Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [243,2,Mod(82,243)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(243, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("243.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 243 = 3^{5} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 243.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.94036476912\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 163.2 | ||
Root | \(-0.173648 + 0.984808i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 243.163 |
Dual form | 243.2.c.f.82.2 |
$q$-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 \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.673648 | − | 1.16679i | 0.476341 | − | 0.825047i | −0.523291 | − | 0.852154i | \(-0.675296\pi\) |
0.999633 | + | 0.0271067i | \(0.00862938\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.0923963 | + | 0.160035i | 0.0461981 | + | 0.0800175i | ||||
\(5\) | 0.826352 | + | 1.43128i | 0.369556 | + | 0.640089i | 0.989496 | − | 0.144560i | \(-0.0461765\pi\) |
−0.619940 | + | 0.784649i | \(0.712843\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.20574 | + | 2.08840i | −0.455726 | + | 0.789340i | −0.998730 | − | 0.0503900i | \(-0.983954\pi\) |
0.543004 | + | 0.839730i | \(0.317287\pi\) | |||||||
\(8\) | 2.94356 | 1.04071 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.22668 | 0.704139 | ||||||||
\(11\) | 2.97178 | − | 5.14728i | 0.896026 | − | 1.55196i | 0.0634960 | − | 0.997982i | \(-0.479775\pi\) |
0.832530 | − | 0.553980i | \(-0.186892\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.61334 | + | 2.79439i | 0.447460 | + | 0.775024i | 0.998220 | − | 0.0596400i | \(-0.0189953\pi\) |
−0.550760 | + | 0.834664i | \(0.685662\pi\) | |||||||
\(14\) | 1.62449 | + | 2.81369i | 0.434162 | + | 0.751991i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.79813 | − | 3.11446i | 0.449533 | − | 0.778615i | ||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.63816 | −1.52290 | −0.761449 | − | 0.648225i | \(-0.775512\pi\) | ||||
−0.761449 | + | 0.648225i | \(0.775512\pi\) | |||||||
\(20\) | −0.152704 | + | 0.264490i | −0.0341456 | + | 0.0591419i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.00387 | − | 6.93491i | −0.853628 | − | 1.47853i | ||||
\(23\) | −1.47178 | − | 2.54920i | −0.306888 | − | 0.531545i | 0.670792 | − | 0.741645i | \(-0.265954\pi\) |
−0.977680 | + | 0.210100i | \(0.932621\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.13429 | − | 1.96464i | 0.226857 | − | 0.392928i | ||||
\(26\) | 4.34730 | 0.852575 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.445622 | −0.0842147 | ||||||||
\(29\) | −0.645430 | + | 1.11792i | −0.119853 | + | 0.207592i | −0.919709 | − | 0.392600i | \(-0.871576\pi\) |
0.799856 | + | 0.600192i | \(0.204909\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.294263 | + | 0.509678i | 0.0528512 | + | 0.0915409i | 0.891241 | − | 0.453531i | \(-0.149836\pi\) |
−0.838389 | + | 0.545072i | \(0.816502\pi\) | |||||||
\(32\) | 0.520945 | + | 0.902302i | 0.0920909 | + | 0.159506i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.02094 | + | 3.50038i | −0.346589 | + | 0.600310i | ||||
\(35\) | −3.98545 | −0.673664 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.0418891 | 0.00688652 | 0.00344326 | − | 0.999994i | \(-0.498904\pi\) | ||||
0.00344326 | + | 0.999994i | \(0.498904\pi\) | |||||||
\(38\) | −4.47178 | + | 7.74535i | −0.725419 | + | 1.25646i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.43242 | + | 4.21307i | 0.384599 | + | 0.666145i | ||||
\(41\) | −2.45084 | − | 4.24497i | −0.382756 | − | 0.662954i | 0.608699 | − | 0.793401i | \(-0.291692\pi\) |
−0.991455 | + | 0.130448i | \(0.958358\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.59240 | − | 4.49016i | 0.395337 | − | 0.684743i | −0.597807 | − | 0.801640i | \(-0.703961\pi\) |
0.993144 | + | 0.116896i | \(0.0372946\pi\) | |||||||
\(44\) | 1.09833 | 0.165579 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.96585 | −0.584733 | ||||||||
\(47\) | −1.86824 | + | 3.23589i | −0.272511 | + | 0.472003i | −0.969504 | − | 0.245075i | \(-0.921187\pi\) |
0.696993 | + | 0.717078i | \(0.254521\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.592396 | + | 1.02606i | 0.0846280 | + | 0.146580i | ||||
\(50\) | −1.52822 | − | 2.64695i | −0.216123 | − | 0.374336i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.298133 | + | 0.516382i | −0.0413437 | + | 0.0716093i | ||||
\(53\) | −11.6382 | −1.59862 | −0.799312 | − | 0.600916i | \(-0.794802\pi\) | ||||
−0.799312 | + | 0.600916i | \(0.794802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.82295 | 1.32453 | ||||||||
\(56\) | −3.54916 | + | 6.14733i | −0.474277 | + | 0.821472i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.869585 | + | 1.50617i | 0.114182 | + | 0.197769i | ||||
\(59\) | −3.67365 | − | 6.36295i | −0.478268 | − | 0.828385i | 0.521421 | − | 0.853299i | \(-0.325402\pi\) |
−0.999690 | + | 0.0249144i | \(0.992069\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.52481 | + | 9.56926i | −0.707380 | + | 1.22522i | 0.258446 | + | 0.966026i | \(0.416790\pi\) |
−0.965826 | + | 0.259192i | \(0.916544\pi\) | |||||||
\(62\) | 0.792919 | 0.100701 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.59627 | 1.07453 | ||||||||
\(65\) | −2.66637 | + | 4.61830i | −0.330723 | + | 0.572829i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.928548 | − | 1.60829i | −0.113440 | − | 0.196484i | 0.803715 | − | 0.595015i | \(-0.202854\pi\) |
−0.917155 | + | 0.398530i | \(0.869520\pi\) | |||||||
\(68\) | −0.277189 | − | 0.480105i | −0.0336141 | − | 0.0582213i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.68479 | + | 4.65020i | −0.320894 | + | 0.555805i | ||||
\(71\) | 5.51249 | 0.654212 | 0.327106 | − | 0.944988i | \(-0.393927\pi\) | ||||
0.327106 | + | 0.944988i | \(0.393927\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.55438 | 0.650091 | 0.325045 | − | 0.945698i | \(-0.394620\pi\) | ||||
0.325045 | + | 0.945698i | \(0.394620\pi\) | |||||||
\(74\) | 0.0282185 | − | 0.0488759i | 0.00328033 | − | 0.00568170i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.613341 | − | 1.06234i | −0.0703550 | − | 0.121858i | ||||
\(77\) | 7.16637 | + | 12.4125i | 0.816684 | + | 1.41454i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.89053 | − | 3.27449i | 0.212701 | − | 0.368409i | −0.739858 | − | 0.672763i | \(-0.765107\pi\) |
0.952559 | + | 0.304354i | \(0.0984406\pi\) | |||||||
\(80\) | 5.94356 | 0.664511 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.60401 | −0.729291 | ||||||||
\(83\) | 1.99273 | − | 3.45150i | 0.218730 | − | 0.378852i | −0.735690 | − | 0.677319i | \(-0.763142\pi\) |
0.954420 | + | 0.298467i | \(0.0964752\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.47906 | − | 4.29385i | −0.268891 | − | 0.465733i | ||||
\(86\) | −3.49273 | − | 6.04958i | −0.376630 | − | 0.652343i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.74763 | − | 15.1513i | 0.932500 | − | 1.61514i | ||||
\(89\) | −8.15064 | −0.863967 | −0.431983 | − | 0.901882i | \(-0.642186\pi\) | ||||
−0.431983 | + | 0.901882i | \(0.642186\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.78106 | −0.815677 | ||||||||
\(92\) | 0.271974 | − | 0.471073i | 0.0283553 | − | 0.0491128i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.51707 | + | 4.35970i | 0.259616 | + | 0.449669i | ||||
\(95\) | −5.48545 | − | 9.50108i | −0.562796 | − | 0.974790i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.130415 | + | 0.225885i | −0.0132416 | + | 0.0229352i | −0.872570 | − | 0.488489i | \(-0.837548\pi\) |
0.859329 | + | 0.511424i | \(0.170882\pi\) | |||||||
\(98\) | 1.59627 | 0.161247 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.419215 | 0.0419215 | ||||||||
\(101\) | 5.51367 | − | 9.54996i | 0.548631 | − | 0.950256i | −0.449738 | − | 0.893161i | \(-0.648483\pi\) |
0.998369 | − | 0.0570958i | \(-0.0181840\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.95336 | + | 3.38332i | 0.192471 | + | 0.333369i | 0.946068 | − | 0.323967i | \(-0.105017\pi\) |
−0.753598 | + | 0.657336i | \(0.771683\pi\) | |||||||
\(104\) | 4.74897 | + | 8.22546i | 0.465675 | + | 0.806573i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.84002 | + | 13.5793i | −0.761490 | + | 1.31894i | ||||
\(107\) | 2.63816 | 0.255040 | 0.127520 | − | 0.991836i | \(-0.459298\pi\) | ||||
0.127520 | + | 0.991836i | \(0.459298\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.95811 | −0.858031 | −0.429016 | − | 0.903297i | \(-0.641140\pi\) | ||||
−0.429016 | + | 0.903297i | \(0.641140\pi\) | |||||||
