Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(218,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 15, 12]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.218");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.ct (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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(160\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{20})\) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 368.14 | ||
Character | \(\chi\) | \(=\) | 825.368 |
Dual form | 825.2.ct.b.482.14 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.493426 | − | 0.968403i | 0.348905 | − | 0.684764i | −0.648145 | − | 0.761517i | \(-0.724455\pi\) |
0.997050 | + | 0.0767523i | \(0.0244551\pi\) | |||||||
\(3\) | 0.511262 | + | 1.65488i | 0.295177 | + | 0.955443i | ||||
\(4\) | 0.481235 | + | 0.662363i | 0.240618 | + | 0.331182i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.85486 | + | 0.321451i | 0.757242 | + | 0.131232i | ||||
\(7\) | −0.654138 | + | 4.13007i | −0.247241 | + | 1.56102i | 0.481634 | + | 0.876372i | \(0.340043\pi\) |
−0.728875 | + | 0.684646i | \(0.759957\pi\) | |||||||
\(8\) | 3.02585 | − | 0.479248i | 1.06980 | − | 0.169440i | ||||
\(9\) | −2.47722 | + | 1.69215i | −0.825741 | + | 0.564049i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.47815 | − | 2.20426i | 0.747191 | − | 0.664610i | ||||
\(12\) | −0.850091 | + | 1.13502i | −0.245400 | + | 0.327653i | ||||
\(13\) | 0.553726 | − | 1.08675i | 0.153576 | − | 0.301410i | −0.801381 | − | 0.598154i | \(-0.795901\pi\) |
0.954957 | + | 0.296745i | \(0.0959010\pi\) | |||||||
\(14\) | 3.67680 | + | 2.67135i | 0.982666 | + | 0.713949i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.522930 | − | 1.60941i | 0.130732 | − | 0.402353i | ||||
\(17\) | −4.50204 | + | 2.29390i | −1.09190 | + | 0.556353i | −0.904735 | − | 0.425975i | \(-0.859931\pi\) |
−0.187169 | + | 0.982328i | \(0.559931\pi\) | |||||||
\(18\) | 0.416355 | + | 3.23390i | 0.0981359 | + | 0.762238i | ||||
\(19\) | 1.57039 | − | 2.16146i | 0.360273 | − | 0.495873i | −0.589952 | − | 0.807438i | \(-0.700853\pi\) |
0.950225 | + | 0.311566i | \(0.100853\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.16918 | + | 1.02903i | −1.56444 | + | 0.224552i | ||||
\(22\) | −0.911829 | − | 3.48749i | −0.194403 | − | 0.743535i | ||||
\(23\) | 0.382388 | − | 0.382388i | 0.0797334 | − | 0.0797334i | −0.666115 | − | 0.745849i | \(-0.732044\pi\) |
0.745849 | + | 0.666115i | \(0.232044\pi\) | |||||||
\(24\) | 2.34010 | + | 4.76239i | 0.477671 | + | 0.972119i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.779188 | − | 1.07246i | −0.152811 | − | 0.210327i | ||||
\(27\) | −4.06680 | − | 3.23436i | −0.782657 | − | 0.622454i | ||||
\(28\) | −3.05040 | + | 1.55426i | −0.576471 | + | 0.293727i | ||||
\(29\) | −4.46296 | + | 3.24253i | −0.828751 | + | 0.602123i | −0.919206 | − | 0.393778i | \(-0.871168\pi\) |
0.0904547 | + | 0.995901i | \(0.471168\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.46761 | + | 7.59452i | 0.443196 | + | 1.36402i | 0.884451 | + | 0.466634i | \(0.154533\pi\) |
−0.441255 | + | 0.897382i | \(0.645467\pi\) | |||||||
\(32\) | 3.03201 | + | 3.03201i | 0.535989 | + | 0.535989i | ||||
\(33\) | 4.91476 | + | 2.97408i | 0.855550 | + | 0.517720i | ||||
\(34\) | 5.49166i | 0.941812i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.31294 | − | 0.826500i | −0.385491 | − | 0.137750i | ||||
\(37\) | 0.212879 | − | 1.34406i | 0.0349970 | − | 0.220963i | −0.963991 | − | 0.265934i | \(-0.914320\pi\) |
0.998988 | + | 0.0449714i | \(0.0143197\pi\) | |||||||
\(38\) | −1.31829 | − | 2.58729i | −0.213855 | − | 0.419714i | ||||
\(39\) | 2.08153 | + | 0.360735i | 0.333312 | + | 0.0577638i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.50451 | − | 4.82355i | 0.547313 | − | 0.753312i | −0.442331 | − | 0.896852i | \(-0.645848\pi\) |
0.989645 | + | 0.143540i | \(0.0458485\pi\) | |||||||
\(42\) | −2.54095 | + | 7.45041i | −0.392077 | + | 1.14962i | ||||
\(43\) | 2.31814 | + | 2.31814i | 0.353512 | + | 0.353512i | 0.861415 | − | 0.507902i | \(-0.169579\pi\) |
−0.507902 | + | 0.861415i | \(0.669579\pi\) | |||||||
\(44\) | 2.65259 | + | 0.580669i | 0.399894 | + | 0.0875391i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.181625 | − | 0.558986i | −0.0267792 | − | 0.0824180i | ||||
\(47\) | −0.934845 | − | 5.90238i | −0.136361 | − | 0.860950i | −0.957123 | − | 0.289680i | \(-0.906451\pi\) |
0.820762 | − | 0.571270i | \(-0.193549\pi\) | |||||||
\(48\) | 2.93073 | + | 0.0425526i | 0.423014 | + | 0.00614194i | ||||
\(49\) | −9.97216 | − | 3.24015i | −1.42459 | − | 0.462879i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.09784 | − | 6.27752i | −0.853868 | − | 0.879029i | ||||
\(52\) | 0.986295 | − | 0.156214i | 0.136774 | − | 0.0216629i | ||||
\(53\) | −2.96098 | − | 1.50870i | −0.406723 | − | 0.207235i | 0.238646 | − | 0.971107i | \(-0.423296\pi\) |
−0.645369 | + | 0.763871i | \(0.723296\pi\) | |||||||
\(54\) | −5.13884 | + | 2.34239i | −0.699307 | + | 0.318758i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.8105i | 1.71187i | ||||||||
\(57\) | 4.37982 | + | 1.49373i | 0.580122 | + | 0.197849i | ||||
\(58\) | 0.937936 | + | 5.92189i | 0.123157 | + | 0.777583i | ||||
\(59\) | 0.878179 | − | 0.638034i | 0.114329 | − | 0.0830650i | −0.529152 | − | 0.848527i | \(-0.677490\pi\) |
0.643481 | + | 0.765462i | \(0.277490\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.837635 | − | 2.57798i | 0.107248 | − | 0.330076i | −0.883003 | − | 0.469367i | \(-0.844482\pi\) |
0.990252 | + | 0.139291i | \(0.0444823\pi\) | |||||||
\(62\) | 8.57214 | + | 1.35769i | 1.08866 | + | 0.172427i | ||||
\(63\) | −5.36824 | − | 11.3380i | −0.676335 | − | 1.42845i | ||||
\(64\) | 7.65111 | − | 2.48600i | 0.956389 | − | 0.310750i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.30518 | − | 3.29198i | 0.653022 | − | 0.405215i | ||||
\(67\) | −1.62430 | + | 1.62430i | −0.198440 | + | 0.198440i | −0.799331 | − | 0.600891i | \(-0.794813\pi\) |
0.600891 | + | 0.799331i | \(0.294813\pi\) | |||||||
\(68\) | −3.68593 | − | 1.87808i | −0.446985 | − | 0.227750i | ||||
\(69\) | 0.828304 | + | 0.437304i | 0.0997161 | + | 0.0526452i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.6181 | + | 5.07463i | 1.85353 | + | 0.602247i | 0.996161 | + | 0.0875402i | \(0.0279006\pi\) |
0.857366 | + | 0.514707i | \(0.172099\pi\) | |||||||
\(72\) | −6.68476 | + | 6.30740i | −0.787806 | + | 0.743334i | ||||
\(73\) | −6.99810 | − | 1.10839i | −0.819066 | − | 0.129727i | −0.267180 | − | 0.963647i | \(-0.586092\pi\) |
−0.551886 | + | 0.833919i | \(0.686092\pi\) | |||||||
\(74\) | −1.19656 | − | 0.869348i | −0.139097 | − | 0.101060i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.18740 | 0.250912 | ||||||||
\(77\) | 7.48269 | + | 11.6768i | 0.852732 | + | 1.33070i | ||||
\(78\) | 1.37642 | − | 1.83777i | 0.155849 | − | 0.208086i | ||||
\(79\) | 7.14001 | − | 2.31993i | 0.803313 | − | 0.261012i | 0.121550 | − | 0.992585i | \(-0.461213\pi\) |
0.681763 | + | 0.731573i | \(0.261213\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.27327 | − | 8.38366i | 0.363696 | − | 0.931518i | ||||
\(82\) | −2.94192 | − | 5.77385i | −0.324881 | − | 0.637615i | ||||
\(83\) | 0.0758170 | + | 0.148799i | 0.00832200 | + | 0.0163328i | 0.895130 | − | 0.445805i | \(-0.147083\pi\) |
−0.886808 | + | 0.462138i | \(0.847083\pi\) | |||||||
\(84\) | −4.13165 | − | 4.25340i | −0.450800 | − | 0.464084i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.38872 | − | 1.10106i | 0.365415 | − | 0.118731i | ||||
\(87\) | −7.64772 | − | 5.72786i | −0.819922 | − | 0.614091i | ||||
\(88\) | 6.44214 | − | 7.85742i | 0.686734 | − | 0.837604i | ||||
\(89\) | 8.05373 | 0.853693 | 0.426847 | − | 0.904324i | \(-0.359624\pi\) | ||||
0.426847 | + | 0.904324i | \(0.359624\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.12613 | + | 2.99781i | 0.432536 | + | 0.314256i | ||||
\(92\) | 0.437298 | + | 0.0692612i | 0.0455915 | + | 0.00722098i | ||||
\(93\) | −11.3064 | + | 7.96637i | −1.17242 | + | 0.826074i | ||||
\(94\) | −6.17716 | − | 2.00708i | −0.637125 | − | 0.207015i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.46745 | + | 6.56776i | −0.353895 | + | 0.670319i | ||||
\(97\) | 9.85915 | + | 5.02349i | 1.00104 | + | 0.510058i | 0.876112 | − | 0.482107i | \(-0.160128\pi\) |
0.124933 | + | 0.992165i | \(0.460128\pi\) | |||||||
\(98\) | −8.05830 | + | 8.05830i | −0.814011 | + | 0.814011i | ||||
\(99\) | −2.40900 | + | 9.65385i | −0.242113 | + | 0.970248i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.53980 | + | 2.12491i | −0.650734 | + | 0.211436i | −0.615738 | − | 0.787951i | \(-0.711142\pi\) |
−0.0349963 | + | 0.999387i | \(0.511142\pi\) | |||||||
\(102\) | −9.08801 | + | 2.80767i | −0.899847 | + | 0.278001i | ||||
\(103\) | −0.238375 | − | 0.0377549i | −0.0234878 | − | 0.00372010i | 0.144680 | − | 0.989479i | \(-0.453785\pi\) |
−0.168167 | + | 0.985758i | \(0.553785\pi\) | |||||||
\(104\) | 1.15467 | − | 3.55372i | 0.113225 | − | 0.348470i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.92205 | + | 2.12300i | −0.283815 | + | 0.206204i | ||||
\(107\) | −2.39327 | − | 15.1105i | −0.231366 | − | 1.46079i | −0.780555 | − | 0.625088i | \(-0.785063\pi\) |
0.549189 | − | 0.835698i | \(-0.314937\pi\) | |||||||
\(108\) | 0.185236 | − | 4.25019i | 0.0178243 | − | 0.408975i | ||||
\(109\) | − | 6.46133i | − | 0.618883i | −0.950918 | − | 0.309442i | \(-0.899858\pi\) | ||
0.950918 | − | 0.309442i | \(-0.100142\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.33309 | − | 0.334880i | 0.221447 | − | 0.0317854i | ||||
\(112\) | 6.30491 | + | 3.21251i | 0.595758 | + | 0.303554i | ||||
\(113\) | 15.9852 | − | 2.53181i | 1.50376 | − | 0.238173i | 0.650440 | − | 0.759557i | \(-0.274584\pi\) |
