Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(181,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.181");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.b (of order \(2\), degree \(1\), 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: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 181.4 | ||
Root | \(-1.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 585.181 |
Dual form | 585.2.b.f.181.1 |
$q$-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 \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.60555i | 1.36277i | 0.731925 | + | 0.681385i | \(0.238622\pi\) | ||||
−0.731925 | + | 0.681385i | \(0.761378\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | 0.632456 | ||||||||
\(11\) | − 3.00000i | − 0.904534i | −0.891883 | − | 0.452267i | \(-0.850615\pi\) | ||||
0.891883 | − | 0.452267i | \(-0.149385\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.60555i | 1.00000i | ||||||||
\(14\) | −7.21110 | −1.92725 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 3.60555 | 0.874475 | 0.437237 | − | 0.899346i | \(-0.355957\pi\) | ||||
0.437237 | + | 0.899346i | \(0.355957\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.21110i | 1.65434i | 0.561951 | + | 0.827170i | \(0.310051\pi\) | ||||
−0.561951 | + | 0.827170i | \(0.689949\pi\) | |||||||
\(20\) | 2.00000i | 0.447214i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.00000 | 1.27920 | ||||||||
\(23\) | −3.60555 | −0.751809 | −0.375905 | − | 0.926658i | \(-0.622668\pi\) | ||||
−0.375905 | + | 0.926658i | \(0.622668\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −7.21110 | −1.41421 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 7.21110i | − 1.36277i | ||||||||
\(29\) | −7.21110 | −1.33907 | −0.669534 | − | 0.742781i | \(-0.733506\pi\) | ||||
−0.669534 | + | 0.742781i | \(0.733506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 7.21110i | − 1.29515i | −0.762001 | − | 0.647576i | \(-0.775783\pi\) | ||||
0.762001 | − | 0.647576i | \(-0.224217\pi\) | |||||||
\(32\) | − 8.00000i | − 1.41421i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.21110i | 1.23669i | ||||||||
\(35\) | 3.60555 | 0.609449 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.60555i | 0.592749i | 0.955072 | + | 0.296374i | \(0.0957776\pi\) | ||||
−0.955072 | + | 0.296374i | \(0.904222\pi\) | |||||||
\(38\) | −14.4222 | −2.33959 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.0000i | 1.71791i | 0.512050 | + | 0.858956i | \(0.328886\pi\) | ||||
−0.512050 | + | 0.858956i | \(0.671114\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 6.00000i | 0.904534i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − 7.21110i | − 1.06322i | ||||||||
\(47\) | 4.00000i | 0.583460i | 0.956501 | + | 0.291730i | \(0.0942309\pi\) | ||||
−0.956501 | + | 0.291730i | \(0.905769\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | − 2.00000i | − 0.282843i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 7.21110i | − 1.00000i | ||||||||
\(53\) | 10.8167 | 1.48578 | 0.742891 | − | 0.669413i | \(-0.233454\pi\) | ||||
0.742891 | + | 0.669413i | \(0.233454\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.00000 | −0.404520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 14.4222i | − 1.89373i | ||||||||
\(59\) | − 12.0000i | − 1.56227i | −0.624364 | − | 0.781133i | \(-0.714642\pi\) | ||||
0.624364 | − | 0.781133i | \(-0.285358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.0000 | 1.66448 | 0.832240 | − | 0.554416i | \(-0.187058\pi\) | ||||
0.832240 | + | 0.554416i | \(0.187058\pi\) | |||||||
\(62\) | 14.4222 | 1.83162 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 3.60555 | 0.447214 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | −7.21110 | −0.874475 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.21110i | 0.861892i | ||||||||
\(71\) | − 5.00000i | − 0.593391i | −0.954972 | − | 0.296695i | \(-0.904115\pi\) | ||||
0.954972 | − | 0.296695i | \(-0.0958846\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 7.21110i | − 0.843996i | −0.906597 | − | 0.421998i | \(-0.861329\pi\) | ||||
0.906597 | − | 0.421998i | \(-0.138671\pi\) | |||||||
\(74\) | −7.21110 | −0.838274 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 14.4222i | − 1.65434i | ||||||||
\(77\) | 10.8167 | 1.23267 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.0000 | 1.46261 | 0.731307 | − | 0.682048i | \(-0.238911\pi\) | ||||
0.731307 | + | 0.682048i | \(0.238911\pi\) | |||||||
\(80\) | 4.00000i | 0.447214i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −22.0000 | −2.42949 | ||||||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 3.60555i | − 0.391077i | ||||||||
\(86\) | − 8.00000i | − 0.862662i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.00000i | 0.317999i | 0.987279 | + | 0.159000i | \(0.0508269\pi\) | ||||
−0.987279 | + | 0.159000i | \(0.949173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.0000 | −1.36277 | ||||||||
\(92\) | 7.21110 | 0.751809 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | 7.21110 | 0.739844 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.60555i | 0.366088i | 0.983105 | + | 0.183044i | \(0.0585951\pi\) | ||||
−0.983105 | + | 0.183044i | \(0.941405\pi\) | |||||||
\(98\) | − 12.0000i | − 1.21218i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.00000 | 0.200000 | ||||||||
\(101\) | 7.21110 | 0.717532 | 0.358766 | − | 0.933428i | \(-0.383198\pi\) | ||||
0.358766 | + | 0.933428i | \(0.383198\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.0000 | 0.985329 | 0.492665 | − | 0.870219i | \(-0.336023\pi\) | ||||
0.492665 | + | 0.870219i | \(0.336023\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 21.6333i | 2.10121i | ||||||||
\(107\) | 3.60555 | 0.348562 | 0.174281 | − | 0.984696i | \(-0.444240\pi\) | ||||
0.174281 | + | 0.984696i | \(0.444240\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.4222i | 1.38140i | 0.723143 | + | 0.690698i | \(0.242697\pi\) | ||||
−0.723143 | + | 0.690698i | \(0.757303\pi\) | |||||||
\(110\) | − 6.00000i | − 0.572078i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 14.4222i | − 1.36277i | ||||||||
\(113\) | 7.21110 | 0.678363 | 0.339182 | − | 0.940721i | \(-0.389850\pi\) | ||||
