Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,3,Mod(17,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([11]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.f (of order \(18\), degree \(6\), 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: | \(4.41418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 54) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 35.4 | ||
Character | \(\chi\) | \(=\) | 162.35 |
Dual form | 162.3.f.a.125.4 |
$q$-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 \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(e\left(\frac{13}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.909039 | − | 1.08335i | 0.454519 | − | 0.541675i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.347296 | − | 1.96962i | −0.0868241 | − | 0.492404i | ||||
\(5\) | −2.86430 | + | 7.86960i | −0.572860 | + | 1.57392i | 0.227103 | + | 0.973871i | \(0.427075\pi\) |
−0.799963 | + | 0.600049i | \(0.795148\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.95208 | + | 11.0708i | −0.278869 | + | 1.58155i | 0.447527 | + | 0.894270i | \(0.352305\pi\) |
−0.726397 | + | 0.687276i | \(0.758806\pi\) | |||||||
\(8\) | −2.44949 | − | 1.41421i | −0.306186 | − | 0.176777i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.92177 | + | 10.2568i | 0.592177 | + | 1.02568i | ||||
\(11\) | −0.538121 | − | 1.47848i | −0.0489201 | − | 0.134407i | 0.912826 | − | 0.408348i | \(-0.133895\pi\) |
−0.961747 | + | 0.273941i | \(0.911673\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.82419 | + | 5.72617i | −0.524937 | + | 0.440475i | −0.866349 | − | 0.499439i | \(-0.833539\pi\) |
0.341412 | + | 0.939914i | \(0.389095\pi\) | |||||||
\(14\) | 10.2191 | + | 12.1786i | 0.729933 | + | 0.869900i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.75877 | + | 1.36808i | −0.234923 | + | 0.0855050i | ||||
\(17\) | 16.9870 | − | 9.80744i | 0.999235 | − | 0.576909i | 0.0912130 | − | 0.995831i | \(-0.470926\pi\) |
0.908022 | + | 0.418923i | \(0.137592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.86486 | − | 8.42619i | 0.256045 | − | 0.443484i | −0.709134 | − | 0.705074i | \(-0.750914\pi\) |
0.965179 | + | 0.261591i | \(0.0842470\pi\) | |||||||
\(20\) | 16.4948 | + | 2.90849i | 0.824742 | + | 0.145424i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.09088 | − | 0.761018i | −0.0950400 | − | 0.0345917i | ||||
\(23\) | 13.8255 | − | 2.43781i | 0.601108 | − | 0.105992i | 0.135190 | − | 0.990820i | \(-0.456835\pi\) |
0.465918 | + | 0.884828i | \(0.345724\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −34.5753 | − | 29.0121i | −1.38301 | − | 1.16048i | ||||
\(26\) | 12.5983i | 0.484550i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 22.4832 | 0.802972 | ||||||||
\(29\) | −7.05122 | + | 8.40331i | −0.243145 | + | 0.289769i | −0.873791 | − | 0.486301i | \(-0.838346\pi\) |
0.630646 | + | 0.776071i | \(0.282790\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.04854 | + | 45.6456i | 0.259630 | + | 1.47244i | 0.783901 | + | 0.620886i | \(0.213227\pi\) |
−0.524271 | + | 0.851552i | \(0.675662\pi\) | |||||||
\(32\) | −1.93476 | + | 5.31570i | −0.0604612 | + | 0.166116i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.81694 | − | 27.3182i | 0.141675 | − | 0.803477i | ||||
\(35\) | −81.5316 | − | 47.0723i | −2.32947 | − | 1.34492i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.89337 | + | 13.6717i | 0.213334 | + | 0.369506i | 0.952756 | − | 0.303737i | \(-0.0982343\pi\) |
−0.739422 | + | 0.673243i | \(0.764901\pi\) | |||||||
\(38\) | −4.70617 | − | 12.9301i | −0.123846 | − | 0.340265i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 18.1454 | − | 15.2258i | 0.453634 | − | 0.380644i | ||||
\(41\) | 6.59742 | + | 7.86250i | 0.160913 | + | 0.191768i | 0.840476 | − | 0.541848i | \(-0.182275\pi\) |
−0.679564 | + | 0.733617i | \(0.737831\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 24.6205 | − | 8.96112i | 0.572569 | − | 0.208398i | −0.0394765 | − | 0.999220i | \(-0.512569\pi\) |
0.612046 | + | 0.790822i | \(0.290347\pi\) | |||||||
\(44\) | −2.72514 | + | 1.57336i | −0.0619350 | + | 0.0357582i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.92691 | − | 17.1939i | 0.215802 | − | 0.373781i | ||||
\(47\) | 42.2938 | + | 7.45754i | 0.899868 | + | 0.158671i | 0.604399 | − | 0.796682i | \(-0.293413\pi\) |
0.295468 | + | 0.955352i | \(0.404524\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −72.7075 | − | 26.4634i | −1.48383 | − | 0.540069i | ||||
\(50\) | −62.8606 | + | 11.0840i | −1.25721 | + | 0.221680i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 13.6484 | + | 11.4523i | 0.262469 | + | 0.220237i | ||||
\(53\) | − | 41.5395i | − | 0.783764i | −0.920016 | − | 0.391882i | \(-0.871824\pi\) | ||
0.920016 | − | 0.391882i | \(-0.128176\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.1764 | 0.239570 | ||||||||
\(56\) | 20.4381 | − | 24.3572i | 0.364966 | − | 0.434950i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.69390 | + | 15.2779i | 0.0464466 | + | 0.263412i | ||||
\(59\) | −20.6989 | + | 56.8698i | −0.350829 | + | 0.963895i | 0.631275 | + | 0.775559i | \(0.282532\pi\) |
−0.982105 | + | 0.188336i | \(0.939690\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.2934 | − | 75.3906i | 0.217924 | − | 1.23591i | −0.657835 | − | 0.753162i | \(-0.728527\pi\) |
0.875759 | − | 0.482748i | \(-0.160361\pi\) | |||||||
\(62\) | 56.7666 | + | 32.7742i | 0.915590 | + | 0.528616i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.00000 | + | 6.92820i | 0.0625000 | + | 0.108253i | ||||
\(65\) | −25.5162 | − | 70.1051i | −0.392556 | − | 1.07854i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.09011 | − | 1.75381i | 0.0311956 | − | 0.0261762i | −0.627057 | − | 0.778974i | \(-0.715741\pi\) |
0.658252 | + | 0.752798i | \(0.271296\pi\) | |||||||
\(68\) | −25.2164 | − | 30.0518i | −0.370830 | − | 0.441938i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −125.111 | + | 45.5367i | −1.78730 | + | 0.650525i | ||||
\(71\) | −65.1324 | + | 37.6042i | −0.917358 | + | 0.529637i | −0.882791 | − | 0.469765i | \(-0.844338\pi\) |
−0.0345668 | + | 0.999402i | \(0.511005\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 33.0777 | − | 57.2922i | 0.453119 | − | 0.784825i | −0.545459 | − | 0.838138i | \(-0.683645\pi\) |
0.998578 | + | 0.0533125i | \(0.0169779\pi\) | |||||||
\(74\) | 21.9866 | + | 3.87684i | 0.297117 | + | 0.0523897i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −18.2859 | − | 6.65552i | −0.240604 | − | 0.0875727i | ||||
\(77\) | 17.4184 | − | 3.07133i | 0.226213 | − | 0.0398875i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 38.8113 | + | 32.5666i | 0.491283 | + | 0.412235i | 0.854486 | − | 0.519475i | \(-0.173872\pi\) |
−0.363203 | + | 0.931710i | \(0.618317\pi\) | |||||||
\(80\) | − | 33.4986i | − | 0.418733i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 14.5152 | 0.177014 | ||||||||
\(83\) | −21.4712 | + | 25.5884i | −0.258689 | + | 0.308294i | −0.879720 | − | 0.475492i | \(-0.842270\pi\) |
0.621030 | + | 0.783787i | \(0.286714\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 28.5248 | + | 161.772i | 0.335586 | + | 1.90320i | ||||
\(86\) | 12.6729 | − | 34.8186i | 0.147360 | − | 0.404868i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.772758 | + | 4.38253i | −0.00878135 | + | 0.0498015i | ||||
\(89\) | 75.2876 | + | 43.4673i | 0.845928 | + | 0.488397i | 0.859275 | − | 0.511514i | \(-0.170915\pi\) |
−0.0133471 | + | 0.999911i | \(0.504249\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −50.0720 | − | 86.7273i | −0.550242 | − | 0.953047i | ||||
\(92\) | −9.60308 | − | 26.3842i | −0.104381 | − | 0.286785i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 46.5258 | − | 39.0398i | 0.494956 | − | 0.415317i | ||||
\(95\) | 52.3763 | + | 62.4197i | 0.551330 | + | 0.657049i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 132.434 | − | 48.2019i | 1.36530 | − | 0.496927i | 0.447608 | − | 0.894230i | \(-0.352276\pi\) |
0.917688 | + | 0.397303i | \(0.130054\pi\) | |||||||
\(98\) | −94.7631 | + | 54.7115i | −0.966970 | + | 0.558281i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −45.1348 | + | 78.1758i | −0.451348 | + | 0.781758i | ||||
\(101\) | 88.8791 | + | 15.6718i | 0.879991 | + | 0.155166i | 0.595348 | − | 0.803468i | \(-0.297014\pi\) |
0.284642 | + | 0.958634i | \(0.408125\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.7299 | + | 7.18111i | 0.191553 | + | 0.0697195i | 0.436015 | − | 0.899939i | \(-0.356389\pi\) |
−0.244463 | + | 0.969659i | \(0.578612\pi\) | |||||||
\(104\) | 24.8138 | − | 4.37534i | 0.238594 | − | 0.0420706i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −45.0018 | − | 37.7610i | −0.424545 | − | 0.356236i | ||||
\(107\) | 21.8959i | 0.204635i | 0.994752 | + | 0.102317i | \(0.0326257\pi\) | ||||
−0.994752 | + | 0.102317i | \(0.967374\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −92.6448 | −0.849953 | −0.424976 | − | 0.905204i | \(-0.639718\pi\) | ||||
