Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [539,2,Mod(67,539)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(539, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("539.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 539 = 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 539.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.30393666895\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.809017 + 1.40126i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 539.67 |
Dual form | 539.2.e.j.177.1 |
$q$-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 \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(442\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.11803 | − | 1.93649i | −0.790569 | − | 1.36931i | −0.925615 | − | 0.378467i | \(-0.876451\pi\) |
0.135045 | − | 0.990839i | \(-0.456882\pi\) | |||||||
\(3\) | −0.618034 | + | 1.07047i | −0.356822 | + | 0.618034i | −0.987428 | − | 0.158069i | \(-0.949473\pi\) |
0.630606 | + | 0.776103i | \(0.282806\pi\) | |||||||
\(4\) | −1.50000 | + | 2.59808i | −0.750000 | + | 1.29904i | ||||
\(5\) | −1.00000 | − | 1.73205i | −0.447214 | − | 0.774597i | 0.550990 | − | 0.834512i | \(-0.314250\pi\) |
−0.998203 | + | 0.0599153i | \(0.980917\pi\) | |||||||
\(6\) | 2.76393 | 1.12837 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 0.736068 | + | 1.27491i | 0.245356 | + | 0.424969i | ||||
\(10\) | −2.23607 | + | 3.87298i | −0.707107 | + | 1.22474i | ||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | −1.85410 | − | 3.21140i | −0.535233 | − | 0.927051i | ||||
\(13\) | −3.23607 | −0.897524 | −0.448762 | − | 0.893651i | \(-0.648135\pi\) | ||||
−0.448762 | + | 0.893651i | \(0.648135\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.47214 | 0.638303 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | −1.61803 | + | 2.80252i | −0.392431 | + | 0.679710i | −0.992770 | − | 0.120036i | \(-0.961699\pi\) |
0.600339 | + | 0.799746i | \(0.295032\pi\) | |||||||
\(18\) | 1.64590 | − | 2.85078i | 0.387942 | − | 0.671935i | ||||
\(19\) | 3.23607 | + | 5.60503i | 0.742405 | + | 1.28588i | 0.951397 | + | 0.307966i | \(0.0996482\pi\) |
−0.208993 | + | 0.977917i | \(0.567018\pi\) | |||||||
\(20\) | 6.00000 | 1.34164 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.23607 | −0.476731 | ||||||||
\(23\) | −1.23607 | − | 2.14093i | −0.257738 | − | 0.446415i | 0.707898 | − | 0.706315i | \(-0.249644\pi\) |
−0.965636 | + | 0.259900i | \(0.916310\pi\) | |||||||
\(24\) | −1.38197 | + | 2.39364i | −0.282093 | + | 0.488599i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 3.61803 | + | 6.26662i | 0.709555 | + | 1.22899i | ||||
\(27\) | −5.52786 | −1.06384 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.47214 | 1.57324 | 0.786618 | − | 0.617440i | \(-0.211830\pi\) | ||||
0.786618 | + | 0.617440i | \(0.211830\pi\) | |||||||
\(30\) | −2.76393 | − | 4.78727i | −0.504623 | − | 0.874032i | ||||
\(31\) | −1.38197 | + | 2.39364i | −0.248208 | + | 0.429910i | −0.963029 | − | 0.269399i | \(-0.913175\pi\) |
0.714820 | + | 0.699308i | \(0.246508\pi\) | |||||||
\(32\) | 3.35410 | − | 5.80948i | 0.592927 | − | 1.02698i | ||||
\(33\) | 0.618034 | + | 1.07047i | 0.107586 | + | 0.186344i | ||||
\(34\) | 7.23607 | 1.24098 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.41641 | −0.736068 | ||||||||
\(37\) | 4.23607 | + | 7.33708i | 0.696405 | + | 1.20621i | 0.969705 | + | 0.244280i | \(0.0785517\pi\) |
−0.273299 | + | 0.961929i | \(0.588115\pi\) | |||||||
\(38\) | 7.23607 | − | 12.5332i | 1.17385 | − | 2.03316i | ||||
\(39\) | 2.00000 | − | 3.46410i | 0.320256 | − | 0.554700i | ||||
\(40\) | −2.23607 | − | 3.87298i | −0.353553 | − | 0.612372i | ||||
\(41\) | 11.2361 | 1.75478 | 0.877390 | − | 0.479779i | \(-0.159283\pi\) | ||||
0.877390 | + | 0.479779i | \(0.159283\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 1.50000 | + | 2.59808i | 0.226134 | + | 0.391675i | ||||
\(45\) | 1.47214 | − | 2.54981i | 0.219453 | − | 0.380104i | ||||
\(46\) | −2.76393 | + | 4.78727i | −0.407520 | + | 0.705845i | ||||
\(47\) | 1.38197 | + | 2.39364i | 0.201580 | + | 0.349148i | 0.949038 | − | 0.315162i | \(-0.102059\pi\) |
−0.747457 | + | 0.664310i | \(0.768726\pi\) | |||||||
\(48\) | −1.23607 | −0.178411 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.23607 | −0.316228 | ||||||||
\(51\) | −2.00000 | − | 3.46410i | −0.280056 | − | 0.485071i | ||||
\(52\) | 4.85410 | − | 8.40755i | 0.673143 | − | 1.16592i | ||||
\(53\) | 0.236068 | − | 0.408882i | 0.0324264 | − | 0.0561642i | −0.849357 | − | 0.527819i | \(-0.823010\pi\) |
0.881783 | + | 0.471655i | \(0.156343\pi\) | |||||||
\(54\) | 6.18034 | + | 10.7047i | 0.841038 | + | 1.45672i | ||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.00000 | −1.05963 | ||||||||
\(58\) | −9.47214 | − | 16.4062i | −1.24375 | − | 2.15424i | ||||
\(59\) | −0.618034 | + | 1.07047i | −0.0804612 | + | 0.139363i | −0.903448 | − | 0.428697i | \(-0.858973\pi\) |
0.822987 | + | 0.568060i | \(0.192306\pi\) | |||||||
\(60\) | −3.70820 | + | 6.42280i | −0.478727 | + | 0.829180i | ||||
\(61\) | −3.61803 | − | 6.26662i | −0.463242 | − | 0.802358i | 0.535878 | − | 0.844295i | \(-0.319981\pi\) |
−0.999120 | + | 0.0419368i | \(0.986647\pi\) | |||||||
\(62\) | 6.18034 | 0.784904 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0000 | −1.62500 | ||||||||
\(65\) | 3.23607 | + | 5.60503i | 0.401385 | + | 0.695219i | ||||
\(66\) | 1.38197 | − | 2.39364i | 0.170108 | − | 0.294636i | ||||
\(67\) | −7.23607 | + | 12.5332i | −0.884026 | + | 1.53118i | −0.0372009 | + | 0.999308i | \(0.511844\pi\) |
−0.846825 | + | 0.531871i | \(0.821489\pi\) | |||||||
\(68\) | −4.85410 | − | 8.40755i | −0.588646 | − | 1.01957i | ||||
\(69\) | 3.05573 | 0.367866 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.4721 | −1.24281 | −0.621407 | − | 0.783488i | \(-0.713439\pi\) | ||||
−0.621407 | + | 0.783488i | \(0.713439\pi\) | |||||||
\(72\) | 1.64590 | + | 2.85078i | 0.193971 | + | 0.335968i | ||||
\(73\) | −0.381966 | + | 0.661585i | −0.0447057 | + | 0.0774326i | −0.887512 | − | 0.460784i | \(-0.847568\pi\) |
0.842807 | + | 0.538216i | \(0.180902\pi\) | |||||||
\(74\) | 9.47214 | − | 16.4062i | 1.10111 | − | 1.90718i | ||||
\(75\) | 0.618034 | + | 1.07047i | 0.0713644 | + | 0.123607i | ||||
\(76\) | −19.4164 | −2.22721 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −8.94427 | −1.01274 | ||||||||
\(79\) | 4.47214 | + | 7.74597i | 0.503155 | + | 0.871489i | 0.999993 | + | 0.00364646i | \(0.00116071\pi\) |
−0.496839 | + | 0.867843i | \(0.665506\pi\) | |||||||
\(80\) | 1.00000 | − | 1.73205i | 0.111803 | − | 0.193649i | ||||
\(81\) | 1.20820 | − | 2.09267i | 0.134245 | − | 0.232519i | ||||
\(82\) | −12.5623 | − | 21.7586i | −1.38727 | − | 2.40283i | ||||
\(83\) | 11.4164 | 1.25311 | 0.626557 | − | 0.779376i | \(-0.284464\pi\) | ||||
0.626557 | + | 0.779376i | \(0.284464\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.47214 | 0.702002 | ||||||||
\(86\) | −8.94427 | − | 15.4919i | −0.964486 | − | 1.67054i | ||||
\(87\) | −5.23607 | + | 9.06914i | −0.561365 | + | 0.972313i | ||||
\(88\) | 1.11803 | − | 1.93649i | 0.119183 | − | 0.206431i | ||||
\(89\) | 1.00000 | + | 1.73205i | 0.106000 | + | 0.183597i | 0.914146 | − | 0.405385i | \(-0.132862\pi\) |
−0.808146 | + | 0.588982i | \(0.799529\pi\) | |||||||
\(90\) | −6.58359 | −0.693972 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.41641 | 0.773214 | ||||||||
\(93\) | −1.70820 | − | 2.95870i | −0.177132 | − | 0.306802i | ||||
\(94\) | 3.09017 | − | 5.35233i | 0.318727 | − | 0.552051i | ||||
\(95\) | 6.47214 | − | 11.2101i | 0.664027 | − | 1.15013i | ||||
\(96\) | 4.14590 | + | 7.18091i | 0.423139 | + | 0.732898i | ||||
\(97\) | −17.4164 | −1.76837 | −0.884184 | − | 0.467139i | \(-0.845285\pi\) | ||||
−0.884184 | + | 0.467139i | \(0.845285\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.47214 | 0.147955 | ||||||||
\(100\) | 1.50000 | + | 2.59808i | 0.150000 | + | 0.259808i | ||||
\(101\) | −2.38197 | + | 4.12569i | −0.237014 | + | 0.410521i | −0.959856 | − | 0.280493i | \(-0.909502\pi\) |
0.722842 | + | 0.691014i | \(0.242836\pi\) | |||||||
\(102\) | −4.47214 | + | 7.74597i | −0.442807 | + | 0.766965i | ||||
\(103\) | 3.85410 | + | 6.67550i | 0.379756 | + | 0.657757i | 0.991027 | − | 0.133665i | \(-0.0426746\pi\) |
−0.611271 | + | 0.791422i | \(0.709341\pi\) | |||||||
\(104\) | −7.23607 | −0.709555 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.05573 | −0.102541 | ||||||||
\(107\) | 2.00000 | + | 3.46410i | 0.193347 | + | 0.334887i | 0.946357 | − | 0.323122i | \(-0.104732\pi\) |
−0.753010 | + | 0.658009i | \(0.771399\pi\) | |||||||
\(108\) | 8.29180 | − | 14.3618i | 0.797878 | − | 1.38197i | ||||
\(109\) | 2.23607 | − | 3.87298i | 0.214176 | − | 0.370965i | −0.738841 | − | 0.673880i | \(-0.764627\pi\) |
0.953018 | + | 0.302915i | \(0.0979599\pi\) | |||||||
\(110\) | 2.23607 | + | 3.87298i | 0.213201 | + | 0.369274i | ||||
\(111\) | −10.4721 | −0.993971 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 8.94427 | + | 15.4919i | 0.837708 | + | 1.45095i | ||||