0.853322 | + | 0.521385i | \(0.174584\pi\) | |||||||
\(114\) | 3.60765 | − | 3.50439i | 0.337888 | − | 0.328216i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.29547 | − | 1.39568i | −0.398824 | − | 0.129586i | ||||
\(117\) | 0.467237 | + | 3.62911i | 0.0431961 | + | 0.335511i | ||||
\(118\) | −0.184558 | − | 1.16525i | −0.0169900 | − | 0.107270i | ||||
\(119\) | −6.52902 | − | 20.0942i | −0.598514 | − | 1.84204i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.28247 | − | 10.9250i | 0.116588 | − | 0.993180i | ||||
\(122\) | −2.08321 | − | 2.08321i | −0.188605 | − | 0.188605i | ||||
\(123\) | 9.77410 | + | 3.33344i | 0.881301 | + | 0.300566i | ||||
\(124\) | −3.84283 | + | 5.28920i | −0.345096 | + | 0.474984i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −13.6286 | − | 0.395843i | −1.21413 | − | 0.0352645i | ||||
\(127\) | −4.43884 | − | 8.71170i | −0.393883 | − | 0.773039i | 0.605863 | − | 0.795569i | \(-0.292828\pi\) |
−0.999746 | + | 0.0225301i | \(0.992828\pi\) | |||||||
\(128\) | 0.0262550 | − | 0.165768i | 0.00232064 | − | 0.0146519i | ||||
\(129\) | −2.65105 | + | 5.02140i | −0.233412 | + | 0.442110i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 9.68231i | − | 0.845947i | −0.906142 | − | 0.422974i | \(-0.860986\pi\) | ||
0.906142 | − | 0.422974i | \(-0.139014\pi\) | |||||||
\(132\) | 0.395235 | + | 4.68659i | 0.0344008 | + | 0.407915i | ||||
\(133\) | 7.89971 | + | 7.89971i | 0.684992 | + | 0.684992i | ||||
\(134\) | 0.771506 | + | 2.37445i | 0.0666480 | + | 0.205121i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.5232 | + | 9.09861i | −1.07385 | + | 0.780199i | ||||
\(137\) | 10.9061 | − | 5.55693i | 0.931770 | − | 0.474761i | 0.0788992 | − | 0.996883i | \(-0.474859\pi\) |
0.852871 | + | 0.522122i | \(0.174859\pi\) | |||||||
\(138\) | 0.832194 | − | 0.586356i | 0.0708410 | − | 0.0499139i | ||||
\(139\) | −3.27216 | − | 4.50374i | −0.277541 | − | 0.382002i | 0.647377 | − | 0.762170i | \(-0.275866\pi\) |
−0.924917 | + | 0.380168i | \(0.875866\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.28975 | − | 4.56471i | 0.782338 | − | 0.384418i | ||||
\(142\) | 12.6207 | − | 12.6207i | 1.05910 | − | 1.05910i | ||||
\(143\) | −1.02326 | − | 3.91368i | −0.0855693 | − | 0.327279i | ||||
\(144\) | 1.42795 | + | 4.87175i | 0.118996 | + | 0.405979i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.52641 | + | 6.23007i | −0.374609 | + | 0.515605i | ||||
\(147\) | 0.263662 | − | 18.1592i | 0.0217465 | − | 1.49775i | ||||
\(148\) | 0.992703 | − | 0.505807i | 0.0815997 | − | 0.0415771i | ||||
\(149\) | −1.96207 | + | 6.03864i | −0.160739 | + | 0.494705i | −0.998697 | − | 0.0510303i | \(-0.983749\pi\) |
0.837958 | + | 0.545735i | \(0.183749\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.67313 | − | 1.21560i | −0.136158 | − | 0.0989244i | 0.517622 | − | 0.855610i | \(-0.326818\pi\) |
−0.653779 | + | 0.756685i | \(0.726818\pi\) | |||||||
\(152\) | 3.71590 | − | 7.29287i | 0.301399 | − | 0.591530i | ||||
\(153\) | 7.27093 | − | 13.3006i | 0.587820 | − | 1.07529i | ||||
\(154\) | 15.0000 | − | 1.48461i | 1.20874 | − | 0.119633i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.762769 | + | 1.55233i | 0.0610704 | + | 0.124286i | ||||
\(157\) | 4.41008 | − | 0.698488i | 0.351962 | − | 0.0557454i | 0.0220499 | − | 0.999757i | \(-0.492981\pi\) |
0.329913 | + | 0.944011i | \(0.392981\pi\) | |||||||
\(158\) | 1.27644 | − | 8.05912i | 0.101548 | − | 0.641149i | ||||
\(159\) | 0.982867 | − | 5.67140i | 0.0779464 | − | 0.449771i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.32915 | + | 1.82942i | 0.104752 | + | 0.144179i | ||||
\(162\) | −6.50365 | − | 7.30656i | −0.510975 | − | 0.574057i | ||||
\(163\) | −10.3568 | + | 20.3264i | −0.811210 | + | 1.59209i | −0.00534819 | + | 0.999986i | \(0.501702\pi\) |
−0.805862 | + | 0.592104i | \(0.798298\pi\) | |||||||
\(164\) | 4.88144 | 0.381176 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.181508 | 0.0140877 | ||||||||
\(167\) | 5.59726 | − | 10.9852i | 0.433129 | − | 0.850064i | −0.566532 | − | 0.824040i | \(-0.691715\pi\) |
0.999661 | − | 0.0260243i | \(-0.00828473\pi\) | |||||||
\(168\) | −21.1997 | + | 6.54951i | −1.63560 | + | 0.505305i | ||||
\(169\) | 6.76680 | + | 9.31370i | 0.520523 | + | 0.716438i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.232702 | + | 8.01175i | −0.0177951 | + | 0.612674i | ||||
\(172\) | −0.419880 | + | 2.65102i | −0.0320155 | + | 0.202138i | ||||
\(173\) | −12.5969 | + | 1.99515i | −0.957725 | + | 0.151689i | −0.615681 | − | 0.787995i | \(-0.711119\pi\) |
−0.342044 | + | 0.939684i | \(0.611119\pi\) | |||||||
\(174\) | −9.32046 | + | 4.57980i | −0.706583 | + | 0.347194i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.25166 | − | 5.14104i | −0.169726 | − | 0.387520i | ||||
\(177\) | 1.50485 | + | 1.12707i | 0.113111 | + | 0.0847161i | ||||
\(178\) | 3.97392 | − | 7.79926i | 0.297858 | − | 0.584579i | ||||
\(179\) | −14.8813 | − | 10.8119i | −1.11228 | − | 0.808119i | −0.129259 | − | 0.991611i | \(-0.541260\pi\) |
−0.983021 | + | 0.183492i | \(0.941260\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.39993 | + | 13.5416i | −0.327044 | + | 1.00654i | 0.643465 | + | 0.765476i | \(0.277496\pi\) |
−0.970509 | + | 0.241064i | \(0.922504\pi\) | |||||||
\(182\) | 4.93903 | − | 2.51656i | 0.366105 | − | 0.186540i | ||||
\(183\) | 4.69448 | + | 0.0681613i | 0.347026 | + | 0.00503863i | ||||
\(184\) | 0.973792 | − | 1.34031i | 0.0717889 | − | 0.0988089i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.13579 | + | 14.8800i | 0.156604 | + | 1.09105i | ||||
\(187\) | −6.10037 | + | 15.6083i | −0.446103 | + | 1.14139i | ||||
\(188\) | 3.45964 | − | 3.45964i | 0.252320 | − | 0.252320i | ||||
\(189\) | 16.0184 | − | 14.6804i | 1.16517 | − | 1.06785i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.65811 | − | 2.28220i | −0.119977 | − | 0.165134i | 0.744804 | − | 0.667283i | \(-0.232543\pi\) |
−0.864781 | + | 0.502149i | \(0.832543\pi\) | |||||||
\(192\) | 8.02573 | + | 11.3906i | 0.579207 | + | 0.822048i | ||||
\(193\) | 14.6680 | − | 7.47371i | 1.05582 | − | 0.537969i | 0.162188 | − | 0.986760i | \(-0.448145\pi\) |
0.893637 | + | 0.448790i | \(0.148145\pi\) | |||||||
\(194\) | 9.72952 | − | 7.06891i | 0.698539 | − | 0.507518i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.65280 | − | 8.16447i | −0.189485 | − | 0.583176i | ||||
\(197\) | 10.6651 | + | 10.6651i | 0.759856 | + | 0.759856i | 0.976296 | − | 0.216440i | \(-0.0694445\pi\) |
−0.216440 | + | 0.976296i | \(0.569445\pi\) | |||||||
\(198\) | 8.16015 | + | 7.09634i | 0.579917 | + | 0.504315i | ||||
\(199\) | 20.8481i | 1.47788i | 0.673771 | + | 0.738940i | \(0.264674\pi\) | ||||
−0.673771 | + | 0.738940i | \(0.735326\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.51846 | − | 1.85757i | −0.248173 | − | 0.131023i | ||||
\(202\) | −1.16914 | + | 7.38164i | −0.0822602 | + | 0.519371i | ||||
\(203\) | −10.4725 | − | 20.5534i | −0.735024 | − | 1.44257i | ||||
\(204\) | 1.22351 | − | 7.05995i | 0.0856626 | − | 0.494295i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.154182 | + | 0.212214i | −0.0107424 | + | 0.0147856i | ||||
\(207\) | −0.300203 | + | 1.59432i | −0.0208656 | + | 0.110813i | ||||
\(208\) | −1.45947 | − | 1.45947i | −0.101196 | − | 0.101196i | ||||
\(209\) | −0.872750 | − | 8.81797i | −0.0603694 | − | 0.609952i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.62698 | − | 20.3957i | −0.456220 | − | 1.40410i | −0.869697 | − | 0.493586i | \(-0.835686\pi\) |
0.413477 | − | 0.910514i | \(-0.364314\pi\) | |||||||
\(212\) | −0.425624 | − | 2.68729i | −0.0292320 | − | 0.184564i | ||||
\(213\) | −0.412940 | + | 28.4405i | −0.0282942 | + | 1.94871i | ||||
\(214\) | −15.8139 | − | 5.13826i | −1.08102 | − | 0.351244i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −13.8556 | − | 7.83771i | −0.942756 | − | 0.533288i | ||||
\(217\) | −32.9800 | + | 5.22352i | −2.23883 | + | 0.354596i | ||||
\(218\) | −6.25717 | − | 3.18819i | −0.423789 | − | 0.215931i | ||||
\(219\) | −1.74361 | − | 12.1477i | −0.117822 | − | 0.820863i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.16278i | 0.414553i | ||||||||
\(222\) | 0.826910 | − | 2.42461i | 0.0554986 | − | 0.162729i | ||||
\(223\) | −3.93131 | − | 24.8213i | −0.263260 | − | 1.66216i | −0.665330 | − | 0.746549i | \(-0.731709\pi\) |
0.402070 | − | 0.915609i | \(-0.368291\pi\) | |||||||
\(224\) | −14.5058 | + | 10.5391i | −0.969208 | + | 0.704171i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.43571 | − | 16.7294i | 0.361578 | − | 1.11282i | ||||
\(227\) | −16.7042 | − | 2.64568i | −1.10869 | − | 0.175600i | −0.424876 | − | 0.905252i | \(-0.639682\pi\) |
−0.683819 | + | 0.729652i | \(0.739682\pi\) | |||||||
\(228\) | 1.11833 | + | 3.61987i | 0.0740634 | + | 0.239732i | ||||
\(229\) | −9.90621 | + | 3.21872i | −0.654621 | + | 0.212699i | −0.617451 | − | 0.786610i | \(-0.711834\pi\) |
−0.0371705 | + | 0.999309i | \(0.511834\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.4981 | + | 18.3528i | −1.01970 | + | 1.20753i | ||||
\(232\) | −11.9503 | + | 11.9503i | −0.784575 | + | 0.784575i | ||||
\(233\) | −6.21436 | − | 3.16637i | −0.407116 | − | 0.207436i | 0.238426 | − | 0.971161i | \(-0.423369\pi\) |
−0.645542 | + | 0.763725i | \(0.723369\pi\) | |||||||
\(234\) | 3.74498 | + | 1.33822i | 0.244817 | + | 0.0874823i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.845221 | + | 0.274629i | 0.0550192 | + | 0.0178768i | ||||
\(237\) | 7.48960 | + | 10.6297i | 0.486502 | + | 0.690475i | ||||
\(238\) | −22.6809 | − | 3.59230i | −1.47019 | − | 0.232854i | ||||
\(239\) | 0.203303 | + | 0.147708i | 0.0131506 | + | 0.00955444i | 0.594341 | − | 0.804213i | \(-0.297413\pi\) |
