Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [729,2,Mod(28,729)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(54))
chi = DirichletCharacter(H, H._module([44]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("729.28");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.g (of order \(27\), degree \(18\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.82109430735\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{27})\) |
Twist minimal: | no (minimal twist has level 81) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{27}]$ |
Embedding invariants
Embedding label | 703.4 | ||
Character | \(\chi\) | \(=\) | 729.703 |
Dual form | 729.2.g.a.28.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{27}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.463223 | − | 0.304667i | −0.327548 | − | 0.215432i | 0.375074 | − | 0.926995i | \(-0.377617\pi\) |
−0.702622 | + | 0.711563i | \(0.747988\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.670406 | − | 1.55417i | −0.335203 | − | 0.777087i | ||||
\(5\) | 0.355980 | + | 0.377317i | 0.159199 | + | 0.168741i | 0.802063 | − | 0.597239i | \(-0.203736\pi\) |
−0.642864 | + | 0.765980i | \(0.722254\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.24586 | + | 0.262503i | −0.848855 | + | 0.0992170i | −0.529387 | − | 0.848380i | \(-0.677578\pi\) |
−0.319468 | + | 0.947597i | \(0.603504\pi\) | |||||||
\(8\) | −0.355511 | + | 2.01620i | −0.125692 | + | 0.712835i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.0499424 | − | 0.283238i | −0.0157932 | − | 0.0895676i | ||||
\(11\) | 0.352258 | + | 1.17662i | 0.106210 | + | 0.354766i | 0.994529 | − | 0.104461i | \(-0.0333117\pi\) |
−0.888319 | + | 0.459227i | \(0.848127\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.226512 | + | 3.88906i | 0.0628232 | + | 1.07863i | 0.871505 | + | 0.490386i | \(0.163144\pi\) |
−0.808682 | + | 0.588246i | \(0.799819\pi\) | |||||||
\(14\) | 1.12031 | + | 0.562641i | 0.299416 | + | 0.150372i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.54412 | + | 1.63667i | −0.386029 | + | 0.409167i | ||||
\(17\) | 6.74697 | + | 2.45569i | 1.63638 | + | 0.595593i | 0.986401 | − | 0.164359i | \(-0.0525555\pi\) |
0.649979 | + | 0.759952i | \(0.274778\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.31557 | − | 0.478829i | 0.301813 | − | 0.109851i | −0.186675 | − | 0.982422i | \(-0.559771\pi\) |
0.488487 | + | 0.872571i | \(0.337549\pi\) | |||||||
\(20\) | 0.347766 | − | 0.806212i | 0.0777628 | − | 0.180274i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.195304 | − | 0.652361i | 0.0416390 | − | 0.139084i | ||||
\(23\) | 1.91236 | + | 0.223523i | 0.398755 | + | 0.0466077i | 0.313107 | − | 0.949718i | \(-0.398630\pi\) |
0.0856474 | + | 0.996326i | \(0.472704\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.275078 | − | 4.72291i | 0.0550156 | − | 0.944581i | ||||
\(26\) | 1.07994 | − | 1.87051i | 0.211794 | − | 0.366838i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.91361 | + | 3.31448i | 0.361639 | + | 0.626377i | ||||
\(29\) | 6.18810 | − | 3.10778i | 1.14910 | − | 0.577100i | 0.230807 | − | 0.972999i | \(-0.425863\pi\) |
0.918294 | + | 0.395899i | \(0.129567\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.11811 | + | 5.53158i | −0.739635 | + | 0.993502i | 0.259977 | + | 0.965615i | \(0.416285\pi\) |
−0.999611 | + | 0.0278867i | \(0.991122\pi\) | |||||||
\(32\) | 5.19815 | − | 1.23198i | 0.918912 | − | 0.217786i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.37718 | − | 3.19311i | −0.407683 | − | 0.547614i | ||||
\(35\) | −0.898529 | − | 0.753956i | −0.151879 | − | 0.127442i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.62954 | − | 3.04555i | 0.596693 | − | 0.500685i | −0.293688 | − | 0.955901i | \(-0.594883\pi\) |
0.890381 | + | 0.455216i | \(0.150438\pi\) | |||||||
\(38\) | −0.755286 | − | 0.179006i | −0.122524 | − | 0.0290386i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.887303 | + | 0.583588i | −0.140295 | + | 0.0922734i | ||||
\(41\) | 1.26157 | − | 0.829746i | 0.197024 | − | 0.129585i | −0.447164 | − | 0.894452i | \(-0.647566\pi\) |
0.644188 | + | 0.764867i | \(0.277196\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.33285 | − | 0.552895i | −0.355756 | − | 0.0843157i | 0.0488519 | − | 0.998806i | \(-0.484444\pi\) |
−0.404608 | + | 0.914490i | \(0.632592\pi\) | |||||||
\(44\) | 1.59252 | − | 1.33629i | 0.240082 | − | 0.201453i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.817749 | − | 0.686173i | −0.120571 | − | 0.101171i | ||||
\(47\) | 6.75172 | + | 9.06914i | 0.984840 | + | 1.32287i | 0.946188 | + | 0.323617i | \(0.104899\pi\) |
0.0386515 | + | 0.999253i | \(0.487694\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.83633 | + | 0.435219i | −0.262334 | + | 0.0621742i | ||||
\(50\) | −1.56633 | + | 2.10395i | −0.221513 | + | 0.297544i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.89243 | − | 2.95929i | 0.817133 | − | 0.410380i | ||||
\(53\) | −3.04317 | − | 5.27093i | −0.418012 | − | 0.724018i | 0.577728 | − | 0.816230i | \(-0.303940\pi\) |
−0.995739 | + | 0.0922118i | \(0.970606\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.318564 | + | 0.551769i | −0.0429551 | + | 0.0744005i | ||||
\(56\) | 0.269168 | − | 4.62143i | 0.0359691 | − | 0.617565i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.81331 | − | 0.445712i | −0.500712 | − | 0.0585248i | ||||
\(59\) | −3.69936 | + | 12.3567i | −0.481616 | + | 1.60871i | 0.279536 | + | 0.960135i | \(0.409819\pi\) |
−0.761152 | + | 0.648574i | \(0.775366\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.26328 | − | 5.24688i | 0.289784 | − | 0.671794i | −0.709681 | − | 0.704524i | \(-0.751161\pi\) |
0.999464 | + | 0.0327296i | \(0.0104200\pi\) | |||||||
\(62\) | 3.59289 | − | 1.30771i | 0.456298 | − | 0.166079i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.44557 | + | 0.526145i | 0.180696 | + | 0.0657681i | ||||
\(65\) | −1.38678 | + | 1.46990i | −0.172008 | + | 0.182318i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0102 | + | 6.03174i | 1.46728 | + | 0.736894i | 0.989895 | − | 0.141802i | \(-0.0452895\pi\) |
0.477382 | + | 0.878696i | \(0.341586\pi\) | |||||||
\(68\) | −0.706625 | − | 12.1323i | −0.0856908 | − | 1.47125i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.186514 | + | 0.623002i | 0.0222927 | + | 0.0744630i | ||||
\(71\) | −0.376160 | − | 2.13331i | −0.0446419 | − | 0.253177i | 0.954317 | − | 0.298796i | \(-0.0965850\pi\) |
−0.998959 | + | 0.0456192i | \(0.985474\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.161233 | − | 0.914398i | 0.0188709 | − | 0.107022i | −0.973917 | − | 0.226903i | \(-0.927140\pi\) |
0.992788 | + | 0.119881i | \(0.0382512\pi\) | |||||||
\(74\) | −2.60917 | + | 0.304968i | −0.303309 | + | 0.0354518i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.62615 | − | 1.72362i | −0.186532 | − | 0.197713i | ||||
\(77\) | −1.09999 | − | 2.55007i | −0.125356 | − | 0.290607i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.48739 | + | 4.26682i | 0.729888 | + | 0.480055i | 0.859259 | − | 0.511542i | \(-0.170925\pi\) |
−0.129371 | + | 0.991596i | \(0.541296\pi\) | |||||||
\(80\) | −1.16722 | −0.130499 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.837183 | −0.0924514 | ||||||||
\(83\) | 3.50271 | + | 2.30377i | 0.384473 | + | 0.252872i | 0.727002 | − | 0.686636i | \(-0.240913\pi\) |
−0.342529 | + | 0.939507i | \(0.611284\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.47521 | + | 3.41993i | 0.160009 | + | 0.370943i | ||||
\(86\) | 0.912180 | + | 0.966854i | 0.0983629 | + | 0.104259i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.49755 | + | 0.291921i | −0.266239 | + | 0.0311189i | ||||
\(89\) | −2.46858 | + | 14.0000i | −0.261669 | + | 1.48400i | 0.516687 | + | 0.856175i | \(0.327165\pi\) |
−0.778356 | + | 0.627824i | \(0.783946\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.52961 | − | 8.67483i | −0.160346 | − | 0.909369i | ||||
\(92\) | −0.934663 | − | 3.12199i | −0.0974454 | − | 0.325490i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.364490 | − | 6.25806i | −0.0375943 | − | 0.645469i | ||||
\(95\) | 0.648988 | + | 0.325934i | 0.0665848 | + | 0.0334401i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.6772 | + | 11.3172i | −1.08410 | + | 1.14908i | −0.0959862 | + | 0.995383i | \(0.530600\pi\) |
−0.988118 | + | 0.153700i | \(0.950881\pi\) | |||||||
\(98\) | 0.983230 | + | 0.357866i | 0.0993212 | + | 0.0361500i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.52463 | + | 2.73874i | −0.752463 | + | 0.273874i | ||||
\(101\) | −3.61117 | + | 8.37164i | −0.359325 | + | 0.833010i | 0.638655 | + | 0.769493i | \(0.279491\pi\) |
−0.997981 | + | 0.0635169i | \(0.979768\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.02856 | − | 10.1161i | 0.298413 | − | 0.996769i | −0.668936 | − | 0.743320i | \(-0.733250\pi\) |
0.967349 | − | 0.253449i | \(-0.0815649\pi\) | |||||||
\(104\) | −7.92167 | − | 0.925910i | −0.776783 | − | 0.0907929i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.196209 | + | 3.36877i | −0.0190575 | + | 0.327204i | ||||
\(107\) | −5.34166 | + | 9.25202i | −0.516398 | + | 0.894427i | 0.483421 | + | 0.875388i | \(0.339394\pi\) |
