Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [729,2,Mod(82,729)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("729.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.e (of order \(9\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.82109430735\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{9})\) |
Coefficient field: | 12.0.101559956668416.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 8x^{6} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | no (minimal twist has level 243) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 325.1 | ||
Root | \(-1.39273 + 0.245576i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 729.325 |
Dual form | 729.2.e.p.406.1 |
$q$-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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{7}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.87642 | + | 1.57450i | −1.32683 | + | 1.11334i | −0.342020 | + | 0.939693i | \(0.611111\pi\) |
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.694593 | − | 3.93923i | 0.347296 | − | 1.96962i | ||||
\(5\) | −2.30177 | + | 0.837775i | −1.02938 | + | 0.374664i | −0.800845 | − | 0.598871i | \(-0.795616\pi\) |
−0.228536 | + | 0.973535i | \(0.573394\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.347296 | + | 1.96962i | 0.131266 | + | 0.744445i | 0.977388 | + | 0.211455i | \(0.0678203\pi\) |
−0.846122 | + | 0.532989i | \(0.821069\pi\) | |||||||
\(8\) | 2.44949 | + | 4.24264i | 0.866025 | + | 1.50000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.00000 | − | 5.19615i | 0.948683 | − | 1.64317i | ||||
\(11\) | 2.30177 | + | 0.837775i | 0.694009 | + | 0.252599i | 0.664851 | − | 0.746976i | \(-0.268495\pi\) |
0.0291582 | + | 0.999575i | \(0.490717\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.766044 | − | 0.642788i | −0.212463 | − | 0.178277i | 0.530346 | − | 0.847781i | \(-0.322062\pi\) |
−0.742808 | + | 0.669504i | \(0.766507\pi\) | |||||||
\(14\) | −3.75284 | − | 3.14900i | −1.00299 | − | 0.841607i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.75877 | − | 1.36808i | −0.939693 | − | 0.342020i | ||||
\(17\) | −3.67423 | + | 6.36396i | −0.891133 | + | 1.54349i | −0.0526138 | + | 0.998615i | \(0.516755\pi\) |
−0.838519 | + | 0.544872i | \(0.816578\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.500000 | + | 0.866025i | 0.114708 | + | 0.198680i | 0.917663 | − | 0.397360i | \(-0.130073\pi\) |
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | 1.70140 | + | 9.64911i | 0.380444 | + | 2.15761i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.63816 | + | 2.05212i | −1.20206 | + | 0.437514i | ||||
\(23\) | 0.425349 | − | 2.41228i | 0.0886915 | − | 0.502994i | −0.907807 | − | 0.419387i | \(-0.862245\pi\) |
0.996499 | − | 0.0836069i | \(-0.0266440\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.766044 | − | 0.642788i | 0.153209 | − | 0.128558i | ||||
\(26\) | 2.44949 | 0.480384 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8.00000 | 1.51186 | ||||||||
\(29\) | 3.75284 | − | 3.14900i | 0.696884 | − | 0.584755i | −0.224001 | − | 0.974589i | \(-0.571912\pi\) |
0.920885 | + | 0.389834i | \(0.127467\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.173648 | + | 0.984808i | −0.0311881 | + | 0.176877i | −0.996423 | − | 0.0845082i | \(-0.973068\pi\) |
0.965235 | + | 0.261385i | \(0.0841792\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.12567 | − | 17.7265i | −0.536048 | − | 3.04008i | ||||
\(35\) | −2.44949 | − | 4.24264i | −0.414039 | − | 0.717137i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | + | 6.92820i | −0.657596 | + | 1.13899i | 0.323640 | + | 0.946180i | \(0.395093\pi\) |
−0.981236 | + | 0.192809i | \(0.938240\pi\) | |||||||
\(38\) | −2.30177 | − | 0.837775i | −0.373396 | − | 0.135905i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9.19253 | − | 7.71345i | −1.45347 | − | 1.21960i | ||||
\(41\) | −3.75284 | − | 3.14900i | −0.586095 | − | 0.491792i | 0.300848 | − | 0.953672i | \(-0.402730\pi\) |
−0.886942 | + | 0.461881i | \(0.847175\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.3366 | − | 3.76222i | −1.57632 | − | 0.573733i | −0.601920 | − | 0.798556i | \(-0.705597\pi\) |
−0.974400 | + | 0.224823i | \(0.927820\pi\) | |||||||
\(44\) | 4.89898 | − | 8.48528i | 0.738549 | − | 1.27920i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | + | 5.19615i | 0.442326 | + | 0.766131i | ||||
\(47\) | −1.70140 | − | 9.64911i | −0.248174 | − | 1.40747i | −0.813003 | − | 0.582259i | \(-0.802169\pi\) |
0.564829 | − | 0.825208i | \(-0.308942\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.81908 | − | 1.02606i | 0.402725 | − | 0.146580i | ||||
\(50\) | −0.425349 | + | 2.41228i | −0.0601535 | + | 0.341147i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.06418 | + | 2.57115i | −0.424925 | + | 0.356554i | ||||
\(53\) | −7.34847 | −1.00939 | −0.504695 | − | 0.863298i | \(-0.668395\pi\) | ||||
−0.504695 | + | 0.863298i | \(0.668395\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.00000 | −0.809040 | ||||||||
\(56\) | −7.50567 | + | 6.29801i | −1.00299 | + | 0.841607i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.08378 | + | 11.8177i | −0.273613 | + | 1.55174i | ||||
\(59\) | −2.30177 | + | 0.837775i | −0.299665 | + | 0.109069i | −0.487477 | − | 0.873136i | \(-0.662083\pi\) |
0.187812 | + | 0.982205i | \(0.439860\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.868241 | + | 4.92404i | 0.111167 | + | 0.630459i | 0.988577 | + | 0.150717i | \(0.0481583\pi\) |
−0.877410 | + | 0.479741i | \(0.840731\pi\) | |||||||
\(62\) | −1.22474 | − | 2.12132i | −0.155543 | − | 0.269408i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.00000 | − | 6.92820i | 0.500000 | − | 0.866025i | ||||
\(65\) | 2.30177 | + | 0.837775i | 0.285499 | + | 0.103913i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.36231 | − | 4.49951i | −0.655111 | − | 0.549703i | 0.253506 | − | 0.967334i | \(-0.418416\pi\) |
−0.908617 | + | 0.417631i | \(0.862861\pi\) | |||||||
\(68\) | 22.5170 | + | 18.8940i | 2.73059 | + | 2.29124i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 11.2763 | + | 4.10424i | 1.34778 | + | 0.490551i | ||||
\(71\) | 3.67423 | − | 6.36396i | 0.436051 | − | 0.755263i | −0.561329 | − | 0.827592i | \(-0.689710\pi\) |
0.997381 | + | 0.0723293i | \(0.0230432\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.50000 | − | 9.52628i | −0.643726 | − | 1.11497i | −0.984594 | − | 0.174855i | \(-0.944054\pi\) |
0.340868 | − | 0.940111i | \(-0.389279\pi\) | |||||||
\(74\) | −3.40280 | − | 19.2982i | −0.395567 | − | 2.24337i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.75877 | − | 1.36808i | 0.431161 | − | 0.156930i | ||||
\(77\) | −0.850699 | + | 4.82455i | −0.0969461 | + | 0.549809i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.36231 | + | 4.49951i | −0.603307 | + | 0.506235i | −0.892507 | − | 0.451034i | \(-0.851055\pi\) |
0.289200 | + | 0.957269i | \(0.406611\pi\) | |||||||
\(80\) | 9.79796 | 1.09545 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 12.0000 | 1.32518 | ||||||||
\(83\) | 9.38209 | − | 7.87251i | 1.02982 | − | 0.864120i | 0.0389889 | − | 0.999240i | \(-0.487586\pi\) |
0.990829 | + | 0.135120i | \(0.0431419\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.12567 | − | 17.7265i | 0.339026 | − | 1.92271i | ||||
\(86\) | 25.3194 | − | 9.21552i | 2.73027 | − | 0.993735i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.08378 | + | 11.8177i | 0.222131 | + | 1.25977i | ||||
\(89\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | − | 1.73205i | 0.104828 | − | 0.181568i | ||||
\(92\) | −9.20707 | − | 3.35110i | −0.959903 | − | 0.349376i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 18.3851 | + | 15.4269i | 1.89627 | + | 1.59116i | ||||
\(95\) | −1.87642 | − | 1.57450i | −0.192516 | − | 0.161540i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.57785 | + | 2.39414i | 0.667879 | + | 0.243088i | 0.653635 | − | 0.756810i | \(-0.273243\pi\) |
0.0142448 | + | 0.999899i | \(0.495466\pi\) | |||||||
\(98\) | −3.67423 | + | 6.36396i | −0.371154 | + | 0.642857i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | − | 3.46410i | −0.200000 | − | 0.346410i | ||||
\(101\) | 0.850699 | + | 4.82455i | 0.0846477 | + | 0.480061i | 0.997432 | + | 0.0716191i | \(0.0228166\pi\) |
−0.912784 | + | 0.408442i | \(0.866072\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.57785 | − | 2.39414i | 0.648135 | − | 0.235902i | 0.00302937 | − | 0.999995i | \(-0.499036\pi\) |
0.645105 | + | 0.764094i | \(0.276813\pi\) | |||||||
\(104\) | 0.850699 | − | 4.82455i | 0.0834179 | − | 0.473086i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.7888 | − | 11.5702i | 1.33929 | − | 1.12379i | ||||
\(107\) | −14.6969 | −1.42081 | −0.710403 | − | 0.703795i | \(-0.751487\pi\) | ||||
−0.710403 | + | 0.703795i | \(0.751487\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00000 | −0.0957826 | −0.0478913 | − | 0.998853i | \(-0.515250\pi\) | ||||
