Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [243,2,Mod(28,243)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(243, 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("243.28");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 243 = 3^{5} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 243.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: | \(1.94036476912\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{9})\) |
Coefficient field: | 12.0.1952986685049.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 55.1 | ||
Root | \(0.500000 - 0.258654i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 243.55 |
Dual form | 243.2.e.c.190.1 |
$q$-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 \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{8}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.390411 | − | 0.142098i | 0.276062 | − | 0.100478i | −0.200279 | − | 0.979739i | \(-0.564185\pi\) |
0.476341 | + | 0.879261i | \(0.341963\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.39986 | + | 1.17462i | −0.699930 | + | 0.587311i | ||||
\(5\) | 0.384663 | + | 2.18153i | 0.172027 | + | 0.975611i | 0.941520 | + | 0.336957i | \(0.109398\pi\) |
−0.769494 | + | 0.638655i | \(0.779491\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.01089 | − | 0.848241i | −0.382082 | − | 0.320605i | 0.431437 | − | 0.902143i | \(-0.358007\pi\) |
−0.813519 | + | 0.581538i | \(0.802451\pi\) | |||||||
\(8\) | −0.795075 | + | 1.37711i | −0.281102 | + | 0.486882i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.460168 | + | 0.797034i | 0.145518 | + | 0.252044i | ||||
\(11\) | −0.905608 | + | 5.13596i | −0.273051 | + | 1.54855i | 0.472034 | + | 0.881580i | \(0.343520\pi\) |
−0.745085 | + | 0.666969i | \(0.767591\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0169695 | + | 0.00617638i | 0.00470648 | + | 0.00171302i | 0.344372 | − | 0.938833i | \(-0.388092\pi\) |
−0.339666 | + | 0.940546i | \(0.610314\pi\) | |||||||
\(14\) | −0.515197 | − | 0.187516i | −0.137692 | − | 0.0501159i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.519924 | − | 2.94863i | 0.129981 | − | 0.737159i | ||||
\(17\) | 1.56640 | + | 2.71308i | 0.379907 | + | 0.658019i | 0.991048 | − | 0.133503i | \(-0.0426226\pi\) |
−0.611141 | + | 0.791522i | \(0.709289\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.208676 | + | 0.361438i | −0.0478736 | + | 0.0829195i | −0.888969 | − | 0.457967i | \(-0.848578\pi\) |
0.841096 | + | 0.540886i | \(0.181911\pi\) | |||||||
\(20\) | −3.10095 | − | 2.60201i | −0.693394 | − | 0.581827i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.376249 | + | 2.13382i | 0.0802166 | + | 0.454931i | ||||
\(23\) | −0.792386 | + | 0.664891i | −0.165224 | + | 0.138639i | −0.721651 | − | 0.692257i | \(-0.756616\pi\) |
0.556427 | + | 0.830897i | \(0.312172\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0873421 | − | 0.0317899i | 0.0174684 | − | 0.00635798i | ||||
\(26\) | 0.00750270 | 0.00147140 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.41147 | 0.455726 | ||||||||
\(29\) | 7.33639 | − | 2.67023i | 1.36233 | − | 0.495849i | 0.445558 | − | 0.895253i | \(-0.353005\pi\) |
0.916775 | + | 0.399404i | \(0.130783\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.85709 | − | 2.39738i | 0.513148 | − | 0.430583i | −0.349087 | − | 0.937090i | \(-0.613508\pi\) |
0.862235 | + | 0.506508i | \(0.169064\pi\) | |||||||
\(32\) | −0.768264 | − | 4.35704i | −0.135811 | − | 0.770224i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.997061 | + | 0.836633i | 0.170995 | + | 0.143481i | ||||
\(35\) | 1.46161 | − | 2.53159i | 0.247058 | − | 0.427916i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.21238 | − | 3.83195i | −0.363713 | − | 0.629969i | 0.624856 | − | 0.780740i | \(-0.285158\pi\) |
−0.988569 | + | 0.150771i | \(0.951824\pi\) | |||||||
\(38\) | −0.0301099 | + | 0.170762i | −0.00488446 | + | 0.0277012i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.31005 | − | 1.20476i | −0.523365 | − | 0.190489i | ||||
\(41\) | 3.45331 | + | 1.25690i | 0.539317 | + | 0.196295i | 0.597294 | − | 0.802023i | \(-0.296243\pi\) |
−0.0579766 | + | 0.998318i | \(0.518465\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.44265 | + | 8.18166i | −0.220002 | + | 1.24769i | 0.652012 | + | 0.758209i | \(0.273925\pi\) |
−0.872013 | + | 0.489482i | \(0.837186\pi\) | |||||||
\(44\) | −4.76508 | − | 8.25337i | −0.718363 | − | 1.24424i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.214876 | + | 0.372177i | −0.0316818 | + | 0.0548745i | ||||
\(47\) | −5.43731 | − | 4.56245i | −0.793114 | − | 0.665501i | 0.153400 | − | 0.988164i | \(-0.450978\pi\) |
−0.946514 | + | 0.322663i | \(0.895422\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.913143 | − | 5.17869i | −0.130449 | − | 0.739813i | ||||
\(50\) | 0.0295820 | − | 0.0248222i | 0.00418353 | − | 0.00351039i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.0310098 | + | 0.0112866i | −0.00430028 | + | 0.00156517i | ||||
\(53\) | −1.30057 | −0.178648 | −0.0893238 | − | 0.996003i | \(-0.528471\pi\) | ||||
−0.0893238 | + | 0.996003i | \(0.528471\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.5526 | −1.55775 | ||||||||
\(56\) | 1.97186 | − | 0.717698i | 0.263501 | − | 0.0959064i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.48477 | − | 2.08497i | 0.326266 | − | 0.273770i | ||||
\(59\) | −0.642813 | − | 3.64557i | −0.0836871 | − | 0.474613i | −0.997632 | − | 0.0687752i | \(-0.978091\pi\) |
0.913945 | − | 0.405838i | \(-0.133020\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.29661 | + | 4.44439i | 0.678162 | + | 0.569045i | 0.915469 | − | 0.402389i | \(-0.131820\pi\) |
−0.237307 | + | 0.971435i | \(0.576265\pi\) | |||||||
\(62\) | 0.774775 | − | 1.34195i | 0.0983965 | − | 0.170428i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.07506 | + | 3.59410i | 0.259382 | + | 0.449263i | ||||
\(65\) | −0.00694645 | + | 0.0393953i | −0.000861601 | + | 0.00488638i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3618 | + | 3.77139i | 1.26590 | + | 0.460748i | 0.885743 | − | 0.464176i | \(-0.153649\pi\) |
0.380152 | + | 0.924924i | \(0.375872\pi\) | |||||||
\(68\) | −5.37958 | − | 1.95801i | −0.652370 | − | 0.237443i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.210896 | − | 1.19605i | 0.0252069 | − | 0.142955i | ||||
\(71\) | 3.04214 | + | 5.26914i | 0.361035 | + | 0.625332i | 0.988132 | − | 0.153610i | \(-0.0490900\pi\) |
−0.627096 | + | 0.778942i | \(0.715757\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.273486 | − | 0.473692i | 0.0320092 | − | 0.0554415i | −0.849577 | − | 0.527465i | \(-0.823143\pi\) |
0.881586 | + | 0.472023i | \(0.156476\pi\) | |||||||
\(74\) | −1.40825 | − | 1.18166i | −0.163705 | − | 0.137365i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.132435 | − | 0.751078i | −0.0151914 | − | 0.0861545i | ||||
\(77\) | 5.27200 | − | 4.42374i | 0.600801 | − | 0.504132i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.459645 | + | 0.167297i | −0.0517141 | + | 0.0188224i | −0.367748 | − | 0.929926i | \(-0.619871\pi\) |
0.316034 | + | 0.948748i | \(0.397649\pi\) | |||||||
\(80\) | 6.63254 | 0.741540 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.52681 | 0.168608 | ||||||||
\(83\) | −4.33543 | + | 1.57797i | −0.475875 | + | 0.173205i | −0.568812 | − | 0.822468i | \(-0.692597\pi\) |
0.0929366 | + | 0.995672i | \(0.470375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.31614 | + | 4.46077i | −0.576616 | + | 0.483838i | ||||
\(86\) | 0.599371 | + | 3.39920i | 0.0646318 | + | 0.366545i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.35275 | − | 5.33059i | −0.677206 | − | 0.568243i | ||||
\(89\) | 1.68653 | − | 2.92116i | 0.178772 | − | 0.309642i | −0.762688 | − | 0.646766i | \(-0.776121\pi\) |
0.941460 | + | 0.337124i | \(0.109454\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0119153 | − | 0.0206379i | −0.00124906 | − | 0.00216344i | ||||
\(92\) | 0.328234 | − | 1.86151i | 0.0342208 | − | 0.194076i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.77110 | − | 1.00860i | −0.285817 | − | 0.104029i | ||||
\(95\) | −0.868758 | − | 0.316202i | −0.0891327 | − | 0.0324417i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.72630 | − | 9.79033i | 0.175279 | − | 0.994057i | −0.762542 | − | 0.646939i | \(-0.776049\pi\) |
0.937821 | − | 0.347119i | \(-0.112840\pi\) | |||||||
\(98\) | −1.09238 | − | 1.89206i | −0.110347 | − | 0.191127i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.0849256 | + | 0.147095i | −0.00849256 | + | 0.0147095i | ||||
\(101\) | 10.5710 | + | 8.87014i | 1.05186 | + | 0.882612i | 0.993288 | − | 0.115671i | \(-0.0369020\pi\) |
0.0585685 | + | 0.998283i | \(0.481346\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.792725 | + | 4.49576i | 0.0781095 | + | 0.442981i | 0.998632 | + | 0.0522911i | \(0.0166524\pi\) |
−0.920522 | + | 0.390690i | \(0.872237\pi\) | |||||||
\(104\) | −0.0219975 | + | 0.0184581i | −0.00215704 | + | 0.00180997i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.507758 | + | 0.184809i | −0.0493178 | + | 0.0179502i | ||||
\(107\) | −11.2965 | −1.09207 | −0.546035 | − | 0.837762i | \(-0.683864\pi\) | ||||
