Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5292,2,Mod(2285,5292)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5292, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5292.2285");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5292.bm (of order \(6\), 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: | \(42.2568327497\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 4625.3 | ||
Root | \(-0.268067 - 1.71118i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5292.4625 |
Dual form | 5292.2.bm.a.2285.3 |
$q$-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 \(\left(\mathbb{Z}/5292\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) | \(2647\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.68574 | −0.753885 | −0.376942 | − | 0.926237i | \(-0.623025\pi\) | ||||
−0.376942 | + | 0.926237i | \(0.623025\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.90538i | − | 1.17752i | −0.808309 | − | 0.588758i | \(-0.799617\pi\) | ||
0.808309 | − | 0.588758i | \(-0.200383\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.24391 | + | 3.02757i | −1.45440 | + | 0.839698i | −0.998727 | − | 0.0504496i | \(-0.983935\pi\) |
−0.455673 | + | 0.890147i | \(0.650601\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.201244 | + | 0.348565i | 0.0488088 | + | 0.0845393i | 0.889398 | − | 0.457134i | \(-0.151124\pi\) |
−0.840589 | + | 0.541674i | \(0.817791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.145617 | + | 0.0840718i | 0.0334067 | + | 0.0192874i | 0.516610 | − | 0.856221i | \(-0.327194\pi\) |
−0.483204 | + | 0.875508i | \(0.660527\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.88395i | 1.85243i | 0.376993 | + | 0.926216i | \(0.376958\pi\) | ||||
−0.376993 | + | 0.926216i | \(0.623042\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.15829 | −0.431658 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.15380 | + | 3.55290i | 1.14273 | + | 0.659757i | 0.947106 | − | 0.320921i | \(-0.103993\pi\) |
0.195627 | + | 0.980678i | \(0.437326\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.44527 | − | 3.14383i | −0.978000 | − | 0.564649i | −0.0763342 | − | 0.997082i | \(-0.524322\pi\) |
−0.901666 | + | 0.432434i | \(0.857655\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.13257 | − | 5.42578i | 0.514992 | − | 0.891992i | −0.484857 | − | 0.874594i | \(-0.661128\pi\) |
0.999849 | − | 0.0173987i | \(-0.00553846\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.64707 | − | 2.85281i | −0.257229 | − | 0.445534i | 0.708269 | − | 0.705942i | \(-0.249476\pi\) |
−0.965499 | + | 0.260408i | \(0.916143\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.80474 | − | 3.12590i | 0.275220 | − | 0.476695i | −0.694971 | − | 0.719038i | \(-0.744583\pi\) |
0.970191 | + | 0.242343i | \(0.0779161\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.38482 | + | 7.59474i | 0.639592 | + | 1.10781i | 0.985522 | + | 0.169546i | \(0.0542301\pi\) |
−0.345930 | + | 0.938260i | \(0.612437\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.94628 | − | 2.85574i | 0.679424 | − | 0.392266i | −0.120214 | − | 0.992748i | \(-0.538358\pi\) |
0.799638 | + | 0.600482i | \(0.205025\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.58345i | 0.887712i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.25163 | − | 3.89994i | 0.293138 | − | 0.507729i | −0.681412 | − | 0.731900i | \(-0.738634\pi\) |
0.974550 | + | 0.224171i | \(0.0719673\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.43678 | + | 2.56157i | −0.568071 | + | 0.327976i | −0.756379 | − | 0.654134i | \(-0.773033\pi\) |
0.188308 | + | 0.982110i | \(0.439700\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.83986 | − | 5.10369i | 1.09645 | − | 0.633035i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.95521 | − | 5.11857i | 0.361036 | − | 0.625332i | −0.627096 | − | 0.778942i | \(-0.715757\pi\) |
0.988132 | + | 0.153610i | \(0.0490899\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4308i | 1.35658i | 0.734792 | + | 0.678292i | \(0.237280\pi\) | ||||
−0.734792 | + | 0.678292i | \(0.762720\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.05559 | − | 3.49620i | 0.708753 | − | 0.409199i | −0.101846 | − | 0.994800i | \(-0.532475\pi\) |
0.810599 | + | 0.585601i | \(0.199142\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.603968 | − | 1.04610i | −0.0679517 | − | 0.117696i | 0.830048 | − | 0.557692i | \(-0.188313\pi\) |
−0.898000 | + | 0.439996i | \(0.854980\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.181350 | + | 0.314108i | −0.0199058 | + | 0.0344779i | −0.875807 | − | 0.482662i | \(-0.839670\pi\) |
0.855901 | + | 0.517140i | \(0.173003\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.339244 | − | 0.587588i | −0.0367962 | − | 0.0637329i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.38526 | − | 2.39934i | 0.146837 | − | 0.254329i | −0.783220 | − | 0.621745i | \(-0.786424\pi\) |
0.930057 | + | 0.367416i | \(0.119757\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.245471 | − | 0.141723i | −0.0251848 | − | 0.0145405i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.508914 | − | 0.293821i | −0.0516723 | − | 0.0298330i | 0.473941 | − | 0.880556i | \(-0.342831\pi\) |