−0.0478913 | + | 0.998853i | \(0.515250\pi\) | |||||||
\(110\) | 11.2585 | − | 9.44701i | 1.07346 | − | 0.900737i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.38919 | − | 7.87846i | 0.131266 | − | 0.744445i | ||||
\(113\) | −9.20707 | + | 3.35110i | −0.866128 | + | 0.315245i | −0.736598 | − | 0.676331i | \(-0.763569\pi\) |
−0.129530 | + | 0.991575i | \(0.541347\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.04189 | + | 5.90885i | 0.0971567 | + | 0.551003i | ||||
\(116\) | −9.79796 | − | 16.9706i | −0.909718 | − | 1.57568i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.00000 | − | 5.19615i | 0.276172 | − | 0.478345i | ||||
\(119\) | −13.8106 | − | 5.02665i | −1.26602 | − | 0.460792i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.83022 | − | 3.21394i | −0.348202 | − | 0.292176i | ||||
\(122\) | −9.38209 | − | 7.87251i | −0.849415 | − | 0.712743i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.75877 | + | 1.36808i | 0.337548 | + | 0.122857i | ||||
\(125\) | 4.89898 | − | 8.48528i | 0.438178 | − | 0.758947i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.50000 | + | 16.4545i | 0.842989 | + | 1.46010i | 0.887357 | + | 0.461084i | \(0.152539\pi\) |
−0.0443678 | + | 0.999015i | \(0.514127\pi\) | |||||||
\(128\) | 3.40280 | + | 19.2982i | 0.300767 | + | 1.70574i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.63816 | + | 2.05212i | −0.494499 | + | 0.179983i | ||||
\(131\) | −2.12675 | + | 12.0614i | −0.185815 | + | 1.05381i | 0.739089 | + | 0.673607i | \(0.235256\pi\) |
−0.924904 | + | 0.380200i | \(0.875855\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.53209 | + | 1.28558i | −0.132849 | + | 0.111474i | ||||
\(134\) | 17.1464 | 1.48123 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −36.0000 | −3.08697 | ||||||||
\(137\) | −7.50567 | + | 6.29801i | −0.641253 | + | 0.538075i | −0.904403 | − | 0.426680i | \(-0.859683\pi\) |
0.263150 | + | 0.964755i | \(0.415239\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.73648 | + | 9.84808i | −0.147286 | + | 0.835303i | 0.818216 | + | 0.574910i | \(0.194963\pi\) |
−0.965503 | + | 0.260393i | \(0.916148\pi\) | |||||||
\(140\) | −18.4141 | + | 6.70220i | −1.55628 | + | 0.566439i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.12567 | + | 17.7265i | 0.262300 | + | 1.48758i | ||||
\(143\) | −1.22474 | − | 2.12132i | −0.102418 | − | 0.177394i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | + | 10.3923i | −0.498273 | + | 0.863034i | ||||
\(146\) | 25.3194 | + | 9.21552i | 2.09545 | + | 0.762682i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 24.5134 | + | 20.5692i | 2.01499 | + | 1.69078i | ||||
\(149\) | −9.38209 | − | 7.87251i | −0.768611 | − | 0.644941i | 0.171742 | − | 0.985142i | \(-0.445060\pi\) |
−0.940353 | + | 0.340201i | \(0.889505\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.69846 | − | 1.71010i | −0.382356 | − | 0.139166i | 0.143689 | − | 0.989623i | \(-0.454103\pi\) |
−0.526045 | + | 0.850457i | \(0.676326\pi\) | |||||||
\(152\) | −2.44949 | + | 4.24264i | −0.198680 | + | 0.344124i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.00000 | − | 10.3923i | −0.483494 | − | 0.837436i | ||||
\(155\) | −0.425349 | − | 2.41228i | −0.0341649 | − | 0.193759i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.9748 | + | 5.81434i | −1.27493 | + | 0.464035i | −0.888751 | − | 0.458391i | \(-0.848426\pi\) |
−0.386175 | + | 0.922426i | \(0.626204\pi\) | |||||||
\(158\) | 2.97745 | − | 16.8859i | 0.236873 | − | 1.34337i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.89898 | 0.386094 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0000 | −0.783260 | −0.391630 | − | 0.920123i | \(-0.628089\pi\) | ||||
−0.391630 | + | 0.920123i | \(0.628089\pi\) | |||||||
\(164\) | −15.0113 | + | 12.5960i | −1.17219 | + | 0.983583i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.20945 | + | 29.5442i | −0.404331 | + | 2.29308i | ||||
\(167\) | 4.60353 | − | 1.67555i | 0.356232 | − | 0.129658i | −0.157704 | − | 0.987486i | \(-0.550409\pi\) |
0.513936 | + | 0.857829i | \(0.328187\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.08378 | − | 11.8177i | −0.160291 | − | 0.909053i | ||||
\(170\) | 22.0454 | + | 38.1838i | 1.69081 | + | 2.92856i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −22.0000 | + | 38.1051i | −1.67748 | + | 2.90549i | ||||
\(173\) | 9.20707 | + | 3.35110i | 0.700001 | + | 0.254779i | 0.667411 | − | 0.744689i | \(-0.267402\pi\) |
0.0325894 | + | 0.999469i | \(0.489625\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.53209 | + | 1.28558i | 0.115815 | + | 0.0971804i | ||||
\(176\) | −7.50567 | − | 6.29801i | −0.565761 | − | 0.474730i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.34847 | + | 12.7279i | −0.549250 | + | 0.951330i | 0.449076 | + | 0.893494i | \(0.351753\pi\) |
−0.998326 | + | 0.0578359i | \(0.981580\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.00000 | − | 6.92820i | −0.297318 | − | 0.514969i | 0.678204 | − | 0.734874i | \(-0.262759\pi\) |
−0.975521 | + | 0.219905i | \(0.929425\pi\) | |||||||
\(182\) | 0.850699 | + | 4.82455i | 0.0630580 | + | 0.357620i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 11.2763 | − | 4.10424i | 0.831301 | − | 0.302569i | ||||
\(185\) | 3.40280 | − | 19.2982i | 0.250178 | − | 1.41883i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.7888 | + | 11.5702i | −1.00834 | + | 0.846095i | ||||
\(188\) | −39.1918 | −2.85836 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | 0.435286 | ||||||||
\(191\) | −7.50567 | + | 6.29801i | −0.543091 | + | 0.455708i | −0.872594 | − | 0.488447i | \(-0.837564\pi\) |
0.329502 | + | 0.944155i | \(0.393119\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.91013 | − | 10.8329i | 0.137494 | − | 0.779768i | −0.835596 | − | 0.549344i | \(-0.814878\pi\) |
0.973090 | − | 0.230424i | \(-0.0740113\pi\) | |||||||
\(194\) | −16.1124 | + | 5.86442i | −1.15680 | + | 0.421041i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.08378 | − | 11.8177i | −0.148841 | − | 0.844121i | ||||
\(197\) | 7.34847 | + | 12.7279i | 0.523557 | + | 0.906827i | 0.999624 | + | 0.0274180i | \(0.00872853\pi\) |
−0.476067 | + | 0.879409i | \(0.657938\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.500000 | − | 0.866025i | 0.0354441 | − | 0.0613909i | −0.847759 | − | 0.530381i | \(-0.822049\pi\) |
0.883203 | + | 0.468990i | \(0.155382\pi\) | |||||||
\(200\) | 4.60353 | + | 1.67555i | 0.325519 | + | 0.118479i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.19253 | − | 7.71345i | −0.646784 | − | 0.542717i | ||||
\(203\) | 7.50567 | + | 6.29801i | 0.526795 | + | 0.442033i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.2763 | + | 4.10424i | 0.787572 | + | 0.286653i | ||||
\(206\) | −8.57321 | + | 14.8492i | −0.597324 | + | 1.03460i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.00000 | + | 3.46410i | 0.138675 | + | 0.240192i | ||||
\(209\) | 0.425349 | + | 2.41228i | 0.0294220 | + | 0.166861i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.939693 | − | 0.342020i | 0.0646911 | − | 0.0235456i | −0.309472 | − | 0.950909i | \(-0.600152\pi\) |
0.374163 | + | 0.927363i | \(0.377930\pi\) | |||||||
\(212\) | −5.10419 | + | 28.9473i | −0.350557 | + | 1.98811i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 27.5776 | − | 23.1404i | 1.88517 | − | 1.58184i | ||||
\(215\) | 26.9444 | 1.83759 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | −0.135769 | ||||||||
\(218\) | 1.87642 | − | 1.57450i | 0.127087 | − | 0.106639i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.16756 | + | 23.6354i | −0.280977 | + | 1.59350i | ||||
\(221\) | 6.90530 | − | 2.51332i | 0.464501 | − | 0.169065i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.21554 | − | 6.89365i | −0.0813984 | − | 0.461633i | −0.998076 | − | 0.0620053i | \(-0.980250\pi\) |
0.916677 | − | 0.399628i | \(-0.130861\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.0000 | − | 20.7846i | 0.798228 | − | 1.38257i | ||||
\(227\) | 9.20707 | + | 3.35110i | 0.611095 | + | 0.222420i | 0.628982 | − | 0.777420i | \(-0.283472\pi\) |
−0.0178875 | + | 0.999840i | \(0.505694\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.766044 | − | 0.642788i | −0.0506216 | − | 0.0424766i | 0.617126 | − | 0.786864i | \(-0.288297\pi\) |
−0.667747 | + | 0.744388i | \(0.732741\pi\) | |||||||
\(230\) | −11.2585 | − | 9.44701i | −0.742364 | − | 0.622917i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 22.5526 | + | 8.20848i | 1.48065 | + | 0.538913i | ||||
\(233\) | −3.67423 | + | 6.36396i | −0.240707 | + | 0.416917i | −0.960916 | − | 0.276840i | \(-0.910713\pi\) |
0.720209 | + | 0.693757i | \(0.244046\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.0000 | + | 20.7846i | 0.782794 | + | 1.35584i | ||||
\(236\) | 1.70140 | + | 9.64911i | 0.110752 | + | 0.628103i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 33.8289 | − | 12.3127i | 2.19280 | − | 0.798115i | ||||
