Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(197,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.197");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.20138089353117696.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3x^{10} - 2x^{9} + 2x^{8} + 4x^{7} + 2x^{6} + 8x^{5} + 8x^{4} - 16x^{3} - 48x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 589.4 | ||
Root | \(1.37925 - 0.312504i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.589 |
Dual form | 784.2.m.h.197.4 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.312504 | − | 1.37925i | 0.220974 | − | 0.975280i | ||||
\(3\) | 0.599978 | + | 0.599978i | 0.346397 | + | 0.346397i | 0.858766 | − | 0.512368i | \(-0.171232\pi\) |
−0.512368 | + | 0.858766i | \(0.671232\pi\) | |||||||
\(4\) | −1.80468 | − | 0.862045i | −0.902341 | − | 0.431023i | ||||
\(5\) | −0.974969 | + | 0.974969i | −0.436020 | + | 0.436020i | −0.890670 | − | 0.454650i | \(-0.849764\pi\) |
0.454650 | + | 0.890670i | \(0.349764\pi\) | |||||||
\(6\) | 1.01502 | − | 0.640026i | 0.414379 | − | 0.261290i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.75295 | + | 2.21972i | −0.619762 | + | 0.784790i | ||||
\(9\) | − | 2.28005i | − | 0.760018i | ||||||
\(10\) | 1.04005 | + | 1.64941i | 0.328892 | + | 0.521590i | ||||
\(11\) | −1.72409 | + | 1.72409i | −0.519833 | + | 0.519833i | −0.917521 | − | 0.397688i | \(-0.869813\pi\) |
0.397688 | + | 0.917521i | \(0.369813\pi\) | |||||||
\(12\) | −0.565561 | − | 1.59998i | −0.163263 | − | 0.461874i | ||||
\(13\) | −1.90592 | − | 1.90592i | −0.528608 | − | 0.528608i | 0.391549 | − | 0.920157i | \(-0.371939\pi\) |
−0.920157 | + | 0.391549i | \(0.871939\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.16992 | −0.302072 | ||||||||
\(16\) | 2.51376 | + | 3.11144i | 0.628439 | + | 0.777859i | ||||
\(17\) | −6.71697 | −1.62910 | −0.814552 | − | 0.580090i | \(-0.803017\pi\) | ||||
−0.814552 | + | 0.580090i | \(0.803017\pi\) | |||||||
\(18\) | −3.14477 | − | 0.712526i | −0.741230 | − | 0.167944i | ||||
\(19\) | −2.94908 | − | 2.94908i | −0.676565 | − | 0.676565i | 0.282656 | − | 0.959221i | \(-0.408784\pi\) |
−0.959221 | + | 0.282656i | \(0.908784\pi\) | |||||||
\(20\) | 2.59998 | − | 0.919042i | 0.581373 | − | 0.205504i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.83917 | + | 2.91674i | 0.392113 | + | 0.621852i | ||||
\(23\) | − | 5.29883i | − | 1.10488i | −0.833552 | − | 0.552441i | \(-0.813697\pi\) | ||
0.833552 | − | 0.552441i | \(-0.186303\pi\) | |||||||
\(24\) | −2.38352 | + | 0.280053i | −0.486533 | + | 0.0571655i | ||||
\(25\) | 3.09887i | 0.619774i | ||||||||
\(26\) | −3.22436 | + | 2.03314i | −0.632349 | + | 0.398732i | ||||
\(27\) | 3.16792 | − | 3.16792i | 0.609666 | − | 0.609666i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.03004 | − | 3.03004i | −0.562663 | − | 0.562663i | 0.367400 | − | 0.930063i | \(-0.380248\pi\) |
−0.930063 | + | 0.367400i | \(0.880248\pi\) | |||||||
\(30\) | −0.365605 | + | 1.61362i | −0.0667501 | + | 0.294605i | ||||
\(31\) | −1.19996 | −0.215518 | −0.107759 | − | 0.994177i | \(-0.534368\pi\) | ||||
−0.107759 | + | 0.994177i | \(0.534368\pi\) | |||||||
\(32\) | 5.07702 | − | 2.49477i | 0.897499 | − | 0.441017i | ||||
\(33\) | −2.06883 | −0.360138 | ||||||||
\(34\) | −2.09908 | + | 9.26441i | −0.359990 | + | 1.58883i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.96551 | + | 4.11477i | −0.327585 | + | 0.685795i | ||||
\(37\) | −2.25002 | + | 2.25002i | −0.369901 | + | 0.369901i | −0.867441 | − | 0.497540i | \(-0.834237\pi\) |
0.497540 | + | 0.867441i | \(0.334237\pi\) | |||||||
\(38\) | −4.98913 | + | 3.14593i | −0.809343 | + | 0.510337i | ||||
\(39\) | − | 2.28702i | − | 0.366217i | ||||||
\(40\) | −0.455088 | − | 3.87323i | −0.0719557 | − | 0.612412i | ||||
\(41\) | − | 3.94994i | − | 0.616877i | −0.951244 | − | 0.308438i | \(-0.900194\pi\) | ||
0.951244 | − | 0.308438i | \(-0.0998064\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.02292 | + | 7.02292i | −1.07098 | + | 1.07098i | −0.0737045 | + | 0.997280i | \(0.523482\pi\) |
−0.997280 | + | 0.0737045i | \(0.976518\pi\) | |||||||
\(44\) | 4.59768 | − | 1.62519i | 0.693126 | − | 0.245007i | ||||
\(45\) | 2.22298 | + | 2.22298i | 0.331383 | + | 0.331383i | ||||
\(46\) | −7.30842 | − | 1.65591i | −1.07757 | − | 0.244150i | ||||
\(47\) | 3.06186 | 0.446619 | 0.223309 | − | 0.974748i | \(-0.428314\pi\) | ||||
0.223309 | + | 0.974748i | \(0.428314\pi\) | |||||||
\(48\) | −0.358595 | + | 3.37499i | −0.0517588 | + | 0.487138i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.27413 | + | 0.968410i | 0.604453 | + | 0.136954i | ||||
\(51\) | −4.03004 | − | 4.03004i | −0.564318 | − | 0.564318i | ||||
\(52\) | 1.79659 | + | 5.08258i | 0.249143 | + | 0.704827i | ||||
\(53\) | −3.01877 | + | 3.01877i | −0.414660 | + | 0.414660i | −0.883358 | − | 0.468698i | \(-0.844723\pi\) |
0.468698 | + | 0.883358i | \(0.344723\pi\) | |||||||
\(54\) | −3.37937 | − | 5.35935i | −0.459874 | − | 0.729315i | ||||
\(55\) | − | 3.36187i | − | 0.453315i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 3.53876i | − | 0.468721i | ||||||
\(58\) | −5.12609 | + | 3.23229i | −0.673088 | + | 0.424420i | ||||
\(59\) | −4.96785 | + | 4.96785i | −0.646759 | + | 0.646759i | −0.952208 | − | 0.305449i | \(-0.901193\pi\) |
0.305449 | + | 0.952208i | \(0.401193\pi\) | |||||||
\(60\) | 2.11133 | + | 1.00852i | 0.272572 | + | 0.130200i | ||||
\(61\) | 9.69194 | + | 9.69194i | 1.24093 | + | 1.24093i | 0.959617 | + | 0.281308i | \(0.0907684\pi\) |
0.281308 | + | 0.959617i | \(0.409232\pi\) | |||||||
\(62\) | −0.374991 | + | 1.65504i | −0.0476240 | + | 0.210191i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.85433 | − | 7.78212i | −0.231791 | − | 0.972766i | ||||
\(65\) | 3.71643 | 0.460967 | ||||||||
\(66\) | −0.646519 | + | 2.85345i | −0.0795810 | + | 0.351235i | ||||
\(67\) | 3.55596 | + | 3.55596i | 0.434430 | + | 0.434430i | 0.890132 | − | 0.455702i | \(-0.150612\pi\) |
−0.455702 | + | 0.890132i | \(0.650612\pi\) | |||||||
\(68\) | 12.1220 | + | 5.79033i | 1.47001 | + | 0.702181i | ||||
\(69\) | 3.17918 | − | 3.17918i | 0.382728 | − | 0.382728i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.5771i | − | 1.37395i | −0.726682 | − | 0.686974i | \(-0.758939\pi\) | ||
0.726682 | − | 0.686974i | \(-0.241061\pi\) | |||||||
\(72\) | 5.06108 | + | 3.99682i | 0.596454 | + | 0.471030i | ||||
\(73\) | − | 10.3271i | − | 1.20869i | −0.796722 | − | 0.604346i | \(-0.793434\pi\) | ||
0.796722 | − | 0.604346i | \(-0.206566\pi\) | |||||||
\(74\) | 2.40020 | + | 3.80648i | 0.279018 | + | 0.442495i | ||||
\(75\) | −1.85925 | + | 1.85925i | −0.214688 | + | 0.214688i | ||||
\(76\) | 2.77991 | + | 7.86439i | 0.318877 | + | 0.902107i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.15439 | − | 0.714705i | −0.357164 | − | 0.0809244i | ||||
\(79\) | 4.06883 | 0.457780 | 0.228890 | − | 0.973452i | \(-0.426490\pi\) | ||||
0.228890 | + | 0.973452i | \(0.426490\pi\) | |||||||
\(80\) | −5.48439 | − | 0.582721i | −0.613173 | − | 0.0651501i | ||||
\(81\) | −3.03880 | −0.337644 | ||||||||
\(82\) | −5.44797 | − | 1.23437i | −0.601627 | − | 0.136314i | ||||
\(83\) | −9.17886 | − | 9.17886i | −1.00751 | − | 1.00751i | −0.999972 | − | 0.00753873i | \(-0.997600\pi\) |
−0.00753873 | − | 0.999972i | \(-0.502400\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.54884 | − | 6.54884i | 0.710322 | − | 0.710322i | ||||
\(86\) | 7.49169 | + | 11.8811i | 0.807850 | + | 1.28117i | ||||
\(87\) | − | 3.63591i | − | 0.389810i | ||||||
\(88\) | −0.804756 | − | 6.84925i | −0.0857873 | − | 0.730132i | ||||
\(89\) | 16.9287i | 1.79444i | 0.441582 | + | 0.897221i | \(0.354417\pi\) | ||||
−0.441582 | + | 0.897221i | \(0.645583\pi\) | |||||||
\(90\) | 3.76075 | − | 2.37136i | 0.396418 | − | 0.249964i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.56783 | + | 9.56270i | −0.476229 | + | 0.996980i | ||||
\(93\) | −0.719947 | − | 0.719947i | −0.0746551 | − | 0.0746551i | ||||
\(94\) | 0.956845 | − | 4.22309i | 0.0986910 | − | 0.435578i | ||||
\(95\) | 5.75052 | 0.589991 | ||||||||
\(96\) | 4.54291 | + | 1.54929i | 0.463659 | + | 0.158124i | ||||
\(97\) | 2.51522 | 0.255382 | 0.127691 | − | 0.991814i | \(-0.459243\pi\) | ||||
0.127691 | + | 0.991814i | \(0.459243\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.93102 | + | 3.93102i | 0.395082 | + | 0.395082i | ||||
\(100\) | 2.67137 | − | 5.59247i | 0.267137 | − | 0.559247i | ||||
\(101\) | 8.56282 | − | 8.56282i | 0.852033 | − | 0.852033i | −0.138351 | − | 0.990383i | \(-0.544180\pi\) |
0.990383 | + | 0.138351i | \(0.0441801\pi\) | |||||||
\(102\) | −6.81785 | + | 4.29904i | −0.675067 | + | 0.425668i | ||||
\(103\) | − | 17.8356i | − | 1.75739i | −0.477382 | − | 0.878696i | \(-0.658414\pi\) | ||
0.477382 | − | 0.878696i | \(-0.341586\pi\) | |||||||
\(104\) | 7.57161 | − | 0.889630i | 0.742457 | − | 0.0872354i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.22027 | + | 5.10703i | 0.312781 | + | 0.496039i | ||||
\(107\) | 8.49285 | − | 8.49285i | 0.821034 | − | 0.821034i | −0.165222 | − | 0.986256i | \(-0.552834\pi\) |
0.986256 | + | 0.165222i | \(0.0528341\pi\) | |||||||
\(108\) | −8.44797 | + | 2.98619i | −0.812906 | + | 0.287347i | ||||
\(109\) | 7.26700 | + | 7.26700i | 0.696052 | + | 0.696052i | 0.963557 | − | 0.267504i | \(-0.0861990\pi\) |
−0.267504 | + | 0.963557i | \(0.586199\pi\) | |||||||
\(110\) | −4.63687 | − | 1.05060i | −0.442109 | − | 0.100171i | ||||