\(115\) | −2.47214 | + | 4.28187i | −0.230528 | + | 0.399286i | ||||
\(116\) | −12.7082 | + | 22.0113i | −1.17993 | + | 2.04369i | ||||
\(117\) | −2.38197 | − | 4.12569i | −0.220213 | − | 0.381420i | ||||
\(118\) | 2.76393 | 0.254441 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 5.52786 | 0.504623 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −8.09017 | + | 14.0126i | −0.732450 | + | 1.26864i | ||||
\(123\) | −6.94427 | + | 12.0278i | −0.626144 | + | 1.08451i | ||||
\(124\) | −4.14590 | − | 7.18091i | −0.372313 | − | 0.644864i | ||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.05573 | 0.271152 | 0.135576 | − | 0.990767i | \(-0.456712\pi\) | ||||
0.135576 | + | 0.990767i | \(0.456712\pi\) | |||||||
\(128\) | 7.82624 | + | 13.5554i | 0.691748 | + | 1.19814i | ||||
\(129\) | −4.94427 | + | 8.56373i | −0.435319 | + | 0.753994i | ||||
\(130\) | 7.23607 | − | 12.5332i | 0.634645 | − | 1.09924i | ||||
\(131\) | 10.9443 | + | 18.9560i | 0.956205 | + | 1.65620i | 0.731585 | + | 0.681750i | \(0.238781\pi\) |
0.224620 | + | 0.974446i | \(0.427886\pi\) | |||||||
\(132\) | −3.70820 | −0.322758 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 32.3607 | 2.79554 | ||||||||
\(135\) | 5.52786 | + | 9.57454i | 0.475763 | + | 0.824045i | ||||
\(136\) | −3.61803 | + | 6.26662i | −0.310244 | + | 0.537358i | ||||
\(137\) | −8.23607 | + | 14.2653i | −0.703655 | + | 1.21877i | 0.263520 | + | 0.964654i | \(0.415116\pi\) |
−0.967175 | + | 0.254112i | \(0.918217\pi\) | |||||||
\(138\) | −3.41641 | − | 5.91739i | −0.290824 | − | 0.503722i | ||||
\(139\) | 1.52786 | 0.129592 | 0.0647959 | − | 0.997899i | \(-0.479360\pi\) | ||||
0.0647959 | + | 0.997899i | \(0.479360\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.41641 | −0.287713 | ||||||||
\(142\) | 11.7082 | + | 20.2792i | 0.982531 | + | 1.70179i | ||||
\(143\) | −1.61803 | + | 2.80252i | −0.135307 | + | 0.234358i | ||||
\(144\) | −0.736068 | + | 1.27491i | −0.0613390 | + | 0.106242i | ||||
\(145\) | −8.47214 | − | 14.6742i | −0.703573 | − | 1.21862i | ||||
\(146\) | 1.70820 | 0.141372 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −25.4164 | −2.08922 | ||||||||
\(149\) | −7.00000 | − | 12.1244i | −0.573462 | − | 0.993266i | −0.996207 | − | 0.0870170i | \(-0.972267\pi\) |
0.422744 | − | 0.906249i | \(-0.361067\pi\) | |||||||
\(150\) | 1.38197 | − | 2.39364i | 0.112837 | − | 0.195440i | ||||
\(151\) | −4.47214 | + | 7.74597i | −0.363937 | + | 0.630358i | −0.988605 | − | 0.150533i | \(-0.951901\pi\) |
0.624668 | + | 0.780891i | \(0.285234\pi\) | |||||||
\(152\) | 7.23607 | + | 12.5332i | 0.586923 | + | 1.01658i | ||||
\(153\) | −4.76393 | −0.385141 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.52786 | 0.444009 | ||||||||
\(156\) | 6.00000 | + | 10.3923i | 0.480384 | + | 0.832050i | ||||
\(157\) | 5.47214 | − | 9.47802i | 0.436724 | − | 0.756428i | −0.560711 | − | 0.828012i | \(-0.689472\pi\) |
0.997435 | + | 0.0715837i | \(0.0228053\pi\) | |||||||
\(158\) | 10.0000 | − | 17.3205i | 0.795557 | − | 1.37795i | ||||
\(159\) | 0.291796 | + | 0.505406i | 0.0231409 | + | 0.0400813i | ||||
\(160\) | −13.4164 | −1.06066 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5.40325 | −0.424520 | ||||||||
\(163\) | 1.70820 | + | 2.95870i | 0.133797 | + | 0.231743i | 0.925137 | − | 0.379633i | \(-0.123950\pi\) |
−0.791340 | + | 0.611376i | \(0.790616\pi\) | |||||||
\(164\) | −16.8541 | + | 29.1922i | −1.31608 | + | 2.27952i | ||||
\(165\) | 1.23607 | − | 2.14093i | 0.0962278 | − | 0.166671i | ||||
\(166\) | −12.7639 | − | 22.1078i | −0.990673 | − | 1.71590i | ||||
\(167\) | −4.94427 | −0.382599 | −0.191300 | − | 0.981532i | \(-0.561270\pi\) | ||||
−0.191300 | + | 0.981532i | \(0.561270\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.52786 | −0.194451 | ||||||||
\(170\) | −7.23607 | − | 12.5332i | −0.554981 | − | 0.961255i | ||||
\(171\) | −4.76393 | + | 8.25137i | −0.364307 | + | 0.630998i | ||||
\(172\) | −12.0000 | + | 20.7846i | −0.914991 | + | 1.58481i | ||||
\(173\) | −6.38197 | − | 11.0539i | −0.485212 | − | 0.840412i | 0.514644 | − | 0.857404i | \(-0.327924\pi\) |
−0.999856 | + | 0.0169925i | \(0.994591\pi\) | |||||||
\(174\) | 23.4164 | 1.77519 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −0.763932 | − | 1.32317i | −0.0574206 | − | 0.0994555i | ||||
\(178\) | 2.23607 | − | 3.87298i | 0.167600 | − | 0.290292i | ||||
\(179\) | 4.47214 | − | 7.74597i | 0.334263 | − | 0.578961i | −0.649080 | − | 0.760720i | \(-0.724846\pi\) |
0.983343 | + | 0.181760i | \(0.0581792\pi\) | |||||||
\(180\) | 4.41641 | + | 7.64944i | 0.329180 | + | 0.570156i | ||||
\(181\) | 25.4164 | 1.88919 | 0.944593 | − | 0.328243i | \(-0.106456\pi\) | ||||
0.944593 | + | 0.328243i | \(0.106456\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.94427 | 0.661180 | ||||||||
\(184\) | −2.76393 | − | 4.78727i | −0.203760 | − | 0.352922i | ||||
\(185\) | 8.47214 | − | 14.6742i | 0.622884 | − | 1.07887i | ||||
\(186\) | −3.81966 | + | 6.61585i | −0.280071 | + | 0.485097i | ||||
\(187\) | 1.61803 | + | 2.80252i | 0.118322 | + | 0.204940i | ||||
\(188\) | −8.29180 | −0.604741 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −28.9443 | −2.09984 | ||||||||
\(191\) | 1.52786 | + | 2.64634i | 0.110552 | + | 0.191482i | 0.915993 | − | 0.401194i | \(-0.131405\pi\) |
−0.805441 | + | 0.592676i | \(0.798071\pi\) | |||||||
\(192\) | 8.03444 | − | 13.9161i | 0.579836 | − | 1.00431i | ||||
\(193\) | −5.94427 | + | 10.2958i | −0.427878 | + | 0.741107i | −0.996684 | − | 0.0813650i | \(-0.974072\pi\) |
0.568806 | + | 0.822472i | \(0.307405\pi\) | |||||||
\(194\) | 19.4721 | + | 33.7267i | 1.39802 | + | 2.42144i | ||||
\(195\) | −8.00000 | −0.572892 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | −1.64590 | − | 2.85078i | −0.116969 | − | 0.202596i | ||||
\(199\) | −1.09017 | + | 1.88823i | −0.0772801 | + | 0.133853i | −0.902076 | − | 0.431578i | \(-0.857957\pi\) |
0.824795 | + | 0.565431i | \(0.191290\pi\) | |||||||
\(200\) | 1.11803 | − | 1.93649i | 0.0790569 | − | 0.136931i | ||||
\(201\) | −8.94427 | − | 15.4919i | −0.630880 | − | 1.09272i | ||||
\(202\) | 10.6525 | 0.749506 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 12.0000 | 0.840168 | ||||||||
\(205\) | −11.2361 | − | 19.4614i | −0.784761 | − | 1.35925i | ||||
\(206\) | 8.61803 | − | 14.9269i | 0.600447 | − | 1.04000i | ||||
\(207\) | 1.81966 | − | 3.15174i | 0.126475 | − | 0.219061i | ||||
\(208\) | −1.61803 | − | 2.80252i | −0.112190 | − | 0.194320i | ||||
\(209\) | 6.47214 | 0.447687 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.8885 | −0.956127 | −0.478063 | − | 0.878325i | \(-0.658661\pi\) | ||||
−0.478063 | + | 0.878325i | \(0.658661\pi\) | |||||||
\(212\) | 0.708204 | + | 1.22665i | 0.0486396 | + | 0.0842463i | ||||
\(213\) | 6.47214 | − | 11.2101i | 0.443463 | − | 0.768101i | ||||
\(214\) | 4.47214 | − | 7.74597i | 0.305709 | − | 0.529503i | ||||
\(215\) | −8.00000 | − | 13.8564i | −0.545595 | − | 0.944999i | ||||
\(216\) | −12.3607 | −0.841038 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.0000 | −0.677285 | ||||||||
\(219\) | −0.472136 | − | 0.817763i | −0.0319040 | − | 0.0552593i | ||||
\(220\) | 3.00000 | − | 5.19615i | 0.202260 | − | 0.350325i | ||||
\(221\) | 5.23607 | − | 9.06914i | 0.352216 | − | 0.610056i | ||||
\(222\) | 11.7082 | + | 20.2792i | 0.785803 | + | 1.36105i | ||||
\(223\) | 10.1803 | 0.681726 | 0.340863 | − | 0.940113i | \(-0.389281\pi\) | ||||
0.340863 | + | 0.940113i | \(0.389281\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.47214 | 0.0981424 | ||||||||
\(226\) | −2.23607 | − | 3.87298i | −0.148741 | − | 0.257627i | ||||
\(227\) | 2.94427 | − | 5.09963i | 0.195418 | − | 0.338474i | −0.751619 | − | 0.659597i | \(-0.770727\pi\) |
0.947038 | + | 0.321123i | \(0.104060\pi\) | |||||||
\(228\) | 12.0000 | − | 20.7846i | 0.794719 | − | 1.37649i | ||||
\(229\) | −2.23607 | − | 3.87298i | −0.147764 | − | 0.255934i | 0.782637 | − | 0.622478i | \(-0.213874\pi\) |
−0.930401 | + | 0.366544i | \(0.880541\pi\) | |||||||
\(230\) | 11.0557 | 0.728993 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.9443 | 1.24375 | ||||||||
\(233\) | −4.70820 | − | 8.15485i | −0.308445 | − | 0.534242i | 0.669578 | − | 0.742742i | \(-0.266475\pi\) |
−0.978022 | + | 0.208500i | \(0.933142\pi\) | |||||||
\(234\) | −5.32624 | + | 9.22531i | −0.348187 | + | 0.603078i | ||||
\(235\) | 2.76393 | − | 4.78727i | 0.180299 | − | 0.312287i | ||||
\(236\) | −1.85410 | − | 3.21140i | −0.120692 | − | 0.209044i | ||||
\(237\) | −11.0557 | −0.718147 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.88854 | −0.639637 | −0.319818 | − | 0.947479i | \(-0.603622\pi\) | ||||
−0.319818 | + | 0.947479i | \(0.603622\pi\) | |||||||
\(240\) | 1.23607 | + | 2.14093i | 0.0797878 | + | 0.138197i | ||||
\(241\) | −6.56231 | + | 11.3662i | −0.422715 | + | 0.732164i | −0.996204 | − | 0.0870491i | \(-0.972256\pi\) |
0.573489 | + | 0.819213i | \(0.305590\pi\) | |||||||
\(242\) | −1.11803 | + | 1.93649i | −0.0718699 | + | 0.124482i | ||||