−0.581191 | + | 0.813767i | \(0.697413\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.42940 | 0.414154 | 0.207077 | − | 0.978325i | \(-0.433605\pi\) | ||||
0.207077 | + | 0.978325i | \(0.433605\pi\) | |||||||
\(242\) | −9.94699 | − | 6.63262i | −0.639416 | − | 0.426361i | ||||
\(243\) | 15.5474 | + | 1.13061i | 0.997366 | + | 0.0725285i | ||||
\(244\) | 2.11066 | − | 0.685793i | 0.135121 | − | 0.0439034i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.05091 | − | 7.82046i | 0.513307 | − | 0.498614i | ||||
\(247\) | −1.47940 | − | 2.90348i | −0.0941317 | − | 0.184744i | ||||
\(248\) | 11.1063 | + | 21.7973i | 0.705250 | + | 1.38413i | ||||
\(249\) | −0.207482 | + | 0.201543i | −0.0131486 | + | 0.0127723i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.3561 | + | 5.96425i | −1.15862 | + | 0.376460i | −0.824386 | − | 0.566029i | \(-0.808479\pi\) |
−0.334239 | + | 0.942488i | \(0.608479\pi\) | |||||||
\(252\) | 4.92649 | − | 9.01197i | 0.310340 | − | 0.567700i | ||||
\(253\) | 0.104733 | − | 1.79050i | 0.00658448 | − | 0.112568i | ||||
\(254\) | −10.6267 | −0.666777 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.8693 | + | 9.35007i | 0.804329 | + | 0.584380i | ||||
\(257\) | −7.34952 | − | 1.16405i | −0.458451 | − | 0.0726115i | −0.0770622 | − | 0.997026i | \(-0.524554\pi\) |
−0.381389 | + | 0.924415i | \(0.624554\pi\) | |||||||
\(258\) | 3.55464 | + | 5.04498i | 0.221302 | + | 0.314087i | ||||
\(259\) | 5.41182 | + | 1.75841i | 0.336274 | + | 0.109262i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.56891 | − | 15.5845i | 0.344707 | − | 0.964654i | ||||
\(262\) | −9.37638 | − | 4.77750i | −0.579275 | − | 0.295155i | ||||
\(263\) | 0.0562110 | − | 0.0562110i | 0.00346612 | − | 0.00346612i | −0.705372 | − | 0.708838i | \(-0.749220\pi\) |
0.708838 | + | 0.705372i | \(0.249220\pi\) | |||||||
\(264\) | 16.2967 | + | 6.64374i | 1.00299 | + | 0.408894i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 11.5480 | − | 3.75218i | 0.708055 | − | 0.230061i | ||||
\(267\) | 4.11756 | + | 13.3279i | 0.251991 | + | 0.815655i | ||||
\(268\) | −1.85755 | − | 0.294207i | −0.113468 | − | 0.0179715i | ||||
\(269\) | 4.02124 | − | 12.3761i | 0.245179 | − | 0.754584i | −0.750428 | − | 0.660953i | \(-0.770152\pi\) |
0.995607 | − | 0.0936318i | \(-0.0298476\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.469264 | + | 0.340940i | −0.0285057 | + | 0.0207106i | −0.601947 | − | 0.798536i | \(-0.705608\pi\) |
0.573441 | + | 0.819247i | \(0.305608\pi\) | |||||||
\(272\) | 1.33759 | + | 8.44518i | 0.0811030 | + | 0.512064i | ||||
\(273\) | −2.85147 | + | 8.36090i | −0.172579 | + | 0.506024i | ||||
\(274\) | − | 13.3034i | − | 0.803689i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.108955 | + | 0.759084i | 0.00655833 | + | 0.0456915i | ||||
\(277\) | 19.0417 | + | 9.70223i | 1.14410 | + | 0.582950i | 0.920118 | − | 0.391642i | \(-0.128093\pi\) |
0.223987 | + | 0.974592i | \(0.428093\pi\) | |||||||
\(278\) | −5.97600 | + | 0.946505i | −0.358417 | + | 0.0567676i | ||||
\(279\) | −18.9639 | − | 14.6378i | −1.13534 | − | 0.876339i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.2788 | − | 4.63947i | −0.851803 | − | 0.276767i | −0.149602 | − | 0.988746i | \(-0.547799\pi\) |
−0.702201 | + | 0.711979i | \(0.747799\pi\) | |||||||
\(282\) | 0.163323 | − | 11.2486i | 0.00972575 | − | 0.669843i | ||||
\(283\) | 1.39140 | + | 8.78495i | 0.0827101 | + | 0.522211i | 0.993905 | + | 0.110236i | \(0.0351608\pi\) |
−0.911195 | + | 0.411975i | \(0.864839\pi\) | |||||||
\(284\) | 4.15473 | + | 12.7869i | 0.246538 | + | 0.758765i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.29493 | − | 0.940185i | −0.253964 | − | 0.0555943i | ||||
\(287\) | 17.6292 | + | 17.6292i | 1.04062 | + | 1.04062i | ||||
\(288\) | −12.6416 | − | 2.38036i | −0.744913 | − | 0.140264i | ||||
\(289\) | 5.01400 | − | 6.90118i | 0.294941 | − | 0.405952i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.27264 | + | 18.8840i | −0.191845 | + | 1.10700i | ||||
\(292\) | −2.63357 | − | 5.16868i | −0.154118 | − | 0.302474i | ||||
\(293\) | 2.02814 | − | 12.8051i | 0.118485 | − | 0.748085i | −0.854880 | − | 0.518825i | \(-0.826370\pi\) |
0.973365 | − | 0.229259i | \(-0.0736304\pi\) | |||||||
\(294\) | −17.4554 | − | 9.21558i | −1.01802 | − | 0.537463i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 4.16896i | − | 0.242316i | ||||||
\(297\) | −17.2075 | + | 0.949051i | −0.998483 | + | 0.0550695i | ||||
\(298\) | 4.87970 | + | 4.87970i | 0.282673 | + | 0.282673i | ||||
\(299\) | −0.203821 | − | 0.627298i | −0.0117873 | − | 0.0362776i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.0904 | + | 8.05768i | −0.639242 | + | 0.464437i | ||||
\(302\) | −2.00276 | + | 1.02046i | −0.115246 | + | 0.0587208i | ||||
\(303\) | −6.86001 | − | 9.73616i | −0.394097 | − | 0.559328i | ||||
\(304\) | −2.65747 | − | 3.65770i | −0.152417 | − | 0.209783i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −9.29270 | − | 13.6041i | −0.531228 | − | 0.777692i | ||||
\(307\) | 2.17577 | − | 2.17577i | 0.124178 | − | 0.124178i | −0.642287 | − | 0.766464i | \(-0.722014\pi\) |
0.766464 | + | 0.642287i | \(0.222014\pi\) | |||||||
\(308\) | −4.13337 | + | 10.5756i | −0.235520 | + | 0.602598i | ||||
\(309\) | −0.0593923 | − | 0.413783i | −0.00337871 | − | 0.0235393i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.64751 | − | 3.64399i | 0.150127 | − | 0.206631i | −0.727330 | − | 0.686288i | \(-0.759239\pi\) |
0.877456 | + | 0.479657i | \(0.159239\pi\) | |||||||
\(312\) | 6.47130 | + | 0.0939597i | 0.366365 | + | 0.00531942i | ||||
\(313\) | −2.31328 | + | 1.17867i | −0.130754 | + | 0.0666226i | −0.518144 | − | 0.855293i | \(-0.673377\pi\) |
0.387390 | + | 0.921916i | \(0.373377\pi\) | |||||||
\(314\) | 1.49963 | − | 4.61538i | 0.0846290 | − | 0.260461i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.97266 | + | 3.61285i | 0.279734 | + | 0.203238i | ||||
\(317\) | 2.43603 | − | 4.78098i | 0.136821 | − | 0.268526i | −0.812422 | − | 0.583070i | \(-0.801851\pi\) |
0.949243 | + | 0.314543i | \(0.101851\pi\) | |||||||
\(318\) | −5.00723 | − | 3.75023i | −0.280791 | − | 0.210302i | ||||
\(319\) | −3.91251 | + | 17.8730i | −0.219058 | + | 1.00070i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 23.7824 | − | 11.6860i | 1.32740 | − | 0.652247i | ||||
\(322\) | 2.42746 | − | 0.384471i | 0.135277 | − | 0.0214258i | ||||
\(323\) | −2.11179 | + | 13.3333i | −0.117503 | + | 0.741884i | ||||
\(324\) | 7.12824 | − | 1.86642i | 0.396013 | − | 0.103690i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.5739 | + | 20.0592i | 0.807171 | + | 1.11098i | ||||
\(327\) | 10.6927 | − | 3.30343i | 0.591307 | − | 0.182680i | ||||
\(328\) | 8.29247 | − | 16.2749i | 0.457875 | − | 0.898631i | ||||
\(329\) | 24.9887 | 1.37767 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.2858 | 0.840182 | 0.420091 | − | 0.907482i | \(-0.361998\pi\) | ||||
0.420091 | + | 0.907482i | \(0.361998\pi\) | |||||||
\(332\) | −0.0620734 | + | 0.121826i | −0.00340672 | + | 0.00668606i | ||||
\(333\) | 1.74701 | + | 3.68977i | 0.0957354 | + | 0.202198i | ||||
\(334\) | −7.87631 | − | 10.8408i | −0.430973 | − | 0.593183i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.09285 | + | 12.0763i | −0.114174 | + | 0.658815i | ||||
\(337\) | 4.61493 | − | 29.1375i | 0.251391 | − | 1.58722i | −0.462274 | − | 0.886737i | \(-0.652967\pi\) |
0.713666 | − | 0.700486i | \(-0.247033\pi\) | |||||||
\(338\) | 12.3583 | − | 1.95737i | 0.672205 | − | 0.106467i | ||||
\(339\) | 12.3625 | + | 25.1591i | 0.671436 | + | 1.36646i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.8554 | + | 13.3811i | 1.23769 | + | 0.724628i | ||||
\(342\) | 7.64378 | + | 4.17856i | 0.413328 | + | 0.225950i | ||||
\(343\) | 6.61653 | − | 12.9857i | 0.357259 | − | 0.701160i | ||||
\(344\) | 8.12531 | + | 5.90338i | 0.438087 | + | 0.318289i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.28353 | + | 13.1833i | −0.230284 | + | 0.708741i | ||||
\(347\) | −9.90827 | + | 5.04852i | −0.531904 | + | 0.271019i | −0.699247 | − | 0.714880i | \(-0.746481\pi\) |
0.167343 | + | 0.985899i | \(0.446481\pi\) | |||||||
\(348\) | 0.113571 | − | 7.82202i | 0.00608807 | − | 0.419304i | ||||
\(349\) | −18.8178 | + | 25.9005i | −1.00730 | + | 1.38642i | −0.0865551 | + | 0.996247i | \(0.527586\pi\) |
−0.920740 | + | 0.390176i | \(0.872414\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.76684 | + | 2.62864i | −0.307811 | + | 0.140306i | ||||
\(352\) | 14.1971 | + | 0.830440i | 0.756710 | + | 0.0442626i | ||||
\(353\) | −8.26410 | + | 8.26410i | −0.439854 | + | 0.439854i | −0.891963 | − | 0.452109i | \(-0.850672\pi\) |
0.452109 | + | 0.891963i | \(0.350672\pi\) | |||||||
\(354\) | 1.83399 | − | 0.901170i | 0.0974756 | − | 0.0478967i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.87574 | + | 5.33449i | 0.205414 | + | 0.282728i | ||||
\(357\) | 29.9154 | − | 21.0781i | 1.58329 | − | 1.11557i | ||||
\(358\) | −17.8131 | + | 9.07622i | −0.941451 | + | 0.479693i | ||||
\(359\) | −0.246254 | + | 0.178914i | −0.0129968 | + | 0.00944272i | −0.594265 | − | 0.804270i | \(-0.702557\pi\) |
0.581268 | + | 0.813712i | \(0.302557\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.66555 | + | 11.2814i | 0.192924 | + | 0.593758i | ||||
\(362\) | 10.9427 | + | 10.9427i | 0.575135 | + | 0.575135i | ||||
\(363\) | 18.7352 | − | 3.46320i | 0.983341 | − | 0.181771i | ||||
\(364\) | 4.17565i | 0.218863i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.38239 | − | 4.51251i | 0.124529 | − | 0.235873i | ||||
\(367\) | 1.56360 | − | 9.87220i | 0.0816194 | − | 0.515325i | −0.912678 | − | 0.408680i | \(-0.865989\pi\) |
0.994297 | − | 0.106645i | \(-0.0340108\pi\) | |||||||
\(368\) | −0.415458 | − | 0.815382i | −0.0216572 | − | 0.0425047i | ||||
