Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(293,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.293");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.x (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.0856109166\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 293.2 | ||
Root | \(-1.61108 - 0.635951i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.293 |
Dual form | 1764.2.x.b.1469.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.55979 | + | 0.753039i | −0.900543 | + | 0.434767i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.09150 | + | 1.89054i | −0.488134 | + | 0.845473i | −0.999907 | − | 0.0136476i | \(-0.995656\pi\) |
0.511773 | + | 0.859121i | \(0.328989\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.86586 | − | 2.34916i | 0.621955 | − | 0.783053i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.26889 | − | 0.732592i | 0.382584 | − | 0.220885i | −0.296358 | − | 0.955077i | \(-0.595772\pi\) |
0.678942 | + | 0.734192i | \(0.262439\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.92752 | − | 1.69021i | −0.811948 | − | 0.468779i | 0.0356837 | − | 0.999363i | \(-0.488639\pi\) |
−0.847632 | + | 0.530585i | \(0.821972\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.278862 | − | 3.77077i | 0.0720017 | − | 0.973610i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.64271 | 0.640952 | 0.320476 | − | 0.947257i | \(-0.396157\pi\) | ||||
0.320476 | + | 0.947257i | \(0.396157\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.94221i | 1.82207i | 0.412331 | + | 0.911034i | \(0.364715\pi\) | ||||
−0.412331 | + | 0.911034i | \(0.635285\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.47245 | + | 2.00482i | 0.724056 | + | 0.418034i | 0.816244 | − | 0.577708i | \(-0.196053\pi\) |
−0.0921879 | + | 0.995742i | \(0.529386\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.117249 | + | 0.203081i | 0.0234498 | + | 0.0406163i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.14134 | + | 5.06925i | −0.219651 | + | 0.975578i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.71261 | + | 3.87553i | −1.24650 | + | 0.719667i | −0.970410 | − | 0.241464i | \(-0.922372\pi\) |
−0.276091 | + | 0.961132i | \(0.589039\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.612252 | − | 0.353484i | −0.109964 | − | 0.0634876i | 0.444009 | − | 0.896022i | \(-0.353556\pi\) |
−0.553973 | + | 0.832534i | \(0.686889\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.42752 | + | 2.09821i | −0.248500 | + | 0.365251i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.83477 | −0.466033 | −0.233016 | − | 0.972473i | \(-0.574860\pi\) | ||||
−0.233016 | + | 0.972473i | \(0.574860\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.83910 | + | 0.431821i | 0.935004 | + | 0.0691467i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.74173 | + | 6.48086i | −0.584360 | + | 1.01214i | 0.410595 | + | 0.911818i | \(0.365321\pi\) |
−0.994955 | + | 0.100323i | \(0.968012\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.27112 | − | 2.20164i | −0.193844 | − | 0.335748i | 0.752677 | − | 0.658390i | \(-0.228762\pi\) |
−0.946521 | + | 0.322642i | \(0.895429\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.40458 | + | 6.09160i | 0.358453 | + | 0.908081i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.27538 | − | 10.8693i | −0.915358 | − | 1.58545i | −0.806376 | − | 0.591403i | \(-0.798574\pi\) |
−0.108983 | − | 0.994044i | \(-0.534759\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.12207 | + | 1.99006i | −0.577205 | + | 0.278665i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2.79062i | − | 0.383321i | −0.981461 | − | 0.191661i | \(-0.938613\pi\) | ||
0.981461 | − | 0.191661i | \(-0.0613873\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.19850i | 0.431286i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.98079 | − | 12.3881i | −0.792176 | − | 1.64085i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.71650 | − | 11.6333i | 0.874414 | − | 1.51453i | 0.0170287 | − | 0.999855i | \(-0.494579\pi\) |
0.857385 | − | 0.514675i | \(-0.172087\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.75061 | + | 3.89747i | −0.864327 | + | 0.499020i | −0.865459 | − | 0.500980i | \(-0.832973\pi\) |
0.00113176 | + | 0.999999i | \(0.499640\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.39079 | − | 3.68972i | 0.792680 | − | 0.457654i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.92029 | + | 5.05809i | −0.356770 | + | 0.617945i | −0.987419 | − | 0.158124i | \(-0.949455\pi\) |
0.630649 | + | 0.776068i | \(0.282789\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.92598 | − | 0.512200i | −0.833791 | − | 0.0616616i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.6854i | − | 1.38680i | −0.720554 | − | 0.693398i | \(-0.756113\pi\) | ||
0.720554 | − | 0.693398i | \(-0.243887\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.57174i | 0.535082i | 0.963547 | + | 0.267541i | \(0.0862110\pi\) | ||||
−0.963547 | + | 0.267541i | \(0.913789\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.335812 | − | 0.228470i | −0.0387762 | − | 0.0263815i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.69189 | − | 8.12659i | −0.527879 | − | 0.914312i | −0.999472 | − | 0.0324963i | \(-0.989654\pi\) |
0.471593 | − | 0.881816i | \(-0.343679\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.03710 | − | 8.76643i | −0.226344 | − | 0.974047i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.70847 | − | 2.95917i | −0.187529 | − | 0.324811i | 0.756896 | − | 0.653535i | \(-0.226715\pi\) |
−0.944426 | + | 0.328724i | \(0.893381\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.88452 | + | 4.99614i | −0.312871 | + | 0.541908i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.55181 | − | 11.0999i | 0.809639 | − | 1.19003i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.23875 | 0.979306 | 0.489653 | − | 0.871918i | \(-0.337124\pi\) | ||||
0.489653 | + | 0.871918i | \(0.337124\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.22117 | + | 0.0903097i | 0.126629 | + | 0.00936468i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.0150 | − | 8.66894i | −1.54051 | − | 0.889414i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.38394 | + | 3.68577i | −0.648191 | + | 0.374233i | −0.787763 | − | 0.615979i | \(-0.788761\pi\) |
0.139572 | + | 0.990212i | \(0.455427\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.646596 | − | 4.34773i | 0.0649853 | − | 0.436964i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.96357 | − | 6.86510i | −0.394390 | − | 0.683103i | 0.598633 | − | 0.801023i | \(-0.295711\pi\) |
−0.993023 | + | 0.117920i | \(0.962377\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.26825 | − | 1.88693i | −0.322031 | − | 0.185924i | 0.330267 | − | 0.943888i | \(-0.392861\pi\) |
−0.652297 | + | 0.757963i | \(0.726195\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.94712i | 0.768277i | 0.923275 | + | 0.384138i | \(0.125501\pi\) | ||||
