Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [833,2,Mod(30,833)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(833, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("833.30");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 833 = 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 833.o (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.65153848837\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 119) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 30.3 | ||
Character | \(\chi\) | \(=\) | 833.30 |
Dual form | 833.2.o.g.361.3 |
$q$-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 \(\left(\mathbb{Z}/833\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36164 | − | 0.786146i | −0.962828 | − | 0.555889i | −0.0657856 | − | 0.997834i | \(-0.520955\pi\) |
−0.897042 | + | 0.441945i | \(0.854289\pi\) | |||||||
\(3\) | −0.526518 | + | 1.96499i | −0.303985 | + | 1.13449i | 0.629830 | + | 0.776733i | \(0.283125\pi\) |
−0.933815 | + | 0.357756i | \(0.883542\pi\) | |||||||
\(4\) | 0.236050 | + | 0.408850i | 0.118025 | + | 0.204425i | ||||
\(5\) | −3.27915 | + | 0.878646i | −1.46648 | + | 0.392942i | −0.901723 | − | 0.432314i | \(-0.857697\pi\) |
−0.564758 | + | 0.825257i | \(0.691030\pi\) | |||||||
\(6\) | 2.26170 | − | 2.26170i | 0.923335 | − | 0.923335i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.40230i | 0.849343i | ||||||||
\(9\) | −0.985896 | − | 0.569207i | −0.328632 | − | 0.189736i | ||||
\(10\) | 5.15578 | + | 1.38149i | 1.63040 | + | 0.436865i | ||||
\(11\) | 4.51148 | + | 1.20885i | 1.36026 | + | 0.364481i | 0.863913 | − | 0.503642i | \(-0.168007\pi\) |
0.496349 | + | 0.868123i | \(0.334673\pi\) | |||||||
\(12\) | −0.927672 | + | 0.248569i | −0.267796 | + | 0.0717557i | ||||
\(13\) | 3.63777 | 1.00894 | 0.504468 | − | 0.863430i | \(-0.331689\pi\) | ||||
0.504468 | + | 0.863430i | \(0.331689\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 6.90613i | − | 1.78315i | ||||||
\(16\) | 2.36066 | − | 4.08878i | 0.590165 | − | 1.02220i | ||||
\(17\) | −4.10399 | + | 0.396526i | −0.995365 | + | 0.0961718i | ||||
\(18\) | 0.894959 | + | 1.55012i | 0.210944 | + | 0.365366i | ||||
\(19\) | 5.36723 | + | 3.09877i | 1.23133 | + | 0.710906i | 0.967306 | − | 0.253611i | \(-0.0816183\pi\) |
0.264020 | + | 0.964517i | \(0.414952\pi\) | |||||||
\(20\) | −1.13328 | − | 1.13328i | −0.253409 | − | 0.253409i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.19270 | − | 5.19270i | −1.10709 | − | 1.10709i | ||||
\(23\) | 0.173950 | + | 0.649191i | 0.0362711 | + | 0.135366i | 0.981687 | − | 0.190500i | \(-0.0610109\pi\) |
−0.945416 | + | 0.325866i | \(0.894344\pi\) | |||||||
\(24\) | −4.72051 | − | 1.26486i | −0.963570 | − | 0.258188i | ||||
\(25\) | 5.65069 | − | 3.26243i | 1.13014 | − | 0.652485i | ||||
\(26\) | −4.95335 | − | 2.85982i | −0.971431 | − | 0.560856i | ||||
\(27\) | −2.67784 | + | 2.67784i | −0.515351 | + | 0.515351i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.95461 | − | 3.95461i | −0.734353 | − | 0.734353i | 0.237126 | − | 0.971479i | \(-0.423795\pi\) |
−0.971479 | + | 0.237126i | \(0.923795\pi\) | |||||||
\(30\) | −5.42922 | + | 9.40369i | −0.991236 | + | 1.71687i | ||||
\(31\) | −1.98218 | + | 7.39761i | −0.356011 | + | 1.32865i | 0.523197 | + | 0.852212i | \(0.324739\pi\) |
−0.879208 | + | 0.476439i | \(0.841927\pi\) | |||||||
\(32\) | −2.26785 | + | 1.30934i | −0.400902 | + | 0.231461i | ||||
\(33\) | −4.75075 | + | 8.22854i | −0.826999 | + | 1.43240i | ||||
\(34\) | 5.89991 | + | 2.68641i | 1.01183 | + | 0.460715i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | − | 0.537445i | − | 0.0895742i | ||||||
\(37\) | 1.32191 | − | 0.354204i | 0.217320 | − | 0.0582307i | −0.148516 | − | 0.988910i | \(-0.547450\pi\) |
0.365836 | + | 0.930679i | \(0.380783\pi\) | |||||||
\(38\) | −4.87217 | − | 8.43884i | −0.790370 | − | 1.36896i | ||||
\(39\) | −1.91535 | + | 7.14819i | −0.306702 | + | 1.14463i | ||||
\(40\) | −2.11077 | − | 7.87752i | −0.333743 | − | 1.24555i | ||||
\(41\) | 0.492170 | − | 0.492170i | 0.0768640 | − | 0.0768640i | −0.667630 | − | 0.744494i | \(-0.732691\pi\) |
0.744494 | + | 0.667630i | \(0.232691\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.64216i | 1.01292i | 0.862264 | + | 0.506460i | \(0.169046\pi\) | ||||
−0.862264 | + | 0.506460i | \(0.830954\pi\) | |||||||
\(44\) | 0.570696 | + | 2.12987i | 0.0860357 | + | 0.321090i | ||||
\(45\) | 3.73303 | + | 1.00026i | 0.556488 | + | 0.149110i | ||||
\(46\) | 0.273500 | − | 1.02072i | 0.0403254 | − | 0.150496i | ||||
\(47\) | −2.16296 | + | 3.74636i | −0.315500 | + | 0.546462i | −0.979544 | − | 0.201232i | \(-0.935506\pi\) |
0.664043 | + | 0.747694i | \(0.268839\pi\) | |||||||
\(48\) | 6.79150 | + | 6.79150i | 0.980268 | + | 0.980268i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −10.2590 | −1.45084 | ||||||||
\(51\) | 1.38166 | − | 8.27309i | 0.193470 | − | 1.15846i | ||||
\(52\) | 0.858695 | + | 1.48730i | 0.119080 | + | 0.206252i | ||||
\(53\) | −3.53287 | + | 2.03970i | −0.485277 | + | 0.280175i | −0.722613 | − | 0.691253i | \(-0.757059\pi\) |
0.237336 | + | 0.971428i | \(0.423726\pi\) | |||||||
\(54\) | 5.75144 | − | 1.54109i | 0.782672 | − | 0.209716i | ||||
\(55\) | −15.8560 | −2.13802 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.91500 | + | 8.91500i | −1.18082 | + | 1.18082i | ||||
\(58\) | 2.27587 | + | 8.49368i | 0.298837 | + | 1.11527i | ||||
\(59\) | −2.36632 | + | 1.36620i | −0.308069 | + | 0.177864i | −0.646062 | − | 0.763285i | \(-0.723585\pi\) |
0.337993 | + | 0.941149i | \(0.390252\pi\) | |||||||
\(60\) | 2.82357 | − | 1.63019i | 0.364522 | − | 0.210457i | ||||
\(61\) | −3.13118 | − | 11.6857i | −0.400907 | − | 1.49620i | −0.811482 | − | 0.584378i | \(-0.801339\pi\) |
0.410575 | − | 0.911827i | \(-0.365328\pi\) | |||||||
\(62\) | 8.51463 | − | 8.51463i | 1.08136 | − | 1.08136i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.32531 | −0.665664 | ||||||||
\(65\) | −11.9288 | + | 3.19631i | −1.47958 | + | 0.396454i | ||||
\(66\) | 12.9377 | − | 7.46956i | 1.59252 | − | 0.919440i | ||||
\(67\) | −6.27952 | − | 10.8764i | −0.767165 | − | 1.32877i | −0.939094 | − | 0.343659i | \(-0.888333\pi\) |
0.171929 | − | 0.985109i | \(-0.445000\pi\) | |||||||
\(68\) | −1.13087 | − | 1.58432i | −0.137138 | − | 0.192127i | ||||
\(69\) | −1.36724 | −0.164597 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.04461 | + | 3.04461i | 0.361328 | + | 0.361328i | 0.864302 | − | 0.502973i | \(-0.167761\pi\) |
−0.502973 | + | 0.864302i | \(0.667761\pi\) | |||||||
\(72\) | 1.36741 | − | 2.36842i | 0.161151 | − | 0.279121i | ||||
\(73\) | −0.427346 | + | 1.59488i | −0.0500170 | + | 0.186666i | −0.986415 | − | 0.164275i | \(-0.947472\pi\) |
0.936398 | + | 0.350941i | \(0.114138\pi\) | |||||||
\(74\) | −2.07842 | − | 0.556911i | −0.241612 | − | 0.0647396i | ||||
\(75\) | 3.43545 | + | 12.8213i | 0.396692 | + | 1.48047i | ||||
\(76\) | 2.92586i | 0.335619i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 8.22754 | − | 8.22754i | 0.931586 | − | 0.931586i | ||||
\(79\) | 2.58942 | + | 9.66384i | 0.291332 | + | 1.08727i | 0.944087 | + | 0.329697i | \(0.106947\pi\) |
−0.652754 | + | 0.757570i | \(0.726387\pi\) | |||||||
\(80\) | −4.14837 | + | 15.4819i | −0.463802 | + | 1.73093i | ||||
\(81\) | −5.55963 | − | 9.62956i | −0.617736 | − | 1.06995i | ||||
\(82\) | −1.05708 | + | 0.283243i | −0.116735 | + | 0.0312789i | ||||
\(83\) | 4.69160i | 0.514970i | 0.966282 | + | 0.257485i | \(0.0828938\pi\) | ||||
−0.966282 | + | 0.257485i | \(0.917106\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.1092 | − | 4.90623i | 1.42189 | − | 0.532155i | ||||
\(86\) | 5.22170 | − | 9.04425i | 0.563071 | − | 0.975267i | ||||
\(87\) | 9.85296 | − | 5.68861i | 1.05635 | − | 0.609883i | ||||
\(88\) | −2.90402 | + | 10.8379i | −0.309569 | + | 1.15533i | ||||
\(89\) | 1.02353 | − | 1.77280i | 0.108494 | − | 0.187917i | −0.806666 | − | 0.591007i | \(-0.798731\pi\) |
0.915160 | + | 0.403090i | \(0.132064\pi\) | |||||||
\(90\) | −4.29671 | − | 4.29671i | −0.452913 | − | 0.452913i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.224361 | + | 0.224361i | −0.0233912 | + | 0.0233912i | ||||
\(93\) | −13.4926 | − | 7.78995i | −1.39912 | − | 0.807780i | ||||
\(94\) | 5.89036 | − | 3.40080i | 0.607545 | − | 0.350766i | ||||
\(95\) | −20.3227 | − | 5.44544i | −2.08506 | − | 0.558690i | ||||
\(96\) | −1.37878 | − | 5.14569i | −0.140722 | − | 0.525180i | ||||
\(97\) | −2.99116 | − | 2.99116i | −0.303706 | − | 0.303706i | 0.538756 | − | 0.842462i | \(-0.318895\pi\) |
−0.842462 | + | 0.538756i | \(0.818895\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.75976 | − | 3.75976i | −0.377870 | − | 0.377870i | ||||
\(100\) | 2.66769 | + | 1.54019i | 0.266769 | + | 0.154019i | ||||
\(101\) | 2.69264 | + | 4.66379i | 0.267928 | + | 0.464065i | 0.968327 | − | 0.249687i | \(-0.0803277\pi\) |
−0.700399 | + | 0.713752i | \(0.746994\pi\) | |||||||
\(102\) | −8.38518 | + | 10.1788i | −0.830256 | + | 1.00785i | ||||
\(103\) | 1.98128 | − | 3.43167i | 0.195221 | − | 0.338133i | −0.751752 | − | 0.659446i | \(-0.770791\pi\) |
0.946973 | + | 0.321313i | \(0.104124\pi\) | |||||||
\(104\) | 8.73903i | 0.856932i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.41401 | 0.622984 | ||||||||
\(107\) | −10.9920 | + | 2.94531i | −1.06264 | + | 0.284734i | −0.747466 | − | 0.664300i | \(-0.768730\pi\) |
−0.315175 | + | 0.949034i | \(0.602063\pi\) | |||||||
\(108\) | −1.72694 | − | 0.462733i | −0.166175 | − | 0.0445265i | ||||
\(109\) | 4.25566 | + | 1.14030i | 0.407619 | + | 0.109221i | 0.456801 | − | 0.889569i | \(-0.348995\pi\) |
−0.0491827 | + | 0.998790i | \(0.515662\pi\) | |||||||