−0.424976 | + | 0.905204i | \(0.639718\pi\) | |||||||
\(110\) | 11.9778 | − | 14.2746i | 0.108889 | − | 0.129769i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.80834 | − | 44.2833i | −0.0697173 | − | 0.395387i | ||||
\(113\) | 52.9813 | − | 145.565i | 0.468861 | − | 1.28819i | −0.449796 | − | 0.893131i | \(-0.648503\pi\) |
0.918657 | − | 0.395055i | \(-0.129274\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20.4158 | + | 115.784i | −0.177529 | + | 1.00681i | ||||
\(116\) | 19.0002 | + | 10.9697i | 0.163794 | + | 0.0945668i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 42.7938 | + | 74.1211i | 0.362659 | + | 0.628145i | ||||
\(119\) | 75.4164 | + | 207.205i | 0.633752 | + | 1.74122i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 90.7951 | − | 76.1861i | 0.750372 | − | 0.629637i | ||||
\(122\) | −69.5902 | − | 82.9344i | −0.570411 | − | 0.679790i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 87.1090 | − | 31.7051i | 0.702492 | − | 0.255686i | ||||
\(125\) | 146.031 | − | 84.3111i | 1.16825 | − | 0.674489i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −115.693 | + | 200.387i | −0.910971 | + | 1.57785i | −0.0982763 | + | 0.995159i | \(0.531333\pi\) |
−0.812695 | + | 0.582689i | \(0.802000\pi\) | |||||||
\(128\) | 11.1418 | + | 1.96460i | 0.0870455 | + | 0.0153485i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −99.1436 | − | 36.0853i | −0.762643 | − | 0.277579i | ||||
\(131\) | 69.0825 | − | 12.1811i | 0.527347 | − | 0.0929856i | 0.0963653 | − | 0.995346i | \(-0.469278\pi\) |
0.430982 | + | 0.902360i | \(0.358167\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 83.7882 | + | 70.3067i | 0.629987 | + | 0.528621i | ||||
\(134\) | − | 3.85860i | − | 0.0287955i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −55.4793 | −0.407936 | ||||||||
\(137\) | −136.898 | + | 163.149i | −0.999257 | + | 1.19087i | −0.0176713 | + | 0.999844i | \(0.505625\pi\) |
−0.981585 | + | 0.191024i | \(0.938819\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.79795 | + | 55.5669i | 0.0704888 | + | 0.399762i | 0.999554 | + | 0.0298471i | \(0.00950205\pi\) |
−0.929066 | + | 0.369915i | \(0.879387\pi\) | |||||||
\(140\) | −64.3987 | + | 176.934i | −0.459991 | + | 1.26381i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −18.4694 | + | 104.745i | −0.130066 | + | 0.737640i | ||||
\(143\) | 12.1382 | + | 7.00802i | 0.0848829 | + | 0.0490071i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −45.9339 | − | 79.5599i | −0.316786 | − | 0.548689i | ||||
\(146\) | −31.9987 | − | 87.9156i | −0.219169 | − | 0.602162i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 24.1867 | − | 20.2950i | 0.163424 | − | 0.137129i | ||||
\(149\) | −18.5161 | − | 22.0666i | −0.124269 | − | 0.148098i | 0.700323 | − | 0.713826i | \(-0.253039\pi\) |
−0.824592 | + | 0.565728i | \(0.808595\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −145.452 | + | 52.9400i | −0.963255 | + | 0.350596i | −0.775308 | − | 0.631583i | \(-0.782405\pi\) |
−0.187947 | + | 0.982179i | \(0.560183\pi\) | |||||||
\(152\) | −23.8329 | + | 13.7599i | −0.156795 | + | 0.0905257i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.5067 | − | 21.6622i | 0.0812122 | − | 0.140664i | ||||
\(155\) | −382.266 | − | 67.4038i | −2.46623 | − | 0.434863i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −200.915 | − | 73.1270i | −1.27971 | − | 0.465777i | −0.389375 | − | 0.921080i | \(-0.627309\pi\) |
−0.890337 | + | 0.455303i | \(0.849531\pi\) | |||||||
\(158\) | 70.5620 | − | 12.4420i | 0.446595 | − | 0.0787467i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −36.2907 | − | 30.4515i | −0.226817 | − | 0.190322i | ||||
\(161\) | 157.818i | 0.980238i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 147.201 | 0.903076 | 0.451538 | − | 0.892252i | \(-0.350876\pi\) | ||||
0.451538 | + | 0.892252i | \(0.350876\pi\) | |||||||
\(164\) | 13.1948 | − | 15.7250i | 0.0804564 | − | 0.0958842i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.20304 | + | 46.5217i | 0.0494159 | + | 0.280251i | ||||
\(167\) | 50.5448 | − | 138.871i | 0.302664 | − | 0.831561i | −0.691371 | − | 0.722500i | \(-0.742993\pi\) |
0.994035 | − | 0.109062i | \(-0.0347846\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −15.5661 | + | 88.2796i | −0.0921070 | + | 0.522364i | ||||
\(170\) | 201.186 | + | 116.155i | 1.18345 | + | 0.683264i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −26.2006 | − | 45.3807i | −0.152329 | − | 0.263841i | ||||
\(173\) | −72.2331 | − | 198.459i | −0.417532 | − | 1.14716i | −0.953097 | − | 0.302666i | \(-0.902123\pi\) |
0.535565 | − | 0.844494i | \(-0.320099\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 388.682 | − | 326.143i | 2.22104 | − | 1.86367i | ||||
\(176\) | 4.04535 | + | 4.82106i | 0.0229849 | + | 0.0273924i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 115.530 | − | 42.0493i | 0.649043 | − | 0.236232i | ||||
\(179\) | 225.133 | − | 129.980i | 1.25772 | − | 0.726147i | 0.285092 | − | 0.958500i | \(-0.407976\pi\) |
0.972632 | + | 0.232353i | \(0.0746424\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 159.698 | − | 276.606i | 0.882311 | − | 1.52821i | 0.0335470 | − | 0.999437i | \(-0.489320\pi\) |
0.848764 | − | 0.528771i | \(-0.177347\pi\) | |||||||
\(182\) | −139.474 | − | 24.5929i | −0.766338 | − | 0.135126i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −37.3130 | − | 13.5808i | −0.202788 | − | 0.0738087i | ||||
\(185\) | −130.200 | + | 22.9578i | −0.703783 | + | 0.124096i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −23.6411 | − | 19.8373i | −0.126423 | − | 0.106082i | ||||
\(188\) | − | 85.8925i | − | 0.456875i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 115.234 | 0.606497 | ||||||||
\(191\) | 25.0422 | − | 29.8442i | 0.131111 | − | 0.156252i | −0.696495 | − | 0.717562i | \(-0.745258\pi\) |
0.827606 | + | 0.561310i | \(0.189702\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −28.3760 | − | 160.928i | −0.147026 | − | 0.833825i | −0.965718 | − | 0.259593i | \(-0.916412\pi\) |
0.818692 | − | 0.574233i | \(-0.194699\pi\) | |||||||
\(194\) | 68.1678 | − | 187.289i | 0.351380 | − | 0.965410i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −26.8716 | + | 152.397i | −0.137100 | + | 0.777533i | ||||
\(197\) | −296.815 | − | 171.366i | −1.50668 | − | 0.869880i | −0.999970 | − | 0.00776089i | \(-0.997530\pi\) |
−0.506706 | − | 0.862119i | \(-0.669137\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 98.8611 | + | 171.232i | 0.496789 | + | 0.860464i | 0.999993 | − | 0.00370331i | \(-0.00117880\pi\) |
−0.503204 | + | 0.864168i | \(0.667845\pi\) | |||||||
\(200\) | 43.6625 | + | 119.962i | 0.218312 | + | 0.599809i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 97.7725 | − | 82.0409i | 0.484022 | − | 0.406143i | ||||
\(203\) | −79.2670 | − | 94.4668i | −0.390478 | − | 0.465353i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −80.7718 | + | 29.3985i | −0.394009 | + | 0.143407i | ||||
\(206\) | 25.7149 | − | 14.8465i | 0.124830 | − | 0.0720705i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 17.8167 | − | 30.8594i | 0.0856571 | − | 0.148363i | ||||
\(209\) | −15.0758 | − | 2.65827i | −0.0721330 | − | 0.0127190i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −214.619 | − | 78.1150i | −1.01715 | − | 0.370213i | −0.220977 | − | 0.975279i | \(-0.570925\pi\) |
−0.796176 | + | 0.605066i | \(0.793147\pi\) | |||||||
\(212\) | −81.8168 | + | 14.4265i | −0.385928 | + | 0.0680496i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 23.7210 | + | 19.9042i | 0.110846 | + | 0.0930105i | ||||
\(215\) | 219.421i | 1.02056i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −521.045 | −2.40113 | ||||||||
\(218\) | −84.2178 | + | 100.367i | −0.386320 | + | 0.460398i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.57610 | − | 25.9524i | −0.0208005 | − | 0.117965i | ||||
\(221\) | −59.7633 | + | 164.198i | −0.270422 | + | 0.742979i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 67.0596 | − | 380.314i | 0.300716 | − | 1.70544i | −0.342301 | − | 0.939590i | \(-0.611206\pi\) |
0.643016 | − | 0.765852i | \(-0.277683\pi\) | |||||||
\(224\) | −55.0724 | − | 31.7961i | −0.245859 | − | 0.141947i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −109.536 | − | 189.722i | −0.484672 | − | 0.839476i | ||||
\(227\) | 63.6795 | + | 174.958i | 0.280527 | + | 0.770740i | 0.997300 | + | 0.0734342i | \(0.0233959\pi\) |
−0.716774 | + | 0.697306i | \(0.754382\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −236.706 | + | 198.620i | −1.03365 | + | 0.867336i | −0.991281 | − | 0.131766i | \(-0.957935\pi\) |
−0.0423704 | + | 0.999102i | \(0.513491\pi\) | |||||||
\(230\) | 106.876 | + | 127.369i | 0.464676 | + | 0.553780i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 29.1560 | − | 10.6119i | 0.125672 | − | 0.0457410i | ||||
\(233\) | 17.8085 | − | 10.2818i | 0.0764315 | − | 0.0441277i | −0.461297 | − | 0.887246i | \(-0.652616\pi\) |