−0.923275 | + | 0.384138i | \(0.874499\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.01028 | −0.0967677 | −0.0483838 | − | 0.998829i | \(-0.515407\pi\) | ||||
−0.0483838 | + | 0.998829i | \(0.515407\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.42163 | − | 2.13469i | 0.419682 | − | 0.202616i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.5557 | − | 6.09431i | −0.992992 | − | 0.573304i | −0.0868250 | − | 0.996224i | \(-0.527672\pi\) |
−0.906167 | + | 0.422919i | \(0.861005\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.58037 | + | 4.37653i | −0.706873 | + | 0.408113i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.43292 | + | 3.72352i | −0.872074 | + | 0.344239i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.42662 | + | 7.66713i | −0.402420 | + | 0.697012i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.955953 | − | 12.9264i | 0.0861954 | − | 1.16554i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.4269 | −1.02206 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.79350 | 0.602826 | 0.301413 | − | 0.953494i | \(-0.402542\pi\) | ||||
0.301413 | + | 0.953494i | \(0.402542\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.64060 | + | 2.47689i | 0.320537 | + | 0.218078i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.86790 | + | 11.8956i | −0.600051 | + | 1.03932i | 0.392761 | + | 0.919640i | \(0.371520\pi\) |
−0.992813 | + | 0.119679i | \(0.961813\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.33783 | − | 7.69085i | −0.717606 | − | 0.661923i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.4028 | + | 10.0475i | −1.48682 | + | 0.858416i | −0.999887 | − | 0.0150235i | \(-0.995218\pi\) |
−0.486933 | + | 0.873439i | \(0.661884\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.51403 | − | 4.91558i | −0.722151 | − | 0.416934i | 0.0933930 | − | 0.995629i | \(-0.470229\pi\) |
−0.815544 | + | 0.578695i | \(0.803562\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.9732 | + | 12.2281i | 1.51362 | + | 1.02980i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.95292 | −0.414184 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 16.9206i | − | 1.40518i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.3512 | − | 10.0177i | −1.42146 | − | 0.820682i | −0.425038 | − | 0.905175i | \(-0.639739\pi\) |
−0.996424 | + | 0.0844939i | \(0.973073\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.1168 | + | 19.2549i | 0.904675 | + | 1.56694i | 0.821353 | + | 0.570420i | \(0.193220\pi\) |
0.0833218 | + | 0.996523i | \(0.473447\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.93094 | − | 6.20815i | 0.398643 | − | 0.501899i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.33655 | − | 0.771657i | 0.107354 | − | 0.0619810i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.95305 | − | 4.01435i | −0.554914 | − | 0.320380i | 0.196188 | − | 0.980566i | \(-0.437144\pi\) |
−0.751102 | + | 0.660187i | \(0.770477\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.10145 | + | 4.35277i | 0.166656 | + | 0.345197i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.4521 | 0.975323 | 0.487661 | − | 0.873033i | \(-0.337850\pi\) | ||||
0.487661 | + | 0.873033i | \(0.337850\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.40860 | − | 4.98898i | −0.187509 | − | 0.388391i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.85984 | − | 17.0777i | 0.762978 | − | 1.32152i | −0.178332 | − | 0.983970i | \(-0.557070\pi\) |
0.941309 | − | 0.337546i | \(-0.109597\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.786412 | − | 1.36211i | −0.0604933 | − | 0.104777i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.6575 | + | 14.8191i | 1.42678 | + | 1.13324i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.913733 | + | 1.58263i | 0.0694699 | + | 0.120325i | 0.898668 | − | 0.438629i | \(-0.144536\pi\) |
−0.829198 | + | 0.558955i | \(0.811203\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.71596 | + | 23.2033i | −0.128980 | + | 1.74407i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.9929i | 1.04588i | 0.852370 | + | 0.522939i | \(0.175164\pi\) | ||||
−0.852370 | + | 0.522939i | \(0.824836\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.3594i | 1.21599i | 0.793942 | + | 0.607994i | \(0.208025\pi\) | ||||
−0.793942 | + | 0.607994i | \(0.791975\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.59456 | − | 11.1627i | 0.561406 | − | 0.825170i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.09415 | − | 5.35923i | 0.227486 | − | 0.394018i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.35330 | − | 1.93603i | 0.245218 | − | 0.141577i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.8326 | − | 6.83153i | 0.856173 | − | 0.494312i | −0.00655557 | − | 0.999979i | \(-0.502087\pi\) |
0.862729 | + | 0.505667i | \(0.168753\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.18885 | − | 3.79119i | 0.157557 | − | 0.272896i | −0.776430 | − | 0.630203i | \(-0.782972\pi\) |
0.933987 | + | 0.357307i | \(0.116305\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.18976 | + | 10.5677i | −0.514869 | + | 0.756768i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.00603i | 0.0716767i | 0.999358 | + | 0.0358384i | \(0.0114101\pi\) | ||||
−0.999358 | + | 0.0358384i | \(0.988590\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.55453i | 0.464638i | 0.972640 | + | 0.232319i | \(0.0746313\pi\) | ||||
−0.972640 | + | 0.232319i | \(0.925369\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.746089 | − | 10.0886i | 0.0526251 | − | 0.711598i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.16820 | − | 14.1477i | −0.570492 | − | 0.988121i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.1888 | − | 4.41661i | 0.777673 | − | 0.306976i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.81840 | + | 10.0778i | 0.402467 | + | 0.697094i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.11202 | + | 15.7825i | −0.627297 | + | 1.08651i | 0.360794 | + | 0.932645i | \(0.382506\pi\) |
−0.988092 | + | 0.153866i | \(0.950828\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.79953 | + | 18.2267i | 0.602934 | + | 1.24887i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.54972 | 0.378487 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.44270 | − | 7.13094i | −0.232636 | − | 0.481864i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.73660 | − | 4.46673i | −0.520420 | − | 0.300464i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.71705 | − | 5.03279i | 0.583737 | − | 0.337021i | −0.178880 | − | 0.983871i | \(-0.557247\pi\) |
0.762617 | + | 0.646850i | \(0.223914\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.695841 | + | 0.103486i | 0.0463894 | + | 0.00689904i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.94372 | − | 17.2230i | −0.659988 | − | 1.14313i | −0.980618 | − | 0.195928i | \(-0.937228\pi\) |
0.320630 | − | 0.947204i | \(-0.396105\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.3854 | − | 8.88275i | −1.01669 | − | 0.586988i | −0.103549 | − | 0.994624i | \(-0.533020\pi\) |
