Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [187,2,Mod(89,187)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(187, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("187.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 187 = 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 187.e (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.49320251780\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 166.2 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 187.166 |
Dual form | 187.2.e.a.89.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).
\(n\) | \(35\) | \(122\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(3\) | 0.414214 | + | 0.414214i | 0.239146 | + | 0.239146i | 0.816497 | − | 0.577350i | \(-0.195913\pi\) |
−0.577350 | + | 0.816497i | \(0.695913\pi\) | |||||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | 2.00000 | + | 2.00000i | 0.894427 | + | 0.894427i | 0.994936 | − | 0.100509i | \(-0.0320471\pi\) |
−0.100509 | + | 0.994936i | \(0.532047\pi\) | |||||||
\(6\) | −0.828427 | + | 0.828427i | −0.338204 | + | 0.338204i | ||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | −0.560734 | − | 0.827996i | \(-0.689481\pi\) |
0.827996 | + | 0.560734i | \(0.189481\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.65685i | − | 0.885618i | ||||||
\(10\) | −4.00000 | + | 4.00000i | −1.26491 | + | 1.26491i | ||||
\(11\) | 0.707107 | − | 0.707107i | 0.213201 | − | 0.213201i | ||||
\(12\) | −0.828427 | − | 0.828427i | −0.239146 | − | 0.239146i | ||||
\(13\) | −3.41421 | −0.946932 | −0.473466 | − | 0.880812i | \(-0.656997\pi\) | ||||
−0.473466 | + | 0.880812i | \(0.656997\pi\) | |||||||
\(14\) | 1.41421 | + | 1.41421i | 0.377964 | + | 0.377964i | ||||
\(15\) | 1.65685i | 0.427798i | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | −2.12132 | − | 3.53553i | −0.514496 | − | 0.857493i | ||||
\(18\) | 5.31371 | 1.25245 | ||||||||
\(19\) | 2.58579i | 0.593220i | 0.954999 | + | 0.296610i | \(0.0958562\pi\) | ||||
−0.954999 | + | 0.296610i | \(0.904144\pi\) | |||||||
\(20\) | −4.00000 | − | 4.00000i | −0.894427 | − | 0.894427i | ||||
\(21\) | 0.585786 | 0.127829 | ||||||||
\(22\) | 1.41421 | + | 1.41421i | 0.301511 | + | 0.301511i | ||||
\(23\) | 3.00000 | − | 3.00000i | 0.625543 | − | 0.625543i | −0.321400 | − | 0.946943i | \(-0.604153\pi\) |
0.946943 | + | 0.321400i | \(0.104153\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000i | 0.600000i | ||||||||
\(26\) | − | 6.82843i | − | 1.33916i | ||||||
\(27\) | 2.34315 | − | 2.34315i | 0.450939 | − | 0.450939i | ||||
\(28\) | −1.41421 | + | 1.41421i | −0.267261 | + | 0.267261i | ||||
\(29\) | 2.70711 | + | 2.70711i | 0.502697 | + | 0.502697i | 0.912275 | − | 0.409578i | \(-0.134324\pi\) |
−0.409578 | + | 0.912275i | \(0.634324\pi\) | |||||||
\(30\) | −3.31371 | −0.604998 | ||||||||
\(31\) | −4.82843 | − | 4.82843i | −0.867211 | − | 0.867211i | 0.124952 | − | 0.992163i | \(-0.460122\pi\) |
−0.992163 | + | 0.124952i | \(0.960122\pi\) | |||||||
\(32\) | − | 8.00000i | − | 1.41421i | ||||||
\(33\) | 0.585786 | 0.101972 | ||||||||
\(34\) | 7.07107 | − | 4.24264i | 1.21268 | − | 0.727607i | ||||
\(35\) | 2.82843 | 0.478091 | ||||||||
\(36\) | 5.31371i | 0.885618i | ||||||||
\(37\) | 6.65685 | + | 6.65685i | 1.09438 | + | 1.09438i | 0.995055 | + | 0.0993251i | \(0.0316684\pi\) |
0.0993251 | + | 0.995055i | \(0.468332\pi\) | |||||||
\(38\) | −5.17157 | −0.838940 | ||||||||
\(39\) | −1.41421 | − | 1.41421i | −0.226455 | − | 0.226455i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.53553 | + | 3.53553i | −0.552158 | + | 0.552158i | −0.927063 | − | 0.374905i | \(-0.877675\pi\) |
0.374905 | + | 0.927063i | \(0.377675\pi\) | |||||||
\(42\) | 1.17157i | 0.180778i | ||||||||
\(43\) | − | 5.41421i | − | 0.825660i | −0.910808 | − | 0.412830i | \(-0.864540\pi\) | ||
0.910808 | − | 0.412830i | \(-0.135460\pi\) | |||||||
\(44\) | −1.41421 | + | 1.41421i | −0.213201 | + | 0.213201i | ||||
\(45\) | 5.31371 | − | 5.31371i | 0.792121 | − | 0.792121i | ||||
\(46\) | 6.00000 | + | 6.00000i | 0.884652 | + | 0.884652i | ||||
\(47\) | 11.4853 | 1.67530 | 0.837650 | − | 0.546207i | \(-0.183929\pi\) | ||||
0.837650 | + | 0.546207i | \(0.183929\pi\) | |||||||
\(48\) | −1.65685 | − | 1.65685i | −0.239146 | − | 0.239146i | ||||
\(49\) | 6.00000i | 0.857143i | ||||||||
\(50\) | −6.00000 | −0.848528 | ||||||||
\(51\) | 0.585786 | − | 2.34315i | 0.0820265 | − | 0.328106i | ||||
\(52\) | 6.82843 | 0.946932 | ||||||||
\(53\) | 3.48528i | 0.478740i | 0.970928 | + | 0.239370i | \(0.0769409\pi\) | ||||
−0.970928 | + | 0.239370i | \(0.923059\pi\) | |||||||
\(54\) | 4.68629 | + | 4.68629i | 0.637723 | + | 0.637723i | ||||
\(55\) | 2.82843 | 0.381385 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.07107 | + | 1.07107i | −0.141866 | + | 0.141866i | ||||
\(58\) | −5.41421 | + | 5.41421i | −0.710921 | + | 0.710921i | ||||
\(59\) | − | 4.65685i | − | 0.606271i | −0.952947 | − | 0.303135i | \(-0.901967\pi\) | ||
0.952947 | − | 0.303135i | \(-0.0980334\pi\) | |||||||
\(60\) | − | 3.31371i | − | 0.427798i | ||||||
\(61\) | −4.82843 | + | 4.82843i | −0.618217 | + | 0.618217i | −0.945074 | − | 0.326857i | \(-0.894010\pi\) |
0.326857 | + | 0.945074i | \(0.394010\pi\) | |||||||
\(62\) | 9.65685 | − | 9.65685i | 1.22642 | − | 1.22642i | ||||
\(63\) | −1.87868 | − | 1.87868i | −0.236691 | − | 0.236691i | ||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | −6.82843 | − | 6.82843i | −0.846962 | − | 0.846962i | ||||
\(66\) | 1.17157i | 0.144211i | ||||||||
\(67\) | 1.00000 | 0.122169 | 0.0610847 | − | 0.998133i | \(-0.480544\pi\) | ||||
0.0610847 | + | 0.998133i | \(0.480544\pi\) | |||||||
\(68\) | 4.24264 | + | 7.07107i | 0.514496 | + | 0.857493i | ||||
\(69\) | 2.48528 | 0.299193 | ||||||||
\(70\) | 5.65685i | 0.676123i | ||||||||
\(71\) | −11.0711 | − | 11.0711i | −1.31389 | − | 1.31389i | −0.918520 | − | 0.395374i | \(-0.870615\pi\) |
−0.395374 | − | 0.918520i | \(-0.629385\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.77817 | − | 5.77817i | −0.676284 | − | 0.676284i | 0.282873 | − | 0.959157i | \(-0.408712\pi\) |
−0.959157 | + | 0.282873i | \(0.908712\pi\) | |||||||
\(74\) | −13.3137 | + | 13.3137i | −1.54769 | + | 1.54769i | ||||
\(75\) | −1.24264 | + | 1.24264i | −0.143488 | + | 0.143488i | ||||
\(76\) | − | 5.17157i | − | 0.593220i | ||||||
\(77\) | − | 1.00000i | − | 0.113961i | ||||||
\(78\) | 2.82843 | − | 2.82843i | 0.320256 | − | 0.320256i | ||||
\(79\) | −2.24264 | + | 2.24264i | −0.252317 | + | 0.252317i | −0.821920 | − | 0.569603i | \(-0.807097\pi\) |
0.569603 | + | 0.821920i | \(0.307097\pi\) | |||||||
\(80\) | −8.00000 | − | 8.00000i | −0.894427 | − | 0.894427i | ||||
\(81\) | −6.02944 | −0.669937 | ||||||||
\(82\) | −7.07107 | − | 7.07107i | −0.780869 | − | 0.780869i | ||||
\(83\) | 4.82843i | 0.529989i | 0.964250 | + | 0.264994i | \(0.0853701\pi\) | ||||
−0.964250 | + | 0.264994i | \(0.914630\pi\) | |||||||
\(84\) | −1.17157 | −0.127829 | ||||||||
\(85\) | 2.82843 | − | 11.3137i | 0.306786 | − | 1.22714i | ||||
\(86\) | 10.8284 | 1.16766 | ||||||||
\(87\) | 2.24264i | 0.240436i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.82843 | −0.193813 | −0.0969064 | − | 0.995293i | \(-0.530895\pi\) | ||||
−0.0969064 | + | 0.995293i | \(0.530895\pi\) | |||||||
\(90\) | 10.6274 | + | 10.6274i | 1.12023 | + | 1.12023i | ||||
\(91\) | −2.41421 | + | 2.41421i | −0.253078 | + | 0.253078i | ||||
\(92\) | −6.00000 | + | 6.00000i | −0.625543 | + | 0.625543i | ||||
\(93\) | − | 4.00000i | − | 0.414781i | ||||||
\(94\) | 22.9706i | 2.36923i | ||||||||
\(95\) | −5.17157 | + | 5.17157i | −0.530592 | + | 0.530592i | ||||
\(96\) | 3.31371 | − | 3.31371i | 0.338204 | − | 0.338204i | ||||
\(97\) | −5.41421 | − | 5.41421i | −0.549730 | − | 0.549730i | 0.376633 | − | 0.926363i | \(-0.377082\pi\) |
−0.926363 | + | 0.376633i | \(0.877082\pi\) | |||||||
\(98\) | −12.0000 | −1.21218 | ||||||||
\(99\) | −1.87868 | − | 1.87868i | −0.188814 | − | 0.188814i | ||||
\(100\) | − | 6.00000i | − | 0.600000i | ||||||
\(101\) | −10.7279 | −1.06747 | −0.533734 | − | 0.845652i | \(-0.679212\pi\) | ||||
−0.533734 | + | 0.845652i | \(0.679212\pi\) | |||||||
\(102\) | 4.68629 | + | 1.17157i | 0.464012 | + | 0.116003i | ||||
\(103\) | 16.6569 | 1.64125 | 0.820624 | − | 0.571468i | \(-0.193626\pi\) | ||||
0.820624 | + | 0.571468i | \(0.193626\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.17157 | + | 1.17157i | 0.114334 | + | 0.114334i | ||||
\(106\) | −6.97056 | −0.677041 | ||||||||
\(107\) | −0.464466 | − | 0.464466i | −0.0449016 | − | 0.0449016i | 0.684299 | − | 0.729201i | \(-0.260108\pi\) |
−0.729201 | + | 0.684299i | \(0.760108\pi\) | |||||||
\(108\) | −4.68629 | + | 4.68629i | −0.450939 | + | 0.450939i | ||||
\(109\) | −10.9497 | + | 10.9497i | −1.04880 | + | 1.04880i | −0.0500488 | + | 0.998747i | \(0.515938\pi\) |
−0.998747 | + | 0.0500488i | \(0.984062\pi\) | |||||||
