Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,3,Mod(13,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([0, 19]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.13");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.k (of order \(20\), degree \(8\), 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: | \(2.04360198270\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{20})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 58.10 | ||
Character | \(\chi\) | \(=\) | 75.58 |
Dual form | 75.3.k.a.22.10 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{20}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.93190 | + | 1.49388i | 1.46595 | + | 0.746939i | 0.991099 | − | 0.133128i | \(-0.0425021\pi\) |
0.474850 | + | 0.880066i | \(0.342502\pi\) | |||||||
\(3\) | −1.71073 | − | 0.270952i | −0.570242 | − | 0.0903175i | ||||
\(4\) | 4.01322 | + | 5.52372i | 1.00331 | + | 1.38093i | ||||
\(5\) | −0.890939 | + | 4.91998i | −0.178188 | + | 0.983996i | ||||
\(6\) | −4.61091 | − | 3.35002i | −0.768484 | − | 0.558337i | ||||
\(7\) | 4.34391 | − | 4.34391i | 0.620559 | − | 0.620559i | −0.325115 | − | 0.945674i | \(-0.605403\pi\) |
0.945674 | + | 0.325115i | \(0.105403\pi\) | |||||||
\(8\) | 1.45557 | + | 9.19012i | 0.181946 | + | 1.14876i | ||||
\(9\) | 2.85317 | + | 0.927051i | 0.317019 | + | 0.103006i | ||||
\(10\) | −9.96199 | + | 13.0939i | −0.996199 | + | 1.30939i | ||||
\(11\) | −4.51369 | − | 13.8917i | −0.410336 | − | 1.26288i | −0.916357 | − | 0.400362i | \(-0.868884\pi\) |
0.506021 | − | 0.862521i | \(-0.331116\pi\) | |||||||
\(12\) | −5.36886 | − | 10.5370i | −0.447405 | − | 0.878081i | ||||
\(13\) | 6.86423 | − | 3.49750i | 0.528018 | − | 0.269039i | −0.169595 | − | 0.985514i | \(-0.554246\pi\) |
0.697612 | + | 0.716475i | \(0.254246\pi\) | |||||||
\(14\) | 19.2252 | − | 6.24664i | 1.37323 | − | 0.446189i | ||||
\(15\) | 2.85723 | − | 8.17534i | 0.190482 | − | 0.545023i | ||||
\(16\) | −1.02182 | + | 3.14483i | −0.0638636 | + | 0.196552i | ||||
\(17\) | −25.6357 | + | 4.06030i | −1.50798 | + | 0.238841i | −0.855039 | − | 0.518564i | \(-0.826467\pi\) |
−0.652945 | + | 0.757405i | \(0.726467\pi\) | |||||||
\(18\) | 6.98030 | + | 6.98030i | 0.387795 | + | 0.387795i | ||||
\(19\) | −1.24222 | + | 1.70977i | −0.0653802 | + | 0.0899881i | −0.840455 | − | 0.541881i | \(-0.817712\pi\) |
0.775075 | + | 0.631870i | \(0.217712\pi\) | |||||||
\(20\) | −30.7522 | + | 14.8237i | −1.53761 | + | 0.741184i | ||||
\(21\) | −8.60824 | + | 6.25425i | −0.409916 | + | 0.297822i | ||||
\(22\) | 7.51883 | − | 47.4720i | 0.341765 | − | 2.15782i | ||||
\(23\) | −2.15443 | + | 4.22830i | −0.0936708 | + | 0.183839i | −0.933088 | − | 0.359649i | \(-0.882897\pi\) |
0.839417 | + | 0.543488i | \(0.182897\pi\) | |||||||
\(24\) | − | 16.1162i | − | 0.671507i | ||||||
\(25\) | −23.4125 | − | 8.76681i | −0.936498 | − | 0.350672i | ||||
\(26\) | 25.3501 | 0.975003 | ||||||||
\(27\) | −4.62981 | − | 2.35900i | −0.171474 | − | 0.0873705i | ||||
\(28\) | 41.4277 | + | 6.56150i | 1.47956 | + | 0.234339i | ||||
\(29\) | 32.6254 | + | 44.9050i | 1.12501 | + | 1.54845i | 0.797208 | + | 0.603704i | \(0.206309\pi\) |
0.327806 | + | 0.944745i | \(0.393691\pi\) | |||||||
\(30\) | 20.5901 | − | 19.7009i | 0.686336 | − | 0.656697i | ||||
\(31\) | 27.1558 | + | 19.7298i | 0.875993 | + | 0.636446i | 0.932188 | − | 0.361974i | \(-0.117897\pi\) |
−0.0561957 | + | 0.998420i | \(0.517897\pi\) | |||||||
\(32\) | 18.6237 | − | 18.6237i | 0.581992 | − | 0.581992i | ||||
\(33\) | 3.95770 | + | 24.9879i | 0.119930 | + | 0.757210i | ||||
\(34\) | −81.2269 | − | 26.3922i | −2.38903 | − | 0.776242i | ||||
\(35\) | 17.5018 | + | 25.2421i | 0.500052 | + | 0.721204i | ||||
\(36\) | 6.32962 | + | 19.4806i | 0.175823 | + | 0.541127i | ||||
\(37\) | −18.7363 | − | 36.7721i | −0.506388 | − | 0.993842i | −0.992763 | − | 0.120092i | \(-0.961681\pi\) |
0.486375 | − | 0.873750i | \(-0.338319\pi\) | |||||||
\(38\) | −6.19627 | + | 3.15716i | −0.163060 | + | 0.0830831i | ||||
\(39\) | −12.6905 | + | 4.12339i | −0.325397 | + | 0.105728i | ||||
\(40\) | −46.5120 | − | 1.02645i | −1.16280 | − | 0.0256613i | ||||
\(41\) | −1.20677 | + | 3.71404i | −0.0294333 | + | 0.0905864i | −0.964694 | − | 0.263373i | \(-0.915165\pi\) |
0.935261 | + | 0.353960i | \(0.115165\pi\) | |||||||
\(42\) | −34.5816 | + | 5.47718i | −0.823371 | + | 0.130409i | ||||
\(43\) | −32.8976 | − | 32.8976i | −0.765060 | − | 0.765060i | 0.212172 | − | 0.977232i | \(-0.431946\pi\) |
−0.977232 | + | 0.212172i | \(0.931946\pi\) | |||||||
\(44\) | 58.6196 | − | 80.6829i | 1.33226 | − | 1.83370i | ||||
\(45\) | −7.10308 | + | 13.2116i | −0.157846 | + | 0.293591i | ||||
\(46\) | −12.6331 | + | 9.17851i | −0.274633 | + | 0.199533i | ||||
\(47\) | −12.8776 | + | 81.3060i | −0.273991 | + | 1.72991i | 0.339846 | + | 0.940481i | \(0.389625\pi\) |
−0.613837 | + | 0.789433i | \(0.710375\pi\) | |||||||
\(48\) | 2.60015 | − | 5.10308i | 0.0541698 | − | 0.106314i | ||||
\(49\) | 11.2608i | 0.229813i | ||||||||
\(50\) | −55.5464 | − | 60.6787i | −1.11093 | − | 1.21357i | ||||
\(51\) | 44.9558 | 0.881487 | ||||||||
\(52\) | 46.8669 | + | 23.8799i | 0.901287 | + | 0.459229i | ||||
\(53\) | −81.1884 | − | 12.8590i | −1.53186 | − | 0.242622i | −0.667159 | − | 0.744916i | \(-0.732490\pi\) |
−0.864697 | + | 0.502293i | \(0.832490\pi\) | |||||||
\(54\) | −10.0501 | − | 13.8327i | −0.186112 | − | 0.256161i | ||||
\(55\) | 72.3684 | − | 9.83061i | 1.31579 | − | 0.178738i | ||||
\(56\) | 46.2440 | + | 33.5982i | 0.825785 | + | 0.599968i | ||||
\(57\) | 2.58837 | − | 2.58837i | 0.0454101 | − | 0.0454101i | ||||
\(58\) | 28.5718 | + | 180.395i | 0.492618 | + | 3.11026i | ||||
\(59\) | −10.7101 | − | 3.47991i | −0.181526 | − | 0.0589815i | 0.216843 | − | 0.976206i | \(-0.430424\pi\) |
−0.398370 | + | 0.917225i | \(0.630424\pi\) | |||||||
\(60\) | 56.6250 | − | 17.0269i | 0.943751 | − | 0.283781i | ||||
\(61\) | −9.84864 | − | 30.3110i | −0.161453 | − | 0.496902i | 0.837304 | − | 0.546737i | \(-0.184130\pi\) |
−0.998757 | + | 0.0498356i | \(0.984130\pi\) | |||||||
\(62\) | 50.1440 | + | 98.4132i | 0.808775 | + | 1.58731i | ||||
\(63\) | 16.4210 | − | 8.36689i | 0.260650 | − | 0.132808i | ||||
\(64\) | 95.0038 | − | 30.8686i | 1.48443 | − | 0.482322i | ||||
\(65\) | 11.0920 | + | 36.8880i | 0.170647 | + | 0.567507i | ||||
\(66\) | −25.7253 | + | 79.1744i | −0.389777 | + | 1.19961i | ||||
\(67\) | −0.351533 | + | 0.0556774i | −0.00524677 | + | 0.000831006i | −0.159057 | − | 0.987269i | \(-0.550845\pi\) |
0.153811 | + | 0.988100i | \(0.450845\pi\) | |||||||
\(68\) | −125.310 | − | 125.310i | −1.84279 | − | 1.84279i | ||||
\(69\) | 4.83131 | − | 6.64972i | 0.0700189 | − | 0.0963728i | ||||
\(70\) | 13.6049 | + | 100.153i | 0.194356 | + | 1.43076i | ||||
\(71\) | 88.5525 | − | 64.3371i | 1.24722 | − | 0.906157i | 0.249161 | − | 0.968462i | \(-0.419845\pi\) |
0.998057 | + | 0.0623051i | \(0.0198452\pi\) | |||||||
\(72\) | −4.36672 | + | 27.5704i | −0.0606488 | + | 0.382922i | ||||
\(73\) | −20.1163 | + | 39.4805i | −0.275566 | + | 0.540828i | −0.986764 | − | 0.162163i | \(-0.948153\pi\) |
0.711198 | + | 0.702992i | \(0.248153\pi\) | |||||||
\(74\) | − | 135.802i | − | 1.83516i | ||||||
\(75\) | 37.6769 | + | 21.3413i | 0.502359 | + | 0.284550i | ||||
\(76\) | −14.4296 | −0.189864 | ||||||||
\(77\) | −79.9515 | − | 40.7373i | −1.03833 | − | 0.529056i | ||||
\(78\) | −43.3670 | − | 6.86866i | −0.555988 | − | 0.0880598i | ||||
\(79\) | 33.1447 | + | 45.6197i | 0.419553 | + | 0.577465i | 0.965516 | − | 0.260344i | \(-0.0838361\pi\) |
−0.545963 | + | 0.837809i | \(0.683836\pi\) | |||||||
\(80\) | −14.5621 | − | 7.82918i | −0.182027 | − | 0.0978648i | ||||
\(81\) | 7.28115 | + | 5.29007i | 0.0898908 | + | 0.0653095i | ||||
\(82\) | −9.08644 | + | 9.08644i | −0.110810 | + | 0.110810i | ||||
\(83\) | −2.71085 | − | 17.1156i | −0.0326608 | − | 0.206212i | 0.965961 | − | 0.258686i | \(-0.0832895\pi\) |
−0.998622 | + | 0.0524736i | \(0.983289\pi\) | |||||||
\(84\) | −69.0935 | − | 22.4499i | −0.822542 | − | 0.267260i | ||||
\(85\) | 2.86327 | − | 129.745i | 0.0336855 | − | 1.52641i | ||||
\(86\) | −47.3074 | − | 145.597i | −0.550087 | − | 1.69299i | ||||
\(87\) | −43.6460 | − | 85.6602i | −0.501679 | − | 0.984600i | ||||
\(88\) | 121.097 | − | 61.7018i | 1.37610 | − | 0.701156i | ||||
\(89\) | −85.2857 | + | 27.7110i | −0.958267 | + | 0.311360i | −0.746070 | − | 0.665867i | \(-0.768062\pi\) |
−0.212196 | + | 0.977227i | \(0.568062\pi\) | |||||||
\(90\) | −40.5620 | + | 28.1239i | −0.450689 | + | 0.312488i | ||||
\(91\) | 14.6248 | − | 45.0105i | 0.160712 | − | 0.494621i | ||||
\(92\) | −32.0022 | + | 5.06865i | −0.347850 | + | 0.0550940i | ||||
\(93\) | −41.1102 | − | 41.1102i | −0.442046 | − | 0.442046i | ||||
\(94\) | −159.217 | + | 219.143i | −1.69380 | + | 2.33131i | ||||
\(95\) | −7.30531 | − | 7.63503i | −0.0768981 | − | 0.0803687i | ||||
\(96\) | −36.9063 | + | 26.8140i | −0.384440 | + | 0.279312i | ||||
\(97\) | 1.37908 | − | 8.70714i | 0.0142173 | − | 0.0897643i | −0.979559 | − | 0.201155i | \(-0.935531\pi\) |
0.993777 | + | 0.111391i | \(0.0355305\pi\) | |||||||
\(98\) | −16.8223 | + | 33.0156i | −0.171656 | + | 0.336894i | ||||
\(99\) | − | 43.8198i | − | 0.442625i | ||||||
\(100\) | −45.5339 | − | 164.507i | −0.455339 | − | 1.64507i | ||||
\(101\) | 4.54639 | 0.0450138 | 0.0225069 | − | 0.999747i | \(-0.492835\pi\) | ||||
0.0225069 | + | 0.999747i | \(0.492835\pi\) | |||||||
\(102\) | 131.806 | + | 67.1585i | 1.29222 | + | 0.658417i | ||||
\(103\) | 98.1209 | + | 15.5408i | 0.952630 | + | 0.150882i | 0.613357 | − | 0.789806i | \(-0.289819\pi\) |
0.339273 | + | 0.940688i | \(0.389819\pi\) | |||||||
\(104\) | 42.1338 | + | 57.9922i | 0.405133 | + | 0.557618i | ||||
\(105\) | −23.1014 | − | 47.9246i | −0.220013 | − | 0.456424i | ||||
\(106\) | −218.826 | − | 158.987i | −2.06440 | − | 1.49987i | ||||
\(107\) | 58.0204 | − | 58.0204i | 0.542247 | − | 0.542247i | −0.381940 | − | 0.924187i | \(-0.624744\pi\) |
0.924187 | + | 0.381940i | \(0.124744\pi\) | |||||||
\(108\) | −5.54994 | − | 35.0410i | −0.0513884 | − | 0.324453i | ||||
\(109\) | 77.8317 | + | 25.2890i | 0.714052 | + | 0.232010i | 0.643442 | − | 0.765494i | \(-0.277506\pi\) |
0.0706096 | + | 0.997504i | \(0.477506\pi\) | |||||||
\(110\) | 226.863 | + | 79.2872i | 2.06239 | + | 0.720793i | ||||
\(111\) | 22.0893 | + | 67.9837i | 0.199002 | + | 0.612466i | ||||