\(110\) | 21.5902 | + | 12.4651i | 2.05854 | + | 1.18850i | ||||
\(111\) | 2.78403i | 0.264248i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.20042 | + | 8.20042i | −0.771430 | + | 0.771430i | −0.978357 | − | 0.206926i | \(-0.933654\pi\) |
0.206926 | + | 0.978357i | \(0.433654\pi\) | |||||||
\(114\) | 19.1475 | − | 5.13057i | 1.79333 | − | 0.480522i | ||||
\(115\) | −1.14082 | − | 1.97595i | −0.106382 | − | 0.184259i | ||||
\(116\) | 0.683359 | − | 2.55033i | 0.0634483 | − | 0.236792i | ||||
\(117\) | −3.58646 | − | 2.07064i | −0.331568 | − | 0.191431i | ||||
\(118\) | 4.29612 | 0.395490 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 16.5906 | 1.51451 | ||||||||
\(121\) | 9.36585 | + | 5.40738i | 0.851441 | + | 0.491580i | ||||
\(122\) | −4.92313 | + | 18.3734i | −0.445719 | + | 1.66345i | ||||
\(123\) | 0.707973 | + | 1.22625i | 0.0638358 | + | 0.110567i | ||||
\(124\) | −3.49241 | + | 0.935789i | −0.313628 | + | 0.0840363i | ||||
\(125\) | −3.66041 | + | 3.66041i | −0.327397 | + | 0.327397i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.12889i | 0.455115i | 0.973765 | + | 0.227558i | \(0.0730740\pi\) | ||||
−0.973765 | + | 0.227558i | \(0.926926\pi\) | |||||||
\(128\) | 11.7869 | + | 6.80515i | 1.04182 | + | 0.601496i | ||||
\(129\) | −13.0518 | − | 3.49722i | −1.14915 | − | 0.307913i | ||||
\(130\) | 18.7555 | + | 5.02553i | 1.64497 | + | 0.440768i | ||||
\(131\) | −8.06881 | + | 2.16203i | −0.704975 | + | 0.188898i | −0.593458 | − | 0.804865i | \(-0.702238\pi\) |
−0.111517 | + | 0.993762i | \(0.535571\pi\) | |||||||
\(132\) | −4.48566 | −0.390426 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 19.7465i | 1.70583i | ||||||||
\(135\) | 6.42818 | − | 11.1339i | 0.553249 | − | 0.958256i | ||||
\(136\) | −0.952577 | − | 9.85904i | −0.0816828 | − | 0.845406i | ||||
\(137\) | 10.0969 | + | 17.4884i | 0.862639 | + | 1.49413i | 0.869373 | + | 0.494157i | \(0.164523\pi\) |
−0.00673433 | + | 0.999977i | \(0.502144\pi\) | |||||||
\(138\) | 1.86170 | + | 1.07485i | 0.158478 | + | 0.0914974i | ||||
\(139\) | 5.51905 | + | 5.51905i | 0.468120 | + | 0.468120i | 0.901305 | − | 0.433185i | \(-0.142610\pi\) |
−0.433185 | + | 0.901305i | \(0.642610\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.22272 | − | 6.22272i | −0.524048 | − | 0.524048i | ||||
\(142\) | −1.75217 | − | 6.53918i | −0.147039 | − | 0.548755i | ||||
\(143\) | 16.4117 | + | 4.39751i | 1.37242 | + | 0.367738i | ||||
\(144\) | −4.65473 | + | 2.68741i | −0.387894 | + | 0.223951i | ||||
\(145\) | 16.4425 | + | 9.49307i | 1.36547 | + | 0.788356i | ||||
\(146\) | 1.83570 | − | 1.83570i | 0.151923 | − | 0.151923i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.456852 | + | 0.456852i | 0.0375530 | + | 0.0375530i | ||||
\(149\) | −0.335290 | + | 0.580739i | −0.0274680 | + | 0.0475760i | −0.879433 | − | 0.476023i | \(-0.842078\pi\) |
0.851965 | + | 0.523599i | \(0.175411\pi\) | |||||||
\(150\) | 5.40153 | − | 20.1588i | 0.441033 | − | 1.64596i | ||||
\(151\) | 9.89318 | − | 5.71183i | 0.805096 | − | 0.464822i | −0.0401543 | − | 0.999193i | \(-0.512785\pi\) |
0.845250 | + | 0.534371i | \(0.179452\pi\) | |||||||
\(152\) | −7.44419 | + | 12.8937i | −0.603803 | + | 1.04582i | ||||
\(153\) | 4.27182 | + | 1.94509i | 0.345356 | + | 0.157251i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 25.9995i | − | 2.08833i | ||||||
\(156\) | −3.37466 | + | 0.904237i | −0.270189 | + | 0.0723969i | ||||
\(157\) | −11.6916 | − | 20.2504i | −0.933090 | − | 1.61616i | −0.778004 | − | 0.628259i | \(-0.783768\pi\) |
−0.155086 | − | 0.987901i | \(-0.549565\pi\) | |||||||
\(158\) | 4.07132 | − | 15.1944i | 0.323897 | − | 1.20880i | ||||
\(159\) | −2.14788 | − | 8.01600i | −0.170338 | − | 0.635710i | ||||
\(160\) | 6.28617 | − | 6.28617i | 0.496965 | − | 0.496965i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 17.4827i | 1.37357i | ||||||||
\(163\) | 3.12576 | + | 11.6655i | 0.244829 | + | 0.913714i | 0.973469 | + | 0.228817i | \(0.0734858\pi\) |
−0.728641 | + | 0.684896i | \(0.759848\pi\) | |||||||
\(164\) | 0.317400 | + | 0.0850472i | 0.0247848 | + | 0.00664107i | ||||
\(165\) | 8.34845 | − | 31.1569i | 0.649926 | − | 2.42556i | ||||
\(166\) | 3.68828 | − | 6.38829i | 0.286266 | − | 0.495827i | ||||
\(167\) | −17.3482 | − | 17.3482i | −1.34244 | − | 1.34244i | −0.893620 | − | 0.448823i | \(-0.851843\pi\) |
−0.448823 | − | 0.893620i | \(-0.648157\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.233365 | 0.0179511 | ||||||||
\(170\) | −21.7071 | − | 3.62521i | −1.66486 | − | 0.278041i | ||||
\(171\) | −3.52768 | − | 6.11013i | −0.269769 | − | 0.467253i | ||||
\(172\) | −2.71565 | + | 1.56788i | −0.207066 | + | 0.119550i | ||||
\(173\) | −3.44376 | + | 0.922753i | −0.261824 | + | 0.0701556i | −0.387343 | − | 0.921936i | \(-0.626607\pi\) |
0.125519 | + | 0.992091i | \(0.459940\pi\) | |||||||
\(174\) | −17.8883 | −1.35611 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.5928 | − | 15.5928i | 1.17535 | − | 1.17535i | ||||
\(177\) | −1.43865 | − | 5.36913i | −0.108136 | − | 0.403568i | ||||
\(178\) | −2.78736 | + | 1.60929i | −0.208922 | + | 0.120621i | ||||
\(179\) | 3.43046 | − | 1.98058i | 0.256405 | − | 0.148035i | −0.366289 | − | 0.930501i | \(-0.619372\pi\) |
0.622693 | + | 0.782466i | \(0.286038\pi\) | |||||||
\(180\) | 0.472224 | + | 1.76236i | 0.0351975 | + | 0.131359i | ||||
\(181\) | −1.36267 | + | 1.36267i | −0.101287 | + | 0.101287i | −0.755934 | − | 0.654648i | \(-0.772817\pi\) |
0.654648 | + | 0.755934i | \(0.272817\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 24.6110 | 1.81930 | ||||||||
\(184\) | −1.55955 | + | 0.417881i | −0.114972 | + | 0.0308066i | ||||
\(185\) | −4.02351 | + | 2.32298i | −0.295814 | + | 0.170789i | ||||
\(186\) | 12.2481 | + | 21.2143i | 0.898072 | + | 1.55551i | ||||
\(187\) | −18.9944 | − | 3.17218i | −1.38901 | − | 0.231973i | ||||
\(188\) | −2.04227 | −0.148948 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 23.3913 | + | 23.3913i | 1.69699 | + | 1.69699i | ||||
\(191\) | 12.5863 | − | 21.8001i | 0.910714 | − | 1.57740i | 0.0976558 | − | 0.995220i | \(-0.468866\pi\) |
0.813058 | − | 0.582183i | \(-0.197801\pi\) | |||||||
\(192\) | 2.80387 | − | 10.4642i | 0.202352 | − | 0.755188i | ||||
\(193\) | −10.8635 | − | 2.91087i | −0.781972 | − | 0.209529i | −0.154318 | − | 0.988021i | \(-0.549318\pi\) |
−0.627654 | + | 0.778493i | \(0.715985\pi\) | |||||||
\(194\) | 1.72141 | + | 6.42438i | 0.123590 | + | 0.461243i | ||||
\(195\) | − | 25.1229i | − | 1.79909i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.0035 | + | 16.0035i | −1.14020 | + | 1.14020i | −0.151789 | + | 0.988413i | \(0.548503\pi\) |
−0.988413 | + | 0.151789i | \(0.951497\pi\) | |||||||
\(198\) | 2.16374 | + | 8.07518i | 0.153770 | + | 0.573878i | ||||
\(199\) | −1.35866 | + | 5.07058i | −0.0963127 | + | 0.359444i | −0.997215 | − | 0.0745776i | \(-0.976239\pi\) |
0.900903 | + | 0.434022i | \(0.142906\pi\) | |||||||
\(200\) | 7.83734 | + | 13.5747i | 0.554184 | + | 0.959874i | ||||
\(201\) | 24.6784 | − | 6.61256i | 1.74068 | − | 0.466414i | ||||
\(202\) | − | 8.46724i | − | 0.595753i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.70860 | − | 1.38797i | 0.259654 | − | 0.0971775i | ||||
\(205\) | −1.18146 | + | 2.04634i | −0.0825164 | + | 0.142923i | ||||
\(206\) | −5.39559 | + | 3.11514i | −0.375928 | + | 0.217042i | ||||
\(207\) | 0.198027 | − | 0.739048i | 0.0137638 | − | 0.0513674i | ||||
\(208\) | 8.58754 | − | 14.8741i | 0.595439 | − | 1.03133i | ||||
\(209\) | 20.4682 | + | 20.4682i | 1.41581 | + | 1.41581i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.87817 | + | 6.87817i | −0.473513 | + | 0.473513i | −0.903050 | − | 0.429536i | \(-0.858677\pi\) |
0.429536 | + | 0.903050i | \(0.358677\pi\) | |||||||
\(212\) | −1.66787 | − | 0.962943i | −0.114550 | − | 0.0661352i | ||||
\(213\) | −7.58567 | + | 4.37959i | −0.519761 | + | 0.300084i | ||||
\(214\) | 17.2827 | + | 4.63088i | 1.18142 | + | 0.316561i | ||||
\(215\) | −5.83610 | − | 21.7806i | −0.398019 | − | 1.48543i | ||||
\(216\) | −6.43299 | − | 6.43299i | −0.437710 | − | 0.437710i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.89826 | − | 4.89826i | −0.331752 | − | 0.331752i | ||||
\(219\) | −2.90891 | − | 1.67946i | −0.196566 | − | 0.113487i | ||||
\(220\) | −3.74280 | − | 6.48272i | −0.252340 | − | 0.437065i | ||||
\(221\) | −14.9294 | + | 1.44247i | −1.00426 | + | 0.0970311i | ||||
\(222\) | 2.18865 | − | 3.79086i | 0.146893 | − | 0.254426i | ||||
\(223\) | − | 17.5438i | − | 1.17482i | −0.809289 | − | 0.587411i | \(-0.800147\pi\) | ||
0.809289 | − | 0.587411i | \(-0.199853\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.42798 | −0.495199 | ||||||||
\(226\) | 17.6128 | − | 4.71933i | 1.17158 | − | 0.313925i | ||||
\(227\) | 8.05931 | + | 2.15948i | 0.534915 | + | 0.143330i | 0.516157 | − | 0.856494i | \(-0.327362\pi\) |
0.0187580 | + | 0.999824i | \(0.494029\pi\) | |||||||
\(228\) | −5.74928 | − | 1.54052i | −0.380756 | − | 0.102023i | ||||
\(229\) | −13.2886 | − | 7.67215i | −0.878132 | − | 0.506990i | −0.00809010 | − | 0.999967i | \(-0.502575\pi\) |
−0.870042 | + | 0.492977i | \(0.835909\pi\) | |||||||
\(230\) | 3.58739i | 0.236546i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.50018 | − | 9.50018i | 0.623717 | − | 0.623717i | ||||
\(233\) | −23.6434 | + | 6.33522i | −1.54893 | + | 0.415034i | −0.929138 | − | 0.369733i | \(-0.879449\pi\) |
−0.619790 | + | 0.784767i | \(0.712782\pi\) | |||||||
\(234\) | 3.25566 | + | 5.63896i | 0.212829 | + | 0.368630i | ||||
\(235\) | 3.80095 | − | 14.1853i | 0.247947 | − | 0.925350i | ||||
\(236\) | −1.11714 | − | 0.644981i | −0.0727196 | − | 0.0419847i | ||||