0.339182 | + | 0.940721i | \(0.389850\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.60555i | 0.336219i | ||||||||
\(116\) | 14.4222 | 1.33907 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 24.0000 | 2.20938 | ||||||||
\(119\) | 13.0000i | 1.19171i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.00000 | 0.181818 | ||||||||
\(122\) | 26.0000i | 2.35393i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 14.4222i | 1.29515i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.21110i | 0.632456i | ||||||||
\(131\) | −21.6333 | −1.89011 | −0.945055 | − | 0.326910i | \(-0.893993\pi\) | ||||
−0.945055 | + | 0.326910i | \(0.893993\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −26.0000 | −2.25449 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 12.0000i | − 1.02523i | −0.858619 | − | 0.512615i | \(-0.828677\pi\) | ||||
0.858619 | − | 0.512615i | \(-0.171323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.00000 | 0.593732 | 0.296866 | − | 0.954919i | \(-0.404058\pi\) | ||||
0.296866 | + | 0.954919i | \(0.404058\pi\) | |||||||
\(140\) | −7.21110 | −0.609449 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.0000 | 0.839181 | ||||||||
\(143\) | 10.8167 | 0.904534 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.21110i | 0.598849i | ||||||||
\(146\) | 14.4222 | 1.19359 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 7.21110i | − 0.592749i | ||||||||
\(149\) | 5.00000i | 0.409616i | 0.978802 | + | 0.204808i | \(0.0656570\pi\) | ||||
−0.978802 | + | 0.204808i | \(0.934343\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.21110i | 0.586831i | 0.955985 | + | 0.293416i | \(0.0947920\pi\) | ||||
−0.955985 | + | 0.293416i | \(0.905208\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 21.6333i | 1.74326i | ||||||||
\(155\) | −7.21110 | −0.579210 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | 0.159617 | 0.0798087 | − | 0.996810i | \(-0.474569\pi\) | ||||
0.0798087 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(158\) | 26.0000i | 2.06845i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.00000 | −0.632456 | ||||||||
\(161\) | − 13.0000i | − 1.02454i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 10.8167i | − 0.847226i | −0.905843 | − | 0.423613i | \(-0.860762\pi\) | ||||
0.905843 | − | 0.423613i | \(-0.139238\pi\) | |||||||
\(164\) | − 22.0000i | − 1.71791i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.0000 | −0.931381 | ||||||||
\(167\) | − 10.0000i | − 0.773823i | −0.922117 | − | 0.386912i | \(-0.873542\pi\) | ||||
0.922117 | − | 0.386912i | \(-0.126458\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 7.21110 | 0.553066 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | 7.21110 | 0.548250 | 0.274125 | − | 0.961694i | \(-0.411612\pi\) | ||||
0.274125 | + | 0.961694i | \(0.411612\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 3.60555i | − 0.272554i | ||||||||
\(176\) | 12.0000i | 0.904534i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.00000 | −0.449719 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.00000 | 0.222988 | 0.111494 | − | 0.993765i | \(-0.464436\pi\) | ||||
0.111494 | + | 0.993765i | \(0.464436\pi\) | |||||||
\(182\) | − 26.0000i | − 1.92725i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.60555 | 0.265085 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 10.8167i | − 0.790992i | ||||||||
\(188\) | − 8.00000i | − 0.583460i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 14.4222i | 1.04630i | ||||||||
\(191\) | 7.21110 | 0.521777 | 0.260889 | − | 0.965369i | \(-0.415984\pi\) | ||||
0.260889 | + | 0.965369i | \(0.415984\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.60555i | 0.259533i | 0.991545 | + | 0.129767i | \(0.0414228\pi\) | ||||
−0.991545 | + | 0.129767i | \(0.958577\pi\) | |||||||
\(194\) | −7.21110 | −0.517727 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.0000 | 0.857143 | ||||||||
\(197\) | 2.00000i | 0.142494i | 0.997459 | + | 0.0712470i | \(0.0226979\pi\) | ||||
−0.997459 | + | 0.0712470i | \(0.977302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.4222i | 1.01474i | ||||||||
\(203\) | − 26.0000i | − 1.82484i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.0000 | 0.768273 | ||||||||
\(206\) | 20.0000i | 1.39347i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 14.4222i | − 1.00000i | ||||||||
\(209\) | 21.6333 | 1.49641 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | −21.6333 | −1.48578 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.21110i | 0.492941i | ||||||||
\(215\) | 4.00000i | 0.272798i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 26.0000 | 1.76500 | ||||||||
\(218\) | −28.8444 | −1.95359 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.00000 | 0.404520 | ||||||||
\(221\) | 13.0000i | 0.874475i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 14.4222i | − 0.965782i | −0.875680 | − | 0.482891i | \(-0.839587\pi\) | ||||
0.875680 | − | 0.482891i | \(-0.160413\pi\) | |||||||
\(224\) | 28.8444 | 1.92725 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.4222i | 0.959351i | ||||||||
\(227\) | 18.0000i | 1.19470i | 0.801980 | + | 0.597351i | \(0.203780\pi\) | ||||
−0.801980 | + | 0.597351i | \(0.796220\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 14.4222i | − 0.953046i | −0.879162 | − | 0.476523i | \(-0.841897\pi\) | ||||
0.879162 | − | 0.476523i | \(-0.158103\pi\) | |||||||
\(230\) | −7.21110 | −0.475486 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.2389 | 1.65345 | 0.826726 | − | 0.562604i | \(-0.190201\pi\) | ||||
0.826726 | + | 0.562604i | \(0.190201\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | 0.260931 | ||||||||
\(236\) | 24.0000i | 1.56227i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −26.0000 | −1.68533 | ||||||||
\(239\) | 7.00000i | 0.452792i | 0.974035 | + | 0.226396i | \(0.0726944\pi\) | ||||
−0.974035 | + | 0.226396i | \(0.927306\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 21.6333i | − 1.39352i | −0.717302 | − | 0.696762i | \(-0.754623\pi\) | ||||
0.717302 | − | 0.696762i | \(-0.245377\pi\) | |||||||
\(242\) | 4.00000i | 0.257130i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −26.0000 | −1.66448 | ||||||||
