Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1368,2,Mod(505,1368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1368, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1368.505");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.s (of order \(3\), 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: | \(10.9235349965\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 577.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1368.577 |
Dual form | 1368.2.s.a.505.1 |
$q$-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 \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).
\(n\) | \(343\) | \(685\) | \(1009\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.00000 | − | 3.46410i | −0.894427 | − | 1.54919i | −0.834512 | − | 0.550990i | \(-0.814250\pi\) |
−0.0599153 | − | 0.998203i | \(-0.519083\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | + | 1.73205i | −0.277350 | + | 0.480384i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) |
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | + | 1.73205i | 0.242536 | + | 0.420084i | 0.961436 | − | 0.275029i | \(-0.0886875\pi\) |
−0.718900 | + | 0.695113i | \(0.755354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.500000 | − | 4.33013i | 0.114708 | − | 0.993399i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | − | 5.19615i | 0.625543 | − | 1.08347i | −0.362892 | − | 0.931831i | \(-0.618211\pi\) |
0.988436 | − | 0.151642i | \(-0.0484560\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.50000 | + | 9.52628i | −1.10000 | + | 1.90526i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | + | 3.46410i | −0.371391 | + | 0.643268i | −0.989780 | − | 0.142605i | \(-0.954452\pi\) |
0.618389 | + | 0.785872i | \(0.287786\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.0000 | −1.79605 | −0.898027 | − | 0.439941i | \(-0.854999\pi\) | ||||
−0.898027 | + | 0.439941i | \(0.854999\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.50000 | + | 7.79423i | 0.702782 | + | 1.21725i | 0.967486 | + | 0.252924i | \(0.0813924\pi\) |
−0.264704 | + | 0.964330i | \(0.585274\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | + | 3.46410i | 0.304997 | + | 0.528271i | 0.977261 | − | 0.212041i | \(-0.0680112\pi\) |
−0.672264 | + | 0.740312i | \(0.734678\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | + | 10.3923i | −0.875190 | + | 1.51587i | −0.0186297 | + | 0.999826i | \(0.505930\pi\) |
−0.856560 | + | 0.516047i | \(0.827403\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.00000 | + | 1.73205i | −0.137361 | + | 0.237915i | −0.926497 | − | 0.376303i | \(-0.877195\pi\) |
0.789136 | + | 0.614218i | \(0.210529\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00000 | + | 10.3923i | 0.809040 | + | 1.40130i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.500000 | − | 0.866025i | −0.0650945 | − | 0.112747i | 0.831641 | − | 0.555313i | \(-0.187402\pi\) |
−0.896736 | + | 0.442566i | \(0.854068\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | − | 6.92820i | 0.512148 | − | 0.887066i | −0.487753 | − | 0.872982i | \(-0.662183\pi\) |
0.999901 | − | 0.0140840i | \(-0.00448323\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.00000 | 0.992278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.50000 | + | 7.79423i | −0.549762 | + | 0.952217i | 0.448528 | + | 0.893769i | \(0.351948\pi\) |
−0.998290 | + | 0.0584478i | \(0.981385\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | − | 5.19615i | −0.356034 | − | 0.616670i | 0.631260 | − | 0.775571i | \(-0.282538\pi\) |
−0.987294 | + | 0.158901i | \(0.949205\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.50000 | + | 7.79423i | 0.526685 | + | 0.912245i | 0.999517 | + | 0.0310925i | \(0.00989865\pi\) |
−0.472831 | + | 0.881153i | \(0.656768\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | + | 3.46410i | 0.225018 | + | 0.389742i | 0.956325 | − | 0.292306i | \(-0.0944227\pi\) |
−0.731307 | + | 0.682048i | \(0.761089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.00000 | 0.548821 | 0.274411 | − | 0.961613i | \(-0.411517\pi\) | ||||
0.274411 | + | 0.961613i | \(0.411517\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | − | 6.92820i | 0.433861 | − | 0.751469i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | + | 15.5885i | −0.953998 | + | 1.65237i | −0.217354 | + | 0.976093i | \(0.569742\pi\) |
−0.736644 | + | 0.676280i | \(0.763591\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.0000 | + | 6.92820i | −1.64157 | + | 0.710819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.500000 | − | 0.866025i | −0.0507673 | − | 0.0879316i | 0.839525 | − | 0.543321i | \(-0.182833\pi\) |
−0.890292 | + | 0.455389i | \(0.849500\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | − | 10.3923i | 0.597022 | − | 1.03407i | −0.396236 | − | 0.918149i | \(-0.629684\pi\) |
0.993258 | − | 0.115924i | \(-0.0369830\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.0000 | −1.37946 | −0.689730 | − | 0.724066i | \(-0.742271\pi\) | ||||
−0.689730 | + | 0.724066i | \(0.742271\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.0000 | −1.54678 | −0.773389 | − | 0.633932i | \(-0.781440\pi\) | ||||