\(237\) | −20.3527 | −1.32205 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.5771 | 0.942916 | 0.471458 | − | 0.881889i | \(-0.343728\pi\) | ||||
0.471458 | + | 0.881889i | \(0.343728\pi\) | |||||||
\(240\) | −28.2377 | − | 16.3030i | −1.82273 | − | 1.05236i | ||||
\(241\) | −3.93803 | + | 14.6969i | −0.253671 | + | 0.946712i | 0.715155 | + | 0.698966i | \(0.246356\pi\) |
−0.968825 | + | 0.247745i | \(0.920310\pi\) | |||||||
\(242\) | −8.50197 | − | 14.7258i | −0.546527 | − | 0.946613i | ||||
\(243\) | 10.8752 | − | 2.91401i | 0.697647 | − | 0.186934i | ||||
\(244\) | 4.03860 | − | 4.03860i | 0.258545 | − | 0.258545i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 2.22628i | − | 0.141942i | ||||||
\(247\) | 19.5247 | + | 11.2726i | 1.24233 | + | 0.717259i | ||||
\(248\) | −17.7713 | − | 4.76181i | −1.12848 | − | 0.302375i | ||||
\(249\) | −9.21896 | − | 2.47021i | −0.584228 | − | 0.156543i | ||||
\(250\) | 7.86180 | − | 2.10656i | 0.497224 | − | 0.133231i | ||||
\(251\) | 1.54033 | 0.0972246 | 0.0486123 | − | 0.998818i | \(-0.484520\pi\) | ||||
0.0486123 | + | 0.998818i | \(0.484520\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.13909i | 0.197353i | ||||||||
\(254\) | 4.03206 | − | 6.98372i | 0.252994 | − | 0.438198i | ||||
\(255\) | 2.73846 | + | 28.3427i | 0.171489 | + | 1.77489i | ||||
\(256\) | −5.37437 | − | 9.30869i | −0.335898 | − | 0.581793i | ||||
\(257\) | 3.48942 | + | 2.01462i | 0.217664 | + | 0.125668i | 0.604868 | − | 0.796326i | \(-0.293226\pi\) |
−0.387204 | + | 0.921994i | \(0.626559\pi\) | |||||||
\(258\) | 15.0226 | + | 15.0226i | 0.935264 | + | 0.935264i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.12260 | − | 4.12260i | −0.255673 | − | 0.255673i | ||||
\(261\) | 1.64784 | + | 6.14983i | 0.101999 | + | 0.380665i | ||||
\(262\) | 12.6865 | + | 3.39934i | 0.783776 | + | 0.210012i | ||||
\(263\) | 15.5660 | − | 8.98703i | 0.959841 | − | 0.554164i | 0.0637166 | − | 0.997968i | \(-0.479705\pi\) |
0.896124 | + | 0.443804i | \(0.146371\pi\) | |||||||
\(264\) | −19.7675 | − | 11.4127i | −1.21660 | − | 0.702406i | ||||
\(265\) | 9.79263 | − | 9.79263i | 0.601557 | − | 0.601557i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.94464 | + | 2.94464i | 0.180209 | + | 0.180209i | ||||
\(268\) | 2.96456 | − | 5.13477i | 0.181089 | − | 0.313656i | ||||
\(269\) | 4.66693 | − | 17.4172i | 0.284548 | − | 1.06195i | −0.664621 | − | 0.747181i | \(-0.731407\pi\) |
0.949169 | − | 0.314767i | \(-0.101926\pi\) | |||||||
\(270\) | −17.5058 | + | 10.1070i | −1.06537 | + | 0.615090i | ||||
\(271\) | −8.35400 | + | 14.4696i | −0.507469 | + | 0.878963i | 0.492493 | + | 0.870316i | \(0.336086\pi\) |
−0.999963 | + | 0.00864660i | \(0.997248\pi\) | |||||||
\(272\) | −8.06683 | + | 17.7164i | −0.489123 | + | 1.07422i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 31.7506i | − | 1.91812i | ||||||
\(275\) | 29.4367 | − | 7.88755i | 1.77510 | − | 0.475637i | ||||
\(276\) | −0.322737 | − | 0.558997i | −0.0194265 | − | 0.0336477i | ||||
\(277\) | −0.270103 | + | 1.00804i | −0.0162289 | + | 0.0605670i | −0.973565 | − | 0.228408i | \(-0.926648\pi\) |
0.957337 | + | 0.288975i | \(0.0933146\pi\) | |||||||
\(278\) | −3.17620 | − | 11.8538i | −0.190496 | − | 0.710941i | ||||
\(279\) | 6.16500 | − | 6.16500i | 0.369089 | − | 0.369089i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3.53036i | − | 0.210604i | −0.994440 | − | 0.105302i | \(-0.966419\pi\) | ||
0.994440 | − | 0.105302i | \(-0.0335809\pi\) | |||||||
\(282\) | 3.58117 | + | 13.3651i | 0.213255 | + | 0.795880i | ||||
\(283\) | 1.76134 | + | 0.471949i | 0.104701 | + | 0.0280545i | 0.310789 | − | 0.950479i | \(-0.399407\pi\) |
−0.206088 | + | 0.978533i | \(0.566073\pi\) | |||||||
\(284\) | −0.526110 | + | 1.96347i | −0.0312189 | + | 0.116510i | ||||
\(285\) | 21.4005 | − | 37.0667i | 1.26766 | − | 2.19564i | ||||
\(286\) | −18.8898 | − | 18.8898i | −1.11698 | − | 1.11698i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.98115 | 0.175666 | ||||||||
\(289\) | 16.6855 | − | 3.25468i | 0.981502 | − | 0.191452i | ||||
\(290\) | −14.9259 | − | 25.8524i | −0.876477 | − | 1.51810i | ||||
\(291\) | 7.45250 | − | 4.30270i | 0.436873 | − | 0.252229i | ||||
\(292\) | −0.752940 | + | 0.201750i | −0.0440625 | + | 0.0118065i | ||||
\(293\) | 14.9585 | 0.873883 | 0.436942 | − | 0.899490i | \(-0.356062\pi\) | ||||
0.436942 | + | 0.899490i | \(0.356062\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.55912 | − | 6.55912i | 0.381887 | − | 0.381887i | ||||
\(296\) | 0.850905 | + | 3.17562i | 0.0494579 | + | 0.184579i | ||||
\(297\) | −15.3181 | + | 8.84393i | −0.888848 | + | 0.513177i | ||||
\(298\) | 0.913091 | − | 0.527174i | 0.0528940 | − | 0.0305383i | ||||
\(299\) | 0.632790 | + | 2.36161i | 0.0365952 | + | 0.136575i | ||||
\(300\) | −4.43105 | + | 4.43105i | −0.255827 | + | 0.255827i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −17.9613 | −1.03356 | ||||||||
\(303\) | −10.5820 | + | 2.83545i | −0.607923 | + | 0.162892i | ||||
\(304\) | 25.3404 | − | 14.6303i | 1.45337 | − | 0.839104i | ||||
\(305\) | 20.5352 | + | 35.5681i | 1.17584 | + | 2.03662i | ||||
\(306\) | −4.28757 | − | 6.00679i | −0.245104 | − | 0.343385i | ||||
\(307\) | −7.16409 | −0.408876 | −0.204438 | − | 0.978879i | \(-0.565537\pi\) | ||||
−0.204438 | + | 0.978879i | \(0.565537\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.70003 | + | 5.70003i | 0.324263 | + | 0.324263i | ||||
\(310\) | −20.4394 | + | 35.4021i | −1.16088 | + | 2.01070i | ||||
\(311\) | −1.62913 | + | 6.08000i | −0.0923796 | + | 0.344765i | −0.996609 | − | 0.0822815i | \(-0.973779\pi\) |
0.904230 | + | 0.427047i | \(0.140446\pi\) | |||||||
\(312\) | −17.1721 | − | 4.60126i | −0.972180 | − | 0.260495i | ||||
\(313\) | 8.11965 | + | 30.3029i | 0.458950 | + | 1.71282i | 0.676209 | + | 0.736710i | \(0.263622\pi\) |
−0.217259 | + | 0.976114i | \(0.569712\pi\) | |||||||
\(314\) | 36.7652i | 2.07478i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.33983 | + | 3.33983i | −0.187880 | + | 0.187880i | ||||
\(317\) | 4.28746 | + | 16.0010i | 0.240808 | + | 0.898708i | 0.975444 | + | 0.220247i | \(0.0706862\pi\) |
−0.734636 | + | 0.678461i | \(0.762647\pi\) | |||||||
\(318\) | −3.37709 | + | 12.6035i | −0.189378 | + | 0.706768i | ||||
\(319\) | −13.0606 | − | 22.6217i | −0.731255 | − | 1.26657i | ||||
\(320\) | 17.4625 | − | 4.67906i | 0.976183 | − | 0.261567i | ||||
\(321\) | − | 23.1500i | − | 1.29211i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.2558 | − | 10.5891i | −1.29399 | − | 0.589192i | ||||
\(324\) | 2.62470 | − | 4.54611i | 0.145817 | − | 0.252562i | ||||
\(325\) | 20.5559 | − | 11.8680i | 1.14024 | − | 0.658316i | ||||
\(326\) | 4.91461 | − | 18.3416i | 0.272195 | − | 1.01585i | ||||
\(327\) | −4.48137 | + | 7.76196i | −0.247820 | + | 0.429237i | ||||
\(328\) | 1.18234 | + | 1.18234i | 0.0652839 | + | 0.0652839i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −35.8614 | + | 35.8614i | −1.97411 | + | 1.97411i | ||||
\(331\) | −4.09885 | − | 2.36647i | −0.225293 | − | 0.130073i | 0.383106 | − | 0.923704i | \(-0.374854\pi\) |
−0.608399 | + | 0.793632i | \(0.708188\pi\) | |||||||
\(332\) | −1.91816 | + | 1.10745i | −0.105273 | + | 0.0607793i | ||||
\(333\) | −1.50488 | − | 0.403231i | −0.0824667 | − | 0.0220969i | ||||
\(334\) | 9.98386 | + | 37.2603i | 0.546293 | + | 2.03879i | ||||
\(335\) | 30.1480 | + | 30.1480i | 1.64716 | + | 1.64716i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.0523 | + | 17.0523i | 0.928898 | + | 0.928898i | 0.997635 | − | 0.0687369i | \(-0.0218969\pi\) |
−0.0687369 | + | 0.997635i | \(0.521897\pi\) | |||||||
\(338\) | −0.317760 | − | 0.183459i | −0.0172838 | − | 0.00997883i | ||||
\(339\) | −11.7961 | − | 20.4314i | −0.640675 | − | 1.10968i | ||||
\(340\) | 5.10034 | + | 4.20159i | 0.276605 | + | 0.227863i | ||||
\(341\) | −17.8852 | + | 30.9780i | −0.968536 | + | 1.67755i | ||||
\(342\) | 11.0931i | 0.599846i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −15.9565 | −0.860316 | ||||||||
\(345\) | 4.48339 | − | 1.20132i | 0.241378 | − | 0.0646770i | ||||
\(346\) | 5.41459 | + | 1.45084i | 0.291090 | + | 0.0779974i | ||||
\(347\) | 22.1256 | + | 5.92855i | 1.18777 | + | 0.318261i | 0.798003 | − | 0.602654i | \(-0.205890\pi\) |
0.389764 | + | 0.920915i | \(0.372557\pi\) | |||||||
\(348\) | 4.65158 | + | 2.68559i | 0.249351 | + | 0.143963i | ||||
\(349\) | − | 10.1897i | − | 0.545442i | −0.962093 | − | 0.272721i | \(-0.912076\pi\) | ||
0.962093 | − | 0.272721i | \(-0.0879235\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.74137 | + | 9.74137i | −0.519956 | + | 0.519956i | ||||
\(352\) | −11.8141 | + | 3.16559i | −0.629696 | + | 0.168726i | ||||
\(353\) | 8.39994 | + | 14.5491i | 0.447084 | + | 0.774372i | 0.998195 | − | 0.0600602i | \(-0.0191293\pi\) |
−0.551111 | + | 0.834432i | \(0.685796\pi\) | |||||||
\(354\) | −2.26198 | + | 8.44183i | −0.120223 | + | 0.448678i | ||||
\(355\) | −12.6589 | − | 7.30860i | −0.671862 | − | 0.387900i | ||||
\(356\) | 0.966416 | 0.0512199 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.22809 | −0.329165 | ||||||||
\(359\) | −24.4581 | − | 14.1209i | −1.29085 | − | 0.745273i | −0.312046 | − | 0.950067i | \(-0.601014\pi\) |
−0.978805 | + | 0.204794i | \(0.934348\pi\) | |||||||
\(360\) | −2.40294 | + | 8.96788i | −0.126646 | + | 0.472649i | ||||
\(361\) | 9.70474 | + | 16.8091i | 0.510776 | + | 0.884689i | ||||
\(362\) | 2.92673 | − | 0.784216i | 0.153826 | − | 0.0412175i | ||||
\(363\) | −15.5567 | + | 15.5567i | −0.816517 | + | 0.816517i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 5.60532i | − | 0.293396i | ||||||
\(366\) | −33.5114 | − | 19.3478i | −1.75167 | − | 1.01133i | ||||
\(367\) | 18.1715 | + | 4.86903i | 0.948543 | + | 0.254161i | 0.699744 | − | 0.714394i | \(-0.253297\pi\) |