\(369\) | −0.519301 | + | 17.8792i | −0.0270337 | + | 0.930752i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.16791 | − | 11.2422i | 0.424057 | − | 0.583664i | ||||
\(372\) | −10.7177 | − | 3.65524i | −0.555685 | − | 0.189515i | ||||
\(373\) | −2.64408 | − | 2.64408i | −0.136906 | − | 0.136906i | 0.635333 | − | 0.772238i | \(-0.280863\pi\) |
−0.772238 | + | 0.635333i | \(0.780863\pi\) | |||||||
\(374\) | 12.1050 | + | 13.6092i | 0.625937 | + | 0.703713i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.65741 | − | 17.4117i | −0.291759 | − | 0.897941i | ||||
\(377\) | 1.05256 | + | 6.64559i | 0.0542095 | + | 0.342265i | ||||
\(378\) | −6.31270 | − | 22.7560i | −0.324690 | − | 1.17044i | ||||
\(379\) | 3.85364 | + | 1.25212i | 0.197948 | + | 0.0643172i | 0.406313 | − | 0.913734i | \(-0.366814\pi\) |
−0.208365 | + | 0.978051i | \(0.566814\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.1474 | − | 11.7997i | 0.622329 | − | 0.604516i | ||||
\(382\) | −3.02824 | + | 0.479627i | −0.154938 | + | 0.0245398i | ||||
\(383\) | 24.4513 | + | 12.4585i | 1.24940 | + | 0.636602i | 0.948416 | − | 0.317027i | \(-0.102685\pi\) |
0.300985 | + | 0.953629i | \(0.402685\pi\) | |||||||
\(384\) | 0.287748 | − | 0.0413018i | 0.0146841 | − | 0.00210768i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 17.8922i | − | 0.910691i | ||||||
\(387\) | −9.66517 | − | 1.81991i | −0.491308 | − | 0.0925112i | ||||
\(388\) | 1.41719 | + | 8.94782i | 0.0719472 | + | 0.454257i | ||||
\(389\) | −3.57077 | + | 2.59432i | −0.181045 | + | 0.131537i | −0.674617 | − | 0.738168i | \(-0.735691\pi\) |
0.493571 | + | 0.869705i | \(0.335691\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.844364 | + | 2.59868i | −0.0427013 | + | 0.131421i | ||||
\(392\) | −31.7271 | − | 5.02509i | −1.60246 | − | 0.253805i | ||||
\(393\) | 16.0230 | − | 4.95019i | 0.808254 | − | 0.249704i | ||||
\(394\) | 15.5905 | − | 5.06567i | 0.785440 | − | 0.255205i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.55365 | + | 3.05014i | −0.379585 | + | 0.153275i | ||||
\(397\) | −2.22251 | + | 2.22251i | −0.111545 | + | 0.111545i | −0.760676 | − | 0.649131i | \(-0.775133\pi\) |
0.649131 | + | 0.760676i | \(0.275133\pi\) | |||||||
\(398\) | 20.1893 | + | 10.2870i | 1.01200 | + | 0.515640i | ||||
\(399\) | −9.03422 | + | 17.1119i | −0.452277 | + | 0.856665i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.9887 | − | 6.49473i | −0.998189 | − | 0.324331i | −0.236047 | − | 0.971742i | \(-0.575852\pi\) |
−0.762142 | + | 0.647410i | \(0.775852\pi\) | |||||||
\(402\) | −3.53498 | + | 2.49071i | −0.176309 | + | 0.124225i | ||||
\(403\) | 9.61971 | + | 1.52361i | 0.479192 | + | 0.0758965i | ||||
\(404\) | −4.55464 | − | 3.30914i | −0.226602 | − | 0.164636i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −25.0714 | −1.24427 | ||||||||
\(407\) | −2.43512 | − | 3.80003i | −0.120704 | − | 0.188361i | ||||
\(408\) | −21.4597 | − | 16.0725i | −1.06241 | − | 0.795707i | ||||
\(409\) | 28.4346 | − | 9.23896i | 1.40600 | − | 0.456837i | 0.494874 | − | 0.868965i | \(-0.335214\pi\) |
0.911126 | + | 0.412127i | \(0.135214\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.7719 | + | 15.2072i | 0.728644 | + | 0.750114i | ||||
\(412\) | −0.0897069 | − | 0.176060i | −0.00441954 | − | 0.00867384i | ||||
\(413\) | 2.06067 | + | 4.04430i | 0.101399 | + | 0.199007i | ||||
\(414\) | 1.39581 | + | 1.07740i | 0.0686005 | + | 0.0529511i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.97394 | − | 1.61613i | 0.243868 | − | 0.0792374i | ||||
\(417\) | 5.78019 | − | 7.71760i | 0.283057 | − | 0.377932i | ||||
\(418\) | −8.96999 | − | 3.50584i | −0.438737 | − | 0.171476i | ||||
\(419\) | −3.58777 | −0.175274 | −0.0876369 | − | 0.996152i | \(-0.527932\pi\) | ||||
−0.0876369 | + | 0.996152i | \(0.527932\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.24117 | + | 2.35485i | 0.157965 | + | 0.114768i | 0.663960 | − | 0.747768i | \(-0.268875\pi\) |
−0.505995 | + | 0.862536i | \(0.668875\pi\) | |||||||
\(422\) | −23.0212 | − | 3.64620i | −1.12066 | − | 0.177494i | ||||
\(423\) | 12.3035 | + | 13.0396i | 0.598218 | + | 0.634008i | ||||
\(424\) | −9.68255 | − | 3.14605i | −0.470226 | − | 0.152786i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 27.3381 | + | 14.4332i | 1.32453 | + | 0.699289i | ||||
\(427\) | 10.0993 | + | 5.14584i | 0.488738 | + | 0.249025i | ||||
\(428\) | 8.85691 | − | 8.85691i | 0.428115 | − | 0.428115i | ||||
\(429\) | 5.95350 | − | 3.69428i | 0.287438 | − | 0.178362i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.6378 | + | 3.78134i | −0.560571 | + | 0.182141i | −0.575578 | − | 0.817747i | \(-0.695223\pi\) |
0.0150070 | + | 0.999887i | \(0.495223\pi\) | |||||||
\(432\) | −7.33208 | + | 4.85382i | −0.352765 | + | 0.233529i | ||||
\(433\) | −0.998249 | − | 0.158107i | −0.0479728 | − | 0.00759815i | 0.132402 | − | 0.991196i | \(-0.457731\pi\) |
−0.180375 | + | 0.983598i | \(0.557731\pi\) | |||||||
\(434\) | −11.2147 | + | 34.5154i | −0.538324 | + | 1.65679i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.27975 | − | 3.10942i | 0.204963 | − | 0.148914i | ||||
\(437\) | −0.226017 | − | 1.42701i | −0.0108119 | − | 0.0682633i | ||||
\(438\) | −12.6242 | − | 4.30545i | −0.603206 | − | 0.205722i | ||||
\(439\) | − | 25.2330i | − | 1.20431i | −0.798380 | − | 0.602153i | \(-0.794310\pi\) | ||
0.798380 | − | 0.602153i | \(-0.205690\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 30.1861 | − | 8.84780i | 1.43743 | − | 0.421324i | ||||
\(442\) | 5.96805 | + | 3.04087i | 0.283871 | + | 0.144640i | ||||
\(443\) | 17.7840 | − | 2.81671i | 0.844945 | − | 0.133826i | 0.281071 | − | 0.959687i | \(-0.409310\pi\) |
0.563874 | + | 0.825861i | \(0.309310\pi\) | |||||||
\(444\) | 1.34458 | + | 1.38420i | 0.0638109 | + | 0.0656912i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −25.9768 | − | 8.44039i | −1.23004 | − | 0.399664i | ||||
\(447\) | −10.9963 | − | 0.159661i | −0.520108 | − | 0.00755169i | ||||
\(448\) | 5.26245 | + | 33.2258i | 0.248627 | + | 1.56977i | ||||
\(449\) | 9.23487 | + | 28.4220i | 0.435820 | + | 1.34132i | 0.892243 | + | 0.451555i | \(0.149130\pi\) |
−0.456423 | + | 0.889763i | \(0.650870\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.94765 | − | 19.6784i | −0.0917110 | − | 0.926617i | ||||
\(452\) | 9.36962 | + | 9.36962i | 0.440710 | + | 0.440710i | ||||
\(453\) | 1.15626 | − | 3.39032i | 0.0543259 | − | 0.159291i | ||||
\(454\) | −10.8044 | + | 14.8709i | −0.507074 | + | 0.697927i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 13.9686 | + | 2.42079i | 0.654139 | + | 0.113364i | ||||
\(457\) | 0.0507311 | + | 0.0995655i | 0.00237310 | + | 0.00465748i | 0.892190 | − | 0.451660i | \(-0.149168\pi\) |
−0.889817 | + | 0.456318i | \(0.849168\pi\) | |||||||
\(458\) | −1.77096 | + | 11.1814i | −0.0827516 | + | 0.522473i | ||||
\(459\) | 25.7282 | + | 5.23238i | 1.20089 | + | 0.244226i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 19.5398i | − | 0.910061i | −0.890476 | − | 0.455031i | \(-0.849628\pi\) | ||
0.890476 | − | 0.455031i | \(-0.150372\pi\) | |||||||
\(462\) | 10.1258 | + | 24.0641i | 0.471094 | + | 1.11957i | ||||
\(463\) | 8.32532 | + | 8.32532i | 0.386911 | + | 0.386911i | 0.873584 | − | 0.486673i | \(-0.161790\pi\) |
−0.486673 | + | 0.873584i | \(0.661790\pi\) | |||||||
\(464\) | 2.88475 | + | 8.87836i | 0.133921 | + | 0.412167i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.13265 | + | 4.45563i | −0.284090 | + | 0.206403i | ||||
\(467\) | −27.4794 | + | 14.0014i | −1.27159 | + | 0.647910i | −0.953855 | − | 0.300268i | \(-0.902924\pi\) |
−0.317740 | + | 0.948178i | \(0.602924\pi\) | |||||||
\(468\) | −2.17894 | + | 2.05593i | −0.100721 | + | 0.0950355i | ||||
\(469\) | −5.64596 | − | 7.77099i | −0.260706 | − | 0.358831i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.41061 | + | 6.94102i | 0.157153 | + | 0.319825i | ||||
\(472\) | 2.35147 | − | 2.35147i | 0.108235 | − | 0.108235i | ||||
\(473\) | 10.8545 | + | 0.634916i | 0.499089 | + | 0.0291935i | ||||
\(474\) | 13.9894 | − | 2.00797i | 0.642556 | − | 0.0922292i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10.1677 | − | 13.9946i | 0.466036 | − | 0.641443i | ||||
\(477\) | 9.88796 | − | 1.27305i | 0.452739 | − | 0.0582888i | ||||
\(478\) | 0.243356 | − | 0.123996i | 0.0111308 | − | 0.00567144i | ||||
\(479\) | −5.98099 | + | 18.4076i | −0.273278 | + | 0.841064i | 0.716392 | + | 0.697698i | \(0.245792\pi\) |
−0.989670 | + | 0.143366i | \(0.954208\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.34278 | − | 0.975589i | −0.0612256 | − | 0.0444830i | ||||
\(482\) | 3.17243 | − | 6.22625i | 0.144500 | − | 0.283598i | ||||
\(483\) | −2.34792 | + | 3.13490i | −0.106834 | + | 0.142643i | ||||
\(484\) | 7.85348 | − | 4.40802i | 0.356976 | − | 0.200365i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.76638 | − | 14.4983i | 0.397651 | − | 0.657655i | ||||
\(487\) | 16.0688 | − | 2.54505i | 0.728147 | − | 0.115327i | 0.218655 | − | 0.975802i | \(-0.429833\pi\) |
0.509492 | + | 0.860475i | \(0.329833\pi\) | |||||||
\(488\) | 1.29907 | − | 8.20201i | 0.0588062 | − | 0.371288i | ||||
\(489\) | −38.9328 | − | 6.74714i | −1.76060 | − | 0.305116i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.6857 | + | 21.5895i | 0.707885 | + | 0.974320i | 0.999840 | + | 0.0178882i | \(0.00569430\pi\) |
−0.291955 | + | 0.956432i | \(0.594306\pi\) | |||||||
\(492\) | 2.49569 | + | 8.07817i | 0.112514 | + | 0.364192i | ||||
\(493\) | 12.6544 | − | 24.8356i | 0.569924 | − | 1.11854i | ||||
\(494\) | −3.54171 | −0.159349 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.5131 | 0.606756 | ||||||||
\(497\) | −31.1749 | + | 61.1843i | −1.39839 | + | 2.74449i | ||||