\(239\) | 0.425349 | − | 2.41228i | 0.0275136 | − | 0.156037i | −0.967956 | − | 0.251121i | \(-0.919201\pi\) |
0.995469 | + | 0.0950838i | \(0.0303119\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.2567 | + | 10.2846i | −0.789524 | + | 0.662489i | −0.945628 | − | 0.325251i | \(-0.894551\pi\) |
0.156103 | + | 0.987741i | \(0.450107\pi\) | |||||||
\(242\) | 12.2474 | 0.787296 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 20.0000 | 1.28037 | ||||||||
\(245\) | −5.62925 | + | 4.72350i | −0.359640 | + | 0.301774i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.173648 | − | 0.984808i | 0.0110490 | − | 0.0626618i | ||||
\(248\) | −4.60353 | + | 1.67555i | −0.292325 | + | 0.106398i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.16756 | + | 23.6354i | 0.263579 | + | 1.49483i | ||||
\(251\) | −3.67423 | − | 6.36396i | −0.231916 | − | 0.401690i | 0.726456 | − | 0.687213i | \(-0.241166\pi\) |
−0.958372 | + | 0.285523i | \(0.907833\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.00000 | − | 5.19615i | 0.188608 | − | 0.326679i | ||||
\(254\) | −43.7336 | − | 15.9177i | −2.74409 | − | 0.998767i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −24.5134 | − | 20.5692i | −1.53209 | − | 1.28558i | ||||
\(257\) | 13.1349 | + | 11.0215i | 0.819334 | + | 0.687503i | 0.952816 | − | 0.303548i | \(-0.0981714\pi\) |
−0.133482 | + | 0.991051i | \(0.542616\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.0351 | − | 5.47232i | −0.934235 | − | 0.340034i | ||||
\(260\) | 4.89898 | − | 8.48528i | 0.303822 | − | 0.526235i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −15.0000 | − | 25.9808i | −0.926703 | − | 1.60510i | ||||
\(263\) | 4.67884 | + | 26.5350i | 0.288510 | + | 1.63622i | 0.692472 | + | 0.721445i | \(0.256522\pi\) |
−0.403962 | + | 0.914776i | \(0.632367\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.9145 | − | 6.15636i | 1.03905 | − | 0.378182i | ||||
\(266\) | 0.850699 | − | 4.82455i | 0.0521597 | − | 0.295812i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −21.4492 | + | 17.9981i | −1.31022 | + | 1.09941i | ||||
\(269\) | 22.0454 | 1.34413 | 0.672066 | − | 0.740491i | \(-0.265407\pi\) | ||||
0.672066 | + | 0.740491i | \(0.265407\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.00000 | −0.425220 | −0.212610 | − | 0.977137i | \(-0.568196\pi\) | ||||
−0.212610 | + | 0.977137i | \(0.568196\pi\) | |||||||
\(272\) | 22.5170 | − | 18.8940i | 1.36529 | − | 1.14562i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.16756 | − | 23.6354i | 0.251771 | − | 1.42787i | ||||
\(275\) | 2.30177 | − | 0.837775i | 0.138802 | − | 0.0505197i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.91013 | + | 10.8329i | 0.114769 | + | 0.650885i | 0.986865 | + | 0.161550i | \(0.0516493\pi\) |
−0.872096 | + | 0.489335i | \(0.837240\pi\) | |||||||
\(278\) | −12.2474 | − | 21.2132i | −0.734553 | − | 1.27228i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12.0000 | − | 20.7846i | 0.717137 | − | 1.24212i | ||||
\(281\) | −11.5088 | − | 4.18887i | −0.686560 | − | 0.249887i | −0.0248982 | − | 0.999690i | \(-0.507926\pi\) |
−0.661661 | + | 0.749803i | \(0.730148\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.0228 | + | 10.9274i | 0.774122 | + | 0.649566i | 0.941761 | − | 0.336283i | \(-0.109170\pi\) |
−0.167639 | + | 0.985849i | \(0.553614\pi\) | |||||||
\(284\) | −22.5170 | − | 18.8940i | −1.33614 | − | 1.12115i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.63816 | + | 2.05212i | 0.333391 | + | 0.121344i | ||||
\(287\) | 4.89898 | − | 8.48528i | 0.289178 | − | 0.500870i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −18.5000 | − | 32.0429i | −1.08824 | − | 1.88488i | ||||
\(290\) | −5.10419 | − | 28.9473i | −0.299729 | − | 1.69985i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −41.3465 | + | 15.0489i | −2.41962 | + | 0.880669i | ||||
\(293\) | −0.850699 | + | 4.82455i | −0.0496984 | + | 0.281853i | −0.999521 | − | 0.0309343i | \(-0.990152\pi\) |
0.949823 | + | 0.312788i | \(0.101263\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.59627 | − | 3.85673i | 0.267605 | − | 0.224547i | ||||
\(296\) | −39.1918 | −2.27798 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 30.0000 | 1.73785 | ||||||||
\(299\) | −1.87642 | + | 1.57450i | −0.108516 | + | 0.0910558i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.82026 | − | 21.6658i | 0.220196 | − | 1.24879i | ||||
\(302\) | 11.5088 | − | 4.18887i | 0.662259 | − | 0.241043i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.694593 | − | 3.93923i | −0.0398376 | − | 0.225930i | ||||
\(305\) | −6.12372 | − | 10.6066i | −0.350643 | − | 0.607332i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.00000 | + | 1.73205i | −0.0570730 | + | 0.0988534i | −0.893150 | − | 0.449758i | \(-0.851510\pi\) |
0.836077 | + | 0.548612i | \(0.184843\pi\) | |||||||
\(308\) | 18.4141 | + | 6.70220i | 1.04924 | + | 0.381893i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.59627 | + | 3.85673i | 0.261050 | + | 0.219047i | ||||
\(311\) | 18.7642 | + | 15.7450i | 1.06402 | + | 0.892818i | 0.994497 | − | 0.104762i | \(-0.0334082\pi\) |
0.0695218 | + | 0.997580i | \(0.477853\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.0351 | + | 5.47232i | 0.849833 | + | 0.309314i | 0.729972 | − | 0.683477i | \(-0.239533\pi\) |
0.119861 | + | 0.992791i | \(0.461755\pi\) | |||||||
\(314\) | 20.8207 | − | 36.0624i | 1.17498 | − | 2.03512i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.0000 | + | 24.2487i | 0.787562 | + | 1.36410i | ||||
\(317\) | −1.70140 | − | 9.64911i | −0.0955600 | − | 0.541948i | −0.994574 | − | 0.104029i | \(-0.966827\pi\) |
0.899014 | − | 0.437919i | \(-0.144284\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.2763 | − | 4.10424i | 0.631352 | − | 0.229793i | ||||
\(320\) | −3.40280 | + | 19.2982i | −0.190222 | + | 1.07880i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.19253 | + | 7.71345i | −0.512280 | + | 0.429854i | ||||
\(323\) | −7.34847 | −0.408880 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 18.7642 | − | 15.7450i | 1.03925 | − | 0.872036i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.16756 | − | 23.6354i | 0.230115 | − | 1.30505i | ||||
\(329\) | 18.4141 | − | 6.70220i | 1.01520 | − | 0.369504i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.21554 | − | 6.89365i | −0.0668120 | − | 0.378910i | −0.999819 | − | 0.0190501i | \(-0.993936\pi\) |
0.933007 | − | 0.359859i | \(-0.117175\pi\) | |||||||
\(332\) | −24.4949 | − | 42.4264i | −1.34433 | − | 2.32845i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.00000 | + | 10.3923i | −0.328305 | + | 0.568642i | ||||
\(335\) | 16.1124 | + | 5.86442i | 0.880313 | + | 0.320408i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.4492 | − | 17.9981i | −1.16841 | − | 0.980416i | −0.168429 | − | 0.985714i | \(-0.553869\pi\) |
−0.999986 | + | 0.00529739i | \(0.998314\pi\) | |||||||
\(338\) | 22.5170 | + | 18.8940i | 1.22476 | + | 1.02770i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −67.6579 | − | 24.6255i | −3.66926 | − | 1.33550i | ||||
\(341\) | −1.22474 | + | 2.12132i | −0.0663237 | + | 0.114876i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 17.3205i | 0.539949 | + | 0.935220i | ||||
\(344\) | −9.35769 | − | 53.0701i | −0.504533 | − | 2.86135i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.5526 | + | 8.20848i | −1.21244 | + | 0.441291i | ||||
\(347\) | 4.25349 | − | 24.1228i | 0.228340 | − | 1.29498i | −0.627857 | − | 0.778328i | \(-0.716068\pi\) |
0.856197 | − | 0.516650i | \(-0.172821\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.3209 | − | 12.8558i | 0.820108 | − | 0.688153i | −0.132889 | − | 0.991131i | \(-0.542425\pi\) |
0.952997 | + | 0.302978i | \(0.0979810\pi\) | |||||||
\(350\) | −4.89898 | −0.261861 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.87642 | + | 1.57450i | −0.0998717 | + | 0.0838023i | −0.691356 | − | 0.722514i | \(-0.742986\pi\) |
0.591485 | + | 0.806316i | \(0.298542\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.12567 | + | 17.7265i | −0.165893 | + | 0.940827i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.25133 | − | 35.4531i | −0.330393 | − | 1.87375i | ||||
\(359\) | 14.6969 | + | 25.4558i | 0.775675 | + | 1.34351i | 0.934414 | + | 0.356188i | \(0.115924\pi\) |
−0.158740 | + | 0.987320i | \(0.550743\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | − | 15.5885i | 0.473684 | − | 0.820445i | ||||
\(362\) | 18.4141 | + | 6.70220i | 0.967826 | + | 0.352260i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.12836 | − | 5.14230i | −0.321213 | − | 0.269530i | ||||
\(365\) | 20.6406 | + | 17.3195i | 1.08038 | + | 0.906545i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.69846 | − | 1.71010i | −0.245258 | − | 0.0892665i | 0.216466 | − | 0.976290i | \(-0.430547\pi\) |
−0.461724 | + | 0.887024i | \(0.652769\pi\) | |||||||