\(243\) | −6.79837 | − | 11.7751i | −0.436116 | − | 0.755375i | ||||
\(244\) | 21.7082 | 1.38973 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 31.0557 | 1.98004 | ||||||||
\(247\) | −10.4721 | − | 18.1383i | −0.666326 | − | 1.15411i | ||||
\(248\) | −3.09017 | + | 5.35233i | −0.196226 | + | 0.339873i | ||||
\(249\) | −7.05573 | + | 12.2209i | −0.447139 | + | 0.774467i | ||||
\(250\) | 13.4164 | + | 23.2379i | 0.848528 | + | 1.46969i | ||||
\(251\) | −4.29180 | −0.270896 | −0.135448 | − | 0.990784i | \(-0.543247\pi\) | ||||
−0.135448 | + | 0.990784i | \(0.543247\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.47214 | −0.155422 | ||||||||
\(254\) | −3.41641 | − | 5.91739i | −0.214364 | − | 0.371290i | ||||
\(255\) | −4.00000 | + | 6.92820i | −0.250490 | + | 0.433861i | ||||
\(256\) | 4.50000 | − | 7.79423i | 0.281250 | − | 0.487139i | ||||
\(257\) | −3.00000 | − | 5.19615i | −0.187135 | − | 0.324127i | 0.757159 | − | 0.653231i | \(-0.226587\pi\) |
−0.944294 | + | 0.329104i | \(0.893253\pi\) | |||||||
\(258\) | 22.1115 | 1.37660 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −19.4164 | −1.20415 | ||||||||
\(261\) | 6.23607 | + | 10.8012i | 0.386003 | + | 0.668577i | ||||
\(262\) | 24.4721 | − | 42.3870i | 1.51189 | − | 2.61868i | ||||
\(263\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(264\) | 1.38197 | + | 2.39364i | 0.0850541 | + | 0.147318i | ||||
\(265\) | −0.944272 | −0.0580062 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.47214 | −0.151292 | ||||||||
\(268\) | −21.7082 | − | 37.5997i | −1.32604 | − | 2.29677i | ||||
\(269\) | 6.70820 | − | 11.6190i | 0.409006 | − | 0.708420i | −0.585772 | − | 0.810476i | \(-0.699209\pi\) |
0.994779 | + | 0.102056i | \(0.0325420\pi\) | |||||||
\(270\) | 12.3607 | − | 21.4093i | 0.752247 | − | 1.30293i | ||||
\(271\) | −5.23607 | − | 9.06914i | −0.318068 | − | 0.550911i | 0.662017 | − | 0.749489i | \(-0.269701\pi\) |
−0.980085 | + | 0.198578i | \(0.936368\pi\) | |||||||
\(272\) | −3.23607 | −0.196215 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 36.8328 | 2.22515 | ||||||||
\(275\) | −0.500000 | − | 0.866025i | −0.0301511 | − | 0.0522233i | ||||
\(276\) | −4.58359 | + | 7.93901i | −0.275900 | + | 0.477873i | ||||
\(277\) | 9.94427 | − | 17.2240i | 0.597493 | − | 1.03489i | −0.395696 | − | 0.918381i | \(-0.629497\pi\) |
0.993190 | − | 0.116508i | \(-0.0371699\pi\) | |||||||
\(278\) | −1.70820 | − | 2.95870i | −0.102451 | − | 0.177451i | ||||
\(279\) | −4.06888 | −0.243598 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.52786 | −0.210455 | −0.105227 | − | 0.994448i | \(-0.533557\pi\) | ||||
−0.105227 | + | 0.994448i | \(0.533557\pi\) | |||||||
\(282\) | 3.81966 | + | 6.61585i | 0.227457 | + | 0.393968i | ||||
\(283\) | 14.9443 | − | 25.8842i | 0.888345 | − | 1.53866i | 0.0465134 | − | 0.998918i | \(-0.485189\pi\) |
0.841831 | − | 0.539741i | \(-0.181478\pi\) | |||||||
\(284\) | 15.7082 | − | 27.2074i | 0.932110 | − | 1.61446i | ||||
\(285\) | 8.00000 | + | 13.8564i | 0.473879 | + | 0.820783i | ||||
\(286\) | 7.23607 | 0.427878 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 9.87539 | 0.581913 | ||||||||
\(289\) | 3.26393 | + | 5.65330i | 0.191996 | + | 0.332547i | ||||
\(290\) | −18.9443 | + | 32.8124i | −1.11245 | + | 1.92681i | ||||
\(291\) | 10.7639 | − | 18.6437i | 0.630993 | − | 1.09291i | ||||
\(292\) | −1.14590 | − | 1.98475i | −0.0670586 | − | 0.116149i | ||||
\(293\) | 25.1246 | 1.46780 | 0.733898 | − | 0.679260i | \(-0.237699\pi\) | ||||
0.733898 | + | 0.679260i | \(0.237699\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.47214 | 0.143933 | ||||||||
\(296\) | 9.47214 | + | 16.4062i | 0.550557 | + | 0.953592i | ||||
\(297\) | −2.76393 | + | 4.78727i | −0.160380 | + | 0.277786i | ||||
\(298\) | −15.6525 | + | 27.1109i | −0.906724 | + | 1.57049i | ||||
\(299\) | 4.00000 | + | 6.92820i | 0.231326 | + | 0.400668i | ||||
\(300\) | −3.70820 | −0.214093 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 20.0000 | 1.15087 | ||||||||
\(303\) | −2.94427 | − | 5.09963i | −0.169144 | − | 0.292966i | ||||
\(304\) | −3.23607 | + | 5.60503i | −0.185601 | + | 0.321471i | ||||
\(305\) | −7.23607 | + | 12.5332i | −0.414336 | + | 0.717651i | ||||
\(306\) | 5.32624 | + | 9.22531i | 0.304481 | + | 0.527376i | ||||
\(307\) | 8.94427 | 0.510477 | 0.255238 | − | 0.966878i | \(-0.417846\pi\) | ||||
0.255238 | + | 0.966878i | \(0.417846\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.52786 | −0.542021 | ||||||||
\(310\) | −6.18034 | − | 10.7047i | −0.351020 | − | 0.607984i | ||||
\(311\) | −4.14590 | + | 7.18091i | −0.235092 | + | 0.407192i | −0.959300 | − | 0.282391i | \(-0.908873\pi\) |
0.724207 | + | 0.689582i | \(0.242206\pi\) | |||||||
\(312\) | 4.47214 | − | 7.74597i | 0.253185 | − | 0.438529i | ||||
\(313\) | 7.47214 | + | 12.9421i | 0.422350 | + | 0.731532i | 0.996169 | − | 0.0874505i | \(-0.0278720\pi\) |
−0.573819 | + | 0.818982i | \(0.694539\pi\) | |||||||
\(314\) | −24.4721 | −1.38104 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −26.8328 | −1.50946 | ||||||||
\(317\) | −7.00000 | − | 12.1244i | −0.393159 | − | 0.680972i | 0.599705 | − | 0.800221i | \(-0.295285\pi\) |
−0.992864 | + | 0.119249i | \(0.961951\pi\) | |||||||
\(318\) | 0.652476 | − | 1.13012i | 0.0365890 | − | 0.0633741i | ||||
\(319\) | 4.23607 | − | 7.33708i | 0.237174 | − | 0.410798i | ||||
\(320\) | 13.0000 | + | 22.5167i | 0.726722 | + | 1.25872i | ||||
\(321\) | −4.94427 | −0.275962 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.9443 | −1.16537 | ||||||||
\(324\) | 3.62461 | + | 6.27801i | 0.201367 | + | 0.348778i | ||||
\(325\) | −1.61803 | + | 2.80252i | −0.0897524 | + | 0.155456i | ||||
\(326\) | 3.81966 | − | 6.61585i | 0.211551 | − | 0.366418i | ||||
\(327\) | 2.76393 | + | 4.78727i | 0.152846 | + | 0.264737i | ||||
\(328\) | 25.1246 | 1.38727 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −5.52786 | −0.304299 | ||||||||
\(331\) | 6.94427 | + | 12.0278i | 0.381692 | + | 0.661109i | 0.991304 | − | 0.131590i | \(-0.0420083\pi\) |
−0.609613 | + | 0.792700i | \(0.708675\pi\) | |||||||
\(332\) | −17.1246 | + | 29.6607i | −0.939835 | + | 1.62784i | ||||
\(333\) | −6.23607 | + | 10.8012i | −0.341734 | + | 0.591901i | ||||
\(334\) | 5.52786 | + | 9.57454i | 0.302471 | + | 0.523896i | ||||
\(335\) | 28.9443 | 1.58139 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.5279 | −0.627963 | −0.313981 | − | 0.949429i | \(-0.601663\pi\) | ||||
−0.313981 | + | 0.949429i | \(0.601663\pi\) | |||||||
\(338\) | 2.82624 | + | 4.89519i | 0.153727 | + | 0.266263i | ||||
\(339\) | −1.23607 | + | 2.14093i | −0.0671340 | + | 0.116279i | ||||
\(340\) | −9.70820 | + | 16.8151i | −0.526501 | + | 0.911927i | ||||
\(341\) | 1.38197 | + | 2.39364i | 0.0748377 | + | 0.129623i | ||||
\(342\) | 21.3050 | 1.15204 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 17.8885 | 0.964486 | ||||||||
\(345\) | −3.05573 | − | 5.29268i | −0.164515 | − | 0.284948i | ||||
\(346\) | −14.2705 | + | 24.7172i | −0.767187 | + | 1.32881i | ||||
\(347\) | −10.4721 | + | 18.1383i | −0.562174 | + | 0.973713i | 0.435133 | + | 0.900366i | \(0.356701\pi\) |
−0.997306 | + | 0.0733471i | \(0.976632\pi\) | |||||||
\(348\) | −15.7082 | − | 27.2074i | −0.842048 | − | 1.45847i | ||||
\(349\) | 7.23607 | 0.387338 | 0.193669 | − | 0.981067i | \(-0.437961\pi\) | ||||
0.193669 | + | 0.981067i | \(0.437961\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.8885 | 0.954820 | ||||||||
\(352\) | −3.35410 | − | 5.80948i | −0.178774 | − | 0.309646i | ||||
\(353\) | 9.94427 | − | 17.2240i | 0.529280 | − | 0.916740i | −0.470137 | − | 0.882594i | \(-0.655795\pi\) |
0.999417 | − | 0.0341465i | \(-0.0108713\pi\) | |||||||
\(354\) | −1.70820 | + | 2.95870i | −0.0907900 | + | 0.157253i | ||||
\(355\) | 10.4721 | + | 18.1383i | 0.555803 | + | 0.962679i | ||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.0000 | −1.05703 | ||||||||
\(359\) | 12.4721 | + | 21.6024i | 0.658254 | + | 1.14013i | 0.981067 | + | 0.193667i | \(0.0620381\pi\) |
−0.322813 | + | 0.946463i | \(0.604629\pi\) | |||||||
\(360\) | 3.29180 | − | 5.70156i | 0.173493 | − | 0.300498i | ||||
\(361\) | −11.4443 | + | 19.8221i | −0.602330 | + | 1.04327i | ||||
\(362\) | −28.4164 | − | 49.2187i | −1.49353 | − | 2.58688i | ||||
\(363\) | 1.23607 | 0.0648767 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.52786 | 0.0799721 | ||||||||
\(366\) | −10.0000 | − | 17.3205i | −0.522708 | − | 0.905357i | ||||
\(367\) | −11.5623 | + | 20.0265i | −0.603547 | + | 1.04537i | 0.388732 | + | 0.921351i | \(0.372913\pi\) |
−0.992279 | + | 0.124024i | \(0.960420\pi\) | |||||||
\(368\) | 1.23607 | − | 2.14093i | 0.0644345 | − | 0.111604i | ||||
\(369\) | 8.27051 | + | 14.3249i | 0.430546 | + | 0.745727i | ||||
\(370\) | −37.8885 | −1.96973 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 10.2492 | 0.531397 | ||||||||
\(373\) | −3.00000 | − | 5.19615i | −0.155334 | − | 0.269047i | 0.777847 | − | 0.628454i | \(-0.216312\pi\) |
−0.933181 | + | 0.359408i | \(0.882979\pi\) | |||||||
\(374\) | 3.61803 | − | 6.26662i | 0.187084 | − | 0.324039i | ||||