−0.525614 | + | 0.850723i | \(0.676164\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.8466 | 1.37779 | 0.688893 | − | 0.724863i | \(-0.258097\pi\) | ||||
0.688893 | + | 0.724863i | \(0.258097\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.0793i | − | 1.19021i | −0.803647 | − | 0.595106i | \(-0.797110\pi\) | ||
0.803647 | − | 0.595106i | \(-0.202890\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.9299 | − | 9.19711i | −1.54000 | − | 0.889118i | −0.998838 | − | 0.0481978i | \(-0.984652\pi\) |
−0.541159 | − | 0.840920i | \(-0.682014\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.51036 | − | 9.54422i | −0.527796 | − | 0.914170i | −0.999475 | − | 0.0323997i | \(-0.989685\pi\) |
0.471679 | − | 0.881771i | \(-0.343648\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.36811 | − | 4.25398i | 0.693133 | − | 0.400181i | −0.111652 | − | 0.993747i | \(-0.535614\pi\) |
0.804785 | + | 0.593567i | \(0.202281\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 14.9760i | − | 1.39652i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.25200 | −0.386545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0670 | 1.07930 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.6312 | −0.943365 | −0.471682 | − | 0.881769i | \(-0.656353\pi\) | ||||
−0.471682 | + | 0.881769i | \(0.656353\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.33480 | 0.553474 | 0.276737 | − | 0.960946i | \(-0.410747\pi\) | ||||
0.276737 | + | 0.960946i | \(0.410747\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 16.6459i | − | 1.42216i | −0.703113 | − | 0.711078i | \(-0.748207\pi\) | ||
0.703113 | − | 0.711078i | \(-0.251793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.24007 | − | 2.44800i | 0.359638 | − | 0.207637i | −0.309284 | − | 0.950970i | \(-0.600089\pi\) |
0.668922 | + | 0.743333i | \(0.266756\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.8238 | + | 20.4795i | 0.988758 | + | 1.71258i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.3737 | − | 5.98926i | −0.861489 | − | 0.497381i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 5.28696i | − | 0.433125i | −0.976269 | − | 0.216562i | \(-0.930516\pi\) | ||
0.976269 | − | 0.216562i | \(-0.0694845\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.5833 | −1.18677 | −0.593385 | − | 0.804919i | \(-0.702209\pi\) | ||||
−0.593385 | + | 0.804919i | \(0.702209\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.17930 | + | 5.29967i | 0.737299 | + | 0.425680i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.4160 | + | 8.90044i | 1.23033 | + | 0.710332i | 0.967099 | − | 0.254400i | \(-0.0818781\pi\) |
0.263232 | + | 0.964732i | \(0.415211\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0482228 | − | 0.0835243i | 0.00377710 | − | 0.00654213i | −0.864131 | − | 0.503267i | \(-0.832131\pi\) |
0.867908 | + | 0.496725i | \(0.165464\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.47872 | − | 4.29327i | −0.191809 | − | 0.332224i | 0.754041 | − | 0.656828i | \(-0.228102\pi\) |
−0.945850 | + | 0.324604i | \(0.894769\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8324 | − | 20.4943i | 0.910185 | − | 1.57649i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.40033 | − | 12.8177i | −0.562637 | − | 0.974515i | −0.997265 | − | 0.0739055i | \(-0.976454\pi\) |
0.434629 | − | 0.900610i | \(-0.356880\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.592751 | + | 0.342225i | −0.0443043 | + | 0.0255791i | −0.521989 | − | 0.852952i | \(-0.674810\pi\) |
0.477684 | + | 0.878532i | \(0.341476\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.84745i | − | 0.583297i | −0.956526 | − | 0.291648i | \(-0.905796\pi\) | ||
0.956526 | − | 0.291648i | \(-0.0942037\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.28070 | + | 9.14644i | −0.388245 | + | 0.672459i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.36128 | − | 0.785934i | 0.0995464 | − | 0.0574732i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.9694 | − | 9.79729i | 1.22786 | − | 0.708907i | 0.261281 | − | 0.965263i | \(-0.415855\pi\) |
0.966582 | + | 0.256356i | \(0.0825219\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.18116 | + | 15.9022i | −0.660875 | + | 1.14467i | 0.319512 | + | 0.947582i | \(0.396481\pi\) |
−0.980386 | + | 0.197086i | \(0.936852\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.92313i | 0.422006i | 0.977485 | + | 0.211003i | \(0.0676730\pi\) | ||||
−0.977485 | + | 0.211003i | \(0.932327\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.6268 | − | 7.86741i | 0.965975 | − | 0.557706i | 0.0679681 | − | 0.997687i | \(-0.478348\pi\) |
0.898007 | + | 0.439982i | \(0.145015\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.77653 | + | 4.80909i | 0.193921 | + | 0.335881i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.328332 | − | 0.568688i | 0.0227112 | − | 0.0393370i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.06619 | + | 8.77489i | 0.348771 | + | 0.604088i | 0.986031 | − | 0.166560i | \(-0.0532659\pi\) |
−0.637261 | + | 0.770648i | \(0.719933\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.04231 | + | 5.26944i | −0.207484 | + | 0.359373i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.11061 | − | 1.21856i | −0.141975 | − | 0.0819693i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.3944 | + | 7.73325i | 0.896955 | + | 0.517857i | 0.876211 | − | 0.481928i | \(-0.160063\pi\) |