−0.913145 | + | 0.407636i | \(0.866353\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.0592i | 1.05208i | 0.850461 | + | 0.526038i | \(0.176323\pi\) | ||||
−0.850461 | + | 0.526038i | \(0.823677\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.3983 | 1.78727 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.4380 | + | 9.14256i | 0.872890 | + | 0.593873i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.11117 | − | 4.10564i | −0.459983 | − | 0.265572i | 0.252054 | − | 0.967713i | \(-0.418894\pi\) |
−0.712037 | + | 0.702142i | \(0.752227\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.6614 | + | 14.2382i | −1.58858 | + | 0.917166i | −0.595037 | + | 0.803698i | \(0.702863\pi\) |
−0.993542 | + | 0.113468i | \(0.963804\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.77890 | + | 12.1397i | 0.627316 | + | 0.778764i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.4240 | − | 23.2510i | 0.854147 | − | 1.47943i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.89322 | + | 3.32912i | 0.310095 | + | 0.210974i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.656343 | −0.0414280 | −0.0207140 | − | 0.999785i | \(-0.506594\pi\) | ||||
−0.0207140 | + | 0.999785i | \(0.506594\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.87486 | 0.369349 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.736951 | − | 9.96507i | 0.0461496 | − | 0.624037i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.82042 | − | 6.61716i | 0.238311 | − | 0.412767i | −0.721918 | − | 0.691978i | \(-0.756739\pi\) |
0.960230 | + | 0.279211i | \(0.0900728\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.42059 | + | 23.0002i | −0.211729 | + | 1.42368i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.73888 | − | 3.31334i | 0.353874 | − | 0.204310i | −0.312516 | − | 0.949913i | \(-0.601172\pi\) |
0.666390 | + | 0.745603i | \(0.267838\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.27577 | + | 3.04597i | 0.324088 | + | 0.187112i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.4105 | + | 6.95714i | −0.881907 | + | 0.425770i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.76693 | 0.534529 | 0.267265 | − | 0.963623i | \(-0.413880\pi\) | ||||
0.267265 | + | 0.963623i | \(0.413880\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.4669i | 1.00029i | 0.865941 | + | 0.500147i | \(0.166721\pi\) | ||||
−0.865941 | + | 0.500147i | \(0.833279\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.297551 | + | 0.171791i | 0.0179430 | + | 0.0103594i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.88732 | + | 15.3933i | 0.533987 | + | 0.924893i | 0.999212 | + | 0.0397001i | \(0.0126402\pi\) |
−0.465225 | + | 0.885193i | \(0.654026\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.97277 | + | 0.778725i | −0.118107 | + | 0.0466210i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.0252 | + | 8.09748i | −0.836676 | + | 0.483055i | −0.856133 | − | 0.516755i | \(-0.827140\pi\) |
0.0194568 | + | 0.999811i | \(0.493806\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.5717 | − | 14.1865i | −1.46063 | − | 0.843298i | −0.461594 | − | 0.887091i | \(-0.652722\pi\) |
−0.999041 | + | 0.0437937i | \(0.986056\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 29.9483 | + | 2.21478i | 1.77398 | + | 0.131192i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.0161 | −0.589181 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.18206 | − | 10.5564i | 0.421020 | − | 0.618826i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.38260 | − | 7.59088i | 0.256034 | − | 0.443464i | −0.709142 | − | 0.705066i | \(-0.750917\pi\) |
0.965176 | + | 0.261602i | \(0.0842507\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.6621 | + | 25.3956i | 0.853663 | + | 1.47859i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.26546 | + | 7.26845i | 0.131455 | + | 0.421758i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.77711 | − | 11.7383i | −0.391931 | − | 0.678844i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.3520 | + | 7.72337i | 0.652156 | + | 0.443696i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 17.0164i | − | 0.974354i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 12.8497i | − | 0.733372i | −0.930345 | − | 0.366686i | \(-0.880492\pi\) | ||
0.930345 | − | 0.366686i | \(-0.119508\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.51871 | + | 0.482080i | 0.370836 | + | 0.0274246i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.29671 | + | 5.71007i | −0.186939 | + | 0.323789i | −0.944228 | − | 0.329291i | \(-0.893190\pi\) |
0.757289 | + | 0.653080i | \(0.226523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.95711 | − | 1.70729i | 0.167146 | − | 0.0965018i | −0.414093 | − | 0.910234i | \(-0.635901\pi\) |
0.581239 | + | 0.813733i | \(0.302568\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.8003 | − | 16.0505i | 1.56142 | − | 0.901485i | 0.564304 | − | 0.825567i | \(-0.309145\pi\) |
0.997114 | − | 0.0759182i | \(-0.0241888\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.67836 | + | 9.83521i | −0.317927 | + | 0.550666i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.98449 | − | 12.3958i | −0.334022 | − | 0.691866i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.9890i | 1.16786i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 0.792700i | − | 0.0439711i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.57583 | − | 0.760783i | 0.0871435 | − | 0.0420714i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.4416 | + | 25.0137i | 0.793784 | + | 1.37487i | 0.923608 | + | 0.383338i | \(0.125225\pi\) |
−0.129824 | + | 0.991537i | \(0.541441\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.28929 | + | 6.65931i | −0.289851 | + | 0.364928i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.37501 | − | 11.0418i | −0.348304 | − | 0.603280i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.82568 | − | 8.35833i | 0.262872 | − | 0.455307i | −0.704132 | − | 0.710069i | \(-0.748664\pi\) |
0.967004 | + | 0.254762i | \(0.0819971\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.0538 | + | 1.55700i | 1.14349 | + | 0.0845647i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.03584 | −0.0560938 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.52806 | − | 12.5348i | 0.459135 | − | 0.674849i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.6758 | − | 6.16367i | −0.573106 | − | 0.330883i | 0.185283 | − | 0.982685i | \(-0.440680\pi\) |
−0.758389 | + | 0.651802i | \(0.774013\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.2211 | − | 5.90115i | 0.547123 | − | 0.315881i | −0.200838 | − | 0.979624i | \(-0.564366\pi\) |
0.747961 | + | 0.663743i | \(0.231033\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.9094 | − | 12.9112i | 0.635676 | − | 0.689151i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.59855 | − | 11.4290i | −0.351205 | − | 0.608305i | 0.635256 | − | 0.772302i | \(-0.280895\pi\) |