\(498\) | 0.0927980 | + | 0.300373i | 0.00415838 | + | 0.0134600i | ||||
\(499\) | −9.21928 | − | 12.6892i | −0.412712 | − | 0.568049i | 0.551166 | − | 0.834396i | \(-0.314183\pi\) |
−0.963877 | + | 0.266347i | \(0.914183\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.0409 | + | 3.64644i | 0.940037 | + | 0.162911i | ||||
\(502\) | −3.28156 | + | 20.7190i | −0.146463 | + | 0.924734i | ||||
\(503\) | −32.8876 | + | 5.20888i | −1.46639 | + | 0.232253i | −0.838009 | − | 0.545657i | \(-0.816280\pi\) |
−0.628377 | + | 0.777909i | \(0.716280\pi\) | |||||||
\(504\) | −21.6772 | − | 31.7344i | −0.965581 | − | 1.41356i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.68225 | − | 0.984902i | −0.0747850 | − | 0.0437842i | ||||
\(507\) | −11.9534 | + | 15.9599i | −0.530869 | + | 0.708806i | ||||
\(508\) | 3.63419 | − | 7.13250i | 0.161241 | − | 0.316453i | ||||
\(509\) | −4.72551 | − | 3.43329i | −0.209455 | − | 0.152178i | 0.478112 | − | 0.878299i | \(-0.341321\pi\) |
−0.687567 | + | 0.726121i | \(0.741321\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.15545 | − | 28.1776i | 0.405013 | − | 1.24650i | ||||
\(512\) | 15.7038 | − | 8.00146i | 0.694014 | − | 0.353618i | ||||
\(513\) | −13.3774 | + | 3.71101i | −0.590627 | + | 0.163845i | ||||
\(514\) | −4.75372 | + | 6.54293i | −0.209677 | + | 0.288596i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.60177 | + | 0.660515i | −0.202582 | + | 0.0290775i | ||||
\(517\) | −15.3271 | − | 12.5663i | −0.674084 | − | 0.552667i | ||||
\(518\) | 4.37318 | − | 4.37318i | 0.192146 | − | 0.192146i | ||||
\(519\) | −9.74205 | − | 19.8263i | −0.427628 | − | 0.870276i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.6507 | − | 21.5414i | −0.685671 | − | 0.943746i | 0.314313 | − | 0.949319i | \(-0.398226\pi\) |
−0.999984 | + | 0.00557374i | \(0.998226\pi\) | |||||||
\(522\) | −12.3442 | − | 13.0827i | −0.540291 | − | 0.572615i | ||||
\(523\) | −20.6026 | + | 10.4976i | −0.900890 | + | 0.459027i | −0.842148 | − | 0.539247i | \(-0.818709\pi\) |
−0.0587425 | + | 0.998273i | \(0.518709\pi\) | |||||||
\(524\) | 6.41321 | − | 4.65947i | 0.280162 | − | 0.203550i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.0266989 | − | 0.0821709i | −0.00116413 | − | 0.00358282i | ||||
\(527\) | −28.5303 | − | 28.5303i | −1.24280 | − | 1.24280i | ||||
\(528\) | 7.35659 | − | 6.35464i | 0.320154 | − | 0.276550i | ||||
\(529\) | 22.7076i | 0.987285i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.09580 | + | 3.06656i | −0.0475535 | + | 0.133077i | ||||
\(532\) | −1.43086 | + | 9.03410i | −0.0620357 | + | 0.391678i | ||||
\(533\) | −3.30145 | − | 6.47945i | −0.143001 | − | 0.280656i | ||||
\(534\) | 14.9385 | + | 2.58888i | 0.646452 | + | 0.112032i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.13646 | + | 5.69334i | −0.178668 | + | 0.245915i | ||||
\(537\) | 10.2841 | − | 30.1544i | 0.443791 | − | 1.30126i | ||||
\(538\) | −10.0009 | − | 10.0009i | −0.431168 | − | 0.431168i | ||||
\(539\) | −31.8547 | + | 13.9517i | −1.37208 | + | 0.600940i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.6196 | + | 38.8390i | 0.542557 | + | 1.66982i | 0.726728 | + | 0.686925i | \(0.241040\pi\) |
−0.184171 | + | 0.982894i | \(0.558960\pi\) | |||||||
\(542\) | 0.0986205 | + | 0.622665i | 0.00423611 | + | 0.0267458i | ||||
\(543\) | −24.6592 | − | 0.358038i | −1.05823 | − | 0.0153649i | ||||
\(544\) | −20.6054 | − | 6.69509i | −0.883448 | − | 0.287050i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.68973 | + | 6.88685i | 0.286294 | + | 0.294730i | ||||
\(547\) | 2.28083 | − | 0.361248i | 0.0975213 | − | 0.0154459i | −0.107483 | − | 0.994207i | \(-0.534279\pi\) |
0.205004 | + | 0.978761i | \(0.434279\pi\) | |||||||
\(548\) | 8.92910 | + | 4.54960i | 0.381432 | + | 0.194349i | ||||
\(549\) | 2.28731 | + | 7.80362i | 0.0976199 | + | 0.333050i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.7385i | 0.627883i | ||||||||
\(552\) | 2.71591 | + | 0.926255i | 0.115597 | + | 0.0394240i | ||||
\(553\) | 4.91091 | + | 31.0063i | 0.208833 | + | 1.31852i | ||||
\(554\) | 18.7913 | − | 13.6527i | 0.798367 | − | 0.580048i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.40843 | − | 4.33471i | 0.0597309 | − | 0.183833i | ||||
\(557\) | 34.2606 | + | 5.42635i | 1.45167 | + | 0.229922i | 0.831927 | − | 0.554885i | \(-0.187238\pi\) |
0.619741 | + | 0.784807i | \(0.287238\pi\) | |||||||
\(558\) | −23.5325 | + | 11.1420i | −0.996211 | + | 0.471679i | ||||
\(559\) | 3.80284 | − | 1.23562i | 0.160843 | − | 0.0522611i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −28.9487 | − | 2.11543i | −1.22221 | − | 0.0893133i | ||||
\(562\) | −11.5384 | + | 11.5384i | −0.486719 | + | 0.486719i | ||||
\(563\) | −29.4779 | − | 15.0198i | −1.24235 | − | 0.633007i | −0.295700 | − | 0.955281i | \(-0.595553\pi\) |
−0.946647 | + | 0.322273i | \(0.895553\pi\) | |||||||
\(564\) | 7.49405 | + | 3.95649i | 0.315556 | + | 0.166598i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.19393 | + | 2.98729i | 0.386450 | + | 0.125565i | ||||
\(567\) | 32.4839 | + | 19.0029i | 1.36420 | + | 0.798046i | ||||
\(568\) | 49.6901 | + | 7.87014i | 2.08495 | + | 0.330224i | ||||
\(569\) | 5.45483 | + | 3.96317i | 0.228678 | + | 0.166145i | 0.696224 | − | 0.717824i | \(-0.254862\pi\) |
−0.467546 | + | 0.883969i | \(0.654862\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.1063 | −1.67840 | −0.839198 | − | 0.543826i | \(-0.816975\pi\) | ||||
−0.839198 | + | 0.543826i | \(0.816975\pi\) | |||||||
\(572\) | 2.09985 | − | 2.56117i | 0.0877992 | − | 0.107088i | ||||
\(573\) | 2.92902 | − | 3.91077i | 0.122362 | − | 0.163375i | ||||
\(574\) | 25.7708 | − | 8.37344i | 1.07565 | − | 0.349501i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −14.7468 | + | 19.1052i | −0.614451 | + | 0.796049i | ||||
\(577\) | −18.3994 | − | 36.1109i | −0.765979 | − | 1.50332i | −0.861426 | − | 0.507884i | \(-0.830428\pi\) |
0.0954466 | − | 0.995435i | \(-0.469572\pi\) | |||||||
\(578\) | −4.20908 | − | 8.26079i | −0.175075 | − | 0.343604i | ||||
\(579\) | 19.8672 | + | 20.4527i | 0.825654 | + | 0.849983i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.664146 | + | 0.215794i | −0.0275534 | + | 0.00895265i | ||||
\(582\) | 16.6725 | + | 12.4871i | 0.691097 | + | 0.517606i | ||||
\(583\) | −10.6633 | + | 2.78800i | −0.441630 | + | 0.115467i | ||||
\(584\) | −21.7064 | −0.898219 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.3998 | − | 8.28245i | −0.470922 | − | 0.342145i | ||||
\(587\) | 5.03076 | + | 0.796794i | 0.207642 | + | 0.0328872i | 0.259389 | − | 0.965773i | \(-0.416479\pi\) |
−0.0517469 | + | 0.998660i | \(0.516479\pi\) | |||||||
\(588\) | 12.1549 | − | 8.56423i | 0.501260 | − | 0.353183i | ||||
\(589\) | 20.2903 | + | 6.59273i | 0.836049 | + | 0.271649i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.1967 | + | 23.1020i | −0.501707 | + | 0.950291i | ||||
\(592\) | −2.05183 | − | 1.04546i | −0.0843297 | − | 0.0429681i | ||||
\(593\) | −18.1298 | + | 18.1298i | −0.744501 | + | 0.744501i | −0.973441 | − | 0.228940i | \(-0.926474\pi\) |
0.228940 | + | 0.973441i | \(0.426474\pi\) | |||||||
\(594\) | −7.57158 | + | 17.1321i | −0.310666 | + | 0.702939i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.94399 | + | 1.60640i | −0.202514 | + | 0.0658007i | ||||
\(597\) | −34.5010 | + | 10.6588i | −1.41203 | + | 0.436237i | ||||
\(598\) | −0.708048 | − | 0.112144i | −0.0289542 | − | 0.00458590i | ||||
\(599\) | 8.80274 | − | 27.0921i | 0.359670 | − | 1.10695i | −0.593581 | − | 0.804774i | \(-0.702286\pi\) |
0.953252 | − | 0.302177i | \(-0.0977135\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.0868 | + | 14.5939i | −0.819358 | + | 0.595298i | −0.916528 | − | 0.399969i | \(-0.869021\pi\) |
0.0971706 | + | 0.995268i | \(0.469021\pi\) | |||||||
\(602\) | 2.33077 | + | 14.7159i | 0.0949950 | + | 0.599775i | ||||
\(603\) | 1.27520 | − | 6.77232i | 0.0519301 | − | 0.275790i | ||||
\(604\) | − | 1.69321i | − | 0.0688959i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.8134 | + | 1.83918i | −0.520510 | + | 0.0747114i | ||||
\(607\) | 23.3703 | + | 11.9078i | 0.948572 | + | 0.483321i | 0.858613 | − | 0.512624i | \(-0.171327\pi\) |
0.0899586 | + | 0.995946i | \(0.471327\pi\) | |||||||
\(608\) | 11.3150 | − | 1.79212i | 0.458885 | − | 0.0726802i | ||||
\(609\) | 28.6591 | − | 27.8388i | 1.16133 | − | 1.12809i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.93205 | − | 2.25236i | −0.280441 | − | 0.0911207i | ||||
\(612\) | 12.3089 | − | 1.58473i | 0.497556 | − | 0.0640590i | ||||
\(613\) | −0.420153 | − | 2.65274i | −0.0169698 | − | 0.107143i | 0.977750 | − | 0.209776i | \(-0.0672734\pi\) |
−0.994719 | + | 0.102633i | \(0.967273\pi\) | |||||||
\(614\) | −1.03344 | − | 3.18060i | −0.0417062 | − | 0.128359i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 28.2376 | + | 31.7463i | 1.13773 | + | 1.27910i | ||||
\(617\) | −18.7260 | − | 18.7260i | −0.753879 | − | 0.753879i | 0.221321 | − | 0.975201i | \(-0.428963\pi\) |
−0.975201 | + | 0.221321i | \(0.928963\pi\) | |||||||
\(618\) | −0.430015 | − | 0.146656i | −0.0172977 | − | 0.00589936i | ||||
\(619\) | 15.8508 | − | 21.8167i | 0.637095 | − | 0.876887i | −0.361361 | − | 0.932426i | \(-0.617688\pi\) |
0.998457 | + | 0.0555393i | \(0.0176878\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.79188 | + | 0.318315i | −0.112034 | + | 0.0127735i | ||||
\(622\) | −2.22250 | − | 4.36189i | −0.0891140 | − | 0.174896i | ||||
\(623\) | −5.26825 | + | 33.2624i | −0.211068 | + | 1.33263i | ||||
\(624\) | 1.66907 | − | 3.16140i | 0.0668161 | − | 0.126557i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.82177i | 0.112781i | ||||||||
\(627\) | 14.1464 | − | 5.95258i | 0.564954 | − | 0.237723i | ||||
\(628\) | 2.58494 | + | 2.58494i | 0.103150 | + | 0.103150i | ||||