0.0207437 | + | 0.999785i | \(0.493397\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 28.0719 | 1.86320 | 0.931600 | − | 0.363486i | \(-0.118414\pi\) | ||||
0.931600 | + | 0.363486i | \(0.118414\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.0264i | 1.12514i | 0.826751 | + | 0.562568i | \(0.190186\pi\) | ||||
−0.826751 | + | 0.562568i | \(0.809814\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.0015 | + | 9.23847i | 1.04829 | + | 0.605233i | 0.922171 | − | 0.386782i | \(-0.126413\pi\) |
0.126122 | + | 0.992015i | \(0.459747\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.39166 | − | 12.8027i | −0.482179 | − | 0.835158i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.06656 | − | 3.50253i | 0.392413 | − | 0.226560i | −0.290792 | − | 0.956786i | \(-0.593919\pi\) |
0.683205 | + | 0.730226i | \(0.260585\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.21759i | 0.400510i | 0.979744 | + | 0.200255i | \(0.0641771\pi\) | ||||
−0.979744 | + | 0.200255i | \(0.935823\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.01813 | −0.0647823 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.81844 | −0.619734 | −0.309867 | − | 0.950780i | \(-0.600285\pi\) | ||||
−0.309867 | + | 0.950780i | \(0.600285\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.6952 | 2.18127 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.33581 | −0.0833254 | −0.0416627 | − | 0.999132i | \(-0.513265\pi\) | ||||
−0.0416627 | + | 0.999132i | \(0.513265\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 20.3502i | − | 1.25485i | −0.778678 | − | 0.627424i | \(-0.784109\pi\) | ||
0.778678 | − | 0.627424i | \(-0.215891\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.33814 | + | 4.81402i | −0.512208 | + | 0.295723i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.3614 | − | 23.1426i | −0.814659 | − | 1.41103i | −0.909572 | − | 0.415546i | \(-0.863591\pi\) |
0.0949131 | − | 0.995486i | \(-0.469743\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.76517 | − | 2.17382i | −0.228718 | − | 0.132050i | 0.381263 | − | 0.924467i | \(-0.375489\pi\) |
−0.609980 | + | 0.792417i | \(0.708823\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.42894i | 0.508284i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.39803 | −0.264252 | −0.132126 | − | 0.991233i | \(-0.542180\pi\) | ||||
−0.132126 | + | 0.991233i | \(0.542180\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.62273 | − | 2.66893i | −0.275769 | − | 0.159215i | 0.355738 | − | 0.934586i | \(-0.384230\pi\) |
−0.631506 | + | 0.775371i | \(0.717563\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5431 | + | 8.97381i | 0.923941 | + | 0.533437i | 0.884890 | − | 0.465800i | \(-0.154233\pi\) |
0.0390505 | + | 0.999237i | \(0.487567\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.41900 | − | 14.5821i | 0.495235 | − | 0.857773i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.1126 | + | 22.7117i | 0.766048 | + | 1.32683i | 0.939691 | + | 0.342026i | \(0.111113\pi\) |
−0.173642 | + | 0.984809i | \(0.555554\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.79566 | + | 6.57428i | −0.220992 | + | 0.382769i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −26.8968 | − | 46.5867i | −1.55548 | − | 2.69418i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.47924 | − | 4.31814i | 0.428260 | − | 0.247256i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.19520i | − | 0.410652i | −0.978694 | − | 0.205326i | \(-0.934175\pi\) | ||
0.978694 | − | 0.205326i | \(-0.0658254\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.08721 | − | 1.88311i | 0.0616503 | − | 0.106781i | −0.833553 | − | 0.552440i | \(-0.813697\pi\) |
0.895203 | + | 0.445658i | \(0.147030\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.2870 | − | 5.93922i | 0.581457 | − | 0.335704i | −0.180255 | − | 0.983620i | \(-0.557692\pi\) |
0.761712 | + | 0.647916i | \(0.224359\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.09969 | + | 4.09901i | −0.398758 | + | 0.230223i | −0.685948 | − | 0.727651i | \(-0.740612\pi\) |
0.287190 | + | 0.957874i | \(0.407279\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.8754 | − | 24.0329i | 0.776875 | − | 1.34559i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0676757i | 0.00376558i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.3179 | − | 6.53438i | 0.627803 | − | 0.362462i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.58540 | − | 14.8704i | −0.471897 | − | 0.817349i | 0.527586 | − | 0.849501i | \(-0.323097\pi\) |
−0.999483 | + | 0.0321526i | \(0.989764\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.98170 | + | 8.62856i | −0.272179 | + | 0.471428i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.95399 | + | 6.84850i | 0.215387 | + | 0.373062i | 0.953392 | − | 0.301733i | \(-0.0975653\pi\) |
−0.738005 | + | 0.674795i | \(0.764232\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.2779 | + | 21.2659i | −0.664883 | + | 1.15161i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.443850 | + | 0.256257i | 0.0238271 | + | 0.0137566i | 0.511866 | − | 0.859065i | \(-0.328954\pi\) |
