Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,2,Mod(223,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("336.223");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.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: | \(2.68297350792\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 223.1 | ||
Root | \(-2.44949i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.223 |
Dual form | 336.2.b.c.223.2 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.44949i | − | 1.09545i | −0.836660 | − | 0.547723i | \(-0.815495\pi\) | ||
0.836660 | − | 0.547723i | \(-0.184505\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | − | 2.44949i | −0.377964 | − | 0.925820i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.44949i | 0.738549i | 0.929320 | + | 0.369274i | \(0.120394\pi\) | ||||
−0.929320 | + | 0.369274i | \(0.879606\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.89898i | − | 1.35873i | −0.733799 | − | 0.679366i | \(-0.762255\pi\) | ||
0.733799 | − | 0.679366i | \(-0.237745\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.44949i | − | 0.632456i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.44949i | − | 0.594089i | −0.954864 | − | 0.297044i | \(-0.903999\pi\) | ||
0.954864 | − | 0.297044i | \(-0.0960009\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | − | 2.44949i | −0.218218 | − | 0.534522i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.34847i | 1.53226i | 0.642685 | + | 0.766131i | \(0.277821\pi\) | ||||
−0.642685 | + | 0.766131i | \(0.722179\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.44949i | 0.426401i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.00000 | + | 2.44949i | −1.01419 | + | 0.414039i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.89898i | − | 0.784465i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.34847i | 1.14764i | 0.818982 | + | 0.573819i | \(0.194539\pi\) | ||||
−0.818982 | + | 0.573819i | \(0.805461\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.89898i | − | 0.747087i | −0.927613 | − | 0.373544i | \(-0.878143\pi\) | ||
0.927613 | − | 0.373544i | \(-0.121857\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 2.44949i | − | 0.365148i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.0000 | −1.75038 | −0.875190 | − | 0.483779i | \(-0.839264\pi\) | ||||
−0.875190 | + | 0.483779i | \(0.839264\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | + | 4.89898i | −0.714286 | + | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 2.44949i | − | 0.342997i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00000 | 0.809040 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.00000 | −0.264906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.0000 | 1.56227 | 0.781133 | − | 0.624364i | \(-0.214642\pi\) | ||||
0.781133 | + | 0.624364i | \(0.214642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | − | 2.44949i | −0.125988 | − | 0.308607i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.0000 | −1.48842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.34847i | 0.884652i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.2474i | 1.45350i | 0.686900 | + | 0.726752i | \(0.258971\pi\) | ||||
−0.686900 | + | 0.726752i | \(0.741029\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.6969i | 1.72015i | 0.510171 | + | 0.860073i | \(0.329582\pi\) | ||||
−0.510171 | + | 0.860073i | \(0.670418\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.00000 | − | 2.44949i | 0.683763 | − | 0.279145i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 9.79796i | − | 1.10236i | −0.834388 | − | 0.551178i | \(-0.814178\pi\) | ||
0.834388 | − | 0.551178i | \(-0.185822\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.00000 | −0.650791 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.00000 | 0.643268 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.2474i | 1.29823i | 0.760692 | + | 0.649113i | \(0.224860\pi\) | ||||
−0.760692 | + | 0.649113i | \(0.775140\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.0000 | + | 4.89898i | −1.25794 | + | 0.513553i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.00000 | 0.829561 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.89898i | 0.502625i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.89898i | − | 0.497416i | −0.968579 | − | 0.248708i | \(-0.919994\pi\) | ||
0.968579 | − | 0.248708i | \(-0.0800060\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.44949i | 0.246183i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.44949i | 0.243733i | 0.992546 | + | 0.121867i | \(0.0388880\pi\) | ||||
−0.992546 | + | 0.121867i | \(0.961112\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.0000 | −1.57653 | −0.788263 | − | 0.615338i | \(-0.789020\pi\) | ||||
−0.788263 | + | 0.615338i | \(0.789020\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.00000 | + | 2.44949i | −0.585540 | + | 0.239046i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 12.2474i | − | 1.18401i | −0.805936 | − | 0.592003i | \(-0.798337\pi\) | ||
0.805936 | − | 0.592003i | \(-0.201663\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.0000 | 1.67851 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 4.89898i | − | 0.452911i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.00000 | + | 2.44949i | −0.550019 | + | 0.224544i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.34847i | 0.662589i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 9.79796i | − | 0.876356i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.79796i | 0.869428i | 0.900568 | + | 0.434714i | \(0.143151\pi\) | ||||
−0.900568 | + | 0.434714i | \(0.856849\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 4.89898i | − | 0.431331i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00000 | + | 4.89898i | 0.173422 | + | 0.424795i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 2.44949i | − | 0.210819i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | 0.512615 | 0.256307 | − | 0.966595i | \(-0.417494\pi\) | ||||
