Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(287,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.287");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.f (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: | \(4.59938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 287.1 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.287 |
Dual form | 576.2.f.a.287.4 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.44949 | −1.09545 | −0.547723 | − | 0.836660i | \(-0.684505\pi\) | ||||
−0.547723 | + | 0.836660i | \(0.684505\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.00000i | − 0.755929i | −0.925820 | − | 0.377964i | \(-0.876624\pi\) | ||||
0.925820 | − | 0.377964i | \(-0.123376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.89898i | 1.47710i | 0.674200 | + | 0.738549i | \(0.264489\pi\) | ||||
−0.674200 | + | 0.738549i | \(0.735511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3.46410i | − 0.960769i | −0.877058 | − | 0.480384i | \(-0.840497\pi\) | ||||
0.877058 | − | 0.480384i | \(-0.159503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 4.24264i | − 1.02899i | −0.857493 | − | 0.514496i | \(-0.827979\pi\) | ||||
0.857493 | − | 0.514496i | \(-0.172021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.92820 | −1.58944 | −0.794719 | − | 0.606977i | \(-0.792382\pi\) | ||||
−0.794719 | + | 0.606977i | \(0.792382\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.48528 | −1.76930 | −0.884652 | − | 0.466252i | \(-0.845604\pi\) | ||||
−0.884652 | + | 0.466252i | \(0.845604\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.34847 | −1.36458 | −0.682288 | − | 0.731083i | \(-0.739015\pi\) | ||||
−0.682288 | + | 0.731083i | \(0.739015\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000i | 0.359211i | 0.983739 | + | 0.179605i | \(0.0574821\pi\) | ||||
−0.983739 | + | 0.179605i | \(0.942518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.89898i | 0.828079i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 6.92820i | − 1.13899i | −0.821995 | − | 0.569495i | \(-0.807139\pi\) | ||||
0.821995 | − | 0.569495i | \(-0.192861\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 4.24264i | − 0.662589i | −0.943527 | − | 0.331295i | \(-0.892515\pi\) | ||||
0.943527 | − | 0.331295i | \(-0.107485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.48528 | 1.23771 | 0.618853 | − | 0.785507i | \(-0.287598\pi\) | ||||
0.618853 | + | 0.785507i | \(0.287598\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.44949 | −0.336463 | −0.168232 | − | 0.985747i | \(-0.553806\pi\) | ||||
−0.168232 | + | 0.985747i | \(0.553806\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 12.0000i | − 1.61808i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.92820i | 0.887066i | 0.896258 | + | 0.443533i | \(0.146275\pi\) | ||||
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.48528i | 1.05247i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.92820 | 0.846415 | 0.423207 | − | 0.906033i | \(-0.360904\pi\) | ||||
0.423207 | + | 0.906033i | \(0.360904\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.48528 | −1.00702 | −0.503509 | − | 0.863990i | \(-0.667958\pi\) | ||||
−0.503509 | + | 0.863990i | \(0.667958\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.79796 | 1.11658 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.0000i | 1.57512i | 0.616236 | + | 0.787562i | \(0.288657\pi\) | ||||
−0.616236 | + | 0.787562i | \(0.711343\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 4.89898i | − 0.537733i | −0.963177 | − | 0.268866i | \(-0.913351\pi\) | ||||
0.963177 | − | 0.268866i | \(-0.0866490\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.3923i | 1.12720i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.24264i | 0.449719i | 0.974391 | + | 0.224860i | \(0.0721923\pi\) | ||||
−0.974391 | + | 0.224860i | \(0.927808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.92820 | −0.726273 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.9706 | 1.74114 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.0000 | −1.62455 | −0.812277 | − | 0.583272i | \(-0.801772\pi\) | ||||
−0.812277 | + | 0.583272i | \(0.801772\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.2474 | 1.21867 | 0.609333 | − | 0.792914i | \(-0.291437\pi\) | ||||
0.609333 | + | 0.792914i | \(0.291437\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000i | 0.197066i | 0.995134 | + | 0.0985329i | \(0.0314150\pi\) | ||||
−0.995134 | + | 0.0985329i | \(0.968585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 19.5959i | − 1.89441i | −0.320630 | − | 0.947204i | \(-0.603895\pi\) | ||||
0.320630 | − | 0.947204i | \(-0.396105\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 10.3923i | − 0.995402i | −0.867349 | − | 0.497701i | \(-0.834178\pi\) | ||||
