Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,2,Mod(577,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.i (of order \(3\), 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: | \(13.7981494693\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 577.1 | ||
Root | \(-1.18614 + 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.577 |
Dual form | 1728.2.i.i.1153.1 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | −1.18614 | + | 2.05446i | −0.530458 | + | 0.918781i | 0.468910 | + | 0.883246i | \(0.344647\pi\) |
−0.999368 | + | 0.0355348i | \(0.988687\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.18614 | − | 3.78651i | −0.826284 | − | 1.43117i | −0.900934 | − | 0.433955i | \(-0.857118\pi\) |
0.0746509 | − | 0.997210i | \(-0.476216\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | 0.780750 | − | 0.624844i | \(-0.214837\pi\) |
−0.931505 | + | 0.363727i | \(0.881504\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.186141 | + | 0.322405i | −0.0516261 | + | 0.0894191i | −0.890684 | − | 0.454624i | \(-0.849774\pi\) |
0.839057 | + | 0.544043i | \(0.183107\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.37228 | 1.30297 | 0.651485 | − | 0.758662i | \(-0.274146\pi\) | ||||
0.651485 | + | 0.758662i | \(0.274146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.627719 | −0.144009 | −0.0720043 | − | 0.997404i | \(-0.522940\pi\) | ||||
−0.0720043 | + | 0.997404i | \(0.522940\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.186141 | + | 0.322405i | −0.0388130 | + | 0.0672261i | −0.884779 | − | 0.466010i | \(-0.845691\pi\) |
0.845966 | + | 0.533236i | \(0.179024\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.313859 | − | 0.543620i | −0.0627719 | − | 0.108724i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.18614 | + | 3.78651i | 0.405956 | + | 0.703137i | 0.994432 | − | 0.105378i | \(-0.0336052\pi\) |
−0.588476 | + | 0.808515i | \(0.700272\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.18614 | + | 5.51856i | −0.572248 | + | 0.991162i | 0.424087 | + | 0.905621i | \(0.360595\pi\) |
−0.996335 | + | 0.0855407i | \(0.972738\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.3723 | 1.75324 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.74456 | −1.43760 | −0.718799 | − | 0.695218i | \(-0.755308\pi\) | ||||
−0.718799 | + | 0.695218i | \(0.755308\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.87228 | + | 10.1711i | −0.917096 | + | 1.58846i | −0.113293 | + | 0.993562i | \(0.536140\pi\) |
−0.803803 | + | 0.594896i | \(0.797193\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.872281 | − | 1.51084i | −0.133022 | − | 0.230400i | 0.791818 | − | 0.610757i | \(-0.209135\pi\) |
−0.924840 | + | 0.380356i | \(0.875801\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.18614 | + | 3.78651i | 0.318881 | + | 0.552319i | 0.980255 | − | 0.197738i | \(-0.0633595\pi\) |
−0.661374 | + | 0.750057i | \(0.730026\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.05842 | + | 10.4935i | −0.865489 | + | 1.49907i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.744563 | 0.102274 | 0.0511368 | − | 0.998692i | \(-0.483716\pi\) | ||||
0.0511368 | + | 0.998692i | \(0.483716\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.37228 | 0.319878 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.50000 | + | 6.06218i | −0.455661 | + | 0.789228i | −0.998726 | − | 0.0504625i | \(-0.983930\pi\) |
0.543065 | + | 0.839691i | \(0.317264\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.18614 | + | 2.05446i | 0.151870 | + | 0.263046i | 0.931915 | − | 0.362677i | \(-0.118137\pi\) |
−0.780045 | + | 0.625723i | \(0.784804\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.441578 | − | 0.764836i | −0.0547710 | − | 0.0948662i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.87228 | + | 3.24289i | −0.228736 | + | 0.396182i | −0.957434 | − | 0.288653i | \(-0.906792\pi\) |
0.728698 | + | 0.684835i | \(0.240126\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.00000 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.1168 | −1.41817 | −0.709085 | − | 0.705123i | \(-0.750892\pi\) | ||||
−0.709085 | + | 0.705123i | \(0.750892\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.18614 | + | 3.78651i | −0.249134 | + | 0.431512i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.18614 | + | 5.51856i | 0.358469 | + | 0.620886i | 0.987705 | − | 0.156328i | \(-0.0499656\pi\) |
−0.629236 | + | 0.777214i | \(0.716632\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.81386 | − | 8.33785i | −0.528390 | − | 0.915198i | −0.999452 | − | 0.0330979i | \(-0.989463\pi\) |
0.471062 | − | 0.882100i | \(-0.343871\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.37228 | + | 11.0371i | −0.691171 | + | 1.19714i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.62772 | 0.170631 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.744563 | − | 1.28962i | 0.0763905 | − | 0.132312i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.872281 | − | 1.51084i | −0.0885667 | − | 0.153402i | 0.818339 | − | 0.574736i | \(-0.194895\pi\) |
−0.906906 | + | 0.421334i | \(0.861562\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.55842 | + | 6.16337i | 0.354076 | + | 0.613278i | 0.986959 | − | 0.160969i | \(-0.0514620\pi\) |
−0.632883 | + | 0.774247i | \(0.718129\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.18614 | − | 10.7147i | 0.609539 | − | 1.05575i | −0.381778 | − | 0.924254i | \(-0.624688\pi\) |
0.991316 | − | 0.131498i | \(-0.0419786\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.8614 | −1.24336 | −0.621680 | − | 0.783272i | \(-0.713549\pi\) | ||||
−0.621680 | + | 0.783272i | \(0.713549\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.74456 | 0.454447 | 0.227223 | − | 0.973843i | \(-0.427035\pi\) | ||||
0.227223 | + | 0.973843i | \(0.427035\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.18614 | + | 3.78651i | −0.205655 | + | 0.356205i | −0.950341 | − | 0.311210i | \(-0.899266\pi\) |