0.256307 | + | 0.966595i | \(0.417494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.0000 | −1.01058 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.0000 | 1.00349 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 14.6969i | − | 1.22051i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.00000 | + | 4.89898i | −0.412393 | + | 0.404061i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.0000 | −1.47462 | −0.737309 | − | 0.675556i | \(-0.763904\pi\) | ||||
−0.737309 | + | 0.675556i | \(0.763904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 14.6969i | − | 1.19602i | −0.801489 | − | 0.598010i | \(-0.795958\pi\) | ||
0.801489 | − | 0.598010i | \(-0.204042\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.44949i | − | 0.198030i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 19.5959i | − | 1.57398i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 19.5959i | − | 1.56392i | −0.623326 | − | 0.781962i | \(-0.714219\pi\) | ||
0.623326 | − | 0.781962i | \(-0.285781\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.0000 | − | 7.34847i | 1.41860 | − | 0.579141i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.5959i | 1.53487i | 0.641126 | + | 0.767435i | \(0.278467\pi\) | ||||
−0.641126 | + | 0.767435i | \(0.721533\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.00000 | 0.467099 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | −0.152944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 7.34847i | − | 0.558694i | −0.960190 | − | 0.279347i | \(-0.909882\pi\) | ||
0.960190 | − | 0.279347i | \(-0.0901179\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | + | 2.44949i | 0.0755929 | + | 0.185164i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.0000 | 0.901975 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 17.1464i | − | 1.28158i | −0.767714 | − | 0.640792i | \(-0.778606\pi\) | ||
0.767714 | − | 0.640792i | \(-0.221394\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.89898i | 0.364138i | 0.983286 | + | 0.182069i | \(0.0582795\pi\) | ||||
−0.983286 | + | 0.182069i | \(0.941721\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 9.79796i | − | 0.720360i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.00000 | 0.438763 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | − | 2.44949i | −0.0727393 | − | 0.178174i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2.44949i | − | 0.177239i | −0.996066 | − | 0.0886194i | \(-0.971755\pi\) | ||
0.996066 | − | 0.0886194i | \(-0.0282455\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.0000 | 1.15171 | 0.575853 | − | 0.817554i | \(-0.304670\pi\) | ||||
0.575853 | + | 0.817554i | \(0.304670\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12.0000 | −0.859338 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.00000 | −0.141776 | −0.0708881 | − | 0.997484i | \(-0.522583\pi\) | ||||
−0.0708881 | + | 0.997484i | \(0.522583\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.00000 | − | 14.6969i | −0.421117 | − | 1.03152i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.0000 | 1.25717 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.34847i | 0.510754i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 4.89898i | − | 0.338869i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.89898i | 0.337260i | 0.985679 | + | 0.168630i | \(0.0539342\pi\) | ||||
−0.985679 | + | 0.168630i | \(0.946066\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.2474i | 0.839181i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.0000 | −0.818393 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.00000 | − | 19.5959i | −0.543075 | − | 1.33026i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.6969i | 0.993127i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.0000 | 0.669650 | 0.334825 | − | 0.942280i | \(-0.391323\pi\) | ||||
0.334825 | + | 0.942280i | \(0.391323\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.0000 | 0.796468 | 0.398234 | − | 0.917284i | \(-0.369623\pi\) | ||||
0.398234 | + | 0.917284i | \(0.369623\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.4949i | 1.61867i | 0.587348 | + | 0.809334i | \(0.300172\pi\) | ||||
−0.587348 | + | 0.809334i | \(0.699828\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.00000 | − | 2.44949i | 0.394771 | − | 0.161165i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −30.0000 | −1.96537 | −0.982683 | − | 0.185296i | \(-0.940675\pi\) | ||||
−0.982683 | + | 0.185296i | \(0.940675\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.3939i | 1.91745i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 9.79796i | − | 0.636446i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 12.2474i | − | 0.792222i | −0.918203 | − | 0.396111i | \(-0.870360\pi\) | ||
0.918203 | − | 0.396111i | \(-0.129640\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4.89898i | − | 0.315571i | −0.987473 | − | 0.157786i | \(-0.949565\pi\) | ||
0.987473 | − | 0.157786i | \(-0.0504355\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.0000 | + | 12.2474i | 0.766652 | + | 0.782461i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.79796i | 0.623429i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.0000 | −1.13165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.00000 | −0.375735 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 22.0454i | − | 1.37515i | −0.726111 | − | 0.687577i | \(-0.758674\pi\) | ||
0.726111 | − | 0.687577i | \(-0.241326\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00000 | − | 9.79796i | −0.248548 | − | 0.608816i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | 0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.44949i | 0.151042i | 0.997144 | + | 0.0755210i | \(0.0240620\pi\) | ||||
−0.997144 | + | 0.0755210i | \(0.975938\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.6969i | 0.902826i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.2474i | 0.749532i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.0454i | 1.34413i | 0.740491 | + | 0.672066i | \(0.234593\pi\) | ||||