−0.773389 | + | 0.633932i | \(0.781440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.00000 | 0.0940721 | 0.0470360 | − | 0.998893i | \(-0.485022\pi\) | ||||
0.0470360 | + | 0.998893i | \(0.485022\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −24.0000 | −2.23801 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 24.0000 | 2.14663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.00000 | − | 5.19615i | 0.266207 | − | 0.461084i | −0.701672 | − | 0.712500i | \(-0.747563\pi\) |
0.967879 | + | 0.251416i | \(0.0808962\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.50000 | − | 12.9904i | −0.655278 | − | 1.13497i | −0.981824 | − | 0.189794i | \(-0.939218\pi\) |
0.326546 | − | 0.945181i | \(-0.394115\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.50000 | − | 7.79423i | 0.384461 | − | 0.665906i | −0.607233 | − | 0.794524i | \(-0.707721\pi\) |
0.991694 | + | 0.128618i | \(0.0410540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.50000 | − | 11.2583i | 0.551323 | − | 0.954919i | −0.446857 | − | 0.894606i | \(-0.647457\pi\) |
0.998179 | − | 0.0603135i | \(-0.0192101\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.00000 | − | 5.19615i | 0.250873 | − | 0.434524i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.0000 | 1.32873 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.00000 | − | 8.66025i | −0.409616 | − | 0.709476i | 0.585231 | − | 0.810867i | \(-0.301004\pi\) |
−0.994847 | + | 0.101391i | \(0.967671\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.00000 | 0.162758 | 0.0813788 | − | 0.996683i | \(-0.474068\pi\) | ||||
0.0813788 | + | 0.996683i | \(0.474068\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.0000 | + | 34.6410i | 1.60644 | + | 2.78243i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.00000 | − | 6.92820i | −0.319235 | − | 0.552931i | 0.661094 | − | 0.750303i | \(-0.270093\pi\) |
−0.980329 | + | 0.197372i | \(0.936759\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.0000 | −0.861586 | −0.430793 | − | 0.902451i | \(-0.641766\pi\) | ||||
−0.430793 | + | 0.902451i | \(0.641766\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.00000 | − | 13.8564i | 0.619059 | − | 1.07224i | −0.370599 | − | 0.928793i | \(-0.620848\pi\) |
0.989658 | − | 0.143448i | \(-0.0458190\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.0000 | − | 22.5167i | −0.988372 | − | 1.71191i | −0.625871 | − | 0.779926i | \(-0.715256\pi\) |
−0.362500 | − | 0.931984i | \(-0.618077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.00000 | −0.672692 | −0.336346 | − | 0.941739i | \(-0.609191\pi\) | ||||
−0.336346 | + | 0.941739i | \(0.609191\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.00000 | + | 12.1244i | −0.520306 | + | 0.901196i | 0.479415 | + | 0.877588i | \(0.340849\pi\) |
−0.999721 | + | 0.0236082i | \(0.992485\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00000 | − | 6.92820i | −0.294086 | − | 0.509372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.00000 | − | 5.19615i | −0.219382 | − | 0.379980i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0000 | −0.868290 | −0.434145 | − | 0.900843i | \(-0.642949\pi\) | ||||
−0.434145 | + | 0.900843i | \(0.642949\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.00000 | + | 5.19615i | 0.215945 | + | 0.374027i | 0.953564 | − | 0.301189i | \(-0.0973836\pi\) |
−0.737620 | + | 0.675216i | \(0.764050\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.00000 | − | 15.5885i | 0.637993 | − | 1.10504i | −0.347879 | − | 0.937539i | \(-0.613098\pi\) |
0.985873 | − | 0.167497i | \(-0.0535685\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.0000 | − | 31.1769i | 1.25717 | − | 2.17749i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.50000 | + | 12.9904i | −0.103757 | + | 0.898563i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.00000 | + | 10.3923i | 0.413057 | + | 0.715436i | 0.995222 | − | 0.0976347i | \(-0.0311277\pi\) |
−0.582165 | + | 0.813070i | \(0.697794\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.00000 | − | 13.8564i | 0.545595 | − | 0.944999i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.00000 | − | 8.66025i | −0.334825 | − | 0.579934i | 0.648626 | − | 0.761107i | \(-0.275344\pi\) |
−0.983451 | + | 0.181173i | \(0.942010\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.0000 | −1.26107 | −0.630537 | − | 0.776159i | \(-0.717165\pi\) | ||||
−0.630537 | + | 0.776159i | \(0.717165\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.00000 | −0.528655 | −0.264327 | − | 0.964433i | \(-0.585150\pi\) | ||||
−0.264327 | + | 0.964433i | \(0.585150\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.50000 | + | 9.52628i | 0.360317 | + | 0.624087i | 0.988013 | − | 0.154371i | \(-0.0493352\pi\) |
−0.627696 | + | 0.778459i | \(0.716002\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 48.0000 | 3.13117 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.5000 | + | 18.1865i | −0.676364 | + | 1.17150i | 0.299704 | + | 0.954032i | \(0.403112\pi\) |