−0.986461 | + | 0.163997i | \(0.947561\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.0916 | + | 12.7546i | 1.17250 | + | 0.676943i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.03311i | 0.318416i | 0.987245 | + | 0.159208i | \(0.0508940\pi\) | ||||
−0.987245 | + | 0.159208i | \(0.949106\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −44.0787 | −2.31993 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.13093 | − | 15.2925i | 0.0593585 | − | 0.802648i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.64304 | − | 4.99006i | −0.452397 | − | 0.261192i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.8755 | − | 8.58836i | 0.776494 | − | 0.448309i | −0.0586924 | − | 0.998276i | \(-0.518693\pi\) |
0.835186 | + | 0.549967i | \(0.185360\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.24302 | + | 20.8823i | 0.429114 | + | 1.08709i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.35902 | + | 4.08595i | −0.122146 | + | 0.211562i | −0.920614 | − | 0.390475i | \(-0.872311\pi\) |
0.798468 | + | 0.602037i | \(0.205644\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.8236 | − | 8.60492i | 0.920405 | − | 0.444356i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.2017 | 1.34946 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.34015 | 0.479771 | 0.239886 | − | 0.970801i | \(-0.422890\pi\) | ||||
0.239886 | + | 0.970801i | \(0.422890\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.5964 | + | 5.11577i | −0.542870 | + | 0.262089i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.85036 | + | 4.93696i | −0.145646 | + | 0.252267i | −0.929614 | − | 0.368535i | \(-0.879860\pi\) |
0.783968 | + | 0.620802i | \(0.213193\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.54375 | − | 1.12191i | −0.383470 | − | 0.0570298i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.63671 | + | 3.83171i | −0.336495 | + | 0.194275i | −0.658721 | − | 0.752387i | \(-0.728902\pi\) |
0.322226 | + | 0.946663i | \(0.395569\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.17668 | + | 5.29816i | 0.464085 | + | 0.267939i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.75464 | − | 23.7263i | 0.0885100 | − | 1.19683i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.4848 | 1.03070 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1.30262i | − | 0.0653766i | −0.999466 | − | 0.0326883i | \(-0.989593\pi\) | ||
0.999466 | − | 0.0326883i | \(-0.0104069\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.18778 | + | 4.72722i | 0.408878 | + | 0.236066i | 0.690308 | − | 0.723516i | \(-0.257475\pi\) |
−0.281429 | + | 0.959582i | \(0.590809\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.19492 | + | 2.06966i | 0.0595233 | + | 0.103097i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.7967 | + | 5.71736i | 0.934018 | + | 0.284098i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.59700 | + | 2.07673i | −0.178296 | + | 0.102940i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.5182 | + | 9.53678i | 0.816771 | + | 0.471563i | 0.849302 | − | 0.527908i | \(-0.177023\pi\) |
−0.0325304 | + | 0.999471i | \(0.510357\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.5785 | − | 28.7769i | 0.965734 | − | 1.41946i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.45921 | 0.366158 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.9817 | + | 1.25585i | 0.831597 | + | 0.0614994i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.20003 | − | 7.27466i | 0.205185 | − | 0.355390i | −0.745007 | − | 0.667057i | \(-0.767554\pi\) |
0.950192 | + | 0.311666i | \(0.100887\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.7178 | + | 34.1522i | 0.960985 | + | 1.66448i | 0.720035 | + | 0.693938i | \(0.244126\pi\) |
0.240951 | + | 0.970537i | \(0.422541\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −37.2427 | − | 5.53874i | −1.81080 | − | 0.269303i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.309855 | + | 0.536685i | 0.0150302 | + | 0.0260331i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.72550 | − | 3.72974i | 0.372991 | − | 0.180074i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.9327i | 0.574777i | 0.957814 | + | 0.287389i | \(0.0927871\pi\) | ||||
−0.957814 | + | 0.287389i | \(0.907213\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 12.2121i | − | 0.586875i | −0.955978 | − | 0.293437i | \(-0.905201\pi\) | ||
0.955978 | − | 0.293437i | \(-0.0947992\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.7419 | + | 26.3925i | 0.610925 | + | 1.26542i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.9227 | + | 27.5789i | −0.761686 | + | 1.31928i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.4639 | + | 8.35076i | −0.690326 | + | 0.398560i | −0.803734 | − | 0.594989i | \(-0.797157\pi\) |
0.113408 | + | 0.993548i | \(0.463823\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.2403 | + | 15.1499i | −1.24672 | + | 0.719791i | −0.970453 | − | 0.241291i | \(-0.922429\pi\) |
−0.276262 | + | 0.961082i | \(0.589096\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.0841 | + | 17.4662i | −0.478033 | + | 0.827977i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 34.6078 | + | 2.55936i | 1.63689 | + | 0.121054i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.1253i | 1.42170i | 0.703343 | + | 0.710851i | \(0.251690\pi\) | ||||
−0.703343 | + | 0.710851i | \(0.748310\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.9646i | 0.516305i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −31.8396 | − | 21.6621i | −1.49595 | − | 1.01778i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.6159 | − | 21.8513i | −0.590146 | − | 1.02216i | −0.994212 | − | 0.107433i | \(-0.965737\pi\) |
0.404067 | − | 0.914730i | \(-0.367596\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.01624 | + | 13.3966i | −0.140786 | + | 0.625299i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.3174 | + | 21.3344i | 0.573680 | + | 0.993643i | 0.996184 | + | 0.0872820i | \(0.0278181\pi\) |
−0.422503 | + | 0.906361i | \(0.638849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.33215 | + | 10.9676i | −0.294280 | + | 0.509708i | −0.974817 | − | 0.223006i | \(-0.928413\pi\) |
0.680537 | + | 0.732713i | \(0.261746\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.50364 | + | 2.21009i | −0.0697298 | + | 0.102491i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.9445 | 0.969198 | 0.484599 | − | 0.874736i | \(-0.338966\pi\) | ||||
0.484599 | + | 0.874736i | \(0.338966\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.8682 | + | 1.02560i | 0.639014 | + | 0.0472573i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.22581 | − | 1.86242i | −0.148323 | − | 0.0856344i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.61291 | + | 0.931217i | −0.0740056 | + | 0.0427271i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.55562 | − | 5.20692i | −0.300161 | − | 0.238409i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.8852 | − | 27.5141i | −0.725816 | − | 1.25715i | −0.958637 | − | 0.284630i | \(-0.908129\pi\) |