0.537729 | + | 0.843118i | \(0.319282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −179.830 | + | 311.475i | −0.765234 | + | 1.32542i | ||||
\(236\) | 119.200 | + | 21.0182i | 0.505086 | + | 0.0890603i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 293.032 | + | 106.655i | 1.23123 | + | 0.448130i | ||||
\(239\) | 101.144 | − | 17.8344i | 0.423197 | − | 0.0746211i | 0.0420061 | − | 0.999117i | \(-0.486625\pi\) |
0.381191 | + | 0.924496i | \(0.375514\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 294.337 | + | 246.978i | 1.22131 | + | 1.02480i | 0.998755 | + | 0.0498853i | \(0.0158856\pi\) |
0.222559 | + | 0.974919i | \(0.428559\pi\) | |||||||
\(242\) | − | 167.619i | − | 0.692641i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −153.107 | −0.627488 | ||||||||
\(245\) | 416.512 | − | 496.380i | 1.70005 | − | 2.02604i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.0511 | + | 85.3589i | 0.0609355 | + | 0.345583i | ||||
\(248\) | 44.8377 | − | 123.191i | 0.180797 | − | 0.496737i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 41.4095 | − | 234.845i | 0.165638 | − | 0.939380i | ||||
\(251\) | −281.668 | − | 162.621i | −1.12218 | − | 0.647893i | −0.180227 | − | 0.983625i | \(-0.557683\pi\) |
−0.941958 | + | 0.335732i | \(0.891016\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.0440 | − | 19.1288i | −0.0436523 | − | 0.0756080i | ||||
\(254\) | 111.919 | + | 307.496i | 0.440627 | + | 1.21061i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.2567 | − | 10.2846i | 0.0478778 | − | 0.0401742i | ||||
\(257\) | 21.5034 | + | 25.6267i | 0.0836708 | + | 0.0997150i | 0.806256 | − | 0.591567i | \(-0.201491\pi\) |
−0.722585 | + | 0.691282i | \(0.757046\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −166.766 | + | 60.6977i | −0.643883 | + | 0.234354i | ||||
\(260\) | −129.218 | + | 74.6043i | −0.496994 | + | 0.286940i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 49.6023 | − | 85.9137i | 0.189322 | − | 0.327915i | ||||
\(263\) | 154.814 | + | 27.2979i | 0.588646 | + | 0.103794i | 0.460035 | − | 0.887901i | \(-0.347837\pi\) |
0.128611 | + | 0.991695i | \(0.458948\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 326.899 | + | 118.982i | 1.23358 | + | 0.448987i | ||||
\(266\) | 152.333 | − | 26.8605i | 0.572682 | − | 0.100979i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.18021 | − | 3.50762i | −0.0155978 | − | 0.0130881i | ||||
\(269\) | 289.194i | 1.07507i | 0.843241 | + | 0.537536i | \(0.180645\pi\) | ||||
−0.843241 | + | 0.537536i | \(0.819355\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 438.046 | 1.61641 | 0.808204 | − | 0.588903i | \(-0.200440\pi\) | ||||
0.808204 | + | 0.588903i | \(0.200440\pi\) | |||||||
\(272\) | −50.4328 | + | 60.1035i | −0.185415 | + | 0.220969i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 52.3016 | + | 296.617i | 0.190882 | + | 1.08255i | ||||
\(275\) | −24.2880 | + | 66.7308i | −0.0883201 | + | 0.242657i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.95396 | − | 16.7527i | 0.0106641 | − | 0.0604791i | −0.979011 | − | 0.203806i | \(-0.934669\pi\) |
0.989675 | + | 0.143327i | \(0.0457800\pi\) | |||||||
\(278\) | 69.1052 | + | 39.8979i | 0.248580 | + | 0.143518i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 133.141 | + | 230.606i | 0.475502 | + | 0.823594i | ||||
\(281\) | −31.3851 | − | 86.2298i | −0.111691 | − | 0.306867i | 0.871236 | − | 0.490864i | \(-0.163319\pi\) |
−0.982927 | + | 0.183996i | \(0.941097\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −335.404 | + | 281.438i | −1.18517 | + | 0.994479i | −0.185243 | + | 0.982693i | \(0.559307\pi\) |
−0.999931 | + | 0.0117863i | \(0.996248\pi\) | |||||||
\(284\) | 96.6861 | + | 115.226i | 0.340444 | + | 0.405725i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.6263 | − | 6.77941i | 0.0651269 | − | 0.0237042i | ||||
\(287\) | −99.9231 | + | 57.6906i | −0.348164 | + | 0.201013i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 47.8719 | − | 82.9166i | 0.165647 | − | 0.286909i | ||||
\(290\) | −127.947 | − | 22.5605i | −0.441196 | − | 0.0777948i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −124.331 | − | 45.2529i | −0.425793 | − | 0.154976i | ||||
\(293\) | −254.746 | + | 44.9185i | −0.869439 | + | 0.153305i | −0.590533 | − | 0.807013i | \(-0.701083\pi\) |
−0.278905 | + | 0.960319i | \(0.589972\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −388.255 | − | 325.784i | −1.31612 | − | 1.10435i | ||||
\(296\) | − | 44.6516i | − | 0.150850i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −40.7377 | −0.136704 | ||||||||
\(299\) | −80.3884 | + | 95.8031i | −0.268857 | + | 0.320412i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 51.1457 | + | 290.062i | 0.169919 | + | 0.963661i | ||||
\(302\) | −74.8685 | + | 205.700i | −0.247909 | + | 0.681124i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.75819 | + | 38.3276i | −0.0222309 | + | 0.126078i | ||||
\(305\) | 555.217 | + | 320.555i | 1.82038 | + | 1.05100i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 106.596 | + | 184.630i | 0.347219 | + | 0.601401i | 0.985754 | − | 0.168192i | \(-0.0537927\pi\) |
−0.638535 | + | 0.769592i | \(0.720459\pi\) | |||||||
\(308\) | −12.0987 | − | 33.2409i | −0.0392815 | − | 0.107925i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −420.516 | + | 352.855i | −1.35650 | + | 1.13824i | ||||
\(311\) | −299.915 | − | 357.425i | −0.964358 | − | 1.14928i | −0.988750 | − | 0.149575i | \(-0.952210\pi\) |
0.0243925 | − | 0.999702i | \(-0.492235\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −88.7107 | + | 32.2881i | −0.283421 | + | 0.103157i | −0.479819 | − | 0.877367i | \(-0.659298\pi\) |
0.196398 | + | 0.980524i | \(0.437075\pi\) | |||||||
\(314\) | −261.861 | + | 151.186i | −0.833953 | + | 0.481483i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 50.6646 | − | 87.7536i | 0.160331 | − | 0.277701i | ||||
\(317\) | 250.991 | + | 44.2565i | 0.791769 | + | 0.139610i | 0.554884 | − | 0.831927i | \(-0.312762\pi\) |
0.236885 | + | 0.971538i | \(0.423874\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.2185 | + | 5.90305i | 0.0508417 | + | 0.0185049i | ||||
\(320\) | −65.9794 | + | 11.6339i | −0.206186 | + | 0.0363561i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 170.973 | + | 143.463i | 0.530971 | + | 0.445537i | ||||
\(323\) | − | 190.847i | − | 0.590859i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 402.076 | 1.23716 | ||||||||
\(326\) | 133.812 | − | 159.471i | 0.410466 | − | 0.489174i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.04106 | − | 28.5893i | −0.0153691 | − | 0.0871625i | ||||
\(329\) | −165.122 | + | 453.669i | −0.501891 | + | 1.37893i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −63.9844 | + | 362.874i | −0.193306 | + | 1.09629i | 0.721504 | + | 0.692410i | \(0.243451\pi\) |
−0.914810 | + | 0.403884i | \(0.867660\pi\) | |||||||
\(332\) | 57.8562 | + | 33.4033i | 0.174266 | + | 0.100612i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −104.498 | − | 180.997i | −0.312870 | − | 0.541906i | ||||
\(335\) | 7.81507 | + | 21.4717i | 0.0233286 | + | 0.0640947i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 150.868 | − | 126.593i | 0.447679 | − | 0.375647i | −0.390895 | − | 0.920435i | \(-0.627834\pi\) |
0.838574 | + | 0.544788i | \(0.183390\pi\) | |||||||
\(338\) | 81.4876 | + | 97.1131i | 0.241087 | + | 0.287317i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 308.723 | − | 112.366i | 0.908008 | − | 0.330488i | ||||
\(341\) | 63.1548 | − | 36.4624i | 0.185205 | − | 0.106928i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 159.483 | − | 276.233i | 0.464966 | − | 0.805344i | ||||
\(344\) | −72.9805 | − | 12.8684i | −0.212153 | − | 0.0374083i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −280.663 | − | 102.153i | −0.811165 | − | 0.295240i | ||||
\(347\) | 263.673 | − | 46.4927i | 0.759864 | − | 0.133985i | 0.219727 | − | 0.975561i | \(-0.429483\pi\) |
0.540137 | + | 0.841577i | \(0.318372\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −395.788 | − | 332.105i | −1.13406 | − | 0.951591i | −0.134834 | − | 0.990868i | \(-0.543050\pi\) |
−0.999228 | + | 0.0392770i | \(0.987495\pi\) | |||||||
\(350\) | − | 717.555i | − | 2.05016i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.90028 | 0.0252849 | ||||||||
\(353\) | 186.396 | − | 222.139i | 0.528035 | − | 0.629288i | −0.434426 | − | 0.900708i | \(-0.643049\pi\) |
0.962461 | + | 0.271420i | \(0.0874932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −109.371 | − | 620.276i | −0.308088 | − | 1.74726i | ||||
\(356\) | 59.4668 | − | 163.384i | 0.167041 | − | 0.458943i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 63.8400 | − | 362.055i | 0.178324 | − | 1.01133i | ||||
\(359\) | −35.8110 | − | 20.6755i | −0.0997520 | − | 0.0575918i | 0.449294 | − | 0.893384i | \(-0.351676\pi\) |
−0.549046 | + | 0.835792i | \(0.685009\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 133.166 | + | 230.651i | 0.368882 | + | 0.638922i | ||||