\(111\) | −2.69992 | −0.256265 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.8351 | −1.30150 | −0.650749 | − | 0.759293i | \(-0.725545\pi\) | ||||
−0.650749 | + | 0.759293i | \(0.725545\pi\) | |||||||
\(114\) | −4.88085 | − | 1.10588i | −0.457134 | − | 0.103575i | ||||
\(115\) | 5.16619 | + | 5.16619i | 0.481750 | + | 0.481750i | ||||
\(116\) | 2.85622 | + | 8.08028i | 0.265194 | + | 0.750235i | ||||
\(117\) | −4.34560 | + | 4.34560i | −0.401751 | + | 0.401751i | ||||
\(118\) | 5.29945 | + | 8.40440i | 0.487854 | + | 0.773688i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.05081 | − | 2.59690i | 0.187213 | − | 0.237063i | ||||
\(121\) | 5.05502i | 0.459547i | ||||||||
\(122\) | 16.3964 | − | 10.3389i | 1.48446 | − | 0.936038i | ||||
\(123\) | 2.36988 | − | 2.36988i | 0.213685 | − | 0.213685i | ||||
\(124\) | 2.16554 | + | 1.03442i | 0.194471 | + | 0.0928934i | ||||
\(125\) | −7.89615 | − | 7.89615i | −0.706253 | − | 0.706253i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.1434 | 1.25502 | 0.627512 | − | 0.778607i | \(-0.284073\pi\) | ||||
0.627512 | + | 0.778607i | \(0.284073\pi\) | |||||||
\(128\) | −11.3130 | + | 0.125645i | −0.999938 | + | 0.0111055i | ||||
\(129\) | −8.42719 | −0.741973 | ||||||||
\(130\) | 1.16140 | − | 5.12590i | 0.101862 | − | 0.449572i | ||||
\(131\) | 3.04995 | + | 3.04995i | 0.266475 | + | 0.266475i | 0.827678 | − | 0.561203i | \(-0.189661\pi\) |
−0.561203 | + | 0.827678i | \(0.689661\pi\) | |||||||
\(132\) | 3.73359 | + | 1.78343i | 0.324967 | + | 0.155228i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.01583 | − | 3.79332i | 0.519688 | − | 0.327693i | ||||
\(135\) | 6.17724i | 0.531652i | ||||||||
\(136\) | 11.7745 | − | 14.9098i | 1.00966 | − | 1.27851i | ||||
\(137\) | 11.5811i | 0.989440i | 0.869052 | + | 0.494720i | \(0.164729\pi\) | ||||
−0.869052 | + | 0.494720i | \(0.835271\pi\) | |||||||
\(138\) | −3.39139 | − | 5.37840i | −0.288694 | − | 0.457840i | ||||
\(139\) | 2.25088 | − | 2.25088i | 0.190917 | − | 0.190917i | −0.605175 | − | 0.796092i | \(-0.706897\pi\) |
0.796092 | + | 0.605175i | \(0.206897\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.83705 | + | 1.83705i | 0.154708 | + | 0.154708i | ||||
\(142\) | −15.9677 | − | 3.61789i | −1.33998 | − | 0.303607i | ||||
\(143\) | 6.57197 | 0.549576 | ||||||||
\(144\) | 7.09424 | − | 5.73149i | 0.591186 | − | 0.477625i | ||||
\(145\) | 5.90838 | 0.490665 | ||||||||
\(146\) | −14.2436 | − | 3.22725i | −1.17881 | − | 0.267089i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.00018 | − | 2.12095i | 0.493212 | − | 0.174341i | ||||
\(149\) | −2.29883 | + | 2.29883i | −0.188327 | + | 0.188327i | −0.794973 | − | 0.606645i | \(-0.792515\pi\) |
0.606645 | + | 0.794973i | \(0.292515\pi\) | |||||||
\(150\) | 1.98336 | + | 3.14541i | 0.161940 | + | 0.256821i | ||||
\(151\) | − | 18.1587i | − | 1.47774i | −0.673850 | − | 0.738868i | \(-0.735361\pi\) | ||
0.673850 | − | 0.738868i | \(-0.264639\pi\) | |||||||
\(152\) | 11.7157 | − | 1.37655i | 0.950270 | − | 0.111653i | ||||
\(153\) | 15.3150i | 1.23815i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.16992 | − | 1.16992i | 0.0939703 | − | 0.0939703i | ||||
\(156\) | −1.97152 | + | 4.12735i | −0.157848 | + | 0.330453i | ||||
\(157\) | 10.8110 | + | 10.8110i | 0.862816 | + | 0.862816i | 0.991664 | − | 0.128849i | \(-0.0411281\pi\) |
−0.128849 | + | 0.991664i | \(0.541128\pi\) | |||||||
\(158\) | 1.27153 | − | 5.61195i | 0.101157 | − | 0.446463i | ||||
\(159\) | −3.62239 | −0.287275 | ||||||||
\(160\) | −2.51761 | + | 7.38226i | −0.199035 | + | 0.583619i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.949637 | + | 4.19127i | −0.0746106 | + | 0.329298i | ||||
\(163\) | −6.43105 | − | 6.43105i | −0.503719 | − | 0.503719i | 0.408873 | − | 0.912591i | \(-0.365922\pi\) |
−0.912591 | + | 0.408873i | \(0.865922\pi\) | |||||||
\(164\) | −3.40503 | + | 7.12838i | −0.265888 | + | 0.556633i | ||||
\(165\) | 2.01705 | − | 2.01705i | 0.157027 | − | 0.157027i | ||||
\(166\) | −15.5284 | + | 9.79154i | −1.20524 | + | 0.759971i | ||||
\(167\) | 0.661950i | 0.0512232i | 0.999672 | + | 0.0256116i | \(0.00815332\pi\) | ||||
−0.999672 | + | 0.0256116i | \(0.991847\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.73492i | − | 0.441148i | ||||||
\(170\) | −6.98597 | − | 11.0791i | −0.535800 | − | 0.849725i | ||||
\(171\) | −6.72405 | + | 6.72405i | −0.514201 | + | 0.514201i | ||||
\(172\) | 18.7282 | − | 6.62006i | 1.42801 | − | 0.504775i | ||||
\(173\) | −6.35590 | − | 6.35590i | −0.483230 | − | 0.483230i | 0.422932 | − | 0.906162i | \(-0.361001\pi\) |
−0.906162 | + | 0.422932i | \(0.861001\pi\) | |||||||
\(174\) | −5.01484 | − | 1.13624i | −0.380174 | − | 0.0861379i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9.69834 | − | 1.03046i | −0.731040 | − | 0.0776735i | ||||
\(177\) | −5.96120 | −0.448071 | ||||||||
\(178\) | 23.3490 | + | 5.29030i | 1.75008 | + | 0.396525i | ||||
\(179\) | −7.61603 | − | 7.61603i | −0.569249 | − | 0.569249i | 0.362669 | − | 0.931918i | \(-0.381866\pi\) |
−0.931918 | + | 0.362669i | \(0.881866\pi\) | |||||||
\(180\) | −2.09546 | − | 5.92809i | −0.156187 | − | 0.441854i | ||||
\(181\) | −13.9902 | + | 13.9902i | −1.03989 | + | 1.03989i | −0.0407146 | + | 0.999171i | \(0.512963\pi\) |
−0.999171 | + | 0.0407146i | \(0.987037\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.6299i | 0.859707i | ||||||||
\(184\) | 11.7619 | + | 9.28858i | 0.867100 | + | 0.684763i | ||||
\(185\) | − | 4.38740i | − | 0.322568i | ||||||
\(186\) | −1.21798 | + | 0.768004i | −0.0893064 | + | 0.0563127i | ||||
\(187\) | 11.5807 | − | 11.5807i | 0.846862 | − | 0.846862i | ||||
\(188\) | −5.52569 | − | 2.63946i | −0.403002 | − | 0.192503i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.79706 | − | 7.93143i | 0.130373 | − | 0.575406i | ||||
\(191\) | −22.4422 | −1.62386 | −0.811929 | − | 0.583756i | \(-0.801582\pi\) | ||||
−0.811929 | + | 0.583756i | \(0.801582\pi\) | |||||||
\(192\) | 3.55655 | − | 5.78166i | 0.256672 | − | 0.417255i | ||||
\(193\) | −6.31408 | −0.454498 | −0.227249 | − | 0.973837i | \(-0.572973\pi\) | ||||
−0.227249 | + | 0.973837i | \(0.572973\pi\) | |||||||
\(194\) | 0.786018 | − | 3.46913i | 0.0564328 | − | 0.249069i | ||||
\(195\) | 2.22978 | + | 2.22978i | 0.159678 | + | 0.159678i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.81709 | − | 3.81709i | 0.271957 | − | 0.271957i | −0.557931 | − | 0.829887i | \(-0.688405\pi\) |
0.829887 | + | 0.557931i | \(0.188405\pi\) | |||||||
\(198\) | 6.65033 | − | 4.19341i | 0.472618 | − | 0.298013i | ||||
\(199\) | − | 25.6304i | − | 1.81689i | −0.418005 | − | 0.908445i | \(-0.637270\pi\) | ||
0.418005 | − | 0.908445i | \(-0.362730\pi\) | |||||||
\(200\) | −6.87863 | − | 5.43216i | −0.486392 | − | 0.384112i | ||||
\(201\) | 4.26700i | 0.300971i | ||||||||
\(202\) | −9.13439 | − | 14.4862i | −0.642693 | − | 1.01925i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.79886 | + | 10.7470i | 0.265973 | + | 0.752441i | ||||
\(205\) | 3.85107 | + | 3.85107i | 0.268970 | + | 0.268970i | ||||
\(206\) | −24.5998 | − | 5.57369i | −1.71395 | − | 0.388338i | ||||
\(207\) | −12.0816 | −0.839729 | ||||||||
\(208\) | 1.13913 | − | 10.7212i | 0.0789847 | − | 0.743380i | ||||
\(209\) | 10.1690 | 0.703401 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.737145 | + | 0.737145i | 0.0507472 | + | 0.0507472i | 0.732025 | − | 0.681278i | \(-0.238575\pi\) |
−0.681278 | + | 0.732025i | \(0.738575\pi\) | |||||||
\(212\) | 8.05024 | − | 2.84561i | 0.552893 | − | 0.195437i | ||||
\(213\) | 6.94600 | − | 6.94600i | 0.475932 | − | 0.475932i | ||||
\(214\) | −9.05974 | − | 14.3678i | −0.619311 | − | 0.982165i | ||||
\(215\) | − | 13.6943i | − | 0.933941i | ||||||
\(216\) | 1.47869 | + | 12.5851i | 0.100612 | + | 0.856307i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 12.2940 | − | 7.75207i | 0.832655 | − | 0.525036i | ||||
\(219\) | 6.19601 | − | 6.19601i | 0.418688 | − | 0.418688i | ||||
\(220\) | −2.89809 | + | 6.06711i | −0.195389 | + | 0.409045i | ||||
\(221\) | 12.8020 | + | 12.8020i | 0.861158 | + | 0.861158i | ||||
\(222\) | −0.843737 | + | 3.72388i | −0.0566279 | + | 0.249930i | ||||
\(223\) | 5.76178 | 0.385838 | 0.192919 | − | 0.981215i | \(-0.438205\pi\) | ||||
0.192919 | + | 0.981215i | \(0.438205\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.06558 | 0.471039 | ||||||||
\(226\) | −4.32353 | + | 19.0821i | −0.287597 | + | 1.26932i | ||||
\(227\) | 18.2179 | + | 18.2179i | 1.20916 | + | 1.20916i | 0.971299 | + | 0.237864i | \(0.0764472\pi\) |
0.237864 | + | 0.971299i | \(0.423553\pi\) | |||||||
\(228\) | −3.05058 | + | 6.38634i | −0.202029 | + | 0.422946i | ||||
\(229\) | −0.512762 | + | 0.512762i | −0.0338843 | + | 0.0338843i | −0.723846 | − | 0.689962i | \(-0.757627\pi\) |
0.689962 | + | 0.723846i | \(0.257627\pi\) | |||||||
\(230\) | 8.73995 | − | 5.51103i | 0.576295 | − | 0.363387i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.0373 | − | 1.41433i | 0.790290 | − | 0.0928556i | ||||
\(233\) | 14.4425i | 0.946160i | 0.881019 | + | 0.473080i | \(0.156858\pi\) | ||||
−0.881019 | + | 0.473080i | \(0.843142\pi\) | |||||||
\(234\) | 4.63567 | + | 7.35171i | 0.303043 | + | 0.480596i | ||||
\(235\) | −2.98522 | + | 2.98522i | −0.194734 | + | 0.194734i | ||||
\(236\) | 13.2479 | − | 4.68288i | 0.862365 | − | 0.304829i | ||||
\(237\) | 2.44121 | + | 2.44121i | 0.158574 | + | 0.158574i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.34716 | −0.475248 | −0.237624 | − | 0.971357i | \(-0.576369\pi\) | ||||
−0.237624 | + | 0.971357i | \(0.576369\pi\) | |||||||