−0.999819 | + | 0.0190389i | \(0.993939\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.00123 | + | 8.66239i | 0.479031 | + | 0.829707i | 0.999711 | − | 0.0240456i | \(-0.00765470\pi\) |
−0.520680 | + | 0.853752i | \(0.674321\pi\) | |||||||
\(110\) | 0.315672 | − | 0.158536i | 0.0300981 | − | 0.0151158i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.03824 | − | 4.08107i | 0.287087 | − | 0.385625i | ||||
\(113\) | 16.6744 | − | 3.95190i | 1.56859 | − | 0.371764i | 0.647799 | − | 0.761811i | \(-0.275689\pi\) |
0.920795 | + | 0.390047i | \(0.127541\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.596424 | + | 0.801136i | 0.0556168 | + | 0.0747063i | ||||
\(116\) | −8.97857 | − | 7.53392i | −0.833640 | − | 0.699507i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.47831 | − | 4.59685i | 0.504320 | − | 0.423174i | ||||
\(119\) | −15.7974 | − | 3.74405i | −1.44814 | − | 0.343216i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.93001 | − | 5.21565i | 0.720910 | − | 0.474150i | ||||
\(122\) | −2.64695 | + | 1.74093i | −0.239644 | + | 0.157616i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 11.3579 | + | 2.69186i | 1.01997 | + | 0.241736i | ||||
\(125\) | 3.86684 | − | 3.24467i | 0.345861 | − | 0.290212i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.19946 | − | 7.71927i | −0.816320 | − | 0.684974i | 0.135787 | − | 0.990738i | \(-0.456644\pi\) |
−0.952107 | + | 0.305764i | \(0.901088\pi\) | |||||||
\(128\) | −6.88954 | − | 9.25426i | −0.608955 | − | 0.817969i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.09022 | − | 0.258386i | 0.0956183 | − | 0.0226619i | ||||
\(131\) | −9.49207 | + | 12.7501i | −0.829326 | + | 1.11398i | 0.162541 | + | 0.986702i | \(0.448031\pi\) |
−0.991867 | + | 0.127277i | \(0.959376\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.82889 | + | 1.42072i | −0.245296 | + | 0.123192i | ||||
\(134\) | −3.72572 | − | 6.45314i | −0.321854 | − | 0.557467i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.34980 | + | 12.7302i | −0.630240 | + | 1.09161i | ||||
\(137\) | 0.0263322 | − | 0.452106i | 0.00224971 | − | 0.0386260i | −0.996996 | − | 0.0774470i | \(-0.975323\pi\) |
0.999246 | + | 0.0388209i | \(0.0123602\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.70831 | − | 0.667205i | −0.484172 | − | 0.0565916i | −0.129494 | − | 0.991580i | \(-0.541335\pi\) |
−0.354678 | + | 0.934989i | \(0.615409\pi\) | |||||||
\(140\) | −0.569400 | + | 1.90193i | −0.0481231 | + | 0.160742i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.475702 | + | 1.10280i | −0.0399200 | + | 0.0925450i | ||||
\(143\) | −4.49618 | + | 1.63647i | −0.375989 | + | 0.136849i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.37546 | + | 1.22857i | 0.280317 | + | 0.102027i | ||||
\(146\) | −0.353274 | + | 0.374448i | −0.0292371 | + | 0.0309896i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.16658 | − | 3.59919i | −0.589089 | − | 0.295852i | ||||
\(149\) | −0.769758 | − | 13.2162i | −0.0630611 | − | 1.08272i | −0.870310 | − | 0.492505i | \(-0.836081\pi\) |
0.807249 | − | 0.590212i | \(-0.200956\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.813561 | − | 2.71748i | −0.0662067 | − | 0.221146i | 0.918484 | − | 0.395459i | \(-0.129415\pi\) |
−0.984690 | + | 0.174314i | \(0.944229\pi\) | |||||||
\(152\) | 0.497716 | + | 2.82269i | 0.0403701 | + | 0.228950i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.267379 | + | 1.51638i | −0.0215460 | + | 0.122193i | ||||
\(155\) | −3.55313 | + | 0.415301i | −0.285394 | + | 0.0333578i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.58966 | − | 10.1644i | −0.765338 | − | 0.811211i | 0.221116 | − | 0.975247i | \(-0.429030\pi\) |
−0.986454 | + | 0.164036i | \(0.947549\pi\) | |||||||
\(158\) | −1.70515 | − | 3.95298i | −0.135654 | − | 0.314482i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.31529 | + | 1.52279i | 0.183040 | + | 0.120387i | ||||
\(161\) | −4.35357 | −0.343109 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.66700 | 0.208896 | 0.104448 | − | 0.994530i | \(-0.466692\pi\) | ||||
0.104448 | + | 0.994530i | \(0.466692\pi\) | |||||||
\(164\) | −2.13533 | − | 1.40443i | −0.166741 | − | 0.109668i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.920655 | − | 2.13432i | −0.0714567 | − | 0.165655i | ||||
\(167\) | −14.2643 | − | 15.1193i | −1.10381 | − | 1.16997i | −0.984184 | − | 0.177147i | \(-0.943313\pi\) |
−0.119622 | − | 0.992820i | \(-0.538168\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.16140 | + | 0.252632i | −0.166262 | + | 0.0194332i | ||||
\(170\) | 0.358585 | − | 2.03364i | 0.0275022 | − | 0.155973i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.704658 | + | 3.99631i | 0.0537297 | + | 0.304716i | ||||
\(173\) | −3.83764 | − | 12.8186i | −0.291770 | − | 0.974580i | −0.970683 | − | 0.240362i | \(-0.922734\pi\) |
0.678913 | − | 0.734218i | \(-0.262451\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.621992 | + | 10.6792i | 0.0470182 | + | 0.807271i | ||||
\(176\) | −2.46967 | − | 1.24032i | −0.186159 | − | 0.0934924i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.40884 | − | 5.73304i | 0.405410 | − | 0.429709i | ||||
\(179\) | −3.77200 | − | 1.37290i | −0.281932 | − | 0.102615i | 0.197184 | − | 0.980367i | \(-0.436820\pi\) |
−0.479116 | + | 0.877752i | \(0.659043\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.3224 | + | 4.48500i | −0.915920 | + | 0.333368i | −0.756614 | − | 0.653862i | \(-0.773148\pi\) |
−0.159306 | + | 0.987229i | \(0.550926\pi\) | |||||||
\(182\) | −1.93438 | + | 4.48440i | −0.143386 | + | 0.332406i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.13053 | + | 3.77624i | −0.0833439 | + | 0.278388i | ||||
\(185\) | 2.44118 | + | 0.285334i | 0.179479 | + | 0.0209781i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.512756 | + | 8.80369i | −0.0374965 | + | 0.643789i | ||||
\(188\) | 9.56863 | − | 16.5734i | 0.697864 | − | 1.20874i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.201325 | − | 0.348705i | −0.0146057 | − | 0.0252977i | ||||
\(191\) | −0.0543345 | + | 0.0272878i | −0.00393151 | + | 0.00197448i | −0.450764 | − | 0.892643i | \(-0.648848\pi\) |
0.446832 | + | 0.894618i | \(0.352552\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.97643 | + | 2.65481i | −0.142267 | + | 0.191097i | −0.867545 | − | 0.497358i | \(-0.834304\pi\) |
0.725279 | + | 0.688455i | \(0.241711\pi\) | |||||||
\(194\) | 8.39388 | − | 1.98939i | 0.602645 | − | 0.142830i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.90750 | + | 2.56221i | 0.136250 | + | 0.183015i | ||||
\(197\) | 11.5875 | + | 9.72308i | 0.825576 | + | 0.692740i | 0.954271 | − | 0.298944i | \(-0.0966343\pi\) |
−0.128695 | + | 0.991684i | \(0.541079\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.76072 | + | 5.67291i | −0.479254 | + | 0.402142i | −0.850157 | − | 0.526530i | \(-0.823493\pi\) |
0.370902 | + | 0.928672i | \(0.379048\pi\) | |||||||
\(200\) | 9.42454 | + | 2.23366i | 0.666416 | + | 0.157943i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.22334 | − | 2.77774i | 0.297153 | − | 0.195441i | ||||
\(203\) | −13.0818 | + | 8.60404i | −0.918163 | + | 0.603885i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.762171 | + | 0.180638i | 0.0532323 | + | 0.0126163i | ||||
\(206\) | −4.48494 | + | 3.76331i | −0.312480 | + | 0.262202i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.71487 | − | 5.63445i | −0.465593 | − | 0.390679i | ||||
\(209\) | 1.02682 | + | 1.37926i | 0.0710268 | + | 0.0954056i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0628 | − | 3.80695i | 1.10581 | − | 0.262081i | 0.363135 | − | 0.931736i | \(-0.381706\pi\) |
0.742672 | + | 0.669655i | \(0.233558\pi\) | |||||||
\(212\) | −6.15179 | + | 8.26328i | −0.422506 | + | 0.567525i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.29316 | − | 2.65833i | 0.361833 | − | 0.181719i | ||||
\(215\) | −0.621831 | − | 1.07704i | −0.0424085 | − | 0.0734537i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.79664 | − | 13.5042i | 0.529270 | − | 0.916723i | ||||
\(218\) | 0.322454 | − | 5.53633i | 0.0218394 | − | 0.374968i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.07111 | + | 0.125195i | 0.0722143 | + | 0.00844065i | ||||
\(221\) | −8.02208 | + | 26.7956i | −0.539624 | + | 1.80247i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.08802 | − | 4.84058i | 0.139824 | − | 0.324149i | −0.833887 | − | 0.551936i | \(-0.813889\pi\) |
0.973711 | + | 0.227786i | \(0.0731487\pi\) | |||||||
\(224\) | −11.3509 | + | 4.13140i | −0.758415 | + | 0.276041i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.92798 | − | 3.24952i | −0.593880 | − | 0.216155i | ||||
\(227\) | −4.65004 | + | 4.92876i | −0.308634 | + | 0.327133i | −0.863061 | − | 0.505099i | \(-0.831456\pi\) |
0.554427 | + | 0.832232i | \(0.312937\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.65641 | − | 3.84519i | −0.505950 | − | 0.254097i | 0.177466 | − | 0.984127i | \(-0.443210\pi\) |
−0.683416 | + | 0.730029i | \(0.739506\pi\) | |||||||
\(230\) | −0.0321978 | − | 0.552815i | −0.00212306 | − | 0.0364516i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.06598 | + | 13.5813i | 0.266945 | + | 0.891657i | ||||
\(233\) | −1.32146 | − | 7.49440i | −0.0865720 | − | 0.490974i | −0.997006 | − | 0.0773205i | \(-0.975364\pi\) |