\(110\) | 5.65685i | 0.539360i | ||||||||
\(111\) | 5.51472i | 0.523434i | ||||||||
\(112\) | −2.82843 | + | 2.82843i | −0.267261 | + | 0.267261i | ||||
\(113\) | −5.41421 | + | 5.41421i | −0.509326 | + | 0.509326i | −0.914320 | − | 0.404993i | \(-0.867274\pi\) |
0.404993 | + | 0.914320i | \(0.367274\pi\) | |||||||
\(114\) | −2.14214 | − | 2.14214i | −0.200629 | − | 0.200629i | ||||
\(115\) | 12.0000 | 1.11901 | ||||||||
\(116\) | −5.41421 | − | 5.41421i | −0.502697 | − | 0.502697i | ||||
\(117\) | 9.07107i | 0.838621i | ||||||||
\(118\) | 9.31371 | 0.857396 | ||||||||
\(119\) | −4.00000 | − | 1.00000i | −0.366679 | − | 0.0916698i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 1.00000i | − | 0.0909091i | ||||||
\(122\) | −9.65685 | − | 9.65685i | −0.874291 | − | 0.874291i | ||||
\(123\) | −2.92893 | −0.264093 | ||||||||
\(124\) | 9.65685 | + | 9.65685i | 0.867211 | + | 0.867211i | ||||
\(125\) | 4.00000 | − | 4.00000i | 0.357771 | − | 0.357771i | ||||
\(126\) | 3.75736 | − | 3.75736i | 0.334732 | − | 0.334732i | ||||
\(127\) | 5.75736i | 0.510883i | 0.966825 | + | 0.255442i | \(0.0822208\pi\) | ||||
−0.966825 | + | 0.255442i | \(0.917779\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.24264 | − | 2.24264i | 0.197454 | − | 0.197454i | ||||
\(130\) | 13.6569 | − | 13.6569i | 1.19779 | − | 1.19779i | ||||
\(131\) | −1.53553 | − | 1.53553i | −0.134160 | − | 0.134160i | 0.636838 | − | 0.770998i | \(-0.280242\pi\) |
−0.770998 | + | 0.636838i | \(0.780242\pi\) | |||||||
\(132\) | −1.17157 | −0.101972 | ||||||||
\(133\) | 1.82843 | + | 1.82843i | 0.158545 | + | 0.158545i | ||||
\(134\) | 2.00000i | 0.172774i | ||||||||
\(135\) | 9.37258 | 0.806664 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.82843 | 0.839699 | 0.419850 | − | 0.907594i | \(-0.362083\pi\) | ||||
0.419850 | + | 0.907594i | \(0.362083\pi\) | |||||||
\(138\) | 4.97056i | 0.423122i | ||||||||
\(139\) | 4.36396 | + | 4.36396i | 0.370146 | + | 0.370146i | 0.867530 | − | 0.497384i | \(-0.165706\pi\) |
−0.497384 | + | 0.867530i | \(0.665706\pi\) | |||||||
\(140\) | −5.65685 | −0.478091 | ||||||||
\(141\) | 4.75736 | + | 4.75736i | 0.400642 | + | 0.400642i | ||||
\(142\) | 22.1421 | − | 22.1421i | 1.85813 | − | 1.85813i | ||||
\(143\) | −2.41421 | + | 2.41421i | −0.201887 | + | 0.201887i | ||||
\(144\) | 10.6274i | 0.885618i | ||||||||
\(145\) | 10.8284i | 0.899252i | ||||||||
\(146\) | 11.5563 | − | 11.5563i | 0.956410 | − | 0.956410i | ||||
\(147\) | −2.48528 | + | 2.48528i | −0.204983 | + | 0.204983i | ||||
\(148\) | −13.3137 | − | 13.3137i | −1.09438 | − | 1.09438i | ||||
\(149\) | 20.2426 | 1.65834 | 0.829171 | − | 0.558995i | \(-0.188813\pi\) | ||||
0.829171 | + | 0.558995i | \(0.188813\pi\) | |||||||
\(150\) | −2.48528 | − | 2.48528i | −0.202922 | − | 0.202922i | ||||
\(151\) | − | 6.48528i | − | 0.527765i | −0.964555 | − | 0.263882i | \(-0.914997\pi\) | ||
0.964555 | − | 0.263882i | \(-0.0850031\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.39340 | + | 5.63604i | −0.759411 | + | 0.455647i | ||||
\(154\) | 2.00000 | 0.161165 | ||||||||
\(155\) | − | 19.3137i | − | 1.55131i | ||||||
\(156\) | 2.82843 | + | 2.82843i | 0.226455 | + | 0.226455i | ||||
\(157\) | −20.3137 | −1.62121 | −0.810605 | − | 0.585593i | \(-0.800862\pi\) | ||||
−0.810605 | + | 0.585593i | \(0.800862\pi\) | |||||||
\(158\) | −4.48528 | − | 4.48528i | −0.356830 | − | 0.356830i | ||||
\(159\) | −1.44365 | + | 1.44365i | −0.114489 | + | 0.114489i | ||||
\(160\) | 16.0000 | − | 16.0000i | 1.26491 | − | 1.26491i | ||||
\(161\) | − | 4.24264i | − | 0.334367i | ||||||
\(162\) | − | 12.0589i | − | 0.947435i | ||||||
\(163\) | −5.00000 | + | 5.00000i | −0.391630 | + | 0.391630i | −0.875268 | − | 0.483638i | \(-0.839315\pi\) |
0.483638 | + | 0.875268i | \(0.339315\pi\) | |||||||
\(164\) | 7.07107 | − | 7.07107i | 0.552158 | − | 0.552158i | ||||
\(165\) | 1.17157 | + | 1.17157i | 0.0912068 | + | 0.0912068i | ||||
\(166\) | −9.65685 | −0.749517 | ||||||||
\(167\) | 2.92893 | + | 2.92893i | 0.226648 | + | 0.226648i | 0.811291 | − | 0.584643i | \(-0.198765\pi\) |
−0.584643 | + | 0.811291i | \(0.698765\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.34315 | −0.103319 | ||||||||
\(170\) | 22.6274 | + | 5.65685i | 1.73544 | + | 0.433861i | ||||
\(171\) | 6.87006 | 0.525366 | ||||||||
\(172\) | 10.8284i | 0.825660i | ||||||||
\(173\) | 0.121320 | + | 0.121320i | 0.00922381 | + | 0.00922381i | 0.711704 | − | 0.702480i | \(-0.247924\pi\) |
−0.702480 | + | 0.711704i | \(0.747924\pi\) | |||||||
\(174\) | −4.48528 | −0.340028 | ||||||||
\(175\) | 2.12132 | + | 2.12132i | 0.160357 | + | 0.160357i | ||||
\(176\) | −2.82843 | + | 2.82843i | −0.213201 | + | 0.213201i | ||||
\(177\) | 1.92893 | − | 1.92893i | 0.144987 | − | 0.144987i | ||||
\(178\) | − | 3.65685i | − | 0.274093i | ||||||
\(179\) | 25.6274i | 1.91548i | 0.287630 | + | 0.957742i | \(0.407133\pi\) | ||||
−0.287630 | + | 0.957742i | \(0.592867\pi\) | |||||||
\(180\) | −10.6274 | + | 10.6274i | −0.792121 | + | 0.792121i | ||||
\(181\) | −13.0711 | + | 13.0711i | −0.971565 | + | 0.971565i | −0.999607 | − | 0.0280419i | \(-0.991073\pi\) |
0.0280419 | + | 0.999607i | \(0.491073\pi\) | |||||||
\(182\) | −4.82843 | − | 4.82843i | −0.357907 | − | 0.357907i | ||||
\(183\) | −4.00000 | −0.295689 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 26.6274i | 1.95769i | ||||||||
\(186\) | 8.00000 | 0.586588 | ||||||||
\(187\) | −4.00000 | − | 1.00000i | −0.292509 | − | 0.0731272i | ||||
\(188\) | −22.9706 | −1.67530 | ||||||||
\(189\) | − | 3.31371i | − | 0.241037i | ||||||
\(190\) | −10.3431 | − | 10.3431i | −0.750371 | − | 0.750371i | ||||
\(191\) | 7.17157 | 0.518917 | 0.259458 | − | 0.965754i | \(-0.416456\pi\) | ||||
0.259458 | + | 0.965754i | \(0.416456\pi\) | |||||||
\(192\) | 3.31371 | + | 3.31371i | 0.239146 | + | 0.239146i | ||||
\(193\) | 9.17157 | − | 9.17157i | 0.660184 | − | 0.660184i | −0.295239 | − | 0.955423i | \(-0.595399\pi\) |
0.955423 | + | 0.295239i | \(0.0953993\pi\) | |||||||
\(194\) | 10.8284 | − | 10.8284i | 0.777436 | − | 0.777436i | ||||
\(195\) | − | 5.65685i | − | 0.405096i | ||||||
\(196\) | − | 12.0000i | − | 0.857143i | ||||||
\(197\) | 13.6569 | − | 13.6569i | 0.973011 | − | 0.973011i | −0.0266347 | − | 0.999645i | \(-0.508479\pi\) |
0.999645 | + | 0.0266347i | \(0.00847908\pi\) | |||||||
\(198\) | 3.75736 | − | 3.75736i | 0.267024 | − | 0.267024i | ||||
\(199\) | −15.4142 | − | 15.4142i | −1.09268 | − | 1.09268i | −0.995241 | − | 0.0974436i | \(-0.968933\pi\) |
−0.0974436 | − | 0.995241i | \(-0.531067\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.414214 | + | 0.414214i | 0.0292164 | + | 0.0292164i | ||||
\(202\) | − | 21.4558i | − | 1.50963i | ||||||
\(203\) | 3.82843 | 0.268703 | ||||||||
\(204\) | −1.17157 | + | 4.68629i | −0.0820265 | + | 0.328106i | ||||
\(205\) | −14.1421 | −0.987730 | ||||||||
\(206\) | 33.3137i | 2.32108i | ||||||||
\(207\) | −7.97056 | − | 7.97056i | −0.553992 | − | 0.553992i | ||||
\(208\) | 13.6569 | 0.946932 | ||||||||
\(209\) | 1.82843 | + | 1.82843i | 0.126475 | + | 0.126475i | ||||
\(210\) | −2.34315 | + | 2.34315i | −0.161692 | + | 0.161692i | ||||
\(211\) | 6.36396 | − | 6.36396i | 0.438113 | − | 0.438113i | −0.453263 | − | 0.891377i | \(-0.649740\pi\) |
0.891377 | + | 0.453263i | \(0.149740\pi\) | |||||||
\(212\) | − | 6.97056i | − | 0.478740i | ||||||
\(213\) | − | 9.17157i | − | 0.628426i | ||||||
\(214\) | 0.928932 | − | 0.928932i | 0.0635005 | − | 0.0635005i | ||||
\(215\) | 10.8284 | − | 10.8284i | 0.738493 | − | 0.738493i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.82843 | −0.463544 | ||||||||
\(218\) | −21.8995 | − | 21.8995i | −1.48322 | − | 1.48322i | ||||
\(219\) | − | 4.78680i | − | 0.323462i | ||||||
\(220\) | −5.65685 | −0.381385 | ||||||||
\(221\) | 7.24264 | + | 12.0711i | 0.487193 | + | 0.811988i | ||||
\(222\) | −11.0294 | −0.740247 | ||||||||
\(223\) | − | 6.00000i | − | 0.401790i | −0.979613 | − | 0.200895i | \(-0.935615\pi\) | ||
0.979613 | − | 0.200895i | \(-0.0643850\pi\) | |||||||
\(224\) | −5.65685 | − | 5.65685i | −0.377964 | − | 0.377964i | ||||
\(225\) | 7.97056 | 0.531371 | ||||||||
\(226\) | −10.8284 | − | 10.8284i | −0.720296 | − | 0.720296i | ||||
\(227\) | −9.77817 | + | 9.77817i | −0.649000 | + | 0.649000i | −0.952751 | − | 0.303751i | \(-0.901761\pi\) |
0.303751 | + | 0.952751i | \(0.401761\pi\) | |||||||
\(228\) | 2.14214 | − | 2.14214i | 0.141866 | − | 0.141866i | ||||
\(229\) | 4.65685i | 0.307734i | 0.988092 | + | 0.153867i | \(0.0491727\pi\) | ||||
−0.988092 | + | 0.153867i | \(0.950827\pi\) | |||||||
\(230\) | 24.0000i | 1.58251i | ||||||||
\(231\) | 0.414214 | − | 0.414214i | 0.0272533 | − | 0.0272533i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.5355 | − | 15.5355i | −1.01777 | − | 1.01777i | −0.999839 | − | 0.0179274i | \(-0.994293\pi\) |
−0.0179274 | − | 0.999839i | \(-0.505707\pi\) | |||||||