−0.976068 | + | 0.217465i | \(0.930221\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.0000 | + | 24.2487i | 0.894427 | + | 1.54919i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.00000 | + | 5.19615i | 0.445399 | + | 0.330623i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.50000 | − | 4.33013i | 0.157799 | − | 0.273315i | −0.776276 | − | 0.630393i | \(-0.782894\pi\) |
0.934075 | + | 0.357078i | \(0.116227\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.00000 | + | 15.5885i | −0.565825 | + | 0.980038i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.50000 | − | 2.59808i | 0.0935674 | − | 0.162064i | −0.815442 | − | 0.578838i | \(-0.803506\pi\) |
0.909010 | + | 0.416775i | \(0.136840\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.00000 | + | 13.8564i | 0.493301 | + | 0.854423i | 0.999970 | − | 0.00771799i | \(-0.00245674\pi\) |
−0.506669 | + | 0.862141i | \(0.669123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.00000 | 0.491436 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.00000 | + | 3.46410i | 0.121942 | + | 0.211210i | 0.920534 | − | 0.390664i | \(-0.127754\pi\) |
−0.798591 | + | 0.601874i | \(0.794421\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.0000 | + | 17.3205i | 0.607457 | + | 1.05215i | 0.991658 | + | 0.128897i | \(0.0411435\pi\) |
−0.384201 | + | 0.923249i | \(0.625523\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.5000 | − | 28.5788i | 0.994987 | − | 1.72337i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.0000 | 0.721010 | 0.360505 | − | 0.932757i | \(-0.382604\pi\) | ||||
0.360505 | + | 0.932757i | \(0.382604\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.50000 | + | 11.2583i | −0.387757 | + | 0.671616i | −0.992148 | − | 0.125073i | \(-0.960084\pi\) |
0.604390 | + | 0.796689i | \(0.293417\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.50000 | − | 11.2583i | −0.386385 | − | 0.669238i | 0.605575 | − | 0.795788i | \(-0.292943\pi\) |
−0.991960 | + | 0.126550i | \(0.959610\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.00000 | 0.233682 | 0.116841 | − | 0.993151i | \(-0.462723\pi\) | ||||
0.116841 | + | 0.993151i | \(0.462723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.00000 | + | 3.46410i | −0.116445 | + | 0.201688i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.00000 | + | 10.3923i | 0.346989 | + | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −32.0000 | −1.83231 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.5000 | − | 21.6506i | −0.713413 | − | 1.23567i | −0.963569 | − | 0.267461i | \(-0.913815\pi\) |
0.250156 | − | 0.968206i | \(-0.419518\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.00000 | 0.113410 | 0.0567048 | − | 0.998391i | \(-0.481941\pi\) | ||||
0.0567048 | + | 0.998391i | \(0.481941\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.50000 | − | 16.4545i | 0.536972 | − | 0.930062i | −0.462093 | − | 0.886831i | \(-0.652902\pi\) |
0.999065 | − | 0.0432311i | \(-0.0137652\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.00000 | − | 5.19615i | 0.168497 | − | 0.291845i | −0.769395 | − | 0.638774i | \(-0.779442\pi\) |
0.937892 | + | 0.346929i | \(0.112775\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.00000 | − | 10.3923i | 0.335936 | − | 0.581857i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.00000 | − | 3.46410i | 0.445132 | − | 0.192748i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.0000 | − | 19.0526i | −0.610170 | − | 1.05685i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.0000 | 0.714545 | 0.357272 | − | 0.934000i | \(-0.383707\pi\) | ||||
0.357272 | + | 0.934000i | \(0.383707\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 36.0000 | 1.96689 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.50000 | − | 2.59808i | −0.0817102 | − | 0.141526i | 0.822274 | − | 0.569091i | \(-0.192705\pi\) |
−0.903985 | + | 0.427565i | \(0.859372\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 30.0000 | 1.62459 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.50000 | − | 7.79423i | −0.241573 | − | 0.418416i | 0.719590 | − | 0.694399i | \(-0.244330\pi\) |
−0.961162 | + | 0.275983i | \(0.910997\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.0000 | −1.49881 | −0.749403 | − | 0.662114i | \(-0.769659\pi\) | ||||
−0.749403 | + | 0.662114i | \(0.769659\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.0000 | −0.585471 | −0.292735 | − | 0.956193i | \(-0.594566\pi\) | ||||
−0.292735 | + | 0.956193i | \(0.594566\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.0000 | + | 20.7846i | −0.636894 | + | 1.10313i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.00000 | − | 1.73205i | −0.0527780 | − | 0.0914141i | 0.838429 | − | 0.545010i | \(-0.183474\pi\) |
−0.891207 | + | 0.453596i | \(0.850141\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5000 | − | 4.33013i | −0.973684 | − | 0.227901i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.0000 | − | 31.1769i | 0.942163 | − | 1.63187i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.0000 | − | 22.5167i | 0.678594 | − | 1.17536i | −0.296810 | − | 0.954937i | \(-0.595923\pi\) |
0.975404 | − | 0.220423i | \(-0.0707439\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.00000 | 0.207112 | 0.103556 | − | 0.994624i | \(-0.466978\pi\) | ||||
