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 | 1469.7 | ||
Root | \(-1.61108 - 0.635951i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1469 |
Dual form | 1764.2.x.a.293.7 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 | \(-0.00434429\pi\) |
−0.511773 | + | 0.859121i | \(0.671011\pi\) | |||||||
\(6\) | 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 | 0.678942 | − | 0.734192i | \(-0.262439\pi\) |
−0.296358 | + | 0.955077i | \(0.595772\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.92752 | − | 1.69021i | 0.811948 | − | 0.468779i | −0.0356837 | − | 0.999363i | \(-0.511361\pi\) |
0.847632 | + | 0.530585i | \(0.178028\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.278862 | + | 3.77077i | 0.0720017 | + | 0.973610i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.64271 | −0.640952 | −0.320476 | − | 0.947257i | \(-0.603843\pi\) | ||||
−0.320476 | + | 0.947257i | \(0.603843\pi\) | |||||||
\(18\) | 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 | −0.0921879 | − | 0.995742i | \(-0.529386\pi\) |
0.816244 | + | 0.577708i | \(0.196053\pi\) | |||||||
\(24\) | 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 | −0.276091 | − | 0.961132i | \(-0.589039\pi\) |
−0.970410 | + | 0.241464i | \(0.922372\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.612252 | − | 0.353484i | 0.109964 | − | 0.0634876i | −0.444009 | − | 0.896022i | \(-0.646444\pi\) |
0.553973 | + | 0.832534i | \(0.313111\pi\) | |||||||
\(32\) | 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 | 0.994955 | + | 0.100323i | \(0.0319876\pi\) |
−0.410595 | + | 0.911818i | \(0.634679\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.27112 | + | 2.20164i | −0.193844 | + | 0.335748i | −0.946521 | − | 0.322642i | \(-0.895429\pi\) |
0.752677 | + | 0.658390i | \(0.228762\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.40458 | + | 6.09160i | −0.358453 | + | 0.908081i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.27538 | − | 10.8693i | 0.915358 | − | 1.58545i | 0.108983 | − | 0.994044i | \(-0.465241\pi\) |
0.806376 | − | 0.591403i | \(-0.201426\pi\) | |||||||
\(48\) | 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 | \(0.0613873\pi\) | ||||
−0.981461 | + | 0.191661i | \(0.938613\pi\) | |||||||
\(54\) | 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 | −0.857385 | − | 0.514675i | \(-0.827913\pi\) |
−0.0170287 | − | 0.999855i | \(-0.505421\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.75061 | + | 3.89747i | 0.864327 | + | 0.499020i | 0.865459 | − | 0.500980i | \(-0.167027\pi\) |
−0.00113176 | + | 0.999999i | \(0.500360\pi\) | |||||||
\(62\) | 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 | 0.630649 | − | 0.776068i | \(-0.282789\pi\) |
−0.987419 | + | 0.158124i | \(0.949455\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.92598 | − | 0.512200i | 0.833791 | − | 0.0616616i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.6854i | 1.38680i | 0.720554 | + | 0.693398i | \(0.243887\pi\) | ||||
−0.720554 | + | 0.693398i | \(0.756113\pi\) | |||||||
\(72\) | 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 | 0.471593 | + | 0.881816i | \(0.343679\pi\) |
−0.999472 | + | 0.0324963i | \(0.989654\pi\) | |||||||
\(80\) | 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 | \(-0.773285\pi\) |
0.944426 | + | 0.328724i | \(0.106619\pi\) | |||||||
\(84\) | 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 | \(-0.662876\pi\) | ||||
−0.489653 | + | 0.871918i | \(0.662876\pi\) | |||||||
\(90\) | 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 | \(-0.211239\pi\) |
−0.139572 | + | 0.990212i | \(0.544573\pi\) | |||||||
\(98\) | 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 | \(-0.704289\pi\) |
0.993023 | + | 0.117920i | \(0.0376226\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.26825 | − | 1.88693i | 0.322031 | − | 0.185924i | −0.330267 | − | 0.943888i | \(-0.607139\pi\) |
0.652297 | + | 0.757963i | \(0.273805\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 7.94712i | − | 0.768277i | −0.923275 | − | 0.384138i | \(-0.874499\pi\) | ||
