i | 0.297345 | − | 0.515016i | −0.678183 | − | 0.734893i | \(-0.737232\pi\) |
0.975528 | + | 0.219877i | \(0.0705656\pi\) | |||||||
\(314\) | 10.4874 | − | 6.05493i | 0.591841 | − | 0.341699i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.271777 | − | 0.470732i | 0.0152887 | − | 0.0264808i | ||||
\(317\) | −1.30489 | − | 0.753380i | −0.0732901 | − | 0.0423140i | 0.462907 | − | 0.886407i | \(-0.346806\pi\) |
−0.536197 | + | 0.844093i | \(0.680140\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.17202i | 0.289578i | ||||||||
\(320\) | 26.6018 | + | 15.3586i | 1.48709 | + | 0.858571i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.23476 | − | 5.42025i | 0.124538 | − | 0.302059i | ||||
\(323\) | 6.32619 | − | 3.65243i | 0.351999 | − | 0.203227i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.9884 | + | 22.0904i | 0.942349 | + | 1.22535i | ||||
\(326\) | 8.09314 | + | 14.0177i | 0.448237 | + | 0.776370i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.18600 | + | 10.7145i | 0.341565 | + | 0.591607i | ||||
\(329\) | 1.44332 | + | 1.87462i | 0.0795729 | + | 0.103351i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.8679 | + | 12.6254i | −1.20197 | + | 0.693957i | −0.960993 | − | 0.276574i | \(-0.910801\pi\) |
−0.240976 | + | 0.970531i | \(0.577467\pi\) | |||||||
\(332\) | − | 0.442569i | − | 0.0242891i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.0635 | + | 22.6266i | 0.714802 | + | 1.23807i | ||||
\(335\) | −11.2760 | − | 19.5306i | −0.616075 | − | 1.06707i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.1811 | 1.75302 | 0.876509 | − | 0.481386i | \(-0.159866\pi\) | ||||
0.876509 | + | 0.481386i | \(0.159866\pi\) | |||||||
\(338\) | 4.56264 | + | 16.8823i | 0.248175 | + | 0.918273i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.55213 | − | 2.62817i | −0.246874 | − | 0.142533i | ||||
\(341\) | 6.58797 | 0.356759 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.17127 | − | 17.0755i | −0.387212 | − | 0.921991i | ||||
\(344\) | 9.77495 | + | 5.64357i | 0.527030 | + | 0.304281i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.7521 | − | 9.67185i | 0.900600 | − | 0.519962i | ||||
\(347\) | −24.7638 | −1.32939 | −0.664695 | − | 0.747115i | \(-0.731438\pi\) | ||||
−0.664695 | + | 0.747115i | \(0.731438\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.0075 | + | 5.77782i | −0.535688 | + | 0.309280i | −0.743330 | − | 0.668925i | \(-0.766755\pi\) |
0.207642 | + | 0.978205i | \(0.433421\pi\) | |||||||
\(350\) | 27.2674 | − | 3.63520i | 1.45750 | − | 0.194310i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.686067 | + | 1.18830i | −0.0365675 | + | 0.0633368i | ||||
\(353\) | 17.3971 | + | 10.0442i | 0.925953 | + | 0.534599i | 0.885529 | − | 0.464583i | \(-0.153796\pi\) |
0.0404237 | + | 0.999183i | \(0.487129\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.3791 | + | 35.2977i | 1.08161 | + | 1.87340i | ||||
\(356\) | 1.44227i | 0.0764399i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.32136 | − | 3.64964i | −0.334094 | − | 0.192890i | ||||
\(359\) | −13.0346 | − | 7.52551i | −0.687938 | − | 0.397181i | 0.114901 | − | 0.993377i | \(-0.463345\pi\) |
−0.802839 | + | 0.596196i | \(0.796678\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.05455 | + | 15.6829i | −0.476555 | + | 0.825418i | ||||
\(362\) | − | 20.8378i | − | 1.09521i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.75537 | − | 0.465248i | −0.0920064 | − | 0.0243856i | ||||
\(365\) | −2.71331 | −0.142021 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.50178 | + | 7.79731i | −0.234991 | + | 0.407016i | −0.959270 | − | 0.282491i | \(-0.908839\pi\) |
0.724279 | + | 0.689507i | \(0.242173\pi\) | |||||||
\(368\) | −5.90223 | −0.307675 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.38956 | − | 2.53431i | −0.228202 | − | 0.131753i | ||||
\(371\) | 0.0279677 | + | 0.209784i | 0.00145201 | + | 0.0108914i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.06953 | + | 13.9768i | 0.417824 | + | 0.723693i | 0.995720 | − | 0.0924174i | \(-0.0294594\pi\) |
−0.577896 | + | 0.816110i | \(0.696126\pi\) | |||||||
\(374\) | −6.65611 | + | 11.5287i | −0.344179 | + | 0.596136i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.31742 | − | 2.28184i | 0.0679409 | − | 0.117677i | ||||
\(377\) | 8.89057 | + | 11.5606i | 0.457888 | + | 0.595400i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.5668 | + | 7.83277i | −0.696878 | + | 0.402342i | −0.806183 | − | 0.591666i | \(-0.798471\pi\) |
0.109306 | + | 0.994008i | \(0.465137\pi\) | |||||||
\(380\) | −0.641068 | −0.0328861 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.52935 | + | 3.19237i | −0.282906 | + | 0.163336i | ||||
\(383\) | −21.3327 | + | 12.3164i | −1.09005 | + | 0.629339i | −0.933589 | − | 0.358345i | \(-0.883341\pi\) |
−0.156459 | + | 0.987685i | \(0.550008\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.59502 | + | 11.9641i | 0.0812896 | + | 0.609747i | ||||
\(386\) | −14.1512 | + | 24.5106i | −0.720277 | + | 1.24756i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.0788960 | − | 0.0455506i | −0.00400534 | − | 0.00231248i | ||||
\(389\) | 9.42834 | + | 16.3304i | 0.478036 | + | 0.827982i | 0.999683 | − | 0.0251791i | \(-0.00801560\pi\) |
−0.521647 | + | 0.853161i | \(0.674682\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.7486 | 0.644724 | ||||||||
\(392\) | −14.5368 | + | 14.6323i | −0.734221 | + | 0.739040i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.90929 | − | 6.77108i | −0.196947 | − | 0.341122i | ||||
\(395\) | −8.82229 | + | 5.09355i | −0.443897 | + | 0.256284i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.5600 | + | 7.25149i | −0.630366 | + | 0.363942i | −0.780894 | − | 0.624664i | \(-0.785236\pi\) |
0.150528 | + | 0.988606i | \(0.451903\pi\) | |||||||
\(398\) | − | 14.2839i | − | 0.715985i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.8467 | − | 23.9831i | −0.692333 | − | 1.19916i | ||||