0.910434 | − | 0.413654i | \(-0.135748\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.01846 | + | 5.77598i | −0.0664370 | + | 0.376783i | ||||
\(236\) | 21.6846 | − | 2.53457i | 1.41155 | − | 0.164986i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.17702 | + | 6.54726i | 0.400397 | + | 0.424396i | ||||
\(239\) | −4.56879 | − | 10.5916i | −0.295530 | − | 0.685116i | 0.704159 | − | 0.710042i | \(-0.251324\pi\) |
−0.999689 | + | 0.0249260i | \(0.992065\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.299604 | + | 0.197052i | 0.0192992 | + | 0.0126933i | 0.559122 | − | 0.829085i | \(-0.311138\pi\) |
−0.539823 | + | 0.841779i | \(0.681509\pi\) | |||||||
\(242\) | −5.26240 | −0.338280 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.67188 | −0.619179 | ||||||||
\(245\) | −0.817915 | − | 0.537951i | −0.0522547 | − | 0.0343684i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.16019 | + | 5.00788i | 0.137449 | + | 0.318644i | ||||
\(248\) | −9.68876 | − | 10.2695i | −0.615237 | − | 0.652113i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.77975 | + | 0.324907i | −0.175807 | + | 0.0205489i | ||||
\(251\) | 1.46695 | − | 8.31946i | 0.0925927 | − | 0.525120i | −0.902866 | − | 0.429923i | \(-0.858541\pi\) |
0.995458 | − | 0.0951969i | \(-0.0303481\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.410642 | + | 2.32887i | 0.0258169 | + | 0.146415i | ||||
\(254\) | 1.90960 | + | 6.37851i | 0.119819 | + | 0.400224i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.193037 | + | 3.31432i | 0.0120648 | + | 0.207145i | ||||
\(257\) | 27.9893 | + | 14.0567i | 1.74592 | + | 0.876835i | 0.968934 | + | 0.247319i | \(0.0795495\pi\) |
0.776988 | + | 0.629516i | \(0.216747\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.35198 | + | 7.79264i | −0.456830 | + | 0.484211i | ||||
\(260\) | 3.21418 | + | 1.16987i | 0.199335 | + | 0.0725520i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.28147 | − | 3.01421i | 0.511631 | − | 0.186218i | ||||
\(263\) | 0.790541 | − | 1.83268i | 0.0487468 | − | 0.113008i | −0.892103 | − | 0.451833i | \(-0.850770\pi\) |
0.940849 | + | 0.338825i | \(0.110030\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.905503 | − | 3.02459i | 0.0556246 | − | 0.185799i | ||||
\(266\) | 1.74326 | + | 0.203757i | 0.106886 | + | 0.0124932i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.32269 | − | 22.7096i | 0.0807959 | − | 1.38721i | ||||
\(269\) | −1.73160 | + | 2.99923i | −0.105578 | + | 0.182866i | −0.913974 | − | 0.405772i | \(-0.867003\pi\) |
0.808396 | + | 0.588639i | \(0.200336\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.7474 | − | 25.5433i | −0.895843 | − | 1.55165i | −0.832758 | − | 0.553638i | \(-0.813239\pi\) |
−0.0630854 | − | 0.998008i | \(-0.520094\pi\) | |||||||
\(272\) | −14.4373 | + | 7.25067i | −0.875388 | + | 0.439636i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.149939 | + | 0.201403i | −0.00905817 | + | 0.0121672i | ||||
\(275\) | 5.65399 | − | 1.34002i | 0.340948 | − | 0.0808062i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.71802 | − | 4.99417i | −0.223394 | − | 0.300071i | 0.676269 | − | 0.736655i | \(-0.263596\pi\) |
−0.899664 | + | 0.436584i | \(0.856188\pi\) | |||||||
\(278\) | 2.44094 | + | 2.04820i | 0.146398 | + | 0.122843i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.83956 | − | 1.54358i | 0.109935 | − | 0.0922464i | ||||
\(281\) | 3.61985 | + | 0.857919i | 0.215942 | + | 0.0511792i | 0.337163 | − | 0.941446i | \(-0.390533\pi\) |
−0.121221 | + | 0.992626i | \(0.538681\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.4175 | + | 7.50939i | −0.678698 | + | 0.446387i | −0.841489 | − | 0.540274i | \(-0.818321\pi\) |
0.162791 | + | 0.986661i | \(0.447950\pi\) | |||||||
\(284\) | −3.06335 | + | 2.01480i | −0.181777 | + | 0.119556i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.58131 | + | 0.611782i | 0.152636 | + | 0.0361754i | ||||
\(287\) | −2.61549 | + | 2.19466i | −0.154388 | + | 0.129547i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 26.4684 | + | 22.2096i | 1.55696 | + | 1.30645i | ||||
\(290\) | −1.18929 | − | 1.59749i | −0.0698374 | − | 0.0938080i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.52923 | + | 0.362433i | −0.0894912 | + | 0.0212098i | ||||
\(293\) | 10.1627 | − | 13.6509i | 0.593712 | − | 0.797494i | −0.399134 | − | 0.916893i | \(-0.630689\pi\) |
0.992846 | + | 0.119399i | \(0.0380967\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.97931 | + | 3.00292i | −0.348129 | + | 0.174837i | ||||
\(296\) | 4.85010 | + | 8.40062i | 0.281906 | + | 0.488276i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.66998 | + | 6.35659i | −0.212596 | + | 0.368227i | ||||
\(299\) | −0.436122 | + | 7.48792i | −0.0252216 | + | 0.433037i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.38438 | + | 0.629344i | 0.310351 | + | 0.0362748i | ||||
\(302\) | −0.451066 | + | 1.50667i | −0.0259559 | + | 0.0866989i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.24771 | + | 2.89252i | −0.0715612 | + | 0.165898i | ||||
\(305\) | 2.78542 | − | 1.01381i | 0.159493 | − | 0.0580506i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.43196 | + | 0.885161i | 0.138799 | + | 0.0505188i | 0.410486 | − | 0.911867i | \(-0.365359\pi\) |
−0.271686 | + | 0.962386i | \(0.587581\pi\) | |||||||
\(308\) | −3.22581 | + | 3.41916i | −0.183807 | + | 0.194825i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.77242 | + | 0.890143i | 0.100667 | + | 0.0505567i | ||||
\(311\) | 0.615800 | + | 10.5729i | 0.0349188 | + | 0.599533i | 0.969698 | + | 0.244305i | \(0.0785598\pi\) |
−0.934780 | + | 0.355228i | \(0.884403\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.25206 | − | 20.8833i | −0.353388 | − | 1.18040i | −0.931286 | − | 0.364288i | \(-0.881312\pi\) |
0.577899 | − | 0.816108i | \(-0.303873\pi\) | |||||||
\(314\) | 1.34538 | + | 7.63006i | 0.0759245 | + | 0.430589i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.28221 | − | 12.9430i | 0.128384 | − | 0.728102i | ||||
\(317\) | −3.56102 | + | 0.416224i | −0.200007 | + | 0.0233775i | −0.215507 | − | 0.976502i | \(-0.569140\pi\) |
0.0154994 | + | 0.999880i | \(0.495066\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.83650 | + | 6.18633i | 0.326781 | + | 0.346368i | ||||
\(320\) | 0.316072 | + | 0.732736i | 0.0176689 | + | 0.0409612i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.01667 | + | 1.32639i | 0.112385 | + | 0.0739167i | ||||
\(323\) | 10.0520 | 0.559307 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.4300 | 1.02231 | ||||||||
\(326\) | −1.23542 | − | 0.812546i | −0.0684234 | − | 0.0450028i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.22443 | + | 2.83856i | 0.0676081 | + | 0.156733i | ||||
\(329\) | −17.5441 | − | 18.5957i | −0.967238 | − | 1.02521i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.12316 | − | 0.481928i | 0.226629 | − | 0.0264892i | −0.00202025 | − | 0.999998i | \(-0.500643\pi\) |
0.228650 | + | 0.973509i | \(0.426569\pi\) | |||||||
\(332\) | 1.23222 | − | 6.98829i | 0.0676270 | − | 0.383532i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.00122 | + | 11.3495i | 0.109502 | + | 0.621016i | ||||
\(335\) | 1.99951 | + | 6.67883i | 0.109245 | + | 0.364903i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.19137 | − | 20.4551i | −0.0648982 | − | 1.11426i | −0.860837 | − | 0.508881i | \(-0.830059\pi\) |
0.795939 | − | 0.605377i | \(-0.206978\pi\) | |||||||
\(338\) | 1.07818 | + | 0.541483i | 0.0586453 | + | 0.0294528i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.32617 | − | 4.58548i | 0.234620 | − | 0.248682i | ||||
\(341\) | −7.95924 | − | 2.89692i | −0.431017 | − | 0.156877i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.8834 | − | 6.87300i | 1.01961 | − | 0.371107i | ||||
\(344\) | 1.94410 | − | 4.50693i | 0.104819 | − | 0.242997i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.12772 | + | 7.10707i | −0.114387 | + | 0.382079i | ||||
\(347\) | 31.0030 | + | 3.62373i | 1.66433 | + | 0.194532i | 0.895543 | − | 0.444976i | \(-0.146788\pi\) |
0.768785 | + | 0.639508i | \(0.220862\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.686708 | + | 11.7903i | −0.0367586 | + | 0.631122i | 0.928743 | + | 0.370724i | \(0.120891\pi\) |
−0.965502 | + | 0.260397i | \(0.916146\pi\) | |||||||
\(350\) | 2.96547 | − | 5.13635i | 0.158511 | − | 0.274549i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.28068 | + | 5.68230i | 0.174861 | + | 0.302867i | ||||
\(353\) | 8.47948 | − | 4.25856i | 0.451317 | − | 0.226660i | −0.208596 | − | 0.978002i | \(-0.566889\pi\) |
0.659913 | + | 0.751342i | \(0.270593\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.671028 | − | 0.901347i | 0.0356145 | − | 0.0478385i | ||||
\(356\) | 23.4134 | − | 5.54908i | 1.24091 | − | 0.294101i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.32900 | + | 1.78516i | 0.0702399 | + | 0.0943486i | ||||
\(359\) | 11.7812 | + | 9.88558i | 0.621787 | + | 0.521741i | 0.898365 | − | 0.439250i | \(-0.144756\pi\) |
−0.276578 | + | 0.960992i | \(0.589200\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0534 | + | 10.9531i | −0.687021 | + | 0.576479i | ||||