\(629\) | 2.12476 | + | 6.53935i | 0.0847198 | + | 0.260741i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.8751 | − | 19.5259i | 1.06988 | − | 0.777314i | 0.0939906 | − | 0.995573i | \(-0.470038\pi\) |
0.975891 | + | 0.218259i | \(0.0700376\pi\) | |||||||
\(632\) | 20.4928 | − | 10.4416i | 0.815160 | − | 0.415345i | ||||
\(633\) | 30.3643 | − | 21.3944i | 1.20687 | − | 0.850350i | ||||
\(634\) | −3.42791 | − | 4.71812i | −0.136140 | − | 0.187380i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.22952 | − | 2.07826i | 0.167711 | − | 0.0824084i | ||||
\(637\) | −9.04307 | + | 9.04307i | −0.358300 | + | 0.358300i | ||||
\(638\) | 15.3777 | + | 12.6079i | 0.608811 | + | 0.499151i | ||||
\(639\) | −47.2765 | + | 13.8572i | −1.87023 | + | 0.548180i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.0768466 | − | 0.105770i | 0.00303526 | − | 0.00417768i | −0.807497 | − | 0.589872i | \(-0.799178\pi\) |
0.810532 | + | 0.585694i | \(0.199178\pi\) | |||||||
\(642\) | 0.418118 | − | 28.7971i | 0.0165018 | − | 1.13653i | ||||
\(643\) | −33.6218 | + | 17.1312i | −1.32591 | + | 0.675587i | −0.966277 | − | 0.257506i | \(-0.917099\pi\) |
−0.359637 | + | 0.933092i | \(0.617099\pi\) | |||||||
\(644\) | −0.572107 | + | 1.76076i | −0.0225442 | + | 0.0693838i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.8700 | + | 8.62405i | 0.467019 | + | 0.339309i | ||||
\(647\) | −15.1064 | + | 29.6481i | −0.593895 | + | 1.16559i | 0.377030 | + | 0.926201i | \(0.376945\pi\) |
−0.970925 | + | 0.239384i | \(0.923055\pi\) | |||||||
\(648\) | 5.88658 | − | 26.9364i | 0.231247 | − | 1.05816i | ||||
\(649\) | 0.769866 | − | 3.51688i | 0.0302199 | − | 0.138050i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25.5057 | − | 51.9072i | −0.999647 | − | 2.03440i | ||||
\(652\) | −18.4476 | + | 2.92181i | −0.722462 | + | 0.114427i | ||||
\(653\) | 4.53843 | − | 28.6545i | 0.177603 | − | 1.12134i | −0.724327 | − | 0.689456i | \(-0.757850\pi\) |
0.901930 | − | 0.431882i | \(-0.142150\pi\) | |||||||
\(654\) | 2.07700 | − | 11.9848i | 0.0812172 | − | 0.468644i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.93047 | − | 8.16258i | −0.231546 | − | 0.318695i | ||||
\(657\) | 19.2114 | − | 9.09609i | 0.749509 | − | 0.354872i | ||||
\(658\) | 12.3301 | − | 24.1992i | 0.480677 | − | 0.943382i | ||||
\(659\) | −30.5605 | −1.19047 | −0.595235 | − | 0.803552i | \(-0.702941\pi\) | ||||
−0.595235 | + | 0.803552i | \(0.702941\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.5197 | −0.837017 | −0.418509 | − | 0.908213i | \(-0.637447\pi\) | ||||
−0.418509 | + | 0.908213i | \(0.637447\pi\) | |||||||
\(662\) | 7.54240 | − | 14.8028i | 0.293144 | − | 0.575327i | ||||
\(663\) | −10.1986 | + | 3.15079i | −0.396082 | + | 0.122367i | ||||
\(664\) | 0.300723 | + | 0.413910i | 0.0116703 | + | 0.0160628i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.43520 | + | 0.128821i | 0.171861 | + | 0.00499170i | ||||
\(667\) | −0.466678 | + | 2.94649i | −0.0180698 | + | 0.114088i | ||||
\(668\) | 9.96982 | − | 1.57906i | 0.385744 | − | 0.0610959i | ||||
\(669\) | 39.0662 | − | 19.1960i | 1.51039 | − | 0.742161i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.60674 | − | 8.23498i | −0.139237 | − | 0.317908i | ||||
\(672\) | −24.8571 | − | 18.6170i | −0.958883 | − | 0.718167i | ||||
\(673\) | 1.77598 | − | 3.48555i | 0.0684589 | − | 0.134358i | −0.854241 | − | 0.519877i | \(-0.825978\pi\) |
0.922700 | + | 0.385519i | \(0.125978\pi\) | |||||||
\(674\) | −25.9398 | − | 18.8463i | −0.999162 | − | 0.725934i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.91263 | + | 8.96416i | −0.112024 | + | 0.344775i | ||||
\(677\) | −12.4420 | + | 6.33951i | −0.478184 | + | 0.243647i | −0.676432 | − | 0.736505i | \(-0.736475\pi\) |
0.198248 | + | 0.980152i | \(0.436475\pi\) | |||||||
\(678\) | 30.4641 | + | 0.442323i | 1.16997 | + | 0.0169873i | ||||
\(679\) | −27.1966 | + | 37.4329i | −1.04371 | + | 1.43654i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.16193 | − | 28.9960i | −0.159486 | − | 1.11113i | ||||
\(682\) | 24.2358 | − | 15.5307i | 0.928035 | − | 0.594700i | ||||
\(683\) | −28.5187 | + | 28.5187i | −1.09124 | + | 1.09124i | −0.0958424 | + | 0.995397i | \(0.530554\pi\) |
−0.995397 | + | 0.0958424i | \(0.969446\pi\) | |||||||
\(684\) | −5.41867 | + | 3.70140i | −0.207188 | + | 0.141527i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.31060 | − | 12.8149i | −0.355480 | − | 0.489277i | ||||
\(687\) | −10.3913 | − | 14.7479i | −0.396451 | − | 0.562669i | ||||
\(688\) | 4.94306 | − | 2.51861i | 0.188452 | − | 0.0960212i | ||||
\(689\) | −3.27915 | + | 2.38244i | −0.124926 | + | 0.0907638i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.21935 | + | 3.75277i | 0.0463862 | + | 0.142762i | 0.971567 | − | 0.236764i | \(-0.0760869\pi\) |
−0.925181 | + | 0.379526i | \(0.876087\pi\) | |||||||
\(692\) | −7.38359 | − | 7.38359i | −0.280682 | − | 0.280682i | ||||
\(693\) | −38.2952 | − | 16.2643i | −1.45471 | − | 0.617829i | ||||
\(694\) | 12.0863i | 0.458789i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −25.8860 | − | 13.6665i | −0.981205 | − | 0.518028i | ||||
\(697\) | −4.71270 | + | 29.7548i | −0.178506 | + | 1.12704i | ||||
\(698\) | 15.7969 | + | 31.0032i | 0.597923 | + | 1.17349i | ||||
\(699\) | 2.06279 | − | 11.9028i | 0.0780219 | − | 0.450206i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.8541 | + | 34.2088i | −0.938727 | + | 1.29205i | 0.0176297 | + | 0.999845i | \(0.494388\pi\) |
−0.956357 | + | 0.292202i | \(0.905612\pi\) | |||||||
\(702\) | −0.299923 | + | 6.88166i | −0.0113199 | + | 0.259732i | ||||
\(703\) | −2.57083 | − | 2.57083i | −0.0969608 | − | 0.0969608i | ||||
\(704\) | 13.4808 | − | 23.0257i | 0.508078 | − | 0.867814i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.92526 | + | 12.0807i | 0.147729 | + | 0.454663i | ||||
\(707\) | −4.49808 | − | 28.3998i | −0.169168 | − | 1.06808i | ||||
\(708\) | −0.0223475 | + | 1.53914i | −0.000839871 | + | 0.0578445i | ||||
\(709\) | 16.9043 | + | 5.49255i | 0.634856 | + | 0.206277i | 0.608725 | − | 0.793381i | \(-0.291681\pi\) |
0.0261310 | + | 0.999659i | \(0.491681\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.7617 | + | 17.8289i | −0.516105 | + | 0.668637i | ||||
\(712\) | 24.3694 | − | 3.85974i | 0.913282 | − | 0.144650i | ||||
\(713\) | 3.84764 | + | 1.96047i | 0.144095 | + | 0.0734201i | ||||
\(714\) | −5.65107 | − | 39.3707i | −0.211486 | − | 1.47341i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 15.0599i | − | 0.562814i | ||||||
\(717\) | −0.140497 | + | 0.411958i | −0.00524697 | + | 0.0153849i | ||||
\(718\) | 0.0517527 | + | 0.326754i | 0.00193140 | + | 0.0121943i | ||||
\(719\) | −1.32092 | + | 0.959704i | −0.0492620 | + | 0.0357909i | −0.612144 | − | 0.790746i | \(-0.709693\pi\) |
0.562882 | + | 0.826537i | \(0.309693\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.311860 | − | 0.959807i | 0.0116143 | − | 0.0357451i | ||||
\(722\) | 12.7336 | + | 2.01681i | 0.473896 | + | 0.0750578i | ||||
\(723\) | 3.28711 | + | 10.6399i | 0.122249 | + | 0.395700i | ||||
\(724\) | −11.0869 | + | 3.60234i | −0.412040 | + | 0.133880i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.89064 | − | 19.8520i | 0.218622 | − | 0.736778i | ||||
\(727\) | −22.3721 | + | 22.3721i | −0.829734 | + | 0.829734i | −0.987480 | − | 0.157746i | \(-0.949577\pi\) |
0.157746 | + | 0.987480i | \(0.449577\pi\) | |||||||
\(728\) | 13.9218 | + | 7.09350i | 0.515975 | + | 0.262902i | ||||
\(729\) | 6.07778 | + | 26.3070i | 0.225103 | + | 0.974335i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.7539 | − | 5.11876i | −0.582679 | − | 0.189324i | ||||
\(732\) | 2.21400 | + | 3.14225i | 0.0818318 | + | 0.116141i | ||||
\(733\) | −30.0516 | − | 4.75971i | −1.10998 | − | 0.175804i | −0.425589 | − | 0.904917i | \(-0.639933\pi\) |
−0.684394 | + | 0.729113i | \(0.739933\pi\) | |||||||
\(734\) | −8.78875 | − | 6.38540i | −0.324399 | − | 0.235689i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.31881 | 0.0854725 | ||||||||
\(737\) | −0.444881 | + | 7.60565i | −0.0163874 | + | 0.280158i | ||||
\(738\) | 17.0580 | + | 9.32494i | 0.627914 | + | 0.343256i | ||||
\(739\) | −11.9617 | + | 3.88660i | −0.440019 | + | 0.142971i | −0.520644 | − | 0.853774i | \(-0.674308\pi\) |
0.0806254 | + | 0.996744i | \(0.474308\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.04853 | − | 3.93265i | 0.148727 | − | 0.144470i | ||||
\(742\) | −6.85669 | − | 13.4570i | −0.251717 | − | 0.494022i | ||||
\(743\) | −20.9964 | − | 41.2077i | −0.770282 | − | 1.51176i | −0.856877 | − | 0.515520i | \(-0.827599\pi\) |
0.0865954 | − | 0.996244i | \(-0.472401\pi\) | |||||||
\(744\) | −30.3936 | + | 29.5236i | −1.11428 | + | 1.08239i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.86520 | + | 1.25588i | −0.141515 | + | 0.0459810i | ||||
\(747\) | −0.439606 | − | 0.240315i | −0.0160844 | − | 0.00879268i | ||||
\(748\) | −13.2741 | + | 3.47060i | −0.485348 | + | 0.126898i | ||||
\(749\) | 63.9728 | 2.33752 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.4528 | + | 17.0395i | 0.855807 | + | 0.621780i | 0.926741 | − | 0.375701i | \(-0.122598\pi\) |
−0.0709343 | + | 0.997481i | \(0.522598\pi\) | |||||||
\(752\) | −9.98822 | − | 1.58198i | −0.364233 | − | 0.0576888i | ||||
\(753\) | −19.2548 | − | 27.3277i | −0.701685 | − | 0.995877i | ||||
\(754\) | 6.95497 | + | 2.25981i | 0.253285 | + | 0.0822973i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 17.4324 | + | 3.54525i | 0.634010 | + | 0.128939i | ||||
\(757\) | 7.08479 | + | 3.60988i | 0.257501 | + | 0.131203i | 0.577976 | − | 0.816054i | \(-0.303843\pi\) |
−0.320475 | + | 0.947257i | \(0.603843\pi\) | |||||||
\(758\) | 3.11405 | − | 3.11405i | 0.113107 | − | 0.113107i | ||||