\(110\) | 6.61721 | − | 11.4613i | 0.630926 | − | 1.09280i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.33615 | + | 7.51044i | 0.409728 | + | 0.709669i | ||||
\(113\) | 7.96451 | + | 13.7949i | 0.749238 | + | 1.29772i | 0.948188 | + | 0.317708i | \(0.102913\pi\) |
−0.198951 | + | 0.980010i | \(0.563753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.43242 | − | 4.21307i | 0.226824 | − | 0.392871i | ||||
\(116\) | −0.238541 | −0.0221480 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.89899 | −0.911275 | ||||||||
\(119\) | 3.61721 | − | 6.26519i | 0.331589 | − | 0.574329i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.1630 | − | 21.0669i | −1.10572 | − | 1.91517i | ||||
\(122\) | 7.44356 | + | 12.8926i | 0.673909 | + | 1.16724i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.0543776 | + | 0.0941848i | −0.00488325 | + | 0.00845804i | ||||
\(125\) | 12.0128 | 1.07446 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.59627 | 0.319117 | 0.159559 | − | 0.987188i | \(-0.448993\pi\) | ||||
0.159559 | + | 0.987188i | \(0.448993\pi\) | |||||||
\(128\) | 4.74897 | − | 8.22546i | 0.419754 | − | 0.727035i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.59240 | + | 6.22221i | 0.315074 | + | 0.545724i | ||||
\(131\) | −8.85369 | − | 15.3350i | −0.773551 | − | 1.33983i | −0.935605 | − | 0.353047i | \(-0.885145\pi\) |
0.162055 | − | 0.986782i | \(-0.448188\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00387 | − | 13.8631i | 0.694024 | − | 1.20208i | ||||
\(134\) | −2.50206 | −0.216145 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.83069 | −0.757225 | ||||||||
\(137\) | −1.96451 | + | 3.40263i | −0.167839 | + | 0.290706i | −0.937660 | − | 0.347554i | \(-0.887012\pi\) |
0.769821 | + | 0.638260i | \(0.220346\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.98293 | − | 10.3627i | −0.507465 | − | 0.878955i | −0.999963 | − | 0.00864157i | \(-0.997249\pi\) |
0.492498 | − | 0.870314i | \(-0.336084\pi\) | |||||||
\(140\) | −0.368241 | − | 0.637812i | −0.0311220 | − | 0.0539049i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.71348 | − | 6.43193i | 0.311628 | − | 0.539756i | ||||
\(143\) | 19.1780 | 1.60374 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.13341 | −0.177170 | ||||||||
\(146\) | 3.74170 | − | 6.48081i | 0.309665 | − | 0.536356i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.00387039 | + | 0.00670372i | 0.000318144 | + | 0.000551042i | ||||
\(149\) | 10.2626 | + | 17.7754i | 0.840748 | + | 1.45622i | 0.889263 | + | 0.457396i | \(0.151218\pi\) |
−0.0485147 | + | 0.998822i | \(0.515449\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00387 | + | 13.8631i | −0.651346 | + | 1.12816i | 0.331451 | + | 0.943472i | \(0.392462\pi\) |
−0.982797 | + | 0.184691i | \(0.940871\pi\) | |||||||
\(152\) | −19.5398 | −1.58489 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 19.3105 | 1.55608 | ||||||||
\(155\) | −0.486329 | + | 0.842347i | −0.0390629 | + | 0.0676590i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.9868 | + | 19.0297i | 0.876842 | + | 1.51873i | 0.854788 | + | 0.518978i | \(0.173687\pi\) |
0.0220541 | + | 0.999757i | \(0.492979\pi\) | |||||||
\(158\) | −2.54710 | − | 4.41171i | −0.202637 | − | 0.350977i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.860967 | + | 1.49124i | −0.0680654 | + | 0.117893i | ||||
\(161\) | 7.09833 | 0.559426 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.5107 | 1.60652 | 0.803262 | − | 0.595625i | \(-0.203096\pi\) | ||||
0.803262 | + | 0.595625i | \(0.203096\pi\) | |||||||
\(164\) | 0.452896 | − | 0.784440i | 0.0353653 | − | 0.0612544i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.68479 | − | 4.65020i | −0.208380 | − | 0.360925i | ||||
\(167\) | 2.14543 | + | 3.71599i | 0.166018 | + | 0.287552i | 0.937016 | − | 0.349285i | \(-0.113576\pi\) |
−0.770998 | + | 0.636837i | \(0.780242\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.29426 | − | 2.24173i | 0.0995587 | − | 0.172441i | ||||
\(170\) | −6.68004 | −0.512336 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.958111 | 0.0730553 | ||||||||
\(173\) | 1.89646 | − | 3.28476i | 0.144185 | − | 0.249736i | −0.784884 | − | 0.619643i | \(-0.787277\pi\) |
0.929069 | + | 0.369907i | \(0.120611\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.73530 | + | 4.73768i | 0.206769 | + | 0.358135i | ||||
\(176\) | −10.6873 | − | 18.5110i | −0.805587 | − | 1.39532i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.49067 | + | 9.51011i | −0.411543 | + | 0.712813i | ||||
\(179\) | −8.27631 | −0.618601 | −0.309300 | − | 0.950964i | \(-0.600095\pi\) | ||||
−0.309300 | + | 0.950964i | \(0.600095\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.72193 | 0.499637 | 0.249819 | − | 0.968293i | \(-0.419629\pi\) | ||||
0.249819 | + | 0.968293i | \(0.419629\pi\) | |||||||
\(182\) | −5.24170 | + | 9.07888i | −0.388540 | + | 0.672972i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.33228 | − | 7.50373i | −0.319380 | − | 0.553182i | ||||
\(185\) | 0.0346151 | + | 0.0599551i | 0.00254495 | + | 0.00440799i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.91534 | + | 15.4418i | −0.651955 | + | 1.12922i | ||||
\(188\) | −0.690474 | −0.0503580 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −14.7811 | −1.07233 | ||||||||
\(191\) | −2.50727 | + | 4.34273i | −0.181420 | + | 0.314229i | −0.942364 | − | 0.334589i | \(-0.891403\pi\) |
0.760944 | + | 0.648817i | \(0.224736\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.93242 | + | 15.4714i | 0.642970 | + | 1.11366i | 0.984766 | + | 0.173882i | \(0.0556312\pi\) |
−0.341797 | + | 0.939774i | \(0.611035\pi\) | |||||||
\(194\) | 0.175708 | + | 0.304334i | 0.0126151 | + | 0.0218499i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.109470 | + | 0.189608i | −0.00781931 | + | 0.0135435i | ||||
\(197\) | −0.723689 | −0.0515607 | −0.0257803 | − | 0.999668i | \(-0.508207\pi\) | ||||
−0.0257803 | + | 0.999668i | \(0.508207\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.1925 | −0.722530 | −0.361265 | − | 0.932463i | \(-0.617655\pi\) | ||||
−0.361265 | + | 0.932463i | \(0.617655\pi\) | |||||||
\(200\) | 3.33884 | − | 5.78304i | 0.236092 | − | 0.408923i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.42855 | − | 12.8666i | −0.522671 | − | 0.905292i | ||||
\(203\) | −1.55644 | − | 2.69583i | −0.109240 | − | 0.189210i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.05051 | − | 7.01568i | 0.282900 | − | 0.489997i | ||||
\(206\) | 5.26352 | 0.366727 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 11.6040 | 0.804593 | ||||||||
\(209\) | −19.7271 | + | 34.1684i | −1.36456 | + | 2.36348i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.43242 | + | 12.8733i | 0.511669 | + | 0.886236i | 0.999909 | + | 0.0135268i | \(0.00430584\pi\) |
−0.488240 | + | 0.872710i | \(0.662361\pi\) | |||||||
\(212\) | −1.07532 | − | 1.86251i | −0.0738534 | − | 0.127918i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.77719 | − | 3.07818i | 0.121486 | − | 0.210420i | ||||
\(215\) | 8.56893 | 0.584396 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.41921 | −0.0963426 | ||||||||
\(218\) | −6.03462 | + | 10.4523i | −0.408716 | + | 0.707916i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.907604 | + | 1.57202i | 0.0611906 | + | 0.105985i | ||||
\(221\) | −4.84002 | − | 8.38316i | −0.325575 | − | 0.563913i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.47431 | − | 9.48178i | 0.366587 | − | 0.634947i | −0.622443 | − | 0.782665i | \(-0.713860\pi\) |
0.989029 | + | 0.147718i | \(0.0471930\pi\) | |||||||
\(224\) | −2.51249 | −0.167873 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 21.4611 | 1.42757 | ||||||||
\(227\) | −8.66637 | + | 15.0106i | −0.575207 | + | 0.996289i | 0.420812 | + | 0.907148i | \(0.361745\pi\) |
−0.996019 | + | 0.0891405i | \(0.971588\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.781059 | − | 1.35283i | −0.0516138 | − | 0.0893978i | 0.839064 | − | 0.544032i | \(-0.183103\pi\) |
−0.890678 | + | 0.454635i | \(0.849770\pi\) | |||||||
\(230\) | −3.27719 | − | 5.67626i | −0.216091 | − | 0.374281i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.89986 | + | 3.29066i | −0.124732 | + | 0.216042i | ||||
\(233\) | −16.7888 | −1.09987 | −0.549935 | − | 0.835207i | \(-0.685348\pi\) | ||||
−0.549935 | + | 0.835207i | \(0.685348\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.17530 | −0.402832 | ||||||||
\(236\) | 0.678863 | − | 1.17582i | 0.0441902 | − | 0.0765397i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.87346 | − | 8.44107i | −0.315899 | − | 0.547153i | ||||