0.744686 | + | 0.667415i | \(0.232599\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.441578 | − | 0.764836i | −0.0411774 | − | 0.0713213i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.7446 | − | 20.3422i | −1.07662 | − | 1.86476i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.3723 | −0.927725 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.74456 | 0.598483 | 0.299242 | − | 0.954177i | \(-0.403266\pi\) | ||||
0.299242 | + | 0.954177i | \(0.403266\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.18614 | + | 15.9109i | −0.802597 | + | 1.39014i | 0.115305 | + | 0.993330i | \(0.463216\pi\) |
−0.917901 | + | 0.396808i | \(0.870118\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.37228 | + | 2.37686i | 0.118992 | + | 0.206100i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.87228 | + | 15.3672i | 0.758010 | + | 1.31291i | 0.943864 | + | 0.330335i | \(0.107162\pi\) |
−0.185854 | + | 0.982577i | \(0.559505\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.87228 | − | 4.97494i | 0.243624 | − | 0.421969i | −0.718120 | − | 0.695919i | \(-0.754997\pi\) |
0.961744 | + | 0.273951i | \(0.0883305\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.372281 | 0.0311317 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.3723 | −0.861371 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.18614 | − | 7.25061i | 0.342942 | − | 0.593993i | −0.642036 | − | 0.766675i | \(-0.721910\pi\) |
0.984978 | + | 0.172682i | \(0.0552432\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.186141 | − | 0.322405i | −0.0151479 | − | 0.0262370i | 0.858352 | − | 0.513061i | \(-0.171489\pi\) |
−0.873500 | + | 0.486824i | \(0.838155\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.55842 | − | 13.0916i | −0.607107 | − | 1.05154i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.55842 | + | 2.69927i | −0.124376 | + | 0.215425i | −0.921489 | − | 0.388405i | \(-0.873026\pi\) |
0.797113 | + | 0.603830i | \(0.206359\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.62772 | 0.128282 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0000 | 0.939913 | 0.469956 | − | 0.882690i | \(-0.344270\pi\) | ||||
0.469956 | + | 0.882690i | \(0.344270\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.55842 | + | 16.5557i | −0.739653 | + | 1.28112i | 0.212999 | + | 0.977052i | \(0.431677\pi\) |
−0.952652 | + | 0.304064i | \(0.901656\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.43070 | + | 11.1383i | 0.494669 | + | 0.856793i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.18614 | + | 14.1788i | 0.622381 | + | 1.07800i | 0.989041 | + | 0.147640i | \(0.0471678\pi\) |
−0.366660 | + | 0.930355i | \(0.619499\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.37228 | + | 2.37686i | −0.103735 | + | 0.179674i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.9783 | 1.71748 | 0.858738 | − | 0.512416i | \(-0.171249\pi\) | ||||
0.858738 | + | 0.512416i | \(0.171249\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.510875 | 0.0379730 | 0.0189865 | − | 0.999820i | \(-0.493956\pi\) | ||||
0.0189865 | + | 0.999820i | \(0.493956\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.3723 | − | 17.9653i | 0.762585 | − | 1.32084i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.68614 | − | 4.65253i | −0.196430 | − | 0.340227i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.93070 | + | 8.54023i | 0.356773 | + | 0.617949i | 0.987420 | − | 0.158121i | \(-0.0505436\pi\) |
−0.630647 | + | 0.776070i | \(0.717210\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.872281 | + | 1.51084i | −0.0627882 | + | 0.108752i | −0.895711 | − | 0.444637i | \(-0.853333\pi\) |
0.832923 | + | 0.553390i | \(0.186666\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.2554 | 1.08690 | 0.543452 | − | 0.839440i | \(-0.317117\pi\) | ||||
0.543452 | + | 0.839440i | \(0.317117\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.2337 | −1.15078 | −0.575388 | − | 0.817881i | \(-0.695149\pi\) | ||||
−0.575388 | + | 0.817881i | \(0.695149\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.55842 | − | 16.5557i | 0.670870 | − | 1.16198i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.9307 | − | 24.1287i | −0.972963 | − | 1.68522i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.313859 | + | 0.543620i | 0.0217101 | + | 0.0376030i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.81386 | + | 8.33785i | −0.331400 | + | 0.574001i | −0.982787 | − | 0.184745i | \(-0.940854\pi\) |
0.651387 | + | 0.758746i | \(0.274188\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.13859 | 0.282250 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.8614 | 1.89136 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.00000 | + | 1.73205i | −0.0672673 | + | 0.116510i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.30298 | + | 12.6491i | 0.489044 | + | 0.847049i | 0.999921 | − | 0.0126050i | \(-0.00401240\pi\) |
−0.510877 | + | 0.859654i | \(0.670679\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.50000 | + | 12.9904i | 0.497792 | + | 0.862202i | 0.999997 | − | 0.00254715i | \(-0.000810783\pi\) |
−0.502204 | + | 0.864749i | \(0.667477\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.3030 | − | 19.5773i | 0.746922 | − | 1.29371i | −0.202369 | − | 0.979309i | \(-0.564864\pi\) |
0.949291 | − | 0.314398i | \(-0.101803\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.37228 | −0.351950 | −0.175975 | − | 0.984395i | \(-0.556308\pi\) | ||||
−0.175975 | + | 0.984395i | \(0.556308\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.3723 | −0.676613 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.93070 | + | 12.0043i | −0.448310 | + | 0.776496i | −0.998276 | − | 0.0586913i | \(-0.981307\pi\) |
0.549966 | + | 0.835187i | \(0.314641\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.87228 | − | 4.97494i | −0.185020 | − | 0.320464i | 0.758563 | − | 0.651599i | \(-0.225902\pi\) |