\(240\) | −2.94089 | − | 3.64013i | −0.189834 | − | 0.234970i | ||||
\(241\) | −3.25347 | −0.209575 | −0.104787 | − | 0.994495i | \(-0.533416\pi\) | ||||
−0.104787 | + | 0.994495i | \(0.533416\pi\) | |||||||
\(242\) | 6.97216 | + | 1.57972i | 0.448187 | + | 0.101548i | ||||
\(243\) | −11.3270 | − | 11.3270i | −0.726625 | − | 0.726625i | ||||
\(244\) | −9.13598 | − | 25.8458i | −0.584871 | − | 1.65461i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.52806 | − | 4.00926i | −0.161184 | − | 0.255621i | ||||
\(247\) | 11.2414i | 0.715275i | ||||||||
\(248\) | 2.10346 | − | 2.66357i | 0.133570 | − | 0.169137i | ||||
\(249\) | − | 11.0142i | − | 0.697998i | ||||||
\(250\) | −13.3584 | + | 8.42321i | −0.844858 | + | 0.532731i | ||||
\(251\) | −2.08074 | + | 2.08074i | −0.131335 | + | 0.131335i | −0.769719 | − | 0.638383i | \(-0.779604\pi\) |
0.638383 | + | 0.769719i | \(0.279604\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.13566 | + | 9.13566i | 0.574354 | + | 0.574354i | ||||
\(254\) | 4.41987 | − | 19.5073i | 0.277328 | − | 1.22400i | ||||
\(255\) | 7.85832 | 0.492107 | ||||||||
\(256\) | −3.36207 | + | 15.6428i | −0.210129 | + | 0.977674i | ||||
\(257\) | −10.9620 | −0.683788 | −0.341894 | − | 0.939738i | \(-0.611068\pi\) | ||||
−0.341894 | + | 0.939738i | \(0.611068\pi\) | |||||||
\(258\) | −2.63353 | + | 11.6232i | −0.163957 | + | 0.723631i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6.70698 | − | 3.20373i | −0.415949 | − | 0.198687i | ||||
\(261\) | −6.90864 | + | 6.90864i | −0.427634 | + | 0.427634i | ||||
\(262\) | 5.15978 | − | 3.25353i | 0.318772 | − | 0.201004i | ||||
\(263\) | − | 10.1931i | − | 0.628534i | −0.949335 | − | 0.314267i | \(-0.898241\pi\) | ||
0.949335 | − | 0.314267i | \(-0.101759\pi\) | |||||||
\(264\) | 3.62656 | − | 4.59223i | 0.223199 | − | 0.282633i | ||||
\(265\) | − | 5.88642i | − | 0.361600i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.1569 | + | 10.1569i | −0.621590 | + | 0.621590i | ||||
\(268\) | −3.35198 | − | 9.48278i | −0.204755 | − | 0.579253i | ||||
\(269\) | −1.75782 | − | 1.75782i | −0.107176 | − | 0.107176i | 0.651485 | − | 0.758661i | \(-0.274146\pi\) |
−0.758661 | + | 0.651485i | \(0.774146\pi\) | |||||||
\(270\) | 8.51999 | + | 1.93041i | 0.518510 | + | 0.117481i | ||||
\(271\) | 5.66166 | 0.343921 | 0.171961 | − | 0.985104i | \(-0.444990\pi\) | ||||
0.171961 | + | 0.985104i | \(0.444990\pi\) | |||||||
\(272\) | −16.8848 | − | 20.8994i | −1.02379 | − | 1.26721i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.9733 | + | 3.61914i | 0.964981 | + | 0.218640i | ||||
\(275\) | −5.34273 | − | 5.34273i | −0.322179 | − | 0.322179i | ||||
\(276\) | −8.47800 | + | 2.99681i | −0.510316 | + | 0.180387i | ||||
\(277\) | 21.3329 | − | 21.3329i | 1.28177 | − | 1.28177i | 0.342106 | − | 0.939662i | \(-0.388860\pi\) |
0.939662 | − | 0.342106i | \(-0.111140\pi\) | |||||||
\(278\) | −2.40112 | − | 3.80794i | −0.144010 | − | 0.228385i | ||||
\(279\) | 2.73596i | 0.163798i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.60009i | − | 0.0954532i | −0.998860 | − | 0.0477266i | \(-0.984802\pi\) | ||
0.998860 | − | 0.0477266i | \(-0.0151976\pi\) | |||||||
\(282\) | 3.10784 | − | 1.95967i | 0.185069 | − | 0.116697i | ||||
\(283\) | −14.3940 | + | 14.3940i | −0.855635 | + | 0.855635i | −0.990820 | − | 0.135186i | \(-0.956837\pi\) |
0.135186 | + | 0.990820i | \(0.456837\pi\) | |||||||
\(284\) | −9.97997 | + | 20.8930i | −0.592203 | + | 1.23977i | ||||
\(285\) | 3.45019 | + | 3.45019i | 0.204371 | + | 0.204371i | ||||
\(286\) | 2.05377 | − | 9.06441i | 0.121442 | − | 0.535990i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5.68821 | − | 11.5759i | −0.335181 | − | 0.682115i | ||||
\(289\) | 28.1177 | 1.65398 | ||||||||
\(290\) | 1.84640 | − | 8.14916i | 0.108424 | − | 0.478535i | ||||
\(291\) | 1.50908 | + | 1.50908i | 0.0884638 | + | 0.0884638i | ||||
\(292\) | −8.90240 | + | 18.6371i | −0.520974 | + | 1.09065i | ||||
\(293\) | −0.267863 | + | 0.267863i | −0.0156487 | + | 0.0156487i | −0.714888 | − | 0.699239i | \(-0.753522\pi\) |
0.699239 | + | 0.714888i | \(0.253522\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 9.68700i | − | 0.563999i | ||||||
\(296\) | −1.05024 | − | 8.93858i | −0.0610442 | − | 0.519544i | ||||
\(297\) | 10.9235i | 0.633849i | ||||||||
\(298\) | 2.45227 | + | 3.88906i | 0.142056 | + | 0.225287i | ||||
\(299\) | −10.0992 | + | 10.0992i | −0.584049 | + | 0.584049i | ||||
\(300\) | 4.95812 | − | 1.75260i | 0.286257 | − | 0.101186i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −25.0455 | − | 5.67468i | −1.44121 | − | 0.326541i | ||||
\(303\) | 10.2750 | 0.590284 | ||||||||
\(304\) | 1.76261 | − | 16.5891i | 0.101092 | − | 0.951452i | ||||
\(305\) | −18.8987 | −1.08214 | ||||||||
\(306\) | 21.1233 | + | 4.78602i | 1.20754 | + | 0.273598i | ||||
\(307\) | 12.3805 | + | 12.3805i | 0.706594 | + | 0.706594i | 0.965817 | − | 0.259223i | \(-0.0834665\pi\) |
−0.259223 | + | 0.965817i | \(0.583466\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.7010 | − | 10.7010i | 0.608756 | − | 0.608756i | ||||
\(310\) | −1.24801 | − | 1.97922i | −0.0708823 | − | 0.112412i | ||||
\(311\) | − | 3.69468i | − | 0.209506i | −0.994498 | − | 0.104753i | \(-0.966595\pi\) | ||
0.994498 | − | 0.104753i | \(-0.0334053\pi\) | |||||||
\(312\) | 5.07656 | + | 4.00904i | 0.287403 | + | 0.226967i | ||||
\(313\) | − | 10.4700i | − | 0.591799i | −0.955219 | − | 0.295900i | \(-0.904381\pi\) | ||
0.955219 | − | 0.295900i | \(-0.0956194\pi\) | |||||||
\(314\) | 18.2897 | − | 11.5327i | 1.03215 | − | 0.650827i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.34295 | − | 3.50752i | −0.413073 | − | 0.197313i | ||||
\(317\) | −15.7941 | − | 15.7941i | −0.887085 | − | 0.887085i | 0.107157 | − | 0.994242i | \(-0.465825\pi\) |
−0.994242 | + | 0.107157i | \(0.965825\pi\) | |||||||
\(318\) | −1.13201 | + | 4.99620i | −0.0634802 | + | 0.280173i | ||||
\(319\) | 10.4481 | 0.584982 | ||||||||
\(320\) | 9.39525 | + | 5.77942i | 0.525210 | + | 0.323079i | ||||
\(321\) | 10.1910 | 0.568809 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.8089 | + | 19.8089i | 1.10219 | + | 1.10219i | ||||
\(324\) | 5.48406 | + | 2.61958i | 0.304670 | + | 0.145532i | ||||
\(325\) | 5.90620 | − | 5.90620i | 0.327617 | − | 0.327617i | ||||
\(326\) | −10.8798 | + | 6.86032i | −0.602576 | + | 0.379958i | ||||
\(327\) | 8.72008i | 0.482221i | ||||||||
\(328\) | 8.76777 | + | 6.92405i | 0.484119 | + | 0.382317i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.15169 | − | 3.41236i | −0.118446 | − | 0.187844i | ||||
\(331\) | 6.76260 | − | 6.76260i | 0.371706 | − | 0.371706i | −0.496392 | − | 0.868098i | \(-0.665342\pi\) |
0.868098 | + | 0.496392i | \(0.165342\pi\) | |||||||
\(332\) | 8.65233 | + | 24.4775i | 0.474858 | + | 1.34338i | ||||
\(333\) | 5.13016 | + | 5.13016i | 0.281131 | + | 0.281131i | ||||
\(334\) | 0.912997 | + | 0.206862i | 0.0499570 | + | 0.0113190i | ||||
\(335\) | −6.93391 | −0.378840 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.1949 | −1.48140 | −0.740700 | − | 0.671836i | \(-0.765506\pi\) | ||||
−0.740700 | + | 0.671836i | \(0.765506\pi\) | |||||||
\(338\) | −7.90991 | − | 1.79219i | −0.430242 | − | 0.0974821i | ||||
\(339\) | −8.30076 | − | 8.30076i | −0.450835 | − | 0.450835i | ||||
\(340\) | −17.4640 | + | 6.17318i | −0.947117 | + | 0.334788i | ||||
\(341\) | 2.06883 | − | 2.06883i | 0.112034 | − | 0.112034i | ||||
\(342\) | 7.17288 | + | 11.3755i | 0.387865 | + | 0.615115i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.27810 | − | 27.8997i | −0.176743 | − | 1.50425i | ||||
\(345\) | 6.19920i | 0.333754i | ||||||||
\(346\) | −10.7526 | + | 6.78015i | −0.578065 | + | 0.364503i | ||||
\(347\) | −4.18157 | + | 4.18157i | −0.224479 | + | 0.224479i | −0.810381 | − | 0.585903i | \(-0.800740\pi\) |
0.585903 | + | 0.810381i | \(0.300740\pi\) | |||||||
\(348\) | −3.13432 | + | 6.56166i | −0.168017 | + | 0.351742i | ||||
\(349\) | 24.5827 | + | 24.5827i | 1.31588 | + | 1.31588i | 0.917004 | + | 0.398877i | \(0.130600\pi\) |
0.398877 | + | 0.917004i | \(0.369400\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.0756 | −0.644548 | ||||||||
\(352\) | −4.45203 | + | 13.0545i | −0.237294 | + | 0.695805i | ||||
\(353\) | −33.3458 | −1.77482 | −0.887409 | − | 0.460982i | \(-0.847497\pi\) | ||||
−0.887409 | + | 0.460982i | \(0.847497\pi\) | |||||||
\(354\) | −1.86290 | + | 8.22201i | −0.0990121 | + | 0.436995i | ||||
\(355\) | 11.2873 | + | 11.2873i | 0.599068 | + | 0.599068i | ||||
\(356\) | 14.5933 | − | 30.5510i | 0.773445 | − | 1.61920i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.8845 | + | 8.12440i | −0.680966 | + | 0.429388i | ||||
\(359\) | 7.89898i | 0.416892i | 0.978034 | + | 0.208446i | \(0.0668406\pi\) | ||||
−0.978034 | + | 0.208446i | \(0.933159\pi\) | |||||||
\(360\) | −8.83118 | + | 1.03762i | −0.465444 | + | 0.0546876i | ||||
\(361\) | − | 1.60588i | − | 0.0845202i | ||||||
\(362\) | 14.9241 | + | 23.6681i | 0.784392 | + | 1.24397i | ||||
\(363\) | −3.03290 | + | 3.03290i | −0.159186 | + | 0.159186i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0686 | + | 10.0686i | 0.527013 | + | 0.527013i | ||||
\(366\) | 16.0406 | + | 3.63439i | 0.838455 | + | 0.189973i | ||||
\(367\) | −29.5941 | −1.54480 | −0.772401 | − | 0.635136i | \(-0.780944\pi\) | ||||
−0.772401 | + | 0.635136i | \(0.780944\pi\) | |||||||
\(368\) | 16.4870 | − | 13.3199i | 0.859442 | − | 0.694350i | ||||
\(369\) | −9.00607 | −0.468837 | ||||||||