\(362\) | −154.489 | − | 424.455i | −0.426765 | − | 1.17253i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −153.430 | + | 128.743i | −0.421510 | + | 0.353689i | ||||
\(365\) | 356.123 | + | 424.410i | 0.975678 | + | 1.16277i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 152.544 | − | 55.5215i | 0.415651 | − | 0.151285i | −0.125725 | − | 0.992065i | \(-0.540126\pi\) |
0.541376 | + | 0.840780i | \(0.317903\pi\) | |||||||
\(368\) | −48.6317 | + | 28.0775i | −0.132151 | + | 0.0762976i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −93.4855 | + | 161.922i | −0.252663 | + | 0.437626i | ||||
\(371\) | 459.876 | + | 81.0886i | 1.23956 | + | 0.218568i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 63.6401 | + | 23.1631i | 0.170617 | + | 0.0620995i | 0.425916 | − | 0.904763i | \(-0.359952\pi\) |
−0.255299 | + | 0.966862i | \(0.582174\pi\) | |||||||
\(374\) | −42.9814 | + | 7.57879i | −0.114924 | + | 0.0202641i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −93.0516 | − | 78.0796i | −0.247478 | − | 0.207659i | ||||
\(377\) | − | 97.7223i | − | 0.259210i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 122.431 | 0.323038 | 0.161519 | − | 0.986870i | \(-0.448361\pi\) | ||||
0.161519 | + | 0.986870i | \(0.448361\pi\) | |||||||
\(380\) | 104.753 | − | 124.839i | 0.275665 | − | 0.328524i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.56733 | − | 54.2590i | −0.0250454 | − | 0.142039i | ||||
\(383\) | 20.6906 | − | 56.8471i | 0.0540226 | − | 0.148426i | −0.909746 | − | 0.415165i | \(-0.863724\pi\) |
0.963769 | + | 0.266739i | \(0.0859462\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −25.7214 | + | 145.873i | −0.0668087 | + | 0.378891i | ||||
\(386\) | −200.137 | − | 115.549i | −0.518489 | − | 0.299350i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −140.933 | − | 244.103i | −0.363229 | − | 0.629132i | ||||
\(389\) | 82.3102 | + | 226.145i | 0.211594 | + | 0.581350i | 0.999402 | − | 0.0345705i | \(-0.0110063\pi\) |
−0.787808 | + | 0.615921i | \(0.788784\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 210.945 | − | 177.004i | 0.539501 | − | 0.452695i | ||||
\(392\) | 140.672 | + | 167.646i | 0.358856 | + | 0.427668i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −455.466 | + | 165.776i | −1.15601 | + | 0.420752i | ||||
\(395\) | −367.453 | + | 212.149i | −0.930261 | + | 0.537087i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.3451 | − | 24.8464i | 0.0361337 | − | 0.0625854i | −0.847393 | − | 0.530966i | \(-0.821829\pi\) |
0.883527 | + | 0.468381i | \(0.155162\pi\) | |||||||
\(398\) | 275.373 | + | 48.5557i | 0.691893 | + | 0.121999i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 169.651 | + | 61.7481i | 0.424129 | + | 0.154370i | ||||
\(401\) | −697.035 | + | 122.906i | −1.73824 | + | 0.306499i | −0.950780 | − | 0.309866i | \(-0.899716\pi\) |
−0.787461 | + | 0.616365i | \(0.788605\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −316.299 | − | 265.406i | −0.784861 | − | 0.658577i | ||||
\(404\) | − | 180.500i | − | 0.446783i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −174.397 | −0.429550 | ||||||||
\(407\) | 15.9657 | − | 19.0272i | 0.0392278 | − | 0.0467499i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.6664 | − | 77.5062i | −0.0334143 | − | 0.189502i | 0.963532 | − | 0.267593i | \(-0.0862284\pi\) |
−0.996946 | + | 0.0780917i | \(0.975117\pi\) | |||||||
\(410\) | −41.5758 | + | 114.229i | −0.101404 | + | 0.278606i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.29189 | − | 41.3543i | 0.0176988 | − | 0.100375i | ||||
\(413\) | −589.190 | − | 340.169i | −1.42661 | − | 0.823653i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −139.871 | − | 242.263i | −0.337037 | − | 0.583766i | ||||
\(416\) | −17.2355 | − | 47.3541i | −0.0414315 | − | 0.113832i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −16.5843 | + | 13.9159i | −0.0396754 | + | 0.0332916i | ||||
\(419\) | −33.8949 | − | 40.3944i | −0.0808948 | − | 0.0964067i | 0.724079 | − | 0.689717i | \(-0.242265\pi\) |
−0.804974 | + | 0.593310i | \(0.797821\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 664.624 | − | 241.903i | 1.57868 | − | 0.574592i | 0.603763 | − | 0.797164i | \(-0.293667\pi\) |
0.974916 | + | 0.222572i | \(0.0714452\pi\) | |||||||
\(422\) | −279.723 | + | 161.498i | −0.662851 | + | 0.382697i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −58.7457 | + | 101.751i | −0.138551 | + | 0.239978i | ||||
\(425\) | −871.865 | − | 153.733i | −2.05145 | − | 0.361725i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 808.686 | + | 294.338i | 1.89388 | + | 0.689315i | ||||
\(428\) | 43.1265 | − | 7.60437i | 0.100763 | − | 0.0177672i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 237.709 | + | 199.462i | 0.552813 | + | 0.463865i | ||||
\(431\) | − | 279.279i | − | 0.647978i | −0.946061 | − | 0.323989i | \(-0.894976\pi\) | ||
0.946061 | − | 0.323989i | \(-0.105024\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 100.836 | 0.232877 | 0.116439 | − | 0.993198i | \(-0.462852\pi\) | ||||
0.116439 | + | 0.993198i | \(0.462852\pi\) | |||||||
\(434\) | −473.650 | + | 564.475i | −1.09136 | + | 1.30063i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 32.1752 | + | 182.475i | 0.0737964 | + | 0.418520i | ||||
\(437\) | 46.7177 | − | 128.356i | 0.106905 | − | 0.293720i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.2883 | − | 98.0470i | 0.0393812 | − | 0.223342i | −0.958765 | − | 0.284199i | \(-0.908272\pi\) |
0.998146 | + | 0.0608574i | \(0.0193835\pi\) | |||||||
\(440\) | −32.2754 | − | 18.6342i | −0.0733531 | − | 0.0423504i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 123.557 | + | 214.007i | 0.279541 | + | 0.484179i | ||||
\(443\) | −117.281 | − | 322.226i | −0.264742 | − | 0.727373i | −0.998832 | − | 0.0483203i | \(-0.984613\pi\) |
0.734090 | − | 0.679052i | \(-0.237609\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −557.716 | + | 467.980i | −1.25330 | + | 1.05164i | ||||
\(446\) | −351.053 | − | 418.369i | −0.787115 | − | 0.938047i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −84.5092 | + | 30.7589i | −0.188637 | + | 0.0686581i | ||||
\(449\) | 433.309 | − | 250.171i | 0.965053 | − | 0.557174i | 0.0673285 | − | 0.997731i | \(-0.478552\pi\) |
0.897725 | + | 0.440557i | \(0.145219\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.07431 | − | 13.9851i | 0.0179031 | − | 0.0310091i | ||||
\(452\) | −305.107 | − | 53.7987i | −0.675016 | − | 0.119024i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 247.428 | + | 90.0564i | 0.544996 | + | 0.198362i | ||||
\(455\) | 825.931 | − | 145.634i | 1.81523 | − | 0.320074i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 88.1631 | + | 73.9776i | 0.192917 | + | 0.161877i | 0.734130 | − | 0.679009i | \(-0.237590\pi\) |
−0.541213 | + | 0.840886i | \(0.682035\pi\) | |||||||
\(458\) | 436.989i | 0.954125i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 235.140 | 0.511173 | ||||||||
\(461\) | −371.972 | + | 443.299i | −0.806880 | + | 0.961602i | −0.999808 | − | 0.0196109i | \(-0.993757\pi\) |
0.192928 | + | 0.981213i | \(0.438202\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −138.386 | − | 784.826i | −0.298890 | − | 1.69509i | −0.650957 | − | 0.759114i | \(-0.725632\pi\) |
0.352067 | − | 0.935975i | \(-0.385479\pi\) | |||||||
\(464\) | 15.0075 | − | 41.2328i | 0.0323437 | − | 0.0888637i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.04990 | − | 28.6394i | 0.0108367 | − | 0.0614579i | ||||
\(467\) | −234.565 | − | 135.426i | −0.502281 | − | 0.289992i | 0.227374 | − | 0.973807i | \(-0.426986\pi\) |
−0.729655 | + | 0.683816i | \(0.760319\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.3360 | + | 26.5628i | 0.0326994 | + | 0.0566371i | ||||
\(470\) | 173.964 | + | 477.961i | 0.370136 | + | 1.01694i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 131.128 | − | 110.029i | 0.277813 | − | 0.233113i | ||||
\(473\) | −26.4976 | − | 31.5786i | −0.0560203 | − | 0.0667624i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −412.665 | + | 150.198i | −0.868769 | + | 0.316206i | ||||
\(476\) | 381.922 | − | 220.503i | 0.802358 | − | 0.463241i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 72.6230 | − | 125.787i | 0.151931 | − | 0.263152i | ||||
\(479\) | 785.792 | + | 138.556i | 1.64048 | + | 0.289262i | 0.916344 | − | 0.400391i | \(-0.131126\pi\) |
0.724140 | + | 0.689653i | \(0.242237\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −132.152 | − | 48.0995i | −0.274745 | − | 0.0999990i | ||||
\(482\) | 535.127 | − | 94.3574i | 1.11022 | − | 0.195762i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −181.590 | − | 152.372i | −0.375186 | − | 0.314819i | ||||
\(485\) | 1180.26i | 2.43354i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −139.213 | −0.285859 | −0.142929 | − | 0.989733i | \(-0.545652\pi\) | ||||
−0.142929 | + | 0.989733i | \(0.545652\pi\) | |||||||
\(488\) | −139.180 | + | 165.869i | −0.285206 | + | 0.339895i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −159.128 | − | 902.458i | −0.324750 | − | 1.84175i | ||||