\(245\) | 6.00000i | 0.383326i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.0000 | −1.65434 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.00000 | −0.126491 | ||||||||
\(251\) | −21.6333 | −1.36548 | −0.682741 | − | 0.730660i | \(-0.739212\pi\) | ||||
−0.682741 | + | 0.730660i | \(0.739212\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.8167i | 0.680037i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | −21.6333 | −1.34945 | −0.674724 | − | 0.738070i | \(-0.735737\pi\) | ||||
−0.674724 | + | 0.738070i | \(0.735737\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.0000 | −0.807781 | ||||||||
\(260\) | −7.21110 | −0.447214 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 43.2666i | − 2.67302i | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 10.8167i | − 0.664462i | ||||||||
\(266\) | − 52.0000i | − 3.18832i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.21110 | 0.439669 | 0.219834 | − | 0.975537i | \(-0.429448\pi\) | ||||
0.219834 | + | 0.975537i | \(0.429448\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 28.8444i | − 1.75217i | −0.482154 | − | 0.876087i | \(-0.660145\pi\) | ||||
0.482154 | − | 0.876087i | \(-0.339855\pi\) | |||||||
\(272\) | −14.4222 | −0.874475 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 24.0000 | 1.44989 | ||||||||
\(275\) | 3.00000i | 0.180907i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.00000 | 0.240337 | 0.120168 | − | 0.992754i | \(-0.461657\pi\) | ||||
0.120168 | + | 0.992754i | \(0.461657\pi\) | |||||||
\(278\) | 14.0000i | 0.839664i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 30.0000i | − 1.78965i | −0.446417 | − | 0.894825i | \(-0.647300\pi\) | ||||
0.446417 | − | 0.894825i | \(-0.352700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.0000 | 1.54554 | 0.772770 | − | 0.634686i | \(-0.218871\pi\) | ||||
0.772770 | + | 0.634686i | \(0.218871\pi\) | |||||||
\(284\) | 10.0000i | 0.593391i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.6333i | 1.27920i | ||||||||
\(287\) | −39.6611 | −2.34112 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.00000 | −0.235294 | ||||||||
\(290\) | −14.4222 | −0.846901 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.4222i | 0.843996i | ||||||||
\(293\) | 12.0000i | 0.701047i | 0.936554 | + | 0.350524i | \(0.113996\pi\) | ||||
−0.936554 | + | 0.350524i | \(0.886004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.0000 | −0.698667 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.0000 | −0.579284 | ||||||||
\(299\) | − 13.0000i | − 0.751809i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 14.4222i | − 0.831282i | ||||||||
\(302\) | −14.4222 | −0.829905 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 28.8444i | − 1.65434i | ||||||||
\(305\) | − 13.0000i | − 0.744378i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0278i | 1.02890i | 0.857521 | + | 0.514449i | \(0.172004\pi\) | ||||
−0.857521 | + | 0.514449i | \(0.827996\pi\) | |||||||
\(308\) | −21.6333 | −1.23267 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − 14.4222i | − 0.819126i | ||||||||
\(311\) | −14.4222 | −0.817808 | −0.408904 | − | 0.912577i | \(-0.634089\pi\) | ||||
−0.408904 | + | 0.912577i | \(0.634089\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.0000 | 1.46961 | 0.734803 | − | 0.678280i | \(-0.237274\pi\) | ||||
0.734803 | + | 0.678280i | \(0.237274\pi\) | |||||||
\(314\) | 4.00000i | 0.225733i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −26.0000 | −1.46261 | ||||||||
\(317\) | 32.0000i | 1.79730i | 0.438667 | + | 0.898650i | \(0.355451\pi\) | ||||
−0.438667 | + | 0.898650i | \(0.644549\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.6333i | 1.21123i | ||||||||
\(320\) | − 8.00000i | − 0.447214i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 26.0000 | 1.44892 | ||||||||
\(323\) | 26.0000i | 1.44668i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 3.60555i | − 0.200000i | ||||||||
\(326\) | 21.6333 | 1.19816 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.4222 | −0.795122 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 28.8444i | − 1.58543i | −0.609591 | − | 0.792716i | \(-0.708666\pi\) | ||||
0.609591 | − | 0.792716i | \(-0.291334\pi\) | |||||||
\(332\) | − 12.0000i | − 0.658586i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 20.0000 | 1.09435 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | − 26.0000i | − 1.41421i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.21110i | 0.391077i | ||||||||
\(341\) | −21.6333 | −1.17151 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.60555i | 0.194681i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.4222i | 0.775343i | ||||||||
\(347\) | −25.2389 | −1.35489 | −0.677446 | − | 0.735572i | \(-0.736913\pi\) | ||||
−0.677446 | + | 0.735572i | \(0.736913\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 7.21110i | − 0.386001i | −0.981199 | − | 0.193001i | \(-0.938178\pi\) | ||||
0.981199 | − | 0.193001i | \(-0.0618220\pi\) | |||||||
\(350\) | 7.21110 | 0.385450 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −24.0000 | −1.27920 | ||||||||
\(353\) | − 24.0000i | − 1.27739i | −0.769460 | − | 0.638696i | \(-0.779474\pi\) | ||||
0.769460 | − | 0.638696i | \(-0.220526\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.00000 | −0.265372 | ||||||||
\(356\) | − 6.00000i | − 0.317999i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 4.00000i | − 0.211112i | −0.994413 | − | 0.105556i | \(-0.966338\pi\) | ||||
0.994413 | − | 0.105556i | \(-0.0336622\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −33.0000 | −1.73684 | ||||||||
\(362\) | 6.00000i | 0.315353i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 26.0000 | 1.36277 | ||||||||
\(365\) | −7.21110 | −0.377446 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.0000 | −0.939592 | −0.469796 | − | 0.882775i | \(-0.655673\pi\) | ||||
−0.469796 | + | 0.882775i | \(0.655673\pi\) | |||||||
\(368\) | 14.4222 | 0.751809 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.21110i | 0.374887i | ||||||||
\(371\) | 39.0000i | 2.02478i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.0000 | −1.34623 | −0.673114 | − | 0.739538i | \(-0.735044\pi\) | ||||
−0.673114 | + | 0.739538i | \(0.735044\pi\) | |||||||