\(234\) | −18.1421 | −1.18599 | ||||||||
\(235\) | 22.9706 | + | 22.9706i | 1.49843 | + | 1.49843i | ||||
\(236\) | 9.31371i | 0.606271i | ||||||||
\(237\) | −1.85786 | −0.120681 | ||||||||
\(238\) | 2.00000 | − | 8.00000i | 0.129641 | − | 0.518563i | ||||
\(239\) | 25.0711 | 1.62171 | 0.810856 | − | 0.585245i | \(-0.199002\pi\) | ||||
0.810856 | + | 0.585245i | \(0.199002\pi\) | |||||||
\(240\) | − | 6.62742i | − | 0.427798i | ||||||
\(241\) | 9.43503 | + | 9.43503i | 0.607764 | + | 0.607764i | 0.942361 | − | 0.334598i | \(-0.108600\pi\) |
−0.334598 | + | 0.942361i | \(0.608600\pi\) | |||||||
\(242\) | 2.00000 | 0.128565 | ||||||||
\(243\) | −9.52691 | − | 9.52691i | −0.611152 | − | 0.611152i | ||||
\(244\) | 9.65685 | − | 9.65685i | 0.618217 | − | 0.618217i | ||||
\(245\) | −12.0000 | + | 12.0000i | −0.766652 | + | 0.766652i | ||||
\(246\) | − | 5.85786i | − | 0.373484i | ||||||
\(247\) | − | 8.82843i | − | 0.561739i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.00000 | + | 2.00000i | −0.126745 | + | 0.126745i | ||||
\(250\) | 8.00000 | + | 8.00000i | 0.505964 | + | 0.505964i | ||||
\(251\) | 6.00000 | 0.378717 | 0.189358 | − | 0.981908i | \(-0.439359\pi\) | ||||
0.189358 | + | 0.981908i | \(0.439359\pi\) | |||||||
\(252\) | 3.75736 | + | 3.75736i | 0.236691 | + | 0.236691i | ||||
\(253\) | − | 4.24264i | − | 0.266733i | ||||||
\(254\) | −11.5147 | −0.722498 | ||||||||
\(255\) | 5.85786 | − | 3.51472i | 0.366834 | − | 0.220100i | ||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 10.5147i | 0.655890i | 0.944697 | + | 0.327945i | \(0.106356\pi\) | ||||
−0.944697 | + | 0.327945i | \(0.893644\pi\) | |||||||
\(258\) | 4.48528 | + | 4.48528i | 0.279241 | + | 0.279241i | ||||
\(259\) | 9.41421 | 0.584971 | ||||||||
\(260\) | 13.6569 | + | 13.6569i | 0.846962 | + | 0.846962i | ||||
\(261\) | 7.19239 | − | 7.19239i | 0.445198 | − | 0.445198i | ||||
\(262\) | 3.07107 | − | 3.07107i | 0.189731 | − | 0.189731i | ||||
\(263\) | − | 5.55635i | − | 0.342619i | −0.985217 | − | 0.171310i | \(-0.945200\pi\) | ||
0.985217 | − | 0.171310i | \(-0.0547998\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.97056 | + | 6.97056i | −0.428198 | + | 0.428198i | ||||
\(266\) | −3.65685 | + | 3.65685i | −0.224216 | + | 0.224216i | ||||
\(267\) | −0.757359 | − | 0.757359i | −0.0463496 | − | 0.0463496i | ||||
\(268\) | −2.00000 | −0.122169 | ||||||||
\(269\) | 16.0711 | + | 16.0711i | 0.979870 | + | 0.979870i | 0.999801 | − | 0.0199311i | \(-0.00634467\pi\) |
−0.0199311 | + | 0.999801i | \(0.506345\pi\) | |||||||
\(270\) | 18.7452i | 1.14079i | ||||||||
\(271\) | −29.3137 | −1.78068 | −0.890340 | − | 0.455295i | \(-0.849534\pi\) | ||||
−0.890340 | + | 0.455295i | \(0.849534\pi\) | |||||||
\(272\) | 8.48528 | + | 14.1421i | 0.514496 | + | 0.857493i | ||||
\(273\) | −2.00000 | −0.121046 | ||||||||
\(274\) | 19.6569i | 1.18751i | ||||||||
\(275\) | 2.12132 | + | 2.12132i | 0.127920 | + | 0.127920i | ||||
\(276\) | −4.97056 | −0.299193 | ||||||||
\(277\) | −10.4645 | − | 10.4645i | −0.628749 | − | 0.628749i | 0.319004 | − | 0.947753i | \(-0.396652\pi\) |
−0.947753 | + | 0.319004i | \(0.896652\pi\) | |||||||
\(278\) | −8.72792 | + | 8.72792i | −0.523466 | + | 0.523466i | ||||
\(279\) | −12.8284 | + | 12.8284i | −0.768018 | + | 0.768018i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.4853i | 0.983429i | 0.870756 | + | 0.491715i | \(0.163630\pi\) | ||||
−0.870756 | + | 0.491715i | \(0.836370\pi\) | |||||||
\(282\) | −9.51472 | + | 9.51472i | −0.566593 | + | 0.566593i | ||||
\(283\) | −1.07107 | + | 1.07107i | −0.0636684 | + | 0.0636684i | −0.738224 | − | 0.674556i | \(-0.764335\pi\) |
0.674556 | + | 0.738224i | \(0.264335\pi\) | |||||||
\(284\) | 22.1421 | + | 22.1421i | 1.31389 | + | 1.31389i | ||||
\(285\) | −4.28427 | −0.253778 | ||||||||
\(286\) | −4.82843 | − | 4.82843i | −0.285511 | − | 0.285511i | ||||
\(287\) | 5.00000i | 0.295141i | ||||||||
\(288\) | −21.2548 | −1.25245 | ||||||||
\(289\) | −8.00000 | + | 15.0000i | −0.470588 | + | 0.882353i | ||||
\(290\) | −21.6569 | −1.27173 | ||||||||
\(291\) | − | 4.48528i | − | 0.262932i | ||||||
\(292\) | 11.5563 | + | 11.5563i | 0.676284 | + | 0.676284i | ||||
\(293\) | 10.9289 | 0.638475 | 0.319238 | − | 0.947675i | \(-0.396573\pi\) | ||||
0.319238 | + | 0.947675i | \(0.396573\pi\) | |||||||
\(294\) | −4.97056 | − | 4.97056i | −0.289889 | − | 0.289889i | ||||
\(295\) | 9.31371 | − | 9.31371i | 0.542265 | − | 0.542265i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.31371i | − | 0.192281i | ||||||
\(298\) | 40.4853i | 2.34525i | ||||||||
\(299\) | −10.2426 | + | 10.2426i | −0.592347 | + | 0.592347i | ||||
\(300\) | 2.48528 | − | 2.48528i | 0.143488 | − | 0.143488i | ||||
\(301\) | −3.82843 | − | 3.82843i | −0.220667 | − | 0.220667i | ||||
\(302\) | 12.9706 | 0.746372 | ||||||||
\(303\) | −4.44365 | − | 4.44365i | −0.255281 | − | 0.255281i | ||||
\(304\) | − | 10.3431i | − | 0.593220i | ||||||
\(305\) | −19.3137 | −1.10590 | ||||||||
\(306\) | −11.2721 | − | 18.7868i | −0.644382 | − | 1.07397i | ||||
\(307\) | −22.2426 | −1.26945 | −0.634727 | − | 0.772736i | \(-0.718888\pi\) | ||||
−0.634727 | + | 0.772736i | \(0.718888\pi\) | |||||||
\(308\) | 2.00000i | 0.113961i | ||||||||
\(309\) | 6.89949 | + | 6.89949i | 0.392499 | + | 0.392499i | ||||
\(310\) | 38.6274 | 2.19389 | ||||||||
\(311\) | 1.65685 | + | 1.65685i | 0.0939516 | + | 0.0939516i | 0.752520 | − | 0.658569i | \(-0.228838\pi\) |
−0.658569 | + | 0.752520i | \(0.728838\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.4142 | + | 10.4142i | −0.588646 | + | 0.588646i | −0.937265 | − | 0.348619i | \(-0.886651\pi\) |
0.348619 | + | 0.937265i | \(0.386651\pi\) | |||||||
\(314\) | − | 40.6274i | − | 2.29274i | ||||||
\(315\) | − | 7.51472i | − | 0.423406i | ||||||
\(316\) | 4.48528 | − | 4.48528i | 0.252317 | − | 0.252317i | ||||
\(317\) | 8.58579 | − | 8.58579i | 0.482226 | − | 0.482226i | −0.423616 | − | 0.905842i | \(-0.639239\pi\) |
0.905842 | + | 0.423616i | \(0.139239\pi\) | |||||||
\(318\) | −2.88730 | − | 2.88730i | −0.161912 | − | 0.161912i | ||||
\(319\) | 3.82843 | 0.214351 | ||||||||
\(320\) | 16.0000 | + | 16.0000i | 0.894427 | + | 0.894427i | ||||
\(321\) | − | 0.384776i | − | 0.0214761i | ||||||
\(322\) | 8.48528 | 0.472866 | ||||||||
\(323\) | 9.14214 | − | 5.48528i | 0.508682 | − | 0.305209i | ||||
\(324\) | 12.0589 | 0.669937 | ||||||||
\(325\) | − | 10.2426i | − | 0.568159i | ||||||
\(326\) | −10.0000 | − | 10.0000i | −0.553849 | − | 0.553849i | ||||
\(327\) | −9.07107 | −0.501631 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.12132 | − | 8.12132i | 0.447743 | − | 0.447743i | ||||
\(330\) | −2.34315 | + | 2.34315i | −0.128986 | + | 0.128986i | ||||
\(331\) | − | 11.6569i | − | 0.640719i | −0.947296 | − | 0.320359i | \(-0.896196\pi\) | ||
0.947296 | − | 0.320359i | \(-0.103804\pi\) | |||||||
\(332\) | − | 9.65685i | − | 0.529989i | ||||||
\(333\) | 17.6863 | − | 17.6863i | 0.969203 | − | 0.969203i | ||||
\(334\) | −5.85786 | + | 5.85786i | −0.320528 | + | 0.320528i | ||||
\(335\) | 2.00000 | + | 2.00000i | 0.109272 | + | 0.109272i | ||||
\(336\) | −2.34315 | −0.127829 | ||||||||
\(337\) | 22.2635 | + | 22.2635i | 1.21277 | + | 1.21277i | 0.970113 | + | 0.242655i | \(0.0780183\pi\) |
0.242655 | + | 0.970113i | \(0.421982\pi\) | |||||||
\(338\) | − | 2.68629i | − | 0.146115i | ||||||
\(339\) | −4.48528 | −0.243607 | ||||||||
\(340\) | −5.65685 | + | 22.6274i | −0.306786 | + | 1.22714i | ||||
\(341\) | −6.82843 | −0.369780 | ||||||||
\(342\) | 13.7401i | 0.742980i | ||||||||
\(343\) | 9.19239 | + | 9.19239i | 0.496342 | + | 0.496342i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.97056 | + | 4.97056i | 0.267606 | + | 0.267606i | ||||
\(346\) | −0.242641 | + | 0.242641i | −0.0130444 | + | 0.0130444i | ||||
\(347\) | 15.4350 | − | 15.4350i | 0.828596 | − | 0.828596i | −0.158727 | − | 0.987323i | \(-0.550739\pi\) |
0.987323 | + | 0.158727i | \(0.0507389\pi\) | |||||||
\(348\) | − | 4.48528i | − | 0.240436i | ||||||
\(349\) | − | 35.6985i | − | 1.91090i | −0.295159 | − | 0.955448i | \(-0.595373\pi\) | ||
0.295159 | − | 0.955448i | \(-0.404627\pi\) | |||||||
\(350\) | −4.24264 | + | 4.24264i | −0.226779 | + | 0.226779i | ||||
\(351\) | −8.00000 | + | 8.00000i | −0.427008 | + | 0.427008i | ||||
\(352\) | −5.65685 | − | 5.65685i | −0.301511 | − | 0.301511i | ||||
\(353\) | −12.1716 | −0.647827 | −0.323914 | − | 0.946087i | \(-0.604999\pi\) | ||||
−0.323914 | + | 0.946087i | \(0.604999\pi\) | |||||||
\(354\) | 3.85786 | + | 3.85786i | 0.205043 | + | 0.205043i | ||||
\(355\) | − | 44.2843i | − | 2.35037i | ||||||
\(356\) | 3.65685 | 0.193813 | ||||||||
\(357\) | −1.24264 | − | 2.07107i | −0.0657675 | − | 0.109613i | ||||
\(358\) | −51.2548 | −2.70890 | ||||||||
\(359\) | − | 32.1421i | − | 1.69640i | −0.529678 | − | 0.848199i | \(-0.677687\pi\) | ||
0.529678 | − | 0.848199i | \(-0.322313\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.3137 | 0.648090 | ||||||||