\(239\) | −2.01455 | − | 3.48930i | −0.130310 | − | 0.225704i | 0.793486 | − | 0.608589i | \(-0.208264\pi\) |
−0.923796 | + | 0.382885i | \(0.874931\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.67617 | − | 2.90322i | 0.107972 | − | 0.187013i | −0.806977 | − | 0.590583i | \(-0.798898\pi\) |
0.914949 | + | 0.403571i | \(0.132231\pi\) | |||||||
\(242\) | −32.7743 | −2.10681 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.04189 | −0.130719 | ||||||||
\(245\) | −0.979055 | + | 1.69577i | −0.0625496 | + | 0.108339i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.7096 | − | 18.5496i | −0.681436 | − | 1.18028i | ||||
\(248\) | 0.866181 | + | 1.50027i | 0.0550026 | + | 0.0952673i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.09240 | − | 14.0164i | 0.511808 | − | 0.886478i | ||||
\(251\) | 23.1506 | 1.46126 | 0.730628 | − | 0.682776i | \(-0.239227\pi\) | ||||
0.730628 | + | 0.682776i | \(0.239227\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.4953 | −1.09992 | ||||||||
\(254\) | 2.42262 | − | 4.19610i | 0.152009 | − | 0.263287i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.19800 | + | 3.80704i | 0.137375 | + | 0.237940i | ||||
\(257\) | 6.00640 | + | 10.4034i | 0.374669 | + | 0.648945i | 0.990277 | − | 0.139107i | \(-0.0444231\pi\) |
−0.615609 | + | 0.788052i | \(0.711090\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.0505072 | + | 0.0874810i | −0.00313836 | + | 0.00543581i | ||||
\(260\) | −0.985452 | −0.0611151 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −23.8571 | −1.47390 | ||||||||
\(263\) | 8.45084 | − | 14.6373i | 0.521101 | − | 0.902573i | −0.478598 | − | 0.878034i | \(-0.658855\pi\) |
0.999699 | − | 0.0245391i | \(-0.00781183\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.61721 | − | 16.6575i | −0.590781 | − | 1.02326i | ||||
\(266\) | −10.7836 | − | 18.6777i | −0.661184 | − | 1.14520i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.171589 | − | 0.297200i | 0.0104815 | − | 0.0181544i | ||||
\(269\) | 7.91447 | 0.482554 | 0.241277 | − | 0.970456i | \(-0.422434\pi\) | ||||
0.241277 | + | 0.970456i | \(0.422434\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.2344 | −1.04692 | −0.523458 | − | 0.852051i | \(-0.675358\pi\) | ||||
−0.523458 | + | 0.852051i | \(0.675358\pi\) | |||||||
\(272\) | −5.39440 | + | 9.34337i | −0.327084 | + | 0.566525i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.64677 | + | 4.58435i | 0.159897 | + | 0.276951i | ||||
\(275\) | −6.74170 | − | 11.6770i | −0.406540 | − | 0.704147i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.2173 | + | 22.8931i | −0.794153 | + | 1.37551i | 0.129222 | + | 0.991616i | \(0.458752\pi\) |
−0.923375 | + | 0.383898i | \(0.874581\pi\) | |||||||
\(278\) | −16.1215 | −0.966906 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −11.7314 | −0.701087 | ||||||||
\(281\) | −9.49794 | + | 16.4509i | −0.566600 | + | 0.981379i | 0.430299 | + | 0.902686i | \(0.358408\pi\) |
−0.996899 | + | 0.0786931i | \(0.974925\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.29339 | + | 14.3646i | 0.492991 | + | 0.853885i | 0.999967 | − | 0.00807493i | \(-0.00257036\pi\) |
−0.506977 | + | 0.861960i | \(0.669237\pi\) | |||||||
\(284\) | 0.509333 | + | 0.882191i | 0.0302234 | + | 0.0523484i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.9192 | − | 22.3767i | 0.763929 | − | 1.32316i | ||||
\(287\) | 11.8203 | 0.697728 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | −1.43717 | + | 2.48925i | −0.0843933 | + | 0.146174i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.513204 | + | 0.888895i | 0.0300330 | + | 0.0520186i | ||||
\(293\) | 9.67886 | + | 16.7643i | 0.565445 | + | 0.979380i | 0.997008 | + | 0.0772970i | \(0.0246290\pi\) |
−0.431563 | + | 0.902083i | \(0.642038\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.07145 | − | 10.5161i | 0.353494 | − | 0.612269i | ||||
\(296\) | 0.123303 | 0.00716685 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 27.6536 | 1.60193 | ||||||||
\(299\) | 4.74897 | − | 8.22546i | 0.274640 | − | 0.475691i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.25150 | + | 10.8279i | 0.360330 | + | 0.624110i | ||||
\(302\) | 10.7836 | + | 18.6777i | 0.620526 | + | 1.07478i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11.9363 | + | 20.6743i | −0.684593 | + | 1.18575i | ||||
\(305\) | −18.2618 | −1.04567 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.8057 | 1.18744 | 0.593722 | − | 0.804670i | \(-0.297658\pi\) | ||||
0.593722 | + | 0.804670i | \(0.297658\pi\) | |||||||
\(308\) | −1.32429 | + | 2.29374i | −0.0754586 | + | 0.130698i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.655230 | + | 1.13489i | 0.0372146 | + | 0.0644575i | ||||
\(311\) | −5.33275 | − | 9.23659i | −0.302392 | − | 0.523759i | 0.674285 | − | 0.738471i | \(-0.264452\pi\) |
−0.976677 | + | 0.214712i | \(0.931119\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.90760 | + | 3.30407i | −0.107824 | + | 0.186757i | −0.914889 | − | 0.403707i | \(-0.867722\pi\) |
0.807064 | + | 0.590463i | \(0.201055\pi\) | |||||||
\(314\) | 29.6049 | 1.67070 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.698711 | 0.0393056 | ||||||||
\(317\) | 13.1946 | − | 22.8537i | 0.741082 | − | 1.28359i | −0.210921 | − | 0.977503i | \(-0.567646\pi\) |
0.952003 | − | 0.306089i | \(-0.0990204\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.83615 | + | 6.64441i | 0.214783 | + | 0.372016i | ||||
\(320\) | 7.10354 | + | 12.3037i | 0.397100 | + | 0.687797i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.78177 | − | 8.28228i | 0.266478 | − | 0.461553i | ||||
\(323\) | 19.9145 | 1.10807 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.31996 | 0.406038 | ||||||||
\(326\) | 13.8170 | − | 23.9318i | 0.765254 | − | 1.32546i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.21419 | − | 12.4953i | −0.398337 | − | 0.689940i | ||||
\(329\) | −4.50521 | − | 7.80326i | −0.248381 | − | 0.430208i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.785807 | − | 1.36106i | 0.0431919 | − | 0.0748105i | −0.843621 | − | 0.536939i | \(-0.819581\pi\) |
0.886813 | + | 0.462128i | \(0.152914\pi\) | |||||||
\(332\) | 0.736482 | 0.0404197 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.78106 | 0.316325 | ||||||||
\(335\) | 1.53462 | − | 2.65803i | 0.0838450 | − | 0.145224i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.00774 | + | 6.94161i | 0.218316 | + | 0.378134i | 0.954293 | − | 0.298872i | \(-0.0966105\pi\) |
−0.735978 | + | 0.677006i | \(0.763277\pi\) | |||||||
\(338\) | −1.74376 | − | 3.02027i | −0.0948478 | − | 0.164281i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.458111 | − | 0.793471i | 0.0248446 | − | 0.0430320i | ||||
\(341\) | 3.49794 | 0.189424 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.7374 | −1.06572 | ||||||||
\(344\) | 7.63088 | − | 13.2171i | 0.411430 | − | 0.712617i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.55509 | − | 4.42555i | −0.137363 | − | 0.237919i | ||||
\(347\) | 9.92262 | + | 17.1865i | 0.532674 | + | 0.922619i | 0.999272 | + | 0.0381490i | \(0.0121462\pi\) |
−0.466598 | + | 0.884470i | \(0.654521\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.54664 | + | 9.60706i | −0.296905 | + | 0.514254i | −0.975426 | − | 0.220327i | \(-0.929288\pi\) |
0.678522 | + | 0.734581i | \(0.262621\pi\) | |||||||
\(350\) | 7.37052 | 0.393971 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.19253 | 0.330063 | ||||||||
\(353\) | −1.43195 | + | 2.48021i | −0.0762151 | + | 0.132008i | −0.901614 | − | 0.432541i | \(-0.857617\pi\) |
0.825399 | + | 0.564550i | \(0.190950\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.55525 | + | 7.88993i | 0.241768 | + | 0.418754i | ||||
\(356\) | −0.753089 | − | 1.30439i | −0.0399136 | − | 0.0691325i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.57532 | + | 9.65674i | −0.294665 | + | 0.510375i | ||||
\(359\) | −28.7888 | −1.51941 | −0.759707 | − | 0.650265i | \(-0.774658\pi\) | ||||
−0.759707 | + | 0.650265i | \(0.774658\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.0651 | 1.31922 | ||||||||
\(362\) | 4.52822 | − | 7.84310i | 0.237998 | − | 0.412224i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.718941 | − | 1.24524i | −0.0376827 | − | 0.0652684i | ||||
\(365\) | 4.58987 | + | 7.94989i | 0.240245 | + | 0.416116i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.49613 | − | 9.51958i | 0.286896 | − | 0.496918i | −0.686171 | − | 0.727440i | \(-0.740710\pi\) |