0.867349 | − | 0.497701i | \(-0.165822\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 4.24264i | − 0.399114i | −0.979886 | − | 0.199557i | \(-0.936050\pi\) | ||||
0.979886 | − | 0.199557i | \(-0.0639503\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.7846 | 1.93817 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.48528 | −0.777844 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.0000 | −1.18182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.79796 | 0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.0000i | 0.887357i | 0.896186 | + | 0.443678i | \(0.146327\pi\) | ||||
−0.896186 | + | 0.443678i | \(0.853673\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 9.79796i | − 0.856052i | −0.903767 | − | 0.428026i | \(-0.859209\pi\) | ||||
0.903767 | − | 0.428026i | \(-0.140791\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.8564i | 1.20150i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.24264i | 0.362473i | 0.983440 | + | 0.181237i | \(0.0580100\pi\) | ||||
−0.983440 | + | 0.181237i | \(0.941990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.92820 | 0.587643 | 0.293821 | − | 0.955860i | \(-0.405073\pi\) | ||||
0.293821 | + | 0.955860i | \(0.405073\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.9706 | 1.41915 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.0000 | 1.49482 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.44949 | 0.200670 | 0.100335 | − | 0.994954i | \(-0.468009\pi\) | ||||
0.100335 | + | 0.994954i | \(0.468009\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 2.00000i | − 0.162758i | −0.996683 | − | 0.0813788i | \(-0.974068\pi\) | ||||
0.996683 | − | 0.0813788i | \(-0.0259324\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 4.89898i | − 0.393496i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.7846i | 1.65879i | 0.558661 | + | 0.829396i | \(0.311315\pi\) | ||||
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.9706i | 1.33747i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.8564 | −1.08532 | −0.542659 | − | 0.839953i | \(-0.682582\pi\) | ||||
−0.542659 | + | 0.839953i | \(0.682582\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.44949 | 0.186231 | 0.0931156 | − | 0.995655i | \(-0.470317\pi\) | ||||
0.0931156 | + | 0.995655i | \(0.470317\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 2.00000i | − 0.151186i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.79796i | 0.732334i | 0.930549 | + | 0.366167i | \(0.119330\pi\) | ||||
−0.930549 | + | 0.366167i | \(0.880670\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 17.3205i | − 1.28742i | −0.765268 | − | 0.643712i | \(-0.777394\pi\) | ||||
0.765268 | − | 0.643712i | \(-0.222606\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.9706i | 1.24770i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.7846 | 1.51992 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0000 | −0.719816 | −0.359908 | − | 0.932988i | \(-0.617192\pi\) | ||||
−0.359908 | + | 0.932988i | \(0.617192\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.44949 | 0.174519 | 0.0872595 | − | 0.996186i | \(-0.472189\pi\) | ||||
0.0872595 | + | 0.996186i | \(0.472189\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 22.0000i | − 1.55954i | −0.626067 | − | 0.779769i | \(-0.715336\pi\) | ||||
0.626067 | − | 0.779769i | \(-0.284664\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.6969i | 1.03152i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.3923i | 0.725830i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 33.9411i | − 2.34776i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.92820 | −0.476957 | −0.238479 | − | 0.971148i | \(-0.576649\pi\) | ||||
−0.238479 | + | 0.971148i | \(0.576649\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000 | 0.271538 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.6969 | −0.988623 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.0000i | 0.669650i | 0.942280 | + | 0.334825i | \(0.108677\pi\) | ||||
−0.942280 | + | 0.334825i | \(0.891323\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 14.6969i | − 0.975470i | −0.872992 | − | 0.487735i | \(-0.837823\pi\) | ||||
0.872992 | − | 0.487735i | \(-0.162177\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 10.3923i | − 0.686743i | −0.939200 | − | 0.343371i | \(-0.888431\pi\) | ||||
0.939200 | − | 0.343371i | \(-0.111569\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 21.2132i | − 1.38972i | −0.719144 | − | 0.694862i | \(-0.755466\pi\) | ||||
0.719144 | − | 0.694862i | \(-0.244534\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.7846 | −1.35584 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.9706 | −1.09773 | −0.548867 | − | 0.835910i | \(-0.684941\pi\) | ||||
−0.548867 | + | 0.835910i | \(0.684941\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.00000 | 0.257663 | 0.128831 | − | 0.991667i | \(-0.458877\pi\) | ||||