\(362\) | 7.07447 | + | 1.67668i | 0.371826 | + | 0.0881244i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.4567 | + | 8.19293i | −0.652911 | + | 0.429426i | ||||
\(365\) | 0.402414 | − | 0.264672i | 0.0210633 | − | 0.0138536i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.45240 | − | 0.818233i | −0.180214 | − | 0.0427114i | 0.139518 | − | 0.990220i | \(-0.455445\pi\) |
−0.319732 | + | 0.947508i | \(0.603593\pi\) | |||||||
\(368\) | −3.31874 | + | 2.78476i | −0.173001 | + | 0.145165i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.04388 | − | 0.875921i | −0.0542688 | − | 0.0455369i | ||||
\(371\) | 8.21818 | + | 11.0389i | 0.426666 | + | 0.573113i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.2434 | + | 6.93082i | −1.51417 | + | 0.358865i | −0.901956 | − | 0.431829i | \(-0.857869\pi\) |
−0.612213 | + | 0.790693i | \(0.709720\pi\) | |||||||
\(374\) | 2.91971 | − | 3.92185i | 0.150975 | − | 0.202794i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −20.6855 | + | 10.3887i | −1.06677 | + | 0.535754i | ||||
\(377\) | 13.4880 | + | 23.3620i | 0.694669 | + | 1.20320i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.7966 | − | 20.4324i | 0.605953 | − | 1.04954i | −0.385947 | − | 0.922521i | \(-0.626125\pi\) |
0.991900 | − | 0.127020i | \(-0.0405414\pi\) | |||||||
\(380\) | 0.0714733 | − | 1.22715i | 0.00366650 | − | 0.0629514i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.0334827 | + | 0.00391357i | 0.00171312 | + | 0.000200236i | ||||
\(383\) | −0.0831461 | + | 0.277727i | −0.00424857 | + | 0.0141912i | −0.960088 | − | 0.279700i | \(-0.909765\pi\) |
0.955839 | + | 0.293891i | \(0.0949503\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.570608 | − | 1.32282i | 0.0290809 | − | 0.0674171i | ||||
\(386\) | 1.72436 | − | 0.627616i | 0.0877676 | − | 0.0319448i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 24.7469 | + | 9.00713i | 1.25633 | + | 0.457268i | ||||
\(389\) | 19.2691 | − | 20.4240i | 0.976982 | − | 1.03554i | −0.0223777 | − | 0.999750i | \(-0.507124\pi\) |
0.999359 | − | 0.0357904i | \(-0.0113949\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.3537 | + | 6.20427i | 0.624755 | + | 0.313764i | ||||
\(392\) | −0.224653 | − | 3.85715i | −0.0113467 | − | 0.194815i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.40531 | − | 8.03428i | −0.121178 | − | 0.404761i | ||||
\(395\) | 0.699438 | + | 3.96671i | 0.0351925 | + | 0.199587i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.686472 | + | 3.89317i | −0.0344530 | + | 0.195393i | −0.997176 | − | 0.0750952i | \(-0.976074\pi\) |
0.962723 | + | 0.270488i | \(0.0871850\pi\) | |||||||
\(398\) | 4.86007 | − | 0.568061i | 0.243613 | − | 0.0284743i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.30508 | + | 7.74293i | 0.365254 | + | 0.387147i | ||||
\(401\) | 0.790666 | + | 1.83297i | 0.0394840 | + | 0.0915341i | 0.936817 | − | 0.349820i | \(-0.113757\pi\) |
−0.897333 | + | 0.441355i | \(0.854498\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.4455 | − | 14.7626i | −1.11809 | − | 0.735379i | ||||
\(404\) | 15.4320 | 0.767768 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.68116 | 0.430839 | ||||||||
\(407\) | 4.86200 | + | 3.19779i | 0.241001 | + | 0.158509i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.74536 | − | 11.0010i | −0.234643 | − | 0.543963i | 0.759689 | − | 0.650287i | \(-0.225351\pi\) |
−0.994332 | + | 0.106324i | \(0.966092\pi\) | |||||||
\(410\) | −0.298021 | − | 0.315884i | −0.0147182 | − | 0.0156004i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −17.7526 | + | 2.07498i | −0.874605 | + | 0.102227i | ||||
\(413\) | 5.06457 | − | 28.7226i | 0.249211 | − | 1.41335i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.377645 | + | 2.14173i | 0.0185379 | + | 0.105133i | ||||
\(416\) | 5.96871 | + | 19.9369i | 0.292640 | + | 0.977486i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.0554328 | − | 0.951745i | −0.00271131 | − | 0.0465514i | ||||
\(419\) | 16.5709 | + | 8.32220i | 0.809540 | + | 0.406566i | 0.804891 | − | 0.593423i | \(-0.202224\pi\) |
0.00464887 | + | 0.999989i | \(0.498520\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.5846 | − | 28.1780i | 1.29565 | − | 1.37331i | 0.407878 | − | 0.913036i | \(-0.366269\pi\) |
0.887776 | − | 0.460276i | \(-0.152250\pi\) | |||||||
\(422\) | −8.60050 | − | 3.13033i | −0.418666 | − | 0.152382i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.7091 | − | 4.26178i | 0.568646 | − | 0.206970i | ||||
\(425\) | 13.4540 | − | 31.1898i | 0.652613 | − | 1.51293i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.70569 | + | 12.3779i | −0.179331 | + | 0.599007i | ||||
\(428\) | 17.9603 | + | 2.09926i | 0.868146 | + | 0.101472i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.0400925 | + | 0.688362i | −0.00193343 | + | 0.0331958i | ||||
\(431\) | −4.62147 | + | 8.00461i | −0.222608 | + | 0.385569i | −0.955599 | − | 0.294670i | \(-0.904790\pi\) |
0.732991 | + | 0.680238i | \(0.238124\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.80798 | + | 10.0597i | 0.279114 | + | 0.483439i | 0.971165 | − | 0.238410i | \(-0.0766261\pi\) |
−0.692051 | + | 0.721848i | \(0.743293\pi\) | |||||||
\(434\) | −7.72586 | + | 3.88007i | −0.370853 | + | 0.186249i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.1100 | − | 13.5801i | 0.484182 | − | 0.650369i | ||||
\(437\) | 2.62287 | − | 0.621633i | 0.125469 | − | 0.0297367i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.55626 | + | 12.8363i | 0.456095 | + | 0.612642i | 0.969377 | − | 0.245578i | \(-0.0789777\pi\) |
−0.513282 | + | 0.858220i | \(0.671570\pi\) | |||||||
\(440\) | −0.999224 | − | 0.838449i | −0.0476362 | − | 0.0399715i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.8797 | − | 9.96829i | 0.565062 | − | 0.474143i | ||||
\(443\) | 3.87119 | + | 0.917488i | 0.183926 | + | 0.0435912i | 0.321546 | − | 0.946894i | \(-0.395797\pi\) |
−0.137621 | + | 0.990485i | \(0.543946\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.16121 | + | 4.05229i | −0.292070 | + | 0.192097i | ||||
\(446\) | −2.44199 | + | 1.60612i | −0.115631 | + | 0.0760520i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.38467 | − | 0.802181i | −0.159910 | − | 0.0378995i | ||||
\(449\) | 21.2890 | − | 17.8636i | 1.00469 | − | 0.843035i | 0.0170628 | − | 0.999854i | \(-0.494568\pi\) |
0.987627 | + | 0.156819i | \(0.0501240\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.42070 | + | 1.19211i | 0.0668980 | + | 0.0561341i | ||||
\(452\) | −17.3205 | − | 23.2655i | −0.814690 | − | 1.09432i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.65564 | − | 0.866402i | 0.171567 | − | 0.0406622i | ||||
\(455\) | 2.72865 | − | 3.66522i | 0.127921 | − | 0.171828i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.41493 | − | 0.710606i | 0.0661877 | − | 0.0332407i | −0.415397 | − | 0.909640i | \(-0.636357\pi\) |
0.481585 | + | 0.876399i | \(0.340061\pi\) | |||||||
\(458\) | 2.37512 | + | 4.11383i | 0.110982 | + | 0.192227i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.845260 | − | 1.46403i | 0.0394104 | − | 0.0682609i | ||||
\(461\) | −1.67892 | + | 28.8259i | −0.0781950 | + | 1.34256i | 0.699824 | + | 0.714315i | \(0.253262\pi\) |
−0.778019 | + | 0.628241i | \(0.783775\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.9507 | + | 1.63060i | 0.648344 | + | 0.0757805i | 0.433907 | − | 0.900957i | \(-0.357135\pi\) |
0.214436 | + | 0.976738i | \(0.431209\pi\) | |||||||
\(464\) | −4.46875 | + | 14.9267i | −0.207456 | + | 0.692953i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.67116 | + | 3.87418i | −0.0774150 | + | 0.179468i | ||||
\(467\) | 8.66429 | − | 3.15354i | 0.400935 | − | 0.145929i | −0.133679 | − | 0.991025i | \(-0.542679\pi\) |
0.534614 | + | 0.845096i | \(0.320457\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.5565 | − | 10.3937i | −1.31862 | − | 0.479938i | ||||
\(470\) | 2.23152 | − | 2.36528i | 0.102932 | − | 0.109102i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −23.5985 | − | 11.8516i | −1.08621 | − | 0.545515i | ||||
\(473\) | −0.171215 | − | 2.93965i | −0.00787247 | − | 0.135165i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.89958 | − | 6.34503i | −0.0871586 | − | 0.291130i | ||||
\(476\) | 4.77174 | + | 27.0619i | 0.218713 | + | 1.24038i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.11055 | + | 6.29825i | −0.0507954 | + | 0.288075i | ||||
\(479\) | −38.0552 | + | 4.44802i | −1.73879 | + | 0.203235i | −0.925532 | − | 0.378670i | \(-0.876381\pi\) |
−0.813256 | + | 0.581906i | \(0.802307\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.6665 | + | 13.4257i | 0.577541 | + | 0.612158i | ||||
\(482\) | −0.0787481 | − | 0.182559i | −0.00358688 | − | 0.00831531i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.4223 | − | 8.82802i | −0.610107 | − | 0.401274i | ||||
\(485\) | −8.07103 | −0.366486 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.8391 | −1.44277 | −0.721384 | − | 0.692535i | \(-0.756494\pi\) | ||||
−0.721384 | + | 0.692535i | \(0.756494\pi\) | |||||||
\(488\) | 9.77415 | + | 6.42856i | 0.442455 | + | 0.291007i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.214981 | + | 0.498383i | 0.00971187 | + | 0.0225146i | ||||
\(491\) | −18.1984 | − | 19.2891i | −0.821280 | − | 0.870506i | 0.172135 | − | 0.985073i | \(-0.444933\pi\) |