\(368\) | −4.89898 | + | 8.48528i | −0.255377 | + | 0.442326i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 24.0000 | + | 41.5692i | 1.24770 | + | 2.16108i | ||||
\(371\) | −2.55210 | − | 14.4737i | −0.132498 | − | 0.751435i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.8892 | + | 11.9707i | −1.70294 | + | 0.619820i | −0.996155 | − | 0.0876084i | \(-0.972078\pi\) |
−0.706785 | + | 0.707428i | \(0.749855\pi\) | |||||||
\(374\) | 7.65629 | − | 43.4210i | 0.395897 | − | 2.24525i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 36.7701 | − | 30.8538i | 1.89627 | − | 1.59116i | ||||
\(377\) | −4.89898 | −0.252310 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.00000 | 0.410932 | 0.205466 | − | 0.978664i | \(-0.434129\pi\) | ||||
0.205466 | + | 0.978664i | \(0.434129\pi\) | |||||||
\(380\) | −7.50567 | + | 6.29801i | −0.385033 | + | 0.323081i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.16756 | − | 23.6354i | 0.213231 | − | 1.20929i | ||||
\(383\) | 32.2247 | − | 11.7288i | 1.64661 | − | 0.599316i | 0.658432 | − | 0.752641i | \(-0.271220\pi\) |
0.988176 | + | 0.153324i | \(0.0489980\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.08378 | − | 11.8177i | −0.106199 | − | 0.602285i | ||||
\(386\) | 13.4722 | + | 23.3345i | 0.685717 | + | 1.18770i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.0000 | − | 24.2487i | 0.710742 | − | 1.23104i | ||||
\(389\) | −25.3194 | − | 9.21552i | −1.28375 | − | 0.467246i | −0.392077 | − | 0.919932i | \(-0.628243\pi\) |
−0.891670 | + | 0.452687i | \(0.850466\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.7888 | + | 11.5702i | 0.697330 | + | 0.585129i | ||||
\(392\) | 11.2585 | + | 9.44701i | 0.568641 | + | 0.477146i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −33.8289 | − | 12.3127i | −1.70428 | − | 0.620306i | ||||
\(395\) | 8.57321 | − | 14.8492i | 0.431365 | − | 0.747146i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.500000 | + | 0.866025i | 0.0250943 | + | 0.0434646i | 0.878300 | − | 0.478110i | \(-0.158678\pi\) |
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | 0.425349 | + | 2.41228i | 0.0213208 | + | 0.120916i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.75877 | + | 1.36808i | −0.187939 | + | 0.0684040i | ||||
\(401\) | −5.95489 | + | 33.7719i | −0.297373 | + | 1.68649i | 0.360024 | + | 0.932943i | \(0.382768\pi\) |
−0.657398 | + | 0.753544i | \(0.728343\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.766044 | − | 0.642788i | 0.0381594 | − | 0.0320195i | ||||
\(404\) | 19.5959 | 0.974933 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −24.0000 | −1.19110 | ||||||||
\(407\) | −15.0113 | + | 12.5960i | −0.744085 | + | 0.624361i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.86215 | + | 27.5746i | −0.240418 | + | 1.36348i | 0.590480 | + | 0.807052i | \(0.298938\pi\) |
−0.830898 | + | 0.556425i | \(0.812173\pi\) | |||||||
\(410\) | −27.6212 | + | 10.0533i | −1.36411 | + | 0.496497i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.86215 | − | 27.5746i | −0.239541 | − | 1.35850i | ||||
\(413\) | −2.44949 | − | 4.24264i | −0.120532 | − | 0.208767i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.0000 | + | 25.9808i | −0.736321 | + | 1.27535i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.59627 | − | 3.85673i | −0.224811 | − | 0.188639i | ||||
\(419\) | −26.2699 | − | 22.0430i | −1.28337 | − | 1.07687i | −0.992771 | − | 0.120026i | \(-0.961702\pi\) |
−0.290596 | − | 0.956846i | \(-0.593853\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.87939 | − | 0.684040i | −0.0915956 | − | 0.0333381i | 0.295816 | − | 0.955245i | \(-0.404409\pi\) |
−0.387412 | + | 0.921907i | \(0.626631\pi\) | |||||||
\(422\) | −1.22474 | + | 2.12132i | −0.0596196 | + | 0.103264i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −18.0000 | − | 31.1769i | −0.874157 | − | 1.51408i | ||||
\(425\) | 1.27605 | + | 7.23683i | 0.0618974 | + | 0.351038i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.39693 | + | 3.42020i | −0.454749 | + | 0.165515i | ||||
\(428\) | −10.2084 | + | 57.8946i | −0.493441 | + | 2.79844i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −50.5589 | + | 42.4240i | −2.43817 | + | 2.04587i | ||||
\(431\) | 7.34847 | 0.353963 | 0.176982 | − | 0.984214i | \(-0.443367\pi\) | ||||
0.176982 | + | 0.984214i | \(0.443367\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.0000 | 0.816968 | 0.408484 | − | 0.912766i | \(-0.366058\pi\) | ||||
0.408484 | + | 0.912766i | \(0.366058\pi\) | |||||||
\(434\) | 3.75284 | − | 3.14900i | 0.180142 | − | 0.151157i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.694593 | + | 3.93923i | −0.0332650 | + | 0.188655i | ||||
\(437\) | 2.30177 | − | 0.837775i | 0.110108 | − | 0.0400762i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.43107 | + | 13.7873i | 0.116029 | + | 0.658032i | 0.986236 | + | 0.165346i | \(0.0528740\pi\) |
−0.870207 | + | 0.492687i | \(0.836015\pi\) | |||||||
\(440\) | −14.6969 | − | 25.4558i | −0.700649 | − | 1.21356i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.00000 | + | 15.5885i | −0.428086 | + | 0.741467i | ||||
\(443\) | −11.5088 | − | 4.18887i | −0.546801 | − | 0.199019i | 0.0538234 | − | 0.998550i | \(-0.482859\pi\) |
−0.600625 | + | 0.799531i | \(0.705081\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.1349 | + | 11.0215i | 0.621957 | + | 0.521884i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 15.0351 | + | 5.47232i | 0.710341 | + | 0.258543i | ||||
\(449\) | 11.0227 | − | 19.0919i | 0.520194 | − | 0.901002i | −0.479531 | − | 0.877525i | \(-0.659193\pi\) |
0.999724 | − | 0.0234766i | \(-0.00747353\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | − | 10.3923i | −0.282529 | − | 0.489355i | ||||
\(452\) | 6.80559 | + | 38.5964i | 0.320108 | + | 1.81542i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −22.5526 | + | 8.20848i | −1.05845 | + | 0.385243i | ||||
\(455\) | −0.850699 | + | 4.82455i | −0.0398814 | + | 0.226179i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.2153 | − | 18.6408i | 1.03919 | − | 0.871982i | 0.0472719 | − | 0.998882i | \(-0.484947\pi\) |
0.991915 | + | 0.126900i | \(0.0405028\pi\) | |||||||
\(458\) | 2.44949 | 0.114457 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 24.0000 | 1.11901 | ||||||||
\(461\) | 20.6406 | − | 17.3195i | 0.961328 | − | 0.806650i | −0.0198402 | − | 0.999803i | \(-0.506316\pi\) |
0.981169 | + | 0.193153i | \(0.0618713\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.29932 | + | 18.7113i | −0.153332 | + | 0.869590i | 0.806963 | + | 0.590603i | \(0.201110\pi\) |
−0.960295 | + | 0.278987i | \(0.910001\pi\) | |||||||
\(464\) | −18.4141 | + | 6.70220i | −0.854855 | + | 0.311142i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.12567 | − | 17.7265i | −0.144794 | − | 0.821166i | ||||
\(467\) | 7.34847 | + | 12.7279i | 0.340047 | + | 0.588978i | 0.984441 | − | 0.175715i | \(-0.0562238\pi\) |
−0.644394 | + | 0.764693i | \(0.722890\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.00000 | − | 12.1244i | 0.323230 | − | 0.559851i | ||||
\(470\) | −55.2424 | − | 20.1066i | −2.54814 | − | 0.927448i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.19253 | − | 7.71345i | −0.423121 | − | 0.355040i | ||||
\(473\) | −20.6406 | − | 17.3195i | −0.949056 | − | 0.796352i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.939693 | + | 0.342020i | 0.0431161 | + | 0.0156930i | ||||
\(476\) | −29.3939 | + | 50.9117i | −1.34727 | + | 2.33353i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.00000 | + | 5.19615i | 0.137217 | + | 0.237666i | ||||
\(479\) | 4.67884 | + | 26.5350i | 0.213782 | + | 1.21242i | 0.883008 | + | 0.469358i | \(0.155515\pi\) |
−0.669226 | + | 0.743059i | \(0.733374\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.51754 | − | 2.73616i | 0.342770 | − | 0.124758i | ||||
\(482\) | 6.80559 | − | 38.5964i | 0.309986 | − | 1.75802i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −15.3209 | + | 12.8558i | −0.696404 | + | 0.584352i | ||||
\(485\) | −17.1464 | −0.778579 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.0000 | 1.58600 | 0.793001 | − | 0.609221i | \(-0.208518\pi\) | ||||
0.793001 | + | 0.609221i | \(0.208518\pi\) | |||||||
\(488\) | −18.7642 | + | 15.7450i | −0.849415 | + | 0.712743i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.12567 | − | 17.7265i | 0.141203 | − | 0.800803i | ||||
\(491\) | −36.8283 | + | 13.4044i | −1.66204 | + | 0.604932i | −0.990681 | − | 0.136203i | \(-0.956510\pi\) |
−0.671356 | + | 0.741135i | \(0.734288\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.25133 | + | 35.4531i | 0.281546 | + | 1.59673i | ||||
\(494\) | 1.22474 | + | 2.12132i | 0.0551039 | + | 0.0954427i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | − | 3.46410i | 0.0898027 | − | 0.155543i | ||||
\(497\) | 13.8106 | + | 5.02665i | 0.619490 | + | 0.225476i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.53209 | + | 1.28558i | 0.0685857 | + | 0.0575503i | 0.676436 | − | 0.736501i | \(-0.263524\pi\) |