−0.546035 | + | 0.837762i | \(0.683864\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.5032 | 1.38915 | 0.694577 | − | 0.719419i | \(-0.255592\pi\) | ||||
0.694577 | + | 0.719419i | \(0.255592\pi\) | |||||||
\(110\) | −4.51026 | + | 1.64160i | −0.430037 | + | 0.156521i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.02674 | + | 2.53974i | −0.286000 | + | 0.239983i | ||||
\(113\) | 2.18075 | + | 12.3676i | 0.205148 | + | 1.16345i | 0.897207 | + | 0.441609i | \(0.145592\pi\) |
−0.692060 | + | 0.721840i | \(0.743297\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.75528 | − | 1.47286i | −0.163681 | − | 0.137345i | ||||
\(116\) | −7.13341 | + | 12.3554i | −0.662321 | + | 1.14717i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.768989 | − | 1.33193i | −0.0707912 | − | 0.122614i | ||||
\(119\) | 0.717884 | − | 4.07132i | 0.0658083 | − | 0.373217i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.2213 | − | 5.54010i | −1.38375 | − | 0.503646i | ||||
\(122\) | 2.69939 | + | 0.982498i | 0.244391 | + | 0.0889512i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.18351 | + | 6.71200i | −0.106282 | + | 0.602755i | ||||
\(125\) | 5.64092 | + | 9.77035i | 0.504539 | + | 0.873887i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.19749 | − | 7.27027i | 0.372467 | − | 0.645132i | −0.617477 | − | 0.786589i | \(-0.711845\pi\) |
0.989944 | + | 0.141456i | \(0.0451785\pi\) | |||||||
\(128\) | 8.09919 | + | 6.79603i | 0.715874 | + | 0.600690i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.00288601 | + | 0.0163674i | 0.000253120 | + | 0.00143552i | ||||
\(131\) | −11.9004 | + | 9.98564i | −1.03974 | + | 0.872449i | −0.991978 | − | 0.126409i | \(-0.959655\pi\) |
−0.0477666 | + | 0.998859i | \(0.515210\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.517536 | − | 0.188368i | 0.0448761 | − | 0.0163335i | ||||
\(134\) | 4.58126 | 0.395761 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.98162 | −0.427170 | ||||||||
\(137\) | −11.2833 | + | 4.10677i | −0.963994 | + | 0.350865i | −0.775597 | − | 0.631228i | \(-0.782551\pi\) |
−0.188396 | + | 0.982093i | \(0.560329\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.70743 | − | 3.95001i | 0.399279 | − | 0.335035i | −0.420936 | − | 0.907090i | \(-0.638298\pi\) |
0.820215 | + | 0.572055i | \(0.193854\pi\) | |||||||
\(140\) | 0.927605 | + | 5.26071i | 0.0783970 | + | 0.444611i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.93642 | + | 1.62485i | 0.162500 | + | 0.136354i | ||||
\(143\) | −0.0470893 | + | 0.0815610i | −0.00393780 | + | 0.00682047i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.64723 | + | 14.9774i | 0.718113 | + | 1.24381i | ||||
\(146\) | 0.0394613 | − | 0.223796i | 0.00326584 | − | 0.0185215i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.59812 | + | 2.76549i | 0.624561 | + | 0.227322i | ||||
\(149\) | −0.829580 | − | 0.301942i | −0.0679618 | − | 0.0247361i | 0.307816 | − | 0.951446i | \(-0.400402\pi\) |
−0.375777 | + | 0.926710i | \(0.622624\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.42834 | − | 8.10051i | 0.116237 | − | 0.659210i | −0.869894 | − | 0.493239i | \(-0.835813\pi\) |
0.986131 | − | 0.165971i | \(-0.0530760\pi\) | |||||||
\(152\) | −0.331826 | − | 0.574740i | −0.0269147 | − | 0.0466176i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.42964 | − | 2.47621i | 0.115204 | − | 0.199539i | ||||
\(155\) | 6.32899 | + | 5.31065i | 0.508356 | + | 0.426562i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.18099 | + | 12.3690i | 0.174062 | + | 0.987155i | 0.939221 | + | 0.343313i | \(0.111549\pi\) |
−0.765159 | + | 0.643841i | \(0.777340\pi\) | |||||||
\(158\) | −0.155678 | + | 0.130629i | −0.0123851 | + | 0.0103923i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.20951 | − | 3.35199i | 0.728076 | − | 0.264998i | ||||
\(161\) | 1.36501 | 0.107578 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.31466 | 0.259624 | 0.129812 | − | 0.991539i | \(-0.458563\pi\) | ||||
0.129812 | + | 0.991539i | \(0.458563\pi\) | |||||||
\(164\) | −6.31054 | + | 2.29685i | −0.492771 | + | 0.179354i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.46837 | + | 1.23211i | −0.113968 | + | 0.0956303i | ||||
\(167\) | −3.57072 | − | 20.2506i | −0.276311 | − | 1.56704i | −0.734767 | − | 0.678320i | \(-0.762708\pi\) |
0.458456 | − | 0.888717i | \(-0.348403\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.95833 | − | 8.35603i | −0.766025 | − | 0.642771i | ||||
\(170\) | −1.44161 | + | 2.49694i | −0.110567 | + | 0.191507i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.59085 | − | 13.1477i | −0.578797 | − | 1.00251i | ||||
\(173\) | 2.43685 | − | 13.8201i | 0.185270 | − | 1.05072i | −0.740337 | − | 0.672236i | \(-0.765334\pi\) |
0.925608 | − | 0.378485i | \(-0.123555\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.115259 | − | 0.0419509i | −0.00871277 | − | 0.00317119i | ||||
\(176\) | 14.6732 | + | 5.34061i | 1.10603 | + | 0.402564i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.243350 | − | 1.38010i | 0.0182398 | − | 0.103443i | ||||
\(179\) | −5.09500 | − | 8.82479i | −0.380818 | − | 0.659596i | 0.610361 | − | 0.792123i | \(-0.291024\pi\) |
−0.991179 | + | 0.132527i | \(0.957691\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.0274 | + | 20.8320i | −0.893987 | + | 1.54843i | −0.0589331 | + | 0.998262i | \(0.518770\pi\) |
−0.835054 | + | 0.550169i | \(0.814563\pi\) | |||||||
\(182\) | −0.00758444 | − | 0.00636410i | −0.000562196 | − | 0.000471739i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.285622 | − | 1.61984i | −0.0210563 | − | 0.119416i | ||||
\(185\) | 7.50851 | − | 6.30039i | 0.552037 | − | 0.463214i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.3528 | + | 5.58796i | −1.12271 | + | 0.408632i | ||||
\(188\) | 12.9706 | 0.945981 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.384104 | −0.0278658 | ||||||||
\(191\) | −10.2862 | + | 3.74388i | −0.744285 | + | 0.270898i | −0.686199 | − | 0.727414i | \(-0.740722\pi\) |
−0.0580861 | + | 0.998312i | \(0.518500\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.27785 | + | 6.94594i | −0.595853 | + | 0.499980i | −0.890110 | − | 0.455747i | \(-0.849372\pi\) |
0.294257 | + | 0.955726i | \(0.404928\pi\) | |||||||
\(194\) | −0.717219 | − | 4.06755i | −0.0514933 | − | 0.292033i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.36128 | + | 6.17684i | 0.525805 | + | 0.441203i | ||||
\(197\) | 11.0367 | − | 19.1161i | 0.786331 | − | 1.36196i | −0.141870 | − | 0.989885i | \(-0.545311\pi\) |
0.928201 | − | 0.372080i | \(-0.121355\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.44338 | − | 11.1603i | −0.456759 | − | 0.791130i | 0.542028 | − | 0.840360i | \(-0.317657\pi\) |
−0.998787 | + | 0.0492301i | \(0.984323\pi\) | |||||||
\(200\) | −0.0256653 | + | 0.145555i | −0.00181481 | + | 0.0102923i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.38747 | + | 1.96088i | 0.379061 | + | 0.137967i | ||||
\(203\) | −9.68131 | − | 3.52371i | −0.679495 | − | 0.247316i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.41361 | + | 8.01700i | −0.0987311 | + | 0.559932i | ||||
\(206\) | 0.948326 | + | 1.64255i | 0.0660730 | + | 0.114442i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.0270347 | − | 0.0468255i | 0.00187452 | − | 0.00324676i | ||||
\(209\) | −1.66735 | − | 1.39907i | −0.115333 | − | 0.0967759i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.16680 | − | 23.6311i | −0.286854 | − | 1.62683i | −0.698586 | − | 0.715526i | \(-0.746187\pi\) |
0.411732 | − | 0.911305i | \(-0.364924\pi\) | |||||||
\(212\) | 1.82062 | − | 1.52768i | 0.125041 | − | 0.104922i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.41026 | + | 1.60520i | −0.301479 | + | 0.109729i | ||||
\(215\) | −18.4035 | −1.25511 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.92177 | −0.334112 | ||||||||
\(218\) | 5.66220 | − | 2.06087i | 0.383492 | − | 0.139580i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 16.1720 | − | 13.5700i | 1.09032 | − | 0.914886i | ||||
\(221\) | 0.00982391 | + | 0.0557142i | 0.000660828 | + | 0.00374774i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.5942 | + | 13.9242i | 1.11123 | + | 0.932432i | 0.998128 | − | 0.0611519i | \(-0.0194774\pi\) |
0.113100 | + | 0.993584i | \(0.463922\pi\) | |||||||
\(224\) | −2.91919 | + | 5.05618i | −0.195047 | + | 0.337831i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.60880 | + | 4.51858i | 0.173535 | + | 0.300571i | ||||
\(227\) | 3.75807 | − | 21.3131i | 0.249432 | − | 1.41460i | −0.560538 | − | 0.828128i | \(-0.689406\pi\) |
0.809970 | − | 0.586471i | \(-0.199483\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.1537 | + | 3.69565i | 0.670976 | + | 0.244215i | 0.654968 | − | 0.755656i | \(-0.272682\pi\) |
0.0160082 | + | 0.999872i | \(0.494904\pi\) | |||||||
\(230\) | −0.894571 | − | 0.325597i | −0.0589862 | − | 0.0214692i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.15578 | + | 12.2261i | −0.141534 | + | 0.802680i | ||||
\(233\) | −3.81950 | − | 6.61557i | −0.250224 | − | 0.433400i | 0.713364 | − | 0.700794i | \(-0.247171\pi\) |
−0.963587 | + | 0.267394i | \(0.913838\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.86160 | − | 13.6167i | 0.512834 | − | 0.888255i | ||||