0.248799 | + | 0.968555i | \(0.419964\pi\) | |||||||
\(368\) | 3.06504 | + | 0.821274i | 0.159776 | + | 0.0428119i | ||||
\(369\) | −0.765374 | + | 0.205081i | −0.0398438 | + | 0.0106761i | ||||
\(370\) | 7.30479 | 0.379758 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 7.35527i | − | 0.381353i | ||||||
\(373\) | −15.4827 | + | 26.8169i | −0.801666 | + | 1.38853i | 0.116853 | + | 0.993149i | \(0.462719\pi\) |
−0.918519 | + | 0.395377i | \(0.870614\pi\) | |||||||
\(374\) | 23.3698 | + | 19.2518i | 1.20843 | + | 0.995485i | ||||
\(375\) | −5.26541 | − | 9.11996i | −0.271905 | − | 0.470953i | ||||
\(376\) | −8.99989 | − | 5.19609i | −0.464134 | − | 0.267968i | ||||
\(377\) | −14.3860 | − | 14.3860i | −0.740915 | − | 0.740915i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.80375 | − | 8.80375i | −0.452218 | − | 0.452218i | 0.443872 | − | 0.896090i | \(-0.353604\pi\) |
−0.896090 | + | 0.443872i | \(0.853604\pi\) | |||||||
\(380\) | −2.57079 | − | 9.59433i | −0.131879 | − | 0.492179i | ||||
\(381\) | −10.0782 | − | 2.70045i | −0.516323 | − | 0.138348i | ||||
\(382\) | −34.2762 | + | 19.7894i | −1.75372 | + | 1.01251i | ||||
\(383\) | 25.8472 | + | 14.9229i | 1.32073 | + | 0.762523i | 0.983845 | − | 0.179023i | \(-0.0572937\pi\) |
0.336884 | + | 0.941546i | \(0.390627\pi\) | |||||||
\(384\) | −19.5781 | + | 19.5781i | −0.999089 | + | 0.999089i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.5039 | + | 12.5039i | 0.636429 | + | 0.636429i | ||||
\(387\) | 3.78076 | − | 6.54847i | 0.192187 | − | 0.332878i | ||||
\(388\) | 0.516874 | − | 1.92900i | 0.0262403 | − | 0.0979300i | ||||
\(389\) | −18.1350 | + | 10.4702i | −0.919479 | + | 0.530861i | −0.883469 | − | 0.468490i | \(-0.844798\pi\) |
−0.0360099 | + | 0.999351i | \(0.511465\pi\) | |||||||
\(390\) | −19.7503 | + | 34.2085i | −1.00009 | + | 1.73221i | ||||
\(391\) | −0.971311 | − | 2.59530i | −0.0491213 | − | 0.131250i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 16.9935i | − | 0.857208i | ||||||
\(394\) | 34.3721 | − | 9.20999i | 1.73164 | − | 0.463992i | ||||
\(395\) | −16.9822 | − | 29.4140i | −0.854467 | − | 1.47998i | ||||
\(396\) | 0.649689 | − | 2.42467i | 0.0326481 | − | 0.121844i | ||||
\(397\) | −7.34029 | − | 27.3943i | −0.368399 | − | 1.37488i | −0.862755 | − | 0.505623i | \(-0.831263\pi\) |
0.494356 | − | 0.869260i | \(-0.335404\pi\) | |||||||
\(398\) | 5.83622 | − | 5.83622i | 0.292543 | − | 0.292543i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 30.8059i | − | 1.54030i | ||||||
\(401\) | 0.846034 | + | 3.15744i | 0.0422489 | + | 0.157675i | 0.983828 | − | 0.179118i | \(-0.0573244\pi\) |
−0.941579 | + | 0.336793i | \(0.890658\pi\) | |||||||
\(402\) | −38.8016 | − | 10.3969i | −1.93525 | − | 0.518548i | ||||
\(403\) | −7.21073 | + | 26.9108i | −0.359192 | + | 1.34052i | ||||
\(404\) | −1.27120 | + | 2.20178i | −0.0632444 | + | 0.109542i | ||||
\(405\) | 26.6918 | + | 26.6918i | 1.32633 | + | 1.32633i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.39193 | 0.316836 | ||||||||
\(408\) | 19.8745 | + | 3.31916i | 0.983934 | + | 0.164323i | ||||
\(409\) | 17.1932 | + | 29.7795i | 0.850149 | + | 1.47250i | 0.881073 | + | 0.472980i | \(0.156822\pi\) |
−0.0309240 | + | 0.999522i | \(0.509845\pi\) | |||||||
\(410\) | 3.21744 | − | 1.85759i | 0.158898 | − | 0.0917399i | ||||
\(411\) | −39.6808 | + | 10.6324i | −1.95731 | + | 0.524459i | ||||
\(412\) | 1.87072 | 0.0921638 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.850642 | + | 0.850642i | −0.0418068 | + | 0.0418068i | ||||
\(415\) | −4.12226 | − | 15.3845i | −0.202354 | − | 0.755194i | ||||
\(416\) | −8.24990 | + | 4.76308i | −0.404485 | + | 0.233529i | ||||
\(417\) | −13.7508 | + | 7.93901i | −0.673378 | + | 0.388775i | ||||
\(418\) | −11.7794 | − | 43.9614i | −0.576150 | − | 2.15022i | ||||
\(419\) | −12.3869 | + | 12.3869i | −0.605140 | + | 0.605140i | −0.941672 | − | 0.336532i | \(-0.890746\pi\) |
0.336532 | + | 0.941672i | \(0.390746\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.1028 | −0.638593 | −0.319296 | − | 0.947655i | \(-0.603447\pi\) | ||||
−0.319296 | + | 0.947655i | \(0.603447\pi\) | |||||||
\(422\) | 14.7729 | − | 3.95838i | 0.719132 | − | 0.192691i | ||||
\(423\) | 4.26491 | − | 2.46234i | 0.207367 | − | 0.119723i | ||||
\(424\) | −4.89998 | − | 8.48702i | −0.237964 | − | 0.412166i | ||||
\(425\) | −21.8967 | + | 15.6296i | −1.06215 | + | 0.758148i | ||||
\(426\) | 13.7720 | 0.667254 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.79886 | − | 3.79886i | −0.183625 | − | 0.183625i | ||||
\(429\) | −17.2821 | + | 29.9335i | −0.834389 | + | 1.44520i | ||||
\(430\) | −9.17606 | + | 34.2455i | −0.442509 | + | 1.65147i | ||||
\(431\) | −25.3873 | − | 6.80250i | −1.22286 | − | 0.327665i | −0.411066 | − | 0.911606i | \(-0.634843\pi\) |
−0.811796 | + | 0.583941i | \(0.801510\pi\) | |||||||
\(432\) | 4.62764 | + | 17.2706i | 0.222648 | + | 0.830932i | ||||
\(433\) | 0.783681i | 0.0376613i | 0.999823 | + | 0.0188307i | \(0.00599434\pi\) | ||||
−0.999823 | + | 0.0188307i | \(0.994006\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −27.3111 | + | 27.3111i | −1.30947 | + | 1.30947i | ||||
\(436\) | 0.538336 | + | 2.00910i | 0.0257816 | + | 0.0962184i | ||||
\(437\) | −1.07806 | + | 4.02338i | −0.0515707 | + | 0.192465i | ||||
\(438\) | 2.64060 | + | 4.57366i | 0.126173 | + | 0.218538i | ||||
\(439\) | −24.2969 | + | 6.51034i | −1.15963 | + | 0.310722i | −0.786818 | − | 0.617185i | \(-0.788273\pi\) |
−0.372812 | + | 0.927907i | \(0.621606\pi\) | |||||||
\(440\) | − | 38.0909i | − | 1.81591i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 21.4625 | + | 9.77254i | 1.02087 | + | 0.464832i | ||||
\(443\) | 6.06586 | − | 10.5064i | 0.288197 | − | 0.499173i | −0.685182 | − | 0.728372i | \(-0.740277\pi\) |
0.973380 | + | 0.229199i | \(0.0736107\pi\) | |||||||
\(444\) | −1.13825 | + | 0.657170i | −0.0540190 | + | 0.0311879i | ||||
\(445\) | −1.79864 | + | 6.71261i | −0.0852637 | + | 0.318208i | ||||
\(446\) | −13.7920 | + | 23.8885i | −0.653071 | + | 1.13115i | ||||
\(447\) | −0.964612 | − | 0.964612i | −0.0456246 | − | 0.0456246i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.1661 | − | 26.1661i | 1.23485 | − | 1.23485i | 0.272777 | − | 0.962077i | \(-0.412058\pi\) |
0.962077 | − | 0.272777i | \(-0.0879421\pi\) | |||||||
\(450\) | 10.1143 | + | 5.83948i | 0.476791 | + | 0.275276i | ||||
\(451\) | 2.81537 | − | 1.62545i | 0.132571 | − | 0.0765397i | ||||
\(452\) | −5.28845 | − | 1.41704i | −0.248748 | − | 0.0666518i | ||||
\(453\) | 6.01476 | + | 22.4474i | 0.282598 | + | 1.05467i | ||||
\(454\) | −9.27624 | − | 9.27624i | −0.435355 | − | 0.435355i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −21.4165 | − | 21.4165i | −1.00292 | − | 1.00292i | ||||
\(457\) | −11.0746 | − | 6.39394i | −0.518050 | − | 0.299096i | 0.218087 | − | 0.975929i | \(-0.430018\pi\) |
−0.736136 | + | 0.676833i | \(0.763352\pi\) | |||||||
\(458\) | 12.0629 | + | 20.8935i | 0.563660 | + | 0.976288i | ||||
\(459\) | 9.92801 | − | 12.0517i | 0.463400 | − | 0.562524i | ||||
\(460\) | 0.538580 | − | 0.932847i | 0.0251114 | − | 0.0434942i | ||||
\(461\) | − | 4.58089i | − | 0.213353i | −0.994294 | − | 0.106677i | \(-0.965979\pi\) | ||
0.994294 | − | 0.106677i | \(-0.0340210\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.53844 | −0.0714973 | −0.0357486 | − | 0.999361i | \(-0.511382\pi\) | ||||
−0.0357486 | + | 0.999361i | \(0.511382\pi\) | |||||||
\(464\) | −25.5051 | + | 6.83406i | −1.18404 | + | 0.317263i | ||||
\(465\) | 51.0889 | + | 13.6892i | 2.36919 | + | 0.634822i | ||||
\(466\) | 37.1743 | + | 9.96081i | 1.72206 | + | 0.461426i | ||||
\(467\) | 9.52860 | + | 5.50134i | 0.440931 | + | 0.254572i | 0.703992 | − | 0.710207i | \(-0.251399\pi\) |
−0.263061 | + | 0.964779i | \(0.584732\pi\) | |||||||
\(468\) | − | 1.95510i | − | 0.0903746i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −16.3273 | + | 16.3273i | −0.753122 | + | 0.753122i | ||||
\(471\) | 45.9478 | − | 12.3117i | 2.11716 | − | 0.567291i | ||||
\(472\) | −3.28202 | − | 5.68462i | −0.151067 | − | 0.261656i | ||||
\(473\) | −8.02935 | + | 29.9660i | −0.369190 | + | 1.37784i | ||||
\(474\) | 27.7132 | + | 16.0002i | 1.27291 | + | 0.734914i | ||||
\(475\) | 40.4380 | 1.85542 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.64405 | 0.212637 | ||||||||
\(478\) | −19.8489 | − | 11.4597i | −0.907866 | − | 0.524156i | ||||
\(479\) | 6.02062 | − | 22.4693i | 0.275089 | − | 1.02665i | −0.680692 | − | 0.732570i | \(-0.738321\pi\) |
0.955781 | − | 0.294078i | \(-0.0950125\pi\) | |||||||
\(480\) | 9.04248 | + | 15.6620i | 0.412731 | + | 0.714871i | ||||
\(481\) | 4.80879 | − | 1.28851i | 0.219262 | − | 0.0587511i | ||||
\(482\) | 16.9161 | − | 16.9161i | 0.770508 | − | 0.770508i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.10564i | 0.232075i | ||||||||
\(485\) | 12.4366 | + | 7.18029i | 0.564718 | + | 0.326040i | ||||
\(486\) | −17.0991 | − | 4.58168i | −0.775629 | − | 0.207829i | ||||
\(487\) | −21.2851 | − | 5.70334i | −0.964522 | − | 0.258443i | −0.258009 | − | 0.966143i | \(-0.583066\pi\) |
−0.706513 | + | 0.707700i | \(0.749733\pi\) | |||||||
\(488\) | 28.0727 | − | 7.52205i | 1.27079 | − | 0.340507i | ||||
\(489\) | −24.5684 | −1.11102 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19.2671i | − | 0.869512i | −0.900548 | − | 0.434756i | \(-0.856835\pi\) | ||
0.900548 | − | 0.434756i | \(-0.143165\pi\) | |||||||
\(492\) | −0.334234 | + | 0.578910i | −0.0150684 | + | 0.0260993i | ||||
\(493\) | 17.7978 | + | 14.6616i | 0.801573 | + | 0.660325i | ||||
\(494\) | −17.7238 | − | 30.6986i | −0.797432 | − | 1.38119i | ||||