\(374\) | 21.6333 | 1.11863 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 26.0000i | − 1.33907i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.6333i | 1.11123i | 0.831440 | + | 0.555614i | \(0.187517\pi\) | ||||
−0.831440 | + | 0.555614i | \(0.812483\pi\) | |||||||
\(380\) | −14.4222 | −0.739844 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.4222i | 0.737904i | ||||||||
\(383\) | 8.00000i | 0.408781i | 0.978889 | + | 0.204390i | \(0.0655212\pi\) | ||||
−0.978889 | + | 0.204390i | \(0.934479\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − 10.8167i | − 0.551268i | ||||||||
\(386\) | −7.21110 | −0.367035 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 7.21110i | − 0.366088i | ||||||||
\(389\) | 28.8444 | 1.46247 | 0.731235 | − | 0.682126i | \(-0.238944\pi\) | ||||
0.731235 | + | 0.682126i | \(0.238944\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.0000 | −0.657438 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.00000 | −0.201517 | ||||||||
\(395\) | − 13.0000i | − 0.654101i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.0278i | 0.904787i | 0.891818 | + | 0.452394i | \(0.149430\pi\) | ||||
−0.891818 | + | 0.452394i | \(0.850570\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | 10.0000i | 0.499376i | 0.968326 | + | 0.249688i | \(0.0803281\pi\) | ||||
−0.968326 | + | 0.249688i | \(0.919672\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.0000 | 1.29515 | ||||||||
\(404\) | −14.4222 | −0.717532 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 52.0000 | 2.58072 | ||||||||
\(407\) | 10.8167 | 0.536162 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 21.6333i | − 1.06970i | −0.844948 | − | 0.534849i | \(-0.820368\pi\) | ||||
0.844948 | − | 0.534849i | \(-0.179632\pi\) | |||||||
\(410\) | 22.0000i | 1.08650i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −20.0000 | −0.985329 | ||||||||
\(413\) | 43.2666 | 2.12901 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | 28.8444 | 1.41421 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 43.2666i | 2.11624i | ||||||||
\(419\) | −21.6333 | −1.05686 | −0.528428 | − | 0.848978i | \(-0.677218\pi\) | ||||
−0.528428 | + | 0.848978i | \(0.677218\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.21110i | 0.351448i | 0.984440 | + | 0.175724i | \(0.0562266\pi\) | ||||
−0.984440 | + | 0.175724i | \(0.943773\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.60555 | −0.174895 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 46.8722i | 2.26830i | ||||||||
\(428\) | −7.21110 | −0.348562 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.00000 | −0.385794 | ||||||||
\(431\) | 24.0000i | 1.15604i | 0.816023 | + | 0.578020i | \(0.196174\pi\) | ||||
−0.816023 | + | 0.578020i | \(0.803826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.0000 | 1.24948 | 0.624740 | − | 0.780833i | \(-0.285205\pi\) | ||||
0.624740 | + | 0.780833i | \(0.285205\pi\) | |||||||
\(434\) | 52.0000i | 2.49608i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − 28.8444i | − 1.38140i | ||||||||
\(437\) | − 26.0000i | − 1.24375i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.0000 | 1.19318 | 0.596592 | − | 0.802544i | \(-0.296521\pi\) | ||||
0.596592 | + | 0.802544i | \(0.296521\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −26.0000 | −1.23669 | ||||||||
\(443\) | −10.8167 | −0.513915 | −0.256957 | − | 0.966423i | \(-0.582720\pi\) | ||||
−0.256957 | + | 0.966423i | \(0.582720\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.00000 | 0.142214 | ||||||||
\(446\) | 28.8444 | 1.36582 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 28.8444i | 1.36277i | ||||||||
\(449\) | − 27.0000i | − 1.27421i | −0.770778 | − | 0.637104i | \(-0.780132\pi\) | ||||
0.770778 | − | 0.637104i | \(-0.219868\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.0000 | 1.55391 | ||||||||
\(452\) | −14.4222 | −0.678363 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −36.0000 | −1.68956 | ||||||||
\(455\) | 13.0000i | 0.609449i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.0278i | 0.843303i | 0.906758 | + | 0.421651i | \(0.138549\pi\) | ||||
−0.906758 | + | 0.421651i | \(0.861451\pi\) | |||||||
\(458\) | 28.8444 | 1.34781 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 7.21110i | − 0.336219i | ||||||||
\(461\) | − 5.00000i | − 0.232873i | −0.993198 | − | 0.116437i | \(-0.962853\pi\) | ||||
0.993198 | − | 0.116437i | \(-0.0371472\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.0278i | 0.837821i | 0.908028 | + | 0.418910i | \(0.137588\pi\) | ||||
−0.908028 | + | 0.418910i | \(0.862412\pi\) | |||||||
\(464\) | 28.8444 | 1.33907 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 50.4777i | 2.33834i | ||||||||
\(467\) | −32.4500 | −1.50161 | −0.750803 | − | 0.660527i | \(-0.770333\pi\) | ||||
−0.750803 | + | 0.660527i | \(0.770333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.00000i | 0.369012i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.0000i | 0.551761i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 7.21110i | − 0.330868i | ||||||||
\(476\) | − 26.0000i | − 1.19171i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14.0000 | −0.640345 | ||||||||
\(479\) | 3.00000i | 0.137073i | 0.997649 | + | 0.0685367i | \(0.0218330\pi\) | ||||
−0.997649 | + | 0.0685367i | \(0.978167\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.0000 | −0.592749 | ||||||||
\(482\) | 43.2666 | 1.97074 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.00000 | −0.181818 | ||||||||
\(485\) | 3.60555 | 0.163720 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 10.8167i | − 0.490149i | −0.969504 | − | 0.245075i | \(-0.921188\pi\) | ||||
0.969504 | − | 0.245075i | \(-0.0788125\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −12.0000 | −0.542105 | ||||||||
\(491\) | −7.21110 | −0.325433 | −0.162716 | − | 0.986673i | \(-0.552026\pi\) | ||||
−0.162716 | + | 0.986673i | \(0.552026\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.0000 | −1.17098 | ||||||||
\(494\) | − 52.0000i | − 2.33959i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 28.8444i | 1.29515i | ||||||||
\(497\) | 18.0278 | 0.808655 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.8444i | 1.29125i | 0.763653 | + | 0.645627i | \(0.223404\pi\) | ||||