\(236\) | 5.18202 | + | 4.34823i | 0.337321 | + | 0.283046i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.298256 | − | 1.69150i | −0.0193331 | − | 0.109643i | ||||
\(239\) | −2.47547 | + | 2.07716i | −0.160125 | + | 0.134360i | −0.719330 | − | 0.694669i | \(-0.755551\pi\) |
0.559205 | + | 0.829029i | \(0.311106\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.9441 | − | 9.07891i | 1.60679 | − | 0.584824i | 0.625988 | − | 0.779832i | \(-0.284696\pi\) |
0.980802 | + | 0.195009i | \(0.0624735\pi\) | |||||||
\(242\) | −6.72979 | −0.432608 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.6350 | −0.808873 | ||||||||
\(245\) | 10.9462 | − | 3.98410i | 0.699329 | − | 0.254535i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.00577350 | + | 0.00484454i | −0.000367359 | + | 0.000308251i | ||||
\(248\) | 1.02986 | + | 5.84063i | 0.0653962 | + | 0.370880i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.59062 | + | 3.01289i | 0.227091 | + | 0.190552i | ||||
\(251\) | 2.24965 | − | 3.89651i | 0.141997 | − | 0.245945i | −0.786252 | − | 0.617906i | \(-0.787981\pi\) |
0.928248 | + | 0.371961i | \(0.121314\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.69726 | − | 4.67179i | −0.169575 | − | 0.293713i | ||||
\(254\) | 0.605656 | − | 3.43485i | 0.0380022 | − | 0.215521i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.67195 | − | 1.33648i | −0.229497 | − | 0.0835301i | ||||
\(257\) | −12.9071 | − | 4.69779i | −0.805121 | − | 0.293040i | −0.0935139 | − | 0.995618i | \(-0.529810\pi\) |
−0.711607 | + | 0.702578i | \(0.752032\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.01394 | + | 5.75033i | −0.0630031 | + | 0.357308i | ||||
\(260\) | −0.0365505 | − | 0.0633073i | −0.00226677 | − | 0.00392615i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.22711 | + | 5.58952i | −0.199372 | + | 0.345322i | ||||
\(263\) | −18.5402 | − | 15.5571i | −1.14324 | − | 0.959292i | −0.143700 | − | 0.989621i | \(-0.545900\pi\) |
−0.999540 | + | 0.0303291i | \(0.990344\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.500283 | − | 2.83725i | −0.0307321 | − | 0.174291i | ||||
\(266\) | 0.175285 | − | 0.147081i | 0.0107474 | − | 0.00901814i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −18.9350 | + | 6.89179i | −1.15664 | + | 0.420983i | ||||
\(269\) | 12.0062 | 0.732032 | 0.366016 | − | 0.930609i | \(-0.380722\pi\) | ||||
0.366016 | + | 0.930609i | \(0.380722\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.71777 | 0.225839 | 0.112919 | − | 0.993604i | \(-0.463980\pi\) | ||||
0.112919 | + | 0.993604i | \(0.463980\pi\) | |||||||
\(272\) | 8.81429 | − | 3.20814i | 0.534445 | − | 0.194522i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.82154 | + | 3.20665i | −0.230868 | + | 0.193721i | ||||
\(275\) | 0.0841740 | + | 0.477374i | 0.00507588 | + | 0.0287868i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.9891 | − | 15.0947i | −1.08086 | − | 0.906950i | −0.0848689 | − | 0.996392i | \(-0.527047\pi\) |
−0.995992 | + | 0.0894421i | \(0.971492\pi\) | |||||||
\(278\) | 1.27654 | − | 2.21104i | 0.0765621 | − | 0.132609i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.32418 | + | 4.02560i | 0.138897 | + | 0.240576i | ||||
\(281\) | −3.53751 | + | 20.0622i | −0.211030 | + | 1.19681i | 0.676633 | + | 0.736320i | \(0.263438\pi\) |
−0.887663 | + | 0.460493i | \(0.847673\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.9004 | − | 3.96741i | −0.647960 | − | 0.235838i | −0.00293048 | − | 0.999996i | \(-0.500933\pi\) |
−0.645030 | + | 0.764157i | \(0.723155\pi\) | |||||||
\(284\) | −10.4478 | − | 3.80269i | −0.619964 | − | 0.225648i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.00679451 | + | 0.0385336i | −0.000401768 | + | 0.00227854i | ||||
\(287\) | −2.42478 | − | 4.19984i | −0.143130 | − | 0.247909i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.59280 | − | 6.22291i | 0.211341 | − | 0.366053i | ||||
\(290\) | 5.50423 | + | 4.61860i | 0.323220 | + | 0.271213i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.173567 | + | 0.984347i | 0.0101572 | + | 0.0576045i | ||||
\(293\) | 24.1872 | − | 20.2955i | 1.41303 | − | 1.18567i | 0.458081 | − | 0.888910i | \(-0.348537\pi\) |
0.954951 | − | 0.296764i | \(-0.0959075\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.70567 | − | 2.80463i | 0.448642 | − | 0.163292i | ||||
\(296\) | 7.03603 | 0.408961 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.366782 | −0.0212471 | ||||||||
\(299\) | −0.0175530 | + | 0.00638876i | −0.00101511 | + | 0.000369472i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.39838 | − | 7.04708i | 0.484075 | − | 0.406187i | ||||
\(302\) | −0.593426 | − | 3.36549i | −0.0341479 | − | 0.193662i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.957252 | + | 0.803230i | 0.0549022 | + | 0.0460684i | ||||
\(305\) | −7.65816 | + | 13.2643i | −0.438505 | + | 0.759513i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.06027 | + | 7.03259i | 0.231732 | + | 0.401371i | 0.958318 | − | 0.285704i | \(-0.0922275\pi\) |
−0.726586 | + | 0.687075i | \(0.758894\pi\) | |||||||
\(308\) | −2.18385 | + | 12.3852i | −0.124436 | + | 0.705714i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.22553 | + | 1.17400i | 0.183198 | + | 0.0666786i | ||||
\(311\) | 22.4103 | + | 8.15669i | 1.27077 | + | 0.462523i | 0.887370 | − | 0.461058i | \(-0.152530\pi\) |
0.383402 | + | 0.923581i | \(0.374752\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.67295 | − | 26.5016i | 0.264131 | − | 1.49796i | −0.507367 | − | 0.861730i | \(-0.669381\pi\) |
0.771498 | − | 0.636231i | \(-0.219508\pi\) | |||||||
\(314\) | 2.60909 | + | 4.51908i | 0.147240 | + | 0.255026i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.446928 | − | 0.774102i | 0.0251417 | − | 0.0435466i | ||||
\(317\) | −6.38294 | − | 5.35592i | −0.358501 | − | 0.300818i | 0.445692 | − | 0.895187i | \(-0.352958\pi\) |
−0.804193 | + | 0.594368i | \(0.797402\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.07028 | + | 40.0976i | 0.395860 | + | 2.24503i | ||||
\(320\) | −7.04246 | + | 5.90933i | −0.393685 | + | 0.330341i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.532913 | − | 0.193964i | 0.0296981 | − | 0.0108092i | ||||
\(323\) | −1.30748 | −0.0727501 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.00167849 | 9.31061e−5 | ||||||||
\(326\) | 1.29408 | − | 0.471006i | 0.0716724 | − | 0.0260866i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.47654 | + | 3.75626i | −0.247176 | + | 0.207405i | ||||
\(329\) | 1.62649 | + | 9.22431i | 0.0896715 | + | 0.508553i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.91820 | − | 4.12686i | −0.270329 | − | 0.226833i | 0.497538 | − | 0.867442i | \(-0.334237\pi\) |
−0.767867 | + | 0.640609i | \(0.778682\pi\) | |||||||
\(332\) | 4.21548 | − | 7.30143i | 0.231355 | − | 0.400718i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.27161 | − | 7.39865i | −0.233732 | − | 0.404836i | ||||
\(335\) | −4.24160 | + | 24.0553i | −0.231743 | + | 1.31428i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.02410 | − | 2.55656i | −0.382627 | − | 0.139265i | 0.143543 | − | 0.989644i | \(-0.454150\pi\) |
−0.526170 | + | 0.850379i | \(0.676373\pi\) | |||||||
\(338\) | −5.07521 | − | 1.84723i | −0.276055 | − | 0.100476i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.20213 | − | 12.4889i | 0.119427 | − | 0.677306i | ||||
\(341\) | 9.72545 | + | 16.8450i | 0.526663 | + | 0.912206i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.08839 | + | 14.0095i | −0.436732 | + | 0.756442i | ||||
\(344\) | −10.1200 | − | 8.49172i | −0.545636 | − | 0.457843i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.01243 | − | 5.74177i | −0.0544285 | − | 0.308680i | ||||
\(347\) | −24.0955 | + | 20.2186i | −1.29352 | + | 1.08539i | −0.302290 | + | 0.953216i | \(0.597751\pi\) |
−0.991227 | + | 0.132173i | \(0.957805\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.1381 | + | 4.05395i | −0.596210 | + | 0.217003i | −0.622459 | − | 0.782653i | \(-0.713866\pi\) |
0.0262485 | + | 0.999655i | \(0.491644\pi\) | |||||||
\(350\) | −0.0509595 | −0.00272390 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 23.0733 | 1.22981 | ||||||||
\(353\) | 7.71214 | − | 2.80699i | 0.410476 | − | 0.149401i | −0.128525 | − | 0.991706i | \(-0.541024\pi\) |
0.539001 | + | 0.842305i | \(0.318802\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.3246 | + | 8.66337i | −0.547973 | + | 0.459804i | ||||
\(356\) | 1.07035 | + | 6.07025i | 0.0567284 | + | 0.321723i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.24312 | − | 2.72130i | −0.171404 | − | 0.143825i | ||||
\(359\) | −8.86365 | + | 15.3523i | −0.467806 | + | 0.810263i | −0.999323 | − | 0.0367840i | \(-0.988289\pi\) |
0.531517 | + | 0.847047i | \(0.321622\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.41291 | + | 16.3036i | 0.495416 | + | 0.858086i | ||||
\(362\) | −1.73543 | + | 9.84210i | −0.0912120 | + | 0.517289i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.0409214 | + | 0.0148942i | 0.00214486 | + | 0.000780667i | ||||
\(365\) | 1.13858 | + | 0.414408i | 0.0595958 | + | 0.0216911i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.52845 | + | 20.0108i | −0.184184 | + | 1.04456i | 0.742816 | + | 0.669495i | \(0.233490\pi\) |