0.232822 | − | 0.972519i | \(-0.425204\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.29884 | + | 4.79134i | 0.378394 | + | 0.218466i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 16.0921i | − | 0.730705i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.5642 | 1.61157 | 0.805784 | − | 0.592210i | \(-0.201744\pi\) | ||||
0.805784 | + | 0.592210i | \(0.201744\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.4226 | + | 9.37691i | −0.878320 | + | 0.424038i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.75734 | + | 1.59195i | 0.124437 | + | 0.0718437i | 0.560926 | − | 0.827866i | \(-0.310445\pi\) |
−0.436490 | + | 0.899709i | \(0.643778\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.7395 | + | 10.2419i | −0.798947 | + | 0.461272i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.51379 | + | 5.96797i | 0.337720 | + | 0.268240i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.0214 | + | 27.7498i | −0.717215 | + | 1.24225i | 0.244884 | + | 0.969552i | \(0.421250\pi\) |
−0.962099 | + | 0.272700i | \(0.912083\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.51904 | + | 34.0625i | −0.112542 | + | 1.52180i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.6608 | −0.519930 | −0.259965 | − | 0.965618i | \(-0.583711\pi\) | ||||
−0.259965 | + | 0.965618i | \(0.583711\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.3050 | 0.770061 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.25235 | + | 1.53239i | 0.100031 | + | 0.0680561i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.4427 | − | 23.2834i | 0.595836 | − | 1.03202i | −0.397592 | − | 0.917562i | \(-0.630154\pi\) |
0.993428 | − | 0.114457i | \(-0.0365127\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −40.2611 | − | 9.06478i | −1.77757 | − | 0.400220i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.13461 | − | 4.11917i | 0.314388 | − | 0.181512i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.9255 | − | 9.19459i | −0.700402 | − | 0.404378i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.61701 | − | 1.78049i | −0.114874 | − | 0.0781549i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.0771 | 1.49294 | 0.746471 | − | 0.665418i | \(-0.231746\pi\) | ||||
0.746471 | + | 0.665418i | \(0.231746\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.43867i | 0.237816i | 0.992905 | + | 0.118908i | \(0.0379394\pi\) | ||||
−0.992905 | + | 0.118908i | \(0.962061\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.61801 | − | 0.934157i | −0.0704815 | − | 0.0406925i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.46140 | − | 5.99532i | −0.150496 | − | 0.260666i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.7964 | − | 37.4843i | −0.642111 | − | 1.62668i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.9080 | − | 12.6486i | 0.948940 | − | 0.547871i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.0243 | − | 8.67429i | −0.649558 | − | 0.375022i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.5372 | − | 21.8259i | −0.454713 | − | 0.941858i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.6658 | −1.01747 | −0.508737 | − | 0.860922i | \(-0.669887\pi\) | ||||
−0.508737 | + | 0.860922i | \(0.669887\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.3193 | − | 25.5172i | −0.528671 | − | 1.09505i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.10273 | − | 1.90998i | 0.0472356 | − | 0.0818145i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0824 | − | 20.9273i | −0.516606 | − | 0.894788i | −0.999814 | − | 0.0192822i | \(-0.993862\pi\) |
0.483208 | − | 0.875505i | \(-0.339471\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.43996 | + | 23.1304i | −0.146814 | + | 0.987182i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −30.7803 | − | 53.3130i | −1.31128 | − | 2.27121i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.790507 | + | 10.6893i | −0.0335552 | + | 0.453734i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 8.50223i | − | 0.360251i | −0.983644 | − | 0.180126i | \(-0.942350\pi\) | ||
0.983644 | − | 0.180126i | \(-0.0576504\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.59381i | 0.363480i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.77253 | + | 5.54496i | −0.159276 | + | 0.234108i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.473776 | − | 0.820605i | 0.0199673 | − | 0.0345844i | −0.855869 | − | 0.517192i | \(-0.826977\pi\) |
0.875836 | + | 0.482608i | \(0.160310\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.0430 | − | 13.3039i | 0.969427 | − | 0.559699i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.7859 | − | 9.11401i | 0.661781 | − | 0.382079i | −0.131175 | − | 0.991359i | \(-0.541875\pi\) |
0.792955 | + | 0.609280i | \(0.208542\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.12121 | − | 10.6023i | 0.256165 | − | 0.443691i | −0.709046 | − | 0.705162i | \(-0.750874\pi\) |
0.965211 | + | 0.261471i | \(0.0842077\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.3118 | + | 19.5661i | −0.556110 | + | 0.817385i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.940253i | 0.0392112i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.8357i | 0.492726i | 0.969178 | + | 0.246363i | \(0.0792355\pi\) | ||||
−0.969178 | + | 0.246363i | \(0.920764\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.559216 | + | 7.56174i | −0.0232402 | + | 0.314255i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.04439 | − | 3.54098i | −0.0846699 | − | 0.146653i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.25660 | − | 21.8975i | 0.134644 | − | 0.905350i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.57681 | − | 6.19521i | −0.147631 | − | 0.255704i | 0.782721 | − | 0.622373i | \(-0.213831\pi\) |
−0.930351 | + | 0.366669i | \(0.880498\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.80745 | − | 4.86264i | 0.115679 | − | 0.200362i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.757580 | − | 1.56919i | −0.0311627 | − | 0.0645480i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.9622 | 1.10721 | 0.553603 | − | 0.832781i | \(-0.313252\pi\) | ||||
0.553603 | + | 0.832781i | \(0.313252\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.93581 | − | 10.2237i | −0.202009 | − | 0.418426i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.5223 | + | 17.6221i | 1.24711 | + | 0.720018i | 0.970532 | − | 0.240974i | \(-0.0774668\pi\) |
0.276576 | + | 0.960992i | \(0.410800\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.39266 | + | 1.95875i | −0.138389 | + | 0.0798991i | −0.567596 | − | 0.823307i | \(-0.692126\pi\) |
0.429207 | + | 0.903206i | \(0.358793\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.43340 | + | 16.2979i | 0.261988 | + | 0.663704i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.66332 | − | 16.7374i | −0.392870 | − | 0.680470i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.5377 | − | 7.23862i | −0.508888 | − | 0.293807i | 0.223488 | − | 0.974707i | \(-0.428256\pi\) |
−0.732376 | + | 0.680900i | \(0.761589\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 42.4267i | 1.71640i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.0352 | 0.526488 | 0.263244 | − | 0.964729i | \(-0.415208\pi\) | ||||