\(112\) | 9.22219 | + | 18.0996i | 0.0823410 | + | 0.161603i | ||||
\(113\) | 168.661 | − | 85.9369i | 1.49257 | − | 0.760504i | 0.498262 | − | 0.867027i | \(-0.333972\pi\) |
0.994310 | + | 0.106523i | \(0.0339718\pi\) | |||||||
\(114\) | 11.4556 | − | 3.72214i | 0.100487 | − | 0.0326503i | ||||
\(115\) | −18.8837 | − | 14.3669i | −0.164206 | − | 0.124930i | ||||
\(116\) | −117.110 | + | 360.428i | −1.00957 | + | 3.10713i | ||||
\(117\) | 22.8272 | − | 3.61547i | 0.195104 | − | 0.0309015i | ||||
\(118\) | −26.2022 | − | 26.2022i | −0.222053 | − | 0.222053i | ||||
\(119\) | −93.7218 | + | 128.997i | −0.787578 | + | 1.08401i | ||||
\(120\) | 79.2913 | + | 14.3585i | 0.660761 | + | 0.119654i | ||||
\(121\) | −74.7153 | + | 54.2839i | −0.617482 | + | 0.448627i | ||||
\(122\) | 16.4057 | − | 103.581i | 0.134473 | − | 0.849028i | ||||
\(123\) | 3.07077 | − | 6.02673i | 0.0249656 | − | 0.0489978i | ||||
\(124\) | 229.181i | 1.84823i | ||||||||
\(125\) | 63.9916 | − | 107.378i | 0.511933 | − | 0.859025i | ||||
\(126\) | 60.6437 | 0.481299 | ||||||||
\(127\) | −99.6529 | − | 50.7757i | −0.784668 | − | 0.399808i | 0.0152756 | − | 0.999883i | \(-0.495137\pi\) |
−0.799944 | + | 0.600075i | \(0.795137\pi\) | |||||||
\(128\) | 220.601 | + | 34.9397i | 1.72344 | + | 0.272967i | ||||
\(129\) | 47.3651 | + | 65.1924i | 0.367171 | + | 0.505368i | ||||
\(130\) | −22.5854 | + | 124.722i | −0.173734 | + | 0.959399i | ||||
\(131\) | −84.3598 | − | 61.2910i | −0.643968 | − | 0.467870i | 0.217243 | − | 0.976118i | \(-0.430294\pi\) |
−0.861211 | + | 0.508247i | \(0.830294\pi\) | |||||||
\(132\) | −122.143 | + | 122.143i | −0.925328 | + | 0.925328i | ||||
\(133\) | 2.03100 | + | 12.8232i | 0.0152707 | + | 0.0964152i | ||||
\(134\) | −1.11384 | − | 0.361907i | −0.00831221 | − | 0.00270080i | ||||
\(135\) | 15.7311 | − | 20.6768i | 0.116527 | − | 0.153162i | ||||
\(136\) | −74.6293 | − | 229.685i | −0.548745 | − | 1.68886i | ||||
\(137\) | 69.3960 | + | 136.197i | 0.506540 | + | 0.994141i | 0.992738 | + | 0.120293i | \(0.0383833\pi\) |
−0.486198 | + | 0.873849i | \(0.661617\pi\) | |||||||
\(138\) | 24.0988 | − | 12.2789i | 0.174629 | − | 0.0889778i | ||||
\(139\) | 149.736 | − | 48.6523i | 1.07724 | − | 0.350016i | 0.283937 | − | 0.958843i | \(-0.408359\pi\) |
0.793303 | + | 0.608827i | \(0.208359\pi\) | |||||||
\(140\) | −69.1920 | + | 197.977i | −0.494228 | + | 1.41412i | ||||
\(141\) | 44.0601 | − | 135.603i | 0.312483 | − | 0.961724i | ||||
\(142\) | 355.739 | − | 56.3435i | 2.50520 | − | 0.396785i | ||||
\(143\) | −79.5693 | − | 79.5693i | −0.556429 | − | 0.556429i | ||||
\(144\) | −5.83084 | + | 8.02546i | −0.0404920 | + | 0.0557324i | ||||
\(145\) | −249.999 | + | 120.509i | −1.72413 | + | 0.831095i | ||||
\(146\) | −117.958 | + | 85.7015i | −0.807931 | + | 0.586996i | ||||
\(147\) | 3.05115 | − | 19.2642i | 0.0207561 | − | 0.131049i | ||||
\(148\) | 127.926 | − | 251.069i | 0.864365 | − | 1.69641i | ||||
\(149\) | 80.4685i | 0.540057i | 0.962852 | + | 0.270028i | \(0.0870331\pi\) | ||||
−0.962852 | + | 0.270028i | \(0.912967\pi\) | |||||||
\(150\) | 78.5837 | + | 118.855i | 0.523891 | + | 0.792368i | ||||
\(151\) | 187.435 | 1.24129 | 0.620647 | − | 0.784090i | \(-0.286870\pi\) | ||||
0.620647 | + | 0.784090i | \(0.286870\pi\) | |||||||
\(152\) | −17.5212 | − | 8.92749i | −0.115271 | − | 0.0587335i | ||||
\(153\) | −76.9072 | − | 12.1809i | −0.502661 | − | 0.0796137i | ||||
\(154\) | −173.553 | − | 238.875i | −1.12697 | − | 1.55114i | ||||
\(155\) | −121.265 | + | 116.028i | −0.782352 | + | 0.748567i | ||||
\(156\) | −73.7061 | − | 53.5506i | −0.472475 | − | 0.343273i | ||||
\(157\) | −90.0864 | + | 90.0864i | −0.573798 | + | 0.573798i | −0.933188 | − | 0.359389i | \(-0.882985\pi\) |
0.359389 | + | 0.933188i | \(0.382985\pi\) | |||||||
\(158\) | 29.0266 | + | 183.267i | 0.183712 | + | 1.15991i | ||||
\(159\) | 135.407 | + | 43.9964i | 0.851616 | + | 0.276707i | ||||
\(160\) | 75.0358 | + | 108.221i | 0.468974 | + | 0.676382i | ||||
\(161\) | 9.00873 | + | 27.7260i | 0.0559549 | + | 0.172211i | ||||
\(162\) | 13.4449 | + | 26.3871i | 0.0829932 | + | 0.162883i | ||||
\(163\) | −30.5160 | + | 15.5487i | −0.187215 | + | 0.0953908i | −0.545086 | − | 0.838380i | \(-0.683503\pi\) |
0.357871 | + | 0.933771i | \(0.383503\pi\) | |||||||
\(164\) | −25.3584 | + | 8.23943i | −0.154624 | + | 0.0502404i | ||||
\(165\) | −126.466 | − | 2.79092i | −0.766462 | − | 0.0169147i | ||||
\(166\) | 17.6207 | − | 54.2310i | 0.106149 | − | 0.326693i | ||||
\(167\) | −58.2426 | + | 9.22473i | −0.348758 | + | 0.0552379i | −0.328356 | − | 0.944554i | \(-0.606495\pi\) |
−0.0204021 | + | 0.999792i | \(0.506495\pi\) | |||||||
\(168\) | −70.0072 | − | 70.0072i | −0.416710 | − | 0.416710i | ||||
\(169\) | −64.4505 | + | 88.7086i | −0.381364 | + | 0.524903i | ||||
\(170\) | 202.218 | − | 376.121i | 1.18951 | − | 2.21248i | ||||
\(171\) | −5.12932 | + | 3.72667i | −0.0299960 | + | 0.0217934i | ||||
\(172\) | 49.6919 | − | 313.742i | 0.288907 | − | 1.82408i | ||||
\(173\) | 35.3231 | − | 69.3255i | 0.204180 | − | 0.400726i | −0.766096 | − | 0.642726i | \(-0.777803\pi\) |
0.970276 | + | 0.242000i | \(0.0778035\pi\) | |||||||
\(174\) | − | 316.349i | − | 1.81810i | ||||||
\(175\) | −139.784 | + | 63.6194i | −0.798765 | + | 0.363539i | ||||
\(176\) | 48.2993 | 0.274428 | ||||||||
\(177\) | 17.3791 | + | 8.85509i | 0.0981869 | + | 0.0500287i | ||||
\(178\) | −291.446 | − | 46.1605i | −1.63734 | − | 0.259329i | ||||
\(179\) | −89.6932 | − | 123.452i | −0.501080 | − | 0.689677i | 0.481304 | − | 0.876554i | \(-0.340163\pi\) |
−0.982383 | + | 0.186877i | \(0.940163\pi\) | |||||||
\(180\) | −101.483 | + | 13.7856i | −0.563797 | + | 0.0765868i | ||||
\(181\) | −26.4190 | − | 19.1945i | −0.145961 | − | 0.106047i | 0.512408 | − | 0.858742i | \(-0.328753\pi\) |
−0.658369 | + | 0.752695i | \(0.728753\pi\) | |||||||
\(182\) | 110.119 | − | 110.119i | 0.605047 | − | 0.605047i | ||||
\(183\) | 8.63549 | + | 54.5223i | 0.0471885 | + | 0.297936i | ||||
\(184\) | −41.9945 | − | 13.6449i | −0.228231 | − | 0.0741568i | ||||
\(185\) | 197.611 | − | 59.4207i | 1.06817 | − | 0.321193i | ||||
\(186\) | −59.1174 | − | 181.945i | −0.317836 | − | 0.978198i | ||||
\(187\) | 172.116 | + | 337.797i | 0.920408 | + | 1.80640i | ||||
\(188\) | −500.792 | + | 255.166i | −2.66379 | + | 1.35727i | ||||
\(189\) | −30.3588 | + | 9.86417i | −0.160628 | + | 0.0521914i | ||||
\(190\) | −10.0127 | − | 33.2984i | −0.0526982 | − | 0.175255i | ||||
\(191\) | 15.5033 | − | 47.7143i | 0.0811692 | − | 0.249813i | −0.902234 | − | 0.431247i | \(-0.858074\pi\) |
0.983403 | + | 0.181434i | \(0.0580738\pi\) | |||||||
\(192\) | −170.889 | + | 27.0662i | −0.890049 | + | 0.140970i | ||||
\(193\) | 49.2763 | + | 49.2763i | 0.255318 | + | 0.255318i | 0.823147 | − | 0.567829i | \(-0.192216\pi\) |
−0.567829 | + | 0.823147i | \(0.692216\pi\) | |||||||
\(194\) | 17.0507 | − | 23.4683i | 0.0878902 | − | 0.120971i | ||||
\(195\) | −8.98054 | − | 66.1106i | −0.0460541 | − | 0.339029i | ||||
\(196\) | −62.2017 | + | 45.1922i | −0.317356 | + | 0.230572i | ||||
\(197\) | −54.5847 | + | 344.634i | −0.277080 | + | 1.74941i | 0.320174 | + | 0.947359i | \(0.396259\pi\) |
−0.597253 | + | 0.802053i | \(0.703741\pi\) | |||||||
\(198\) | 65.4615 | − | 128.475i | 0.330613 | − | 0.648865i | ||||
\(199\) | − | 39.9002i | − | 0.200504i | −0.994962 | − | 0.100252i | \(-0.968035\pi\) | ||
0.994962 | − | 0.100252i | \(-0.0319648\pi\) | |||||||
\(200\) | 46.4895 | − | 227.924i | 0.232448 | − | 1.13962i | ||||
\(201\) | 0.616463 | 0.00306698 | ||||||||
\(202\) | 13.3296 | + | 6.79175i | 0.0659879 | + | 0.0336225i | ||||
\(203\) | 336.786 | + | 53.3416i | 1.65904 | + | 0.262766i | ||||
\(204\) | 180.418 | + | 248.324i | 0.884401 | + | 1.21727i | ||||
\(205\) | −17.1979 | − | 9.24625i | −0.0838920 | − | 0.0451037i | ||||
\(206\) | 264.464 | + | 192.145i | 1.28381 | + | 0.932741i | ||||
\(207\) | −10.0668 | + | 10.0668i | −0.0486319 | + | 0.0486319i | ||||
\(208\) | 3.98506 | + | 25.1607i | 0.0191589 | + | 0.120965i | ||||
\(209\) | 29.3587 | + | 9.53923i | 0.140472 | + | 0.0456422i | ||||
\(210\) | 3.86244 | − | 175.021i | 0.0183926 | − | 0.833431i | ||||
\(211\) | 59.1092 | + | 181.919i | 0.280138 | + | 0.862177i | 0.987814 | + | 0.155640i | \(0.0497439\pi\) |
−0.707676 | + | 0.706538i | \(0.750256\pi\) | |||||||
\(212\) | −254.797 | − | 500.068i | −1.20187 | − | 2.35881i | ||||
\(213\) | −168.921 | + | 86.0697i | −0.793058 | + | 0.404083i | ||||
\(214\) | 256.785 | − | 83.4346i | 1.19993 | − | 0.389882i | ||||
\(215\) | 191.165 | − | 132.546i | 0.889141 | − | 0.616492i | ||||
\(216\) | 14.9405 | − | 45.9822i | 0.0691690 | − | 0.212880i | ||||
\(217\) | 203.667 | − | 32.2577i | 0.938557 | − | 0.148653i | ||||
\(218\) | 190.416 | + | 190.416i | 0.873467 | + | 0.873467i | ||||
\(219\) | 45.1108 | − | 62.0897i | 0.205985 | − | 0.283515i | ||||
\(220\) | 344.732 | + | 360.291i | 1.56696 | + | 1.63769i | ||||
\(221\) | −161.769 | + | 117.532i | −0.731985 | + | 0.531818i | ||||
\(222\) | −36.7959 | + | 232.320i | −0.165747 | + | 1.04649i | ||||
\(223\) | 82.3253 | − | 161.572i | 0.369172 | − | 0.724540i | −0.629449 | − | 0.777042i | \(-0.716719\pi\) |
0.998621 | + | 0.0525014i | \(0.0167194\pi\) | |||||||
\(224\) | − | 161.800i | − | 0.722320i | ||||||
\(225\) | −58.6724 | − | 46.7177i | −0.260766 | − | 0.207634i | ||||
\(226\) | 622.875 | 2.75608 | ||||||||
\(227\) | −266.514 | − | 135.796i | −1.17407 | − | 0.598220i | −0.245509 | − | 0.969394i | \(-0.578955\pi\) |
−0.928563 | + | 0.371174i | \(0.878955\pi\) | |||||||
\(228\) | 24.6852 | + | 3.90975i | 0.108268 | + | 0.0171480i | ||||
\(229\) | −128.483 | − | 176.841i | −0.561060 | − | 0.772232i | 0.430401 | − | 0.902638i | \(-0.358372\pi\) |
−0.991461 | + | 0.130405i | \(0.958372\pi\) | |||||||
\(230\) | −33.9027 | − | 70.3323i | −0.147403 | − | 0.305792i | ||||
\(231\) | 125.737 | + | 91.3535i | 0.544317 | + | 0.395470i | ||||
\(232\) | −365.194 | + | 365.194i | −1.57411 | + | 1.57411i | ||||
\(233\) | −28.5917 | − | 180.521i | −0.122711 | − | 0.774767i | −0.969905 | − | 0.243484i | \(-0.921710\pi\) |
0.847194 | − | 0.531284i | \(-0.178290\pi\) | |||||||
\(234\) | 72.3280 | + | 23.5008i | 0.309094 | + | 0.100431i | ||||
\(235\) | −388.551 | − | 135.796i | −1.65341 | − | 0.577856i | ||||
\(236\) | −23.7598 | − | 73.1250i | −0.100677 | − | 0.309852i | ||||
\(237\) | −44.3407 | − | 87.0235i | −0.187092 | − | 0.367188i | ||||