\(495\) | 15.6323 | + | 9.02533i | 0.702621 | + | 0.405658i | ||||
\(496\) | 25.5680 | + | 25.5680i | 1.14804 | + | 1.14804i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 10.6110 | + | 10.6110i | 0.475490 | + | 0.475490i | ||||
\(499\) | 10.9640 | + | 40.9180i | 0.490814 | + | 1.83174i | 0.552314 | + | 0.833636i | \(0.313745\pi\) |
−0.0614998 | + | 0.998107i | \(0.519588\pi\) | |||||||
\(500\) | −2.36060 | − | 0.632522i | −0.105569 | − | 0.0282872i | ||||
\(501\) | 43.2232 | − | 24.9549i | 1.93107 | − | 1.11490i | ||||
\(502\) | −2.09738 | − | 1.21092i | −0.0936106 | − | 0.0540461i | ||||
\(503\) | −7.89613 | + | 7.89613i | −0.352071 | + | 0.352071i | −0.860880 | − | 0.508809i | \(-0.830086\pi\) |
0.508809 | + | 0.860880i | \(0.330086\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.9274 | − | 12.9274i | −0.575262 | − | 0.575262i | ||||
\(506\) | 2.46778 | − | 4.27432i | 0.109706 | − | 0.190017i | ||||
\(507\) | −0.122871 | + | 0.458560i | −0.00545688 | + | 0.0203653i | ||||
\(508\) | −2.09695 | + | 1.21067i | −0.0930371 | + | 0.0537150i | ||||
\(509\) | 16.8980 | − | 29.2682i | 0.748991 | − | 1.29729i | −0.199315 | − | 0.979935i | \(-0.563872\pi\) |
0.948307 | − | 0.317356i | \(-0.102795\pi\) | |||||||
\(510\) | 18.5527 | − | 40.7455i | 0.821527 | − | 1.80424i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 10.3205i | − | 0.456104i | ||||||
\(513\) | −22.6706 | + | 6.07457i | −1.00093 | + | 0.268199i | ||||
\(514\) | −3.16756 | − | 5.48638i | −0.139715 | − | 0.241994i | ||||
\(515\) | −3.48168 | + | 12.9938i | −0.153421 | + | 0.572576i | ||||
\(516\) | −1.65103 | − | 6.16175i | −0.0726827 | − | 0.271256i | ||||
\(517\) | −14.2869 | + | 14.2869i | −0.628338 | + | 0.628338i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 7.25281i | − | 0.318363i | ||||||
\(520\) | −7.67851 | − | 28.6566i | −0.336725 | − | 1.25667i | ||||
\(521\) | −14.3162 | − | 3.83601i | −0.627203 | − | 0.168059i | −0.0688031 | − | 0.997630i | \(-0.521918\pi\) |
−0.558400 | + | 0.829572i | \(0.688585\pi\) | |||||||
\(522\) | 2.59089 | − | 9.66932i | 0.113400 | − | 0.423215i | ||||
\(523\) | 1.37970 | − | 2.38971i | 0.0603300 | − | 0.104495i | −0.834283 | − | 0.551337i | \(-0.814118\pi\) |
0.894613 | + | 0.446842i | \(0.147451\pi\) | |||||||
\(524\) | −2.78859 | − | 2.78859i | −0.121820 | − | 0.121820i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.2605 | −1.23221 | ||||||||
\(527\) | 5.20152 | − | 31.1457i | 0.226582 | − | 1.35673i | ||||
\(528\) | 22.4298 | + | 38.8496i | 0.976132 | + | 1.69071i | ||||
\(529\) | 19.5274 | − | 11.2741i | 0.849017 | − | 0.490180i | ||||
\(530\) | −21.0325 | + | 5.63565i | −0.913594 | + | 0.244797i | ||||
\(531\) | 3.11059 | 0.134988 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.79040 | − | 1.79040i | 0.0775508 | − | 0.0775508i | ||||
\(534\) | −1.69464 | − | 6.32447i | −0.0733341 | − | 0.273686i | ||||
\(535\) | 33.4567 | − | 19.3162i | 1.44646 | − | 0.835113i | ||||
\(536\) | 26.1285 | − | 15.0853i | 1.12858 | − | 0.651586i | ||||
\(537\) | 2.08562 | + | 7.78364i | 0.0900011 | + | 0.335889i | ||||
\(538\) | −20.0472 | + | 20.0472i | −0.864296 | + | 0.864296i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 6.06948 | 0.261189 | ||||||||
\(541\) | −10.7745 | + | 2.88703i | −0.463233 | + | 0.124123i | −0.482885 | − | 0.875684i | \(-0.660411\pi\) |
0.0196516 | + | 0.999807i | \(0.493744\pi\) | |||||||
\(542\) | 22.7504 | − | 13.1349i | 0.977211 | − | 0.564193i | ||||
\(543\) | −1.96017 | − | 3.39511i | −0.0841189 | − | 0.145698i | ||||
\(544\) | 8.78804 | − | 6.27279i | 0.376784 | − | 0.268944i | ||||
\(545\) | −14.9569 | −0.640683 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.17129 | + | 5.17129i | 0.221108 | + | 0.221108i | 0.808965 | − | 0.587857i | \(-0.200028\pi\) |
−0.587857 | + | 0.808965i | \(0.700028\pi\) | |||||||
\(548\) | −4.76676 | + | 8.25627i | −0.203626 | + | 0.352690i | ||||
\(549\) | −3.56458 | + | 13.3032i | −0.152133 | + | 0.567767i | ||||
\(550\) | −46.2831 | − | 12.4015i | −1.97352 | − | 0.528803i | ||||
\(551\) | −8.97086 | − | 33.4797i | −0.382172 | − | 1.42628i | ||||
\(552\) | − | 3.28453i | − | 0.139799i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.16025 | − | 1.16025i | 0.0492942 | − | 0.0492942i | ||||
\(555\) | −2.44618 | − | 9.12925i | −0.103834 | − | 0.387515i | ||||
\(556\) | −0.953695 | + | 3.55924i | −0.0404457 | + | 0.150945i | ||||
\(557\) | −7.67715 | − | 13.2972i | −0.325291 | − | 0.563421i | 0.656280 | − | 0.754518i | \(-0.272129\pi\) |
−0.981571 | + | 0.191096i | \(0.938796\pi\) | |||||||
\(558\) | −13.2411 | + | 3.54795i | −0.560542 | + | 0.150197i | ||||
\(559\) | 24.1626i | 1.02197i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.2342 | − | 35.6537i | 0.685409 | − | 1.50530i | ||||
\(562\) | −2.77538 | + | 4.80710i | −0.117072 | + | 0.202775i | ||||
\(563\) | −5.73828 | + | 3.31299i | −0.241839 | + | 0.139626i | −0.616022 | − | 0.787729i | \(-0.711257\pi\) |
0.374182 | + | 0.927355i | \(0.377923\pi\) | |||||||
\(564\) | 1.07529 | − | 4.01304i | 0.0452779 | − | 0.168979i | ||||
\(565\) | 19.6851 | − | 34.0957i | 0.828160 | − | 1.43442i | ||||
\(566\) | −2.02730 | − | 2.02730i | −0.0852136 | − | 0.0852136i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.31407 | + | 7.31407i | −0.306892 | + | 0.306892i | ||||
\(569\) | 32.0150 | + | 18.4838i | 1.34214 | + | 0.774883i | 0.987121 | − | 0.159977i | \(-0.0511420\pi\) |
0.355016 | + | 0.934860i | \(0.384475\pi\) | |||||||
\(570\) | −58.2797 | + | 33.6478i | −2.44107 | + | 1.40935i | ||||
\(571\) | 35.3394 | + | 9.46916i | 1.47891 | + | 0.396272i | 0.905975 | − | 0.423331i | \(-0.139139\pi\) |
0.572932 | + | 0.819603i | \(0.305806\pi\) | |||||||
\(572\) | 2.07606 | + | 7.74797i | 0.0868045 | + | 0.323959i | ||||
\(573\) | 36.2102 | + | 36.2102i | 1.51270 | + | 1.51270i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.10087 | + | 3.10087i | 0.129315 | + | 0.129315i | ||||
\(576\) | 5.25020 | + | 3.03120i | 0.218758 | + | 0.126300i | ||||
\(577\) | −3.35458 | − | 5.81030i | −0.139653 | − | 0.241886i | 0.787712 | − | 0.616043i | \(-0.211265\pi\) |
−0.927365 | + | 0.374157i | \(0.877932\pi\) | |||||||
\(578\) | −25.2784 | − | 8.68554i | −1.05144 | − | 0.361271i | ||||
\(579\) | 11.4397 | − | 19.8141i | 0.475416 | − | 0.823444i | ||||
\(580\) | 8.96335i | 0.372183i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −13.5302 | −0.560845 | ||||||||
\(583\) | −18.4041 | + | 4.93138i | −0.762222 | + | 0.204237i | ||||
\(584\) | −3.83138 | − | 1.02661i | −0.158543 | − | 0.0424816i | ||||
\(585\) | 13.5799 | + | 3.63873i | 0.561460 | + | 0.150443i | ||||
\(586\) | −20.3681 | − | 11.7595i | −0.841399 | − | 0.485782i | ||||
\(587\) | − | 0.653601i | − | 0.0269770i | −0.999909 | − | 0.0134885i | \(-0.995706\pi\) | ||
0.999909 | − | 0.0134885i | \(-0.00429365\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33.5623 | + | 33.5623i | −1.38291 | + | 1.38291i | ||||
\(590\) | −14.0876 | + | 3.77477i | −0.579978 | + | 0.155405i | ||||
\(591\) | −23.0206 | − | 39.8729i | −0.946941 | − | 1.64015i | ||||
\(592\) | 1.67231 | − | 6.24114i | 0.0687315 | − | 0.256509i | ||||
\(593\) | −23.9967 | − | 13.8545i | −0.985428 | − | 0.568937i | −0.0815231 | − | 0.996671i | \(-0.525978\pi\) |
−0.903904 | + | 0.427735i | \(0.859312\pi\) | |||||||
\(594\) | 27.8105 | 1.14108 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.316581 | −0.0129677 | ||||||||
\(597\) | −9.24829 | − | 5.33950i | −0.378507 | − | 0.218531i | ||||
\(598\) | 0.994931 | − | 3.71313i | 0.0406857 | − | 0.151841i | ||||
\(599\) | 3.77268 | + | 6.53448i | 0.154148 | + | 0.266992i | 0.932748 | − | 0.360528i | \(-0.117404\pi\) |
−0.778601 | + | 0.627520i | \(0.784070\pi\) | |||||||
\(600\) | −30.8006 | + | 8.25300i | −1.25743 | + | 0.336927i | ||||
\(601\) | 12.8735 | − | 12.8735i | 0.525119 | − | 0.525119i | −0.393994 | − | 0.919113i | \(-0.628907\pi\) |
0.919113 | + | 0.393994i | \(0.128907\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.2974i | 0.582234i | ||||||||
\(604\) | 4.67057 | + | 2.69655i | 0.190043 | + | 0.109721i | ||||
\(605\) | −35.4632 | − | 9.50234i | −1.44178 | − | 0.386325i | ||||
\(606\) | 16.6381 | + | 4.45815i | 0.675875 | + | 0.181100i | ||||
\(607\) | 11.8126 | − | 3.16518i | 0.479458 | − | 0.128470i | −0.0109920 | − | 0.999940i | \(-0.503499\pi\) |
0.490450 | + | 0.871469i | \(0.336832\pi\) | |||||||
\(608\) | −16.2294 | −0.658189 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 64.5748i | − | 2.61456i | ||||||
\(611\) | −7.86835 | + | 13.6284i | −0.318319 | + | 0.551345i | ||||
\(612\) | 0.213111 | + | 2.20567i | 0.00861451 | + | 0.0891590i | ||||
\(613\) | 19.7050 | + | 34.1300i | 0.795876 | + | 1.37850i | 0.922282 | + | 0.386519i | \(0.126322\pi\) |
−0.126406 | + | 0.991979i | \(0.540344\pi\) | |||||||
\(614\) | 9.75495 | + | 5.63202i | 0.393678 | + | 0.227290i | ||||
\(615\) | −3.39899 | − | 3.39899i | −0.137060 | − | 0.137060i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.4142 | + | 10.4142i | 0.419260 | + | 0.419260i | 0.884948 | − | 0.465689i | \(-0.154193\pi\) |
−0.465689 | + | 0.884948i | \(0.654193\pi\) | |||||||
\(618\) | −3.28036 | − | 12.2425i | −0.131955 | − | 0.492464i | ||||
\(619\) | −35.7331 | − | 9.57465i | −1.43623 | − | 0.384838i | −0.545021 | − | 0.838423i | \(-0.683478\pi\) |
−0.891213 | + | 0.453585i | \(0.850145\pi\) | |||||||
\(620\) | 10.6299 | − | 6.13719i | 0.426908 | − | 0.246475i | ||||
\(621\) | −2.20424 | − | 1.27262i | −0.0884531 | − | 0.0510684i | ||||
\(622\) | 6.99806 | − | 6.99806i | 0.280597 | − | 0.280597i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 24.7059 | + | 24.7059i | 0.989028 | + | 0.989028i | ||||