\(401\) | 20.9889i | 1.04814i | 0.851676 | + | 0.524069i | \(0.175587\pi\) | ||||
−0.851676 | + | 0.524069i | \(0.824413\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.7255 | − | 11.3245i | 0.733531 | − | 0.564116i | ||||
\(404\) | −0.273971 | + | 0.474532i | −0.0136306 | + | 0.0236089i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 14.2699 | − | 1.90241i | 0.708201 | − | 0.0944152i | ||||
\(407\) | 0.675191 | − | 1.16947i | 0.0334680 | − | 0.0579683i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 21.4276i | − | 1.05953i | −0.848146 | − | 0.529763i | \(-0.822281\pi\) | ||
0.848146 | − | 0.529763i | \(-0.177719\pi\) | |||||||
\(410\) | − | 20.1521i | − | 0.995242i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.07891 | + | 1.86873i | −0.0531542 | + | 0.0920657i | ||||
\(413\) | −11.2796 | + | 27.3580i | −0.555035 | + | 1.34620i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.14723 | + | 7.18321i | −0.203580 | + | 0.352610i | ||||
\(416\) | 0.509155 | + | 3.83545i | 0.0249634 | + | 0.188048i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.62357i | 0.0794113i | ||||||||
\(419\) | 3.98203 | + | 6.89708i | 0.194535 | + | 0.336944i | 0.946748 | − | 0.321976i | \(-0.104347\pi\) |
−0.752213 | + | 0.658920i | \(0.771014\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.81786i | 0.137334i | 0.997640 | + | 0.0686670i | \(0.0218746\pi\) | ||||
−0.997640 | + | 0.0686670i | \(0.978125\pi\) | |||||||
\(422\) | −5.43530 | + | 3.13807i | −0.264586 | + | 0.152759i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.204122 | − | 0.117850i | 0.00991306 | − | 0.00572331i | ||||
\(425\) | 29.9082 | + | 51.8026i | 1.45076 | + | 2.51279i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.66555 | − | 19.9941i | −0.128995 | − | 0.967582i | ||||
\(428\) | 1.25110 | 0.0604742 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.19253 | − | 15.9219i | −0.443303 | − | 0.767823i | ||||
\(431\) | −4.96775 | − | 2.86813i | −0.239288 | − | 0.138153i | 0.375561 | − | 0.926797i | \(-0.377450\pi\) |
−0.614849 | + | 0.788645i | \(0.710783\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.2628 | + | 21.2398i | −0.589314 | + | 1.02072i | 0.405009 | + | 0.914313i | \(0.367268\pi\) |
−0.994322 | + | 0.106409i | \(0.966065\pi\) | |||||||
\(434\) | −2.42324 | − | 18.1765i | −0.116319 | − | 0.872502i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.962653 | + | 0.555788i | −0.0461027 | + | 0.0266174i | ||||
\(437\) | 1.34652 | − | 0.777413i | 0.0644128 | − | 0.0371887i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.6423 | −1.74884 | −0.874420 | − | 0.485169i | \(-0.838758\pi\) | ||||
−0.874420 | + | 0.485169i | \(0.838758\pi\) | |||||||
\(440\) | 11.6412 | − | 6.72108i | 0.554975 | − | 0.320415i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.93973 | + | 37.2108i | 0.234959 | + | 1.76994i | ||||
\(443\) | 13.5467 | − | 23.4635i | 0.643622 | − | 1.11479i | −0.340996 | − | 0.940065i | \(-0.610764\pi\) |
0.984618 | − | 0.174721i | \(-0.0559022\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.5152 | − | 23.4090i | 0.640682 | − | 1.10969i | ||||
\(446\) | 16.2943 | + | 28.2226i | 0.771558 | + | 1.33638i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 21.0592 | + | 8.68267i | 0.994953 | + | 0.410218i | ||||
\(449\) | −23.7571 | − | 13.7162i | −1.12117 | − | 0.647307i | −0.179470 | − | 0.983764i | \(-0.557438\pi\) |
−0.941699 | + | 0.336456i | \(0.890772\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.36892 | 0.252812 | ||||||||
\(452\) | 0.621768 | − | 1.07693i | 0.0292455 | − | 0.0506547i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −20.6832 | −0.970712 | ||||||||
\(455\) | 24.1312 | + | 24.0006i | 1.13129 | + | 1.12516i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 39.6639i | 1.85540i | 0.373327 | + | 0.927700i | \(0.378217\pi\) | ||||
−0.373327 | + | 0.927700i | \(0.621783\pi\) | |||||||
\(458\) | 10.9982 | − | 19.0495i | 0.513913 | − | 0.890123i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.968913 | − | 0.559402i | −0.0451758 | − | 0.0260823i | ||||
\(461\) | 4.23988 | + | 2.44790i | 0.197471 | + | 0.114010i | 0.595475 | − | 0.803374i | \(-0.296964\pi\) |
−0.398004 | + | 0.917384i | \(0.630297\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.71193i | − | 0.218982i | −0.993988 | − | 0.109491i | \(-0.965078\pi\) | ||
0.993988 | − | 0.109491i | \(-0.0349221\pi\) | |||||||
\(464\) | −7.24638 | − | 12.5511i | −0.336405 | − | 0.582670i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 33.9140 | + | 19.5803i | 1.57104 | + | 0.907038i | ||||
\(467\) | −16.0081 | + | 27.7268i | −0.740765 | + | 1.28304i | 0.211383 | + | 0.977403i | \(0.432203\pi\) |
−0.952147 | + | 0.305639i | \(0.901130\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.2025 | − | 13.2513i | −0.471110 | − | 0.611887i | ||||
\(470\) | −3.71678 | + | 2.14588i | −0.171442 | + | 0.0989822i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 32.9563 | 1.51693 | ||||||||
\(473\) | 4.24191 | − | 2.44907i | 0.195043 | − | 0.112608i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.31788 | + | 3.64763i | 0.289884 | + | 0.167365i | ||||
\(476\) | −3.60366 | − | 1.48578i | −0.165174 | − | 0.0681008i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11.6417 | −0.532480 | ||||||||
\(479\) | −15.6097 | − | 9.01224i | −0.713224 | − | 0.411780i | 0.0990298 | − | 0.995084i | \(-0.468426\pi\) |
−0.812254 | + | 0.583305i | \(0.801759\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.501083 | − | 3.77464i | −0.0228474 | − | 0.172109i | ||||
\(482\) | −24.4807 | −1.11506 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.891390 | − | 1.54393i | −0.0405177 | − | 0.0701788i | ||||
\(485\) | 0.853693 | + | 1.47864i | 0.0387642 | + | 0.0671416i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 17.6004i | − | 0.797550i | −0.917049 | − | 0.398775i | \(-0.869435\pi\) | ||
0.917049 | − | 0.398775i | \(-0.130565\pi\) | |||||||