0.128831 | + | 0.991667i | \(0.458877\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.34847 | −0.469476 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.0000i | 1.52708i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.6969i | 0.927663i | 0.885924 | + | 0.463831i | \(0.153526\pi\) | ||||
−0.885924 | + | 0.463831i | \(0.846474\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 41.5692i | − 2.61343i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.2132i | 1.32324i | 0.749838 | + | 0.661622i | \(0.230131\pi\) | ||||
−0.749838 | + | 0.661622i | \(0.769869\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.8564 | −0.860995 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.9706 | −1.04645 | −0.523225 | − | 0.852195i | \(-0.675271\pi\) | ||||
−0.523225 | + | 0.852195i | \(0.675271\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.0454 | −1.34413 | −0.672066 | − | 0.740491i | \(-0.734593\pi\) | ||||
−0.672066 | + | 0.740491i | \(0.734593\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 14.0000i | − 0.850439i | −0.905090 | − | 0.425220i | \(-0.860197\pi\) | ||||
0.905090 | − | 0.425220i | \(-0.139803\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.89898i | 0.295420i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.3923i | 0.624413i | 0.950014 | + | 0.312207i | \(0.101068\pi\) | ||||
−0.950014 | + | 0.312207i | \(0.898932\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 12.7279i | − 0.759284i | −0.925133 | − | 0.379642i | \(-0.876047\pi\) | ||||
0.925133 | − | 0.379642i | \(-0.123953\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.48528 | −0.500870 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.0454 | −1.28791 | −0.643953 | − | 0.765065i | \(-0.722707\pi\) | ||||
−0.643953 | + | 0.765065i | \(0.722707\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 29.3939i | 1.69989i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 16.9706i | − 0.971732i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.7846 | −1.18624 | −0.593120 | − | 0.805114i | \(-0.702104\pi\) | ||||
−0.593120 | + | 0.805114i | \(0.702104\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.9706 | 0.962312 | 0.481156 | − | 0.876635i | \(-0.340217\pi\) | ||||
0.481156 | + | 0.876635i | \(0.340217\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.00000 | −0.113047 | −0.0565233 | − | 0.998401i | \(-0.518002\pi\) | ||||
−0.0565233 | + | 0.998401i | \(0.518002\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.1464 | 0.963039 | 0.481520 | − | 0.876435i | \(-0.340085\pi\) | ||||
0.481520 | + | 0.876435i | \(0.340085\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 36.0000i | − 2.01561i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.3939i | 1.63552i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 3.46410i | − 0.192154i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 16.9706i | − 0.935617i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.92820 | 0.380808 | 0.190404 | − | 0.981706i | \(-0.439020\pi\) | ||||
0.190404 | + | 0.981706i | \(0.439020\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.9706 | −0.927201 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.0000 | 1.08947 | 0.544735 | − | 0.838608i | \(-0.316630\pi\) | ||||
0.544735 | + | 0.838608i | \(0.316630\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.79796 | −0.530589 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 20.0000i | − 1.07990i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 4.89898i | − 0.262991i | −0.991317 | − | 0.131495i | \(-0.958022\pi\) | ||||
0.991317 | − | 0.131495i | \(-0.0419779\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 6.92820i | − 0.370858i | −0.982658 | − | 0.185429i | \(-0.940632\pi\) | ||||
0.982658 | − | 0.185429i | \(-0.0593675\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.6985i | 1.58069i | 0.612661 | + | 0.790345i | \(0.290099\pi\) | ||||
−0.612661 | + | 0.790345i | \(0.709901\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.7846 | 1.10313 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.48528 | 0.447836 | 0.223918 | − | 0.974608i | \(-0.428115\pi\) | ||||
0.223918 | + | 0.974608i | \(0.428115\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.0000 | 1.52632 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.79796 | −0.512849 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.00000i | 0.104399i | 0.998637 | + | 0.0521996i | \(0.0166232\pi\) | ||||
−0.998637 | + | 0.0521996i | \(0.983377\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.89898i | 0.254342i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 6.92820i | − 0.358729i | −0.983783 | − | 0.179364i | \(-0.942596\pi\) | ||||
0.983783 | − | 0.179364i | \(-0.0574041\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.4558i | 1.31104i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.6410 | −1.77939 | −0.889695 | − | 0.456556i | \(-0.849083\pi\) | ||||