0.263244 | + | 0.964729i | \(0.415208\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 23.3944 | + | 15.9165i | 0.943355 | + | 0.641814i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.14491 | − | 1.81571i | −0.126609 | − | 0.0730979i | 0.435358 | − | 0.900258i | \(-0.356622\pi\) |
−0.561967 | + | 0.827160i | \(0.689955\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.2737 | + | 8.24091i | −0.573708 | + | 0.331230i | −0.758629 | − | 0.651523i | \(-0.774130\pi\) |
0.184921 | + | 0.982753i | \(0.440797\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.1262 | + | 15.3145i | −0.566864 | + | 0.614551i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.8863 | − | 20.5876i | 0.475450 | − | 0.823504i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.6644 | − | 11.3377i | −0.665512 | − | 0.452783i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.49147 | −0.298704 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.8383 | −1.38689 | −0.693446 | − | 0.720508i | \(-0.743909\pi\) | ||||
−0.693446 | + | 0.720508i | \(0.743909\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.32798 | − | 31.4790i | 0.0925289 | − | 1.25118i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.41512 | + | 12.8434i | −0.294260 | + | 0.509673i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27.4508 | − | 21.8033i | −1.08594 | − | 0.862525i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.25538 | + | 4.18889i | −0.286570 | + | 0.165451i | −0.636394 | − | 0.771364i | \(-0.719575\pi\) |
0.349824 | + | 0.936815i | \(0.386241\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.0021 | + | 10.3935i | 0.709934 | + | 0.409881i | 0.811037 | − | 0.584995i | \(-0.198904\pi\) |
−0.101103 | + | 0.994876i | \(0.532237\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.65637 | + | 4.17915i | −0.340844 | + | 0.164554i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.49540 | 0.373303 | 0.186651 | − | 0.982426i | \(-0.440237\pi\) | ||||
0.186651 | + | 0.982426i | \(0.440237\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 19.6818i | − | 0.772579i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.64747 | + | 3.83792i | 0.260136 | + | 0.150189i | 0.624396 | − | 0.781108i | \(-0.285345\pi\) |
−0.364261 | + | 0.931297i | \(0.618678\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.9927 | − | 25.9680i | −0.585811 | − | 1.01465i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.7397 | + | 8.53025i | 0.418997 | + | 0.332797i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.0493 | − | 21.9678i | 1.48219 | − | 0.855743i | 0.482395 | − | 0.875954i | \(-0.339767\pi\) |
0.999796 | + | 0.0202102i | \(0.00643354\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.1649 | + | 12.7969i | 0.862115 | + | 0.497742i | 0.864720 | − | 0.502254i | \(-0.167496\pi\) |
−0.00260513 | + | 0.999997i | \(0.500829\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.4311 | + | 1.14118i | 0.599292 | + | 0.0443197i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.0789 | −1.20338 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.80684 | + | 14.4144i | −0.379155 | + | 0.557291i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.71051 | + | 9.89089i | −0.220452 | + | 0.381834i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.64671 | − | 13.2445i | −0.294759 | − | 0.510538i | 0.680170 | − | 0.733055i | \(-0.261906\pi\) |
−0.974929 | + | 0.222517i | \(0.928573\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.16329 | + | 0.362580i | −0.0447751 | + | 0.0139557i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.6459 | + | 39.2238i | 0.870352 | + | 1.50749i | 0.861633 | + | 0.507532i | \(0.169442\pi\) |
0.00871898 | + | 0.999962i | \(0.497225\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.4797 | + | 19.3762i | 1.09134 | + | 0.742499i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.8157i | 1.06434i | 0.846638 | + | 0.532169i | \(0.178623\pi\) | ||||
−0.846638 | + | 0.532169i | \(0.821377\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 43.8674i | − | 1.67609i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 30.6869 | + | 2.26940i | 1.17078 | + | 0.0865831i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.71672 | + | 8.16961i | −0.179693 | + | 0.311237i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.1115 | + | 8.14729i | −0.536828 | + | 0.309938i | −0.743792 | − | 0.668411i | \(-0.766975\pi\) |
0.206965 | + | 0.978348i | \(0.433641\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.5862 | − | 10.7307i | 0.705013 | − | 0.407040i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.88831 | + | 17.1271i | −0.374546 | + | 0.648733i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.0932 | − | 25.0490i | −0.457408 | − | 0.947439i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 0.393403i | − | 0.0148586i | −0.999972 | − | 0.00742932i | \(-0.997635\pi\) | ||
0.999972 | − | 0.00742932i | \(-0.00236485\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 22.5143i | − | 0.849143i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −42.7356 | + | 20.6320i | −1.60951 | + | 0.777047i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.3183 | + | 28.2641i | 0.612846 | + | 1.06148i | 0.990758 | + | 0.135639i | \(0.0433087\pi\) |
−0.377912 | + | 0.925841i | \(0.623358\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −27.8451 | − | 4.14112i | −1.04427 | − | 0.155304i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.41734 | − | 2.45491i | −0.0530799 | − | 0.0919372i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.40612 | − | 9.36368i | 0.202178 | − | 0.350182i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.1836 | + | 1.04893i | 0.529697 | + | 0.0391729i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.213207 | 0.00795130 | 0.00397565 | − | 0.999992i | \(-0.498735\pi\) | ||||
0.00397565 | + | 0.999992i | \(0.498735\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 27.7445 | − | 40.7796i | 1.03183 | − | 1.51661i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.57409 | − | 0.908804i | −0.0584604 | − | 0.0337521i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.8208 | + | 18.3717i | −1.18017 | + | 0.681370i | −0.956053 | − | 0.293193i | \(-0.905282\pi\) |
−0.224114 | + | 0.974563i | \(0.571949\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.3947 | − | 11.5715i | −0.903507 | − | 0.428574i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.35920 | − | 5.81831i | −0.124245 | − | 0.215198i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.41829 | + | 5.43765i | 0.347873 | + | 0.200844i | 0.663748 | − | 0.747956i | \(-0.268965\pi\) |
−0.315875 | + | 0.948801i | \(0.602298\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.55753i | 0.315221i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.8256 | −0.508584 | −0.254292 | − | 0.967127i | \(-0.581842\pi\) | ||||