\(238\) | −467.488 | + | 238.197i | −1.96424 | + | 1.00083i | ||||
\(239\) | −434.275 | + | 141.105i | −1.81705 | + | 0.590396i | −0.817149 | + | 0.576427i | \(0.804447\pi\) |
−0.999902 | + | 0.0139688i | \(0.995553\pi\) | |||||||
\(240\) | 22.7905 | + | 17.3392i | 0.0949605 | + | 0.0722468i | ||||
\(241\) | −123.592 | + | 380.378i | −0.512831 | + | 1.57833i | 0.274363 | + | 0.961626i | \(0.411533\pi\) |
−0.787194 | + | 0.616706i | \(0.788467\pi\) | |||||||
\(242\) | −300.151 | + | 47.5393i | −1.24029 | + | 0.196443i | ||||
\(243\) | −11.0227 | − | 11.0227i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 127.905 | − | 176.046i | 0.524200 | − | 0.721499i | ||||
\(245\) | −55.4031 | − | 10.0327i | −0.226135 | − | 0.0409499i | ||||
\(246\) | 18.0064 | − | 13.0824i | 0.0731967 | − | 0.0531805i | ||||
\(247\) | −2.54698 | + | 16.0810i | −0.0103116 | + | 0.0651051i | ||||
\(248\) | −141.792 | + | 278.283i | −0.571743 | + | 1.12211i | ||||
\(249\) | 30.0147i | 0.120541i | ||||||||
\(250\) | 348.027 | − | 219.226i | 1.39211 | − | 0.876905i | ||||
\(251\) | 153.360 | 0.610995 | 0.305497 | − | 0.952193i | \(-0.401177\pi\) | ||||
0.305497 | + | 0.952193i | \(0.401177\pi\) | |||||||
\(252\) | 112.117 | + | 57.1266i | 0.444910 | + | 0.226693i | ||||
\(253\) | 68.4628 | + | 10.8434i | 0.270604 | + | 0.0428595i | ||||
\(254\) | −216.319 | − | 297.738i | −0.851652 | − | 1.17220i | ||||
\(255\) | −40.0529 | + | 221.182i | −0.157070 | + | 0.867380i | ||||
\(256\) | 271.323 | + | 197.128i | 1.05986 | + | 0.770030i | ||||
\(257\) | 208.413 | − | 208.413i | 0.810947 | − | 0.810947i | −0.173829 | − | 0.984776i | \(-0.555614\pi\) |
0.984776 | + | 0.173829i | \(0.0556139\pi\) | |||||||
\(258\) | 41.4801 | + | 261.895i | 0.160776 | + | 1.01510i | ||||
\(259\) | −241.124 | − | 78.3459i | −0.930981 | − | 0.302494i | ||||
\(260\) | −159.244 | + | 209.309i | −0.612478 | + | 0.805034i | ||||
\(261\) | 51.4566 | + | 158.367i | 0.197152 | + | 0.606770i | ||||
\(262\) | −155.773 | − | 305.722i | −0.594554 | − | 1.16688i | ||||
\(263\) | −9.36797 | + | 4.77322i | −0.0356197 | + | 0.0181491i | −0.471710 | − | 0.881754i | \(-0.656363\pi\) |
0.436090 | + | 0.899903i | \(0.356363\pi\) | |||||||
\(264\) | −223.881 | + | 72.7434i | −0.848035 | + | 0.275543i | ||||
\(265\) | 135.600 | − | 387.989i | 0.511698 | − | 1.46411i | ||||
\(266\) | −13.2016 | + | 40.6305i | −0.0496302 | + | 0.152746i | ||||
\(267\) | 153.409 | − | 24.2976i | 0.574565 | − | 0.0910022i | ||||
\(268\) | −1.71833 | − | 1.71833i | −0.00641167 | − | 0.00641167i | ||||
\(269\) | 270.816 | − | 372.747i | 1.00675 | − | 1.38568i | 0.0856627 | − | 0.996324i | \(-0.472699\pi\) |
0.921089 | − | 0.389351i | \(-0.127301\pi\) | |||||||
\(270\) | 77.0107 | − | 37.1220i | 0.285225 | − | 0.137489i | ||||
\(271\) | 120.422 | − | 87.4918i | 0.444362 | − | 0.322848i | −0.343004 | − | 0.939334i | \(-0.611444\pi\) |
0.787366 | + | 0.616486i | \(0.211444\pi\) | |||||||
\(272\) | 13.4261 | − | 84.7689i | 0.0493606 | − | 0.311651i | ||||
\(273\) | −37.2147 | + | 73.0380i | −0.136318 | + | 0.267538i | ||||
\(274\) | 502.986i | 1.83572i | ||||||||
\(275\) | −16.1095 | + | 364.810i | −0.0585798 | + | 1.32658i | ||||
\(276\) | 56.1203 | 0.203335 | ||||||||
\(277\) | −229.696 | − | 117.036i | −0.829229 | − | 0.422513i | −0.0127710 | − | 0.999918i | \(-0.504065\pi\) |
−0.816458 | + | 0.577405i | \(0.804065\pi\) | |||||||
\(278\) | 511.692 | + | 81.0441i | 1.84062 | + | 0.291526i | ||||
\(279\) | 59.1895 | + | 81.4673i | 0.212149 | + | 0.291998i | ||||
\(280\) | −206.503 | + | 197.586i | −0.737511 | + | 0.705663i | ||||
\(281\) | −64.5890 | − | 46.9267i | −0.229854 | − | 0.166999i | 0.466897 | − | 0.884312i | \(-0.345372\pi\) |
−0.696751 | + | 0.717313i | \(0.745372\pi\) | |||||||
\(282\) | 331.754 | − | 331.754i | 1.17643 | − | 1.17643i | ||||
\(283\) | 5.52224 | + | 34.8661i | 0.0195132 | + | 0.123202i | 0.995522 | − | 0.0945291i | \(-0.0301345\pi\) |
−0.976009 | + | 0.217731i | \(0.930135\pi\) | |||||||
\(284\) | 710.761 | + | 230.940i | 2.50268 | + | 0.813170i | ||||
\(285\) | 10.4287 | + | 15.0408i | 0.0365918 | + | 0.0527749i | ||||
\(286\) | −114.422 | − | 352.156i | −0.400078 | − | 1.23131i | ||||
\(287\) | 10.8914 | + | 21.3756i | 0.0379491 | + | 0.0744793i | ||||
\(288\) | 70.4018 | − | 35.8715i | 0.244451 | − | 0.124554i | ||||
\(289\) | 365.849 | − | 118.871i | 1.26591 | − | 0.411320i | ||||
\(290\) | −912.998 | − | 20.1485i | −3.14827 | − | 0.0694775i | ||||
\(291\) | −4.71844 | + | 14.5219i | −0.0162146 | + | 0.0499033i | ||||
\(292\) | −298.810 | + | 47.3269i | −1.02332 | + | 0.162078i | ||||
\(293\) | −16.7371 | − | 16.7371i | −0.0571231 | − | 0.0571231i | 0.677968 | − | 0.735091i | \(-0.262861\pi\) |
−0.735091 | + | 0.677968i | \(0.762861\pi\) | |||||||
\(294\) | 37.7240 | − | 51.9226i | 0.128313 | − | 0.176608i | ||||
\(295\) | 26.6631 | − | 49.5929i | 0.0903834 | − | 0.168112i | ||||
\(296\) | 310.668 | − | 225.714i | 1.04955 | − | 0.762546i | ||||
\(297\) | −11.8731 | + | 74.9638i | −0.0399768 | + | 0.252403i | ||||
\(298\) | −120.210 | + | 235.925i | −0.403389 | + | 0.791696i | ||||
\(299\) | 36.5592i | 0.122271i | ||||||||
\(300\) | 33.3224 | + | 293.764i | 0.111075 | + | 0.979214i | ||||
\(301\) | −285.809 | −0.949530 | ||||||||
\(302\) | 549.541 | + | 280.005i | 1.81967 | + | 0.927170i | ||||
\(303\) | −7.77763 | − | 1.23186i | −0.0256688 | − | 0.00406553i | ||||
\(304\) | −4.10763 | − | 5.65367i | −0.0135119 | − | 0.0185976i | ||||
\(305\) | 157.904 | − | 21.4499i | 0.517718 | − | 0.0703275i | ||||
\(306\) | −207.287 | − | 150.603i | −0.677409 | − | 0.492167i | ||||
\(307\) | 14.0410 | − | 14.0410i | 0.0457363 | − | 0.0457363i | −0.683869 | − | 0.729605i | \(-0.739704\pi\) |
0.729605 | + | 0.683869i | \(0.239704\pi\) | |||||||
\(308\) | −95.8413 | − | 605.118i | −0.311173 | − | 1.96467i | ||||
\(309\) | −163.647 | − | 53.1722i | −0.529603 | − | 0.172078i | ||||
\(310\) | −528.867 | + | 159.028i | −1.70602 | + | 0.512992i | ||||
\(311\) | −59.5063 | − | 183.142i | −0.191339 | − | 0.588880i | −1.00000 | 0.000605266i | \(-0.999807\pi\) | |
0.808661 | − | 0.588275i | \(-0.200193\pi\) | |||||||
\(312\) | −56.3663 | − | 110.625i | −0.180661 | − | 0.354568i | ||||
\(313\) | 141.673 | − | 72.1860i | 0.452629 | − | 0.230626i | −0.212787 | − | 0.977099i | \(-0.568254\pi\) |
0.665416 | + | 0.746473i | \(0.268254\pi\) | |||||||
\(314\) | −398.702 | + | 129.546i | −1.26975 | + | 0.412567i | ||||
\(315\) | 26.5349 | + | 88.2452i | 0.0842378 | + | 0.280143i | ||||
\(316\) | −118.974 | + | 366.164i | −0.376500 | + | 1.15875i | ||||
\(317\) | 378.338 | − | 59.9228i | 1.19349 | − | 0.189031i | 0.472093 | − | 0.881549i | \(-0.343499\pi\) |
0.721401 | + | 0.692518i | \(0.243499\pi\) | |||||||
\(318\) | 331.274 | + | 331.274i | 1.04174 | + | 1.04174i | ||||
\(319\) | 476.547 | − | 655.911i | 1.49388 | − | 2.05615i | ||||
\(320\) | 67.2304 | + | 494.919i | 0.210095 | + | 1.54662i | ||||
\(321\) | −114.978 | + | 83.5363i | −0.358187 | + | 0.260238i | ||||
\(322\) | −15.0066 | + | 94.7479i | −0.0466043 | + | 0.294248i | ||||
\(323\) | 24.9031 | − | 48.8751i | 0.0770994 | − | 0.151316i | ||||
\(324\) | 61.4493i | 0.189658i | ||||||||
\(325\) | −191.370 | + | 21.7076i | −0.588832 | + | 0.0667928i | ||||
\(326\) | −112.698 | −0.345699 | ||||||||
\(327\) | −126.297 | − | 64.3513i | −0.386228 | − | 0.196793i | ||||
\(328\) | −35.8890 | − | 5.68426i | −0.109418 | − | 0.0173301i | ||||
\(329\) | 297.247 | + | 409.125i | 0.903486 | + | 1.24354i | ||||
\(330\) | −366.617 | − | 197.108i | −1.11096 | − | 0.597296i | ||||
\(331\) | −450.680 | − | 327.439i | −1.36157 | − | 0.989240i | −0.998343 | − | 0.0575405i | \(-0.981674\pi\) |
−0.363229 | − | 0.931700i | \(-0.618326\pi\) | |||||||
\(332\) | 83.6628 | − | 83.6628i | 0.251996 | − | 0.251996i | ||||
\(333\) | −19.3683 | − | 122.287i | −0.0581631 | − | 0.367227i | ||||
\(334\) | −184.542 | − | 59.9614i | −0.552521 | − | 0.179525i | ||||
\(335\) | 0.0392630 | − | 1.77914i | 0.000117203 | − | 0.00531088i | ||||
\(336\) | −10.8725 | − | 33.4622i | −0.0323587 | − | 0.0995899i | ||||
\(337\) | 86.1758 | + | 169.130i | 0.255715 | + | 0.501868i | 0.982799 | − | 0.184680i | \(-0.0591250\pi\) |
−0.727084 | + | 0.686548i | \(0.759125\pi\) | |||||||
\(338\) | −321.482 | + | 163.803i | −0.951131 | + | 0.484625i | ||||
\(339\) | −311.817 | + | 101.316i | −0.919814 | + | 0.298866i | ||||
\(340\) | 728.165 | − | 504.878i | 2.14166 | − | 1.48494i | ||||
\(341\) | 151.508 | − | 466.295i | 0.444306 | − | 1.36743i | ||||
\(342\) | −20.6058 | + | 3.26365i | −0.0602510 | + | 0.00954282i | ||||
\(343\) | 261.768 | + | 261.768i | 0.763172 | + | 0.763172i | ||||
\(344\) | 254.448 | − | 350.217i | 0.739674 | − | 1.01807i | ||||
\(345\) | 28.4121 | + | 29.6944i | 0.0823540 | + | 0.0860708i | ||||
\(346\) | 207.128 | − | 150.487i | 0.598635 | − | 0.434934i | ||||
\(347\) | 23.6780 | − | 149.497i | 0.0682362 | − | 0.430827i | −0.929793 | − | 0.368082i | \(-0.880015\pi\) |
0.998030 | − | 0.0627447i | \(-0.0199854\pi\) | |||||||
\(348\) | 298.002 | − | 584.862i | 0.856327 | − | 1.68064i | ||||
\(349\) | 124.533i | 0.356829i | 0.983955 | + | 0.178415i | \(0.0570968\pi\) | ||||
−0.983955 | + | 0.178415i | \(0.942903\pi\) | |||||||
\(350\) | −504.872 | − | 22.2944i | −1.44249 | − | 0.0636982i | ||||
\(351\) | −40.0307 | −0.114048 | ||||||||
\(352\) | −342.777 | − | 174.654i | −0.973800 | − | 0.496176i | ||||
\(353\) | −367.421 | − | 58.1938i | −1.04085 | − | 0.164855i | −0.387470 | − | 0.921882i | \(-0.626651\pi\) |
−0.653383 | + | 0.757027i | \(0.726651\pi\) | |||||||
\(354\) | 37.7253 | + | 51.9244i | 0.106569 | + | 0.146679i | ||||
\(355\) | 237.643 | + | 492.997i | 0.669416 | + | 1.38872i | ||||
\(356\) | −495.338 | − | 359.884i | −1.39140 | − | 1.01091i | ||||
\(357\) | 195.284 | − | 195.284i | 0.547015 | − | 0.547015i | ||||
\(358\) | −78.5492 | − | 495.940i | −0.219411 | − | 1.38531i | ||||
\(359\) | −232.340 | − | 75.4918i | −0.647186 | − | 0.210283i | −0.0330130 | − | 0.999455i | \(-0.510510\pi\) |
−0.614173 | + | 0.789171i | \(0.710510\pi\) | |||||||
\(360\) | −131.755 | − | 46.0477i | −0.365987 | − | 0.127910i | ||||
\(361\) | 110.175 | + | 339.084i | 0.305194 | + | 0.939290i | ||||
\(362\) | −48.7835 | − | 95.7430i | −0.134761 | − | 0.264483i | ||||
\(363\) | 142.526 | − | 72.6206i | 0.392633 | − | 0.200057i | ||||
\(364\) | 307.318 | − | 99.8537i | 0.844280 | − | 0.274323i | ||||
\(365\) | −176.321 | − | 134.147i | −0.483071 | − | 0.367525i | ||||