0.973067 | + | 0.230522i | \(0.0740434\pi\) | |||||||
\(368\) | −10.5858 | −0.551825 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.0932736 | 0.00484906 | ||||||||
\(371\) | 14.0326 | − | 24.3051i | 0.728534 | − | 1.26186i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.7049 | − | 28.9337i | −0.864945 | − | 1.49813i | −0.867102 | − | 0.498131i | \(-0.834020\pi\) |
0.00215708 | − | 0.999998i | \(-0.499313\pi\) | |||||||
\(374\) | 12.0116 | + | 20.8047i | 0.621106 | + | 1.07579i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.49928 | + | 9.52504i | −0.283604 | + | 0.491216i | ||||
\(377\) | −4.16519 | −0.214518 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.9394 | 1.07559 | 0.537794 | − | 0.843077i | \(-0.319258\pi\) | ||||
0.537794 | + | 0.843077i | \(0.319258\pi\) | |||||||
\(380\) | 1.01367 | − | 1.75573i | 0.0520002 | − | 0.0900670i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.37804 | + | 5.85094i | 0.172836 | + | 0.299360i | ||||
\(383\) | −2.05556 | − | 3.56033i | −0.105034 | − | 0.181925i | 0.808718 | − | 0.588197i | \(-0.200162\pi\) |
−0.913752 | + | 0.406272i | \(0.866829\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.8439 | + | 20.5142i | −0.603621 | + | 1.04550i | ||||
\(386\) | 24.0692 | 1.22509 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.0481994 | −0.00244695 | ||||||||
\(389\) | 8.54710 | − | 14.8040i | 0.433355 | − | 0.750593i | −0.563804 | − | 0.825908i | \(-0.690663\pi\) |
0.997160 | + | 0.0753148i | \(0.0239962\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.41534 | + | 7.64760i | 0.223294 | + | 0.386756i | ||||
\(392\) | 1.74376 | + | 3.02027i | 0.0880730 | + | 0.152547i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.487511 | + | 0.844395i | −0.0245605 | + | 0.0425400i | ||||
\(395\) | 6.24897 | 0.314420 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.4020 | 1.12432 | 0.562162 | − | 0.827027i | \(-0.309970\pi\) | ||||
0.562162 | + | 0.827027i | \(0.309970\pi\) | |||||||
\(398\) | −6.86618 | + | 11.8926i | −0.344171 | + | 0.596121i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.07919 | − | 7.06537i | −0.203960 | − | 0.353268i | ||||
\(401\) | −7.29086 | − | 12.6281i | −0.364088 | − | 0.630619i | 0.624541 | − | 0.780992i | \(-0.285286\pi\) |
−0.988629 | + | 0.150373i | \(0.951953\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.949493 | + | 1.64457i | −0.0472976 | + | 0.0819219i | ||||
\(404\) | 2.03777 | 0.101383 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.19396 | −0.208143 | ||||||||
\(407\) | 0.124485 | − | 0.215615i | 0.00617050 | − | 0.0106876i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.75150 | + | 15.1580i | 0.432734 | + | 0.749517i | 0.997108 | − | 0.0760026i | \(-0.0242157\pi\) |
−0.564374 | + | 0.825519i | \(0.690882\pi\) | |||||||
\(410\) | −5.45723 | − | 9.45221i | −0.269514 | − | 0.466811i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.360967 | + | 0.625213i | −0.0177836 | + | 0.0308020i | ||||
\(413\) | 17.7178 | 0.871837 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.58677 | 0.323332 | ||||||||
\(416\) | −1.68092 | + | 2.91144i | −0.0824140 | + | 0.142745i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 26.5783 | + | 46.0350i | 1.29999 | + | 2.25165i | ||||
\(419\) | 9.43107 | + | 16.3351i | 0.460738 | + | 0.798022i | 0.998998 | − | 0.0447571i | \(-0.0142514\pi\) |
−0.538260 | + | 0.842779i | \(0.680918\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.1668 | − | 28.0018i | 0.787924 | − | 1.36472i | −0.139313 | − | 0.990248i | \(-0.544489\pi\) |
0.927237 | − | 0.374475i | \(-0.122177\pi\) | |||||||
\(422\) | 20.0273 | 0.974916 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −34.2576 | −1.66370 | ||||||||
\(425\) | −3.40286 | + | 5.89392i | −0.165063 | + | 0.285897i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.3229 | − | 23.0760i | −0.644743 | − | 1.11673i | ||||
\(428\) | 0.243756 | + | 0.422197i | 0.0117824 | + | 0.0204077i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.77244 | − | 9.99816i | 0.278372 | − | 0.482154i | ||||
\(431\) | −34.3164 | −1.65297 | −0.826483 | − | 0.562962i | \(-0.809662\pi\) | ||||
−0.826483 | + | 0.562962i | \(0.809662\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.0669 | −1.20464 | −0.602318 | − | 0.798256i | \(-0.705756\pi\) | ||||
−0.602318 | + | 0.798256i | \(0.705756\pi\) | |||||||
\(434\) | −0.956052 | + | 1.65593i | −0.0458919 | + | 0.0794872i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.827696 | − | 1.43361i | −0.0396394 | − | 0.0686575i | ||||
\(437\) | 9.76991 | + | 16.9220i | 0.467358 | + | 0.809489i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.6040 | − | 20.0987i | 0.553829 | − | 0.959260i | −0.444165 | − | 0.895945i | \(-0.646499\pi\) |
0.997994 | − | 0.0633148i | \(-0.0201672\pi\) | |||||||
\(440\) | 28.9145 | 1.37844 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.0419 | −0.620339 | ||||||||
\(443\) | −2.06077 | + | 3.56937i | −0.0979103 | + | 0.169586i | −0.910820 | − | 0.412805i | \(-0.864549\pi\) |
0.812909 | + | 0.582390i | \(0.197883\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.73530 | − | 11.6659i | −0.319284 | − | 0.553016i | ||||
\(446\) | −7.37551 | − | 12.7748i | −0.349241 | − | 0.604903i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10.3648 | + | 17.9524i | −0.489693 | + | 0.848172i | ||||
\(449\) | −18.3414 | −0.865585 | −0.432793 | − | 0.901494i | \(-0.642472\pi\) | ||||
−0.432793 | + | 0.901494i | \(0.642472\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.1334 | −1.37184 | ||||||||
\(452\) | −1.47178 | + | 2.54920i | −0.0692268 | + | 0.119904i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.6762 | + | 20.2237i | 0.547990 | + | 0.949147i | ||||
\(455\) | −6.42989 | − | 11.1369i | −0.301438 | − | 0.522106i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.73055 | − | 16.8538i | 0.455176 | − | 0.788388i | −0.543522 | − | 0.839395i | \(-0.682910\pi\) |
0.998698 | + | 0.0510067i | \(0.0162430\pi\) | |||||||
\(458\) | −2.10464 | −0.0983432 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.898986 | 0.0419154 | ||||||||
\(461\) | 13.8746 | − | 24.0316i | 0.646206 | − | 1.11926i | −0.337815 | − | 0.941212i | \(-0.609688\pi\) |
0.984022 | − | 0.178050i | \(-0.0569788\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.3430 | − | 33.5031i | −0.898946 | − | 1.55702i | −0.828843 | − | 0.559481i | \(-0.811001\pi\) |
−0.0701028 | − | 0.997540i | \(-0.522333\pi\) | |||||||
\(464\) | 2.32114 | + | 4.02033i | 0.107756 | + | 0.186639i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.3097 | + | 19.5891i | −0.523914 | + | 0.907445i | ||||
\(467\) | −29.7638 | −1.37731 | −0.688653 | − | 0.725091i | \(-0.741798\pi\) | ||||
−0.688653 | + | 0.725091i | \(0.741798\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.47834 | 0.206791 | ||||||||
\(470\) | −4.15998 | + | 7.20529i | −0.191885 | + | 0.332355i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10.8136 | − | 18.7297i | −0.497737 | − | 0.862106i | ||||
\(473\) | −15.4081 | − | 26.6876i | −0.708464 | − | 1.22710i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.52956 | + | 13.0416i | −0.345480 | + | 0.598389i | ||||
\(476\) | 1.33687 | 0.0612752 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.42839 | −0.248289 | ||||||||
\(479\) | −18.8380 | + | 32.6283i | −0.860728 | + | 1.49083i | 0.0104984 | + | 0.999945i | \(0.496658\pi\) |
−0.871227 | + | 0.490881i | \(0.836675\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0675813 | + | 0.117054i | 0.00308144 | + | 0.00533722i | ||||
\(482\) | −2.25830 | − | 3.91150i | −0.102863 | − | 0.178164i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.24763 | − | 3.89300i | 0.102165 | − | 0.176955i | ||||
\(485\) | −0.431074 | −0.0195741 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.763823 | −0.0346121 | −0.0173061 | − | 0.999850i | \(-0.505509\pi\) | ||||
−0.0173061 | + | 0.999850i | \(0.505509\pi\) | |||||||
\(488\) | −16.2626 | + | 28.1677i | −0.736175 | + | 1.27509i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.31908 | + | 2.28471i | 0.0595899 | + | 0.103213i | ||||
\(491\) | −0.248970 | − | 0.431229i | −0.0112359 | − | 0.0194611i | 0.860353 | − | 0.509699i | \(-0.170243\pi\) |
−0.871589 | + | 0.490238i | \(0.836910\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.93629 | − | 3.35375i | 0.0872061 | − | 0.151045i | ||||
\(494\) | −28.8580 | −1.29838 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.11650 | 0.0950335 | ||||||||