−0.889695 | + | 0.456556i | \(0.849083\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.9706 | −0.867155 | −0.433578 | − | 0.901116i | \(-0.642749\pi\) | ||||
−0.433578 | + | 0.901116i | \(0.642749\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.0000 | −1.22315 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.9444 | −1.36613 | −0.683067 | − | 0.730355i | \(-0.739354\pi\) | ||||
−0.683067 | + | 0.730355i | \(0.739354\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.0000i | 1.82060i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 34.2929i | − 1.72546i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.7846i | 1.04315i | 0.853206 | + | 0.521575i | \(0.174655\pi\) | ||||
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 38.1838i | − 1.90681i | −0.301699 | − | 0.953403i | \(-0.597554\pi\) | ||||
0.301699 | − | 0.953403i | \(-0.402446\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.92820 | 0.345118 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.9411 | 1.68240 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.00000 | −0.395575 | −0.197787 | − | 0.980245i | \(-0.563376\pi\) | ||||
−0.197787 | + | 0.980245i | \(0.563376\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000i | 0.589057i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.6969i | 0.717992i | 0.933339 | + | 0.358996i | \(0.116881\pi\) | ||||
−0.933339 | + | 0.358996i | \(0.883119\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 3.46410i | − 0.168830i | −0.996431 | − | 0.0844150i | \(-0.973098\pi\) | ||||
0.996431 | − | 0.0844150i | \(-0.0269021\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 4.24264i | − 0.205798i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.8564 | 0.670559 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.4558 | −1.22616 | −0.613082 | − | 0.790019i | \(-0.710071\pi\) | ||||
−0.613082 | + | 0.790019i | \(0.710071\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.0000 | 0.480569 | 0.240285 | − | 0.970702i | \(-0.422759\pi\) | ||||
0.240285 | + | 0.970702i | \(0.422759\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 58.7878 | 2.81220 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0000i | 0.668184i | 0.942541 | + | 0.334092i | \(0.108430\pi\) | ||||
−0.942541 | + | 0.334092i | \(0.891570\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 14.6969i | − 0.698273i | −0.937072 | − | 0.349136i | \(-0.886475\pi\) | ||||
0.937072 | − | 0.349136i | \(-0.113525\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 10.3923i | − 0.492642i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.24264i | 0.200223i | 0.994976 | + | 0.100111i | \(0.0319199\pi\) | ||||
−0.994976 | + | 0.100111i | \(0.968080\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.7846 | 0.978709 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.9706 | 0.795592 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.0000 | −1.49690 | −0.748448 | − | 0.663193i | \(-0.769201\pi\) | ||||
−0.748448 | + | 0.663193i | \(0.769201\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.44949 | −0.114084 | −0.0570421 | − | 0.998372i | \(-0.518167\pi\) | ||||
−0.0570421 | + | 0.998372i | \(0.518167\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 26.0000i | − 1.20832i | −0.796862 | − | 0.604161i | \(-0.793508\pi\) | ||||
0.796862 | − | 0.604161i | \(-0.206492\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 34.2929i | − 1.58688i | −0.608646 | − | 0.793442i | \(-0.708287\pi\) | ||||
0.608646 | − | 0.793442i | \(-0.291713\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 13.8564i | − 0.639829i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.92820 | −0.317888 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.48528 | −0.387702 | −0.193851 | − | 0.981031i | \(-0.562098\pi\) | ||||
−0.193851 | + | 0.981031i | \(0.562098\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.0000 | −1.09431 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 39.1918 | 1.77961 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.0000i | 0.453143i | 0.973995 | + | 0.226572i | \(0.0727517\pi\) | ||||
−0.973995 | + | 0.226572i | \(0.927248\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 9.79796i | − 0.442176i | −0.975254 | − | 0.221088i | \(-0.929039\pi\) | ||||
0.975254 | − | 0.221088i | \(-0.0709608\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.1769i | 1.40414i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.9706i | 0.761234i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.48528 | 0.378340 | 0.189170 | − | 0.981944i | \(-0.439420\pi\) | ||||
0.189170 | + | 0.981944i | \(0.439420\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.0000 | −1.33498 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.2474 | 0.542859 | 0.271429 | − | 0.962458i | \(-0.412504\pi\) | ||||