−0.927000 | + | 0.375062i | \(0.877622\pi\) | |||||||
\(368\) | 1.54854 | + | 2.68215i | 0.0807232 | + | 0.139817i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.03613 | − | 3.52668i | 0.105853 | − | 0.183343i | ||||
\(371\) | 1.31474 | + | 1.10320i | 0.0682581 | + | 0.0572753i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.68116 | − | 9.53435i | −0.0870474 | − | 0.493670i | −0.996896 | − | 0.0787298i | \(-0.974914\pi\) |
0.909849 | − | 0.414940i | \(-0.136198\pi\) | |||||||
\(374\) | −5.19986 | + | 4.36320i | −0.268878 | + | 0.225616i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.6061 | − | 3.86029i | 0.546966 | − | 0.199079i | ||||
\(377\) | 0.140987 | 0.00726119 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.12905 | −0.212095 | −0.106048 | − | 0.994361i | \(-0.533820\pi\) | ||||
−0.106048 | + | 0.994361i | \(0.533820\pi\) | |||||||
\(380\) | 1.58756 | − | 0.577824i | 0.0814400 | − | 0.0296417i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.48385 | + | 2.92330i | −0.178249 | + | 0.149569i | ||||
\(383\) | 0.824861 | + | 4.67802i | 0.0421484 | + | 0.239036i | 0.998603 | − | 0.0528469i | \(-0.0168295\pi\) |
−0.956454 | + | 0.291882i | \(0.905718\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.6785 | + | 9.79940i | 0.595190 | + | 0.499424i | ||||
\(386\) | −2.24476 | + | 3.88803i | −0.114255 | + | 0.197896i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.08336 | + | 15.7328i | 0.461138 | + | 0.798714i | ||||
\(389\) | −3.78784 | + | 21.4819i | −0.192051 | + | 1.08918i | 0.724505 | + | 0.689270i | \(0.242069\pi\) |
−0.916556 | + | 0.399907i | \(0.869043\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.04509 | − | 1.10832i | −0.153997 | − | 0.0560503i | ||||
\(392\) | 7.85765 | + | 2.85995i | 0.396871 | + | 0.144449i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.59248 | − | 9.03141i | 0.0802281 | − | 0.454996i | ||||
\(395\) | −0.541773 | − | 0.938378i | −0.0272595 | − | 0.0472149i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.4245 | − | 30.1802i | 0.874512 | − | 1.51470i | 0.0172294 | − | 0.999852i | \(-0.494515\pi\) |
0.857282 | − | 0.514847i | \(-0.172151\pi\) | |||||||
\(398\) | −4.10141 | − | 3.44149i | −0.205585 | − | 0.172507i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.0483256 | − | 0.274068i | −0.00241628 | − | 0.0137034i | ||||
\(401\) | −14.4216 | + | 12.1012i | −0.720181 | + | 0.604304i | −0.927435 | − | 0.373983i | \(-0.877992\pi\) |
0.207254 | + | 0.978287i | \(0.433547\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0632904 | − | 0.0230358i | 0.00315272 | − | 0.00114750i | ||||
\(404\) | −25.2170 | −1.25459 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.28040 | −0.212433 | ||||||||
\(407\) | 21.6843 | − | 7.89243i | 1.07485 | − | 0.391213i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.87201 | + | 4.08810i | −0.240905 | + | 0.202144i | −0.755244 | − | 0.655443i | \(-0.772482\pi\) |
0.514339 | + | 0.857587i | \(0.328037\pi\) | |||||||
\(410\) | 0.587309 | + | 3.33079i | 0.0290051 | + | 0.164496i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.39053 | − | 5.36229i | −0.314839 | − | 0.264181i | ||||
\(413\) | −2.44251 | + | 4.23055i | −0.120188 | + | 0.208172i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.11007 | − | 8.85090i | −0.250843 | − | 0.434474i | ||||
\(416\) | 0.0138737 | − | 0.0786817i | 0.000680215 | − | 0.00385769i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.849756 | − | 0.309286i | −0.0415629 | − | 0.0151277i | ||||
\(419\) | 22.8514 | + | 8.31724i | 1.11636 | + | 0.406324i | 0.833324 | − | 0.552784i | \(-0.186435\pi\) |
0.283040 | + | 0.959108i | \(0.408657\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.38746 | + | 7.86865i | −0.0676204 | + | 0.383495i | 0.932150 | + | 0.362072i | \(0.117931\pi\) |
−0.999771 | + | 0.0214224i | \(0.993181\pi\) | |||||||
\(422\) | −4.98469 | − | 8.63373i | −0.242651 | − | 0.420283i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.03405 | − | 1.79103i | 0.0502181 | − | 0.0869803i | ||||
\(425\) | 0.223061 | + | 0.187170i | 0.0108200 | + | 0.00907910i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.58441 | − | 8.98561i | −0.0766748 | − | 0.434844i | ||||
\(428\) | 15.8135 | − | 13.2691i | 0.764373 | − | 0.641385i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.18492 | + | 2.61510i | −0.346487 | + | 0.126111i | ||||
\(431\) | 9.87124 | 0.475481 | 0.237740 | − | 0.971329i | \(-0.423593\pi\) | ||||
0.237740 | + | 0.971329i | \(0.423593\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.10369 | −0.293325 | −0.146662 | − | 0.989187i | \(-0.546853\pi\) | ||||
−0.146662 | + | 0.989187i | \(0.546853\pi\) | |||||||
\(434\) | −1.92151 | + | 0.699373i | −0.0922356 | + | 0.0335710i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −20.3024 | + | 17.0358i | −0.972310 | + | 0.815865i | ||||
\(437\) | −0.0749645 | − | 0.425145i | −0.00358604 | − | 0.0203374i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.5933 | − | 9.72796i | −0.553320 | − | 0.464290i | 0.322744 | − | 0.946486i | \(-0.395395\pi\) |
−0.876063 | + | 0.482196i | \(0.839839\pi\) | |||||||
\(440\) | 9.18520 | − | 15.9092i | 0.437887 | − | 0.758443i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.0117522 | + | 0.0203554i | 0.000558996 | + | 0.000968210i | ||||
\(443\) | −0.125512 | + | 0.711813i | −0.00596324 | + | 0.0338192i | −0.987644 | − | 0.156713i | \(-0.949910\pi\) |
0.981681 | + | 0.190532i | \(0.0610214\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.02135 | + | 2.55556i | 0.332844 | + | 0.121145i | ||||
\(446\) | 8.45714 | + | 3.07815i | 0.400457 | + | 0.145754i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.951004 | − | 5.39341i | 0.0449307 | − | 0.254815i | ||||
\(449\) | −0.834224 | − | 1.44492i | −0.0393695 | − | 0.0681899i | 0.845669 | − | 0.533707i | \(-0.179202\pi\) |
−0.885039 | + | 0.465517i | \(0.845868\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.58275 | + | 16.5978i | −0.451234 | + | 0.781560i | ||||
\(452\) | −17.5800 | − | 14.7514i | −0.826896 | − | 0.693848i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.56135 | − | 8.85487i | −0.0732779 | − | 0.415580i | ||||
\(455\) | 0.0404388 | − | 0.0339322i | 0.00189580 | − | 0.00159077i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.4150 | + | 3.79076i | −0.487195 | + | 0.177324i | −0.573926 | − | 0.818907i | \(-0.694580\pi\) |
0.0867310 | + | 0.996232i | \(0.472358\pi\) | |||||||
\(458\) | 4.48926 | 0.209769 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.18720 | 0.195229 | ||||||||
\(461\) | 20.5646 | − | 7.48490i | 0.957789 | − | 0.348607i | 0.184622 | − | 0.982810i | \(-0.440894\pi\) |
0.773167 | + | 0.634203i | \(0.218672\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.0375 | − | 15.9744i | 0.884749 | − | 0.742393i | −0.0824009 | − | 0.996599i | \(-0.526259\pi\) |
0.967150 | + | 0.254207i | \(0.0818143\pi\) | |||||||
\(464\) | −4.05916 | − | 23.0206i | −0.188442 | − | 1.06871i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.43123 | − | 2.04004i | −0.112625 | − | 0.0945032i | ||||
\(467\) | 5.91777 | − | 10.2499i | 0.273842 | − | 0.474308i | −0.696001 | − | 0.718041i | \(-0.745039\pi\) |
0.969842 | + | 0.243734i | \(0.0783722\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.27564 | − | 12.6018i | −0.335958 | − | 0.581896i | ||||
\(470\) | 1.13435 | − | 6.43321i | 0.0523236 | − | 0.296742i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.53144 | + | 2.01328i | 0.254605 | + | 0.0926687i | ||||
\(473\) | −40.7142 | − | 14.8187i | −1.87204 | − | 0.681367i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.00673613 | + | 0.0382025i | −0.000309075 | + | 0.00175285i | ||||
\(476\) | 3.77733 | + | 6.54252i | 0.173134 | + | 0.299876i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.671288 | + | 1.16270i | −0.0307040 | + | 0.0531809i | ||||
\(479\) | 2.21184 | + | 1.85595i | 0.101062 | + | 0.0848007i | 0.691918 | − | 0.721976i | \(-0.256766\pi\) |
−0.590857 | + | 0.806776i | \(0.701210\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0138753 | − | 0.0786906i | −0.000632658 | − | 0.00358798i | ||||
\(482\) | 8.44834 | − | 7.08900i | 0.384811 | − | 0.322895i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 27.8152 | − | 10.1239i | 1.26433 | − | 0.460178i | ||||
\(485\) | 22.0220 | 0.999966 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.75903 | 0.396910 | 0.198455 | − | 0.980110i | \(-0.436408\pi\) | ||||
0.198455 | + | 0.980110i | \(0.436408\pi\) | |||||||
\(488\) | −10.3316 | + | 3.76040i | −0.467690 | + | 0.170225i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.70739 | − | 3.11087i | 0.167483 | − | 0.140535i | ||||
\(491\) | −3.91977 | − | 22.2301i | −0.176897 | − | 1.00323i | −0.935932 | − | 0.352181i | \(-0.885440\pi\) |
0.759035 | − | 0.651050i | \(-0.225671\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.7362 | + | 15.7216i | 0.843838 | + | 0.708064i | ||||
\(494\) | −0.00156564 | + | 0.00271176i | −7.04413e−5 | + | 0.000122008i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.58354 | − | 9.67097i | −0.250708 | − | 0.434239i | ||||
\(497\) | 1.39422 | − | 7.90701i | 0.0625393 | − | 0.354678i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.8051 | + | 8.66433i | 1.06566 | + | 0.387869i | 0.814552 | − | 0.580090i | \(-0.196983\pi\) |