−0.763653 | + | 0.645627i | \(0.776596\pi\) | |||||||
\(500\) | − 2.00000i | − 0.0894427i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 43.2666i | − 1.93108i | ||||||||
\(503\) | 14.4222 | 0.643054 | 0.321527 | − | 0.946900i | \(-0.395804\pi\) | ||||
0.321527 | + | 0.946900i | \(0.395804\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − 7.21110i | − 0.320890i | ||||||||
\(506\) | −21.6333 | −0.961718 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 15.0000i | − 0.664863i | −0.943127 | − | 0.332432i | \(-0.892131\pi\) | ||||
0.943127 | − | 0.332432i | \(-0.107869\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.0000 | 1.15017 | ||||||||
\(512\) | 32.0000i | 1.41421i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 43.2666i | − 1.90841i | ||||||||
\(515\) | − 10.0000i | − 0.440653i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.0000 | 0.527759 | ||||||||
\(518\) | − 26.0000i | − 1.14237i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.8444 | 1.26370 | 0.631848 | − | 0.775092i | \(-0.282297\pi\) | ||||
0.631848 | + | 0.775092i | \(0.282297\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.0000 | −1.48672 | −0.743358 | − | 0.668894i | \(-0.766768\pi\) | ||||
−0.743358 | + | 0.668894i | \(0.766768\pi\) | |||||||
\(524\) | 43.2666 | 1.89011 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 26.0000i | − 1.13258i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.0000 | −0.434783 | ||||||||
\(530\) | 21.6333 | 0.939691 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 52.0000 | 2.25449 | ||||||||
\(533\) | −39.6611 | −1.71791 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 3.60555i | − 0.155882i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14.4222i | 0.621785i | ||||||||
\(539\) | 18.0000i | 0.775315i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 7.21110i | − 0.310030i | −0.987912 | − | 0.155015i | \(-0.950457\pi\) | ||||
0.987912 | − | 0.155015i | \(-0.0495425\pi\) | |||||||
\(542\) | 57.6888 | 2.47795 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 28.8444i | − 1.23669i | ||||||||
\(545\) | 14.4222 | 0.617779 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 24.0000i | 1.02523i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.00000 | −0.255841 | ||||||||
\(551\) | − 52.0000i | − 2.21527i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 46.8722i | 1.99321i | ||||||||
\(554\) | 8.00000i | 0.339887i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.0000 | −0.593732 | ||||||||
\(557\) | 42.0000i | 1.77960i | 0.456354 | + | 0.889799i | \(0.349155\pi\) | ||||
−0.456354 | + | 0.889799i | \(0.650845\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 14.4222i | − 0.609994i | ||||||||
\(560\) | −14.4222 | −0.609449 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 60.0000 | 2.53095 | ||||||||
\(563\) | −32.4500 | −1.36760 | −0.683801 | − | 0.729668i | \(-0.739675\pi\) | ||||
−0.683801 | + | 0.729668i | \(0.739675\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 7.21110i | − 0.303373i | ||||||||
\(566\) | 52.0000i | 2.18572i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −43.2666 | −1.81383 | −0.906915 | − | 0.421313i | \(-0.861569\pi\) | ||||
−0.906915 | + | 0.421313i | \(0.861569\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.0000 | −0.544033 | −0.272017 | − | 0.962293i | \(-0.587691\pi\) | ||||
−0.272017 | + | 0.962293i | \(0.587691\pi\) | |||||||
\(572\) | −21.6333 | −0.904534 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − 79.3221i | − 3.31084i | ||||||||
\(575\) | 3.60555 | 0.150362 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.60555i | 0.150101i | 0.997180 | + | 0.0750505i | \(0.0239118\pi\) | ||||
−0.997180 | + | 0.0750505i | \(0.976088\pi\) | |||||||
\(578\) | − 8.00000i | − 0.332756i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 14.4222i | − 0.598849i | ||||||||
\(581\) | −21.6333 | −0.897501 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 32.4500i | − 1.34394i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.0000 | −0.991431 | ||||||||
\(587\) | − 28.0000i | − 1.15568i | −0.816149 | − | 0.577842i | \(-0.803895\pi\) | ||||
0.816149 | − | 0.577842i | \(-0.196105\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 52.0000 | 2.14262 | ||||||||
\(590\) | − 24.0000i | − 0.988064i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 14.4222i | − 0.592749i | ||||||||
\(593\) | 4.00000i | 0.164260i | 0.996622 | + | 0.0821302i | \(0.0261723\pi\) | ||||
−0.996622 | + | 0.0821302i | \(0.973828\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.0000 | 0.532948 | ||||||||
\(596\) | − 10.0000i | − 0.409616i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 26.0000 | 1.06322 | ||||||||
\(599\) | 7.21110 | 0.294638 | 0.147319 | − | 0.989089i | \(-0.452936\pi\) | ||||
0.147319 | + | 0.989089i | \(0.452936\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.0000 | −0.530281 | −0.265141 | − | 0.964210i | \(-0.585418\pi\) | ||||
−0.265141 | + | 0.964210i | \(0.585418\pi\) | |||||||
\(602\) | 28.8444 | 1.17561 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − 14.4222i | − 0.586831i | ||||||||
\(605\) | − 2.00000i | − 0.0813116i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.0000 | −0.811775 | −0.405887 | − | 0.913923i | \(-0.633038\pi\) | ||||
−0.405887 | + | 0.913923i | \(0.633038\pi\) | |||||||
\(608\) | 57.6888 | 2.33959 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 26.0000 | 1.05271 | ||||||||
\(611\) | −14.4222 | −0.583460 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.60555i | 0.145627i | 0.997346 | + | 0.0728134i | \(0.0231978\pi\) | ||||
−0.997346 | + | 0.0728134i | \(0.976802\pi\) | |||||||
\(614\) | −36.0555 | −1.45508 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.0000i | 1.36879i | 0.729112 | + | 0.684394i | \(0.239933\pi\) | ||||
−0.729112 | + | 0.684394i | \(0.760067\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 14.4222i | − 0.579677i | −0.957076 | − | 0.289839i | \(-0.906398\pi\) | ||||
0.957076 | − | 0.289839i | \(-0.0936017\pi\) | |||||||
\(620\) | 14.4222 | 0.579210 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 28.8444i | − 1.15656i | ||||||||