0.271429 | + | 0.962458i | \(0.412504\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 8.00000i | − 0.353899i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 4.89898i | − 0.215875i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 41.5692i | 1.82821i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.2132i | 0.929367i | 0.885477 | + | 0.464684i | \(0.153832\pi\) | ||||
−0.885477 | + | 0.464684i | \(0.846168\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.92820 | 0.302949 | 0.151475 | − | 0.988461i | \(-0.451598\pi\) | ||||
0.151475 | + | 0.988461i | \(0.451598\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.48528 | 0.369625 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 49.0000 | 2.13043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.6969 | −0.636595 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 48.0000i | 2.07522i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.6969i | 0.633042i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.3205i | 0.744667i | 0.928099 | + | 0.372333i | \(0.121442\pi\) | ||||
−0.928099 | + | 0.372333i | \(0.878558\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 25.4558i | 1.09041i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.7128 | 1.18491 | 0.592457 | − | 0.805602i | \(-0.298158\pi\) | ||||
0.592457 | + | 0.805602i | \(0.298158\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 50.9117 | 2.16891 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.0000 | 1.19068 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.9444 | 1.14167 | 0.570835 | − | 0.821065i | \(-0.306620\pi\) | ||||
0.570835 | + | 0.821065i | \(0.306620\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 24.4949i | − 1.03234i | −0.856487 | − | 0.516168i | \(-0.827358\pi\) | ||||
0.856487 | − | 0.516168i | \(-0.172642\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.3923i | 0.437208i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 38.1838i | 1.60075i | 0.599502 | + | 0.800373i | \(0.295365\pi\) | ||||
−0.599502 | + | 0.800373i | \(0.704635\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.8564 | 0.579873 | 0.289936 | − | 0.957046i | \(-0.406366\pi\) | ||||
0.289936 | + | 0.957046i | \(0.406366\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.48528 | −0.353861 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.0000 | −1.08239 | −0.541197 | − | 0.840896i | \(-0.682029\pi\) | ||||
−0.541197 | + | 0.840896i | \(0.682029\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.79796 | −0.406488 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 12.0000i | − 0.496989i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 19.5959i | − 0.808810i | −0.914580 | − | 0.404405i | \(-0.867479\pi\) | ||||
0.914580 | − | 0.404405i | \(-0.132521\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 13.8564i | − 0.570943i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 29.6985i | − 1.21957i | −0.792567 | − | 0.609785i | \(-0.791256\pi\) | ||||
0.792567 | − | 0.609785i | \(-0.208744\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.7846 | 0.852086 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.48528 | −0.346699 | −0.173350 | − | 0.984860i | \(-0.555459\pi\) | ||||
−0.173350 | + | 0.984860i | \(0.555459\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0000 | 0.571072 | 0.285536 | − | 0.958368i | \(-0.407828\pi\) | ||||
0.285536 | + | 0.958368i | \(0.407828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 31.8434 | 1.29462 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 38.0000i | − 1.54237i | −0.636610 | − | 0.771186i | \(-0.719664\pi\) | ||||
0.636610 | − | 0.771186i | \(-0.280336\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 29.3939i | − 1.18915i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.92820i | 0.279827i | 0.990164 | + | 0.139914i | \(0.0446825\pi\) | ||||
−0.990164 | + | 0.139914i | \(0.955317\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 12.7279i | − 0.512407i | −0.966623 | − | 0.256203i | \(-0.917528\pi\) | ||||
0.966623 | − | 0.256203i | \(-0.0824717\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.8564 | 0.556936 | 0.278468 | − | 0.960446i | \(-0.410173\pi\) | ||||
0.278468 | + | 0.960446i | \(0.410173\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.48528 | 0.339956 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29.3939 | −1.17201 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 14.0000i | − 0.557331i | −0.960388 | − | 0.278666i | \(-0.910108\pi\) | ||||
0.960388 | − | 0.278666i | \(-0.0898921\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 24.4949i | − 0.972050i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 10.3923i | − 0.411758i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.7279i | 0.502723i | 0.967893 | + | 0.251361i | \(0.0808782\pi\) | ||||