\(370\) | −6.05133 | − | 1.37108i | −0.314594 | − | 0.0712791i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.678649 | + | 1.91990i | 0.0351863 | + | 0.0995424i | ||||
\(373\) | −4.31630 | + | 4.31630i | −0.223490 | + | 0.223490i | −0.809966 | − | 0.586477i | \(-0.800515\pi\) |
0.586477 | + | 0.809966i | \(0.300515\pi\) | |||||||
\(374\) | −12.3537 | − | 19.5917i | −0.638793 | − | 1.01306i | ||||
\(375\) | − | 9.47503i | − | 0.489289i | ||||||
\(376\) | −5.36729 | + | 6.79648i | −0.276797 | + | 0.350502i | ||||
\(377\) | 11.5500i | 0.594857i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.1468 | + | 15.1468i | −0.778037 | + | 0.778037i | −0.979497 | − | 0.201460i | \(-0.935432\pi\) |
0.201460 | + | 0.979497i | \(0.435432\pi\) | |||||||
\(380\) | −10.3779 | − | 4.95721i | −0.532373 | − | 0.254300i | ||||
\(381\) | 8.48573 | + | 8.48573i | 0.434737 | + | 0.434737i | ||||
\(382\) | −7.01327 | + | 30.9534i | −0.358830 | + | 1.58372i | ||||
\(383\) | −6.62147 | −0.338341 | −0.169171 | − | 0.985587i | \(-0.554109\pi\) | ||||
−0.169171 | + | 0.985587i | \(0.554109\pi\) | |||||||
\(384\) | −6.86294 | − | 6.71217i | −0.350223 | − | 0.342529i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.97318 | + | 8.70872i | −0.100432 | + | 0.443262i | ||||
\(387\) | 16.0126 | + | 16.0126i | 0.813967 | + | 0.813967i | ||||
\(388\) | −4.53918 | − | 2.16824i | −0.230442 | − | 0.110076i | ||||
\(389\) | −25.6610 | + | 25.6610i | −1.30106 | + | 1.30106i | −0.373386 | + | 0.927676i | \(0.621803\pi\) |
−0.927676 | + | 0.373386i | \(0.878197\pi\) | |||||||
\(390\) | 3.77225 | − | 2.37861i | 0.191015 | − | 0.120446i | ||||
\(391\) | 35.5921i | 1.79997i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.65981i | 0.184613i | ||||||||
\(394\) | −4.07188 | − | 6.45760i | −0.205138 | − | 0.325329i | ||||
\(395\) | −3.96699 | + | 3.96699i | −0.199601 | + | 0.199601i | ||||
\(396\) | −3.70552 | − | 10.4830i | −0.186209 | − | 0.526788i | ||||
\(397\) | 9.47099 | + | 9.47099i | 0.475336 | + | 0.475336i | 0.903636 | − | 0.428301i | \(-0.140888\pi\) |
−0.428301 | + | 0.903636i | \(0.640888\pi\) | |||||||
\(398\) | −35.3508 | − | 8.00960i | −1.77198 | − | 0.401485i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.64193 | + | 7.78980i | −0.482097 | + | 0.389490i | ||||
\(401\) | 17.5138 | 0.874598 | 0.437299 | − | 0.899316i | \(-0.355935\pi\) | ||||
0.437299 | + | 0.899316i | \(0.355935\pi\) | |||||||
\(402\) | 5.88527 | + | 1.33346i | 0.293531 | + | 0.0665067i | ||||
\(403\) | 2.28702 | + | 2.28702i | 0.113925 | + | 0.113925i | ||||
\(404\) | −22.8347 | + | 8.07163i | −1.13607 | + | 0.401579i | ||||
\(405\) | 2.96274 | − | 2.96274i | 0.147220 | − | 0.147220i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 7.75847i | − | 0.384573i | ||||||
\(408\) | 16.0100 | − | 1.88111i | 0.792614 | − | 0.0931286i | ||||
\(409\) | 10.3755i | 0.513037i | 0.966539 | + | 0.256519i | \(0.0825755\pi\) | ||||
−0.966539 | + | 0.256519i | \(0.917425\pi\) | |||||||
\(410\) | 6.51508 | − | 4.10813i | 0.321757 | − | 0.202886i | ||||
\(411\) | −6.94840 | + | 6.94840i | −0.342739 | + | 0.342739i | ||||
\(412\) | −15.3751 | + | 32.1875i | −0.757476 | + | 1.58577i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.77555 | + | 16.6636i | −0.185558 | + | 0.818971i | ||||
\(415\) | 17.8982 | 0.878589 | ||||||||
\(416\) | −14.4312 | − | 4.92157i | −0.707550 | − | 0.241300i | ||||
\(417\) | 2.70096 | 0.132266 | ||||||||
\(418\) | 3.17784 | − | 14.0256i | 0.155433 | − | 0.686013i | ||||
\(419\) | −12.6045 | − | 12.6045i | −0.615771 | − | 0.615771i | 0.328673 | − | 0.944444i | \(-0.393399\pi\) |
−0.944444 | + | 0.328673i | \(0.893399\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.6588 | + | 17.6588i | −0.860635 | + | 0.860635i | −0.991412 | − | 0.130777i | \(-0.958253\pi\) |
0.130777 | + | 0.991412i | \(0.458253\pi\) | |||||||
\(422\) | 1.24707 | − | 0.786350i | 0.0607065 | − | 0.0382789i | ||||
\(423\) | − | 6.98121i | − | 0.339438i | ||||||
\(424\) | −1.40908 | − | 11.9926i | −0.0684308 | − | 0.582412i | ||||
\(425\) | − | 20.8150i | − | 1.00968i | ||||||
\(426\) | −7.40964 | − | 11.7509i | −0.358998 | − | 0.569335i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −22.6481 | + | 8.00567i | −1.09474 | + | 0.386969i | ||||
\(429\) | 3.94304 | + | 3.94304i | 0.190372 | + | 0.190372i | ||||
\(430\) | −18.8879 | − | 4.27951i | −0.910853 | − | 0.206377i | ||||
\(431\) | 9.58438 | 0.461663 | 0.230832 | − | 0.972994i | \(-0.425855\pi\) | ||||
0.230832 | + | 0.972994i | \(0.425855\pi\) | |||||||
\(432\) | 17.8201 | + | 1.89340i | 0.857372 | + | 0.0910964i | ||||
\(433\) | 0.958633 | 0.0460690 | 0.0230345 | − | 0.999735i | \(-0.492667\pi\) | ||||
0.0230345 | + | 0.999735i | \(0.492667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.54490 | + | 3.54490i | 0.169965 | + | 0.169965i | ||||
\(436\) | −6.85014 | − | 19.3791i | −0.328062 | − | 0.928091i | ||||
\(437\) | −15.6266 | + | 15.6266i | −0.747524 | + | 0.747524i | ||||
\(438\) | −6.60960 | − | 10.4822i | −0.315819 | − | 0.500857i | ||||
\(439\) | 9.97389i | 0.476028i | 0.971262 | + | 0.238014i | \(0.0764964\pi\) | ||||
−0.971262 | + | 0.238014i | \(0.923504\pi\) | |||||||
\(440\) | 7.46242 | + | 5.89319i | 0.355757 | + | 0.280947i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 21.6579 | − | 13.6566i | 1.03016 | − | 0.649576i | ||||
\(443\) | −15.4846 | + | 15.4846i | −0.735697 | + | 0.735697i | −0.971742 | − | 0.236045i | \(-0.924149\pi\) |
0.236045 | + | 0.971742i | \(0.424149\pi\) | |||||||
\(444\) | 4.87250 | + | 2.32746i | 0.231239 | + | 0.110456i | ||||
\(445\) | −16.5050 | − | 16.5050i | −0.782412 | − | 0.782412i | ||||
\(446\) | 1.80058 | − | 7.94696i | 0.0852600 | − | 0.376300i | ||||
\(447\) | −2.75849 | −0.130472 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.77877 | −0.414296 | −0.207148 | − | 0.978310i | \(-0.566418\pi\) | ||||
−0.207148 | + | 0.978310i | \(0.566418\pi\) | |||||||
\(450\) | 2.20803 | − | 9.74523i | 0.104087 | − | 0.459395i | ||||
\(451\) | 6.81005 | + | 6.81005i | 0.320673 | + | 0.320673i | ||||
\(452\) | 24.9680 | + | 11.9265i | 1.17439 | + | 0.560975i | ||||
\(453\) | 10.8948 | − | 10.8948i | 0.511884 | − | 0.511884i | ||||
\(454\) | 30.8202 | − | 19.4339i | 1.44646 | − | 0.912078i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.85507 | + | 6.20328i | 0.367847 | + | 0.290495i | ||||
\(457\) | 1.87158i | 0.0875486i | 0.999041 | + | 0.0437743i | \(0.0139383\pi\) | ||||
−0.999041 | + | 0.0437743i | \(0.986062\pi\) | |||||||
\(458\) | 0.546989 | + | 0.867469i | 0.0255591 | + | 0.0405342i | ||||
\(459\) | −21.2788 | + | 21.2788i | −0.993209 | + | 0.993209i | ||||
\(460\) | −4.86984 | − | 13.7768i | −0.227058 | − | 0.642348i | ||||
\(461\) | −13.2713 | − | 13.2713i | −0.618107 | − | 0.618107i | 0.326939 | − | 0.945046i | \(-0.393983\pi\) |
−0.945046 | + | 0.326939i | \(0.893983\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.89824 | −0.0882189 | −0.0441095 | − | 0.999027i | \(-0.514045\pi\) | ||||
−0.0441095 | + | 0.999027i | \(0.514045\pi\) | |||||||
\(464\) | 1.81099 | − | 17.0445i | 0.0840733 | − | 0.791272i | ||||
\(465\) | 1.40385 | 0.0651021 | ||||||||
\(466\) | 19.9199 | + | 4.51335i | 0.922771 | + | 0.209077i | ||||
\(467\) | −1.08393 | − | 1.08393i | −0.0501585 | − | 0.0501585i | 0.681583 | − | 0.731741i | \(-0.261292\pi\) |
−0.731741 | + | 0.681583i | \(0.761292\pi\) | |||||||
\(468\) | 11.5885 | − | 4.09633i | 0.535681 | − | 0.189353i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.18448 | + | 5.05027i | 0.146889 | + | 0.232952i | ||||
\(471\) | 12.9728i | 0.597754i | ||||||||
\(472\) | −2.31885 | − | 19.7356i | −0.106734 | − | 0.908406i | ||||
\(473\) | − | 24.2163i | − | 1.11347i | ||||||
\(474\) | 4.12994 | − | 2.60416i | 0.189694 | − | 0.119613i | ||||
\(475\) | 9.13880 | − | 9.13880i | 0.419317 | − | 0.419317i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.88296 | + | 6.88296i | 0.315149 | + | 0.315149i | ||||
\(478\) | −2.29602 | + | 10.1336i | −0.105018 | + | 0.463500i | ||||
\(479\) | 28.2972 | 1.29293 | 0.646466 | − | 0.762942i | \(-0.276246\pi\) | ||||
0.646466 | + | 0.762942i | \(0.276246\pi\) | |||||||
\(480\) | −5.93971 | + | 2.91868i | −0.271109 | + | 0.133219i | ||||
\(481\) | 8.57672 | 0.391065 | ||||||||
\(482\) | −1.01672 | + | 4.48737i | −0.0463105 | + | 0.204394i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.35766 | − | 9.12271i | 0.198075 | − | 0.414668i | ||||
\(485\) | −2.45227 | + | 2.45227i | −0.111352 | + | 0.111352i | ||||
\(486\) | −19.1625 | + | 12.0830i | −0.869228 | + | 0.548097i | ||||
\(487\) | 6.19712i | 0.280818i | 0.990094 | + | 0.140409i | \(0.0448418\pi\) | ||||
−0.990094 | + | 0.140409i | \(0.955158\pi\) | |||||||
\(488\) | −38.5029 | + | 4.52392i | −1.74294 | + | 0.204788i | ||||
\(489\) | − | 7.71698i | − | 0.348974i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.5658 | − | 21.5658i | 0.973249 | − | 0.973249i | −0.0264026 | − | 0.999651i | \(-0.508405\pi\) |
0.999651 | + | 0.0264026i | \(0.00840519\pi\) | |||||||
\(492\) | −6.31982 | + | 2.23393i | −0.284919 | + | 0.100713i | ||||
\(493\) | 20.3527 | + | 20.3527i | 0.916638 | + | 0.916638i | ||||
\(494\) | 15.5048 | + | 3.51299i | 0.697593 | + | 0.158057i | ||||
\(495\) | −7.66525 | −0.344527 | ||||||||
\(496\) | −3.01640 | − | 3.73359i | −0.135440 | − | 0.167643i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −15.1914 | − | 3.44199i | −0.680743 | − | 0.154239i | ||||
\(499\) | 2.45487 | + | 2.45487i | 0.109895 | + | 0.109895i | 0.759916 | − | 0.650021i | \(-0.225240\pi\) |