−0.943583 | + | 0.331135i | \(0.892568\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.3723 | − | 24.8935i | −0.918211 | − | 1.59039i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.116844 | − | 0.202380i | 0.00743460 | − | 0.0128771i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.88316 | 0.623819 | 0.311910 | − | 0.950112i | \(-0.399031\pi\) | ||||
0.311910 | + | 0.950112i | \(0.399031\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.372281 | 0.0234051 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.24456 | − | 3.88770i | 0.140012 | − | 0.242508i | −0.787489 | − | 0.616329i | \(-0.788619\pi\) |
0.927501 | + | 0.373821i | \(0.121953\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.1168 | + | 33.1113i | 1.18786 | + | 2.05744i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.5584 | − | 18.2877i | −0.651060 | − | 1.12767i | −0.982866 | − | 0.184322i | \(-0.940991\pi\) |
0.331806 | − | 0.943348i | \(-0.392342\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.883156 | + | 1.52967i | −0.0542518 | + | 0.0939669i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.7446 | −0.777050 | −0.388525 | − | 0.921438i | \(-0.627015\pi\) | ||||
−0.388525 | + | 0.921438i | \(0.627015\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.4891 | −1.30537 | −0.652686 | − | 0.757629i | \(-0.726358\pi\) | ||||
−0.652686 | + | 0.757629i | \(0.726358\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.313859 | + | 0.543620i | −0.0189264 | + | 0.0327815i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.5584 | + | 25.2159i | 0.874731 | + | 1.51508i | 0.857049 | + | 0.515235i | \(0.172295\pi\) |
0.0176816 | + | 0.999844i | \(0.494371\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.93070 | − | 12.0043i | −0.413451 | − | 0.716118i | 0.581813 | − | 0.813322i | \(-0.302343\pi\) |
−0.995264 | + | 0.0972040i | \(0.969010\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.9307 | − | 20.6646i | 0.709207 | − | 1.22838i | −0.255945 | − | 0.966691i | \(-0.582387\pi\) |
0.965152 | − | 0.261691i | \(-0.0842800\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 51.3505 | 3.03113 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.8614 | 0.697730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.81386 | + | 16.9981i | −0.573332 | + | 0.993040i | 0.422889 | + | 0.906182i | \(0.361016\pi\) |
−0.996221 | + | 0.0868582i | \(0.972317\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.30298 | − | 14.3812i | −0.483418 | − | 0.837305i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.0692967 | − | 0.120025i | −0.00400753 | − | 0.00694125i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.81386 | + | 6.60580i | −0.219827 | + | 0.380752i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.62772 | −0.322242 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −31.3723 | −1.79051 | −0.895255 | − | 0.445553i | \(-0.853007\pi\) | ||||
−0.895255 | + | 0.445553i | \(0.853007\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.44158 | + | 9.42509i | −0.308564 | + | 0.534448i | −0.978048 | − | 0.208378i | \(-0.933182\pi\) |
0.669485 | + | 0.742826i | \(0.266515\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.61684 | − | 9.72866i | −0.317483 | − | 0.549896i | 0.662479 | − | 0.749080i | \(-0.269504\pi\) |
−0.979962 | + | 0.199184i | \(0.936171\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.3030 | − | 26.5055i | −0.859501 | − | 1.48870i | −0.872405 | − | 0.488783i | \(-0.837441\pi\) |
0.0129041 | − | 0.999917i | \(-0.495892\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.18614 | − | 3.78651i | 0.122400 | − | 0.212004i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.37228 | −0.187639 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.233688 | 0.0129627 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.55842 | − | 16.5557i | 0.526973 | − | 0.912744i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.9307 | − | 27.5928i | −0.875631 | − | 1.51664i | −0.856089 | − | 0.516828i | \(-0.827113\pi\) |
−0.0195412 | − | 0.999809i | \(-0.506221\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.44158 | − | 7.69304i | −0.242669 | − | 0.420316i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.98913 | − | 17.3017i | 0.544142 | − | 0.942482i | −0.454518 | − | 0.890738i | \(-0.650188\pi\) |
0.998660 | − | 0.0517446i | \(-0.0164782\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.37228 | 0.345078 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 22.3723 | 1.20799 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.3614 | + | 24.8747i | −0.770961 | + | 1.33534i | 0.166076 | + | 0.986113i | \(0.446890\pi\) |
−0.937037 | + | 0.349230i | \(0.886443\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.44158 | + | 14.6212i | 0.451867 | + | 0.782657i | 0.998502 | − | 0.0547140i | \(-0.0174247\pi\) |
−0.546635 | + | 0.837371i | \(0.684091\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.9891 | − | 20.7658i | −0.638117 | − | 1.10525i | −0.985846 | − | 0.167656i | \(-0.946380\pi\) |
0.347729 | − | 0.937595i | \(-0.386953\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.74456 | + | 8.21782i | −0.251815 | + | 0.436157i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.2337 | −1.06789 | −0.533947 | − | 0.845518i | \(-0.679292\pi\) | ||||
−0.533947 | + | 0.845518i | \(0.679292\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6060 | −0.979262 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.3723 | − | 24.8935i | 0.752280 | − | 1.30299i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.81386 | − | 15.2661i | −0.460080 | − | 0.796881i | 0.538885 | − | 0.842380i | \(-0.318846\pi\) |
−0.998964 | + | 0.0454981i | \(0.985513\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.62772 | − | 2.81929i | −0.0845069 | − | 0.146370i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.5584 | − | 18.2877i | 0.546694 | − | 0.946902i | −0.451804 | − | 0.892117i | \(-0.649219\pi\) |
