Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [867,2,Mod(616,867)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(867, 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("867.616");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 867 = 3 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 867.e (of order \(4\), 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: | \(6.92302985525\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.722204136308736.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 18x^{8} + 69x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 616.4 | ||
Root | \(1.08335 - 1.08335i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 867.616 |
Dual form | 867.2.e.j.829.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/867\mathbb{Z}\right)^\times\).
\(n\) | \(290\) | \(292\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.34730i | − | 0.952682i | −0.879261 | − | 0.476341i | \(-0.841963\pi\) | ||
0.879261 | − | 0.476341i | \(-0.158037\pi\) | |||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0.184793 | 0.0923963 | ||||||||
\(5\) | 1.79046 | − | 1.79046i | 0.800717 | − | 0.800717i | −0.182491 | − | 0.983208i | \(-0.558416\pi\) |
0.983208 | + | 0.182491i | \(0.0584160\pi\) | |||||||
\(6\) | −0.952682 | − | 0.952682i | −0.388931 | − | 0.388931i | ||||
\(7\) | −0.130668 | − | 0.130668i | −0.0493879 | − | 0.0493879i | 0.681982 | − | 0.731369i | \(-0.261118\pi\) |
−0.731369 | + | 0.681982i | \(0.761118\pi\) | |||||||
\(8\) | − | 2.94356i | − | 1.04071i | ||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −2.41228 | − | 2.41228i | −0.762829 | − | 0.762829i | ||||
\(11\) | 2.52718 | + | 2.52718i | 0.761975 | + | 0.761975i | 0.976679 | − | 0.214704i | \(-0.0688788\pi\) |
−0.214704 | + | 0.976679i | \(0.568879\pi\) | |||||||
\(12\) | 0.130668 | − | 0.130668i | 0.0377206 | − | 0.0377206i | ||||
\(13\) | 6.53209 | 1.81168 | 0.905838 | − | 0.423625i | \(-0.139242\pi\) | ||||
0.905838 | + | 0.423625i | \(0.139242\pi\) | |||||||
\(14\) | −0.176049 | + | 0.176049i | −0.0470510 | + | 0.0470510i | ||||
\(15\) | − | 2.53209i | − | 0.653783i | ||||||
\(16\) | −3.59627 | −0.899067 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −1.34730 | −0.317561 | ||||||||
\(19\) | 4.63816i | 1.06407i | 0.846724 | + | 0.532033i | \(0.178572\pi\) | ||||
−0.846724 | + | 0.532033i | \(0.821428\pi\) | |||||||
\(20\) | 0.330863 | − | 0.330863i | 0.0739832 | − | 0.0739832i | ||||
\(21\) | −0.184793 | −0.0403250 | ||||||||
\(22\) | 3.40487 | − | 3.40487i | 0.725920 | − | 0.725920i | ||||
\(23\) | −2.19632 | − | 2.19632i | −0.457965 | − | 0.457965i | 0.440022 | − | 0.897987i | \(-0.354971\pi\) |
−0.897987 | + | 0.440022i | \(0.854971\pi\) | |||||||
\(24\) | −2.08141 | − | 2.08141i | −0.424867 | − | 0.424867i | ||||
\(25\) | − | 1.41147i | − | 0.282295i | ||||||
\(26\) | − | 8.80066i | − | 1.72595i | ||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | −0.0241465 | − | 0.0241465i | −0.00456326 | − | 0.00456326i | ||||
\(29\) | −4.49369 | + | 4.49369i | −0.834457 | + | 0.834457i | −0.988123 | − | 0.153666i | \(-0.950892\pi\) |
0.153666 | + | 0.988123i | \(0.450892\pi\) | |||||||
\(30\) | −3.41147 | −0.622847 | ||||||||
\(31\) | −5.24070 | + | 5.24070i | −0.941258 | + | 0.941258i | −0.998368 | − | 0.0571098i | \(-0.981812\pi\) |
0.0571098 | + | 0.998368i | \(0.481812\pi\) | |||||||
\(32\) | − | 1.04189i | − | 0.184182i | ||||||
\(33\) | 3.57398 | 0.622150 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.467911 | −0.0790914 | ||||||||
\(36\) | − | 0.184793i | − | 0.0307988i | ||||||
\(37\) | −5.93752 | + | 5.93752i | −0.976123 | + | 0.976123i | −0.999722 | − | 0.0235987i | \(-0.992488\pi\) |
0.0235987 | + | 0.999722i | \(0.492488\pi\) | |||||||
\(38\) | 6.24897 | 1.01372 | ||||||||
\(39\) | 4.61888 | − | 4.61888i | 0.739613 | − | 0.739613i | ||||
\(40\) | −5.27032 | − | 5.27032i | −0.833311 | − | 0.833311i | ||||
\(41\) | −5.08042 | − | 5.08042i | −0.793428 | − | 0.793428i | 0.188622 | − | 0.982050i | \(-0.439598\pi\) |
−0.982050 | + | 0.188622i | \(0.939598\pi\) | |||||||
\(42\) | 0.248970i | 0.0384170i | ||||||||
\(43\) | 4.93582i | 0.752706i | 0.926476 | + | 0.376353i | \(0.122822\pi\) | ||||
−0.926476 | + | 0.376353i | \(0.877178\pi\) | |||||||
\(44\) | 0.467005 | + | 0.467005i | 0.0704036 | + | 0.0704036i | ||||
\(45\) | −1.79046 | − | 1.79046i | −0.266906 | − | 0.266906i | ||||
\(46\) | −2.95910 | + | 2.95910i | −0.436295 | + | 0.436295i | ||||
\(47\) | 9.04963 | 1.32002 | 0.660012 | − | 0.751255i | \(-0.270551\pi\) | ||||
0.660012 | + | 0.751255i | \(0.270551\pi\) | |||||||
\(48\) | −2.54294 | + | 2.54294i | −0.367042 | + | 0.367042i | ||||
\(49\) | − | 6.96585i | − | 0.995122i | ||||||
\(50\) | −1.90167 | −0.268937 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.20708 | 0.167392 | ||||||||
\(53\) | − | 7.65270i | − | 1.05118i | −0.850738 | − | 0.525590i | \(-0.823845\pi\) | ||
0.850738 | − | 0.525590i | \(-0.176155\pi\) | |||||||
\(54\) | −0.952682 | + | 0.952682i | −0.129644 | + | 0.129644i | ||||
\(55\) | 9.04963 | 1.22025 | ||||||||
\(56\) | −0.384630 | + | 0.384630i | −0.0513983 | + | 0.0513983i | ||||
\(57\) | 3.27967 | + | 3.27967i | 0.434403 | + | 0.434403i | ||||
\(58\) | 6.05433 | + | 6.05433i | 0.794973 | + | 0.794973i | ||||
\(59\) | 6.55438i | 0.853307i | 0.904415 | + | 0.426654i | \(0.140308\pi\) | ||||
−0.904415 | + | 0.426654i | \(0.859692\pi\) | |||||||
\(60\) | − | 0.467911i | − | 0.0604071i | ||||||
\(61\) | −2.11103 | − | 2.11103i | −0.270290 | − | 0.270290i | 0.558927 | − | 0.829217i | \(-0.311213\pi\) |
−0.829217 | + | 0.558927i | \(0.811213\pi\) | |||||||
\(62\) | 7.06078 | + | 7.06078i | 0.896720 | + | 0.896720i | ||||
\(63\) | −0.130668 | + | 0.130668i | −0.0164626 | + | 0.0164626i | ||||
\(64\) | −8.59627 | −1.07453 | ||||||||
\(65\) | 11.6954 | − | 11.6954i | 1.45064 | − | 1.45064i | ||||
\(66\) | − | 4.81521i | − | 0.592711i | ||||||
\(67\) | −13.5175 | −1.65143 | −0.825715 | − | 0.564087i | \(-0.809228\pi\) | ||||
−0.825715 | + | 0.564087i | \(0.809228\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.10607 | −0.373927 | ||||||||
\(70\) | 0.630415i | 0.0753490i | ||||||||
\(71\) | −2.55323 | + | 2.55323i | −0.303013 | + | 0.303013i | −0.842191 | − | 0.539179i | \(-0.818735\pi\) |
0.539179 | + | 0.842191i | \(0.318735\pi\) | |||||||
\(72\) | −2.94356 | −0.346902 | ||||||||
\(73\) | −5.94781 | + | 5.94781i | −0.696139 | + | 0.696139i | −0.963575 | − | 0.267437i | \(-0.913823\pi\) |
0.267437 | + | 0.963575i | \(0.413823\pi\) | |||||||
\(74\) | 7.99960 | + | 7.99960i | 0.929935 | + | 0.929935i | ||||
\(75\) | −0.998063 | − | 0.998063i | −0.115246 | − | 0.115246i | ||||
\(76\) | 0.857097i | 0.0983157i | ||||||||
\(77\) | − | 0.660444i | − | 0.0752646i | ||||||
\(78\) | −6.22301 | − | 6.22301i | −0.704617 | − | 0.704617i | ||||
\(79\) | −5.53166 | − | 5.53166i | −0.622360 | − | 0.622360i | 0.323774 | − | 0.946134i | \(-0.395048\pi\) |
−0.946134 | + | 0.323774i | \(0.895048\pi\) | |||||||
\(80\) | −6.43896 | + | 6.43896i | −0.719898 | + | 0.719898i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −6.84483 | + | 6.84483i | −0.755885 | + | 0.755885i | ||||
\(83\) | 2.51249i | 0.275781i | 0.990447 | + | 0.137891i | \(0.0440323\pi\) | ||||
−0.990447 | + | 0.137891i | \(0.955968\pi\) | |||||||
\(84\) | −0.0341483 | −0.00372588 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.65002 | 0.717090 | ||||||||
\(87\) | 6.35504i | 0.681331i | ||||||||
\(88\) | 7.43893 | − | 7.43893i | 0.792992 | − | 0.792992i | ||||
\(89\) | −1.32770 | −0.140735 | −0.0703677 | − | 0.997521i | \(-0.522417\pi\) | ||||
−0.0703677 | + | 0.997521i | \(0.522417\pi\) | |||||||
\(90\) | −2.41228 | + | 2.41228i | −0.254276 | + | 0.254276i | ||||
\(91\) | −0.853535 | − | 0.853535i | −0.0894748 | − | 0.0894748i | ||||
\(92\) | −0.405864 | − | 0.405864i | −0.0423142 | − | 0.0423142i | ||||
\(93\) | 7.41147i | 0.768534i | ||||||||
\(94\) | − | 12.1925i | − | 1.25756i | ||||||
\(95\) | 8.30442 | + | 8.30442i | 0.852015 | + | 0.852015i | ||||
\(96\) | −0.736727 | − | 0.736727i | −0.0751919 | − | 0.0751919i | ||||
\(97\) | 6.19339 | − | 6.19339i | 0.628843 | − | 0.628843i | −0.318934 | − | 0.947777i | \(-0.603325\pi\) |
0.947777 | + | 0.318934i | \(0.103325\pi\) | |||||||
\(98\) | −9.38507 | −0.948035 | ||||||||
\(99\) | 2.52718 | − | 2.52718i | 0.253992 | − | 0.253992i | ||||
\(100\) | − | 0.260830i | − | 0.0260830i | ||||||
\(101\) | −11.0273 | −1.09726 | −0.548631 | − | 0.836065i | \(-0.684851\pi\) | ||||
−0.548631 | + | 0.836065i | \(0.684851\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.27126 | 0.617926 | 0.308963 | − | 0.951074i | \(-0.400018\pi\) | ||||
0.308963 | + | 0.951074i | \(0.400018\pi\) | |||||||
\(104\) | − | 19.2276i | − | 1.88542i | ||||||
\(105\) | −0.330863 | + | 0.330863i | −0.0322889 | + | 0.0322889i | ||||
\(106\) | −10.3105 | −1.00144 | ||||||||
\(107\) | −2.51332 | + | 2.51332i | −0.242972 | + | 0.242972i | −0.818079 | − | 0.575106i | \(-0.804961\pi\) |
0.575106 | + | 0.818079i | \(0.304961\pi\) | |||||||
\(108\) | −0.130668 | − | 0.130668i | −0.0125735 | − | 0.0125735i | ||||