−0.488039 | + | 0.872822i | \(0.662288\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.74612 | + | 3.31752i | 0.307583 | + | 0.177583i | 0.645844 | − | 0.763469i | \(-0.276506\pi\) |
−0.338262 | + | 0.941052i | \(0.609839\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0687 | 0.961702 | 0.480851 | − | 0.876802i | \(-0.340328\pi\) | ||||
0.480851 | + | 0.876802i | \(0.340328\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 19.2693i | − | 1.02271i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.52677 | + | 0.881479i | 0.0805796 | + | 0.0465227i | 0.539748 | − | 0.841826i | \(-0.318519\pi\) |
−0.459169 | + | 0.888349i | \(0.651853\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.48586 | − | 16.4300i | −0.499256 | − | 0.864737i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.2081 | + | 5.89367i | −0.534318 | + | 0.308489i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 33.4417i | − | 1.74564i | −0.488038 | − | 0.872822i | \(-0.662287\pi\) | ||
0.488038 | − | 0.872822i | \(-0.337713\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.5688 | 1.32390 | 0.661952 | − | 0.749546i | \(-0.269728\pi\) | ||||
0.661952 | + | 0.749546i | \(0.269728\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −43.0267 | −2.21599 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.7920 | 1.32485 | 0.662423 | − | 0.749130i | \(-0.269528\pi\) | ||||
0.662423 | + | 0.749130i | \(0.269528\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.8316 | 1.67762 | 0.838808 | − | 0.544427i | \(-0.183253\pi\) | ||||
0.838808 | + | 0.544427i | \(0.183253\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.1544i | 1.02187i | 0.859619 | + | 0.510935i | \(0.170701\pi\) | ||||
−0.859619 | + | 0.510935i | \(0.829299\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.09663 | + | 1.78784i | −0.156603 | + | 0.0904150i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.01813 | + | 1.76346i | 0.0512278 | + | 0.0887291i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.2125 | + | 17.4432i | 1.51632 | + | 0.875449i | 0.999816 | + | 0.0191652i | \(0.00610086\pi\) |
0.516506 | + | 0.856284i | \(0.327232\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.66245i | 0.482520i | 0.970461 | + | 0.241260i | \(0.0775606\pi\) | ||||
−0.970461 | + | 0.241260i | \(0.922439\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38.0727 | 1.89654 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.1897 | − | 12.2339i | −1.05034 | − | 0.606412i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.1202 | − | 18.5446i | −1.58824 | − | 0.916973i | −0.993597 | − | 0.112986i | \(-0.963958\pi\) |
−0.594647 | − | 0.803987i | \(-0.702708\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.305709 | − | 0.529504i | 0.0150067 | − | 0.0259923i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.84193 | − | 3.19031i | −0.0899841 | − | 0.155857i | 0.817520 | − | 0.575900i | \(-0.195348\pi\) |
−0.907504 | + | 0.420043i | \(0.862015\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.55139 | + | 14.8114i | −0.416769 | + | 0.721866i | −0.995612 | − | 0.0935732i | \(-0.970171\pi\) |
0.578843 | + | 0.815439i | \(0.303504\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.434342 | − | 0.752303i | −0.0210687 | − | 0.0364921i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.3242 | − | 15.7756i | 1.31616 | − | 0.759885i | 0.333051 | − | 0.942909i | \(-0.391922\pi\) |
0.983108 | + | 0.183024i | \(0.0585887\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10.0692i | − | 0.483893i | −0.970290 | − | 0.241947i | \(-0.922214\pi\) | ||
0.970290 | − | 0.241947i | \(-0.0777859\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.746890 | + | 1.29365i | −0.0357286 | + | 0.0618837i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.1966 | + | 13.9699i | −1.15484 | + | 0.666748i | −0.950062 | − | 0.312060i | \(-0.898981\pi\) |
−0.204779 | + | 0.978808i | \(0.565648\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.1930 | − | 17.4319i | 1.43451 | − | 0.828215i | 0.437050 | − | 0.899437i | \(-0.356023\pi\) |
0.997460 | + | 0.0712223i | \(0.0226900\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.33518 | + | 4.04466i | −0.110698 | + | 0.191735i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.2411i | 1.09682i | 0.836211 | + | 0.548408i | \(0.184766\pi\) | ||||
−0.836211 | + | 0.548408i | \(0.815234\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.1413 | + | 6.43244i | −0.524624 | + | 0.302892i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.10938 | + | 5.38560i | 0.145451 | + | 0.251928i | 0.929541 | − | 0.368719i | \(-0.120203\pi\) |
−0.784090 | + | 0.620647i | \(0.786870\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.17165 | − | 3.76140i | 0.101144 | − | 0.175186i | −0.811012 | − | 0.585029i | \(-0.801083\pi\) |
0.912156 | + | 0.409843i | \(0.134416\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.57451 | + | 6.19124i | 0.166122 | + | 0.287731i | 0.937053 | − | 0.349187i | \(-0.113542\pi\) |
−0.770931 | + | 0.636918i | \(0.780209\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.944451 | + | 1.63584i | −0.0437040 | + | 0.0756975i | −0.887050 | − | 0.461673i | \(-0.847249\pi\) |