0.998498 | − | 0.0547851i | \(-0.0174474\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.62772 | −0.0838318 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.88316 | 0.302197 | 0.151099 | − | 0.988519i | \(-0.451719\pi\) | ||||
0.151099 | + | 0.988519i | \(0.451719\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.6753 | − | 18.4901i | 0.545481 | − | 0.944800i | −0.453096 | − | 0.891462i | \(-0.649680\pi\) |
0.998576 | − | 0.0533383i | \(-0.0169862\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.18614 | − | 8.98266i | −0.264310 | − | 0.457799i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.30298 | − | 9.18504i | −0.268872 | − | 0.465700i | 0.699699 | − | 0.714438i | \(-0.253318\pi\) |
−0.968571 | + | 0.248738i | \(0.919984\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.00000 | + | 1.73205i | −0.0505722 | + | 0.0875936i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.1168 | −0.760611 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2337 | 0.915123 | 0.457561 | − | 0.889178i | \(-0.348723\pi\) | ||||
0.457561 | + | 0.889178i | \(0.348723\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.61684 | + | 14.9248i | −0.430305 | + | 0.745310i | −0.996899 | − | 0.0786871i | \(-0.974927\pi\) |
0.566595 | + | 0.823997i | \(0.308261\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.18614 | − | 2.05446i | −0.0590859 | − | 0.102340i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.37228 | + | 7.57301i | 0.216726 | + | 0.375380i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.87228 | + | 4.97494i | −0.142025 | + | 0.245995i | −0.928259 | − | 0.371934i | \(-0.878695\pi\) |
0.786234 | + | 0.617929i | \(0.212028\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 30.6060 | 1.50602 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.8397 | 1.12115 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.30298 | − | 10.9171i | 0.307921 | − | 0.533335i | −0.669986 | − | 0.742373i | \(-0.733700\pi\) |
0.977907 | + | 0.209039i | \(0.0670334\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.5584 | − | 30.4121i | −0.855745 | − | 1.48219i | −0.875952 | − | 0.482398i | \(-0.839766\pi\) |
0.0202069 | − | 0.999796i | \(-0.493568\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.68614 | − | 2.92048i | −0.0817898 | − | 0.141664i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.18614 | − | 8.98266i | 0.250975 | − | 0.434701i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.25544 | 0.0604723 | 0.0302361 | − | 0.999543i | \(-0.490374\pi\) | ||||
0.0302361 | + | 0.999543i | \(0.490374\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.1168 | 1.54344 | 0.771719 | − | 0.635964i | \(-0.219397\pi\) | ||||
0.771719 | + | 0.635964i | \(0.219397\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.116844 | − | 0.202380i | 0.00558941 | − | 0.00968113i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.55842 | − | 6.16337i | −0.169834 | − | 0.294161i | 0.768527 | − | 0.639817i | \(-0.220990\pi\) |
−0.938361 | + | 0.345656i | \(0.887657\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.3614 | − | 26.6067i | −0.729842 | − | 1.26412i | −0.956950 | − | 0.290254i | \(-0.906260\pi\) |
0.227107 | − | 0.973870i | \(-0.427073\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.11684 | − | 12.3267i | 0.337371 | − | 0.584343i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.8832 | 0.749572 | 0.374786 | − | 0.927111i | \(-0.377716\pi\) | ||||
0.374786 | + | 0.927111i | \(0.377716\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.7446 | 0.553030 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.93070 | + | 3.34408i | −0.0905128 | + | 0.156773i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.87228 | + | 3.24289i | 0.0875816 | + | 0.151696i | 0.906488 | − | 0.422231i | \(-0.138753\pi\) |
−0.818907 | + | 0.573927i | \(0.805419\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.44158 | + | 5.96099i | 0.160290 | + | 0.277631i | 0.934973 | − | 0.354720i | \(-0.115424\pi\) |
−0.774682 | + | 0.632350i | \(0.782090\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.6753 | + | 35.8106i | −0.960861 | + | 1.66426i | −0.240515 | + | 0.970645i | \(0.577316\pi\) |
−0.720346 | + | 0.693615i | \(0.756017\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.37228 | 0.341148 | 0.170574 | − | 0.985345i | \(-0.445438\pi\) | ||||
0.170574 | + | 0.985345i | \(0.445438\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.3723 | 0.756002 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.872281 | + | 1.51084i | −0.0401075 | + | 0.0694683i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.197015 | + | 0.341241i | 0.00903969 | + | 0.0156572i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.30298 | − | 9.18504i | −0.242300 | − | 0.419675i | 0.719069 | − | 0.694938i | \(-0.244568\pi\) |
−0.961369 | + | 0.275263i | \(0.911235\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.62772 | − | 2.81929i | 0.0742176 | − | 0.128549i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.13859 | 0.187924 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.74456 | 0.305625 | 0.152813 | − | 0.988255i | \(-0.451167\pi\) | ||||
0.152813 | + | 0.988255i | \(0.451167\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.127719 | + | 0.221215i | −0.00576386 | + | 0.00998330i | −0.868893 | − | 0.495000i | \(-0.835168\pi\) |
0.863129 | + | 0.504983i | \(0.168501\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.7446 | + | 20.3422i | 0.528948 | + | 0.916166i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.74456 | − | 15.1460i | −0.392247 | − | 0.679392i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.98913 | + | 17.3017i | −0.447175 | + | 0.774529i | −0.998201 | − | 0.0599587i | \(-0.980903\pi\) |
0.551026 | + | 0.834488i | \(0.314236\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.51087 | −0.290306 | −0.145153 | − | 0.989409i | \(-0.546367\pi\) | ||||