−0.607850 | + | 0.794052i | \(0.707968\pi\) | |||||||
\(500\) | −30.0227 | − | 25.1920i | −1.34266 | − | 1.12662i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 16.9145 | + | 6.15636i | 0.754930 | + | 0.274772i | ||||
\(503\) | −7.34847 | + | 12.7279i | −0.327652 | + | 0.567510i | −0.982045 | − | 0.188644i | \(-0.939591\pi\) |
0.654393 | + | 0.756154i | \(0.272924\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.00000 | − | 10.3923i | −0.266996 | − | 0.462451i | ||||
\(506\) | 2.55210 | + | 14.4737i | 0.113455 | + | 0.643433i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 71.4166 | − | 25.9935i | 3.16860 | − | 1.15328i | ||||
\(509\) | 1.70140 | − | 9.64911i | 0.0754131 | − | 0.427689i | −0.923603 | − | 0.383349i | \(-0.874771\pi\) |
0.999017 | − | 0.0443397i | \(-0.0141184\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.8530 | − | 14.1413i | 0.745532 | − | 0.625575i | ||||
\(512\) | 39.1918 | 1.73205 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −42.0000 | −1.85254 | ||||||||
\(515\) | −13.1349 | + | 11.0215i | −0.578794 | + | 0.485666i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.16756 | − | 23.6354i | 0.183289 | − | 1.03948i | ||||
\(518\) | 36.8283 | − | 13.4044i | 1.61814 | − | 0.588955i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.08378 | + | 11.8177i | 0.0913797 | + | 0.518240i | ||||
\(521\) | 11.0227 | + | 19.0919i | 0.482913 | + | 0.836431i | 0.999808 | − | 0.0196188i | \(-0.00624525\pi\) |
−0.516894 | + | 0.856049i | \(0.672912\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.5000 | − | 21.6506i | 0.546587 | − | 0.946716i | −0.451918 | − | 0.892059i | \(-0.649260\pi\) |
0.998505 | − | 0.0546569i | \(-0.0174065\pi\) | |||||||
\(524\) | 46.0353 | + | 16.7555i | 2.01106 | + | 0.731967i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −50.5589 | − | 42.4240i | −2.20447 | − | 1.84977i | ||||
\(527\) | −5.62925 | − | 4.72350i | −0.245214 | − | 0.205759i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.9748 | + | 5.81434i | 0.694555 | + | 0.252797i | ||||
\(530\) | −22.0454 | + | 38.1838i | −0.957591 | + | 1.65860i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.00000 | + | 6.92820i | 0.173422 | + | 0.300376i | ||||
\(533\) | 0.850699 | + | 4.82455i | 0.0368479 | + | 0.208975i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.8289 | − | 12.3127i | 1.46255 | − | 0.532326i | ||||
\(536\) | 5.95489 | − | 33.7719i | 0.257212 | − | 1.45872i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −41.3664 | + | 34.7105i | −1.78343 | + | 1.49648i | ||||
\(539\) | 7.34847 | 0.316521 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.0000 | −1.20381 | −0.601907 | − | 0.798566i | \(-0.705592\pi\) | ||||
−0.601907 | + | 0.798566i | \(0.705592\pi\) | |||||||
\(542\) | 13.1349 | − | 11.0215i | 0.564193 | − | 0.473414i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.30177 | − | 0.837775i | 0.0985969 | − | 0.0358863i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.25743 | − | 12.8025i | −0.0965206 | − | 0.547395i | −0.994271 | − | 0.106891i | \(-0.965911\pi\) |
0.897750 | − | 0.440505i | \(-0.145201\pi\) | |||||||
\(548\) | 19.5959 | + | 33.9411i | 0.837096 | + | 1.44989i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.00000 | + | 5.19615i | −0.127920 | + | 0.221565i | ||||
\(551\) | 4.60353 | + | 1.67555i | 0.196117 | + | 0.0713808i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.7246 | − | 8.99903i | −0.456057 | − | 0.382678i | ||||
\(554\) | −20.6406 | − | 17.3195i | −0.876935 | − | 0.735836i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 37.5877 | + | 13.6808i | 1.59407 | + | 0.580195i | ||||
\(557\) | 3.67423 | − | 6.36396i | 0.155682 | − | 0.269650i | −0.777625 | − | 0.628728i | \(-0.783576\pi\) |
0.933307 | + | 0.359079i | \(0.116909\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.50000 | + | 9.52628i | 0.232625 | + | 0.402919i | ||||
\(560\) | 3.40280 | + | 19.2982i | 0.143794 | + | 0.815498i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 28.1908 | − | 10.2606i | 1.18916 | − | 0.432817i | ||||
\(563\) | −2.12675 | + | 12.0614i | −0.0896317 | + | 0.508327i | 0.906629 | + | 0.421929i | \(0.138647\pi\) |
−0.996261 | + | 0.0863979i | \(0.972464\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.3851 | − | 15.4269i | 0.773466 | − | 0.649015i | ||||
\(566\) | −41.6413 | −1.75032 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 36.0000 | 1.51053 | ||||||||
\(569\) | 9.38209 | − | 7.87251i | 0.393318 | − | 0.330033i | −0.424586 | − | 0.905387i | \(-0.639580\pi\) |
0.817904 | + | 0.575355i | \(0.195136\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.73648 | + | 9.84808i | −0.0726695 | + | 0.412129i | 0.926673 | + | 0.375869i | \(0.122656\pi\) |
−0.999342 | + | 0.0362604i | \(0.988455\pi\) | |||||||
\(572\) | −9.20707 | + | 3.35110i | −0.384967 | + | 0.140117i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.16756 | + | 23.6354i | 0.173950 | + | 0.986522i | ||||
\(575\) | −1.22474 | − | 2.12132i | −0.0510754 | − | 0.0884652i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.5000 | − | 21.6506i | 0.520382 | − | 0.901328i | −0.479337 | − | 0.877631i | \(-0.659123\pi\) |
0.999719 | − | 0.0236970i | \(-0.00754370\pi\) | |||||||
\(578\) | 85.1654 | + | 30.9977i | 3.54241 | + | 1.28933i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 36.7701 | + | 30.8538i | 1.52680 | + | 1.28113i | ||||
\(581\) | 18.7642 | + | 15.7450i | 0.778469 | + | 0.653213i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.9145 | − | 6.15636i | −0.700526 | − | 0.254970i | ||||
\(584\) | 26.9444 | − | 46.6690i | 1.11497 | − | 1.93118i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | − | 10.3923i | −0.247858 | − | 0.429302i | ||||
\(587\) | −0.425349 | − | 2.41228i | −0.0175560 | − | 0.0995653i | 0.974771 | − | 0.223209i | \(-0.0716532\pi\) |
−0.992327 | + | 0.123644i | \(0.960542\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.939693 | + | 0.342020i | −0.0387194 | + | 0.0140927i | ||||
\(590\) | −2.55210 | + | 14.4737i | −0.105068 | + | 0.595871i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 24.5134 | − | 20.5692i | 1.00750 | − | 0.845389i | ||||
\(593\) | −7.34847 | −0.301765 | −0.150883 | − | 0.988552i | \(-0.548212\pi\) | ||||
−0.150883 | + | 0.988552i | \(0.548212\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 36.0000 | 1.47586 | ||||||||
\(596\) | −37.5284 | + | 31.4900i | −1.53722 | + | 1.28988i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.04189 | − | 5.90885i | 0.0426060 | − | 0.241631i | ||||
\(599\) | −36.8283 | + | 13.4044i | −1.50476 | + | 0.547689i | −0.957289 | − | 0.289134i | \(-0.906633\pi\) |
−0.547474 | + | 0.836823i | \(0.684411\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.21554 | − | 6.89365i | −0.0495828 | − | 0.281198i | 0.949928 | − | 0.312468i | \(-0.101156\pi\) |
−0.999511 | + | 0.0312703i | \(0.990045\pi\) | |||||||
\(602\) | 26.9444 | + | 46.6690i | 1.09817 | + | 1.90209i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.0000 | + | 17.3205i | −0.406894 | + | 0.704761i | ||||
\(605\) | 11.5088 | + | 4.18887i | 0.467901 | + | 0.170302i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.7060 | + | 28.2827i | 1.36808 | + | 1.14796i | 0.973393 | + | 0.229143i | \(0.0735924\pi\) |
0.394690 | + | 0.918814i | \(0.370852\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 28.1908 | + | 10.2606i | 1.14141 | + | 0.415440i | ||||
\(611\) | −4.89898 | + | 8.48528i | −0.198191 | + | 0.343278i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.50000 | − | 9.52628i | −0.222143 | − | 0.384763i | 0.733316 | − | 0.679888i | \(-0.237972\pi\) |
−0.955458 | + | 0.295126i | \(0.904638\pi\) | |||||||
\(614\) | −0.850699 | − | 4.82455i | −0.0343314 | − | 0.194703i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.5526 | + | 8.20848i | −0.908671 | + | 0.330729i | ||||
\(617\) | 4.25349 | − | 24.1228i | 0.171239 | − | 0.971146i | −0.771156 | − | 0.636646i | \(-0.780321\pi\) |
0.942396 | − | 0.334500i | \(-0.108568\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.5362 | + | 31.4966i | −1.50871 | + | 1.26595i | −0.642481 | + | 0.766302i | \(0.722095\pi\) |
−0.866226 | + | 0.499653i | \(0.833461\pi\) | |||||||
\(620\) | −9.79796 | −0.393496 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −60.0000 | −2.40578 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.03580 | + | 28.5594i | −0.201432 | + | 1.14238i | ||||
\(626\) | −36.8283 | + | 13.4044i | −1.47195 | + | 0.535747i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.8081 | + | 66.9669i | 0.471194 | + | 2.67227i | ||||
\(629\) | −29.3939 | − | 50.9117i | −1.17201 | − | 2.02998i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.0000 | + | 38.1051i | −0.875806 | + | 1.51694i | −0.0199047 | + | 0.999802i | \(0.506336\pi\) |