0.103556 | + | 0.994624i | \(0.466978\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.00000 | − | 6.92820i | −0.206010 | − | 0.356821i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0000 | −0.616399 | −0.308199 | − | 0.951322i | \(-0.599726\pi\) | ||||
−0.308199 | + | 0.951322i | \(0.599726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.00000 | − | 6.92820i | −0.204390 | − | 0.354015i | 0.745548 | − | 0.666452i | \(-0.232188\pi\) |
−0.949938 | + | 0.312437i | \(0.898855\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.00000 | − | 3.46410i | 0.101404 | − | 0.175637i | −0.810859 | − | 0.585241i | \(-0.801000\pi\) |
0.912263 | + | 0.409604i | \(0.134333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.00000 | − | 13.8564i | 0.402524 | − | 0.697191i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.00000 | + | 12.1244i | 0.351320 | + | 0.608504i | 0.986481 | − | 0.163876i | \(-0.0523996\pi\) |
−0.635161 | + | 0.772380i | \(0.719066\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.50000 | − | 2.59808i | −0.0749064 | − | 0.129742i | 0.826139 | − | 0.563466i | \(-0.190532\pi\) |
−0.901046 | + | 0.433724i | \(0.857199\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.0000 | − | 17.3205i | 0.498135 | − | 0.862796i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.00000 | −0.297409 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.5000 | − | 30.3109i | 0.865319 | − | 1.49878i | −0.00141047 | − | 0.999999i | \(-0.500449\pi\) |
0.866730 | − | 0.498778i | \(-0.166218\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.0000 | − | 17.3205i | −0.490881 | − | 0.850230i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0000 | + | 19.0526i | 0.536107 | + | 0.928565i | 0.999109 | + | 0.0422075i | \(0.0134391\pi\) |
−0.463002 | + | 0.886357i | \(0.653228\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −22.0000 | −1.06716 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.0000 | + | 25.9808i | −0.722525 | + | 1.25145i | 0.237460 | + | 0.971397i | \(0.423685\pi\) |
−0.959985 | + | 0.280052i | \(0.909648\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.00000 | + | 8.66025i | −0.240285 | + | 0.416185i | −0.960795 | − | 0.277259i | \(-0.910574\pi\) |
0.720511 | + | 0.693444i | \(0.243907\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21.0000 | − | 15.5885i | −1.00457 | − | 0.745697i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.00000 | + | 12.1244i | 0.334092 | + | 0.578664i | 0.983310 | − | 0.181938i | \(-0.0582371\pi\) |
−0.649218 | + | 0.760602i | \(0.724904\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.500000 | − | 0.866025i | 0.0237557 | − | 0.0411461i | −0.853903 | − | 0.520432i | \(-0.825771\pi\) |
0.877659 | + | 0.479286i | \(0.159104\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 72.0000 | 3.41313 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.0000 | −1.55737 | −0.778683 | − | 0.627417i | \(-0.784112\pi\) | ||||
−0.778683 | + | 0.627417i | \(0.784112\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.5000 | − | 23.3827i | −0.635690 | − | 1.10105i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0000 | −0.514558 | −0.257279 | − | 0.966337i | \(-0.582826\pi\) | ||||
−0.257279 | + | 0.966337i | \(0.582826\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.00000 | + | 5.19615i | 0.139724 | + | 0.242009i | 0.927392 | − | 0.374091i | \(-0.122045\pi\) |
−0.787668 | + | 0.616100i | \(0.788712\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.0000 | −1.58011 | −0.790057 | − | 0.613033i | \(-0.789949\pi\) | ||||
−0.790057 | + | 0.613033i | \(0.789949\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.00000 | −0.231372 | −0.115686 | − | 0.993286i | \(-0.536907\pi\) | ||||
−0.115686 | + | 0.993286i | \(0.536907\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.00000 | − | 10.3923i | −0.275880 | − | 0.477839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 38.5000 | + | 28.5788i | 1.76650 | + | 1.31129i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.0000 | − | 17.3205i | 0.456912 | − | 0.791394i | −0.541884 | − | 0.840453i | \(-0.682289\pi\) |
0.998796 | + | 0.0490589i | \(0.0156222\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | + | 3.46410i | −0.0911922 | + | 0.157949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.00000 | + | 3.46410i | −0.0908153 | + | 0.157297i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.0000 | −1.17817 | −0.589086 | − | 0.808070i | \(-0.700512\pi\) | ||||
−0.589086 | + | 0.808070i | \(0.700512\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.00000 | + | 13.8564i | 0.361035 | + | 0.625331i | 0.988131 | − | 0.153611i | \(-0.0490902\pi\) |
−0.627096 | + | 0.778942i | \(0.715757\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.00000 | −0.360302 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.50000 | − | 6.06218i | −0.156682 | − | 0.271380i | 0.776989 | − | 0.629515i | \(-0.216746\pi\) |
−0.933670 | + | 0.358134i | \(0.883413\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.00000 | + | 5.19615i | −0.133763 | + | 0.231685i | −0.925124 | − | 0.379664i | \(-0.876040\pi\) |