\(491\) | 73.6069 | − | 202.233i | 0.149912 | − | 0.411881i | −0.841892 | − | 0.539646i | \(-0.818558\pi\) |
0.991804 | + | 0.127765i | \(0.0407804\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −37.3639 | + | 211.901i | −0.0757889 | + | 0.429820i | ||||
\(494\) | 106.156 | + | 61.2890i | 0.214890 | + | 0.124067i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −92.6994 | − | 160.560i | −0.186894 | − | 0.323710i | ||||
\(497\) | −289.166 | − | 794.476i | −0.581822 | − | 1.59854i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −363.724 | + | 305.201i | −0.728906 | + | 0.611624i | −0.929833 | − | 0.367982i | \(-0.880049\pi\) |
0.200927 | + | 0.979606i | \(0.435604\pi\) | |||||||
\(500\) | −216.777 | − | 258.344i | −0.433553 | − | 0.516689i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −432.223 | + | 157.316i | −0.861002 | + | 0.313379i | ||||
\(503\) | 696.911 | − | 402.362i | 1.38551 | − | 0.799924i | 0.392704 | − | 0.919665i | \(-0.371540\pi\) |
0.992805 | + | 0.119740i | \(0.0382063\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −377.907 | + | 654.554i | −0.748331 | + | 1.29615i | ||||
\(506\) | −30.7627 | − | 5.42429i | −0.0607958 | − | 0.0107199i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 434.865 | + | 158.278i | 0.856033 | + | 0.311571i | ||||
\(509\) | −924.707 | + | 163.051i | −1.81671 | + | 0.320336i | −0.975439 | − | 0.220272i | \(-0.929306\pi\) |
−0.841275 | + | 0.540607i | \(0.818194\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 569.702 | + | 478.036i | 1.11488 | + | 0.935492i | ||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 47.3102 | 0.0920431 | ||||||||
\(515\) | −113.025 | + | 134.698i | −0.219466 | + | 0.261549i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.7334 | − | 66.5434i | −0.0226952 | − | 0.128711i | ||||
\(518\) | −85.8396 | + | 235.842i | −0.165713 | + | 0.455294i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −36.6420 | + | 207.807i | −0.0704654 | + | 0.399629i | ||||
\(521\) | 832.809 | + | 480.823i | 1.59848 | + | 0.922884i | 0.991780 | + | 0.127955i | \(0.0408414\pi\) |
0.606703 | + | 0.794929i | \(0.292492\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.2517 | − | 33.3450i | −0.0368102 | − | 0.0637572i | 0.847033 | − | 0.531540i | \(-0.178386\pi\) |
−0.883844 | + | 0.467783i | \(0.845053\pi\) | |||||||
\(524\) | −47.9842 | − | 131.836i | −0.0915729 | − | 0.251595i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 170.305 | − | 142.903i | 0.323774 | − | 0.271679i | ||||
\(527\) | 584.387 | + | 696.445i | 1.10889 | + | 1.32153i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −311.896 | + | 113.521i | −0.589596 | + | 0.214595i | ||||
\(530\) | 426.063 | − | 245.987i | 0.803892 | − | 0.464127i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 109.378 | − | 189.448i | 0.205597 | − | 0.356105i | ||||
\(533\) | −90.0441 | − | 15.8772i | −0.168938 | − | 0.0297884i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −172.312 | − | 62.7165i | −0.322079 | − | 0.117227i | ||||
\(536\) | −7.59995 | + | 1.34008i | −0.0141790 | + | 0.00250014i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 313.299 | + | 262.889i | 0.582340 | + | 0.488641i | ||||
\(539\) | 121.737i | 0.225857i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.4860 | −0.0304731 | −0.0152366 | − | 0.999884i | \(-0.504850\pi\) | ||||
−0.0152366 | + | 0.999884i | \(0.504850\pi\) | |||||||
\(542\) | 398.201 | − | 474.558i | 0.734689 | − | 0.875568i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 19.2678 | + | 109.273i | 0.0354187 | + | 0.200869i | ||||
\(545\) | 265.363 | − | 729.078i | 0.486904 | − | 1.33776i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.02809 | − | 45.5295i | 0.0146766 | − | 0.0832350i | −0.976590 | − | 0.215111i | \(-0.930989\pi\) |
0.991266 | + | 0.131876i | \(0.0420999\pi\) | |||||||
\(548\) | 368.885 | + | 212.976i | 0.673147 | + | 0.388642i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 50.2141 | + | 86.9733i | 0.0912983 | + | 0.158133i | ||||
\(551\) | 36.5047 | + | 100.296i | 0.0662517 | + | 0.182025i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −436.302 | + | 366.101i | −0.788972 | + | 0.662026i | ||||
\(554\) | −15.4638 | − | 18.4290i | −0.0279130 | − | 0.0332654i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 106.043 | − | 38.5964i | 0.190724 | − | 0.0694179i | ||||
\(557\) | −62.2086 | + | 35.9161i | −0.111685 | + | 0.0644814i | −0.554802 | − | 0.831982i | \(-0.687206\pi\) |
0.443117 | + | 0.896464i | \(0.353873\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −116.702 | + | 202.133i | −0.208769 | + | 0.361598i | ||||
\(560\) | 370.857 | + | 65.3921i | 0.662245 | + | 0.116772i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −121.947 | − | 44.3852i | −0.216988 | − | 0.0789772i | ||||
\(563\) | 342.983 | − | 60.4772i | 0.609206 | − | 0.107420i | 0.139470 | − | 0.990226i | \(-0.455460\pi\) |
0.469736 | + | 0.882807i | \(0.344349\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 993.784 | + | 833.884i | 1.75891 | + | 1.47590i | ||||
\(566\) | 619.198i | 1.09399i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 212.722 | 0.374510 | ||||||||
\(569\) | −218.985 | + | 260.976i | −0.384859 | + | 0.458657i | −0.923342 | − | 0.383980i | \(-0.874553\pi\) |
0.538483 | + | 0.842637i | \(0.318998\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −93.4096 | − | 529.752i | −0.163589 | − | 0.927762i | −0.950507 | − | 0.310704i | \(-0.899435\pi\) |
0.786917 | − | 0.617058i | \(-0.211676\pi\) | |||||||
\(572\) | 9.58754 | − | 26.3415i | 0.0167614 | − | 0.0460516i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −28.3348 | + | 160.695i | −0.0493638 | + | 0.279956i | ||||
\(575\) | −548.746 | − | 316.819i | −0.954341 | − | 0.550989i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −146.659 | − | 254.021i | −0.254175 | − | 0.440244i | 0.710496 | − | 0.703701i | \(-0.248471\pi\) |
−0.964671 | + | 0.263457i | \(0.915137\pi\) | |||||||
\(578\) | −46.3103 | − | 127.237i | −0.0801216 | − | 0.220132i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −140.750 | + | 118.103i | −0.242672 | + | 0.203626i | ||||
\(581\) | −241.371 | − | 287.655i | −0.415441 | − | 0.495103i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −61.4151 | + | 22.3533i | −0.105343 | + | 0.0383418i | ||||
\(584\) | −162.047 | + | 93.5578i | −0.277478 | + | 0.160202i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −182.911 | + | 316.811i | −0.312135 | + | 0.540634i | ||||
\(587\) | −462.413 | − | 81.5359i | −0.787757 | − | 0.138903i | −0.234724 | − | 0.972062i | \(-0.575419\pi\) |
−0.553033 | + | 0.833159i | \(0.686530\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 423.773 | + | 154.241i | 0.719479 | + | 0.261869i | ||||
\(590\) | −705.877 | + | 124.465i | −1.19640 | + | 0.210958i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −48.3734 | − | 40.5901i | −0.0817118 | − | 0.0685643i | ||||
\(593\) | − | 880.585i | − | 1.48497i | −0.669864 | − | 0.742483i | \(-0.733648\pi\) | ||
0.669864 | − | 0.742483i | \(-0.266352\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1846.64 | −3.10359 | ||||||||
\(596\) | −37.0322 | + | 44.1332i | −0.0621345 | + | 0.0740490i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 30.7122 | + | 174.178i | 0.0513582 | + | 0.291267i | ||||
\(599\) | −117.916 | + | 323.972i | −0.196855 | + | 0.540855i | −0.998367 | − | 0.0571238i | \(-0.981807\pi\) |
0.801512 | + | 0.597979i | \(0.204029\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 108.241 | − | 613.865i | 0.180102 | − | 1.02141i | −0.751987 | − | 0.659177i | \(-0.770905\pi\) |
0.932089 | − | 0.362229i | \(-0.117984\pi\) | |||||||
\(602\) | 360.732 | + | 208.269i | 0.599223 | + | 0.345961i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 154.786 | + | 268.098i | 0.256269 | + | 0.443870i | ||||
\(605\) | 339.490 | + | 932.741i | 0.561140 | + | 1.54172i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 725.795 | − | 609.015i | 1.19571 | − | 1.00332i | 0.195967 | − | 0.980610i | \(-0.437215\pi\) |
0.999742 | − | 0.0227086i | \(-0.00722899\pi\) | |||||||
\(608\) | 35.3788 | + | 42.1628i | 0.0581888 | + | 0.0693467i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 851.987 | − | 310.098i | 1.39670 | − | 0.508358i | ||||
\(611\) | −331.324 | + | 191.290i | −0.542265 | + | 0.313077i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 352.677 | − | 610.854i | 0.575329 | − | 0.996499i | −0.420677 | − | 0.907211i | \(-0.638207\pi\) |
0.996006 | − | 0.0892887i | \(-0.0284594\pi\) | |||||||
\(614\) | 296.919 | + | 52.3549i | 0.483582 | + | 0.0852685i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −47.0097 | − | 17.1101i | −0.0763145 | − | 0.0277762i | ||||
\(617\) | 876.465 | − | 154.544i | 1.42053 | − | 0.250477i | 0.589976 | − | 0.807421i | \(-0.299137\pi\) |