−0.740491 | + | 0.672066i | \(0.765407\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.0000 | + | 4.89898i | −0.726273 | + | 0.296500i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 2.44949i | − | 0.147710i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.00000 | −0.480673 | −0.240337 | − | 0.970690i | \(-0.577258\pi\) | ||||
−0.240337 | + | 0.970690i | \(0.577258\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.00000 | 0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.0000 | −0.832214 | −0.416107 | − | 0.909316i | \(-0.636606\pi\) | ||||
−0.416107 | + | 0.909316i | \(0.636606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.89898i | 0.290191i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.0000 | − | 7.34847i | 1.06251 | − | 0.433766i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.0000 | 0.647059 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 4.89898i | − | 0.287183i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.0454i | 1.28791i | 0.765065 | + | 0.643953i | \(0.222707\pi\) | ||||
−0.765065 | + | 0.643953i | \(0.777293\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 29.3939i | − | 1.71138i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.44949i | 0.142134i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 36.0000 | 2.08193 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.0000 | + | 4.89898i | −0.691669 | + | 0.282372i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.44949i | 0.140720i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.0000 | −1.48390 | −0.741949 | − | 0.670456i | \(-0.766098\pi\) | ||||
−0.741949 | + | 0.670456i | \(0.766098\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.0000 | −0.910208 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.79796i | 0.553813i | 0.960897 | + | 0.276907i | \(0.0893093\pi\) | ||||
−0.960897 | + | 0.276907i | \(0.910691\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.00000 | + | 2.44949i | −0.338062 | + | 0.138013i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.0000 | −1.01098 | −0.505490 | − | 0.862832i | \(-0.668688\pi\) | ||||
−0.505490 | + | 0.862832i | \(0.668688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.6969i | 0.822871i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 12.2474i | − | 0.683586i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.89898i | 0.272587i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.89898i | 0.271746i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.00000 | 0.110600 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.0000 | + | 29.3939i | 0.661581 | + | 1.62054i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 24.4949i | − | 1.34636i | −0.739478 | − | 0.673181i | \(-0.764928\pi\) | ||
0.739478 | − | 0.673181i | \(-0.235072\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.00000 | 0.219199 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.5959i | 1.06118i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0000 | + | 7.34847i | 0.917914 | + | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.0000 | 0.969087 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 17.1464i | − | 0.920468i | −0.887798 | − | 0.460234i | \(-0.847765\pi\) | ||
0.887798 | − | 0.460234i | \(-0.152235\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.5959i | 1.04895i | 0.851427 | + | 0.524473i | \(0.175738\pi\) | ||||
−0.851427 | + | 0.524473i | \(0.824262\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 4.89898i | − | 0.261488i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.44949i | 0.130373i | 0.997873 | + | 0.0651866i | \(0.0207643\pi\) | ||||
−0.997873 | + | 0.0651866i | \(0.979236\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.0000 | 1.59223 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.00000 | + | 2.44949i | −0.317554 | + | 0.129641i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.2474i | 0.646396i | 0.946331 | + | 0.323198i | \(0.104758\pi\) | ||||
−0.946331 | + | 0.323198i | \(0.895242\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.00000 | 0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.0000 | 1.88433 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.0000 | −0.730794 | −0.365397 | − | 0.930852i | \(-0.619067\pi\) | ||||
−0.365397 | + | 0.930852i | \(0.619067\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.34847i | 0.382546i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.00000 | + | 14.6969i | 0.311504 | + | 0.763027i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 9.79796i | − | 0.505964i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 29.3939i | − | 1.51386i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.2929i | 1.76151i | 0.473576 | + | 0.880753i | \(0.342963\pi\) | ||||
−0.473576 | + | 0.880753i | \(0.657037\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.79796i | 0.501965i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.0000 | −0.613171 | −0.306586 | − | 0.951843i | \(-0.599187\pi\) | ||||
−0.306586 | + | 0.951843i | \(0.599187\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00000 | − | 14.6969i | −0.305788 | − | 0.749025i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 4.89898i | − | 0.249029i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.0000 | −1.52106 | −0.760530 | − | 0.649303i | \(-0.775061\pi\) | ||||
−0.760530 | + | 0.649303i | \(0.775061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0000 | 0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −24.0000 | −1.20757 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 9.79796i | − | 0.491745i | −0.969302 | − | 0.245873i | \(-0.920925\pi\) | ||
0.969302 | − | 0.245873i | \(-0.0790745\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.00000 | + | 4.89898i | 0.100125 | + | 0.245256i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0000 | −0.898877 | −0.449439 | − | 0.893311i | \(-0.648376\pi\) | ||||