\(623\) | −10.8167 | −0.433360 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 52.0000i | 2.07834i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.00000 | −0.159617 | ||||||||
\(629\) | 13.0000i | 0.518344i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.8444i | 1.14828i | 0.818758 | + | 0.574139i | \(0.194663\pi\) | ||||
−0.818758 | + | 0.574139i | \(0.805337\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −64.0000 | −2.54176 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 21.6333i | − 0.857143i | ||||||||
\(638\) | −43.2666 | −1.71294 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.2666 | 1.70893 | 0.854464 | − | 0.519510i | \(-0.173886\pi\) | ||||
0.854464 | + | 0.519510i | \(0.173886\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.2389i | 0.995323i | 0.867371 | + | 0.497662i | \(0.165808\pi\) | ||||
−0.867371 | + | 0.497662i | \(0.834192\pi\) | |||||||
\(644\) | 26.0000i | 1.02454i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −52.0000 | −2.04591 | ||||||||
\(647\) | 18.0278 | 0.708744 | 0.354372 | − | 0.935104i | \(-0.384695\pi\) | ||||
0.354372 | + | 0.935104i | \(0.384695\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −36.0000 | −1.41312 | ||||||||
\(650\) | 7.21110 | 0.282843 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 21.6333i | 0.847226i | ||||||||
\(653\) | 7.21110 | 0.282192 | 0.141096 | − | 0.989996i | \(-0.454937\pi\) | ||||
0.141096 | + | 0.989996i | \(0.454937\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.6333i | 0.845283i | ||||||||
\(656\) | − 44.0000i | − 1.71791i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 28.8444i | − 1.12447i | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.21110i | 0.280479i | 0.990118 | + | 0.140240i | \(0.0447873\pi\) | ||||
−0.990118 | + | 0.140240i | \(0.955213\pi\) | |||||||
\(662\) | 57.6888 | 2.24214 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 26.0000i | 1.00824i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.0000 | 1.00672 | ||||||||
\(668\) | 20.0000i | 0.773823i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 39.0000i | − 1.50558i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.0000 | 1.54189 | 0.770943 | − | 0.636904i | \(-0.219785\pi\) | ||||
0.770943 | + | 0.636904i | \(0.219785\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 26.0000 | 1.00000 | ||||||||
\(677\) | 10.8167 | 0.415718 | 0.207859 | − | 0.978159i | \(-0.433351\pi\) | ||||
0.207859 | + | 0.978159i | \(0.433351\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.0000 | −0.498894 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 43.2666i | − 1.65676i | ||||||||
\(683\) | − 38.0000i | − 1.45403i | −0.686622 | − | 0.727015i | \(-0.740907\pi\) | ||||
0.686622 | − | 0.727015i | \(-0.259093\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | −7.21110 | −0.275321 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 16.0000 | 0.609994 | ||||||||
\(689\) | 39.0000i | 1.48578i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 14.4222i | − 0.548647i | −0.961638 | − | 0.274323i | \(-0.911546\pi\) | ||||
0.961638 | − | 0.274323i | \(-0.0884538\pi\) | |||||||
\(692\) | −14.4222 | −0.548250 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − 50.4777i | − 1.91611i | ||||||||
\(695\) | − 7.00000i | − 0.265525i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39.6611i | 1.50227i | ||||||||
\(698\) | 14.4222 | 0.545889 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.21110i | 0.272554i | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −26.0000 | −0.980609 | ||||||||
\(704\) | − 24.0000i | − 0.904534i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 48.0000 | 1.80650 | ||||||||
\(707\) | 26.0000i | 0.977831i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 28.8444i | − 1.08327i | −0.840612 | − | 0.541637i | \(-0.817805\pi\) | ||||
0.840612 | − | 0.541637i | \(-0.182195\pi\) | |||||||
\(710\) | − 10.0000i | − 0.375293i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26.0000i | 0.973708i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 10.8167i | − 0.404520i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.00000 | 0.298557 | ||||||||
\(719\) | −21.6333 | −0.806786 | −0.403393 | − | 0.915027i | \(-0.632169\pi\) | ||||
−0.403393 | + | 0.915027i | \(0.632169\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36.0555i | 1.34278i | ||||||||
\(722\) | − 66.0000i | − 2.45627i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.00000 | −0.222988 | ||||||||
\(725\) | 7.21110 | 0.267814 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.0000 | 0.964287 | 0.482143 | − | 0.876092i | \(-0.339858\pi\) | ||||
0.482143 | + | 0.876092i | \(0.339858\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − 14.4222i | − 0.533790i | ||||||||
\(731\) | −14.4222 | −0.533425 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 32.4500i | − 1.19857i | −0.800537 | − | 0.599283i | \(-0.795452\pi\) | ||||
0.800537 | − | 0.599283i | \(-0.204548\pi\) | |||||||
\(734\) | − 36.0000i | − 1.32878i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 28.8444i | 1.06322i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.6333i | 0.795794i | 0.917430 | + | 0.397897i | \(0.130260\pi\) | ||||
−0.917430 | + | 0.397897i | \(0.869740\pi\) | |||||||
\(740\) | −7.21110 | −0.265085 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −78.0000 | −2.86347 | ||||||||
\(743\) | 2.00000i | 0.0733729i | 0.999327 | + | 0.0366864i | \(0.0116803\pi\) | ||||
−0.999327 | + | 0.0366864i | \(0.988320\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.00000 | 0.183186 | ||||||||
\(746\) | − 52.0000i | − 1.90386i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 21.6333i | 0.790992i | ||||||||
\(749\) | 13.0000i | 0.475010i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.0000 | 0.912263 | 0.456131 | − | 0.889912i | \(-0.349235\pi\) | ||||
0.456131 | + | 0.889912i | \(0.349235\pi\) | |||||||
\(752\) | − 16.0000i | − 0.583460i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 52.0000 | 1.89373 | ||||||||
\(755\) | 7.21110 | 0.262439 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | −43.2666 | −1.57151 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.0000i | 1.37750i | 0.724999 | + | 0.688749i | \(0.241840\pi\) | ||||