−0.967893 | + | 0.251361i | \(0.919122\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −41.5692 | −1.63933 | −0.819665 | − | 0.572843i | \(-0.805840\pi\) | ||||
−0.819665 | + | 0.572843i | \(0.805840\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 42.4264 | 1.66795 | 0.833977 | − | 0.551799i | \(-0.186058\pi\) | ||||
0.833977 | + | 0.551799i | \(0.186058\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.44949 | 0.0958559 | 0.0479280 | − | 0.998851i | \(-0.484738\pi\) | ||||
0.0479280 | + | 0.998851i | \(0.484738\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.0000i | 0.937758i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.1918i | 1.52670i | 0.645987 | + | 0.763349i | \(0.276446\pi\) | ||||
−0.645987 | + | 0.763349i | \(0.723554\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.92820i | 0.269476i | 0.990881 | + | 0.134738i | \(0.0430193\pi\) | ||||
−0.990881 | + | 0.134738i | \(0.956981\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 33.9411i | − 1.31618i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 62.3538 | 2.41435 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.9411 | −1.31028 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.00000 | −0.0770943 | −0.0385472 | − | 0.999257i | \(-0.512273\pi\) | ||||
−0.0385472 | + | 0.999257i | \(0.512273\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.7423 | 1.41212 | 0.706062 | − | 0.708150i | \(-0.250470\pi\) | ||||
0.706062 | + | 0.708150i | \(0.250470\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.0000i | 1.22805i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.0908i | 1.68709i | 0.537060 | + | 0.843544i | \(0.319535\pi\) | ||||
−0.537060 | + | 0.843544i | \(0.680465\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 10.3923i | − 0.397070i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.48528i | 0.323263i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.5692 | −1.58137 | −0.790684 | − | 0.612225i | \(-0.790275\pi\) | ||||
−0.790684 | + | 0.612225i | \(0.790275\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.9706 | −0.643730 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.0000 | −0.681799 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.1464 | −0.647612 | −0.323806 | − | 0.946124i | \(-0.604962\pi\) | ||||
−0.323806 | + | 0.946124i | \(0.604962\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 48.0000i | 1.81035i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 24.4949i | − 0.921225i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 24.2487i | − 0.910679i | −0.890318 | − | 0.455340i | \(-0.849518\pi\) | ||||
0.890318 | − | 0.455340i | \(-0.150482\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 16.9706i | − 0.635553i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −41.5692 | −1.55460 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.4558 | −0.949343 | −0.474671 | − | 0.880163i | \(-0.657433\pi\) | ||||
−0.474671 | + | 0.880163i | \(0.657433\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.00000 | 0.148968 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.34847 | −0.272915 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 14.0000i | − 0.519231i | −0.965712 | − | 0.259616i | \(-0.916404\pi\) | ||||
0.965712 | − | 0.259616i | \(-0.0835959\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.3923i | 0.383849i | 0.981410 | + | 0.191924i | \(0.0614728\pi\) | ||||
−0.981410 | + | 0.191924i | \(0.938527\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.9411i | 1.25024i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.5692 | −1.52915 | −0.764574 | − | 0.644536i | \(-0.777051\pi\) | ||||
−0.764574 | + | 0.644536i | \(0.777051\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.9411 | −1.24518 | −0.622590 | − | 0.782549i | \(-0.713919\pi\) | ||||
−0.622590 | + | 0.782549i | \(0.713919\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.00000 | −0.219823 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −39.1918 | −1.43204 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 46.0000i | − 1.67856i | −0.543696 | − | 0.839282i | \(-0.682976\pi\) | ||||
0.543696 | − | 0.839282i | \(-0.317024\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.89898i | 0.178292i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.3205i | 0.629525i | 0.949171 | + | 0.314762i | \(0.101925\pi\) | ||||
−0.949171 | + | 0.314762i | \(0.898075\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.7279i | 0.461387i | 0.973026 | + | 0.230693i | \(0.0740994\pi\) | ||||
−0.973026 | + | 0.230693i | \(0.925901\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.7846 | −0.752453 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.0000 | 0.937584 | 0.468792 | − | 0.883309i | \(-0.344689\pi\) | ||||
0.468792 | + | 0.883309i | \(0.344689\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.34847 | 0.264306 | 0.132153 | − | 0.991229i | \(-0.457811\pi\) | ||||
