Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5292,2,Mod(881,5292)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5292, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5292.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5292.x (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(42.2568327497\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 881.3 | ||
Root | \(-1.61108 - 0.635951i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5292.881 |
Dual form | 5292.2.x.a.4409.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5292\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) | \(2647\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 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 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.26889 | + | 0.732592i | −0.382584 | + | 0.220885i | −0.678942 | − | 0.734192i | \(-0.737561\pi\) |
0.296358 | + | 0.955077i | \(0.404228\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.92752 | + | 1.69021i | 0.811948 | + | 0.468779i | 0.847632 | − | 0.530585i | \(-0.178028\pi\) |
−0.0356837 | + | 0.999363i | \(0.511361\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 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 | \(-0.635285\pi\) | ||
0.412331 | − | 0.911034i | \(-0.364715\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.47245 | − | 2.00482i | −0.724056 | − | 0.418034i | 0.0921879 | − | 0.995742i | \(-0.470614\pi\) |
−0.816244 | + | 0.577708i | \(0.803947\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.117249 | + | 0.203081i | 0.0234498 | + | 0.0406163i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.71261 | − | 3.87553i | 1.24650 | − | 0.719667i | 0.276091 | − | 0.961132i | \(-0.410961\pi\) |
0.970410 | + | 0.241464i | \(0.0776276\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.612252 | + | 0.353484i | 0.109964 | + | 0.0634876i | 0.553973 | − | 0.832534i | \(-0.313111\pi\) |
−0.444009 | + | 0.896022i | \(0.646444\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 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 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 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 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 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 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 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 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 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 | −0.00113176 | − | 0.999999i | \(-0.500360\pi\) |
0.865459 | + | 0.500980i | \(0.167027\pi\) | |||||||
\(62\) | 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 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | \(-0.913789\pi\) | ||
0.963547 | − | 0.267541i | \(-0.0862110\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 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 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 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 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 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 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.0150 | + | 8.66894i | 1.54051 | + | 0.889414i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.38394 | − | 3.68577i | 0.648191 | − | 0.374233i | −0.139572 | − | 0.990212i | \(-0.544573\pi\) |
0.787763 | + | 0.615979i | \(0.211239\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 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 | 0.652297 | − | 0.757963i | \(-0.273805\pi\) |
−0.330267 | + | 0.943888i | \(0.607139\pi\) | |||||||
\(104\) | 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 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.5557 | + | 6.09431i | 0.992992 | + | 0.573304i | 0.906167 | − | 0.422919i | \(-0.138995\pi\) |
0.0868250 | + | 0.996224i | \(0.472328\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.58037 | − | 4.37653i | 0.706873 | − | 0.408113i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.42662 | + | 7.66713i | −0.402420 | + | 0.697012i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 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 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.4028 | − | 10.0475i | 1.48682 | − | 0.858416i | 0.486933 | − | 0.873439i | \(-0.338116\pi\) |
0.999887 | + | 0.0150235i | \(0.00478229\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.51403 | + | 4.91558i | 0.722151 | + | 0.416934i | 0.815544 | − | 0.578695i | \(-0.196438\pi\) |
−0.0933930 | + | 0.995629i | \(0.529771\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 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 | \(-0.0269274\pi\) |
0.425038 | + | 0.905175i | \(0.360261\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.33655 | + | 0.771657i | −0.107354 | + | 0.0619810i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.95305 | + | 4.01435i | 0.554914 | + | 0.320380i | 0.751102 | − | 0.660187i | \(-0.229523\pi\) |
−0.196188 | + | 0.980566i | \(0.562856\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 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 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 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 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 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 | \(-0.791975\pi\) | ||
0.793942 | − | 0.607994i | \(-0.208025\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 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 | \(-0.831247\pi\) |
0.00655557 | + | 0.999979i | \(0.497913\pi\) | |||||||
\(192\) | 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 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 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 | \(-0.925369\pi\) | ||
0.972640 | − | 0.232319i | \(-0.0746313\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.16820 | − | 14.1477i | −0.570492 | − | 0.988121i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.54972 | 0.378487 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.73660 | + | 4.46673i | 0.520420 | + | 0.300464i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.71705 | + | 5.03279i | −0.583737 | + | 0.337021i | −0.762617 | − | 0.646850i | \(-0.776086\pi\) |