\(625\) | −7.52528 | + | 13.0342i | −0.301011 | + | 0.521367i | ||||
\(626\) | 12.7665 | − | 47.6451i | 0.510250 | − | 1.90428i | ||||
\(627\) | −50.9967 | + | 29.4429i | −2.03661 | + | 1.17584i | ||||
\(628\) | 5.51960 | − | 9.56022i | 0.220256 | − | 0.381494i | ||||
\(629\) | −5.28464 | + | 1.97782i | −0.210713 | + | 0.0788609i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.7794i | 1.26512i | 0.774512 | + | 0.632559i | \(0.217996\pi\) | ||||
−0.774512 | + | 0.632559i | \(0.782004\pi\) | |||||||
\(632\) | −23.2155 | + | 6.22057i | −0.923462 | + | 0.247441i | ||||
\(633\) | −9.89407 | − | 17.1370i | −0.393254 | − | 0.681136i | ||||
\(634\) | 6.74114 | − | 25.1583i | 0.267725 | − | 0.999163i | ||||
\(635\) | −4.50648 | − | 16.8184i | −0.178834 | − | 0.667418i | ||||
\(636\) | 2.77034 | − | 2.77034i | 0.109851 | − | 0.109851i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 41.0702i | 1.62599i | ||||||||
\(639\) | −1.26865 | − | 4.73468i | −0.0501871 | − | 0.187301i | ||||
\(640\) | −44.6302 | − | 11.9586i | −1.76417 | − | 0.472707i | ||||
\(641\) | −4.90532 | + | 18.3069i | −0.193749 | + | 0.723080i | 0.798839 | + | 0.601545i | \(0.205448\pi\) |
−0.992587 | + | 0.121534i | \(0.961219\pi\) | |||||||
\(642\) | −18.1993 | + | 31.5221i | −0.718269 | + | 1.24408i | ||||
\(643\) | −19.0600 | − | 19.0600i | −0.751652 | − | 0.751652i | 0.223135 | − | 0.974787i | \(-0.428371\pi\) |
−0.974787 | + | 0.223135i | \(0.928371\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 45.8716 | 1.80619 | ||||||||
\(646\) | 23.3416 | + | 32.7010i | 0.918362 | + | 1.28660i | ||||
\(647\) | −0.408070 | − | 0.706798i | −0.0160429 | − | 0.0277871i | 0.857893 | − | 0.513829i | \(-0.171773\pi\) |
−0.873935 | + | 0.486042i | \(0.838440\pi\) | |||||||
\(648\) | 23.1331 | − | 13.3559i | 0.908755 | − | 0.524670i | ||||
\(649\) | −12.3271 | + | 3.30304i | −0.483882 | + | 0.129656i | ||||
\(650\) | −37.3198 | −1.46380 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.03161 | + | 4.03161i | −0.157890 | + | 0.157890i | ||||
\(653\) | 6.86267 | + | 25.6118i | 0.268557 | + | 1.00227i | 0.960037 | + | 0.279873i | \(0.0902924\pi\) |
−0.691480 | + | 0.722396i | \(0.743041\pi\) | |||||||
\(654\) | 12.2041 | − | 7.04602i | 0.477216 | − | 0.275521i | ||||
\(655\) | 24.5592 | − | 14.1793i | 0.959607 | − | 0.554029i | ||||
\(656\) | −0.850530 | − | 3.17422i | −0.0332076 | − | 0.123932i | ||||
\(657\) | 1.32913 | − | 1.32913i | 0.0518544 | − | 0.0518544i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.6995 | −0.611566 | −0.305783 | − | 0.952101i | \(-0.598918\pi\) | ||||
−0.305783 | + | 0.952101i | \(0.598918\pi\) | |||||||
\(660\) | 14.7091 | − | 3.94130i | 0.572553 | − | 0.153415i | ||||
\(661\) | −13.4338 | + | 7.75601i | −0.522515 | + | 0.301674i | −0.737963 | − | 0.674841i | \(-0.764212\pi\) |
0.215448 | + | 0.976515i | \(0.430879\pi\) | |||||||
\(662\) | 3.72078 | + | 6.44458i | 0.144612 | + | 0.250476i | ||||
\(663\) | 5.02614 | − | 30.0956i | 0.195199 | − | 1.16882i | ||||
\(664\) | −11.2707 | −0.437386 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.73211 | + | 1.73211i | 0.0671179 | + | 0.0671179i | ||||
\(667\) | 1.87939 | − | 3.25520i | 0.0727703 | − | 0.126042i | ||||
\(668\) | 2.99778 | − | 11.1879i | 0.115988 | − | 0.432871i | ||||
\(669\) | 34.4735 | + | 9.23715i | 1.33282 | + | 0.357129i | ||||
\(670\) | −17.3501 | − | 64.7516i | −0.670295 | − | 2.50157i | ||||
\(671\) | − | 56.5050i | − | 2.18135i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.7151 | − | 25.7151i | 0.991243 | − | 0.991243i | −0.00871919 | − | 0.999962i | \(-0.502775\pi\) |
0.999962 | + | 0.00871919i | \(0.00277544\pi\) | |||||||
\(674\) | −9.81357 | − | 36.6248i | −0.378005 | − | 1.41073i | ||||
\(675\) | −6.39539 | + | 23.8679i | −0.246159 | + | 0.918676i | ||||
\(676\) | 0.0550857 | + | 0.0954112i | 0.00211868 | + | 0.00366966i | ||||
\(677\) | 27.6865 | − | 7.41857i | 1.06408 | − | 0.285119i | 0.316020 | − | 0.948752i | \(-0.397653\pi\) |
0.748058 | + | 0.663634i | \(0.230987\pi\) | |||||||
\(678\) | 37.0938i | 1.42458i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 11.7863 | + | 31.4923i | 0.451982 | + | 1.20768i | ||||
\(681\) | −8.48674 | + | 14.6995i | −0.325213 | + | 0.563285i | ||||
\(682\) | 48.7065 | − | 28.1207i | 1.86507 | − | 1.07680i | ||||
\(683\) | 5.11944 | − | 19.1060i | 0.195890 | − | 0.731071i | −0.796145 | − | 0.605106i | \(-0.793131\pi\) |
0.992035 | − | 0.125965i | \(-0.0402026\pi\) | |||||||
\(684\) | 1.66542 | − | 2.88459i | 0.0636789 | − | 0.110295i | ||||
\(685\) | −48.4754 | − | 48.4754i | −1.85215 | − | 1.85215i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.0724 | − | 22.0724i | 0.842114 | − | 0.842114i | ||||
\(688\) | 27.1583 | + | 15.6799i | 1.03540 | + | 0.597790i | ||||
\(689\) | −12.8518 | + | 7.41997i | −0.489613 | + | 0.282678i | ||||
\(690\) | −7.04920 | − | 1.88883i | −0.268358 | − | 0.0719064i | ||||
\(691\) | 9.75631 | + | 36.4110i | 0.371147 | + | 1.38514i | 0.858893 | + | 0.512155i | \(0.171153\pi\) |
−0.487745 | + | 0.872986i | \(0.662181\pi\) | |||||||
\(692\) | −1.19017 | − | 1.19017i | −0.0452434 | − | 0.0452434i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25.4665 | − | 25.4665i | −0.966697 | − | 0.966697i | ||||
\(695\) | −22.9471 | − | 13.2485i | −0.870433 | − | 0.502544i | ||||
\(696\) | 13.6658 | + | 23.6698i | 0.517999 | + | 0.897201i | ||||
\(697\) | −1.82470 | + | 2.21502i | −0.0691155 | + | 0.0838998i | ||||
\(698\) | −8.01058 | + | 13.8747i | −0.303205 | + | 0.525166i | ||||
\(699\) | − | 49.7946i | − | 1.88341i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.4612 | 0.470652 | 0.235326 | − | 0.971916i | \(-0.424384\pi\) | ||||
0.235326 | + | 0.971916i | \(0.424384\pi\) | |||||||
\(702\) | 20.9224 | − | 5.60615i | 0.789666 | − | 0.211590i | ||||
\(703\) | 8.19256 | + | 2.19519i | 0.308988 | + | 0.0827932i | ||||
\(704\) | −24.0250 | − | 6.43748i | −0.905477 | − | 0.242622i | ||||
\(705\) | 25.8728 | + | 14.9377i | 0.974427 | + | 0.562586i | ||||
\(706\) | − | 26.4143i | − | 0.994116i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.85558 | − | 1.85558i | 0.0697368 | − | 0.0697368i | ||||
\(709\) | 13.9469 | − | 3.73707i | 0.523788 | − | 0.140349i | 0.0127698 | − | 0.999918i | \(-0.495935\pi\) |
0.511018 | + | 0.859570i | \(0.329268\pi\) | |||||||
\(710\) | 11.4912 | + | 19.9034i | 0.431259 | + | 0.746962i | ||||
\(711\) | 2.94783 | − | 11.0015i | 0.110552 | − | 0.412587i | ||||
\(712\) | 4.25882 | + | 2.45883i | 0.159606 | + | 0.0921485i | ||||
\(713\) | −5.14726 | −0.192766 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −57.6804 | −2.15712 | ||||||||
\(716\) | 1.61952 | + | 0.935030i | 0.0605243 | + | 0.0349437i | ||||
\(717\) | −7.67512 | + | 28.6439i | −0.286633 | + | 1.06973i | ||||
\(718\) | 22.2022 | + | 38.4553i | 0.828578 | + | 1.43514i | ||||
\(719\) | 8.93538 | − | 2.39423i | 0.333233 | − | 0.0892896i | −0.0883228 | − | 0.996092i | \(-0.528151\pi\) |
0.421556 | + | 0.906802i | \(0.361484\pi\) | |||||||
\(720\) | 12.9023 | − | 12.9023i | 0.480840 | − | 0.480840i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 30.5173i | − | 1.13574i | ||||||
\(723\) | −26.8059 | − | 15.4764i | −0.996922 | − | 0.575573i | ||||
\(724\) | −0.878788 | − | 0.235470i | −0.0326599 | − | 0.00875119i | ||||
\(725\) | −35.2479 | − | 9.44465i | −1.30907 | − | 0.350765i | ||||
\(726\) | 33.4126 | − | 8.95288i | 1.24006 | − | 0.332273i | ||||
\(727\) | 33.0618 | 1.22619 | 0.613096 | − | 0.790008i | \(-0.289924\pi\) | ||||
0.613096 | + | 0.790008i | \(0.289924\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 10.4537i | − | 0.387175i | ||||||
\(730\) | −4.40660 | + | 7.63246i | −0.163096 | + | 0.282490i | ||||
\(731\) | −2.63379 | − | 27.2594i | −0.0974143 | − | 1.00822i | ||||
\(732\) | 5.80942 | + | 10.0622i | 0.214722 | + | 0.371910i | ||||
\(733\) | −1.57407 | − | 0.908789i | −0.0581396 | − | 0.0335669i | 0.470648 | − | 0.882321i | \(-0.344020\pi\) |
−0.528788 | + | 0.848754i | \(0.677353\pi\) | |||||||
\(734\) | −20.9153 | − | 20.9153i | −0.771998 | − | 0.771998i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.24450 | − | 1.24450i | −0.0458730 | − | 0.0458730i | ||||
\(737\) | −15.1819 | − | 56.6598i | −0.559234 | − | 2.08709i | ||||
\(738\) | 1.20339 | + | 0.322448i | 0.0442974 | + | 0.0118695i | ||||
\(739\) | −26.1195 | + | 15.0801i | −0.960820 | + | 0.554730i | −0.896425 | − | 0.443195i | \(-0.853845\pi\) |
−0.0643946 | + | 0.997925i | \(0.520512\pi\) | |||||||
\(740\) | −1.89950 | − | 1.09668i | −0.0698270 | − | 0.0403146i | ||||
\(741\) | −32.4307 | + | 32.4307i | −1.19137 | + | 1.19137i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.0426 | + | 28.0426i | 1.02878 | + | 1.02878i | 0.999573 | + | 0.0292082i | \(0.00929860\pi\) |
0.0292082 | + | 0.999573i | \(0.490701\pi\) | |||||||
\(744\) | 18.7138 | − | 32.4133i | 0.686082 | − | 1.18833i | ||||
\(745\) | 0.589202 | − | 2.19893i | 0.0215867 | − | 0.0805627i | ||||
\(746\) | 42.1640 | − | 24.3434i | 1.54373 | − | 0.891274i | ||||
\(747\) | 2.67049 | − | 4.62543i | 0.0977082 | − | 0.169236i | ||||
\(748\) | −3.18668 | − | 8.51467i | −0.116517 | − | 0.311327i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 16.5575i | 0.604595i | ||||||||
\(751\) | 40.4055 | − | 10.8266i | 1.47442 | − | 0.395069i | 0.569974 | − | 0.821663i | \(-0.306953\pi\) |
0.904443 | + | 0.426594i | \(0.140287\pi\) | |||||||
\(752\) | 10.2120 | + | 17.6878i | 0.372394 | + | 0.645006i | ||||
\(753\) | −0.811010 | + | 3.02673i | −0.0295549 | + | 0.110300i | ||||
\(754\) | 8.27910 | + | 30.8980i | 0.301507 | + | 1.12524i | ||||
\(755\) | −27.4226 | + | 27.4226i | −0.998009 | + | 0.998009i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.9024i | 1.08682i | 0.839467 | + | 0.543411i | \(0.182867\pi\) | ||||