−0.855901 | + | 0.517139i | \(0.826997\pi\) | |||||||
\(632\) | −32.2247 | − | 11.7288i | −1.28183 | − | 0.466549i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18.3851 | + | 15.4269i | 0.730164 | + | 0.612681i | ||||
\(635\) | −35.6519 | − | 29.9155i | −1.41480 | − | 1.18716i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.81908 | − | 1.02606i | −0.111696 | − | 0.0406540i | ||||
\(638\) | −14.6969 | + | 25.4558i | −0.581857 | + | 1.00781i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −24.0000 | − | 41.5692i | −0.948683 | − | 1.64317i | ||||
\(641\) | −2.97745 | − | 16.8859i | −0.117602 | − | 0.666954i | −0.985429 | − | 0.170088i | \(-0.945595\pi\) |
0.867827 | − | 0.496867i | \(-0.165516\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.7083 | + | 12.9968i | −1.40820 | + | 0.512542i | −0.930601 | − | 0.366036i | \(-0.880715\pi\) |
−0.477598 | + | 0.878578i | \(0.658492\pi\) | |||||||
\(644\) | 3.40280 | − | 19.2982i | 0.134089 | − | 0.760456i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.7888 | − | 11.5702i | 0.542513 | − | 0.455223i | ||||
\(647\) | −36.7423 | −1.44449 | −0.722245 | − | 0.691637i | \(-0.756890\pi\) | ||||
−0.722245 | + | 0.691637i | \(0.756890\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.00000 | −0.235521 | ||||||||
\(650\) | 1.87642 | − | 1.57450i | 0.0735992 | − | 0.0617570i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.94593 | + | 39.3923i | −0.272023 | + | 1.54272i | ||||
\(653\) | −9.20707 | + | 3.35110i | −0.360300 | + | 0.131139i | −0.515826 | − | 0.856693i | \(-0.672515\pi\) |
0.155526 | + | 0.987832i | \(0.450293\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.20945 | − | 29.5442i | −0.203550 | − | 1.15439i | ||||
\(656\) | 9.79796 | + | 16.9706i | 0.382546 | + | 0.662589i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −24.0000 | + | 41.5692i | −0.935617 | + | 1.62054i | ||||
\(659\) | −18.4141 | − | 6.70220i | −0.717313 | − | 0.261081i | −0.0425284 | − | 0.999095i | \(-0.513541\pi\) |
−0.674785 | + | 0.738015i | \(0.735764\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.42649 | + | 7.07066i | 0.327752 | + | 0.275017i | 0.791783 | − | 0.610802i | \(-0.209153\pi\) |
−0.464031 | + | 0.885819i | \(0.653597\pi\) | |||||||
\(662\) | 13.1349 | + | 11.0215i | 0.510503 | + | 0.428363i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 56.3816 | + | 20.5212i | 2.18803 | + | 0.796377i | ||||
\(665\) | 2.44949 | − | 4.24264i | 0.0949871 | − | 0.164523i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.00000 | − | 10.3923i | −0.232321 | − | 0.402392i | ||||
\(668\) | −3.40280 | − | 19.2982i | −0.131658 | − | 0.746670i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −39.4671 | + | 14.3648i | −1.52475 | + | 0.554962i | ||||
\(671\) | −2.12675 | + | 12.0614i | −0.0821022 | + | 0.465625i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.2153 | − | 18.6408i | 0.856336 | − | 0.718552i | −0.104839 | − | 0.994489i | \(-0.533433\pi\) |
0.961176 | + | 0.275938i | \(0.0889883\pi\) | |||||||
\(674\) | 68.5857 | 2.64182 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −48.0000 | −1.84615 | ||||||||
\(677\) | −35.6519 | + | 29.9155i | −1.37022 | + | 1.14975i | −0.397538 | + | 0.917586i | \(0.630135\pi\) |
−0.972677 | + | 0.232162i | \(0.925420\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.43107 | + | 13.7873i | −0.0932961 | + | 0.529108i | ||||
\(680\) | 82.8636 | − | 30.1599i | 3.17768 | − | 1.15658i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.04189 | − | 5.90885i | −0.0398960 | − | 0.226261i | ||||
\(683\) | −11.0227 | − | 19.0919i | −0.421772 | − | 0.730531i | 0.574341 | − | 0.818616i | \(-0.305258\pi\) |
−0.996113 | + | 0.0880857i | \(0.971925\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.0000 | − | 20.7846i | 0.458496 | − | 0.794139i | ||||
\(686\) | −46.0353 | − | 16.7555i | −1.75764 | − | 0.639728i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 33.7060 | + | 28.2827i | 1.28503 | + | 1.07827i | ||||
\(689\) | 5.62925 | + | 4.72350i | 0.214457 | + | 0.179951i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.1656 | − | 16.0749i | −1.68014 | − | 0.611520i | −0.686808 | − | 0.726839i | \(-0.740989\pi\) |
−0.993329 | + | 0.115319i | \(0.963211\pi\) | |||||||
\(692\) | 19.5959 | − | 33.9411i | 0.744925 | − | 1.29025i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.0000 | + | 51.9615i | 1.13878 | + | 1.97243i | ||||
\(695\) | −4.25349 | − | 24.1228i | −0.161344 | − | 0.915029i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.8289 | − | 12.3127i | 1.28136 | − | 0.466378i | ||||
\(698\) | −8.50699 | + | 48.2455i | −0.321994 | + | 1.82612i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.12836 | − | 5.14230i | 0.231630 | − | 0.194361i | ||||
\(701\) | 14.6969 | 0.555096 | 0.277548 | − | 0.960712i | \(-0.410478\pi\) | ||||
0.277548 | + | 0.960712i | \(0.410478\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.00000 | −0.301726 | ||||||||
\(704\) | 15.0113 | − | 12.5960i | 0.565761 | − | 0.474730i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.04189 | − | 5.90885i | 0.0392120 | − | 0.222382i | ||||
\(707\) | −9.20707 | + | 3.35110i | −0.346267 | + | 0.126031i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.21554 | − | 6.89365i | −0.0456505 | − | 0.258897i | 0.953438 | − | 0.301590i | \(-0.0975173\pi\) |
−0.999088 | + | 0.0426932i | \(0.986406\pi\) | |||||||
\(710\) | −22.0454 | − | 38.1838i | −0.827349 | − | 1.43301i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.30177 | + | 0.837775i | 0.0862019 | + | 0.0313749i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.59627 | + | 3.85673i | 0.171891 | + | 0.144233i | ||||
\(716\) | 45.0340 | + | 37.7880i | 1.68300 | + | 1.41221i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −67.6579 | − | 24.6255i | −2.52497 | − | 0.919014i | ||||
\(719\) | −18.3712 | + | 31.8198i | −0.685129 | + | 1.18668i | 0.288267 | + | 0.957550i | \(0.406921\pi\) |
−0.973396 | + | 0.229128i | \(0.926412\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.00000 | + | 12.1244i | 0.260694 | + | 0.451535i | ||||
\(722\) | 7.65629 | + | 43.4210i | 0.284938 | + | 1.61596i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −30.0702 | + | 10.9446i | −1.11755 | + | 0.406755i | ||||
\(725\) | 0.850699 | − | 4.82455i | 0.0315942 | − | 0.179179i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.7246 | − | 8.99903i | 0.397754 | − | 0.333755i | −0.421871 | − | 0.906656i | \(-0.638626\pi\) |
0.819625 | + | 0.572901i | \(0.194182\pi\) | |||||||
\(728\) | 9.79796 | 0.363137 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −66.0000 | −2.44277 | ||||||||
\(731\) | 61.9218 | − | 51.9586i | 2.29026 | − | 1.92176i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.95202 | − | 16.7417i | 0.109035 | − | 0.618370i | −0.880496 | − | 0.474053i | \(-0.842790\pi\) |
0.989532 | − | 0.144317i | \(-0.0460984\pi\) | |||||||
\(734\) | 11.5088 | − | 4.18887i | 0.424799 | − | 0.154614i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.57321 | − | 14.8492i | −0.315798 | − | 0.546979i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.500000 | − | 0.866025i | 0.0183928 | − | 0.0318573i | −0.856683 | − | 0.515844i | \(-0.827478\pi\) |
0.875075 | + | 0.483987i | \(0.160812\pi\) | |||||||
\(740\) | −73.6566 | − | 26.8088i | −2.70767 | − | 0.985511i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 27.5776 | + | 23.1404i | 1.01241 | + | 0.849509i | ||||
\(743\) | 24.3934 | + | 20.4685i | 0.894908 | + | 0.750917i | 0.969189 | − | 0.246320i | \(-0.0792215\pi\) |
−0.0742802 | + | 0.997237i | \(0.523666\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.1908 | + | 10.2606i | 1.03283 | + | 0.375919i | ||||
\(746\) | 42.8661 | − | 74.2462i | 1.56944 | − | 2.71835i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 36.0000 | + | 62.3538i | 1.31629 | + | 2.27988i | ||||
\(749\) | −5.10419 | − | 28.9473i | −0.186503 | − | 1.05771i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.4320 | + | 8.89252i | −0.891537 | + | 0.324493i | −0.746856 | − | 0.664986i | \(-0.768438\pi\) |
−0.144680 | + | 0.989478i | \(0.546215\pi\) | |||||||
\(752\) | −6.80559 | + | 38.5964i | −0.248174 | + | 1.40747i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.19253 | − | 7.71345i | 0.334772 | − | 0.280907i | ||||
\(755\) | 12.2474 | 0.445730 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.00000 | −0.254419 | −0.127210 | − | 0.991876i | \(-0.540602\pi\) | ||||
−0.127210 | + | 0.991876i | \(0.540602\pi\) | |||||||
\(758\) | −15.0113 | + | 12.5960i | −0.545237 | + | 0.457508i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.08378 | − | 11.8177i | 0.0755866 | − | 0.428673i | ||||
\(761\) | −2.30177 | + | 0.837775i | −0.0834390 | + | 0.0303693i | −0.383402 | − | 0.923581i | \(-0.625248\pi\) |
0.299963 | + | 0.953951i | \(0.403026\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.347296 | − | 1.96962i | −0.0125730 | − | 0.0713049i | ||||