0.843346 | + | 0.537371i | \(0.180583\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.2078 | − | 7.04818i | −0.561316 | − | 0.324076i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.314283 | − | 0.181451i | −0.0144203 | − | 0.00832555i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.4498 | −0.477465 | −0.238732 | − | 0.971085i | \(-0.576732\pi\) | ||||
−0.238732 | + | 0.971085i | \(0.576732\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 37.9364i | 1.72975i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.857895 | + | 0.495306i | 0.0389550 | + | 0.0224907i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.8298 | − | 20.4898i | −0.536060 | − | 0.928483i | −0.999111 | − | 0.0421513i | \(-0.986579\pi\) |
0.463052 | − | 0.886331i | \(-0.346754\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.6767 | − | 6.74152i | 0.526960 | − | 0.304241i | −0.212817 | − | 0.977092i | \(-0.568264\pi\) |
0.739778 | + | 0.672851i | \(0.234931\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.86000i | 0.128808i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.0807 | −0.540807 | −0.270403 | − | 0.962747i | \(-0.587157\pi\) | ||||
−0.270403 | + | 0.962747i | \(0.587157\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.5283 | −0.915310 | −0.457655 | − | 0.889130i | \(-0.651310\pi\) | ||||
−0.457655 | + | 0.889130i | \(0.651310\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.3417 | −1.03869 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.18085 | 0.362610 | 0.181305 | − | 0.983427i | \(-0.441968\pi\) | ||||
0.181305 | + | 0.983427i | \(0.441968\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.3626i | 0.897283i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.6603 | − | 17.1244i | 1.30446 | − | 0.753131i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.8746 | − | 24.0314i | −0.607856 | − | 1.05284i | −0.991593 | − | 0.129395i | \(-0.958697\pi\) |
0.383738 | − | 0.923442i | \(-0.374637\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.8843 | − | 11.4802i | −0.869478 | − | 0.501993i | −0.00230311 | − | 0.999997i | \(-0.500733\pi\) |
−0.867175 | + | 0.498004i | \(0.834066\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 2.53071i | − | 0.110239i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −55.9246 | −2.43151 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.2742 | + | 9.97325i | 0.748228 | + | 0.431990i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.8536 | + | 15.5039i | 1.16098 | + | 0.670292i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.60405 | + | 4.51035i | −0.111957 | + | 0.193915i | −0.916559 | − | 0.399899i | \(-0.869045\pi\) |
0.804602 | + | 0.593814i | \(0.202379\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.28902 | + | 16.0890i | 0.397898 | + | 0.689179i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.6224 | − | 18.3985i | 0.454181 | − | 0.786664i | −0.544460 | − | 0.838787i | \(-0.683265\pi\) |
0.998641 | + | 0.0521229i | \(0.0165988\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.597397 | + | 1.03472i | 0.0254500 | + | 0.0440807i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.0945 | − | 6.40543i | 0.470090 | − | 0.271407i | −0.246187 | − | 0.969222i | \(-0.579178\pi\) |
0.716277 | + | 0.697816i | \(0.245844\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.8559i | 0.924406i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.7396 | + | 32.4580i | −0.789781 | + | 1.36794i | 0.136319 | + | 0.990665i | \(0.456473\pi\) |
−0.926101 | + | 0.377277i | \(0.876861\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.4207 | + | 7.17109i | −0.522542 | + | 0.301690i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.94906 | + | 3.43469i | −0.249397 | + | 0.143990i | −0.619488 | − | 0.785006i | \(-0.712660\pi\) |
0.370091 | + | 0.928996i | \(0.379327\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.0847909 | + | 0.146862i | −0.00354839 | + | 0.00614599i | −0.867794 | − | 0.496924i | \(-0.834463\pi\) |
0.864246 | + | 0.503070i | \(0.167796\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 19.1741i | − | 0.799617i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.41193 | − | 3.12458i | 0.225302 | − | 0.130078i | −0.383101 | − | 0.923706i | \(-0.625144\pi\) |
0.608403 | + | 0.793628i | \(0.291811\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.1527 | − | 19.3171i | −0.461900 | − | 0.800033i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.7881 | − | 18.6855i | 0.445273 | − | 0.771235i | −0.552799 | − | 0.833315i | \(-0.686440\pi\) |
0.998071 | + | 0.0620801i | \(0.0197734\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.528615 | − | 0.915588i | −0.0217812 | − | 0.0377261i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.13036 | − | 7.15399i | 0.169613 | − | 0.293779i | −0.768671 | − | 0.639645i | \(-0.779081\pi\) |
0.938284 | + | 0.345866i | \(0.112415\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.7618 | − | 17.7603i | −1.25689 | − | 0.725667i | −0.284422 | − | 0.958699i | \(-0.591802\pi\) |
−0.972469 | + | 0.233033i | \(0.925135\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.8981 | − | 20.7258i | −1.46432 | − | 0.845423i | −0.465109 | − | 0.885254i | \(-0.653985\pi\) |