\(362\) | −26.1421 | − | 26.1421i | −1.37400 | − | 1.37400i | ||||
\(363\) | 0.414214 | − | 0.414214i | 0.0217406 | − | 0.0217406i | ||||
\(364\) | 4.82843 | − | 4.82843i | 0.253078 | − | 0.253078i | ||||
\(365\) | − | 23.1127i | − | 1.20977i | ||||||
\(366\) | − | 8.00000i | − | 0.418167i | ||||||
\(367\) | −12.8284 | + | 12.8284i | −0.669638 | + | 0.669638i | −0.957632 | − | 0.287994i | \(-0.907012\pi\) |
0.287994 | + | 0.957632i | \(0.407012\pi\) | |||||||
\(368\) | −12.0000 | + | 12.0000i | −0.625543 | + | 0.625543i | ||||
\(369\) | 9.39340 | + | 9.39340i | 0.489001 | + | 0.489001i | ||||
\(370\) | −53.2548 | −2.76859 | ||||||||
\(371\) | 2.46447 | + | 2.46447i | 0.127949 | + | 0.127949i | ||||
\(372\) | 8.00000i | 0.414781i | ||||||||
\(373\) | 28.7279 | 1.48748 | 0.743738 | − | 0.668472i | \(-0.233051\pi\) | ||||
0.743738 | + | 0.668472i | \(0.233051\pi\) | |||||||
\(374\) | 2.00000 | − | 8.00000i | 0.103418 | − | 0.413670i | ||||
\(375\) | 3.31371 | 0.171119 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.24264 | − | 9.24264i | −0.476020 | − | 0.476020i | ||||
\(378\) | 6.62742 | 0.340878 | ||||||||
\(379\) | −24.5563 | − | 24.5563i | −1.26137 | − | 1.26137i | −0.950427 | − | 0.310948i | \(-0.899353\pi\) |
−0.310948 | − | 0.950427i | \(-0.600647\pi\) | |||||||
\(380\) | 10.3431 | − | 10.3431i | 0.530592 | − | 0.530592i | ||||
\(381\) | −2.38478 | + | 2.38478i | −0.122176 | + | 0.122176i | ||||
\(382\) | 14.3431i | 0.733859i | ||||||||
\(383\) | 31.4558i | 1.60732i | 0.595090 | + | 0.803659i | \(0.297117\pi\) | ||||
−0.595090 | + | 0.803659i | \(0.702883\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.00000 | − | 2.00000i | 0.101929 | − | 0.101929i | ||||
\(386\) | 18.3431 | + | 18.3431i | 0.933642 | + | 0.933642i | ||||
\(387\) | −14.3848 | −0.731219 | ||||||||
\(388\) | 10.8284 | + | 10.8284i | 0.549730 | + | 0.549730i | ||||
\(389\) | − | 9.00000i | − | 0.456318i | −0.973624 | − | 0.228159i | \(-0.926729\pi\) | ||
0.973624 | − | 0.228159i | \(-0.0732706\pi\) | |||||||
\(390\) | 11.3137 | 0.572892 | ||||||||
\(391\) | −16.9706 | − | 4.24264i | −0.858238 | − | 0.214560i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 1.27208i | − | 0.0641678i | ||||||
\(394\) | 27.3137 | + | 27.3137i | 1.37604 | + | 1.37604i | ||||
\(395\) | −8.97056 | −0.451358 | ||||||||
\(396\) | 3.75736 | + | 3.75736i | 0.188814 | + | 0.188814i | ||||
\(397\) | −0.272078 | + | 0.272078i | −0.0136552 | + | 0.0136552i | −0.713901 | − | 0.700246i | \(-0.753074\pi\) |
0.700246 | + | 0.713901i | \(0.253074\pi\) | |||||||
\(398\) | 30.8284 | − | 30.8284i | 1.54529 | − | 1.54529i | ||||
\(399\) | 1.51472i | 0.0758308i | ||||||||
\(400\) | − | 12.0000i | − | 0.600000i | ||||||
\(401\) | −8.48528 | + | 8.48528i | −0.423735 | + | 0.423735i | −0.886487 | − | 0.462753i | \(-0.846862\pi\) |
0.462753 | + | 0.886487i | \(0.346862\pi\) | |||||||
\(402\) | −0.828427 | + | 0.828427i | −0.0413182 | + | 0.0413182i | ||||
\(403\) | 16.4853 | + | 16.4853i | 0.821190 | + | 0.821190i | ||||
\(404\) | 21.4558 | 1.06747 | ||||||||
\(405\) | −12.0589 | − | 12.0589i | −0.599210 | − | 0.599210i | ||||
\(406\) | 7.65685i | 0.380003i | ||||||||
\(407\) | 9.41421 | 0.466645 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.1421 | 0.501496 | 0.250748 | − | 0.968052i | \(-0.419323\pi\) | ||||
0.250748 | + | 0.968052i | \(0.419323\pi\) | |||||||
\(410\) | − | 28.2843i | − | 1.39686i | ||||||
\(411\) | 4.07107 | + | 4.07107i | 0.200811 | + | 0.200811i | ||||
\(412\) | −33.3137 | −1.64125 | ||||||||
\(413\) | −3.29289 | − | 3.29289i | −0.162033 | − | 0.162033i | ||||
\(414\) | 15.9411 | − | 15.9411i | 0.783464 | − | 0.783464i | ||||
\(415\) | −9.65685 | + | 9.65685i | −0.474036 | + | 0.474036i | ||||
\(416\) | 27.3137i | 1.33916i | ||||||||
\(417\) | 3.61522i | 0.177038i | ||||||||
\(418\) | −3.65685 | + | 3.65685i | −0.178863 | + | 0.178863i | ||||
\(419\) | 8.34315 | − | 8.34315i | 0.407589 | − | 0.407589i | −0.473308 | − | 0.880897i | \(-0.656940\pi\) |
0.880897 | + | 0.473308i | \(0.156940\pi\) | |||||||
\(420\) | −2.34315 | − | 2.34315i | −0.114334 | − | 0.114334i | ||||
\(421\) | −20.3137 | −0.990030 | −0.495015 | − | 0.868885i | \(-0.664837\pi\) | ||||
−0.495015 | + | 0.868885i | \(0.664837\pi\) | |||||||
\(422\) | 12.7279 | + | 12.7279i | 0.619586 | + | 0.619586i | ||||
\(423\) | − | 30.5147i | − | 1.48368i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.6066 | − | 6.36396i | 0.514496 | − | 0.308697i | ||||
\(426\) | 18.3431 | 0.888728 | ||||||||
\(427\) | 6.82843i | 0.330451i | ||||||||
\(428\) | 0.928932 | + | 0.928932i | 0.0449016 | + | 0.0449016i | ||||
\(429\) | −2.00000 | −0.0965609 | ||||||||
\(430\) | 21.6569 | + | 21.6569i | 1.04439 | + | 1.04439i | ||||
\(431\) | 6.84924 | − | 6.84924i | 0.329916 | − | 0.329916i | −0.522638 | − | 0.852555i | \(-0.675052\pi\) |
0.852555 | + | 0.522638i | \(0.175052\pi\) | |||||||
\(432\) | −9.37258 | + | 9.37258i | −0.450939 | + | 0.450939i | ||||
\(433\) | − | 11.4853i | − | 0.551947i | −0.961165 | − | 0.275974i | \(-0.911000\pi\) | ||
0.961165 | − | 0.275974i | \(-0.0890003\pi\) | |||||||
\(434\) | − | 13.6569i | − | 0.655550i | ||||||
\(435\) | −4.48528 | + | 4.48528i | −0.215053 | + | 0.215053i | ||||
\(436\) | 21.8995 | − | 21.8995i | 1.04880 | − | 1.04880i | ||||
\(437\) | 7.75736 | + | 7.75736i | 0.371085 | + | 0.371085i | ||||
\(438\) | 9.57359 | 0.457444 | ||||||||
\(439\) | 13.7782 | + | 13.7782i | 0.657596 | + | 0.657596i | 0.954811 | − | 0.297214i | \(-0.0960576\pi\) |
−0.297214 | + | 0.954811i | \(0.596058\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.9411 | 0.759101 | ||||||||
\(442\) | −24.1421 | + | 14.4853i | −1.14832 | + | 0.688995i | ||||
\(443\) | 12.9706 | 0.616250 | 0.308125 | − | 0.951346i | \(-0.400298\pi\) | ||||
0.308125 | + | 0.951346i | \(0.400298\pi\) | |||||||
\(444\) | − | 11.0294i | − | 0.523434i | ||||||
\(445\) | −3.65685 | − | 3.65685i | −0.173352 | − | 0.173352i | ||||
\(446\) | 12.0000 | 0.568216 | ||||||||
\(447\) | 8.38478 | + | 8.38478i | 0.396586 | + | 0.396586i | ||||
\(448\) | 5.65685 | − | 5.65685i | 0.267261 | − | 0.267261i | ||||
\(449\) | −11.3137 | + | 11.3137i | −0.533927 | + | 0.533927i | −0.921739 | − | 0.387812i | \(-0.873231\pi\) |
0.387812 | + | 0.921739i | \(0.373231\pi\) | |||||||
\(450\) | 15.9411i | 0.751472i | ||||||||
\(451\) | 5.00000i | 0.235441i | ||||||||
\(452\) | 10.8284 | − | 10.8284i | 0.509326 | − | 0.509326i | ||||
\(453\) | 2.68629 | − | 2.68629i | 0.126213 | − | 0.126213i | ||||
\(454\) | −19.5563 | − | 19.5563i | −0.917825 | − | 0.917825i | ||||
\(455\) | −9.65685 | −0.452720 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 36.4853i | 1.70671i | 0.521331 | + | 0.853355i | \(0.325436\pi\) | ||||
−0.521331 | + | 0.853355i | \(0.674564\pi\) | |||||||
\(458\) | −9.31371 | −0.435201 | ||||||||
\(459\) | −13.2548 | − | 3.31371i | −0.618683 | − | 0.154671i | ||||
\(460\) | −24.0000 | −1.11901 | ||||||||
\(461\) | − | 33.6985i | − | 1.56949i | −0.619816 | − | 0.784747i | \(-0.712793\pi\) | ||
0.619816 | − | 0.784747i | \(-0.287207\pi\) | |||||||
\(462\) | 0.828427 | + | 0.828427i | 0.0385419 | + | 0.0385419i | ||||
\(463\) | 40.1127 | 1.86420 | 0.932098 | − | 0.362207i | \(-0.117977\pi\) | ||||
0.932098 | + | 0.362207i | \(0.117977\pi\) | |||||||
\(464\) | −10.8284 | − | 10.8284i | −0.502697 | − | 0.502697i | ||||
\(465\) | 8.00000 | − | 8.00000i | 0.370991 | − | 0.370991i | ||||
\(466\) | 31.0711 | − | 31.0711i | 1.43934 | − | 1.43934i | ||||
\(467\) | 28.1127i | 1.30090i | 0.759549 | + | 0.650450i | \(0.225420\pi\) | ||||
−0.759549 | + | 0.650450i | \(0.774580\pi\) | |||||||
\(468\) | − | 18.1421i | − | 0.838621i | ||||||
\(469\) | 0.707107 | − | 0.707107i | 0.0326512 | − | 0.0326512i | ||||
\(470\) | −45.9411 | + | 45.9411i | −2.11911 | + | 2.11911i | ||||
\(471\) | −8.41421 | − | 8.41421i | −0.387706 | − | 0.387706i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.82843 | − | 3.82843i | −0.176031 | − | 0.176031i | ||||
\(474\) | − | 3.71573i | − | 0.170669i | ||||||
\(475\) | −7.75736 | −0.355932 | ||||||||
\(476\) | 8.00000 | + | 2.00000i | 0.366679 | + | 0.0916698i | ||||
\(477\) | 9.25988 | 0.423981 | ||||||||
\(478\) | 50.1421i | 2.29345i | ||||||||
\(479\) | 18.9497 | + | 18.9497i | 0.865836 | + | 0.865836i | 0.992008 | − | 0.126172i | \(-0.0402692\pi\) |
−0.126172 | + | 0.992008i | \(0.540269\pi\) | |||||||
\(480\) | 13.2548 | 0.604998 | ||||||||
\(481\) | −22.7279 | − | 22.7279i | −1.03630 | − | 1.03630i | ||||
\(482\) | −18.8701 | + | 18.8701i | −0.859508 | + | 0.859508i | ||||
\(483\) | 1.75736 | − | 1.75736i | 0.0799626 | − | 0.0799626i | ||||
\(484\) | 2.00000i | 0.0909091i | ||||||||
\(485\) | − | 21.6569i | − | 0.983387i | ||||||
\(486\) | 19.0538 | − | 19.0538i | 0.864299 | − | 0.864299i | ||||
\(487\) | 5.82843 | − | 5.82843i | 0.264111 | − | 0.264111i | −0.562611 | − | 0.826722i | \(-0.690203\pi\) |