\(488\) | −19.4545 | + | 11.2321i | −0.880666 | + | 0.508453i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 32.4229 | − | 8.80146i | 1.46472 | − | 0.397609i | ||||
\(491\) | −1.93180 | − | 3.34598i | −0.0871810 | − | 0.151002i | 0.819138 | − | 0.573597i | \(-0.194453\pi\) |
−0.906318 | + | 0.422595i | \(0.861119\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.6519 | + | 27.1099i | 0.704926 | + | 1.22097i | ||||
\(494\) | 2.79087 | + | 3.62902i | 0.125567 | + | 0.163277i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15.9872 | + | 9.23023i | −0.717848 | + | 0.414450i | ||||
\(497\) | 18.4390 | + | 23.9490i | 0.827103 | + | 1.07426i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.9528 | − | 6.32363i | −0.490317 | − | 0.283084i | 0.234389 | − | 0.972143i | \(-0.424691\pi\) |
−0.724706 | + | 0.689058i | \(0.758024\pi\) | |||||||
\(500\) | − | 1.85351i | − | 0.0828917i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.4908 | − | 10.6757i | −0.825287 | − | 0.476480i | ||||
\(503\) | 11.0180 | − | 19.0837i | 0.491268 | − | 0.850902i | −0.508681 | − | 0.860955i | \(-0.669867\pi\) |
0.999949 | + | 0.0100533i | \(0.00320011\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.89351 | − | 5.13467i | 0.395756 | − | 0.228490i | ||||
\(506\) | −1.41674 | + | 2.45387i | −0.0629818 | + | 0.109088i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.40075 | + | 2.42617i | 0.0621482 | + | 0.107644i | ||||
\(509\) | − | 15.6702i | − | 0.694568i | −0.937760 | − | 0.347284i | \(-0.887104\pi\) | ||
0.937760 | − | 0.347284i | \(-0.112896\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.99446 | + | 0.265895i | −0.0882299 | + | 0.0117625i | ||||
\(512\) | − | 24.9600i | − | 1.10309i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 32.7249i | − | 1.44344i | ||||||
\(515\) | 35.0230 | − | 20.2206i | 1.54330 | − | 0.891025i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.571705 | − | 0.990222i | −0.0251436 | − | 0.0435499i | ||||
\(518\) | −3.47497 | − | 1.43272i | −0.152681 | − | 0.0629503i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 14.4673 | − | 35.0341i | 0.634435 | − | 1.53635i | ||||
\(521\) | −12.6207 | − | 21.8598i | −0.552925 | − | 0.957694i | −0.998062 | − | 0.0622317i | \(-0.980178\pi\) |
0.445137 | − | 0.895463i | \(-0.353155\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.2477 | −0.579279 | −0.289640 | − | 0.957136i | \(-0.593535\pi\) | ||||
−0.289640 | + | 0.957136i | \(0.593535\pi\) | |||||||
\(524\) | 1.06479 | − | 1.84426i | 0.0465154 | − | 0.0805670i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.9812 | + | 10.3815i | 0.784019 | + | 0.452654i | ||||
\(527\) | 34.5318 | − | 19.9369i | 1.50423 | − | 0.868466i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.2865 | −0.882021 | ||||||||
\(530\) | −0.383920 | −0.0166764 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.471226 | + | 0.0628224i | −0.0204303 | + | 0.00272370i | ||||
\(533\) | 12.0007 | − | 9.22903i | 0.519807 | − | 0.399754i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.3063 | − | 11.7238i | −0.877916 | − | 0.506865i | ||||
\(536\) | −9.31258 | + | 16.1299i | −0.402242 | + | 0.696704i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.5427i | 0.756320i | ||||||||
\(539\) | 2.34488 | + | 8.63809i | 0.101001 | + | 0.372069i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.4737 | − | 7.20170i | −0.536287 | − | 0.309625i | 0.207286 | − | 0.978280i | \(-0.433537\pi\) |
−0.743573 | + | 0.668655i | \(0.766870\pi\) | |||||||
\(542\) | 36.2816 | 1.55843 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.30488i | 0.356069i | ||||||||
\(545\) | 20.8328 | 0.892377 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.00679 | 0.0858042 | 0.0429021 | − | 0.999079i | \(-0.486340\pi\) | ||||
0.0429021 | + | 0.999079i | \(0.486340\pi\) | |||||||
\(548\) | 3.35631i | 0.143375i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −13.2947 | −0.566889 | ||||||||
\(551\) | 3.30634 | + | 1.90892i | 0.140855 | + | 0.0813226i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.98581 | + | 4.60864i | −0.254542 | + | 0.195979i | ||||
\(554\) | − | 17.0863i | − | 0.725928i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.557497 | − | 0.965614i | 0.0236432 | − | 0.0409512i | ||||
\(557\) | 7.42977 | + | 4.28958i | 0.314810 | + | 0.181755i | 0.649077 | − | 0.760723i | \(-0.275155\pi\) |
−0.334267 | + | 0.942478i | \(0.608489\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.27170 | − | 12.7659i | 0.222969 | − | 0.539942i | ||||
\(560\) | −20.6333 | − | 26.7989i | −0.871915 | − | 1.13246i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −35.9466 | −1.51631 | ||||||||
\(563\) | −12.7744 | −0.538375 | −0.269188 | − | 0.963088i | \(-0.586755\pi\) | ||||
−0.269188 | + | 0.963088i | \(0.586755\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.1835 | + | 11.6530i | −0.849126 | + | 0.490243i | ||||
\(566\) | 17.1747 | + | 9.91583i | 0.721908 | + | 0.416794i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.8306 | − | 29.1515i | 0.706196 | − | 1.22317i | ||||
\(569\) | −5.79116 | −0.242778 | −0.121389 | − | 0.992605i | \(-0.538735\pi\) | ||||
−0.121389 | + | 0.992605i | \(0.538735\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.0666 | − | 38.2204i | −0.923458 | − | 1.59948i | −0.794023 | − | 0.607888i | \(-0.792017\pi\) |
−0.129435 | − | 0.991588i | \(-0.541316\pi\) | |||||||
\(572\) | 0.811204 | + | 0.334987i | 0.0339182 | + | 0.0140065i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.97484 | − | 14.8131i | −0.0824281 | − | 0.618287i | ||||
\(575\) | 6.36592 | + | 11.0261i | 0.265477 | + | 0.459820i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.3343 | − | 5.96649i | 0.430221 | − | 0.248388i | −0.269220 | − | 0.963079i | \(-0.586766\pi\) |
0.699441 | + | 0.714691i | \(0.253432\pi\) | |||||||
\(578\) | 57.7037i | 2.40016i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 2.74719i | − | 0.114071i | ||||||
\(581\) | −2.34455 | + | 5.68654i | −0.0972685 | + | 0.235918i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 0.102284i | − | 0.00423617i | ||||||