−0.993416 | + | 0.114567i | \(0.963452\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 49.3827 | − | 5.77201i | 2.22408 | − | 0.259958i | ||||
\(494\) | 0.525085 | − | 2.97790i | 0.0236247 | − | 0.133982i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.69452 | − | 15.2814i | −0.120988 | − | 0.686155i | ||||
\(497\) | 1.40480 | + | 4.69237i | 0.0630140 | + | 0.210481i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.394547 | + | 6.77412i | 0.0176624 | + | 0.303251i | 0.995558 | + | 0.0941553i | \(0.0300150\pi\) |
−0.977895 | + | 0.209096i | \(0.932948\pi\) | |||||||
\(500\) | −7.63513 | − | 3.83451i | −0.341453 | − | 0.171484i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.21418 | + | 3.40684i | −0.143456 | + | 0.152055i | ||||
\(503\) | −24.9170 | − | 9.06903i | −1.11099 | − | 0.404368i | −0.279635 | − | 0.960106i | \(-0.590213\pi\) |
−0.831357 | + | 0.555738i | \(0.812436\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.44427 | + | 1.61758i | −0.197768 | + | 0.0719815i | ||||
\(506\) | 0.519309 | − | 1.20389i | 0.0230861 | − | 0.0535196i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.82972 | + | 19.4726i | −0.258652 | + | 0.863958i | ||||
\(509\) | −6.91186 | − | 0.807881i | −0.306363 | − | 0.0358087i | −0.0384775 | − | 0.999259i | \(-0.512251\pi\) |
−0.267885 | + | 0.963451i | \(0.586325\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.122074 | + | 2.09594i | −0.00540025 | + | 0.0927187i | ||||
\(512\) | −10.6169 | + | 18.3890i | −0.469204 | + | 0.812685i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.68265 | − | 15.0388i | −0.382975 | − | 0.663333i | ||||
\(515\) | 4.89509 | − | 2.45841i | 0.215703 | − | 0.108330i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.29262 | + | 11.1389i | −0.364709 | + | 0.489889i | ||||
\(518\) | 5.77977 | − | 1.36983i | 0.253948 | − | 0.0601869i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.47060 | − | 3.31859i | −0.108343 | − | 0.145530i | ||||
\(521\) | −5.56140 | − | 4.66657i | −0.243649 | − | 0.204446i | 0.512783 | − | 0.858518i | \(-0.328615\pi\) |
−0.756432 | + | 0.654073i | \(0.773059\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.0663 | + | 15.1594i | −0.789983 | + | 0.662875i | −0.945741 | − | 0.324920i | \(-0.894662\pi\) |
0.155758 | + | 0.987795i | \(0.450218\pi\) | |||||||
\(524\) | 26.1794 | + | 6.20463i | 1.14365 | + | 0.271050i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.924553 | + | 0.608088i | −0.0403124 | + | 0.0265139i | ||||
\(527\) | −41.3686 | + | 27.2086i | −1.80205 | + | 1.18522i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.7729 | − | 4.44925i | −0.816212 | − | 0.193446i | ||||
\(530\) | −1.34094 | + | 1.12518i | −0.0582468 | + | 0.0488749i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.10456 | + | 3.44414i | 0.177955 | + | 0.149322i | ||||
\(533\) | 3.51269 | + | 4.71837i | 0.152152 | + | 0.204375i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.39247 | + | 1.27804i | −0.233137 | + | 0.0552545i | ||||
\(536\) | −16.4310 | + | 22.0706i | −0.709709 | + | 0.953305i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.71588 | − | 0.861749i | 0.0739770 | − | 0.0371527i | ||||
\(539\) | −1.15895 | − | 2.00737i | −0.0499197 | − | 0.0864634i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.4179 | + | 18.0443i | −0.447900 | + | 0.775785i | −0.998249 | − | 0.0591491i | \(-0.981161\pi\) |
0.550349 | + | 0.834935i | \(0.314495\pi\) | |||||||
\(542\) | −0.950841 | + | 16.3253i | −0.0408421 | + | 0.701232i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 38.0971 | + | 4.45292i | 1.63340 | + | 0.190917i | ||||
\(545\) | −1.48813 | + | 4.97069i | −0.0637444 | + | 0.212921i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.27790 | + | 19.1903i | −0.353937 | + | 0.820519i | 0.644498 | + | 0.764606i | \(0.277066\pi\) |
−0.998436 | + | 0.0559131i | \(0.982193\pi\) | |||||||
\(548\) | −0.720305 | + | 0.262170i | −0.0307699 | + | 0.0111993i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.02732 | − | 1.10185i | −0.129085 | − | 0.0469832i | ||||
\(551\) | 6.65279 | − | 7.05155i | 0.283418 | − | 0.300406i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.6898 | − | 7.87972i | −0.667199 | − | 0.335080i | ||||
\(554\) | 0.200717 | + | 3.44617i | 0.00852764 | + | 0.146414i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.78993 | + | 9.31900i | 0.118319 | + | 0.395214i | ||||
\(557\) | −5.21184 | − | 29.5578i | −0.220833 | − | 1.25240i | −0.870493 | − | 0.492180i | \(-0.836200\pi\) |
0.649661 | − | 0.760224i | \(-0.274911\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.62182 | − | 9.19782i | 0.0685959 | − | 0.389026i | ||||
\(560\) | 2.62141 | − | 0.306399i | 0.110775 | − | 0.0129477i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.41542 | − | 1.50025i | −0.0597058 | − | 0.0632844i | ||||
\(563\) | −1.65639 | − | 3.83994i | −0.0698085 | − | 0.161834i | 0.879740 | − | 0.475456i | \(-0.157717\pi\) |
−0.949548 | + | 0.313622i | \(0.898458\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.42688 | + | 4.88473i | 0.312451 | + | 0.205502i | ||||
\(566\) | 7.57670 | 0.318472 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.43491 | 0.186085 | ||||||||
\(569\) | −23.6347 | − | 15.5448i | −0.990818 | − | 0.651671i | −0.0529260 | − | 0.998598i | \(-0.516855\pi\) |
−0.937892 | + | 0.346927i | \(0.887225\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.09054 | − | 9.48294i | −0.171184 | − | 0.396849i | 0.810928 | − | 0.585146i | \(-0.198963\pi\) |
−0.982112 | + | 0.188297i | \(0.939703\pi\) | |||||||
\(572\) | 5.55763 | + | 5.89074i | 0.232376 | + | 0.246304i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.88020 | − | 0.219763i | 0.0784779 | − | 0.00917275i | ||||
\(575\) | 1.58173 | − | 8.97041i | 0.0659625 | − | 0.374092i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.09162 | + | 6.19086i | 0.0454446 | + | 0.257729i | 0.999063 | − | 0.0432907i | \(-0.0137842\pi\) |
−0.953618 | + | 0.301020i | \(0.902673\pi\) | |||||||
\(578\) | −5.49424 | − | 18.3520i | −0.228530 | − | 0.763344i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.353520 | − | 6.06970i | −0.0146791 | − | 0.252030i | ||||
\(581\) | −8.47135 | − | 4.25447i | −0.351451 | − | 0.176505i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.12992 | − | 5.43740i | 0.212460 | − | 0.225194i | ||||
\(584\) | 1.78629 | + | 0.650157i | 0.0739173 | + | 0.0269037i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.86658 | + | 3.22717i | −0.366275 | + | 0.133313i | ||||
\(587\) | 1.75202 | − | 4.06163i | 0.0723135 | − | 0.167642i | −0.878225 | − | 0.478247i | \(-0.841272\pi\) |
0.950539 | + | 0.310605i | \(0.100532\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.76899 | + | 9.24906i | −0.114094 | + | 0.381101i | ||||
\(590\) | 3.68464 | + | 0.430673i | 0.151694 | + | 0.0177305i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.619887 | + | 10.6430i | −0.0254772 | + | 0.437427i | ||||
\(593\) | 2.41323 | − | 4.17983i | 0.0990993 | − | 0.171645i | −0.812213 | − | 0.583361i | \(-0.801737\pi\) |
0.911312 | + | 0.411716i | \(0.135071\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.21086 | − | 7.29343i | −0.172629 | − | 0.299001i | ||||
\(596\) | −20.0243 | + | 10.0566i | −0.820227 | + | 0.411934i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.48334 | − | 3.33571i | 0.101551 | − | 0.136407i | ||||
\(599\) | −25.1459 | + | 5.95970i | −1.02744 | + | 0.243507i | −0.709574 | − | 0.704631i | \(-0.751113\pi\) |
−0.317861 | + | 0.948137i | \(0.602965\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.2678 | + | 27.2243i | 0.826739 | + | 1.11050i | 0.992245 | + | 0.124295i | \(0.0396668\pi\) |
−0.165506 | + | 0.986209i | \(0.552926\pi\) | |||||||
\(602\) | −2.30243 | − | 1.93197i | −0.0938401 | − | 0.0787412i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.67803 | + | 3.08623i | −0.149657 | + | 0.125577i | ||||
\(605\) | 4.79088 | + | 1.13546i | 0.194777 | + | 0.0461630i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.8325 | − | 22.9097i | 1.41381 | − | 0.929875i | 0.413998 | − | 0.910278i | \(-0.364132\pi\) |
0.999808 | − | 0.0195968i | \(-0.00623825\pi\) | |||||||
\(608\) | 6.24863 | − | 4.10979i | 0.253415 | − | 0.166674i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.59915 | − | 0.379005i | −0.0647476 | − | 0.0153455i | ||||
\(611\) | −33.7411 | + | 28.3121i | −1.36502 | + | 1.14539i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.53038 | + | 1.28414i | 0.0618116 | + | 0.0518661i | 0.673170 | − | 0.739488i | \(-0.264932\pi\) |
−0.611358 | + | 0.791354i | \(0.709377\pi\) | |||||||
\(614\) | −0.856862 | − | 1.15096i | −0.0345801 | − | 0.0464492i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.53251 | − | 1.31123i | 0.222911 | − | 0.0528309i | ||||
\(617\) | 18.7421 | − | 25.1750i | 0.754527 | − | 1.01351i | −0.244511 | − | 0.969647i | \(-0.578627\pi\) |
0.999038 | − | 0.0438590i | \(-0.0139652\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.02506 | + | 2.52368i | −0.201974 | + | 0.101435i | −0.546911 | − | 0.837190i | \(-0.684197\pi\) |
0.344937 | + | 0.938626i | \(0.387900\pi\) | |||||||
\(620\) | 3.02749 | + | 5.24376i | 0.121587 | + | 0.210595i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.93595 | − | 5.08522i | 0.117721 | − | 0.203899i | ||||