−0.724999 | + | 0.688749i | \(0.758160\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −52.0000 | −1.88253 | ||||||||
\(764\) | −14.4222 | −0.521777 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.0000 | −0.578103 | ||||||||
\(767\) | 43.2666 | 1.56227 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 7.21110i | − 0.260039i | −0.991511 | − | 0.130020i | \(-0.958496\pi\) | ||||
0.991511 | − | 0.130020i | \(-0.0415040\pi\) | |||||||
\(770\) | 21.6333 | 0.779610 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 7.21110i | − 0.259533i | ||||||||
\(773\) | − 18.0000i | − 0.647415i | −0.946157 | − | 0.323708i | \(-0.895071\pi\) | ||||
0.946157 | − | 0.323708i | \(-0.104929\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.21110i | 0.259030i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 57.6888i | 2.06824i | ||||||||
\(779\) | −79.3221 | −2.84201 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.0000 | −0.536742 | ||||||||
\(782\) | − 26.0000i | − 0.929758i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 24.0000 | 0.857143 | ||||||||
\(785\) | − 2.00000i | − 0.0713831i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 28.8444i | − 1.02819i | −0.857733 | − | 0.514096i | \(-0.828127\pi\) | ||||
0.857733 | − | 0.514096i | \(-0.171873\pi\) | |||||||
\(788\) | − 4.00000i | − 0.142494i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 26.0000 | 0.925038 | ||||||||
\(791\) | 26.0000i | 0.924454i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 46.8722i | 1.66448i | ||||||||
\(794\) | −36.0555 | −1.27956 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.6611 | 1.40487 | 0.702433 | − | 0.711749i | \(-0.252097\pi\) | ||||
0.702433 | + | 0.711749i | \(0.252097\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.4222i | 0.510221i | ||||||||
\(800\) | 8.00000i | 0.282843i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −20.0000 | −0.706225 | ||||||||
\(803\) | −21.6333 | −0.763423 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.0000 | −0.458190 | ||||||||
\(806\) | 52.0000i | 1.83162i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.6333 | 0.760587 | 0.380293 | − | 0.924866i | \(-0.375823\pi\) | ||||
0.380293 | + | 0.924866i | \(0.375823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 28.8444i | − 1.01286i | −0.862280 | − | 0.506432i | \(-0.830964\pi\) | ||||
0.862280 | − | 0.506432i | \(-0.169036\pi\) | |||||||
\(812\) | 52.0000i | 1.82484i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 21.6333i | 0.758247i | ||||||||
\(815\) | −10.8167 | −0.378891 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 28.8444i | − 1.00914i | ||||||||
\(818\) | 43.2666 | 1.51278 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22.0000 | −0.768273 | ||||||||
\(821\) | 15.0000i | 0.523504i | 0.965135 | + | 0.261752i | \(0.0843002\pi\) | ||||
−0.965135 | + | 0.261752i | \(0.915700\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.0000 | 1.04573 | 0.522867 | − | 0.852414i | \(-0.324862\pi\) | ||||
0.522867 | + | 0.852414i | \(0.324862\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 86.5332i | 3.01088i | ||||||||
\(827\) | 4.00000i | 0.139094i | 0.997579 | + | 0.0695468i | \(0.0221553\pi\) | ||||
−0.997579 | + | 0.0695468i | \(0.977845\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.0000 | −0.903017 | −0.451509 | − | 0.892267i | \(-0.649114\pi\) | ||||
−0.451509 | + | 0.892267i | \(0.649114\pi\) | |||||||
\(830\) | 12.0000i | 0.416526i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 28.8444i | 1.00000i | ||||||||
\(833\) | −21.6333 | −0.749550 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.0000 | −0.346064 | ||||||||
\(836\) | −43.2666 | −1.49641 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 43.2666i | − 1.49462i | ||||||||
\(839\) | − 51.0000i | − 1.76072i | −0.474310 | − | 0.880358i | \(-0.657302\pi\) | ||||
0.474310 | − | 0.880358i | \(-0.342698\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.0000 | 0.793103 | ||||||||
\(842\) | −14.4222 | −0.497022 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.0000i | 0.447214i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.21110i | 0.247776i | ||||||||
\(848\) | −43.2666 | −1.48578 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 7.21110i | − 0.247339i | ||||||||
\(851\) | − 13.0000i | − 0.445634i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 54.0833i | 1.85178i | 0.377798 | + | 0.925888i | \(0.376681\pi\) | ||||
−0.377798 | + | 0.925888i | \(0.623319\pi\) | |||||||
\(854\) | −93.7443 | −3.20787 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.0278 | −0.615816 | −0.307908 | − | 0.951416i | \(-0.599629\pi\) | ||||
−0.307908 | + | 0.951416i | \(0.599629\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.0000 | −0.443554 | −0.221777 | − | 0.975097i | \(-0.571186\pi\) | ||||
−0.221777 | + | 0.975097i | \(0.571186\pi\) | |||||||
\(860\) | − 8.00000i | − 0.272798i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −48.0000 | −1.63489 | ||||||||
\(863\) | − 6.00000i | − 0.204242i | −0.994772 | − | 0.102121i | \(-0.967437\pi\) | ||||
0.994772 | − | 0.102121i | \(-0.0325630\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 7.21110i | − 0.245185i | ||||||||
\(866\) | 52.0000i | 1.76703i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −52.0000 | −1.76500 | ||||||||
\(869\) | − 39.0000i | − 1.32298i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 52.0000 | 1.75893 | ||||||||
\(875\) | −3.60555 | −0.121890 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50.4777i | 1.70451i | 0.523125 | + | 0.852256i | \(0.324766\pi\) | ||||
−0.523125 | + | 0.852256i | \(0.675234\pi\) | |||||||
\(878\) | 50.0000i | 1.68742i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 12.0000 | 0.404520 | ||||||||
\(881\) | −43.2666 | −1.45769 | −0.728845 | − | 0.684679i | \(-0.759942\pi\) | ||||
−0.728845 | + | 0.684679i | \(0.759942\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.0000 | −0.874970 | −0.437485 | − | 0.899226i | \(-0.644131\pi\) | ||||
−0.437485 | + | 0.899226i | \(0.644131\pi\) | |||||||
\(884\) | − 26.0000i | − 0.874475i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − 21.6333i | − 0.726785i | ||||||||