0.826722 | + | 0.562611i | \(0.190203\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.14214 | −0.187314 | ||||||||
\(490\) | −24.0000 | − | 24.0000i | −1.08421 | − | 1.08421i | ||||
\(491\) | 38.3848i | 1.73228i | 0.499801 | + | 0.866140i | \(0.333407\pi\) | ||||
−0.499801 | + | 0.866140i | \(0.666593\pi\) | |||||||
\(492\) | 5.85786 | 0.264093 | ||||||||
\(493\) | 3.82843 | − | 15.3137i | 0.172424 | − | 0.689695i | ||||
\(494\) | 17.6569 | 0.794419 | ||||||||
\(495\) | − | 7.51472i | − | 0.337761i | ||||||
\(496\) | 19.3137 | + | 19.3137i | 0.867211 | + | 0.867211i | ||||
\(497\) | −15.6569 | −0.702306 | ||||||||
\(498\) | −4.00000 | − | 4.00000i | −0.179244 | − | 0.179244i | ||||
\(499\) | −9.07107 | + | 9.07107i | −0.406077 | + | 0.406077i | −0.880368 | − | 0.474291i | \(-0.842704\pi\) |
0.474291 | + | 0.880368i | \(0.342704\pi\) | |||||||
\(500\) | −8.00000 | + | 8.00000i | −0.357771 | + | 0.357771i | ||||
\(501\) | 2.42641i | 0.108404i | ||||||||
\(502\) | 12.0000i | 0.535586i | ||||||||
\(503\) | 16.0208 | − | 16.0208i | 0.714333 | − | 0.714333i | −0.253106 | − | 0.967439i | \(-0.581452\pi\) |
0.967439 | + | 0.253106i | \(0.0814521\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.4558 | − | 21.4558i | −0.954773 | − | 0.954773i | ||||
\(506\) | 8.48528 | 0.377217 | ||||||||
\(507\) | −0.556349 | − | 0.556349i | −0.0247083 | − | 0.0247083i | ||||
\(508\) | − | 11.5147i | − | 0.510883i | ||||||
\(509\) | 40.3137 | 1.78687 | 0.893437 | − | 0.449189i | \(-0.148287\pi\) | ||||
0.893437 | + | 0.449189i | \(0.148287\pi\) | |||||||
\(510\) | 7.02944 | + | 11.7157i | 0.311269 | + | 0.518781i | ||||
\(511\) | −8.17157 | −0.361489 | ||||||||
\(512\) | 32.0000i | 1.41421i | ||||||||
\(513\) | 6.05887 | + | 6.05887i | 0.267506 | + | 0.267506i | ||||
\(514\) | −21.0294 | −0.927569 | ||||||||
\(515\) | 33.3137 | + | 33.3137i | 1.46798 | + | 1.46798i | ||||
\(516\) | −4.48528 | + | 4.48528i | −0.197454 | + | 0.197454i | ||||
\(517\) | 8.12132 | − | 8.12132i | 0.357175 | − | 0.357175i | ||||
\(518\) | 18.8284i | 0.827274i | ||||||||
\(519\) | 0.100505i | 0.00441168i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.24264 | − | 3.24264i | 0.142063 | − | 0.142063i | −0.632499 | − | 0.774561i | \(-0.717971\pi\) |
0.774561 | + | 0.632499i | \(0.217971\pi\) | |||||||
\(522\) | 14.3848 | + | 14.3848i | 0.629605 | + | 0.629605i | ||||
\(523\) | −6.34315 | −0.277366 | −0.138683 | − | 0.990337i | \(-0.544287\pi\) | ||||
−0.138683 | + | 0.990337i | \(0.544287\pi\) | |||||||
\(524\) | 3.07107 | + | 3.07107i | 0.134160 | + | 0.134160i | ||||
\(525\) | 1.75736i | 0.0766974i | ||||||||
\(526\) | 11.1127 | 0.484537 | ||||||||
\(527\) | −6.82843 | + | 27.3137i | −0.297451 | + | 1.18980i | ||||
\(528\) | −2.34315 | −0.101972 | ||||||||
\(529\) | 5.00000i | 0.217391i | ||||||||
\(530\) | −13.9411 | − | 13.9411i | −0.605564 | − | 0.605564i | ||||
\(531\) | −12.3726 | −0.536924 | ||||||||
\(532\) | −3.65685 | − | 3.65685i | −0.158545 | − | 0.158545i | ||||
\(533\) | 12.0711 | − | 12.0711i | 0.522856 | − | 0.522856i | ||||
\(534\) | 1.51472 | − | 1.51472i | 0.0655483 | − | 0.0655483i | ||||
\(535\) | − | 1.85786i | − | 0.0803225i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.6152 | + | 10.6152i | −0.458081 | + | 0.458081i | ||||
\(538\) | −32.1421 | + | 32.1421i | −1.38575 | + | 1.38575i | ||||
\(539\) | 4.24264 | + | 4.24264i | 0.182743 | + | 0.182743i | ||||
\(540\) | −18.7452 | −0.806664 | ||||||||
\(541\) | 5.43503 | + | 5.43503i | 0.233670 | + | 0.233670i | 0.814223 | − | 0.580553i | \(-0.197163\pi\) |
−0.580553 | + | 0.814223i | \(0.697163\pi\) | |||||||
\(542\) | − | 58.6274i | − | 2.51826i | ||||||
\(543\) | −10.8284 | −0.464692 | ||||||||
\(544\) | −28.2843 | + | 16.9706i | −1.21268 | + | 0.727607i | ||||
\(545\) | −43.7990 | −1.87614 | ||||||||
\(546\) | − | 4.00000i | − | 0.171184i | ||||||
\(547\) | −6.10051 | − | 6.10051i | −0.260839 | − | 0.260839i | 0.564556 | − | 0.825395i | \(-0.309047\pi\) |
−0.825395 | + | 0.564556i | \(0.809047\pi\) | |||||||
\(548\) | −19.6569 | −0.839699 | ||||||||
\(549\) | 12.8284 | + | 12.8284i | 0.547504 | + | 0.547504i | ||||
\(550\) | −4.24264 | + | 4.24264i | −0.180907 | + | 0.180907i | ||||
\(551\) | −7.00000 | + | 7.00000i | −0.298210 | + | 0.298210i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.17157i | 0.134869i | ||||||||
\(554\) | 20.9289 | − | 20.9289i | 0.889185 | − | 0.889185i | ||||
\(555\) | −11.0294 | + | 11.0294i | −0.468174 | + | 0.468174i | ||||
\(556\) | −8.72792 | − | 8.72792i | −0.370146 | − | 0.370146i | ||||
\(557\) | 24.2843 | 1.02896 | 0.514479 | − | 0.857503i | \(-0.327985\pi\) | ||||
0.514479 | + | 0.857503i | \(0.327985\pi\) | |||||||
\(558\) | −25.6569 | − | 25.6569i | −1.08614 | − | 1.08614i | ||||
\(559\) | 18.4853i | 0.781844i | ||||||||
\(560\) | −11.3137 | −0.478091 | ||||||||
\(561\) | −1.24264 | − | 2.07107i | −0.0524643 | − | 0.0874406i | ||||
\(562\) | −32.9706 | −1.39078 | ||||||||
\(563\) | − | 16.8701i | − | 0.710988i | −0.934679 | − | 0.355494i | \(-0.884313\pi\) | ||
0.934679 | − | 0.355494i | \(-0.115687\pi\) | |||||||
\(564\) | −9.51472 | − | 9.51472i | −0.400642 | − | 0.400642i | ||||
\(565\) | −21.6569 | −0.911111 | ||||||||
\(566\) | −2.14214 | − | 2.14214i | −0.0900407 | − | 0.0900407i | ||||
\(567\) | −4.26346 | + | 4.26346i | −0.179048 | + | 0.179048i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 19.5147i | − | 0.818100i | −0.912512 | − | 0.409050i | \(-0.865860\pi\) | ||
0.912512 | − | 0.409050i | \(-0.134140\pi\) | |||||||
\(570\) | − | 8.56854i | − | 0.358897i | ||||||
\(571\) | −12.2635 | + | 12.2635i | −0.513210 | + | 0.513210i | −0.915508 | − | 0.402299i | \(-0.868211\pi\) |
0.402299 | + | 0.915508i | \(0.368211\pi\) | |||||||
\(572\) | 4.82843 | − | 4.82843i | 0.201887 | − | 0.201887i | ||||
\(573\) | 2.97056 | + | 2.97056i | 0.124097 | + | 0.124097i | ||||
\(574\) | −10.0000 | −0.417392 | ||||||||
\(575\) | 9.00000 | + | 9.00000i | 0.375326 | + | 0.375326i | ||||
\(576\) | − | 21.2548i | − | 0.885618i | ||||||
\(577\) | 21.6863 | 0.902812 | 0.451406 | − | 0.892319i | \(-0.350923\pi\) | ||||
0.451406 | + | 0.892319i | \(0.350923\pi\) | |||||||
\(578\) | −30.0000 | − | 16.0000i | −1.24784 | − | 0.665512i | ||||
\(579\) | 7.59798 | 0.315761 | ||||||||
\(580\) | − | 21.6569i | − | 0.899252i | ||||||
\(581\) | 3.41421 | + | 3.41421i | 0.141645 | + | 0.141645i | ||||
\(582\) | 8.97056 | 0.371842 | ||||||||
\(583\) | 2.46447 | + | 2.46447i | 0.102068 | + | 0.102068i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −18.1421 | + | 18.1421i | −0.750085 | + | 0.750085i | ||||
\(586\) | 21.8579i | 0.902940i | ||||||||
\(587\) | 37.1127i | 1.53180i | 0.642957 | + | 0.765902i | \(0.277707\pi\) | ||||
−0.642957 | + | 0.765902i | \(0.722293\pi\) | |||||||
\(588\) | 4.97056 | − | 4.97056i | 0.204983 | − | 0.204983i | ||||
\(589\) | 12.4853 | − | 12.4853i | 0.514447 | − | 0.514447i | ||||
\(590\) | 18.6274 | + | 18.6274i | 0.766879 | + | 0.766879i | ||||
\(591\) | 11.3137 | 0.465384 | ||||||||
\(592\) | −26.6274 | − | 26.6274i | −1.09438 | − | 1.09438i | ||||
\(593\) | 25.3137i | 1.03951i | 0.854316 | + | 0.519755i | \(0.173977\pi\) | ||||
−0.854316 | + | 0.519755i | \(0.826023\pi\) | |||||||
\(594\) | 6.62742 | 0.271926 | ||||||||
\(595\) | −6.00000 | − | 10.0000i | −0.245976 | − | 0.409960i | ||||
\(596\) | −40.4853 | −1.65834 | ||||||||
\(597\) | − | 12.7696i | − | 0.522623i | ||||||
\(598\) | −20.4853 | − | 20.4853i | −0.837705 | − | 0.837705i | ||||
\(599\) | −5.97056 | −0.243951 | −0.121975 | − | 0.992533i | \(-0.538923\pi\) | ||||
−0.121975 | + | 0.992533i | \(0.538923\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.3137 | + | 19.3137i | −0.787823 | + | 0.787823i | −0.981137 | − | 0.193314i | \(-0.938076\pi\) |
0.193314 | + | 0.981137i | \(0.438076\pi\) | |||||||
\(602\) | 7.65685 | − | 7.65685i | 0.312070 | − | 0.312070i | ||||
\(603\) | − | 2.65685i | − | 0.108195i | ||||||
\(604\) | 12.9706i | 0.527765i | ||||||||
\(605\) | 2.00000 | − | 2.00000i | 0.0813116 | − | 0.0813116i | ||||
\(606\) | 8.88730 | − | 8.88730i | 0.361022 | − | 0.361022i | ||||
\(607\) | 32.7279 | + | 32.7279i | 1.32839 | + | 1.32839i | 0.906779 | + | 0.421606i | \(0.138534\pi\) |
0.421606 | + | 0.906779i | \(0.361466\pi\) | |||||||
\(608\) | 20.6863 | 0.838940 | ||||||||
\(609\) | 1.58579 | + | 1.58579i | 0.0642593 | + | 0.0642593i | ||||
\(610\) | − | 38.6274i | − | 1.56398i | ||||||
\(611\) | −39.2132 | −1.58640 | ||||||||
\(612\) | 18.7868 | − | 11.2721i | 0.759411 | − | 0.455647i | ||||
\(613\) | 11.2721 | 0.455275 | 0.227637 | − | 0.973746i | \(-0.426900\pi\) | ||||
0.227637 | + | 0.973746i | \(0.426900\pi\) | |||||||
\(614\) | − | 44.4853i | − | 1.79528i | ||||||
\(615\) | −5.85786 | − | 5.85786i | −0.236212 | − | 0.236212i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.9706 | + | 16.9706i | 0.683209 | + | 0.683209i | 0.960722 | − | 0.277513i | \(-0.0895101\pi\) |