−0.839467 | + | 0.543411i | \(0.817133\pi\) | |||||||
\(758\) | 5.06654 | + | 18.9086i | 0.184025 | + | 0.686791i | ||||
\(759\) | −6.16828 | − | 1.65279i | −0.223894 | − | 0.0599923i | ||||
\(760\) | 13.0816 | − | 48.8212i | 0.474520 | − | 1.77093i | ||||
\(761\) | 14.9404 | − | 25.8775i | 0.541588 | − | 0.938058i | −0.457225 | − | 0.889351i | \(-0.651157\pi\) |
0.998813 | − | 0.0487070i | \(-0.0155101\pi\) | |||||||
\(762\) | 11.6000 | + | 11.6000i | 0.420224 | + | 0.420224i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 11.8840 | 0.429948 | ||||||||
\(765\) | −15.7170 | − | 2.62483i | −0.568248 | − | 0.0949008i | ||||
\(766\) | −23.4631 | − | 40.6393i | −0.847756 | − | 1.46836i | ||||
\(767\) | −8.60813 | + | 4.96991i | −0.310822 | + | 0.179453i | ||||
\(768\) | 21.1212 | − | 5.65941i | 0.762146 | − | 0.204216i | ||||
\(769\) | 35.8821 | 1.29394 | 0.646971 | − | 0.762514i | \(-0.276035\pi\) | ||||
0.646971 | + | 0.762514i | \(0.276035\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.79594 | + | 5.79594i | −0.208736 | + | 0.208736i | ||||
\(772\) | −1.37422 | − | 5.12866i | −0.0494592 | − | 0.184584i | ||||
\(773\) | 11.4284 | − | 6.59820i | 0.411052 | − | 0.237321i | −0.280190 | − | 0.959945i | \(-0.590397\pi\) |
0.691241 | + | 0.722624i | \(0.257064\pi\) | |||||||
\(774\) | −10.2961 | + | 5.94446i | −0.370086 | + | 0.213669i | ||||
\(775\) | 12.9335 | + | 48.2683i | 0.464584 | + | 1.73385i | ||||
\(776\) | 7.18567 | − | 7.18567i | 0.257950 | − | 0.257950i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 32.9245 | 1.18040 | ||||||||
\(779\) | 4.16670 | − | 1.11647i | 0.149288 | − | 0.0400015i | ||||
\(780\) | 10.2715 | − | 5.93026i | 0.367779 | − | 0.212337i | ||||
\(781\) | 10.0552 | + | 17.4161i | 0.359804 | + | 0.623199i | ||||
\(782\) | −0.717702 | + | 4.29746i | −0.0256650 | + | 0.153677i | ||||
\(783\) | 21.1797 | 0.756899 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 56.1314 | + | 56.1314i | 2.00342 | + | 2.00342i | ||||
\(786\) | −13.3594 | + | 23.1391i | −0.476513 | + | 0.825344i | ||||
\(787\) | 7.42724 | − | 27.7189i | 0.264753 | − | 0.988070i | −0.697649 | − | 0.716440i | \(-0.745770\pi\) |
0.962402 | − | 0.271631i | \(-0.0875629\pi\) | |||||||
\(788\) | −10.3207 | − | 2.76541i | −0.367658 | − | 0.0985137i | ||||
\(789\) | 9.46367 | + | 35.3189i | 0.336916 | + | 1.25739i | ||||
\(790\) | 53.4019i | 1.89995i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 9.03209 | − | 9.03209i | 0.320941 | − | 0.320941i | ||||
\(793\) | −11.3905 | − | 42.5100i | −0.404489 | − | 1.50957i | ||||
\(794\) | −11.5411 | + | 43.0719i | −0.409577 | + | 1.52856i | ||||
\(795\) | 14.0864 | + | 24.3984i | 0.499595 | + | 0.865323i | ||||
\(796\) | −2.39382 | + | 0.641422i | −0.0848467 | + | 0.0227346i | ||||
\(797\) | 10.8120i | 0.382980i | 0.981495 | + | 0.191490i | \(0.0613320\pi\) | ||||
−0.981495 | + | 0.191490i | \(0.938668\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.39125 | − | 16.2327i | 0.261484 | − | 0.574272i | ||||
\(800\) | −8.54326 | + | 14.7974i | −0.302050 | + | 0.523166i | ||||
\(801\) | −2.01819 | + | 1.16520i | −0.0713091 | + | 0.0411703i | ||||
\(802\) | 1.33021 | − | 4.96442i | 0.0469714 | − | 0.175300i | ||||
\(803\) | −3.85592 | + | 6.67865i | −0.136073 | + | 0.235684i | ||||
\(804\) | 8.52888 | + | 8.52888i | 0.300790 | + | 0.300790i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 30.9743 | − | 30.9743i | 1.09102 | − | 1.09102i | ||||
\(807\) | 31.7675 | + | 18.3410i | 1.11827 | + | 0.645633i | ||||
\(808\) | −11.2039 | + | 6.46855i | −0.394150 | + | 0.227563i | ||||
\(809\) | −49.2510 | − | 13.1968i | −1.73157 | − | 0.463974i | −0.751029 | − | 0.660269i | \(-0.770442\pi\) |
−0.980545 | + | 0.196295i | \(0.937109\pi\) | |||||||
\(810\) | −15.3611 | − | 57.3284i | −0.539734 | − | 2.01432i | ||||
\(811\) | 10.8591 | + | 10.8591i | 0.381315 | + | 0.381315i | 0.871576 | − | 0.490261i | \(-0.163098\pi\) |
−0.490261 | + | 0.871576i | \(0.663098\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.0340 | − | 24.0340i | −0.842910 | − | 0.842910i | ||||
\(814\) | −8.70353 | − | 5.02499i | −0.305059 | − | 0.176126i | ||||
\(815\) | −20.4997 | − | 35.5065i | −0.718074 | − | 1.24374i | ||||
\(816\) | −30.5653 | − | 25.1793i | −1.07000 | − | 0.881450i | ||||
\(817\) | −20.5825 | + | 35.6500i | −0.720091 | + | 1.24723i | ||||
\(818\) | − | 54.0654i | − | 1.89035i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.11553 | −0.0389560 | ||||||||
\(821\) | −13.4603 | + | 3.60669i | −0.469769 | + | 0.125874i | −0.485935 | − | 0.873995i | \(-0.661521\pi\) |
0.0161658 | + | 0.999869i | \(0.494854\pi\) | |||||||
\(822\) | 62.3897 | + | 16.7173i | 2.17609 | + | 0.583082i | ||||
\(823\) | −11.8562 | − | 3.17686i | −0.413281 | − | 0.110738i | 0.0461864 | − | 0.998933i | \(-0.485293\pi\) |
−0.459468 | + | 0.888194i | \(0.651960\pi\) | |||||||
\(824\) | 8.24392 | + | 4.75963i | 0.287190 | + | 0.165810i | ||||
\(825\) | 61.9959i | 2.15842i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.8528 | − | 11.8528i | 0.412162 | − | 0.412162i | −0.470329 | − | 0.882491i | \(-0.655865\pi\) |
0.882491 | + | 0.470329i | \(0.155865\pi\) | |||||||
\(828\) | 0.348904 | − | 0.0934886i | 0.0121253 | − | 0.00324895i | ||||
\(829\) | 21.7133 | + | 37.6085i | 0.754134 | + | 1.30620i | 0.945804 | + | 0.324739i | \(0.105276\pi\) |
−0.191670 | + | 0.981459i | \(0.561390\pi\) | |||||||
\(830\) | −6.48139 | + | 24.1889i | −0.224972 | + | 0.839608i | ||||
\(831\) | −1.83857 | − | 1.06150i | −0.0637793 | − | 0.0368230i | ||||
\(832\) | −19.3722 | −0.671612 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 24.9649 | 0.864463 | ||||||||
\(835\) | 72.1303 | + | 41.6444i | 2.49617 | + | 1.44117i | ||||
\(836\) | −3.53691 | + | 13.1999i | −0.122327 | + | 0.456529i | ||||
\(837\) | −14.5017 | − | 25.1176i | −0.501251 | − | 0.868192i | ||||
\(838\) | 26.6045 | − | 7.12865i | 0.919036 | − | 0.246255i | ||||
\(839\) | 4.20215 | − | 4.20215i | 0.145074 | − | 0.145074i | −0.630839 | − | 0.775914i | \(-0.717289\pi\) |
0.775914 | + | 0.630839i | \(0.217289\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.27792i | 0.0785488i | ||||||||
\(842\) | 17.8414 | + | 10.3007i | 0.614855 | + | 0.354987i | ||||
\(843\) | 6.93714 | + | 1.85880i | 0.238928 | + | 0.0640205i | ||||
\(844\) | −4.43574 | − | 1.18855i | −0.152684 | − | 0.0409117i | ||||
\(845\) | −0.765238 | + | 0.205045i | −0.0263250 | + | 0.00705376i | ||||
\(846\) | −7.74305 | −0.266211 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 19.2602i | 0.661397i | ||||||||
\(849\) | −1.85475 | + | 3.21253i | −0.0636549 | + | 0.110254i | ||||
\(850\) | 42.1027 | − | 4.06795i | 1.44411 | − | 0.139530i | ||||
\(851\) | 0.459891 | + | 0.796555i | 0.0157649 | + | 0.0273056i | ||||
\(852\) | −3.58119 | − | 2.06760i | −0.122690 | − | 0.0708349i | ||||
\(853\) | −9.18348 | − | 9.18348i | −0.314436 | − | 0.314436i | 0.532189 | − | 0.846625i | \(-0.321370\pi\) |
−0.846625 | + | 0.532189i | \(0.821370\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.9364 | + | 16.9364i | 0.579214 | + | 0.579214i | ||||
\(856\) | −7.07553 | − | 26.4062i | −0.241837 | − | 0.902546i | ||||
\(857\) | 27.8122 | + | 7.45226i | 0.950048 | + | 0.254564i | 0.700382 | − | 0.713768i | \(-0.253013\pi\) |
0.249665 | + | 0.968332i | \(0.419679\pi\) | |||||||
\(858\) | 47.0642 | − | 27.1725i | 1.60675 | − | 0.927655i | ||||
\(859\) | −7.14240 | − | 4.12366i | −0.243695 | − | 0.140698i | 0.373179 | − | 0.927760i | \(-0.378268\pi\) |
−0.616874 | + | 0.787062i | \(0.711601\pi\) | |||||||
\(860\) | 7.52741 | − | 7.52741i | 0.256683 | − | 0.256683i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 29.2207 | + | 29.2207i | 0.995260 | + | 0.995260i | ||||
\(863\) | 17.8414 | − | 30.9022i | 0.607329 | − | 1.05192i | −0.384350 | − | 0.923188i | \(-0.625574\pi\) |
0.991679 | − | 0.128737i | \(-0.0410924\pi\) | |||||||
\(864\) | 2.56673 | − | 9.57915i | 0.0873218 | − | 0.325889i | ||||
\(865\) | 10.4818 | − | 6.05169i | 0.356393 | − | 0.205764i | ||||
\(866\) | 0.616088 | − | 1.06710i | 0.0209355 | − | 0.0362614i | ||||
\(867\) | −2.38981 | + | 34.5006i | −0.0811621 | + | 1.17170i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 46.7284i | 1.58515i | ||||||||
\(870\) | 58.6584 | − | 15.7175i | 1.98871 | − | 0.532872i | ||||
\(871\) | −22.8434 | − | 39.5660i | −0.774020 | − | 1.34064i | ||||
\(872\) | −2.73935 | + | 10.2234i | −0.0927662 | + | 0.346208i | ||||
\(873\) | 1.24638 | + | 4.65156i | 0.0421836 | + | 0.157431i | ||||
\(874\) | 4.63090 | − | 4.63090i | 0.156643 | − | 0.156643i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 1.58575i | − | 0.0535774i | ||||||
\(877\) | −3.64250 | − | 13.5940i | −0.122998 | − | 0.459036i | 0.876762 | − | 0.480925i | \(-0.159699\pi\) |
−0.999760 | + | 0.0218882i | \(0.993032\pi\) | |||||||
\(878\) | 38.2019 | + | 10.2362i | 1.28925 | + | 0.345454i | ||||
\(879\) | −7.87590 | + | 29.3933i | −0.265648 | + | 0.991410i | ||||
\(880\) | −37.4306 | + | 64.8316i | −1.26178 | + | 2.18547i | ||||
\(881\) | 10.4454 | + | 10.4454i | 0.351914 | + | 0.351914i | 0.860821 | − | 0.508907i | \(-0.169950\pi\) |
−0.508907 | + | 0.860821i | \(0.669950\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.72305 | 0.158943 | 0.0794717 | − | 0.996837i | \(-0.474677\pi\) | ||||
0.0794717 | + | 0.996837i | \(0.474677\pi\) | |||||||
\(884\) | −4.11383 | − | 5.76339i | −0.138363 | − | 0.193844i | ||||
\(885\) | 9.43513 | + | 16.3421i | 0.317158 | + | 0.549334i | ||||
\(886\) | −16.5191 | + | 9.53729i | −0.554969 | + | 0.320412i | ||||
\(887\) | 43.5827 | − | 11.6779i | 1.46336 | − | 0.392107i | 0.562713 | − | 0.826652i | \(-0.309758\pi\) |