0.923275 | − | 0.384138i | \(-0.125501\pi\) | |||||||
\(108\) | 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 | −0.906167 | − | 0.422919i | \(-0.861005\pi\) |
−0.0868250 | + | 0.996224i | \(0.527672\pi\) | |||||||
\(114\) | 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 | 0.992813 | + | 0.119679i | \(0.0381865\pi\) |
−0.392761 | + | 0.919640i | \(0.628480\pi\) | |||||||
\(132\) | 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 | −0.486933 | − | 0.873439i | \(-0.661884\pi\) |
−0.999887 | + | 0.0150235i | \(0.995218\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.51403 | − | 4.91558i | 0.722151 | − | 0.416934i | −0.0933930 | − | 0.995629i | \(-0.529771\pi\) |
0.815544 | + | 0.578695i | \(0.196438\pi\) | |||||||
\(140\) | 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 | −0.996424 | − | 0.0844939i | \(-0.973073\pi\) |
−0.425038 | + | 0.905175i | \(0.639739\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.1168 | − | 19.2549i | 0.904675 | − | 1.56694i | 0.0833218 | − | 0.996523i | \(-0.473447\pi\) |
0.821353 | − | 0.570420i | \(-0.193220\pi\) | |||||||
\(152\) | 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 | \(-0.562856\pi\) |
0.751102 | + | 0.660187i | \(0.229523\pi\) | |||||||
\(158\) | 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 | −0.941309 | − | 0.337546i | \(-0.890403\pi\) |
0.178332 | − | 0.983970i | \(-0.442930\pi\) | |||||||
\(168\) | 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 | \(-0.855464\pi\) |
0.829198 | + | 0.558955i | \(0.188797\pi\) | |||||||
\(174\) | 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 | \(-0.824836\pi\) | ||
0.852370 | − | 0.522939i | \(-0.175164\pi\) | |||||||
\(180\) | 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 | 0.862729 | − | 0.505667i | \(-0.168753\pi\) |
−0.00655557 | + | 0.999979i | \(0.502087\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.18885 | + | 3.79119i | 0.157557 | + | 0.272896i | 0.933987 | − | 0.357307i | \(-0.116305\pi\) |
−0.776430 | + | 0.630203i | \(0.782972\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.18976 | + | 10.5677i | 0.514869 | + | 0.756768i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.00603i | − | 0.0716767i | −0.999358 | − | 0.0358384i | \(-0.988590\pi\) | ||
0.999358 | − | 0.0358384i | \(-0.0114101\pi\) | |||||||
\(198\) | 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 | −0.988092 | − | 0.153866i | \(-0.950828\pi\) |
0.360794 | − | 0.932645i | \(-0.382506\pi\) | |||||||
\(212\) | 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 | \(-0.442753\pi\) |
−0.762617 | + | 0.646850i | \(0.776086\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.695841 | − | 0.103486i | 0.0463894 | − | 0.00689904i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.94372 | − | 17.2230i | 0.659988 | − | 1.14313i | −0.320630 | − | 0.947204i | \(-0.603895\pi\) |
0.980618 | − | 0.195928i | \(-0.0627720\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.3854 | − | 8.88275i | 1.01669 | − | 0.586988i | 0.103549 | − | 0.994624i | \(-0.466980\pi\) |
0.913145 | + | 0.407636i | \(0.133647\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 16.0592i | − | 1.05208i | −0.850461 | − | 0.526038i | \(-0.823677\pi\) | ||
0.850461 | − | 0.526038i | \(-0.176323\pi\) | |||||||
\(234\) | 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 | −0.712037 | − | 0.702142i | \(-0.752227\pi\) |
0.252054 | + | 0.967713i | \(0.418894\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.6614 | + | 14.2382i | 1.58858 | + | 0.917166i | 0.993542 | + | 0.113468i | \(0.0361959\pi\) |
0.595037 | + | 0.803698i | \(0.297137\pi\) | |||||||
\(242\) | 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 | \(-0.493406\pi\) | ||||
0.0207140 | + | 0.999785i | \(0.493406\pi\) | |||||||
\(252\) | 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 | \(-0.243261\pi\) |
−0.960230 | + | 0.279211i | \(0.909927\pi\) | |||||||
\(258\) | 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 | 0.666390 | − | 0.745603i | \(-0.267838\pi\) |
−0.312516 | + | 0.949913i | \(0.601172\pi\) | |||||||
