Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [465,2,Mod(32,465)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(465, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("465.32");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 465 = 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 465.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.71304369399\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(30\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 32.22 | ||
Character | \(\chi\) | \(=\) | 465.32 |
Dual form | 465.2.k.b.218.22 |
$q$-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 \(\left(\mathbb{Z}/465\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(406\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00031 | − | 1.00031i | 0.707325 | − | 0.707325i | −0.258647 | − | 0.965972i | \(-0.583277\pi\) |
0.965972 | + | 0.258647i | \(0.0832765\pi\) | |||||||
\(3\) | 0.708168 | + | 1.58066i | 0.408861 | + | 0.912597i | ||||
\(4\) | − | 0.00123647i | − | 0.000618237i | ||||||
\(5\) | 1.98035 | + | 1.03838i | 0.885638 | + | 0.464377i | ||||
\(6\) | 2.28954 | + | 0.872765i | 0.934701 | + | 0.356305i | ||||
\(7\) | −1.66917 | − | 1.66917i | −0.630886 | − | 0.630886i | 0.317405 | − | 0.948290i | \(-0.397189\pi\) |
−0.948290 | + | 0.317405i | \(0.897189\pi\) | |||||||
\(8\) | 1.99938 | + | 1.99938i | 0.706888 | + | 0.706888i | ||||
\(9\) | −1.99699 | + | 2.23875i | −0.665665 | + | 0.746251i | ||||
\(10\) | 3.01966 | − | 0.942258i | 0.954900 | − | 0.297968i | ||||
\(11\) | − | 0.488628i | − | 0.147327i | −0.997283 | − | 0.0736634i | \(-0.976531\pi\) | ||
0.997283 | − | 0.0736634i | \(-0.0234691\pi\) | |||||||
\(12\) | 0.00195445 | 0.000875632i | 0.000564201 | 0.000252773i | ||||||
\(13\) | 0.606001 | − | 0.606001i | 0.168074 | − | 0.168074i | −0.618058 | − | 0.786132i | \(-0.712080\pi\) |
0.786132 | + | 0.618058i | \(0.212080\pi\) | |||||||
\(14\) | −3.33937 | −0.892483 | ||||||||
\(15\) | −0.238909 | + | 3.86561i | −0.0616860 | + | 0.998096i | ||||
\(16\) | 4.00247 | 1.00062 | ||||||||
\(17\) | 0.560255 | − | 0.560255i | 0.135882 | − | 0.135882i | −0.635894 | − | 0.771776i | \(-0.719369\pi\) |
0.771776 | + | 0.635894i | \(0.219369\pi\) | |||||||
\(18\) | 0.241832 | + | 4.23706i | 0.0570004 | + | 0.998684i | ||||
\(19\) | 1.46112i | 0.335205i | 0.985855 | + | 0.167602i | \(0.0536025\pi\) | ||||
−0.985855 | + | 0.167602i | \(0.946397\pi\) | |||||||
\(20\) | 0.00128393 | − | 0.00244865i | 0.000287095 | − | 0.000547534i | ||||
\(21\) | 1.45634 | − | 3.82044i | 0.317799 | − | 0.833689i | ||||
\(22\) | −0.488779 | − | 0.488779i | −0.104208 | − | 0.104208i | ||||
\(23\) | −3.42811 | − | 3.42811i | −0.714810 | − | 0.714810i | 0.252728 | − | 0.967537i | \(-0.418672\pi\) |
−0.967537 | + | 0.252728i | \(0.918672\pi\) | |||||||
\(24\) | −1.74445 | + | 4.57625i | −0.356084 | + | 0.934123i | ||||
\(25\) | 2.84354 | + | 4.11270i | 0.568708 | + | 0.822540i | ||||
\(26\) | − | 1.21238i | − | 0.237767i | ||||||
\(27\) | −4.95292 | − | 1.57116i | −0.953190 | − | 0.302370i | ||||
\(28\) | −0.00206388 | + | 0.00206388i | −0.000390037 | + | 0.000390037i | ||||
\(29\) | 0.216767 | 0.0402527 | 0.0201263 | − | 0.999797i | \(-0.493593\pi\) | ||||
0.0201263 | + | 0.999797i | \(0.493593\pi\) | |||||||
\(30\) | 3.62782 | + | 4.10578i | 0.662346 | + | 0.749610i | ||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 0.00494590 | − | 0.00494590i | 0.000874319 | − | 0.000874319i | ||||
\(33\) | 0.772356 | − | 0.346031i | 0.134450 | − | 0.0602362i | ||||
\(34\) | − | 1.12086i | − | 0.192225i | ||||||
\(35\) | −1.57230 | − | 5.03875i | −0.265767 | − | 0.851705i | ||||
\(36\) | 0.00276816 | + | 0.00246923i | 0.000461360 | + | 0.000411539i | ||||
\(37\) | 5.23298 | + | 5.23298i | 0.860296 | + | 0.860296i | 0.991372 | − | 0.131076i | \(-0.0418433\pi\) |
−0.131076 | + | 0.991372i | \(0.541843\pi\) | |||||||
\(38\) | 1.46158 | + | 1.46158i | 0.237099 | + | 0.237099i | ||||
\(39\) | 1.38703 | + | 0.528733i | 0.222103 | + | 0.0846650i | ||||
\(40\) | 1.88335 | + | 6.03558i | 0.297784 | + | 0.954309i | ||||
\(41\) | − | 7.11630i | − | 1.11138i | −0.831390 | − | 0.555690i | \(-0.812454\pi\) | ||
0.831390 | − | 0.555690i | \(-0.187546\pi\) | |||||||
\(42\) | −2.36483 | − | 5.27841i | −0.364902 | − | 0.814477i | ||||
\(43\) | 4.14486 | − | 4.14486i | 0.632084 | − | 0.632084i | −0.316506 | − | 0.948591i | \(-0.602510\pi\) |
0.948591 | + | 0.316506i | \(0.102510\pi\) | |||||||
\(44\) | −0.000604176 | 0 | −9.10829e−5 | 0 | ||||||
\(45\) | −6.27941 | + | 2.35987i | −0.936080 | + | 0.351788i | ||||
\(46\) | −6.85833 | −1.01121 | ||||||||
\(47\) | 6.37862 | − | 6.37862i | 0.930418 | − | 0.930418i | −0.0673142 | − | 0.997732i | \(-0.521443\pi\) |
0.997732 | + | 0.0673142i | \(0.0214430\pi\) | |||||||
\(48\) | 2.83442 | + | 6.32656i | 0.409114 | + | 0.913160i | ||||
\(49\) | − | 1.42776i | − | 0.203966i | ||||||
\(50\) | 6.95839 | + | 1.26955i | 0.984065 | + | 0.179542i | ||||
\(51\) | 1.28233 | + | 0.488820i | 0.179562 | + | 0.0684485i | ||||
\(52\) | −0.000749304 | 0 | 0.000749304i | −0.000103910 | 0 | 0.000103910i | ||||
\(53\) | −6.92873 | − | 6.92873i | −0.951734 | − | 0.951734i | 0.0471539 | − | 0.998888i | \(-0.484985\pi\) |
−0.998888 | + | 0.0471539i | \(0.984985\pi\) | |||||||
\(54\) | −6.52610 | + | 3.38280i | −0.888090 | + | 0.460341i | ||||
\(55\) | 0.507381 | − | 0.967652i | 0.0684152 | − | 0.130478i | ||||
\(56\) | − | 6.67460i | − | 0.891931i | ||||||
\(57\) | −2.30955 | + | 1.03472i | −0.305907 | + | 0.137052i | ||||
\(58\) | 0.216834 | − | 0.216834i | 0.0284717 | − | 0.0284717i | ||||
\(59\) | −9.51422 | −1.23865 | −0.619323 | − | 0.785136i | \(-0.712593\pi\) | ||||
−0.619323 | + | 0.785136i | \(0.712593\pi\) | |||||||
\(60\) | 0.00477972 | 0.000295405i | 0.000617060 | 3.81366e-5i | ||||||
\(61\) | 3.65071 | 0.467425 | 0.233713 | − | 0.972306i | \(-0.424912\pi\) | ||||
0.233713 | + | 0.972306i | \(0.424912\pi\) | |||||||
\(62\) | −1.00031 | + | 1.00031i | −0.127039 | + | 0.127039i | ||||
\(63\) | 7.07017 | − | 0.403534i | 0.890757 | − | 0.0508404i | ||||
\(64\) | 7.99505i | 0.999381i | ||||||||
\(65\) | 1.82935 | − | 0.570833i | 0.226903 | − | 0.0708031i | ||||
\(66\) | 0.426457 | − | 1.11873i | 0.0524933 | − | 0.137707i | ||||
\(67\) | −4.73394 | − | 4.73394i | −0.578342 | − | 0.578342i | 0.356104 | − | 0.934446i | \(-0.384105\pi\) |
−0.934446 | + | 0.356104i | \(0.884105\pi\) | |||||||
\(68\) | −0.000692741 | 0 | 0.000692741i | −8.40072e−5 | 0 | 8.40072e-5i | ||||
\(69\) | 2.99101 | − | 7.84636i | 0.360075 | − | 0.944591i | ||||
\(70\) | −6.61310 | − | 3.46753i | −0.790416 | − | 0.414449i | ||||
\(71\) | 0.0865773i | 0.0102748i | 0.999987 | + | 0.00513742i | \(0.00163530\pi\) | ||||
−0.999987 | + | 0.00513742i | \(0.998365\pi\) | |||||||
\(72\) | −8.46887 | + | 0.483365i | −0.998066 | + | 0.0569652i | ||||
\(73\) | 1.94880 | − | 1.94880i | 0.228090 | − | 0.228090i | −0.583804 | − | 0.811895i | \(-0.698436\pi\) |
0.811895 | + | 0.583804i | \(0.198436\pi\) | |||||||
\(74\) | 10.4692 | 1.21702 | ||||||||
\(75\) | −4.48709 | + | 7.40716i | −0.518124 | + | 0.855305i | ||||
\(76\) | 0.00180664 | 0.000207236 | ||||||||
\(77\) | −0.815601 | + | 0.815601i | −0.0929464 | + | 0.0929464i | ||||
\(78\) | 1.91636 | − | 0.858567i | 0.216985 | − | 0.0972135i | ||||
\(79\) | − | 8.96053i | − | 1.00814i | −0.863663 | − | 0.504069i | \(-0.831836\pi\) | ||
0.863663 | − | 0.504069i | \(-0.168164\pi\) | |||||||
\(80\) | 7.92628 | + | 4.15608i | 0.886185 | + | 0.464664i | ||||
\(81\) | −1.02402 | − | 8.94155i | −0.113780 | − | 0.993506i | ||||
\(82\) | −7.11850 | − | 7.11850i | −0.786107 | − | 0.786107i | ||||
\(83\) | 0.345948 | + | 0.345948i | 0.0379727 | + | 0.0379727i | 0.725838 | − | 0.687865i | \(-0.241452\pi\) |
−0.687865 | + | 0.725838i | \(0.741452\pi\) | |||||||
\(84\) | −0.00472388 | − | 0.00180073i | −0.000515417 | − | 0.000196475i | ||||
\(85\) | 1.69126 | − | 0.527742i | 0.183443 | − | 0.0572417i | ||||
\(86\) | − | 8.29227i | − | 0.894179i | ||||||
\(87\) | 0.153508 | + | 0.342636i | 0.0164578 | + | 0.0367344i | ||||
\(88\) | 0.976954 | − | 0.976954i | 0.104144 | − | 0.104144i | ||||
\(89\) | −12.2175 | −1.29505 | −0.647525 | − | 0.762044i | \(-0.724196\pi\) | ||||
−0.647525 | + | 0.762044i | \(0.724196\pi\) | |||||||
\(90\) | −3.92076 | + | 8.64195i | −0.413284 | + | 0.910942i | ||||
\(91\) | −2.02303 | −0.212071 | ||||||||
\(92\) | −0.00423877 | + | 0.00423877i | −0.000441922 | + | 0.000441922i | ||||
\(93\) | −0.708168 | − | 1.58066i | −0.0734337 | − | 0.163907i | ||||
\(94\) | − | 12.7612i | − | 1.31622i | ||||||
\(95\) | −1.51720 | + | 2.89353i | −0.155661 | + | 0.296870i | ||||
\(96\) | 0.0113203 | + | 0.00431527i | 0.00115538 | + | 0.000440425i | ||||
\(97\) | −1.33436 | − | 1.33436i | −0.135484 | − | 0.135484i | 0.636113 | − | 0.771596i | \(-0.280541\pi\) |
−0.771596 | + | 0.636113i | \(0.780541\pi\) | |||||||
\(98\) | −1.42821 | − | 1.42821i | −0.144271 | − | 0.144271i | ||||
\(99\) | 1.09392 | + | 0.975787i | 0.109943 | + | 0.0980703i | ||||
\(100\) | 0.00508525 | − | 0.00351596i | 0.000508525 | − | 0.000351596i | ||||
\(101\) | 13.5503i | 1.34830i | 0.738593 | + | 0.674152i | \(0.235491\pi\) | ||||
−0.738593 | + | 0.674152i | \(0.764509\pi\) | |||||||
\(102\) | 1.77170 | − | 0.793755i | 0.175424 | − | 0.0785935i | ||||
\(103\) | −3.23911 | + | 3.23911i | −0.319159 | + | 0.319159i | −0.848444 | − | 0.529285i | \(-0.822460\pi\) |
0.529285 | + | 0.848444i | \(0.322460\pi\) | |||||||
\(104\) | 2.42325 | 0.237620 | ||||||||
\(105\) | 6.85112 | − | 6.05357i | 0.668601 | − | 0.590767i | ||||
\(106\) | −13.8617 | −1.34637 | ||||||||
\(107\) | −5.66961 | + | 5.66961i | −0.548102 | + | 0.548102i | −0.925891 | − | 0.377790i | \(-0.876684\pi\) |
0.377790 | + | 0.925891i | \(0.376684\pi\) | |||||||
\(108\) | −0.00194270 | + | 0.00612416i | −0.000186937 | + | 0.000589298i | ||||
\(109\) | 14.9745i | 1.43430i | 0.696921 | + | 0.717148i | \(0.254553\pi\) | ||||
−0.696921 | + | 0.717148i | \(0.745447\pi\) | |||||||