\(109\) | −2.54294 | − | 2.54294i | −0.243570 | − | 0.243570i | 0.574755 | − | 0.818325i | \(-0.305097\pi\) |
−0.818325 | + | 0.574755i | \(0.805097\pi\) | |||||||
\(110\) | − | 12.1925i | − | 1.16251i | ||||||
\(111\) | 8.39693i | 0.797001i | ||||||||
\(112\) | 0.469917 | + | 0.469917i | 0.0444030 | + | 0.0444030i | ||||
\(113\) | 3.32987 | + | 3.32987i | 0.313247 | + | 0.313247i | 0.846166 | − | 0.532919i | \(-0.178905\pi\) |
−0.532919 | + | 0.846166i | \(0.678905\pi\) | |||||||
\(114\) | 4.41869 | − | 4.41869i | 0.413848 | − | 0.413848i | ||||
\(115\) | −7.86484 | −0.733400 | ||||||||
\(116\) | −0.830400 | + | 0.830400i | −0.0771007 | + | 0.0771007i | ||||
\(117\) | − | 6.53209i | − | 0.603892i | ||||||
\(118\) | 8.83069 | 0.812931 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −7.45336 | −0.680396 | ||||||||
\(121\) | 1.77332i | 0.161211i | ||||||||
\(122\) | −2.84419 | + | 2.84419i | −0.257501 | + | 0.257501i | ||||
\(123\) | −7.18479 | −0.647831 | ||||||||
\(124\) | −0.968443 | + | 0.968443i | −0.0869687 | + | 0.0869687i | ||||
\(125\) | 6.42510 | + | 6.42510i | 0.574679 | + | 0.574679i | ||||
\(126\) | 0.176049 | + | 0.176049i | 0.0156837 | + | 0.0156837i | ||||
\(127\) | 7.76651i | 0.689166i | 0.938756 | + | 0.344583i | \(0.111980\pi\) | ||||
−0.938756 | + | 0.344583i | \(0.888020\pi\) | |||||||
\(128\) | 9.49794i | 0.839507i | ||||||||
\(129\) | 3.49015 | + | 3.49015i | 0.307291 | + | 0.307291i | ||||
\(130\) | −15.7572 | − | 15.7572i | −1.38200 | − | 1.38200i | ||||
\(131\) | 3.50110 | − | 3.50110i | 0.305893 | − | 0.305893i | −0.537421 | − | 0.843314i | \(-0.680601\pi\) |
0.843314 | + | 0.537421i | \(0.180601\pi\) | |||||||
\(132\) | 0.660444 | 0.0574843 | ||||||||
\(133\) | 0.606059 | − | 0.606059i | 0.0525520 | − | 0.0525520i | ||||
\(134\) | 18.2121i | 1.57329i | ||||||||
\(135\) | −2.53209 | −0.217928 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.5885 | −0.990075 | −0.495037 | − | 0.868872i | \(-0.664846\pi\) | ||||
−0.495037 | + | 0.868872i | \(0.664846\pi\) | |||||||
\(138\) | 4.18479i | 0.356233i | ||||||||
\(139\) | −1.90179 | + | 1.90179i | −0.161308 | + | 0.161308i | −0.783146 | − | 0.621838i | \(-0.786386\pi\) |
0.621838 | + | 0.783146i | \(0.286386\pi\) | |||||||
\(140\) | −0.0864665 | −0.00730775 | ||||||||
\(141\) | 6.39905 | − | 6.39905i | 0.538898 | − | 0.538898i | ||||
\(142\) | 3.43996 | + | 3.43996i | 0.288675 | + | 0.288675i | ||||
\(143\) | 16.5078 | + | 16.5078i | 1.38045 | + | 1.38045i | ||||
\(144\) | 3.59627i | 0.299689i | ||||||||
\(145\) | 16.0915i | 1.33633i | ||||||||
\(146\) | 8.01346 | + | 8.01346i | 0.663199 | + | 0.663199i | ||||
\(147\) | −4.92560 | − | 4.92560i | −0.406257 | − | 0.406257i | ||||
\(148\) | −1.09721 | + | 1.09721i | −0.0901901 | + | 0.0901901i | ||||
\(149\) | 15.9290 | 1.30496 | 0.652478 | − | 0.757808i | \(-0.273730\pi\) | ||||
0.652478 | + | 0.757808i | \(0.273730\pi\) | |||||||
\(150\) | −1.34469 | + | 1.34469i | −0.109793 | + | 0.109793i | ||||
\(151\) | 1.38919i | 0.113050i | 0.998401 | + | 0.0565252i | \(0.0180021\pi\) | ||||
−0.998401 | + | 0.0565252i | \(0.981998\pi\) | |||||||
\(152\) | 13.6527 | 1.10738 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.889814 | −0.0717033 | ||||||||
\(155\) | 18.7665i | 1.50736i | ||||||||
\(156\) | 0.853535 | − | 0.853535i | 0.0683375 | − | 0.0683375i | ||||
\(157\) | −1.78106 | −0.142144 | −0.0710720 | − | 0.997471i | \(-0.522642\pi\) | ||||
−0.0710720 | + | 0.997471i | \(0.522642\pi\) | |||||||
\(158\) | −7.45279 | + | 7.45279i | −0.592912 | + | 0.592912i | ||||
\(159\) | −5.41128 | − | 5.41128i | −0.429142 | − | 0.429142i | ||||
\(160\) | −1.86546 | − | 1.86546i | −0.147477 | − | 0.147477i | ||||
\(161\) | 0.573978i | 0.0452358i | ||||||||
\(162\) | 1.34730i | 0.105854i | ||||||||
\(163\) | 2.22784 | + | 2.22784i | 0.174498 | + | 0.174498i | 0.788952 | − | 0.614454i | \(-0.210624\pi\) |
−0.614454 | + | 0.788952i | \(0.710624\pi\) | |||||||
\(164\) | −0.938823 | − | 0.938823i | −0.0733097 | − | 0.0733097i | ||||
\(165\) | 6.39905 | − | 6.39905i | 0.498166 | − | 0.498166i | ||||
\(166\) | 3.38507 | 0.262732 | ||||||||
\(167\) | 17.2168 | − | 17.2168i | 1.33228 | − | 1.33228i | 0.428946 | − | 0.903330i | \(-0.358885\pi\) |
0.903330 | − | 0.428946i | \(-0.141115\pi\) | |||||||
\(168\) | 0.543948i | 0.0419665i | ||||||||
\(169\) | 29.6682 | 2.28217 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.63816 | 0.354689 | ||||||||
\(172\) | 0.912103i | 0.0695472i | ||||||||
\(173\) | 10.6556 | − | 10.6556i | 0.810127 | − | 0.810127i | −0.174526 | − | 0.984653i | \(-0.555839\pi\) |
0.984653 | + | 0.174526i | \(0.0558392\pi\) | |||||||
\(174\) | 8.56212 | 0.649093 | ||||||||
\(175\) | −0.184435 | + | 0.184435i | −0.0139419 | + | 0.0139419i | ||||
\(176\) | −9.08843 | − | 9.08843i | −0.685066 | − | 0.685066i | ||||
\(177\) | 4.63464 | + | 4.63464i | 0.348361 | + | 0.348361i | ||||
\(178\) | 1.78880i | 0.134076i | ||||||||
\(179\) | − | 16.9017i | − | 1.26329i | −0.775258 | − | 0.631645i | \(-0.782380\pi\) | ||
0.775258 | − | 0.631645i | \(-0.217620\pi\) | |||||||
\(180\) | −0.330863 | − | 0.330863i | −0.0246611 | − | 0.0246611i | ||||
\(181\) | 7.54355 | + | 7.54355i | 0.560707 | + | 0.560707i | 0.929508 | − | 0.368801i | \(-0.120232\pi\) |
−0.368801 | + | 0.929508i | \(0.620232\pi\) | |||||||
\(182\) | −1.14997 | + | 1.14997i | −0.0852411 | + | 0.0852411i | ||||
\(183\) | −2.98545 | −0.220691 | ||||||||
\(184\) | −6.46501 | + | 6.46501i | −0.476607 | + | 0.476607i | ||||
\(185\) | 21.2618i | 1.56320i | ||||||||
\(186\) | 9.98545 | 0.732169 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.67230 | 0.121965 | ||||||||
\(189\) | 0.184793i | 0.0134417i | ||||||||
\(190\) | 11.1885 | − | 11.1885i | 0.811700 | − | 0.811700i | ||||
\(191\) | −1.77837 | −0.128678 | −0.0643392 | − | 0.997928i | \(-0.520494\pi\) | ||||
−0.0643392 | + | 0.997928i | \(0.520494\pi\) | |||||||
\(192\) | −6.07848 | + | 6.07848i | −0.438676 | + | 0.438676i | ||||
\(193\) | 3.58449 | + | 3.58449i | 0.258017 | + | 0.258017i | 0.824247 | − | 0.566230i | \(-0.191599\pi\) |
−0.566230 | + | 0.824247i | \(0.691599\pi\) | |||||||
\(194\) | −8.34433 | − | 8.34433i | −0.599088 | − | 0.599088i | ||||
\(195\) | − | 16.5398i | − | 1.18444i | ||||||
\(196\) | − | 1.28724i | − | 0.0919455i | ||||||
\(197\) | −5.68838 | − | 5.68838i | −0.405280 | − | 0.405280i | 0.474809 | − | 0.880089i | \(-0.342517\pi\) |
−0.880089 | + | 0.474809i | \(0.842517\pi\) | |||||||
\(198\) | −3.40487 | − | 3.40487i | −0.241973 | − | 0.241973i | ||||
\(199\) | 8.44347 | − | 8.44347i | 0.598542 | − | 0.598542i | −0.341382 | − | 0.939924i | \(-0.610895\pi\) |
0.939924 | + | 0.341382i | \(0.110895\pi\) | |||||||
\(200\) | −4.15476 | −0.293786 | ||||||||
\(201\) | −9.55834 | + | 9.55834i | −0.674194 | + | 0.674194i | ||||
\(202\) | 14.8571i | 1.04534i | ||||||||
\(203\) | 1.17436 | 0.0824242 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.1925 | −1.27062 | ||||||||
\(206\) | − | 8.44924i | − | 0.588687i | ||||||
\(207\) | −2.19632 | + | 2.19632i | −0.152655 | + | 0.152655i | ||||
\(208\) | −23.4911 | −1.62882 | ||||||||
\(209\) | −11.7215 | + | 11.7215i | −0.810791 | + | 0.810791i | ||||
\(210\) | 0.445771 | + | 0.445771i | 0.0307611 | + | 0.0307611i | ||||
\(211\) | 1.80074 | + | 1.80074i | 0.123968 | + | 0.123968i | 0.766369 | − | 0.642401i | \(-0.222061\pi\) |
−0.642401 | + | 0.766369i | \(0.722061\pi\) | |||||||
\(212\) | − | 1.41416i | − | 0.0971251i | ||||||
\(213\) | 3.61081i | 0.247409i | ||||||||
\(214\) | 3.38619 | + | 3.38619i | 0.231475 | + | 0.231475i | ||||
\(215\) | 8.83738 | + | 8.83738i | 0.602704 | + | 0.602704i | ||||
\(216\) | −2.08141 | + | 2.08141i | −0.141622 | + | 0.141622i | ||||
\(217\) | 1.36959 | 0.0929735 | ||||||||
\(218\) | −3.42610 | + | 3.42610i | −0.232045 | + | 0.232045i | ||||
\(219\) | 8.41147i | 0.568395i | ||||||||
\(220\) | 1.67230 | 0.112747 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 11.3131 | 0.759289 | ||||||||
\(223\) | 4.44562i | 0.297701i | 0.988860 | + | 0.148850i | \(0.0475573\pi\) | ||||
−0.988860 | + | 0.148850i | \(0.952443\pi\) | |||||||
\(224\) | −0.136142 | + | 0.136142i | −0.00909634 | + | 0.00909634i | ||||
\(225\) | −1.41147 | −0.0940983 | ||||||||
\(226\) | 4.48632 | − | 4.48632i | 0.298425 | − | 0.298425i | ||||
\(227\) | −5.31761 | − | 5.31761i | −0.352942 | − | 0.352942i | 0.508261 | − | 0.861203i | \(-0.330288\pi\) |
−0.861203 | + | 0.508261i | \(0.830288\pi\) | |||||||
\(228\) | 0.606059 | + | 0.606059i | 0.0401372 | + | 0.0401372i | ||||
\(229\) | − | 13.7374i | − | 0.907794i | −0.891054 | − | 0.453897i | \(-0.850033\pi\) | ||
0.891054 | − | 0.453897i | \(-0.149967\pi\) | |||||||
\(230\) | 10.5963i | 0.698697i | ||||||||
\(231\) | −0.467005 | − | 0.467005i | −0.0307267 | − | 0.0307267i | ||||
\(232\) | 13.2275 | + | 13.2275i | 0.868425 | + | 0.868425i | ||||
\(233\) | 14.5136 | − | 14.5136i | 0.950815 | − | 0.950815i | −0.0480306 | − | 0.998846i | \(-0.515294\pi\) |
0.998846 | + | 0.0480306i | \(0.0152945\pi\) | |||||||
\(234\) | −8.80066 | −0.575317 | ||||||||