0.178880 | + | 0.983871i | \(0.442753\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 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 | 0.913145 | − | 0.407636i | \(-0.133647\pi\) |
0.103549 | + | 0.994624i | \(0.466980\pi\) | |||||||
\(230\) | 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 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.11117 | + | 4.10564i | 0.459983 | + | 0.265572i | 0.712037 | − | 0.702142i | \(-0.247773\pi\) |
−0.252054 | + | 0.967713i | \(0.581106\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.6614 | − | 14.2382i | 1.58858 | − | 0.917166i | 0.595037 | − | 0.803698i | \(-0.297137\pi\) |
0.993542 | − | 0.113468i | \(-0.0361959\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.4240 | − | 23.2510i | 0.854147 | − | 1.47943i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | 0 | ||||||||
\(256\) | 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 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.73888 | + | 3.31334i | −0.353874 | + | 0.204310i | −0.666390 | − | 0.745603i | \(-0.732162\pi\) |
0.312516 | + | 0.949913i | \(0.398828\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.27577 | − | 3.04597i | −0.324088 | − | 0.187112i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 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 | \(-0.833279\pi\) | ||
0.865941 | − | 0.500147i | \(-0.166721\pi\) | |||||||
\(272\) | 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 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.0252 | − | 8.09748i | 0.836676 | − | 0.483055i | −0.0194568 | − | 0.999811i | \(-0.506194\pi\) |
0.856133 | + | 0.516755i | \(0.172860\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.5717 | + | 14.1865i | 1.46063 | + | 0.843298i | 0.999041 | − | 0.0437937i | \(-0.0139444\pi\) |
0.461594 | + | 0.887091i | \(0.347278\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.0161 | −0.589181 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 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 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.77711 | − | 11.7383i | −0.391931 | − | 0.678844i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.0164i | 0.974354i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.8497i | 0.733372i | 0.930345 | + | 0.366686i | \(0.119508\pi\) | ||||
−0.930345 | + | 0.366686i | \(0.880492\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | −0.581239 | − | 0.813733i | \(-0.697432\pi\) |
0.414093 | + | 0.910234i | \(0.364099\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.8003 | + | 16.0505i | −1.56142 | + | 0.901485i | −0.564304 | + | 0.825567i | \(0.690855\pi\) |
−0.997114 | + | 0.0759182i | \(0.975811\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.67836 | + | 9.83521i | −0.317927 | + | 0.550666i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 20.9890i | − | 1.16786i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.792700i | 0.0439711i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.03584 | −0.0560938 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.6758 | + | 6.16367i | 0.573106 | + | 0.330883i | 0.758389 | − | 0.651802i | \(-0.225987\pi\) |
−0.185283 | + | 0.982685i | \(0.559320\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.2211 | + | 5.90115i | −0.547123 | + | 0.315881i | −0.747961 | − | 0.663743i | \(-0.768967\pi\) |
0.200838 | + | 0.979624i | \(0.435634\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 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 | \(-0.949106\pi\) | ||
0.987245 | − | 0.159208i | \(-0.0508940\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −44.0787 | −2.31993 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.64304 | + | 4.99006i | 0.452397 | + | 0.261192i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.8755 | + | 8.58836i | −0.776494 | + | 0.448309i | −0.835186 | − | 0.549967i | \(-0.814640\pi\) |
0.0586924 | + | 0.998276i | \(0.481307\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 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 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 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 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.63671 | − | 3.83171i | 0.336495 | − | 0.194275i | −0.322226 | − | 0.946663i | \(-0.604431\pi\) |
0.658721 | + | 0.752387i | \(0.271098\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.17668 | − | 5.29816i | −0.464085 | − | 0.267939i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.4848 | 1.03070 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.30262i | 0.0653766i | 0.999466 | + | 0.0326883i | \(0.0104069\pi\) | ||||
−0.999466 | + | 0.0326883i | \(0.989593\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.18778 | − | 4.72722i | −0.408878 | − | 0.236066i | 0.281429 | − | 0.959582i | \(-0.409191\pi\) |
−0.690308 | + | 0.723516i | \(0.742525\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.19492 | + | 2.06966i | 0.0595233 | + | 0.103097i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.59700 | − | 2.07673i | 0.178296 | − | 0.102940i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.5182 | − | 9.53678i | −0.816771 | − | 0.471563i | 0.0325304 | − | 0.999471i | \(-0.489643\pi\) |
−0.849302 | + | 0.527908i | \(0.822977\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.45921 | 0.366158 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.309855 | + | 0.536685i | 0.0150302 | + | 0.0260331i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | \(0.0947992\pi\) | ||||
−0.955978 | + | 0.293437i | \(0.905201\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.9227 | + | 27.5789i | −0.761686 | + | 1.31928i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.4639 | − | 8.35076i | 0.690326 | − | 0.398560i | −0.113408 | − | 0.993548i | \(-0.536177\pi\) |
0.803734 | + | 0.594989i | \(0.202843\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.2403 | − | 15.1499i | 1.24672 | − | 0.719791i | 0.276262 | − | 0.961082i | \(-0.410904\pi\) |