\(497\) | −6.64661 | + | 11.5123i | −0.298141 | + | 0.516396i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.48293 | − | 7.76466i | −0.200683 | − | 0.347594i | 0.748065 | − | 0.663625i | \(-0.230983\pi\) |
−0.948749 | + | 0.316031i | \(0.897650\pi\) | |||||||
\(500\) | 1.10994 | + | 1.92247i | 0.0496379 | + | 0.0859754i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.5954 | − | 27.0120i | 0.696056 | − | 1.20560i | ||||
\(503\) | −18.3618 | −0.818714 | −0.409357 | − | 0.912374i | \(-0.634247\pi\) | ||||
−0.409357 | + | 0.912374i | \(0.634247\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.2249 | 0.810999 | ||||||||
\(506\) | −11.7856 | + | 20.4133i | −0.523936 | + | 0.907483i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.332282 | + | 0.575529i | 0.0147426 | + | 0.0255350i | ||||
\(509\) | −14.1853 | − | 24.5696i | −0.628751 | − | 1.08903i | −0.987803 | − | 0.155710i | \(-0.950233\pi\) |
0.359052 | − | 0.933317i | \(-0.383100\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.69712 | + | 11.5998i | −0.296263 | + | 0.513143i | ||||
\(512\) | 24.9186 | 1.10126 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16.1848 | 0.713881 | ||||||||
\(515\) | −3.22833 | + | 5.59163i | −0.142257 | + | 0.246397i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.1040 | + | 19.2327i | 0.488354 | + | 0.845853i | ||||
\(518\) | 0.0680482 | + | 0.117863i | 0.00298986 | + | 0.00517860i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.84864 | + | 13.5942i | −0.344186 | + | 0.596147i | ||||
\(521\) | 32.6382 | 1.42990 | 0.714952 | − | 0.699174i | \(-0.246449\pi\) | ||||
0.714952 | + | 0.699174i | \(0.246449\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.0232 | −0.963008 | −0.481504 | − | 0.876444i | \(-0.659909\pi\) | ||||
−0.481504 | + | 0.876444i | \(0.659909\pi\) | |||||||
\(524\) | 1.63610 | − | 2.83380i | 0.0714732 | − | 0.123795i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.3858 | − | 19.7208i | −0.496444 | − | 0.859866i | ||||
\(527\) | −0.882789 | − | 1.52904i | −0.0384549 | − | 0.0666058i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.16772 | − | 12.4149i | 0.311640 | − | 0.539776i | ||||
\(530\) | −25.9145 | −1.12565 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.95811 | 0.128250 | ||||||||
\(533\) | 7.90807 | − | 13.6972i | 0.342537 | − | 0.593291i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.18004 | + | 3.77595i | 0.0942516 | + | 0.163248i | ||||
\(536\) | −2.73324 | − | 4.73411i | −0.118058 | − | 0.204482i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.33157 | − | 9.23454i | 0.229860 | − | 0.398129i | ||||
\(539\) | 7.04189 | 0.303316 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.7870 | −0.678738 | −0.339369 | − | 0.940653i | \(-0.610214\pi\) | ||||
−0.339369 | + | 0.940653i | \(0.610214\pi\) | |||||||
\(542\) | −11.6099 | + | 20.1090i | −0.498690 | + | 0.863756i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.56283 | − | 2.70691i | −0.0670059 | − | 0.116058i | ||||
\(545\) | −7.40255 | − | 12.8216i | −0.317090 | − | 0.549217i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.7096 | − | 23.7457i | 0.586180 | − | 1.01529i | −0.408547 | − | 0.912737i | \(-0.633964\pi\) |
0.994727 | − | 0.102557i | \(-0.0327024\pi\) | |||||||
\(548\) | −0.726053 | −0.0310154 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −18.1661 | −0.774606 | ||||||||
\(551\) | 4.28446 | − | 7.42091i | 0.182524 | − | 0.316141i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.55896 | + | 7.89636i | 0.193867 | + | 0.335787i | ||||
\(554\) | 17.8077 | + | 30.8438i | 0.756576 | + | 1.31043i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.10560 | − | 1.91496i | 0.0468879 | − | 0.0812122i | ||||
\(557\) | −29.4020 | −1.24580 | −0.622901 | − | 0.782301i | \(-0.714046\pi\) | ||||
−0.622901 | + | 0.782301i | \(0.714046\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.7297 | 0.707590 | ||||||||
\(560\) | −7.16637 | + | 12.4125i | −0.302835 | + | 0.524525i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.7965 | + | 22.1643i | 0.539789 | + | 0.934943i | ||||
\(563\) | −5.18526 | − | 8.98113i | −0.218533 | − | 0.378510i | 0.735827 | − | 0.677170i | \(-0.236794\pi\) |
−0.954360 | + | 0.298660i | \(0.903460\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.1630 | + | 22.7989i | −0.553770 | + | 0.959158i | ||||
\(566\) | 22.3473 | 0.939327 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.2264 | 0.680843 | ||||||||
\(569\) | −16.4846 | + | 28.5521i | −0.691069 | + | 1.19697i | 0.280419 | + | 0.959878i | \(0.409527\pi\) |
−0.971488 | + | 0.237089i | \(0.923807\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.368708 | + | 0.638620i | 0.0154299 | + | 0.0267254i | 0.873637 | − | 0.486578i | \(-0.161755\pi\) |
−0.858207 | + | 0.513303i | \(0.828422\pi\) | |||||||
\(572\) | 1.77197 | + | 3.06915i | 0.0740900 | + | 0.128328i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.96270 | − | 13.7918i | 0.332357 | − | 0.575658i | ||||
\(575\) | −6.67768 | −0.278479 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.3432 | 0.805267 | 0.402634 | − | 0.915361i | \(-0.368095\pi\) | ||||
0.402634 | + | 0.915361i | \(0.368095\pi\) | |||||||
\(578\) | −5.38919 | + | 9.33434i | −0.224161 | + | 0.388257i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.197119 | − | 0.341420i | −0.00818492 | − | 0.0141767i | ||||
\(581\) | 4.80541 | + | 8.32321i | 0.199362 | + | 0.345305i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −34.5861 | + | 59.9048i | −1.43241 | + | 2.48100i | ||||
\(584\) | 16.3497 | 0.676554 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26.0806 | 1.07738 | ||||||||
\(587\) | −15.9561 | + | 27.6367i | −0.658577 | + | 1.14069i | 0.322408 | + | 0.946601i | \(0.395508\pi\) |
−0.980984 | + | 0.194087i | \(0.937825\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.95336 | − | 3.38332i | −0.0804869 | − | 0.139407i | ||||
\(590\) | −8.18004 | − | 14.1683i | −0.336767 | − | 0.583298i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.0753221 | − | 0.130462i | 0.00309572 | − | 0.00536194i | ||||
\(593\) | −31.6783 | −1.30087 | −0.650436 | − | 0.759561i | \(-0.725414\pi\) | ||||
−0.650436 | + | 0.759561i | \(0.725414\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.9564 | 0.490163 | ||||||||
\(596\) | −1.89646 | + | 3.28476i | −0.0776820 | + | 0.134549i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.39827 | − | 11.0821i | −0.261645 | − | 0.453182i | ||||
\(599\) | −6.31180 | − | 10.9324i | −0.257893 | − | 0.446684i | 0.707784 | − | 0.706429i | \(-0.249695\pi\) |
−0.965677 | + | 0.259745i | \(0.916362\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.45424 | − | 7.71497i | 0.181692 | − | 0.314700i | −0.760765 | − | 0.649028i | \(-0.775176\pi\) |
0.942457 | + | 0.334328i | \(0.108509\pi\) | |||||||
\(602\) | 16.8452 | 0.686561 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.95811 | −0.120364 | ||||||||
\(605\) | 20.1018 | − | 34.8173i | 0.817254 | − | 1.41553i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.5621 | + | 28.6864i | 0.672236 | + | 1.16435i | 0.977269 | + | 0.212005i | \(0.0679992\pi\) |
−0.305033 | + | 0.952342i | \(0.598668\pi\) | |||||||
\(608\) | −3.45811 | − | 5.98962i | −0.140245 | − | 0.242911i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.3020 | + | 21.3077i | −0.498094 | + | 0.862723i | ||||
\(611\) | −12.0564 | −0.487751 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.6800 | 0.714090 | 0.357045 | − | 0.934087i | \(-0.383784\pi\) | ||||
0.357045 | + | 0.934087i | \(0.383784\pi\) | |||||||
\(614\) | 14.0157 | − | 24.2760i | 0.565629 | − | 0.979698i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 21.0947 | + | 36.5370i | 0.849929 | + | 1.47212i | ||||
\(617\) | −12.8662 | − | 22.2849i | −0.517973 | − | 0.897155i | −0.999782 | − | 0.0208793i | \(-0.993353\pi\) |
0.481809 | − | 0.876276i | \(-0.339980\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.8974 | + | 24.0710i | −0.558583 | + | 0.967495i | 0.439032 | + | 0.898472i | \(0.355322\pi\) |
−0.997615 | + | 0.0690232i | \(0.978012\pi\) | |||||||
\(620\) | −0.179740 | −0.00721854 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −14.3696 | −0.576168 | ||||||||
\(623\) | 9.82753 | − | 17.0218i | 0.393732 | − | 0.681964i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.25537 | + | 7.37051i | 0.170215 | + | 0.294820i | ||||
\(626\) | 2.57011 | + | 4.45156i | 0.102722 | + | 0.177920i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.03028 | + | 3.51654i | −0.0810169 | + | 0.140325i | ||||
\(629\) | −0.125667 | −0.00501068 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.8138 | 1.06744 | 0.533720 | − | 0.845661i | \(-0.320794\pi\) | ||||