\(264\) | 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 | \(-0.586120\pi\) | ||||
−0.267265 | + | 0.963623i | \(0.586120\pi\) | |||||||
\(270\) | 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 | −0.465225 | − | 0.885193i | \(-0.654026\pi\) |
0.999212 | − | 0.0397001i | \(-0.0126402\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.97277 | + | 0.778725i | 0.118107 | + | 0.0466210i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.0252 | − | 8.09748i | −0.836676 | − | 0.483055i | 0.0194568 | − | 0.999811i | \(-0.493806\pi\) |
−0.856133 | + | 0.516755i | \(0.827140\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.5717 | − | 14.1865i | 1.46063 | − | 0.843298i | 0.461594 | − | 0.887091i | \(-0.347278\pi\) |
0.999041 | + | 0.0437937i | \(0.0139444\pi\) | |||||||
\(284\) | 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 | \(-0.249083\pi\) |
−0.965176 | + | 0.261602i | \(0.915749\pi\) | |||||||
\(294\) | 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 | \(-0.106810\pi\) |
−0.757289 | + | 0.653080i | \(0.773477\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.95711 | − | 1.70729i | −0.167146 | − | 0.0965018i | 0.414093 | − | 0.910234i | \(-0.364099\pi\) |
−0.581239 | + | 0.813733i | \(0.697432\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.8003 | + | 16.0505i | 1.56142 | + | 0.901485i | 0.997114 | + | 0.0759182i | \(0.0241888\pi\) |
0.564304 | + | 0.825567i | \(0.309145\pi\) | |||||||
\(318\) | 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 | −0.129824 | − | 0.991537i | \(-0.541441\pi\) |
0.923608 | − | 0.383338i | \(-0.125225\pi\) | |||||||
\(332\) | 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 | 0.967004 | − | 0.254762i | \(-0.0819971\pi\) |
−0.704132 | + | 0.710069i | \(0.748664\pi\) | |||||||
\(338\) | 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 | −0.758389 | − | 0.651802i | \(-0.774013\pi\) |
0.185283 | + | 0.982685i | \(0.440680\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.2211 | − | 5.90115i | −0.547123 | − | 0.315881i | 0.200838 | − | 0.979624i | \(-0.435634\pi\) |
−0.747961 | + | 0.663743i | \(0.768967\pi\) | |||||||
\(350\) | 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 | \(-0.719105\pi\) |
0.986461 | + | 0.163997i | \(0.0524386\pi\) | |||||||
\(354\) | 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 | \(-0.949106\pi\) | ||
0.987245 | − | 0.159208i | \(-0.0508940\pi\) | |||||||
\(360\) | 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 | \(-0.481307\pi\) |
−0.835186 | + | 0.549967i | \(0.814640\pi\) | |||||||
\(368\) | 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 | 0.798468 | − | 0.602037i | \(-0.205644\pi\) |
−0.920614 | + | 0.390475i | \(0.872311\pi\) | |||||||
\(374\) | 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 | \(-0.120140\pi\) |
−0.783968 | + | 0.620802i | \(0.786807\pi\) | |||||||
\(384\) | 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 | 0.322226 | − | 0.946663i | \(-0.395569\pi\) |
−0.658721 | + | 0.752387i | \(0.728902\pi\) | |||||||
\(390\) | 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 | −0.281429 | − | 0.959582i | \(-0.590809\pi\) |
0.690308 | + | 0.723516i | \(0.257475\pi\) | |||||||
\(402\) | 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 | \(-0.822977\pi\) |
0.0325304 | + | 0.999471i | \(0.489643\pi\) | |||||||
\(410\) | 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 | \(-0.232446\pi\) |
−0.950192 | + | 0.311666i | \(0.899113\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.7178 | − | 34.1522i | 0.960985 | − | 1.66448i | 0.240951 | − | 0.970537i | \(-0.422541\pi\) |
0.720035 | − | 0.693938i | \(-0.244126\pi\) | |||||||
\(422\) | 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 | \(-0.907213\pi\) | ||
0.957814 | − | 0.287389i | \(-0.0927871\pi\) | |||||||
\(432\) | 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 | \(-0.202843\pi\) |
−0.113408 | + | 0.993548i | \(0.536177\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.2403 | − | 15.1499i | −1.24672 | − | 0.719791i | −0.276262 | − | 0.961082i | \(-0.589096\pi\) |
−0.970453 | + | 0.241291i | \(0.922429\pi\) | |||||||