−0.277513 | + | 0.960722i | \(0.589510\pi\) | |||||||
\(618\) | −13.7990 | + | 13.7990i | −0.555077 | + | 0.555077i | ||||
\(619\) | −21.0711 | + | 21.0711i | −0.846918 | + | 0.846918i | −0.989747 | − | 0.142830i | \(-0.954380\pi\) |
0.142830 | + | 0.989747i | \(0.454380\pi\) | |||||||
\(620\) | 38.6274i | 1.55131i | ||||||||
\(621\) | − | 14.0589i | − | 0.564163i | ||||||
\(622\) | −3.31371 | + | 3.31371i | −0.132868 | + | 0.132868i | ||||
\(623\) | −1.29289 | + | 1.29289i | −0.0517987 | + | 0.0517987i | ||||
\(624\) | 5.65685 | + | 5.65685i | 0.226455 | + | 0.226455i | ||||
\(625\) | 31.0000 | 1.24000 | ||||||||
\(626\) | −20.8284 | − | 20.8284i | −0.832471 | − | 0.832471i | ||||
\(627\) | 1.51472i | 0.0604920i | ||||||||
\(628\) | 40.6274 | 1.62121 | ||||||||
\(629\) | 9.41421 | − | 37.6569i | 0.375369 | − | 1.50148i | ||||
\(630\) | 15.0294 | 0.598787 | ||||||||
\(631\) | − | 9.34315i | − | 0.371945i | −0.982555 | − | 0.185972i | \(-0.940457\pi\) | ||
0.982555 | − | 0.185972i | \(-0.0595435\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.27208 | 0.209546 | ||||||||
\(634\) | 17.1716 | + | 17.1716i | 0.681970 | + | 0.681970i | ||||
\(635\) | −11.5147 | + | 11.5147i | −0.456948 | + | 0.456948i | ||||
\(636\) | 2.88730 | − | 2.88730i | 0.114489 | − | 0.114489i | ||||
\(637\) | − | 20.4853i | − | 0.811656i | ||||||
\(638\) | 7.65685i | 0.303138i | ||||||||
\(639\) | −29.4142 | + | 29.4142i | −1.16361 | + | 1.16361i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.41421 | + | 4.41421i | 0.174351 | + | 0.174351i | 0.788888 | − | 0.614537i | \(-0.210657\pi\) |
−0.614537 | + | 0.788888i | \(0.710657\pi\) | |||||||
\(642\) | 0.769553 | 0.0303718 | ||||||||
\(643\) | 5.72792 | + | 5.72792i | 0.225887 | + | 0.225887i | 0.810972 | − | 0.585085i | \(-0.198939\pi\) |
−0.585085 | + | 0.810972i | \(0.698939\pi\) | |||||||
\(644\) | 8.48528i | 0.334367i | ||||||||
\(645\) | 8.97056 | 0.353216 | ||||||||
\(646\) | 10.9706 | + | 18.2843i | 0.431631 | + | 0.719385i | ||||
\(647\) | −28.4558 | −1.11871 | −0.559357 | − | 0.828927i | \(-0.688952\pi\) | ||||
−0.559357 | + | 0.828927i | \(0.688952\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.29289 | − | 3.29289i | −0.129257 | − | 0.129257i | ||||
\(650\) | 20.4853 | 0.803499 | ||||||||
\(651\) | −2.82843 | − | 2.82843i | −0.110855 | − | 0.110855i | ||||
\(652\) | 10.0000 | − | 10.0000i | 0.391630 | − | 0.391630i | ||||
\(653\) | 1.89949 | − | 1.89949i | 0.0743330 | − | 0.0743330i | −0.668963 | − | 0.743296i | \(-0.733261\pi\) |
0.743296 | + | 0.668963i | \(0.233261\pi\) | |||||||
\(654\) | − | 18.1421i | − | 0.709414i | ||||||
\(655\) | − | 6.14214i | − | 0.239993i | ||||||
\(656\) | 14.1421 | − | 14.1421i | 0.552158 | − | 0.552158i | ||||
\(657\) | −15.3518 | + | 15.3518i | −0.598930 | + | 0.598930i | ||||
\(658\) | 16.2426 | + | 16.2426i | 0.633204 | + | 0.633204i | ||||
\(659\) | 42.5269 | 1.65661 | 0.828307 | − | 0.560275i | \(-0.189305\pi\) | ||||
0.828307 | + | 0.560275i | \(0.189305\pi\) | |||||||
\(660\) | −2.34315 | − | 2.34315i | −0.0912068 | − | 0.0912068i | ||||
\(661\) | − | 21.0000i | − | 0.816805i | −0.912802 | − | 0.408403i | \(-0.866086\pi\) | ||
0.912802 | − | 0.408403i | \(-0.133914\pi\) | |||||||
\(662\) | 23.3137 | 0.906113 | ||||||||
\(663\) | −2.00000 | + | 8.00000i | −0.0776736 | + | 0.310694i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.31371i | 0.283613i | ||||||||
\(666\) | 35.3726 | + | 35.3726i | 1.37066 | + | 1.37066i | ||||
\(667\) | 16.2426 | 0.628918 | ||||||||
\(668\) | −5.85786 | − | 5.85786i | −0.226648 | − | 0.226648i | ||||
\(669\) | 2.48528 | − | 2.48528i | 0.0960865 | − | 0.0960865i | ||||
\(670\) | −4.00000 | + | 4.00000i | −0.154533 | + | 0.154533i | ||||
\(671\) | 6.82843i | 0.263609i | ||||||||
\(672\) | − | 4.68629i | − | 0.180778i | ||||||
\(673\) | 20.9497 | − | 20.9497i | 0.807553 | − | 0.807553i | −0.176710 | − | 0.984263i | \(-0.556545\pi\) |
0.984263 | + | 0.176710i | \(0.0565453\pi\) | |||||||
\(674\) | −44.5269 | + | 44.5269i | −1.71511 | + | 1.71511i | ||||
\(675\) | 7.02944 | + | 7.02944i | 0.270563 | + | 0.270563i | ||||
\(676\) | 2.68629 | 0.103319 | ||||||||
\(677\) | −27.9203 | − | 27.9203i | −1.07306 | − | 1.07306i | −0.997111 | − | 0.0759533i | \(-0.975800\pi\) |
−0.0759533 | − | 0.997111i | \(-0.524200\pi\) | |||||||
\(678\) | − | 8.97056i | − | 0.344512i | ||||||
\(679\) | −7.65685 | −0.293843 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.10051 | −0.310412 | ||||||||
\(682\) | − | 13.6569i | − | 0.522948i | ||||||
\(683\) | −36.2132 | − | 36.2132i | −1.38566 | − | 1.38566i | −0.834204 | − | 0.551455i | \(-0.814073\pi\) |
−0.551455 | − | 0.834204i | \(-0.685927\pi\) | |||||||
\(684\) | −13.7401 | −0.525366 | ||||||||
\(685\) | 19.6569 | + | 19.6569i | 0.751050 | + | 0.751050i | ||||
\(686\) | −18.3848 | + | 18.3848i | −0.701934 | + | 0.701934i | ||||
\(687\) | −1.92893 | + | 1.92893i | −0.0735934 | + | 0.0735934i | ||||
\(688\) | 21.6569i | 0.825660i | ||||||||
\(689\) | − | 11.8995i | − | 0.453335i | ||||||
\(690\) | −9.94113 | + | 9.94113i | −0.378452 | + | 0.378452i | ||||
\(691\) | 27.2426 | − | 27.2426i | 1.03636 | − | 1.03636i | 0.0370453 | − | 0.999314i | \(-0.488205\pi\) |
0.999314 | − | 0.0370453i | \(-0.0117946\pi\) | |||||||
\(692\) | −0.242641 | − | 0.242641i | −0.00922381 | − | 0.00922381i | ||||
\(693\) | −2.65685 | −0.100926 | ||||||||
\(694\) | 30.8701 | + | 30.8701i | 1.17181 | + | 1.17181i | ||||
\(695\) | 17.4558i | 0.662138i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.0000 | + | 5.00000i | 0.757554 | + | 0.189389i | ||||
\(698\) | 71.3970 | 2.70242 | ||||||||
\(699\) | − | 12.8701i | − | 0.486790i | ||||||
\(700\) | −4.24264 | − | 4.24264i | −0.160357 | − | 0.160357i | ||||
\(701\) | −9.85786 | −0.372326 | −0.186163 | − | 0.982519i | \(-0.559605\pi\) | ||||
−0.186163 | + | 0.982519i | \(0.559605\pi\) | |||||||
\(702\) | −16.0000 | − | 16.0000i | −0.603881 | − | 0.603881i | ||||
\(703\) | −17.2132 | + | 17.2132i | −0.649208 | + | 0.649208i | ||||
\(704\) | 5.65685 | − | 5.65685i | 0.213201 | − | 0.213201i | ||||
\(705\) | 19.0294i | 0.716690i | ||||||||
\(706\) | − | 24.3431i | − | 0.916166i | ||||||
\(707\) | −7.58579 | + | 7.58579i | −0.285293 | + | 0.285293i | ||||
\(708\) | −3.85786 | + | 3.85786i | −0.144987 | + | 0.144987i | ||||
\(709\) | 12.0711 | + | 12.0711i | 0.453338 | + | 0.453338i | 0.896461 | − | 0.443123i | \(-0.146129\pi\) |
−0.443123 | + | 0.896461i | \(0.646129\pi\) | |||||||
\(710\) | 88.5685 | 3.32392 | ||||||||
\(711\) | 5.95837 | + | 5.95837i | 0.223456 | + | 0.223456i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28.9706 | −1.08496 | ||||||||
\(714\) | 4.14214 | − | 2.48528i | 0.155016 | − | 0.0930093i | ||||
\(715\) | −9.65685 | −0.361146 | ||||||||
\(716\) | − | 51.2548i | − | 1.91548i | ||||||
\(717\) | 10.3848 | + | 10.3848i | 0.387827 | + | 0.387827i | ||||
\(718\) | 64.2843 | 2.39907 | ||||||||
\(719\) | −16.5563 | − | 16.5563i | −0.617448 | − | 0.617448i | 0.327428 | − | 0.944876i | \(-0.393818\pi\) |
−0.944876 | + | 0.327428i | \(0.893818\pi\) | |||||||
\(720\) | −21.2548 | + | 21.2548i | −0.792121 | + | 0.792121i | ||||
\(721\) | 11.7782 | − | 11.7782i | 0.438642 | − | 0.438642i | ||||
\(722\) | 24.6274i | 0.916538i | ||||||||
\(723\) | 7.81623i | 0.290689i | ||||||||
\(724\) | 26.1421 | − | 26.1421i | 0.971565 | − | 0.971565i | ||||
\(725\) | −8.12132 | + | 8.12132i | −0.301618 | + | 0.301618i | ||||
\(726\) | 0.828427 | + | 0.828427i | 0.0307458 | + | 0.0307458i | ||||
\(727\) | −5.14214 | −0.190711 | −0.0953556 | − | 0.995443i | \(-0.530399\pi\) | ||||
−0.0953556 | + | 0.995443i | \(0.530399\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.1960i | 0.377628i | ||||||||
\(730\) | 46.2254 | 1.71088 | ||||||||
\(731\) | −19.1421 | + | 11.4853i | −0.707997 | + | 0.424798i | ||||
\(732\) | 8.00000 | 0.295689 | ||||||||
\(733\) | − | 33.7990i | − | 1.24839i | −0.781267 | − | 0.624197i | \(-0.785426\pi\) | ||
0.781267 | − | 0.624197i | \(-0.214574\pi\) | |||||||
\(734\) | −25.6569 | − | 25.6569i | −0.947012 | − | 0.947012i | ||||
\(735\) | −9.94113 | −0.366684 | ||||||||
\(736\) | −24.0000 | − | 24.0000i | −0.884652 | − | 0.884652i | ||||
\(737\) | 0.707107 | − | 0.707107i | 0.0260466 | − | 0.0260466i | ||||
\(738\) | −18.7868 | + | 18.7868i | −0.691552 | + | 0.691552i | ||||
\(739\) | − | 35.3137i | − | 1.29904i | −0.760346 | − | 0.649518i | \(-0.774971\pi\) | ||
0.760346 | − | 0.649518i | \(-0.225029\pi\) | |||||||
\(740\) | − | 53.2548i | − | 1.95769i | ||||||
\(741\) | 3.65685 | − | 3.65685i | 0.134338 | − | 0.134338i | ||||
\(742\) | −4.92893 | + | 4.92893i | −0.180947 | + | 0.180947i | ||||
\(743\) | −5.43503 | − | 5.43503i | −0.199392 | − | 0.199392i | 0.600347 | − | 0.799739i | \(-0.295029\pi\) |