0.533720 | + | 0.845661i | \(0.320794\pi\) | |||||||
\(632\) | 5.56489 | − | 9.63868i | 0.221360 | − | 0.383406i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −17.7770 | − | 30.7907i | −0.706016 | − | 1.22286i | ||||
\(635\) | 2.97178 | + | 5.14728i | 0.117932 | + | 0.204263i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.91147 | + | 3.31077i | −0.0757354 | + | 0.131177i | ||||
\(638\) | 10.3369 | 0.409240 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 15.6973 | 0.620490 | ||||||||
\(641\) | 6.34524 | − | 10.9903i | 0.250622 | − | 0.434090i | −0.713075 | − | 0.701087i | \(-0.752698\pi\) |
0.963697 | + | 0.266998i | \(0.0860316\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.73829 | − | 13.4031i | −0.305168 | − | 0.528567i | 0.672130 | − | 0.740433i | \(-0.265379\pi\) |
−0.977299 | + | 0.211866i | \(0.932046\pi\) | |||||||
\(644\) | 0.655859 | + | 1.13598i | 0.0258445 | + | 0.0447639i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.4153 | − | 23.2361i | 0.527820 | − | 0.914210i | ||||
\(647\) | −11.1506 | −0.438377 | −0.219189 | − | 0.975683i | \(-0.570341\pi\) | ||||
−0.219189 | + | 0.975683i | \(0.570341\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −43.6691 | −1.71416 | ||||||||
\(650\) | 4.93107 | − | 8.54087i | 0.193413 | − | 0.335001i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.89512 | + | 3.28244i | 0.0742184 | + | 0.128550i | ||||
\(653\) | 22.2961 | + | 38.6179i | 0.872513 | + | 1.51124i | 0.859389 | + | 0.511323i | \(0.170844\pi\) |
0.0131240 | + | 0.999914i | \(0.495822\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.6325 | − | 25.3443i | 0.571740 | − | 0.990283i | ||||
\(656\) | −17.6277 | −0.688247 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.1397 | −0.473255 | ||||||||
\(659\) | −7.04829 | + | 12.2080i | −0.274562 | + | 0.475556i | −0.970025 | − | 0.243007i | \(-0.921866\pi\) |
0.695462 | + | 0.718563i | \(0.255200\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.0574 | − | 31.2763i | −0.702350 | − | 1.21651i | −0.967639 | − | 0.252337i | \(-0.918801\pi\) |
0.265289 | − | 0.964169i | \(-0.414533\pi\) | |||||||
\(662\) | −1.05871 | − | 1.83375i | −0.0411481 | − | 0.0712706i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.86571 | − | 10.1597i | 0.227634 | − | 0.394273i | ||||
\(665\) | 26.4561 | 1.02592 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.79973 | 0.147126 | ||||||||
\(668\) | −0.396459 | + | 0.686688i | −0.0153395 | + | 0.0265687i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.06758 | − | 3.58116i | −0.0798776 | − | 0.138352i | ||||
\(671\) | 32.8371 | + | 56.8755i | 1.26766 | + | 2.19565i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.12108 | + | 1.94177i | −0.0432145 | + | 0.0748497i | −0.886824 | − | 0.462108i | \(-0.847093\pi\) |
0.843609 | + | 0.536958i | \(0.180427\pi\) | |||||||
\(674\) | 10.7992 | 0.415971 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.478340 | 0.0183977 | ||||||||
\(677\) | 17.5881 | − | 30.4635i | 0.675966 | − | 1.17081i | −0.300219 | − | 0.953870i | \(-0.597060\pi\) |
0.976185 | − | 0.216938i | \(-0.0696068\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.314492 | − | 0.544717i | −0.0120691 | − | 0.0209043i | ||||
\(680\) | −7.29726 | − | 12.6392i | −0.279837 | − | 0.484692i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.35638 | − | 4.08137i | 0.0902305 | − | 0.156284i | ||||
\(683\) | 17.7638 | 0.679714 | 0.339857 | − | 0.940477i | \(-0.389621\pi\) | ||||
0.339857 | + | 0.940477i | \(0.389621\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.49350 | −0.248104 | ||||||||
\(686\) | −13.2961 | + | 23.0295i | −0.507646 | + | 0.879269i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.32295 | − | 16.1478i | −0.355434 | − | 0.615630i | ||||
\(689\) | −18.7763 | − | 32.5215i | −0.715320 | − | 1.23897i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.0153 | − | 38.1317i | 0.837502 | − | 1.45060i | −0.0544745 | − | 0.998515i | \(-0.517348\pi\) |
0.891977 | − | 0.452081i | \(-0.149318\pi\) | |||||||
\(692\) | 0.700903 | 0.0266443 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 26.7374 | 1.01494 | ||||||||
\(695\) | 9.88800 | − | 17.1265i | 0.375073 | − | 0.649646i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.35251 | + | 12.7349i | 0.278496 | + | 0.482370i | ||||
\(698\) | 7.47296 | + | 12.9436i | 0.282856 | + | 0.489921i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.505463 | + | 0.875488i | −0.0191047 | + | 0.0330903i | ||||
\(701\) | 30.1052 | 1.13706 | 0.568530 | − | 0.822663i | \(-0.307512\pi\) | ||||
0.568530 | + | 0.822663i | \(0.307512\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.278066 | −0.0104875 | ||||||||
\(704\) | 25.5462 | − | 44.2474i | 0.962810 | − | 1.66764i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.92926 | + | 3.34158i | 0.0726088 | + | 0.125762i | ||||
\(707\) | 13.2961 | + | 23.0295i | 0.500050 | + | 0.866113i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.3687 | − | 21.4232i | 0.464517 | − | 0.804566i | −0.534663 | − | 0.845065i | \(-0.679561\pi\) |
0.999180 | + | 0.0404991i | \(0.0128948\pi\) | |||||||
\(710\) | 12.2746 | 0.460656 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −23.9919 | −0.899136 | ||||||||
\(713\) | 0.866181 | − | 1.50027i | 0.0324388 | − | 0.0561856i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.8478 | + | 27.4491i | 0.592673 | + | 1.02654i | ||||
\(716\) | −0.764700 | − | 1.32450i | −0.0285782 | − | 0.0494989i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19.3935 | + | 33.5906i | −0.723760 | + | 1.25359i | ||||
\(719\) | 43.5526 | 1.62424 | 0.812119 | − | 0.583491i | \(-0.198314\pi\) | ||||
0.812119 | + | 0.583491i | \(0.198314\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.42097 | −0.350855 | ||||||||
\(722\) | 16.8851 | − | 29.2458i | 0.628397 | − | 1.08842i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.621082 | + | 1.07574i | 0.0230823 | + | 0.0399797i | ||||
\(725\) | 1.46420 | + | 2.53607i | 0.0543791 | + | 0.0941874i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.2686 | + | 17.7857i | −0.380840 | + | 0.659635i | −0.991183 | − | 0.132503i | \(-0.957699\pi\) |
0.610342 | + | 0.792138i | \(0.291032\pi\) | |||||||
\(728\) | −22.9040 | −0.848880 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.3678 | 0.457754 | ||||||||
\(731\) | −7.77719 | + | 13.4705i | −0.287650 | + | 0.498224i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.00299 | − | 12.1295i | −0.258661 | − | 0.448015i | 0.707222 | − | 0.706991i | \(-0.249948\pi\) |
−0.965884 | + | 0.258977i | \(0.916615\pi\) | |||||||
\(734\) | −7.40492 | − | 12.8257i | −0.273320 | − | 0.473405i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.53343 | − | 2.65598i | 0.0565231 | − | 0.0979009i | ||||
\(737\) | −11.0378 | −0.406581 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.9813 | −1.54431 | −0.772154 | − | 0.635435i | \(-0.780821\pi\) | ||||
−0.772154 | + | 0.635435i | \(0.780821\pi\) | |||||||
\(740\) | −0.00639661 | + | 0.0110793i | −0.000235144 | + | 0.000407282i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −18.9060 | − | 32.7462i | −0.694062 | − | 1.20215i | ||||
\(743\) | 13.9311 | + | 24.1293i | 0.511082 | + | 0.885219i | 0.999918 | + | 0.0128435i | \(0.00408832\pi\) |
−0.488836 | + | 0.872376i | \(0.662578\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.9611 | + | 29.3775i | −0.621407 | + | 1.07631i | ||||
\(746\) | −45.0128 | −1.64804 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.29498 | −0.120476 | ||||||||
\(749\) | −3.18092 | + | 5.50952i | −0.116228 | + | 0.201313i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.4525 | + | 45.8170i | 0.965265 | + | 1.67189i | 0.708902 | + | 0.705307i | \(0.249191\pi\) |
0.256363 | + | 0.966580i | \(0.417476\pi\) | |||||||
\(752\) | 6.71869 | + | 11.6371i | 0.245006 | + | 0.424362i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.80587 | + | 4.85992i | −0.102184 | + | 0.176988i | ||||
\(755\) | −26.4561 | −0.962834 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.4858 | −1.50783 | −0.753913 | − | 0.656975i | \(-0.771836\pi\) | ||||
−0.753913 | + | 0.656975i | \(0.771836\pi\) | |||||||
\(758\) | 14.1058 | − | 24.4320i | 0.512346 | − | 0.887410i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −16.1468 | − | 27.9670i | −0.585705 | − | 1.01447i | ||||
\(761\) | −22.6937 | − | 39.3067i | −0.822647 | − | 1.42487i | −0.903705 | − | 0.428156i | \(-0.859163\pi\) |