\(110\) | −0.460414 | − | 1.47549i | −0.0438987 | − | 0.140682i | ||||
\(111\) | −4.56575 | + | 11.9774i | −0.433361 | + | 1.13684i | ||||
\(112\) | −6.68079 | − | 6.68079i | −0.631276 | − | 0.631276i | ||||
\(113\) | 0.606854 | + | 0.606854i | 0.0570880 | + | 0.0570880i | 0.735074 | − | 0.677986i | \(-0.237147\pi\) |
−0.677986 | + | 0.735074i | \(0.737147\pi\) | |||||||
\(114\) | −1.27522 | + | 3.34530i | −0.119435 | + | 0.313316i | ||||
\(115\) | −3.22917 | − | 10.3485i | −0.301121 | − | 0.965004i | ||||
\(116\) | 0 | 0.000268027i | 0 | 2.48857e-5i | ||||||
\(117\) | 0.146505 | + | 2.56687i | 0.0135444 | + | 0.237307i | ||||
\(118\) | −9.51716 | + | 9.51716i | −0.876126 | + | 0.876126i | ||||
\(119\) | −1.87032 | −0.171452 | ||||||||
\(120\) | −8.20649 | + | 7.25115i | −0.749147 | + | 0.661937i | ||||
\(121\) | 10.7612 | 0.978295 | ||||||||
\(122\) | 3.65184 | − | 3.65184i | 0.330622 | − | 0.330622i | ||||
\(123\) | 11.2485 | − | 5.03954i | 1.01424 | − | 0.454400i | ||||
\(124\) | 0.00123647i | 0.000111039i | ||||||||
\(125\) | 1.36065 | + | 11.0972i | 0.121701 | + | 0.992567i | ||||
\(126\) | 6.66870 | − | 7.47601i | 0.594095 | − | 0.666016i | ||||
\(127\) | 7.09372 | + | 7.09372i | 0.629466 | + | 0.629466i | 0.947934 | − | 0.318468i | \(-0.103168\pi\) |
−0.318468 | + | 0.947934i | \(0.603168\pi\) | |||||||
\(128\) | 8.00741 | + | 8.00741i | 0.707762 | + | 0.707762i | ||||
\(129\) | 9.48688 | + | 3.61637i | 0.835273 | + | 0.318403i | ||||
\(130\) | 1.25891 | − | 2.40092i | 0.110413 | − | 0.210575i | ||||
\(131\) | 13.4920i | 1.17881i | 0.807839 | + | 0.589403i | \(0.200637\pi\) | ||||
−0.807839 | + | 0.589403i | \(0.799363\pi\) | |||||||
\(132\) | −0.000427858 | 0 | 0.000954999i | −3.72403e−5 | 0 | 8.31220e-5i | ||||
\(133\) | 2.43886 | − | 2.43886i | 0.211476 | − | 0.211476i | ||||
\(134\) | −9.47080 | −0.818153 | ||||||||
\(135\) | −8.17704 | − | 8.25446i | −0.703767 | − | 0.710430i | ||||
\(136\) | 2.24033 | 0.192107 | ||||||||
\(137\) | 12.2568 | − | 12.2568i | 1.04717 | − | 1.04717i | 0.0483356 | − | 0.998831i | \(-0.484608\pi\) |
0.998831 | − | 0.0483356i | \(-0.0153917\pi\) | |||||||
\(138\) | −4.85686 | − | 10.8407i | −0.413443 | − | 0.922823i | ||||
\(139\) | − | 1.52125i | − | 0.129031i | −0.997917 | − | 0.0645155i | \(-0.979450\pi\) | ||
0.997917 | − | 0.0645155i | \(-0.0205502\pi\) | |||||||
\(140\) | −0.00623029 | + | 0.00194411i | −0.000526556 | + | 0.000164307i | ||||
\(141\) | 14.5996 | + | 5.56532i | 1.22951 | + | 0.468684i | ||||
\(142\) | 0.0866040 | + | 0.0866040i | 0.00726765 | + | 0.00726765i | ||||
\(143\) | −0.296109 | − | 0.296109i | −0.0247619 | − | 0.0247619i | ||||
\(144\) | −7.99291 | + | 8.96054i | −0.666076 | + | 0.746712i | ||||
\(145\) | 0.429274 | + | 0.225086i | 0.0356493 | + | 0.0186924i | ||||
\(146\) | − | 3.89881i | − | 0.322668i | ||||||
\(147\) | 2.25682 | − | 1.01110i | 0.186139 | − | 0.0833940i | ||||
\(148\) | 0.00647044 | − | 0.00647044i | 0.000531867 | − | 0.000531867i | ||||
\(149\) | −19.3963 | −1.58900 | −0.794502 | − | 0.607261i | \(-0.792268\pi\) | ||||
−0.794502 | + | 0.607261i | \(0.792268\pi\) | |||||||
\(150\) | 2.92098 | + | 11.8979i | 0.238497 | + | 0.971462i | ||||
\(151\) | −18.4786 | −1.50376 | −0.751882 | − | 0.659298i | \(-0.770854\pi\) | ||||
−0.751882 | + | 0.659298i | \(0.770854\pi\) | |||||||
\(152\) | −2.92134 | + | 2.92134i | −0.236952 | + | 0.236952i | ||||
\(153\) | 0.135446 | + | 2.37310i | 0.0109502 | + | 0.191854i | ||||
\(154\) | 1.63171i | 0.131487i | ||||||||
\(155\) | −1.98035 | − | 1.03838i | −0.159065 | − | 0.0834046i | ||||
\(156\) | 0.000653764 | − | 0.00171503i | 5.23430e−5 | − | 0.000137312i | ||||
\(157\) | 16.0623 | + | 16.0623i | 1.28191 | + | 1.28191i | 0.939578 | + | 0.342336i | \(0.111218\pi\) |
0.342336 | + | 0.939578i | \(0.388782\pi\) | |||||||
\(158\) | −8.96330 | − | 8.96330i | −0.713082 | − | 0.713082i | ||||
\(159\) | 6.04528 | − | 15.8587i | 0.479422 | − | 1.25768i | ||||
\(160\) | 0.0149303 | − | 0.00465887i | 0.00118034 | − | 0.000368316i | ||||
\(161\) | 11.4442i | 0.901927i | ||||||||
\(162\) | −9.96866 | − | 7.91998i | −0.783212 | − | 0.622252i | ||||
\(163\) | 3.67219 | − | 3.67219i | 0.287628 | − | 0.287628i | −0.548514 | − | 0.836142i | \(-0.684806\pi\) |
0.836142 | + | 0.548514i | \(0.184806\pi\) | |||||||
\(164\) | −0.00879913 | −0.000687096 | ||||||||
\(165\) | 1.88884 | + | 0.116737i | 0.147046 | + | 0.00908800i | ||||
\(166\) | 0.692110 | 0.0537181 | ||||||||
\(167\) | 14.2829 | − | 14.2829i | 1.10524 | − | 1.10524i | 0.111477 | − | 0.993767i | \(-0.464442\pi\) |
0.993767 | − | 0.111477i | \(-0.0355581\pi\) | |||||||
\(168\) | 10.5503 | − | 4.72674i | 0.813973 | − | 0.364676i | ||||
\(169\) | 12.2655i | 0.943502i | ||||||||
\(170\) | 1.16387 | − | 2.21968i | 0.0892650 | − | 0.170242i | ||||
\(171\) | −3.27110 | − | 2.91786i | −0.250147 | − | 0.223134i | ||||
\(172\) | −0.00512501 | − | 0.00512501i | −0.000390778 | − | 0.000390778i | ||||
\(173\) | 3.63506 | + | 3.63506i | 0.276369 | + | 0.276369i | 0.831658 | − | 0.555289i | \(-0.187392\pi\) |
−0.555289 | + | 0.831658i | \(0.687392\pi\) | |||||||
\(174\) | 0.496297 | + | 0.189187i | 0.0376242 | + | 0.0143422i | ||||
\(175\) | 2.11844 | − | 11.6111i | 0.160139 | − | 0.877718i | ||||
\(176\) | − | 1.95572i | − | 0.147418i | ||||||
\(177\) | −6.73767 | − | 15.0388i | −0.506434 | − | 1.13038i | ||||
\(178\) | −12.2212 | + | 12.2212i | −0.916021 | + | 0.916021i | ||||
\(179\) | −20.8745 | −1.56023 | −0.780116 | − | 0.625635i | \(-0.784840\pi\) | ||||
−0.780116 | + | 0.625635i | \(0.784840\pi\) | |||||||
\(180\) | 0.00291792 | + | 0.00776433i | 0.000217489 | + | 0.000578719i | ||||
\(181\) | −19.2211 | −1.42870 | −0.714348 | − | 0.699791i | \(-0.753277\pi\) | ||||
−0.714348 | + | 0.699791i | \(0.753277\pi\) | |||||||
\(182\) | −2.02366 | + | 2.02366i | −0.150004 | + | 0.150004i | ||||
\(183\) | 2.58532 | + | 5.77054i | 0.191112 | + | 0.426571i | ||||
\(184\) | − | 13.7082i | − | 1.01058i | ||||||
\(185\) | 4.92929 | + | 15.7969i | 0.362409 | + | 1.16141i | ||||
\(186\) | −2.28954 | − | 0.872765i | −0.167877 | − | 0.0639942i | ||||
\(187\) | −0.273756 | − | 0.273756i | −0.0200190 | − | 0.0200190i | ||||
\(188\) | −0.00788700 | − | 0.00788700i | −0.000575219 | − | 0.000575219i | ||||
\(189\) | 5.64472 | + | 10.8898i | 0.410593 | + | 0.792115i | ||||
\(190\) | 1.37676 | + | 4.41210i | 0.0998804 | + | 0.320087i | ||||
\(191\) | − | 24.3776i | − | 1.76390i | −0.471339 | − | 0.881952i | \(-0.656229\pi\) | ||
0.471339 | − | 0.881952i | \(-0.343771\pi\) | |||||||
\(192\) | −12.6375 | + | 5.66184i | −0.912032 | + | 0.408608i | ||||
\(193\) | −5.95019 | + | 5.95019i | −0.428304 | + | 0.428304i | −0.888050 | − | 0.459746i | \(-0.847940\pi\) |
0.459746 | + | 0.888050i | \(0.347940\pi\) | |||||||
\(194\) | −2.66954 | −0.191662 | ||||||||
\(195\) | 2.19778 | + | 2.48734i | 0.157386 | + | 0.178122i | ||||
\(196\) | −0.00176539 | −0.000126100 | ||||||||
\(197\) | 15.7539 | − | 15.7539i | 1.12242 | − | 1.12242i | 0.131046 | − | 0.991376i | \(-0.458167\pi\) |
0.991376 | − | 0.131046i | \(-0.0418334\pi\) | |||||||
\(198\) | 2.07034 | − | 0.118166i | 0.147133 | − | 0.00839769i | ||||
\(199\) | 4.09660i | 0.290400i | 0.989402 | + | 0.145200i | \(0.0463826\pi\) | ||||
−0.989402 | + | 0.145200i | \(0.953617\pi\) | |||||||
\(200\) | −2.53753 | + | 13.9082i | −0.179431 | + | 0.983456i | ||||
\(201\) | 4.13034 | − | 10.8352i | 0.291332 | − | 0.764255i | ||||
\(202\) | 13.5545 | + | 13.5545i | 0.953689 | + | 0.953689i | ||||
\(203\) | −0.361821 | − | 0.361821i | −0.0253948 | − | 0.0253948i | ||||
\(204\) | 0.000604413 | − | 0.00158557i | 4.23174e−5 | − | 0.000111012i | ||||
\(205\) | 7.38942 | − | 14.0927i | 0.516099 | − | 0.984280i | ||||
\(206\) | 6.48022i | 0.451499i | ||||||||
\(207\) | 14.5206 | − | 0.828771i | 1.00925 | − | 0.0576035i | ||||
\(208\) | 2.42550 | − | 2.42550i | 0.168178 | − | 0.168178i | ||||
\(209\) | 0.713946 | 0.0493847 | ||||||||
\(210\) | 0.797803 | − | 12.9087i | 0.0550537 | − | 0.890783i | ||||
\(211\) | −0.945083 | −0.0650622 | −0.0325311 | − | 0.999471i | \(-0.510357\pi\) | ||||
−0.0325311 | + | 0.999471i | \(0.510357\pi\) | |||||||
\(212\) | −0.00856719 | + | 0.00856719i | −0.000588397 | + | 0.000588397i | ||||
\(213\) | −0.136850 | + | 0.0613113i | −0.00937677 | + | 0.00420098i | ||||
\(214\) | 11.3427i | 0.775372i | ||||||||
\(215\) | 12.5122 | − | 3.90432i | 0.853323 | − | 0.266272i | ||||
\(216\) | −6.76143 | − | 13.0441i | −0.460057 | − | 0.887541i | ||||
\(217\) | 1.66917 | + | 1.66917i | 0.113310 | + | 0.113310i | ||||
\(218\) | 14.9791 | + | 14.9791i | 1.01451 | + | 1.01451i | ||||
\(219\) | 4.46049 | + | 1.70032i | 0.301412 | + | 0.114897i | ||||
\(220\) | −0.00119648 | 0.000627363i | −8.06665e−5 | 4.22968e-5i | ||||||
\(221\) | − | 0.679030i | − | 0.0456765i | ||||||
\(222\) | 7.41395 | + | 16.5483i | 0.497592 | + | 1.11065i | ||||
\(223\) | 3.30852 | − | 3.30852i | 0.221555 | − | 0.221555i | −0.587598 | − | 0.809153i | \(-0.699926\pi\) |
0.809153 | + | 0.587598i | \(0.199926\pi\) | |||||||
\(224\) | −0.0165111 | −0.00110319 | ||||||||
\(225\) | −14.8858 | − | 1.84705i | −0.992390 | − | 0.123137i | ||||
\(226\) | 1.21408 | 0.0807596 | ||||||||
\(227\) | 4.51141 | − | 4.51141i | 0.299433 | − | 0.299433i | −0.541359 | − | 0.840792i | \(-0.682090\pi\) |
0.840792 | + | 0.541359i | \(0.182090\pi\) | |||||||
\(228\) | 0.00127941 | + | 0.00285569i | 8.47308e−5 | + | 0.000189123i | ||||
\(229\) | 23.0217i | 1.52132i | 0.649151 | + | 0.760660i | \(0.275124\pi\) | ||||
−0.649151 | + | 0.760660i | \(0.724876\pi\) | |||||||
\(230\) | −13.5819 | − | 7.12155i | −0.895562 | − | 0.469581i | ||||
\(231\) | −1.86677 | − | 0.711608i | −0.122825 | − | 0.0468204i | ||||
\(232\) | 0.433400 | + | 0.433400i | 0.0284541 | + | 0.0284541i | ||||
\(233\) | −19.6190 | − | 19.6190i | −1.28528 | − | 1.28528i | −0.937618 | − | 0.347666i | \(-0.886974\pi\) |
−0.347666 | − | 0.937618i | \(-0.613026\pi\) | |||||||
\(234\) | 2.71421 | + | 2.42111i | 0.177433 | + | 0.158273i | ||||