−0.254292 | + | 0.967127i | \(0.581842\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.42961 | + | 46.3753i | −0.125990 | + | 1.70364i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.8751 | − | 9.16552i | −0.582403 | − | 0.336250i | 0.179685 | − | 0.983724i | \(-0.442492\pi\) |
−0.762088 | + | 0.647474i | \(0.775825\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 37.8776 | − | 21.8687i | 1.38773 | − | 0.801206i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.1393 | − | 1.50792i | −0.370979 | − | 0.0551720i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.97084 | − | 17.2700i | 0.363841 | − | 0.630191i | −0.624748 | − | 0.780826i | \(-0.714798\pi\) |
0.988589 | + | 0.150635i | \(0.0481318\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.02375 | − | 0.494252i | 0.0373077 | − | 0.0180115i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −48.5362 | −1.76641 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.9292 | −1.70567 | −0.852836 | − | 0.522178i | \(-0.825119\pi\) | ||||
−0.852836 | + | 0.522178i | \(0.825119\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.16352 | + | 4.42400i | −0.332615 | + | 0.160581i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.7769 | + | 46.3789i | −0.970661 | + | 1.68123i | −0.277093 | + | 0.960843i | \(0.589371\pi\) |
−0.693568 | + | 0.720391i | \(0.743962\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.35460 | + | 16.0983i | 0.229751 | + | 0.582036i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −39.3254 | + | 22.7045i | −1.41996 | + | 0.819813i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.7306 | + | 20.0517i | 1.25242 | + | 0.723085i | 0.971589 | − | 0.236673i | \(-0.0760570\pi\) |
0.280830 | + | 0.959758i | \(0.409390\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.976058 | + | 13.1983i | −0.0351519 | + | 0.475325i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.6475 | −0.562801 | −0.281401 | − | 0.959590i | \(-0.590799\pi\) | ||||
−0.281401 | + | 0.959590i | \(0.590799\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 0.165783i | − | 0.00595509i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −51.4724 | − | 29.7176i | −1.84419 | − | 1.06474i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.56060 | − | 14.8274i | −0.306322 | − | 0.530566i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.9847 | − | 38.4512i | −0.428297 | − | 1.37413i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.1785 | − | 8.76333i | 0.541745 | − | 0.312777i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.9920 | + | 23.0894i | 1.42556 | + | 0.823048i | 0.996766 | − | 0.0803536i | \(-0.0256050\pi\) |
0.428795 | + | 0.903402i | \(0.358938\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.45635 | + | 9.48971i | −0.229852 | + | 0.337843i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.3501 | 0.935719 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.5228 | − | 0.778197i | −0.373206 | − | 0.0275998i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.9388 | − | 29.3388i | 0.600002 | − | 1.03923i | −0.392818 | − | 0.919616i | \(-0.628500\pi\) |
0.992820 | − | 0.119618i | \(-0.0381669\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.5840 | − | 28.7244i | −0.586701 | − | 1.01620i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.2383 | − | 21.7033i | 0.609084 | − | 0.766848i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.34922 | + | 5.80102i | 0.118191 | + | 0.204714i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.6745 | + | 6.60184i | −0.481366 | + | 0.232396i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 39.0142i | − | 1.37167i | −0.727758 | − | 0.685834i | \(-0.759438\pi\) | ||
0.727758 | − | 0.685834i | \(-0.240562\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.73397i | 0.271577i | 0.990738 | + | 0.135788i | \(0.0433567\pi\) | ||||
−0.990738 | + | 0.135788i | \(0.956643\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.4002 | − | 25.6849i | −0.434895 | − | 0.900807i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.5915 | + | 23.5411i | −0.476088 | + | 0.824609i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.4859 | − | 10.0955i | 0.611755 | − | 0.353197i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.443638 | − | 0.256134i | 0.0154831 | − | 0.00893915i | −0.492238 | − | 0.870460i | \(-0.663821\pi\) |
0.507722 | + | 0.861521i | \(0.330488\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.1753 | − | 41.8728i | 0.842698 | − | 1.45960i | −0.0449080 | − | 0.998991i | \(-0.514299\pi\) |
0.887606 | − | 0.460604i | \(-0.152367\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.593482 | − | 0.0438900i | −0.0206624 | − | 0.00152805i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 17.3086i | − | 0.601879i | −0.953643 | − | 0.300940i | \(-0.902700\pi\) | ||
0.953643 | − | 0.300940i | \(-0.0973003\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 38.1288i | − | 1.32427i | −0.749385 | − | 0.662134i | \(-0.769651\pi\) | ||
0.749385 | − | 0.662134i | \(-0.230349\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.4541 | − | 17.3177i | −0.882991 | − | 0.600746i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.5241 | + | 37.2808i | 0.744871 | + | 1.29015i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.49069 | − | 2.70022i | 0.0860908 | − | 0.0933332i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.2026 | + | 26.3317i | 0.524852 | + | 0.909071i | 0.999581 | + | 0.0289389i | \(0.00921281\pi\) |
−0.474729 | + | 0.880132i | \(0.657454\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.5394 | − | 26.9151i | 0.535842 | − | 0.928106i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.7787 | − | 23.1919i | 0.543446 | − | 0.798771i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.43348 | 0.118115 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 49.0095 | + | 3.62442i | 1.68200 | + | 0.124390i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.84358 | − | 5.68319i | −0.337434 | − | 0.194817i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.7143 | + | 16.0008i | −0.948919 | + | 0.547858i | −0.892745 | − | 0.450563i | \(-0.851223\pi\) |
−0.0561738 | + | 0.998421i | \(0.517890\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −48.3807 | + | 19.0976i | −1.65459 | + | 0.653126i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.5774 | + | 39.1053i | 0.771230 | + | 1.33581i | 0.936889 | + | 0.349627i | \(0.113692\pi\) |
−0.165659 | + | 0.986183i | \(0.552975\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.7911 | − | 9.11701i | −0.538786 | − | 0.311068i | 0.205801 | − | 0.978594i | \(-0.434020\pi\) |
−0.744587 | + | 0.667526i | \(0.767353\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.64373i | 0.260195i | 0.991501 | + | 0.130098i | \(0.0415291\pi\) | ||||