−0.650021 | + | 0.759916i | \(0.725240\pi\) | |||||||
\(500\) | 7.44320 | + | 21.0569i | 0.332870 | + | 0.941692i | ||||
\(501\) | −0.397156 | + | 0.397156i | −0.0177436 | + | 0.0177436i | ||||
\(502\) | 2.21963 | + | 3.52012i | 0.0990671 | + | 0.157110i | ||||
\(503\) | 13.1803i | 0.587680i | 0.955855 | + | 0.293840i | \(0.0949332\pi\) | ||||
−0.955855 | + | 0.293840i | \(0.905067\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.6970i | 0.743006i | ||||||||
\(506\) | 15.4553 | − | 9.74546i | 0.687073 | − | 0.433238i | ||||
\(507\) | 3.44082 | − | 3.44082i | 0.152812 | − | 0.152812i | ||||
\(508\) | −25.5243 | − | 12.1923i | −1.13246 | − | 0.540944i | ||||
\(509\) | 1.53507 | + | 1.53507i | 0.0680410 | + | 0.0680410i | 0.740308 | − | 0.672267i | \(-0.234679\pi\) |
−0.672267 | + | 0.740308i | \(0.734679\pi\) | |||||||
\(510\) | 2.45576 | − | 10.8386i | 0.108743 | − | 0.479942i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 20.5247 | + | 9.52558i | 0.907072 | + | 0.420975i | ||||
\(513\) | −18.6849 | −0.824957 | ||||||||
\(514\) | −3.42566 | + | 15.1193i | −0.151099 | + | 0.666885i | ||||
\(515\) | 17.3891 | + | 17.3891i | 0.766257 | + | 0.766257i | ||||
\(516\) | 15.2084 | + | 7.26462i | 0.669513 | + | 0.319807i | ||||
\(517\) | −5.27893 | + | 5.27893i | −0.232167 | + | 0.232167i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 7.62680i | − | 0.334779i | ||||||
\(520\) | −6.51472 | + | 8.24945i | −0.285689 | + | 0.361762i | ||||
\(521\) | − | 10.0170i | − | 0.438854i | −0.975629 | − | 0.219427i | \(-0.929581\pi\) | ||
0.975629 | − | 0.219427i | \(-0.0704189\pi\) | |||||||
\(522\) | 7.36979 | + | 11.6877i | 0.322567 | + | 0.511559i | ||||
\(523\) | 16.3284 | − | 16.3284i | 0.713992 | − | 0.713992i | −0.253376 | − | 0.967368i | \(-0.581541\pi\) |
0.967368 | + | 0.253376i | \(0.0815409\pi\) | |||||||
\(524\) | −2.87500 | − | 8.13339i | −0.125595 | − | 0.355309i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.0589 | − | 3.18539i | −0.612997 | − | 0.138890i | ||||
\(527\) | 8.06007 | 0.351102 | ||||||||
\(528\) | −5.20054 | − | 6.43704i | −0.226324 | − | 0.280136i | ||||
\(529\) | −5.07755 | −0.220763 | ||||||||
\(530\) | −8.11887 | − | 1.83953i | −0.352661 | − | 0.0799042i | ||||
\(531\) | 11.3270 | + | 11.3270i | 0.491548 | + | 0.491548i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.52828 | + | 7.52828i | −0.326086 | + | 0.326086i | ||||
\(534\) | 10.8348 | + | 17.1830i | 0.468869 | + | 0.743579i | ||||
\(535\) | 16.5605i | 0.715974i | ||||||||
\(536\) | −14.1267 | + | 1.65982i | −0.610179 | + | 0.0716934i | ||||
\(537\) | − | 9.13891i | − | 0.394373i | ||||||
\(538\) | −2.97380 | + | 1.87515i | −0.128210 | + | 0.0808436i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.32506 | − | 11.1480i | 0.229154 | − | 0.479732i | ||||
\(541\) | −6.69916 | − | 6.69916i | −0.288020 | − | 0.288020i | 0.548277 | − | 0.836297i | \(-0.315284\pi\) |
−0.836297 | + | 0.548277i | \(0.815284\pi\) | |||||||
\(542\) | 1.76929 | − | 7.80887i | 0.0759977 | − | 0.335420i | ||||
\(543\) | −16.7877 | −0.720427 | ||||||||
\(544\) | −34.1022 | + | 16.7573i | −1.46212 | + | 0.718463i | ||||
\(545\) | −14.1702 | −0.606985 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.2058 | − | 21.2058i | −0.906695 | − | 0.906695i | 0.0893091 | − | 0.996004i | \(-0.471534\pi\) |
−0.996004 | + | 0.0893091i | \(0.971534\pi\) | |||||||
\(548\) | 9.98343 | − | 20.9002i | 0.426471 | − | 0.892812i | ||||
\(549\) | 22.0981 | − | 22.0981i | 0.943125 | − | 0.943125i | ||||
\(550\) | −9.03861 | + | 5.69936i | −0.385408 | + | 0.243021i | ||||
\(551\) | 17.8716i | 0.761357i | ||||||||
\(552\) | 1.48395 | + | 12.6298i | 0.0631611 | + | 0.537561i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −22.7568 | − | 36.0900i | −0.966844 | − | 1.53332i | ||||
\(555\) | 2.63234 | − | 2.63234i | 0.111737 | − | 0.111737i | ||||
\(556\) | −6.00248 | + | 2.12176i | −0.254562 | + | 0.0899827i | ||||
\(557\) | −16.9582 | − | 16.9582i | −0.718543 | − | 0.718543i | 0.249764 | − | 0.968307i | \(-0.419647\pi\) |
−0.968307 | + | 0.249764i | \(0.919647\pi\) | |||||||
\(558\) | 3.77359 | + | 0.855000i | 0.159749 | + | 0.0361950i | ||||
\(559\) | 26.7703 | 1.13226 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.8963 | 0.586702 | ||||||||
\(562\) | −2.20693 | − | 0.500034i | −0.0930936 | − | 0.0210927i | ||||
\(563\) | −7.49559 | − | 7.49559i | −0.315901 | − | 0.315901i | 0.531289 | − | 0.847191i | \(-0.321708\pi\) |
−0.847191 | + | 0.531289i | \(0.821708\pi\) | |||||||
\(564\) | −1.73167 | − | 4.89891i | −0.0729165 | − | 0.206281i | ||||
\(565\) | 13.4888 | − | 13.4888i | 0.567478 | − | 0.567478i | ||||
\(566\) | 15.3548 | + | 24.3512i | 0.645410 | + | 1.02356i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 25.6979 | + | 20.2941i | 1.07826 | + | 0.851520i | ||||
\(569\) | − | 44.0529i | − | 1.84679i | −0.383848 | − | 0.923396i | \(-0.625401\pi\) | ||
0.383848 | − | 0.923396i | \(-0.374599\pi\) | |||||||
\(570\) | 5.83688 | − | 3.68048i | 0.244480 | − | 0.154159i | ||||
\(571\) | 9.43664 | − | 9.43664i | 0.394911 | − | 0.394911i | −0.481523 | − | 0.876434i | \(-0.659916\pi\) |
0.876434 | + | 0.481523i | \(0.159916\pi\) | |||||||
\(572\) | −11.8603 | − | 5.66533i | −0.495905 | − | 0.236880i | ||||
\(573\) | −13.4648 | − | 13.4648i | −0.562500 | − | 0.562500i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.4204 | 0.684777 | ||||||||
\(576\) | −17.7437 | + | 4.22797i | −0.739319 | + | 0.176165i | ||||
\(577\) | −16.4631 | −0.685369 | −0.342685 | − | 0.939450i | \(-0.611336\pi\) | ||||
−0.342685 | + | 0.939450i | \(0.611336\pi\) | |||||||
\(578\) | 8.78690 | − | 38.7815i | 0.365487 | − | 1.61310i | ||||
\(579\) | −3.78831 | − | 3.78831i | −0.157437 | − | 0.157437i | ||||
\(580\) | −10.6628 | − | 5.09330i | −0.442747 | − | 0.211488i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.55300 | − | 1.60981i | 0.105825 | − | 0.0667287i | ||||
\(583\) | − | 10.4093i | − | 0.431108i | ||||||
\(584\) | 22.9232 | + | 18.1028i | 0.948570 | + | 0.749101i | ||||
\(585\) | − | 8.47366i | − | 0.350343i | ||||||
\(586\) | 0.285743 | + | 0.453160i | 0.0118039 | + | 0.0187199i | ||||
\(587\) | 21.5452 | − | 21.5452i | 0.889267 | − | 0.889267i | −0.105186 | − | 0.994453i | \(-0.533544\pi\) |
0.994453 | + | 0.105186i | \(0.0335438\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.53876 | + | 3.53876i | 0.145812 | + | 0.145812i | ||||
\(590\) | −13.3608 | − | 3.02723i | −0.550057 | − | 0.124629i | ||||
\(591\) | 4.58034 | 0.188410 | ||||||||
\(592\) | −12.6568 | − | 1.34479i | −0.520190 | − | 0.0552706i | ||||
\(593\) | −26.2918 | −1.07967 | −0.539837 | − | 0.841770i | \(-0.681514\pi\) | ||||
−0.539837 | + | 0.841770i | \(0.681514\pi\) | |||||||
\(594\) | 15.0663 | + | 3.41366i | 0.618180 | + | 0.140064i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.13034 | − | 2.16696i | 0.251109 | − | 0.0887620i | ||||
\(597\) | 15.3777 | − | 15.3777i | 0.629366 | − | 0.629366i | ||||
\(598\) | 10.7733 | + | 17.0853i | 0.440552 | + | 0.698671i | ||||
\(599\) | 27.8214i | 1.13675i | 0.822769 | + | 0.568376i | \(0.192428\pi\) | ||||
−0.822769 | + | 0.568376i | \(0.807572\pi\) | |||||||
\(600\) | −0.867846 | − | 7.38620i | −0.0354297 | − | 0.301541i | ||||
\(601\) | − | 18.3631i | − | 0.749047i | −0.927217 | − | 0.374523i | \(-0.877806\pi\) | ||
0.927217 | − | 0.374523i | \(-0.122194\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.10778 | − | 8.10778i | 0.330174 | − | 0.330174i | ||||
\(604\) | −15.6536 | + | 32.7707i | −0.636938 | + | 1.33342i | ||||
\(605\) | −4.92849 | − | 4.92849i | −0.200372 | − | 0.200372i | ||||
\(606\) | 3.21099 | − | 14.1718i | 0.130437 | − | 0.575692i | ||||
\(607\) | −9.91188 | −0.402311 | −0.201155 | − | 0.979559i | \(-0.564470\pi\) | ||||
−0.201155 | + | 0.979559i | \(0.564470\pi\) | |||||||
\(608\) | −22.3298 | − | 7.61526i | −0.905593 | − | 0.308839i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.90592 | + | 26.0661i | −0.239124 | + | 1.05539i | ||||
\(611\) | −5.83567 | − | 5.83567i | −0.236086 | − | 0.236086i | ||||
\(612\) | 13.2023 | − | 27.6388i | 0.533670 | − | 1.11723i | ||||
\(613\) | 30.5010 | − | 30.5010i | 1.23193 | − | 1.23193i | 0.268702 | − | 0.963223i | \(-0.413405\pi\) |
0.963223 | − | 0.268702i | \(-0.0865948\pi\) | |||||||
\(614\) | 20.9449 | − | 13.2069i | 0.845266 | − | 0.532988i | ||||
\(615\) | 4.62112i | 0.186341i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.78309i | − | 0.313336i | −0.987651 | − | 0.156668i | \(-0.949925\pi\) | ||
0.987651 | − | 0.156668i | \(-0.0500752\pi\) | |||||||
\(618\) | −11.4152 | − | 18.1034i | −0.459188 | − | 0.728227i | ||||
\(619\) | −27.6514 | + | 27.6514i | −1.11140 | + | 1.11140i | −0.118441 | + | 0.992961i | \(0.537790\pi\) |
−0.992961 | + | 0.118441i | \(0.962210\pi\) | |||||||
\(620\) | −3.11986 | + | 1.10281i | −0.125297 | + | 0.0442899i | ||||
\(621\) | −16.7862 | − | 16.7862i | −0.673608 | − | 0.673608i | ||||
\(622\) | −5.09591 | − | 1.15460i | −0.204327 | − | 0.0462954i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 7.11593 | − | 5.74902i | 0.284865 | − | 0.230145i | ||||
\(625\) | −0.0973335 | −0.00389334 | ||||||||
\(626\) | −14.4408 | − | 3.27192i | −0.577170 | − | 0.130772i | ||||
\(627\) | 6.10115 | + | 6.10115i | 0.243656 | + | 0.243656i | ||||
\(628\) | −10.1909 | − | 28.8301i | −0.406661 | − | 1.15045i | ||||
\(629\) | 15.1133 | − | 15.1133i | 0.602607 | − | 0.602607i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 6.10120i | − | 0.242885i | −0.992598 | − | 0.121442i | \(-0.961248\pi\) | ||