−0.999206 | + | 0.0398308i | \(0.987318\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.16776 | 0.291411 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.41990i | 0.0982206i | 0.998793 | + | 0.0491103i | \(0.0156386\pi\) | ||||
−0.998793 | + | 0.0491103i | \(0.984361\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −45.9873 | − | 26.5508i | −1.86045 | − | 1.07413i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.3228 | + | 36.9321i | 0.861219 | + | 1.49168i | 0.870753 | + | 0.491720i | \(0.163632\pi\) |
−0.00953416 | + | 0.999955i | \(0.503035\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.2535 | + | 7.65193i | −0.533567 | + | 0.308055i | −0.742468 | − | 0.669882i | \(-0.766345\pi\) |
0.208901 | + | 0.977937i | \(0.433011\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.6178i | 1.11005i | 0.831833 | + | 0.555026i | \(0.187292\pi\) | ||||
−0.831833 | + | 0.555026i | \(0.812708\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.55034 | −0.382014 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.52164 | 0.100545 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.28775 | 0.329930 | 0.164965 | − | 0.986299i | \(-0.447249\pi\) | ||||
0.164965 | + | 0.986299i | \(0.447249\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.9214 | 0.711188 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.91088i | 0.391456i | 0.980658 | + | 0.195728i | \(0.0627070\pi\) | ||||
−0.980658 | + | 0.195728i | \(0.937293\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.83668 | + | 3.94716i | −0.269612 | + | 0.155661i | −0.628711 | − | 0.777639i | \(-0.716417\pi\) |
0.359099 | + | 0.933299i | \(0.383084\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.15966 | + | 3.74063i | 0.0849049 | + | 0.147060i | 0.905351 | − | 0.424665i | \(-0.139608\pi\) |
−0.820446 | + | 0.571724i | \(0.806275\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.2308 | − | 8.79348i | −0.597859 | − | 0.345174i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.3997i | 1.69836i | 0.528102 | + | 0.849181i | \(0.322904\pi\) | ||||
−0.528102 | + | 0.849181i | \(0.677096\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.6788 | −0.417256 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.34894 | + | 5.39761i | 0.364183 | + | 0.210261i | 0.670914 | − | 0.741535i | \(-0.265902\pi\) |
−0.306731 | + | 0.951796i | \(0.599235\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.39495 | − | 1.96008i | −0.132048 | − | 0.0762381i | 0.432521 | − | 0.901624i | \(-0.357624\pi\) |
−0.564569 | + | 0.825386i | \(0.690958\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.5638 | + | 54.6701i | −1.22216 | + | 2.11683i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.0039 | + | 17.3273i | 0.386197 | + | 0.668913i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.3404 | + | 21.3742i | −0.475687 | + | 0.823915i | −0.999612 | − | 0.0278497i | \(-0.991134\pi\) |
0.523925 | + | 0.851765i | \(0.324467\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.36327 | + | 12.7536i | 0.282994 | + | 0.490159i | 0.972121 | − | 0.234481i | \(-0.0753392\pi\) |
−0.689127 | + | 0.724641i | \(0.742006\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.60128 | − | 0.924499i | 0.0612712 | − | 0.0353750i | −0.469051 | − | 0.883171i | \(-0.655404\pi\) |
0.530323 | + | 0.847796i | \(0.322071\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.0606i | 1.07214i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17.2919 | + | 29.9505i | −0.658769 | + | 1.14102i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.7613 | − | 19.4921i | 1.28434 | − | 0.741514i | 0.306701 | − | 0.951806i | \(-0.400775\pi\) |
0.977639 | + | 0.210292i | \(0.0674415\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.14764 | + | 4.12669i | −0.271126 | + | 0.156534i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.662926 | − | 1.14822i | 0.0251101 | − | 0.0434920i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 25.4389i | − | 0.960813i | −0.877046 | − | 0.480406i | \(-0.840489\pi\) | ||
0.877046 | − | 0.480406i | \(-0.159511\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.912310 | − | 0.526722i | 0.0344084 | − | 0.0198657i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.14517 | + | 12.3758i | 0.268342 | + | 0.464783i | 0.968434 | − | 0.249270i | \(-0.0801908\pi\) |
−0.700092 | + | 0.714053i | \(0.746857\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.9296 | − | 48.3756i | 1.04597 | − | 1.81168i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.9319 | − | 34.5230i | −0.745410 | − | 1.29109i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.7344 | + | 28.9848i | −0.624088 | + | 1.08095i | 0.364629 | + | 0.931153i | \(0.381196\pi\) |
−0.988716 | + | 0.149799i | \(0.952137\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.2817 | − | 7.66819i | −0.493269 | − | 0.284789i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.1354 | − | 7.00636i | −0.450076 | − | 0.259851i | 0.257786 | − | 0.966202i | \(-0.417007\pi\) |
−0.707862 | + | 0.706350i | \(0.750340\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.45277 | 0.0537326 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 27.3077i | − | 1.00863i | −0.863519 | − | 0.504316i | \(-0.831745\pi\) | ||