\(375\) | 7.41641 | − | 12.8456i | 0.382982 | − | 0.663344i | ||||
\(376\) | 3.09017 | + | 5.35233i | 0.159363 | + | 0.276025i | ||||
\(377\) | −27.4164 | −1.41202 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 37.3050 | 1.91623 | 0.958113 | − | 0.286389i | \(-0.0924551\pi\) | ||||
0.958113 | + | 0.286389i | \(0.0924551\pi\) | |||||||
\(380\) | 19.4164 | + | 33.6302i | 0.996041 | + | 1.72519i | ||||
\(381\) | −1.88854 | + | 3.27105i | −0.0967530 | + | 0.167581i | ||||
\(382\) | 3.41641 | − | 5.91739i | 0.174799 | − | 0.302760i | ||||
\(383\) | −2.32624 | − | 4.02916i | −0.118865 | − | 0.205881i | 0.800453 | − | 0.599395i | \(-0.204592\pi\) |
−0.919318 | + | 0.393515i | \(0.871259\pi\) | |||||||
\(384\) | −19.3475 | −0.987324 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.5836 | 1.35307 | ||||||||
\(387\) | 5.88854 | + | 10.1993i | 0.299332 | + | 0.518457i | ||||
\(388\) | 26.1246 | − | 45.2492i | 1.32628 | − | 2.29718i | ||||
\(389\) | −7.94427 | + | 13.7599i | −0.402791 | + | 0.697654i | −0.994062 | − | 0.108819i | \(-0.965293\pi\) |
0.591271 | + | 0.806473i | \(0.298626\pi\) | |||||||
\(390\) | 8.94427 | + | 15.4919i | 0.452911 | + | 0.784465i | ||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27.0557 | −1.36478 | ||||||||
\(394\) | 2.23607 | + | 3.87298i | 0.112651 | + | 0.195118i | ||||
\(395\) | 8.94427 | − | 15.4919i | 0.450035 | − | 0.779484i | ||||
\(396\) | −2.20820 | + | 3.82472i | −0.110966 | + | 0.192199i | ||||
\(397\) | −17.9443 | − | 31.0804i | −0.900597 | − | 1.55988i | −0.826721 | − | 0.562613i | \(-0.809796\pi\) |
−0.0738766 | − | 0.997267i | \(-0.523537\pi\) | |||||||
\(398\) | 4.87539 | 0.244381 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −11.4721 | − | 19.8703i | −0.572891 | − | 0.992277i | −0.996267 | − | 0.0863225i | \(-0.972488\pi\) |
0.423376 | − | 0.905954i | \(-0.360845\pi\) | |||||||
\(402\) | −20.0000 | + | 34.6410i | −0.997509 | + | 1.72774i | ||||
\(403\) | 4.47214 | − | 7.74597i | 0.222773 | − | 0.385854i | ||||
\(404\) | −7.14590 | − | 12.3771i | −0.355522 | − | 0.615782i | ||||
\(405\) | −4.83282 | −0.240145 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.47214 | 0.419948 | ||||||||
\(408\) | −4.47214 | − | 7.74597i | −0.221404 | − | 0.383482i | ||||
\(409\) | 4.56231 | − | 7.90215i | 0.225592 | − | 0.390736i | −0.730905 | − | 0.682479i | \(-0.760902\pi\) |
0.956497 | + | 0.291743i | \(0.0942352\pi\) | |||||||
\(410\) | −25.1246 | + | 43.5171i | −1.24082 | + | 2.14916i | ||||
\(411\) | −10.1803 | − | 17.6329i | −0.502159 | − | 0.869765i | ||||
\(412\) | −23.1246 | −1.13927 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.13777 | −0.399949 | ||||||||
\(415\) | −11.4164 | − | 19.7738i | −0.560409 | − | 0.970658i | ||||
\(416\) | −10.8541 | + | 18.7999i | −0.532166 | + | 0.921739i | ||||
\(417\) | −0.944272 | + | 1.63553i | −0.0462412 | + | 0.0800921i | ||||
\(418\) | −7.23607 | − | 12.5332i | −0.353928 | − | 0.613021i | ||||
\(419\) | −24.6525 | −1.20435 | −0.602176 | − | 0.798363i | \(-0.705700\pi\) | ||||
−0.602176 | + | 0.798363i | \(0.705700\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.3607 | 1.08979 | 0.544896 | − | 0.838503i | \(-0.316569\pi\) | ||||
0.544896 | + | 0.838503i | \(0.316569\pi\) | |||||||
\(422\) | 15.5279 | + | 26.8950i | 0.755885 | + | 1.30923i | ||||
\(423\) | −2.03444 | + | 3.52376i | −0.0989179 | + | 0.171331i | ||||
\(424\) | 0.527864 | − | 0.914287i | 0.0256353 | − | 0.0444017i | ||||
\(425\) | 1.61803 | + | 2.80252i | 0.0784862 | + | 0.135942i | ||||
\(426\) | −28.9443 | −1.40235 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | −2.00000 | − | 3.46410i | −0.0965609 | − | 0.167248i | ||||
\(430\) | −17.8885 | + | 30.9839i | −0.862662 | + | 1.49417i | ||||
\(431\) | −6.00000 | + | 10.3923i | −0.289010 | + | 0.500580i | −0.973574 | − | 0.228373i | \(-0.926659\pi\) |
0.684564 | + | 0.728953i | \(0.259993\pi\) | |||||||
\(432\) | −2.76393 | − | 4.78727i | −0.132980 | − | 0.230328i | ||||
\(433\) | 8.47214 | 0.407145 | 0.203572 | − | 0.979060i | \(-0.434745\pi\) | ||||
0.203572 | + | 0.979060i | \(0.434745\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 20.9443 | 1.00420 | ||||||||
\(436\) | 6.70820 | + | 11.6190i | 0.321265 | + | 0.556447i | ||||
\(437\) | 8.00000 | − | 13.8564i | 0.382692 | − | 0.662842i | ||||
\(438\) | −1.05573 | + | 1.82857i | −0.0504446 | + | 0.0873727i | ||||
\(439\) | 5.23607 | + | 9.06914i | 0.249904 | + | 0.432846i | 0.963499 | − | 0.267712i | \(-0.0862676\pi\) |
−0.713595 | + | 0.700558i | \(0.752934\pi\) | |||||||
\(440\) | −4.47214 | −0.213201 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −23.4164 | −1.11380 | ||||||||
\(443\) | 12.4721 | + | 21.6024i | 0.592569 | + | 1.02636i | 0.993885 | + | 0.110420i | \(0.0352196\pi\) |
−0.401316 | + | 0.915940i | \(0.631447\pi\) | |||||||
\(444\) | 15.7082 | − | 27.2074i | 0.745478 | − | 1.29121i | ||||
\(445\) | 2.00000 | − | 3.46410i | 0.0948091 | − | 0.164214i | ||||
\(446\) | −11.3820 | − | 19.7141i | −0.538952 | − | 0.933492i | ||||
\(447\) | 17.3050 | 0.818496 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.4721 | −1.34368 | −0.671842 | − | 0.740695i | \(-0.734496\pi\) | ||||
−0.671842 | + | 0.740695i | \(0.734496\pi\) | |||||||
\(450\) | −1.64590 | − | 2.85078i | −0.0775884 | − | 0.134387i | ||||
\(451\) | 5.61803 | − | 9.73072i | 0.264543 | − | 0.458202i | ||||
\(452\) | −3.00000 | + | 5.19615i | −0.141108 | + | 0.244406i | ||||
\(453\) | −5.52786 | − | 9.57454i | −0.259722 | − | 0.449851i | ||||
\(454\) | −13.1672 | −0.617967 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −17.8885 | −0.837708 | ||||||||
\(457\) | 14.4164 | + | 24.9700i | 0.674371 | + | 1.16805i | 0.976652 | + | 0.214826i | \(0.0689185\pi\) |
−0.302281 | + | 0.953219i | \(0.597748\pi\) | |||||||
\(458\) | −5.00000 | + | 8.66025i | −0.233635 | + | 0.404667i | ||||
\(459\) | 8.94427 | − | 15.4919i | 0.417483 | − | 0.723102i | ||||
\(460\) | −7.41641 | − | 12.8456i | −0.345792 | − | 0.598929i | ||||
\(461\) | 12.1803 | 0.567295 | 0.283647 | − | 0.958929i | \(-0.408455\pi\) | ||||
0.283647 | + | 0.958929i | \(0.408455\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.52786 | −0.256902 | −0.128451 | − | 0.991716i | \(-0.541000\pi\) | ||||
−0.128451 | + | 0.991716i | \(0.541000\pi\) | |||||||
\(464\) | 4.23607 | + | 7.33708i | 0.196655 | + | 0.340616i | ||||
\(465\) | −3.41641 | + | 5.91739i | −0.158432 | + | 0.274412i | ||||
\(466\) | −10.5279 | + | 18.2348i | −0.487694 | + | 0.844711i | ||||
\(467\) | 12.0344 | + | 20.8443i | 0.556888 | + | 0.964558i | 0.997754 | + | 0.0669848i | \(0.0213379\pi\) |
−0.440866 | + | 0.897573i | \(0.645329\pi\) | |||||||
\(468\) | 14.2918 | 0.660639 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −12.3607 | −0.570156 | ||||||||
\(471\) | 6.76393 | + | 11.7155i | 0.311666 | + | 0.539821i | ||||
\(472\) | −1.38197 | + | 2.39364i | −0.0636101 | + | 0.110176i | ||||
\(473\) | 4.00000 | − | 6.92820i | 0.183920 | − | 0.318559i | ||||
\(474\) | 12.3607 | + | 21.4093i | 0.567745 | + | 0.983363i | ||||
\(475\) | 6.47214 | 0.296962 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.695048 | 0.0318241 | ||||||||
\(478\) | 11.0557 | + | 19.1491i | 0.505677 | + | 0.875859i | ||||
\(479\) | 6.76393 | − | 11.7155i | 0.309052 | − | 0.535294i | −0.669103 | − | 0.743169i | \(-0.733322\pi\) |
0.978155 | + | 0.207876i | \(0.0666550\pi\) | |||||||
\(480\) | 8.29180 | − | 14.3618i | 0.378467 | − | 0.655524i | ||||
\(481\) | −13.7082 | − | 23.7433i | −0.625040 | − | 1.08260i | ||||
\(482\) | 29.3475 | 1.33674 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.00000 | 0.136364 | ||||||||
\(485\) | 17.4164 | + | 30.1661i | 0.790838 | + | 1.36977i | ||||
\(486\) | −15.2016 | + | 26.3300i | −0.689560 | + | 1.19435i | ||||
\(487\) | 18.1803 | − | 31.4893i | 0.823830 | − | 1.42692i | −0.0789805 | − | 0.996876i | \(-0.525166\pi\) |
0.902810 | − | 0.430039i | \(-0.141500\pi\) | |||||||
\(488\) | −8.09017 | − | 14.0126i | −0.366225 | − | 0.634320i | ||||
\(489\) | −4.22291 | −0.190967 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | −20.8328 | − | 36.0835i | −0.939216 | − | 1.62677i | ||||
\(493\) | −13.7082 | + | 23.7433i | −0.617386 | + | 1.06934i | ||||
\(494\) | −23.4164 | + | 40.5584i | −1.05355 | + | 1.82481i | ||||
\(495\) | −1.47214 | − | 2.54981i | −0.0661676 | − | 0.114606i | ||||
\(496\) | −2.76393 | −0.124104 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 31.5542 | 1.41398 | ||||||||
\(499\) | −0.763932 | − | 1.32317i | −0.0341983 | − | 0.0592332i | 0.848420 | − | 0.529324i | \(-0.177554\pi\) |
−0.882618 | + | 0.470091i | \(0.844221\pi\) | |||||||
\(500\) | 18.0000 | − | 31.1769i | 0.804984 | − | 1.39427i | ||||
\(501\) | 3.05573 | − | 5.29268i | 0.136520 | − | 0.236459i | ||||
\(502\) | 4.79837 | + | 8.31103i | 0.214162 | + | 0.370939i | ||||
\(503\) | −23.4164 | −1.04409 | −0.522043 | − | 0.852919i | \(-0.674830\pi\) | ||||
−0.522043 | + | 0.852919i | \(0.674830\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.52786 | 0.423984 | ||||||||