0.992598 | − | 0.121442i | \(-0.0387520\pi\) | |||||||
\(632\) | −7.13246 | + | 9.03168i | −0.283714 | + | 0.359261i | ||||
\(633\) | 0.884542i | 0.0351574i | ||||||||
\(634\) | −26.7198 | + | 16.8483i | −1.06118 | + | 0.669133i | ||||
\(635\) | −13.7894 | + | 13.7894i | −0.547215 | + | 0.547215i | ||||
\(636\) | 6.53727 | + | 3.12267i | 0.259220 | + | 0.123822i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.26508 | − | 14.4106i | 0.129266 | − | 0.570521i | ||||
\(639\) | −26.3964 | −1.04422 | ||||||||
\(640\) | 10.9073 | − | 11.1523i | 0.431151 | − | 0.440835i | ||||
\(641\) | 8.80169 | 0.347646 | 0.173823 | − | 0.984777i | \(-0.444388\pi\) | ||||
0.173823 | + | 0.984777i | \(0.444388\pi\) | |||||||
\(642\) | 3.18474 | − | 14.0560i | 0.125692 | − | 0.554747i | ||||
\(643\) | −20.3898 | − | 20.3898i | −0.804095 | − | 0.804095i | 0.179638 | − | 0.983733i | \(-0.442507\pi\) |
−0.983733 | + | 0.179638i | \(0.942507\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.21625 | − | 8.21625i | 0.323515 | − | 0.323515i | ||||
\(646\) | 33.5118 | − | 21.1311i | 1.31850 | − | 0.831392i | ||||
\(647\) | − | 50.8466i | − | 1.99898i | −0.0318632 | − | 0.999492i | \(-0.510144\pi\) | ||
0.0318632 | − | 0.999492i | \(-0.489856\pi\) | |||||||
\(648\) | 5.32686 | − | 6.74529i | 0.209259 | − | 0.264980i | ||||
\(649\) | − | 17.1300i | − | 0.672413i | ||||||
\(650\) | −6.30044 | − | 9.99187i | −0.247124 | − | 0.391913i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.06215 | + | 17.1499i | 0.237412 | + | 0.671641i | ||||
\(653\) | −1.69069 | − | 1.69069i | −0.0661618 | − | 0.0661618i | 0.673252 | − | 0.739413i | \(-0.264897\pi\) |
−0.739413 | + | 0.673252i | \(0.764897\pi\) | |||||||
\(654\) | 12.0272 | + | 2.72506i | 0.470301 | + | 0.106558i | ||||
\(655\) | −5.94722 | −0.232377 | ||||||||
\(656\) | 12.2900 | − | 9.92918i | 0.479843 | − | 0.387669i | ||||
\(657\) | −23.5463 | −0.918627 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.01195 | − | 3.01195i | −0.117329 | − | 0.117329i | 0.646005 | − | 0.763334i | \(-0.276439\pi\) |
−0.763334 | + | 0.646005i | \(0.776439\pi\) | |||||||
\(660\) | −5.37892 | + | 1.90134i | −0.209374 | + | 0.0740097i | ||||
\(661\) | −1.93721 | + | 1.93721i | −0.0753488 | + | 0.0753488i | −0.743777 | − | 0.668428i | \(-0.766967\pi\) |
0.668428 | + | 0.743777i | \(0.266967\pi\) | |||||||
\(662\) | −7.21400 | − | 11.4407i | −0.280380 | − | 0.444655i | ||||
\(663\) | 15.3619i | 0.596606i | ||||||||
\(664\) | 36.4646 | − | 4.28443i | 1.41510 | − | 0.166268i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.67899 | − | 5.47259i | 0.336304 | − | 0.212059i | ||||
\(667\) | −16.0556 | + | 16.0556i | −0.621676 | + | 0.621676i | ||||
\(668\) | 0.570631 | − | 1.19461i | 0.0220784 | − | 0.0462208i | ||||
\(669\) | 3.45694 | + | 3.45694i | 0.133653 | + | 0.133653i | ||||
\(670\) | −2.16688 | + | 9.56362i | −0.0837137 | + | 0.369475i | ||||
\(671\) | −33.4196 | −1.29015 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.6937 | 0.682041 | 0.341021 | − | 0.940056i | \(-0.389227\pi\) | ||||
0.341021 | + | 0.940056i | \(0.389227\pi\) | |||||||
\(674\) | −8.49852 | + | 37.5087i | −0.327351 | + | 1.44478i | ||||
\(675\) | 9.81696 | + | 9.81696i | 0.377855 | + | 0.377855i | ||||
\(676\) | −4.94376 | + | 10.3497i | −0.190145 | + | 0.398066i | ||||
\(677\) | −11.2232 | + | 11.2232i | −0.431342 | + | 0.431342i | −0.889085 | − | 0.457742i | \(-0.848658\pi\) |
0.457742 | + | 0.889085i | \(0.348658\pi\) | |||||||
\(678\) | −14.0429 | + | 8.85483i | −0.539314 | + | 0.340068i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.05681 | + | 26.0164i | 0.117223 | + | 0.997684i | ||||
\(681\) | 21.8606i | 0.837702i | ||||||||
\(682\) | −2.20693 | − | 3.49997i | −0.0845076 | − | 0.134021i | ||||
\(683\) | 6.78769 | − | 6.78769i | 0.259724 | − | 0.259724i | −0.565218 | − | 0.824942i | \(-0.691208\pi\) |
0.824942 | + | 0.565218i | \(0.191208\pi\) | |||||||
\(684\) | 17.9312 | − | 6.33834i | 0.685617 | − | 0.242352i | ||||
\(685\) | −11.2912 | − | 11.2912i | −0.431415 | − | 0.431415i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.615292 | −0.0234749 | ||||||||
\(688\) | −39.5052 | − | 4.19746i | −1.50612 | − | 0.160027i | ||||
\(689\) | 11.5071 | 0.438385 | ||||||||
\(690\) | 8.55028 | + | 1.93728i | 0.325503 | + | 0.0737509i | ||||
\(691\) | 34.3472 | + | 34.3472i | 1.30663 | + | 1.30663i | 0.923833 | + | 0.382795i | \(0.125038\pi\) |
0.382795 | + | 0.923833i | \(0.374962\pi\) | |||||||
\(692\) | 5.99130 | + | 16.9494i | 0.227755 | + | 0.644321i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.46069 | + | 7.07421i | 0.169326 | + | 0.268533i | ||||
\(695\) | 4.38908i | 0.166487i | ||||||||
\(696\) | 8.07071 | + | 6.37357i | 0.305919 | + | 0.241590i | ||||
\(697\) | 26.5316i | 1.00496i | ||||||||
\(698\) | 41.5880 | − | 26.2236i | 1.57413 | − | 0.992577i | ||||
\(699\) | −8.66519 | + | 8.66519i | −0.327747 | + | 0.327747i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.68514 | + | 4.68514i | 0.176955 | + | 0.176955i | 0.790027 | − | 0.613072i | \(-0.210066\pi\) |
−0.613072 | + | 0.790027i | \(0.710066\pi\) | |||||||
\(702\) | −3.77368 | + | 16.6553i | −0.142428 | + | 0.628615i | ||||
\(703\) | 13.2709 | 0.500523 | ||||||||
\(704\) | 16.6141 | + | 10.2201i | 0.626168 | + | 0.385183i | ||||
\(705\) | −3.58214 | −0.134911 | ||||||||
\(706\) | −10.4207 | + | 45.9923i | −0.392189 | + | 1.73094i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.7581 | + | 5.13883i | 0.404313 | + | 0.193129i | ||||
\(709\) | 17.0134 | − | 17.0134i | 0.638951 | − | 0.638951i | −0.311346 | − | 0.950297i | \(-0.600780\pi\) |
0.950297 | + | 0.311346i | \(0.100780\pi\) | |||||||
\(710\) | 19.0954 | − | 12.0407i | 0.716637 | − | 0.451880i | ||||
\(711\) | − | 9.27715i | − | 0.347920i | ||||||
\(712\) | −37.5771 | − | 29.6752i | −1.40826 | − | 1.11213i | ||||
\(713\) | 6.35836i | 0.238122i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.40747 | + | 6.40747i | −0.239626 | + | 0.239626i | ||||
\(716\) | 7.17915 | + | 20.3099i | 0.268298 | + | 0.759016i | ||||
\(717\) | −4.40814 | − | 4.40814i | −0.164625 | − | 0.164625i | ||||
\(718\) | 10.8947 | + | 2.46847i | 0.406587 | + | 0.0921223i | ||||
\(719\) | 24.5042 | 0.913853 | 0.456927 | − | 0.889504i | \(-0.348950\pi\) | ||||
0.456927 | + | 0.889504i | \(0.348950\pi\) | |||||||
\(720\) | −1.32863 | + | 12.5047i | −0.0495152 | + | 0.466023i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.21492 | − | 0.501845i | −0.0824308 | − | 0.0186768i | ||||
\(723\) | −1.95201 | − | 1.95201i | −0.0725961 | − | 0.0725961i | ||||
\(724\) | 37.3081 | − | 13.1877i | 1.38655 | − | 0.490117i | ||||
\(725\) | 9.38968 | − | 9.38968i | 0.348724 | − | 0.348724i | ||||
\(726\) | 3.23535 | + | 5.13094i | 0.120075 | + | 0.190427i | ||||
\(727\) | − | 41.6544i | − | 1.54488i | −0.635090 | − | 0.772438i | \(-0.719037\pi\) | ||
0.635090 | − | 0.772438i | \(-0.280963\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 4.47546i | − | 0.165758i | ||||||
\(730\) | 17.0336 | − | 10.7407i | 0.630442 | − | 0.397529i | ||||
\(731\) | 47.1727 | − | 47.1727i | 1.74475 | − | 1.74475i | ||||
\(732\) | 10.0255 | − | 20.9883i | 0.370553 | − | 0.775749i | ||||
\(733\) | −18.5348 | − | 18.5348i | −0.684598 | − | 0.684598i | 0.276434 | − | 0.961033i | \(-0.410847\pi\) |
−0.961033 | + | 0.276434i | \(0.910847\pi\) | |||||||
\(734\) | −9.24829 | + | 40.8178i | −0.341361 | + | 1.50661i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.2193 | − | 26.9022i | −0.487272 | − | 0.991630i | ||||
\(737\) | −12.2616 | −0.451662 | ||||||||
\(738\) | −2.81444 | + | 12.4217i | −0.103601 | + | 0.457247i | ||||
\(739\) | 4.93924 | + | 4.93924i | 0.181693 | + | 0.181693i | 0.792093 | − | 0.610400i | \(-0.208991\pi\) |
−0.610400 | + | 0.792093i | \(0.708991\pi\) | |||||||
\(740\) | −3.78213 | + | 7.91786i | −0.139034 | + | 0.291066i | ||||
\(741\) | −6.74461 | + | 6.74461i | −0.247769 | + | 0.247769i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 17.8484i | − | 0.654796i | −0.944887 | − | 0.327398i | \(-0.893828\pi\) | ||
0.944887 | − | 0.327398i | \(-0.106172\pi\) | |||||||
\(744\) | 2.86011 | − | 0.336051i | 0.104857 | − | 0.0123202i | ||||
\(745\) | − | 4.48257i | − | 0.164229i | ||||||
\(746\) | 4.60441 | + | 7.30214i | 0.168580 | + | 0.267350i | ||||
\(747\) | −20.9283 | + | 20.9283i | −0.765726 | + | 0.765726i | ||||
\(748\) | −30.8825 | + | 10.9164i | −1.12918 | + | 0.399142i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −13.0685 | − | 2.96099i | −0.477193 | − | 0.108120i | ||||
\(751\) | 18.3471 | 0.669495 | 0.334747 | − | 0.942308i | \(-0.391349\pi\) | ||||
0.334747 | + | 0.942308i | \(0.391349\pi\) | |||||||
\(752\) | 7.69677 | + | 9.52679i | 0.280672 | + | 0.347406i | ||||
\(753\) | −2.49680 | −0.0909885 | ||||||||
\(754\) | 15.9304 | + | 3.60943i | 0.580152 | + | 0.131448i | ||||
\(755\) | 17.7042 | + | 17.7042i | 0.644322 | + | 0.644322i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.90437 | − | 4.90437i | 0.178252 | − | 0.178252i | −0.612341 | − | 0.790594i | \(-0.709772\pi\) |
0.790594 | + | 0.612341i | \(0.209772\pi\) | |||||||
\(758\) | 16.1578 | + | 25.6247i | 0.586878 | + | 0.930730i | ||||
\(759\) | 10.9624i | 0.397909i | ||||||||
\(760\) | −10.0804 | + | 12.7646i | −0.365654 | + | 0.463019i | ||||
\(761\) | 3.48443i | 0.126311i | 0.998004 | + | 0.0631553i | \(0.0201163\pi\) | ||||
−0.998004 | + | 0.0631553i | \(0.979884\pi\) | |||||||