0.791361 | + | 0.611349i | \(0.209373\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −48.0000 | −2.13597 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.00000 | − | 13.8564i | 0.354594 | − | 0.614174i | −0.632455 | − | 0.774597i | \(-0.717953\pi\) |
0.987048 | + | 0.160423i | \(0.0512858\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.0000 | + | 48.4974i | 1.23383 | + | 2.13705i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.0000 | − | 31.1769i | 0.791639 | − | 1.37116i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.00000 | −0.0438108 | −0.0219054 | − | 0.999760i | \(-0.506973\pi\) | ||||
−0.0219054 | + | 0.999760i | \(0.506973\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.0000 | + | 17.3205i | −0.437269 | + | 0.757373i | −0.997478 | − | 0.0709788i | \(-0.977388\pi\) |
0.560208 | + | 0.828352i | \(0.310721\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.0000 | − | 17.3205i | −0.435607 | − | 0.754493i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.0000 | −0.779667 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.0000 | + | 55.4256i | 1.38348 | + | 2.39626i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.0000 | 0.904534 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | + | 3.46410i | −0.0859867 | + | 0.148933i | −0.905811 | − | 0.423681i | \(-0.860738\pi\) |
0.819825 | + | 0.572615i | \(0.194071\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.0000 | + | 24.2487i | −0.598597 | + | 1.03680i | 0.394432 | + | 0.918925i | \(0.370941\pi\) |
−0.993028 | + | 0.117875i | \(0.962392\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.0000 | + | 10.3923i | 0.596420 | + | 0.442727i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.0000 | + | 34.6410i | −0.847427 | + | 1.46779i | 0.0360693 | + | 0.999349i | \(0.488516\pi\) |
−0.883497 | + | 0.468438i | \(0.844817\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.0000 | −0.463595 | −0.231797 | − | 0.972764i | \(-0.574461\pi\) | ||||
−0.231797 | + | 0.972764i | \(0.574461\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.00000 | − | 3.46410i | −0.0841406 | − | 0.145736i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 46.0000 | 1.92842 | 0.964210 | − | 0.265139i | \(-0.0854179\pi\) | ||||
0.964210 | + | 0.265139i | \(0.0854179\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.0000 | 0.711428 | 0.355714 | − | 0.934595i | \(-0.384238\pi\) | ||||
0.355714 | + | 0.934595i | \(0.384238\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 33.0000 | + | 57.1577i | 1.37620 | + | 2.38364i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.0000 | −1.54033 | −0.770165 | − | 0.637845i | \(-0.779826\pi\) | ||||
−0.770165 | + | 0.637845i | \(0.779826\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.00000 | − | 5.19615i | 0.124247 | − | 0.215203i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.00000 | + | 3.46410i | 0.0825488 | + | 0.142979i | 0.904344 | − | 0.426804i | \(-0.140361\pi\) |
−0.821795 | + | 0.569783i | \(0.807027\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.00000 | + | 43.3013i | −0.206021 | + | 1.78420i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.5000 | + | 18.1865i | −0.431183 | + | 0.746831i | −0.996976 | − | 0.0777165i | \(-0.975237\pi\) |
0.565792 | + | 0.824548i | \(0.308570\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.0000 | − | 32.9090i | 0.776319 | − | 1.34462i | −0.157731 | − | 0.987482i | \(-0.550418\pi\) |
0.934050 | − | 0.357142i | \(-0.116249\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.0000 | −0.530281 | −0.265141 | − | 0.964210i | \(-0.585418\pi\) | ||||
−0.265141 | + | 0.964210i | \(0.585418\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.00000 | + | 6.92820i | 0.162623 | + | 0.281672i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0000 | − | 20.7846i | −0.485468 | − | 0.840855i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.0000 | + | 19.0526i | 0.444286 | + | 0.769526i | 0.998002 | − | 0.0631797i | \(-0.0201241\pi\) |
−0.553716 | + | 0.832705i | \(0.686791\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.50000 | − | 2.59808i | 0.0603877 | − | 0.104595i | −0.834251 | − | 0.551385i | \(-0.814100\pi\) |
0.894639 | + | 0.446790i | \(0.147433\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.0000 | −0.803868 | −0.401934 | − | 0.915669i | \(-0.631662\pi\) | ||||
−0.401934 | + | 0.915669i | \(0.631662\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.5000 | − | 35.5070i | −0.820000 | − | 1.42028i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.00000 | + | 3.46410i | 0.0797452 | + | 0.138123i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.00000 | − | 6.92820i | 0.159237 | − | 0.275807i | −0.775356 | − | 0.631524i | \(-0.782430\pi\) |
0.934594 | + | 0.355716i | \(0.115763\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.0000 | −0.952411 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.00000 | − | 12.1244i | 0.277350 | − | 0.480384i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5000 | + | 28.5788i | 0.651711 | + | 1.12880i | 0.982708 | + | 0.185164i | \(0.0592817\pi\) |