\(235\) | 16.2030 | − | 16.2030i | 1.05697 | − | 1.05697i | ||||
\(236\) | 1.21120i | 0.0788424i | ||||||||
\(237\) | −7.82295 | −0.508155 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.9145 | 1.67627 | 0.838134 | − | 0.545465i | \(-0.183647\pi\) | ||||
0.838134 | + | 0.545465i | \(0.183647\pi\) | |||||||
\(240\) | 9.10607i | 0.587794i | ||||||||
\(241\) | −8.04498 | + | 8.04498i | −0.518223 | + | 0.518223i | −0.917033 | − | 0.398810i | \(-0.869423\pi\) |
0.398810 | + | 0.917033i | \(0.369423\pi\) | |||||||
\(242\) | 2.38919 | 0.153583 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | −0.390103 | − | 0.390103i | −0.0249738 | − | 0.0249738i | ||||
\(245\) | −12.4721 | − | 12.4721i | −0.796811 | − | 0.796811i | ||||
\(246\) | 9.68004i | 0.617177i | ||||||||
\(247\) | 30.2968i | 1.92774i | ||||||||
\(248\) | 15.4263 | + | 15.4263i | 0.979574 | + | 0.979574i | ||||
\(249\) | 1.77660 | + | 1.77660i | 0.112587 | + | 0.112587i | ||||
\(250\) | 8.65652 | − | 8.65652i | 0.547486 | − | 0.547486i | ||||
\(251\) | 0.859785 | 0.0542691 | 0.0271346 | − | 0.999632i | \(-0.491362\pi\) | ||||
0.0271346 | + | 0.999632i | \(0.491362\pi\) | |||||||
\(252\) | −0.0241465 | + | 0.0241465i | −0.00152109 | + | 0.00152109i | ||||
\(253\) | − | 11.1010i | − | 0.697915i | ||||||
\(254\) | 10.4638 | 0.656557 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.39599 | −0.274750 | ||||||||
\(257\) | 0.0300295i | 0.00187319i | 1.00000 | 0.000936594i | \(0.000298127\pi\) | |||||
−1.00000 | 0.000936594i | \(0.999702\pi\) | ||||||||
\(258\) | 4.70227 | − | 4.70227i | 0.292751 | − | 0.292751i | ||||
\(259\) | 1.55169 | 0.0964173 | ||||||||
\(260\) | 2.16123 | − | 2.16123i | 0.134034 | − | 0.134034i | ||||
\(261\) | 4.49369 | + | 4.49369i | 0.278152 | + | 0.278152i | ||||
\(262\) | −4.71702 | − | 4.71702i | −0.291418 | − | 0.291418i | ||||
\(263\) | − | 12.2422i | − | 0.754884i | −0.926033 | − | 0.377442i | \(-0.876804\pi\) | ||
0.926033 | − | 0.377442i | \(-0.123196\pi\) | |||||||
\(264\) | − | 10.5202i | − | 0.647475i | ||||||
\(265\) | −13.7018 | − | 13.7018i | −0.841697 | − | 0.841697i | ||||
\(266\) | −0.816541 | − | 0.816541i | −0.0500653 | − | 0.0500653i | ||||
\(267\) | −0.938823 | + | 0.938823i | −0.0574550 | + | 0.0574550i | ||||
\(268\) | −2.49794 | −0.152586 | ||||||||
\(269\) | −15.2503 | + | 15.2503i | −0.929827 | + | 0.929827i | −0.997694 | − | 0.0678676i | \(-0.978380\pi\) |
0.0678676 | + | 0.997694i | \(0.478380\pi\) | |||||||
\(270\) | 3.41147i | 0.207616i | ||||||||
\(271\) | 3.39693 | 0.206349 | 0.103174 | − | 0.994663i | \(-0.467100\pi\) | ||||
0.103174 | + | 0.994663i | \(0.467100\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.20708 | −0.0730559 | ||||||||
\(274\) | 15.6132i | 0.943227i | ||||||||
\(275\) | 3.56705 | − | 3.56705i | 0.215102 | − | 0.215102i | ||||
\(276\) | −0.573978 | −0.0345494 | ||||||||
\(277\) | 11.2551 | − | 11.2551i | 0.676255 | − | 0.676255i | −0.282896 | − | 0.959151i | \(-0.591295\pi\) |
0.959151 | + | 0.282896i | \(0.0912950\pi\) | |||||||
\(278\) | 2.56228 | + | 2.56228i | 0.153675 | + | 0.153675i | ||||
\(279\) | 5.24070 | + | 5.24070i | 0.313753 | + | 0.313753i | ||||
\(280\) | 1.37733i | 0.0823110i | ||||||||
\(281\) | 16.0155i | 0.955404i | 0.878522 | + | 0.477702i | \(0.158530\pi\) | ||||
−0.878522 | + | 0.477702i | \(0.841470\pi\) | |||||||
\(282\) | −8.62142 | − | 8.62142i | −0.513398 | − | 0.513398i | ||||
\(283\) | 18.9757 | + | 18.9757i | 1.12799 | + | 1.12799i | 0.990504 | + | 0.137487i | \(0.0439024\pi\) |
0.137487 | + | 0.990504i | \(0.456098\pi\) | |||||||
\(284\) | −0.471818 | + | 0.471818i | −0.0279973 | + | 0.0279973i | ||||
\(285\) | 11.7442 | 0.695668 | ||||||||
\(286\) | 22.2409 | − | 22.2409i | 1.31513 | − | 1.31513i | ||||
\(287\) | 1.32770i | 0.0783714i | ||||||||
\(288\) | −1.04189 | −0.0613939 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 21.6800 | 1.27310 | ||||||||
\(291\) | − | 8.75877i | − | 0.513448i | ||||||
\(292\) | −1.09911 | + | 1.09911i | −0.0643206 | + | 0.0643206i | ||||
\(293\) | −2.40879 | −0.140723 | −0.0703614 | − | 0.997522i | \(-0.522415\pi\) | ||||
−0.0703614 | + | 0.997522i | \(0.522415\pi\) | |||||||
\(294\) | −6.63624 | + | 6.63624i | −0.387034 | + | 0.387034i | ||||
\(295\) | 11.7353 | + | 11.7353i | 0.683257 | + | 0.683257i | ||||
\(296\) | 17.4775 | + | 17.4775i | 1.01586 | + | 1.01586i | ||||
\(297\) | − | 3.57398i | − | 0.207383i | ||||||
\(298\) | − | 21.4611i | − | 1.24321i | ||||||
\(299\) | −14.3466 | − | 14.3466i | −0.829683 | − | 0.829683i | ||||
\(300\) | −0.184435 | − | 0.184435i | −0.0106483 | − | 0.0106483i | ||||
\(301\) | 0.644954 | − | 0.644954i | 0.0371745 | − | 0.0371745i | ||||
\(302\) | 1.87164 | 0.107701 | ||||||||
\(303\) | −7.79751 | + | 7.79751i | −0.447955 | + | 0.447955i | ||||
\(304\) | − | 16.6800i | − | 0.956666i | ||||||
\(305\) | −7.55943 | −0.432852 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.41921 | −0.366364 | −0.183182 | − | 0.983079i | \(-0.558640\pi\) | ||||
−0.183182 | + | 0.983079i | \(0.558640\pi\) | |||||||
\(308\) | − | 0.122045i | − | 0.00695417i | ||||||
\(309\) | 4.43445 | − | 4.43445i | 0.252267 | − | 0.252267i | ||||
\(310\) | 25.2841 | 1.43604 | ||||||||
\(311\) | −0.384630 | + | 0.384630i | −0.0218103 | + | 0.0218103i | −0.717928 | − | 0.696118i | \(-0.754909\pi\) |
0.696118 | + | 0.717928i | \(0.254909\pi\) | |||||||
\(312\) | −13.5960 | − | 13.5960i | −0.769721 | − | 0.769721i | ||||
\(313\) | −11.7511 | − | 11.7511i | −0.664211 | − | 0.664211i | 0.292159 | − | 0.956370i | \(-0.405626\pi\) |
−0.956370 | + | 0.292159i | \(0.905626\pi\) | |||||||
\(314\) | 2.39961i | 0.135418i | ||||||||
\(315\) | 0.467911i | 0.0263638i | ||||||||
\(316\) | −1.02221 | − | 1.02221i | −0.0575038 | − | 0.0575038i | ||||
\(317\) | −18.4253 | − | 18.4253i | −1.03487 | − | 1.03487i | −0.999370 | − | 0.0355007i | \(-0.988697\pi\) |
−0.0355007 | − | 0.999370i | \(-0.511303\pi\) | |||||||
\(318\) | −7.29060 | + | 7.29060i | −0.408836 | + | 0.408836i | ||||
\(319\) | −22.7128 | −1.27167 | ||||||||
\(320\) | −15.3912 | + | 15.3912i | −0.860397 | + | 0.860397i | ||||
\(321\) | 3.55438i | 0.198386i | ||||||||
\(322\) | 0.773318 | 0.0430953 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.184793 | −0.0102663 | ||||||||
\(325\) | − | 9.21987i | − | 0.511427i | ||||||
\(326\) | 3.00156 | − | 3.00156i | 0.166241 | − | 0.166241i | ||||
\(327\) | −3.59627 | −0.198874 | ||||||||
\(328\) | −14.9545 | + | 14.9545i | −0.825725 | + | 0.825725i | ||||
\(329\) | −1.18250 | − | 1.18250i | −0.0651932 | − | 0.0651932i | ||||
\(330\) | −8.62142 | − | 8.62142i | −0.474594 | − | 0.474594i | ||||
\(331\) | 22.5107i | 1.23730i | 0.785666 | + | 0.618651i | \(0.212320\pi\) | ||||
−0.785666 | + | 0.618651i | \(0.787680\pi\) | |||||||
\(332\) | 0.464289i | 0.0254812i | ||||||||
\(333\) | 5.93752 | + | 5.93752i | 0.325374 | + | 0.325374i | ||||
\(334\) | −23.1961 | − | 23.1961i | −1.26924 | − | 1.26924i | ||||
\(335\) | −24.2026 | + | 24.2026i | −1.32233 | + | 1.32233i | ||||
\(336\) | 0.664563 | 0.0362549 | ||||||||
\(337\) | 0.351437 | − | 0.351437i | 0.0191440 | − | 0.0191440i | −0.697470 | − | 0.716614i | \(-0.745691\pi\) |
0.716614 | + | 0.697470i | \(0.245691\pi\) | |||||||
\(338\) | − | 39.9718i | − | 2.17418i | ||||||
\(339\) | 4.70914 | 0.255765 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.4884 | −1.43443 | ||||||||
\(342\) | − | 6.24897i | − | 0.337906i | ||||||
\(343\) | −1.82489 | + | 1.82489i | −0.0985348 | + | 0.0985348i | ||||
\(344\) | 14.5289 | 0.783346 | ||||||||
\(345\) | −5.56128 | + | 5.56128i | −0.299409 | + | 0.299409i | ||||
\(346\) | −14.3562 | − | 14.3562i | −0.771794 | − | 0.771794i | ||||
\(347\) | 9.80392 | + | 9.80392i | 0.526302 | + | 0.526302i | 0.919468 | − | 0.393166i | \(-0.128620\pi\) |
−0.393166 | + | 0.919468i | \(0.628620\pi\) | |||||||
\(348\) | 1.17436i | 0.0629525i | ||||||||
\(349\) | − | 27.0479i | − | 1.44784i | −0.689884 | − | 0.723920i | \(-0.742339\pi\) | ||
0.689884 | − | 0.723920i | \(-0.257661\pi\) | |||||||
\(350\) | 0.248488 | + | 0.248488i | 0.0132822 | + | 0.0132822i | ||||
\(351\) | −4.61888 | − | 4.61888i | −0.246538 | − | 0.246538i | ||||
\(352\) | 2.63305 | − | 2.63305i | 0.140342 | − | 0.140342i | ||||
\(353\) | −8.96997 | −0.477423 | −0.238712 | − | 0.971090i | \(-0.576725\pi\) | ||||
−0.238712 | + | 0.971090i | \(0.576725\pi\) | |||||||
\(354\) | 6.24424 | − | 6.24424i | 0.331878 | − | 0.331878i | ||||
\(355\) | 9.14290i | 0.485255i | ||||||||
\(356\) | −0.245348 | −0.0130034 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −22.7716 | −1.20351 | ||||||||
\(359\) | 6.12567i | 0.323300i | 0.986848 | + | 0.161650i | \(0.0516816\pi\) | ||||
−0.986848 | + | 0.161650i | \(0.948318\pi\) | |||||||
\(360\) | −5.27032 | + | 5.27032i | −0.277770 | + | 0.277770i | ||||
\(361\) | −2.51249 | −0.132236 | ||||||||
\(362\) | 10.1634 | − | 10.1634i | 0.534176 | − | 0.534176i | ||||
\(363\) | 1.25393 | + | 1.25393i | 0.0658140 | + | 0.0658140i | ||||
\(364\) | −0.157727 | − | 0.157727i | −0.00826714 | − | 0.00826714i | ||||
\(365\) | 21.2986i | 1.11482i | ||||||||