\(762\) | 14.3558 | − | 9.05215i | 0.520056 | − | 0.327925i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 40.5010 | + | 19.3462i | 1.46527 | + | 0.699920i | ||||
\(765\) | −14.9317 | − | 14.9317i | −0.539857 | − | 0.539857i | ||||
\(766\) | −2.06924 | + | 9.13269i | −0.0747646 | + | 0.329978i | ||||
\(767\) | 18.9367 | 0.683764 | ||||||||
\(768\) | −11.4025 | + | 7.36816i | −0.411452 | + | 0.265875i | ||||
\(769\) | 13.5559 | 0.488837 | 0.244418 | − | 0.969670i | \(-0.421403\pi\) | ||||
0.244418 | + | 0.969670i | \(0.421403\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.57694 | − | 6.57694i | −0.236863 | − | 0.236863i | ||||
\(772\) | 11.3949 | + | 5.44303i | 0.410112 | + | 0.195899i | ||||
\(773\) | −20.3801 | + | 20.3801i | −0.733022 | + | 0.733022i | −0.971217 | − | 0.238195i | \(-0.923444\pi\) |
0.238195 | + | 0.971217i | \(0.423444\pi\) | |||||||
\(774\) | 27.0895 | − | 17.0815i | 0.973711 | − | 0.613980i | ||||
\(775\) | − | 3.71851i | − | 0.133573i | ||||||
\(776\) | −4.40906 | + | 5.58310i | −0.158276 | + | 0.200422i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27.3738 | + | 43.4121i | 0.981399 | + | 1.55640i | ||||
\(779\) | −11.6487 | + | 11.6487i | −0.417357 | + | 0.417357i | ||||
\(780\) | −2.10187 | − | 5.94621i | −0.0752590 | − | 0.212909i | ||||
\(781\) | 19.9599 | + | 19.9599i | 0.714223 | + | 0.714223i | ||||
\(782\) | 49.0905 | + | 11.1227i | 1.75547 | + | 0.397746i | ||||
\(783\) | −19.1978 | −0.686073 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.0809 | −0.752409 | ||||||||
\(786\) | 5.04780 | + | 1.14371i | 0.180049 | + | 0.0407946i | ||||
\(787\) | −27.7178 | − | 27.7178i | −0.988034 | − | 0.988034i | 0.0118952 | − | 0.999929i | \(-0.496214\pi\) |
−0.999929 | + | 0.0118952i | \(0.996214\pi\) | |||||||
\(788\) | −10.1791 | + | 3.59813i | −0.362617 | + | 0.128178i | ||||
\(789\) | 6.11565 | − | 6.11565i | 0.217723 | − | 0.217723i | ||||
\(790\) | 4.23178 | + | 6.71118i | 0.150560 | + | 0.238773i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −15.6166 | + | 1.83489i | −0.554913 | + | 0.0651999i | ||||
\(793\) | − | 36.9442i | − | 1.31193i | ||||||
\(794\) | 16.0226 | − | 10.1032i | 0.568622 | − | 0.358548i | ||||
\(795\) | 3.53172 | − | 3.53172i | 0.125257 | − | 0.125257i | ||||
\(796\) | −22.0946 | + | 46.2547i | −0.783121 | + | 1.63945i | ||||
\(797\) | 2.87837 | + | 2.87837i | 0.101957 | + | 0.101957i | 0.756245 | − | 0.654288i | \(-0.227032\pi\) |
−0.654288 | + | 0.756245i | \(0.727032\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.5664 | −0.727588 | ||||||||
\(800\) | 7.73096 | + | 15.7330i | 0.273331 | + | 0.556246i | ||||
\(801\) | 38.5984 | 1.36381 | ||||||||
\(802\) | 5.47314 | − | 24.1560i | 0.193263 | − | 0.852978i | ||||
\(803\) | 17.8048 | + | 17.8048i | 0.628318 | + | 0.628318i | ||||
\(804\) | 3.67835 | − | 7.70058i | 0.129725 | − | 0.271578i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.86909 | − | 2.43968i | 0.136283 | − | 0.0859341i | ||||
\(807\) | − | 2.10931i | − | 0.0742511i | ||||||
\(808\) | 3.99688 | + | 34.0173i | 0.140610 | + | 1.19672i | ||||
\(809\) | − | 21.5478i | − | 0.757581i | −0.925482 | − | 0.378791i | \(-0.876340\pi\) | ||
0.925482 | − | 0.378791i | \(-0.123660\pi\) | |||||||
\(810\) | −3.16050 | − | 5.01223i | −0.111049 | − | 0.176112i | ||||
\(811\) | −20.4977 | + | 20.4977i | −0.719772 | + | 0.719772i | −0.968558 | − | 0.248787i | \(-0.919968\pi\) |
0.248787 | + | 0.968558i | \(0.419968\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.39687 | + | 3.39687i | 0.119134 | + | 0.119134i | ||||
\(814\) | −10.7009 | − | 2.42455i | −0.375066 | − | 0.0849806i | ||||
\(815\) | 12.5402 | 0.439263 | ||||||||
\(816\) | 2.40867 | − | 22.6697i | 0.0843205 | − | 0.793599i | ||||
\(817\) | 41.4222 | 1.44918 | ||||||||
\(818\) | 14.3105 | + | 3.24240i | 0.500355 | + | 0.113368i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.63016 | − | 10.2698i | −0.126771 | − | 0.358635i | ||||
\(821\) | −9.10771 | + | 9.10771i | −0.317861 | + | 0.317861i | −0.847945 | − | 0.530084i | \(-0.822160\pi\) |
0.530084 | + | 0.847945i | \(0.322160\pi\) | |||||||
\(822\) | 7.41221 | + | 11.7550i | 0.258530 | + | 0.410003i | ||||
\(823\) | 41.4587i | 1.44516i | 0.691287 | + | 0.722580i | \(0.257044\pi\) | ||||
−0.691287 | + | 0.722580i | \(0.742956\pi\) | |||||||
\(824\) | 39.5900 | + | 31.2649i | 1.37918 | + | 1.08916i | ||||
\(825\) | − | 6.41104i | − | 0.223204i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.8134 | − | 14.8134i | 0.515111 | − | 0.515111i | −0.400977 | − | 0.916088i | \(-0.631329\pi\) |
0.916088 | + | 0.400977i | \(0.131329\pi\) | |||||||
\(828\) | 21.8034 | + | 10.4149i | 0.757722 | + | 0.361942i | ||||
\(829\) | −17.2948 | − | 17.2948i | −0.600675 | − | 0.600675i | 0.339817 | − | 0.940492i | \(-0.389635\pi\) |
−0.940492 | + | 0.339817i | \(0.889635\pi\) | |||||||
\(830\) | 5.59327 | − | 24.6862i | 0.194145 | − | 0.856870i | ||||
\(831\) | 25.5985 | 0.888002 | ||||||||
\(832\) | −11.2979 | + | 18.3663i | −0.391685 | + | 0.636738i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.844060 | − | 3.72530i | 0.0292274 | − | 0.128997i | ||||
\(835\) | −0.645381 | − | 0.645381i | −0.0223343 | − | 0.0223343i | ||||
\(836\) | −18.3517 | − | 8.76610i | −0.634708 | − | 0.303182i | ||||
\(837\) | −3.80136 | + | 3.80136i | −0.131394 | + | 0.131394i | ||||
\(838\) | −21.3238 | + | 13.4459i | −0.736618 | + | 0.464479i | ||||
\(839\) | − | 26.6645i | − | 0.920562i | −0.887773 | − | 0.460281i | \(-0.847749\pi\) | ||
0.887773 | − | 0.460281i | \(-0.152251\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 10.6378i | − | 0.366820i | ||||||
\(842\) | 18.8375 | + | 29.8743i | 0.649182 | + | 1.02954i | ||||
\(843\) | 0.960018 | − | 0.960018i | 0.0330648 | − | 0.0330648i | ||||
\(844\) | −0.694860 | − | 1.96577i | −0.0239181 | − | 0.0676645i | ||||
\(845\) | 5.59137 | + | 5.59137i | 0.192349 | + | 0.192349i | ||||
\(846\) | −9.62886 | − | 2.18166i | −0.331047 | − | 0.0750069i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −16.9812 | − | 1.80426i | −0.583136 | − | 0.0619586i | ||||
\(849\) | −17.2722 | −0.592779 | ||||||||
\(850\) | −28.7092 | − | 6.50478i | −0.984717 | − | 0.223112i | ||||
\(851\) | 11.9224 | + | 11.9224i | 0.408696 | + | 0.408696i | ||||
\(852\) | −18.5231 | + | 6.54755i | −0.634590 | + | 0.224315i | ||||
\(853\) | 12.4072 | − | 12.4072i | 0.424815 | − | 0.424815i | −0.462043 | − | 0.886858i | \(-0.652883\pi\) |
0.886858 | + | 0.462043i | \(0.152883\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 13.1115i | − | 0.448404i | ||||||
\(856\) | 3.96422 | + | 33.7393i | 0.135494 | + | 1.15319i | ||||
\(857\) | − | 2.47165i | − | 0.0844298i | −0.999109 | − | 0.0422149i | \(-0.986559\pi\) | ||
0.999109 | − | 0.0422149i | \(-0.0134414\pi\) | |||||||
\(858\) | 6.67066 | − | 4.20623i | 0.227733 | − | 0.143598i | ||||
\(859\) | −18.9839 | + | 18.9839i | −0.647723 | + | 0.647723i | −0.952442 | − | 0.304719i | \(-0.901437\pi\) |
0.304719 | + | 0.952442i | \(0.401437\pi\) | |||||||
\(860\) | −11.8051 | + | 24.7138i | −0.402550 | + | 0.842733i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.99516 | − | 13.2193i | 0.102016 | − | 0.450251i | ||||
\(863\) | −35.3848 | −1.20451 | −0.602255 | − | 0.798303i | \(-0.705731\pi\) | ||||
−0.602255 | + | 0.798303i | \(0.705731\pi\) | |||||||
\(864\) | 8.18035 | − | 23.9868i | 0.278301 | − | 0.816047i | ||||
\(865\) | 12.3936 | 0.421395 | ||||||||
\(866\) | 0.299577 | − | 1.32220i | 0.0101800 | − | 0.0449301i | ||||
\(867\) | 16.8700 | + | 16.8700i | 0.572935 | + | 0.572935i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.01504 | + | 7.01504i | −0.237969 | + | 0.237969i | ||||
\(870\) | 5.99712 | − | 3.78152i | 0.203321 | − | 0.128206i | ||||
\(871\) | − | 13.5548i | − | 0.459286i | ||||||
\(872\) | −28.8694 | + | 3.39203i | −0.977641 | + | 0.114869i | ||||
\(873\) | − | 5.73484i | − | 0.194095i | ||||||
\(874\) | 16.6697 | + | 26.4365i | 0.563862 | + | 0.894228i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.5231 | + | 5.84059i | −0.558263 | + | 0.197335i | ||||
\(877\) | 4.32355 | + | 4.32355i | 0.145996 | + | 0.145996i | 0.776327 | − | 0.630331i | \(-0.217081\pi\) |
−0.630331 | + | 0.776327i | \(0.717081\pi\) | |||||||
\(878\) | 13.7565 | + | 3.11688i | 0.464260 | + | 0.105190i | ||||
\(879\) | −0.321424 | −0.0108414 | ||||||||
\(880\) | 10.4603 | − | 8.45092i | 0.352615 | − | 0.284881i | ||||
\(881\) | 26.3944 | 0.889249 | 0.444625 | − | 0.895717i | \(-0.353337\pi\) | ||||
0.444625 | + | 0.895717i | \(0.353337\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.3078 | − | 29.3078i | −0.986286 | − | 0.986286i | 0.0136216 | − | 0.999907i | \(-0.495664\pi\) |
−0.999907 | + | 0.0136216i | \(0.995664\pi\) | |||||||
\(884\) | −12.0677 | − | 34.1395i | −0.405879 | − | 1.14824i | ||||
\(885\) | 5.81199 | − | 5.81199i | 0.195368 | − | 0.195368i | ||||
\(886\) | 16.5182 | + | 26.1962i | 0.554940 | + | 0.880080i | ||||
\(887\) | 18.2241i | 0.611904i | 0.952047 | + | 0.305952i | \(0.0989747\pi\) | ||||
−0.952047 | + | 0.305952i | \(0.901025\pi\) | |||||||
\(888\) | 4.73283 | − | 5.99308i | 0.158823 | − | 0.201114i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −27.9225 | + | 17.6067i | −0.935963 | + | 0.590178i | ||||
\(891\) | 5.23916 | − | 5.23916i | 0.175519 | − | 0.175519i | ||||
\(892\) | −10.3982 | − | 4.96692i | −0.348157 | − | 0.166305i | ||||
\(893\) | −9.02967 | − | 9.02967i | −0.302166 | − | 0.302166i | ||||
\(894\) | −0.862040 | + | 3.80466i | −0.0288309 | + | 0.127247i | ||||