0.863519 | − | 0.504316i | \(-0.168255\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −19.9899 | − | 11.5412i | −0.736339 | − | 0.425126i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.3157 | + | 45.5801i | 0.968039 | + | 1.67669i | 0.701220 | + | 0.712945i | \(0.252639\pi\) |
0.266819 | + | 0.963747i | \(0.414027\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.9523 | − | 17.8703i | 1.13553 | − | 0.655599i | 0.190211 | − | 0.981743i | \(-0.439083\pi\) |
0.945320 | + | 0.326144i | \(0.105750\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.91243i | 0.326526i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.1282 | −1.20887 | −0.604433 | − | 0.796656i | \(-0.706600\pi\) | ||||
−0.604433 | + | 0.796656i | \(0.706600\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.5836 | 0.894687 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.6903 | −0.497584 | −0.248792 | − | 0.968557i | \(-0.580034\pi\) | ||||
−0.248792 | + | 0.968557i | \(0.580034\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.0347 | −0.472509 | −0.236255 | − | 0.971691i | \(-0.575920\pi\) | ||||
−0.236255 | + | 0.971691i | \(0.575920\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.2679i | 0.984588i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.4866 | − | 10.6732i | 0.666642 | − | 0.384886i | −0.128161 | − | 0.991753i | \(-0.540907\pi\) |
0.794803 | + | 0.606867i | \(0.207574\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.73940 | − | 9.94093i | −0.206432 | − | 0.357550i | 0.744156 | − | 0.668006i | \(-0.232852\pi\) |
−0.950588 | + | 0.310455i | \(0.899518\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.7525 | + | 6.78529i | 0.422161 | + | 0.243735i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 0.553889i | − | 0.0198451i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44.6416 | 1.59740 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.9873 | − | 15.0038i | −0.927528 | − | 0.535509i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.6808 | − | 20.6003i | −1.27188 | − | 0.734322i | −0.296541 | − | 0.955020i | \(-0.595833\pi\) |
−0.975342 | + | 0.220698i | \(0.929166\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.5107 | − | 26.8653i | 0.550801 | − | 0.954016i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.0066 | + | 43.3127i | 0.885779 | + | 1.53421i | 0.844819 | + | 0.535053i | \(0.179708\pi\) |
0.0409600 | + | 0.999161i | \(0.486958\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.76484 | + | 3.05679i | −0.0624355 | + | 0.108141i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.6540 | − | 23.6494i | −0.481838 | − | 0.834568i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.8995 | + | 25.3454i | −1.54343 | + | 0.891097i | −0.544807 | + | 0.838562i | \(0.683397\pi\) |
−0.998619 | + | 0.0525356i | \(0.983270\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 8.96566i | − | 0.314827i | −0.987533 | − | 0.157413i | \(-0.949684\pi\) | ||
0.987533 | − | 0.157413i | \(-0.0503155\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.0812910 | + | 0.140800i | −0.00284750 | + | 0.00493201i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.525599 | − | 0.303455i | 0.0183884 | − | 0.0106165i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.2190 | − | 16.2922i | 0.984849 | − | 0.568603i | 0.0811184 | − | 0.996704i | \(-0.474151\pi\) |
0.903731 | + | 0.428102i | \(0.140817\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.0877 | − | 17.4724i | 0.351636 | − | 0.609051i | −0.634901 | − | 0.772594i | \(-0.718959\pi\) |
0.986536 | + | 0.163543i | \(0.0522923\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 0.253288i | − | 0.00880770i | −0.999990 | − | 0.00440385i | \(-0.998598\pi\) | ||
0.999990 | − | 0.00440385i | \(-0.00140179\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.10909 | − | 3.52708i | 0.212177 | − | 0.122501i | −0.390146 | − | 0.920753i | \(-0.627575\pi\) |
0.602323 | + | 0.798253i | \(0.294242\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.17848 | + | 7.23733i | 0.144602 | + | 0.250458i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.0936 | + | 29.6069i | −0.590136 | + | 1.02215i | 0.404078 | + | 0.914725i | \(0.367592\pi\) |
−0.994214 | + | 0.107420i | \(0.965741\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.7462 | + | 18.6130i | 0.370558 | + | 0.641826i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.9463 | + | 34.5480i | −0.686174 | + | 1.18849i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 48.2024 | + | 27.8296i | 1.65236 | + | 0.953988i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.7586 | + | 12.5623i | 0.745000 | + | 0.430126i | 0.823884 | − | 0.566758i | \(-0.191802\pi\) |
−0.0788844 | + | 0.996884i | \(0.525136\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.1907 | 1.44121 | 0.720604 | − | 0.693347i | \(-0.243865\pi\) | ||||
0.720604 | + | 0.693347i | \(0.243865\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 4.71278i | − | 0.160798i | −0.996763 | − | 0.0803990i | \(-0.974381\pi\) | ||
0.996763 | − | 0.0803990i | \(-0.0256195\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.8409 | − | 17.8060i | −1.04984 | − | 0.606123i | −0.127232 | − | 0.991873i | \(-0.540609\pi\) |