\(366\) | −56.1313 | + | 172.754i | −0.153364 | + | 0.472006i | ||||
\(367\) | −170.553 | + | 27.0130i | −0.464723 | + | 0.0736049i | −0.384405 | − | 0.923164i | \(-0.625593\pi\) |
−0.0803176 | + | 0.996769i | \(0.525593\pi\) | |||||||
\(368\) | −11.0959 | − | 11.0959i | −0.0301518 | − | 0.0301518i | ||||
\(369\) | −6.88621 | + | 9.47806i | −0.0186618 | + | 0.0256858i | ||||
\(370\) | 668.143 | + | 120.991i | 1.80579 | + | 0.327004i | ||||
\(371\) | −408.534 | + | 296.817i | −1.10117 | + | 0.800046i | ||||
\(372\) | 62.0972 | − | 392.066i | 0.166928 | − | 1.05394i | ||||
\(373\) | −17.9357 | + | 35.2007i | −0.0480849 | + | 0.0943718i | −0.913799 | − | 0.406168i | \(-0.866865\pi\) |
0.865714 | + | 0.500539i | \(0.166865\pi\) | |||||||
\(374\) | 1247.51i | 3.33558i | ||||||||
\(375\) | −138.567 | + | 166.356i | −0.369511 | + | 0.443616i | ||||
\(376\) | −765.956 | −2.03712 | ||||||||
\(377\) | 381.004 | + | 194.131i | 1.01062 | + | 0.514937i | ||||
\(378\) | −103.745 | − | 16.4316i | −0.274457 | − | 0.0434697i | ||||
\(379\) | −52.2973 | − | 71.9811i | −0.137988 | − | 0.189924i | 0.734431 | − | 0.678684i | \(-0.237449\pi\) |
−0.872418 | + | 0.488760i | \(0.837449\pi\) | |||||||
\(380\) | 12.8559 | − | 70.9936i | 0.0338314 | − | 0.186825i | ||||
\(381\) | 156.721 | + | 113.864i | 0.411341 | + | 0.298857i | ||||
\(382\) | 116.734 | − | 116.734i | 0.305585 | − | 0.305585i | ||||
\(383\) | −50.0372 | − | 315.922i | −0.130645 | − | 0.824863i | −0.962779 | − | 0.270288i | \(-0.912881\pi\) |
0.832134 | − | 0.554575i | \(-0.187119\pi\) | |||||||
\(384\) | −367.920 | − | 119.545i | −0.958126 | − | 0.311314i | ||||
\(385\) | 271.659 | − | 357.066i | 0.705608 | − | 0.927443i | ||||
\(386\) | 70.8604 | + | 218.086i | 0.183576 | + | 0.564989i | ||||
\(387\) | −63.3646 | − | 124.360i | −0.163733 | − | 0.321344i | ||||
\(388\) | 53.6304 | − | 27.3260i | 0.138223 | − | 0.0704279i | ||||
\(389\) | −77.7419 | + | 25.2599i | −0.199851 | + | 0.0649354i | −0.407232 | − | 0.913325i | \(-0.633506\pi\) |
0.207381 | + | 0.978260i | \(0.433506\pi\) | |||||||
\(390\) | 72.4311 | − | 207.245i | 0.185721 | − | 0.531399i | ||||
\(391\) | 38.0621 | − | 117.143i | 0.0973456 | − | 0.299599i | ||||
\(392\) | −103.488 | + | 16.3909i | −0.264001 | + | 0.0418136i | ||||
\(393\) | 127.710 | + | 127.710i | 0.324961 | + | 0.324961i | ||||
\(394\) | −674.878 | + | 928.889i | −1.71289 | + | 2.35759i | ||||
\(395\) | −253.978 | + | 122.427i | −0.642983 | + | 0.309941i | ||||
\(396\) | 242.049 | − | 175.859i | 0.611234 | − | 0.444088i | ||||
\(397\) | 8.70402 | − | 54.9550i | 0.0219245 | − | 0.138426i | −0.974298 | − | 0.225263i | \(-0.927676\pi\) |
0.996223 | + | 0.0868371i | \(0.0276760\pi\) | |||||||
\(398\) | 59.6060 | − | 116.983i | 0.149764 | − | 0.293928i | ||||
\(399\) | − | 22.4873i | − | 0.0563592i | ||||||
\(400\) | 51.4934 | − | 64.6702i | 0.128734 | − | 0.161675i | ||||
\(401\) | 706.598 | 1.76209 | 0.881045 | − | 0.473032i | \(-0.156840\pi\) | ||||
0.881045 | + | 0.473032i | \(0.156840\pi\) | |||||||
\(402\) | 1.80741 | + | 0.920921i | 0.00449604 | + | 0.00229085i | ||||
\(403\) | 255.409 | + | 40.4527i | 0.633768 | + | 0.100379i | ||||
\(404\) | 18.2457 | + | 25.1130i | 0.0451626 | + | 0.0621609i | ||||
\(405\) | −32.5141 | + | 31.1100i | −0.0802817 | + | 0.0768149i | ||||
\(406\) | 907.735 | + | 659.508i | 2.23580 | + | 1.62440i | ||||
\(407\) | −426.258 | + | 426.258i | −1.04732 | + | 1.04732i | ||||
\(408\) | 65.4365 | + | 413.150i | 0.160383 | + | 1.01262i | ||||
\(409\) | 225.857 | + | 73.3853i | 0.552217 | + | 0.179426i | 0.571816 | − | 0.820382i | \(-0.306239\pi\) |
−0.0195993 | + | 0.999808i | \(0.506239\pi\) | |||||||
\(410\) | −36.6096 | − | 52.8006i | −0.0892918 | − | 0.128782i | ||||
\(411\) | −81.8146 | − | 251.799i | −0.199062 | − | 0.612651i | ||||
\(412\) | 307.938 | + | 604.362i | 0.747421 | + | 1.46690i | ||||
\(413\) | −61.6400 | + | 31.4071i | −0.149249 | + | 0.0760463i | ||||
\(414\) | −44.5534 | + | 14.4763i | −0.107617 | + | 0.0349669i | ||||
\(415\) | 86.6238 | + | 1.91166i | 0.208732 | + | 0.00460640i | ||||
\(416\) | 62.7011 | − | 192.974i | 0.150724 | − | 0.463880i | ||||
\(417\) | −269.340 | + | 42.6593i | −0.645900 | + | 0.102301i | ||||
\(418\) | 71.8264 | + | 71.8264i | 0.171833 | + | 0.171833i | ||||
\(419\) | 140.550 | − | 193.451i | 0.335443 | − | 0.461697i | −0.607661 | − | 0.794197i | \(-0.707892\pi\) |
0.943103 | + | 0.332500i | \(0.107892\pi\) | |||||||
\(420\) | 172.011 | − | 319.938i | 0.409550 | − | 0.761756i | ||||
\(421\) | −392.951 | + | 285.496i | −0.933375 | + | 0.678137i | −0.946817 | − | 0.321773i | \(-0.895721\pi\) |
0.0134415 | + | 0.999910i | \(0.495721\pi\) | |||||||
\(422\) | −98.4630 | + | 621.671i | −0.233325 | + | 1.47315i | ||||
\(423\) | −112.117 | + | 220.041i | −0.265051 | + | 0.520193i | ||||
\(424\) | − | 764.848i | − | 1.80389i | ||||||
\(425\) | 635.791 | + | 129.682i | 1.49598 | + | 0.305134i | ||||
\(426\) | −623.838 | −1.46441 | ||||||||
\(427\) | −174.450 | − | 88.8867i | −0.408548 | − | 0.208166i | ||||
\(428\) | 553.338 | + | 87.6401i | 1.29285 | + | 0.204767i | ||||
\(429\) | 114.562 | + | 157.681i | 0.267044 | + | 0.367554i | ||||
\(430\) | 758.484 | − | 103.033i | 1.76392 | − | 0.239613i | ||||
\(431\) | −224.130 | − | 162.840i | −0.520023 | − | 0.377819i | 0.296589 | − | 0.955005i | \(-0.404151\pi\) |
−0.816613 | + | 0.577186i | \(0.804151\pi\) | |||||||
\(432\) | 12.1495 | − | 12.1495i | 0.0281238 | − | 0.0281238i | ||||
\(433\) | 78.8616 | + | 497.912i | 0.182128 | + | 1.14991i | 0.894154 | + | 0.447760i | \(0.147778\pi\) |
−0.712026 | + | 0.702154i | \(0.752222\pi\) | |||||||
\(434\) | 645.320 | + | 209.677i | 1.48691 | + | 0.483127i | ||||
\(435\) | 460.332 | − | 138.420i | 1.05824 | − | 0.318206i | ||||
\(436\) | 172.666 | + | 531.411i | 0.396023 | + | 1.21883i | ||||
\(437\) | −4.55316 | − | 8.93609i | −0.0104191 | − | 0.0204487i | ||||
\(438\) | 225.015 | − | 114.651i | 0.513732 | − | 0.261760i | ||||
\(439\) | −644.964 | + | 209.562i | −1.46917 | + | 0.477361i | −0.930856 | − | 0.365385i | \(-0.880937\pi\) |
−0.538310 | + | 0.842747i | \(0.680937\pi\) | |||||||
\(440\) | 195.682 | + | 650.765i | 0.444732 | + | 1.47901i | ||||
\(441\) | −10.4394 | + | 32.1291i | −0.0236720 | + | 0.0728550i | ||||
\(442\) | −649.867 | + | 102.929i | −1.47029 | + | 0.232871i | ||||
\(443\) | 229.580 | + | 229.580i | 0.518238 | + | 0.518238i | 0.917038 | − | 0.398800i | \(-0.130573\pi\) |
−0.398800 | + | 0.917038i | \(0.630573\pi\) | |||||||
\(444\) | −286.874 | + | 394.849i | −0.646113 | + | 0.889299i | ||||
\(445\) | −60.3533 | − | 444.293i | −0.135625 | − | 0.998412i | ||||
\(446\) | 482.739 | − | 350.730i | 1.08237 | − | 0.786391i | ||||
\(447\) | 21.8031 | − | 137.660i | 0.0487766 | − | 0.307963i | ||||
\(448\) | 278.598 | − | 546.779i | 0.621870 | − | 1.22049i | ||||
\(449\) | − | 72.7747i | − | 0.162082i | −0.996711 | − | 0.0810409i | \(-0.974176\pi\) | ||
0.996711 | − | 0.0810409i | \(-0.0258244\pi\) | |||||||
\(450\) | −102.231 | − | 224.621i | −0.227180 | − | 0.499158i | ||||
\(451\) | 57.0414 | 0.126478 | ||||||||
\(452\) | 1151.56 | + | 586.751i | 2.54771 | + | 1.29812i | ||||
\(453\) | −320.650 | − | 50.7860i | −0.707838 | − | 0.112110i | ||||
\(454\) | −578.531 | − | 796.280i | −1.27430 | − | 1.75392i | ||||
\(455\) | 208.421 | + | 112.055i | 0.458068 | + | 0.246275i | ||||
\(456\) | 27.5550 | + | 20.0199i | 0.0604277 | + | 0.0439033i | ||||
\(457\) | 209.874 | − | 209.874i | 0.459243 | − | 0.459243i | −0.439164 | − | 0.898407i | \(-0.644725\pi\) |
0.898407 | + | 0.439164i | \(0.144725\pi\) | |||||||
\(458\) | −112.519 | − | 710.418i | −0.245675 | − | 1.55113i | ||||
\(459\) | 128.267 | + | 41.6764i | 0.279448 | + | 0.0907982i | ||||
\(460\) | 3.57435 | − | 161.966i | 0.00777032 | − | 0.352100i | ||||
\(461\) | 41.7392 | + | 128.460i | 0.0905406 | + | 0.278655i | 0.986066 | − | 0.166355i | \(-0.0531999\pi\) |
−0.895525 | + | 0.445011i | \(0.853200\pi\) | |||||||
\(462\) | 232.178 | + | 455.675i | 0.502550 | + | 0.986310i | ||||
\(463\) | −657.694 | + | 335.112i | −1.42051 | + | 0.723784i | −0.984373 | − | 0.176099i | \(-0.943652\pi\) |
−0.436133 | + | 0.899882i | \(0.643652\pi\) | |||||||
\(464\) | −174.556 | + | 56.7167i | −0.376198 | + | 0.122234i | ||||
\(465\) | 238.888 | − | 165.635i | 0.513739 | − | 0.356204i | ||||
\(466\) | 185.848 | − | 571.981i | 0.398815 | − | 1.22743i | ||||
\(467\) | −193.470 | + | 30.6426i | −0.414282 | + | 0.0656158i | −0.360096 | − | 0.932915i | \(-0.617256\pi\) |
−0.0541855 | + | 0.998531i | \(0.517256\pi\) | |||||||
\(468\) | 111.581 | + | 111.581i | 0.238422 | + | 0.238422i | ||||
\(469\) | −1.28517 | + | 1.76889i | −0.00274024 | + | 0.00377162i | ||||
\(470\) | −936.328 | − | 978.588i | −1.99219 | − | 2.08210i | ||||
\(471\) | 178.522 | − | 129.704i | 0.379028 | − | 0.275380i | ||||
\(472\) | 16.3915 | − | 103.492i | 0.0347278 | − | 0.219263i | ||||
\(473\) | −308.514 | + | 605.494i | −0.652250 | + | 1.28011i | ||||
\(474\) | − | 321.384i | − | 0.678025i | ||||||
\(475\) | 44.0728 | − | 29.1397i | 0.0927848 | − | 0.0613467i | ||||
\(476\) | −1088.67 | −2.28712 | ||||||||
\(477\) | −219.723 | − | 111.955i | −0.460636 | − | 0.234706i | ||||
\(478\) | −1484.04 | − | 235.049i | −3.10469 | − | 0.491735i | ||||
\(479\) | −84.2910 | − | 116.017i | −0.175973 | − | 0.242206i | 0.711915 | − | 0.702265i | \(-0.247828\pi\) |
−0.887888 | + | 0.460060i | \(0.847828\pi\) | |||||||
\(480\) | −99.0430 | − | 205.468i | −0.206340 | − | 0.428058i | ||||
\(481\) | −257.221 | − | 186.882i | −0.534763 | − | 0.388528i | ||||
\(482\) | −930.598 | + | 930.598i | −1.93070 | + | 1.93070i | ||||
\(483\) | −7.89904 | − | 49.8726i | −0.0163541 | − | 0.103256i | ||||
\(484\) | −599.698 | − | 194.854i | −1.23905 | − | 0.402590i | ||||
\(485\) | 41.6103 | + | 14.5426i | 0.0857944 | + | 0.0299847i | ||||
\(486\) | −15.8509 | − | 48.7840i | −0.0326150 | − | 0.100379i | ||||
\(487\) | 152.898 | + | 300.080i | 0.313959 | + | 0.616180i | 0.993026 | − | 0.117897i | \(-0.0376152\pi\) |
−0.679067 | + | 0.734077i | \(0.737615\pi\) | |||||||
\(488\) | 264.226 | − | 134.630i | 0.541447 | − | 0.275881i | ||||
\(489\) | 56.4176 | − | 18.3312i | 0.115373 | − | 0.0374871i | ||||
\(490\) | −147.449 | − | 112.180i | −0.300916 | − | 0.228939i | ||||
\(491\) | 196.552 | − | 604.925i | 0.400310 | − | 1.23203i | −0.524439 | − | 0.851448i | \(-0.675725\pi\) |