0.132153 | + | 0.991229i | \(0.457811\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.00000i | 0.0718421i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29.3939i | 1.05314i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 41.5692i | − 1.48746i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 50.9117i | − 1.81712i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.6410 | 1.23482 | 0.617409 | − | 0.786642i | \(-0.288182\pi\) | ||||
0.617409 | + | 0.786642i | \(0.288182\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.48528 | −0.301702 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.0000 | 0.852265 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.9444 | −0.954419 | −0.477210 | − | 0.878790i | \(-0.658352\pi\) | ||||
−0.477210 | + | 0.878790i | \(0.658352\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 36.0000i | − 1.27359i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.5959i | 0.691525i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 41.5692i | − 1.46512i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 38.1838i | − 1.34247i | −0.741245 | − | 0.671235i | \(-0.765764\pi\) | ||||
0.741245 | − | 0.671235i | \(-0.234236\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.7846 | 0.729846 | 0.364923 | − | 0.931038i | \(-0.381095\pi\) | ||||
0.364923 | + | 0.931038i | \(0.381095\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 33.9411 | 1.18891 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.34847 | −0.256463 | −0.128232 | − | 0.991744i | \(-0.540930\pi\) | ||||
−0.128232 | + | 0.991744i | \(0.540930\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 26.0000i | − 0.906303i | −0.891434 | − | 0.453152i | \(-0.850300\pi\) | ||||
0.891434 | − | 0.453152i | \(-0.149700\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.3939i | 1.02213i | 0.859543 | + | 0.511063i | \(0.170748\pi\) | ||||
−0.859543 | + | 0.511063i | \(0.829252\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.0333i | 1.56407i | 0.623233 | + | 0.782036i | \(0.285819\pi\) | ||||
−0.623233 | + | 0.782036i | \(0.714181\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 12.7279i | − 0.440996i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.4558 | −0.878833 | −0.439417 | − | 0.898283i | \(-0.644815\pi\) | ||||
−0.439417 | + | 0.898283i | \(0.644815\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.44949 | −0.0842650 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.0000i | 0.893371i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 58.7878i | 2.01522i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 48.4974i | − 1.66052i | −0.557376 | − | 0.830260i | \(-0.688192\pi\) | ||||
0.557376 | − | 0.830260i | \(-0.311808\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 4.24264i | − 0.144926i | −0.997371 | − | 0.0724629i | \(-0.976914\pi\) | ||||
0.997371 | − | 0.0724629i | \(-0.0230859\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.7128 | −0.945549 | −0.472774 | − | 0.881183i | \(-0.656747\pi\) | ||||
−0.472774 | + | 0.881183i | \(0.656747\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.9411 | 1.15537 | 0.577685 | − | 0.816260i | \(-0.303956\pi\) | ||||
0.577685 | + | 0.816260i | \(0.303956\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | −0.204006 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −68.5857 | −2.32661 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 24.0000i | − 0.813209i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 19.5959i | − 0.662463i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 6.92820i | − 0.233949i | −0.993135 | − | 0.116974i | \(-0.962680\pi\) | ||||
0.993135 | − | 0.116974i | \(-0.0373195\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.2132i | 0.714691i | 0.933972 | + | 0.357345i | \(0.116318\pi\) | ||||
−0.933972 | + | 0.357345i | \(0.883682\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.7128 | 0.932610 | 0.466305 | − | 0.884624i | \(-0.345585\pi\) | ||||
0.466305 | + | 0.884624i | \(0.345585\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.9706 | 0.569816 | 0.284908 | − | 0.958555i | \(-0.408037\pi\) | ||||
0.284908 | + | 0.958555i | \(0.408037\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.0000 | 0.670778 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −58.7878 | −1.96726 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 24.0000i | − 0.802232i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 14.6969i | − 0.490170i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.3923i | 0.346218i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 42.4264i | 1.41030i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −55.4256 | −1.84038 | −0.920189 | − | 0.391475i | \(-0.871965\pi\) | ||||
−0.920189 | + | 0.391475i | \(0.871965\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.9411 | −1.12452 | −0.562260 | − | 0.826961i | \(-0.690068\pi\) | ||||