\(623\) | 1.86903 | − | 32.0901i | 0.0748813 | − | 1.28566i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.8938 | − | 2.44214i | −0.835753 | − | 0.0976855i | ||||
\(626\) | −3.46636 | + | 11.5784i | −0.138544 | + | 0.462768i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.36836 | + | 21.7183i | −0.373838 | + | 0.866655i | ||||
\(629\) | 31.9673 | − | 11.6352i | 1.27462 | − | 0.463924i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.397697 | − | 0.144750i | −0.0158321 | − | 0.00576240i | 0.334092 | − | 0.942540i | \(-0.391570\pi\) |
−0.349924 | + | 0.936778i | \(0.613793\pi\) | |||||||
\(632\) | −10.9091 | + | 11.5630i | −0.433941 | + | 0.459951i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.77636 | + | 0.892121i | 0.0705482 | + | 0.0354307i | ||||
\(635\) | −0.362217 | − | 6.21902i | −0.0143741 | − | 0.246794i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.10855 | − | 7.04304i | −0.0835437 | − | 0.279055i | ||||
\(638\) | −0.818834 | − | 4.64384i | −0.0324180 | − | 0.183851i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.03925 | − | 5.89388i | 0.0410800 | − | 0.232976i | ||||
\(641\) | −11.5838 | + | 1.35395i | −0.457532 | + | 0.0534778i | −0.341738 | − | 0.939795i | \(-0.611015\pi\) |
−0.115794 | + | 0.993273i | \(0.536941\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.1862 | − | 30.9355i | −1.15099 | − | 1.21998i | −0.971709 | − | 0.236181i | \(-0.924104\pi\) |
−0.179281 | − | 0.983798i | \(-0.557377\pi\) | |||||||
\(644\) | 2.91866 | + | 6.76621i | 0.115011 | + | 0.266626i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.65631 | − | 3.06250i | −0.183200 | − | 0.120492i | ||||
\(647\) | −14.1553 | −0.556501 | −0.278251 | − | 0.960508i | \(-0.589755\pi\) | ||||
−0.278251 | + | 0.960508i | \(0.589755\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.8424 | −0.621867 | ||||||||
\(650\) | −8.53720 | − | 5.61500i | −0.334856 | − | 0.220239i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.78797 | − | 4.14498i | −0.0700224 | − | 0.162330i | ||||
\(653\) | −7.94103 | − | 8.41700i | −0.310756 | − | 0.329383i | 0.553106 | − | 0.833111i | \(-0.313443\pi\) |
−0.863862 | + | 0.503729i | \(0.831961\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.18981 | + | 0.957252i | −0.320002 | + | 0.0374029i | ||||
\(656\) | −0.589989 | + | 3.34599i | −0.0230352 | + | 0.130639i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.46136 | + | 13.9590i | 0.0959536 | + | 0.544180i | ||||
\(659\) | 1.23393 | + | 4.12161i | 0.0480670 | + | 0.160555i | 0.978654 | − | 0.205517i | \(-0.0658876\pi\) |
−0.930587 | + | 0.366072i | \(0.880702\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.170582 | − | 2.92879i | −0.00663489 | − | 0.113917i | 0.993365 | − | 0.115008i | \(-0.0366895\pi\) |
−0.999999 | + | 0.00109179i | \(0.999652\pi\) | |||||||
\(662\) | −2.05677 | − | 1.03295i | −0.0799387 | − | 0.0401467i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.89012 | + | 6.24316i | −0.228581 | + | 0.242282i | ||||
\(665\) | −1.54309 | − | 0.561641i | −0.0598387 | − | 0.0217795i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.5285 | − | 4.56001i | 0.485107 | − | 0.176564i | ||||
\(668\) | −13.9352 | + | 32.3053i | −0.539167 | + | 1.24993i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.10860 | − | 3.70297i | 0.0428289 | − | 0.143058i | ||||
\(671\) | 6.97087 | + | 0.814778i | 0.269107 | + | 0.0314541i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.936690 | + | 16.0824i | −0.0361068 | + | 0.619929i | 0.930915 | + | 0.365236i | \(0.119012\pi\) |
−0.967022 | + | 0.254693i | \(0.918025\pi\) | |||||||
\(674\) | −5.68011 | + | 9.83823i | −0.218790 | + | 0.378955i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.84165 | + | 3.18983i | 0.0708327 | + | 0.122686i | ||||
\(677\) | 18.1338 | − | 9.10714i | 0.696939 | − | 0.350016i | −0.0648017 | − | 0.997898i | \(-0.520641\pi\) |
0.761740 | + | 0.647882i | \(0.224345\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.0087 | − | 28.2195i | 0.806239 | − | 1.08297i | ||||
\(680\) | −7.41972 | + | 1.75851i | −0.284533 | + | 0.0674356i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.80431 | + | 3.76684i | 0.107382 | + | 0.144240i | ||||
\(683\) | −25.4821 | − | 21.3820i | −0.975044 | − | 0.818159i | 0.00829016 | − | 0.999966i | \(-0.497361\pi\) |
−0.983334 | + | 0.181806i | \(0.941806\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.179961 | − | 0.151005i | 0.00687596 | − | 0.00576962i | ||||
\(686\) | −10.8412 | − | 2.56941i | −0.413919 | − | 0.0981006i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.50710 | − | 2.96436i | 0.171831 | − | 0.113015i | ||||
\(689\) | 19.8097 | − | 13.0290i | 0.754688 | − | 0.496366i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.78847 | + | 1.37189i | 0.220204 | + | 0.0521893i | 0.339237 | − | 0.940701i | \(-0.389831\pi\) |
−0.119033 | + | 0.992890i | \(0.537979\pi\) | |||||||
\(692\) | −17.3496 | + | 14.5580i | −0.659532 | + | 0.553413i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.2573 | − | 11.1242i | −0.503239 | − | 0.422268i | ||||
\(695\) | −1.78030 | − | 2.39135i | −0.0675305 | − | 0.0907092i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.5494 | − | 2.50024i | 0.399585 | − | 0.0947035i | ||||
\(698\) | 3.91022 | − | 5.25233i | 0.148004 | − | 0.198804i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 16.1803 | − | 8.12608i | 0.611560 | − | 0.307137i | ||||
\(701\) | −2.41414 | − | 4.18141i | −0.0911806 | − | 0.157929i | 0.816828 | − | 0.576882i | \(-0.195731\pi\) |
−0.908008 | + | 0.418952i | \(0.862397\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.31663 | − | 5.74456i | 0.125089 | − | 0.216660i | ||||
\(704\) | −0.109861 | + | 1.88623i | −0.00414053 | + | 0.0710901i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.22533 | − | 0.610754i | −0.196658 | − | 0.0229860i | ||||
\(707\) | 5.91261 | − | 19.7495i | 0.222367 | − | 0.742756i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.5159 | − | 29.0152i | 0.470046 | − | 1.08969i | −0.504074 | − | 0.863660i | \(-0.668166\pi\) |
0.974120 | − | 0.226029i | \(-0.0725745\pi\) | |||||||
\(710\) | −0.585446 | + | 0.213085i | −0.0219714 | + | 0.00799694i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −27.3493 | − | 9.95432i | −1.02496 | − | 0.373054i | ||||
\(713\) | −9.11174 | + | 9.65788i | −0.341238 | + | 0.361691i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.21802 | − | 1.11393i | −0.0829493 | − | 0.0416587i | ||||
\(716\) | 0.395050 | + | 6.78274i | 0.0147637 | + | 0.253483i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.44551 | − | 8.16856i | −0.0912655 | − | 0.304848i | ||||
\(719\) | −0.209547 | − | 1.18840i | −0.00781477 | − | 0.0443198i | 0.980651 | − | 0.195764i | \(-0.0627187\pi\) |
−0.988466 | + | 0.151444i | \(0.951608\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.14621 | + | 23.5144i | −0.154413 | + | 0.875720i | ||||
\(722\) | 9.38368 | − | 1.09679i | 0.349224 | − | 0.0408185i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15.2315 | + | 16.1445i | 0.566075 | + | 0.600004i | ||||
\(725\) | −12.9755 | − | 30.0807i | −0.481900 | − | 1.11717i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.6307 | + | 14.8845i | 0.839328 | + | 0.552034i | 0.894821 | − | 0.446425i | \(-0.147303\pi\) |
−0.0554936 | + | 0.998459i | \(0.517673\pi\) | |||||||
\(728\) | 18.0340 | 0.668385 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.267044 | −0.00988375 | ||||||||
\(731\) | −14.3819 | − | 9.45912i | −0.531934 | − | 0.349858i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.72184 | + | 17.9012i | 0.285213 | + | 0.661198i | 0.999242 | − | 0.0389179i | \(-0.0123911\pi\) |
−0.714030 | + | 0.700116i | \(0.753132\pi\) | |||||||
\(734\) | 1.34994 | + | 1.43085i | 0.0498272 | + | 0.0528138i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.2161 | − | 1.19409i | 0.376571 | − | 0.0440148i | ||||
\(737\) | −2.86641 | + | 16.2562i | −0.105585 | + | 0.598805i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.48150 | + | 14.0733i | 0.0912834 | + | 0.517694i | 0.995823 | + | 0.0913044i | \(0.0291036\pi\) |
−0.904540 | + | 0.426390i | \(0.859785\pi\) | |||||||
\(740\) | −1.19313 | − | 3.98532i | −0.0438602 | − | 0.146503i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.443657 | − | 7.61729i | −0.0162872 | − | 0.279640i | ||||
\(743\) | −11.7806 | − | 5.91644i | −0.432189 | − | 0.217053i | 0.219386 | − | 0.975638i | \(-0.429595\pi\) |
−0.651574 | + | 0.758585i | \(0.725891\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.71270 | − | 4.99517i | 0.172660 | − | 0.183009i | ||||
\(746\) | 15.6578 | + | 5.69899i | 0.573274 | + | 0.208655i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 14.0262 | − | 5.10513i | 0.512849 | − | 0.186662i | ||||
\(749\) | 9.56793 | − | 22.1810i | 0.349605 | − | 0.810474i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.8223 | − | 42.8296i | 0.467894 | − | 1.56287i | −0.320220 | − | 0.947343i | \(-0.603757\pi\) |
0.788113 | − | 0.615530i | \(-0.211058\pi\) | |||||||
\(752\) | −25.2686 | − | 2.95348i | −0.921452 | − | 0.107702i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.869641 | − | 14.9312i | 0.0316705 | − | 0.543761i | ||||