0.924748 | − | 0.380579i | \(-0.124275\pi\) | |||||||
\(492\) | 45.6137 | − | 7.22450i | 0.0927108 | − | 0.0146839i | ||||
\(493\) | −1018.70 | − | 1018.70i | −2.06634 | − | 2.06634i | ||||
\(494\) | −31.4905 | + | 43.3429i | −0.0637459 | + | 0.0877387i | ||||
\(495\) | 215.593 | + | 39.0408i | 0.435541 | + | 0.0788704i | ||||
\(496\) | −89.7953 | + | 65.2401i | −0.181039 | + | 0.131532i | ||||
\(497\) | 105.189 | − | 664.139i | 0.211649 | − | 1.33630i | ||||
\(498\) | −44.8382 | + | 88.0000i | −0.0900366 | + | 0.176707i | ||||
\(499\) | − | 220.616i | − | 0.442116i | −0.975261 | − | 0.221058i | \(-0.929049\pi\) | ||
0.975261 | − | 0.221058i | \(-0.0709511\pi\) | |||||||
\(500\) | 849.940 | − | 77.4601i | 1.69988 | − | 0.154920i | ||||
\(501\) | 102.137 | 0.203866 | ||||||||
\(502\) | 449.635 | + | 229.100i | 0.895687 | + | 0.456375i | ||||
\(503\) | −377.227 | − | 59.7469i | −0.749954 | − | 0.118781i | −0.230255 | − | 0.973130i | \(-0.573956\pi\) |
−0.519699 | + | 0.854349i | \(0.673956\pi\) | |||||||
\(504\) | 100.795 | + | 138.732i | 0.199989 | + | 0.275262i | ||||
\(505\) | −4.05056 | + | 22.3682i | −0.00802091 | + | 0.0442934i | ||||
\(506\) | 184.527 | + | 134.067i | 0.364678 | + | 0.264954i | ||||
\(507\) | 134.293 | − | 134.293i | 0.264878 | − | 0.264878i | ||||
\(508\) | −119.458 | − | 754.229i | −0.235154 | − | 1.48470i | ||||
\(509\) | −54.3299 | − | 17.6528i | −0.106738 | − | 0.0346814i | 0.255161 | − | 0.966899i | \(-0.417872\pi\) |
−0.361899 | + | 0.932217i | \(0.617872\pi\) | |||||||
\(510\) | −447.850 | + | 588.649i | −0.878137 | + | 1.15421i | ||||
\(511\) | 84.1163 | + | 258.883i | 0.164611 | + | 0.506621i | ||||
\(512\) | 95.4111 | + | 187.255i | 0.186350 | + | 0.365732i | ||||
\(513\) | 9.78462 | − | 4.98551i | 0.0190733 | − | 0.00971835i | ||||
\(514\) | 922.391 | − | 299.703i | 1.79454 | − | 0.583080i | ||||
\(515\) | −163.880 | + | 468.907i | −0.318214 | + | 0.910499i | ||||
\(516\) | −170.019 | + | 523.263i | −0.329493 | + | 1.01408i | ||||
\(517\) | 1187.60 | − | 188.098i | 2.29711 | − | 0.363826i | ||||
\(518\) | −589.912 | − | 589.912i | −1.13883 | − | 1.13883i | ||||
\(519\) | −79.2121 | + | 109.026i | −0.152624 | + | 0.210070i | ||||
\(520\) | −322.860 | + | 155.630i | −0.620884 | + | 0.299289i | ||||
\(521\) | 37.2208 | − | 27.0425i | 0.0714410 | − | 0.0519050i | −0.551492 | − | 0.834181i | \(-0.685941\pi\) |
0.622933 | + | 0.782276i | \(0.285941\pi\) | |||||||
\(522\) | −85.7155 | + | 541.186i | −0.164206 | + | 1.03675i | ||||
\(523\) | 138.623 | − | 272.063i | 0.265053 | − | 0.520197i | −0.719671 | − | 0.694315i | \(-0.755707\pi\) |
0.984725 | + | 0.174118i | \(0.0557075\pi\) | |||||||
\(524\) | − | 711.954i | − | 1.35869i | ||||||
\(525\) | 256.370 | − | 70.9606i | 0.488324 | − | 0.135163i | ||||
\(526\) | −34.5965 | −0.0657729 | ||||||||
\(527\) | −776.267 | − | 395.528i | −1.47299 | − | 0.750527i | ||||
\(528\) | −82.6269 | − | 13.0868i | −0.156490 | − | 0.0247856i | ||||
\(529\) | 297.701 | + | 409.751i | 0.562763 | + | 0.774576i | ||||
\(530\) | 977.173 | − | 934.974i | 1.84372 | − | 1.76410i | ||||
\(531\) | −27.3316 | − | 19.8575i | −0.0514719 | − | 0.0373965i | ||||
\(532\) | −62.6811 | + | 62.6811i | −0.117822 | + | 0.117822i | ||||
\(533\) | 4.70635 | + | 29.7147i | 0.00882992 | + | 0.0557499i | ||||
\(534\) | 486.077 | + | 157.936i | 0.910257 | + | 0.295760i | ||||
\(535\) | 233.767 | + | 337.152i | 0.436947 | + | 0.630191i | ||||
\(536\) | −1.02336 | − | 3.14959i | −0.00190926 | − | 0.00587610i | ||||
\(537\) | 119.991 | + | 235.495i | 0.223447 | + | 0.438539i | ||||
\(538\) | 1350.84 | − | 688.289i | 2.51086 | − | 1.27935i | ||||
\(539\) | 156.432 | − | 50.8279i | 0.290227 | − | 0.0943004i | ||||
\(540\) | 177.346 | + | 3.91375i | 0.328418 | + | 0.00724769i | ||||
\(541\) | −72.3805 | + | 222.764i | −0.133790 | + | 0.411764i | −0.995400 | − | 0.0958075i | \(-0.969457\pi\) |
0.861610 | + | 0.507571i | \(0.169457\pi\) | |||||||
\(542\) | 483.768 | − | 76.6213i | 0.892560 | − | 0.141368i | ||||
\(543\) | 39.9948 | + | 39.9948i | 0.0736553 | + | 0.0736553i | ||||
\(544\) | −401.815 | + | 553.051i | −0.738630 | + | 1.01664i | ||||
\(545\) | −193.765 | + | 360.399i | −0.355532 | + | 0.661283i | ||||
\(546\) | −218.220 | + | 158.546i | −0.399669 | + | 0.290377i | ||||
\(547\) | −126.813 | + | 800.663i | −0.231833 | + | 1.46374i | 0.547332 | + | 0.836916i | \(0.315644\pi\) |
−0.779164 | + | 0.626819i | \(0.784356\pi\) | |||||||
\(548\) | −473.815 | + | 929.914i | −0.864626 | + | 1.69692i | ||||
\(549\) | − | 95.6126i | − | 0.174158i | ||||||
\(550\) | −592.212 | + | 1045.52i | −1.07675 | + | 1.90095i | ||||
\(551\) | −117.306 | −0.212896 | ||||||||
\(552\) | 68.1440 | + | 34.7211i | 0.123449 | + | 0.0629006i | ||||
\(553\) | 342.146 | + | 54.1906i | 0.618708 | + | 0.0979938i | ||||
\(554\) | −498.609 | − | 686.276i | −0.900016 | − | 1.23877i | ||||
\(555\) | −354.159 | + | 48.1094i | −0.638124 | + | 0.0866835i | ||||
\(556\) | 869.667 | + | 631.850i | 1.56415 | + | 1.13642i | ||||
\(557\) | 581.702 | − | 581.702i | 1.04435 | − | 1.04435i | 0.0453787 | − | 0.998970i | \(-0.485551\pi\) |
0.998970 | − | 0.0453787i | \(-0.0144494\pi\) | |||||||
\(558\) | 51.8354 | + | 327.276i | 0.0928949 | + | 0.586516i | ||||
\(559\) | −340.876 | − | 110.757i | −0.609796 | − | 0.198135i | ||||
\(560\) | −97.2660 | + | 29.2474i | −0.173689 | + | 0.0522275i | ||||
\(561\) | −202.917 | − | 624.514i | −0.361706 | − | 1.11322i | ||||
\(562\) | −119.266 | − | 234.072i | −0.212217 | − | 0.416499i | ||||
\(563\) | −376.119 | + | 191.642i | −0.668062 | + | 0.340395i | −0.754911 | − | 0.655827i | \(-0.772320\pi\) |
0.0868492 | + | 0.996221i | \(0.472320\pi\) | |||||||
\(564\) | 925.857 | − | 300.829i | 1.64159 | − | 0.533385i | ||||
\(565\) | 272.542 | + | 906.372i | 0.482375 | + | 1.60420i | ||||
\(566\) | −35.8950 | + | 110.473i | −0.0634187 | + | 0.195183i | ||||
\(567\) | 54.6083 | − | 8.64910i | 0.0963109 | − | 0.0152542i | ||||
\(568\) | 720.161 | + | 720.161i | 1.26789 | + | 1.26789i | ||||
\(569\) | −470.636 | + | 647.774i | −0.827128 | + | 1.13844i | 0.161323 | + | 0.986902i | \(0.448424\pi\) |
−0.988451 | + | 0.151542i | \(0.951576\pi\) | |||||||
\(570\) | 8.10664 | + | 59.6773i | 0.0142222 | + | 0.104697i | ||||
\(571\) | 545.948 | − | 396.655i | 0.956127 | − | 0.694667i | 0.00387883 | − | 0.999992i | \(-0.498765\pi\) |
0.952248 | + | 0.305326i | \(0.0987653\pi\) | |||||||
\(572\) | 120.190 | − | 758.848i | 0.210122 | − | 1.32666i | ||||
\(573\) | −39.4503 | + | 77.4255i | −0.0688486 | + | 0.135123i | ||||
\(574\) | 78.9414i | 0.137529i | ||||||||
\(575\) | 87.5092 | − | 80.1075i | 0.152190 | − | 0.139317i | ||||
\(576\) | 299.679 | 0.520276 | ||||||||
\(577\) | −809.001 | − | 412.206i | −1.40208 | − | 0.714396i | −0.420831 | − | 0.907139i | \(-0.638262\pi\) |
−0.981249 | + | 0.192743i | \(0.938262\pi\) | |||||||
\(578\) | 1250.21 | + | 198.014i | 2.16299 | + | 0.342585i | ||||
\(579\) | −70.9468 | − | 97.6498i | −0.122533 | − | 0.168653i | ||||
\(580\) | −1668.96 | − | 897.298i | −2.87752 | − | 1.54707i | ||||
\(581\) | −86.1245 | − | 62.5731i | −0.148235 | − | 0.107699i | ||||
\(582\) | −35.5279 | + | 35.5279i | −0.0610445 | + | 0.0610445i | ||||
\(583\) | 187.826 | + | 1185.89i | 0.322172 | + | 2.03411i | ||||
\(584\) | −392.111 | − | 127.405i | −0.671423 | − | 0.218159i | ||||
\(585\) | −2.54958 | + | 115.530i | −0.00435826 | + | 0.197488i | ||||
\(586\) | −24.0682 | − | 74.0745i | −0.0410721 | − | 0.126407i | ||||
\(587\) | 54.6357 | + | 107.229i | 0.0930761 | + | 0.182672i | 0.932851 | − | 0.360263i | \(-0.117313\pi\) |
−0.839775 | + | 0.542935i | \(0.817313\pi\) | |||||||
\(588\) | 118.655 | − | 60.4578i | 0.201794 | − | 0.102819i | ||||
\(589\) | −67.4671 | + | 21.9214i | −0.114545 | + | 0.0372180i | ||||
\(590\) | 152.259 | − | 105.570i | 0.258066 | − | 0.178932i | ||||
\(591\) | 186.759 | − | 574.785i | 0.316005 | − | 0.972563i | ||||
\(592\) | 134.787 | − | 21.3482i | 0.227681 | − | 0.0360612i | ||||
\(593\) | 255.390 | + | 255.390i | 0.430674 | + | 0.430674i | 0.888858 | − | 0.458183i | \(-0.151500\pi\) |
−0.458183 | + | 0.888858i | \(0.651500\pi\) | |||||||
\(594\) | −146.797 | + | 202.049i | −0.247134 | + | 0.340150i | ||||
\(595\) | −551.162 | − | 576.038i | −0.926323 | − | 0.968131i | ||||
\(596\) | −444.486 | + | 322.938i | −0.745781 | + | 0.541842i | ||||
\(597\) | −10.8111 | + | 68.2584i | −0.0181090 | + | 0.114336i | ||||
\(598\) | −54.6149 | + | 107.188i | −0.0913293 | + | 0.179244i | ||||
\(599\) | − | 546.766i | − | 0.912799i | −0.889775 | − | 0.456399i | \(-0.849139\pi\) | ||
0.889775 | − | 0.456399i | \(-0.150861\pi\) | |||||||
\(600\) | −141.287 | + | 377.319i | −0.235479 | + | 0.628865i | ||||
\(601\) | −768.536 | −1.27876 | −0.639381 | − | 0.768890i | \(-0.720809\pi\) | ||||
−0.639381 | + | 0.768890i | \(0.720809\pi\) | |||||||
\(602\) | −837.962 | − | 426.963i | −1.39196 | − | 0.709241i | ||||
\(603\) | −1.05460 | − | 0.167032i | −0.00174892 | − | 0.000277002i | ||||
\(604\) | 752.219 | + | 1035.34i | 1.24540 | + | 1.71414i | ||||
\(605\) | −200.509 | − | 415.962i | −0.331420 | − | 0.687540i | ||||
\(606\) | −20.9630 | − | 15.2305i | −0.0345924 | − | 0.0251328i | ||||
\(607\) | −163.485 | + | 163.485i | −0.269333 | + | 0.269333i | −0.828832 | − | 0.559498i | \(-0.810994\pi\) |
0.559498 | + | 0.828832i | \(0.310994\pi\) | |||||||
\(608\) | 8.70754 | + | 54.9772i | 0.0143216 | + | 0.0904231i | ||||
\(609\) | −561.695 | − | 182.506i | −0.922323 | − | 0.299681i | ||||
\(610\) | 495.002 | + | 173.000i | 0.811479 | + | 0.283607i | ||||
\(611\) | 195.973 | + | 603.142i | 0.320741 | + | 0.987140i | ||||
\(612\) | −241.361 | − | 473.699i | −0.394381 | − | 0.774017i | ||||
\(613\) | 530.506 | − | 270.306i | 0.865426 | − | 0.440957i | 0.0358546 | − | 0.999357i | \(-0.488585\pi\) |
0.829572 | + | 0.558400i | \(0.188585\pi\) | |||||||
\(614\) | 62.1425 | − | 20.1913i | 0.101209 | − | 0.0328849i | ||||
\(615\) | 26.9155 | + | 20.4776i | 0.0437651 | + | 0.0332969i | ||||
\(616\) | 258.006 | − | 794.060i | 0.418840 | − | 1.28906i | ||||
\(617\) | 319.636 | − | 50.6254i | 0.518049 | − | 0.0820509i | 0.108065 | − | 0.994144i | \(-0.465534\pi\) |
0.409984 | + | 0.912093i | \(0.365534\pi\) | |||||||
\(618\) | −400.364 | − | 400.364i | −0.647839 | − | 0.647839i | ||||
\(619\) | 6.19820 | − | 8.53110i | 0.0100133 | − | 0.0137821i | −0.803981 | − | 0.594655i | \(-0.797289\pi\) |
0.813994 | + | 0.580873i | \(0.197289\pi\) | |||||||