\(584\) | 1.12043 | + | 1.94064i | 0.0463637 | + | 0.0803043i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.79091 | + | 13.4943i | −0.321840 | + | 0.557443i | ||||
\(587\) | −17.6250 | + | 10.1758i | −0.727462 | + | 0.420000i | −0.817493 | − | 0.575939i | \(-0.804637\pi\) |
0.0900312 | + | 0.995939i | \(0.471303\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.43152 | − | 4.21152i | 0.100189 | − | 0.173533i | ||||
\(590\) | −46.4889 | − | 26.8404i | −1.91392 | − | 1.10500i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.78397i | 0.155520i | ||||||||
\(593\) | −15.7443 | − | 9.09000i | −0.646543 | − | 0.373282i | 0.140588 | − | 0.990068i | \(-0.455101\pi\) |
−0.787130 | + | 0.616787i | \(0.788434\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 44.5670 | + | 57.8846i | 1.82707 | + | 2.37304i | ||||
\(596\) | −1.72759 | + | 0.997422i | −0.0707646 | + | 0.0408560i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.05141 | + | 7.92026i | 0.0429955 | + | 0.323884i | ||||
\(599\) | −19.1341 | − | 33.1412i | −0.781797 | − | 1.35411i | −0.930894 | − | 0.365290i | \(-0.880970\pi\) |
0.149096 | − | 0.988823i | \(-0.452364\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.4360 | + | 23.2718i | 0.548064 | + | 0.949275i | 0.998407 | + | 0.0564195i | \(0.0179684\pi\) |
−0.450343 | + | 0.892856i | \(0.648698\pi\) | |||||||
\(602\) | −8.31740 | − | 10.8028i | −0.338992 | − | 0.440290i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.777170 | + | 0.448699i | −0.0316226 | + | 0.0182573i | ||||
\(605\) | 33.4122i | 1.35840i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.70105 | + | 8.14245i | 0.190810 | + | 0.330492i | 0.945519 | − | 0.325568i | \(-0.105555\pi\) |
−0.754709 | + | 0.656059i | \(0.772222\pi\) | |||||||
\(608\) | 0.506435 | + | 0.877171i | 0.0205386 | + | 0.0355740i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 36.5908 | 1.48152 | ||||||||
\(611\) | −2.98005 | − | 1.23061i | −0.120560 | − | 0.0497853i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.5089 | + | 6.64469i | 0.464842 | + | 0.268376i | 0.714078 | − | 0.700066i | \(-0.246846\pi\) |
−0.249236 | + | 0.968443i | \(0.580180\pi\) | |||||||
\(614\) | 39.4602 | 1.59248 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.89843 | − | 6.08123i | 0.318237 | − | 0.245020i | ||||
\(617\) | 9.72211 | + | 5.61306i | 0.391397 | + | 0.225973i | 0.682765 | − | 0.730638i | \(-0.260777\pi\) |
−0.291368 | + | 0.956611i | \(0.594110\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.04109 | + | 4.64253i | −0.323199 | + | 0.186599i | −0.652817 | − | 0.757515i | \(-0.726413\pi\) |
0.329619 | + | 0.944114i | \(0.393080\pi\) | |||||||
\(620\) | −3.49929 | −0.140535 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.175512 | + | 0.101332i | −0.00703740 | + | 0.00406304i | ||||
\(623\) | 7.64055 | − | 18.5316i | 0.306112 | − | 0.742453i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.95363 | − | 3.38379i | 0.0781452 | − | 0.135351i | ||||
\(626\) | 12.2571 | + | 7.07665i | 0.489893 | + | 0.282840i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.856848 | − | 1.48410i | −0.0341920 | − | 0.0592222i | ||||
\(629\) | − | 8.17322i | − | 0.325888i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.00894 | + | 5.20132i | 0.358640 | + | 0.207061i | 0.668484 | − | 0.743726i | \(-0.266943\pi\) |
−0.309844 | + | 0.950787i | \(0.600277\pi\) | |||||||
\(632\) | 7.28611 | + | 4.20664i | 0.289826 | + | 0.167331i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.01347 | − | 1.75538i | 0.0402499 | − | 0.0697149i | ||||
\(635\) | − | 52.5046i | − | 2.08358i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.0900 | + | 15.2772i | 0.795994 | + | 0.605305i | ||||
\(638\) | −6.95754 | −0.275452 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.8322 | + | 29.1542i | −0.665351 | + | 1.15242i | ||||
\(641\) | 14.8591 | 0.586899 | 0.293449 | − | 0.955975i | \(-0.405197\pi\) | ||||
0.293449 | + | 0.955975i | \(0.405197\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.98945 | + | 1.14861i | 0.0784563 | + | 0.0452968i | 0.538715 | − | 0.842488i | \(-0.318910\pi\) |
−0.460259 | + | 0.887785i | \(0.652243\pi\) | |||||||
\(644\) | −0.767033 | − | 0.316247i | −0.0302254 | − | 0.0124619i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.91334 | + | 8.51016i | 0.193313 | + | 0.334828i | ||||
\(647\) | −3.99932 | + | 6.92703i | −0.157230 | + | 0.272330i | −0.933869 | − | 0.357616i | \(-0.883590\pi\) |
0.776639 | + | 0.629946i | \(0.216923\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.15081 | − | 12.3856i | 0.280694 | − | 0.486176i | ||||
\(650\) | −29.7166 | + | 22.8533i | −1.16558 | + | 0.896380i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.98368 | − | 1.14528i | 0.0776871 | − | 0.0448526i | ||||
\(653\) | −3.98444 | −0.155923 | −0.0779615 | − | 0.996956i | \(-0.524841\pi\) | ||||
−0.0779615 | + | 0.996956i | \(0.524841\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −34.5645 | + | 19.9558i | −1.35055 | + | 0.779738i | ||||
\(656\) | −13.0289 | + | 7.52225i | −0.508694 | + | 0.293695i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.52178 | + | 1.94159i | −0.0983094 | + | 0.0756912i | ||||
\(659\) | −13.7501 | + | 23.8159i | −0.535629 | + | 0.927737i | 0.463504 | + | 0.886095i | \(0.346592\pi\) |
−0.999133 | + | 0.0416417i | \(0.986741\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.05023 | + | 3.49310i | 0.235327 | + | 0.135866i | 0.613027 | − | 0.790062i | \(-0.289952\pi\) |
−0.377700 | + | 0.925928i | \(0.623285\pi\) | |||||||
\(662\) | −16.9841 | − | 29.4173i | −0.660105 | − | 1.14333i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.85019 | 0.265839 | ||||||||
\(665\) | 8.23704 | + | 3.39612i | 0.319419 | + | 0.131696i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.33148 | + | 5.77029i | 0.128995 | + | 0.223427i | ||||