−0.330997 | + | 0.943632i | \(0.607385\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.50000 | − | 4.33013i | −0.0985904 | − | 0.170764i | 0.812511 | − | 0.582946i | \(-0.198100\pi\) |
−0.911101 | + | 0.412182i | \(0.864767\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.0000 | 0.550397 | 0.275198 | − | 0.961387i | \(-0.411256\pi\) | ||||
0.275198 | + | 0.961387i | \(0.411256\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.50000 | + | 2.59808i | 0.0588802 | + | 0.101983i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −36.0000 | −1.40879 | −0.704394 | − | 0.709809i | \(-0.748781\pi\) | ||||
−0.704394 | + | 0.709809i | \(0.748781\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.0000 | + | 51.9615i | −1.17220 | + | 2.03030i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.00000 | − | 10.3923i | 0.233727 | − | 0.404827i | −0.725175 | − | 0.688565i | \(-0.758241\pi\) |
0.958902 | + | 0.283738i | \(0.0915745\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.0000 | + | 17.3205i | −0.388955 | + | 0.673690i | −0.992309 | − | 0.123784i | \(-0.960497\pi\) |
0.603354 | + | 0.797473i | \(0.293830\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0000 | + | 20.7846i | 0.464642 | + | 0.804783i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0000 | + | 20.7846i | −0.463255 | + | 0.802381i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.0000 | 1.15642 | 0.578208 | − | 0.815890i | \(-0.303752\pi\) | ||||
0.578208 | + | 0.815890i | \(0.303752\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.00000 | 0.0768662 | 0.0384331 | − | 0.999261i | \(-0.487763\pi\) | ||||
0.0384331 | + | 0.999261i | \(0.487763\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.0000 | 1.07139 | 0.535695 | − | 0.844411i | \(-0.320050\pi\) | ||||
0.535695 | + | 0.844411i | \(0.320050\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.0000 | −1.37549 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.00000 | − | 3.46410i | −0.0761939 | − | 0.131972i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.0000 | 1.36950 | 0.684752 | − | 0.728776i | \(-0.259910\pi\) | ||||
0.684752 | + | 0.728776i | \(0.259910\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −52.0000 | −1.97247 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.00000 | + | 15.5885i | −0.340899 | + | 0.590455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.00000 | − | 10.3923i | −0.226617 | − | 0.392512i | 0.730186 | − | 0.683248i | \(-0.239433\pi\) |
−0.956803 | + | 0.290736i | \(0.906100\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.00000 | − | 8.66025i | 0.0377157 | − | 0.326628i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.00000 | + | 15.5885i | −0.338002 | + | 0.585437i | −0.984057 | − | 0.177854i | \(-0.943084\pi\) |
0.646055 | + | 0.763291i | \(0.276418\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −30.0000 | + | 51.9615i | −1.12351 | + | 1.94597i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.0000 | −0.897549 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.0000 | − | 29.4449i | −0.633993 | − | 1.09811i | −0.986728 | − | 0.162385i | \(-0.948081\pi\) |
0.352735 | − | 0.935723i | \(-0.385252\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22.0000 | − | 38.1051i | −0.817059 | − | 1.41519i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.00000 | + | 6.92820i | 0.148352 | + | 0.256953i | 0.930618 | − | 0.365991i | \(-0.119270\pi\) |
−0.782267 | + | 0.622944i | \(0.785937\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.00000 | + | 6.92820i | −0.147945 | + | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.0000 | 0.812589 | 0.406294 | − | 0.913742i | \(-0.366821\pi\) | ||||
0.406294 | + | 0.913742i | \(0.366821\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.5000 | − | 23.3827i | 0.497279 | − | 0.861312i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.50000 | + | 4.33013i | 0.0919640 | + | 0.159286i | 0.908337 | − | 0.418238i | \(-0.137352\pi\) |
−0.816373 | + | 0.577524i | \(0.804019\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.00000 | − | 5.19615i | −0.110059 | − | 0.190628i | 0.805735 | − | 0.592277i | \(-0.201771\pi\) |
−0.915794 | + | 0.401648i | \(0.868437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.0000 | + | 34.6410i | −0.732743 | + | 1.26915i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.0000 | + | 32.9090i | −0.693320 | + | 1.20087i | 0.277424 | + | 0.960748i | \(0.410519\pi\) |
−0.970744 | + | 0.240118i | \(0.922814\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.00000 | − | 6.92820i | −0.145575 | − | 0.252143i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.00000 | − | 12.1244i | −0.254419 | − | 0.440667i | 0.710318 | − | 0.703881i | \(-0.248551\pi\) |
−0.964738 | + | 0.263213i | \(0.915218\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.0000 | −0.616250 | −0.308125 | − | 0.951346i | \(-0.599701\pi\) | ||||
−0.308125 | + | 0.951346i | \(0.599701\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.00000 | 0.0722158 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.00000 | + | 1.73205i | −0.0360609 | + | 0.0624593i | −0.883493 | − | 0.468445i | \(-0.844814\pi\) |