\(366\) | 4.02229i | 0.210248i | ||||||||
\(367\) | 12.6723 | + | 12.6723i | 0.661486 | + | 0.661486i | 0.955730 | − | 0.294244i | \(-0.0950678\pi\) |
−0.294244 | + | 0.955730i | \(0.595068\pi\) | |||||||
\(368\) | 7.89856 | + | 7.89856i | 0.411741 | + | 0.411741i | ||||
\(369\) | −5.08042 | + | 5.08042i | −0.264476 | + | 0.264476i | ||||
\(370\) | 28.6459 | 1.48923 | ||||||||
\(371\) | −0.999964 | + | 0.999964i | −0.0519155 | + | 0.0519155i | ||||
\(372\) | 1.36959i | 0.0710097i | ||||||||
\(373\) | −15.5389 | −0.804574 | −0.402287 | − | 0.915514i | \(-0.631785\pi\) | ||||
−0.402287 | + | 0.915514i | \(0.631785\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.08647 | 0.469223 | ||||||||
\(376\) | − | 26.6382i | − | 1.37376i | ||||||
\(377\) | −29.3532 | + | 29.3532i | −1.51177 | + | 1.51177i | ||||
\(378\) | 0.248970 | 0.0128057 | ||||||||
\(379\) | 26.8762 | − | 26.8762i | 1.38054 | − | 1.38054i | 0.536876 | − | 0.843661i | \(-0.319604\pi\) |
0.843661 | − | 0.536876i | \(-0.180396\pi\) | |||||||
\(380\) | 1.53459 | + | 1.53459i | 0.0787230 | + | 0.0787230i | ||||
\(381\) | 5.49175 | + | 5.49175i | 0.281351 | + | 0.281351i | ||||
\(382\) | 2.39599i | 0.122590i | ||||||||
\(383\) | − | 21.2686i | − | 1.08677i | −0.839483 | − | 0.543387i | \(-0.817142\pi\) | ||
0.839483 | − | 0.543387i | \(-0.182858\pi\) | |||||||
\(384\) | 6.71606 | + | 6.71606i | 0.342727 | + | 0.342727i | ||||
\(385\) | −1.18250 | − | 1.18250i | −0.0602657 | − | 0.0602657i | ||||
\(386\) | 4.82937 | − | 4.82937i | 0.245808 | − | 0.245808i | ||||
\(387\) | 4.93582 | 0.250902 | ||||||||
\(388\) | 1.14449 | − | 1.14449i | 0.0581028 | − | 0.0581028i | ||||
\(389\) | 13.8016i | 0.699769i | 0.936793 | + | 0.349884i | \(0.113779\pi\) | ||||
−0.936793 | + | 0.349884i | \(0.886221\pi\) | |||||||
\(390\) | −22.2841 | −1.12840 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −20.5044 | −1.03563 | ||||||||
\(393\) | − | 4.95130i | − | 0.249760i | ||||||
\(394\) | −7.66393 | + | 7.66393i | −0.386103 | + | 0.386103i | ||||
\(395\) | −19.8084 | −0.996669 | ||||||||
\(396\) | 0.467005 | − | 0.467005i | 0.0234679 | − | 0.0234679i | ||||
\(397\) | 20.1965 | + | 20.1965i | 1.01363 | + | 1.01363i | 0.999906 | + | 0.0137259i | \(0.00436921\pi\) |
0.0137259 | + | 0.999906i | \(0.495631\pi\) | |||||||
\(398\) | −11.3759 | − | 11.3759i | −0.570220 | − | 0.570220i | ||||
\(399\) | − | 0.857097i | − | 0.0429085i | ||||||
\(400\) | 5.07604i | 0.253802i | ||||||||
\(401\) | −18.9339 | − | 18.9339i | −0.945515 | − | 0.945515i | 0.0530753 | − | 0.998591i | \(-0.483098\pi\) |
−0.998591 | + | 0.0530753i | \(0.983098\pi\) | |||||||
\(402\) | 12.8779 | + | 12.8779i | 0.642292 | + | 0.642292i | ||||
\(403\) | −34.2327 | + | 34.2327i | −1.70525 | + | 1.70525i | ||||
\(404\) | −2.03777 | −0.101383 | ||||||||
\(405\) | −1.79046 | + | 1.79046i | −0.0889685 | + | 0.0889685i | ||||
\(406\) | − | 1.58222i | − | 0.0785240i | ||||||
\(407\) | −30.0104 | −1.48756 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 38.8357 | 1.92030 | 0.960152 | − | 0.279479i | \(-0.0901616\pi\) | ||||
0.960152 | + | 0.279479i | \(0.0901616\pi\) | |||||||
\(410\) | 24.5107i | 1.21050i | ||||||||
\(411\) | −8.19433 | + | 8.19433i | −0.404196 | + | 0.404196i | ||||
\(412\) | 1.15888 | 0.0570940 | ||||||||
\(413\) | 0.856448 | − | 0.856448i | 0.0421430 | − | 0.0421430i | ||||
\(414\) | 2.95910 | + | 2.95910i | 0.145432 | + | 0.145432i | ||||
\(415\) | 4.49850 | + | 4.49850i | 0.220823 | + | 0.220823i | ||||
\(416\) | − | 6.80571i | − | 0.333677i | ||||||
\(417\) | 2.68954i | 0.131707i | ||||||||
\(418\) | 15.7923 | + | 15.7923i | 0.772427 | + | 0.772427i | ||||
\(419\) | −13.4598 | − | 13.4598i | −0.657556 | − | 0.657556i | 0.297245 | − | 0.954801i | \(-0.403932\pi\) |
−0.954801 | + | 0.297245i | \(0.903932\pi\) | |||||||
\(420\) | −0.0611410 | + | 0.0611410i | −0.00298338 | + | 0.00298338i | ||||
\(421\) | −6.41653 | −0.312722 | −0.156361 | − | 0.987700i | \(-0.549976\pi\) | ||||
−0.156361 | + | 0.987700i | \(0.549976\pi\) | |||||||
\(422\) | 2.42614 | − | 2.42614i | 0.118102 | − | 0.118102i | ||||
\(423\) | − | 9.04963i | − | 0.440008i | ||||||
\(424\) | −22.5262 | −1.09397 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.86484 | 0.235702 | ||||||||
\(427\) | 0.551689i | 0.0266981i | ||||||||
\(428\) | −0.464444 | + | 0.464444i | −0.0224497 | + | 0.0224497i | ||||
\(429\) | 23.3455 | 1.12713 | ||||||||
\(430\) | 11.9066 | − | 11.9066i | 0.574186 | − | 0.574186i | ||||
\(431\) | −6.11714 | − | 6.11714i | −0.294652 | − | 0.294652i | 0.544262 | − | 0.838915i | \(-0.316810\pi\) |
−0.838915 | + | 0.544262i | \(0.816810\pi\) | |||||||
\(432\) | 2.54294 | + | 2.54294i | 0.122347 | + | 0.122347i | ||||
\(433\) | − | 23.3182i | − | 1.12060i | −0.828289 | − | 0.560301i | \(-0.810686\pi\) | ||
0.828289 | − | 0.560301i | \(-0.189314\pi\) | |||||||
\(434\) | − | 1.84524i | − | 0.0885742i | ||||||
\(435\) | 11.3784 | + | 11.3784i | 0.545554 | + | 0.545554i | ||||
\(436\) | −0.469917 | − | 0.469917i | −0.0225050 | − | 0.0225050i | ||||
\(437\) | 10.1869 | − | 10.1869i | 0.487304 | − | 0.487304i | ||||
\(438\) | 11.3327 | 0.541500 | ||||||||
\(439\) | −9.33334 | + | 9.33334i | −0.445456 | + | 0.445456i | −0.893841 | − | 0.448385i | \(-0.852000\pi\) |
0.448385 | + | 0.893841i | \(0.352000\pi\) | |||||||
\(440\) | − | 26.6382i | − | 1.26992i | ||||||
\(441\) | −6.96585 | −0.331707 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.5235 | −1.45022 | −0.725108 | − | 0.688635i | \(-0.758210\pi\) | ||||
−0.725108 | + | 0.688635i | \(0.758210\pi\) | |||||||
\(444\) | 1.55169i | 0.0736399i | ||||||||
\(445\) | −2.37718 | + | 2.37718i | −0.112689 | + | 0.112689i | ||||
\(446\) | 5.98957 | 0.283614 | ||||||||
\(447\) | 11.2635 | − | 11.2635i | 0.532746 | − | 0.532746i | ||||
\(448\) | 1.12326 | + | 1.12326i | 0.0530689 | + | 0.0530689i | ||||
\(449\) | 1.91755 | + | 1.91755i | 0.0904949 | + | 0.0904949i | 0.750905 | − | 0.660410i | \(-0.229618\pi\) |
−0.660410 | + | 0.750905i | \(0.729618\pi\) | |||||||
\(450\) | 1.90167i | 0.0896458i | ||||||||
\(451\) | − | 25.6783i | − | 1.20914i | ||||||
\(452\) | 0.615334 | + | 0.615334i | 0.0289429 | + | 0.0289429i | ||||
\(453\) | 0.982302 | + | 0.982302i | 0.0461526 | + | 0.0461526i | ||||
\(454\) | −7.16439 | + | 7.16439i | −0.336241 | + | 0.336241i | ||||
\(455\) | −3.05644 | −0.143288 | ||||||||
\(456\) | 9.65392 | − | 9.65392i | 0.452086 | − | 0.452086i | ||||
\(457\) | − | 26.2668i | − | 1.22871i | −0.789030 | − | 0.614355i | \(-0.789416\pi\) | ||
0.789030 | − | 0.614355i | \(-0.210584\pi\) | |||||||
\(458\) | −18.5084 | −0.864839 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.45336 | −0.0677634 | ||||||||
\(461\) | − | 25.5202i | − | 1.18860i | −0.804245 | − | 0.594298i | \(-0.797430\pi\) | ||
0.804245 | − | 0.594298i | \(-0.202570\pi\) | |||||||
\(462\) | −0.629194 | + | 0.629194i | −0.0292727 | + | 0.0292727i | ||||
\(463\) | 2.82564 | 0.131318 | 0.0656592 | − | 0.997842i | \(-0.479085\pi\) | ||||
0.0656592 | + | 0.997842i | \(0.479085\pi\) | |||||||
\(464\) | 16.1605 | − | 16.1605i | 0.750233 | − | 0.750233i | ||||
\(465\) | 13.2699 | + | 13.2699i | 0.615378 | + | 0.615378i | ||||
\(466\) | −19.5541 | − | 19.5541i | −0.905825 | − | 0.905825i | ||||
\(467\) | 32.9992i | 1.52702i | 0.645796 | + | 0.763510i | \(0.276526\pi\) | ||||
−0.645796 | + | 0.763510i | \(0.723474\pi\) | |||||||
\(468\) | − | 1.20708i | − | 0.0557973i | ||||||
\(469\) | 1.76631 | + | 1.76631i | 0.0815607 | + | 0.0815607i | ||||
\(470\) | −21.8302 | − | 21.8302i | −1.00695 | − | 1.00695i | ||||
\(471\) | −1.25940 | + | 1.25940i | −0.0580300 | + | 0.0580300i | ||||
\(472\) | 19.2932 | 0.888043 | ||||||||
\(473\) | −12.4737 | + | 12.4737i | −0.573543 | + | 0.573543i | ||||
\(474\) | 10.5398i | 0.484110i | ||||||||
\(475\) | 6.54664 | 0.300380 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.65270 | −0.350393 | ||||||||
\(478\) | − | 34.9145i | − | 1.59695i | ||||||
\(479\) | 24.6206 | − | 24.6206i | 1.12495 | − | 1.12495i | 0.133958 | − | 0.990987i | \(-0.457231\pi\) |
0.990987 | − | 0.133958i | \(-0.0427688\pi\) | |||||||
\(480\) | −2.63816 | −0.120415 | ||||||||
\(481\) | −38.7844 | + | 38.7844i | −1.76842 | + | 1.76842i | ||||
\(482\) | 10.8390 | + | 10.8390i | 0.493702 | + | 0.493702i | ||||
\(483\) | 0.405864 | + | 0.405864i | 0.0184674 | + | 0.0184674i | ||||
\(484\) | 0.327696i | 0.0148953i | ||||||||
\(485\) | − | 22.1780i | − | 1.00705i | ||||||
\(486\) | 0.952682 | + | 0.952682i | 0.0432146 | + | 0.0432146i | ||||
\(487\) | 15.2612 | + | 15.2612i | 0.691553 | + | 0.691553i | 0.962574 | − | 0.271021i | \(-0.0873612\pi\) |
−0.271021 | + | 0.962574i | \(0.587361\pi\) | |||||||
\(488\) | −6.21396 | + | 6.21396i | −0.281293 | + | 0.281293i | ||||
\(489\) | 3.15064 | 0.142477 | ||||||||
\(490\) | −16.8036 | + | 16.8036i | −0.759107 | + | 0.759107i | ||||
\(491\) | − | 34.3209i | − | 1.54888i | −0.632647 | − | 0.774440i | \(-0.718032\pi\) | ||
0.632647 | − | 0.774440i | \(-0.281968\pi\) | |||||||
\(492\) | −1.32770 | −0.0598572 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 40.8188 | 1.83653 | ||||||||