\(235\) | 19.2553 | − | 6.00845i | 1.25608 | − | 0.391948i | ||||
\(236\) | 0.0117641i | 0.000765777i | ||||||||
\(237\) | 14.1636 | − | 6.34556i | 0.920023 | − | 0.412189i | ||||
\(238\) | −1.87090 | + | 1.87090i | −0.121272 | + | 0.121272i | ||||
\(239\) | 8.66511 | 0.560499 | 0.280250 | − | 0.959927i | \(-0.409583\pi\) | ||||
0.280250 | + | 0.959927i | \(0.409583\pi\) | |||||||
\(240\) | −0.956225 | + | 15.4720i | −0.0617241 | + | 0.998712i | ||||
\(241\) | −19.4767 | −1.25460 | −0.627302 | − | 0.778776i | \(-0.715841\pi\) | ||||
−0.627302 | + | 0.778776i | \(0.715841\pi\) | |||||||
\(242\) | 10.7646 | − | 10.7646i | 0.691973 | − | 0.691973i | ||||
\(243\) | 13.4084 | − | 7.95076i | 0.860150 | − | 0.510042i | ||||
\(244\) | − | 0.00451401i | − | 0.000288980i | ||||||
\(245\) | 1.48256 | − | 2.82747i | 0.0947173 | − | 0.180640i | ||||
\(246\) | 6.21086 | − | 16.2931i | 0.395990 | − | 1.03881i | ||||
\(247\) | 0.885442 | + | 0.885442i | 0.0563394 | + | 0.0563394i | ||||
\(248\) | −1.99938 | − | 1.99938i | −0.126961 | − | 0.126961i | ||||
\(249\) | −0.301838 | + | 0.791817i | −0.0191282 | + | 0.0501794i | ||||
\(250\) | 12.4617 | + | 9.73959i | 0.788150 | + | 0.615986i | ||||
\(251\) | 6.66638i | 0.420778i | 0.977618 | + | 0.210389i | \(0.0674731\pi\) | ||||
−0.977618 | + | 0.210389i | \(0.932527\pi\) | |||||||
\(252\) | −0.000498959 | − | 0.00874208i | −3.14315e−5 | − | 0.000550699i | ||||
\(253\) | −1.67507 | + | 1.67507i | −0.105311 | + | 0.105311i | ||||
\(254\) | 14.1918 | 0.890474 | ||||||||
\(255\) | 2.03188 | + | 2.29958i | 0.127241 | + | 0.144005i | ||||
\(256\) | 0.0296754 | 0.00185471 | ||||||||
\(257\) | −4.13272 | + | 4.13272i | −0.257792 | + | 0.257792i | −0.824155 | − | 0.566364i | \(-0.808350\pi\) |
0.566364 | + | 0.824155i | \(0.308350\pi\) | |||||||
\(258\) | 13.1073 | − | 5.87233i | 0.816024 | − | 0.365595i | ||||
\(259\) | − | 17.4694i | − | 1.08550i | ||||||
\(260\) | −0.000705820 | − | 0.00226194i | −4.37731e−5 | − | 0.000140280i | ||||
\(261\) | −0.432883 | + | 0.485288i | −0.0267948 | + | 0.0300386i | ||||
\(262\) | 13.4962 | + | 13.4962i | 0.833799 | + | 0.833799i | ||||
\(263\) | 2.14753 | + | 2.14753i | 0.132423 | + | 0.132423i | 0.770211 | − | 0.637789i | \(-0.220151\pi\) |
−0.637789 | + | 0.770211i | \(0.720151\pi\) | |||||||
\(264\) | 2.23608 | + | 0.852387i | 0.137621 | + | 0.0524608i | ||||
\(265\) | −6.52663 | − | 20.9159i | −0.400928 | − | 1.28485i | ||||
\(266\) | − | 4.87923i | − | 0.299165i | ||||||
\(267\) | −8.65203 | − | 19.3117i | −0.529496 | − | 1.18186i | ||||
\(268\) | −0.00585339 | + | 0.00585339i | −0.000357553 | + | 0.000357553i | ||||
\(269\) | 16.1691 | 0.985846 | 0.492923 | − | 0.870073i | \(-0.335928\pi\) | ||||
0.492923 | + | 0.870073i | \(0.335928\pi\) | |||||||
\(270\) | −16.4366 | − | 0.0774414i | −1.00030 | − | 0.00471293i | ||||
\(271\) | 27.6629 | 1.68040 | 0.840200 | − | 0.542277i | \(-0.182438\pi\) | ||||
0.840200 | + | 0.542277i | \(0.182438\pi\) | |||||||
\(272\) | 2.24241 | − | 2.24241i | 0.135966 | − | 0.135966i | ||||
\(273\) | −1.43265 | − | 3.19773i | −0.0867078 | − | 0.193536i | ||||
\(274\) | − | 24.5211i | − | 1.48138i | ||||||
\(275\) | 2.00958 | − | 1.38943i | 0.121182 | − | 0.0837860i | ||||
\(276\) | −0.00970183 | − | 0.00369830i | −0.000583981 | − | 0.000222612i | ||||
\(277\) | 16.0299 | + | 16.0299i | 0.963141 | + | 0.963141i | 0.999344 | − | 0.0362031i | \(-0.0115263\pi\) |
−0.0362031 | + | 0.999344i | \(0.511526\pi\) | |||||||
\(278\) | −1.52172 | − | 1.52172i | −0.0912669 | − | 0.0912669i | ||||
\(279\) | 1.99699 | − | 2.23875i | 0.119557 | − | 0.134031i | ||||
\(280\) | 6.93076 | − | 13.2180i | 0.414192 | − | 0.789928i | ||||
\(281\) | 27.0910i | 1.61611i | 0.589104 | + | 0.808057i | \(0.299481\pi\) | ||||
−0.589104 | + | 0.808057i | \(0.700519\pi\) | |||||||
\(282\) | 20.1711 | − | 9.03707i | 1.20117 | − | 0.538150i | ||||
\(283\) | −7.86447 | + | 7.86447i | −0.467494 | + | 0.467494i | −0.901102 | − | 0.433608i | \(-0.857240\pi\) |
0.433608 | + | 0.901102i | \(0.357240\pi\) | |||||||
\(284\) | 0.000107051 | 0 | 6.35228e−6 | 0 | ||||||
\(285\) | −5.64813 | − | 0.349075i | −0.334567 | − | 0.0206774i | ||||
\(286\) | −0.592401 | −0.0350294 | ||||||||
\(287\) | −11.8783 | + | 11.8783i | −0.701154 | + | 0.701154i | ||||
\(288\) | 0.00119571 | + | 0.0209496i | 7.04577e−5 | + | 0.00123447i | ||||
\(289\) | 16.3722i | 0.963072i | ||||||||
\(290\) | 0.654563 | − | 0.204251i | 0.0384372 | − | 0.0119940i | ||||
\(291\) | 1.16422 | − | 3.05412i | 0.0682479 | − | 0.179036i | ||||
\(292\) | −0.00240965 | − | 0.00240965i | −0.000141014 | − | 0.000141014i | ||||
\(293\) | 10.7917 | + | 10.7917i | 0.630460 | + | 0.630460i | 0.948183 | − | 0.317723i | \(-0.102918\pi\) |
−0.317723 | + | 0.948183i | \(0.602918\pi\) | |||||||
\(294\) | 1.24610 | − | 3.26892i | 0.0726742 | − | 0.190648i | ||||
\(295\) | −18.8415 | − | 9.87936i | −1.09699 | − | 0.575199i | ||||
\(296\) | 20.9254i | 1.21627i | ||||||||
\(297\) | −0.767714 | + | 2.42014i | −0.0445473 | + | 0.140431i | ||||
\(298\) | −19.4023 | + | 19.4023i | −1.12394 | + | 1.12394i | ||||
\(299\) | −4.15487 | −0.240282 | ||||||||
\(300\) | 0.00915877 | + | 0.00554817i | 0.000528782 | + | 0.000320324i | ||||
\(301\) | −13.8369 | −0.797546 | ||||||||
\(302\) | −18.4843 | + | 18.4843i | −1.06365 | + | 1.06365i | ||||
\(303\) | −21.4184 | + | 9.59588i | −1.23046 | + | 0.551269i | ||||
\(304\) | 5.84811i | 0.335412i | ||||||||
\(305\) | 7.22967 | + | 3.79082i | 0.413970 | + | 0.217062i | ||||
\(306\) | 2.50932 | + | 2.23835i | 0.143448 | + | 0.127958i | ||||
\(307\) | 12.8025 | + | 12.8025i | 0.730678 | + | 0.730678i | 0.970754 | − | 0.240076i | \(-0.0771723\pi\) |
−0.240076 | + | 0.970754i | \(0.577172\pi\) | |||||||
\(308\) | 0.00100847 | + | 0.00100847i | 5.74629e−5 | + | 5.74629e-5i | ||||
\(309\) | −7.41378 | − | 2.82611i | −0.421755 | − | 0.160772i | ||||
\(310\) | −3.01966 | + | 0.942258i | −0.171505 | + | 0.0535167i | ||||
\(311\) | 21.6644i | 1.22847i | 0.789121 | + | 0.614237i | \(0.210536\pi\) | ||||
−0.789121 | + | 0.614237i | \(0.789464\pi\) | |||||||
\(312\) | 1.71607 | + | 3.83035i | 0.0971534 | + | 0.216851i | ||||
\(313\) | 15.5220 | − | 15.5220i | 0.877353 | − | 0.877353i | −0.115907 | − | 0.993260i | \(-0.536977\pi\) |
0.993260 | + | 0.115907i | \(0.0369774\pi\) | |||||||
\(314\) | 32.1346 | 1.81346 | ||||||||
\(315\) | 14.4204 | + | 6.54238i | 0.812497 | + | 0.368621i | ||||
\(316\) | −0.0110795 | −0.000623268 | ||||||||
\(317\) | −13.7279 | + | 13.7279i | −0.771035 | + | 0.771035i | −0.978288 | − | 0.207252i | \(-0.933548\pi\) |
0.207252 | + | 0.978288i | \(0.433548\pi\) | |||||||
\(318\) | −9.81644 | − | 21.9107i | −0.550479 | − | 1.22869i | ||||
\(319\) | − | 0.105919i | − | 0.00593030i | ||||||
\(320\) | −8.30189 | + | 15.8330i | −0.464090 | + | 0.885089i | ||||
\(321\) | −12.9768 | − | 4.94671i | −0.724293 | − | 0.276098i | ||||
\(322\) | 11.4477 | + | 11.4477i | 0.637956 | + | 0.637956i | ||||
\(323\) | 0.818603 | + | 0.818603i | 0.0455483 | + | 0.0455483i | ||||
\(324\) | −0.0110560 | + | 0.00126618i | −0.000614222 | + | 7.03433e-5i | ||||
\(325\) | 4.21549 | + | 0.769111i | 0.233833 | + | 0.0426626i | ||||
\(326\) | − | 7.34665i | − | 0.406893i | ||||||
\(327\) | −23.6696 | + | 10.6045i | −1.30893 | + | 0.586428i | ||||
\(328\) | 14.2282 | − | 14.2282i | 0.785621 | − | 0.785621i | ||||
\(329\) | −21.2940 | −1.17397 | ||||||||
\(330\) | 2.00620 | − | 1.77265i | 0.110438 | − | 0.0975814i | ||||
\(331\) | −16.4734 | −0.905461 | −0.452731 | − | 0.891647i | \(-0.649550\pi\) | ||||
−0.452731 | + | 0.891647i | \(0.649550\pi\) | |||||||
\(332\) | 0.000427756 | 0 | 0.000427756i | 2.34762e−5 | 0 | 2.34762e-5i | ||||
\(333\) | −22.1656 | + | 1.26511i | −1.21467 | + | 0.0693277i | ||||
\(334\) | − | 28.5746i | − | 1.56353i | ||||||
\(335\) | −4.45921 | − | 14.2905i | −0.243633 | − | 0.780771i | ||||
\(336\) | 5.82896 | − | 15.2912i | 0.317996 | − | 0.834204i | ||||
\(337\) | 18.6177 | + | 18.6177i | 1.01417 | + | 1.01417i | 0.999898 | + | 0.0142748i | \(0.00454395\pi\) |
0.0142748 | + | 0.999898i | \(0.495456\pi\) | |||||||
\(338\) | 12.2693 | + | 12.2693i | 0.667363 | + | 0.667363i | ||||
\(339\) | −0.529477 | + | 1.38899i | −0.0287573 | + | 0.0754394i | ||||
\(340\) | −0.000652540 | − | 0.00209120i | −3.53889e−5 | − | 0.000113411i | ||||
\(341\) | 0.488628i | 0.0264607i | ||||||||
\(342\) | −6.19087 | + | 0.353347i | −0.334764 | + | 0.0191068i | ||||
\(343\) | −14.0673 | + | 14.0673i | −0.759565 | + | 0.759565i | ||||
\(344\) | 16.5743 | 0.893626 | ||||||||
\(345\) | 14.0707 | − | 12.4327i | 0.757542 | − | 0.669355i | ||||
\(346\) | 7.27238 | 0.390965 | ||||||||
\(347\) | −21.7272 | + | 21.7272i | −1.16637 | + | 1.16637i | −0.183322 | + | 0.983053i | \(0.558685\pi\) |
−0.983053 | + | 0.183322i | \(0.941315\pi\) | |||||||
\(348\) | 0.000423661 | 0 | 0.000189808i | 2.27106e−5 | 0 | 1.01748e-5i | ||||
\(349\) | 2.53205i | 0.135537i | 0.997701 | + | 0.0677687i | \(0.0215880\pi\) | ||||
−0.997701 | + | 0.0677687i | \(0.978412\pi\) | |||||||
\(350\) | −9.49562 | − | 13.7338i | −0.507562 | − | 0.734102i | ||||
\(351\) | −3.95360 | + | 2.04935i | −0.211028 | + | 0.109386i | ||||
\(352\) | −0.00241670 | − | 0.00241670i | −0.000128811 | − | 0.000128811i | ||||
\(353\) | −5.70119 | − | 5.70119i | −0.303444 | − | 0.303444i | 0.538916 | − | 0.842360i | \(-0.318834\pi\) |
−0.842360 | + | 0.538916i | \(0.818834\pi\) | |||||||
\(354\) | −21.7832 | − | 8.30368i | −1.15776 | − | 0.441336i | ||||
\(355\) | −0.0899000 | + | 0.171453i | −0.00477140 | + | 0.00909978i | ||||
\(356\) | 0.0151066i | 0.000800648i | ||||||||
\(357\) | −1.32450 | − | 2.95635i | −0.0701000 | − | 0.156466i | ||||
\(358\) | −20.8809 | + | 20.8809i | −1.10359 | + | 1.10359i | ||||
\(359\) | −16.7850 | −0.885877 | −0.442938 | − | 0.896552i | \(-0.646064\pi\) | ||||
−0.442938 | + | 0.896552i | \(0.646064\pi\) | |||||||
\(360\) | −17.2732 | − | 7.83667i | −0.910378 | − | 0.413029i | ||||
\(361\) | 16.8651 | 0.887638 | ||||||||