0.830550 | + | 0.556943i | \(0.188026\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −376.539 | − | 315.954i | −0.608303 | − | 0.510426i | 0.285800 | − | 0.958289i | \(-0.407741\pi\) |
−0.894102 | + | 0.447863i | \(0.852185\pi\) | |||||||
\(620\) | 776.326i | 1.25214i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −659.851 | −1.06085 | ||||||||
\(623\) | −628.186 | + | 748.643i | −1.00832 | + | 1.20167i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 49.2783 | + | 279.471i | 0.0788452 | + | 0.447154i | ||||
\(626\) | −45.6622 | + | 125.456i | −0.0729428 | + | 0.200409i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −74.2551 | + | 421.121i | −0.118241 | + | 0.670575i | ||||
\(629\) | 268.169 | + | 154.828i | 0.426342 | + | 0.246149i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.7611 | + | 25.5670i | 0.0233932 | + | 0.0405183i | 0.877485 | − | 0.479604i | \(-0.159220\pi\) |
−0.854092 | + | 0.520122i | \(0.825886\pi\) | |||||||
\(632\) | −49.0119 | − | 134.659i | −0.0775504 | − | 0.213068i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 276.106 | − | 231.680i | 0.435498 | − | 0.365426i | ||||
\(635\) | −1245.58 | − | 1484.43i | −1.96155 | − | 2.33768i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 647.704 | − | 235.745i | 1.01680 | − | 0.370086i | ||||
\(638\) | 21.1383 | − | 12.2042i | 0.0331322 | − | 0.0191289i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −47.3742 | + | 82.0545i | −0.0740222 | + | 0.128210i | ||||
\(641\) | 94.3541 | + | 16.6372i | 0.147198 | + | 0.0259550i | 0.246762 | − | 0.969076i | \(-0.420634\pi\) |
−0.0995634 | + | 0.995031i | \(0.531745\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 537.766 | + | 195.731i | 0.836339 | + | 0.304402i | 0.724458 | − | 0.689319i | \(-0.242090\pi\) |
0.111881 | + | 0.993722i | \(0.464313\pi\) | |||||||
\(644\) | 310.841 | − | 54.8097i | 0.482673 | − | 0.0851083i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −206.755 | − | 173.488i | −0.320054 | − | 0.268557i | ||||
\(647\) | 419.943i | 0.649061i | 0.945875 | + | 0.324531i | \(0.105206\pi\) | ||||
−0.945875 | + | 0.324531i | \(0.894794\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 95.2192 | 0.146717 | ||||||||
\(650\) | 365.503 | − | 435.590i | 0.562313 | − | 0.670138i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −51.1225 | − | 289.930i | −0.0784087 | − | 0.444678i | ||||
\(653\) | 425.980 | − | 1170.37i | 0.652343 | − | 1.79230i | 0.0434334 | − | 0.999056i | \(-0.486170\pi\) |
0.608909 | − | 0.793240i | \(-0.291607\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −102.013 | + | 578.542i | −0.155744 | + | 0.883270i | ||||
\(656\) | −35.5547 | − | 20.5275i | −0.0541993 | − | 0.0312920i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 341.380 | + | 591.288i | 0.518815 | + | 0.898614i | ||||
\(659\) | −159.051 | − | 436.990i | −0.241353 | − | 0.663111i | −0.999934 | − | 0.0115322i | \(-0.996329\pi\) |
0.758581 | − | 0.651579i | \(-0.225893\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −250.507 | + | 210.201i | −0.378982 | + | 0.318004i | −0.812303 | − | 0.583236i | \(-0.801786\pi\) |
0.433320 | + | 0.901240i | \(0.357342\pi\) | |||||||
\(662\) | 334.955 | + | 399.184i | 0.505974 | + | 0.602996i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 88.7810 | − | 32.3137i | 0.133706 | − | 0.0486651i | ||||
\(665\) | −793.280 | + | 458.000i | −1.19290 | + | 0.688722i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −77.0009 | + | 133.369i | −0.115444 | + | 0.199954i | ||||
\(668\) | −291.076 | − | 51.3245i | −0.435742 | − | 0.0768332i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 30.3656 | + | 11.0522i | 0.0453218 | + | 0.0164958i | ||||
\(671\) | −118.617 | + | 20.9153i | −0.176776 | + | 0.0311704i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −221.219 | − | 185.625i | −0.328706 | − | 0.275817i | 0.463466 | − | 0.886115i | \(-0.346605\pi\) |
−0.792172 | + | 0.610297i | \(0.791050\pi\) | |||||||
\(674\) | − | 278.521i | − | 0.413235i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 179.283 | 0.265211 | ||||||||
\(677\) | −110.656 | + | 131.875i | −0.163450 | + | 0.194793i | −0.841553 | − | 0.540175i | \(-0.818358\pi\) |
0.678102 | + | 0.734967i | \(0.262803\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 275.113 | + | 1560.24i | 0.405174 | + | 2.29786i | ||||
\(680\) | 158.909 | − | 436.600i | 0.233690 | − | 0.642059i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 17.9086 | − | 101.565i | 0.0262589 | − | 0.148922i | ||||
\(683\) | 113.042 | + | 65.2651i | 0.165509 | + | 0.0955565i | 0.580466 | − | 0.814284i | \(-0.302870\pi\) |
−0.414958 | + | 0.909841i | \(0.636204\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −891.799 | − | 1544.64i | −1.30190 | − | 2.25495i | ||||
\(686\) | −154.281 | − | 423.883i | −0.224899 | − | 0.617905i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −80.2832 | + | 67.3656i | −0.116691 | + | 0.0979151i | ||||
\(689\) | 237.862 | + | 283.473i | 0.345228 | + | 0.411427i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −259.558 | + | 94.4713i | −0.375626 | + | 0.136717i | −0.522932 | − | 0.852374i | \(-0.675162\pi\) |
0.147306 | + | 0.989091i | \(0.452940\pi\) | |||||||
\(692\) | −365.801 | + | 211.195i | −0.528614 | + | 0.305196i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 189.321 | − | 327.914i | 0.272797 | − | 0.472498i | ||||
\(695\) | −465.354 | − | 82.0544i | −0.669574 | − | 0.118064i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 189.181 | + | 68.8564i | 0.271422 | + | 0.0987897i | ||||
\(698\) | −719.573 | + | 126.880i | −1.03091 | + | 0.181777i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −777.364 | − | 652.286i | −1.11052 | − | 0.931837i | ||||
\(701\) | − | 865.652i | − | 1.23488i | −0.786617 | − | 0.617441i | \(-0.788170\pi\) | ||
0.786617 | − | 0.617441i | \(-0.211830\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 153.601 | 0.218493 | ||||||||
\(704\) | 8.09070 | − | 9.64212i | 0.0114925 | − | 0.0136962i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −71.2123 | − | 403.865i | −0.100867 | − | 0.572047i | ||||
\(707\) | −346.999 | + | 953.372i | −0.490805 | + | 1.34847i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.7944 | + | 112.259i | −0.0279187 | + | 0.158335i | −0.995580 | − | 0.0939188i | \(-0.970061\pi\) |
0.967661 | + | 0.252254i | \(0.0811717\pi\) | |||||||
\(710\) | −771.399 | − | 445.367i | −1.08648 | − | 0.627278i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −122.944 | − | 212.945i | −0.172674 | − | 0.299081i | ||||
\(713\) | 222.550 | + | 611.451i | 0.312132 | + | 0.857575i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −89.9179 | + | 75.4501i | −0.125759 | + | 0.105525i | ||||
\(716\) | −334.199 | − | 398.283i | −0.466758 | − | 0.556261i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −54.9523 | + | 20.0010i | −0.0765353 | + | 0.0278566i | ||||
\(719\) | 117.571 | − | 67.8798i | 0.163521 | − | 0.0944086i | −0.416006 | − | 0.909362i | \(-0.636571\pi\) |
0.579527 | + | 0.814953i | \(0.303237\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −118.015 | + | 204.408i | −0.163683 | + | 0.283507i | ||||
\(722\) | 370.929 | + | 65.4048i | 0.513752 | + | 0.0905883i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −600.270 | − | 218.480i | −0.829102 | − | 0.301768i | ||||
\(725\) | 487.596 | − | 85.9763i | 0.672546 | − | 0.118588i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 76.0522 | + | 63.8154i | 0.104611 | + | 0.0877790i | 0.693593 | − | 0.720367i | \(-0.256027\pi\) |
−0.588982 | + | 0.808146i | \(0.700471\pi\) | |||||||
\(728\) | 283.250i | 0.389080i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 783.514 | 1.07331 | ||||||||
\(731\) | 330.342 | − | 393.686i | 0.451904 | − | 0.538559i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −132.435 | − | 751.078i | −0.180676 | − | 1.02466i | −0.931387 | − | 0.364032i | \(-0.881400\pi\) |
0.750711 | − | 0.660631i | \(-0.229711\pi\) | |||||||
\(734\) | 78.5192 | − | 215.730i | 0.106974 | − | 0.293910i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.7903 | + | 78.2088i | −0.0187368 | + | 0.106262i | ||||
\(737\) | −3.71769 | − | 2.14641i | −0.00504436 | − | 0.00291236i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 436.285 | + | 755.668i | 0.590373 | + | 1.02256i | 0.994182 | + | 0.107712i | \(0.0343525\pi\) |
−0.403810 | + | 0.914843i | \(0.632314\pi\) | |||||||
\(740\) | 90.4359 | + | 248.471i | 0.122211 | + | 0.335771i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 505.893 | − | 424.494i | 0.681796 | − | 0.572095i | ||||
\(743\) | 515.245 | + | 614.045i | 0.693466 | + | 0.826441i | 0.991770 | − | 0.128030i | \(-0.0408654\pi\) |
−0.298304 | + | 0.954471i | \(0.596421\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 226.691 | − | 82.5088i | 0.304283 | − | 0.110750i | ||||
\(746\) | 82.9451 | − | 47.8884i | 0.111186 | − | 0.0641935i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −30.8613 | + | 53.4534i | −0.0412584 | + | 0.0714617i | ||||