\(668\) | 3.20195 | − | 1.84865i | 0.123887 | − | 0.0715263i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 26.2731 | − | 15.1688i | 1.01502 | − | 0.586022i | ||||
\(671\) | 9.74849i | 0.376336i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.72783 | + | 4.72474i | 0.105150 | + | 0.182125i | 0.913800 | − | 0.406166i | \(-0.133134\pi\) |
−0.808649 | + | 0.588291i | \(0.799801\pi\) | |||||||
\(674\) | 43.2909i | 1.66750i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.38905 | − | 0.645671i | 0.0918866 | − | 0.0248335i | ||||
\(677\) | 16.8961 | − | 29.2649i | 0.649371 | − | 1.12474i | −0.333903 | − | 0.942607i | \(-0.608366\pi\) |
0.983273 | − | 0.182135i | \(-0.0583009\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.772421 | + | 1.00324i | 0.0296428 | + | 0.0385007i | ||||
\(680\) | 40.6795 | − | 70.4590i | 1.55999 | − | 2.70198i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.86231i | 0.339355i | ||||||||
\(683\) | 12.2988i | 0.470602i | 0.971923 | + | 0.235301i | \(0.0756076\pi\) | ||||
−0.971923 | + | 0.235301i | \(0.924392\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.4514 | − | 54.4754i | 1.20170 | − | 2.08140i | ||||
\(686\) | 22.9704 | − | 9.64698i | 0.877015 | − | 0.368323i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.86265 | + | 11.8865i | −0.261636 | + | 0.453167i | ||||
\(689\) | −0.175823 | − | 0.228627i | −0.00669834 | − | 0.00870998i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 11.0897i | − | 0.421871i | −0.977500 | − | 0.210935i | \(-0.932349\pi\) | ||
0.977500 | − | 0.210935i | \(-0.0676509\pi\) | |||||||
\(692\) | −1.36869 | − | 2.37064i | −0.0520297 | − | 0.0901181i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 33.3129i | − | 1.26454i | ||||||
\(695\) | −18.0972 | + | 10.4484i | −0.686465 | + | 0.396331i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28.1419 | − | 16.2478i | 1.06595 | − | 0.615428i | ||||
\(698\) | −7.77247 | − | 13.4623i | −0.294193 | − | 0.509556i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.514427 | − | 3.85868i | −0.0194435 | − | 0.145844i | ||||
\(701\) | −10.6470 | −0.402133 | −0.201066 | − | 0.979578i | \(-0.564441\pi\) | ||||
−0.201066 | + | 0.979578i | \(0.564441\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.498406 | − | 0.863265i | −0.0187977 | − | 0.0325587i | ||||
\(704\) | −9.53396 | − | 5.50443i | −0.359325 | − | 0.207456i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.5117 | + | 23.4030i | −0.508521 | + | 0.880784i | ||||
\(707\) | 6.03413 | − | 4.64585i | 0.226937 | − | 0.174725i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.2532 | − | 20.3535i | 1.32396 | − | 0.764391i | 0.339605 | − | 0.940568i | \(-0.389707\pi\) |
0.984358 | + | 0.176178i | \(0.0563733\pi\) | |||||||
\(710\) | −47.4833 | + | 27.4145i | −1.78202 | + | 1.02885i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −22.3237 | −0.836618 | ||||||||
\(713\) | 7.35003 | − | 4.24354i | 0.275261 | − | 0.158922i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.0273 | − | 13.0387i | −0.375001 | − | 0.487621i | ||||
\(716\) | −0.516470 | + | 0.894552i | −0.0193014 | + | 0.0334310i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.1235 | − | 17.5344i | 0.377806 | − | 0.654380i | ||||
\(719\) | 4.88769 | + | 8.46572i | 0.182280 | + | 0.315718i | 0.942657 | − | 0.333764i | \(-0.108319\pi\) |
−0.760377 | + | 0.649482i | \(0.774986\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.7627 | − | 18.2956i | 0.884968 | − | 0.681363i | ||||
\(722\) | −21.0971 | − | 12.1804i | −0.785153 | − | 0.453308i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.94881 | −0.109592 | ||||||||
\(725\) | −15.6313 | + | 27.0743i | −0.580533 | + | 1.00551i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.2091 | −0.452811 | −0.226406 | − | 0.974033i | \(-0.572697\pi\) | ||||
−0.226406 | + | 0.974033i | \(0.572697\pi\) | |||||||
\(728\) | 7.20122 | − | 27.1701i | 0.266895 | − | 1.00699i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 3.65002i | − | 0.135093i | ||||||
\(731\) | 14.8231 | − | 25.6743i | 0.548251 | − | 0.949598i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.3256 | − | 11.1577i | −0.713809 | − | 0.412118i | 0.0986608 | − | 0.995121i | \(-0.468544\pi\) |
−0.812470 | + | 0.583003i | \(0.801877\pi\) | |||||||
\(734\) | −10.4891 | − | 6.05591i | −0.387161 | − | 0.223528i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.76768i | 0.0651576i | ||||||||
\(737\) | 4.04126 | + | 6.99968i | 0.148862 | + | 0.257836i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.6960 | − | 21.1865i | −1.34989 | − | 0.779357i | −0.361653 | − | 0.932313i | \(-0.617787\pi\) |
−0.988233 | + | 0.152956i | \(0.951121\pi\) | |||||||
\(740\) | −0.358637 | + | 0.621178i | −0.0131838 | + | 0.0228350i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.282206 | + | 0.0376229i | −0.0103601 | + | 0.00138118i | ||||
\(743\) | 26.8296 | − | 15.4901i | 0.984282 | − | 0.568276i | 0.0807220 | − | 0.996737i | \(-0.474277\pi\) |
0.903560 | + | 0.428461i | \(0.140944\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 37.3866 | 1.36974 | ||||||||
\(746\) | −18.8020 | + | 10.8553i | −0.688390 | + | 0.397442i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.63146 | + | 0.941923i | 0.0596520 | + | 0.0344401i | ||||
\(749\) | −16.0753 | − | 6.62783i | −0.587379 | − | 0.242176i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.5660 | −0.823444 | −0.411722 | − | 0.911309i | \(-0.635073\pi\) | ||||
−0.411722 | + | 0.911309i | \(0.635073\pi\) | |||||||
\(752\) | 2.77475 | + | 1.60200i | 0.101185 | + | 0.0584190i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −15.5516 | + | 11.9598i | −0.566356 | + | 0.435551i | ||||
\(755\) | 16.8187 | 0.612095 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.1404 | − | 27.9560i | −0.586633 | − | 1.01608i | −0.994670 | − | 0.103112i | \(-0.967120\pi\) |
0.408037 | − | 0.912965i | \(-0.366213\pi\) | |||||||
\(758\) | −10.5368 | − | 18.2504i | −0.382716 | − | 0.662883i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 9.92260i | − | 0.359931i | ||||||