−0.799739 | + | 0.600347i | \(0.795029\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40.4853 | + | 40.4853i | 1.48327 | + | 1.48327i | ||||
\(746\) | 57.4558i | 2.10361i | ||||||||
\(747\) | 12.8284 | 0.469368 | ||||||||
\(748\) | 8.00000 | + | 2.00000i | 0.292509 | + | 0.0731272i | ||||
\(749\) | −0.656854 | −0.0240009 | ||||||||
\(750\) | 6.62742i | 0.241999i | ||||||||
\(751\) | −19.3848 | − | 19.3848i | −0.707361 | − | 0.707361i | 0.258619 | − | 0.965979i | \(-0.416733\pi\) |
−0.965979 | + | 0.258619i | \(0.916733\pi\) | |||||||
\(752\) | −45.9411 | −1.67530 | ||||||||
\(753\) | 2.48528 | + | 2.48528i | 0.0905687 | + | 0.0905687i | ||||
\(754\) | 18.4853 | − | 18.4853i | 0.673194 | − | 0.673194i | ||||
\(755\) | 12.9706 | − | 12.9706i | 0.472047 | − | 0.472047i | ||||
\(756\) | 6.62742i | 0.241037i | ||||||||
\(757\) | − | 17.1716i | − | 0.624111i | −0.950064 | − | 0.312056i | \(-0.898982\pi\) | ||
0.950064 | − | 0.312056i | \(-0.101018\pi\) | |||||||
\(758\) | 49.1127 | − | 49.1127i | 1.78385 | − | 1.78385i | ||||
\(759\) | 1.75736 | − | 1.75736i | 0.0637881 | − | 0.0637881i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.92893 | 0.178674 | 0.0893368 | − | 0.996001i | \(-0.471525\pi\) | ||||
0.0893368 | + | 0.996001i | \(0.471525\pi\) | |||||||
\(762\) | −4.76955 | − | 4.76955i | −0.172783 | − | 0.172783i | ||||
\(763\) | 15.4853i | 0.560605i | ||||||||
\(764\) | −14.3431 | −0.518917 | ||||||||
\(765\) | −30.0589 | − | 7.51472i | −1.08678 | − | 0.271695i | ||||
\(766\) | −62.9117 | −2.27309 | ||||||||
\(767\) | 15.8995i | 0.574097i | ||||||||
\(768\) | 6.62742 | + | 6.62742i | 0.239146 | + | 0.239146i | ||||
\(769\) | −14.0416 | −0.506354 | −0.253177 | − | 0.967420i | \(-0.581476\pi\) | ||||
−0.253177 | + | 0.967420i | \(0.581476\pi\) | |||||||
\(770\) | 4.00000 | + | 4.00000i | 0.144150 | + | 0.144150i | ||||
\(771\) | −4.35534 | + | 4.35534i | −0.156854 | + | 0.156854i | ||||
\(772\) | −18.3431 | + | 18.3431i | −0.660184 | + | 0.660184i | ||||
\(773\) | 41.5980i | 1.49618i | 0.663600 | + | 0.748088i | \(0.269028\pi\) | ||||
−0.663600 | + | 0.748088i | \(0.730972\pi\) | |||||||
\(774\) | − | 28.7696i | − | 1.03410i | ||||||
\(775\) | 14.4853 | − | 14.4853i | 0.520327 | − | 0.520327i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.89949 | + | 3.89949i | 0.139894 | + | 0.139894i | ||||
\(778\) | 18.0000 | 0.645331 | ||||||||
\(779\) | −9.14214 | − | 9.14214i | −0.327551 | − | 0.327551i | ||||
\(780\) | 11.3137i | 0.405096i | ||||||||
\(781\) | −15.6569 | −0.560246 | ||||||||
\(782\) | 8.48528 | − | 33.9411i | 0.303433 | − | 1.21373i | ||||
\(783\) | 12.6863 | 0.453371 | ||||||||
\(784\) | − | 24.0000i | − | 0.857143i | ||||||
\(785\) | −40.6274 | − | 40.6274i | −1.45005 | − | 1.45005i | ||||
\(786\) | 2.54416 | 0.0907470 | ||||||||
\(787\) | −8.36396 | − | 8.36396i | −0.298143 | − | 0.298143i | 0.542143 | − | 0.840286i | \(-0.317613\pi\) |
−0.840286 | + | 0.542143i | \(0.817613\pi\) | |||||||
\(788\) | −27.3137 | + | 27.3137i | −0.973011 | + | 0.973011i | ||||
\(789\) | 2.30152 | − | 2.30152i | 0.0819361 | − | 0.0819361i | ||||
\(790\) | − | 17.9411i | − | 0.638317i | ||||||
\(791\) | 7.65685i | 0.272246i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.4853 | − | 16.4853i | 0.585410 | − | 0.585410i | ||||
\(794\) | −0.544156 | − | 0.544156i | −0.0193114 | − | 0.0193114i | ||||
\(795\) | −5.77460 | −0.204804 | ||||||||
\(796\) | 30.8284 | + | 30.8284i | 1.09268 | + | 1.09268i | ||||
\(797\) | 19.5147i | 0.691247i | 0.938373 | + | 0.345623i | \(0.112333\pi\) | ||||
−0.938373 | + | 0.345623i | \(0.887667\pi\) | |||||||
\(798\) | −3.02944 | −0.107241 | ||||||||
\(799\) | −24.3640 | − | 40.6066i | −0.861935 | − | 1.43656i | ||||
\(800\) | 24.0000 | 0.848528 | ||||||||
\(801\) | 4.85786i | 0.171644i | ||||||||
\(802\) | −16.9706 | − | 16.9706i | −0.599251 | − | 0.599251i | ||||
\(803\) | −8.17157 | −0.288369 | ||||||||
\(804\) | −0.828427 | − | 0.828427i | −0.0292164 | − | 0.0292164i | ||||
\(805\) | 8.48528 | − | 8.48528i | 0.299067 | − | 0.299067i | ||||
\(806\) | −32.9706 | + | 32.9706i | −1.16134 | + | 1.16134i | ||||
\(807\) | 13.3137i | 0.468665i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32.6066 | + | 32.6066i | −1.14639 | + | 1.14639i | −0.159129 | + | 0.987258i | \(0.550869\pi\) |
−0.987258 | + | 0.159129i | \(0.949131\pi\) | |||||||
\(810\) | 24.1177 | − | 24.1177i | 0.847411 | − | 0.847411i | ||||
\(811\) | −23.0711 | − | 23.0711i | −0.810135 | − | 0.810135i | 0.174519 | − | 0.984654i | \(-0.444163\pi\) |
−0.984654 | + | 0.174519i | \(0.944163\pi\) | |||||||
\(812\) | −7.65685 | −0.268703 | ||||||||
\(813\) | −12.1421 | − | 12.1421i | −0.425843 | − | 0.425843i | ||||
\(814\) | 18.8284i | 0.659936i | ||||||||
\(815\) | −20.0000 | −0.700569 | ||||||||
\(816\) | −2.34315 | + | 9.37258i | −0.0820265 | + | 0.328106i | ||||
\(817\) | 14.0000 | 0.489798 | ||||||||
\(818\) | 20.2843i | 0.709223i | ||||||||
\(819\) | 6.41421 | + | 6.41421i | 0.224131 | + | 0.224131i | ||||
\(820\) | 28.2843 | 0.987730 | ||||||||
\(821\) | −17.1716 | − | 17.1716i | −0.599292 | − | 0.599292i | 0.340832 | − | 0.940124i | \(-0.389291\pi\) |
−0.940124 | + | 0.340832i | \(0.889291\pi\) | |||||||
\(822\) | −8.14214 | + | 8.14214i | −0.283990 | + | 0.283990i | ||||
\(823\) | 20.6274 | − | 20.6274i | 0.719027 | − | 0.719027i | −0.249379 | − | 0.968406i | \(-0.580227\pi\) |
0.968406 | + | 0.249379i | \(0.0802266\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.75736i | 0.0611834i | ||||||||
\(826\) | 6.58579 | − | 6.58579i | 0.229149 | − | 0.229149i | ||||
\(827\) | 14.7487 | − | 14.7487i | 0.512864 | − | 0.512864i | −0.402539 | − | 0.915403i | \(-0.631872\pi\) |
0.915403 | + | 0.402539i | \(0.131872\pi\) | |||||||
\(828\) | 15.9411 | + | 15.9411i | 0.553992 | + | 0.553992i | ||||
\(829\) | 32.9706 | 1.14511 | 0.572557 | − | 0.819865i | \(-0.305951\pi\) | ||||
0.572557 | + | 0.819865i | \(0.305951\pi\) | |||||||
\(830\) | −19.3137 | − | 19.3137i | −0.670389 | − | 0.670389i | ||||
\(831\) | − | 8.66905i | − | 0.300726i | ||||||
\(832\) | −27.3137 | −0.946932 | ||||||||
\(833\) | 21.2132 | − | 12.7279i | 0.734994 | − | 0.440996i | ||||
\(834\) | −7.23045 | −0.250370 | ||||||||
\(835\) | 11.7157i | 0.405440i | ||||||||
\(836\) | −3.65685 | − | 3.65685i | −0.126475 | − | 0.126475i | ||||
\(837\) | −22.6274 | −0.782118 | ||||||||
\(838\) | 16.6863 | + | 16.6863i | 0.576418 | + | 0.576418i | ||||
\(839\) | −25.3848 | + | 25.3848i | −0.876380 | + | 0.876380i | −0.993158 | − | 0.116778i | \(-0.962743\pi\) |
0.116778 | + | 0.993158i | \(0.462743\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 14.3431i | − | 0.494591i | ||||||
\(842\) | − | 40.6274i | − | 1.40011i | ||||||
\(843\) | −6.82843 | + | 6.82843i | −0.235184 | + | 0.235184i | ||||
\(844\) | −12.7279 | + | 12.7279i | −0.438113 | + | 0.438113i | ||||
\(845\) | −2.68629 | − | 2.68629i | −0.0924112 | − | 0.0924112i | ||||
\(846\) | 61.0294 | 2.09824 | ||||||||
\(847\) | −0.707107 | − | 0.707107i | −0.0242965 | − | 0.0242965i | ||||
\(848\) | − | 13.9411i | − | 0.478740i | ||||||
\(849\) | −0.887302 | −0.0304521 | ||||||||
\(850\) | 12.7279 | + | 21.2132i | 0.436564 | + | 0.727607i | ||||
\(851\) | 39.9411 | 1.36916 | ||||||||
\(852\) | 18.3431i | 0.628426i | ||||||||
\(853\) | 15.9203 | + | 15.9203i | 0.545101 | + | 0.545101i | 0.925020 | − | 0.379919i | \(-0.124048\pi\) |
−0.379919 | + | 0.925020i | \(0.624048\pi\) | |||||||
\(854\) | −13.6569 | −0.467328 | ||||||||
\(855\) | 13.7401 | + | 13.7401i | 0.469902 | + | 0.469902i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.4558 | − | 39.4558i | 1.34779 | − | 1.34779i | 0.459724 | − | 0.888062i | \(-0.347948\pi\) |
0.888062 | − | 0.459724i | \(-0.152052\pi\) | |||||||
\(858\) | − | 4.00000i | − | 0.136558i | ||||||
\(859\) | − | 10.3137i | − | 0.351899i | −0.984399 | − | 0.175950i | \(-0.943700\pi\) | ||
0.984399 | − | 0.175950i | \(-0.0562996\pi\) | |||||||
\(860\) | −21.6569 | + | 21.6569i | −0.738493 | + | 0.738493i | ||||
\(861\) | −2.07107 | + | 2.07107i | −0.0705818 | + | 0.0705818i | ||||
\(862\) | 13.6985 | + | 13.6985i | 0.466572 | + | 0.466572i | ||||
\(863\) | −30.6863 | −1.04457 | −0.522287 | − | 0.852770i | \(-0.674921\pi\) | ||||
−0.522287 | + | 0.852770i | \(0.674921\pi\) | |||||||
\(864\) | −18.7452 | − | 18.7452i | −0.637723 | − | 0.637723i | ||||
\(865\) | 0.485281i | 0.0165001i | ||||||||
\(866\) | 22.9706 | 0.780571 | ||||||||
\(867\) | −9.52691 | + | 2.89949i | −0.323551 | + | 0.0984720i | ||||
\(868\) | 13.6569 | 0.463544 | ||||||||
\(869\) | 3.17157i | 0.107588i | ||||||||
\(870\) | −8.97056 | − | 8.97056i | −0.304131 | − | 0.304131i | ||||
\(871\) | −3.41421 | −0.115686 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.3848 | + | 14.3848i | −0.486851 | + | 0.486851i | ||||
\(874\) | −15.5147 | + | 15.5147i | −0.524793 | + | 0.524793i | ||||
\(875\) | − | 5.65685i | − | 0.191237i | ||||||
\(876\) | 9.57359i | 0.323462i | ||||||||