0.847432 | + | 0.530904i | \(0.178148\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.0000 | − | 45.0333i | 0.935155 | − | 1.61974i | 0.160798 | − | 0.986987i | \(-0.448593\pi\) |
0.774357 | − | 0.632749i | \(-0.218073\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 55.0000 | − | 95.2628i | 1.97566 | − | 3.42194i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 36.0000 | − | 15.5885i | 1.28983 | − | 0.558514i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.00000 | + | 15.5885i | 0.322045 | + | 0.557799i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.0000 | + | 27.7128i | −0.571064 | + | 0.989113i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.0000 | 1.46149 | 0.730746 | − | 0.682649i | \(-0.239172\pi\) | ||||
0.730746 | + | 0.682649i | \(0.239172\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.00000 | + | 13.8564i | 0.284088 | + | 0.492055i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.0000 | −1.48772 | −0.743858 | − | 0.668338i | \(-0.767006\pi\) | ||||
−0.743858 | + | 0.668338i | \(0.767006\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.5000 | − | 23.3827i | −0.476405 | − | 0.825157i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.0000 | −0.738321 | −0.369160 | − | 0.929366i | \(-0.620355\pi\) | ||||
−0.369160 | + | 0.929366i | \(0.620355\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 22.0000 | + | 38.1051i | 0.770626 | + | 1.33476i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.0000 | − | 6.92820i | 0.559769 | − | 0.242387i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.0000 | + | 32.9090i | −0.663105 | + | 1.14853i | 0.316691 | + | 0.948529i | \(0.397428\pi\) |
−0.979795 | + | 0.200002i | \(0.935905\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.0000 | − | 22.5167i | 0.453152 | − | 0.784881i | −0.545428 | − | 0.838157i | \(-0.683633\pi\) |
0.998580 | + | 0.0532760i | \(0.0169663\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.5000 | + | 47.6314i | −0.956269 | + | 1.65631i | −0.224831 | + | 0.974398i | \(0.572183\pi\) |
−0.731438 | + | 0.681908i | \(0.761150\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.0000 | −0.416777 | −0.208389 | − | 0.978046i | \(-0.566822\pi\) | ||||
−0.208389 | + | 0.978046i | \(0.566822\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.00000 | − | 12.1244i | −0.242536 | − | 0.420084i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −64.0000 | −2.21481 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.50000 | + | 11.2583i | 0.224138 | + | 0.388218i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.0000 | − | 31.1769i | 0.619219 | − | 1.07252i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.00000 | − | 10.3923i | 0.205677 | − | 0.356244i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.0000 | − | 36.3731i | −0.719026 | − | 1.24539i | −0.961386 | − | 0.275204i | \(-0.911255\pi\) |
0.242360 | − | 0.970186i | \(-0.422079\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.5000 | − | 30.3109i | −0.597789 | − | 1.03540i | −0.993147 | − | 0.116873i | \(-0.962713\pi\) |
0.395358 | − | 0.918527i | \(-0.370620\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.5000 | + | 25.1147i | −0.494734 | + | 0.856904i | −0.999982 | − | 0.00607046i | \(-0.998068\pi\) |
0.505248 | + | 0.862974i | \(0.331401\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.00000 | −0.204242 | −0.102121 | − | 0.994772i | \(-0.532563\pi\) | ||||
−0.102121 | + | 0.994772i | \(0.532563\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −52.0000 | + | 90.0666i | −1.76805 | + | 3.06236i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.00000 | − | 10.3923i | −0.203536 | − | 0.352535i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.00000 | − | 15.5885i | −0.304953 | − | 0.528195i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.0000 | − | 34.6410i | −0.675352 | − | 1.16974i | −0.976366 | − | 0.216124i | \(-0.930658\pi\) |
0.301014 | − | 0.953620i | \(-0.402675\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.00000 | −0.235836 | −0.117918 | − | 0.993023i | \(-0.537622\pi\) | ||||
−0.117918 | + | 0.993023i | \(0.537622\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.5000 | − | 37.2391i | 0.723533 | − | 1.25320i | −0.236043 | − | 0.971743i | \(-0.575850\pi\) |
0.959575 | − | 0.281453i | \(-0.0908162\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.0000 | − | 27.7128i | 0.537227 | − | 0.930505i | −0.461825 | − | 0.886971i | \(-0.652805\pi\) |
0.999052 | − | 0.0435339i | \(-0.0138616\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 42.0000 | + | 31.1769i | 1.40548 | + | 1.04330i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.0000 | + | 31.1769i | 0.601674 | + | 1.04213i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.0000 | − | 34.6410i | 0.667037 | − | 1.15534i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.00000 | −0.133259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 56.0000 | 1.86150 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.5000 | − | 42.4352i | −0.813509 | − | 1.40904i | −0.910393 | − | 0.413744i | \(-0.864221\pi\) |
0.0968843 | − | 0.995296i | \(-0.469112\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.0000 | 0.463841 | 0.231920 | − | 0.972735i | \(-0.425499\pi\) | ||||