\(759\) | 3.01660 | − | 0.742094i | 0.109495 | − | 0.0269363i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.3219 | + | 6.92791i | −0.772919 | + | 0.251137i | −0.668814 | − | 0.743430i | \(-0.733198\pi\) |
−0.104105 | + | 0.994566i | \(0.533198\pi\) | |||||||
\(762\) | −5.43301 | − | 17.5858i | −0.196817 | − | 0.637067i | ||||
\(763\) | 26.6857 | + | 4.22660i | 0.966088 | + | 0.153013i | ||||
\(764\) | 0.713701 | − | 2.19655i | 0.0258208 | − | 0.0794683i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.1298 | − | 17.5313i | 0.871844 | − | 0.633432i | ||||
\(767\) | −0.207112 | − | 1.30766i | −0.00747839 | − | 0.0472167i | ||||
\(768\) | −8.89364 | + | 26.0774i | −0.320921 | + | 0.940986i | ||||
\(769\) | − | 16.0651i | − | 0.579321i | −0.957129 | − | 0.289661i | \(-0.906458\pi\) | ||
0.957129 | − | 0.289661i | \(-0.0935424\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.83117 | − | 12.7577i | −0.0659481 | − | 0.459457i | ||||
\(772\) | 12.0091 | + | 6.11892i | 0.432215 | + | 0.220225i | ||||
\(773\) | −10.9438 | + | 1.73332i | −0.393620 | + | 0.0623433i | −0.350107 | − | 0.936710i | \(-0.613855\pi\) |
−0.0435127 | + | 0.999053i | \(0.513855\pi\) | |||||||
\(774\) | −6.53145 | + | 8.46179i | −0.234768 | + | 0.304153i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 32.2399 | + | 10.4754i | 1.15734 | + | 0.376044i | ||||
\(777\) | −0.143088 | + | 9.85489i | −0.00513324 | + | 0.353542i | ||||
\(778\) | 0.750434 | + | 4.73805i | 0.0269043 | + | 0.169867i | ||||
\(779\) | −4.92244 | − | 15.1497i | −0.176365 | − | 0.542795i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.8898 | − | 21.8507i | 1.78520 | − | 0.781878i | ||||
\(782\) | 2.09994 | + | 2.09994i | 0.0750938 | + | 0.0750938i | ||||
\(783\) | 28.6375 | + | 1.24811i | 1.02342 | + | 0.0446036i | ||||
\(784\) | −10.4295 | + | 14.3549i | −0.372481 | + | 0.512676i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.11239 | − | 17.9593i | 0.111015 | − | 0.640587i | ||||
\(787\) | −12.4914 | − | 24.5158i | −0.445272 | − | 0.873895i | −0.999147 | − | 0.0412951i | \(-0.986852\pi\) |
0.553875 | − | 0.832600i | \(-0.313148\pi\) | |||||||
\(788\) | −1.93175 | + | 12.1966i | −0.0688157 | + | 0.434485i | ||||
\(789\) | 0.121761 | + | 0.0642837i | 0.00433480 | + | 0.00228856i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 67.6761i | 2.40629i | ||||||||
\(792\) | −2.66269 | + | 30.3656i | −0.0946145 | + | 1.07900i | ||||
\(793\) | −2.33779 | − | 2.33779i | −0.0830174 | − | 0.0830174i | ||||
\(794\) | 1.05564 | + | 3.24894i | 0.0374634 | + | 0.115300i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.8090 | + | 10.0328i | −0.489447 | + | 0.355604i | ||||
\(797\) | −11.8258 | + | 6.02556i | −0.418892 | + | 0.213436i | −0.650715 | − | 0.759322i | \(-0.725531\pi\) |
0.231823 | + | 0.972758i | \(0.425531\pi\) | |||||||
\(798\) | 12.1135 | + | 17.1922i | 0.428812 | + | 0.608597i | ||||
\(799\) | 17.7482 | + | 24.4283i | 0.627886 | + | 0.864211i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.9509 | + | 13.6281i | −0.704930 | + | 0.481525i | ||||
\(802\) | −16.1525 | + | 16.1525i | −0.570364 | + | 0.570364i | ||||
\(803\) | −19.7855 | + | 12.6789i | −0.698216 | + | 0.447428i | ||||
\(804\) | −0.462818 | − | 3.22443i | −0.0163223 | − | 0.113717i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.22209 | − | 8.56397i | 0.219164 | − | 0.301653i | ||||
\(807\) | 22.5368 | + | 0.327222i | 0.793333 | + | 0.0115188i | ||||
\(808\) | −18.7701 | + | 9.56385i | −0.660330 | + | 0.336455i | ||||
\(809\) | 9.68288 | − | 29.8008i | 0.340432 | − | 1.04774i | −0.623552 | − | 0.781782i | \(-0.714311\pi\) |
0.963984 | − | 0.265960i | \(-0.0856889\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.91658 | + | 2.84556i | 0.137530 | + | 0.0999212i | 0.654423 | − | 0.756129i | \(-0.272912\pi\) |
−0.516893 | + | 0.856050i | \(0.672912\pi\) | |||||||
\(812\) | 8.57409 | − | 16.8276i | 0.300891 | − | 0.590533i | ||||
\(813\) | −0.804130 | − | 0.602263i | −0.0282021 | − | 0.0211223i | ||||
\(814\) | −4.88152 | + | 0.483143i | −0.171097 | + | 0.0169342i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −13.2919 | + | 6.53123i | −0.465308 | + | 0.228639i | ||||
\(817\) | 8.65094 | − | 1.37017i | 0.302658 | − | 0.0479363i | ||||
\(818\) | 5.08333 | − | 32.0949i | 0.177735 | − | 1.12217i | ||||
\(819\) | −15.2941 | − | 0.444217i | −0.534419 | − | 0.0155222i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.3775 | − | 41.8111i | −1.06018 | − | 1.45922i | −0.879634 | − | 0.475650i | \(-0.842213\pi\) |
−0.180548 | − | 0.983566i | \(-0.557787\pi\) | |||||||
\(822\) | 22.0155 | − | 6.80153i | 0.767879 | − | 0.237231i | ||||
\(823\) | 2.41656 | − | 4.74277i | 0.0842361 | − | 0.165323i | −0.845046 | − | 0.534694i | \(-0.820427\pi\) |
0.929282 | + | 0.369371i | \(0.120427\pi\) | |||||||
\(824\) | −0.739382 | −0.0257576 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.93330 | 0.171652 | ||||||||
\(827\) | 22.6677 | − | 44.4880i | 0.788235 | − | 1.54700i | −0.0481406 | − | 0.998841i | \(-0.515330\pi\) |
0.836375 | − | 0.548157i | \(-0.184670\pi\) | |||||||
\(828\) | −1.20049 | + | 0.568398i | −0.0417197 | + | 0.0197532i | ||||
\(829\) | −28.7195 | − | 39.5290i | −0.997468 | − | 1.37290i | −0.926866 | − | 0.375393i | \(-0.877508\pi\) |
−0.0706026 | − | 0.997505i | \(-0.522492\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.32069 | + | 36.4720i | −0.219262 | + | 1.26520i | ||||
\(832\) | 1.53497 | − | 9.69139i | 0.0532154 | − | 0.335989i | ||||
\(833\) | 52.3276 | − | 8.28788i | 1.81304 | − | 0.287158i | ||||
\(834\) | −4.62165 | − | 9.40562i | −0.160035 | − | 0.325690i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.42070 | − | 4.82160i | 0.187479 | − | 0.166758i | ||||
\(837\) | 14.5282 | − | 38.8666i | 0.502167 | − | 1.34342i | ||||
\(838\) | −1.77030 | + | 3.47441i | −0.0611539 | + | 0.120021i | ||||
\(839\) | 4.54256 | + | 3.30037i | 0.156827 | + | 0.113941i | 0.663431 | − | 0.748237i | \(-0.269100\pi\) |
−0.506604 | + | 0.862179i | \(0.669100\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.442520 | − | 1.36194i | 0.0152593 | − | 0.0469633i | ||||
\(842\) | 3.87972 | − | 1.97682i | 0.133704 | − | 0.0681256i | ||||
\(843\) | 0.377530 | − | 26.0016i | 0.0130028 | − | 0.895544i | ||||
\(844\) | 10.3203 | − | 14.2046i | 0.355238 | − | 0.488943i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 18.6985 | − | 5.48068i | 0.642867 | − | 0.188430i | ||||
\(847\) | 44.2820 | + | 12.4431i | 1.52155 | + | 0.427551i | ||||
\(848\) | −3.97650 | + | 3.97650i | −0.136554 | + | 0.136554i | ||||
\(849\) | −13.8266 | + | 6.79400i | −0.474529 | + | 0.233170i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.432551 | − | 0.595356i | −0.0148277 | − | 0.0204085i | ||||
\(852\) | −19.0366 | + | 13.4130i | −0.652184 | + | 0.459523i | ||||
\(853\) | 3.64385 | − | 1.85663i | 0.124763 | − | 0.0635699i | −0.390495 | − | 0.920605i | \(-0.627696\pi\) |
0.515258 | + | 0.857035i | \(0.327696\pi\) | |||||||
\(854\) | 9.96650 | − | 7.24108i | 0.341046 | − | 0.247785i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.4834 | − | 44.5752i | −0.495031 | − | 1.52355i | ||||
\(857\) | 20.3472 | + | 20.3472i | 0.695048 | + | 0.695048i | 0.963338 | − | 0.268290i | \(-0.0864587\pi\) |
−0.268290 | + | 0.963338i | \(0.586459\pi\) | |||||||
\(858\) | −0.639942 | − | 7.58825i | −0.0218473 | − | 0.259059i | ||||
\(859\) | − | 51.3158i | − | 1.75087i | −0.483333 | − | 0.875437i | \(-0.660574\pi\) | ||
0.483333 | − | 0.875437i | \(-0.339426\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20.1609 | + | 38.1872i | −0.687083 | + | 1.30141i | ||||
\(862\) | −2.08052 | + | 13.1359i | −0.0708626 | + | 0.447409i | ||||
\(863\) | 10.2425 | + | 20.1021i | 0.348660 | + | 0.684283i | 0.997028 | − | 0.0770439i | \(-0.0245481\pi\) |
−0.648368 | + | 0.761327i | \(0.724548\pi\) | |||||||
\(864\) | −2.52397 | − | 22.1372i | −0.0858671 | − | 0.753124i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.645674 | + | 0.888694i | −0.0219409 | + | 0.0301990i | ||||
\(867\) | 13.9841 | + | 4.76923i | 0.474923 | + | 0.161972i | ||||
\(868\) | −19.3310 | − | 19.3310i | −0.656137 | − | 0.656137i | ||||
\(869\) | 12.5803 | − | 21.4876i | 0.426757 | − | 0.728916i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.865789 | + | 2.66462i | 0.0293361 | + | 0.0902874i | ||||
\(872\) | −3.09658 | − | 19.5510i | −0.104863 | − | 0.662082i | ||||
\(873\) | −32.9238 | + | 4.23884i | −1.11430 | + | 0.143463i | ||||
\(874\) | −1.49345 | − | 0.485251i | −0.0505166 | − | 0.0164138i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.20708 | − | 7.00079i | 0.243505 | − | 0.236535i | ||||
\(877\) | −33.3679 | + | 5.28496i | −1.12676 | + | 0.178460i | −0.691868 | − | 0.722024i | \(-0.743212\pi\) |
−0.434887 | + | 0.900485i | \(0.643212\pi\) | |||||||
\(878\) | −24.4357 | − | 12.4506i | −0.824666 | − | 0.420189i | ||||
\(879\) | 22.2278 | − | 3.19047i | 0.749726 | − | 0.107612i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.0213i | 0.708226i | 0.935203 | + | 0.354113i | \(0.115217\pi\) | ||||
−0.935203 | + | 0.354113i | \(0.884783\pi\) | |||||||
\(882\) | 6.32636 | − | 33.5980i | 0.213020 | − | 1.13130i | ||||
\(883\) | −5.72459 | − | 36.1437i | −0.192648 | − | 1.21633i | −0.874567 | − | 0.484904i | \(-0.838855\pi\) |
0.681919 | − | 0.731427i | \(-0.261145\pi\) | |||||||
\(884\) | −4.08200 | + | 2.96574i | −0.137292 | + | 0.0997488i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.04739 | − | 18.6120i | 0.203166 | − | 0.625281i | ||||
\(887\) | 43.4370 | + | 6.87974i | 1.45847 | + | 0.230999i | 0.834742 | − | 0.550641i | \(-0.185617\pi\) |
0.623729 | + | 0.781640i | \(0.285617\pi\) | |||||||
\(888\) | 6.89911 | − | 2.13143i | 0.231519 | − | 0.0715261i | ||||