\(495\) | − | 9.04963i | − | 0.406751i | ||||||
\(496\) | 18.8470 | − | 18.8470i | 0.846254 | − | 0.846254i | ||||
\(497\) | 0.667252 | 0.0299303 | ||||||||
\(498\) | 2.39360 | − | 2.39360i | 0.107260 | − | 0.107260i | ||||
\(499\) | −12.8313 | − | 12.8313i | −0.574408 | − | 0.574408i | 0.358949 | − | 0.933357i | \(-0.383135\pi\) |
−0.933357 | + | 0.358949i | \(0.883135\pi\) | |||||||
\(500\) | 1.18731 | + | 1.18731i | 0.0530982 | + | 0.0530982i | ||||
\(501\) | − | 24.3482i | − | 1.08780i | ||||||
\(502\) | − | 1.15839i | − | 0.0517013i | ||||||
\(503\) | −17.8296 | − | 17.8296i | −0.794981 | − | 0.794981i | 0.187318 | − | 0.982299i | \(-0.440021\pi\) |
−0.982299 | + | 0.187318i | \(0.940021\pi\) | |||||||
\(504\) | 0.384630 | + | 0.384630i | 0.0171328 | + | 0.0171328i | ||||
\(505\) | −19.7440 | + | 19.7440i | −0.878596 | + | 0.878596i | ||||
\(506\) | −14.9564 | −0.664891 | ||||||||
\(507\) | 20.9786 | − | 20.9786i | 0.931691 | − | 0.931691i | ||||
\(508\) | 1.43519i | 0.0636764i | ||||||||
\(509\) | −2.82026 | −0.125006 | −0.0625029 | − | 0.998045i | \(-0.519908\pi\) | ||||
−0.0625029 | + | 0.998045i | \(0.519908\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.55438 | 0.0687616 | ||||||||
\(512\) | 24.9186i | 1.10126i | ||||||||
\(513\) | 3.27967 | − | 3.27967i | 0.144801 | − | 0.144801i | ||||
\(514\) | 0.0404586 | 0.00178455 | ||||||||
\(515\) | 11.2284 | − | 11.2284i | 0.494783 | − | 0.494783i | ||||
\(516\) | 0.644954 | + | 0.644954i | 0.0283925 | + | 0.0283925i | ||||
\(517\) | 22.8701 | + | 22.8701i | 1.00582 | + | 1.00582i | ||||
\(518\) | − | 2.09059i | − | 0.0918550i | ||||||
\(519\) | − | 15.0692i | − | 0.661466i | ||||||
\(520\) | −34.4262 | − | 34.4262i | −1.50969 | − | 1.50969i | ||||
\(521\) | 0.744101 | + | 0.744101i | 0.0325997 | + | 0.0325997i | 0.723219 | − | 0.690619i | \(-0.242662\pi\) |
−0.690619 | + | 0.723219i | \(0.742662\pi\) | |||||||
\(522\) | 6.05433 | − | 6.05433i | 0.264991 | − | 0.264991i | ||||
\(523\) | −15.0915 | −0.659906 | −0.329953 | − | 0.943997i | \(-0.607033\pi\) | ||||
−0.329953 | + | 0.943997i | \(0.607033\pi\) | |||||||
\(524\) | 0.646977 | − | 0.646977i | 0.0282633 | − | 0.0282633i | ||||
\(525\) | 0.260830i | 0.0113835i | ||||||||
\(526\) | −16.4938 | −0.719165 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −12.8530 | −0.559354 | ||||||||
\(529\) | − | 13.3523i | − | 0.580537i | ||||||
\(530\) | −18.4604 | + | 18.4604i | −0.801870 | + | 0.801870i | ||||
\(531\) | 6.55438 | 0.284436 | ||||||||
\(532\) | 0.111995 | − | 0.111995i | 0.00485560 | − | 0.00485560i | ||||
\(533\) | −33.1857 | − | 33.1857i | −1.43743 | − | 1.43743i | ||||
\(534\) | 1.26487 | + | 1.26487i | 0.0547364 | + | 0.0547364i | ||||
\(535\) | 9.00000i | 0.389104i | ||||||||
\(536\) | 39.7897i | 1.71865i | ||||||||
\(537\) | −11.9513 | − | 11.9513i | −0.515736 | − | 0.515736i | ||||
\(538\) | 20.5467 | + | 20.5467i | 0.885830 | + | 0.885830i | ||||
\(539\) | 17.6040 | − | 17.6040i | 0.758257 | − | 0.758257i | ||||
\(540\) | −0.467911 | −0.0201357 | ||||||||
\(541\) | −13.6600 | + | 13.6600i | −0.587291 | + | 0.587291i | −0.936897 | − | 0.349606i | \(-0.886315\pi\) |
0.349606 | + | 0.936897i | \(0.386315\pi\) | |||||||
\(542\) | − | 4.57667i | − | 0.196585i | ||||||
\(543\) | 10.6682 | 0.457816 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.10607 | −0.390061 | ||||||||
\(546\) | 1.62630i | 0.0695991i | ||||||||
\(547\) | 11.8383 | − | 11.8383i | 0.506168 | − | 0.506168i | −0.407180 | − | 0.913348i | \(-0.633488\pi\) |
0.913348 | + | 0.407180i | \(0.133488\pi\) | |||||||
\(548\) | −2.14147 | −0.0914792 | ||||||||
\(549\) | −2.11103 | + | 2.11103i | −0.0900967 | + | 0.0900967i | ||||
\(550\) | −4.80588 | − | 4.80588i | −0.204923 | − | 0.204923i | ||||
\(551\) | −20.8424 | − | 20.8424i | −0.887918 | − | 0.887918i | ||||
\(552\) | 9.14290i | 0.389148i | ||||||||
\(553\) | 1.44562i | 0.0614741i | ||||||||
\(554\) | −15.1640 | − | 15.1640i | −0.644256 | − | 0.644256i | ||||
\(555\) | 15.0343 | + | 15.0343i | 0.638172 | + | 0.638172i | ||||
\(556\) | −0.351437 | + | 0.351437i | −0.0149042 | + | 0.0149042i | ||||
\(557\) | 19.8084 | 0.839309 | 0.419654 | − | 0.907684i | \(-0.362151\pi\) | ||||
0.419654 | + | 0.907684i | \(0.362151\pi\) | |||||||
\(558\) | 7.06078 | − | 7.06078i | 0.298907 | − | 0.298907i | ||||
\(559\) | 32.2412i | 1.36366i | ||||||||
\(560\) | 1.68273 | 0.0711085 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 21.5776 | 0.910196 | ||||||||
\(563\) | 35.4020i | 1.49202i | 0.665937 | + | 0.746008i | \(0.268032\pi\) | ||||
−0.665937 | + | 0.746008i | \(0.731968\pi\) | |||||||
\(564\) | 1.18250 | − | 1.18250i | 0.0497921 | − | 0.0497921i | ||||
\(565\) | 11.9240 | 0.501645 | ||||||||
\(566\) | 25.5659 | − | 25.5659i | 1.07462 | − | 1.07462i | ||||
\(567\) | 0.130668 | + | 0.130668i | 0.00548754 | + | 0.00548754i | ||||
\(568\) | 7.51560 | + | 7.51560i | 0.315347 | + | 0.315347i | ||||
\(569\) | − | 18.0060i | − | 0.754850i | −0.926040 | − | 0.377425i | \(-0.876810\pi\) | ||
0.926040 | − | 0.377425i | \(-0.123190\pi\) | |||||||
\(570\) | − | 15.8229i | − | 0.662750i | ||||||
\(571\) | 9.82325 | + | 9.82325i | 0.411090 | + | 0.411090i | 0.882118 | − | 0.471028i | \(-0.156117\pi\) |
−0.471028 | + | 0.882118i | \(0.656117\pi\) | |||||||
\(572\) | 3.05052 | + | 3.05052i | 0.127549 | + | 0.127549i | ||||
\(573\) | −1.25750 | + | 1.25750i | −0.0525327 | + | 0.0525327i | ||||
\(574\) | 1.78880 | 0.0746631 | ||||||||
\(575\) | −3.10005 | + | 3.10005i | −0.129281 | + | 0.129281i | ||||
\(576\) | 8.59627i | 0.358178i | ||||||||
\(577\) | −4.15570 | −0.173004 | −0.0865020 | − | 0.996252i | \(-0.527569\pi\) | ||||
−0.0865020 | + | 0.996252i | \(0.527569\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.06923 | 0.210670 | ||||||||
\(580\) | 2.97359i | 0.123472i | ||||||||
\(581\) | 0.328302 | − | 0.328302i | 0.0136203 | − | 0.0136203i | ||||
\(582\) | −11.8007 | −0.489153 | ||||||||
\(583\) | 19.3398 | − | 19.3398i | 0.800972 | − | 0.800972i | ||||
\(584\) | 17.5078 | + | 17.5078i | 0.724476 | + | 0.724476i | ||||
\(585\) | −11.6954 | − | 11.6954i | −0.483546 | − | 0.483546i | ||||
\(586\) | 3.24535i | 0.134064i | ||||||||
\(587\) | 25.9341i | 1.07041i | 0.844721 | + | 0.535207i | \(0.179766\pi\) | ||||
−0.844721 | + | 0.535207i | \(0.820234\pi\) | |||||||
\(588\) | −0.910214 | − | 0.910214i | −0.0375366 | − | 0.0375366i | ||||
\(589\) | −24.3072 | − | 24.3072i | −1.00156 | − | 1.00156i | ||||
\(590\) | 15.8110 | − | 15.8110i | 0.650927 | − | 0.650927i | ||||
\(591\) | −8.04458 | −0.330910 | ||||||||
\(592\) | 21.3529 | − | 21.3529i | 0.877600 | − | 0.877600i | ||||
\(593\) | − | 37.6459i | − | 1.54593i | −0.634448 | − | 0.772966i | \(-0.718772\pi\) | ||
0.634448 | − | 0.772966i | \(-0.281228\pi\) | |||||||
\(594\) | −4.81521 | −0.197570 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.94356 | 0.120573 | ||||||||
\(597\) | − | 11.9409i | − | 0.488707i | ||||||
\(598\) | −19.3291 | + | 19.3291i | −0.790425 | + | 0.790425i | ||||
\(599\) | 9.59720 | 0.392131 | 0.196065 | − | 0.980591i | \(-0.437183\pi\) | ||||
0.196065 | + | 0.980591i | \(0.437183\pi\) | |||||||
\(600\) | −2.93786 | + | 2.93786i | −0.119938 | + | 0.119938i | ||||
\(601\) | −19.9139 | − | 19.9139i | −0.812305 | − | 0.812305i | 0.172674 | − | 0.984979i | \(-0.444759\pi\) |
−0.984979 | + | 0.172674i | \(0.944759\pi\) | |||||||
\(602\) | −0.868945 | − | 0.868945i | −0.0354155 | − | 0.0354155i | ||||
\(603\) | 13.5175i | 0.550477i | ||||||||
\(604\) | 0.256711i | 0.0104454i | ||||||||
\(605\) | 3.17505 | + | 3.17505i | 0.129084 | + | 0.129084i | ||||
\(606\) | 10.5056 | + | 10.5056i | 0.426759 | + | 0.426759i | ||||
\(607\) | 11.5036 | − | 11.5036i | 0.466917 | − | 0.466917i | −0.433997 | − | 0.900914i | \(-0.642897\pi\) |
0.900914 | + | 0.433997i | \(0.142897\pi\) | |||||||
\(608\) | 4.83244 | 0.195981 | ||||||||
\(609\) | 0.830400 | − | 0.830400i | 0.0336495 | − | 0.0336495i | ||||
\(610\) | 10.1848i | 0.412370i | ||||||||
\(611\) | 59.1130 | 2.39146 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.12330 | −0.166539 | −0.0832693 | − | 0.996527i | \(-0.526536\pi\) | ||||
−0.0832693 | + | 0.996527i | \(0.526536\pi\) | |||||||
\(614\) | 8.64858i | 0.349028i | ||||||||
\(615\) | −12.8641 | + | 12.8641i | −0.518729 | + | 0.518729i | ||||
\(616\) | −1.94406 | −0.0783284 | ||||||||
\(617\) | −8.97519 | + | 8.97519i | −0.361328 | + | 0.361328i | −0.864302 | − | 0.502974i | \(-0.832239\pi\) |
0.502974 | + | 0.864302i | \(0.332239\pi\) | |||||||
\(618\) | −5.97452 | − | 5.97452i | −0.240330 | − | 0.240330i | ||||
\(619\) | −18.3310 | − | 18.3310i | −0.736785 | − | 0.736785i | 0.235169 | − | 0.971954i | \(-0.424436\pi\) |
−0.971954 | + | 0.235169i | \(0.924436\pi\) | |||||||
\(620\) | 3.46791i | 0.139275i | ||||||||
\(621\) | 3.10607i | 0.124642i | ||||||||
\(622\) | 0.518210 | + | 0.518210i | 0.0207783 | + | 0.0207783i | ||||
\(623\) | 0.173487 | + | 0.173487i | 0.00695063 | + | 0.00695063i | ||||
\(624\) | −16.6107 | + | 16.6107i | −0.664962 | + | 0.664962i | ||||
\(625\) | 30.0651 | 1.20260 | ||||||||