\(749\) | −242.406 | − | 42.7427i | −0.323639 | − | 0.0570663i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −814.474 | − | 296.444i | −1.08452 | − | 0.394733i | −0.262931 | − | 0.964815i | \(-0.584689\pi\) |
−0.821588 | + | 0.570082i | \(0.806911\pi\) | |||||||
\(752\) | −169.175 | + | 29.8301i | −0.224967 | + | 0.0396677i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −105.867 | − | 88.8333i | −0.140408 | − | 0.117816i | ||||
\(755\) | − | 1296.28i | − | 1.71693i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −305.290 | −0.403289 | −0.201644 | − | 0.979459i | \(-0.564629\pi\) | ||||
−0.201644 | + | 0.979459i | \(0.564629\pi\) | |||||||
\(758\) | 111.295 | − | 132.636i | 0.146827 | − | 0.174981i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −40.0205 | − | 226.968i | −0.0526586 | − | 0.298642i | ||||
\(761\) | −210.316 | + | 577.838i | −0.276367 | + | 0.759313i | 0.721399 | + | 0.692519i | \(0.243499\pi\) |
−0.997767 | + | 0.0667941i | \(0.978723\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 180.851 | − | 1025.65i | 0.237026 | − | 1.34424i | ||||
\(764\) | −67.4786 | − | 38.9588i | −0.0883228 | − | 0.0509932i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −42.7767 | − | 74.0914i | −0.0558443 | − | 0.0967251i | ||||
\(767\) | −184.393 | − | 506.616i | −0.240408 | − | 0.660516i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 105.505 | − | 88.5291i | 0.137198 | − | 0.115122i | −0.571606 | − | 0.820528i | \(-0.693680\pi\) |
0.708804 | + | 0.705406i | \(0.249235\pi\) | |||||||
\(770\) | 134.650 | + | 160.470i | 0.174870 | + | 0.208402i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −307.112 | + | 111.780i | −0.397813 | + | 0.144792i | ||||
\(773\) | 154.674 | − | 89.3010i | 0.200096 | − | 0.115525i | −0.396604 | − | 0.917990i | \(-0.629812\pi\) |
0.596700 | + | 0.802464i | \(0.296478\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1045.99 | − | 1811.71i | 1.34967 | − | 2.33769i | ||||
\(776\) | −392.563 | − | 69.2194i | −0.505880 | − | 0.0892003i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 319.818 | + | 116.404i | 0.411077 | + | 0.149620i | ||||
\(779\) | 98.3465 | − | 17.3411i | 0.126247 | − | 0.0222608i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 90.6461 | + | 76.0611i | 0.116064 | + | 0.0973894i | ||||
\(782\) | − | 389.430i | − | 0.497993i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 309.495 | 0.394764 | ||||||||
\(785\) | 1150.96 | − | 1371.66i | 1.46619 | − | 1.74734i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −108.344 | − | 614.451i | −0.137668 | − | 0.780752i | −0.972965 | − | 0.230953i | \(-0.925816\pi\) |
0.835297 | − | 0.549798i | \(-0.185295\pi\) | |||||||
\(788\) | −234.443 | + | 644.127i | −0.297516 | + | 0.817420i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −104.197 | + | 590.932i | −0.131895 | + | 0.748016i | ||||
\(791\) | 1508.10 | + | 870.702i | 1.90658 | + | 1.10076i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 340.983 | + | 590.599i | 0.429991 | + | 0.744766i | ||||
\(794\) | −13.8771 | − | 38.1271i | −0.0174775 | − | 0.0480190i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 302.928 | − | 254.187i | 0.380563 | − | 0.319330i | ||||
\(797\) | 487.894 | + | 581.449i | 0.612163 | + | 0.729547i | 0.979702 | − | 0.200461i | \(-0.0642440\pi\) |
−0.367539 | + | 0.930008i | \(0.619800\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 791.584 | − | 288.113i | 0.990718 | − | 0.360592i | ||||
\(800\) | 221.115 | − | 127.661i | 0.276393 | − | 0.159576i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −500.481 | + | 866.859i | −0.624042 | + | 1.08087i | ||||
\(803\) | −102.505 | − | 18.0744i | −0.127653 | − | 0.0225086i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1241.97 | − | 452.039i | −1.54282 | − | 0.561539i | ||||
\(806\) | −575.056 | + | 101.398i | −0.713469 | + | 0.125804i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −195.545 | − | 164.082i | −0.242011 | − | 0.203072i | ||||
\(809\) | − | 1035.21i | − | 1.27961i | −0.768537 | − | 0.639805i | \(-0.779015\pi\) | ||
0.768537 | − | 0.639805i | \(-0.220985\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1435.70 | 1.77029 | 0.885144 | − | 0.465318i | \(-0.154060\pi\) | ||||
0.885144 | + | 0.465318i | \(0.154060\pi\) | |||||||
\(812\) | −158.534 | + | 188.934i | −0.195239 | + | 0.232677i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.09967 | − | 34.5929i | −0.00749345 | − | 0.0424975i | ||||
\(815\) | −421.629 | + | 1158.42i | −0.517336 | + | 1.42137i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 44.2671 | − | 251.051i | 0.0541825 | − | 0.307284i | ||||
\(818\) | −96.3897 | − | 55.6506i | −0.117836 | − | 0.0680325i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 85.9555 | + | 148.879i | 0.104824 | + | 0.181560i | ||||
\(821\) | 2.84183 | + | 7.80786i | 0.00346142 | + | 0.00951018i | 0.941411 | − | 0.337261i | \(-0.109500\pi\) |
−0.937950 | + | 0.346771i | \(0.887278\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −518.097 | + | 434.735i | −0.629522 | + | 0.528232i | −0.900781 | − | 0.434275i | \(-0.857005\pi\) |
0.271258 | + | 0.962507i | \(0.412560\pi\) | |||||||
\(824\) | −38.1726 | − | 45.4924i | −0.0463260 | − | 0.0552092i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −904.118 | + | 329.072i | −1.09457 | + | 0.398392i | ||||
\(827\) | −1123.27 | + | 648.518i | −1.35824 | + | 0.784181i | −0.989387 | − | 0.145305i | \(-0.953584\pi\) |
−0.368855 | + | 0.929487i | \(0.620250\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −367.050 | + | 635.750i | −0.442763 | + | 0.766888i | −0.997893 | − | 0.0648754i | \(-0.979335\pi\) |
0.555130 | + | 0.831763i | \(0.312668\pi\) | |||||||
\(830\) | −389.603 | − | 68.6976i | −0.469402 | − | 0.0827682i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −66.9688 | − | 24.3747i | −0.0804914 | − | 0.0292965i | ||||
\(833\) | −1494.62 | + | 263.542i | −1.79426 | + | 0.316377i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 948.082 | + | 795.535i | 1.13543 | + | 0.952737i | ||||
\(836\) | 30.6167i | 0.0366229i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −74.5731 | −0.0889894 | ||||||||
\(839\) | −447.625 | + | 533.458i | −0.533522 | + | 0.635826i | −0.963722 | − | 0.266907i | \(-0.913998\pi\) |
0.430201 | + | 0.902733i | \(0.358443\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 125.142 | + | 709.716i | 0.148802 | + | 0.843896i | ||||
\(842\) | 342.103 | − | 939.920i | 0.406298 | − | 1.11629i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −79.3201 | + | 449.846i | −0.0939811 | + | 0.532993i | ||||
\(845\) | −650.139 | − | 375.358i | −0.769396 | − | 0.444211i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 666.203 | + | 1153.90i | 0.786544 | + | 1.36233i | ||||
\(848\) | 56.8293 | + | 156.137i | 0.0670157 | + | 0.184124i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −959.106 | + | 804.786i | −1.12836 | + | 0.946807i | ||||
\(851\) | 142.459 | + | 169.776i | 0.167401 | + | 0.199501i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1214.78 | + | 442.144i | −1.42413 | + | 0.518340i | −0.935242 | − | 0.354009i | \(-0.884818\pi\) |
−0.488885 | + | 0.872348i | \(0.662596\pi\) | |||||||
\(854\) | 1054.00 | − | 608.526i | 1.23419 | − | 0.712559i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 30.9655 | − | 53.6338i | 0.0361747 | − | 0.0626564i | ||||
\(857\) | 169.817 | + | 29.9433i | 0.198153 | + | 0.0349397i | 0.271844 | − | 0.962341i | \(-0.412367\pi\) |
−0.0736908 | + | 0.997281i | \(0.523478\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 602.703 | + | 219.366i | 0.701633 | + | 0.255373i | 0.668108 | − | 0.744064i | \(-0.267104\pi\) |
0.0335249 | + | 0.999438i | \(0.489327\pi\) | |||||||
\(860\) | 432.174 | − | 76.2040i | 0.502528 | − | 0.0886093i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −302.557 | − | 253.875i | −0.350994 | − | 0.294519i | ||||
\(863\) | − | 222.895i | − | 0.258280i | −0.991626 | − | 0.129140i | \(-0.958778\pi\) | ||
0.991626 | − | 0.129140i | \(-0.0412216\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1768.69 | 2.04473 | ||||||||
\(866\) | 91.6638 | − | 109.241i | 0.105847 | − | 0.126144i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 180.957 | + | 1026.26i | 0.208476 | + | 1.18233i | ||||
\(869\) | 27.2637 | − | 74.9064i | 0.0313736 | − | 0.0861984i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.22067 | + | 23.9366i | −0.00484578 | + | 0.0274818i | ||||
\(872\) | 226.933 | + | 131.020i | 0.260244 | + | 0.150252i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −96.5861 | − | 167.292i | −0.110510 | − | 0.191410i | ||||
\(875\) | 648.328 | + | 1781.27i | 0.740947 | + | 2.03573i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 685.259 | − | 575.001i | 0.781368 | − | 0.655645i | −0.162225 | − | 0.986754i | \(-0.551867\pi\) |
0.943593 | + | 0.331108i | \(0.107423\pi\) | |||||||
\(878\) | −90.5035 | − | 107.858i | −0.103079 | − | 0.122845i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −49.5269 | + | 18.0263i | −0.0562806 | + | 0.0204845i | ||||