−0.562260 | + | 0.826961i | \(0.690068\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.0000 | 0.794284 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19.5959 | −0.647114 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 26.0000i | − 0.857661i | −0.903385 | − | 0.428830i | \(-0.858926\pi\) | ||||
0.903385 | − | 0.428830i | \(-0.141074\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.3939i | 0.967511i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 6.92820i | − 0.227798i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 38.1838i | − 1.25277i | −0.779514 | − | 0.626384i | \(-0.784534\pi\) | ||||
0.779514 | − | 0.626384i | \(-0.215466\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.7846 | −0.681188 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −50.9117 | −1.66499 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.0000 | −0.457360 | −0.228680 | − | 0.973502i | \(-0.573441\pi\) | ||||
−0.228680 | + | 0.973502i | \(0.573441\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 56.3383 | 1.83657 | 0.918287 | − | 0.395914i | \(-0.129572\pi\) | ||||
0.918287 | + | 0.395914i | \(0.129572\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.0000i | 1.17232i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 19.5959i | − 0.636782i | −0.947960 | − | 0.318391i | \(-0.896858\pi\) | ||||
0.947960 | − | 0.318391i | \(-0.103142\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 13.8564i | − 0.449798i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.2132i | 0.687163i | 0.939123 | + | 0.343582i | \(0.111640\pi\) | ||||
−0.939123 | + | 0.343582i | \(0.888360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.48528 | 0.274004 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.0000 | 0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.4949 | 0.788519 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.0000i | 0.836104i | 0.908423 | + | 0.418052i | \(0.137287\pi\) | ||||
−0.908423 | + | 0.418052i | \(0.862713\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.89898i | 0.157216i | 0.996906 | + | 0.0786079i | \(0.0250475\pi\) | ||||
−0.996906 | + | 0.0786079i | \(0.974952\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 13.8564i | − 0.444216i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 29.6985i | − 0.950139i | −0.879948 | − | 0.475069i | \(-0.842423\pi\) | ||||
0.879948 | − | 0.475069i | \(-0.157577\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.7846 | −0.664279 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −50.9117 | −1.62383 | −0.811915 | − | 0.583775i | \(-0.801575\pi\) | ||||
−0.811915 | + | 0.583775i | \(0.801575\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.00000 | −0.191176 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.0000i | 1.58830i | 0.607720 | + | 0.794151i | \(0.292084\pi\) | ||||
−0.607720 | + | 0.794151i | \(0.707916\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 53.8888i | 1.70839i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.7846i | 0.658255i | 0.944285 | + | 0.329128i | \(0.106755\pi\) | ||||
−0.944285 | + | 0.329128i | \(0.893245\pi\) | |||||||
\(998\) | 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 | 576.2.f.a.287.1 | ✓ | 8 | |
3.2 | odd | 2 | inner | 576.2.f.a.287.5 | yes | 8 | |
4.3 | odd | 2 | inner | 576.2.f.a.287.3 | yes | 8 | |
8.3 | odd | 2 | inner | 576.2.f.a.287.8 | yes | 8 | |
8.5 | even | 2 | inner | 576.2.f.a.287.6 | yes | 8 | |
12.11 | even | 2 | inner | 576.2.f.a.287.7 | yes | 8 | |
16.3 | odd | 4 | 2304.2.c.j.2303.6 | 8 | |||
16.5 | even | 4 | 2304.2.c.j.2303.3 | 8 | |||
16.11 | odd | 4 | 2304.2.c.j.2303.1 | 8 | |||
16.13 | even | 4 | 2304.2.c.j.2303.8 | 8 | |||
24.5 | odd | 2 | inner | 576.2.f.a.287.2 | yes | 8 | |
24.11 | even | 2 | inner | 576.2.f.a.287.4 | yes | 8 | |
48.5 | odd | 4 | 2304.2.c.j.2303.7 | 8 | |||
48.11 | even | 4 | 2304.2.c.j.2303.5 | 8 | |||
48.29 | odd | 4 | 2304.2.c.j.2303.4 | 8 | |||
48.35 | even | 4 | 2304.2.c.j.2303.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.2.f.a.287.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
576.2.f.a.287.2 | yes | 8 | 24.5 | odd | 2 | inner | |
576.2.f.a.287.3 | yes | 8 | 4.3 | odd | 2 | inner | |
576.2.f.a.287.4 | yes | 8 | 24.11 | even | 2 | inner | |
576.2.f.a.287.5 | yes | 8 | 3.2 | odd | 2 | inner | |
576.2.f.a.287.6 | yes | 8 | 8.5 | even | 2 | inner | |
576.2.f.a.287.7 | yes | 8 | 12.11 | even | 2 | inner | |
576.2.f.a.287.8 | yes | 8 | 8.3 | odd | 2 | inner | |
2304.2.c.j.2303.1 | 8 | 16.11 | odd | 4 | |||
2304.2.c.j.2303.2 | 8 | 48.35 | even | 4 | |||
2304.2.c.j.2303.3 | 8 | 16.5 | even | 4 | |||
2304.2.c.j.2303.4 | 8 | 48.29 | odd | 4 | |||
2304.2.c.j.2303.5 | 8 | 48.11 | even | 4 | |||
2304.2.c.j.2303.6 | 8 | 16.3 | odd | 4 | |||
2304.2.c.j.2303.7 | 8 | 48.5 | odd | 4 | |||
2304.2.c.j.2303.8 | 8 | 16.13 | even | 4 |