\(761\) | 25.7657 | − | 14.8758i | 0.934006 | − | 0.539249i | 0.0459296 | − | 0.998945i | \(-0.485375\pi\) |
0.888076 | + | 0.459696i | \(0.152042\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.3134 | − | 2.04154i | 0.554383 | − | 0.0739086i | ||||
\(764\) | 0.451761 | + | 0.782473i | 0.0163441 | + | 0.0283089i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.5684 | − | 28.6972i | −0.598639 | − | 1.03687i | ||||
\(767\) | −5.30687 | − | 39.9764i | −0.191620 | − | 1.44347i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.2090 | + | 20.9053i | −1.30573 | + | 0.753863i | −0.981380 | − | 0.192075i | \(-0.938478\pi\) |
−0.324349 | + | 0.945938i | \(0.605145\pi\) | |||||||
\(770\) | −16.0944 | + | 2.14566i | −0.580003 | + | 0.0773242i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.46856 | + | 2.00257i | 0.124836 | + | 0.0720742i | ||||
\(773\) | − | 41.4336i | − | 1.49026i | −0.666917 | − | 0.745132i | \(-0.732387\pi\) | ||
0.666917 | − | 0.745132i | \(-0.267613\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34.4864 | + | 19.9107i | 1.23879 | + | 0.715215i | ||||
\(776\) | 0.705044 | − | 1.22117i | 0.0253096 | − | 0.0438375i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −21.9680 | + | 12.6832i | −0.787592 | + | 0.454716i | ||||
\(779\) | 1.98159 | − | 3.43221i | 0.0709978 | − | 0.122972i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.30376 | − | 12.6505i | −0.261349 | − | 0.452670i | ||||
\(782\) | 17.1497i | 0.613273i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −17.7930 | − | 17.6770i | −0.635464 | − | 0.631320i | ||||
\(785\) | 32.1175i | 1.14632i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.8627i | 0.850612i | 0.905050 | + | 0.425306i | \(0.139833\pi\) | ||||
−0.905050 | + | 0.425306i | \(0.860167\pi\) | |||||||
\(788\) | −0.958193 | + | 0.553213i | −0.0341342 | + | 0.0197074i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.85198 | − | 11.8680i | −0.243782 | − | 0.422243i | ||||
\(791\) | −13.6942 | + | 10.5436i | −0.486911 | + | 0.374887i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.7574 | + | 21.7900i | 0.595073 | + | 0.773785i | ||||
\(794\) | −9.75490 | − | 16.8960i | −0.346188 | − | 0.599616i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.02135 | −0.0716447 | ||||||||
\(797\) | −25.4115 | + | 44.0141i | −0.900123 | + | 1.55906i | −0.0727899 | + | 0.997347i | \(0.523190\pi\) |
−0.827333 | + | 0.561712i | \(0.810143\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.99335 | − | 3.46026i | −0.212029 | − | 0.122415i | ||||
\(800\) | −7.18279 | + | 4.14699i | −0.253950 | + | 0.146618i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −28.2349 | −0.997008 | ||||||||
\(803\) | 0.972438 | 0.0343166 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.48602 | + | 12.3206i | 0.334338 | + | 0.434246i | ||||
\(806\) | 15.2341 | + | 19.8092i | 0.536598 | + | 0.697748i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.34493 | − | 4.24060i | −0.258394 | − | 0.149184i | ||||
\(809\) | 2.20588 | − | 3.82070i | 0.0775547 | − | 0.134329i | −0.824640 | − | 0.565658i | \(-0.808622\pi\) |
0.902194 | + | 0.431330i | \(0.141955\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 17.6493i | − | 0.619750i | −0.950777 | − | 0.309875i | \(-0.899713\pi\) | ||
0.950777 | − | 0.309875i | \(-0.100287\pi\) | |||||||
\(812\) | −0.269215 | − | 2.01937i | −0.00944760 | − | 0.0708658i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.57320 | + | 0.908285i | 0.0551405 | + | 0.0318354i | ||||
\(815\) | −42.9288 | −1.50373 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 3.61566i | − | 0.126496i | ||||||
\(818\) | 28.8249 | 1.00784 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.85178 | −0.0995884 | ||||||||
\(821\) | 3.56043i | 0.124260i | 0.998068 | + | 0.0621299i | \(0.0197893\pi\) | ||||
−0.998068 | + | 0.0621299i | \(0.980211\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.8665 | −0.762217 | −0.381109 | − | 0.924530i | \(-0.624458\pi\) | ||||
−0.381109 | + | 0.924530i | \(0.624458\pi\) | |||||||
\(824\) | −28.9247 | − | 16.6997i | −1.00764 | − | 0.581760i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −36.8026 | − | 15.1737i | −1.28053 | − | 0.527960i | ||||
\(827\) | 18.1361i | 0.630653i | 0.948983 | + | 0.315327i | \(0.102114\pi\) | ||||
−0.948983 | + | 0.315327i | \(0.897886\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.4497 | − | 26.7596i | 0.536590 | − | 0.929401i | −0.462495 | − | 0.886622i | \(-0.653046\pi\) |
0.999085 | − | 0.0427787i | \(-0.0136210\pi\) | |||||||
\(830\) | −9.66305 | − | 5.57896i | −0.335409 | − | 0.193649i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −30.7724 | + | 4.08504i | −1.06684 | + | 0.141623i | ||||
\(833\) | 38.4322 | + | 38.1816i | 1.33160 | + | 1.32291i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −69.2933 | −2.39799 | ||||||||
\(836\) | 0.229755 | 0.00794625 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.27813 | + | 5.35673i | −0.320508 | + | 0.185045i | ||||
\(839\) | 13.3333 | + | 7.69796i | 0.460315 | + | 0.265763i | 0.712177 | − | 0.702000i | \(-0.247709\pi\) |
−0.251862 | + | 0.967763i | \(0.581043\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.31965 | − | 10.9459i | 0.217919 | − | 0.377446i | ||||
\(842\) | −3.79065 | −0.130635 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.444076 | + | 0.769163i | 0.0152857 | + | 0.0264757i | ||||
\(845\) | −44.8265 | − | 11.9076i | −1.54208 | − | 0.409636i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.27428 | + | 24.5602i | 0.112506 | + | 0.843897i | ||||
\(848\) | 0.143307 | + | 0.248216i | 0.00492119 | + | 0.00852376i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −69.6862 | + | 40.2333i | −2.39022 | + | 1.37999i | ||||
\(851\) | − | 1.73966i | − | 0.0596347i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.7772i | 0.814116i | 0.913402 | + | 0.407058i | \(0.133445\pi\) | ||||