\(506\) | 2.76393 | + | 4.78727i | 0.122872 | + | 0.212820i | ||||
\(507\) | 1.56231 | − | 2.70599i | 0.0693844 | − | 0.120177i | ||||
\(508\) | −4.58359 | + | 7.93901i | −0.203364 | + | 0.352237i | ||||
\(509\) | 20.2361 | + | 35.0499i | 0.896948 | + | 1.55356i | 0.831375 | + | 0.555712i | \(0.187554\pi\) |
0.0655728 | + | 0.997848i | \(0.479113\pi\) | |||||||
\(510\) | 17.8885 | 0.792118 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11.1803 | 0.494106 | ||||||||
\(513\) | −17.8885 | − | 30.9839i | −0.789799 | − | 1.36797i | ||||
\(514\) | −6.70820 | + | 11.6190i | −0.295886 | + | 0.512490i | ||||
\(515\) | 7.70820 | − | 13.3510i | 0.339664 | − | 0.588315i | ||||
\(516\) | −14.8328 | − | 25.6912i | −0.652978 | − | 1.13099i | ||||
\(517\) | 2.76393 | 0.121558 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.7771 | 0.692537 | ||||||||
\(520\) | 7.23607 | + | 12.5332i | 0.317323 | + | 0.549619i | ||||
\(521\) | 15.1803 | − | 26.2931i | 0.665063 | − | 1.15192i | −0.314206 | − | 0.949355i | \(-0.601738\pi\) |
0.979268 | − | 0.202568i | \(-0.0649286\pi\) | |||||||
\(522\) | 13.9443 | − | 24.1522i | 0.610324 | − | 1.05711i | ||||
\(523\) | 22.0000 | + | 38.1051i | 0.961993 | + | 1.66622i | 0.717486 | + | 0.696573i | \(0.245293\pi\) |
0.244507 | + | 0.969648i | \(0.421374\pi\) | |||||||
\(524\) | −65.6656 | −2.86862 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.47214 | − | 7.74597i | −0.194809 | − | 0.337420i | ||||
\(528\) | −0.618034 | + | 1.07047i | −0.0268965 | + | 0.0465861i | ||||
\(529\) | 8.44427 | − | 14.6259i | 0.367142 | − | 0.635909i | ||||
\(530\) | 1.05573 | + | 1.82857i | 0.0458579 | + | 0.0794282i | ||||
\(531\) | −1.81966 | −0.0789665 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.3607 | −1.57496 | ||||||||
\(534\) | 2.76393 | + | 4.78727i | 0.119607 | + | 0.207165i | ||||
\(535\) | 4.00000 | − | 6.92820i | 0.172935 | − | 0.299532i | ||||
\(536\) | −16.1803 | + | 28.0252i | −0.698884 | + | 1.21050i | ||||
\(537\) | 5.52786 | + | 9.57454i | 0.238545 | + | 0.413172i | ||||
\(538\) | −30.0000 | −1.29339 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −33.1672 | −1.42729 | ||||||||
\(541\) | −10.4164 | − | 18.0417i | −0.447836 | − | 0.775675i | 0.550409 | − | 0.834895i | \(-0.314472\pi\) |
−0.998245 | + | 0.0592201i | \(0.981139\pi\) | |||||||
\(542\) | −11.7082 | + | 20.2792i | −0.502910 | + | 0.871066i | ||||
\(543\) | −15.7082 | + | 27.2074i | −0.674104 | + | 1.16758i | ||||
\(544\) | 10.8541 | + | 18.7999i | 0.465366 | + | 0.806037i | ||||
\(545\) | −8.94427 | −0.383131 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0000 | 1.19719 | 0.598597 | − | 0.801050i | \(-0.295725\pi\) | ||||
0.598597 | + | 0.801050i | \(0.295725\pi\) | |||||||
\(548\) | −24.7082 | − | 42.7959i | −1.05548 | − | 1.82815i | ||||
\(549\) | 5.32624 | − | 9.22531i | 0.227318 | − | 0.393727i | ||||
\(550\) | −1.11803 | + | 1.93649i | −0.0476731 | + | 0.0825723i | ||||
\(551\) | 27.4164 | + | 47.4866i | 1.16798 | + | 2.02300i | ||||
\(552\) | 6.83282 | 0.290824 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −44.4721 | −1.88944 | ||||||||
\(555\) | 10.4721 | + | 18.1383i | 0.444517 | + | 0.769927i | ||||
\(556\) | −2.29180 | + | 3.96951i | −0.0971938 | + | 0.168345i | ||||
\(557\) | 19.4721 | − | 33.7267i | 0.825061 | − | 1.42905i | −0.0768119 | − | 0.997046i | \(-0.524474\pi\) |
0.901873 | − | 0.432002i | \(-0.142193\pi\) | |||||||
\(558\) | 4.54915 | + | 7.87936i | 0.192581 | + | 0.333560i | ||||
\(559\) | −25.8885 | −1.09497 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.00000 | −0.168880 | ||||||||
\(562\) | 3.94427 | + | 6.83168i | 0.166379 | + | 0.288177i | ||||
\(563\) | 6.29180 | − | 10.8977i | 0.265168 | − | 0.459284i | −0.702440 | − | 0.711743i | \(-0.747906\pi\) |
0.967608 | + | 0.252459i | \(0.0812394\pi\) | |||||||
\(564\) | 5.12461 | − | 8.87609i | 0.215785 | − | 0.373751i | ||||
\(565\) | −2.00000 | − | 3.46410i | −0.0841406 | − | 0.145736i | ||||
\(566\) | −66.8328 | −2.80919 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −23.4164 | −0.982531 | ||||||||
\(569\) | −3.76393 | − | 6.51932i | −0.157792 | − | 0.273304i | 0.776280 | − | 0.630388i | \(-0.217104\pi\) |
−0.934072 | + | 0.357084i | \(0.883771\pi\) | |||||||
\(570\) | 17.8885 | − | 30.9839i | 0.749269 | − | 1.29777i | ||||
\(571\) | 7.52786 | − | 13.0386i | 0.315031 | − | 0.545650i | −0.664413 | − | 0.747366i | \(-0.731318\pi\) |
0.979444 | + | 0.201716i | \(0.0646516\pi\) | |||||||
\(572\) | −4.85410 | − | 8.40755i | −0.202960 | − | 0.351537i | ||||
\(573\) | −3.77709 | −0.157790 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.47214 | −0.103095 | ||||||||
\(576\) | −9.56888 | − | 16.5738i | −0.398703 | − | 0.690575i | ||||
\(577\) | −9.76393 | + | 16.9116i | −0.406478 | + | 0.704040i | −0.994492 | − | 0.104810i | \(-0.966576\pi\) |
0.588014 | + | 0.808850i | \(0.299910\pi\) | |||||||
\(578\) | 7.29837 | − | 12.6412i | 0.303572 | − | 0.525803i | ||||
\(579\) | −7.34752 | − | 12.7263i | −0.305353 | − | 0.528886i | ||||
\(580\) | 50.8328 | 2.11072 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −48.1378 | −1.99537 | ||||||||
\(583\) | −0.236068 | − | 0.408882i | −0.00977694 | − | 0.0169342i | ||||
\(584\) | −0.854102 | + | 1.47935i | −0.0353430 | + | 0.0612159i | ||||
\(585\) | −4.76393 | + | 8.25137i | −0.196964 | + | 0.341152i | ||||
\(586\) | −28.0902 | − | 48.6536i | −1.16039 | − | 2.00986i | ||||
\(587\) | −27.1246 | −1.11955 | −0.559776 | − | 0.828644i | \(-0.689113\pi\) | ||||
−0.559776 | + | 0.828644i | \(0.689113\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.8885 | −0.737085 | ||||||||
\(590\) | −2.76393 | − | 4.78727i | −0.113789 | − | 0.197089i | ||||
\(591\) | 1.23607 | − | 2.14093i | 0.0508450 | − | 0.0880662i | ||||
\(592\) | −4.23607 | + | 7.33708i | −0.174101 | + | 0.301552i | ||||
\(593\) | −22.8541 | − | 39.5845i | −0.938505 | − | 1.62554i | −0.768260 | − | 0.640137i | \(-0.778877\pi\) |
−0.170245 | − | 0.985402i | \(-0.554456\pi\) | |||||||
\(594\) | 12.3607 | 0.507165 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 42.0000 | 1.72039 | ||||||||
\(597\) | −1.34752 | − | 2.33398i | −0.0551505 | − | 0.0955235i | ||||
\(598\) | 8.94427 | − | 15.4919i | 0.365758 | − | 0.633512i | ||||
\(599\) | 11.7082 | − | 20.2792i | 0.478384 | − | 0.828586i | −0.521309 | − | 0.853368i | \(-0.674556\pi\) |
0.999693 | + | 0.0247824i | \(0.00788929\pi\) | |||||||
\(600\) | 1.38197 | + | 2.39364i | 0.0564185 | + | 0.0977198i | ||||
\(601\) | 37.1246 | 1.51434 | 0.757172 | − | 0.653215i | \(-0.226580\pi\) | ||||
0.757172 | + | 0.653215i | \(0.226580\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −21.3050 | −0.867605 | ||||||||
\(604\) | −13.4164 | − | 23.2379i | −0.545906 | − | 0.945537i | ||||
\(605\) | −1.00000 | + | 1.73205i | −0.0406558 | + | 0.0704179i | ||||
\(606\) | −6.58359 | + | 11.4031i | −0.267440 | + | 0.463220i | ||||
\(607\) | 6.47214 | + | 11.2101i | 0.262696 | + | 0.455003i | 0.966957 | − | 0.254938i | \(-0.0820551\pi\) |
−0.704262 | + | 0.709941i | \(0.748722\pi\) | |||||||
\(608\) | 43.4164 | 1.76077 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 32.3607 | 1.31025 | ||||||||
\(611\) | −4.47214 | − | 7.74597i | −0.180923 | − | 0.313368i | ||||
\(612\) | 7.14590 | − | 12.3771i | 0.288856 | − | 0.500313i | ||||
\(613\) | −7.65248 | + | 13.2545i | −0.309081 | + | 0.535343i | −0.978162 | − | 0.207846i | \(-0.933355\pi\) |
0.669081 | + | 0.743190i | \(0.266688\pi\) | |||||||
\(614\) | −10.0000 | − | 17.3205i | −0.403567 | − | 0.698999i | ||||
\(615\) | 27.7771 | 1.12008 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.58359 | 0.265045 | 0.132523 | − | 0.991180i | \(-0.457692\pi\) | ||||
0.132523 | + | 0.991180i | \(0.457692\pi\) | |||||||
\(618\) | 10.6525 | + | 18.4506i | 0.428505 | + | 0.742193i | ||||
\(619\) | 5.56231 | − | 9.63420i | 0.223568 | − | 0.387231i | −0.732321 | − | 0.680960i | \(-0.761563\pi\) |
0.955889 | + | 0.293729i | \(0.0948962\pi\) | |||||||
\(620\) | −8.29180 | + | 14.3618i | −0.333007 | + | 0.576784i | ||||
\(621\) | 6.83282 | + | 11.8348i | 0.274191 | + | 0.474914i | ||||
\(622\) | 18.5410 | 0.743427 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | 16.7082 | − | 28.9395i | 0.667794 | − | 1.15665i | ||||
\(627\) | −4.00000 | + | 6.92820i | −0.159745 | + | 0.276686i | ||||
\(628\) | 16.4164 | + | 28.4341i | 0.655086 | + | 1.13464i | ||||
\(629\) | −27.4164 | −1.09316 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.0000 | −0.955425 | −0.477712 | − | 0.878516i | \(-0.658534\pi\) | ||||
−0.477712 | + | 0.878516i | \(0.658534\pi\) | |||||||
\(632\) | 10.0000 | + | 17.3205i | 0.397779 | + | 0.688973i | ||||
\(633\) | 8.58359 | − | 14.8672i | 0.341167 | − | 0.590919i | ||||
\(634\) | −15.6525 | + | 27.1109i | −0.621639 | + | 1.07671i | ||||
\(635\) | −3.05573 | − | 5.29268i | −0.121263 | − | 0.210033i | ||||
\(636\) | −1.75078 | −0.0694228 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −18.9443 | −0.750011 | ||||||||
\(639\) | −7.70820 | − | 13.3510i | −0.304932 | − | 0.528157i | ||||