\(626\) | −15.8322 | + | 15.8322i | −0.632782 | + | 0.632782i | ||||
\(627\) | 16.5767i | 0.662008i | ||||||||
\(628\) | −0.329126 | −0.0131336 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0.630415 | 0.0251163 | ||||||||
\(631\) | 30.1411i | 1.19990i | 0.800037 | + | 0.599950i | \(0.204813\pi\) | ||||
−0.800037 | + | 0.599950i | \(0.795187\pi\) | |||||||
\(632\) | −16.2828 | + | 16.2828i | −0.647695 | + | 0.647695i | ||||
\(633\) | 2.54664 | 0.101220 | ||||||||
\(634\) | −24.8244 | + | 24.8244i | −0.985903 | + | 0.985903i | ||||
\(635\) | 13.9056 | + | 13.9056i | 0.551827 | + | 0.551827i | ||||
\(636\) | −0.999964 | − | 0.999964i | −0.0396511 | − | 0.0396511i | ||||
\(637\) | − | 45.5016i | − | 1.80284i | ||||||
\(638\) | 30.6008i | 1.21150i | ||||||||
\(639\) | 2.55323 | + | 2.55323i | 0.101004 | + | 0.101004i | ||||
\(640\) | 17.0057 | + | 17.0057i | 0.672208 | + | 0.672208i | ||||
\(641\) | 0.422865 | − | 0.422865i | 0.0167022 | − | 0.0167022i | −0.698706 | − | 0.715409i | \(-0.746241\pi\) |
0.715409 | + | 0.698706i | \(0.246241\pi\) | |||||||
\(642\) | 4.78880 | 0.188999 | ||||||||
\(643\) | −23.0394 | + | 23.0394i | −0.908586 | + | 0.908586i | −0.996158 | − | 0.0875723i | \(-0.972089\pi\) |
0.0875723 | + | 0.996158i | \(0.472089\pi\) | |||||||
\(644\) | 0.106067i | 0.00417962i | ||||||||
\(645\) | 12.4979 | 0.492106 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.8648 | −0.545083 | −0.272542 | − | 0.962144i | \(-0.587864\pi\) | ||||
−0.272542 | + | 0.962144i | \(0.587864\pi\) | |||||||
\(648\) | 2.94356i | 0.115634i | ||||||||
\(649\) | −16.5641 | + | 16.5641i | −0.650199 | + | 0.650199i | ||||
\(650\) | −12.4219 | −0.487227 | ||||||||
\(651\) | 0.968443 | − | 0.968443i | 0.0379563 | − | 0.0379563i | ||||
\(652\) | 0.411689 | + | 0.411689i | 0.0161230 | + | 0.0161230i | ||||
\(653\) | −1.05796 | − | 1.05796i | −0.0414013 | − | 0.0414013i | 0.686103 | − | 0.727504i | \(-0.259320\pi\) |
−0.727504 | + | 0.686103i | \(0.759320\pi\) | |||||||
\(654\) | 4.84524i | 0.189464i | ||||||||
\(655\) | − | 12.5371i | − | 0.489867i | ||||||
\(656\) | 18.2705 | + | 18.2705i | 0.713344 | + | 0.713344i | ||||
\(657\) | 5.94781 | + | 5.94781i | 0.232046 | + | 0.232046i | ||||
\(658\) | −1.59317 | + | 1.59317i | −0.0621084 | + | 0.0621084i | ||||
\(659\) | −49.3441 | −1.92217 | −0.961087 | − | 0.276246i | \(-0.910909\pi\) | ||||
−0.961087 | + | 0.276246i | \(0.910909\pi\) | |||||||
\(660\) | 1.18250 | − | 1.18250i | 0.0460287 | − | 0.0460287i | ||||
\(661\) | 45.9077i | 1.78560i | 0.450452 | + | 0.892801i | \(0.351263\pi\) | ||||
−0.450452 | + | 0.892801i | \(0.648737\pi\) | |||||||
\(662\) | 30.3286 | 1.17876 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.39567 | 0.287008 | ||||||||
\(665\) | − | 2.17024i | − | 0.0841585i | ||||||
\(666\) | 7.99960 | − | 7.99960i | 0.309978 | − | 0.309978i | ||||
\(667\) | 19.7392 | 0.764304 | ||||||||
\(668\) | 3.18154 | − | 3.18154i | 0.123097 | − | 0.123097i | ||||
\(669\) | 3.14353 | + | 3.14353i | 0.121536 | + | 0.121536i | ||||
\(670\) | 32.6080 | + | 32.6080i | 1.25976 | + | 1.25976i | ||||
\(671\) | − | 10.6699i | − | 0.411908i | ||||||
\(672\) | 0.192533i | 0.00742713i | ||||||||
\(673\) | 24.6049 | + | 24.6049i | 0.948448 | + | 0.948448i | 0.998735 | − | 0.0502868i | \(-0.0160135\pi\) |
−0.0502868 | + | 0.998735i | \(0.516014\pi\) | |||||||
\(674\) | −0.473490 | − | 0.473490i | −0.0182381 | − | 0.0182381i | ||||
\(675\) | −0.998063 | + | 0.998063i | −0.0384155 | + | 0.0384155i | ||||
\(676\) | 5.48246 | 0.210864 | ||||||||
\(677\) | −10.0321 | + | 10.0321i | −0.385564 | + | 0.385564i | −0.873102 | − | 0.487538i | \(-0.837895\pi\) |
0.487538 | + | 0.873102i | \(0.337895\pi\) | |||||||
\(678\) | − | 6.34461i | − | 0.243663i | ||||||
\(679\) | −1.61856 | −0.0621145 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.52023 | −0.288176 | ||||||||
\(682\) | 35.6878i | 1.36656i | ||||||||
\(683\) | 31.4867 | − | 31.4867i | 1.20480 | − | 1.20480i | 0.232117 | − | 0.972688i | \(-0.425435\pi\) |
0.972688 | − | 0.232117i | \(-0.0745652\pi\) | |||||||
\(684\) | 0.857097 | 0.0327719 | ||||||||
\(685\) | −20.7488 | + | 20.7488i | −0.792769 | + | 0.792769i | ||||
\(686\) | 2.45867 | + | 2.45867i | 0.0938724 | + | 0.0938724i | ||||
\(687\) | −9.71382 | − | 9.71382i | −0.370605 | − | 0.370605i | ||||
\(688\) | − | 17.7505i | − | 0.676733i | ||||||
\(689\) | − | 49.9881i | − | 1.90440i | ||||||
\(690\) | 7.49269 | + | 7.49269i | 0.285242 | + | 0.285242i | ||||
\(691\) | 4.23403 | + | 4.23403i | 0.161070 | + | 0.161070i | 0.783041 | − | 0.621971i | \(-0.213668\pi\) |
−0.621971 | + | 0.783041i | \(0.713668\pi\) | |||||||
\(692\) | 1.96907 | − | 1.96907i | 0.0748527 | − | 0.0748527i | ||||
\(693\) | −0.660444 | −0.0250882 | ||||||||
\(694\) | 13.2088 | − | 13.2088i | 0.501399 | − | 0.501399i | ||||
\(695\) | 6.81016i | 0.258324i | ||||||||
\(696\) | 18.7065 | 0.709066 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −36.4415 | −1.37933 | ||||||||
\(699\) | − | 20.5253i | − | 0.776337i | ||||||
\(700\) | −0.0340821 | + | 0.0340821i | −0.00128818 | + | 0.00128818i | ||||
\(701\) | −15.4739 | −0.584441 | −0.292221 | − | 0.956351i | \(-0.594394\pi\) | ||||
−0.292221 | + | 0.956351i | \(0.594394\pi\) | |||||||
\(702\) | −6.22301 | + | 6.22301i | −0.234872 | + | 0.234872i | ||||
\(703\) | −27.5392 | − | 27.5392i | −1.03866 | − | 1.03866i | ||||
\(704\) | −21.7243 | − | 21.7243i | −0.818767 | − | 0.818767i | ||||
\(705\) | − | 22.9145i | − | 0.863009i | ||||||
\(706\) | 12.0852i | 0.454833i | ||||||||
\(707\) | 1.44092 | + | 1.44092i | 0.0541914 | + | 0.0541914i | ||||
\(708\) | 0.856448 | + | 0.856448i | 0.0321873 | + | 0.0321873i | ||||
\(709\) | 22.6262 | − | 22.6262i | 0.849744 | − | 0.849744i | −0.140357 | − | 0.990101i | \(-0.544825\pi\) |
0.990101 | + | 0.140357i | \(0.0448250\pi\) | |||||||
\(710\) | 12.3182 | 0.462294 | ||||||||
\(711\) | −5.53166 | + | 5.53166i | −0.207453 | + | 0.207453i | ||||
\(712\) | 3.90816i | 0.146464i | ||||||||
\(713\) | 23.0205 | 0.862126 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 59.1130 | 2.21070 | ||||||||
\(716\) | − | 3.12330i | − | 0.116723i | ||||||
\(717\) | 18.3243 | − | 18.3243i | 0.684333 | − | 0.684333i | ||||
\(718\) | 8.25309 | 0.308003 | ||||||||
\(719\) | −16.5013 | + | 16.5013i | −0.615395 | + | 0.615395i | −0.944347 | − | 0.328952i | \(-0.893305\pi\) |
0.328952 | + | 0.944347i | \(0.393305\pi\) | |||||||
\(720\) | 6.43896 | + | 6.43896i | 0.239966 | + | 0.239966i | ||||
\(721\) | −0.819453 | − | 0.819453i | −0.0305180 | − | 0.0305180i | ||||
\(722\) | 3.38507i | 0.125979i | ||||||||
\(723\) | 11.3773i | 0.423127i | ||||||||
\(724\) | 1.39399 | + | 1.39399i | 0.0518073 | + | 0.0518073i | ||||
\(725\) | 6.34273 | + | 6.34273i | 0.235563 | + | 0.235563i | ||||
\(726\) | 1.68941 | − | 1.68941i | 0.0626999 | − | 0.0626999i | ||||
\(727\) | 4.75372 | 0.176306 | 0.0881528 | − | 0.996107i | \(-0.471904\pi\) | ||||
0.0881528 | + | 0.996107i | \(0.471904\pi\) | |||||||
\(728\) | −2.51244 | + | 2.51244i | −0.0931170 | + | 0.0931170i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 28.6955 | 1.06207 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.551689 | −0.0203910 | ||||||||
\(733\) | − | 0.982764i | − | 0.0362992i | −0.999835 | − | 0.0181496i | \(-0.994222\pi\) | ||
0.999835 | − | 0.0181496i | \(-0.00577752\pi\) | |||||||
\(734\) | 17.0733 | − | 17.0733i | 0.630186 | − | 0.630186i | ||||
\(735\) | −17.6382 | −0.650593 | ||||||||
\(736\) | −2.28832 | + | 2.28832i | −0.0843487 | + | 0.0843487i | ||||
\(737\) | −34.1613 | − | 34.1613i | −1.25835 | − | 1.25835i | ||||
\(738\) | 6.84483 | + | 6.84483i | 0.251962 | + | 0.251962i | ||||
\(739\) | 9.95636i | 0.366250i | 0.983090 | + | 0.183125i | \(0.0586214\pi\) | ||||
−0.983090 | + | 0.183125i | \(0.941379\pi\) | |||||||
\(740\) | 3.92902i | 0.144433i | ||||||||
\(741\) | 21.4231 | + | 21.4231i | 0.786997 | + | 0.786997i | ||||
\(742\) | 1.34725 | + | 1.34725i | 0.0494590 | + | 0.0494590i | ||||
\(743\) | −32.8990 | + | 32.8990i | −1.20695 | + | 1.20695i | −0.234937 | + | 0.972011i | \(0.575488\pi\) |
−0.972011 | + | 0.234937i | \(0.924512\pi\) | |||||||
\(744\) | 21.8161 | 0.799819 | ||||||||
\(745\) | 28.5202 | − | 28.5202i | 1.04490 | − | 1.04490i | ||||
\(746\) | 20.9355i | 0.766503i | ||||||||
\(747\) | 2.51249 | 0.0919271 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.656822 | 0.0239998 | ||||||||
\(750\) | − | 12.2422i | − | 0.447021i | ||||||
\(751\) | 9.41549 | − | 9.41549i | 0.343576 | − | 0.343576i | −0.514134 | − | 0.857710i | \(-0.671887\pi\) |
0.857710 | + | 0.514134i | \(0.171887\pi\) | |||||||
\(752\) | −32.5449 | −1.18679 | ||||||||
\(753\) | 0.607960 | − | 0.607960i | 0.0221553 | − | 0.0221553i | ||||
\(754\) | 39.5474 | + | 39.5474i | 1.44023 | + | 1.44023i | ||||
\(755\) | 2.48728 | + | 2.48728i | 0.0905213 | + | 0.0905213i | ||||
\(756\) | 0.0341483i | 0.00124196i | ||||||||
\(757\) | 45.0874i | 1.63873i | 0.573273 | + | 0.819365i | \(0.305674\pi\) | ||||
−0.573273 | + | 0.819365i | \(0.694326\pi\) | |||||||
\(758\) | −36.2102 | − | 36.2102i | −1.31521 | − | 1.31521i | ||||