0.251108 | + | 0.967959i | \(0.419205\pi\) | |||||||
\(500\) | −19.3730 | − | 7.05118i | −0.866385 | − | 0.315338i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.324602 | − | 1.84091i | 0.0144877 | − | 0.0821637i | ||||
\(503\) | −1.87207 | − | 3.24252i | −0.0834714 | − | 0.144577i | 0.821267 | − | 0.570543i | \(-0.193267\pi\) |
−0.904739 | + | 0.425967i | \(0.859934\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.2842 | + | 26.4731i | −0.680139 | + | 1.17804i | ||||
\(506\) | −1.71689 | − | 1.44064i | −0.0763250 | − | 0.0640443i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.66392 | + | 15.1078i | 0.118192 | + | 0.670302i | ||||
\(509\) | 18.6531 | − | 15.6518i | 0.826784 | − | 0.693754i | −0.127766 | − | 0.991804i | \(-0.540781\pi\) |
0.954550 | + | 0.298050i | \(0.0963363\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.678271 | + | 0.246871i | −0.0300050 | + | 0.0109209i | ||||
\(512\) | −22.7690 | −1.00626 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.70660 | −0.251707 | ||||||||
\(515\) | −9.50273 | + | 3.45871i | −0.418740 | + | 0.152409i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28.3566 | − | 23.7940i | 1.24712 | − | 1.04646i | ||||
\(518\) | 0.421257 | + | 2.38907i | 0.0185090 | + | 0.104970i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.0487287 | − | 0.0408882i | −0.00213689 | − | 0.00179307i | ||||
\(521\) | −9.81046 | + | 16.9922i | −0.429804 | + | 0.744443i | −0.996856 | − | 0.0792397i | \(-0.974751\pi\) |
0.567051 | + | 0.823682i | \(0.308084\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.4077 | − | 18.0267i | −0.455097 | − | 0.788251i | 0.543597 | − | 0.839346i | \(-0.317062\pi\) |
−0.998694 | + | 0.0510956i | \(0.983729\pi\) | |||||||
\(524\) | 4.92957 | − | 27.9570i | 0.215349 | − | 1.22131i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.44893 | − | 3.43913i | −0.411993 | − | 0.149953i | ||||
\(527\) | 10.9796 | + | 3.99626i | 0.478280 | + | 0.174080i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.80811 | + | 21.5969i | −0.165570 | + | 0.938995i | ||||
\(530\) | −0.598482 | − | 1.03660i | −0.0259964 | − | 0.0450271i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.503217 | + | 0.871598i | −0.0218172 | + | 0.0377886i | ||||
\(533\) | 0.0508378 | + | 0.0426579i | 0.00220203 | + | 0.00184772i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.34534 | − | 24.6436i | −0.187865 | − | 1.06544i | ||||
\(536\) | −13.4320 | + | 11.2708i | −0.580175 | + | 0.486825i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.68735 | − | 1.70606i | 0.202086 | − | 0.0735533i | ||||
\(539\) | 27.4245 | 1.18126 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.6272 | −1.31676 | −0.658382 | − | 0.752684i | \(-0.728759\pi\) | ||||
−0.658382 | + | 0.752684i | \(0.728759\pi\) | |||||||
\(542\) | 1.45146 | − | 0.528288i | 0.0623455 | − | 0.0226919i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.6176 | − | 8.90922i | 0.455226 | − | 0.381980i | ||||
\(545\) | 5.57884 | + | 31.6392i | 0.238971 | + | 1.35527i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.3491 | + | 14.5576i | 0.741795 | + | 0.622440i | 0.933319 | − | 0.359048i | \(-0.116899\pi\) |
−0.191524 | + | 0.981488i | \(0.561343\pi\) | |||||||
\(548\) | 10.9711 | − | 19.0025i | 0.468661 | − | 0.811745i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.100696 | + | 0.174411i | 0.00429370 | + | 0.00743691i | ||||
\(551\) | −0.565809 | + | 3.20886i | −0.0241043 | + | 0.136702i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.606561 | + | 0.220770i | 0.0257936 | + | 0.00938810i | ||||
\(554\) | −9.16806 | − | 3.33690i | −0.389513 | − | 0.141771i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.94998 | + | 11.0589i | −0.0826978 | + | 0.469002i | ||||
\(557\) | −18.2259 | − | 31.5682i | −0.772256 | − | 1.33759i | −0.936324 | − | 0.351138i | \(-0.885795\pi\) |
0.164067 | − | 0.986449i | \(-0.447539\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.0750139 | + | 0.129928i | −0.00317275 | + | 0.00549537i | ||||
\(560\) | −6.70480 | − | 5.62599i | −0.283329 | − | 0.237742i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.46972 | + | 8.33519i | 0.0619963 | + | 0.351599i | ||||
\(563\) | 20.3126 | − | 17.0443i | 0.856075 | − | 0.718332i | −0.105044 | − | 0.994468i | \(-0.533498\pi\) |
0.961119 | + | 0.276136i | \(0.0890539\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.1416 | + | 9.51475i | −1.09978 | + | 0.400288i | ||||
\(566\) | −4.81938 | −0.202574 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.67492 | −0.405950 | ||||||||
\(569\) | −21.5823 | + | 7.85531i | −0.904777 | + | 0.329312i | −0.752165 | − | 0.658974i | \(-0.770991\pi\) |
−0.152612 | + | 0.988286i | \(0.548768\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.67549 | + | 3.08410i | −0.153814 | + | 0.129066i | −0.716447 | − | 0.697641i | \(-0.754233\pi\) |
0.562633 | + | 0.826707i | \(0.309788\pi\) | |||||||
\(572\) | −0.0298850 | − | 0.169486i | −0.00124955 | − | 0.00708657i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.54345 | − | 1.29511i | −0.0644223 | − | 0.0540567i | ||||
\(575\) | −0.0480718 | + | 0.0832628i | −0.00200473 | + | 0.00347230i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.15666 | + | 3.73545i | 0.0897831 | + | 0.155509i | 0.907419 | − | 0.420226i | \(-0.138049\pi\) |
−0.817636 | + | 0.575735i | \(0.804716\pi\) | |||||||
\(578\) | 0.518404 | − | 2.94002i | 0.0215628 | − | 0.122289i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −29.6977 | − | 10.8091i | −1.23313 | − | 0.448823i | ||||
\(581\) | 5.72116 | + | 2.08233i | 0.237354 | + | 0.0863897i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.17781 | − | 6.67969i | 0.0487799 | − | 0.276645i | ||||
\(584\) | 0.434885 | + | 0.753242i | 0.0179957 | + | 0.0311694i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.55900 | − | 11.3605i | 0.270950 | − | 0.469299i | ||||
\(587\) | 32.0377 | + | 26.8828i | 1.32234 | + | 1.10957i | 0.985804 | + | 0.167900i | \(0.0536985\pi\) |
0.336532 | + | 0.941672i | \(0.390746\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.270298 | + | 1.53294i | 0.0111374 | + | 0.0631635i | ||||
\(590\) | 2.60984 | − | 2.18992i | 0.107446 | − | 0.0901575i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.4493 | + | 4.53117i | −0.511663 | + | 0.186230i | ||||
\(593\) | −31.5370 | −1.29507 | −0.647536 | − | 0.762035i | \(-0.724200\pi\) | ||||
−0.647536 | + | 0.762035i | \(0.724200\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.15786 | 0.375436 | ||||||||
\(596\) | 1.51596 | − | 0.551766i | 0.0620963 | − | 0.0226012i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.00594504 | + | 0.00498848i | −0.000243111 | + | 0.000203994i | ||||
\(599\) | −2.19323 | − | 12.4384i | −0.0896129 | − | 0.508220i | −0.996266 | − | 0.0863420i | \(-0.972482\pi\) |
0.906653 | − | 0.421878i | \(-0.138629\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.7368 | + | 13.2048i | 0.641919 | + | 0.538634i | 0.904607 | − | 0.426247i | \(-0.140165\pi\) |
−0.262688 | + | 0.964881i | \(0.584609\pi\) | |||||||
\(602\) | 2.27744 | − | 3.94465i | 0.0928216 | − | 0.160772i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.51556 | + | 13.0173i | 0.305804 | + | 0.529668i | ||||
\(605\) | 6.23084 | − | 35.3369i | 0.253320 | − | 1.43665i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.1338 | − | 4.41636i | −0.492497 | − | 0.179254i | 0.0838192 | − | 0.996481i | \(-0.473288\pi\) |
−0.576316 | + | 0.817227i | \(0.695510\pi\) | |||||||
\(608\) | 1.73512 | + | 0.631531i | 0.0703683 | + | 0.0256120i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.10500 | + | 6.26674i | −0.0447400 | + | 0.253733i | ||||
\(611\) | −0.0640889 | − | 0.111005i | −0.00259276 | − | 0.00449079i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.5799 | − | 26.9851i | 0.629265 | − | 1.08992i | −0.358434 | − | 0.933555i | \(-0.616689\pi\) |
0.987699 | − | 0.156364i | \(-0.0499774\pi\) | |||||||
\(614\) | 2.58449 | + | 2.16864i | 0.104301 | + | 0.0875193i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.90034 | + | 10.7773i | 0.0765667 | + | 0.434231i | ||||
\(617\) | −5.47016 | + | 4.59001i | −0.220220 | + | 0.184787i | −0.746223 | − | 0.665696i | \(-0.768135\pi\) |
0.526003 | + | 0.850483i | \(0.323690\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.42596 | − | 3.43077i | 0.378861 | − | 0.137894i | −0.145568 | − | 0.989348i | \(-0.546501\pi\) |
0.524429 | + | 0.851454i | \(0.324279\pi\) | |||||||
\(620\) | −15.0977 | −0.606338 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9.90827 | 0.397285 | ||||||||
\(623\) | −4.18276 | + | 1.52240i | −0.167579 | + | 0.0609936i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.7885 | + | 15.7654i | −0.751539 | + | 0.630616i | ||||
\(626\) | −1.94145 | − | 11.0105i | −0.0775961 | − | 0.440070i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17.5820 | − | 14.7530i | −0.701598 | − | 0.588711i | ||||
\(629\) | 6.93093 | − | 12.0047i | 0.276354 | − | 0.478660i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.53780 | + | 6.12765i | 0.140838 | + | 0.243938i | 0.927812 | − | 0.373047i | \(-0.121687\pi\) |