0.231920 | + | 0.972735i | \(0.425499\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.0000 | −0.496428 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.0000 | −0.857661 | −0.428830 | − | 0.903385i | \(-0.641074\pi\) | ||||
−0.428830 | + | 0.903385i | \(0.641074\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.0000 | 0.394985 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.0000 | + | 19.0526i | −0.361678 | + | 0.626444i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.5000 | + | 18.1865i | 0.344494 | + | 0.596681i | 0.985262 | − | 0.171054i | \(-0.0547172\pi\) |
−0.640768 | + | 0.767735i | \(0.721384\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.50000 | + | 30.3109i | −0.114708 | + | 0.993399i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.0000 | + | 20.7846i | −0.392442 | + | 0.679729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.50000 | + | 9.52628i | −0.179677 | + | 0.311210i | −0.941770 | − | 0.336258i | \(-0.890839\pi\) |
0.762093 | + | 0.647468i | \(0.224172\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.00000 | + | 8.66025i | −0.162995 | + | 0.282316i | −0.935942 | − | 0.352155i | \(-0.885449\pi\) |
0.772946 | + | 0.634472i | \(0.218782\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 54.0000 | 1.75848 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.0000 | − | 24.2487i | −0.454939 | − | 0.787977i | 0.543746 | − | 0.839250i | \(-0.317006\pi\) |
−0.998685 | + | 0.0512727i | \(0.983672\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.0000 | −0.584305 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.500000 | + | 0.866025i | 0.0161966 | + | 0.0280533i | 0.874010 | − | 0.485908i | \(-0.161511\pi\) |
−0.857814 | + | 0.513961i | \(0.828178\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.0000 | + | 41.5692i | 0.776622 | + | 1.34515i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 69.0000 | 2.22581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.0000 | − | 20.7846i | 0.386294 | − | 0.669080i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.0000 | − | 46.7654i | −0.868261 | − | 1.50387i | −0.863772 | − | 0.503883i | \(-0.831904\pi\) |
−0.00448958 | − | 0.999990i | \(-0.501429\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.5000 | + | 45.8993i | 0.850425 | + | 1.47298i | 0.880825 | + | 0.473442i | \(0.156989\pi\) |
−0.0303994 | + | 0.999538i | \(0.509678\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47.0000 | 1.50366 | 0.751832 | − | 0.659355i | \(-0.229171\pi\) | ||||
0.751832 | + | 0.659355i | \(0.229171\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.0000 | − | 46.7654i | 0.862924 | − | 1.49463i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.0000 | + | 27.7128i | 0.510321 | + | 0.883901i | 0.999928 | + | 0.0119587i | \(0.00380665\pi\) |
−0.489608 | + | 0.871943i | \(0.662860\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.0000 | − | 62.3538i | −1.14706 | − | 1.98676i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.0000 | 0.763156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.00000 | − | 6.92820i | −0.127064 | − | 0.220082i | 0.795474 | − | 0.605988i | \(-0.207222\pi\) |
−0.922538 | + | 0.385906i | \(0.873889\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −72.0000 | −2.28255 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.0000 | − | 27.7128i | 0.506725 | − | 0.877674i | −0.493245 | − | 0.869891i | \(-0.664189\pi\) |
0.999970 | − | 0.00778294i | \(-0.00247741\pi\) | |||||||
\(998\) | 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 \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1368.2.s.a.577.1 | 2 | ||
3.2 | odd | 2 | 152.2.i.b.121.1 | yes | 2 | ||
4.3 | odd | 2 | 2736.2.s.a.577.1 | 2 | |||
12.11 | even | 2 | 304.2.i.d.273.1 | 2 | |||
19.11 | even | 3 | inner | 1368.2.s.a.505.1 | 2 | ||
24.5 | odd | 2 | 1216.2.i.f.577.1 | 2 | |||
24.11 | even | 2 | 1216.2.i.b.577.1 | 2 | |||
57.11 | odd | 6 | 152.2.i.b.49.1 | ✓ | 2 | ||
57.26 | odd | 6 | 2888.2.a.d.1.1 | 1 | |||
57.50 | even | 6 | 2888.2.a.a.1.1 | 1 | |||
76.11 | odd | 6 | 2736.2.s.a.1873.1 | 2 | |||
228.11 | even | 6 | 304.2.i.d.49.1 | 2 | |||
228.83 | even | 6 | 5776.2.a.e.1.1 | 1 | |||
228.107 | odd | 6 | 5776.2.a.j.1.1 | 1 | |||
456.11 | even | 6 | 1216.2.i.b.961.1 | 2 | |||
456.125 | odd | 6 | 1216.2.i.f.961.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.i.b.49.1 | ✓ | 2 | 57.11 | odd | 6 | ||
152.2.i.b.121.1 | yes | 2 | 3.2 | odd | 2 | ||
304.2.i.d.49.1 | 2 | 228.11 | even | 6 | |||
304.2.i.d.273.1 | 2 | 12.11 | even | 2 | |||
1216.2.i.b.577.1 | 2 | 24.11 | even | 2 | |||
1216.2.i.b.961.1 | 2 | 456.11 | even | 6 | |||
1216.2.i.f.577.1 | 2 | 24.5 | odd | 2 | |||
1216.2.i.f.961.1 | 2 | 456.125 | odd | 6 | |||
1368.2.s.a.505.1 | 2 | 19.11 | even | 3 | inner | ||
1368.2.s.a.577.1 | 2 | 1.1 | even | 1 | trivial | ||
2736.2.s.a.577.1 | 2 | 4.3 | odd | 2 | |||
2736.2.s.a.1873.1 | 2 | 76.11 | odd | 6 | |||
2888.2.a.a.1.1 | 1 | 57.50 | even | 6 | |||
2888.2.a.d.1.1 | 1 | 57.26 | odd | 6 | |||
5776.2.a.e.1.1 | 1 | 228.83 | even | 6 | |||
5776.2.a.j.1.1 | 1 | 228.107 | odd | 6 |