\(877\) | −11.5563 | + | 11.5563i | −0.390230 | + | 0.390230i | −0.874769 | − | 0.484539i | \(-0.838987\pi\) |
0.484539 | + | 0.874769i | \(0.338987\pi\) | |||||||
\(878\) | −27.5563 | + | 27.5563i | −0.929982 | + | 0.929982i | ||||
\(879\) | 4.52691 | + | 4.52691i | 0.152689 | + | 0.152689i | ||||
\(880\) | −11.3137 | −0.381385 | ||||||||
\(881\) | −15.4142 | − | 15.4142i | −0.519318 | − | 0.519318i | 0.398047 | − | 0.917365i | \(-0.369688\pi\) |
−0.917365 | + | 0.398047i | \(0.869688\pi\) | |||||||
\(882\) | 31.8823i | 1.07353i | ||||||||
\(883\) | 20.6569 | 0.695158 | 0.347579 | − | 0.937651i | \(-0.387004\pi\) | ||||
0.347579 | + | 0.937651i | \(0.387004\pi\) | |||||||
\(884\) | −14.4853 | − | 24.1421i | −0.487193 | − | 0.811988i | ||||
\(885\) | 7.71573 | 0.259361 | ||||||||
\(886\) | 25.9411i | 0.871509i | ||||||||
\(887\) | −3.51472 | − | 3.51472i | −0.118013 | − | 0.118013i | 0.645634 | − | 0.763647i | \(-0.276593\pi\) |
−0.763647 | + | 0.645634i | \(0.776593\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.07107 | + | 4.07107i | 0.136539 | + | 0.136539i | ||||
\(890\) | 7.31371 | − | 7.31371i | 0.245156 | − | 0.245156i | ||||
\(891\) | −4.26346 | + | 4.26346i | −0.142831 | + | 0.142831i | ||||
\(892\) | 12.0000i | 0.401790i | ||||||||
\(893\) | 29.6985i | 0.993822i | ||||||||
\(894\) | −16.7696 | + | 16.7696i | −0.560858 | + | 0.560858i | ||||
\(895\) | −51.2548 | + | 51.2548i | −1.71326 | + | 1.71326i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.48528 | −0.283315 | ||||||||
\(898\) | −22.6274 | − | 22.6274i | −0.755087 | − | 0.755087i | ||||
\(899\) | − | 26.1421i | − | 0.871889i | ||||||
\(900\) | −15.9411 | −0.531371 | ||||||||
\(901\) | 12.3223 | − | 7.39340i | 0.410516 | − | 0.246310i | ||||
\(902\) | −10.0000 | −0.332964 | ||||||||
\(903\) | − | 3.17157i | − | 0.105543i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −52.2843 | −1.73799 | ||||||||
\(906\) | 5.37258 | + | 5.37258i | 0.178492 | + | 0.178492i | ||||
\(907\) | 10.7279 | − | 10.7279i | 0.356215 | − | 0.356215i | −0.506201 | − | 0.862416i | \(-0.668951\pi\) |
0.862416 | + | 0.506201i | \(0.168951\pi\) | |||||||
\(908\) | 19.5563 | − | 19.5563i | 0.649000 | − | 0.649000i | ||||
\(909\) | 28.5025i | 0.945369i | ||||||||
\(910\) | − | 19.3137i | − | 0.640243i | ||||||
\(911\) | 5.24264 | − | 5.24264i | 0.173696 | − | 0.173696i | −0.614905 | − | 0.788601i | \(-0.710806\pi\) |
0.788601 | + | 0.614905i | \(0.210806\pi\) | |||||||
\(912\) | 4.28427 | − | 4.28427i | 0.141866 | − | 0.141866i | ||||
\(913\) | 3.41421 | + | 3.41421i | 0.112994 | + | 0.112994i | ||||
\(914\) | −72.9706 | −2.41365 | ||||||||
\(915\) | −8.00000 | − | 8.00000i | −0.264472 | − | 0.264472i | ||||
\(916\) | − | 9.31371i | − | 0.307734i | ||||||
\(917\) | −2.17157 | −0.0717117 | ||||||||
\(918\) | 6.62742 | − | 26.5097i | 0.218737 | − | 0.874949i | ||||
\(919\) | 18.0416 | 0.595138 | 0.297569 | − | 0.954700i | \(-0.403824\pi\) | ||||
0.297569 | + | 0.954700i | \(0.403824\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.21320 | − | 9.21320i | −0.303585 | − | 0.303585i | ||||
\(922\) | 67.3970 | 2.21960 | ||||||||
\(923\) | 37.7990 | + | 37.7990i | 1.24417 | + | 1.24417i | ||||
\(924\) | −0.828427 | + | 0.828427i | −0.0272533 | + | 0.0272533i | ||||
\(925\) | −19.9706 | + | 19.9706i | −0.656628 | + | 0.656628i | ||||
\(926\) | 80.2254i | 2.63637i | ||||||||
\(927\) | − | 44.2548i | − | 1.45352i | ||||||
\(928\) | 21.6569 | − | 21.6569i | 0.710921 | − | 0.710921i | ||||
\(929\) | −18.1716 | + | 18.1716i | −0.596190 | + | 0.596190i | −0.939296 | − | 0.343107i | \(-0.888521\pi\) |
0.343107 | + | 0.939296i | \(0.388521\pi\) | |||||||
\(930\) | 16.0000 | + | 16.0000i | 0.524661 | + | 0.524661i | ||||
\(931\) | −15.5147 | −0.508474 | ||||||||
\(932\) | 31.0711 | + | 31.0711i | 1.01777 | + | 1.01777i | ||||
\(933\) | 1.37258i | 0.0449364i | ||||||||
\(934\) | −56.2254 | −1.83975 | ||||||||
\(935\) | −6.00000 | − | 10.0000i | −0.196221 | − | 0.327035i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.6863i | 0.610455i | 0.952280 | + | 0.305227i | \(0.0987324\pi\) | ||||
−0.952280 | + | 0.305227i | \(0.901268\pi\) | |||||||
\(938\) | 1.41421 | + | 1.41421i | 0.0461757 | + | 0.0461757i | ||||
\(939\) | −8.62742 | −0.281545 | ||||||||
\(940\) | −45.9411 | − | 45.9411i | −1.49843 | − | 1.49843i | ||||
\(941\) | −3.05025 | + | 3.05025i | −0.0994354 | + | 0.0994354i | −0.755074 | − | 0.655639i | \(-0.772399\pi\) |
0.655639 | + | 0.755074i | \(0.272399\pi\) | |||||||
\(942\) | 16.8284 | − | 16.8284i | 0.548300 | − | 0.548300i | ||||
\(943\) | 21.2132i | 0.690797i | ||||||||
\(944\) | 18.6274i | 0.606271i | ||||||||
\(945\) | 6.62742 | − | 6.62742i | 0.215590 | − | 0.215590i | ||||
\(946\) | 7.65685 | − | 7.65685i | 0.248946 | − | 0.248946i | ||||
\(947\) | 8.10051 | + | 8.10051i | 0.263231 | + | 0.263231i | 0.826365 | − | 0.563134i | \(-0.190405\pi\) |
−0.563134 | + | 0.826365i | \(0.690405\pi\) | |||||||
\(948\) | 3.71573 | 0.120681 | ||||||||
\(949\) | 19.7279 | + | 19.7279i | 0.640395 | + | 0.640395i | ||||
\(950\) | − | 15.5147i | − | 0.503364i | ||||||
\(951\) | 7.11270 | 0.230645 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.6569 | −1.34940 | −0.674699 | − | 0.738093i | \(-0.735727\pi\) | ||||
−0.674699 | + | 0.738093i | \(0.735727\pi\) | |||||||
\(954\) | 18.5198i | 0.599600i | ||||||||
\(955\) | 14.3431 | + | 14.3431i | 0.464133 | + | 0.464133i | ||||
\(956\) | −50.1421 | −1.62171 | ||||||||
\(957\) | 1.58579 | + | 1.58579i | 0.0512612 | + | 0.0512612i | ||||
\(958\) | −37.8995 | + | 37.8995i | −1.22448 | + | 1.22448i | ||||
\(959\) | 6.94975 | − | 6.94975i | 0.224419 | − | 0.224419i | ||||
\(960\) | 13.2548i | 0.427798i | ||||||||
\(961\) | 15.6274i | 0.504110i | ||||||||
\(962\) | 45.4558 | − | 45.4558i | 1.46556 | − | 1.46556i | ||||
\(963\) | −1.23402 | + | 1.23402i | −0.0397657 | + | 0.0397657i | ||||
\(964\) | −18.8701 | − | 18.8701i | −0.607764 | − | 0.607764i | ||||
\(965\) | 36.6863 | 1.18097 | ||||||||
\(966\) | 3.51472 | + | 3.51472i | 0.113084 | + | 0.113084i | ||||
\(967\) | − | 23.2132i | − | 0.746486i | −0.927734 | − | 0.373243i | \(-0.878246\pi\) | ||
0.927734 | − | 0.373243i | \(-0.121754\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.05887 | + | 1.51472i | 0.194639 | + | 0.0486598i | ||||
\(970\) | 43.3137 | 1.39072 | ||||||||
\(971\) | 56.4264i | 1.81081i | 0.424549 | + | 0.905405i | \(0.360433\pi\) | ||||
−0.424549 | + | 0.905405i | \(0.639567\pi\) | |||||||
\(972\) | 19.0538 | + | 19.0538i | 0.611152 | + | 0.611152i | ||||
\(973\) | 6.17157 | 0.197852 | ||||||||
\(974\) | 11.6569 | + | 11.6569i | 0.373510 | + | 0.373510i | ||||
\(975\) | 4.24264 | − | 4.24264i | 0.135873 | − | 0.135873i | ||||
\(976\) | 19.3137 | − | 19.3137i | 0.618217 | − | 0.618217i | ||||
\(977\) | − | 30.8579i | − | 0.987231i | −0.869680 | − | 0.493615i | \(-0.835675\pi\) | ||
0.869680 | − | 0.493615i | \(-0.164325\pi\) | |||||||
\(978\) | − | 8.28427i | − | 0.264902i | ||||||
\(979\) | −1.29289 | + | 1.29289i | −0.0413210 | + | 0.0413210i | ||||
\(980\) | 24.0000 | − | 24.0000i | 0.766652 | − | 0.766652i | ||||
\(981\) | 29.0919 | + | 29.0919i | 0.928832 | + | 0.928832i | ||||
\(982\) | −76.7696 | −2.44981 | ||||||||
\(983\) | 9.75736 | + | 9.75736i | 0.311211 | + | 0.311211i | 0.845379 | − | 0.534167i | \(-0.179375\pi\) |
−0.534167 | + | 0.845379i | \(0.679375\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 54.6274 | 1.74057 | ||||||||
\(986\) | 30.6274 | + | 7.65685i | 0.975376 | + | 0.243844i | ||||
\(987\) | 6.72792 | 0.214152 | ||||||||
\(988\) | 17.6569i | 0.561739i | ||||||||
\(989\) | −16.2426 | − | 16.2426i | −0.516486 | − | 0.516486i | ||||
\(990\) | 15.0294 | 0.477667 | ||||||||
\(991\) | 38.4558 | + | 38.4558i | 1.22159 | + | 1.22159i | 0.967067 | + | 0.254524i | \(0.0819186\pi\) |
0.254524 | + | 0.967067i | \(0.418081\pi\) | |||||||
\(992\) | −38.6274 | + | 38.6274i | −1.22642 | + | 1.22642i | ||||
\(993\) | 4.82843 | − | 4.82843i | 0.153226 | − | 0.153226i | ||||
\(994\) | − | 31.3137i | − | 0.993211i | ||||||
\(995\) | − | 61.6569i | − | 1.95465i | ||||||
\(996\) | 4.00000 | − | 4.00000i | 0.126745 | − | 0.126745i | ||||
\(997\) | −8.46447 | + | 8.46447i | −0.268072 | + | 0.268072i | −0.828323 | − | 0.560251i | \(-0.810705\pi\) |
0.560251 | + | 0.828323i | \(0.310705\pi\) | |||||||
\(998\) | −18.1421 | − | 18.1421i | −0.574279 | − | 0.574279i | ||||
\(999\) | 31.1960 | 0.986996 |
(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 | 187.2.e.a.166.2 | yes | 4 | |
17.2 | even | 8 | 3179.2.a.i.1.1 | 2 | |||
17.4 | even | 4 | inner | 187.2.e.a.89.2 | ✓ | 4 | |
17.15 | even | 8 | 3179.2.a.h.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
187.2.e.a.89.2 | ✓ | 4 | 17.4 | even | 4 | inner | |
187.2.e.a.166.2 | yes | 4 | 1.1 | even | 1 | trivial | |
3179.2.a.h.1.2 | 2 | 17.15 | even | 8 | |||
3179.2.a.i.1.1 | 2 | 17.2 | even | 8 |