−0.913402 | + | 0.407058i | \(0.866555\pi\) | |||||||
\(854\) | 26.8966 | − | 3.58577i | 0.920382 | − | 0.122702i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.3648i | 0.661877i | ||||||||
\(857\) | 15.0525 | + | 26.0717i | 0.514184 | + | 0.890592i | 0.999865 | + | 0.0164561i | \(0.00523837\pi\) |
−0.485681 | + | 0.874136i | \(0.661428\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.56717 | − | 13.1067i | 0.258188 | − | 0.447195i | −0.707568 | − | 0.706645i | \(-0.750208\pi\) |
0.965757 | + | 0.259450i | \(0.0835411\pi\) | |||||||
\(860\) | −2.25315 | + | 1.30086i | −0.0768318 | + | 0.0443589i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.85828 | − | 6.68274i | 0.131414 | − | 0.227615i | ||||
\(863\) | −15.8186 | − | 9.13287i | −0.538471 | − | 0.310886i | 0.205988 | − | 0.978555i | \(-0.433959\pi\) |
−0.744459 | + | 0.667668i | \(0.767293\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 51.3029i | 1.74435i | ||||||||
\(866\) | −28.5724 | − | 16.4963i | −0.970929 | − | 0.560566i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.57221 | + | 0.342919i | −0.0873064 | + | 0.0116394i | ||||
\(869\) | 3.16186 | − | 1.82550i | 0.107259 | − | 0.0619259i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.0654 | + | 8.69895i | 0.713772 | + | 0.294753i | ||||
\(872\) | −8.60263 | − | 14.9002i | −0.291322 | − | 0.504584i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.04580 | + | 1.81137i | 0.0353746 | + | 0.0612706i | ||||
\(875\) | −9.81919 | + | 23.8157i | −0.331949 | + | 0.805118i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.05906 | + | 3.49820i | −0.204600 | + | 0.118126i | −0.598799 | − | 0.800899i | \(-0.704355\pi\) |
0.394199 | + | 0.919025i | \(0.371022\pi\) | |||||||
\(878\) | − | 49.2922i | − | 1.66353i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.17292 | + | 14.1559i | 0.275509 | + | 0.477195i | ||||
\(881\) | −12.8873 | − | 22.3215i | −0.434184 | − | 0.752029i | 0.563045 | − | 0.826427i | \(-0.309630\pi\) |
−0.997229 | + | 0.0743977i | \(0.976297\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.4526 | −0.553674 | −0.276837 | − | 0.960917i | \(-0.589286\pi\) | ||||
−0.276837 | + | 0.960917i | \(0.589286\pi\) | |||||||
\(884\) | 5.26580 | − | 0.699034i | 0.177108 | − | 0.0235111i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31.5637 | + | 18.2233i | 1.06040 | + | 0.612225i | ||||
\(887\) | −55.2455 | −1.85496 | −0.927481 | − | 0.373871i | \(-0.878030\pi\) | ||||
−0.927481 | + | 0.373871i | \(0.878030\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.14527 | − | 38.5943i | −0.172567 | − | 1.29441i | ||||
\(890\) | 31.4904 | + | 18.1810i | 1.05556 | + | 0.609429i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.99385 | − | 2.30585i | 0.133724 | − | 0.0772056i | ||||
\(893\) | −0.844032 | −0.0282444 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.7654 | − | 9.67949i | 0.560404 | − | 0.323550i | ||||
\(896\) | −9.51575 | + | 23.0798i | −0.317899 | + | 0.771041i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.4514 | − | 31.9587i | 0.615731 | − | 1.06648i | ||||
\(899\) | 18.0478 | + | 10.4199i | 0.601927 | + | 0.347523i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.309538 | − | 0.536136i | −0.0103122 | − | 0.0178613i | ||||
\(902\) | 7.22241i | 0.240480i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.6691 | + | 9.62388i | 0.554405 | + | 0.320086i | ||||
\(905\) | 47.8614 | + | 27.6328i | 1.59097 | + | 0.918544i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.9212 | − | 41.4327i | 0.794290 | − | 1.37575i | −0.128998 | − | 0.991645i | \(-0.541176\pi\) |
0.923289 | − | 0.384107i | \(-0.125490\pi\) | |||||||
\(908\) | 2.92694i | 0.0971338i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −32.2862 | + | 32.4619i | −1.07028 | + | 1.07610i | ||||
\(911\) | 23.0711 | 0.764380 | 0.382190 | − | 0.924084i | \(-0.375170\pi\) | ||||
0.382190 | + | 0.924084i | \(0.375170\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.48635 | − | 2.57443i | 0.0491909 | − | 0.0852011i | ||||
\(914\) | −53.3569 | −1.76489 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.69574 | − | 1.55638i | −0.0890697 | − | 0.0514244i | ||||
\(917\) | −23.4515 | + | 18.0560i | −0.774438 | + | 0.596262i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.7184 | + | 37.6174i | 0.716424 | + | 1.24088i | 0.962408 | + | 0.271609i | \(0.0875557\pi\) |
−0.245984 | + | 0.969274i | \(0.579111\pi\) | |||||||
\(920\) | 8.65856 | − | 14.9971i | 0.285464 | − | 0.494439i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.29298 | + | 5.70360i | −0.108448 | + | 0.187838i | ||||
\(923\) | −38.0714 | − | 15.7216i | −1.25313 | − | 0.517482i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.06892 | − | 4.08124i | 0.232425 | − | 0.134190i | ||||
\(926\) | 6.33861 | 0.208300 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.75897 | + | 2.17024i | −0.123394 | + | 0.0712418i | ||||
\(929\) | −11.0695 | + | 6.39095i | −0.363177 | + | 0.209680i | −0.670474 | − | 0.741933i | \(-0.733909\pi\) |
0.307296 | + | 0.951614i | \(0.400576\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.38757 | + | 1.68917i | 0.209344 | + | 0.0553603i | ||||
\(932\) | 2.77085 | − | 4.79926i | 0.0907623 | − | 0.157205i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −37.2988 | − | 21.5345i | −1.22045 | − | 0.704629i | ||||
\(935\) | −17.6532 | − | 30.5762i | −0.577320 | − | 0.999948i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.2533 | 0.530971 | 0.265486 | − | 0.964115i | \(-0.414468\pi\) | ||||
0.265486 | + | 0.964115i | \(0.414468\pi\) | |||||||
\(938\) | 17.8260 | − | 13.7247i | 0.582038 | − | 0.448128i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.303669 | + | 0.525971i | 0.00990460 | + | 0.0171553i | ||||
\(941\) | −39.1000 | + | 22.5744i | −1.27462 | + | 0.735905i | −0.975855 | − | 0.218420i | \(-0.929910\pi\) |
−0.298770 | + | 0.954325i | \(0.596576\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.98997 | − | 3.45831i | 0.195060 | − | 0.112618i | ||||