−0.145153 | + | 0.989409i | \(0.546367\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.8832 | −0.751291 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.5584 | − | 26.9480i | 0.689615 | − | 1.19445i | −0.282348 | − | 0.959312i | \(-0.591113\pi\) |
0.971962 | − | 0.235136i | \(-0.0755535\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.4891 | + | 45.8805i | 1.17181 | + | 2.02963i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.6753 | + | 25.4183i | 0.646669 | + | 1.12006i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.18614 | − | 3.78651i | 0.0961464 | − | 0.166530i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.1168 | −0.530849 | −0.265424 | − | 0.964132i | \(-0.585512\pi\) | ||||
−0.265424 | + | 0.964132i | \(0.585512\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.4891 | 0.589838 | 0.294919 | − | 0.955522i | \(-0.404707\pi\) | ||||
0.294919 | + | 0.955522i | \(0.404707\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.1168 | + | 29.6472i | −0.745621 | + | 1.29145i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4307 | + | 19.7986i | 0.496987 | + | 0.860807i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.18614 | − | 3.78651i | −0.0946923 | − | 0.164012i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.2554 | − | 26.4232i | 0.659550 | − | 1.14237i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.1168 | 0.521909 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.23369 | −0.0960337 | −0.0480169 | − | 0.998847i | \(-0.515290\pi\) | ||||
−0.0480169 | + | 0.998847i | \(0.515290\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.62772 | + | 9.74749i | −0.241065 | + | 0.417537i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.12772 | − | 14.0776i | −0.347516 | − | 0.601916i | 0.638291 | − | 0.769795i | \(-0.279641\pi\) |
−0.985808 | + | 0.167879i | \(0.946308\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.37228 | − | 2.37686i | −0.0584611 | − | 0.101258i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.9307 | − | 24.1287i | 0.592394 | − | 1.02606i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.0000 | −0.593199 | −0.296600 | − | 0.955002i | \(-0.595853\pi\) | ||||
−0.296600 | + | 0.955002i | \(0.595853\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.649468 | 0.0274696 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.87228 | + | 8.43904i | −0.205342 | + | 0.355663i | −0.950242 | − | 0.311514i | \(-0.899164\pi\) |
0.744900 | + | 0.667177i | \(0.232497\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.18614 | − | 8.98266i | −0.218183 | − | 0.377903i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.6168 | + | 23.5851i | 0.570848 | + | 0.988737i | 0.996479 | + | 0.0838407i | \(0.0267187\pi\) |
−0.425631 | + | 0.904897i | \(0.639948\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.2446 | + | 22.9403i | −0.554268 | + | 0.960020i | 0.443692 | + | 0.896179i | \(0.353668\pi\) |
−0.997960 | + | 0.0638407i | \(0.979665\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.233688 | 0.00974546 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.8614 | 0.618688 | 0.309344 | − | 0.950950i | \(-0.399890\pi\) | ||||
0.309344 | + | 0.950950i | \(0.399890\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.0475 | + | 36.4554i | −0.873199 | + | 1.51243i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.372281 | − | 0.644810i | −0.0154183 | − | 0.0267053i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.61684 | − | 7.99661i | −0.190558 | − | 0.330055i | 0.754878 | − | 0.655866i | \(-0.227696\pi\) |
−0.945435 | + | 0.325810i | \(0.894363\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.00000 | − | 3.46410i | 0.0824086 | − | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.0000 | 1.06769 | 0.533846 | − | 0.845582i | \(-0.320746\pi\) | ||||
0.533846 | + | 0.845582i | \(0.320746\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 55.7228 | 2.28441 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.9307 | − | 34.5210i | 0.814346 | − | 1.41049i | −0.0954498 | − | 0.995434i | \(-0.530429\pi\) |
0.909796 | − | 0.415055i | \(-0.136238\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.98913 | − | 5.17732i | −0.121929 | − | 0.211187i | 0.798599 | − | 0.601863i | \(-0.205575\pi\) |
−0.920528 | + | 0.390676i | \(0.872241\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.8614 | + | 20.5446i | 0.482235 | + | 0.835255i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.55842 | − | 9.62747i | 0.225609 | − | 0.390767i | −0.730893 | − | 0.682492i | \(-0.760896\pi\) |
0.956502 | + | 0.291725i | \(0.0942294\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.62772 | −0.0658504 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.7446 | 0.514748 | 0.257374 | − | 0.966312i | \(-0.417143\pi\) | ||||
0.257374 | + | 0.966312i | \(0.417143\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.9891 | − | 32.8901i | 0.764473 | − | 1.32411i | −0.176051 | − | 0.984381i | \(-0.556332\pi\) |
0.940525 | − | 0.339726i | \(-0.110334\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.6168 | + | 18.3889i | 0.426727 | + | 0.739113i | 0.996580 | − | 0.0826338i | \(-0.0263332\pi\) |
−0.569853 | + | 0.821747i | \(0.693000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.1168 | + | 22.7190i | 0.525515 | + | 0.910219i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.8723 | − | 24.0275i | 0.554891 | − | 0.961100i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −46.9783 | −1.87315 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.0000 | −1.27390 | −0.636950 | − | 0.770905i | \(-0.719804\pi\) | ||||
−0.636950 | + | 0.770905i | \(0.719804\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.00000 | + | 13.8564i | −0.317470 | + | 0.549875i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.25544 | − | 3.90653i | −0.0893637 | − | 0.154782i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.61684 | + | 2.80046i | 0.0638615 | + | 0.110611i | 0.896188 | − | 0.443674i | \(-0.146325\pi\) |