\(444\) | 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 | \(-0.748310\pi\) | ||
0.703343 | − | 0.710851i | \(-0.251690\pi\) | |||||||
\(450\) | 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 | 0.404067 | + | 0.914730i | \(0.367596\pi\) |
−0.994212 | + | 0.107433i | \(0.965737\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.01624 | − | 13.3966i | −0.140786 | − | 0.625299i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.3174 | + | 21.3344i | −0.573680 | + | 0.993643i | 0.422503 | + | 0.906361i | \(0.361151\pi\) |
−0.996184 | + | 0.0872820i | \(0.972182\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.33215 | − | 10.9676i | −0.294280 | − | 0.509708i | 0.680537 | − | 0.732713i | \(-0.261746\pi\) |
−0.974817 | + | 0.223006i | \(0.928413\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.50364 | + | 2.21009i | 0.0697298 | + | 0.102491i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.9445 | −0.969198 | −0.484599 | − | 0.874736i | \(-0.661034\pi\) | ||||
−0.484599 | + | 0.874736i | \(0.661034\pi\) | |||||||
\(468\) | 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 | −0.232822 | − | 0.972519i | \(-0.574796\pi\) |
0.958637 | − | 0.284630i | \(-0.0918707\pi\) | |||||||
\(480\) | 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 | −0.436490 | − | 0.899709i | \(-0.643778\pi\) |
0.560926 | + | 0.827866i | \(0.310445\pi\) | |||||||
\(492\) | 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 | −0.962099 | − | 0.272700i | \(-0.912083\pi\) |
0.244884 | − | 0.969552i | \(-0.421250\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.51904 | − | 34.0625i | −0.112542 | − | 1.52180i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.6608 | 0.519930 | 0.259965 | − | 0.965618i | \(-0.416289\pi\) | ||||
0.259965 | + | 0.965618i | \(0.416289\pi\) | |||||||
\(504\) | 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 | −0.993428 | − | 0.114457i | \(-0.963487\pi\) |
0.397592 | − | 0.917562i | \(-0.369846\pi\) | |||||||
\(510\) | 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 | \(-0.768254\pi\) | ||||
−0.746471 | + | 0.665418i | \(0.768254\pi\) | |||||||
\(522\) | 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 | 0.483208 | + | 0.875505i | \(0.339471\pi\) |
−0.999814 | + | 0.0192822i | \(0.993862\pi\) | |||||||
\(548\) | 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 | \(0.0576504\pi\) | ||||
−0.983644 | + | 0.180126i | \(0.942350\pi\) | |||||||
\(558\) | 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 | \(-0.173023\pi\) |
−0.875836 | + | 0.482608i | \(0.839690\pi\) | |||||||
\(564\) | 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 | 0.792955 | − | 0.609280i | \(-0.208542\pi\) |
−0.131175 | + | 0.991359i | \(0.541875\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.12121 | + | 10.6023i | 0.256165 | + | 0.443691i | 0.965211 | − | 0.261471i | \(-0.0842077\pi\) |
−0.709046 | + | 0.705162i | \(0.750874\pi\) | |||||||
\(572\) | 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 | \(-0.786169\pi\) |
0.930351 | + | 0.366669i | \(0.119502\pi\) | |||||||
\(588\) | 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 | \(-0.686748\pi\) | ||||
−0.553603 | + | 0.832781i | \(0.686748\pi\) | |||||||
\(594\) | 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 | 0.276576 | − | 0.960992i | \(-0.410800\pi\) |
0.970532 | + | 0.240974i | \(0.0774668\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.39266 | + | 1.95875i | 0.138389 | + | 0.0798991i | 0.567596 | − | 0.823307i | \(-0.307874\pi\) |
−0.429207 | + | 0.903206i | \(0.641207\pi\) | |||||||
\(602\) | 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 | \(-0.571744\pi\) |
0.732376 | + | 0.680900i | \(0.238411\pi\) | |||||||
\(608\) | 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 | −0.561967 | − | 0.827160i | \(-0.689955\pi\) |
0.435358 | + | 0.900258i | \(0.356622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.2737 | + | 8.24091i | 0.573708 | + | 0.331230i | 0.758629 | − | 0.651523i | \(-0.225870\pi\) |
−0.184921 | + | 0.982753i | \(0.559203\pi\) | |||||||