\(620\) | −1127.57 | − | 204.186i | −1.81866 | − | 0.329333i | ||||
\(621\) | 19.9492 | − | 14.4939i | 0.0321243 | − | 0.0233396i | ||||
\(622\) | 99.1246 | − | 625.848i | 0.159364 | − | 1.00619i | ||||
\(623\) | −250.100 | + | 490.848i | −0.401444 | + | 0.787878i | ||||
\(624\) | − | 44.1228i | − | 0.0707096i | ||||||
\(625\) | 471.286 | + | 410.505i | 0.754058 | + | 0.656808i | ||||
\(626\) | 523.208 | 0.835795 | ||||||||
\(627\) | −47.6401 | − | 24.2738i | −0.0759810 | − | 0.0387142i | ||||
\(628\) | −859.149 | − | 136.076i | −1.36807 | − | 0.216681i | ||||
\(629\) | 629.625 | + | 866.605i | 1.00099 | + | 1.37775i | ||||
\(630\) | −54.0298 | + | 298.366i | −0.0857616 | + | 0.473597i | ||||
\(631\) | −25.4826 | − | 18.5142i | −0.0403844 | − | 0.0293410i | 0.567410 | − | 0.823435i | \(-0.307946\pi\) |
−0.607794 | + | 0.794094i | \(0.707946\pi\) | |||||||
\(632\) | −371.006 | + | 371.006i | −0.587035 | + | 0.587035i | ||||
\(633\) | −51.8282 | − | 327.230i | −0.0818770 | − | 0.516951i | ||||
\(634\) | 1198.77 | + | 389.502i | 1.89080 | + | 0.614357i | ||||
\(635\) | 338.600 | − | 445.052i | 0.533228 | − | 0.700870i | ||||
\(636\) | 300.394 | + | 924.518i | 0.472318 | + | 1.45364i | ||||
\(637\) | 39.3848 | + | 77.2970i | 0.0618285 | + | 0.121345i | ||||
\(638\) | 2377.04 | − | 1211.16i | 3.72576 | − | 1.89837i | ||||
\(639\) | 312.299 | − | 101.472i | 0.488731 | − | 0.158798i | ||||
\(640\) | −368.445 | + | 1054.22i | −0.575695 | + | 1.64722i | ||||
\(641\) | −347.695 | + | 1070.09i | −0.542425 | + | 1.66941i | 0.184609 | + | 0.982812i | \(0.440898\pi\) |
−0.727034 | + | 0.686601i | \(0.759102\pi\) | |||||||
\(642\) | −461.896 | + | 73.1572i | −0.719465 | + | 0.113952i | ||||
\(643\) | 737.920 | + | 737.920i | 1.14762 | + | 1.14762i | 0.987019 | + | 0.160602i | \(0.0513436\pi\) |
0.160602 | + | 0.987019i | \(0.448656\pi\) | |||||||
\(644\) | −116.997 | + | 161.032i | −0.181672 | + | 0.250050i | ||||
\(645\) | −362.945 | + | 174.953i | −0.562706 | + | 0.271245i | ||||
\(646\) | 146.027 | − | 106.095i | 0.226048 | − | 0.164233i | ||||
\(647\) | 167.580 | − | 1058.06i | 0.259011 | − | 1.63533i | −0.424525 | − | 0.905416i | \(-0.639559\pi\) |
0.683536 | − | 0.729916i | \(-0.260441\pi\) | |||||||
\(648\) | −38.0181 | + | 74.6147i | −0.0586699 | + | 0.115146i | ||||
\(649\) | 164.488i | 0.253449i | ||||||||
\(650\) | −593.507 | − | 222.239i | −0.913088 | − | 0.341907i | ||||
\(651\) | −357.159 | −0.548631 | ||||||||
\(652\) | −208.354 | − | 106.162i | −0.319562 | − | 0.162825i | ||||
\(653\) | −375.029 | − | 59.3987i | −0.574317 | − | 0.0909628i | −0.137481 | − | 0.990504i | \(-0.543901\pi\) |
−0.436835 | + | 0.899542i | \(0.643901\pi\) | |||||||
\(654\) | −274.156 | − | 377.343i | −0.419198 | − | 0.576977i | ||||
\(655\) | 376.710 | − | 360.442i | 0.575130 | − | 0.550293i | ||||
\(656\) | −10.4469 | − | 7.59015i | −0.0159252 | − | 0.0115704i | ||||
\(657\) | −93.9956 | + | 93.9956i | −0.143068 | + | 0.143068i | ||||
\(658\) | 260.315 | + | 1643.56i | 0.395615 | + | 2.49782i | ||||
\(659\) | 329.556 | + | 107.079i | 0.500085 | + | 0.162487i | 0.548188 | − | 0.836355i | \(-0.315318\pi\) |
−0.0481033 | + | 0.998842i | \(0.515318\pi\) | |||||||
\(660\) | −492.121 | − | 709.765i | −0.745637 | − | 1.07540i | ||||
\(661\) | −246.800 | − | 759.573i | −0.373374 | − | 1.14913i | −0.944569 | − | 0.328312i | \(-0.893520\pi\) |
0.571195 | − | 0.820814i | \(-0.306480\pi\) | |||||||
\(662\) | −832.197 | − | 1633.28i | −1.25709 | − | 2.46719i | ||||
\(663\) | 308.587 | − | 157.233i | 0.465441 | − | 0.237154i | ||||
\(664\) | 153.349 | − | 49.8260i | 0.230947 | − | 0.0750392i | ||||
\(665\) | −64.8995 | − | 1.43224i | −0.0975933 | − | 0.00215374i | ||||
\(666\) | 125.895 | − | 387.466i | 0.189032 | − | 0.581781i | ||||
\(667\) | −260.161 | + | 41.2055i | −0.390047 | + | 0.0617773i | ||||
\(668\) | −284.695 | − | 284.695i | −0.426191 | − | 0.426191i | ||||
\(669\) | −184.615 | + | 254.100i | −0.275956 | + | 0.379821i | ||||
\(670\) | 2.77294 | − | 5.15761i | 0.00413871 | − | 0.00769793i | ||||
\(671\) | −376.618 | + | 273.629i | −0.561279 | + | 0.407793i | ||||
\(672\) | −43.8400 | + | 276.795i | −0.0652382 | + | 0.411898i | ||||
\(673\) | 32.9059 | − | 64.5815i | 0.0488944 | − | 0.0959606i | −0.865267 | − | 0.501312i | \(-0.832851\pi\) |
0.914161 | + | 0.405352i | \(0.132851\pi\) | |||||||
\(674\) | 624.607i | 0.926716i | ||||||||
\(675\) | 87.7142 | + | 95.8187i | 0.129947 | + | 0.141954i | ||||
\(676\) | −748.656 | −1.10748 | ||||||||
\(677\) | −529.170 | − | 269.626i | −0.781640 | − | 0.398265i | 0.0171675 | − | 0.999853i | \(-0.494535\pi\) |
−0.798807 | + | 0.601587i | \(0.794535\pi\) | |||||||
\(678\) | −1065.57 | − | 168.770i | −1.57164 | − | 0.248923i | ||||
\(679\) | −31.8325 | − | 43.8136i | −0.0468814 | − | 0.0645267i | ||||
\(680\) | 1196.54 | − | 162.539i | 1.75961 | − | 0.239028i | ||||
\(681\) | 419.139 | + | 304.522i | 0.615476 | + | 0.447169i | ||||
\(682\) | 1140.79 | − | 1140.79i | 1.67272 | − | 1.67272i | ||||
\(683\) | 114.459 | + | 722.664i | 0.167582 | + | 1.05807i | 0.917847 | + | 0.396935i | \(0.129926\pi\) |
−0.750264 | + | 0.661138i | \(0.770074\pi\) | |||||||
\(684\) | −41.1702 | − | 13.3770i | −0.0601904 | − | 0.0195570i | ||||
\(685\) | −731.916 | + | 220.084i | −1.06849 | + | 0.321290i | ||||
\(686\) | 376.428 | + | 1158.53i | 0.548729 | + | 1.68881i | ||||
\(687\) | 171.883 | + | 337.340i | 0.250194 | + | 0.491033i | ||||
\(688\) | 137.073 | − | 69.8421i | 0.199234 | − | 0.101515i | ||||
\(689\) | −602.270 | + | 195.689i | −0.874122 | + | 0.284019i | ||||
\(690\) | 38.9416 | + | 129.505i | 0.0564371 | + | 0.187689i | ||||
\(691\) | 161.872 | − | 498.191i | 0.234257 | − | 0.720970i | −0.762962 | − | 0.646444i | \(-0.776255\pi\) |
0.997219 | − | 0.0745265i | \(-0.0237445\pi\) | |||||||
\(692\) | 524.694 | − | 83.1034i | 0.758229 | − | 0.120092i | ||||
\(693\) | −190.350 | − | 190.350i | −0.274675 | − | 0.274675i | ||||
\(694\) | 292.751 | − | 402.938i | 0.421832 | − | 0.580602i | ||||
\(695\) | 105.962 | + | 780.046i | 0.152464 | + | 1.12237i | ||||
\(696\) | 723.697 | − | 525.797i | 1.03979 | − | 0.755455i | ||||
\(697\) | 15.8562 | − | 100.112i | 0.0227492 | − | 0.143633i | ||||
\(698\) | −186.038 | + | 365.119i | −0.266530 | + | 0.523094i | ||||
\(699\) | 316.569i | 0.452888i | ||||||||
\(700\) | −912.400 | − | 516.809i | −1.30343 | − | 0.738299i | ||||
\(701\) | −699.523 | −0.997893 | −0.498947 | − | 0.866633i | \(-0.666280\pi\) | ||||
−0.498947 | + | 0.866633i | \(0.666280\pi\) | |||||||
\(702\) | −117.366 | − | 59.8009i | −0.167188 | − | 0.0851865i | ||||
\(703\) | 86.1468 | + | 13.6443i | 0.122542 | + | 0.0194087i | ||||
\(704\) | −857.636 | − | 1180.43i | −1.21823 | − | 1.67675i | ||||
\(705\) | 627.910 | + | 337.589i | 0.890652 | + | 0.478850i | ||||
\(706\) | −990.308 | − | 719.501i | −1.40270 | − | 1.01912i | ||||
\(707\) | 19.7491 | − | 19.7491i | 0.0279337 | − | 0.0279337i | ||||
\(708\) | 20.8330 | + | 131.535i | 0.0294252 | + | 0.185783i | ||||
\(709\) | 145.144 | + | 47.1600i | 0.204716 | + | 0.0665162i | 0.409580 | − | 0.912274i | \(-0.365675\pi\) |
−0.204864 | + | 0.978790i | \(0.565675\pi\) | |||||||
\(710\) | −39.7327 | + | 1800.43i | −0.0559616 | + | 2.53581i | ||||
\(711\) | 52.2756 | + | 160.888i | 0.0735240 | + | 0.226284i | ||||
\(712\) | −378.807 | − | 743.451i | −0.532032 | − | 1.04417i | ||||
\(713\) | −141.929 | + | 72.3163i | −0.199059 | + | 0.101425i | ||||
\(714\) | 864.285 | − | 280.823i | 1.21048 | − | 0.393310i | ||||
\(715\) | 462.371 | − | 320.588i | 0.646673 | − | 0.448375i | ||||
\(716\) | 321.957 | − | 990.882i | 0.449661 | − | 1.38391i | ||||
\(717\) | 781.159 | − | 123.723i | 1.08948 | − | 0.172557i | ||||
\(718\) | −568.421 | − | 568.421i | −0.791673 | − | 0.791673i | ||||
\(719\) | 431.478 | − | 593.879i | 0.600109 | − | 0.825979i | −0.395610 | − | 0.918419i | \(-0.629467\pi\) |
0.995718 | + | 0.0924401i | \(0.0294667\pi\) | |||||||
\(720\) | −34.2902 | − | 35.8378i | −0.0476253 | − | 0.0497748i | ||||
\(721\) | 493.737 | − | 358.721i | 0.684794 | − | 0.497532i | ||||
\(722\) | −183.527 | + | 1158.75i | −0.254193 | + | 1.60491i | ||||
\(723\) | 314.497 | − | 617.235i | 0.434989 | − | 0.853714i | ||||
\(724\) | − | 222.963i | − | 0.307960i | ||||||
\(725\) | −370.167 | − | 1337.36i | −0.510575 | − | 1.84463i | ||||
\(726\) | 526.358 | 0.725010 | ||||||||
\(727\) | 1179.77 | + | 601.120i | 1.62279 | + | 0.826851i | 0.998975 | + | 0.0452756i | \(0.0144166\pi\) |
0.623811 | + | 0.781575i | \(0.285583\pi\) | |||||||
\(728\) | 434.939 | + | 68.8876i | 0.597444 | + | 0.0946258i | ||||
\(729\) | 15.8702 | + | 21.8435i | 0.0217698 | + | 0.0299636i | ||||
\(730\) | −316.556 | − | 656.706i | −0.433639 | − | 0.899597i | ||||
\(731\) | 976.927 | + | 709.779i | 1.33643 | + | 0.970970i | ||||
\(732\) | −266.510 | + | 266.510i | −0.364085 | + | 0.364085i | ||||
\(733\) | −133.600 | − | 843.514i | −0.182264 | − | 1.15077i | −0.893915 | − | 0.448237i | \(-0.852052\pi\) |
0.711651 | − | 0.702533i | \(-0.247948\pi\) | |||||||
\(734\) | −540.399 | − | 175.586i | −0.736238 | − | 0.239218i | ||||
\(735\) | 92.0611 | + | 32.1748i | 0.125253 | + | 0.0437753i | ||||
\(736\) | 38.6233 | + | 118.870i | 0.0524773 | + | 0.161509i | ||||
\(737\) | 2.36017 | + | 4.63209i | 0.00320240 | + | 0.00628506i | ||||
\(738\) | −34.3487 | + | 17.5016i | −0.0465430 | + | 0.0237148i | ||||
\(739\) | 32.3337 | − | 10.5059i | 0.0437534 | − | 0.0142163i | −0.287059 | − | 0.957913i | \(-0.592677\pi\) |
0.330812 | + | 0.943697i | \(0.392677\pi\) | |||||||
\(740\) | 1121.28 | + | 853.081i | 1.51524 | + | 1.15281i | ||||
\(741\) | 8.71436 | − | 26.8200i | 0.0117603 | − | 0.0361944i | ||||
\(742\) | −1641.19 | + | 259.938i | −2.21184 | + | 0.350321i | ||||
\(743\) | −327.809 | − | 327.809i | −0.441197 | − | 0.441197i | 0.451217 | − | 0.892414i | \(-0.350990\pi\) |
−0.892414 | + | 0.451217i | \(0.850990\pi\) | |||||||
\(744\) | 317.969 | − | 437.647i | 0.427378 | − | 0.588235i | ||||
\(745\) | −395.904 | − | 71.6925i | −0.531414 | − | 0.0962316i | ||||
\(746\) | −105.171 | + | 76.4112i | −0.140980 | + | 0.102428i | ||||
\(747\) | 8.13255 | − | 51.3469i | 0.0108869 | − | 0.0687375i | ||||
\(748\) | −1175.16 | + | 2306.38i | −1.57107 | + | 3.08339i | ||||
\(749\) | − | 504.071i | − | 0.672993i | ||||||
\(750\) | −654.778 | + | 280.737i | −0.873038 | + | 0.374317i | ||||