−0.832327 | + | 0.554285i | \(0.812992\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.50000 | − | 2.59808i | 0.0591542 | − | 0.102458i | −0.834932 | − | 0.550353i | \(-0.814493\pi\) |
0.894086 | + | 0.447895i | \(0.147826\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.7228 | −1.32578 | −0.662890 | − | 0.748717i | \(-0.730670\pi\) | ||||
−0.662890 | + | 0.748717i | \(0.730670\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.00000 | 0.274774 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.4416 | − | 19.8174i | 0.447744 | − | 0.775515i | −0.550495 | − | 0.834838i | \(-0.685561\pi\) |
0.998239 | + | 0.0593237i | \(0.0188944\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.7921 | − | 37.7450i | −0.851488 | − | 1.47482i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.55842 | − | 16.5557i | −0.372343 | − | 0.644917i | 0.617582 | − | 0.786506i | \(-0.288112\pi\) |
−0.989926 | + | 0.141589i | \(0.954779\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.0475 | + | 39.9195i | −0.896446 | + | 1.55269i | −0.0644406 | + | 0.997922i | \(0.520526\pi\) |
−0.832005 | + | 0.554768i | \(0.812807\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.51087 | −0.252481 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.62772 | −0.0630255 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.18614 | − | 2.05446i | 0.0457905 | − | 0.0793114i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.186141 | + | 0.322405i | 0.00717520 | + | 0.0124278i | 0.869591 | − | 0.493773i | \(-0.164383\pi\) |
−0.862416 | + | 0.506201i | \(0.831049\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.3030 | + | 17.8453i | 0.395976 | + | 0.685850i | 0.993225 | − | 0.116205i | \(-0.0370731\pi\) |
−0.597249 | + | 0.802056i | \(0.703740\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.81386 | + | 6.60580i | −0.146362 | + | 0.253507i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.3723 | −0.588204 | −0.294102 | − | 0.955774i | \(-0.595021\pi\) | ||||
−0.294102 | + | 0.955774i | \(0.595021\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −42.0951 | −1.60837 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.138593 | + | 0.240051i | −0.00527999 | + | 0.00914521i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.55842 | + | 13.0916i | 0.287536 | + | 0.498027i | 0.973221 | − | 0.229872i | \(-0.0738306\pi\) |
−0.685685 | + | 0.727898i | \(0.740497\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.81386 | + | 11.8020i | 0.258464 | + | 0.447674i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.5475 | + | 54.6420i | −1.19495 | + | 2.06971i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.4891 | −1.34041 | −0.670203 | − | 0.742178i | \(-0.733793\pi\) | ||||
−0.670203 | + | 0.742178i | \(0.733793\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.48913 | 0.207026 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.5584 | − | 26.9480i | 0.585135 | − | 1.01348i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.3030 | − | 24.7735i | −0.537160 | − | 0.930388i | −0.999055 | − | 0.0434539i | \(-0.986164\pi\) |
0.461896 | − | 0.886934i | \(-0.347169\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.18614 | − | 2.05446i | −0.0444213 | − | 0.0769400i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.441578 | + | 0.764836i | −0.0165141 | + | 0.0286032i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −45.4891 | −1.69646 | −0.848229 | − | 0.529630i | \(-0.822331\pi\) | ||||
−0.848229 | + | 0.529630i | \(0.822331\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −54.0951 | −2.01461 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.37228 | − | 2.37686i | 0.0509652 | − | 0.0882744i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.44158 | − | 9.42509i | −0.201817 | − | 0.349557i | 0.747297 | − | 0.664490i | \(-0.231351\pi\) |
−0.949114 | + | 0.314933i | \(0.898018\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.68614 | − | 8.11663i | −0.173323 | − | 0.300205i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.9307 | + | 32.7889i | −0.699221 | + | 1.21109i | 0.269515 | + | 0.962996i | \(0.413137\pi\) |
−0.968737 | + | 0.248091i | \(0.920197\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.74456 | 0.137933 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.1168 | −1.54929 | −0.774647 | − | 0.632394i | \(-0.782072\pi\) | ||||
−0.774647 | + | 0.632394i | \(0.782072\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.8139 | − | 30.8545i | 0.653527 | − | 1.13194i | −0.328734 | − | 0.944423i | \(-0.606622\pi\) |
0.982261 | − | 0.187520i | \(-0.0600448\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.93070 | + | 17.2005i | 0.363833 | + | 0.630177i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 28.1168 | + | 48.6998i | 1.02737 | + | 1.77945i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.8139 | − | 32.5866i | 0.686527 | − | 1.18910i | −0.286427 | − | 0.958102i | \(-0.592467\pi\) |
0.972954 | − | 0.230998i | \(-0.0741992\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.883156 | 0.0321413 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.51087 | −0.309333 | −0.154667 | − | 0.987967i | \(-0.549430\pi\) | ||||
−0.154667 | + | 0.987967i | \(0.549430\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.67527 | + | 16.7581i | −0.350728 | + | 0.607479i | −0.986377 | − | 0.164499i | \(-0.947399\pi\) |
0.635649 | + | 0.771978i | \(0.280733\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.3723 | − | 17.9653i | −0.375502 | − | 0.650388i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.30298 | − | 2.25684i | −0.0470480 | − | 0.0814896i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.5584 | + | 28.6800i | −0.597112 | + | 1.03423i | 0.396133 | + | 0.918193i | \(0.370352\pi\) |
−0.993245 | + | 0.116035i | \(0.962981\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.9783 | 1.04228 | 0.521138 | − | 0.853473i | \(-0.325508\pi\) | ||||