0.0810582 | − | 0.996709i | \(-0.474170\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.8011 | − | 18.7081i | 0.391027 | − | 0.677279i | ||||
\(764\) | −0.926651 | −0.0335251 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.53890 | −0.200128 | ||||||||
\(767\) | 11.8537 | − | 20.5312i | 0.428012 | − | 0.741339i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.55825 | − | 4.43102i | −0.0922528 | − | 0.159787i | 0.816206 | − | 0.577761i | \(-0.196073\pi\) |
−0.908459 | + | 0.417975i | \(0.862740\pi\) | |||||||
\(770\) | 15.9572 | + | 27.6387i | 0.575059 | + | 0.996031i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.65064 | + | 2.85900i | −0.0594080 | + | 0.102898i | ||||
\(773\) | 52.6427 | 1.89343 | 0.946713 | − | 0.322077i | \(-0.104381\pi\) | ||||
0.946713 | + | 0.322077i | \(0.104381\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.33511 | 0.0479587 | ||||||||
\(776\) | −0.383885 | + | 0.664908i | −0.0137807 | + | 0.0238688i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.5155 | − | 19.9454i | −0.412850 | − | 0.715077i | ||||
\(779\) | 16.2690 | + | 28.1788i | 0.582899 | + | 1.00961i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.3819 | − | 28.3743i | 0.586191 | − | 1.01531i | ||||
\(782\) | 11.8976 | 0.425456 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.26083 | 0.152172 | ||||||||
\(785\) | −18.1579 | + | 31.4504i | −0.648084 | + | 1.12251i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.3812 | + | 17.9808i | 0.370050 | + | 0.640945i | 0.989573 | − | 0.144034i | \(-0.0460073\pi\) |
−0.619523 | + | 0.784978i | \(0.712674\pi\) | |||||||
\(788\) | −0.0668661 | − | 0.115816i | −0.00238201 | − | 0.00412576i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.20961 | − | 7.29125i | 0.149771 | − | 0.259411i | ||||
\(791\) | −38.4124 | −1.36579 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.6536 | −1.26610 | ||||||||
\(794\) | 15.0911 | − | 26.1385i | 0.535561 | − | 0.927620i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.941752 | − | 1.63116i | −0.0333795 | − | 0.0578150i | ||||
\(797\) | −22.7900 | − | 39.4734i | −0.807263 | − | 1.39822i | −0.914753 | − | 0.404014i | \(-0.867615\pi\) |
0.107490 | − | 0.994206i | \(-0.465719\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.60472 | − | 9.70766i | 0.198281 | − | 0.343432i | ||||
\(800\) | 2.36360 | 0.0835658 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.6459 | −0.693721 | ||||||||
\(803\) | 16.5064 | − | 28.5899i | 0.582498 | − | 1.00892i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.86571 | + | 10.1597i | 0.206739 | + | 0.358083i | ||||
\(806\) | 1.27925 | + | 2.21572i | 0.0450596 | + | 0.0780455i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.2298 | − | 28.1109i | 0.570964 | − | 0.988938i | ||||
\(809\) | 4.21120 | 0.148058 | 0.0740290 | − | 0.997256i | \(-0.476414\pi\) | ||||
0.0740290 | + | 0.997256i | \(0.476414\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.3618 | 0.398968 | 0.199484 | − | 0.979901i | \(-0.436073\pi\) | ||||
0.199484 | + | 0.979901i | \(0.436073\pi\) | |||||||
\(812\) | 0.287618 | − | 0.498169i | 0.0100934 | − | 0.0174823i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.167718 | − | 0.290497i | −0.00587853 | − | 0.0101819i | ||||
\(815\) | 16.9491 | + | 29.3567i | 0.593700 | + | 1.02832i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.2087 | + | 29.8064i | −0.602057 | + | 1.04279i | ||||
\(818\) | 23.5817 | 0.824515 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.49701 | 0.0522778 | ||||||||
\(821\) | 0.821137 | − | 1.42225i | 0.0286579 | − | 0.0496369i | −0.851341 | − | 0.524613i | \(-0.824210\pi\) |
0.879999 | + | 0.474976i | \(0.157543\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.60947 | − | 9.71589i | −0.195534 | − | 0.338675i | 0.751542 | − | 0.659686i | \(-0.229311\pi\) |
−0.947075 | + | 0.321011i | \(0.895977\pi\) | |||||||
\(824\) | 5.74985 | + | 9.95903i | 0.200305 | + | 0.346939i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.9356 | − | 20.6730i | 0.415292 | − | 0.719306i | ||||
\(827\) | 9.61318 | 0.334283 | 0.167141 | − | 0.985933i | \(-0.446546\pi\) | ||||
0.167141 | + | 0.985933i | \(0.446546\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.4938 | 1.16329 | 0.581644 | − | 0.813443i | \(-0.302410\pi\) | ||||
0.581644 | + | 0.813443i | \(0.302410\pi\) | |||||||
\(830\) | 4.43717 | − | 7.68540i | 0.154016 | − | 0.266764i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13.8687 | + | 24.0213i | 0.480811 | + | 0.832789i | ||||
\(833\) | −1.77719 | − | 3.07818i | −0.0615759 | − | 0.106653i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.54576 | + | 6.14144i | −0.122706 | + | 0.212533i | ||||
\(836\) | −7.29086 | −0.252160 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.4129 | 0.877874 | ||||||||
\(839\) | −15.9971 | + | 27.7077i | −0.552280 | + | 0.956577i | 0.445830 | + | 0.895118i | \(0.352909\pi\) |
−0.998110 | + | 0.0614591i | \(0.980425\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.6668 | + | 23.6717i | 0.471270 | + | 0.816264i | ||||
\(842\) | −21.7815 | − | 37.7267i | −0.750641 | − | 1.30015i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.37346 | + | 2.37889i | −0.0472763 | + | 0.0818849i | ||||
\(845\) | 4.27807 | 0.147170 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 58.6614 | 2.01563 | ||||||||
\(848\) | −20.9270 | + | 36.2466i | −0.718635 | + | 1.24471i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.58466 | + | 7.94086i | 0.157252 | + | 0.272369i | ||||
\(851\) | −0.0616516 | − | 0.106784i | −0.00211339 | − | 0.00366050i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.6211 | + | 30.5206i | −0.603334 | + | 1.04501i | 0.388978 | + | 0.921247i | \(0.372828\pi\) |
−0.992312 | + | 0.123759i | \(0.960505\pi\) | |||||||
\(854\) | −35.8999 | −1.22847 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.76558 | 0.265422 | ||||||||
\(857\) | −10.6245 | + | 18.4021i | −0.362925 | + | 0.628605i | −0.988441 | − | 0.151606i | \(-0.951555\pi\) |
0.625515 | + | 0.780212i | \(0.284889\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.9192 | − | 44.8934i | −0.884352 | − | 1.53174i | −0.846454 | − | 0.532461i | \(-0.821267\pi\) |
−0.0378979 | − | 0.999282i | \(-0.512066\pi\) | |||||||
\(860\) | 0.791737 | + | 1.37133i | 0.0269980 | + | 0.0467619i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.1172 | + | 40.0402i | −0.787375 | + | 1.36377i | ||||
\(863\) | 22.6783 | 0.771978 | 0.385989 | − | 0.922503i | \(-0.373860\pi\) | ||||
0.385989 | + | 0.922503i | \(0.373860\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.26857 | 0.213138 | ||||||||
\(866\) | −16.8862 | + | 29.2478i | −0.573818 | + | 0.993882i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.131130 | − | 0.227124i | −0.00445085 | − | 0.00770909i | ||||
\(869\) | −11.2365 | − | 19.4622i | −0.381172 | − | 0.660208i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.99613 | − | 5.18945i | 0.101520 | − | 0.175838i | ||||
\(872\) | −26.3688 | −0.892959 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 26.3259 | 0.890488 | ||||||||
\(875\) | −14.4843 | + | 25.0875i | −0.489658 | + | 0.848112i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.566704 | − | 0.981560i | −0.0191362 | − | 0.0331449i | 0.856299 | − | 0.516481i | \(-0.172758\pi\) |
−0.875435 | + | 0.483336i | \(0.839425\pi\) | |||||||
\(878\) | −15.6340 | − | 27.0789i | −0.527623 | − | 0.913870i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 17.6630 | − | 30.5932i | 0.595419 | − | 1.03130i | ||||
\(881\) | 30.8289 | 1.03865 | 0.519327 | − | 0.854576i | \(-0.326183\pi\) | ||||
0.519327 | + | 0.854576i | \(0.326183\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.33511 | −0.314152 | −0.157076 | − | 0.987587i | \(-0.550207\pi\) | ||||
−0.157076 | + | 0.987587i | \(0.550207\pi\) | |||||||
\(884\) | 0.894400 | − | 1.54915i | 0.0300819 | − | 0.0521034i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.77647 | + | 4.80899i | 0.0932775 | + | 0.161561i | ||||
\(887\) | −7.04710 | − | 12.2059i | −0.236619 | − | 0.409835i | 0.723123 | − | 0.690719i | \(-0.242706\pi\) |
−0.959742 | + | 0.280884i | \(0.909373\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.33615 | + | 7.51044i | −0.145430 | + | 0.251892i | ||||
\(890\) | −18.1489 | −0.608352 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.02322 | 0.0677425 | ||||||||
\(893\) | 12.4017 | − | 21.4803i | 0.415006 | − | 0.718812i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.83915 | − | 11.8457i | −0.228607 | − | 0.395960i | ||||