−0.449439 | + | 0.893311i | \(0.648376\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 39.1918i | − | 1.95228i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 2.44949i | − | 0.121716i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.79796i | 0.485667i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.89898i | − | 0.242239i | −0.992638 | − | 0.121119i | \(-0.961352\pi\) | ||
0.992638 | − | 0.121119i | \(-0.0386484\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | 0.295958 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.0000 | − | 29.3939i | −0.590481 | − | 1.44638i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.00000 | −0.195881 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −36.0000 | −1.75872 | −0.879358 | − | 0.476162i | \(-0.842028\pi\) | ||||
−0.879358 | + | 0.476162i | \(0.842028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.00000 | −0.389896 | −0.194948 | − | 0.980814i | \(-0.562454\pi\) | ||||
−0.194948 | + | 0.980814i | \(0.562454\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.0000 | −0.583460 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.44949i | 0.118818i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.0000 | 0.579365 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.1464i | 0.825914i | 0.910750 | + | 0.412957i | \(0.135504\pi\) | ||||
−0.910750 | + | 0.412957i | \(0.864496\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.79796i | 0.470860i | 0.971891 | + | 0.235430i | \(0.0756498\pi\) | ||||
−0.971891 | + | 0.235430i | \(0.924350\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 14.6969i | − | 0.704664i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 14.6969i | − | 0.703050i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.0000 | 1.05000 | 0.525001 | − | 0.851101i | \(-0.324065\pi\) | ||||
0.525001 | + | 0.851101i | \(0.324065\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | + | 4.89898i | −0.238095 | + | 0.233285i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 2.44949i | − | 0.116379i | −0.998306 | − | 0.0581894i | \(-0.981467\pi\) | ||
0.998306 | − | 0.0581894i | \(-0.0185327\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 30.0000 | 1.42214 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.0000 | −0.851371 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0000 | −0.847587 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 14.6969i | − | 0.690522i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.0000 | + | 29.3939i | 0.562569 | + | 1.37801i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.0000 | 1.77757 | 0.888783 | − | 0.458329i | \(-0.151552\pi\) | ||||
0.888783 | + | 0.458329i | \(0.151552\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 2.44949i | − | 0.114332i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.44949i | − | 0.114084i | −0.998372 | − | 0.0570421i | \(-0.981833\pi\) | ||
0.998372 | − | 0.0570421i | \(-0.0181669\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.79796i | 0.455350i | 0.973737 | + | 0.227675i | \(0.0731123\pi\) | ||||
−0.973737 | + | 0.227675i | \(0.926888\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 19.5959i | − | 0.908739i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.0000 | 1.11059 | 0.555294 | − | 0.831654i | \(-0.312606\pi\) | ||||
0.555294 | + | 0.831654i | \(0.312606\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 19.5959i | − | 0.902932i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.0000 | 0.551761 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00000 | 0.0917663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.0000 | −1.09659 | −0.548294 | − | 0.836286i | \(-0.684723\pi\) | ||||
−0.548294 | + | 0.836286i | \(0.684723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 19.5959i | − | 0.893497i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18.0000 | − | 7.34847i | 0.819028 | − | 0.334367i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.0000 | −0.544892 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.89898i | 0.221994i | 0.993821 | + | 0.110997i | \(0.0354044\pi\) | ||||
−0.993821 | + | 0.110997i | \(0.964596\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.5959i | 0.886158i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.7423i | 1.65816i | 0.559131 | + | 0.829079i | \(0.311135\pi\) | ||||
−0.559131 | + | 0.829079i | \(0.688865\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 14.6969i | − | 0.661917i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.00000 | 0.269680 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 30.0000 | − | 12.2474i | 1.34568 | − | 0.549373i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 14.6969i | − | 0.657925i | −0.944343 | − | 0.328963i | \(-0.893301\pi\) | ||
0.944343 | − | 0.328963i | \(-0.106699\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.0000 | 0.536120 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.0000 | 0.535054 | 0.267527 | − | 0.963550i | \(-0.413794\pi\) | ||||
0.267527 | + | 0.963550i | \(0.413794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.0000 | −0.488527 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 17.1464i | − | 0.760002i | −0.924986 | − | 0.380001i | \(-0.875924\pi\) | ||
0.924986 | − | 0.380001i | \(-0.124076\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.0000 | − | 14.6969i | 1.59255 | − | 0.650154i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.00000 | −0.0883022 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 39.1918i | 1.72700i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 29.3939i | − | 1.29274i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 7.34847i | − | 0.322562i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.44949i | 0.107314i | 0.998559 | + | 0.0536570i | \(0.0170878\pi\) | ||||