0.900650 | + | 0.434545i | \(0.143091\pi\) | |||||||
\(888\) | −6.68809 | −0.224437 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.72620 | − | 7.72620i | 0.258983 | − | 0.258983i | ||||
\(891\) | −13.4415 | − | 50.1643i | −0.450307 | − | 1.68057i | ||||
\(892\) | 7.17281 | − | 4.14122i | 0.240163 | − | 0.138658i | ||||
\(893\) | −23.2182 | + | 13.4050i | −0.776967 | + | 0.448582i | ||||
\(894\) | 0.555133 | + | 2.07178i | 0.0185664 | + | 0.0692908i | ||||
\(895\) | −9.50877 | + | 9.50877i | −0.317843 | + | 0.317843i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.97371 | −0.166067 | ||||||||
\(898\) | −56.1993 | + | 15.0585i | −1.87539 | + | 0.502510i | ||||
\(899\) | 37.0935 | − | 21.4159i | 1.23714 | − | 0.714261i | ||||
\(900\) | −1.75337 | − | 3.03693i | −0.0584458 | − | 0.101231i | ||||
\(901\) | 13.6901 | − | 9.77180i | 0.456082 | − | 0.325546i | ||||
\(902\) | −5.11138 | −0.170190 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.6999 | − | 19.6999i | −0.655209 | − | 0.655209i | ||||
\(905\) | 3.27110 | − | 5.66571i | 0.108735 | − | 0.188335i | ||||
\(906\) | 9.45696 | − | 35.2938i | 0.314186 | − | 1.17256i | ||||
\(907\) | −32.7157 | − | 8.76614i | −1.08631 | − | 0.291075i | −0.329129 | − | 0.944285i | \(-0.606755\pi\) |
−0.757177 | + | 0.653210i | \(0.773422\pi\) | |||||||
\(908\) | 1.01949 | + | 3.80480i | 0.0338330 | + | 0.126267i | ||||
\(909\) | − | 6.13069i | − | 0.203342i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.16704 | − | 7.16704i | 0.237455 | − | 0.237455i | −0.578341 | − | 0.815795i | \(-0.696300\pi\) |
0.815795 | + | 0.578341i | \(0.196300\pi\) | |||||||
\(912\) | 15.4062 | + | 57.4968i | 0.510151 | + | 1.90391i | ||||
\(913\) | −5.67143 | + | 21.1661i | −0.187697 | + | 0.700494i | ||||
\(914\) | 10.0531 | + | 17.4126i | 0.332528 | + | 0.575956i | ||||
\(915\) | −80.7032 | + | 21.6243i | −2.66796 | + | 0.714879i | ||||
\(916\) | − | 7.24404i | − | 0.239350i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −22.9928 | + | 8.60524i | −0.758876 | + | 0.284015i | ||||
\(919\) | 3.95035 | − | 6.84221i | 0.130310 | − | 0.225704i | −0.793486 | − | 0.608589i | \(-0.791736\pi\) |
0.923796 | + | 0.382885i | \(0.125069\pi\) | |||||||
\(920\) | 4.74684 | − | 2.74059i | 0.156499 | − | 0.0903546i | ||||
\(921\) | 3.77202 | − | 14.0774i | 0.124292 | − | 0.463866i | ||||
\(922\) | −3.60125 | + | 6.23754i | −0.118601 | + | 0.205423i | ||||
\(923\) | 11.0756 | + | 11.0756i | 0.364557 | + | 0.364557i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.31412 | − | 6.31412i | 0.207607 | − | 0.207607i | ||||
\(926\) | 2.09481 | + | 1.20944i | 0.0688396 | + | 0.0397446i | ||||
\(927\) | −3.90666 | + | 2.25551i | −0.128312 | + | 0.0740808i | ||||
\(928\) | 14.1464 | + | 3.79052i | 0.464378 | + | 0.124430i | ||||
\(929\) | −2.37065 | − | 8.84740i | −0.0777786 | − | 0.290274i | 0.916070 | − | 0.401018i | \(-0.131343\pi\) |
−0.993849 | + | 0.110744i | \(0.964677\pi\) | |||||||
\(930\) | −58.8031 | − | 58.8031i | −1.92823 | − | 1.92823i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −8.17117 | − | 8.17117i | −0.267656 | − | 0.267656i | ||||
\(933\) | −11.0894 | − | 6.40246i | −0.363050 | − | 0.209607i | ||||
\(934\) | −8.64971 | − | 14.9817i | −0.283027 | − | 0.490217i | ||||
\(935\) | 65.0728 | − | 6.28731i | 2.12811 | − | 0.205617i | ||||
\(936\) | 4.97432 | − | 8.61577i | 0.162591 | − | 0.281615i | ||||
\(937\) | 53.4400i | 1.74581i | 0.487891 | + | 0.872905i | \(0.337766\pi\) | ||||
−0.487891 | + | 0.872905i | \(0.662234\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −63.8202 | −2.08269 | ||||||||
\(940\) | 6.69690 | − | 1.79443i | 0.218429 | − | 0.0585278i | ||||
\(941\) | −48.4370 | − | 12.9787i | −1.57900 | − | 0.423092i | −0.640384 | − | 0.768055i | \(-0.721225\pi\) |
−0.938616 | + | 0.344963i | \(0.887892\pi\) | |||||||
\(942\) | −72.2432 | − | 19.3575i | −2.35381 | − | 0.630702i | ||||
\(943\) | 0.405125 | + | 0.233899i | 0.0131927 | + | 0.00761679i | ||||
\(944\) | 12.9005i | 0.419876i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 34.4907 | − | 34.4907i | 1.12139 | − | 1.12139i | ||||
\(947\) | 14.1735 | − | 3.79776i | 0.460575 | − | 0.123411i | −0.0210682 | − | 0.999778i | \(-0.506707\pi\) |
0.481643 | + | 0.876367i | \(0.340040\pi\) | |||||||
\(948\) | −4.80426 | − | 8.32123i | −0.156035 | − | 0.270261i | ||||
\(949\) | −1.55458 | + | 5.80179i | −0.0504640 | + | 0.188334i | ||||
\(950\) | −55.0622 | − | 31.7902i | −1.78645 | − | 1.03141i | ||||
\(951\) | −33.6993 | −1.09278 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.66197 | −0.151016 | −0.0755080 | − | 0.997145i | \(-0.524058\pi\) | ||||
−0.0755080 | + | 0.997145i | \(0.524058\pi\) | |||||||
\(954\) | −6.32355 | − | 3.65090i | −0.204732 | − | 0.118202i | ||||
\(955\) | −22.1178 | + | 82.5449i | −0.715716 | + | 2.67109i | ||||
\(956\) | 3.44093 | + | 5.95986i | 0.111288 | + | 0.192756i | ||||
\(957\) | 51.3281 | − | 13.7533i | 1.65920 | − | 0.444581i | ||||
\(958\) | −25.8621 | + | 25.8621i | −0.835566 | + | 0.835566i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 36.7773i | 1.18698i | ||||||||
\(961\) | −23.9488 | − | 13.8269i | −0.772543 | − | 0.446028i | ||||
\(962\) | −7.56082 | − | 2.02592i | −0.243771 | − | 0.0653181i | ||||
\(963\) | 12.5135 | + | 3.35298i | 0.403242 | + | 0.108048i | ||||
\(964\) | −6.93841 | + | 1.85914i | −0.223471 | + | 0.0598789i | ||||
\(965\) | 38.1807 | 1.22908 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.2606i | 0.490748i | 0.969428 | + | 0.245374i | \(0.0789108\pi\) | ||||
−0.969428 | + | 0.245374i | \(0.921089\pi\) | |||||||
\(968\) | −12.9902 | + | 22.4996i | −0.417520 | + | 0.723165i | ||||
\(969\) | 33.0521 | − | 40.1221i | 1.06179 | − | 1.28891i | ||||
\(970\) | −11.2895 | − | 19.5540i | −0.362484 | − | 0.627841i | ||||
\(971\) | 16.1056 | + | 9.29856i | 0.516852 | + | 0.298405i | 0.735646 | − | 0.677366i | \(-0.236879\pi\) |
−0.218793 | + | 0.975771i | \(0.570212\pi\) | |||||||
\(972\) | 3.75850 | + | 3.75850i | 0.120554 | + | 0.120554i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 24.4991 | + | 24.4991i | 0.785003 | + | 0.785003i | ||||
\(975\) | 12.4974 | + | 46.6409i | 0.400237 | + | 1.49370i | ||||
\(976\) | −55.1721 | − | 14.7833i | −1.76602 | − | 0.473202i | ||||
\(977\) | 18.8317 | − | 10.8725i | 0.602479 | − | 0.347842i | −0.167537 | − | 0.985866i | \(-0.553581\pi\) |
0.770016 | + | 0.638024i | \(0.220248\pi\) | |||||||
\(978\) | 33.4534 | + | 19.3143i | 1.06972 | + | 0.617605i | ||||
\(979\) | 6.76068 | − | 6.76068i | 0.216072 | − | 0.216072i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.54657 | − | 3.54657i | −0.113233 | − | 0.113233i | ||||
\(982\) | −15.1467 | + | 26.2349i | −0.483352 | + | 0.837190i | ||||
\(983\) | −0.924420 | + | 3.44998i | −0.0294844 | + | 0.110037i | −0.979100 | − | 0.203380i | \(-0.934807\pi\) |
0.949615 | + | 0.313418i | \(0.101474\pi\) | |||||||
\(984\) | −2.94581 | + | 1.70077i | −0.0939091 | + | 0.0542185i | ||||
\(985\) | 38.4165 | − | 66.5393i | 1.22405 | − | 2.12012i | ||||
\(986\) | −12.7081 | − | 33.9556i | −0.404710 | − | 1.08137i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.6436i | 0.338618i | ||||||||
\(989\) | −4.31203 | + | 1.15540i | −0.137114 | + | 0.0367397i | ||||
\(990\) | −14.1904 | − | 24.5786i | −0.451002 | − | 0.781159i | ||||
\(991\) | −0.109827 | + | 0.409880i | −0.00348877 | + | 0.0130203i | −0.967648 | − | 0.252303i | \(-0.918812\pi\) |
0.964160 | + | 0.265323i | \(0.0854787\pi\) | |||||||
\(992\) | −5.19071 | − | 19.3720i | −0.164805 | − | 0.615062i | ||||
\(993\) | 6.80821 | − | 6.80821i | 0.216052 | − | 0.216052i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 17.8210i | − | 0.564963i | ||||||
\(996\) | −1.16619 | − | 4.35227i | −0.0369520 | − | 0.137907i | ||||
\(997\) | 36.1631 | + | 9.68988i | 1.14530 | + | 0.306882i | 0.781079 | − | 0.624432i | \(-0.214669\pi\) |
0.364218 | + | 0.931314i | \(0.381336\pi\) | |||||||
\(998\) | 17.2385 | − | 64.3351i | 0.545676 | − | 2.03649i | ||||
\(999\) | −2.59135 | + | 4.48836i | −0.0819868 | + | 0.142005i |
(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 | 833.2.o.g.30.3 | 40 | ||
7.2 | even | 3 | 119.2.g.a.64.8 | ✓ | 20 | ||
7.3 | odd | 6 | 833.2.o.f.557.8 | 40 | |||
7.4 | even | 3 | inner | 833.2.o.g.557.8 | 40 | ||
7.5 | odd | 6 | 833.2.g.h.540.8 | 20 | |||
7.6 | odd | 2 | 833.2.o.f.30.3 | 40 | |||
17.4 | even | 4 | inner | 833.2.o.g.667.8 | 40 | ||
21.2 | odd | 6 | 1071.2.n.c.64.3 | 20 | |||
119.2 | even | 24 | 2023.2.a.m.1.3 | 10 | |||
119.4 | even | 12 | inner | 833.2.o.g.361.3 | 40 | ||
119.38 | odd | 12 | 833.2.o.f.361.3 | 40 | |||
119.55 | odd | 4 | 833.2.o.f.667.8 | 40 | |||
119.72 | even | 12 | 119.2.g.a.106.3 | yes | 20 | ||
119.89 | odd | 12 | 833.2.g.h.344.3 | 20 | |||
119.100 | even | 24 | 2023.2.a.n.1.3 | 10 | |||
357.191 | odd | 12 | 1071.2.n.c.820.8 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
119.2.g.a.64.8 | ✓ | 20 | 7.2 | even | 3 | ||
119.2.g.a.106.3 | yes | 20 | 119.72 | even | 12 | ||
833.2.g.h.344.3 | 20 | 119.89 | odd | 12 | |||
833.2.g.h.540.8 | 20 | 7.5 | odd | 6 | |||
833.2.o.f.30.3 | 40 | 7.6 | odd | 2 | |||
833.2.o.f.361.3 | 40 | 119.38 | odd | 12 | |||
833.2.o.f.557.8 | 40 | 7.3 | odd | 6 | |||
833.2.o.f.667.8 | 40 | 119.55 | odd | 4 | |||
833.2.o.g.30.3 | 40 | 1.1 | even | 1 | trivial | ||
833.2.o.g.361.3 | 40 | 119.4 | even | 12 | inner | ||
833.2.o.g.557.8 | 40 | 7.4 | even | 3 | inner | ||
833.2.o.g.667.8 | 40 | 17.4 | even | 4 | inner | ||
1071.2.n.c.64.3 | 20 | 21.2 | odd | 6 | |||
1071.2.n.c.820.8 | 20 | 357.191 | odd | 12 | |||
2023.2.a.m.1.3 | 10 | 119.2 | even | 24 | |||
2023.2.a.n.1.3 | 10 | 119.100 | even | 24 |