\(362\) | −19.2271 | + | 19.2271i | −1.01055 | + | 1.01055i | ||||
\(363\) | 7.62077 | + | 17.0099i | 0.399987 | + | 0.892788i | ||||
\(364\) | 0.00250143i | 0.000131110i | ||||||||
\(365\) | 5.88290 | − | 1.83571i | 0.307925 | − | 0.0960855i | ||||
\(366\) | 8.35844 | + | 3.18621i | 0.436903 | + | 0.166546i | ||||
\(367\) | −25.1508 | − | 25.1508i | −1.31286 | − | 1.31286i | −0.919299 | − | 0.393560i | \(-0.871243\pi\) |
−0.393560 | − | 0.919299i | \(-0.628757\pi\) | |||||||
\(368\) | −13.7209 | − | 13.7209i | −0.715252 | − | 0.715252i | ||||
\(369\) | 15.9316 | + | 14.2112i | 0.829368 | + | 0.739807i | ||||
\(370\) | 20.7326 | + | 10.8710i | 1.07784 | + | 0.565155i | ||||
\(371\) | 23.1304i | 1.20087i | ||||||||
\(372\) | −0.00195445 | 0.000875632i | −0.000101334 | 4.53994e-5i | ||||||
\(373\) | −1.28708 | + | 1.28708i | −0.0666427 | + | 0.0666427i | −0.739643 | − | 0.673000i | \(-0.765005\pi\) |
0.673000 | + | 0.739643i | \(0.265005\pi\) | |||||||
\(374\) | −0.547682 | −0.0283200 | ||||||||
\(375\) | −16.5774 | + | 10.0094i | −0.856054 | + | 0.516886i | ||||
\(376\) | 25.5066 | 1.31540 | ||||||||
\(377\) | 0.131361 | − | 0.131361i | 0.00676544 | − | 0.00676544i | ||||
\(378\) | 16.5396 | + | 5.24669i | 0.850706 | + | 0.269861i | ||||
\(379\) | − | 26.9785i | − | 1.38579i | −0.721038 | − | 0.692896i | \(-0.756335\pi\) | ||
0.721038 | − | 0.692896i | \(-0.243665\pi\) | |||||||
\(380\) | 0.00357778 | + | 0.00187598i | 0.000183536 | + | 9.62357e-5i | ||||
\(381\) | −6.18924 | + | 16.2363i | −0.317084 | + | 0.831812i | ||||
\(382\) | −24.3852 | − | 24.3852i | −1.24765 | − | 1.24765i | ||||
\(383\) | −9.28532 | − | 9.28532i | −0.474458 | − | 0.474458i | 0.428896 | − | 0.903354i | \(-0.358903\pi\) |
−0.903354 | + | 0.428896i | \(0.858903\pi\) | |||||||
\(384\) | −6.98643 | + | 18.3276i | −0.356525 | + | 0.935277i | ||||
\(385\) | −2.46208 | + | 0.768270i | −0.125479 | + | 0.0391547i | ||||
\(386\) | 11.9041i | 0.605901i | ||||||||
\(387\) | 1.00205 | + | 17.5566i | 0.0509370 | + | 0.892450i | ||||
\(388\) | −0.00164990 | + | 0.00164990i | −8.37611e−5 | + | 8.37611e-5i | ||||
\(389\) | −5.45183 | −0.276419 | −0.138209 | − | 0.990403i | \(-0.544135\pi\) | ||||
−0.138209 | + | 0.990403i | \(0.544135\pi\) | |||||||
\(390\) | 4.68657 | + | 0.289647i | 0.237314 | + | 0.0146669i | ||||
\(391\) | −3.84123 | −0.194259 | ||||||||
\(392\) | 2.85465 | − | 2.85465i | 0.144181 | − | 0.144181i | ||||
\(393\) | −21.3264 | + | 9.55464i | −1.07577 | + | 0.481968i | ||||
\(394\) | − | 31.5176i | − | 1.58783i | ||||||
\(395\) | 9.30442 | − | 17.7449i | 0.468156 | − | 0.892845i | ||||
\(396\) | 0.00120654 | − | 0.00135260i | 6.06307e−5 | − | 6.79707e-5i | ||||
\(397\) | 12.6464 | + | 12.6464i | 0.634706 | + | 0.634706i | 0.949245 | − | 0.314538i | \(-0.101850\pi\) |
−0.314538 | + | 0.949245i | \(0.601850\pi\) | |||||||
\(398\) | 4.09787 | + | 4.09787i | 0.205408 | + | 0.205408i | ||||
\(399\) | 5.58214 | + | 2.12789i | 0.279457 | + | 0.106528i | ||||
\(400\) | 11.3812 | + | 16.4610i | 0.569059 | + | 0.823048i | ||||
\(401\) | − | 23.2395i | − | 1.16053i | −0.814429 | − | 0.580264i | \(-0.802950\pi\) | ||
0.814429 | − | 0.580264i | \(-0.197050\pi\) | |||||||
\(402\) | −6.70692 | − | 14.9701i | −0.334511 | − | 0.746643i | ||||
\(403\) | −0.606001 | + | 0.606001i | −0.0301870 | + | 0.0301870i | ||||
\(404\) | 0.0167546 | 0.000833571 | ||||||||
\(405\) | 7.25680 | − | 18.7707i | 0.360593 | − | 0.932723i | ||||
\(406\) | −0.723865 | −0.0359248 | ||||||||
\(407\) | 2.55698 | − | 2.55698i | 0.126745 | − | 0.126745i | ||||
\(408\) | 1.58653 | + | 3.54120i | 0.0785449 | + | 0.175316i | ||||
\(409\) | − | 20.9451i | − | 1.03567i | −0.855480 | − | 0.517835i | \(-0.826738\pi\) | ||
0.855480 | − | 0.517835i | \(-0.173262\pi\) | |||||||
\(410\) | −6.70540 | − | 21.4888i | −0.331156 | − | 1.06126i | ||||
\(411\) | 28.0537 | + | 10.6940i | 1.38379 | + | 0.527495i | ||||
\(412\) | 0.00400508 | + | 0.00400508i | 0.000197316 | + | 0.000197316i | ||||
\(413\) | 15.8808 | + | 15.8808i | 0.781444 | + | 0.781444i | ||||
\(414\) | 13.6961 | − | 15.3541i | 0.673125 | − | 0.754613i | ||||
\(415\) | 0.325872 | + | 1.04432i | 0.0159964 | + | 0.0512637i | ||||
\(416\) | − | 0.00599443i | − | 0.000293901i | ||||||
\(417\) | 2.40459 | − | 1.07730i | 0.117753 | − | 0.0527558i | ||||
\(418\) | 0.714167 | − | 0.714167i | 0.0349310 | − | 0.0349310i | ||||
\(419\) | 8.76420 | 0.428159 | 0.214080 | − | 0.976816i | \(-0.431325\pi\) | ||||
0.214080 | + | 0.976816i | \(0.431325\pi\) | |||||||
\(420\) | −0.00748508 | − | 0.00847124i | −0.000365234 | − | 0.000413354i | ||||
\(421\) | 6.41350 | 0.312575 | 0.156287 | − | 0.987712i | \(-0.450047\pi\) | ||||
0.156287 | + | 0.987712i | \(0.450047\pi\) | |||||||
\(422\) | −0.945375 | + | 0.945375i | −0.0460202 | + | 0.0460202i | ||||
\(423\) | 1.54208 | + | 27.0182i | 0.0749785 | + | 1.31367i | ||||
\(424\) | − | 27.7063i | − | 1.34554i | ||||||
\(425\) | 3.89727 | + | 0.711052i | 0.189045 | + | 0.0344911i | ||||
\(426\) | −0.0755616 | + | 0.198222i | −0.00366097 | + | 0.00960389i | ||||
\(427\) | −6.09364 | − | 6.09364i | −0.294892 | − | 0.294892i | ||||
\(428\) | 0.00701032 | + | 0.00701032i | 0.000338857 | + | 0.000338857i | ||||
\(429\) | 0.258354 | − | 0.677744i | 0.0124734 | − | 0.0327218i | ||||
\(430\) | 8.61052 | − | 16.4216i | 0.415236 | − | 0.791918i | ||||
\(431\) | 2.35265i | 0.113323i | 0.998393 | + | 0.0566616i | \(0.0180456\pi\) | ||||
−0.998393 | + | 0.0566616i | \(0.981954\pi\) | |||||||
\(432\) | −19.8239 | − | 6.28854i | −0.953779 | − | 0.302557i | ||||
\(433\) | 16.6004 | − | 16.6004i | 0.797762 | − | 0.797762i | −0.184980 | − | 0.982742i | \(-0.559222\pi\) |
0.982742 | + | 0.184980i | \(0.0592221\pi\) | |||||||
\(434\) | 3.33937 | 0.160295 | ||||||||
\(435\) | −0.0517876 | + | 0.837937i | −0.00248302 | + | 0.0401760i | ||||
\(436\) | 0.0185156 | 0.000886735 | ||||||||
\(437\) | 5.00889 | − | 5.00889i | 0.239608 | − | 0.239608i | ||||
\(438\) | 6.16271 | − | 2.76102i | 0.294466 | − | 0.131927i | ||||
\(439\) | 11.3213i | 0.540337i | 0.962813 | + | 0.270169i | \(0.0870795\pi\) | ||||
−0.962813 | + | 0.270169i | \(0.912921\pi\) | |||||||
\(440\) | 2.94915 | − | 0.920258i | 0.140595 | − | 0.0438716i | ||||
\(441\) | 3.19641 | + | 2.85124i | 0.152210 | + | 0.135773i | ||||
\(442\) | −0.679240 | − | 0.679240i | −0.0323082 | − | 0.0323082i | ||||
\(443\) | 0.123239 | + | 0.123239i | 0.00585525 | + | 0.00585525i | 0.710028 | − | 0.704173i | \(-0.248682\pi\) |
−0.704173 | + | 0.710028i | \(0.748682\pi\) | |||||||
\(444\) | 0.0148098 | + | 0.00564543i | 0.000702840 | + | 0.000267920i | ||||
\(445\) | −24.1948 | − | 12.6864i | −1.14694 | − | 0.601391i | ||||
\(446\) | − | 6.61909i | − | 0.313423i | ||||||
\(447\) | −13.7358 | − | 30.6590i | −0.649682 | − | 1.45012i | ||||
\(448\) | 13.3451 | − | 13.3451i | 0.630495 | − | 0.630495i | ||||
\(449\) | −5.58480 | −0.263563 | −0.131782 | − | 0.991279i | \(-0.542070\pi\) | ||||
−0.131782 | + | 0.991279i | \(0.542070\pi\) | |||||||
\(450\) | −16.7381 | + | 13.0428i | −0.789040 | + | 0.614844i | ||||
\(451\) | −3.47722 | −0.163736 | ||||||||
\(452\) | 0.000750360 | 0 | 0.000750360i | 3.52940e−5 | 0 | 3.52940e-5i | ||||
\(453\) | −13.0859 | − | 29.2084i | −0.614831 | − | 1.37233i | ||||
\(454\) | − | 9.02561i | − | 0.423593i | ||||||
\(455\) | −4.00630 | − | 2.10067i | −0.187818 | − | 0.0984811i | ||||
\(456\) | −6.68647 | − | 2.54886i | −0.313123 | − | 0.119361i | ||||
\(457\) | −18.7342 | − | 18.7342i | −0.876347 | − | 0.876347i | 0.116808 | − | 0.993155i | \(-0.462734\pi\) |
−0.993155 | + | 0.116808i | \(0.962734\pi\) | |||||||
\(458\) | 23.0289 | + | 23.0289i | 1.07607 | + | 1.07607i | ||||
\(459\) | −3.65515 | + | 1.89465i | −0.170608 | + | 0.0884346i | ||||
\(460\) | −0.0127957 | + | 0.00399278i | −0.000596601 | + | 0.000186164i | ||||
\(461\) | − | 1.80178i | − | 0.0839173i | −0.999119 | − | 0.0419587i | \(-0.986640\pi\) | ||
0.999119 | − | 0.0419587i | \(-0.0133598\pi\) | |||||||
\(462\) | −2.57918 | + | 1.15552i | −0.119994 | + | 0.0537598i | ||||
\(463\) | −28.8896 | + | 28.8896i | −1.34261 | + | 1.34261i | −0.449162 | + | 0.893450i | \(0.648277\pi\) |
−0.893450 | + | 0.449162i | \(0.851723\pi\) | |||||||
\(464\) | 0.867605 | 0.0402775 | ||||||||
\(465\) | 0.238909 | − | 3.86561i | 0.0110791 | − | 0.179263i | ||||
\(466\) | −39.2502 | −1.81823 | ||||||||
\(467\) | −1.77213 | + | 1.77213i | −0.0820043 | + | 0.0820043i | −0.746919 | − | 0.664915i | \(-0.768468\pi\) |
0.664915 | + | 0.746919i | \(0.268468\pi\) | |||||||
\(468\) | 0.00317386 | 0.000181150i | 0.000146712 | 8.37366e-6i | ||||||
\(469\) | 15.8035i | 0.729736i | ||||||||
\(470\) | 13.2509 | − | 25.2716i | 0.611220 | − | 1.16569i | ||||
\(471\) | −14.0143 | + | 36.7640i | −0.645745 | + | 1.69399i | ||||
\(472\) | −19.0226 | − | 19.0226i | −0.875584 | − | 0.875584i | ||||
\(473\) | −2.02529 | − | 2.02529i | −0.0931230 | − | 0.0931230i | ||||
\(474\) | 7.82043 | − | 20.5155i | 0.359204 | − | 0.942307i | ||||
\(475\) | −6.00916 | + | 4.15477i | −0.275719 | + | 0.190634i | ||||
\(476\) | 0.00231260i | 0.000105998i | ||||||||
\(477\) | 29.3483 | − | 1.67507i | 1.34377 | − | 0.0766962i | ||||
\(478\) | 8.66779 | − | 8.66779i | 0.396455 | − | 0.396455i | ||||
\(479\) | 36.3824 | 1.66236 | 0.831178 | − | 0.556007i | \(-0.187667\pi\) | ||||
0.831178 | + | 0.556007i | \(0.187667\pi\) | |||||||
\(480\) | 0.0179373 | + | 0.0203005i | 0.000818721 | + | 0.000926587i | ||||
\(481\) | 6.34237 | 0.289187 | ||||||||
\(482\) | −19.4827 | + | 19.4827i | −0.887414 | + | 0.887414i | ||||
\(483\) | −18.0894 | + | 8.10440i | −0.823095 | + | 0.368763i | ||||
\(484\) | − | 0.0133060i | − | 0.000604818i | ||||||
\(485\) | −1.25692 | − | 4.02806i | −0.0570739 | − | 0.182905i | ||||
\(486\) | 5.45933 | − | 21.3658i | 0.247640 | − | 0.969171i | ||||
\(487\) | −16.8813 | − | 16.8813i | −0.764966 | − | 0.764966i | 0.212250 | − | 0.977215i | \(-0.431921\pi\) |
−0.977215 | + | 0.212250i | \(0.931921\pi\) | |||||||
\(488\) | 7.29916 | + | 7.29916i | 0.330417 | + | 0.330417i | ||||