\(755\) | 0.735741 | − | 1.27434i | 0.0267764 | − | 0.0463780i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.72638 | + | 8.18632i | 0.171783 | + | 0.297537i | 0.939043 | − | 0.343799i | \(-0.111714\pi\) |
−0.767260 | + | 0.641336i | \(0.778381\pi\) | |||||||
\(758\) | −11.6895 | + | 5.87071i | −0.424583 | + | 0.213234i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.887871 | + | 1.19262i | −0.0322065 | + | 0.0432608i | ||||
\(761\) | 1.90438 | − | 0.451347i | 0.0690338 | − | 0.0163613i | −0.195954 | − | 0.980613i | \(-0.562780\pi\) |
0.264988 | + | 0.964252i | \(0.414632\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.5060 | − | 18.1417i | −0.488949 | − | 0.656773i | ||||
\(764\) | 0.0788362 | + | 0.0661515i | 0.00285219 | + | 0.00239328i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.123129 | − | 0.103318i | 0.00444885 | − | 0.00373303i | ||||
\(767\) | −48.8940 | − | 11.5881i | −1.76546 | − | 0.418422i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.2670 | + | 12.0144i | −0.658725 | + | 0.433250i | −0.834371 | − | 0.551203i | \(-0.814169\pi\) |
0.175646 | + | 0.984453i | \(0.443799\pi\) | |||||||
\(770\) | −0.667338 | + | 0.438915i | −0.0240492 | + | 0.0158174i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.45105 | + | 1.29192i | 0.196187 | + | 0.0464973i | ||||
\(773\) | 13.5712 | − | 11.3876i | 0.488122 | − | 0.409583i | −0.365231 | − | 0.930917i | \(-0.619010\pi\) |
0.853353 | + | 0.521334i | \(0.174565\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.9923 | + | 20.9711i | 0.897751 | + | 0.753303i | ||||
\(776\) | −19.0218 | − | 25.5507i | −0.682844 | − | 0.917218i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.1484 | + | 3.59024i | −0.543097 | + | 0.128716i | ||||
\(779\) | 1.26238 | − | 1.69566i | 0.0452293 | − | 0.0607535i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.37760 | − | 1.19407i | 0.0850771 | − | 0.0427273i | ||||
\(782\) | −3.83230 | − | 6.63773i | −0.137043 | − | 0.237365i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.12321 | − | 3.67750i | 0.0758288 | − | 0.131339i | ||||
\(785\) | 0.421489 | − | 7.23669i | 0.0150436 | − | 0.258289i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.8109 | − | 2.31556i | −0.706182 | − | 0.0825408i | −0.244581 | − | 0.969629i | \(-0.578650\pi\) |
−0.461600 | + | 0.887088i | \(0.652725\pi\) | |||||||
\(788\) | 7.34303 | − | 24.5274i | 0.261585 | − | 0.873753i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.884528 | − | 2.05057i | 0.0314701 | − | 0.0729559i | ||||
\(791\) | −36.4109 | + | 13.2525i | −1.29462 | + | 0.471205i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.9181 | + | 7.61357i | 0.742824 | + | 0.270366i | ||||
\(794\) | 1.50411 | − | 1.59426i | 0.0533789 | − | 0.0565783i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.3491 | + | 6.70418i | 0.473147 | + | 0.237623i | ||||
\(797\) | 0.996262 | + | 17.1052i | 0.0352894 | + | 0.605896i | 0.968876 | + | 0.247545i | \(0.0796238\pi\) |
−0.933587 | + | 0.358351i | \(0.883339\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.2826 | + | 77.7693i | 0.823679 | + | 2.75128i | ||||
\(800\) | −4.38865 | − | 24.8893i | −0.155162 | − | 0.879968i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.192190 | − | 1.08996i | 0.00678646 | − | 0.0384879i | ||||
\(803\) | 1.13270 | − | 0.132394i | 0.0399721 | − | 0.00467207i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.54979 | − | 1.64268i | −0.0546228 | − | 0.0578967i | ||||
\(806\) | 5.89959 | + | 13.6768i | 0.207804 | + | 0.481744i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.5951 | − | 10.2571i | −0.548634 | − | 0.360843i | ||||
\(809\) | −48.2164 | −1.69520 | −0.847600 | − | 0.530636i | \(-0.821953\pi\) | ||||
−0.847600 | + | 0.530636i | \(0.821953\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.8518 | 0.416172 | 0.208086 | − | 0.978110i | \(-0.433277\pi\) | ||||
0.208086 | + | 0.978110i | \(0.433277\pi\) | |||||||
\(812\) | 22.1423 | + | 14.5632i | 0.777042 | + | 0.511069i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.27793 | − | 2.96258i | −0.0447915 | − | 0.103838i | ||||
\(815\) | 0.949400 | + | 1.00631i | 0.0332560 | + | 0.0352493i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.33377 | + | 0.389661i | −0.116634 | + | 0.0136325i | ||||
\(818\) | −1.15347 | + | 6.54166i | −0.0403302 | + | 0.228724i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.230221 | − | 1.30565i | −0.00803966 | − | 0.0455952i | ||||
\(821\) | 7.85507 | + | 26.2378i | 0.274144 | + | 0.915705i | 0.978568 | + | 0.205925i | \(0.0660203\pi\) |
−0.704424 | + | 0.709780i | \(0.748795\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.678059 | − | 11.6418i | −0.0236356 | − | 0.405808i | −0.989289 | − | 0.145973i | \(-0.953369\pi\) |
0.965653 | − | 0.259835i | \(-0.0836683\pi\) | |||||||
\(824\) | 19.3194 | + | 9.70258i | 0.673024 | + | 0.338005i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.0968 | + | 11.7620i | −0.386108 | + | 0.409251i | ||||
\(827\) | 32.4874 | + | 11.8244i | 1.12970 | + | 0.411176i | 0.838182 | − | 0.545390i | \(-0.183619\pi\) |
0.291515 | + | 0.956566i | \(0.405841\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.0937 | + | 6.94953i | −0.663150 | + | 0.241367i | −0.651596 | − | 0.758566i | \(-0.725900\pi\) |
−0.0115545 | + | 0.999933i | \(0.503678\pi\) | |||||||
\(830\) | 0.477580 | − | 1.10716i | 0.0165770 | − | 0.0384299i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.71877 | + | 5.74110i | −0.0595877 | + | 0.199037i | ||||
\(833\) | −13.4585 | − | 1.57307i | −0.466308 | − | 0.0545036i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.626952 | − | 10.7644i | 0.0216966 | − | 0.372516i | ||||
\(836\) | 1.45523 | − | 2.52053i | 0.0503301 | − | 0.0871742i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.14051 | − | 8.90362i | −0.177576 | − | 0.307571i | ||||
\(839\) | −9.14041 | + | 4.59049i | −0.315562 | + | 0.158481i | −0.599529 | − | 0.800353i | \(-0.704646\pi\) |
0.283967 | + | 0.958834i | \(0.408349\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.3167 | − | 15.2010i | 0.390231 | − | 0.524171i | ||||
\(842\) | −20.8995 | + | 4.95327i | −0.720244 | + | 0.170701i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.6852 | − | 22.4122i | −0.574330 | − | 0.771459i | ||||
\(845\) | −0.864740 | − | 0.725603i | −0.0297480 | − | 0.0249615i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.4406 | + | 13.7953i | −0.564904 | + | 0.474011i | ||||
\(848\) | 13.3258 | + | 3.15827i | 0.457609 | + | 0.108455i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −15.7347 | + | 10.3489i | −0.539695 | + | 0.354963i | ||||
\(851\) | 7.62174 | − | 5.01290i | 0.261270 | − | 0.171840i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.64759 | − | 1.10150i | −0.159131 | − | 0.0377146i | 0.150278 | − | 0.988644i | \(-0.451983\pi\) |
−0.309409 | + | 0.950929i | \(0.600131\pi\) | |||||||
\(854\) | 5.48769 | − | 4.60472i | 0.187785 | − | 0.157570i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.7549 | − | 14.0591i | −0.572672 | − | 0.480529i | ||||
\(857\) | 5.65608 | + | 7.59744i | 0.193208 | + | 0.259524i | 0.888162 | − | 0.459531i | \(-0.151983\pi\) |
−0.694954 | + | 0.719055i | \(0.744575\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.5203 | − | 9.60350i | 1.38254 | − | 0.327667i | 0.528965 | − | 0.848644i | \(-0.322580\pi\) |
0.853571 | + | 0.520976i | \(0.174432\pi\) | |||||||
\(860\) | −1.25703 | + | 1.68849i | −0.0428645 | + | 0.0575770i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.57951 | − | 2.29992i | 0.155979 | − | 0.0783354i | ||||
\(863\) | −9.29605 | − | 16.1012i | −0.316441 | − | 0.548092i | 0.663302 | − | 0.748352i | \(-0.269155\pi\) |
−0.979743 | + | 0.200260i | \(0.935821\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.47056 | − | 6.01118i | 0.118002 | − | 0.204386i | ||||
\(866\) | 0.374469 | − | 6.42939i | 0.0127250 | − | 0.218480i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −26.2148 | − | 3.06407i | −0.889787 | − | 0.104001i | ||||
\(869\) | −2.73521 | + | 9.13624i | −0.0927857 | + | 0.309926i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.7374 | + | 48.0746i | −0.702659 | + | 1.62895i | ||||
\(872\) | −19.2431 | + | 7.00393i | −0.651655 | + | 0.237183i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.40437 | − | 0.511148i | −0.0475034 | − | 0.0172898i | ||||
\(875\) | −7.83265 | + | 8.30213i | −0.264792 | + | 0.280663i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.6571 | + | 11.8811i | 0.798845 | + | 0.401195i | 0.800896 | − | 0.598803i | \(-0.204357\pi\) |
−0.00205156 | + | 0.999998i | \(0.500653\pi\) | |||||||
\(878\) | −0.515893 | − | 8.85754i | −0.0174105 | − | 0.298927i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.411163 | − | 1.37338i | −0.0138603 | − | 0.0462966i | ||||
\(881\) | 2.07452 | + | 11.7652i | 0.0698924 | + | 0.396380i | 0.999605 | + | 0.0280945i | \(0.00894392\pi\) |
−0.929713 | + | 0.368285i | \(0.879945\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.35734 | − | 7.69784i | 0.0456780 | − | 0.259053i | −0.953414 | − | 0.301666i | \(-0.902457\pi\) |
0.999092 | + | 0.0426131i | \(0.0135683\pi\) | |||||||