\(889\) | 38.8835 | − | 12.6340i | 1.30411 | − | 0.423732i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.3681 | − | 27.9911i | −0.347345 | − | 0.937737i | ||||
\(892\) | 14.5488 | − | 14.5488i | 0.487131 | − | 0.487131i | ||||
\(893\) | −14.2258 | − | 7.24842i | −0.476049 | − | 0.242559i | ||||
\(894\) | −5.58049 | + | 10.5701i | −0.186640 | + | 0.353517i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.667457 | + | 0.216870i | 0.0222982 | + | 0.00724511i | ||||
\(897\) | 0.933893 | − | 0.658012i | 0.0311818 | − | 0.0219704i | ||||
\(898\) | 32.0807 | + | 5.08108i | 1.07055 | + | 0.169558i | ||||
\(899\) | −35.6383 | − | 25.8927i | −1.18860 | − | 0.863571i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.7913 | 0.559398 | ||||||||
\(902\) | −20.0176 | − | 7.82371i | −0.666513 | − | 0.260501i | ||||
\(903\) | −19.0046 | − | 14.2337i | −0.632432 | − | 0.473668i | ||||
\(904\) | 47.1556 | − | 15.3218i | 1.56837 | − | 0.509595i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.71267 | − | 2.79260i | −0.0901223 | − | 0.0927779i | ||||
\(907\) | 6.16955 | + | 12.1084i | 0.204856 | + | 0.402053i | 0.970461 | − | 0.241258i | \(-0.0775600\pi\) |
−0.765605 | + | 0.643311i | \(0.777560\pi\) | |||||||
\(908\) | −6.28623 | − | 12.3374i | −0.208616 | − | 0.409432i | ||||
\(909\) | 12.6049 | − | 16.3302i | 0.418077 | − | 0.541638i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.8195 | − | 12.2883i | 1.25301 | − | 0.407129i | 0.394014 | − | 0.919104i | \(-0.371086\pi\) |
0.859000 | + | 0.511975i | \(0.171086\pi\) | |||||||
\(912\) | 4.69437 | − | 6.26783i | 0.155446 | − | 0.207548i | ||||
\(913\) | 0.515879 | + | 0.201627i | 0.0170731 | + | 0.00667287i | ||||
\(914\) | 0.121452 | 0.00401726 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.89918 | − | 5.01255i | −0.227955 | − | 0.165619i | ||||
\(917\) | 39.9886 | + | 6.33357i | 1.32054 | + | 0.209153i | ||||
\(918\) | 17.7620 | − | 22.3335i | 0.586234 | − | 0.737115i | ||||
\(919\) | −52.9287 | − | 17.1976i | −1.74596 | − | 0.567296i | −0.750361 | − | 0.661029i | \(-0.770120\pi\) |
−0.995597 | + | 0.0937325i | \(0.970120\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.71301 | + | 2.48824i | 0.155299 | + | 0.0819902i | ||||
\(922\) | −18.9224 | − | 9.64147i | −0.623178 | − | 0.317525i | ||||
\(923\) | 14.1630 | − | 14.1630i | 0.466180 | − | 0.466180i | ||||
\(924\) | −19.6145 | − | 1.43333i | −0.645268 | − | 0.0471530i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 12.1702 | − | 3.95434i | 0.399938 | − | 0.129948i | ||||
\(927\) | 0.654394 | − | 0.309838i | 0.0214931 | − | 0.0101764i | ||||
\(928\) | −23.3632 | − | 3.70036i | −0.766933 | − | 0.121470i | ||||
\(929\) | −9.74897 | + | 30.0043i | −0.319853 | + | 0.984408i | 0.653857 | + | 0.756618i | \(0.273150\pi\) |
−0.973710 | + | 0.227790i | \(0.926850\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.6636 | + | 16.4661i | −0.742771 | + | 0.539655i | ||||
\(932\) | −0.893277 | − | 5.63993i | −0.0292603 | − | 0.184742i | ||||
\(933\) | 7.38391 | + | 2.51827i | 0.241738 | + | 0.0824444i | ||||
\(934\) | 33.5198i | 1.09680i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.15303 | + | 10.7572i | 0.103060 | + | 0.351611i | ||||
\(937\) | 25.9806 | + | 13.2378i | 0.848749 | + | 0.432459i | 0.823564 | − | 0.567223i | \(-0.191982\pi\) |
0.0251854 | + | 0.999683i | \(0.491982\pi\) | |||||||
\(938\) | −10.3113 | + | 1.63315i | −0.336676 | + | 0.0533243i | ||||
\(939\) | −3.13325 | − | 3.22558i | −0.102250 | − | 0.105263i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.4628 | + | 4.37432i | 0.438874 | + | 0.142599i | 0.520116 | − | 0.854096i | \(-0.325889\pi\) |
−0.0812422 | + | 0.996694i | \(0.525889\pi\) | |||||||
\(942\) | 8.40459 | + | 0.122030i | 0.273836 | + | 0.00397595i | ||||
\(943\) | −0.504383 | − | 3.18455i | −0.0164250 | − | 0.103703i | ||||
\(944\) | −0.567634 | − | 1.74700i | −0.0184749 | − | 0.0568600i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.97073 | − | 10.1982i | 0.194125 | − | 0.331573i | ||||
\(947\) | −35.6162 | − | 35.6162i | −1.15737 | − | 1.15737i | −0.985039 | − | 0.172331i | \(-0.944870\pi\) |
−0.172331 | − | 0.985039i | \(-0.555130\pi\) | |||||||
\(948\) | −3.43648 | + | 10.0762i | −0.111612 | + | 0.327261i | ||||
\(949\) | −5.07957 | + | 6.99143i | −0.164890 | + | 0.226951i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.15736 | + | 1.58699i | 0.296948 | + | 0.0514618i | ||||
\(952\) | −29.3860 | − | 57.6732i | −0.952405 | − | 1.86920i | ||||
\(953\) | 4.76638 | − | 30.0938i | 0.154398 | − | 0.974833i | −0.781843 | − | 0.623475i | \(-0.785720\pi\) |
0.936241 | − | 0.351357i | \(-0.114280\pi\) | |||||||
\(954\) | 3.64615 | − | 10.2037i | 0.118049 | − | 0.330357i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.205742i | 0.00665419i | ||||||||
\(957\) | −31.5779 | + | 2.66307i | −1.02077 | + | 0.0860849i | ||||
\(958\) | 14.8748 | + | 14.8748i | 0.480583 | + | 0.480583i | ||||
\(959\) | 15.8164 | + | 48.6779i | 0.510738 | + | 1.57189i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.5081 | + | 19.2592i | −0.855099 | + | 0.621266i | ||||
\(962\) | −1.60733 | + | 0.818974i | −0.0518223 | + | 0.0264048i | ||||
\(963\) | 31.4978 | + | 33.3823i | 1.01500 | + | 1.07573i | ||||
\(964\) | 3.09405 | + | 4.25860i | 0.0996527 | + | 0.137160i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.87732 | + | 3.82057i | 0.0604017 | + | 0.122925i | ||||
\(967\) | 16.4265 | − | 16.4265i | 0.528241 | − | 0.528241i | −0.391807 | − | 0.920047i | \(-0.628150\pi\) |
0.920047 | + | 0.391807i | \(0.128150\pi\) | |||||||
\(968\) | −1.35521 | − | 33.6720i | −0.0435582 | − | 1.08226i | ||||
\(969\) | −23.1446 | + | 3.32206i | −0.743512 | + | 0.106720i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.95130 | + | 10.9440i | −0.255169 | + | 0.351211i | −0.917313 | − | 0.398166i | \(-0.869647\pi\) |
0.662144 | + | 0.749377i | \(0.269647\pi\) | |||||||
\(972\) | 6.73308 | + | 10.8421i | 0.215964 | + | 0.347761i | ||||
\(973\) | 20.7412 | − | 10.5682i | 0.664932 | − | 0.338800i | ||||
\(974\) | 5.46413 | − | 16.8169i | 0.175082 | − | 0.538847i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.71100 | − | 2.69620i | −0.118786 | − | 0.0863032i | ||||
\(977\) | −16.2585 | + | 31.9091i | −0.520155 | + | 1.02086i | 0.470232 | + | 0.882543i | \(0.344170\pi\) |
−0.990388 | + | 0.138320i | \(0.955830\pi\) | |||||||
\(978\) | −25.7444 | + | 34.3734i | −0.823215 | + | 1.09914i | ||||
\(979\) | 19.9584 | − | 17.7525i | 0.637872 | − | 0.567373i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.9335 | + | 16.0062i | 0.349081 | + | 0.511037i | ||||
\(982\) | 28.6471 | − | 4.53725i | 0.914165 | − | 0.144789i | ||||
\(983\) | −5.00429 | + | 31.5958i | −0.159612 | + | 1.00775i | 0.769687 | + | 0.638422i | \(0.220412\pi\) |
−0.929299 | + | 0.369329i | \(0.879588\pi\) | |||||||
\(984\) | 31.1725 | + | 5.40228i | 0.993745 | + | 0.172218i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −17.8069 | − | 24.5091i | −0.567086 | − | 0.780527i | ||||
\(987\) | 12.7758 | + | 41.3532i | 0.406658 | + | 1.31629i | ||||
\(988\) | 1.21122 | − | 2.37715i | 0.0385340 | − | 0.0756273i | ||||
\(989\) | 1.77285 | 0.0563735 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.4020 | −1.12458 | −0.562290 | − | 0.826940i | \(-0.690080\pi\) | ||||
−0.562290 | + | 0.826940i | \(0.690080\pi\) | |||||||
\(992\) | −15.5449 | + | 30.5085i | −0.493550 | + | 0.968646i | ||||
\(993\) | 7.81503 | + | 25.2960i | 0.248002 | + | 0.802745i | ||||
\(994\) | 43.8685 | + | 60.3798i | 1.39142 | + | 1.91513i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.233342 | − | 0.0404388i | −0.00739374 | − | 0.00128135i | ||||
\(997\) | 1.76124 | − | 11.1201i | 0.0557792 | − | 0.352176i | −0.943975 | − | 0.330016i | \(-0.892946\pi\) |
0.999754 | − | 0.0221597i | \(-0.00705422\pi\) | |||||||
\(998\) | −16.8373 | + | 2.66677i | −0.532977 | + | 0.0844152i | ||||
\(999\) | −5.21293 | + | 4.77751i | −0.164930 | + | 0.151154i |
(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 | 825.2.ct.b.368.14 | 160 | ||
3.2 | odd | 2 | inner | 825.2.ct.b.368.7 | 160 | ||
5.2 | odd | 4 | inner | 825.2.ct.b.632.14 | 160 | ||
5.3 | odd | 4 | 165.2.v.a.137.7 | yes | 160 | ||
5.4 | even | 2 | 165.2.v.a.38.7 | ✓ | 160 | ||
11.9 | even | 5 | inner | 825.2.ct.b.218.7 | 160 | ||
15.2 | even | 4 | inner | 825.2.ct.b.632.7 | 160 | ||
15.8 | even | 4 | 165.2.v.a.137.14 | yes | 160 | ||
15.14 | odd | 2 | 165.2.v.a.38.14 | yes | 160 | ||
33.20 | odd | 10 | inner | 825.2.ct.b.218.14 | 160 | ||
55.9 | even | 10 | 165.2.v.a.53.14 | yes | 160 | ||
55.42 | odd | 20 | inner | 825.2.ct.b.482.7 | 160 | ||
55.53 | odd | 20 | 165.2.v.a.152.14 | yes | 160 | ||
165.53 | even | 20 | 165.2.v.a.152.7 | yes | 160 | ||
165.119 | odd | 10 | 165.2.v.a.53.7 | yes | 160 | ||
165.152 | even | 20 | inner | 825.2.ct.b.482.14 | 160 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.v.a.38.7 | ✓ | 160 | 5.4 | even | 2 | ||
165.2.v.a.38.14 | yes | 160 | 15.14 | odd | 2 | ||
165.2.v.a.53.7 | yes | 160 | 165.119 | odd | 10 | ||
165.2.v.a.53.14 | yes | 160 | 55.9 | even | 10 | ||
165.2.v.a.137.7 | yes | 160 | 5.3 | odd | 4 | ||
165.2.v.a.137.14 | yes | 160 | 15.8 | even | 4 | ||
165.2.v.a.152.7 | yes | 160 | 165.53 | even | 20 | ||
165.2.v.a.152.14 | yes | 160 | 55.53 | odd | 20 | ||
825.2.ct.b.218.7 | 160 | 11.9 | even | 5 | inner | ||
825.2.ct.b.218.14 | 160 | 33.20 | odd | 10 | inner | ||
825.2.ct.b.368.7 | 160 | 3.2 | odd | 2 | inner | ||
825.2.ct.b.368.14 | 160 | 1.1 | even | 1 | trivial | ||
825.2.ct.b.482.7 | 160 | 55.42 | odd | 20 | inner | ||
825.2.ct.b.482.14 | 160 | 165.152 | even | 20 | inner | ||
825.2.ct.b.632.7 | 160 | 15.2 | even | 4 | inner | ||
825.2.ct.b.632.14 | 160 | 5.2 | odd | 4 | inner |