−0.998559 | + | 0.0536570i | \(0.982912\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.0000 | 0.874539 | 0.437269 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437269 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.00000 | + | 2.44949i | 0.0436436 | + | 0.106904i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 19.5959i | − | 0.853612i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −31.0000 | −1.34783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 36.0000 | 1.55933 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.0000 | −1.29701 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 17.1464i | − | 0.739923i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.0000 | − | 12.2474i | −0.516877 | − | 0.527535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.0000 | 0.687894 | 0.343947 | − | 0.938989i | \(-0.388236\pi\) | ||||
0.343947 | + | 0.938989i | \(0.388236\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.89898i | 0.210235i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 4.89898i | − | 0.209849i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 29.3939i | − | 1.25679i | −0.777894 | − | 0.628396i | \(-0.783712\pi\) | ||
0.777894 | − | 0.628396i | \(-0.216288\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.0000 | −0.511217 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.0000 | + | 9.79796i | −1.02058 | + | 0.416652i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 9.79796i | − | 0.415900i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.00000 | 0.254228 | 0.127114 | − | 0.991888i | \(-0.459429\pi\) | ||||
0.127114 | + | 0.991888i | \(0.459429\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.0000 | −1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.00000 | 0.253320 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.0000 | −1.01148 | −0.505740 | − | 0.862686i | \(-0.668780\pi\) | ||||
−0.505740 | + | 0.862686i | \(0.668780\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 14.6969i | − | 0.618305i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | − | 2.44949i | −0.0419961 | − | 0.102869i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.00000 | −0.251533 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 19.5959i | − | 0.820064i | −0.912071 | − | 0.410032i | \(-0.865518\pi\) | ||
0.912071 | − | 0.410032i | \(-0.134482\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 2.44949i | − | 0.102329i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 7.34847i | − | 0.306452i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.0000 | 0.664937 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 14.6969i | − | 0.608685i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.0000 | −0.496139 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0000 | −0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.0000 | 0.740421 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 46.5403i | 1.91118i | 0.294697 | + | 0.955591i | \(0.404781\pi\) | ||||
−0.294697 | + | 0.955591i | \(0.595219\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.00000 | + | 14.6969i | 0.245976 | + | 0.602516i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.00000 | −0.0818546 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.44949i | 0.100083i | 0.998747 | + | 0.0500417i | \(0.0159354\pi\) | ||||
−0.998747 | + | 0.0500417i | \(0.984065\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.5959i | − | 0.799334i | −0.916660 | − | 0.399667i | \(-0.869126\pi\) | ||
0.916660 | − | 0.399667i | \(-0.130874\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 12.2474i | − | 0.497930i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.0000 | −0.568242 | −0.284121 | − | 0.958788i | \(-0.591702\pi\) | ||||
−0.284121 | + | 0.958788i | \(0.591702\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.00000 | − | 14.6969i | −0.243132 | − | 0.595550i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 58.7878i | 2.37830i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.0000 | 1.05013 | 0.525065 | − | 0.851062i | \(-0.324041\pi\) | ||||
0.525065 | + | 0.851062i | \(0.324041\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18.0000 | 0.725830 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.0000 | −1.69086 | −0.845428 | − | 0.534089i | \(-0.820655\pi\) | ||||
−0.845428 | + | 0.534089i | \(0.820655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.34847i | 0.294884i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 30.0000 | − | 12.2474i | 1.20192 | − | 0.490684i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 4.89898i | − | 0.195646i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 9.79796i | − | 0.390670i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 19.5959i | − | 0.780101i | −0.920793 | − | 0.390051i | \(-0.872458\pi\) | ||
0.920793 | − | 0.390051i | \(-0.127542\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.89898i | 0.194717i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.0000 | 0.952411 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.0000 | + | 24.4949i | 0.950915 | + | 0.970523i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.2474i | 0.484502i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.00000 | −0.236986 | −0.118493 | − | 0.992955i | \(-0.537806\pi\) | ||||
−0.118493 | + | 0.992955i | \(0.537806\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.0000 | −0.552106 | −0.276053 | − | 0.961142i | \(-0.589027\pi\) | ||||
−0.276053 | + | 0.961142i | \(0.589027\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.0000 | −0.472500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.0000 | −0.943537 | −0.471769 | − | 0.881722i | \(-0.656384\pi\) | ||||
−0.471769 | + | 0.881722i | \(0.656384\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.3939i | 1.15381i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.00000 | − | 19.5959i | −0.313545 | − | 0.768025i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.00000 | −0.234798 | −0.117399 | − | 0.993085i | \(-0.537456\pi\) | ||||
−0.117399 | + | 0.993085i | \(0.537456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.6969i | 0.573382i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.34847i | 0.286256i | 0.989704 | + | 0.143128i | \(0.0457160\pi\) | ||||