\(764\) | 19.5959 | + | 33.9411i | 0.708955 | + | 1.22795i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −42.0000 | + | 72.7461i | −1.51752 | + | 2.62842i | ||||
\(767\) | 2.30177 | + | 0.837775i | 0.0831120 | + | 0.0302503i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.3436 | − | 23.7831i | −1.02210 | − | 0.857642i | −0.0322082 | − | 0.999481i | \(-0.510254\pi\) |
−0.989890 | + | 0.141839i | \(0.954698\pi\) | |||||||
\(770\) | 22.5170 | + | 18.8940i | 0.811457 | + | 0.680893i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −41.3465 | − | 15.0489i | −1.48809 | − | 0.541621i | ||||
\(773\) | −22.0454 | + | 38.1838i | −0.792918 | + | 1.37337i | 0.131235 | + | 0.991351i | \(0.458106\pi\) |
−0.924153 | + | 0.382023i | \(0.875227\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.500000 | + | 0.866025i | 0.0179605 | + | 0.0311086i | ||||
\(776\) | 5.95489 | + | 33.7719i | 0.213768 | + | 1.21234i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 62.0197 | − | 22.5733i | 2.22351 | − | 0.809293i | ||||
\(779\) | 0.850699 | − | 4.82455i | 0.0304794 | − | 0.172858i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.7888 | − | 11.5702i | 0.493402 | − | 0.414013i | ||||
\(782\) | −44.0908 | −1.57668 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12.0000 | −0.428571 | ||||||||
\(785\) | 31.8991 | − | 26.7665i | 1.13853 | − | 0.955338i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.34120 | + | 24.6202i | −0.154747 | + | 0.877615i | 0.804269 | + | 0.594265i | \(0.202557\pi\) |
−0.959017 | + | 0.283350i | \(0.908554\pi\) | |||||||
\(788\) | 55.2424 | − | 20.1066i | 1.96793 | − | 0.716268i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.29322 | + | 41.3619i | 0.259481 | + | 1.47159i | ||||
\(791\) | −9.79796 | − | 16.9706i | −0.348375 | − | 0.603404i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.50000 | − | 4.33013i | 0.0887776 | − | 0.153767i | ||||
\(794\) | −2.30177 | − | 0.837775i | −0.0816867 | − | 0.0297315i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.06418 | − | 2.57115i | −0.108607 | − | 0.0911320i | ||||
\(797\) | −31.8991 | − | 26.7665i | −1.12992 | − | 0.948119i | −0.130861 | − | 0.991401i | \(-0.541774\pi\) |
−0.999063 | + | 0.0432816i | \(0.986219\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 67.6579 | + | 24.6255i | 2.39356 | + | 0.871186i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −42.0000 | − | 72.7461i | −1.48307 | − | 2.56876i | ||||
\(803\) | −4.67884 | − | 26.5350i | −0.165113 | − | 0.936401i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.2763 | + | 4.10424i | −0.397438 | + | 0.144656i | ||||
\(806\) | −0.425349 | + | 2.41228i | −0.0149823 | + | 0.0849688i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −18.3851 | + | 15.4269i | −0.646784 | + | 0.542717i | ||||
\(809\) | −22.0454 | −0.775075 | −0.387538 | − | 0.921854i | \(-0.626674\pi\) | ||||
−0.387538 | + | 0.921854i | \(0.626674\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.0000 | 1.22902 | 0.614508 | − | 0.788911i | \(-0.289355\pi\) | ||||
0.614508 | + | 0.788911i | \(0.289355\pi\) | |||||||
\(812\) | 30.0227 | − | 25.1920i | 1.05359 | − | 0.884067i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.33511 | − | 47.2708i | 0.292146 | − | 1.65684i | ||||
\(815\) | 23.0177 | − | 8.37775i | 0.806274 | − | 0.293460i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.91013 | − | 10.8329i | −0.0668270 | − | 0.378995i | ||||
\(818\) | −34.2929 | − | 59.3970i | −1.19902 | − | 2.07677i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 24.0000 | − | 41.5692i | 0.838116 | − | 1.45166i | ||||
\(821\) | 36.8283 | + | 13.4044i | 1.28532 | + | 0.467817i | 0.892187 | − | 0.451667i | \(-0.149170\pi\) |
0.393129 | + | 0.919483i | \(0.371393\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.8116 | + | 22.4976i | 0.934592 | + | 0.784216i | 0.976636 | − | 0.214900i | \(-0.0689425\pi\) |
−0.0420440 | + | 0.999116i | \(0.513387\pi\) | |||||||
\(824\) | 26.2699 | + | 22.0430i | 0.915154 | + | 0.767905i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.2763 | + | 4.10424i | 0.392353 | + | 0.142805i | ||||
\(827\) | −11.0227 | + | 19.0919i | −0.383297 | + | 0.663890i | −0.991531 | − | 0.129868i | \(-0.958545\pi\) |
0.608234 | + | 0.793757i | \(0.291878\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.5000 | + | 32.0429i | 0.642532 | + | 1.11290i | 0.984866 | + | 0.173319i | \(0.0554492\pi\) |
−0.342334 | + | 0.939578i | \(0.611217\pi\) | |||||||
\(830\) | −12.7605 | − | 72.3683i | −0.442923 | − | 2.51194i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.51754 | + | 2.73616i | −0.260624 | + | 0.0948593i | ||||
\(833\) | −3.82814 | + | 21.7105i | −0.132637 | + | 0.752224i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.19253 | + | 7.71345i | −0.318121 | + | 0.266935i | ||||
\(836\) | 9.79796 | 0.338869 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 84.0000 | 2.90173 | ||||||||
\(839\) | 3.75284 | − | 3.14900i | 0.129562 | − | 0.108716i | −0.575704 | − | 0.817658i | \(-0.695272\pi\) |
0.705266 | + | 0.708943i | \(0.250827\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.868241 | + | 4.92404i | −0.0299393 | + | 0.169794i | ||||
\(842\) | 4.60353 | − | 1.67555i | 0.158648 | − | 0.0577433i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.694593 | − | 3.93923i | −0.0239089 | − | 0.135594i | ||||
\(845\) | 14.6969 | + | 25.4558i | 0.505590 | + | 0.875708i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.00000 | − | 8.66025i | 0.171802 | − | 0.297570i | ||||
\(848\) | 27.6212 | + | 10.0533i | 0.948516 | + | 0.345232i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13.7888 | − | 11.5702i | −0.472952 | − | 0.396854i | ||||
\(851\) | 15.0113 | + | 12.5960i | 0.514582 | + | 0.431786i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.2160 | + | 4.44626i | 0.418268 | + | 0.152237i | 0.542576 | − | 0.840007i | \(-0.317449\pi\) |
−0.124308 | + | 0.992244i | \(0.539671\pi\) | |||||||
\(854\) | 12.2474 | − | 21.2132i | 0.419099 | − | 0.725901i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −36.0000 | − | 62.3538i | −1.23045 | − | 2.13121i | ||||
\(857\) | −4.25349 | − | 24.1228i | −0.145297 | − | 0.824018i | −0.967129 | − | 0.254288i | \(-0.918159\pi\) |
0.821832 | − | 0.569730i | \(-0.192952\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.4320 | + | 8.89252i | −0.833609 | + | 0.303409i | −0.723339 | − | 0.690493i | \(-0.757394\pi\) |
−0.110270 | + | 0.993902i | \(0.535172\pi\) | |||||||
\(860\) | 18.7154 | − | 106.140i | 0.638189 | − | 3.61935i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.7888 | + | 11.5702i | −0.469648 | + | 0.394082i | ||||
\(863\) | 7.34847 | 0.250145 | 0.125072 | − | 0.992148i | \(-0.460084\pi\) | ||||
0.125072 | + | 0.992148i | \(0.460084\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.0000 | −0.816024 | ||||||||
\(866\) | −31.8991 | + | 26.7665i | −1.08398 | + | 0.909564i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.38919 | + | 7.87846i | −0.0471520 | + | 0.267412i | ||||
\(869\) | −16.1124 | + | 5.86442i | −0.546575 | + | 0.198937i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.21554 | + | 6.89365i | 0.0411869 | + | 0.233583i | ||||
\(872\) | −2.44949 | − | 4.24264i | −0.0829502 | − | 0.143674i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.00000 | + | 5.19615i | −0.101477 | + | 0.175762i | ||||
\(875\) | 18.4141 | + | 6.70220i | 0.622512 | + | 0.226576i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.12836 | + | 5.14230i | 0.206940 | + | 0.173643i | 0.740367 | − | 0.672203i | \(-0.234652\pi\) |
−0.533427 | + | 0.845846i | \(0.679096\pi\) | |||||||
\(878\) | −26.2699 | − | 22.0430i | −0.886565 | − | 0.743916i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 22.5526 | + | 8.20848i | 0.760249 | + | 0.276708i | ||||
\(881\) | 18.3712 | − | 31.8198i | 0.618941 | − | 1.07204i | −0.370739 | − | 0.928737i | \(-0.620896\pi\) |
0.989679 | − | 0.143299i | \(-0.0457712\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.50000 | − | 14.7224i | −0.286048 | − | 0.495449i | 0.686815 | − | 0.726832i | \(-0.259008\pi\) |
−0.972863 | + | 0.231383i | \(0.925675\pi\) | |||||||
\(884\) | −5.10419 | − | 28.9473i | −0.171673 | − | 0.973604i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28.1908 | − | 10.2606i | 0.947088 | − | 0.344712i | ||||
\(887\) | 2.97745 | − | 16.8859i | 0.0999729 | − | 0.566974i | −0.893137 | − | 0.449785i | \(-0.851501\pi\) |
0.993110 | − | 0.117189i | \(-0.0373883\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.1097 | + | 24.4259i | −0.976308 | + | 0.819219i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −28.0000 | −0.937509 | ||||||||
\(893\) | 7.50567 | − | 6.29801i | 0.251168 | − | 0.210755i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.25133 | − | 35.4531i | 0.208959 | − | 1.18507i | ||||