\(489\) | 8.40502 | + | 3.20397i | 0.380088 | + | 0.144888i | ||||
\(490\) | −1.34532 | − | 4.31136i | −0.0607755 | − | 0.194767i | ||||
\(491\) | 3.75278i | 0.169361i | 0.996408 | + | 0.0846803i | \(0.0269869\pi\) | ||||
−0.996408 | + | 0.0846803i | \(0.973013\pi\) | |||||||
\(492\) | −0.00623126 | − | 0.0139085i | −0.000280927 | − | 0.000627042i | ||||
\(493\) | 0.121445 | − | 0.121445i | 0.00546961 | − | 0.00546961i | ||||
\(494\) | 1.77143 | 0.0797005 | ||||||||
\(495\) | 1.15310 | + | 3.06830i | 0.0518279 | + | 0.137910i | ||||
\(496\) | −4.00247 | −0.179716 | ||||||||
\(497\) | 0.144512 | − | 0.144512i | 0.00648224 | − | 0.00648224i | ||||
\(498\) | 0.490130 | + | 1.09399i | 0.0219633 | + | 0.0490230i | ||||
\(499\) | − | 6.14567i | − | 0.275118i | −0.990494 | − | 0.137559i | \(-0.956074\pi\) | ||
0.990494 | − | 0.137559i | \(-0.0439257\pi\) | |||||||
\(500\) | 0.0137214 | − | 0.00168241i | 0.000613642 | − | 7.52399e-5i | ||||
\(501\) | 32.6912 | + | 12.4618i | 1.46053 | + | 0.556750i | ||||
\(502\) | 6.66844 | + | 6.66844i | 0.297627 | + | 0.297627i | ||||
\(503\) | −10.0046 | − | 10.0046i | −0.446084 | − | 0.446084i | 0.447966 | − | 0.894050i | \(-0.352148\pi\) |
−0.894050 | + | 0.447966i | \(0.852148\pi\) | |||||||
\(504\) | 14.9428 | + | 13.3291i | 0.665604 | + | 0.593727i | ||||
\(505\) | −14.0703 | + | 26.8342i | −0.626121 | + | 1.19411i | ||||
\(506\) | 3.35117i | 0.148978i | ||||||||
\(507\) | −19.3877 | + | 8.68606i | −0.861037 | + | 0.385761i | ||||
\(508\) | 0.00877120 | − | 0.00877120i | 0.000389159 | − | 0.000389159i | ||||
\(509\) | −8.38449 | −0.371636 | −0.185818 | − | 0.982584i | \(-0.559494\pi\) | ||||
−0.185818 | + | 0.982584i | \(0.559494\pi\) | |||||||
\(510\) | 4.33279 | + | 0.267782i | 0.191859 | + | 0.0118576i | ||||
\(511\) | −6.50576 | −0.287798 | ||||||||
\(512\) | −15.9851 | + | 15.9851i | −0.706450 | + | 0.706450i | ||||
\(513\) | 2.29566 | − | 7.23684i | 0.101356 | − | 0.319514i | ||||
\(514\) | 8.26799i | 0.364685i | ||||||||
\(515\) | −9.77798 | + | 3.05114i | −0.430869 | + | 0.134449i | ||||
\(516\) | 0.00447154 | − | 0.0117303i | 0.000196849 | − | 0.000516397i | ||||
\(517\) | −3.11677 | − | 3.11677i | −0.137076 | − | 0.137076i | ||||
\(518\) | −17.4748 | − | 17.4748i | −0.767799 | − | 0.767799i | ||||
\(519\) | −3.17158 | + | 8.32005i | −0.139217 | + | 0.365210i | ||||
\(520\) | 4.79888 | + | 2.51625i | 0.210445 | + | 0.110345i | ||||
\(521\) | − | 16.8731i | − | 0.739225i | −0.929186 | − | 0.369613i | \(-0.879490\pi\) | ||
0.929186 | − | 0.369613i | \(-0.120510\pi\) | |||||||
\(522\) | 0.0524213 | + | 0.918455i | 0.00229442 | + | 0.0401997i | ||||
\(523\) | 7.41293 | − | 7.41293i | 0.324145 | − | 0.324145i | −0.526210 | − | 0.850355i | \(-0.676387\pi\) |
0.850355 | + | 0.526210i | \(0.176387\pi\) | |||||||
\(524\) | 0.0166826 | 0.000728781 | ||||||||
\(525\) | 19.8535 | − | 4.87409i | 0.866477 | − | 0.212723i | ||||
\(526\) | 4.29640 | 0.187332 | ||||||||
\(527\) | −0.560255 | + | 0.560255i | −0.0244051 | + | 0.0244051i | ||||
\(528\) | 3.09133 | − | 1.38498i | 0.134533 | − | 0.0602735i | ||||
\(529\) | 0.503846i | 0.0219063i | ||||||||
\(530\) | −27.4510 | − | 14.3937i | −1.19240 | − | 0.625224i | ||||
\(531\) | 18.9999 | − | 21.3000i | 0.824523 | − | 0.924341i | ||||
\(532\) | −0.00301559 | − | 0.00301559i | −0.000130742 | − | 0.000130742i | ||||
\(533\) | −4.31249 | − | 4.31249i | −0.186794 | − | 0.186794i | ||||
\(534\) | −27.9724 | − | 10.6630i | −1.21048 | − | 0.461432i | ||||
\(535\) | −17.1150 | + | 5.34059i | −0.739945 | + | 0.230894i | ||||
\(536\) | − | 18.9299i | − | 0.817647i | ||||||
\(537\) | −14.7826 | − | 32.9955i | −0.637918 | − | 1.42386i | ||||
\(538\) | 16.1741 | − | 16.1741i | 0.697314 | − | 0.697314i | ||||
\(539\) | −0.697646 | −0.0300497 | ||||||||
\(540\) | −0.0102064 | + | 0.0101107i | −0.000439215 | + | 0.000435095i | ||||
\(541\) | 5.37201 | 0.230961 | 0.115480 | − | 0.993310i | \(-0.463159\pi\) | ||||
0.115480 | + | 0.993310i | \(0.463159\pi\) | |||||||
\(542\) | 27.6714 | − | 27.6714i | 1.18859 | − | 1.18859i | ||||
\(543\) | −13.6118 | − | 30.3821i | −0.584138 | − | 1.30382i | ||||
\(544\) | − | 0.00554193i | − | 0.000237608i | ||||||
\(545\) | −15.5492 | + | 29.6547i | −0.666054 | + | 1.27027i | ||||
\(546\) | −4.63181 | − | 1.76563i | −0.198223 | − | 0.0755621i | ||||
\(547\) | 1.42656 | + | 1.42656i | 0.0609951 | + | 0.0609951i | 0.736946 | − | 0.675951i | \(-0.236267\pi\) |
−0.675951 | + | 0.736946i | \(0.736267\pi\) | |||||||
\(548\) | −0.0151552 | − | 0.0151552i | −0.000647397 | − | 0.000647397i | ||||
\(549\) | −7.29045 | + | 8.17303i | −0.311149 | + | 0.348817i | ||||
\(550\) | 0.620338 | − | 3.40006i | 0.0264513 | − | 0.144979i | ||||
\(551\) | 0.316724i | 0.0134929i | ||||||||
\(552\) | 21.6680 | − | 9.70771i | 0.922253 | − | 0.413187i | ||||
\(553\) | −14.9566 | + | 14.9566i | −0.636020 | + | 0.636020i | ||||
\(554\) | 32.0696 | 1.36251 | ||||||||
\(555\) | −21.4788 | + | 18.9784i | −0.911726 | + | 0.805589i | ||||
\(556\) | −0.00188099 | −7.97718e−5 | ||||||||
\(557\) | −15.6580 | + | 15.6580i | −0.663449 | + | 0.663449i | −0.956191 | − | 0.292742i | \(-0.905432\pi\) |
0.292742 | + | 0.956191i | \(0.405432\pi\) | |||||||
\(558\) | −0.241832 | − | 4.23706i | −0.0102376 | − | 0.179369i | ||||
\(559\) | − | 5.02357i | − | 0.212474i | ||||||
\(560\) | −6.29309 | − | 20.1675i | −0.265931 | − | 0.852231i | ||||
\(561\) | 0.238851 | − | 0.626582i | 0.0100843 | − | 0.0264543i | ||||
\(562\) | 27.0994 | + | 27.0994i | 1.14312 | + | 1.14312i | ||||
\(563\) | −22.2250 | − | 22.2250i | −0.936673 | − | 0.936673i | 0.0614379 | − | 0.998111i | \(-0.480431\pi\) |
−0.998111 | + | 0.0614379i | \(0.980431\pi\) | |||||||
\(564\) | 0.00688137 | − | 0.0180520i | 0.000289758 | − | 0.000760127i | ||||
\(565\) | 0.571637 | + | 1.83193i | 0.0240489 | + | 0.0770697i | ||||
\(566\) | 15.7338i | 0.661341i | ||||||||
\(567\) | −13.2157 | + | 16.6342i | −0.555006 | + | 0.698571i | ||||
\(568\) | −0.173101 | + | 0.173101i | −0.00726315 | + | 0.00726315i | ||||
\(569\) | 36.0307 | 1.51048 | 0.755242 | − | 0.655446i | \(-0.227519\pi\) | ||||
0.755242 | + | 0.655446i | \(0.227519\pi\) | |||||||
\(570\) | −5.99906 | + | 5.30070i | −0.251273 | + | 0.222022i | ||||
\(571\) | −35.3321 | −1.47860 | −0.739302 | − | 0.673374i | \(-0.764844\pi\) | ||||
−0.739302 | + | 0.673374i | \(0.764844\pi\) | |||||||
\(572\) | −0.000366131 | 0 | 0.000366131i | −1.53087e−5 | 0 | 1.53087e-5i | ||||
\(573\) | 38.5328 | − | 17.2635i | 1.60973 | − | 0.721192i | ||||
\(574\) | 23.7639i | 0.991888i | ||||||||
\(575\) | 4.35081 | − | 23.8467i | 0.181441 | − | 0.994477i | ||||
\(576\) | −17.8989 | − | 15.9661i | −0.745789 | − | 0.665253i | ||||
\(577\) | 0.737957 | + | 0.737957i | 0.0307216 | + | 0.0307216i | 0.722301 | − | 0.691579i | \(-0.243085\pi\) |
−0.691579 | + | 0.722301i | \(0.743085\pi\) | |||||||
\(578\) | 16.3773 | + | 16.3773i | 0.681205 | + | 0.681205i | ||||
\(579\) | −13.6190 | − | 5.19151i | −0.565986 | − | 0.215752i | ||||
\(580\) | 0.000278314 | 0 | 0.000530786i | 1.15563e−5 | 0 | 2.20397e-5i | ||||
\(581\) | − | 1.15489i | − | 0.0479129i | ||||||
\(582\) | −1.89049 | − | 4.21965i | −0.0783632 | − | 0.174910i | ||||
\(583\) | −3.38557 | + | 3.38557i | −0.140216 | + | 0.140216i | ||||
\(584\) | 7.79281 | 0.322469 | ||||||||
\(585\) | −2.37525 | + | 5.23541i | −0.0982044 | + | 0.216458i | ||||
\(586\) | 21.5901 | 0.891881 | ||||||||
\(587\) | 3.85573 | − | 3.85573i | 0.159143 | − | 0.159143i | −0.623044 | − | 0.782187i | \(-0.714104\pi\) |
0.782187 | + | 0.623044i | \(0.214104\pi\) | |||||||
\(588\) | −0.00125020 | − | 0.00279049i | −5.15572e−5 | − | 0.000115078i | ||||
\(589\) | − | 1.46112i | − | 0.0602046i | ||||||
\(590\) | −28.7297 | + | 8.96486i | −1.18278 | + | 0.369077i | ||||
\(591\) | 36.0581 | + | 13.7452i | 1.48323 | + | 0.565404i | ||||
\(592\) | 20.9448 | + | 20.9448i | 0.860827 | + | 0.860827i | ||||
\(593\) | −27.6856 | − | 27.6856i | −1.13691 | − | 1.13691i | −0.989001 | − | 0.147910i | \(-0.952745\pi\) |
−0.147910 | − | 0.989001i | \(-0.547255\pi\) | |||||||
\(594\) | 1.65293 | + | 3.18884i | 0.0678207 | + | 0.130840i | ||||
\(595\) | −3.70388 | − | 1.94210i | −0.151844 | − | 0.0796183i | ||||
\(596\) | 0.0239830i | 0.000982382i | ||||||||
\(597\) | −6.47535 | + | 2.90108i | −0.265018 | + | 0.118733i | ||||
\(598\) | −4.15616 | + | 4.15616i | −0.169958 | + | 0.169958i | ||||
\(599\) | −43.2024 | −1.76520 | −0.882600 | − | 0.470124i | \(-0.844209\pi\) | ||||
−0.882600 | + | 0.470124i | \(0.844209\pi\) | |||||||
\(600\) | −23.7811 | + | 5.83835i | −0.970861 | + | 0.238349i | ||||
\(601\) | 13.9160 | 0.567646 | 0.283823 | − | 0.958877i | \(-0.408397\pi\) | ||||
0.283823 | + | 0.958877i | \(0.408397\pi\) | |||||||
\(602\) | −13.8412 | + | 13.8412i | −0.564125 | + | 0.564125i | ||||
\(603\) | 20.0518 | − | 1.14446i | 0.816571 | − | 0.0466062i | ||||
\(604\) | 0.0228483i | 0.000929683i | ||||||||
\(605\) | 21.3110 | + | 11.1742i | 0.866415 | + | 0.454298i | ||||
\(606\) | −11.8262 | + | 31.0239i | −0.480407 | + | 1.26026i | ||||
\(607\) | 15.2786 | + | 15.2786i | 0.620137 | + | 0.620137i | 0.945566 | − | 0.325429i | \(-0.105509\pi\) |
−0.325429 | + | 0.945566i | \(0.605509\pi\) | |||||||
\(608\) | 0.00722657 | + | 0.00722657i | 0.000293076 | + | 0.000293076i | ||||
\(609\) | 0.315687 | − | 0.828147i | 0.0127923 | − | 0.0335582i | ||||
\(610\) | 11.0239 | − | 3.43991i | 0.446344 | − | 0.139278i | ||||
\(611\) | − | 7.73090i | − | 0.312759i | ||||||
\(612\) | 0.00293428 | 0.000167475i | 0.000118611 | 6.76979e-6i | ||||||
\(613\) | −4.86567 | + | 4.86567i | −0.196523 | + | 0.196523i | −0.798507 | − | 0.601985i | \(-0.794377\pi\) |
0.601985 | + | 0.798507i | \(0.294377\pi\) | |||||||
\(614\) | 25.6130 | 1.03365 | ||||||||
\(615\) | 27.5088 | + | 1.70015i | 1.10926 | + | 0.0685565i | ||||
\(616\) | −3.26140 | −0.131405 | ||||||||
\(617\) | 16.5719 | − | 16.5719i | 0.667160 | − | 0.667160i | −0.289897 | − | 0.957058i | \(-0.593621\pi\) |