0.970453 | + | 0.241291i | \(0.0775708\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.0841 | + | 17.4662i | −0.478033 | + | 0.827977i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 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 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 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 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 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 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 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 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 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 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 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 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.75734 | − | 1.59195i | −0.124437 | − | 0.0718437i | 0.436490 | − | 0.899709i | \(-0.356222\pi\) |
−0.560926 | + | 0.827866i | \(0.689555\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.7395 | − | 10.2419i | 0.798947 | − | 0.461272i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 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 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 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 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 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 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 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 | \(-0.962061\pi\) | ||
0.992905 | − | 0.118908i | \(-0.0379394\pi\) | |||||||
\(524\) | 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 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 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 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 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 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −30.7803 | − | 53.3130i | −1.31128 | − | 2.27121i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 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 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 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 | −0.792955 | − | 0.609280i | \(-0.791458\pi\) |
0.131175 | + | 0.991359i | \(0.458125\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 0.940253i | − | 0.0392112i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 11.8357i | − | 0.492726i | −0.969178 | − | 0.246363i | \(-0.920764\pi\) | ||
0.969178 | − | 0.246363i | \(-0.0792355\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.04439 | − | 3.54098i | −0.0846699 | − | 0.146653i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 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 | 0 | ||||||||
\(592\) | 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 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.5223 | − | 17.6221i | −1.24711 | − | 0.720018i | −0.276576 | − | 0.960992i | \(-0.589200\pi\) |
−0.970532 | + | 0.240974i | \(0.922533\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.39266 | − | 1.95875i | 0.138389 | − | 0.0798991i | −0.429207 | − | 0.903206i | \(-0.641207\pi\) |
0.567596 | + | 0.823307i | \(0.307874\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.66332 | − | 16.7374i | −0.392870 | − | 0.680470i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.5377 | + | 7.23862i | 0.508888 | + | 0.293807i | 0.732376 | − | 0.680900i | \(-0.238411\pi\) |
−0.223488 | + | 0.974707i | \(0.571744\pi\) | |||||||
\(608\) | 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 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.14491 | + | 1.81571i | 0.126609 | + | 0.0730979i | 0.561967 | − | 0.827160i | \(-0.310045\pi\) |
−0.435358 | + | 0.900258i | \(0.643378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.2737 | − | 8.24091i | 0.573708 | − | 0.331230i | −0.184921 | − | 0.982753i | \(-0.559203\pi\) |
0.758629 | + | 0.651523i | \(0.225870\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.8863 | − | 20.5876i | 0.475450 | − | 0.823504i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.41512 | + | 12.8434i | −0.294260 | + | 0.509673i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.25538 | − | 4.18889i | 0.286570 | − | 0.165451i | −0.349824 | − | 0.936815i | \(-0.613759\pi\) |
0.636394 | + | 0.771364i | \(0.280425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.0021 | − | 10.3935i | −0.709934 | − | 0.409881i | 0.101103 | − | 0.994876i | \(-0.467763\pi\) |
−0.811037 | + | 0.584995i | \(0.801096\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 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 | 0.364261 | − | 0.931297i | \(-0.381322\pi\) |
−0.624396 | + | 0.781108i | \(0.714655\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.9927 | − | 25.9680i | −0.585811 | − | 1.01465i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.0493 | + | 21.9678i | −1.48219 | + | 0.855743i | −0.999796 | − | 0.0202102i | \(-0.993566\pi\) |
−0.482395 | + | 0.875954i | \(0.660233\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.1649 | − | 12.7969i | −0.862115 | − | 0.497742i | 0.00260513 | − | 0.999997i | \(-0.499171\pi\) |
−0.864720 | + | 0.502254i | \(0.832504\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.0789 | −1.20338 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 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 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 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 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.71672 | + | 8.16961i | −0.179693 | + | 0.311237i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.1115 | − | 8.14729i | 0.536828 | − | 0.309938i | −0.206965 | − | 0.978348i | \(-0.566359\pi\) |
0.743792 | + | 0.668411i | \(0.233025\pi\) | |||||||
\(692\) | 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 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 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 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 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 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.57409 | + | 0.908804i | 0.0584604 | + | 0.0337521i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.8208 | − | 18.3717i | 1.18017 | − | 0.681370i | 0.224114 | − | 0.974563i | \(-0.428051\pi\) |