−0.786975 | + | 0.616985i | \(0.788354\pi\) | |||||||
\(632\) | 0.135066 | − | 0.765996i | 0.00537263 | − | 0.0304697i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.25303 | − | 1.18401i | −0.129194 | − | 0.0470229i | ||||
\(635\) | 17.4750 | + | 6.36037i | 0.693473 | + | 0.252403i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0164900 | − | 0.0935195i | 0.000653358 | − | 0.00370538i | ||||
\(638\) | 8.45809 | + | 14.6498i | 0.334859 | + | 0.579993i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.7103 | + | 20.2828i | −0.462890 | + | 0.801750i | ||||
\(641\) | −3.83881 | − | 3.22114i | −0.151624 | − | 0.127228i | 0.563820 | − | 0.825898i | \(-0.309331\pi\) |
−0.715444 | + | 0.698670i | \(0.753776\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.284506 | + | 1.61351i | 0.0112198 | + | 0.0636307i | 0.989904 | − | 0.141742i | \(-0.0452704\pi\) |
−0.978684 | + | 0.205373i | \(0.934159\pi\) | |||||||
\(644\) | −1.91082 | + | 1.60337i | −0.0752968 | + | 0.0631815i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.510454 | + | 0.185790i | −0.0200835 | + | 0.00730981i | ||||
\(647\) | 34.4927 | 1.35605 | 0.678024 | − | 0.735040i | \(-0.262836\pi\) | ||||
0.678024 | + | 0.735040i | \(0.262836\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.3056 | 0.757813 | ||||||||
\(650\) | 0.000655302 | 0 | 0.000238510i | 2.57031e−5 | 0 | 9.35515e-6i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.64006 | + | 3.89347i | −0.181719 | + | 0.152480i | ||||
\(653\) | 6.73071 | + | 38.1717i | 0.263393 | + | 1.49378i | 0.773573 | + | 0.633708i | \(0.218468\pi\) |
−0.510180 | + | 0.860068i | \(0.670421\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.3617 | − | 22.1201i | −1.03004 | − | 0.864302i | ||||
\(656\) | 5.50161 | − | 9.52907i | 0.214802 | − | 0.372048i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.94575 | + | 3.37015i | 0.0758534 | + | 0.131382i | ||||
\(659\) | 1.63089 | − | 9.24924i | 0.0635305 | − | 0.360299i | −0.936425 | − | 0.350868i | \(-0.885887\pi\) |
0.999956 | − | 0.00943154i | \(-0.00300220\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.6912 | + | 8.25891i | 0.882584 | + | 0.321234i | 0.743252 | − | 0.669012i | \(-0.233282\pi\) |
0.139332 | + | 0.990246i | \(0.455505\pi\) | |||||||
\(662\) | −2.50654 | − | 0.912305i | −0.0974193 | − | 0.0354577i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.27396 | − | 7.22497i | 0.0494391 | − | 0.280383i | ||||
\(665\) | 0.610007 | + | 1.05656i | 0.0236551 | + | 0.0409718i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.03784 | + | 6.99375i | −0.156346 | + | 0.270799i | ||||
\(668\) | 28.7853 | + | 24.1537i | 1.11374 | + | 0.934536i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.76224 | + | 9.99417i | 0.0680814 | + | 0.386109i | ||||
\(671\) | −27.6228 | + | 23.1783i | −1.06637 | + | 0.894788i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.8700 | − | 9.05195i | 0.958669 | − | 0.348927i | 0.185157 | − | 0.982709i | \(-0.440721\pi\) |
0.773512 | + | 0.633782i | \(0.218498\pi\) | |||||||
\(674\) | −3.10557 | −0.119622 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.7554 | 0.913671 | ||||||||
\(677\) | −29.1933 | + | 10.6255i | −1.12199 | + | 0.408371i | −0.835378 | − | 0.549676i | \(-0.814751\pi\) |
−0.286611 | + | 0.958047i | \(0.592529\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.0497 | + | 8.43267i | −0.385671 | + | 0.323616i | ||||
\(680\) | −1.91624 | − | 10.8676i | −0.0734846 | − | 0.416752i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.19055 | + | 5.19449i | 0.237048 | + | 0.198907i | ||||
\(683\) | −19.0681 | + | 33.0268i | −0.729619 | + | 1.26374i | 0.227425 | + | 0.973796i | \(0.426969\pi\) |
−0.957044 | + | 0.289942i | \(0.906364\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.2993 | − | 23.0351i | −0.508140 | − | 0.880125i | ||||
\(686\) | −1.16707 | + | 6.61880i | −0.0445590 | + | 0.252707i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 23.3747 | + | 8.50768i | 0.891150 | + | 0.324352i | ||||
\(689\) | −0.0220700 | − | 0.00803284i | −0.000840802 | − | 0.000306027i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.71815 | − | 32.4293i | 0.217529 | − | 1.23367i | −0.658935 | − | 0.752200i | \(-0.728993\pi\) |
0.876464 | − | 0.481468i | \(-0.159896\pi\) | |||||||
\(692\) | 12.8221 | + | 22.2085i | 0.487424 | + | 0.844242i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.53414 | + | 11.3175i | −0.248033 | + | 0.429605i | ||||
\(695\) | 10.4278 | + | 8.75000i | 0.395551 | + | 0.331906i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.99918 | + | 11.3379i | 0.0757244 | + | 0.429455i | ||||
\(698\) | −3.77238 | + | 3.16541i | −0.142787 | + | 0.119812i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.210623 | − | 0.0766606i | 0.00796081 | − | 0.00289750i | ||||
\(701\) | −2.30710 | −0.0871381 | −0.0435690 | − | 0.999050i | \(-0.513873\pi\) | ||||
−0.0435690 | + | 0.999050i | \(0.513873\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.84668 | 0.0696490 | ||||||||
\(704\) | −20.3384 | + | 7.40255i | −0.766530 | + | 0.278994i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.61203 | − | 2.19176i | 0.0983051 | − | 0.0824878i | ||||
\(707\) | −3.16217 | − | 17.9336i | −0.118926 | − | 0.674461i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.54298 | − | 7.16841i | −0.320838 | − | 0.269215i | 0.468116 | − | 0.883667i | \(-0.344933\pi\) |
−0.788954 | + | 0.614452i | \(0.789377\pi\) | |||||||
\(710\) | −2.79979 | + | 4.84937i | −0.105074 | + | 0.181994i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.68184 | + | 4.64508i | 0.100506 | + | 0.174082i | ||||
\(713\) | −0.669920 | + | 3.79930i | −0.0250887 | + | 0.142285i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.196042 | − | 0.0713533i | −0.00733154 | − | 0.00266846i | ||||
\(716\) | 17.4981 | + | 6.36878i | 0.653934 | + | 0.238013i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.27894 | + | 7.25321i | −0.0477295 | + | 0.270687i | ||||
\(719\) | 16.0850 | + | 27.8600i | 0.599869 | + | 1.03900i | 0.992840 | + | 0.119453i | \(0.0381140\pi\) |
−0.392971 | + | 0.919551i | \(0.628553\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.01213 | − | 5.21717i | 0.112178 | − | 0.194297i | ||||
\(722\) | 5.99161 | + | 5.02756i | 0.222985 | + | 0.187106i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.63311 | − | 43.2895i | −0.283682 | − | 1.60884i | ||||
\(725\) | 0.555889 | − | 0.466446i | 0.0206452 | − | 0.0173234i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.04193 | − | 1.83511i | 0.186995 | − | 0.0680605i | −0.246826 | − | 0.969060i | \(-0.579387\pi\) |
0.433820 | + | 0.900999i | \(0.357165\pi\) | |||||||
\(728\) | 0.0378942 | 0.00140445 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.503399 | 0.0186316 | ||||||||
\(731\) | −24.4573 | + | 8.90171i | −0.904584 | + | 0.329242i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.1815 | + | 9.38235i | −0.412996 | + | 0.346545i | −0.825491 | − | 0.564415i | \(-0.809102\pi\) |
0.412495 | + | 0.910960i | \(0.364657\pi\) | |||||||
\(734\) | 1.46595 | + | 8.31382i | 0.0541093 | + | 0.306869i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.50572 | + | 2.94165i | 0.129223 | + | 0.108431i | ||||
\(737\) | −28.7534 | + | 49.8023i | −1.05915 | + | 1.83449i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.6083 | + | 37.4266i | 0.794873 | + | 1.37676i | 0.922920 | + | 0.384992i | \(0.125796\pi\) |
−0.128047 | + | 0.991768i | \(0.540871\pi\) | |||||||
\(740\) | −3.11029 | + | 17.6393i | −0.114336 | + | 0.648434i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.670052 | + | 0.243879i | 0.0245984 | + | 0.00895308i | ||||
\(743\) | −7.62298 | − | 2.77454i | −0.279660 | − | 0.101788i | 0.198382 | − | 0.980125i | \(-0.436431\pi\) |
−0.478042 | + | 0.878337i | \(0.658653\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.339588 | − | 1.92590i | 0.0124416 | − | 0.0705596i | ||||
\(746\) | −2.01116 | − | 3.48342i | −0.0736336 | − | 0.127537i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 14.9280 | − | 25.8561i | 0.545823 | − | 0.945393i | ||||
\(749\) | 11.4195 | + | 9.58213i | 0.417261 | + | 0.350123i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.52037 | + | 8.62244i | 0.0554790 | + | 0.314637i | 0.999901 | − | 0.0140996i | \(-0.00448819\pi\) |
−0.944422 | + | 0.328737i | \(0.893377\pi\) | |||||||
\(752\) | −16.2800 | + | 13.6605i | −0.593670 | + | 0.498148i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.0550428 | − | 0.0200339i | 0.00200454 | − | 0.000729593i | ||||
\(755\) | 18.2210 | 0.663129 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.1511 | −1.16855 | −0.584276 | − | 0.811555i | \(-0.698622\pi\) | ||||
−0.584276 | + | 0.811555i | \(0.698622\pi\) | |||||||
\(758\) | −1.61203 | + | 0.586730i | −0.0585514 | + | 0.0213110i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.12617 | − | 0.944972i | 0.0408506 | − | 0.0342777i | ||||
\(761\) | −4.26235 | − | 24.1730i | −0.154510 | − | 0.876271i | −0.959232 | − | 0.282619i | \(-0.908797\pi\) |
0.804722 | − | 0.593652i | \(-0.202314\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.6612 | − | 12.3022i | −0.530771 | − | 0.445370i | ||||