0.957058 | + | 0.289897i | \(0.0936212\pi\) | |||||||
\(618\) | −10.2431 | + | 4.58909i | −0.412036 | + | 0.184600i | ||||
\(619\) | 22.9117i | 0.920899i | 0.887686 | + | 0.460450i | \(0.152312\pi\) | ||||
−0.887686 | + | 0.460450i | \(0.847688\pi\) | |||||||
\(620\) | −0.00128393 | + | 0.00244865i | −5.15638e−5 | + | 9.83400e-5i | ||||
\(621\) | 11.5930 | + | 22.3653i | 0.465213 | + | 0.897487i | ||||
\(622\) | 21.6711 | + | 21.6711i | 0.868931 | + | 0.868931i | ||||
\(623\) | 20.3930 | + | 20.3930i | 0.817028 | + | 0.817028i | ||||
\(624\) | 5.55156 | + | 2.11624i | 0.222240 | + | 0.0847173i | ||||
\(625\) | −8.82856 | + | 23.3892i | −0.353143 | + | 0.935570i | ||||
\(626\) | − | 31.0535i | − | 1.24115i | ||||||
\(627\) | 0.505594 | + | 1.12851i | 0.0201915 | + | 0.0450683i | ||||
\(628\) | 0.0198607 | − | 0.0198607i | 0.000792527 | − | 0.000792527i | ||||
\(629\) | 5.86360 | 0.233797 | ||||||||
\(630\) | 20.9693 | − | 7.88046i | 0.835435 | − | 0.313965i | ||||
\(631\) | −5.03474 | −0.200430 | −0.100215 | − | 0.994966i | \(-0.531953\pi\) | ||||
−0.100215 | + | 0.994966i | \(0.531953\pi\) | |||||||
\(632\) | 17.9155 | − | 17.9155i | 0.712641 | − | 0.712641i | ||||
\(633\) | −0.669278 | − | 1.49386i | −0.0266014 | − | 0.0593756i | ||||
\(634\) | 27.4643i | 1.09075i | ||||||||
\(635\) | 6.68205 | + | 21.4140i | 0.265169 | + | 0.849788i | ||||
\(636\) | −0.0196089 | − | 0.00747483i | −0.000777542 | − | 0.000296396i | ||||
\(637\) | −0.865227 | − | 0.865227i | −0.0342815 | − | 0.0342815i | ||||
\(638\) | −0.105951 | − | 0.105951i | −0.00419465 | − | 0.00419465i | ||||
\(639\) | −0.193825 | − | 0.172894i | −0.00766760 | − | 0.00683959i | ||||
\(640\) | 7.54272 | + | 24.1722i | 0.298152 | + | 0.955489i | ||||
\(641\) | 2.56260i | 0.101216i | 0.998719 | + | 0.0506082i | \(0.0161160\pi\) | ||||
−0.998719 | + | 0.0506082i | \(0.983884\pi\) | |||||||
\(642\) | −17.9290 | + | 8.03256i | −0.707602 | + | 0.317020i | ||||
\(643\) | 27.8538 | − | 27.8538i | 1.09845 | − | 1.09845i | 0.103856 | − | 0.994592i | \(-0.466882\pi\) |
0.994592 | − | 0.103856i | \(-0.0331181\pi\) | |||||||
\(644\) | 0.0141504 | 0.000557605 | ||||||||
\(645\) | 15.0321 | + | 17.0126i | 0.591890 | + | 0.669872i | ||||
\(646\) | 1.63771 | 0.0644349 | ||||||||
\(647\) | −8.41427 | + | 8.41427i | −0.330799 | + | 0.330799i | −0.852890 | − | 0.522091i | \(-0.825152\pi\) |
0.522091 | + | 0.852890i | \(0.325152\pi\) | |||||||
\(648\) | 15.8302 | − | 19.9250i | 0.621867 | − | 0.782727i | ||||
\(649\) | 4.64891i | 0.182486i | ||||||||
\(650\) | 4.98614 | − | 3.44744i | 0.195572 | − | 0.135220i | ||||
\(651\) | −1.45634 | + | 3.82044i | −0.0570785 | + | 0.149735i | ||||
\(652\) | −0.00454057 | − | 0.00454057i | −0.000177822 | − | 0.000177822i | ||||
\(653\) | 15.4098 | + | 15.4098i | 0.603031 | + | 0.603031i | 0.941116 | − | 0.338085i | \(-0.109779\pi\) |
−0.338085 | + | 0.941116i | \(0.609779\pi\) | |||||||
\(654\) | −13.0692 | + | 34.2847i | −0.511046 | + | 1.34064i | ||||
\(655\) | −14.0099 | + | 26.7189i | −0.547410 | + | 1.04399i | ||||
\(656\) | − | 28.4828i | − | 1.11207i | ||||||
\(657\) | 0.471138 | + | 8.25464i | 0.0183808 | + | 0.322044i | ||||
\(658\) | −21.3005 | + | 21.3005i | −0.830382 | + | 0.830382i | ||||
\(659\) | 1.48765 | 0.0579506 | 0.0289753 | − | 0.999580i | \(-0.490776\pi\) | ||||
0.0289753 | + | 0.999580i | \(0.490776\pi\) | |||||||
\(660\) | 0.000144343 | − | 0.00233551i | 5.61854e−6 | − | 9.09095e-5i | ||||
\(661\) | −10.9973 | −0.427747 | −0.213873 | − | 0.976861i | \(-0.568608\pi\) | ||||
−0.213873 | + | 0.976861i | \(0.568608\pi\) | |||||||
\(662\) | −16.4785 | + | 16.4785i | −0.640456 | + | 0.640456i | ||||
\(663\) | 1.07332 | − | 0.480868i | 0.0416842 | − | 0.0186754i | ||||
\(664\) | 1.38336i | 0.0536849i | ||||||||
\(665\) | 7.36225 | − | 2.29733i | 0.285496 | − | 0.0890865i | ||||
\(666\) | −20.9069 | + | 23.4379i | −0.810126 | + | 0.908201i | ||||
\(667\) | −0.743101 | − | 0.743101i | −0.0287730 | − | 0.0287730i | ||||
\(668\) | −0.0176604 | − | 0.0176604i | −0.000683303 | − | 0.000683303i | ||||
\(669\) | 7.57265 | + | 2.88667i | 0.292776 | + | 0.111605i | ||||
\(670\) | −18.7555 | − | 9.83428i | −0.724587 | − | 0.379931i | ||||
\(671\) | − | 1.78384i | − | 0.0688643i | ||||||
\(672\) | −0.0116926 | − | 0.0260984i | −0.000451052 | − | 0.00100677i | ||||
\(673\) | 9.80668 | − | 9.80668i | 0.378020 | − | 0.378020i | −0.492367 | − | 0.870387i | \(-0.663868\pi\) |
0.870387 | + | 0.492367i | \(0.163868\pi\) | |||||||
\(674\) | 37.2470 | 1.43470 | ||||||||
\(675\) | −7.62211 | − | 24.8375i | −0.293375 | − | 0.955997i | ||||
\(676\) | 0.0151660 | 0.000583308 | ||||||||
\(677\) | −25.2317 | + | 25.2317i | −0.969733 | + | 0.969733i | −0.999555 | − | 0.0298219i | \(-0.990506\pi\) |
0.0298219 | + | 0.999555i | \(0.490506\pi\) | |||||||
\(678\) | 0.859776 | + | 1.91906i | 0.0330195 | + | 0.0737010i | ||||
\(679\) | 4.45454i | 0.170949i | ||||||||
\(680\) | 4.43662 | + | 2.32631i | 0.170137 | + | 0.0892099i | ||||
\(681\) | 10.3259 | + | 3.93619i | 0.395688 | + | 0.150835i | ||||
\(682\) | 0.488779 | + | 0.488779i | 0.0187163 | + | 0.0187163i | ||||
\(683\) | −31.5979 | − | 31.5979i | −1.20906 | − | 1.20906i | −0.971331 | − | 0.237731i | \(-0.923596\pi\) |
−0.237731 | − | 0.971331i | \(-0.576404\pi\) | |||||||
\(684\) | −0.00360786 | + | 0.00404463i | −0.000137950 | + | 0.000154650i | ||||
\(685\) | 36.9998 | − | 11.5455i | 1.41369 | − | 0.441130i | ||||
\(686\) | 28.1434i | 1.07452i | ||||||||
\(687\) | −36.3896 | + | 16.3033i | −1.38835 | + | 0.622009i | ||||
\(688\) | 16.5897 | − | 16.5897i | 0.632475 | − | 0.632475i | ||||
\(689\) | −8.39763 | −0.319924 | ||||||||
\(690\) | 1.63852 | − | 26.5116i | 0.0623772 | − | 1.00928i | ||||
\(691\) | 23.7307 | 0.902758 | 0.451379 | − | 0.892332i | \(-0.350932\pi\) | ||||
0.451379 | + | 0.892332i | \(0.350932\pi\) | |||||||
\(692\) | 0.00449466 | − | 0.00449466i | 0.000170861 | − | 0.000170861i | ||||
\(693\) | −0.197178 | − | 3.45468i | −0.00749016 | − | 0.131233i | ||||
\(694\) | 43.4677i | 1.65001i | ||||||||
\(695\) | 1.57964 | − | 3.01261i | 0.0599191 | − | 0.114275i | ||||
\(696\) | −0.378140 | + | 0.991980i | −0.0143333 | + | 0.0376009i | ||||
\(697\) | −3.98695 | − | 3.98695i | −0.151016 | − | 0.151016i | ||||
\(698\) | 2.53283 | + | 2.53283i | 0.0958690 | + | 0.0958690i | ||||
\(699\) | 17.1175 | − | 44.9046i | 0.647443 | − | 1.69845i | ||||
\(700\) | −0.0143569 | − | 0.00261939i | −0.000542638 | − | 9.90037e-5i | ||||
\(701\) | − | 9.19645i | − | 0.347345i | −0.984803 | − | 0.173672i | \(-0.944437\pi\) | ||
0.984803 | − | 0.173672i | \(-0.0555634\pi\) | |||||||
\(702\) | −1.90484 | + | 6.00481i | −0.0718936 | + | 0.226637i | ||||
\(703\) | −7.64603 | + | 7.64603i | −0.288375 | + | 0.288375i | ||||
\(704\) | 3.90660 | 0.147236 | ||||||||
\(705\) | 23.1333 | + | 26.1812i | 0.871252 | + | 0.986039i | ||||
\(706\) | −11.4059 | −0.429267 | ||||||||
\(707\) | 22.6177 | − | 22.6177i | 0.850625 | − | 0.850625i | ||||
\(708\) | −0.0185951 | + | 0.00833096i | −0.000698846 | + | 0.000313097i | ||||
\(709\) | − | 37.0608i | − | 1.39185i | −0.718115 | − | 0.695924i | \(-0.754995\pi\) | ||
0.718115 | − | 0.695924i | \(-0.245005\pi\) | |||||||
\(710\) | 0.0815782 | + | 0.261434i | 0.00306157 | + | 0.00981143i | ||||
\(711\) | 20.0604 | + | 17.8941i | 0.752324 | + | 0.671082i | ||||
\(712\) | −24.4274 | − | 24.4274i | −0.915455 | − | 0.915455i | ||||
\(713\) | 3.42811 | + | 3.42811i | 0.128384 | + | 0.128384i | ||||
\(714\) | −4.28217 | − | 1.63235i | −0.160256 | − | 0.0610891i | ||||
\(715\) | −0.278925 | − | 0.893871i | −0.0104312 | − | 0.0334289i | ||||
\(716\) | 0.0258108i | 0.000964593i | ||||||||
\(717\) | 6.13636 | + | 13.6966i | 0.229167 | + | 0.511510i | ||||
\(718\) | −16.7902 | + | 16.7902i | −0.626603 | + | 0.626603i | ||||
\(719\) | 22.4294 | 0.836477 | 0.418238 | − | 0.908337i | \(-0.362648\pi\) | ||||
0.418238 | + | 0.908337i | \(0.362648\pi\) | |||||||
\(720\) | −25.1332 | + | 9.44530i | −0.936658 | + | 0.352006i | ||||
\(721\) | 10.8132 | 0.402706 | ||||||||
\(722\) | 16.8703 | − | 16.8703i | 0.627849 | − | 0.627849i | ||||
\(723\) | −13.7928 | − | 30.7861i | −0.512959 | − | 1.14495i | ||||
\(724\) | 0.0237664i | 0.000883273i | ||||||||
\(725\) | 0.616386 | + | 0.891498i | 0.0228920 | + | 0.0331094i | ||||
\(726\) | 24.6383 | + | 9.39203i | 0.914413 | + | 0.348571i | ||||
\(727\) | 17.7622 | + | 17.7622i | 0.658763 | + | 0.658763i | 0.955087 | − | 0.296325i | \(-0.0957610\pi\) |
−0.296325 | + | 0.955087i | \(0.595761\pi\) | |||||||
\(728\) | −4.04481 | − | 4.04481i | −0.149911 | − | 0.149911i | ||||
\(729\) | 22.0629 | + | 15.5637i | 0.817144 | + | 0.576433i | ||||
\(730\) | 4.04845 | − | 7.72100i | 0.149840 | − | 0.285767i | ||||
\(731\) | − | 4.64435i | − | 0.171778i | ||||||
\(732\) | 0.00713513 | − | 0.00319668i | 0.000263722 | − | 0.000118153i | ||||
\(733\) | 14.5129 | − | 14.5129i | 0.536046 | − | 0.536046i | −0.386319 | − | 0.922365i | \(-0.626254\pi\) |
0.922365 | + | 0.386319i | \(0.126254\pi\) | |||||||
\(734\) | −50.3171 | −1.85724 | ||||||||
\(735\) | 5.51918 | + | 0.341105i | 0.203578 | + | 0.0125819i | ||||
\(736\) | −0.0339101 | −0.00124994 | ||||||||
\(737\) | −2.31313 | + | 2.31313i | −0.0852054 | + | 0.0852054i | ||||
\(738\) | 30.1522 | − | 1.72095i | 1.10992 | − | 0.0633491i | ||||
\(739\) | 32.9388i | 1.21167i | 0.795589 | + | 0.605837i | \(0.207162\pi\) | ||||
−0.795589 | + | 0.605837i | \(0.792838\pi\) | |||||||
\(740\) | 0.0195325 | − | 0.00609494i | 0.000718028 | − | 0.000224055i | ||||
\(741\) | −0.772544 | + | 2.02663i | −0.0283801 | + | 0.0744501i | ||||
\(742\) | 23.1375 | + | 23.1375i | 0.849406 | + | 0.849406i | ||||
\(743\) | 3.09833 | + | 3.09833i | 0.113667 | + | 0.113667i | 0.761652 | − | 0.647986i | \(-0.224388\pi\) |
−0.647986 | + | 0.761652i | \(0.724388\pi\) | |||||||
\(744\) | 1.74445 | − | 4.57625i | 0.0639547 | − | 0.167773i | ||||
\(745\) | −38.4113 | − | 20.1407i | −1.40728 | − | 0.737897i | ||||
\(746\) | 2.57496i | 0.0942761i | ||||||||