\(759\) | −7.84960 | − | 7.84960i | −0.284923 | − | 0.284923i | ||||
\(760\) | 24.4446 | − | 24.4446i | 0.886698 | − | 0.886698i | ||||
\(761\) | −24.0036 | −0.870131 | −0.435065 | − | 0.900399i | \(-0.643275\pi\) | ||||
−0.435065 | + | 0.900399i | \(0.643275\pi\) | |||||||
\(762\) | 7.39902 | − | 7.39902i | 0.268038 | − | 0.268038i | ||||
\(763\) | 0.664563i | 0.0240588i | ||||||||
\(764\) | −0.328630 | −0.0118894 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −28.6551 | −1.03535 | ||||||||
\(767\) | 42.8138i | 1.54592i | ||||||||
\(768\) | −3.10844 | + | 3.10844i | −0.112166 | + | 0.112166i | ||||
\(769\) | 30.5773 | 1.10264 | 0.551322 | − | 0.834292i | \(-0.314123\pi\) | ||||
0.551322 | + | 0.834292i | \(0.314123\pi\) | |||||||
\(770\) | −1.59317 | + | 1.59317i | −0.0574140 | + | 0.0574140i | ||||
\(771\) | 0.0212341 | + | 0.0212341i | 0.000764726 | + | 0.000764726i | ||||
\(772\) | 0.662386 | + | 0.662386i | 0.0238398 | + | 0.0238398i | ||||
\(773\) | 45.3346i | 1.63057i | 0.579058 | + | 0.815286i | \(0.303421\pi\) | ||||
−0.579058 | + | 0.815286i | \(0.696579\pi\) | |||||||
\(774\) | − | 6.65002i | − | 0.239030i | ||||||
\(775\) | 7.39712 | + | 7.39712i | 0.265712 | + | 0.265712i | ||||
\(776\) | −18.2306 | − | 18.2306i | −0.654441 | − | 0.654441i | ||||
\(777\) | 1.09721 | − | 1.09721i | 0.0393622 | − | 0.0393622i | ||||
\(778\) | 18.5948 | 0.666657 | ||||||||
\(779\) | 23.5638 | − | 23.5638i | 0.844259 | − | 0.844259i | ||||
\(780\) | − | 3.05644i | − | 0.109438i | ||||||
\(781\) | −12.9050 | −0.461776 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.35504 | 0.227110 | ||||||||
\(784\) | 25.0511i | 0.894681i | ||||||||
\(785\) | −3.18891 | + | 3.18891i | −0.113817 | + | 0.113817i | ||||
\(786\) | −6.67087 | −0.237942 | ||||||||
\(787\) | 13.2542 | − | 13.2542i | 0.472460 | − | 0.472460i | −0.430250 | − | 0.902710i | \(-0.641575\pi\) |
0.902710 | + | 0.430250i | \(0.141575\pi\) | |||||||
\(788\) | −1.05117 | − | 1.05117i | −0.0374464 | − | 0.0374464i | ||||
\(789\) | −8.65652 | − | 8.65652i | −0.308180 | − | 0.308180i | ||||
\(790\) | 26.6878i | 0.949509i | ||||||||
\(791\) | − | 0.870214i | − | 0.0309412i | ||||||
\(792\) | −7.43893 | − | 7.43893i | −0.264331 | − | 0.264331i | ||||
\(793\) | −13.7895 | − | 13.7895i | −0.489678 | − | 0.489678i | ||||
\(794\) | 27.2106 | − | 27.2106i | 0.965669 | − | 0.965669i | ||||
\(795\) | −19.3773 | −0.687243 | ||||||||
\(796\) | 1.56029 | − | 1.56029i | 0.0553030 | − | 0.0553030i | ||||
\(797\) | 44.5681i | 1.57868i | 0.613954 | + | 0.789342i | \(0.289578\pi\) | ||||
−0.613954 | + | 0.789342i | \(0.710422\pi\) | |||||||
\(798\) | −1.15476 | −0.0408782 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −1.47060 | −0.0519935 | ||||||||
\(801\) | 1.32770i | 0.0469118i | ||||||||
\(802\) | −25.5096 | + | 25.5096i | −0.900776 | + | 0.900776i | ||||
\(803\) | −30.0624 | −1.06088 | ||||||||
\(804\) | −1.76631 | + | 1.76631i | −0.0622930 | + | 0.0622930i | ||||
\(805\) | 1.02768 | + | 1.02768i | 0.0362211 | + | 0.0362211i | ||||
\(806\) | 46.1216 | + | 46.1216i | 1.62457 | + | 1.62457i | ||||
\(807\) | 21.5672i | 0.759200i | ||||||||
\(808\) | 32.4597i | 1.14193i | ||||||||
\(809\) | −5.98582 | − | 5.98582i | −0.210450 | − | 0.210450i | 0.594009 | − | 0.804459i | \(-0.297545\pi\) |
−0.804459 | + | 0.594009i | \(0.797545\pi\) | |||||||
\(810\) | 2.41228 | + | 2.41228i | 0.0847588 | + | 0.0847588i | ||||
\(811\) | 7.72965 | − | 7.72965i | 0.271425 | − | 0.271425i | −0.558249 | − | 0.829674i | \(-0.688527\pi\) |
0.829674 | + | 0.558249i | \(0.188527\pi\) | |||||||
\(812\) | 0.217014 | 0.00761568 | ||||||||
\(813\) | 2.40199 | − | 2.40199i | 0.0842415 | − | 0.0842415i | ||||
\(814\) | 40.4329i | 1.41717i | ||||||||
\(815\) | 7.97771 | 0.279447 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.8931 | −0.800929 | ||||||||
\(818\) | − | 52.3233i | − | 1.82944i | ||||||
\(819\) | −0.853535 | + | 0.853535i | −0.0298249 | + | 0.0298249i | ||||
\(820\) | −3.36184 | −0.117401 | ||||||||
\(821\) | −8.88691 | + | 8.88691i | −0.310155 | + | 0.310155i | −0.844970 | − | 0.534814i | \(-0.820382\pi\) |
0.534814 | + | 0.844970i | \(0.320382\pi\) | |||||||
\(822\) | 11.0402 | + | 11.0402i | 0.385071 | + | 0.385071i | ||||
\(823\) | 36.2530 | + | 36.2530i | 1.26370 | + | 1.26370i | 0.949286 | + | 0.314415i | \(0.101808\pi\) |
0.314415 | + | 0.949286i | \(0.398192\pi\) | |||||||
\(824\) | − | 18.4598i | − | 0.643079i | ||||||
\(825\) | − | 5.04458i | − | 0.175630i | ||||||
\(826\) | −1.15389 | − | 1.15389i | −0.0401489 | − | 0.0401489i | ||||
\(827\) | −20.1849 | − | 20.1849i | −0.701899 | − | 0.701899i | 0.262919 | − | 0.964818i | \(-0.415315\pi\) |
−0.964818 | + | 0.262919i | \(0.915315\pi\) | |||||||
\(828\) | −0.405864 | + | 0.405864i | −0.0141047 | + | 0.0141047i | ||||
\(829\) | −4.09865 | −0.142352 | −0.0711760 | − | 0.997464i | \(-0.522675\pi\) | ||||
−0.0711760 | + | 0.997464i | \(0.522675\pi\) | |||||||
\(830\) | 6.06082 | − | 6.06082i | 0.210374 | − | 0.210374i | ||||
\(831\) | − | 15.9172i | − | 0.552160i | ||||||
\(832\) | −56.1516 | −1.94671 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3.62361 | 0.125475 | ||||||||
\(835\) | − | 61.6519i | − | 2.13355i | ||||||
\(836\) | −2.16604 | + | 2.16604i | −0.0749141 | + | 0.0749141i | ||||
\(837\) | 7.41147 | 0.256178 | ||||||||
\(838\) | −18.1344 | + | 18.1344i | −0.626442 | + | 0.626442i | ||||
\(839\) | 26.4436 | + | 26.4436i | 0.912935 | + | 0.912935i | 0.996502 | − | 0.0835670i | \(-0.0266313\pi\) |
−0.0835670 | + | 0.996502i | \(0.526631\pi\) | |||||||
\(840\) | 0.973916 | + | 0.973916i | 0.0336033 | + | 0.0336033i | ||||
\(841\) | − | 11.3865i | − | 0.392638i | ||||||
\(842\) | 8.64496i | 0.297925i | ||||||||
\(843\) | 11.3247 | + | 11.3247i | 0.390042 | + | 0.390042i | ||||
\(844\) | 0.332764 | + | 0.332764i | 0.0114542 | + | 0.0114542i | ||||
\(845\) | 53.1196 | − | 53.1196i | 1.82737 | − | 1.82737i | ||||
\(846\) | −12.1925 | −0.419188 | ||||||||
\(847\) | 0.231716 | − | 0.231716i | 0.00796186 | − | 0.00796186i | ||||
\(848\) | 27.5212i | 0.945081i | ||||||||
\(849\) | 26.8357 | 0.921000 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.0814 | 0.894059 | ||||||||
\(852\) | 0.667252i | 0.0228597i | ||||||||
\(853\) | 39.7808 | − | 39.7808i | 1.36207 | − | 1.36207i | 0.490793 | − | 0.871276i | \(-0.336707\pi\) |
0.871276 | − | 0.490793i | \(-0.163293\pi\) | |||||||
\(854\) | 0.743289 | 0.0254348 | ||||||||
\(855\) | 8.30442 | − | 8.30442i | 0.284005 | − | 0.284005i | ||||
\(856\) | 7.39813 | + | 7.39813i | 0.252863 | + | 0.252863i | ||||
\(857\) | −12.6008 | − | 12.6008i | −0.430436 | − | 0.430436i | 0.458341 | − | 0.888777i | \(-0.348444\pi\) |
−0.888777 | + | 0.458341i | \(0.848444\pi\) | |||||||
\(858\) | − | 31.4534i | − | 1.07380i | ||||||
\(859\) | 5.45935i | 0.186271i | 0.995653 | + | 0.0931353i | \(0.0296889\pi\) | ||||
−0.995653 | + | 0.0931353i | \(0.970311\pi\) | |||||||
\(860\) | 1.63308 | + | 1.63308i | 0.0556876 | + | 0.0556876i | ||||
\(861\) | 0.938823 | + | 0.938823i | 0.0319950 | + | 0.0319950i | ||||
\(862\) | −8.24161 | + | 8.24161i | −0.280710 | + | 0.280710i | ||||
\(863\) | −8.23947 | −0.280475 | −0.140237 | − | 0.990118i | \(-0.544787\pi\) | ||||
−0.140237 | + | 0.990118i | \(0.544787\pi\) | |||||||
\(864\) | −0.736727 | + | 0.736727i | −0.0250640 | + | 0.0250640i | ||||
\(865\) | − | 38.1566i | − | 1.29736i | ||||||
\(866\) | −31.4165 | −1.06758 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.253089 | 0.00859040 | ||||||||
\(869\) | − | 27.9590i | − | 0.948446i | ||||||
\(870\) | 15.3301 | − | 15.3301i | 0.519739 | − | 0.519739i | ||||
\(871\) | −88.2978 | −2.99186 | ||||||||
\(872\) | −7.48532 | + | 7.48532i | −0.253485 | + | 0.253485i | ||||
\(873\) | −6.19339 | − | 6.19339i | −0.209614 | − | 0.209614i | ||||
\(874\) | −13.7247 | − | 13.7247i | −0.464246 | − | 0.464246i | ||||
\(875\) | − | 1.67911i | − | 0.0567643i | ||||||
\(876\) | 1.55438i | 0.0525176i | ||||||||
\(877\) | 5.76315 | + | 5.76315i | 0.194608 | + | 0.194608i | 0.797684 | − | 0.603076i | \(-0.206058\pi\) |
−0.603076 | + | 0.797684i | \(0.706058\pi\) | |||||||
\(878\) | 12.5748 | + | 12.5748i | 0.424378 | + | 0.424378i | ||||
\(879\) | −1.70327 | + | 1.70327i | −0.0574498 | + | 0.0574498i | ||||
\(880\) | −32.5449 | −1.09709 | ||||||||
\(881\) | −13.3327 | + | 13.3327i | −0.449191 | + | 0.449191i | −0.895086 | − | 0.445894i | \(-0.852886\pi\) |
0.445894 | + | 0.895086i | \(0.352886\pi\) | |||||||
\(882\) | 9.38507i | 0.316012i | ||||||||
\(883\) | 17.2189 | 0.579463 | 0.289732 | − | 0.957108i | \(-0.406434\pi\) | ||||
0.289732 | + | 0.957108i | \(0.406434\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.5963 | 0.557877 | ||||||||
\(886\) | 41.1242i | 1.38160i | ||||||||
\(887\) | 7.91242 | − | 7.91242i | 0.265673 | − | 0.265673i | −0.561681 | − | 0.827354i | \(-0.689845\pi\) |
0.827354 | + | 0.561681i | \(0.189845\pi\) | |||||||
\(888\) | 24.7169 | 0.829444 | ||||||||
\(889\) | 1.01483 | − | 1.01483i | 0.0340365 | − | 0.0340365i | ||||
\(890\) | 3.20277 | + | 3.20277i | 0.107357 | + | 0.107357i | ||||