\(751\) | 436.259 | 0.580905 | 0.290452 | − | 0.956889i | \(-0.406194\pi\) | ||||
0.290452 | + | 0.956889i | \(0.406194\pi\) | |||||||
\(752\) | −242.535 | − | 123.578i | −0.322520 | − | 0.164332i | ||||
\(753\) | −262.356 | − | 41.5532i | −0.348415 | − | 0.0551835i | ||||
\(754\) | 827.057 | + | 1138.35i | 1.09689 | + | 1.50974i | ||||
\(755\) | −166.993 | + | 922.178i | −0.221183 | + | 1.22143i | ||||
\(756\) | −176.323 | − | 128.106i | −0.233232 | − | 0.169453i | ||||
\(757\) | −667.784 | + | 667.784i | −0.882145 | + | 0.882145i | −0.993752 | − | 0.111607i | \(-0.964400\pi\) |
0.111607 | + | 0.993752i | \(0.464400\pi\) | |||||||
\(758\) | −45.7996 | − | 289.167i | −0.0604216 | − | 0.381487i | ||||
\(759\) | −114.183 | − | 37.1003i | −0.150439 | − | 0.0488805i | ||||
\(760\) | 59.5334 | − | 78.2500i | 0.0783334 | − | 0.102961i | ||||
\(761\) | 265.924 | + | 818.431i | 0.349440 | + | 1.07547i | 0.959163 | + | 0.282853i | \(0.0912807\pi\) |
−0.609723 | + | 0.792615i | \(0.708719\pi\) | |||||||
\(762\) | 289.391 | + | 567.961i | 0.379778 | + | 0.745356i | ||||
\(763\) | 447.947 | − | 228.241i | 0.587087 | − | 0.299136i | ||||
\(764\) | 325.779 | − | 105.852i | 0.426412 | − | 0.138550i | ||||
\(765\) | 128.449 | − | 367.529i | 0.167908 | − | 0.480431i | ||||
\(766\) | 325.245 | − | 1001.00i | 0.424602 | − | 1.30679i | ||||
\(767\) | −85.6873 | + | 13.5715i | −0.111717 | + | 0.0176943i | ||||
\(768\) | −410.747 | − | 410.747i | −0.534827 | − | 0.534827i | ||||
\(769\) | 534.634 | − | 735.861i | 0.695233 | − | 0.956907i | −0.304757 | − | 0.952430i | \(-0.598575\pi\) |
0.999990 | − | 0.00447640i | \(-0.00142489\pi\) | |||||||
\(770\) | 1329.89 | − | 641.055i | 1.72713 | − | 0.832539i | ||||
\(771\) | −413.009 | + | 300.068i | −0.535679 | + | 0.389194i | ||||
\(772\) | −74.4320 | + | 469.945i | −0.0964146 | + | 0.608738i | ||||
\(773\) | −330.014 | + | 647.689i | −0.426926 | + | 0.837889i | 0.572907 | + | 0.819620i | \(0.305816\pi\) |
−0.999833 | + | 0.0182691i | \(0.994184\pi\) | |||||||
\(774\) | − | 459.270i | − | 0.593372i | ||||||
\(775\) | −462.816 | − | 699.993i | −0.597181 | − | 0.903217i | ||||
\(776\) | 82.0270 | 0.105705 | ||||||||
\(777\) | 391.269 | + | 199.362i | 0.503564 | + | 0.256579i | ||||
\(778\) | −265.666 | − | 42.0774i | −0.341474 | − | 0.0540841i | ||||
\(779\) | −4.85110 | − | 6.67697i | −0.00622734 | − | 0.00857120i | ||||
\(780\) | 329.136 | − | 314.923i | 0.421969 | − | 0.403747i | ||||
\(781\) | −1293.45 | − | 939.748i | −1.65615 | − | 1.20326i | ||||
\(782\) | 286.592 | − | 286.592i | 0.366486 | − | 0.366486i | ||||
\(783\) | −45.1182 | − | 284.865i | −0.0576222 | − | 0.363812i | ||||
\(784\) | −35.4134 | − | 11.5065i | −0.0451702 | − | 0.0146767i | ||||
\(785\) | −362.962 | − | 523.485i | −0.462372 | − | 0.666860i | ||||
\(786\) | 183.649 | + | 565.214i | 0.233650 | + | 0.719102i | ||||
\(787\) | −665.324 | − | 1305.77i | −0.845393 | − | 1.65918i | −0.747774 | − | 0.663953i | \(-0.768877\pi\) |
−0.0976189 | − | 0.995224i | \(-0.531123\pi\) | |||||||
\(788\) | −2122.72 | + | 1081.58i | −2.69381 | + | 1.37257i | ||||
\(789\) | 17.3194 | − | 5.62740i | 0.0219510 | − | 0.00713232i | ||||
\(790\) | −927.529 | − | 20.4692i | −1.17409 | − | 0.0259103i | ||||
\(791\) | 359.345 | − | 1105.95i | 0.454292 | − | 1.39817i | ||||
\(792\) | 402.710 | − | 63.7829i | 0.508472 | − | 0.0805340i | ||||
\(793\) | −173.616 | − | 173.616i | −0.218936 | − | 0.218936i | ||||
\(794\) | 107.615 | − | 148.120i | 0.135536 | − | 0.186549i | ||||
\(795\) | −337.101 | + | 627.002i | −0.424026 | + | 0.788681i | ||||
\(796\) | 220.398 | − | 160.128i | 0.276882 | − | 0.201166i | ||||
\(797\) | −118.617 | + | 748.917i | −0.148829 | + | 0.939669i | 0.794368 | + | 0.607436i | \(0.207802\pi\) |
−0.943197 | + | 0.332233i | \(0.892198\pi\) | |||||||
\(798\) | 33.5933 | − | 65.9306i | 0.0420969 | − | 0.0826198i | ||||
\(799\) | − | 2136.62i | − | 2.67412i | ||||||
\(800\) | −599.298 | + | 272.757i | −0.749123 | + | 0.340946i | ||||
\(801\) | −269.024 | −0.335860 | ||||||||
\(802\) | 2071.68 | + | 1055.57i | 2.58314 | + | 1.31617i | ||||
\(803\) | 639.250 | + | 101.247i | 0.796078 | + | 0.126086i | ||||
\(804\) | 2.47400 | + | 3.40517i | 0.00307712 | + | 0.00423529i | ||||
\(805\) | −144.438 | + | 19.6206i | −0.179426 | + | 0.0243734i | ||||
\(806\) | 688.401 | + | 500.152i | 0.854095 | + | 0.620536i | ||||
\(807\) | −564.289 | + | 564.289i | −0.699243 | + | 0.699243i | ||||
\(808\) | 6.61760 | + | 41.7819i | 0.00819010 | + | 0.0517102i | ||||
\(809\) | −684.508 | − | 222.410i | −0.846116 | − | 0.274920i | −0.146298 | − | 0.989241i | \(-0.546736\pi\) |
−0.699818 | + | 0.714321i | \(0.746736\pi\) | |||||||
\(810\) | −141.803 | + | 42.6393i | −0.175065 | + | 0.0526412i | ||||
\(811\) | −27.5305 | − | 84.7302i | −0.0339464 | − | 0.104476i | 0.932648 | − | 0.360789i | \(-0.117492\pi\) |
−0.966594 | + | 0.256312i | \(0.917492\pi\) | |||||||
\(812\) | 1056.95 | + | 2074.38i | 1.30166 | + | 2.55466i | ||||
\(813\) | −229.715 | + | 117.046i | −0.282553 | + | 0.143968i | ||||
\(814\) | −1886.52 | + | 612.968i | −2.31760 | + | 0.753032i | ||||
\(815\) | −49.3114 | − | 163.991i | −0.0605048 | − | 0.201216i | ||||
\(816\) | −45.9367 | + | 141.379i | −0.0562950 | + | 0.173258i | ||||
\(817\) | 97.1136 | − | 15.3813i | 0.118866 | − | 0.0188265i | ||||
\(818\) | 552.560 | + | 552.560i | 0.675502 | + | 0.675502i | ||||
\(819\) | 83.4540 | − | 114.865i | 0.101897 | − | 0.140250i | ||||
\(820\) | −17.9451 | − | 132.104i | −0.0218843 | − | 0.161102i | ||||
\(821\) | 543.123 | − | 394.602i | 0.661538 | − | 0.480635i | −0.205644 | − | 0.978627i | \(-0.565929\pi\) |
0.867182 | + | 0.497991i | \(0.165929\pi\) | |||||||
\(822\) | 136.285 | − | 860.471i | 0.165797 | − | 1.04680i | ||||
\(823\) | 558.523 | − | 1096.16i | 0.678643 | − | 1.33191i | −0.252620 | − | 0.967566i | \(-0.581292\pi\) |
0.931263 | − | 0.364347i | \(-0.118708\pi\) | |||||||
\(824\) | 924.364i | 1.12180i | ||||||||
\(825\) | 126.405 | − | 619.725i | 0.153218 | − | 0.751182i | ||||
\(826\) | −227.641 | −0.275594 | ||||||||
\(827\) | 150.479 | + | 76.6727i | 0.181957 | + | 0.0927119i | 0.542596 | − | 0.839994i | \(-0.317441\pi\) |
−0.360639 | + | 0.932705i | \(0.617441\pi\) | |||||||
\(828\) | −96.0065 | − | 15.2059i | −0.115950 | − | 0.0183647i | ||||
\(829\) | 637.618 | + | 877.605i | 0.769141 | + | 1.05863i | 0.996398 | + | 0.0847965i | \(0.0270240\pi\) |
−0.227258 | + | 0.973835i | \(0.572976\pi\) | |||||||
\(830\) | 251.116 | + | 135.010i | 0.302550 | + | 0.162663i | ||||
\(831\) | 361.236 | + | 262.454i | 0.434701 | + | 0.315829i | ||||
\(832\) | 544.165 | − | 544.165i | 0.654045 | − | 0.654045i | ||||
\(833\) | −45.7223 | − | 288.679i | −0.0548888 | − | 0.346554i | ||||
\(834\) | −853.406 | − | 277.289i | −1.02327 | − | 0.332480i | ||||
\(835\) | 6.50516 | − | 294.771i | 0.00779061 | − | 0.353020i | ||||
\(836\) | 65.1310 | + | 200.453i | 0.0779079 | + | 0.239776i | ||||
\(837\) | −79.1832 | − | 155.406i | −0.0946036 | − | 0.185670i | ||||
\(838\) | 701.072 | − | 357.214i | 0.836601 | − | 0.426270i | ||||
\(839\) | 1156.94 | − | 375.911i | 1.37895 | − | 0.448047i | 0.476623 | − | 0.879108i | \(-0.341861\pi\) |
0.902323 | + | 0.431061i | \(0.141861\pi\) | |||||||
\(840\) | 406.807 | − | 282.062i | 0.484294 | − | 0.335788i | ||||
\(841\) | −692.161 | + | 2130.25i | −0.823021 | + | 2.53300i | ||||
\(842\) | −1578.59 | + | 250.024i | −1.87481 | + | 0.296940i | ||||
\(843\) | 97.7792 | + | 97.7792i | 0.115990 | + | 0.115990i | ||||
\(844\) | −767.654 | + | 1056.59i | −0.909543 | + | 1.25188i | ||||
\(845\) | −379.023 | − | 396.129i | −0.448548 | − | 0.468792i | ||||
\(846\) | −657.430 | + | 477.651i | −0.777104 | + | 0.564599i | ||||
\(847\) | −88.7525 | + | 560.361i | −0.104785 | + | 0.661584i | ||||
\(848\) | 123.399 | − | 242.184i | 0.145518 | − | 0.285595i | ||||
\(849\) | − | 61.1426i | − | 0.0720172i | ||||||
\(850\) | 1670.35 | + | 1330.01i | 1.96511 | + | 1.56472i | ||||
\(851\) | 195.850 | 0.230141 | ||||||||
\(852\) | −1153.34 | − | 587.658i | −1.35369 | − | 0.689740i | ||||
\(853\) | −182.560 | − | 28.9147i | −0.214021 | − | 0.0338977i | 0.0485029 | − | 0.998823i | \(-0.484555\pi\) |
−0.262524 | + | 0.964925i | \(0.584555\pi\) | |||||||
\(854\) | −378.684 | − | 521.214i | −0.443424 | − | 0.610320i | ||||
\(855\) | −13.7652 | − | 28.5564i | −0.0160997 | − | 0.0333993i | ||||
\(856\) | 617.668 | + | 448.762i | 0.721574 | + | 0.524254i | ||||
\(857\) | 203.015 | − | 203.015i | 0.236890 | − | 0.236890i | −0.578671 | − | 0.815561i | \(-0.696428\pi\) |
0.815561 | + | 0.578671i | \(0.196428\pi\) | |||||||
\(858\) | 100.328 | + | 633.446i | 0.116932 | + | 0.738282i | ||||
\(859\) | −1263.62 | − | 410.575i | −1.47103 | − | 0.477968i | −0.539614 | − | 0.841913i | \(-0.681430\pi\) |
−0.931421 | + | 0.363944i | \(0.881430\pi\) | |||||||
\(860\) | 1499.33 | + | 524.009i | 1.74341 | + | 0.609313i | ||||
\(861\) | −12.8404 | − | 39.5188i | −0.0149134 | − | 0.0458987i | ||||
\(862\) | −413.864 | − | 812.253i | −0.480120 | − | 0.942289i | ||||
\(863\) | 1200.75 | − | 611.814i | 1.39137 | − | 0.708938i | 0.412032 | − | 0.911169i | \(-0.364819\pi\) |
0.979338 | + | 0.202231i | \(0.0648192\pi\) | |||||||
\(864\) | −130.158 | + | 42.2908i | −0.150646 | + | 0.0489477i | ||||
\(865\) | 309.610 | + | 235.554i | 0.357930 | + | 0.272317i | ||||
\(866\) | −512.606 | + | 1577.64i | −0.591924 | + | 1.82175i | ||||
\(867\) | −658.076 | + | 104.229i | −0.759026 | + | 0.120218i | ||||
\(868\) | 995.543 | + | 995.543i | 1.14694 | + | 1.14694i | ||||
\(869\) | 484.132 | − | 666.350i | 0.557113 | − | 0.766801i | ||||
\(870\) | 1556.43 | + | 281.848i | 1.78900 | + | 0.323963i | ||||
\(871\) | −2.21828 | + | 1.61167i | −0.00254681 | + | 0.00185037i | ||||
\(872\) | −119.120 | + | 752.092i | −0.136605 | + | 0.862491i | ||||
\(873\) | 12.0067 | − | 23.5645i | 0.0137534 | − | 0.0269925i | ||||
\(874\) | − | 33.0016i | − | 0.0377592i | ||||||
\(875\) | −188.467 | − | 744.416i | −0.215391 | − | 0.850761i | ||||
\(876\) | 524.006 | 0.598181 | ||||||||
\(877\) | 892.419 | + | 454.710i | 1.01758 | + | 0.518484i | 0.881485 | − | 0.472212i | \(-0.156544\pi\) |
0.136096 | + | 0.990696i | \(0.456544\pi\) | |||||||
\(878\) | −2204.03 | − | 349.084i | −2.51028 | − | 0.397590i | ||||
\(879\) | 24.0976 | + | 33.1675i | 0.0274148 | + | 0.0377332i | ||||
\(880\) | −43.0318 | + | 237.632i | −0.0488997 | + | 0.270036i | ||||
\(881\) | 610.778 | + | 443.756i | 0.693278 | + | 0.503696i | 0.877736 | − | 0.479145i | \(-0.159053\pi\) |