\(895\) | 14.8508 | 0.496407 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.1185 | −0.404626 | ||||||||
\(898\) | −2.74340 | + | 12.1081i | −0.0915485 | + | 0.404054i | ||||
\(899\) | 3.63591 | + | 3.63591i | 0.121264 | + | 0.121264i | ||||
\(900\) | −12.7511 | − | 6.09085i | −0.425038 | − | 0.203028i | ||||
\(901\) | 20.2770 | − | 20.2770i | 0.675525 | − | 0.675525i | ||||
\(902\) | 11.5210 | − | 7.26462i | 0.383606 | − | 0.241885i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 24.2523 | − | 30.7101i | 0.806618 | − | 1.02140i | ||||
\(905\) | − | 27.2801i | − | 0.906821i | ||||||
\(906\) | −11.6221 | − | 18.4314i | −0.386117 | − | 0.612343i | ||||
\(907\) | −13.0697 | + | 13.0697i | −0.433974 | + | 0.433974i | −0.889978 | − | 0.456004i | \(-0.849280\pi\) |
0.456004 | + | 0.889978i | \(0.349280\pi\) | |||||||
\(908\) | −17.1728 | − | 48.5821i | −0.569900 | − | 1.61225i | ||||
\(909\) | −19.5237 | − | 19.5237i | −0.647560 | − | 0.647560i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.3908 | 0.708708 | 0.354354 | − | 0.935111i | \(-0.384701\pi\) | ||||
0.354354 | + | 0.935111i | \(0.384701\pi\) | |||||||
\(912\) | 11.0106 | − | 8.89559i | 0.364599 | − | 0.294562i | ||||
\(913\) | 31.6504 | 1.04747 | ||||||||
\(914\) | 2.58138 | + | 0.584876i | 0.0853844 | + | 0.0193460i | ||||
\(915\) | −11.3388 | − | 11.3388i | −0.374849 | − | 0.374849i | ||||
\(916\) | 1.36740 | − | 0.483348i | 0.0451801 | − | 0.0159703i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 22.6991 | + | 35.9986i | 0.749184 | + | 1.18813i | ||||
\(919\) | − | 10.5692i | − | 0.348645i | −0.984689 | − | 0.174322i | \(-0.944227\pi\) | ||
0.984689 | − | 0.174322i | \(-0.0557735\pi\) | |||||||
\(920\) | −20.5236 | + | 2.41143i | −0.676643 | + | 0.0795025i | ||||
\(921\) | 14.8561i | 0.489525i | ||||||||
\(922\) | −22.4519 | + | 14.1572i | −0.739412 | + | 0.466241i | ||||
\(923\) | −22.0650 | + | 22.0650i | −0.726279 | + | 0.726279i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.97251 | − | 6.97251i | −0.229255 | − | 0.229255i | ||||
\(926\) | −0.593210 | + | 2.61816i | −0.0194941 | + | 0.0860381i | ||||
\(927\) | −40.6661 | −1.33565 | ||||||||
\(928\) | −22.9428 | − | 7.82431i | −0.753134 | − | 0.256846i | ||||
\(929\) | 17.5372 | 0.575378 | 0.287689 | − | 0.957724i | \(-0.407113\pi\) | ||||
0.287689 | + | 0.957724i | \(0.407113\pi\) | |||||||
\(930\) | 0.438710 | − | 1.93627i | 0.0143859 | − | 0.0634928i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 12.4501 | − | 26.0641i | 0.407817 | − | 0.853759i | ||||
\(933\) | 2.21673 | − | 2.21673i | 0.0725725 | − | 0.0725725i | ||||
\(934\) | −1.83375 | + | 1.15629i | −0.0600023 | + | 0.0378348i | ||||
\(935\) | 22.5816i | 0.738497i | ||||||||
\(936\) | −2.02840 | − | 17.2637i | −0.0663005 | − | 0.564280i | ||||
\(937\) | − | 43.7391i | − | 1.42890i | −0.699689 | − | 0.714448i | \(-0.746678\pi\) | ||
0.699689 | − | 0.714448i | \(-0.253322\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.28177 | − | 6.28177i | 0.204998 | − | 0.204998i | ||||
\(940\) | 7.96078 | − | 2.81398i | 0.259652 | − | 0.0917819i | ||||
\(941\) | −7.61563 | − | 7.61563i | −0.248262 | − | 0.248262i | 0.571995 | − | 0.820257i | \(-0.306170\pi\) |
−0.820257 | + | 0.571995i | \(0.806170\pi\) | |||||||
\(942\) | 17.8928 | + | 4.05405i | 0.582978 | + | 0.132088i | ||||
\(943\) | −20.9300 | −0.681576 | ||||||||
\(944\) | −27.9451 | − | 2.96919i | −0.909536 | − | 0.0966389i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −33.4004 | − | 7.56769i | −1.08594 | − | 0.246047i | ||||
\(947\) | 9.69441 | + | 9.69441i | 0.315026 | + | 0.315026i | 0.846853 | − | 0.531827i | \(-0.178494\pi\) |
−0.531827 | + | 0.846853i | \(0.678494\pi\) | |||||||
\(948\) | −2.30117 | − | 6.51004i | −0.0747387 | − | 0.211436i | ||||
\(949\) | −19.6826 | + | 19.6826i | −0.638924 | + | 0.638924i | ||||
\(950\) | −9.74882 | − | 15.4606i | −0.316293 | − | 0.501610i | ||||
\(951\) | − | 18.9522i | − | 0.614568i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.19629i | 0.103538i | 0.998659 | + | 0.0517690i | \(0.0164860\pi\) | ||||
−0.998659 | + | 0.0517690i | \(0.983514\pi\) | |||||||
\(954\) | 11.6443 | − | 7.34239i | 0.376998 | − | 0.237719i | ||||
\(955\) | 21.8804 | − | 21.8804i | 0.708034 | − | 0.708034i | ||||
\(956\) | 13.2593 | + | 6.33359i | 0.428836 | + | 0.204843i | ||||
\(957\) | 6.26864 | + | 6.26864i | 0.202636 | + | 0.202636i | ||||
\(958\) | 8.84300 | − | 39.0290i | 0.285704 | − | 1.26097i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.16942 | + | 9.10447i | 0.0700177 | + | 0.293845i | ||||
\(961\) | −29.5601 | −0.953552 | ||||||||
\(962\) | 2.68026 | − | 11.8295i | 0.0864151 | − | 0.381397i | ||||
\(963\) | −19.3641 | − | 19.3641i | −0.624001 | − | 0.624001i | ||||
\(964\) | 5.87149 | + | 2.80464i | 0.189108 | + | 0.0903314i | ||||
\(965\) | 6.15604 | − | 6.15604i | 0.198170 | − | 0.198170i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.7940i | 0.829479i | 0.909940 | + | 0.414739i | \(0.136127\pi\) | ||||
−0.909940 | + | 0.414739i | \(0.863873\pi\) | |||||||
\(968\) | −11.2207 | − | 8.86120i | −0.360648 | − | 0.284810i | ||||
\(969\) | 23.7698i | 0.763595i | ||||||||
\(970\) | 2.61595 | + | 4.14864i | 0.0839932 | + | 0.133205i | ||||
\(971\) | 11.9004 | − | 11.9004i | 0.381901 | − | 0.381901i | −0.489885 | − | 0.871787i | \(-0.662961\pi\) |
0.871787 | + | 0.489885i | \(0.162961\pi\) | |||||||
\(972\) | 10.6772 | + | 30.2059i | 0.342472 | + | 0.968855i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.54740 | + | 1.93663i | 0.273876 | + | 0.0620535i | ||||
\(975\) | 7.08719 | 0.226972 | ||||||||
\(976\) | −5.79269 | + | 54.5190i | −0.185419 | + | 1.74511i | ||||
\(977\) | 2.74136 | 0.0877038 | 0.0438519 | − | 0.999038i | \(-0.486037\pi\) | ||||
0.0438519 | + | 0.999038i | \(0.486037\pi\) | |||||||
\(978\) | −10.6437 | − | 2.41159i | −0.340347 | − | 0.0771141i | ||||
\(979\) | −29.1867 | − | 29.1867i | −0.932810 | − | 0.932810i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.5691 | − | 16.5691i | 0.529012 | − | 0.529012i | ||||
\(982\) | −23.0053 | − | 36.4840i | −0.734127 | − | 1.16425i | ||||
\(983\) | 44.6295i | 1.42346i | 0.702454 | + | 0.711729i | \(0.252088\pi\) | ||||
−0.702454 | + | 0.711729i | \(0.747912\pi\) | |||||||
\(984\) | 1.10619 | + | 9.41474i | 0.0352641 | + | 0.300131i | ||||
\(985\) | 7.44310i | 0.237157i | ||||||||
\(986\) | 34.4318 | − | 21.7112i | 1.09653 | − | 0.691425i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.69062 | − | 20.2872i | 0.308300 | − | 0.645422i | ||||
\(989\) | 37.2132 | + | 37.2132i | 1.18331 | + | 1.18331i | ||||
\(990\) | −2.39542 | + | 10.5723i | −0.0761315 | + | 0.336010i | ||||
\(991\) | 1.08451 | 0.0344508 | 0.0172254 | − | 0.999852i | \(-0.494517\pi\) | ||||
0.0172254 | + | 0.999852i | \(0.494517\pi\) | |||||||
\(992\) | −6.09220 | + | 2.99361i | −0.193428 | + | 0.0950473i | ||||
\(993\) | 8.11482 | 0.257516 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.9888 | + | 24.9888i | 0.792200 | + | 0.792200i | ||||
\(996\) | −9.49476 | + | 19.8772i | −0.300853 | + | 0.629832i | ||||
\(997\) | −29.3910 | + | 29.3910i | −0.930823 | + | 0.930823i | −0.997757 | − | 0.0669342i | \(-0.978678\pi\) |
0.0669342 | + | 0.997757i | \(0.478678\pi\) | |||||||
\(998\) | 4.15305 | − | 2.61874i | 0.131463 | − | 0.0828946i | ||||
\(999\) | 14.2557i | 0.451031i |
(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 | 784.2.m.h.589.4 | 12 | ||
7.2 | even | 3 | 784.2.x.m.557.1 | 24 | |||
7.3 | odd | 6 | 784.2.x.l.765.5 | 24 | |||
7.4 | even | 3 | 784.2.x.m.765.5 | 24 | |||
7.5 | odd | 6 | 784.2.x.l.557.1 | 24 | |||
7.6 | odd | 2 | 112.2.m.d.29.4 | ✓ | 12 | ||
16.5 | even | 4 | inner | 784.2.m.h.197.4 | 12 | ||
28.27 | even | 2 | 448.2.m.d.337.5 | 12 | |||
56.13 | odd | 2 | 896.2.m.g.673.5 | 12 | |||
56.27 | even | 2 | 896.2.m.h.673.2 | 12 | |||
112.5 | odd | 12 | 784.2.x.l.165.5 | 24 | |||
112.13 | odd | 4 | 896.2.m.g.225.5 | 12 | |||
112.27 | even | 4 | 448.2.m.d.113.5 | 12 | |||
112.37 | even | 12 | 784.2.x.m.165.5 | 24 | |||
112.53 | even | 12 | 784.2.x.m.373.1 | 24 | |||
112.69 | odd | 4 | 112.2.m.d.85.4 | yes | 12 | ||
112.83 | even | 4 | 896.2.m.h.225.2 | 12 | |||
112.101 | odd | 12 | 784.2.x.l.373.1 | 24 | |||
224.27 | even | 8 | 7168.2.a.bi.1.5 | 12 | |||
224.69 | odd | 8 | 7168.2.a.bj.1.8 | 12 | |||
224.139 | even | 8 | 7168.2.a.bi.1.8 | 12 | |||
224.181 | odd | 8 | 7168.2.a.bj.1.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.m.d.29.4 | ✓ | 12 | 7.6 | odd | 2 | ||
112.2.m.d.85.4 | yes | 12 | 112.69 | odd | 4 | ||
448.2.m.d.113.5 | 12 | 112.27 | even | 4 | |||
448.2.m.d.337.5 | 12 | 28.27 | even | 2 | |||
784.2.m.h.197.4 | 12 | 16.5 | even | 4 | inner | ||
784.2.m.h.589.4 | 12 | 1.1 | even | 1 | trivial | ||
784.2.x.l.165.5 | 24 | 112.5 | odd | 12 | |||
784.2.x.l.373.1 | 24 | 112.101 | odd | 12 | |||
784.2.x.l.557.1 | 24 | 7.5 | odd | 6 | |||
784.2.x.l.765.5 | 24 | 7.3 | odd | 6 | |||
784.2.x.m.165.5 | 24 | 112.37 | even | 12 | |||
784.2.x.m.373.1 | 24 | 112.53 | even | 12 | |||
784.2.x.m.557.1 | 24 | 7.2 | even | 3 | |||
784.2.x.m.765.5 | 24 | 7.4 | even | 3 | |||
896.2.m.g.225.5 | 12 | 112.13 | odd | 4 | |||
896.2.m.g.673.5 | 12 | 56.13 | odd | 2 | |||
896.2.m.h.225.2 | 12 | 112.83 | even | 4 | |||
896.2.m.h.673.2 | 12 | 56.27 | even | 2 | |||
7168.2.a.bi.1.5 | 12 | 224.27 | even | 8 | |||
7168.2.a.bi.1.8 | 12 | 224.139 | even | 8 | |||
7168.2.a.bj.1.5 | 12 | 224.181 | odd | 8 | |||
7168.2.a.bj.1.8 | 12 | 224.69 | odd | 8 |