\(896\) | 11.4520 | + | 19.8355i | 0.382585 | + | 0.662657i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.3557 | + | 21.4006i | −0.412314 | + | 0.714149i | ||||
\(899\) | −0.759704 | −0.0253376 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.9145 | 1.16317 | ||||||||
\(902\) | −19.6257 | + | 33.9927i | −0.653463 | + | 1.13183i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 23.4440 | + | 40.6063i | 0.779737 | + | 1.35054i | ||||
\(905\) | 5.55468 | + | 9.62099i | 0.184644 | + | 0.319813i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.36959 | − | 7.56834i | 0.145090 | − | 0.251303i | −0.784317 | − | 0.620361i | \(-0.786986\pi\) |
0.929406 | + | 0.369058i | \(0.120320\pi\) | |||||||
\(908\) | −3.20296 | −0.106294 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −17.3259 | −0.574349 | ||||||||
\(911\) | −10.3255 | + | 17.8842i | −0.342098 | + | 0.592532i | −0.984822 | − | 0.173566i | \(-0.944471\pi\) |
0.642724 | + | 0.766098i | \(0.277804\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.8439 | − | 20.5142i | −0.391976 | − | 0.678922i | ||||
\(914\) | −13.1099 | − | 22.7071i | −0.433638 | − | 0.751083i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.144334 | − | 0.249994i | 0.00476893 | − | 0.00826002i | ||||
\(917\) | 42.7009 | 1.41011 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.36009 | −0.0778522 | −0.0389261 | − | 0.999242i | \(-0.512394\pi\) | ||||
−0.0389261 | + | 0.999242i | \(0.512394\pi\) | |||||||
\(920\) | 7.15998 | − | 12.4014i | 0.236057 | − | 0.408864i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18.6932 | − | 32.3777i | −0.615629 | − | 1.06630i | ||||
\(923\) | 8.89352 | + | 15.4040i | 0.292734 | + | 0.507030i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.0475142 | − | 0.0822969i | 0.00156226 | − | 0.00270591i | ||||
\(926\) | −52.1215 | −1.71282 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.34493 | −0.0441496 | ||||||||
\(929\) | −13.4101 | + | 23.2270i | −0.439972 | + | 0.762054i | −0.997687 | − | 0.0679787i | \(-0.978345\pi\) |
0.557715 | + | 0.830033i | \(0.311678\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.93242 | − | 6.81115i | −0.128880 | − | 0.223226i | ||||
\(932\) | −1.55122 | − | 2.68680i | −0.0508120 | − | 0.0880089i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −20.0503 | + | 34.7282i | −0.656067 | + | 1.13634i | ||||
\(935\) | −29.4688 | −0.963734 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.93313 | 0.0631527 | 0.0315764 | − | 0.999501i | \(-0.489947\pi\) | ||||
0.0315764 | + | 0.999501i | \(0.489947\pi\) | |||||||
\(938\) | 3.01683 | − | 5.22530i | 0.0985029 | − | 0.170612i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.570574 | − | 0.988264i | −0.0186101 | − | 0.0322336i | ||||
\(941\) | 5.95517 | + | 10.3147i | 0.194133 | + | 0.336248i | 0.946616 | − | 0.322363i | \(-0.104477\pi\) |
−0.752483 | + | 0.658612i | \(0.771144\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.21419 | + | 12.4953i | −0.234926 | + | 0.406905i | ||||
\(944\) | −26.4228 | −0.859990 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −41.5185 | −1.34988 | ||||||||
\(947\) | −0.157918 | + | 0.273522i | −0.00513165 | + | 0.00888828i | −0.868580 | − | 0.495549i | \(-0.834967\pi\) |
0.863448 | + | 0.504438i | \(0.168300\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.96110 | + | 15.5211i | 0.290890 | + | 0.503836i | ||||
\(950\) | 10.1446 | + | 17.5709i | 0.329133 | + | 0.570075i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.6475 | − | 18.4420i | 0.345087 | − | 0.597708i | ||||
\(953\) | −3.25133 | −0.105321 | −0.0526605 | − | 0.998612i | \(-0.516770\pi\) | ||||
−0.0526605 | + | 0.998612i | \(0.516770\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.28756 | −0.268179 | ||||||||
\(956\) | 0.372273 | − | 0.644796i | 0.0120402 | − | 0.0208542i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25.3803 | + | 43.9600i | 0.820001 | + | 1.42028i | ||||
\(959\) | −4.73736 | − | 8.20535i | −0.152977 | − | 0.264964i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3268 | − | 26.5468i | 0.494414 | − | 0.856349i | ||||
\(962\) | 0.182104 | 0.00587127 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.619489 | 0.0199524 | ||||||||
\(965\) | −14.7626 | + | 25.5696i | −0.475226 | + | 0.823116i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.48380 | − | 9.49823i | −0.176347 | − | 0.305442i | 0.764279 | − | 0.644885i | \(-0.223095\pi\) |
−0.940627 | + | 0.339443i | \(0.889761\pi\) | |||||||
\(968\) | −35.8025 | − | 62.0117i | −1.15073 | − | 1.99313i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.290393 | + | 0.502975i | −0.00932394 | + | 0.0161495i | ||||
\(971\) | −23.3868 | −0.750519 | −0.375259 | − | 0.926920i | \(-0.622446\pi\) | ||||
−0.375259 | + | 0.926920i | \(0.622446\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.8553 | 0.925060 | ||||||||
\(974\) | −0.514548 | + | 0.891223i | −0.0164872 | + | 0.0285566i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 19.8687 | + | 34.4136i | 0.635982 | + | 1.10155i | ||||
\(977\) | −25.0881 | − | 43.4539i | −0.802640 | − | 1.39021i | −0.917873 | − | 0.396875i | \(-0.870095\pi\) |
0.115233 | − | 0.993339i | \(-0.463239\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.2219 | + | 41.9536i | −0.774136 | + | 1.34084i | ||||
\(980\) | −0.361844 | −0.0115587 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.670874 | −0.0214084 | ||||||||
\(983\) | −7.34730 | + | 12.7259i | −0.234342 | + | 0.405893i | −0.959081 | − | 0.283131i | \(-0.908627\pi\) |
0.724739 | + | 0.689024i | \(0.241960\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.598021 | − | 1.03580i | −0.0190545 | − | 0.0330034i | ||||
\(986\) | −2.60876 | − | 4.51850i | −0.0830797 | − | 0.143898i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.97906 | − | 3.42782i | 0.0629621 | − | 0.109054i | ||||
\(989\) | −15.2618 | −0.485296 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.00000 | 0.0635321 | 0.0317660 | − | 0.999495i | \(-0.489887\pi\) | ||||
0.0317660 | + | 0.999495i | \(0.489887\pi\) | |||||||
\(992\) | −0.306589 | + | 0.531028i | −0.00973422 | + | 0.0168602i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.95496 | + | 15.5104i | 0.284034 | + | 0.491961i | ||||
\(995\) | −8.42262 | − | 14.5884i | −0.267015 | − | 0.462483i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.9432 | − | 39.7387i | 0.726617 | − | 1.25854i | −0.231688 | − | 0.972790i | \(-0.574425\pi\) |
0.958305 | − | 0.285747i | \(-0.0922418\pi\) | |||||||
\(998\) | −12.0797 | −0.382375 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 243.2.c.f.163.2 | 6 | ||
3.2 | odd | 2 | 243.2.c.e.163.2 | 6 | |||
9.2 | odd | 6 | 243.2.a.f.1.2 | yes | 3 | ||
9.4 | even | 3 | inner | 243.2.c.f.82.2 | 6 | ||
9.5 | odd | 6 | 243.2.c.e.82.2 | 6 | |||
9.7 | even | 3 | 243.2.a.e.1.2 | ✓ | 3 | ||
27.2 | odd | 18 | 729.2.e.c.325.1 | 6 | |||
27.4 | even | 9 | 729.2.e.g.163.1 | 6 | |||
27.5 | odd | 18 | 729.2.e.c.406.1 | 6 | |||
27.7 | even | 9 | 729.2.e.a.82.1 | 6 | |||
27.11 | odd | 18 | 729.2.e.b.568.1 | 6 | |||
27.13 | even | 9 | 729.2.e.a.649.1 | 6 | |||
27.14 | odd | 18 | 729.2.e.i.649.1 | 6 | |||
27.16 | even | 9 | 729.2.e.g.568.1 | 6 | |||
27.20 | odd | 18 | 729.2.e.i.82.1 | 6 | |||
27.22 | even | 9 | 729.2.e.h.406.1 | 6 | |||
27.23 | odd | 18 | 729.2.e.b.163.1 | 6 | |||
27.25 | even | 9 | 729.2.e.h.325.1 | 6 | |||
36.7 | odd | 6 | 3888.2.a.bd.1.2 | 3 | |||
36.11 | even | 6 | 3888.2.a.bk.1.2 | 3 | |||
45.29 | odd | 6 | 6075.2.a.bq.1.2 | 3 | |||
45.34 | even | 6 | 6075.2.a.bv.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
243.2.a.e.1.2 | ✓ | 3 | 9.7 | even | 3 | ||
243.2.a.f.1.2 | yes | 3 | 9.2 | odd | 6 | ||
243.2.c.e.82.2 | 6 | 9.5 | odd | 6 | |||
243.2.c.e.163.2 | 6 | 3.2 | odd | 2 | |||
243.2.c.f.82.2 | 6 | 9.4 | even | 3 | inner | ||
243.2.c.f.163.2 | 6 | 1.1 | even | 1 | trivial | ||
729.2.e.a.82.1 | 6 | 27.7 | even | 9 | |||
729.2.e.a.649.1 | 6 | 27.13 | even | 9 | |||
729.2.e.b.163.1 | 6 | 27.23 | odd | 18 | |||
729.2.e.b.568.1 | 6 | 27.11 | odd | 18 | |||
729.2.e.c.325.1 | 6 | 27.2 | odd | 18 | |||
729.2.e.c.406.1 | 6 | 27.5 | odd | 18 | |||
729.2.e.g.163.1 | 6 | 27.4 | even | 9 | |||
729.2.e.g.568.1 | 6 | 27.16 | even | 9 | |||
729.2.e.h.325.1 | 6 | 27.25 | even | 9 | |||
729.2.e.h.406.1 | 6 | 27.22 | even | 9 | |||
729.2.e.i.82.1 | 6 | 27.20 | odd | 18 | |||
729.2.e.i.649.1 | 6 | 27.14 | odd | 18 | |||
3888.2.a.bd.1.2 | 3 | 36.7 | odd | 6 | |||
3888.2.a.bk.1.2 | 3 | 36.11 | even | 6 | |||
6075.2.a.bq.1.2 | 3 | 45.29 | odd | 6 | |||
6075.2.a.bv.1.2 | 3 | 45.34 | even | 6 |