\(884\) | 47.0231 | − | 5.49622i | 1.58156 | − | 0.184858i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.51370 | − | 1.60442i | −0.0508536 | − | 0.0539017i | ||||
\(887\) | 5.57323 | + | 12.9202i | 0.187131 | + | 0.433818i | 0.985794 | − | 0.167961i | \(-0.0537182\pi\) |
−0.798663 | + | 0.601779i | \(0.794459\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.6870 | + | 14.9215i | 0.760899 | + | 0.500451i | ||||
\(890\) | 4.08862 | 0.137051 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.92294 | −0.298762 | ||||||||
\(893\) | 13.2249 | + | 8.69817i | 0.442555 | + | 0.291073i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.824741 | − | 1.91196i | −0.0275681 | − | 0.0639099i | ||||
\(896\) | 17.9022 | + | 18.9753i | 0.598071 | + | 0.633919i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.3040 | + | 1.78878i | −0.510701 | + | 0.0596924i | ||||
\(899\) | −8.29234 | + | 47.0282i | −0.276565 | + | 1.56848i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.58839 | − | 43.0359i | −0.252806 | − | 1.43373i | ||||
\(902\) | −0.294905 | − | 0.985050i | −0.00981925 | − | 0.0327986i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.03991 | + | 35.0239i | 0.0678464 | + | 1.16488i | ||||
\(905\) | −6.07882 | − | 3.05290i | −0.202067 | − | 0.101482i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.1204 | − | 30.8658i | 0.966926 | − | 1.02488i | −0.0327513 | − | 0.999464i | \(-0.510427\pi\) |
0.999677 | − | 0.0254177i | \(-0.00809158\pi\) | |||||||
\(908\) | 10.7776 | + | 3.92271i | 0.357666 | + | 0.130180i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.38065 | + | 0.866484i | −0.0789176 | + | 0.0287237i | ||||
\(911\) | −13.9697 | + | 32.3854i | −0.462837 | + | 1.07298i | 0.513767 | + | 0.857930i | \(0.328250\pi\) |
−0.976604 | + | 0.215047i | \(0.931010\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.47681 | + | 4.93290i | −0.0488754 | + | 0.163255i | ||||
\(914\) | −0.871927 | − | 0.101914i | −0.0288408 | − | 0.00337100i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.843203 | + | 14.4772i | −0.0278602 | + | 0.478341i | ||||
\(917\) | 17.9709 | − | 31.1266i | 0.593452 | − | 1.02789i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.19629 | + | 10.7323i | 0.204397 | + | 0.354026i | 0.949940 | − | 0.312431i | \(-0.101143\pi\) |
−0.745544 | + | 0.666457i | \(0.767810\pi\) | |||||||
\(920\) | −1.82729 | + | 0.917699i | −0.0602439 | + | 0.0302556i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.56001 | − | 12.8413i | 0.314842 | − | 0.422906i | ||||
\(923\) | 8.21136 | − | 1.94613i | 0.270280 | − | 0.0640576i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.3854 | − | 17.9798i | −0.440110 | − | 0.591171i | ||||
\(926\) | −5.96549 | − | 5.00564i | −0.196038 | − | 0.164496i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 28.3379 | − | 23.7784i | 0.930239 | − | 0.780563i | ||||
\(929\) | 27.2216 | + | 6.45164i | 0.893113 | + | 0.211672i | 0.651453 | − | 0.758689i | \(-0.274160\pi\) |
0.241660 | + | 0.970361i | \(0.422308\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.20743 | + | 1.45185i | −0.0723457 | + | 0.0475825i | ||||
\(932\) | −10.7617 | + | 7.07807i | −0.352511 | + | 0.231850i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.97428 | − | 1.17893i | −0.162763 | − | 0.0385756i | ||||
\(935\) | −3.50431 | + | 2.94047i | −0.114603 | + | 0.0961636i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.5096 | − | 28.1179i | −1.09471 | − | 0.918572i | −0.0976531 | − | 0.995221i | \(-0.531134\pi\) |
−0.997058 | + | 0.0766487i | \(0.975578\pi\) | |||||||
\(938\) | 10.0614 | + | 13.5148i | 0.328517 | + | 0.441275i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.65966 | − | 2.28938i | 0.315063 | − | 0.0746714i | ||||
\(941\) | −15.3652 | + | 20.6391i | −0.500892 | + | 0.672814i | −0.978616 | − | 0.205695i | \(-0.934054\pi\) |
0.477724 | + | 0.878510i | \(0.341462\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.59804 | − | 1.30478i | 0.0846037 | − | 0.0424896i | ||||
\(944\) | −14.5116 | − | 25.1349i | −0.472313 | − | 0.818071i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.816302 | + | 1.41388i | −0.0265403 | + | 0.0459691i | ||||
\(947\) | −0.553709 | + | 9.50681i | −0.0179931 | + | 0.308930i | 0.977289 | + | 0.211910i | \(0.0679682\pi\) |
−0.995282 | + | 0.0970203i | \(0.969069\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.59267 | + | 0.419923i | 0.116623 | + | 0.0136313i | ||||
\(950\) | −1.05319 | + | 3.51790i | −0.0341700 | + | 0.114136i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 13.1649 | − | 30.5197i | 0.426677 | − | 0.989148i | ||||
\(953\) | 45.3519 | − | 16.5068i | 1.46909 | − | 0.534706i | 0.521239 | − | 0.853411i | \(-0.325470\pi\) |
0.947854 | + | 0.318704i | \(0.103248\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.0296382 | − | 0.0107874i | −0.000959070 | − | 0.000349073i | ||||
\(956\) | −13.3983 | + | 14.2014i | −0.433333 | + | 0.459306i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 18.9832 | + | 9.53374i | 0.613320 | + | 0.308021i | ||||
\(959\) | 0.0595410 | + | 1.02228i | 0.00192268 | + | 0.0330111i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.74867 | − | 15.8617i | −0.153183 | − | 0.511667i | ||||
\(962\) | −1.77705 | − | 10.0781i | −0.0572943 | − | 0.324932i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.105398 | − | 0.597742i | 0.00339464 | − | 0.0192520i | ||||
\(965\) | −1.70528 | + | 0.199318i | −0.0548948 | + | 0.00641628i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.1290 | + | 14.9758i | 0.454356 | + | 0.481590i | 0.913538 | − | 0.406753i | \(-0.133339\pi\) |
−0.459182 | + | 0.888342i | \(0.651857\pi\) | |||||||
\(968\) | 7.69660 | + | 17.8427i | 0.247378 | + | 0.573487i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.73869 | + | 2.45897i | 0.120042 | + | 0.0789529i | ||||
\(971\) | 55.4615 | 1.77984 | 0.889921 | − | 0.456114i | \(-0.150759\pi\) | ||||
0.889921 | + | 0.456114i | \(0.150759\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.9952 | 0.416607 | ||||||||
\(974\) | 14.7486 | + | 9.70032i | 0.472576 | + | 0.310818i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.09263 | + | 11.8060i | 0.163011 | + | 0.377902i | ||||
\(977\) | 30.4294 | + | 32.2533i | 0.973524 | + | 1.03188i | 0.999481 | + | 0.0322122i | \(0.0102552\pi\) |
−0.0259570 | + | 0.999663i | \(0.508263\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.3423 | + | 2.02703i | −0.554264 | + | 0.0647841i | ||||
\(980\) | −0.287735 | + | 1.63183i | −0.00919137 | + | 0.0521269i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.55314 | + | 14.4796i | 0.0814741 | + | 0.462063i | ||||
\(983\) | −17.0485 | − | 56.9459i | −0.543762 | − | 1.81629i | −0.576863 | − | 0.816841i | \(-0.695723\pi\) |
0.0331008 | − | 0.999452i | \(-0.489462\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.456243 | + | 7.83339i | 0.0145371 | + | 0.249593i | ||||
\(986\) | −24.6337 | − | 12.3715i | −0.784498 | − | 0.393990i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.33492 | − | 6.71462i | 0.201541 | − | 0.213620i | ||||
\(989\) | −4.33766 | − | 1.57878i | −0.137929 | − | 0.0502022i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.3541 | + | 7.77226i | −0.678335 | + | 0.246894i | −0.658133 | − | 0.752902i | \(-0.728653\pi\) |
−0.0202027 | + | 0.999796i | \(0.506431\pi\) | |||||||
\(992\) | −14.5917 | + | 33.8274i | −0.463288 | + | 1.07402i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.778871 | − | 2.60161i | 0.0247043 | − | 0.0825180i | ||||
\(995\) | −4.54717 | − | 0.531488i | −0.144155 | − | 0.0168493i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.14316 | − | 19.6274i | 0.0362044 | − | 0.621605i | −0.930592 | − | 0.366058i | \(-0.880707\pi\) |
0.966797 | − | 0.255547i | \(-0.0822557\pi\) | |||||||
\(998\) | 1.88108 | − | 3.25813i | 0.0595447 | − | 0.103134i | ||||
\(999\) | 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 | 729.2.g.a.703.4 | 144 | ||
3.2 | odd | 2 | 729.2.g.d.703.5 | 144 | |||
9.2 | odd | 6 | 81.2.g.a.79.5 | yes | 144 | ||
9.4 | even | 3 | 729.2.g.b.460.5 | 144 | |||
9.5 | odd | 6 | 729.2.g.c.460.4 | 144 | |||
9.7 | even | 3 | 243.2.g.a.235.4 | 144 | |||
81.13 | even | 27 | 243.2.g.a.91.4 | 144 | |||
81.14 | odd | 54 | 729.2.g.d.28.5 | 144 | |||
81.38 | odd | 54 | 6561.2.a.c.1.33 | 72 | |||
81.40 | even | 27 | 729.2.g.b.271.5 | 144 | |||
81.41 | odd | 54 | 729.2.g.c.271.4 | 144 | |||
81.43 | even | 27 | 6561.2.a.d.1.40 | 72 | |||
81.67 | even | 27 | inner | 729.2.g.a.28.4 | 144 | ||
81.68 | odd | 54 | 81.2.g.a.40.5 | ✓ | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
81.2.g.a.40.5 | ✓ | 144 | 81.68 | odd | 54 | ||
81.2.g.a.79.5 | yes | 144 | 9.2 | odd | 6 | ||
243.2.g.a.91.4 | 144 | 81.13 | even | 27 | |||
243.2.g.a.235.4 | 144 | 9.7 | even | 3 | |||
729.2.g.a.28.4 | 144 | 81.67 | even | 27 | inner | ||
729.2.g.a.703.4 | 144 | 1.1 | even | 1 | trivial | ||
729.2.g.b.271.5 | 144 | 81.40 | even | 27 | |||
729.2.g.b.460.5 | 144 | 9.4 | even | 3 | |||
729.2.g.c.271.4 | 144 | 81.41 | odd | 54 | |||
729.2.g.c.460.4 | 144 | 9.5 | odd | 6 | |||
729.2.g.d.28.5 | 144 | 81.14 | odd | 54 | |||
729.2.g.d.703.5 | 144 | 3.2 | odd | 2 | |||
6561.2.a.c.1.33 | 72 | 81.38 | odd | 54 | |||
6561.2.a.d.1.40 | 72 | 81.43 | even | 27 |