−0.989704 | + | 0.143128i | \(0.954284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.3939i | 1.14329i | 0.820501 | + | 0.571645i | \(0.193694\pi\) | ||||
−0.820501 | + | 0.571645i | \(0.806306\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.0000 | −0.466041 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.0000 | − | 4.89898i | 0.465340 | − | 0.189974i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44.0908i | 1.70720i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.0000 | 0.386622 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.00000 | −0.308377 | −0.154189 | − | 0.988041i | \(-0.549276\pi\) | ||||
−0.154189 | + | 0.988041i | \(0.549276\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 12.2474i | − | 0.470708i | −0.971910 | − | 0.235354i | \(-0.924375\pi\) | ||
0.971910 | − | 0.235354i | \(-0.0756249\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0000 | + | 4.89898i | −0.460518 | + | 0.188006i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.0000 | 0.459841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.34847i | 0.281181i | 0.990068 | + | 0.140591i | \(0.0449002\pi\) | ||||
−0.990068 | + | 0.140591i | \(0.955100\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 14.6969i | − | 0.561541i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.4949i | 0.934539i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.3939i | 1.11982i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.00000 | − | 2.44949i | 0.227921 | − | 0.0930484i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.79796i | 0.371658i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | 0.681799 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −30.0000 | −1.13470 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.00000 | −0.301726 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 29.3939i | 1.10704i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00000 | − | 2.44949i | 0.225653 | − | 0.0921225i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.0000 | −0.375558 | −0.187779 | − | 0.982211i | \(-0.560129\pi\) | ||||
−0.187779 | + | 0.982211i | \(0.560129\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 9.79796i | − | 0.367452i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 58.7878i | 2.20162i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 29.3939i | − | 1.09927i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 12.2474i | − | 0.457389i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.0000 | 0.895049 | 0.447524 | − | 0.894272i | \(-0.352306\pi\) | ||||
0.447524 | + | 0.894272i | \(0.352306\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | + | 39.1918i | 0.595871 | + | 1.45958i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 4.89898i | − | 0.182195i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.00000 | −0.222834 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0000 | 1.18681 | 0.593407 | − | 0.804902i | \(-0.297782\pi\) | ||||
0.593407 | + | 0.804902i | \(0.297782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | −0.443836 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 4.89898i | − | 0.180948i | −0.995899 | − | 0.0904740i | \(-0.971162\pi\) | ||
0.995899 | − | 0.0904740i | \(-0.0288382\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.0000 | + | 12.2474i | 0.442627 | + | 0.451754i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.79796i | 0.360424i | 0.983628 | + | 0.180212i | \(0.0576783\pi\) | ||||
−0.983628 | + | 0.180212i | \(0.942322\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.79796i | 0.359937i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 12.2474i | − | 0.449315i | −0.974438 | − | 0.224658i | \(-0.927874\pi\) | ||
0.974438 | − | 0.224658i | \(-0.0721264\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 44.0908i | 1.61536i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −30.0000 | + | 12.2474i | −1.09618 | + | 0.447512i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.2929i | 1.25136i | 0.780078 | + | 0.625682i | \(0.215179\pi\) | ||||
−0.780078 | + | 0.625682i | \(0.784821\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −36.0000 | −1.31017 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0000 | −0.363456 | −0.181728 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181728 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.0000 | −0.653359 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 41.6413i | − | 1.50950i | −0.656014 | − | 0.754748i | \(-0.727759\pi\) | ||
0.656014 | − | 0.754748i | \(-0.272241\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.00000 | − | 4.89898i | −0.0724049 | − | 0.177355i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.00000 | −0.216930 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 58.7878i | − | 2.12270i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.79796i | 0.353323i | 0.984272 | + | 0.176662i | \(0.0565299\pi\) | ||||
−0.984272 | + | 0.176662i | \(0.943470\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 22.0454i | − | 0.793946i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 22.0454i | − | 0.792918i | −0.918052 | − | 0.396459i | \(-0.870239\pi\) | ||
0.918052 | − | 0.396459i | \(-0.129761\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.00000 | −0.287368 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.00000 | − | 9.79796i | −0.143499 | − | 0.351500i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 14.6969i | − | 0.526572i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.0000 | −1.07348 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.00000 | 0.214423 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −48.0000 | −1.71319 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.0000 | 0.712923 | 0.356462 | − | 0.934310i | \(-0.383983\pi\) | ||||