−0.991501 | + | 0.130098i | \(0.958471\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.98937 | −0.135643 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.6229 | − | 7.54249i | 0.530583 | − | 0.256157i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.9069 | − | 6.87448i | −0.403915 | − | 0.233201i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.0984 | − | 9.87179i | 0.579358 | − | 0.334493i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.25311 | + | 21.8741i | −0.110101 | + | 0.740325i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.01581 | + | 13.8838i | −0.270675 | + | 0.468822i | −0.969035 | − | 0.246924i | \(-0.920580\pi\) |
0.698360 | + | 0.715747i | \(0.253913\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.11969 | + | 15.1404i | −0.0377660 | + | 0.510674i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.7532 | −0.833958 | −0.416979 | − | 0.908916i | \(-0.636911\pi\) | ||||
−0.416979 | + | 0.908916i | \(0.636911\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.6958 | −0.393595 | −0.196798 | − | 0.980444i | \(-0.563054\pi\) | ||||
−0.196798 | + | 0.980444i | \(0.563054\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −41.9937 | − | 28.5705i | −1.41160 | − | 0.960387i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.5429 | + | 47.7058i | −0.924801 | + | 1.60180i | −0.132921 | + | 0.991127i | \(0.542436\pi\) |
−0.791880 | + | 0.610676i | \(0.790898\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.00706 | − | 9.63124i | −0.301748 | − | 0.322659i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 86.3261 | − | 49.8404i | 2.88879 | − | 1.66785i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.4541 | − | 15.2733i | −0.884262 | − | 0.510529i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.4102 | + | 13.2058i | 0.648089 | + | 0.440929i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.47975 | 0.182760 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 7.37481i | − | 0.245691i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30.9281 | − | 17.8563i | −1.02808 | − | 0.593565i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.9383 | + | 22.4098i | 0.429610 | + | 0.744107i | 0.996839 | − | 0.0794540i | \(-0.0253177\pi\) |
−0.567228 | + | 0.823560i | \(0.691984\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −23.5227 | − | 3.49830i | −0.780199 | − | 0.116031i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.86306 | + | 2.23034i | −0.127989 | + | 0.0738944i | −0.562627 | − | 0.826711i | \(-0.690209\pi\) |
0.434639 | + | 0.900605i | \(0.356876\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.33572 | − | 2.50323i | −0.143491 | − | 0.0828448i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.8140 | + | 26.5419i | 0.423617 | + | 0.877448i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.4704 | 1.40097 | 0.700485 | − | 0.713667i | \(-0.252967\pi\) | ||||
0.700485 | + | 0.713667i | \(0.252967\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.67634 | + | 20.0428i | 0.318846 | + | 0.660433i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −19.7507 | + | 34.2091i | −0.650101 | + | 1.12601i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.332373 | − | 0.575688i | −0.0109284 | − | 0.0189285i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.5308 | + | 4.15690i | −0.345877 | + | 0.136530i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.72508 | − | 13.3802i | −0.253452 | − | 0.438991i | 0.711022 | − | 0.703170i | \(-0.248233\pi\) |
−0.964474 | + | 0.264178i | \(0.914899\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.842259 | − | 11.3890i | 0.0275743 | − | 0.372861i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.45272i | 0.276433i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.1410i | 1.50736i | 0.657241 | + | 0.753680i | \(0.271723\pi\) | ||||
−0.657241 | + | 0.753680i | \(0.728277\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.32681 | + | 4.88983i | −0.108566 | + | 0.159574i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.5052 | + | 35.5161i | −0.668451 | + | 1.15779i | 0.309886 | + | 0.950774i | \(0.399709\pi\) |
−0.978337 | + | 0.207017i | \(0.933624\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.9859 | + | 15.0030i | −0.846218 | + | 0.488564i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.50657 | − | 4.91127i | 0.276426 | − | 0.159595i | −0.355378 | − | 0.934723i | \(-0.615648\pi\) |
0.631804 | + | 0.775128i | \(0.282315\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.72718 | − | 13.3839i | 0.250835 | − | 0.434459i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31.2758 | + | 45.9700i | −1.01419 | + | 1.49068i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 17.0826i | − | 0.553359i | −0.960962 | − | 0.276679i | \(-0.910766\pi\) | ||
0.960962 | − | 0.276679i | \(-0.0892340\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29.8265i | 0.965163i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.45073 | − | 19.6169i | 0.0468955 | − | 0.634123i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.2501 | − | 26.4139i | −0.491939 | − | 0.852063i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.6690 | + | 14.8282i | 0.601602 | + | 0.477834i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.77826 | + | 8.27619i | 0.153818 | + | 0.266420i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.3240 | − | 36.9343i | 0.685735 | − | 1.18773i | −0.287471 | − | 0.957789i | \(-0.592814\pi\) |
0.973205 | − | 0.229938i | \(-0.0738523\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.8055 | − | 32.7383i | −0.507746 | − | 1.05171i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.5124 | 0.754549 | 0.377275 | − | 0.926101i | \(-0.376861\pi\) | ||||
0.377275 | + | 0.926101i | \(0.376861\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.596934 | + | 1.23644i | 0.0191172 | + | 0.0395978i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.1944 | + | 17.4327i | 0.966003 | + | 0.557722i | 0.898015 | − | 0.439964i | \(-0.145009\pi\) |
0.0679878 | + | 0.997686i | \(0.478342\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.7229 | − | 6.76824i | 0.374666 | − | 0.216314i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.88505 | + | 2.37332i | −0.0601851 | + | 0.0757742i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.1804 | + | 22.8292i | 0.420390 | + | 0.728137i | 0.995978 | − | 0.0896033i | \(-0.0285599\pi\) |
−0.575587 | + | 0.817740i | \(0.695227\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.90194 | − | 1.09808i | −0.0606008 | − | 0.0349879i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 10.1935i | − | 0.324133i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.161043 | −0.00511568 | −0.00255784 | − | 0.999997i | \(-0.500814\pi\) | ||||
−0.00255784 | + | 0.999997i | \(0.500814\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −41.3621 | − | 28.1408i | −1.31259 | − | 0.893022i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.3916 | − | 7.15427i | −0.392839 | − | 0.226806i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.5820 | − | 8.41890i | 0.461816 | − | 0.266629i | −0.250992 | − | 0.967989i | \(-0.580757\pi\) |
0.712807 | + | 0.701360i | \(0.247423\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.23544 | − | 14.3701i | 0.102365 | − | 0.454651i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))