\(747\) | −1.46535 | + | 0.0836355i | −0.0536143 | + | 0.00306006i | ||||
\(748\) | −0.000338493 | 0 | 0.000338493i | −1.23765e−5 | 0 | 1.23765e-5i | ||||
\(749\) | 18.9270 | 0.691579 | ||||||||
\(750\) | −6.57000 | + | 26.5951i | −0.239903 | + | 0.971115i | ||||
\(751\) | 30.1178 | 1.09901 | 0.549507 | − | 0.835489i | \(-0.314816\pi\) | ||||
0.549507 | + | 0.835489i | \(0.314816\pi\) | |||||||
\(752\) | 25.5303 | − | 25.5303i | 0.930992 | − | 0.930992i | ||||
\(753\) | −10.5373 | + | 4.72092i | −0.384001 | + | 0.172040i | ||||
\(754\) | − | 0.262803i | − | 0.00957073i | ||||||
\(755\) | −36.5939 | − | 19.1877i | −1.33179 | − | 0.698314i | ||||
\(756\) | 0.0134649 | − | 0.00697955i | 0.000489715 | − | 0.000253844i | ||||
\(757\) | −21.3145 | − | 21.3145i | −0.774689 | − | 0.774689i | 0.204233 | − | 0.978922i | \(-0.434530\pi\) |
−0.978922 | + | 0.204233i | \(0.934530\pi\) | |||||||
\(758\) | −26.9868 | − | 26.9868i | −0.980205 | − | 0.980205i | ||||
\(759\) | −3.83395 | − | 1.46149i | −0.139164 | − | 0.0530487i | ||||
\(760\) | −8.81874 | + | 2.75181i | −0.319889 | + | 0.0998187i | ||||
\(761\) | − | 14.3563i | − | 0.520417i | −0.965552 | − | 0.260208i | \(-0.916209\pi\) | ||
0.965552 | − | 0.260208i | \(-0.0837913\pi\) | |||||||
\(762\) | 10.0502 | + | 22.4325i | 0.364080 | + | 0.812644i | ||||
\(763\) | 24.9949 | − | 24.9949i | 0.904877 | − | 0.904877i | ||||
\(764\) | −0.0301423 | −0.00109051 | ||||||||
\(765\) | −2.19595 | + | 4.84020i | −0.0793946 | + | 0.174998i | ||||
\(766\) | −18.5764 | −0.671192 | ||||||||
\(767\) | −5.76563 | + | 5.76563i | −0.208185 | + | 0.208185i | ||||
\(768\) | 0.0210152 | + | 0.0469068i | 0.000758319 | + | 0.00169260i | ||||
\(769\) | 38.8955i | 1.40261i | 0.712862 | + | 0.701304i | \(0.247399\pi\) | ||||
−0.712862 | + | 0.701304i | \(0.752601\pi\) | |||||||
\(770\) | −1.69433 | + | 3.23134i | −0.0610594 | + | 0.116450i | ||||
\(771\) | −9.45910 | − | 3.60578i | −0.340661 | − | 0.129859i | ||||
\(772\) | 0.00735726 | + | 0.00735726i | 0.000264794 | + | 0.000264794i | ||||
\(773\) | 11.8920 | + | 11.8920i | 0.427727 | + | 0.427727i | 0.887853 | − | 0.460127i | \(-0.152196\pi\) |
−0.460127 | + | 0.887853i | \(0.652196\pi\) | |||||||
\(774\) | 18.5643 | + | 16.5596i | 0.667282 | + | 0.595223i | ||||
\(775\) | −2.84354 | − | 4.11270i | −0.102143 | − | 0.147732i | ||||
\(776\) | − | 5.33579i | − | 0.191544i | ||||||
\(777\) | 27.6133 | − | 12.3713i | 0.990621 | − | 0.443818i | ||||
\(778\) | −5.45352 | + | 5.45352i | −0.195518 | + | 0.195518i | ||||
\(779\) | 10.3978 | 0.372540 | ||||||||
\(780\) | 0.00307553 | − | 0.00271750i | 0.000110122 | − | 9.73022e-5i | ||||
\(781\) | 0.0423041 | 0.00151376 | ||||||||
\(782\) | −3.84242 | + | 3.84242i | −0.137405 | + | 0.137405i | ||||
\(783\) | −1.07363 | − | 0.340577i | −0.0383684 | − | 0.0121712i | ||||
\(784\) | − | 5.71459i | − | 0.204092i | ||||||
\(785\) | 15.1302 | + | 48.4878i | 0.540020 | + | 1.73060i | ||||
\(786\) | −11.7754 | + | 30.8906i | −0.420014 | + | 1.10183i | ||||
\(787\) | 18.9654 | + | 18.9654i | 0.676044 | + | 0.676044i | 0.959103 | − | 0.283059i | \(-0.0913491\pi\) |
−0.283059 | + | 0.959103i | \(0.591349\pi\) | |||||||
\(788\) | −0.0194793 | − | 0.0194793i | −0.000693923 | − | 0.000693923i | ||||
\(789\) | −1.87371 | + | 4.91534i | −0.0667059 | + | 0.174991i | ||||
\(790\) | −8.44313 | − | 27.0577i | −0.300393 | − | 0.962671i | ||||
\(791\) | − | 2.02588i | − | 0.0720321i | ||||||
\(792\) | 0.236186 | + | 4.13813i | 0.00839250 | + | 0.147042i | ||||
\(793\) | 2.21233 | − | 2.21233i | 0.0785622 | − | 0.0785622i | ||||
\(794\) | 25.3007 | 0.897888 | ||||||||
\(795\) | 28.4391 | − | 25.1284i | 1.00863 | − | 0.891213i | ||||
\(796\) | 0.00506534 | 0.000179536 | ||||||||
\(797\) | 25.5972 | − | 25.5972i | 0.906701 | − | 0.906701i | −0.0893038 | − | 0.996004i | \(-0.528464\pi\) |
0.996004 | + | 0.0893038i | \(0.0284642\pi\) | |||||||
\(798\) | 7.71242 | − | 3.45532i | 0.273017 | − | 0.122317i | ||||
\(799\) | − | 7.14731i | − | 0.252854i | ||||||
\(800\) | 0.0344048 | + | 0.00627712i | 0.00121639 | + | 0.000221930i | ||||
\(801\) | 24.3982 | − | 27.3519i | 0.862069 | − | 0.966432i | ||||
\(802\) | −23.2467 | − | 23.2467i | −0.820870 | − | 0.820870i | ||||
\(803\) | −0.952240 | − | 0.952240i | −0.0336038 | − | 0.0336038i | ||||
\(804\) | −0.0133974 | − | 0.00510706i | −0.000472491 | − | 0.000180112i | ||||
\(805\) | −11.8834 | + | 22.6634i | −0.418834 | + | 0.798780i | ||||
\(806\) | 1.21238i | 0.0427041i | ||||||||
\(807\) | 11.4504 | + | 25.5579i | 0.403074 | + | 0.899680i | ||||
\(808\) | −27.0922 | + | 27.0922i | −0.953100 | + | 0.953100i | ||||
\(809\) | 13.9192 | 0.489372 | 0.244686 | − | 0.969602i | \(-0.421315\pi\) | ||||
0.244686 | + | 0.969602i | \(0.421315\pi\) | |||||||
\(810\) | −11.5175 | − | 26.0355i | −0.404682 | − | 0.914795i | ||||
\(811\) | 40.5704 | 1.42462 | 0.712310 | − | 0.701865i | \(-0.247649\pi\) | ||||
0.712310 | + | 0.701865i | \(0.247649\pi\) | |||||||
\(812\) | −0.000447382 | 0 | 0.000447382i | −1.57000e−5 | 0 | 1.57000e-5i | ||||
\(813\) | 19.5900 | + | 43.7257i | 0.687050 | + | 1.53353i | ||||
\(814\) | − | 5.11554i | − | 0.179299i | ||||||
\(815\) | 11.0853 | − | 3.45908i | 0.388302 | − | 0.121166i | ||||
\(816\) | 5.13249 | + | 1.95649i | 0.179673 | + | 0.0684908i | ||||
\(817\) | 6.05615 | + | 6.05615i | 0.211878 | + | 0.211878i | ||||
\(818\) | −20.9516 | − | 20.9516i | −0.732556 | − | 0.732556i | ||||
\(819\) | 4.03999 | − | 4.52907i | 0.141169 | − | 0.158258i | ||||
\(820\) | −0.0174253 | − | 0.00913683i | −0.000608518 | − | 0.000319072i | ||||
\(821\) | − | 22.8010i | − | 0.795762i | −0.917437 | − | 0.397881i | \(-0.869746\pi\) | ||
0.917437 | − | 0.397881i | \(-0.130254\pi\) | |||||||
\(822\) | 38.7596 | − | 17.3651i | 1.35190 | − | 0.605677i | ||||
\(823\) | −22.5406 | + | 22.5406i | −0.785717 | + | 0.785717i | −0.980789 | − | 0.195072i | \(-0.937506\pi\) |
0.195072 | + | 0.980789i | \(0.437506\pi\) | |||||||
\(824\) | −12.9524 | −0.451219 | ||||||||
\(825\) | 3.61935 | + | 2.19252i | 0.126009 | + | 0.0763336i | ||||
\(826\) | 31.7715 | 1.10547 | ||||||||
\(827\) | −1.41043 | + | 1.41043i | −0.0490454 | + | 0.0490454i | −0.731204 | − | 0.682159i | \(-0.761041\pi\) |
0.682159 | + | 0.731204i | \(0.261041\pi\) | |||||||
\(828\) | −0.00102475 | − | 0.0179543i | −3.56127e−5 | − | 0.000623957i | ||||
\(829\) | − | 33.0090i | − | 1.14645i | −0.819398 | − | 0.573225i | \(-0.805692\pi\) | ||
0.819398 | − | 0.573225i | \(-0.194308\pi\) | |||||||
\(830\) | 1.37062 | + | 0.718672i | 0.0475748 | + | 0.0249455i | ||||
\(831\) | −13.9860 | + | 36.6897i | −0.485168 | + | 1.27275i | ||||
\(832\) | 4.84501 | + | 4.84501i | 0.167970 | + | 0.167970i | ||||
\(833\) | −0.799913 | − | 0.799913i | −0.0277153 | − | 0.0277153i | ||||
\(834\) | 1.32770 | − | 3.48297i | 0.0459744 | − | 0.120605i | ||||
\(835\) | 43.1161 | − | 13.4540i | 1.49210 | − | 0.465596i | ||||
\(836\) | 0 | 0.000882776i | 0 | 3.05315e-5i | ||||||
\(837\) | 4.95292 | + | 1.57116i | 0.171198 | + | 0.0543073i | ||||
\(838\) | 8.76691 | − | 8.76691i | 0.302848 | − | 0.302848i | ||||
\(839\) | 37.0786 | 1.28009 | 0.640047 | − | 0.768336i | \(-0.278915\pi\) | ||||
0.640047 | + | 0.768336i | \(0.278915\pi\) | |||||||
\(840\) | 25.8014 | + | 1.59462i | 0.890233 | + | 0.0550196i | ||||
\(841\) | −28.9530 | −0.998380 | ||||||||
\(842\) | 6.41548 | − | 6.41548i | 0.221092 | − | 0.221092i | ||||
\(843\) | −42.8218 | + | 19.1850i | −1.47486 | + | 0.660767i | ||||
\(844\) | 0.00116857i | 4.02239e-5i | ||||||||
\(845\) | −12.7363 | + | 24.2900i | −0.438141 | + | 0.835601i | ||||
\(846\) | 28.5691 | + | 25.4840i | 0.982227 | + | 0.876159i | ||||
\(847\) | −17.9623 | − | 17.9623i | −0.617192 | − | 0.617192i | ||||
\(848\) | −27.7320 | − | 27.7320i | −0.952322 | − | 0.952322i | ||||
\(849\) | −18.0004 | − | 6.86171i | −0.617774 | − | 0.235493i | ||||
\(850\) | 4.60975 | − | 3.18720i | 0.158113 | − | 0.109320i | ||||
\(851\) | − | 35.8784i | − | 1.22990i | ||||||
\(852\) | 7.58098e−5 | 0 | 0.000169211i | 2.59720e−6 | 0 | 5.79707e-6i | ||||
\(853\) | 37.3086 | − | 37.3086i | 1.27742 | − | 1.27742i | 0.335315 | − | 0.942106i | \(-0.391157\pi\) |
0.942106 | − | 0.335315i | \(-0.108843\pi\) | |||||||
\(854\) | −12.1911 | −0.417169 | ||||||||
\(855\) | −3.44806 | − | 9.17500i | −0.117921 | − | 0.313778i | ||||
\(856\) | −22.6714 | −0.774893 | ||||||||
\(857\) | −4.08616 | + | 4.08616i | −0.139580 | + | 0.139580i | −0.773444 | − | 0.633864i | \(-0.781468\pi\) |
0.633864 | + | 0.773444i | \(0.281468\pi\) | |||||||
\(858\) | −0.419520 | − | 0.936386i | −0.0143222 | − | 0.0319677i | ||||
\(859\) | − | 9.31165i | − | 0.317709i | −0.987302 | − | 0.158855i | \(-0.949220\pi\) | ||
0.987302 | − | 0.158855i | \(-0.0507801\pi\) | |||||||
\(860\) | −0.00482759 | − | 0.0154710i | −0.000164619 | − | 0.000527556i | ||||
\(861\) | −27.1874 | − | 10.3638i | −0.926545 | − | 0.353196i | ||||
\(862\) | 2.35338 | + | 2.35338i | 0.0801563 | + | 0.0801563i | ||||
\(863\) | 14.5615 | + | 14.5615i | 0.495680 | + | 0.495680i | 0.910090 | − | 0.414411i | \(-0.136012\pi\) |
−0.414411 | + | 0.910090i | \(0.636012\pi\) | |||||||
\(864\) | −0.0322675 | + | 0.0167258i | −0.00109776 | + | 0.000569024i | ||||
\(865\) | 3.42411 | + | 10.9733i | 0.116423 | + | 0.373102i | ||||
\(866\) | − | 33.2110i | − | 1.12855i | ||||||
\(867\) | −25.8790 | + | 11.5943i | −0.878896 | + | 0.393763i | ||||
\(868\) | 0.00206388 | − | 0.00206388i | 7.00527e−5 | − | 7.00527e-5i | ||||
\(869\) | −4.37836 | −0.148526 | ||||||||
\(870\) | 0.786392 | + | 0.889999i | 0.0266612 | + | 0.0301738i | ||||
\(871\) | −5.73754 | −0.194409 | ||||||||
\(872\) | −29.9397 | + | 29.9397i | −1.01389 | + | 1.01389i | ||||
\(873\) | 5.65201 | − | 0.322591i | 0.191292 | − | 0.0109181i | ||||
\(874\) | − | 10.0209i | − | 0.338961i | ||||||
\(875\) | 16.2520 | − | 20.7943i | 0.549417 | − | 0.702975i | ||||
\(876\) | 0.00210241 | − | 0.00551528i | 7.10337e−5 | − | 0.000186344i | ||||