\(896\) | −36.8283 | + | 13.4044i | −1.23035 | + | 0.447809i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.37700 | + | 53.1796i | 0.312915 | + | 1.77463i | ||||
\(899\) | 2.44949 | + | 4.24264i | 0.0816951 | + | 0.141500i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.0000 | − | 46.7654i | 0.899500 | − | 1.55798i | ||||
\(902\) | 27.6212 | + | 10.0533i | 0.919686 | + | 0.334738i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −36.7701 | − | 30.8538i | −1.22296 | − | 1.02618i | ||||
\(905\) | 15.0113 | + | 12.5960i | 0.498994 | + | 0.418706i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.57785 | + | 2.39414i | 0.218414 | + | 0.0794961i | 0.448910 | − | 0.893577i | \(-0.351813\pi\) |
−0.230496 | + | 0.973073i | \(0.574035\pi\) | |||||||
\(908\) | 19.5959 | − | 33.9411i | 0.650313 | − | 1.12638i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.00000 | − | 10.3923i | −0.198898 | − | 0.344502i | ||||
\(911\) | 2.12675 | + | 12.0614i | 0.0704623 | + | 0.399611i | 0.999557 | + | 0.0297691i | \(0.00947719\pi\) |
−0.929095 | + | 0.369842i | \(0.879412\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.1908 | − | 10.2606i | 0.932979 | − | 0.339576i | ||||
\(914\) | −12.3351 | + | 69.9560i | −0.408010 | + | 2.31394i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.06418 | + | 2.57115i | −0.101243 | + | 0.0849532i | ||||
\(917\) | −24.4949 | −0.808893 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.0000 | 0.659739 | 0.329870 | − | 0.944027i | \(-0.392995\pi\) | ||||
0.329870 | + | 0.944027i | \(0.392995\pi\) | |||||||
\(920\) | −22.5170 | + | 18.8940i | −0.742364 | + | 0.622917i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11.4608 | + | 64.9973i | −0.377441 | + | 2.14057i | ||||
\(923\) | −6.90530 | + | 2.51332i | −0.227291 | + | 0.0827271i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.38919 | + | 7.87846i | 0.0456761 | + | 0.259042i | ||||
\(926\) | −23.2702 | − | 40.3051i | −0.764705 | − | 1.32451i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.3194 | − | 9.21552i | −0.830704 | − | 0.302352i | −0.108556 | − | 0.994090i | \(-0.534623\pi\) |
−0.722148 | + | 0.691739i | \(0.756845\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.29813 | + | 1.92836i | 0.0753183 | + | 0.0631995i | ||||
\(932\) | 22.5170 | + | 18.8940i | 0.737569 | + | 0.618894i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −33.8289 | − | 12.3127i | −1.10692 | − | 0.402885i | ||||
\(935\) | 22.0454 | − | 38.1838i | 0.720962 | − | 1.24874i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.00000 | − | 6.92820i | −0.130674 | − | 0.226335i | 0.793262 | − | 0.608880i | \(-0.208381\pi\) |
−0.923937 | + | 0.382545i | \(0.875048\pi\) | |||||||
\(938\) | 5.95489 | + | 33.7719i | 0.194434 | + | 1.10269i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 90.2105 | − | 32.8339i | 2.94234 | − | 1.07092i | ||||
\(941\) | 1.70140 | − | 9.64911i | 0.0554640 | − | 0.314552i | −0.944436 | − | 0.328695i | \(-0.893391\pi\) |
0.999900 | + | 0.0141435i | \(0.00450217\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.19253 | + | 7.71345i | −0.299350 | + | 0.251185i | ||||
\(944\) | 9.79796 | 0.318896 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 66.0000 | 2.14585 | ||||||||
\(947\) | −18.7642 | + | 15.7450i | −0.609754 | + | 0.511644i | −0.894564 | − | 0.446940i | \(-0.852514\pi\) |
0.284810 | + | 0.958584i | \(0.408069\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.91013 | + | 10.8329i | −0.0620054 | + | 0.351650i | ||||
\(950\) | −2.30177 | + | 0.837775i | −0.0746792 | + | 0.0271810i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −12.5027 | − | 70.9062i | −0.405214 | − | 2.29808i | ||||
\(953\) | 14.6969 | + | 25.4558i | 0.476081 | + | 0.824596i | 0.999624 | − | 0.0274030i | \(-0.00872374\pi\) |
−0.523544 | + | 0.851999i | \(0.675390\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.0000 | − | 20.7846i | 0.388311 | − | 0.672574i | ||||
\(956\) | −9.20707 | − | 3.35110i | −0.297778 | − | 0.108382i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −50.5589 | − | 42.4240i | −1.63348 | − | 1.37066i | ||||
\(959\) | −15.0113 | − | 12.5960i | −0.484742 | − | 0.406746i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.1908 | + | 10.2606i | 0.909380 | + | 0.330987i | ||||
\(962\) | −9.79796 | + | 16.9706i | −0.315899 | + | 0.547153i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 32.0000 | + | 55.4256i | 1.03065 | + | 1.78514i | ||||
\(965\) | 4.67884 | + | 26.5350i | 0.150617 | + | 0.854193i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.57785 | − | 2.39414i | 0.211529 | − | 0.0769904i | −0.234082 | − | 0.972217i | \(-0.575208\pi\) |
0.445612 | + | 0.895226i | \(0.352986\pi\) | |||||||
\(968\) | 4.25349 | − | 24.1228i | 0.136712 | − | 0.775335i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 32.1739 | − | 26.9971i | 1.03304 | − | 0.866824i | ||||
\(971\) | −29.3939 | −0.943294 | −0.471647 | − | 0.881787i | \(-0.656340\pi\) | ||||
−0.471647 | + | 0.881787i | \(0.656340\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.0000 | −0.641171 | ||||||||
\(974\) | −65.6746 | + | 55.1076i | −2.10435 | + | 1.76576i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.47296 | − | 19.6962i | 0.111167 | − | 0.630459i | ||||
\(977\) | −23.0177 | + | 8.37775i | −0.736401 | + | 0.268028i | −0.682872 | − | 0.730538i | \(-0.739269\pi\) |
−0.0535290 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 14.6969 | + | 25.4558i | 0.469476 | + | 0.813157i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 48.0000 | − | 83.1384i | 1.53174 | − | 2.65305i | ||||
\(983\) | −4.60353 | − | 1.67555i | −0.146830 | − | 0.0534417i | 0.267560 | − | 0.963541i | \(-0.413783\pi\) |
−0.414390 | + | 0.910100i | \(0.636005\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.5776 | − | 23.1404i | −0.878695 | − | 0.737313i | ||||
\(986\) | −67.5510 | − | 56.6821i | −2.15126 | − | 1.80512i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.75877 | − | 1.36808i | −0.119582 | − | 0.0435244i | ||||
\(989\) | −13.4722 | + | 23.3345i | −0.428391 | + | 0.741995i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.50000 | + | 6.06218i | 0.111181 | + | 0.192571i | 0.916247 | − | 0.400614i | \(-0.131203\pi\) |
−0.805066 | + | 0.593186i | \(0.797870\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −33.8289 | + | 12.3127i | −1.07299 | + | 0.390536i | ||||
\(995\) | −0.425349 | + | 2.41228i | −0.0134845 | + | 0.0764743i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.3022 | − | 32.1394i | 1.21304 | − | 1.01786i | 0.213885 | − | 0.976859i | \(-0.431388\pi\) |
0.999159 | − | 0.0410055i | \(-0.0130561\pi\) | |||||||
\(998\) | −4.89898 | −0.155074 | ||||||||
\(999\) | 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 | 729.2.e.p.325.1 | 12 | ||
3.2 | odd | 2 | inner | 729.2.e.p.325.2 | 12 | ||
9.2 | odd | 6 | inner | 729.2.e.p.568.1 | 12 | ||
9.4 | even | 3 | inner | 729.2.e.p.82.1 | 12 | ||
9.5 | odd | 6 | inner | 729.2.e.p.82.2 | 12 | ||
9.7 | even | 3 | inner | 729.2.e.p.568.2 | 12 | ||
27.2 | odd | 18 | inner | 729.2.e.p.163.1 | 12 | ||
27.4 | even | 9 | 243.2.a.d.1.1 | ✓ | 2 | ||
27.5 | odd | 18 | 243.2.c.c.82.1 | 4 | |||
27.7 | even | 9 | inner | 729.2.e.p.649.1 | 12 | ||
27.11 | odd | 18 | inner | 729.2.e.p.406.2 | 12 | ||
27.13 | even | 9 | 243.2.c.c.163.2 | 4 | |||
27.14 | odd | 18 | 243.2.c.c.163.1 | 4 | |||
27.16 | even | 9 | inner | 729.2.e.p.406.1 | 12 | ||
27.20 | odd | 18 | inner | 729.2.e.p.649.2 | 12 | ||
27.22 | even | 9 | 243.2.c.c.82.2 | 4 | |||
27.23 | odd | 18 | 243.2.a.d.1.2 | yes | 2 | ||
27.25 | even | 9 | inner | 729.2.e.p.163.2 | 12 | ||
108.23 | even | 18 | 3888.2.a.z.1.1 | 2 | |||
108.31 | odd | 18 | 3888.2.a.z.1.2 | 2 | |||
135.4 | even | 18 | 6075.2.a.bn.1.2 | 2 | |||
135.104 | odd | 18 | 6075.2.a.bn.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
243.2.a.d.1.1 | ✓ | 2 | 27.4 | even | 9 | ||
243.2.a.d.1.2 | yes | 2 | 27.23 | odd | 18 | ||
243.2.c.c.82.1 | 4 | 27.5 | odd | 18 | |||
243.2.c.c.82.2 | 4 | 27.22 | even | 9 | |||
243.2.c.c.163.1 | 4 | 27.14 | odd | 18 | |||
243.2.c.c.163.2 | 4 | 27.13 | even | 9 | |||
729.2.e.p.82.1 | 12 | 9.4 | even | 3 | inner | ||
729.2.e.p.82.2 | 12 | 9.5 | odd | 6 | inner | ||
729.2.e.p.163.1 | 12 | 27.2 | odd | 18 | inner | ||
729.2.e.p.163.2 | 12 | 27.25 | even | 9 | inner | ||
729.2.e.p.325.1 | 12 | 1.1 | even | 1 | trivial | ||
729.2.e.p.325.2 | 12 | 3.2 | odd | 2 | inner | ||
729.2.e.p.406.1 | 12 | 27.16 | even | 9 | inner | ||
729.2.e.p.406.2 | 12 | 27.11 | odd | 18 | inner | ||
729.2.e.p.568.1 | 12 | 9.2 | odd | 6 | inner | ||
729.2.e.p.568.2 | 12 | 9.7 | even | 3 | inner | ||
729.2.e.p.649.1 | 12 | 27.7 | even | 9 | inner | ||
729.2.e.p.649.2 | 12 | 27.20 | odd | 18 | inner | ||
3888.2.a.z.1.1 | 2 | 108.23 | even | 18 | |||
3888.2.a.z.1.2 | 2 | 108.31 | odd | 18 | |||
6075.2.a.bn.1.1 | 2 | 135.104 | odd | 18 | |||
6075.2.a.bn.1.2 | 2 | 135.4 | even | 18 |