−0.184458 | + | 0.982840i | \(0.559053\pi\) | |||||||
\(882\) | −78.6040 | + | 78.6040i | −0.0891202 | + | 0.0891202i | ||||
\(883\) | −143.134 | − | 903.715i | −0.162100 | − | 1.02346i | −0.925835 | − | 0.377929i | \(-0.876636\pi\) |
0.763735 | − | 0.645530i | \(-0.223364\pi\) | |||||||
\(884\) | −1298.43 | − | 421.884i | −1.46881 | − | 0.477245i | ||||
\(885\) | −59.0506 | + | 77.6155i | −0.0667238 | + | 0.0877011i | ||||
\(886\) | 330.140 | + | 1016.07i | 0.372619 | + | 1.14680i | ||||
\(887\) | 668.313 | + | 1311.64i | 0.753453 | + | 1.47874i | 0.873947 | + | 0.486021i | \(0.161552\pi\) |
−0.120494 | + | 0.992714i | \(0.538448\pi\) | |||||||
\(888\) | −592.626 | + | 301.958i | −0.667372 | + | 0.340043i | ||||
\(889\) | −653.449 | + | 212.318i | −0.735038 | + | 0.238828i | ||||
\(890\) | 486.770 | − | 1392.78i | 0.546932 | − | 1.56492i | ||||
\(891\) | 40.6232 | − | 125.025i | 0.0455929 | − | 0.140320i | ||||
\(892\) | 1222.87 | − | 193.684i | 1.37093 | − | 0.217134i | ||||
\(893\) | −123.018 | − | 123.018i | −0.137758 | − | 0.137758i | ||||
\(894\) | 269.571 | − | 371.033i | 0.301534 | − | 0.415025i | ||||
\(895\) | 687.294 | − | 331.301i | 0.767926 | − | 0.370169i | ||||
\(896\) | 1110.05 | − | 806.495i | 1.23889 | − | 0.900106i | ||||
\(897\) | 9.90580 | − | 62.5427i | 0.0110433 | − | 0.0697243i | ||||
\(898\) | 108.716 | − | 213.368i | 0.121065 | − | 0.237604i | ||||
\(899\) | 1863.12i | 2.07244i | ||||||||
\(900\) | 22.5905 | − | 511.579i | 0.0251006 | − | 0.568421i | ||||
\(901\) | 2133.53 | 2.36796 | ||||||||
\(902\) | 167.240 | + | 85.2128i | 0.185410 | + | 0.0944710i | ||||
\(903\) | 488.940 | + | 77.4405i | 0.541462 | + | 0.0857592i | ||||
\(904\) | 1035.27 | + | 1424.92i | 1.14521 | + | 1.57624i | ||||
\(905\) | 117.974 | − | 112.880i | 0.130358 | − | 0.124729i | ||||
\(906\) | −864.247 | − | 627.912i | −0.953914 | − | 0.693059i | ||||
\(907\) | −511.441 | + | 511.441i | −0.563882 | + | 0.563882i | −0.930408 | − | 0.366526i | \(-0.880547\pi\) |
0.366526 | + | 0.930408i | \(0.380547\pi\) | |||||||
\(908\) | −319.482 | − | 2017.13i | −0.351853 | − | 2.22151i | ||||
\(909\) | 12.9716 | + | 4.21474i | 0.0142702 | + | 0.00463667i | ||||
\(910\) | 443.672 | + | 639.890i | 0.487552 | + | 0.703176i | ||||
\(911\) | −196.843 | − | 605.821i | −0.216074 | − | 0.665007i | −0.999076 | − | 0.0429874i | \(-0.986312\pi\) |
0.783002 | − | 0.622019i | \(-0.213688\pi\) | |||||||
\(912\) | 5.49515 | + | 10.7848i | 0.00602539 | + | 0.0118255i | ||||
\(913\) | −225.530 | + | 114.913i | −0.247020 | + | 0.125863i | ||||
\(914\) | 928.856 | − | 301.803i | 1.01625 | − | 0.330201i | ||||
\(915\) | −275.943 | − | 6.08964i | −0.301577 | − | 0.00665534i | ||||
\(916\) | 461.193 | − | 1419.41i | 0.503486 | − | 1.54957i | ||||
\(917\) | −632.694 | + | 100.209i | −0.689961 | + | 0.109279i | ||||
\(918\) | 313.805 | + | 313.805i | 0.341836 | + | 0.341836i | ||||
\(919\) | −576.765 | + | 793.848i | −0.627600 | + | 0.863818i | −0.997879 | − | 0.0651032i | \(-0.979262\pi\) |
0.370278 | + | 0.928921i | \(0.379262\pi\) | |||||||
\(920\) | 104.547 | − | 194.456i | 0.113638 | − | 0.211365i | ||||
\(921\) | −27.8248 | + | 20.2159i | −0.0302115 | + | 0.0219500i | ||||
\(922\) | −69.5284 | + | 438.985i | −0.0754105 | + | 0.476123i | ||||
\(923\) | 382.826 | − | 751.338i | 0.414762 | − | 0.814017i | ||||
\(924\) | 1061.16i | 1.14844i | ||||||||
\(925\) | 116.289 | + | 1025.18i | 0.125718 | + | 1.10831i | ||||
\(926\) | −2428.91 | −2.62301 | ||||||||
\(927\) | 265.548 | + | 135.304i | 0.286460 | + | 0.145959i | ||||
\(928\) | 1443.91 | + | 228.692i | 1.55593 | + | 0.246436i | ||||
\(929\) | −503.341 | − | 692.790i | −0.541810 | − | 0.745737i | 0.447063 | − | 0.894503i | \(-0.352470\pi\) |
−0.988873 | + | 0.148765i | \(0.952470\pi\) | |||||||
\(930\) | 947.835 | − | 128.755i | 1.01918 | − | 0.138446i | ||||
\(931\) | −19.2535 | − | 13.9885i | −0.0206804 | − | 0.0150252i | ||||
\(932\) | 882.402 | − | 882.402i | 0.946784 | − | 0.946784i | ||||
\(933\) | 52.1764 | + | 329.429i | 0.0559232 | + | 0.353085i | ||||
\(934\) | −613.010 | − | 199.179i | −0.656327 | − | 0.213254i | ||||
\(935\) | −1815.30 | + | 545.852i | −1.94150 | + | 0.583799i | ||||
\(936\) | 66.4532 | + | 204.522i | 0.0709970 | + | 0.218506i | ||||
\(937\) | −80.6308 | − | 158.247i | −0.0860521 | − | 0.168887i | 0.843970 | − | 0.536390i | \(-0.180213\pi\) |
−0.930022 | + | 0.367504i | \(0.880213\pi\) | |||||||
\(938\) | −6.41050 | + | 3.26631i | −0.00683422 | + | 0.00348221i | ||||
\(939\) | −261.923 | + | 85.1038i | −0.278938 | + | 0.0906324i | ||||
\(940\) | −809.239 | − | 2691.23i | −0.860892 | − | 2.86301i | ||||
\(941\) | −254.617 | + | 783.630i | −0.270581 | + | 0.832763i | 0.719774 | + | 0.694209i | \(0.244245\pi\) |
−0.990355 | + | 0.138554i | \(0.955755\pi\) | |||||||
\(942\) | 717.171 | − | 113.589i | 0.761328 | − | 0.120583i | ||||
\(943\) | −13.1042 | − | 13.1042i | −0.0138963 | − | 0.0138963i | ||||
\(944\) | 21.8875 | − | 30.1255i | 0.0231859 | − | 0.0319126i | ||||
\(945\) | −21.4837 | − | 158.153i | −0.0227341 | − | 0.167358i | ||||
\(946\) | −1809.07 | + | 1314.36i | −1.91233 | + | 1.38939i | ||||
\(947\) | 34.8644 | − | 220.125i | 0.0368156 | − | 0.232444i | −0.962419 | − | 0.271570i | \(-0.912457\pi\) |
0.999234 | + | 0.0391254i | \(0.0124572\pi\) | |||||||
\(948\) | 302.745 | − | 594.170i | 0.319351 | − | 0.626762i | ||||
\(949\) | 341.360i | 0.359705i | ||||||||
\(950\) | 172.748 | − | 19.5953i | 0.181840 | − | 0.0206266i | ||||
\(951\) | −663.469 | −0.697654 | ||||||||
\(952\) | −1321.92 | − | 673.550i | −1.38857 | − | 0.707510i | ||||
\(953\) | −794.568 | − | 125.847i | −0.833754 | − | 0.132054i | −0.275060 | − | 0.961427i | \(-0.588698\pi\) |
−0.558694 | + | 0.829374i | \(0.688698\pi\) | |||||||
\(954\) | −476.960 | − | 656.479i | −0.499958 | − | 0.688133i | ||||
\(955\) | 220.941 | + | 118.787i | 0.231352 | + | 0.124384i | ||||
\(956\) | −2522.26 | − | 1832.53i | −2.63835 | − | 1.91688i | ||||
\(957\) | −992.962 | + | 992.962i | −1.03758 | + | 1.03758i | ||||
\(958\) | −73.8181 | − | 466.069i | −0.0770544 | − | 0.486502i | ||||
\(959\) | 893.080 | + | 290.179i | 0.931261 | + | 0.302585i | ||||
\(960\) | 19.0868 | − | 864.887i | 0.0198820 | − | 0.900924i | ||||
\(961\) | 51.2046 | + | 157.592i | 0.0532826 | + | 0.163987i | ||||
\(962\) | −474.968 | − | 932.176i | −0.493729 | − | 0.968998i | ||||
\(963\) | 219.330 | − | 111.754i | 0.227757 | − | 0.116048i | ||||
\(964\) | −2597.11 | + | 843.851i | −2.69409 | + | 0.875364i | ||||
\(965\) | −286.341 | + | 198.536i | −0.296726 | + | 0.205737i | ||||
\(966\) | 51.3443 | − | 158.022i | 0.0531515 | − | 0.163583i | ||||
\(967\) | 193.991 | − | 30.7251i | 0.200611 | − | 0.0317736i | −0.0553203 | − | 0.998469i | \(-0.517618\pi\) |
0.255931 | + | 0.966695i | \(0.417618\pi\) | |||||||
\(968\) | −607.629 | − | 607.629i | −0.627716 | − | 0.627716i | ||||
\(969\) | −55.8452 | + | 76.8644i | −0.0576318 | + | 0.0793234i | ||||
\(970\) | 100.272 | + | 104.798i | 0.103374 | + | 0.108039i | ||||
\(971\) | −465.952 | + | 338.534i | −0.479868 | + | 0.348645i | −0.801275 | − | 0.598297i | \(-0.795844\pi\) |
0.321406 | + | 0.946941i | \(0.395844\pi\) | |||||||
\(972\) | 16.6498 | − | 105.123i | 0.0171295 | − | 0.108151i | ||||
\(973\) | 439.100 | − | 861.783i | 0.451285 | − | 0.885697i | ||||
\(974\) | 1108.21i | 1.13780i | ||||||||
\(975\) | 333.264 | + | 14.7164i | 0.341809 | + | 0.0150938i | ||||
\(976\) | 105.387 | 0.107978 | ||||||||
\(977\) | −478.563 | − | 243.840i | −0.489829 | − | 0.249581i | 0.191588 | − | 0.981475i | \(-0.438636\pi\) |
−0.681418 | + | 0.731895i | \(0.738636\pi\) | |||||||
\(978\) | 192.795 | + | 30.5357i | 0.197132 | + | 0.0312226i | ||||
\(979\) | 769.907 | + | 1059.69i | 0.786422 | + | 1.08242i | ||||
\(980\) | −166.927 | − | 346.295i | −0.170334 | − | 0.353362i | ||||
\(981\) | 198.623 | + | 144.308i | 0.202470 | + | 0.147103i | ||||
\(982\) | 1479.96 | − | 1479.96i | 1.50708 | − | 1.50708i | ||||
\(983\) | −81.0532 | − | 511.749i | −0.0824549 | − | 0.520600i | −0.993998 | − | 0.109396i | \(-0.965108\pi\) |
0.911543 | − | 0.411204i | \(-0.134892\pi\) | |||||||
\(984\) | 59.8561 | + | 19.4484i | 0.0608294 | + | 0.0197647i | ||||
\(985\) | −1646.96 | − | 575.604i | −1.67204 | − | 0.584369i | ||||
\(986\) | −1464.92 | − | 4508.55i | −1.48572 | − | 4.57257i | ||||
\(987\) | −397.655 | − | 780.441i | −0.402892 | − | 0.790720i | ||||
\(988\) | −99.0484 | + | 50.4677i | −0.100251 | + | 0.0510807i | ||||
\(989\) | 209.976 | − | 68.2255i | 0.212312 | − | 0.0689843i | ||||
\(990\) | 573.774 | + | 436.533i | 0.579570 | + | 0.440942i | ||||
\(991\) | −372.803 | + | 1147.37i | −0.376189 | + | 1.15779i | 0.566485 | + | 0.824072i | \(0.308303\pi\) |
−0.942673 | + | 0.333717i | \(0.891697\pi\) | |||||||
\(992\) | 873.185 | − | 138.299i | 0.880226 | − | 0.139414i | ||||
\(993\) | 682.271 | + | 682.271i | 0.687080 | + | 0.687080i | ||||
\(994\) | 1300.55 | − | 1790.05i | 1.30840 | − | 1.80085i | ||||
\(995\) | 196.308 | + | 35.5487i | 0.197295 | + | 0.0357273i | ||||
\(996\) | −165.793 | + | 120.455i | −0.166459 | + | 0.120939i | ||||
\(997\) | 24.0632 | − | 151.929i | 0.0241356 | − | 0.152386i | −0.972677 | − | 0.232161i | \(-0.925420\pi\) |
0.996813 | + | 0.0797753i | \(0.0254203\pi\) | |||||||
\(998\) | 329.573 | − | 646.824i | 0.330234 | − | 0.648120i | ||||
\(999\) | 214.447i | 0.214662i |
(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 | 75.3.k.a.58.10 | yes | 80 | |
3.2 | odd | 2 | 225.3.r.b.208.1 | 80 | |||
5.2 | odd | 4 | 375.3.k.c.232.1 | 80 | |||
5.3 | odd | 4 | 375.3.k.b.232.10 | 80 | |||
5.4 | even | 2 | 375.3.k.a.268.1 | 80 | |||
25.3 | odd | 20 | 375.3.k.a.7.1 | 80 | |||
25.4 | even | 10 | 375.3.k.b.118.10 | 80 | |||
25.21 | even | 5 | 375.3.k.c.118.1 | 80 | |||
25.22 | odd | 20 | inner | 75.3.k.a.22.10 | ✓ | 80 | |
75.47 | even | 20 | 225.3.r.b.172.1 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.3.k.a.22.10 | ✓ | 80 | 25.22 | odd | 20 | inner | |
75.3.k.a.58.10 | yes | 80 | 1.1 | even | 1 | trivial | |
225.3.r.b.172.1 | 80 | 75.47 | even | 20 | |||
225.3.r.b.208.1 | 80 | 3.2 | odd | 2 | |||
375.3.k.a.7.1 | 80 | 25.3 | odd | 20 | |||
375.3.k.a.268.1 | 80 | 5.4 | even | 2 | |||
375.3.k.b.118.10 | 80 | 25.4 | even | 10 | |||
375.3.k.b.232.10 | 80 | 5.3 | odd | 4 | |||
375.3.k.c.118.1 | 80 | 25.21 | even | 5 | |||
375.3.k.c.232.1 | 80 | 5.2 | odd | 4 |