\(944\) | 40.0752i | 1.30434i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.29455 | + | 5.70633i | 0.107115 | + | 0.185529i | ||||
\(947\) | 19.8557i | 0.645225i | 0.946531 | + | 0.322612i | \(0.104561\pi\) | ||||
−0.946531 | + | 0.322612i | \(0.895439\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.17361 | − | 1.67160i | 0.0705583 | − | 0.0542623i | ||||
\(950\) | −4.90689 | + | 8.49898i | −0.159200 | + | 0.275743i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 22.9973 | − | 55.7784i | 0.745348 | − | 1.80779i | ||||
\(953\) | −7.86433 | + | 13.6214i | −0.254751 | + | 0.441241i | −0.964828 | − | 0.262883i | \(-0.915327\pi\) |
0.710077 | + | 0.704124i | \(0.248660\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 16.9335i | − | 0.547954i | ||||||
\(956\) | 1.64745i | 0.0532823i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.1235 | − | 20.9985i | 0.391693 | − | 0.678432i | ||||
\(959\) | 17.7804 | − | 43.1251i | 0.574160 | − | 1.39258i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.22744 | + | 3.85804i | −0.0718529 | + | 0.124453i | ||||
\(962\) | 5.07775 | − | 0.674070i | 0.163713 | − | 0.0217329i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.46432i | 0.111578i | ||||||||
\(965\) | −37.5315 | − | 65.0064i | −1.20818 | − | 2.09263i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.1912i | 1.67835i | 0.543858 | + | 0.839177i | \(0.316963\pi\) | ||||
−0.543858 | + | 0.839177i | \(0.683037\pi\) | |||||||
\(968\) | 23.8974 | − | 13.7972i | 0.768091 | − | 0.443458i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.98910 | + | 1.14841i | −0.0638663 | + | 0.0368732i | ||||
\(971\) | −11.2292 | − | 19.4495i | −0.360362 | − | 0.624165i | 0.627658 | − | 0.778489i | \(-0.284013\pi\) |
−0.988020 | + | 0.154324i | \(0.950680\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.2787 | + | 9.45372i | −0.393637 | + | 0.303072i | ||||
\(974\) | 23.6765 | 0.758645 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.6584 | − | 23.6570i | −0.437193 | − | 0.757241i | ||||
\(977\) | 35.5369 | + | 20.5172i | 1.13693 | + | 0.656405i | 0.945668 | − | 0.325135i | \(-0.105410\pi\) |
0.191259 | + | 0.981540i | \(0.438743\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.84378 | + | 8.38967i | −0.154808 | + | 0.268135i | ||||
\(980\) | −1.24552 | − | 4.58825i | −0.0397866 | − | 0.146566i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.50110 | − | 2.59871i | 0.143636 | − | 0.0829282i | ||||
\(983\) | 23.2379 | − | 13.4164i | 0.741173 | − | 0.427916i | −0.0813229 | − | 0.996688i | \(-0.525915\pi\) |
0.822496 | + | 0.568772i | \(0.192581\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.7362 | 0.660711 | ||||||||
\(986\) | −36.4689 | + | 21.0553i | −1.16141 | + | 0.670539i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.513552 | − | 0.394943i | 0.0163383 | − | 0.0125648i | ||||
\(989\) | 3.15506 | − | 5.46473i | 0.100325 | − | 0.173768i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.18755 | + | 8.98510i | −0.164788 | + | 0.285421i | −0.936580 | − | 0.350454i | \(-0.886027\pi\) |
0.771792 | + | 0.635875i | \(0.219361\pi\) | |||||||
\(992\) | 2.76439 | + | 4.78807i | 0.0877696 | + | 0.152021i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −32.2168 | + | 24.8047i | −1.02186 | + | 0.786756i | ||||
\(995\) | 32.8079 | + | 18.9417i | 1.04008 | + | 0.600491i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53.9097 | −1.70734 | −0.853669 | − | 0.520816i | \(-0.825628\pi\) | ||||
−0.853669 | + | 0.520816i | \(0.825628\pi\) | |||||||
\(998\) | 8.50671 | − | 14.7341i | 0.269275 | − | 0.466398i | ||||
\(999\) | 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 | 819.2.bm.f.478.5 | 12 | ||
3.2 | odd | 2 | 91.2.k.b.23.2 | yes | 12 | ||
7.4 | even | 3 | 819.2.do.e.361.2 | 12 | |||
13.4 | even | 6 | 819.2.do.e.667.2 | 12 | |||
21.2 | odd | 6 | 637.2.q.g.491.2 | 12 | |||
21.5 | even | 6 | 637.2.q.i.491.2 | 12 | |||
21.11 | odd | 6 | 91.2.u.b.88.5 | yes | 12 | ||
21.17 | even | 6 | 637.2.u.g.361.5 | 12 | |||
21.20 | even | 2 | 637.2.k.i.569.2 | 12 | |||
39.2 | even | 12 | 1183.2.e.j.170.9 | 24 | |||
39.11 | even | 12 | 1183.2.e.j.170.4 | 24 | |||
39.17 | odd | 6 | 91.2.u.b.30.5 | yes | 12 | ||
91.4 | even | 6 | inner | 819.2.bm.f.550.2 | 12 | ||
273.2 | even | 12 | 8281.2.a.cp.1.4 | 12 | |||
273.11 | even | 12 | 1183.2.e.j.508.4 | 24 | |||
273.17 | even | 6 | 637.2.k.i.459.5 | 12 | |||
273.89 | odd | 12 | 8281.2.a.co.1.9 | 12 | |||
273.95 | odd | 6 | 91.2.k.b.4.5 | ✓ | 12 | ||
273.128 | even | 12 | 8281.2.a.cp.1.9 | 12 | |||
273.158 | even | 12 | 1183.2.e.j.508.9 | 24 | |||
273.173 | even | 6 | 637.2.q.i.589.2 | 12 | |||
273.212 | odd | 6 | 637.2.q.g.589.2 | 12 | |||
273.236 | odd | 12 | 8281.2.a.co.1.4 | 12 | |||
273.251 | even | 6 | 637.2.u.g.30.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.5 | ✓ | 12 | 273.95 | odd | 6 | ||
91.2.k.b.23.2 | yes | 12 | 3.2 | odd | 2 | ||
91.2.u.b.30.5 | yes | 12 | 39.17 | odd | 6 | ||
91.2.u.b.88.5 | yes | 12 | 21.11 | odd | 6 | ||
637.2.k.i.459.5 | 12 | 273.17 | even | 6 | |||
637.2.k.i.569.2 | 12 | 21.20 | even | 2 | |||
637.2.q.g.491.2 | 12 | 21.2 | odd | 6 | |||
637.2.q.g.589.2 | 12 | 273.212 | odd | 6 | |||
637.2.q.i.491.2 | 12 | 21.5 | even | 6 | |||
637.2.q.i.589.2 | 12 | 273.173 | even | 6 | |||
637.2.u.g.30.5 | 12 | 273.251 | even | 6 | |||
637.2.u.g.361.5 | 12 | 21.17 | even | 6 | |||
819.2.bm.f.478.5 | 12 | 1.1 | even | 1 | trivial | ||
819.2.bm.f.550.2 | 12 | 91.4 | even | 6 | inner | ||
819.2.do.e.361.2 | 12 | 7.4 | even | 3 | |||
819.2.do.e.667.2 | 12 | 13.4 | even | 6 | |||
1183.2.e.j.170.4 | 24 | 39.11 | even | 12 | |||
1183.2.e.j.170.9 | 24 | 39.2 | even | 12 | |||
1183.2.e.j.508.4 | 24 | 273.11 | even | 12 | |||
1183.2.e.j.508.9 | 24 | 273.158 | even | 12 | |||
8281.2.a.co.1.4 | 12 | 273.236 | odd | 12 | |||
8281.2.a.co.1.9 | 12 | 273.89 | odd | 12 | |||
8281.2.a.cp.1.4 | 12 | 273.2 | even | 12 | |||
8281.2.a.cp.1.9 | 12 | 273.128 | even | 12 |