−0.922603 | + | 0.385750i | \(0.873943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.4750 | + | 21.6074i | 0.424163 | + | 0.734672i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.08543 | + | 2.35873i | −0.138589 | + | 0.0800143i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.7884i | 1.21264i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.9064 | 1.38131 | 0.690655 | − | 0.723184i | \(-0.257322\pi\) | ||||
0.690655 | + | 0.723184i | \(0.257322\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.4443 | 1.26153 | 0.630765 | − | 0.775974i | \(-0.282741\pi\) | ||||
0.630765 | + | 0.775974i | \(0.282741\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.8357 | −1.67711 | −0.838553 | − | 0.544821i | \(-0.816598\pi\) | ||||
−0.838553 | + | 0.544821i | \(0.816598\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.8965 | 0.970248 | 0.485124 | − | 0.874445i | \(-0.338774\pi\) | ||||
0.485124 | + | 0.874445i | \(0.338774\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.47456i | 0.0493443i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.999223 | − | 0.576902i | 0.0334003 | − | 0.0192837i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −22.3394 | − | 38.6930i | −0.745062 | − | 1.29048i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.99082 | + | 1.14940i | 0.0663238 | + | 0.0382920i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.2287i | 0.439738i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.8700 | −0.493749 | −0.246874 | − | 0.969048i | \(-0.579403\pi\) | ||||
−0.246874 | + | 0.969048i | \(0.579403\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.81616 | − | 4.51266i | −0.258961 | − | 0.149511i | 0.364899 | − | 0.931047i | \(-0.381103\pi\) |
−0.623861 | + | 0.781536i | \(0.714437\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.22671 | + | 0.708243i | 0.0405982 | + | 0.0234394i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.2083 | − | 22.8774i | 0.435702 | − | 0.754657i | −0.561651 | − | 0.827374i | \(-0.689834\pi\) |
0.997353 | + | 0.0727170i | \(0.0231670\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −34.6075 | − | 59.9420i | −1.13912 | − | 1.97302i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.76100 | + | 11.7104i | −0.222300 | + | 0.385036i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.1259 | + | 19.2706i | 0.365029 | + | 0.632249i | 0.988781 | − | 0.149373i | \(-0.0477257\pi\) |
−0.623752 | + | 0.781623i | \(0.714392\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.29476 | + | 1.32488i | −0.0750465 | + | 0.0433281i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.6822i | 0.479647i | 0.970817 | + | 0.239823i | \(0.0770896\pi\) | ||||
−0.970817 | + | 0.239823i | \(0.922910\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.0396 | − | 39.9058i | 0.751070 | − | 1.30089i | −0.196235 | − | 0.980557i | \(-0.562871\pi\) |
0.947305 | − | 0.320334i | \(-0.103795\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.3442 | − | 14.6325i | 0.825322 | − | 0.476500i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.96116 | + | 4.01903i | −0.226207 | + | 0.130601i | −0.608821 | − | 0.793308i | \(-0.708357\pi\) |
0.382614 | + | 0.923908i | \(0.375024\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.1700 | + | 36.6675i | −0.687206 | + | 1.19028i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.9348i | 1.77951i | 0.456437 | + | 0.889756i | \(0.349125\pi\) | ||||
−0.456437 | + | 0.889756i | \(0.650875\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.6060 | + | 16.5157i | −0.925667 | + | 0.534434i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.26733 | + | 7.39124i | 0.137656 | + | 0.238427i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.4770 | − | 26.8070i | 0.498223 | − | 0.862948i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.5917 | − | 46.0582i | −0.855132 | − | 1.48113i | −0.876522 | − | 0.481361i | \(-0.840143\pi\) |
0.0213900 | − | 0.999771i | \(-0.493191\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.61403 | − | 13.1879i | 0.244346 | − | 0.423219i | −0.717602 | − | 0.696454i | \(-0.754760\pi\) |
0.961947 | + | 0.273234i | \(0.0880935\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.49418 | − | 0.862667i | −0.0478031 | − | 0.0275992i | 0.475908 | − | 0.879495i | \(-0.342120\pi\) |
−0.523711 | + | 0.851896i | \(0.675453\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.37033 | − | 5.40997i | −0.299477 | − | 0.172903i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −60.2383 | −1.92130 | −0.960651 | − | 0.277758i | \(-0.910409\pi\) | ||||
−0.960651 | + | 0.277758i | \(0.910409\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 9.98485i | − | 0.318144i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.7703 | + | 16.0332i | 0.883044 | + | 0.509826i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.87312 | − | 4.97639i | −0.0912676 | − | 0.158080i | 0.816777 | − | 0.576953i | \(-0.195759\pi\) |
−0.908045 | + | 0.418873i | \(0.862425\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.9711 | + | 13.2624i | −0.728234 | + | 0.420446i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.0259240i | 0.000821020i | 1.00000 | 0.000410510i | \(0.000130669\pi\) | |||||
−1.00000 | 0.000410510i | \(0.999869\pi\) | ||||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))