\(640\) | 15.6525 | − | 27.1109i | 0.618718 | − | 1.07165i | ||||
\(641\) | 7.76393 | − | 13.4475i | 0.306657 | − | 0.531145i | −0.670972 | − | 0.741483i | \(-0.734123\pi\) |
0.977629 | + | 0.210337i | \(0.0674563\pi\) | |||||||
\(642\) | 5.52786 | + | 9.57454i | 0.218167 | + | 0.377877i | ||||
\(643\) | −11.1246 | −0.438712 | −0.219356 | − | 0.975645i | \(-0.570396\pi\) | ||||
−0.219356 | + | 0.975645i | \(0.570396\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.7771 | 0.778722 | ||||||||
\(646\) | 23.4164 | + | 40.5584i | 0.921306 | + | 1.59575i | ||||
\(647\) | 18.0344 | − | 31.2366i | 0.709007 | − | 1.22804i | −0.256219 | − | 0.966619i | \(-0.582477\pi\) |
0.965226 | − | 0.261417i | \(-0.0841899\pi\) | |||||||
\(648\) | 2.70163 | − | 4.67935i | 0.106130 | − | 0.183822i | ||||
\(649\) | 0.618034 | + | 1.07047i | 0.0242600 | + | 0.0420195i | ||||
\(650\) | 7.23607 | 0.283822 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.2492 | −0.401391 | ||||||||
\(653\) | −12.5279 | − | 21.6989i | −0.490253 | − | 0.849143i | 0.509684 | − | 0.860362i | \(-0.329762\pi\) |
−0.999937 | + | 0.0112183i | \(0.996429\pi\) | |||||||
\(654\) | 6.18034 | − | 10.7047i | 0.241670 | − | 0.418585i | ||||
\(655\) | 21.8885 | − | 37.9121i | 0.855256 | − | 1.48135i | ||||
\(656\) | 5.61803 | + | 9.73072i | 0.219347 | + | 0.379921i | ||||
\(657\) | −1.12461 | −0.0438753 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.8885 | −0.696839 | −0.348419 | − | 0.937339i | \(-0.613281\pi\) | ||||
−0.348419 | + | 0.937339i | \(0.613281\pi\) | |||||||
\(660\) | 3.70820 | + | 6.42280i | 0.144342 | + | 0.250007i | ||||
\(661\) | −20.4164 | + | 35.3623i | −0.794106 | + | 1.37543i | 0.129299 | + | 0.991606i | \(0.458727\pi\) |
−0.923405 | + | 0.383827i | \(0.874606\pi\) | |||||||
\(662\) | 15.5279 | − | 26.8950i | 0.603508 | − | 1.04531i | ||||
\(663\) | 6.47214 | + | 11.2101i | 0.251357 | + | 0.435363i | ||||
\(664\) | 25.5279 | 0.990673 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 27.8885 | 1.08066 | ||||||||
\(667\) | −10.4721 | − | 18.1383i | −0.405483 | − | 0.702317i | ||||
\(668\) | 7.41641 | − | 12.8456i | 0.286949 | − | 0.497011i | ||||
\(669\) | −6.29180 | + | 10.8977i | −0.243255 | + | 0.421330i | ||||
\(670\) | −32.3607 | − | 56.0503i | −1.25020 | − | 2.16541i | ||||
\(671\) | −7.23607 | −0.279345 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.4164 | −0.825542 | −0.412771 | − | 0.910835i | \(-0.635439\pi\) | ||||
−0.412771 | + | 0.910835i | \(0.635439\pi\) | |||||||
\(674\) | 12.8885 | + | 22.3236i | 0.496448 | + | 0.859873i | ||||
\(675\) | −2.76393 | + | 4.78727i | −0.106384 | + | 0.184262i | ||||
\(676\) | 3.79180 | − | 6.56758i | 0.145838 | − | 0.252599i | ||||
\(677\) | −4.85410 | − | 8.40755i | −0.186558 | − | 0.323128i | 0.757542 | − | 0.652786i | \(-0.226400\pi\) |
−0.944101 | + | 0.329658i | \(0.893067\pi\) | |||||||
\(678\) | 5.52786 | 0.212296 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 14.4721 | 0.554981 | ||||||||
\(681\) | 3.63932 | + | 6.30349i | 0.139459 | + | 0.241550i | ||||
\(682\) | 3.09017 | − | 5.35233i | 0.118329 | − | 0.204951i | ||||
\(683\) | 2.94427 | − | 5.09963i | 0.112659 | − | 0.195132i | −0.804182 | − | 0.594383i | \(-0.797396\pi\) |
0.916842 | + | 0.399251i | \(0.130730\pi\) | |||||||
\(684\) | −14.2918 | − | 24.7541i | −0.546460 | − | 0.946497i | ||||
\(685\) | 32.9443 | 1.25874 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.52786 | 0.210901 | ||||||||
\(688\) | 4.00000 | + | 6.92820i | 0.152499 | + | 0.264135i | ||||
\(689\) | −0.763932 | + | 1.32317i | −0.0291035 | + | 0.0504087i | ||||
\(690\) | −6.83282 | + | 11.8348i | −0.260121 | + | 0.450543i | ||||
\(691\) | 9.27051 | + | 16.0570i | 0.352667 | + | 0.610837i | 0.986716 | − | 0.162456i | \(-0.0519416\pi\) |
−0.634049 | + | 0.773293i | \(0.718608\pi\) | |||||||
\(692\) | 38.2918 | 1.45564 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 46.8328 | 1.77775 | ||||||||
\(695\) | −1.52786 | − | 2.64634i | −0.0579552 | − | 0.100381i | ||||
\(696\) | −11.7082 | + | 20.2792i | −0.443798 | + | 0.768681i | ||||
\(697\) | −18.1803 | + | 31.4893i | −0.688629 | + | 1.19274i | ||||
\(698\) | −8.09017 | − | 14.0126i | −0.306217 | − | 0.530384i | ||||
\(699\) | 11.6393 | 0.440240 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.5279 | −0.586479 | −0.293240 | − | 0.956039i | \(-0.594733\pi\) | ||||
−0.293240 | + | 0.956039i | \(0.594733\pi\) | |||||||
\(702\) | −20.0000 | − | 34.6410i | −0.754851 | − | 1.30744i | ||||
\(703\) | −27.4164 | + | 47.4866i | −1.03403 | + | 1.79099i | ||||
\(704\) | −6.50000 | + | 11.2583i | −0.244978 | + | 0.424314i | ||||
\(705\) | 3.41641 | + | 5.91739i | 0.128669 | + | 0.222862i | ||||
\(706\) | −44.4721 | −1.67373 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.58359 | 0.172262 | ||||||||
\(709\) | 7.47214 | + | 12.9421i | 0.280622 | + | 0.486051i | 0.971538 | − | 0.236883i | \(-0.0761260\pi\) |
−0.690916 | + | 0.722935i | \(0.742793\pi\) | |||||||
\(710\) | 23.4164 | − | 40.5584i | 0.878802 | − | 1.52213i | ||||
\(711\) | −6.58359 | + | 11.4031i | −0.246904 | + | 0.427650i | ||||
\(712\) | 2.23607 | + | 3.87298i | 0.0838002 | + | 0.145146i | ||||
\(713\) | 6.83282 | 0.255891 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.47214 | 0.242044 | ||||||||
\(716\) | 13.4164 | + | 23.2379i | 0.501395 | + | 0.868441i | ||||
\(717\) | 6.11146 | − | 10.5854i | 0.228237 | − | 0.395317i | ||||
\(718\) | 27.8885 | − | 48.3044i | 1.04079 | − | 1.80270i | ||||
\(719\) | −25.7426 | − | 44.5876i | −0.960039 | − | 1.66284i | −0.722392 | − | 0.691484i | \(-0.756957\pi\) |
−0.237647 | − | 0.971352i | \(-0.576376\pi\) | |||||||
\(720\) | 2.94427 | 0.109727 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 51.1803 | 1.90474 | ||||||||
\(723\) | −8.11146 | − | 14.0495i | −0.301668 | − | 0.522505i | ||||
\(724\) | −38.1246 | + | 66.0338i | −1.41689 | + | 2.45413i | ||||
\(725\) | 4.23607 | − | 7.33708i | 0.157324 | − | 0.272492i | ||||
\(726\) | −1.38197 | − | 2.39364i | −0.0512896 | − | 0.0888361i | ||||
\(727\) | −25.0132 | −0.927687 | −0.463843 | − | 0.885917i | \(-0.653530\pi\) | ||||
−0.463843 | + | 0.885917i | \(0.653530\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.0557 | 0.890953 | ||||||||
\(730\) | −1.70820 | − | 2.95870i | −0.0632235 | − | 0.109506i | ||||
\(731\) | −12.9443 | + | 22.4201i | −0.478761 | + | 0.829239i | ||||
\(732\) | −13.4164 | + | 23.2379i | −0.495885 | + | 0.858898i | ||||
\(733\) | 4.38197 | + | 7.58979i | 0.161852 | + | 0.280335i | 0.935533 | − | 0.353240i | \(-0.114920\pi\) |
−0.773681 | + | 0.633575i | \(0.781587\pi\) | |||||||
\(734\) | 51.7082 | 1.90858 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.5836 | −0.611279 | ||||||||
\(737\) | 7.23607 | + | 12.5332i | 0.266544 | + | 0.461668i | ||||
\(738\) | 18.4934 | − | 32.0315i | 0.680752 | − | 1.17910i | ||||
\(739\) | −12.4721 | + | 21.6024i | −0.458795 | + | 0.794656i | −0.998898 | − | 0.0469430i | \(-0.985052\pi\) |
0.540103 | + | 0.841599i | \(0.318385\pi\) | |||||||
\(740\) | 25.4164 | + | 44.0225i | 0.934326 | + | 1.61830i | ||||
\(741\) | 25.8885 | 0.951039 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.88854 | 0.0692840 | 0.0346420 | − | 0.999400i | \(-0.488971\pi\) | ||||
0.0346420 | + | 0.999400i | \(0.488971\pi\) | |||||||
\(744\) | −3.81966 | − | 6.61585i | −0.140036 | − | 0.242549i | ||||
\(745\) | −14.0000 | + | 24.2487i | −0.512920 | + | 0.888404i | ||||
\(746\) | −6.70820 | + | 11.6190i | −0.245605 | + | 0.425400i | ||||
\(747\) | 8.40325 | + | 14.5549i | 0.307459 | + | 0.532534i | ||||
\(748\) | −9.70820 | −0.354967 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −33.1672 | −1.21109 | ||||||||
\(751\) | −14.7639 | − | 25.5719i | −0.538744 | − | 0.933131i | −0.998972 | − | 0.0453307i | \(-0.985566\pi\) |
0.460229 | − | 0.887800i | \(-0.347767\pi\) | |||||||
\(752\) | −1.38197 | + | 2.39364i | −0.0503951 | + | 0.0872869i | ||||
\(753\) | 2.65248 | − | 4.59422i | 0.0966616 | − | 0.167423i | ||||
\(754\) | 30.6525 | + | 53.0916i | 1.11630 | + | 1.93348i | ||||
\(755\) | 17.8885 | 0.651031 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.8885 | 0.577479 | 0.288739 | − | 0.957408i | \(-0.406764\pi\) | ||||
0.288739 | + | 0.957408i | \(0.406764\pi\) | |||||||
\(758\) | −41.7082 | − | 72.2407i | −1.51491 | − | 2.62390i | ||||
\(759\) | 1.52786 | − | 2.64634i | 0.0554580 | − | 0.0960560i | ||||
\(760\) | 14.4721 | − | 25.0665i | 0.524960 | − | 0.909257i | ||||
\(761\) | −15.7984 | − | 27.3636i | −0.572691 | − | 0.991929i | −0.996288 | − | 0.0860788i | \(-0.972566\pi\) |
0.423598 | − | 0.905850i | \(-0.360767\pi\) | |||||||
\(762\) | 8.44582 | 0.305960 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −9.16718 | −0.331657 | ||||||||
\(765\) | 4.76393 | + | 8.25137i | 0.172240 | + | 0.298329i | ||||
\(766\) | −5.20163 | + | 9.00948i | −0.187942 | + | 0.325526i | ||||
\(767\) | 2.00000 | − | 3.46410i | 0.0722158 | − | 0.125081i | ||||
\(768\) | 5.56231 | + | 9.63420i | 0.200712 | + | 0.347644i | ||||