\(881\) | −600.708 | + | 346.819i | −0.681847 | + | 0.393665i | −0.800551 | − | 0.599265i | \(-0.795460\pi\) |
0.118703 | + | 0.992930i | \(0.462126\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −357.452 | + | 619.125i | −0.404815 | + | 0.701161i | −0.994300 | − | 0.106619i | \(-0.965998\pi\) |
0.589485 | + | 0.807780i | \(0.299331\pi\) | |||||||
\(884\) | 344.163 | + | 60.6852i | 0.389325 | + | 0.0686484i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −455.696 | − | 165.860i | −0.514330 | − | 0.187201i | ||||
\(887\) | 1637.53 | − | 288.740i | 1.84614 | − | 0.325524i | 0.862553 | − | 0.505966i | \(-0.168864\pi\) |
0.983586 | + | 0.180442i | \(0.0577529\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1992.60 | − | 1671.99i | −2.24140 | − | 1.88076i | ||||
\(890\) | 1029.61i | 1.15687i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −772.361 | −0.865876 | ||||||||
\(893\) | 268.592 | − | 320.095i | 0.300775 | − | 0.358450i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 378.046 | + | 2144.01i | 0.422398 | + | 2.39554i | ||||
\(896\) | −43.4996 | + | 119.514i | −0.0485486 | + | 0.133386i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 122.872 | − | 696.840i | 0.136828 | − | 0.775992i | ||||
\(899\) | −440.326 | − | 254.222i | −0.489795 | − | 0.282783i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −407.396 | − | 705.631i | −0.452160 | − | 0.783164i | ||||
\(902\) | −7.81092 | − | 21.4603i | −0.00865955 | − | 0.0237919i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −335.637 | + | 281.633i | −0.371280 | + | 0.311541i | ||||
\(905\) | 1719.35 | + | 2049.04i | 1.89984 | + | 2.26414i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.6374 | − | 8.23933i | 0.0249585 | − | 0.00908416i | −0.329511 | − | 0.944152i | \(-0.606884\pi\) |
0.354469 | + | 0.935068i | \(0.384662\pi\) | |||||||
\(908\) | 322.484 | − | 186.186i | 0.355159 | − | 0.205051i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 593.031 | − | 1027.16i | 0.651682 | − | 1.12875i | ||||
\(911\) | 324.675 | + | 57.2490i | 0.356394 | + | 0.0628419i | 0.348979 | − | 0.937131i | \(-0.386528\pi\) |
0.00741541 | + | 0.999973i | \(0.497640\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 49.3860 | + | 17.9750i | 0.0540920 | + | 0.0196879i | ||||
\(914\) | 160.287 | − | 28.2630i | 0.175369 | − | 0.0309223i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 473.412 | + | 397.240i | 0.516826 | + | 0.433668i | ||||
\(917\) | 788.579i | 0.859955i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −174.813 | −0.190220 | −0.0951102 | − | 0.995467i | \(-0.530320\pi\) | ||||
−0.0951102 | + | 0.995467i | \(0.530320\pi\) | |||||||
\(920\) | 213.751 | − | 254.739i | 0.232338 | − | 0.276890i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 142.111 | + | 805.951i | 0.154133 | + | 0.874134i | ||||
\(923\) | 229.148 | − | 629.578i | 0.248264 | − | 0.682099i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 123.730 | − | 701.707i | 0.133762 | − | 0.758602i | ||||
\(926\) | −976.040 | − | 563.517i | −1.05404 | − | 0.608550i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −31.0271 | − | 53.7406i | −0.0334344 | − | 0.0579101i | ||||
\(929\) | 46.7382 | + | 128.412i | 0.0503102 | + | 0.138226i | 0.962303 | − | 0.271981i | \(-0.0876787\pi\) |
−0.911992 | + | 0.410207i | \(0.865456\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −576.698 | + | 483.907i | −0.619439 | + | 0.519771i | ||||
\(932\) | −26.4360 | − | 31.5051i | −0.0283648 | − | 0.0338038i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −359.943 | + | 131.008i | −0.385378 | + | 0.140266i | ||||
\(935\) | 223.827 | − | 129.226i | 0.239387 | − | 0.138210i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −288.732 | + | 500.099i | −0.308145 | + | 0.533723i | −0.977957 | − | 0.208808i | \(-0.933042\pi\) |
0.669811 | + | 0.742531i | \(0.266375\pi\) | |||||||
\(938\) | 42.7179 | + | 7.53231i | 0.0455414 | + | 0.00803018i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 675.939 | + | 246.022i | 0.719085 | + | 0.261725i | ||||
\(941\) | 1294.60 | − | 228.273i | 1.37577 | − | 0.242585i | 0.563620 | − | 0.826034i | \(-0.309408\pi\) |
0.812150 | + | 0.583449i | \(0.198297\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 110.380 | + | 92.6197i | 0.117052 | + | 0.0982181i | ||||
\(944\) | − | 242.078i | − | 0.256439i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −58.2981 | −0.0616259 | ||||||||
\(947\) | 395.028 | − | 470.776i | 0.417136 | − | 0.497123i | −0.516029 | − | 0.856571i | \(-0.672590\pi\) |
0.933165 | + | 0.359448i | \(0.117035\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 102.337 | + | 580.381i | 0.107837 | + | 0.611571i | ||||
\(950\) | −212.412 | + | 583.597i | −0.223592 | + | 0.614313i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 108.300 | − | 614.201i | 0.113761 | − | 0.645169i | ||||
\(953\) | −684.011 | − | 394.914i | −0.717745 | − | 0.414391i | 0.0961768 | − | 0.995364i | \(-0.469339\pi\) |
−0.813922 | + | 0.580974i | \(0.802672\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 163.133 | + | 282.555i | 0.170820 | + | 0.295869i | ||||
\(956\) | −70.2540 | − | 193.021i | −0.0734874 | − | 0.201905i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 864.421 | − | 725.335i | 0.902318 | − | 0.757135i | ||||
\(959\) | −1538.96 | − | 1834.06i | −1.60475 | − | 1.91247i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1115.69 | + | 406.079i | −1.16097 | + | 0.422559i | ||||
\(962\) | −172.240 | + | 99.4430i | −0.179044 | + | 0.103371i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 384.229 | − | 665.505i | 0.398578 | − | 0.690358i | ||||
\(965\) | 1347.72 | + | 237.639i | 1.39660 | + | 0.246258i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1642.98 | − | 597.996i | −1.69905 | − | 0.618403i | −0.703333 | − | 0.710861i | \(-0.748305\pi\) |
−0.995717 | + | 0.0924577i | \(0.970528\pi\) | |||||||
\(968\) | −330.145 | + | 58.2135i | −0.341059 | + | 0.0601379i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1278.64 | + | 1072.91i | 1.31819 | + | 1.10609i | ||||
\(971\) | 1254.82i | 1.29230i | 0.763211 | + | 0.646149i | \(0.223622\pi\) | ||||
−0.763211 | + | 0.646149i | \(0.776378\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −634.298 | −0.651899 | ||||||||
\(974\) | −126.550 | + | 150.817i | −0.129928 | + | 0.154843i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 53.1736 | + | 301.562i | 0.0544811 | + | 0.308978i | ||||
\(977\) | −239.287 | + | 657.435i | −0.244920 | + | 0.672912i | 0.754934 | + | 0.655801i | \(0.227669\pi\) |
−0.999854 | + | 0.0171106i | \(0.994553\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.7515 | − | 134.702i | 0.0242610 | − | 0.137591i | ||||
\(980\) | −1122.33 | − | 647.978i | −1.14524 | − | 0.661202i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −152.178 | − | 263.580i | −0.154968 | − | 0.268412i | ||||
\(983\) | −129.688 | − | 356.315i | −0.131931 | − | 0.362477i | 0.856084 | − | 0.516837i | \(-0.172891\pi\) |
−0.988015 | + | 0.154360i | \(0.950668\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2198.75 | − | 1844.97i | 2.23224 | − | 1.87307i | ||||
\(986\) | 195.598 | + | 233.105i | 0.198376 | + | 0.236415i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 162.897 | − | 59.2897i | 0.164876 | − | 0.0600098i | ||||
\(989\) | 318.545 | − | 183.912i | 0.322088 | − | 0.185957i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −298.374 | + | 516.798i | −0.301083 | + | 0.521492i | −0.976382 | − | 0.216053i | \(-0.930682\pi\) |
0.675298 | + | 0.737545i | \(0.264015\pi\) | |||||||
\(992\) | −258.210 | − | 45.5294i | −0.260293 | − | 0.0458966i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1123.56 | − | 408.942i | −1.13034 | − | 0.411410i | ||||
\(995\) | −1630.70 | + | 287.536i | −1.63889 | + | 0.288981i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 865.580 | + | 726.308i | 0.868185 | + | 0.728494i | 0.963715 | − | 0.266933i | \(-0.0860102\pi\) |
−0.0955301 | + | 0.995427i | \(0.530455\pi\) | |||||||
\(998\) | 671.480i | 0.672825i | ||||||||
\(999\) | 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 | 162.3.f.a.35.4 | 36 | ||
3.2 | odd | 2 | 54.3.f.a.11.3 | yes | 36 | ||
12.11 | even | 2 | 432.3.bc.c.65.1 | 36 | |||
27.5 | odd | 18 | inner | 162.3.f.a.125.4 | 36 | ||
27.7 | even | 9 | 1458.3.b.c.1457.1 | 36 | |||
27.20 | odd | 18 | 1458.3.b.c.1457.36 | 36 | |||
27.22 | even | 9 | 54.3.f.a.5.3 | ✓ | 36 | ||
108.103 | odd | 18 | 432.3.bc.c.113.1 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
54.3.f.a.5.3 | ✓ | 36 | 27.22 | even | 9 | ||
54.3.f.a.11.3 | yes | 36 | 3.2 | odd | 2 | ||
162.3.f.a.35.4 | 36 | 1.1 | even | 1 | trivial | ||
162.3.f.a.125.4 | 36 | 27.5 | odd | 18 | inner | ||
432.3.bc.c.65.1 | 36 | 12.11 | even | 2 | |||
432.3.bc.c.113.1 | 36 | 108.103 | odd | 18 | |||
1458.3.b.c.1457.1 | 36 | 27.7 | even | 9 | |||
1458.3.b.c.1457.36 | 36 | 27.20 | odd | 18 |