\(887\) | 25.2389 | 0.847438 | 0.423719 | − | 0.905794i | \(-0.360724\pi\) | ||||
0.423719 | + | 0.905794i | \(0.360724\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 6.00000i | 0.201120i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 28.8444i | 0.965782i | ||||||||
\(893\) | −28.8444 | −0.965241 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 54.0000 | 1.80200 | ||||||||
\(899\) | 52.0000i | 1.73430i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39.0000 | 1.29928 | ||||||||
\(902\) | 66.0000i | 2.19756i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 3.00000i | − 0.0997234i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.0000 | 1.72663 | 0.863316 | − | 0.504664i | \(-0.168384\pi\) | ||||
0.863316 | + | 0.504664i | \(0.168384\pi\) | |||||||
\(908\) | − 36.0000i | − 1.19470i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −26.0000 | −0.861892 | ||||||||
\(911\) | 36.0555 | 1.19457 | 0.597286 | − | 0.802028i | \(-0.296246\pi\) | ||||
0.597286 | + | 0.802028i | \(0.296246\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.0000 | 0.595713 | ||||||||
\(914\) | −36.0555 | −1.19261 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 28.8444i | 0.953046i | ||||||||
\(917\) | − 78.0000i | − 2.57579i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.0000 | 0.428830 | 0.214415 | − | 0.976743i | \(-0.431215\pi\) | ||||
0.214415 | + | 0.976743i | \(0.431215\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10.0000 | 0.329332 | ||||||||
\(923\) | 18.0278 | 0.593391 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 3.60555i | − 0.118550i | ||||||||
\(926\) | −36.0555 | −1.18486 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 57.6888i | 1.89373i | ||||||||
\(929\) | 5.00000i | 0.164045i | 0.996630 | + | 0.0820223i | \(0.0261379\pi\) | ||||
−0.996630 | + | 0.0820223i | \(0.973862\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 43.2666i | − 1.41801i | ||||||||
\(932\) | −50.4777 | −1.65345 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 64.8999i | − 2.12359i | ||||||||
\(935\) | −10.8167 | −0.353742 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52.0000 | −1.69877 | −0.849383 | − | 0.527777i | \(-0.823026\pi\) | ||||
−0.849383 | + | 0.527777i | \(0.823026\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.00000 | −0.260931 | ||||||||
\(941\) | − 59.0000i | − 1.92335i | −0.274201 | − | 0.961673i | \(-0.588413\pi\) | ||||
0.274201 | − | 0.961673i | \(-0.411587\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 39.6611i | − 1.29154i | ||||||||
\(944\) | 48.0000i | 1.56227i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.0000 | −0.780307 | ||||||||
\(947\) | − 42.0000i | − 1.36482i | −0.730971 | − | 0.682408i | \(-0.760933\pi\) | ||||
0.730971 | − | 0.682408i | \(-0.239067\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.0000 | 0.843996 | ||||||||
\(950\) | 14.4222 | 0.467918 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.8167 | −0.350386 | −0.175193 | − | 0.984534i | \(-0.556055\pi\) | ||||
−0.175193 | + | 0.984534i | \(0.556055\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 7.21110i | − 0.233346i | ||||||||
\(956\) | − 14.0000i | − 0.452792i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.00000 | −0.193851 | ||||||||
\(959\) | 43.2666 | 1.39715 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.0000 | −0.677419 | ||||||||
\(962\) | − 26.0000i | − 0.838274i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 43.2666i | 1.39352i | ||||||||
\(965\) | 3.60555 | 0.116067 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.4222i | 0.463787i | 0.972741 | + | 0.231893i | \(0.0744921\pi\) | ||||
−0.972741 | + | 0.231893i | \(0.925508\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.21110i | 0.231535i | ||||||||
\(971\) | 21.6333 | 0.694246 | 0.347123 | − | 0.937820i | \(-0.387159\pi\) | ||||
0.347123 | + | 0.937820i | \(0.387159\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.2389i | 0.809121i | ||||||||
\(974\) | 21.6333 | 0.693176 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −52.0000 | −1.66448 | ||||||||
\(977\) | 2.00000i | 0.0639857i | 0.999488 | + | 0.0319928i | \(0.0101854\pi\) | ||||
−0.999488 | + | 0.0319928i | \(0.989815\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.00000 | 0.287641 | ||||||||
\(980\) | − 12.0000i | − 0.383326i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 14.4222i | − 0.460231i | ||||||||
\(983\) | 4.00000i | 0.127580i | 0.997963 | + | 0.0637901i | \(0.0203188\pi\) | ||||
−0.997963 | + | 0.0637901i | \(0.979681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.00000 | 0.0637253 | ||||||||
\(986\) | − 52.0000i | − 1.65602i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 52.0000 | 1.65434 | ||||||||
\(989\) | 14.4222 | 0.458599 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.00000 | −0.158830 | −0.0794151 | − | 0.996842i | \(-0.525305\pi\) | ||||
−0.0794151 | + | 0.996842i | \(0.525305\pi\) | |||||||
\(992\) | −57.6888 | −1.83162 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 36.0555i | 1.14361i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.00000 | −0.190022 | −0.0950110 | − | 0.995476i | \(-0.530289\pi\) | ||||
−0.0950110 | + | 0.995476i | \(0.530289\pi\) | |||||||
\(998\) | −57.6888 | −1.82611 | ||||||||
\(999\) | 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 | 585.2.b.f.181.4 | yes | 4 | |
3.2 | odd | 2 | inner | 585.2.b.f.181.2 | yes | 4 | |
13.5 | odd | 4 | 7605.2.a.bl.1.1 | 2 | |||
13.8 | odd | 4 | 7605.2.a.w.1.2 | 2 | |||
13.12 | even | 2 | inner | 585.2.b.f.181.1 | ✓ | 4 | |
39.5 | even | 4 | 7605.2.a.w.1.1 | 2 | |||
39.8 | even | 4 | 7605.2.a.bl.1.2 | 2 | |||
39.38 | odd | 2 | inner | 585.2.b.f.181.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.b.f.181.1 | ✓ | 4 | 13.12 | even | 2 | inner | |
585.2.b.f.181.2 | yes | 4 | 3.2 | odd | 2 | inner | |
585.2.b.f.181.3 | yes | 4 | 39.38 | odd | 2 | inner | |
585.2.b.f.181.4 | yes | 4 | 1.1 | even | 1 | trivial | |
7605.2.a.w.1.1 | 2 | 39.5 | even | 4 | |||
7605.2.a.w.1.2 | 2 | 13.8 | odd | 4 | |||
7605.2.a.bl.1.1 | 2 | 13.5 | odd | 4 | |||
7605.2.a.bl.1.2 | 2 | 39.8 | even | 4 |