\(769\) | −18.2918 | −0.659619 | −0.329810 | − | 0.944047i | \(-0.606985\pi\) | ||||
−0.329810 | + | 0.944047i | \(0.606985\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.41641 | 0.267095 | ||||||||
\(772\) | −17.8328 | − | 30.8873i | −0.641817 | − | 1.11166i | ||||
\(773\) | −19.1803 | + | 33.2213i | −0.689869 | + | 1.19489i | 0.282011 | + | 0.959411i | \(0.408999\pi\) |
−0.971880 | + | 0.235477i | \(0.924335\pi\) | |||||||
\(774\) | 13.1672 | − | 22.8062i | 0.473285 | − | 0.819753i | ||||
\(775\) | 1.38197 | + | 2.39364i | 0.0496417 | + | 0.0859819i | ||||
\(776\) | −38.9443 | −1.39802 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 35.5279 | 1.27374 | ||||||||
\(779\) | 36.3607 | + | 62.9785i | 1.30276 | + | 2.25644i | ||||
\(780\) | 12.0000 | − | 20.7846i | 0.429669 | − | 0.744208i | ||||
\(781\) | −5.23607 | + | 9.06914i | −0.187361 | + | 0.324519i | ||||
\(782\) | −8.94427 | − | 15.4919i | −0.319847 | − | 0.553990i | ||||
\(783\) | −46.8328 | −1.67367 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.8885 | −0.781236 | ||||||||
\(786\) | 30.2492 | + | 52.3932i | 1.07895 | + | 1.86880i | ||||
\(787\) | −21.7082 | + | 37.5997i | −0.773814 | + | 1.34028i | 0.161645 | + | 0.986849i | \(0.448320\pi\) |
−0.935459 | + | 0.353436i | \(0.885013\pi\) | |||||||
\(788\) | 3.00000 | − | 5.19615i | 0.106871 | − | 0.185105i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −40.0000 | −1.42314 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.29180 | 0.116969 | ||||||||
\(793\) | 11.7082 | + | 20.2792i | 0.415771 | + | 0.720136i | ||||
\(794\) | −40.1246 | + | 69.4979i | −1.42397 | + | 2.46639i | ||||
\(795\) | 0.583592 | − | 1.01081i | 0.0206979 | − | 0.0358498i | ||||
\(796\) | −3.27051 | − | 5.66469i | −0.115920 | − | 0.200780i | ||||
\(797\) | 14.9443 | 0.529353 | 0.264677 | − | 0.964337i | \(-0.414735\pi\) | ||||
0.264677 | + | 0.964337i | \(0.414735\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.94427 | −0.316426 | ||||||||
\(800\) | −3.35410 | − | 5.80948i | −0.118585 | − | 0.205396i | ||||
\(801\) | −1.47214 | + | 2.54981i | −0.0520154 | + | 0.0900933i | ||||
\(802\) | −25.6525 | + | 44.4314i | −0.905820 | + | 1.56893i | ||||
\(803\) | 0.381966 | + | 0.661585i | 0.0134793 | + | 0.0233468i | ||||
\(804\) | 53.6656 | 1.89264 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.0000 | −0.704470 | ||||||||
\(807\) | 8.29180 | + | 14.3618i | 0.291885 | + | 0.505560i | ||||
\(808\) | −5.32624 | + | 9.22531i | −0.187376 | + | 0.324545i | ||||
\(809\) | −10.5279 | + | 18.2348i | −0.370140 | + | 0.641101i | −0.989587 | − | 0.143937i | \(-0.954024\pi\) |
0.619447 | + | 0.785039i | \(0.287357\pi\) | |||||||
\(810\) | 5.40325 | + | 9.35871i | 0.189851 | + | 0.328831i | ||||
\(811\) | 34.8328 | 1.22315 | 0.611573 | − | 0.791188i | \(-0.290537\pi\) | ||||
0.611573 | + | 0.791188i | \(0.290537\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.9443 | 0.453975 | ||||||||
\(814\) | −9.47214 | − | 16.4062i | −0.331998 | − | 0.575038i | ||||
\(815\) | 3.41641 | − | 5.91739i | 0.119672 | − | 0.207277i | ||||
\(816\) | 2.00000 | − | 3.46410i | 0.0700140 | − | 0.121268i | ||||
\(817\) | 25.8885 | + | 44.8403i | 0.905725 | + | 1.56876i | ||||
\(818\) | −20.4033 | −0.713383 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 67.4164 | 2.35428 | ||||||||
\(821\) | −22.4164 | − | 38.8264i | −0.782338 | − | 1.35505i | −0.930576 | − | 0.366098i | \(-0.880694\pi\) |
0.148238 | − | 0.988952i | \(-0.452640\pi\) | |||||||
\(822\) | −22.7639 | + | 39.4283i | −0.793983 | + | 1.37522i | ||||
\(823\) | 7.05573 | − | 12.2209i | 0.245947 | − | 0.425993i | −0.716450 | − | 0.697638i | \(-0.754234\pi\) |
0.962398 | + | 0.271645i | \(0.0875677\pi\) | |||||||
\(824\) | 8.61803 | + | 14.9269i | 0.300223 | + | 0.520002i | ||||
\(825\) | 1.23607 | 0.0430344 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.9443 | −0.450116 | −0.225058 | − | 0.974345i | \(-0.572257\pi\) | ||||
−0.225058 | + | 0.974345i | \(0.572257\pi\) | |||||||
\(828\) | 5.45898 | + | 9.45523i | 0.189713 | + | 0.328592i | ||||
\(829\) | 18.4164 | − | 31.8982i | 0.639628 | − | 1.10787i | −0.345886 | − | 0.938277i | \(-0.612422\pi\) |
0.985514 | − | 0.169592i | \(-0.0542450\pi\) | |||||||
\(830\) | −25.5279 | + | 44.2156i | −0.886085 | + | 1.53474i | ||||
\(831\) | 12.2918 | + | 21.2900i | 0.426398 | + | 0.738542i | ||||
\(832\) | 42.0689 | 1.45848 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.22291 | 0.146227 | ||||||||
\(835\) | 4.94427 | + | 8.56373i | 0.171104 | + | 0.296360i | ||||
\(836\) | −9.70820 | + | 16.8151i | −0.335765 | + | 0.581562i | ||||
\(837\) | 7.63932 | − | 13.2317i | 0.264054 | − | 0.457354i | ||||
\(838\) | 27.5623 | + | 47.7393i | 0.952124 | + | 1.64913i | ||||
\(839\) | −44.0689 | −1.52143 | −0.760713 | − | 0.649088i | \(-0.775151\pi\) | ||||
−0.760713 | + | 0.649088i | \(0.775151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.7771 | 1.47507 | ||||||||
\(842\) | −25.0000 | − | 43.3013i | −0.861557 | − | 1.49226i | ||||
\(843\) | 2.18034 | − | 3.77646i | 0.0750949 | − | 0.130068i | ||||
\(844\) | 20.8328 | − | 36.0835i | 0.717095 | − | 1.24205i | ||||
\(845\) | 2.52786 | + | 4.37839i | 0.0869612 | + | 0.150621i | ||||
\(846\) | 9.09830 | 0.312806 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.472136 | 0.0162132 | ||||||||
\(849\) | 18.4721 | + | 31.9947i | 0.633962 | + | 1.09805i | ||||
\(850\) | 3.61803 | − | 6.26662i | 0.124098 | − | 0.214943i | ||||
\(851\) | 10.4721 | − | 18.1383i | 0.358980 | − | 0.621772i | ||||
\(852\) | 19.4164 | + | 33.6302i | 0.665195 | + | 1.15215i | ||||
\(853\) | 30.6525 | 1.04952 | 0.524760 | − | 0.851250i | \(-0.324155\pi\) | ||||
0.524760 | + | 0.851250i | \(0.324155\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19.0557 | 0.651692 | ||||||||
\(856\) | 4.47214 | + | 7.74597i | 0.152854 | + | 0.264752i | ||||
\(857\) | 7.61803 | − | 13.1948i | 0.260227 | − | 0.450727i | −0.706075 | − | 0.708137i | \(-0.749536\pi\) |
0.966302 | + | 0.257410i | \(0.0828692\pi\) | |||||||
\(858\) | −4.47214 | + | 7.74597i | −0.152676 | + | 0.264443i | ||||
\(859\) | −13.2705 | − | 22.9852i | −0.452784 | − | 0.784245i | 0.545774 | − | 0.837933i | \(-0.316236\pi\) |
−0.998558 | + | 0.0536877i | \(0.982902\pi\) | |||||||
\(860\) | 48.0000 | 1.63679 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 26.8328 | 0.913929 | ||||||||
\(863\) | 1.52786 | + | 2.64634i | 0.0520091 | + | 0.0900824i | 0.890858 | − | 0.454282i | \(-0.150104\pi\) |
−0.838849 | + | 0.544365i | \(0.816771\pi\) | |||||||
\(864\) | −18.5410 | + | 32.1140i | −0.630778 | + | 1.09254i | ||||
\(865\) | −12.7639 | + | 22.1078i | −0.433987 | + | 0.751687i | ||||
\(866\) | −9.47214 | − | 16.4062i | −0.321876 | − | 0.557506i | ||||
\(867\) | −8.06888 | −0.274034 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.94427 | 0.303414 | ||||||||
\(870\) | −23.4164 | − | 40.5584i | −0.793891 | − | 1.37506i | ||||
\(871\) | 23.4164 | − | 40.5584i | 0.793435 | − | 1.37427i | ||||
\(872\) | 5.00000 | − | 8.66025i | 0.169321 | − | 0.293273i | ||||
\(873\) | −12.8197 | − | 22.2043i | −0.433880 | − | 0.751502i | ||||
\(874\) | −35.7771 | −1.21018 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.83282 | 0.0957120 | ||||||||
\(877\) | −7.29180 | − | 12.6298i | −0.246226 | − | 0.426477i | 0.716249 | − | 0.697845i | \(-0.245857\pi\) |
−0.962476 | + | 0.271368i | \(0.912524\pi\) | |||||||
\(878\) | 11.7082 | − | 20.2792i | 0.395133 | − | 0.684390i | ||||
\(879\) | −15.5279 | + | 26.8950i | −0.523742 | + | 0.907148i | ||||
\(880\) | −1.00000 | − | 1.73205i | −0.0337100 | − | 0.0583874i | ||||
\(881\) | −2.58359 | −0.0870434 | −0.0435217 | − | 0.999052i | \(-0.513858\pi\) | ||||
−0.0435217 | + | 0.999052i | \(0.513858\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.94427 | −0.300999 | −0.150499 | − | 0.988610i | \(-0.548088\pi\) | ||||
−0.150499 | + | 0.988610i | \(0.548088\pi\) | |||||||
\(884\) | 15.7082 | + | 27.2074i | 0.528324 | + | 0.915084i | ||||
\(885\) | −1.52786 | + | 2.64634i | −0.0513586 | + | 0.0889557i | ||||
\(886\) | 27.8885 | − | 48.3044i | 0.936934 | − | 1.62282i | ||||
\(887\) | −2.18034 | − | 3.77646i | −0.0732086 | − | 0.126801i | 0.827097 | − | 0.562059i | \(-0.189991\pi\) |
−0.900306 | + | 0.435258i | \(0.856657\pi\) | |||||||
\(888\) | −23.4164 | −0.785803 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8.94427 | −0.299813 | ||||||||
\(891\) | −1.20820 | − | 2.09267i | −0.0404764 | − | 0.0701071i | ||||
\(892\) | −15.2705 | + | 26.4493i | −0.511294 | + | 0.885588i | ||||
\(893\) | −8.94427 | + | 15.4919i | −0.299309 | + | 0.518418i | ||||
\(894\) | −19.3475 | − | 33.5109i | −0.647078 | − | 1.12077i | ||||
\(895\) | −17.8885 | −0.597948 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.88854 | −0.330169 | ||||||||
\(898\) | 31.8328 | + | 55.1361i | 1.06227 | + | 1.83991i | ||||
\(899\) | −11.7082 | + | 20.2792i | −0.390490 | + | 0.676349i | ||||
\(900\) | −2.20820 | + | 3.82472i | −0.0736068 | + | 0.127491i | ||||
\(901\) | 0.763932 | + | 1.32317i | 0.0254503 | + | 0.0440812i | ||||