0.356462 | + | 0.934310i | \(0.383983\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.44949i | 0.0872041i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.00000 | − | 14.6969i | −0.213335 | − | 0.522563i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14.6969i | 0.521247i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.7423i | 1.30148i | 0.759300 | + | 0.650740i | \(0.225541\pi\) | ||||
−0.759300 | + | 0.650740i | \(0.774459\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.3939i | 1.03988i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.2474i | 0.432742i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −36.0000 | −1.27041 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.0000 | − | 44.0908i | −0.634417 | − | 1.55400i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.0454i | 0.776035i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.0000 | 0.632846 | 0.316423 | − | 0.948618i | \(-0.397518\pi\) | ||||
0.316423 | + | 0.948618i | \(0.397518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.0000 | −0.561144 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 48.0000 | 1.68137 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.79796i | 0.342787i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.0000 | + | 4.89898i | −0.419314 | + | 0.171184i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.0000 | 0.628204 | 0.314102 | − | 0.949389i | \(-0.398297\pi\) | ||||
0.314102 | + | 0.949389i | \(0.398297\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.5959i | 0.683071i | 0.939869 | + | 0.341535i | \(0.110947\pi\) | ||||
−0.939869 | + | 0.341535i | \(0.889053\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 2.44949i | − | 0.0852803i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 46.5403i | − | 1.61836i | −0.587557 | − | 0.809182i | \(-0.699910\pi\) | ||
0.587557 | − | 0.809182i | \(-0.300090\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 4.89898i | − | 0.170149i | −0.996375 | − | 0.0850743i | \(-0.972887\pi\) | ||
0.996375 | − | 0.0850743i | \(-0.0271128\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.00000 | −0.277517 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.0000 | + | 12.2474i | 0.415775 | + | 0.424349i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 29.3939i | − | 1.01722i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.00000 | 0.276520 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.0000 | 0.414286 | 0.207143 | − | 0.978311i | \(-0.433583\pi\) | ||||
0.207143 | + | 0.978311i | \(0.433583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.00000 | 0.206651 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.9444i | 0.926915i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.00000 | − | 12.2474i | −0.171802 | − | 0.420827i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.0000 | −0.480479 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.3939i | 1.00761i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 29.3939i | − | 1.00643i | −0.864162 | − | 0.503214i | \(-0.832151\pi\) | ||
0.864162 | − | 0.503214i | \(-0.167849\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.89898i | 0.167542i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 22.0454i | − | 0.753057i | −0.926405 | − | 0.376528i | \(-0.877118\pi\) | ||
0.926405 | − | 0.376528i | \(-0.122882\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.0000 | 0.750630 | 0.375315 | − | 0.926897i | \(-0.377534\pi\) | ||||
0.375315 | + | 0.926897i | \(0.377534\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.0000 | − | 7.34847i | 0.613438 | − | 0.250435i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 51.4393i | − | 1.75101i | −0.483206 | − | 0.875507i | \(-0.660528\pi\) | ||
0.483206 | − | 0.875507i | \(-0.339472\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.0000 | −0.612018 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.0000 | 0.373580 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.0000 | 0.814144 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 4.89898i | − | 0.165805i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.0000 | + | 9.79796i | −0.811348 | + | 0.331231i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.0000 | −0.742887 | −0.371444 | − | 0.928456i | \(-0.621137\pi\) | ||||
−0.371444 | + | 0.928456i | \(0.621137\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.0454i | 0.743573i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.44949i | 0.0825254i | 0.999148 | + | 0.0412627i | \(0.0131381\pi\) | ||||
−0.999148 | + | 0.0412627i | \(0.986862\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.2929i | 1.15405i | 0.816728 | + | 0.577023i | \(0.195786\pi\) | ||||
−0.816728 | + | 0.577023i | \(0.804214\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 29.3939i | − | 0.988064i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.0000 | 0.402921 | 0.201460 | − | 0.979497i | \(-0.435431\pi\) | ||||
0.201460 | + | 0.979497i | \(0.435431\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.0000 | − | 9.79796i | 0.804934 | − | 0.328613i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.44949i | 0.0820610i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.0000 | 0.803129 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −42.0000 | −1.40391 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 36.0000 | 1.20201 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 48.0000 | 1.60089 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.6969i | 0.489626i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.0000 | + | 4.89898i | −0.399335 | + | 0.163028i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.0000 | 0.398893 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.4949i | 0.813340i | 0.913575 | + | 0.406670i | \(0.133310\pi\) | ||||
−0.913575 | + | 0.406670i | \(0.866690\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.44949i | 0.0812444i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 7.34847i | − | 0.243466i | −0.992563 | − | 0.121733i | \(-0.961155\pi\) | ||
0.992563 | − | 0.121733i | \(-0.0388451\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 14.6969i | − | 0.484807i | −0.970175 | − | 0.242404i | \(-0.922064\pi\) | ||