\(764\) | 10.0016 | − | 17.3233i | 0.361846 | − | 0.626736i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.986770 | + | 1.70914i | 0.0356535 | + | 0.0617536i | ||||
\(767\) | 0.0116082 | − | 0.0658336i | 0.000419150 | − | 0.00237712i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.5199 | − | 10.7444i | −1.06451 | − | 0.387451i | −0.250392 | − | 0.968145i | \(-0.580559\pi\) |
−0.814122 | + | 0.580693i | \(0.802782\pi\) | |||||||
\(770\) | 5.95187 | + | 2.16630i | 0.214491 | + | 0.0780682i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.42898 | − | 19.4467i | 0.123412 | − | 0.699902i | ||||
\(773\) | −14.3573 | − | 24.8675i | −0.516395 | − | 0.894422i | −0.999819 | − | 0.0190355i | \(-0.993940\pi\) |
0.483424 | − | 0.875386i | \(-0.339393\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.173332 | − | 0.300219i | 0.00622625 | − | 0.0107842i | ||||
\(776\) | 12.1098 | + | 10.1614i | 0.434717 | + | 0.364771i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.57372 | + | 8.92501i | 0.0564206 | + | 0.319977i | ||||
\(779\) | −1.17492 | + | 0.985872i | −0.0420958 | + | 0.0353225i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.8171 | + | 10.8525i | −1.06694 | + | 0.388334i | ||||
\(782\) | −1.34633 | −0.0481446 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −15.7448 | −0.562315 | ||||||||
\(785\) | −26.1445 | + | 9.51581i | −0.933136 | + | 0.339634i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.7348 | + | 24.9505i | −1.05993 | + | 0.889388i | −0.994103 | − | 0.108443i | \(-0.965413\pi\) |
−0.0658285 | + | 0.997831i | \(0.520969\pi\) | |||||||
\(788\) | 7.00437 | + | 39.7238i | 0.249521 | + | 1.41510i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.344855 | − | 0.289368i | −0.0122694 | − | 0.0102952i | ||||
\(791\) | 8.28623 | − | 14.3522i | 0.294625 | − | 0.510305i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0624304 | + | 0.108133i | 0.00221697 | + | 0.00383990i | ||||
\(794\) | 2.51418 | − | 14.2586i | 0.0892250 | − | 0.506020i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.1289 | + | 8.05427i | 0.784339 | + | 0.285476i | ||||
\(797\) | 3.79081 | + | 1.37974i | 0.134278 | + | 0.0488730i | 0.408285 | − | 0.912855i | \(-0.366127\pi\) |
−0.274007 | + | 0.961728i | \(0.588349\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.86129 | − | 21.8985i | 0.136603 | − | 0.774712i | ||||
\(800\) | −0.205612 | − | 0.356130i | −0.00726948 | − | 0.0125911i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.91080 | + | 6.77371i | −0.138095 | + | 0.239188i | ||||
\(803\) | 2.18519 | + | 1.83359i | 0.0771138 | + | 0.0647061i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.525068 | + | 2.97781i | 0.0185062 | + | 0.104954i | ||||
\(806\) | 0.0214359 | − | 0.0179869i | 0.000755047 | − | 0.000633560i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −20.6199 | + | 7.50504i | −0.725406 | + | 0.264026i | ||||
\(809\) | −29.9454 | −1.05283 | −0.526413 | − | 0.850229i | \(-0.676463\pi\) | ||||
−0.526413 | + | 0.850229i | \(0.676463\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.2173 | 0.709927 | 0.354963 | − | 0.934880i | \(-0.384493\pi\) | ||||
0.354963 | + | 0.934880i | \(0.384493\pi\) | |||||||
\(812\) | 17.6915 | − | 6.43918i | 0.620850 | − | 0.225971i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.34428 | − | 6.16258i | 0.257417 | − | 0.215998i | ||||
\(815\) | 1.27503 | + | 7.23104i | 0.0446623 | + | 0.253292i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.65611 | − | 2.22874i | −0.0929256 | − | 0.0779739i | ||||
\(818\) | −1.32117 | + | 2.28834i | −0.0461938 | + | 0.0800099i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.43809 | − | 12.8831i | −0.259749 | − | 0.449899i | ||||
\(821\) | 4.66656 | − | 26.4654i | 0.162864 | − | 0.923648i | −0.788375 | − | 0.615194i | \(-0.789078\pi\) |
0.951239 | − | 0.308453i | \(-0.0998114\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.6640 | − | 7.88504i | −0.755159 | − | 0.274855i | −0.0643839 | − | 0.997925i | \(-0.520508\pi\) |
−0.690775 | + | 0.723070i | \(0.742730\pi\) | |||||||
\(824\) | −6.82144 | − | 2.48280i | −0.237636 | − | 0.0864925i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.352429 | + | 1.99873i | −0.0122626 | + | 0.0695446i | ||||
\(827\) | 2.55476 | + | 4.42498i | 0.0888378 | + | 0.153872i | 0.907020 | − | 0.421087i | \(-0.138351\pi\) |
−0.818182 | + | 0.574959i | \(0.805018\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.2991 | − | 26.4988i | 0.531360 | − | 0.920343i | −0.467970 | − | 0.883744i | \(-0.655014\pi\) |
0.999330 | − | 0.0365985i | \(-0.0116523\pi\) | |||||||
\(830\) | −3.25272 | − | 2.72936i | −0.112904 | − | 0.0947373i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.0130140 | + | 0.0738063i | 0.000451181 | + | 0.00255877i | ||||
\(833\) | 12.6199 | − | 10.5893i | 0.437252 | − | 0.366898i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 42.8038 | − | 15.5793i | 1.48129 | − | 0.539144i | ||||
\(836\) | 3.97744 | 0.137563 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.1033 | 0.349013 | ||||||||
\(839\) | 52.9129 | − | 19.2587i | 1.82676 | − | 0.664884i | 0.833004 | − | 0.553267i | \(-0.186619\pi\) |
0.993751 | − | 0.111617i | \(-0.0356030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.4772 | − | 20.5388i | 0.844042 | − | 0.708235i | ||||
\(842\) | 0.576441 | + | 3.26916i | 0.0198655 | + | 0.112663i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 33.5905 | + | 28.1858i | 1.15623 | + | 0.970195i | ||||
\(845\) | 14.3984 | − | 24.9387i | 0.495318 | − | 0.857917i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.6878 | + | 18.5118i | 0.367237 | + | 0.636073i | ||||
\(848\) | −0.676200 | + | 3.83492i | −0.0232208 | + | 0.131692i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.113682 | + | 0.0413768i | 0.00389926 | + | 0.00141921i | ||||
\(851\) | 4.30089 | + | 1.56539i | 0.147433 | + | 0.0536610i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.90880 | + | 44.8531i | −0.270792 | + | 1.53574i | 0.481226 | + | 0.876597i | \(0.340192\pi\) |
−0.752018 | + | 0.659143i | \(0.770919\pi\) | |||||||
\(854\) | −1.89540 | − | 3.28294i | −0.0648594 | − | 0.112340i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.98154 | − | 15.5565i | 0.306983 | − | 0.531710i | ||||
\(857\) | −13.3975 | − | 11.2418i | −0.457649 | − | 0.384013i | 0.384616 | − | 0.923077i | \(-0.374334\pi\) |
−0.842265 | + | 0.539063i | \(0.818778\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.18575 | + | 18.0673i | 0.108697 | + | 0.616448i | 0.989679 | + | 0.143300i | \(0.0457714\pi\) |
−0.880983 | + | 0.473148i | \(0.843117\pi\) | |||||||
\(860\) | 25.7623 | − | 21.6171i | 0.878488 | − | 0.737139i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.85383 | − | 1.40268i | 0.131262 | − | 0.0477755i | ||||
\(863\) | 4.65373 | 0.158415 | 0.0792073 | − | 0.996858i | \(-0.474761\pi\) | ||||
0.0792073 | + | 0.996858i | \(0.474761\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.0863 | 1.05697 | ||||||||
\(866\) | −2.38294 | + | 0.867321i | −0.0809758 | + | 0.0294728i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.88980 | − | 5.78123i | 0.233855 | − | 0.196228i | ||||
\(869\) | −0.442973 | − | 2.51222i | −0.0150268 | − | 0.0852213i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.152541 | + | 0.127997i | 0.00516864 | + | 0.00433700i | ||||
\(872\) | −11.5311 | + | 19.9725i | −0.390493 | + | 0.676354i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.0896791 | − | 0.155329i | −0.00303344 | − | 0.00525407i | ||||
\(875\) | 2.58524 | − | 14.6617i | 0.0873972 | − | 0.495654i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.44594 | + | 1.25422i | 0.116361 | + | 0.0423520i | 0.399545 | − | 0.916714i | \(-0.369168\pi\) |
−0.283183 | + | 0.959066i | \(0.591390\pi\) | |||||||
\(878\) | −5.90848 | − | 2.15051i | −0.199402 | − | 0.0725763i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.00648 | + | 34.0644i | −0.202478 | + | 1.14831i | ||||
\(881\) | −19.1504 | − | 33.1694i | −0.645193 | − | 1.11751i | −0.984257 | − | 0.176744i | \(-0.943444\pi\) |
0.339064 | − | 0.940763i | \(-0.389890\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.3071 | + | 19.5844i | −0.380513 | + | 0.659069i | −0.991136 | − | 0.132853i | \(-0.957586\pi\) |
0.610622 | + | 0.791922i | \(0.290919\pi\) | |||||||
\(884\) | −0.0791952 | − | 0.0664527i | −0.00266362 | − | 0.00223504i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.0521459 | + | 0.295734i | 0.00175188 | + | 0.00993538i | ||||
\(887\) | −1.45285 | + | 1.21908i | −0.0487818 | + | 0.0409328i | −0.666853 | − | 0.745190i | \(-0.732359\pi\) |
0.618071 | + | 0.786122i | \(0.287915\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.4102 | + | 3.78899i | −0.349146 | + | 0.127079i | ||||
\(890\) | 3.10435 | 0.104058 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −39.5852 | −1.32541 | ||||||||
\(893\) | 2.78368 | − | 1.01318i | 0.0931522 | − | 0.0339046i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.2917 | − | 14.5095i | 0.577998 | − | 0.484998i | ||||
\(896\) | −2.42276 | − | 13.7401i | −0.0809386 | − | 0.459026i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.531009 | − | 0.445570i | −0.0177200 | − | 0.0148689i | ||||