\(902\) | −25.1246 | −0.836558 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.47214 | 0.148741 | ||||||||
\(905\) | −25.4164 | − | 44.0225i | −0.844870 | − | 1.46336i | ||||
\(906\) | −12.3607 | + | 21.4093i | −0.410656 | + | 0.711277i | ||||
\(907\) | −11.2361 | + | 19.4614i | −0.373088 | + | 0.646207i | −0.990039 | − | 0.140795i | \(-0.955034\pi\) |
0.616951 | + | 0.787001i | \(0.288368\pi\) | |||||||
\(908\) | 8.83282 | + | 15.2989i | 0.293127 | + | 0.507711i | ||||
\(909\) | −7.01316 | −0.232612 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.4721 | 1.40716 | 0.703582 | − | 0.710614i | \(-0.251583\pi\) | ||||
0.703582 | + | 0.710614i | \(0.251583\pi\) | |||||||
\(912\) | −4.00000 | − | 6.92820i | −0.132453 | − | 0.229416i | ||||
\(913\) | 5.70820 | − | 9.88690i | 0.188914 | − | 0.327209i | ||||
\(914\) | 32.2361 | − | 55.8345i | 1.06627 | − | 1.84684i | ||||
\(915\) | −8.94427 | − | 15.4919i | −0.295689 | − | 0.512148i | ||||
\(916\) | 13.4164 | 0.443291 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −40.0000 | −1.32020 | ||||||||
\(919\) | −20.9443 | − | 36.2765i | −0.690888 | − | 1.19665i | −0.971547 | − | 0.236845i | \(-0.923887\pi\) |
0.280660 | − | 0.959807i | \(-0.409447\pi\) | |||||||
\(920\) | −5.52786 | + | 9.57454i | −0.182248 | + | 0.315663i | ||||
\(921\) | −5.52786 | + | 9.57454i | −0.182149 | + | 0.315492i | ||||
\(922\) | −13.6180 | − | 23.5871i | −0.448486 | − | 0.776801i | ||||
\(923\) | 33.8885 | 1.11546 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.47214 | 0.278562 | ||||||||
\(926\) | 6.18034 | + | 10.7047i | 0.203099 | + | 0.351777i | ||||
\(927\) | −5.67376 | + | 9.82724i | −0.186351 | + | 0.322769i | ||||
\(928\) | 28.4164 | − | 49.2187i | 0.932814 | − | 1.61568i | ||||
\(929\) | −26.1246 | − | 45.2492i | −0.857121 | − | 1.48458i | −0.874664 | − | 0.484731i | \(-0.838918\pi\) |
0.0175428 | − | 0.999846i | \(-0.494416\pi\) | |||||||
\(930\) | 15.2786 | 0.501006 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 28.2492 | 0.925334 | ||||||||
\(933\) | −5.12461 | − | 8.87609i | −0.167772 | − | 0.290590i | ||||
\(934\) | 26.9098 | − | 46.6092i | 0.880517 | − | 1.52510i | ||||
\(935\) | 3.23607 | − | 5.60503i | 0.105831 | − | 0.183304i | ||||
\(936\) | −5.32624 | − | 9.22531i | −0.174094 | − | 0.301539i | ||||
\(937\) | 10.6525 | 0.348001 | 0.174001 | − | 0.984746i | \(-0.444331\pi\) | ||||
0.174001 | + | 0.984746i | \(0.444331\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.4721 | −0.602815 | ||||||||
\(940\) | 8.29180 | + | 14.3618i | 0.270449 | + | 0.468431i | ||||
\(941\) | 3.79837 | − | 6.57898i | 0.123823 | − | 0.214469i | −0.797449 | − | 0.603386i | \(-0.793818\pi\) |
0.921272 | + | 0.388918i | \(0.127151\pi\) | |||||||
\(942\) | 15.1246 | − | 26.1966i | 0.492786 | − | 0.853531i | ||||
\(943\) | −13.8885 | − | 24.0557i | −0.452273 | − | 0.783360i | ||||
\(944\) | −1.23607 | −0.0402306 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.8885 | −0.581607 | ||||||||
\(947\) | 2.58359 | + | 4.47491i | 0.0839555 | + | 0.145415i | 0.904946 | − | 0.425527i | \(-0.139911\pi\) |
−0.820990 | + | 0.570942i | \(0.806578\pi\) | |||||||
\(948\) | 16.5836 | − | 28.7236i | 0.538610 | − | 0.932900i | ||||
\(949\) | 1.23607 | − | 2.14093i | 0.0401245 | − | 0.0694976i | ||||
\(950\) | −7.23607 | − | 12.5332i | −0.234769 | − | 0.406632i | ||||
\(951\) | 17.3050 | 0.561152 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.9443 | 0.743238 | 0.371619 | − | 0.928385i | \(-0.378803\pi\) | ||||
0.371619 | + | 0.928385i | \(0.378803\pi\) | |||||||
\(954\) | −0.777088 | − | 1.34596i | −0.0251591 | − | 0.0435769i | ||||
\(955\) | 3.05573 | − | 5.29268i | 0.0988810 | − | 0.171267i | ||||
\(956\) | 14.8328 | − | 25.6912i | 0.479728 | − | 0.830912i | ||||
\(957\) | 5.23607 | + | 9.06914i | 0.169258 | + | 0.293164i | ||||
\(958\) | −30.2492 | −0.977308 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −32.1378 | −1.03724 | ||||||||
\(961\) | 11.6803 | + | 20.2309i | 0.376785 | + | 0.652611i | ||||
\(962\) | −30.6525 | + | 53.0916i | −0.988275 | + | 1.71174i | ||||
\(963\) | −2.94427 | + | 5.09963i | −0.0948778 | + | 0.164333i | ||||
\(964\) | −19.6869 | − | 34.0987i | −0.634073 | − | 1.09825i | ||||
\(965\) | 23.7771 | 0.765412 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.8885 | −0.446625 | −0.223313 | − | 0.974747i | \(-0.571687\pi\) | ||||
−0.223313 | + | 0.974747i | \(0.571687\pi\) | |||||||
\(968\) | −1.11803 | − | 1.93649i | −0.0359350 | − | 0.0622412i | ||||
\(969\) | 12.9443 | − | 22.4201i | 0.415830 | − | 0.720239i | ||||
\(970\) | 38.9443 | − | 67.4535i | 1.25043 | − | 2.16580i | ||||
\(971\) | 5.56231 | + | 9.63420i | 0.178503 | + | 0.309176i | 0.941368 | − | 0.337382i | \(-0.109541\pi\) |
−0.762865 | + | 0.646558i | \(0.776208\pi\) | |||||||
\(972\) | 40.7902 | 1.30835 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −81.3050 | −2.60518 | ||||||||
\(975\) | −2.00000 | − | 3.46410i | −0.0640513 | − | 0.110940i | ||||
\(976\) | 3.61803 | − | 6.26662i | 0.115810 | − | 0.200590i | ||||
\(977\) | −11.4721 | + | 19.8703i | −0.367026 | + | 0.635708i | −0.989099 | − | 0.147251i | \(-0.952957\pi\) |
0.622073 | + | 0.782959i | \(0.286291\pi\) | |||||||
\(978\) | 4.72136 | + | 8.17763i | 0.150972 | + | 0.261492i | ||||
\(979\) | 2.00000 | 0.0639203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.58359 | 0.210198 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.9098 | − | 18.8964i | 0.347970 | − | 0.602701i | −0.637919 | − | 0.770103i | \(-0.720205\pi\) |
0.985889 | + | 0.167402i | \(0.0535379\pi\) | |||||||
\(984\) | −15.5279 | + | 26.8950i | −0.495010 | + | 0.857383i | ||||
\(985\) | 2.00000 | + | 3.46410i | 0.0637253 | + | 0.110375i | ||||
\(986\) | 61.3050 | 1.95235 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 62.8328 | 1.99898 | ||||||||
\(989\) | −9.88854 | − | 17.1275i | −0.314437 | − | 0.544622i | ||||
\(990\) | −3.29180 | + | 5.70156i | −0.104620 | + | 0.181207i | ||||
\(991\) | −27.1246 | + | 46.9812i | −0.861642 | + | 1.49241i | 0.00870185 | + | 0.999962i | \(0.497230\pi\) |
−0.870344 | + | 0.492445i | \(0.836103\pi\) | |||||||
\(992\) | 9.27051 | + | 16.0570i | 0.294339 | + | 0.509810i | ||||
\(993\) | −17.1672 | −0.544784 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.36068 | 0.138243 | ||||||||
\(996\) | −21.1672 | − | 36.6626i | −0.670708 | − | 1.16170i | ||||
\(997\) | 0.673762 | − | 1.16699i | 0.0213383 | − | 0.0369589i | −0.855159 | − | 0.518366i | \(-0.826541\pi\) |
0.876497 | + | 0.481407i | \(0.159874\pi\) | |||||||
\(998\) | −1.70820 | + | 2.95870i | −0.0540723 | + | 0.0936559i | ||||
\(999\) | −23.4164 | − | 40.5584i | −0.740862 | − | 1.28321i |
(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 | 539.2.e.j.67.1 | 4 | ||
7.2 | even | 3 | inner | 539.2.e.j.177.1 | 4 | ||
7.3 | odd | 6 | 77.2.a.d.1.2 | ✓ | 2 | ||
7.4 | even | 3 | 539.2.a.f.1.2 | 2 | |||
7.5 | odd | 6 | 539.2.e.i.177.1 | 4 | |||
7.6 | odd | 2 | 539.2.e.i.67.1 | 4 | |||
21.11 | odd | 6 | 4851.2.a.y.1.1 | 2 | |||
21.17 | even | 6 | 693.2.a.h.1.1 | 2 | |||
28.3 | even | 6 | 1232.2.a.m.1.2 | 2 | |||
28.11 | odd | 6 | 8624.2.a.ce.1.1 | 2 | |||
35.3 | even | 12 | 1925.2.b.h.1849.2 | 4 | |||
35.17 | even | 12 | 1925.2.b.h.1849.3 | 4 | |||
35.24 | odd | 6 | 1925.2.a.r.1.1 | 2 | |||
56.3 | even | 6 | 4928.2.a.bv.1.1 | 2 | |||
56.45 | odd | 6 | 4928.2.a.bm.1.2 | 2 | |||
77.3 | odd | 30 | 847.2.f.n.372.1 | 4 | |||
77.10 | even | 6 | 847.2.a.f.1.1 | 2 | |||
77.17 | even | 30 | 847.2.f.m.729.1 | 4 | |||
77.24 | even | 30 | 847.2.f.m.323.1 | 4 | |||
77.31 | odd | 30 | 847.2.f.a.323.1 | 4 | |||
77.32 | odd | 6 | 5929.2.a.m.1.1 | 2 | |||
77.38 | odd | 30 | 847.2.f.a.729.1 | 4 | |||
77.52 | even | 30 | 847.2.f.b.372.1 | 4 | |||
77.59 | odd | 30 | 847.2.f.n.148.1 | 4 | |||
77.73 | even | 30 | 847.2.f.b.148.1 | 4 | |||
231.164 | odd | 6 | 7623.2.a.bl.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.a.d.1.2 | ✓ | 2 | 7.3 | odd | 6 | ||
539.2.a.f.1.2 | 2 | 7.4 | even | 3 | |||
539.2.e.i.67.1 | 4 | 7.6 | odd | 2 | |||
539.2.e.i.177.1 | 4 | 7.5 | odd | 6 | |||
539.2.e.j.67.1 | 4 | 1.1 | even | 1 | trivial | ||
539.2.e.j.177.1 | 4 | 7.2 | even | 3 | inner | ||
693.2.a.h.1.1 | 2 | 21.17 | even | 6 | |||
847.2.a.f.1.1 | 2 | 77.10 | even | 6 | |||
847.2.f.a.323.1 | 4 | 77.31 | odd | 30 | |||
847.2.f.a.729.1 | 4 | 77.38 | odd | 30 | |||
847.2.f.b.148.1 | 4 | 77.73 | even | 30 | |||
847.2.f.b.372.1 | 4 | 77.52 | even | 30 | |||
847.2.f.m.323.1 | 4 | 77.24 | even | 30 | |||
847.2.f.m.729.1 | 4 | 77.17 | even | 30 | |||
847.2.f.n.148.1 | 4 | 77.59 | odd | 30 | |||
847.2.f.n.372.1 | 4 | 77.3 | odd | 30 | |||
1232.2.a.m.1.2 | 2 | 28.3 | even | 6 | |||
1925.2.a.r.1.1 | 2 | 35.24 | odd | 6 | |||
1925.2.b.h.1849.2 | 4 | 35.3 | even | 12 | |||
1925.2.b.h.1849.3 | 4 | 35.17 | even | 12 | |||
4851.2.a.y.1.1 | 2 | 21.11 | odd | 6 | |||
4928.2.a.bm.1.2 | 2 | 56.45 | odd | 6 | |||
4928.2.a.bv.1.1 | 2 | 56.3 | even | 6 | |||
5929.2.a.m.1.1 | 2 | 77.32 | odd | 6 | |||
7623.2.a.bl.1.2 | 2 | 231.164 | odd | 6 | |||
8624.2.a.ce.1.1 | 2 | 28.11 | odd | 6 |