\(891\) | −2.52718 | − | 2.52718i | −0.0846639 | − | 0.0846639i | ||||
\(892\) | 0.821518i | 0.0275065i | ||||||||
\(893\) | 41.9736i | 1.40459i | ||||||||
\(894\) | −15.1753 | − | 15.1753i | −0.507538 | − | 0.507538i | ||||
\(895\) | −30.2617 | − | 30.2617i | −1.01154 | − | 1.01154i | ||||
\(896\) | 1.24108 | − | 1.24108i | 0.0414615 | − | 0.0414615i | ||||
\(897\) | −20.2891 | −0.677433 | ||||||||
\(898\) | 2.58351 | − | 2.58351i | 0.0862129 | − | 0.0862129i | ||||
\(899\) | − | 47.1002i | − | 1.57088i | ||||||
\(900\) | −0.260830 | −0.00869433 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −34.5963 | −1.15193 | ||||||||
\(903\) | − | 0.912103i | − | 0.0303529i | ||||||
\(904\) | 9.80167 | − | 9.80167i | 0.325999 | − | 0.325999i | ||||
\(905\) | 27.0128 | 0.897936 | ||||||||
\(906\) | 1.32345 | − | 1.32345i | 0.0439688 | − | 0.0439688i | ||||
\(907\) | 29.0477 | + | 29.0477i | 0.964513 | + | 0.964513i | 0.999392 | − | 0.0348783i | \(-0.0111044\pi\) |
−0.0348783 | + | 0.999392i | \(0.511104\pi\) | |||||||
\(908\) | −0.982654 | − | 0.982654i | −0.0326105 | − | 0.0326105i | ||||
\(909\) | 11.0273i | 0.365754i | ||||||||
\(910\) | 4.11793i | 0.136508i | ||||||||
\(911\) | 27.1308 | + | 27.1308i | 0.898884 | + | 0.898884i | 0.995337 | − | 0.0964535i | \(-0.0307499\pi\) |
−0.0964535 | + | 0.995337i | \(0.530750\pi\) | |||||||
\(912\) | −11.7946 | − | 11.7946i | −0.390557 | − | 0.390557i | ||||
\(913\) | −6.34952 | + | 6.34952i | −0.210138 | + | 0.210138i | ||||
\(914\) | −35.3892 | −1.17057 | ||||||||
\(915\) | −5.34532 | + | 5.34532i | −0.176711 | + | 0.176711i | ||||
\(916\) | − | 2.53857i | − | 0.0838768i | ||||||
\(917\) | −0.914964 | −0.0302148 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.7110 | 0.749167 | 0.374584 | − | 0.927193i | \(-0.377786\pi\) | ||||
0.374584 | + | 0.927193i | \(0.377786\pi\) | |||||||
\(920\) | 23.1506i | 0.763254i | ||||||||
\(921\) | −4.53907 | + | 4.53907i | −0.149567 | + | 0.149567i | ||||
\(922\) | −34.3833 | −1.13235 | ||||||||
\(923\) | −16.6779 | + | 16.6779i | −0.548961 | + | 0.548961i | ||||
\(924\) | −0.0862990 | − | 0.0862990i | −0.00283903 | − | 0.00283903i | ||||
\(925\) | 8.38066 | + | 8.38066i | 0.275554 | + | 0.275554i | ||||
\(926\) | − | 3.80697i | − | 0.125105i | ||||||
\(927\) | − | 6.27126i | − | 0.205975i | ||||||
\(928\) | 4.68193 | + | 4.68193i | 0.153692 | + | 0.153692i | ||||
\(929\) | −15.2339 | − | 15.2339i | −0.499807 | − | 0.499807i | 0.411571 | − | 0.911378i | \(-0.364980\pi\) |
−0.911378 | + | 0.411571i | \(0.864980\pi\) | |||||||
\(930\) | 17.8785 | − | 17.8785i | 0.586260 | − | 0.586260i | ||||
\(931\) | 32.3087 | 1.05888 | ||||||||
\(932\) | 2.68200 | − | 2.68200i | 0.0878518 | − | 0.0878518i | ||||
\(933\) | 0.543948i | 0.0178081i | ||||||||
\(934\) | 44.4597 | 1.45476 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −19.2276 | −0.628474 | ||||||||
\(937\) | − | 37.5476i | − | 1.22663i | −0.789840 | − | 0.613313i | \(-0.789837\pi\) | ||
0.789840 | − | 0.613313i | \(-0.210163\pi\) | |||||||
\(938\) | 2.37974 | − | 2.37974i | 0.0777014 | − | 0.0777014i | ||||
\(939\) | −16.6186 | −0.542326 | ||||||||
\(940\) | 2.99419 | − | 2.99419i | 0.0976597 | − | 0.0976597i | ||||
\(941\) | 27.4877 | + | 27.4877i | 0.896074 | + | 0.896074i | 0.995086 | − | 0.0990120i | \(-0.0315682\pi\) |
−0.0990120 | + | 0.995086i | \(0.531568\pi\) | |||||||
\(942\) | 1.69678 | + | 1.69678i | 0.0552842 | + | 0.0552842i | ||||
\(943\) | 22.3164i | 0.726723i | ||||||||
\(944\) | − | 23.5713i | − | 0.767180i | ||||||
\(945\) | 0.330863 | + | 0.330863i | 0.0107630 | + | 0.0107630i | ||||
\(946\) | 16.8058 | + | 16.8058i | 0.546404 | + | 0.546404i | ||||
\(947\) | −33.6097 | + | 33.6097i | −1.09217 | + | 1.09217i | −0.0968710 | + | 0.995297i | \(0.530883\pi\) |
−0.995297 | + | 0.0968710i | \(0.969117\pi\) | |||||||
\(948\) | −1.44562 | −0.0469516 | ||||||||
\(949\) | −38.8516 | + | 38.8516i | −1.26118 | + | 1.26118i | ||||
\(950\) | − | 8.82026i | − | 0.286167i | ||||||
\(951\) | −26.0574 | −0.844968 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.6332 | 1.57538 | 0.787692 | − | 0.616069i | \(-0.211276\pi\) | ||||
0.787692 | + | 0.616069i | \(0.211276\pi\) | |||||||
\(954\) | 10.3105i | 0.333813i | ||||||||
\(955\) | −3.18410 | + | 3.18410i | −0.103035 | + | 0.103035i | ||||
\(956\) | 4.78880 | 0.154881 | ||||||||
\(957\) | −16.0603 | + | 16.0603i | −0.519157 | + | 0.519157i | ||||
\(958\) | −33.1713 | − | 33.1713i | −1.07172 | − | 1.07172i | ||||
\(959\) | 1.51425 | + | 1.51425i | 0.0488977 | + | 0.0488977i | ||||
\(960\) | 21.7665i | 0.702511i | ||||||||
\(961\) | − | 23.9299i | − | 0.771934i | ||||||
\(962\) | 52.2541 | + | 52.2541i | 1.68474 | + | 1.68474i | ||||
\(963\) | 2.51332 | + | 2.51332i | 0.0809908 | + | 0.0809908i | ||||
\(964\) | −1.48665 | + | 1.48665i | −0.0478819 | + | 0.0478819i | ||||
\(965\) | 12.8357 | 0.413197 | ||||||||
\(966\) | 0.546819 | − | 0.546819i | 0.0175936 | − | 0.0175936i | ||||
\(967\) | 1.39281i | 0.0447897i | 0.999749 | + | 0.0223948i | \(0.00712909\pi\) | ||||
−0.999749 | + | 0.0223948i | \(0.992871\pi\) | |||||||
\(968\) | 5.21987 | 0.167773 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −29.8803 | −0.959399 | ||||||||
\(971\) | 13.0892i | 0.420051i | 0.977696 | + | 0.210025i | \(0.0673547\pi\) | ||||
−0.977696 | + | 0.210025i | \(0.932645\pi\) | |||||||
\(972\) | −0.130668 | + | 0.130668i | −0.00419118 | + | 0.00419118i | ||||
\(973\) | 0.497007 | 0.0159333 | ||||||||
\(974\) | 20.5614 | − | 20.5614i | 0.658830 | − | 0.658830i | ||||
\(975\) | −6.51944 | − | 6.51944i | −0.208789 | − | 0.208789i | ||||
\(976\) | 7.59184 | + | 7.59184i | 0.243009 | + | 0.243009i | ||||
\(977\) | − | 3.40230i | − | 0.108849i | −0.998518 | − | 0.0544247i | \(-0.982668\pi\) | ||
0.998518 | − | 0.0544247i | \(-0.0173325\pi\) | |||||||
\(978\) | − | 4.24485i | − | 0.135735i | ||||||
\(979\) | −3.35533 | − | 3.35533i | −0.107237 | − | 0.107237i | ||||
\(980\) | −2.30474 | − | 2.30474i | −0.0736223 | − | 0.0736223i | ||||
\(981\) | −2.54294 | + | 2.54294i | −0.0811900 | + | 0.0811900i | ||||
\(982\) | −46.2404 | −1.47559 | ||||||||
\(983\) | 10.3677 | − | 10.3677i | 0.330680 | − | 0.330680i | −0.522165 | − | 0.852845i | \(-0.674875\pi\) |
0.852845 | + | 0.522165i | \(0.174875\pi\) | |||||||
\(984\) | 21.1489i | 0.674202i | ||||||||
\(985\) | −20.3696 | −0.649029 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.67230 | −0.0532300 | ||||||||
\(988\) | 5.59863i | 0.178116i | ||||||||
\(989\) | 10.8406 | − | 10.8406i | 0.344713 | − | 0.344713i | ||||
\(990\) | −12.1925 | −0.387504 | ||||||||
\(991\) | −32.9988 | + | 32.9988i | −1.04824 | + | 1.04824i | −0.0494659 | + | 0.998776i | \(0.515752\pi\) |
−0.998776 | + | 0.0494659i | \(0.984248\pi\) | |||||||
\(992\) | 5.46023 | + | 5.46023i | 0.173363 | + | 0.173363i | ||||
\(993\) | 15.9175 | + | 15.9175i | 0.505126 | + | 0.505126i | ||||
\(994\) | − | 0.898986i | − | 0.0285141i | ||||||
\(995\) | − | 30.2354i | − | 0.958525i | ||||||
\(996\) | 0.328302 | + | 0.328302i | 0.0104026 | + | 0.0104026i | ||||
\(997\) | −1.09597 | − | 1.09597i | −0.0347097 | − | 0.0347097i | 0.689539 | − | 0.724249i | \(-0.257813\pi\) |
−0.724249 | + | 0.689539i | \(0.757813\pi\) | |||||||
\(998\) | −17.2876 | + | 17.2876i | −0.547228 | + | 0.547228i | ||||
\(999\) | 8.39693 | 0.265667 |
(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 | 867.2.e.j.616.4 | 12 | ||
17.2 | even | 8 | 867.2.d.d.577.3 | 6 | |||
17.3 | odd | 16 | 867.2.h.l.733.4 | 24 | |||
17.4 | even | 4 | inner | 867.2.e.j.829.3 | 12 | ||
17.5 | odd | 16 | 867.2.h.l.712.4 | 24 | |||
17.6 | odd | 16 | 867.2.h.l.688.4 | 24 | |||
17.7 | odd | 16 | 867.2.h.l.757.3 | 24 | |||
17.8 | even | 8 | 867.2.a.i.1.2 | ✓ | 3 | ||
17.9 | even | 8 | 867.2.a.j.1.2 | yes | 3 | ||
17.10 | odd | 16 | 867.2.h.l.757.4 | 24 | |||
17.11 | odd | 16 | 867.2.h.l.688.3 | 24 | |||
17.12 | odd | 16 | 867.2.h.l.712.3 | 24 | |||
17.13 | even | 4 | inner | 867.2.e.j.829.4 | 12 | ||
17.14 | odd | 16 | 867.2.h.l.733.3 | 24 | |||
17.15 | even | 8 | 867.2.d.d.577.4 | 6 | |||
17.16 | even | 2 | inner | 867.2.e.j.616.3 | 12 | ||
51.8 | odd | 8 | 2601.2.a.y.1.2 | 3 | |||
51.26 | odd | 8 | 2601.2.a.z.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
867.2.a.i.1.2 | ✓ | 3 | 17.8 | even | 8 | ||
867.2.a.j.1.2 | yes | 3 | 17.9 | even | 8 | ||
867.2.d.d.577.3 | 6 | 17.2 | even | 8 | |||
867.2.d.d.577.4 | 6 | 17.15 | even | 8 | |||
867.2.e.j.616.3 | 12 | 17.16 | even | 2 | inner | ||
867.2.e.j.616.4 | 12 | 1.1 | even | 1 | trivial | ||
867.2.e.j.829.3 | 12 | 17.4 | even | 4 | inner | ||
867.2.e.j.829.4 | 12 | 17.13 | even | 4 | inner | ||
867.2.h.l.688.3 | 24 | 17.11 | odd | 16 | |||
867.2.h.l.688.4 | 24 | 17.6 | odd | 16 | |||
867.2.h.l.712.3 | 24 | 17.12 | odd | 16 | |||
867.2.h.l.712.4 | 24 | 17.5 | odd | 16 | |||
867.2.h.l.733.3 | 24 | 17.14 | odd | 16 | |||
867.2.h.l.733.4 | 24 | 17.3 | odd | 16 | |||
867.2.h.l.757.3 | 24 | 17.7 | odd | 16 | |||
867.2.h.l.757.4 | 24 | 17.10 | odd | 16 | |||
2601.2.a.y.1.2 | 3 | 51.8 | odd | 8 | |||
2601.2.a.z.1.2 | 3 | 51.26 | odd | 8 |