\(877\) | −18.7018 | − | 18.7018i | −0.631515 | − | 0.631515i | 0.316933 | − | 0.948448i | \(-0.397347\pi\) |
−0.948448 | + | 0.316933i | \(0.897347\pi\) | |||||||
\(878\) | 11.3248 | + | 11.3248i | 0.382194 | + | 0.382194i | ||||
\(879\) | −9.41574 | + | 24.7005i | −0.317585 | + | 0.833126i | ||||
\(880\) | 2.03078 | − | 3.87300i | 0.0684575 | − | 0.130559i | ||||
\(881\) | − | 17.4925i | − | 0.589338i | −0.955599 | − | 0.294669i | \(-0.904791\pi\) | ||
0.955599 | − | 0.294669i | \(-0.0952093\pi\) | |||||||
\(882\) | 6.04952 | − | 0.345279i | 0.203698 | − | 0.0116262i | ||||
\(883\) | −35.1699 | + | 35.1699i | −1.18356 | + | 1.18356i | −0.204746 | + | 0.978815i | \(0.565637\pi\) |
−0.978815 | + | 0.204746i | \(0.934363\pi\) | |||||||
\(884\) | −0.000839603 | 0 | −2.82389e−5 | 0 | ||||||
\(885\) | 2.27303 | − | 36.7782i | 0.0764071 | − | 1.23629i | ||||
\(886\) | 0.246554 | 0.00828313 | ||||||||
\(887\) | −18.3427 | + | 18.3427i | −0.615887 | + | 0.615887i | −0.944474 | − | 0.328587i | \(-0.893428\pi\) |
0.328587 | + | 0.944474i | \(0.393428\pi\) | |||||||
\(888\) | −33.0761 | + | 14.8187i | −1.10996 | + | 0.497284i | ||||
\(889\) | − | 23.6812i | − | 0.794242i | ||||||
\(890\) | −36.8926 | + | 11.5120i | −1.23664 | + | 0.385884i | ||||
\(891\) | −4.36909 | + | 0.500366i | −0.146370 | + | 0.0167629i | ||||
\(892\) | −0.00409090 | − | 0.00409090i | −0.000136974 | − | 0.000136974i | ||||
\(893\) | 9.31996 | + | 9.31996i | 0.311881 | + | 0.311881i | ||||
\(894\) | −44.4085 | − | 16.9284i | −1.48524 | − | 0.566170i | ||||
\(895\) | −41.3387 | − | 21.6756i | −1.38180 | − | 0.724536i | ||||
\(896\) | − | 26.7314i | − | 0.893034i | ||||||
\(897\) | −2.94235 | − | 6.56745i | −0.0982422 | − | 0.219281i | ||||
\(898\) | −5.58653 | + | 5.58653i | −0.186425 | + | 0.186425i | ||||
\(899\) | −0.216767 | −0.00722959 | ||||||||
\(900\) | −0.00228384 | + | 0.0184060i | −7.61279e−5 | + | 0.000613532i | ||||
\(901\) | −7.76371 | −0.258647 | ||||||||
\(902\) | −3.47830 | + | 3.47830i | −0.115815 | + | 0.115815i | ||||
\(903\) | −9.79886 | − | 21.8715i | −0.326086 | − | 0.727838i | ||||
\(904\) | 2.42667i | 0.0807097i | ||||||||
\(905\) | −38.0645 | − | 19.9588i | −1.26531 | − | 0.663453i | ||||
\(906\) | −42.3074 | − | 16.1274i | −1.40557 | − | 0.535798i | ||||
\(907\) | −26.2609 | − | 26.2609i | −0.871980 | − | 0.871980i | 0.120708 | − | 0.992688i | \(-0.461484\pi\) |
−0.992688 | + | 0.120708i | \(0.961484\pi\) | |||||||
\(908\) | −0.00557825 | − | 0.00557825i | −0.000185121 | − | 0.000185121i | ||||
\(909\) | −30.3357 | − | 27.0598i | −1.00617 | − | 0.897518i | ||||
\(910\) | −6.10887 | + | 1.90622i | −0.202507 | + | 0.0631906i | ||||
\(911\) | − | 11.9878i | − | 0.397172i | −0.980083 | − | 0.198586i | \(-0.936365\pi\) | ||
0.980083 | − | 0.198586i | \(-0.0636349\pi\) | |||||||
\(912\) | −9.24389 | + | 4.14145i | −0.306096 | + | 0.137137i | ||||
\(913\) | 0.169040 | − | 0.169040i | 0.00559440 | − | 0.00559440i | ||||
\(914\) | −37.4799 | −1.23972 | ||||||||
\(915\) | −0.872186 | + | 14.1122i | −0.0288336 | + | 0.466535i | ||||
\(916\) | 0.0284658 | 0.000940536 | ||||||||
\(917\) | 22.5205 | − | 22.5205i | 0.743692 | − | 0.743692i | ||||
\(918\) | −1.76105 | + | 5.55152i | −0.0581233 | + | 0.183227i | ||||
\(919\) | − | 26.1006i | − | 0.860978i | −0.902596 | − | 0.430489i | \(-0.858341\pi\) | ||
0.902596 | − | 0.430489i | \(-0.141659\pi\) | |||||||
\(920\) | 14.2343 | − | 27.1470i | 0.469291 | − | 0.895009i | ||||
\(921\) | −11.1701 | + | 29.3028i | −0.368069 | + | 0.965561i | ||||
\(922\) | −1.80234 | − | 1.80234i | −0.0593569 | − | 0.0593569i | ||||
\(923\) | 0.0524659 | + | 0.0524659i | 0.00172694 | + | 0.00172694i | ||||
\(924\) | −0.000879885 | 0.00230822i | −2.89461e−5 | 7.59348e-5i | ||||||
\(925\) | −6.64147 | + | 36.4018i | −0.218370 | + | 1.19688i | ||||
\(926\) | 57.7970i | 1.89933i | ||||||||
\(927\) | −0.783079 | − | 13.7201i | −0.0257197 | − | 0.450626i | ||||
\(928\) | 0.00107211 | − | 0.00107211i | 3.51937e−5 | − | 3.51937e-5i | ||||
\(929\) | 15.4055 | 0.505437 | 0.252718 | − | 0.967540i | \(-0.418675\pi\) | ||||
0.252718 | + | 0.967540i | \(0.418675\pi\) | |||||||
\(930\) | −3.62782 | − | 4.10578i | −0.118961 | − | 0.134634i | ||||
\(931\) | 2.08614 | 0.0683705 | ||||||||
\(932\) | −0.0242584 | + | 0.0242584i | −0.000794611 | + | 0.000794611i | ||||
\(933\) | −34.2441 | + | 15.3420i | −1.12110 | + | 0.502276i | ||||
\(934\) | 3.54535i | 0.116007i | ||||||||
\(935\) | −0.257870 | − | 0.826395i | −0.00843324 | − | 0.0270260i | ||||
\(936\) | −4.83922 | + | 5.42506i | −0.158175 | + | 0.177324i | ||||
\(937\) | −38.8342 | − | 38.8342i | −1.26866 | − | 1.26866i | −0.946782 | − | 0.321874i | \(-0.895687\pi\) |
−0.321874 | − | 0.946782i | \(-0.604313\pi\) | |||||||
\(938\) | 15.8083 | + | 15.8083i | 0.516161 | + | 0.516161i | ||||
\(939\) | 35.5272 | + | 13.5428i | 1.15939 | + | 0.441954i | ||||
\(940\) | −0.00742930 | − | 0.0238087i | −0.000242317 | − | 0.000776554i | ||||
\(941\) | 41.2021i | 1.34315i | 0.740937 | + | 0.671574i | \(0.234382\pi\) | ||||
−0.740937 | + | 0.671574i | \(0.765618\pi\) | |||||||
\(942\) | 22.7567 | + | 50.7940i | 0.741453 | + | 1.65496i | ||||
\(943\) | −24.3955 | + | 24.3955i | −0.794425 | + | 0.794425i | ||||
\(944\) | −38.0804 | −1.23941 | ||||||||
\(945\) | −0.129223 | + | 27.4269i | −0.00420361 | + | 0.892197i | ||||
\(946\) | −4.05184 | −0.131737 | ||||||||
\(947\) | 16.9664 | − | 16.9664i | 0.551332 | − | 0.551332i | −0.375493 | − | 0.926825i | \(-0.622527\pi\) |
0.926825 | + | 0.375493i | \(0.122527\pi\) | |||||||
\(948\) | −0.00784613 | − | 0.0175129i | −0.000254830 | − | 0.000568793i | ||||
\(949\) | − | 2.36195i | − | 0.0766723i | ||||||
\(950\) | −1.85497 | + | 10.1671i | −0.0601832 | + | 0.329863i | ||||
\(951\) | −31.4208 | − | 11.9775i | −1.01889 | − | 0.388398i | ||||
\(952\) | −3.73948 | − | 3.73948i | −0.121197 | − | 0.121197i | ||||
\(953\) | 19.9054 | + | 19.9054i | 0.644799 | + | 0.644799i | 0.951731 | − | 0.306932i | \(-0.0993025\pi\) |
−0.306932 | + | 0.951731i | \(0.599303\pi\) | |||||||
\(954\) | 27.6818 | − | 31.0330i | 0.896232 | − | 1.00473i | ||||
\(955\) | 25.3132 | − | 48.2762i | 0.819116 | − | 1.56218i | ||||
\(956\) | − | 0.0107142i | − | 0.000346522i | ||||||
\(957\) | 0.167422 | − | 0.0750081i | 0.00541197 | − | 0.00242467i | ||||
\(958\) | 36.3937 | − | 36.3937i | 1.17583 | − | 1.17583i | ||||
\(959\) | −40.9172 | −1.32129 | ||||||||
\(960\) | −30.9057 | − | 1.91009i | −0.997478 | − | 0.0616478i | ||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 6.34433 | − | 6.34433i | 0.204550 | − | 0.204550i | ||||
\(963\) | −1.37067 | − | 24.0150i | −0.0441692 | − | 0.773873i | ||||
\(964\) | 0.0240824i | 0.000775643i | ||||||||
\(965\) | −17.9620 | + | 5.60488i | −0.578217 | + | 0.180428i | ||||
\(966\) | −9.98807 | + | 26.2019i | −0.321361 | + | 0.843031i | ||||
\(967\) | 10.1993 | + | 10.1993i | 0.327986 | + | 0.327986i | 0.851820 | − | 0.523834i | \(-0.175499\pi\) |
−0.523834 | + | 0.851820i | \(0.675499\pi\) | |||||||
\(968\) | 21.5158 | + | 21.5158i | 0.691545 | + | 0.691545i | ||||
\(969\) | −0.714227 | + | 1.87364i | −0.0229443 | + | 0.0601901i | ||||
\(970\) | −5.28662 | − | 2.77200i | −0.169743 | − | 0.0890035i | ||||
\(971\) | − | 52.2148i | − | 1.67565i | −0.545937 | − | 0.837826i | \(-0.683826\pi\) | ||
0.545937 | − | 0.837826i | \(-0.316174\pi\) | |||||||
\(972\) | −0.00983091 | − | 0.0165792i | −0.000315327 | − | 0.000531777i | ||||
\(973\) | −2.53923 | + | 2.53923i | −0.0814038 | + | 0.0814038i | ||||
\(974\) | −33.7731 | −1.08216 | ||||||||
\(975\) | 1.76957 | + | 7.20792i | 0.0566715 | + | 0.230838i | ||||
\(976\) | 14.6119 | 0.467714 | ||||||||
\(977\) | 16.2313 | − | 16.2313i | 0.519287 | − | 0.519287i | −0.398069 | − | 0.917356i | \(-0.630319\pi\) |
0.917356 | + | 0.398069i | \(0.130319\pi\) | |||||||
\(978\) | 11.6126 | − | 5.20266i | 0.371329 | − | 0.166363i | ||||
\(979\) | 5.96980i | 0.190796i | ||||||||
\(980\) | −0.00349609 | − | 0.00183315i | −0.000111679 | − | 5.85578e-5i | ||||
\(981\) | −33.5242 | − | 29.9040i | −1.07034 | − | 0.954760i | ||||
\(982\) | 3.75394 | + | 3.75394i | 0.119793 | + | 0.119793i | ||||
\(983\) | −3.80734 | − | 3.80734i | −0.121435 | − | 0.121435i | 0.643777 | − | 0.765213i | \(-0.277366\pi\) |
−0.765213 | + | 0.643777i | \(0.777366\pi\) | |||||||
\(984\) | 32.5660 | + | 12.4140i | 1.03817 | + | 0.395745i | ||||
\(985\) | 47.5568 | − | 14.8397i | 1.51529 | − | 0.472832i | ||||
\(986\) | − | 0.242965i | − | 0.00773758i | ||||||
\(987\) | −15.0797 | − | 33.6586i | −0.479993 | − | 1.07136i | ||||
\(988\) | 0.00109483 | − | 0.00109483i | 3.48311e−5 | − | 3.48311e-5i | ||||
\(989\) | −28.4180 | −0.903640 | ||||||||
\(990\) | 4.22270 | + | 1.91579i | 0.134206 | + | 0.0608879i | ||||
\(991\) | 26.4153 | 0.839111 | 0.419555 | − | 0.907730i | \(-0.362186\pi\) | ||||
0.419555 | + | 0.907730i | \(0.362186\pi\) | |||||||
\(992\) | −0.00494590 | + | 0.00494590i | −0.000157032 | + | 0.000157032i | ||||
\(993\) | −11.6660 | − | 26.0389i | −0.370208 | − | 0.826321i | ||||
\(994\) | − | 0.289113i | − | 0.00917011i | ||||||
\(995\) | −4.25382 | + | 8.11269i | −0.134855 | + | 0.257190i | ||||
\(996\) | 0.000979061 | 0 | 0.000373215i | 3.10227e−5 | 0 | 1.18258e-5i | ||||
\(997\) | −1.90689 | − | 1.90689i | −0.0603917 | − | 0.0603917i | 0.676266 | − | 0.736658i | \(-0.263597\pi\) |
−0.736658 | + | 0.676266i | \(0.763597\pi\) | |||||||
\(998\) | −6.14757 | − | 6.14757i | −0.194598 | − | 0.194598i | ||||
\(999\) | −17.6967 | − | 34.1404i | −0.559898 | − | 1.08015i |
(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 | 465.2.k.b.32.22 | yes | 60 | |
3.2 | odd | 2 | inner | 465.2.k.b.32.9 | ✓ | 60 | |
5.3 | odd | 4 | inner | 465.2.k.b.218.9 | yes | 60 | |
15.8 | even | 4 | inner | 465.2.k.b.218.22 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
465.2.k.b.32.9 | ✓ | 60 | 3.2 | odd | 2 | inner | |
465.2.k.b.32.22 | yes | 60 | 1.1 | even | 1 | trivial | |
465.2.k.b.218.9 | yes | 60 | 5.3 | odd | 4 | inner | |
465.2.k.b.218.22 | yes | 60 | 15.8 | even | 4 | inner |