\(620\) | 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 | 0.349824 | − | 0.936815i | \(-0.386241\pi\) |
−0.636394 | + | 0.771364i | \(0.719575\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.0021 | + | 10.3935i | −0.709934 | + | 0.409881i | −0.811037 | − | 0.584995i | \(-0.801096\pi\) |
0.101103 | + | 0.994876i | \(0.467763\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.65637 | − | 4.17915i | −0.340844 | − | 0.164554i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.49540 | −0.373303 | −0.186651 | − | 0.982426i | \(-0.559763\pi\) | ||||
−0.186651 | + | 0.982426i | \(0.559763\pi\) | |||||||
\(648\) | 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 | −0.364261 | − | 0.931297i | \(-0.618678\pi\) |
0.624396 | + | 0.781108i | \(0.285345\pi\) | |||||||
\(654\) | 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 | 0.999796 | − | 0.0202102i | \(-0.00643354\pi\) |
0.482395 | + | 0.875954i | \(0.339767\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.1649 | + | 12.7969i | −0.862115 | + | 0.497742i | −0.864720 | − | 0.502254i | \(-0.832504\pi\) |
0.00260513 | + | 0.999997i | \(0.499171\pi\) | |||||||
\(662\) | 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 | −0.974929 | − | 0.222517i | \(-0.928573\pi\) |
0.680170 | + | 0.733055i | \(0.261906\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.16329 | + | 0.362580i | 0.0447751 | + | 0.0139557i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.6459 | + | 39.2238i | −0.870352 | + | 1.50749i | −0.00871898 | + | 0.999962i | \(0.502775\pi\) |
−0.861633 | + | 0.507532i | \(0.830558\pi\) | |||||||
\(678\) | 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 | \(-0.821377\pi\) | ||
0.846638 | − | 0.532169i | \(-0.178623\pi\) | |||||||
\(684\) | 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 | \(-0.233025\pi\) |
−0.206965 | + | 0.978348i | \(0.566359\pi\) | |||||||
\(692\) | 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 | \(0.00236485\pi\) | ||||
−0.999972 | + | 0.00742932i | \(0.997635\pi\) | |||||||
\(702\) | 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 | −0.377912 | − | 0.925841i | \(-0.623358\pi\) |
0.990758 | − | 0.135639i | \(-0.0433087\pi\) | |||||||
\(710\) | 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 | \(-0.501265\pi\) | ||||
−0.00397565 | + | 0.999992i | \(0.501265\pi\) | |||||||
\(720\) | 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 | \(-0.0947180\pi\) |
0.224114 | + | 0.974563i | \(0.428051\pi\) | |||||||
\(728\) | 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 | \(-0.731035\pi\) |
0.315875 | + | 0.948801i | \(0.397702\pi\) | |||||||
\(734\) | 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 | −0.762088 | − | 0.647474i | \(-0.775825\pi\) |
0.179685 | + | 0.983724i | \(0.442492\pi\) | |||||||
\(744\) | 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 | 0.988589 | − | 0.150635i | \(-0.0481318\pi\) |
−0.624748 | + | 0.780826i | \(0.714798\pi\) | |||||||
\(752\) | 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 | 0.693568 | + | 0.720391i | \(0.256038\pi\) |
0.277093 | + | 0.960843i | \(0.410629\pi\) | |||||||
\(762\) | 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 | \(-0.923943\pi\) |
−0.280830 | + | 0.959758i | \(0.590610\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.976058 | − | 13.1983i | −0.0351519 | − | 0.475325i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.6475 | 0.562801 | 0.281401 | − | 0.959590i | \(-0.409201\pi\) | ||||
0.281401 | + | 0.959590i | \(0.409201\pi\) | |||||||
\(774\) | 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 | \(-0.974395\pi\) |
−0.428795 | + | 0.903402i | \(0.641062\pi\) | |||||||
\(788\) | 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 | −0.992820 | − | 0.119618i | \(-0.961833\pi\) |
0.392818 | − | 0.919616i | \(-0.371500\pi\) | |||||||
\(798\) | 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 | \(0.240562\pi\) | ||||
−0.727758 | + | 0.685834i | \(0.759438\pi\) | |||||||
\(810\) | 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 | 0.507722 | − | 0.861521i | \(-0.330488\pi\) |