\(899\) | 14.5592 | − | 25.2172i | 0.485575 | − | 0.841041i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.03722 | − | 3.52856i | −0.0678695 | − | 0.117553i | ||||
\(902\) | −1.38269 | + | 7.84165i | −0.0460387 | + | 0.261098i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18.7655 | − | 6.83007i | −0.624130 | − | 0.227165i | ||||
\(905\) | −50.0722 | − | 18.2248i | −1.66446 | − | 0.605812i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.13409 | − | 6.43172i | 0.0376567 | − | 0.213562i | −0.960173 | − | 0.279405i | \(-0.909863\pi\) |
0.997830 | + | 0.0658435i | \(0.0209738\pi\) | |||||||
\(908\) | 19.7740 | + | 34.2497i | 0.656225 | + | 1.13661i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.0109660 | − | 0.0189938i | 0.000363521 | − | 0.000629637i | ||||
\(911\) | −32.9683 | − | 27.6637i | −1.09229 | − | 0.916540i | −0.0954074 | − | 0.995438i | \(-0.530415\pi\) |
−0.996883 | + | 0.0788981i | \(0.974860\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.17818 | − | 23.6956i | −0.138277 | − | 0.784210i | ||||
\(914\) | −3.52748 | + | 2.95991i | −0.116679 | + | 0.0979050i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18.5548 | + | 6.75339i | −0.613067 | + | 0.223138i | ||||
\(917\) | 20.5003 | 0.676980 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.7911 | −0.553887 | −0.276943 | − | 0.960886i | \(-0.589321\pi\) | ||||
−0.276943 | + | 0.960886i | \(0.589321\pi\) | |||||||
\(920\) | 3.42387 | − | 1.24619i | 0.112882 | − | 0.0410856i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.96505 | − | 5.84437i | 0.229382 | − | 0.192474i | ||||
\(923\) | 0.0190793 | + | 0.108204i | 0.000628001 | + | 0.00356157i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.315051 | − | 0.264359i | −0.0103588 | − | 0.00869208i | ||||
\(926\) | 5.16253 | − | 8.94176i | 0.169651 | − | 0.293844i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −17.2706 | − | 29.9135i | −0.566935 | − | 0.981960i | ||||
\(929\) | −2.01432 | + | 11.4238i | −0.0660877 | + | 0.374802i | 0.933769 | + | 0.357876i | \(0.116499\pi\) |
−0.999857 | + | 0.0169258i | \(0.994612\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.06232 | + | 0.750625i | 0.0675900 | + | 0.0246007i | ||||
\(932\) | 13.1176 | + | 4.77440i | 0.429680 | + | 0.156391i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.853874 | − | 4.84256i | 0.0279396 | − | 0.158453i | ||||
\(935\) | −18.0960 | − | 31.3432i | −0.591802 | − | 1.02503i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.8976 | + | 41.3919i | −0.780702 | + | 1.35222i | 0.150832 | + | 0.988559i | \(0.451805\pi\) |
−0.931533 | + | 0.363656i | \(0.881528\pi\) | |||||||
\(938\) | −4.63117 | − | 3.88601i | −0.151213 | − | 0.126883i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.98932 | + | 28.2959i | 0.162734 | + | 0.922909i | ||||
\(941\) | 8.62593 | − | 7.23801i | 0.281197 | − | 0.235953i | −0.491270 | − | 0.871008i | \(-0.663467\pi\) |
0.772467 | + | 0.635055i | \(0.219023\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.57206 | + | 1.30012i | −0.116322 | + | 0.0423379i | ||||
\(944\) | −11.0837 | −0.360743 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18.0010 | −0.585261 | ||||||||
\(947\) | −6.88973 | + | 2.50766i | −0.223886 | + | 0.0814879i | −0.451528 | − | 0.892257i | \(-0.649121\pi\) |
0.227642 | + | 0.973745i | \(0.426899\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.00756662 | − | 0.00634915i | 0.000245623 | − | 0.000206102i | ||||
\(950\) | 0.00279864 | + | 0.0158719i | 9.07998e−5 | + | 0.000514951i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.03589 | + | 4.22561i | 0.163214 | + | 0.136953i | ||||
\(953\) | 12.4377 | − | 21.5427i | 0.402895 | − | 0.697835i | −0.591179 | − | 0.806541i | \(-0.701337\pi\) |
0.994074 | + | 0.108705i | \(0.0346705\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.1241 | − | 20.9996i | −0.392328 | − | 0.679531i | ||||
\(956\) | 1.02543 | − | 5.81547i | 0.0331646 | − | 0.188086i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.12725 | + | 0.410286i | 0.0364199 | + | 0.0132558i | ||||
\(959\) | 14.8897 | + | 5.41941i | 0.480814 | + | 0.175002i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.96758 | + | 16.8300i | −0.0957283 | + | 0.542902i | ||||
\(962\) | −0.0165988 | − | 0.0287500i | −0.000535168 | − | 0.000926937i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −24.2540 | + | 42.0091i | −0.781167 | + | 1.35302i | ||||
\(965\) | −18.3370 | − | 15.3866i | −0.590288 | − | 0.495311i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.90924 | − | 33.5130i | −0.190028 | − | 1.07770i | −0.919323 | − | 0.393505i | \(-0.871263\pi\) |
0.729294 | − | 0.684200i | \(-0.239849\pi\) | |||||||
\(968\) | 19.7314 | − | 16.5566i | 0.634192 | − | 0.532150i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.59761 | − | 3.12927i | 0.276053 | − | 0.100475i | ||||
\(971\) | −34.2476 | −1.09906 | −0.549530 | − | 0.835474i | \(-0.685193\pi\) | ||||
−0.549530 | + | 0.835474i | \(0.685193\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.10928 | −0.259971 | ||||||||
\(974\) | 3.41962 | − | 1.24464i | 0.109572 | − | 0.0398808i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15.8587 | − | 13.3070i | 0.507625 | − | 0.425948i | ||||
\(977\) | −4.06637 | − | 23.0615i | −0.130095 | − | 0.737804i | −0.978151 | − | 0.207897i | \(-0.933338\pi\) |
0.848056 | − | 0.529907i | \(-0.177773\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.4756 | + | 11.3074i | 0.430682 | + | 0.361386i | ||||
\(980\) | −10.6434 | + | 18.4349i | −0.339990 | + | 0.588880i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.68917 | − | 8.12188i | −0.149637 | − | 0.259180i | ||||
\(983\) | −5.76566 | + | 32.6987i | −0.183896 | + | 1.04293i | 0.743470 | + | 0.668770i | \(0.233179\pi\) |
−0.927366 | + | 0.374157i | \(0.877932\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 45.9478 | + | 16.7236i | 1.46402 | + | 0.532859i | ||||
\(986\) | 9.54883 | + | 3.47549i | 0.304097 | + | 0.110682i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.00239159 | − | 0.0135634i | 7.60865e−5 | − | 0.000431508i | ||||
\(989\) | −4.29678 | − | 7.44223i | −0.136630 | − | 0.236649i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.0903 | − | 24.4051i | 0.447594 | − | 0.775255i | −0.550635 | − | 0.834746i | \(-0.685614\pi\) |
0.998229 | + | 0.0594912i | \(0.0189478\pi\) | |||||||
\(992\) | −12.6405 | − | 10.6066i | −0.401336 | − | 0.336761i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.579251 | − | 3.28510i | −0.0183727 | − | 0.104197i | ||||
\(995\) | 21.8680 | − | 18.3494i | 0.693261 | − | 0.581715i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.2398 | − | 15.3740i | 1.33775 | − | 0.486901i | 0.428646 | − | 0.903472i | \(-0.358991\pi\) |
0.909103 | + | 0.416571i | \(0.136768\pi\) | |||||||
\(998\) | 10.5249 | 0.333161 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 243.2.e.c.55.1 | 12 | ||
3.2 | odd | 2 | 243.2.e.b.55.2 | 12 | |||
9.2 | odd | 6 | 81.2.e.a.46.1 | 12 | |||
9.4 | even | 3 | 243.2.e.d.217.2 | 12 | |||
9.5 | odd | 6 | 243.2.e.a.217.1 | 12 | |||
9.7 | even | 3 | 27.2.e.a.16.2 | ✓ | 12 | ||
27.2 | odd | 18 | 729.2.a.d.1.3 | 6 | |||
27.4 | even | 9 | inner | 243.2.e.c.190.1 | 12 | ||
27.5 | odd | 18 | 243.2.e.a.28.1 | 12 | |||
27.7 | even | 9 | 729.2.c.e.487.3 | 12 | |||
27.11 | odd | 18 | 729.2.c.b.244.4 | 12 | |||
27.13 | even | 9 | 27.2.e.a.22.2 | yes | 12 | ||
27.14 | odd | 18 | 81.2.e.a.37.1 | 12 | |||
27.16 | even | 9 | 729.2.c.e.244.3 | 12 | |||
27.20 | odd | 18 | 729.2.c.b.487.4 | 12 | |||
27.22 | even | 9 | 243.2.e.d.28.2 | 12 | |||
27.23 | odd | 18 | 243.2.e.b.190.2 | 12 | |||
27.25 | even | 9 | 729.2.a.a.1.4 | 6 | |||
36.7 | odd | 6 | 432.2.u.c.97.1 | 12 | |||
45.7 | odd | 12 | 675.2.u.b.124.3 | 24 | |||
45.34 | even | 6 | 675.2.l.c.151.1 | 12 | |||
45.43 | odd | 12 | 675.2.u.b.124.2 | 24 | |||
108.67 | odd | 18 | 432.2.u.c.49.1 | 12 | |||
135.13 | odd | 36 | 675.2.u.b.49.3 | 24 | |||
135.67 | odd | 36 | 675.2.u.b.49.2 | 24 | |||
135.94 | even | 18 | 675.2.l.c.76.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.2.e.a.16.2 | ✓ | 12 | 9.7 | even | 3 | ||
27.2.e.a.22.2 | yes | 12 | 27.13 | even | 9 | ||
81.2.e.a.37.1 | 12 | 27.14 | odd | 18 | |||
81.2.e.a.46.1 | 12 | 9.2 | odd | 6 | |||
243.2.e.a.28.1 | 12 | 27.5 | odd | 18 | |||
243.2.e.a.217.1 | 12 | 9.5 | odd | 6 | |||
243.2.e.b.55.2 | 12 | 3.2 | odd | 2 | |||
243.2.e.b.190.2 | 12 | 27.23 | odd | 18 | |||
243.2.e.c.55.1 | 12 | 1.1 | even | 1 | trivial | ||
243.2.e.c.190.1 | 12 | 27.4 | even | 9 | inner | ||
243.2.e.d.28.2 | 12 | 27.22 | even | 9 | |||
243.2.e.d.217.2 | 12 | 9.4 | even | 3 | |||
432.2.u.c.49.1 | 12 | 108.67 | odd | 18 | |||
432.2.u.c.97.1 | 12 | 36.7 | odd | 6 | |||
675.2.l.c.76.1 | 12 | 135.94 | even | 18 | |||
675.2.l.c.151.1 | 12 | 45.34 | even | 6 | |||
675.2.u.b.49.2 | 24 | 135.67 | odd | 36 | |||
675.2.u.b.49.3 | 24 | 135.13 | odd | 36 | |||
675.2.u.b.124.2 | 24 | 45.43 | odd | 12 | |||
675.2.u.b.124.3 | 24 | 45.7 | odd | 12 | |||
729.2.a.a.1.4 | 6 | 27.25 | even | 9 | |||
729.2.a.d.1.3 | 6 | 27.2 | odd | 18 | |||
729.2.c.b.244.4 | 12 | 27.11 | odd | 18 | |||
729.2.c.b.487.4 | 12 | 27.20 | odd | 18 | |||
729.2.c.e.244.3 | 12 | 27.16 | even | 9 | |||
729.2.c.e.487.3 | 12 | 27.7 | even | 9 |