0.970175 | − | 0.242404i | \(-0.0779358\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.0000 | −0.856729 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 60.0000 | 1.97492 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.0000 | −0.525509 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 12.2474i | − | 0.401826i | −0.979609 | − | 0.200913i | \(-0.935609\pi\) | ||
0.979609 | − | 0.200913i | \(-0.0643908\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.0000 | − | 9.79796i | 0.327737 | − | 0.321115i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.0000 | −0.785725 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 14.6969i | − | 0.480641i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 39.1918i | − | 1.28034i | −0.768233 | − | 0.640171i | \(-0.778864\pi\) | ||
0.768233 | − | 0.640171i | \(-0.221136\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.79796i | 0.319744i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 12.2474i | − | 0.399255i | −0.979872 | − | 0.199628i | \(-0.936027\pi\) | ||
0.979872 | − | 0.199628i | \(-0.0639733\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −54.0000 | −1.75848 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.00000 | + | 2.44949i | −0.195180 | + | 0.0796819i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 26.9444i | − | 0.875575i | −0.899078 | − | 0.437787i | \(-0.855762\pi\) | ||
0.899078 | − | 0.437787i | \(-0.144238\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 72.0000 | 2.33722 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.0000 | −0.583077 | −0.291539 | − | 0.956559i | \(-0.594167\pi\) | ||||
−0.291539 | + | 0.956559i | \(0.594167\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.00000 | −0.194155 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.6969i | 0.475085i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.00000 | − | 14.6969i | −0.193750 | − | 0.474589i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 12.2474i | − | 0.394669i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 39.1918i | − | 1.26163i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 58.7878i | 1.89049i | 0.326366 | + | 0.945243i | \(0.394176\pi\) | ||||
−0.326366 | + | 0.945243i | \(0.605824\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.89898i | 0.157378i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.0000 | −1.15529 | −0.577647 | − | 0.816286i | \(-0.696029\pi\) | ||||
−0.577647 | + | 0.816286i | \(0.696029\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.00000 | + | 9.79796i | 0.128234 | + | 0.314108i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.89898i | 0.156893i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.00000 | 0.191957 | 0.0959785 | − | 0.995383i | \(-0.469402\pi\) | ||||
0.0959785 | + | 0.995383i | \(0.469402\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.0000 | −0.958804 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.0000 | 0.382741 | 0.191370 | − | 0.981518i | \(-0.438707\pi\) | ||||
0.191370 | + | 0.981518i | \(0.438707\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 44.0908i | − | 1.40485i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.0000 | + | 29.3939i | 0.381964 | + | 0.935617i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 36.0000 | 1.14473 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 14.6969i | − | 0.466864i | −0.972373 | − | 0.233432i | \(-0.925004\pi\) | ||
0.972373 | − | 0.233432i | \(-0.0749956\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 24.4949i | − | 0.777322i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.89898i | 0.155308i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.00000 | 0.126554 |
(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 | 336.2.b.c.223.1 | yes | 2 | |
3.2 | odd | 2 | 1008.2.b.d.559.2 | 2 | |||
4.3 | odd | 2 | 336.2.b.b.223.1 | ✓ | 2 | ||
7.2 | even | 3 | 2352.2.bl.m.31.1 | 4 | |||
7.3 | odd | 6 | 2352.2.bl.n.607.1 | 4 | |||
7.4 | even | 3 | 2352.2.bl.m.607.2 | 4 | |||
7.5 | odd | 6 | 2352.2.bl.n.31.2 | 4 | |||
7.6 | odd | 2 | 336.2.b.b.223.2 | yes | 2 | ||
8.3 | odd | 2 | 1344.2.b.d.895.2 | 2 | |||
8.5 | even | 2 | 1344.2.b.a.895.2 | 2 | |||
12.11 | even | 2 | 1008.2.b.e.559.2 | 2 | |||
21.20 | even | 2 | 1008.2.b.e.559.1 | 2 | |||
24.5 | odd | 2 | 4032.2.b.d.3583.1 | 2 | |||
24.11 | even | 2 | 4032.2.b.f.3583.1 | 2 | |||
28.3 | even | 6 | 2352.2.bl.m.607.1 | 4 | |||
28.11 | odd | 6 | 2352.2.bl.n.607.2 | 4 | |||
28.19 | even | 6 | 2352.2.bl.m.31.2 | 4 | |||
28.23 | odd | 6 | 2352.2.bl.n.31.1 | 4 | |||
28.27 | even | 2 | inner | 336.2.b.c.223.2 | yes | 2 | |
56.13 | odd | 2 | 1344.2.b.d.895.1 | 2 | |||
56.27 | even | 2 | 1344.2.b.a.895.1 | 2 | |||
84.83 | odd | 2 | 1008.2.b.d.559.1 | 2 | |||
168.83 | odd | 2 | 4032.2.b.d.3583.2 | 2 | |||
168.125 | even | 2 | 4032.2.b.f.3583.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.b.b.223.1 | ✓ | 2 | 4.3 | odd | 2 | ||
336.2.b.b.223.2 | yes | 2 | 7.6 | odd | 2 | ||
336.2.b.c.223.1 | yes | 2 | 1.1 | even | 1 | trivial | |
336.2.b.c.223.2 | yes | 2 | 28.27 | even | 2 | inner | |
1008.2.b.d.559.1 | 2 | 84.83 | odd | 2 | |||
1008.2.b.d.559.2 | 2 | 3.2 | odd | 2 | |||
1008.2.b.e.559.1 | 2 | 21.20 | even | 2 | |||
1008.2.b.e.559.2 | 2 | 12.11 | even | 2 | |||
1344.2.b.a.895.1 | 2 | 56.27 | even | 2 | |||
1344.2.b.a.895.2 | 2 | 8.5 | even | 2 | |||
1344.2.b.d.895.1 | 2 | 56.13 | odd | 2 | |||
1344.2.b.d.895.2 | 2 | 8.3 | odd | 2 | |||
2352.2.bl.m.31.1 | 4 | 7.2 | even | 3 | |||
2352.2.bl.m.31.2 | 4 | 28.19 | even | 6 | |||
2352.2.bl.m.607.1 | 4 | 28.3 | even | 6 | |||
2352.2.bl.m.607.2 | 4 | 7.4 | even | 3 | |||
2352.2.bl.n.31.1 | 4 | 28.23 | odd | 6 | |||
2352.2.bl.n.31.2 | 4 | 7.5 | odd | 6 | |||
2352.2.bl.n.607.1 | 4 | 7.3 | odd | 6 | |||
2352.2.bl.n.607.2 | 4 | 28.11 | odd | 6 | |||
4032.2.b.d.3583.1 | 2 | 24.5 | odd | 2 | |||
4032.2.b.d.3583.2 | 2 | 168.83 | odd | 2 | |||
4032.2.b.f.3583.1 | 2 | 24.11 | even | 2 | |||
4032.2.b.f.3583.2 | 2 | 168.125 | even | 2 |