0.521138 | + | 0.853473i | \(0.325508\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.00000 | 0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.68614 | − | 6.38458i | 0.132070 | − | 0.228751i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.00000 | − | 3.46410i | −0.0715656 | − | 0.123955i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.69702 | − | 6.40342i | −0.131952 | − | 0.228548i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.4198 | − | 37.1002i | 0.763534 | − | 1.32248i | −0.177484 | − | 0.984124i | \(-0.556796\pi\) |
0.941018 | − | 0.338357i | \(-0.109871\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.1168 | 0.679717 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.883156 | −0.0313618 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.69702 | + | 2.93932i | −0.0601114 | + | 0.104116i | −0.894515 | − | 0.447038i | \(-0.852479\pi\) |
0.834404 | + | 0.551154i | \(0.185812\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.7446 | + | 20.3422i | 0.415493 | + | 0.719655i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.05842 | + | 10.4935i | 0.213797 | + | 0.370307i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.93070 | + | 3.34408i | −0.0680484 | + | 0.117863i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.1386 | −0.461928 | −0.230964 | − | 0.972962i | \(-0.574188\pi\) | ||||
−0.230964 | + | 0.972962i | \(0.574188\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.3505 | −0.363456 | −0.181728 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181728 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.2337 | + | 24.6535i | −0.498584 | + | 0.863573i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.547547 | + | 0.948380i | 0.0191563 | + | 0.0331796i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.81386 | − | 16.9981i | −0.342506 | − | 0.593238i | 0.642391 | − | 0.766377i | \(-0.277942\pi\) |
−0.984897 | + | 0.173139i | \(0.944609\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.4416 | + | 21.5494i | −0.433686 | + | 0.751166i | −0.997187 | − | 0.0749488i | \(-0.976121\pi\) |
0.563501 | + | 0.826115i | \(0.309454\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.9783 | 1.07722 | 0.538610 | − | 0.842555i | \(-0.318950\pi\) | ||||
0.538610 | + | 0.842555i | \(0.318950\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.4891 | −0.537960 | −0.268980 | − | 0.963146i | \(-0.586686\pi\) | ||||
−0.268980 | + | 0.963146i | \(0.586686\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −32.5475 | + | 56.3740i | −1.12771 | + | 1.95324i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.6753 | − | 39.2747i | −0.784710 | − | 1.35916i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.0475 | + | 26.0631i | 0.519499 | + | 0.899799i | 0.999743 | + | 0.0226638i | \(0.00721474\pi\) |
−0.480244 | + | 0.877135i | \(0.659452\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.94158 | − | 8.55906i | 0.170399 | − | 0.295140i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −30.5109 | −1.04961 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −43.7228 | −1.50233 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.62772 | − | 2.81929i | 0.0557975 | − | 0.0966441i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.5584 | + | 28.6800i | 0.566950 | + | 0.981985i | 0.996865 | + | 0.0791165i | \(0.0252099\pi\) |
−0.429916 | + | 0.902869i | \(0.641457\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.5584 | + | 32.1441i | 0.633944 | + | 1.09802i | 0.986738 | + | 0.162322i | \(0.0518982\pi\) |
−0.352794 | + | 0.935701i | \(0.614768\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.24456 | + | 2.15565i | −0.0424639 | + | 0.0735497i | −0.886476 | − | 0.462774i | \(-0.846854\pi\) |
0.844012 | + | 0.536324i | \(0.180187\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.9783 | 0.646027 | 0.323014 | − | 0.946394i | \(-0.395304\pi\) | ||||
0.323014 | + | 0.946394i | \(0.395304\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38.8397 | −1.32059 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.18614 | − | 5.51856i | 0.108082 | − | 0.187204i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.697015 | − | 1.20727i | −0.0236175 | − | 0.0409066i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.6753 | + | 39.2747i | 0.766564 | + | 1.32773i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.9307 | − | 24.1287i | 0.470406 | − | 0.814768i | −0.529021 | − | 0.848609i | \(-0.677441\pi\) |
0.999427 | + | 0.0338410i | \(0.0107740\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.9783 | −0.841539 | −0.420769 | − | 0.907168i | \(-0.638240\pi\) | ||||
−0.420769 | + | 0.907168i | \(0.638240\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.8397 | −1.07149 | −0.535745 | − | 0.844380i | \(-0.679969\pi\) | ||||
−0.535745 | + | 0.844380i | \(0.679969\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.93070 | − | 10.2723i | 0.199134 | − | 0.344909i | −0.749114 | − | 0.662441i | \(-0.769521\pi\) |
0.948248 | + | 0.317531i | \(0.102854\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.7446 | − | 25.5383i | −0.494517 | − | 0.856528i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.37228 | − | 2.37686i | −0.0459216 | − | 0.0795386i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.2554 | + | 47.2078i | −0.911049 | + | 1.57798i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.8614 | −0.929230 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.00000 | 0.133259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.605969 | + | 1.04957i | −0.0201431 | + | 0.0348889i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.5000 | + | 32.0429i | 0.614282 | + | 1.06397i | 0.990510 | + | 0.137441i | \(0.0438878\pi\) |
−0.376228 | + | 0.926527i | \(0.622779\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.441578 | − | 0.764836i | −0.0146301 | − | 0.0253401i | 0.858618 | − | 0.512617i | \(-0.171324\pi\) |