0.956053 | + | 0.293193i | \(0.0947180\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.35920 | − | 5.81831i | −0.124245 | − | 0.215198i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.41829 | − | 5.43765i | −0.347873 | − | 0.200844i | 0.315875 | − | 0.948801i | \(-0.397702\pi\) |
−0.663748 | + | 0.747956i | \(0.731035\pi\) | |||||||
\(734\) | 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 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.8751 | + | 9.16552i | 0.582403 | + | 0.336250i | 0.762088 | − | 0.647474i | \(-0.224175\pi\) |
−0.179685 | + | 0.983724i | \(0.557508\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −37.8776 | + | 21.8687i | −1.38773 | + | 0.801206i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 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 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 39.3254 | − | 22.7045i | 1.41996 | − | 0.819813i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.7306 | − | 20.0517i | −1.25242 | − | 0.723085i | −0.280830 | − | 0.959758i | \(-0.590610\pi\) |
−0.971589 | + | 0.236673i | \(0.923943\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.1785 | + | 8.76333i | −0.541745 | + | 0.312777i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.9920 | − | 23.0894i | −1.42556 | − | 0.823048i | −0.428795 | − | 0.903402i | \(-0.641062\pi\) |
−0.996766 | + | 0.0803536i | \(0.974395\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.3501 | 0.935719 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 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 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.34922 | + | 5.80102i | 0.118191 | + | 0.204714i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 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 | \(-0.956643\pi\) | ||
0.990738 | − | 0.135788i | \(-0.0433567\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 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 | \(-0.669512\pi\) |
0.492238 | + | 0.870460i | \(0.336179\pi\) | |||||||
\(822\) | 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 | 0 | ||||||||
\(826\) | 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 | \(0.230349\pi\) | ||||
−0.749385 | + | 0.662134i | \(0.769651\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.5241 | + | 37.2808i | 0.744871 | + | 1.29015i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.43348 | 0.118115 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.84358 | + | 5.68319i | 0.337434 | + | 0.194817i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.7143 | − | 16.0008i | 0.948919 | − | 0.547858i | 0.0561738 | − | 0.998421i | \(-0.482110\pi\) |
0.892745 | + | 0.450563i | \(0.148777\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 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 | 0.744587 | − | 0.667526i | \(-0.232647\pi\) |
−0.205801 | + | 0.978594i | \(0.565980\pi\) | |||||||
\(860\) | 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 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 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 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 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 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 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 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 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 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 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 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 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 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.86306 | − | 2.23034i | 0.127989 | − | 0.0738944i | −0.434639 | − | 0.900605i | \(-0.643124\pi\) |
0.562627 | + | 0.826711i | \(0.309791\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.33572 | + | 2.50323i | 0.143491 | + | 0.0828448i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 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 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 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 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 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 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 8.45272i | − | 0.276433i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 46.1410i | − | 1.50736i | −0.657241 | − | 0.753680i | \(-0.728277\pi\) | ||
0.657241 | − | 0.753680i | \(-0.271723\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 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 | −0.631804 | − | 0.775128i | \(-0.717685\pi\) |
0.355378 | + | 0.934723i | \(0.384352\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.72718 | − | 13.3839i | 0.250835 | − | 0.434459i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 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 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.2501 | − | 26.4139i | −0.491939 | − | 0.852063i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 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 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 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 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.1944 | − | 17.4327i | −0.966003 | − | 0.557722i | −0.0679878 | − | 0.997686i | \(-0.521658\pi\) |
−0.898015 | + | 0.439964i | \(0.854991\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.7229 | + | 6.76824i | −0.374666 | + | 0.216314i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.3916 | + | 7.15427i | 0.392839 | + | 0.226806i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.5820 | + | 8.41890i | −0.461816 | + | 0.266629i | −0.712807 | − | 0.701360i | \(-0.752577\pi\) |
0.250992 | + | 0.967989i | \(0.419243\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))