−0.492238 | + | 0.870460i | \(0.663821\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.1753 | + | 41.8728i | 0.842698 | + | 1.45960i | 0.887606 | + | 0.460604i | \(0.152367\pi\) |
−0.0449080 | + | 0.998991i | \(0.514299\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.593482 | − | 0.0438900i | 0.0206624 | − | 0.00152805i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.3086i | 0.601879i | 0.953643 | + | 0.300940i | \(0.0973003\pi\) | ||||
−0.953643 | + | 0.300940i | \(0.902700\pi\) | |||||||
\(828\) | 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 | 0.474729 | + | 0.880132i | \(0.342546\pi\) |
−0.999581 | + | 0.0289389i | \(0.990787\pi\) | |||||||
\(840\) | 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 | \(-0.148777\pi\) |
0.0561738 | + | 0.998421i | \(0.482110\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −48.3807 | − | 19.0976i | −1.65459 | − | 0.653126i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.5774 | + | 39.1053i | −0.771230 | + | 1.33581i | 0.165659 | + | 0.986183i | \(0.447025\pi\) |
−0.936889 | + | 0.349627i | \(0.886308\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.7911 | − | 9.11701i | 0.538786 | − | 0.311068i | −0.205801 | − | 0.978594i | \(-0.565980\pi\) |
0.744587 | + | 0.667526i | \(0.232647\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 7.64373i | − | 0.260195i | −0.991501 | − | 0.130098i | \(-0.958471\pi\) | ||
0.991501 | − | 0.130098i | \(-0.0415291\pi\) | |||||||
\(864\) | 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 | 0.698360 | − | 0.715747i | \(-0.253913\pi\) |
−0.969035 | + | 0.246924i | \(0.920580\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.11969 | − | 15.1404i | −0.0377660 | − | 0.510674i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.7532 | 0.833958 | 0.416979 | − | 0.908916i | \(-0.363089\pi\) | ||||
0.416979 | + | 0.908916i | \(0.363089\pi\) | |||||||
\(882\) | 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 | 0.791880 | + | 0.610676i | \(0.209102\pi\) |
0.132921 | + | 0.991127i | \(0.457564\pi\) | |||||||
\(888\) | 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 | −0.567228 | − | 0.823560i | \(-0.691984\pi\) |
0.996839 | + | 0.0794540i | \(0.0253177\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 23.5227 | − | 3.49830i | 0.780199 | − | 0.116031i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.86306 | − | 2.23034i | −0.127989 | − | 0.0738944i | 0.434639 | − | 0.900605i | \(-0.356876\pi\) |
−0.562627 | + | 0.826711i | \(0.690209\pi\) | |||||||
\(912\) | 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 | \(-0.751767\pi\) |
0.964474 | + | 0.264178i | \(0.0851008\pi\) | |||||||
\(930\) | 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 | 0.978337 | + | 0.207017i | \(0.0663756\pi\) |
−0.309886 | + | 0.950774i | \(0.600291\pi\) | |||||||
\(942\) | 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 | 0.631804 | − | 0.775128i | \(-0.282315\pi\) |
−0.355378 | + | 0.934723i | \(0.615648\pi\) | |||||||
\(948\) | 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 | \(0.0892340\pi\) | ||||
−0.960962 | + | 0.276679i | \(0.910766\pi\) | |||||||
\(954\) | 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 | 0.973205 | + | 0.229938i | \(0.0738523\pi\) |
−0.287471 | + | 0.957789i | \(0.592814\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.8055 | − | 32.7383i | 0.507746 | − | 1.05171i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.5124 | −0.754549 | −0.377275 | − | 0.926101i | \(-0.623139\pi\) | ||||
−0.377275 | + | 0.926101i | \(0.623139\pi\) | |||||||
\(972\) | 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 | 0.0679878 | − | 0.997686i | \(-0.478342\pi\) |
0.898015 | + | 0.439964i | \(0.145009\pi\) | |||||||
\(978\) | 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 | \(-0.971440\pi\) |
0.575587 | + | 0.817740i | \(0.304773\pi\) | |||||||
\(984\) | 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 | \(-0.419243\pi\) |
−0.712807 | + | 0.701360i | \(0.752577\pi\) | |||||||
\(998\) | 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 \(a_p\))