−0.873248 | + | 0.487276i | \(0.837990\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.81386 | + | 8.33785i | −0.159315 | + | 0.275943i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 80.3288 | 2.65269 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.2337 | 1.19524 | 0.597620 | − | 0.801780i | \(-0.296113\pi\) | ||||
0.597620 | + | 0.801780i | \(0.296113\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.744563 | + | 1.28962i | −0.0245076 | + | 0.0424484i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.74456 | + | 4.75372i | 0.0902407 | + | 0.156301i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.7921 | + | 32.5489i | 0.616549 | + | 1.06789i | 0.990111 | + | 0.140289i | \(0.0448032\pi\) |
−0.373561 | + | 0.927605i | \(0.621864\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.80298 | − | 6.58696i | 0.124638 | − | 0.215879i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.7446 | 0.416792 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.0000 | 0.980057 | 0.490029 | − | 0.871706i | \(-0.336986\pi\) | ||||
0.490029 | + | 0.871706i | \(0.336986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.4198 | + | 23.2438i | −0.437474 | + | 0.757727i | −0.997494 | − | 0.0707520i | \(-0.977460\pi\) |
0.560020 | + | 0.828479i | \(0.310793\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.18614 | − | 3.78651i | −0.0711905 | − | 0.123306i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.8723 | + | 46.5442i | 0.873232 | + | 1.51248i | 0.858634 | + | 0.512588i | \(0.171313\pi\) |
0.0145974 | + | 0.999893i | \(0.495353\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.25544 | − | 3.90653i | 0.0732146 | − | 0.126811i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.88316 | 0.255360 | 0.127680 | − | 0.991815i | \(-0.459247\pi\) | ||||
0.127680 | + | 0.991815i | \(0.459247\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.3940 | −0.757013 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 38.7921 | − | 67.1899i | 1.25266 | − | 2.16968i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.80298 | − | 8.31901i | −0.154935 | − | 0.268355i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.06930 | − | 3.58413i | −0.0666130 | − | 0.115377i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.18614 | − | 7.25061i | 0.134617 | − | 0.233164i | −0.790834 | − | 0.612031i | \(-0.790353\pi\) |
0.925451 | + | 0.378867i | \(0.123686\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.48913 | −0.176154 | −0.0880772 | − | 0.996114i | \(-0.528072\pi\) | ||||
−0.0880772 | + | 0.996114i | \(0.528072\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.1168 | −0.805209 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.127719 | − | 0.221215i | 0.00408608 | − | 0.00707730i | −0.863975 | − | 0.503534i | \(-0.832033\pi\) |
0.868061 | + | 0.496457i | \(0.165366\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.00000 | + | 5.19615i | 0.0958804 | + | 0.166070i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.5584 | + | 47.7326i | 0.878977 | + | 1.52243i | 0.852465 | + | 0.522785i | \(0.175107\pi\) |
0.0265123 | + | 0.999648i | \(0.491560\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.0951 | + | 31.3416i | −0.576558 | + | 0.998627i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.649468 | 0.0206519 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.9783 | 1.61938 | 0.809689 | − | 0.586860i | \(-0.199636\pi\) | ||||
0.809689 | + | 0.586860i | \(0.199636\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.2554 | − | 33.3514i | 0.610438 | − | 1.05731i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.6753 | + | 42.7388i | 0.781474 | + | 1.35355i | 0.931083 | + | 0.364807i | \(0.118865\pi\) |
−0.149610 | + | 0.988745i | \(0.547802\pi\) | |||||||
\(998\) | 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 | 1728.2.i.i.577.1 | 4 | ||
3.2 | odd | 2 | 576.2.i.j.193.1 | 4 | |||
4.3 | odd | 2 | 1728.2.i.j.577.1 | 4 | |||
8.3 | odd | 2 | 432.2.i.d.145.2 | 4 | |||
8.5 | even | 2 | 216.2.i.b.145.2 | 4 | |||
9.2 | odd | 6 | 576.2.i.j.385.1 | 4 | |||
9.4 | even | 3 | 5184.2.a.bp.1.2 | 2 | |||
9.5 | odd | 6 | 5184.2.a.bt.1.1 | 2 | |||
9.7 | even | 3 | inner | 1728.2.i.i.1153.1 | 4 | ||
12.11 | even | 2 | 576.2.i.l.193.2 | 4 | |||
24.5 | odd | 2 | 72.2.i.b.49.2 | yes | 4 | ||
24.11 | even | 2 | 144.2.i.d.49.1 | 4 | |||
36.7 | odd | 6 | 1728.2.i.j.1153.1 | 4 | |||
36.11 | even | 6 | 576.2.i.l.385.2 | 4 | |||
36.23 | even | 6 | 5184.2.a.bs.1.1 | 2 | |||
36.31 | odd | 6 | 5184.2.a.bo.1.2 | 2 | |||
72.5 | odd | 6 | 648.2.a.f.1.2 | 2 | |||
72.11 | even | 6 | 144.2.i.d.97.1 | 4 | |||
72.13 | even | 6 | 648.2.a.g.1.1 | 2 | |||
72.29 | odd | 6 | 72.2.i.b.25.2 | ✓ | 4 | ||
72.43 | odd | 6 | 432.2.i.d.289.2 | 4 | |||
72.59 | even | 6 | 1296.2.a.n.1.2 | 2 | |||
72.61 | even | 6 | 216.2.i.b.73.2 | 4 | |||
72.67 | odd | 6 | 1296.2.a.p.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.2.i.b.25.2 | ✓ | 4 | 72.29 | odd | 6 | ||
72.2.i.b.49.2 | yes | 4 | 24.5 | odd | 2 | ||
144.2.i.d.49.1 | 4 | 24.11 | even | 2 | |||
144.2.i.d.97.1 | 4 | 72.11 | even | 6 | |||
216.2.i.b.73.2 | 4 | 72.61 | even | 6 | |||
216.2.i.b.145.2 | 4 | 8.5 | even | 2 | |||
432.2.i.d.145.2 | 4 | 8.3 | odd | 2 | |||
432.2.i.d.289.2 | 4 | 72.43 | odd | 6 | |||
576.2.i.j.193.1 | 4 | 3.2 | odd | 2 | |||
576.2.i.j.385.1 | 4 | 9.2 | odd | 6 | |||
576.2.i.l.193.2 | 4 | 12.11 | even | 2 | |||
576.2.i.l.385.2 | 4 | 36.11 | even | 6 | |||
648.2.a.f.1.2 | 2 | 72.5 | odd | 6 | |||
648.2.a.g.1.1 | 2 | 72.13 | even | 6 | |||
1296.2.a.n.1.2 | 2 | 72.59 | even | 6 | |||
1296.2.a.p.1.1 | 2 | 72.67 | odd | 6 | |||
1728.2.i.i.577.1 | 4 | 1.1 | even | 1 | trivial | ||
1728.2.i.i.1153.1 | 4 | 9.7 | even | 3 | inner | ||
1728.2.i.j.577.1 | 4 | 4.3 | odd | 2 | |||
1728.2.i.j.1153.1 | 4 | 36.7 | odd | 6 | |||
5184.2.a.bo.1.2 | 2 | 36.31 | odd | 6 | |||
5184.2.a.bp.1.2 | 2 | 9.4 | even | 3 | |||
5184.2.a.bs.1.1 | 2 | 36.23 | even | 6 | |||
5184.2.a.bt.1.1 | 2 | 9.5 | odd | 6 |