Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(289,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("2880.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.d (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: | \(22.9969157821\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 289.3 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.289 |
Dual form | 2880.2.d.f.289.2 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.41421 | + | 1.73205i | −0.632456 | + | 0.774597i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.82843i | − | 1.06904i | −0.845154 | − | 0.534522i | \(-0.820491\pi\) | ||
0.845154 | − | 0.534522i | \(-0.179509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000i | 0.603023i | 0.953463 | + | 0.301511i | \(0.0974911\pi\) | ||||
−0.953463 | + | 0.301511i | \(0.902509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.82843 | 0.784465 | 0.392232 | − | 0.919866i | \(-0.371703\pi\) | ||||
0.392232 | + | 0.919866i | \(0.371703\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.89898i | 1.18818i | 0.804400 | + | 0.594089i | \(0.202487\pi\) | ||||
−0.804400 | + | 0.594089i | \(0.797513\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.65685i | − | 1.17954i | −0.807573 | − | 0.589768i | \(-0.799219\pi\) | ||
0.807573 | − | 0.589768i | \(-0.200781\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | − | 4.89898i | −0.200000 | − | 0.979796i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.46410i | 0.643268i | 0.946864 | + | 0.321634i | \(0.104232\pi\) | ||||
−0.946864 | + | 0.321634i | \(0.895768\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.46410 | 0.622171 | 0.311086 | − | 0.950382i | \(-0.399307\pi\) | ||||
0.311086 | + | 0.950382i | \(0.399307\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.89898 | + | 4.00000i | 0.828079 | + | 0.676123i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.82843 | 0.464991 | 0.232495 | − | 0.972598i | \(-0.425311\pi\) | ||||
0.232495 | + | 0.972598i | \(0.425311\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.00000 | −1.24939 | −0.624695 | − | 0.780869i | \(-0.714777\pi\) | ||||
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.79796 | −1.49417 | −0.747087 | − | 0.664726i | \(-0.768548\pi\) | ||||
−0.747087 | + | 0.664726i | \(0.768548\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.48528 | 1.16554 | 0.582772 | − | 0.812636i | \(-0.301968\pi\) | ||||
0.582772 | + | 0.812636i | \(0.301968\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.46410 | − | 2.82843i | −0.467099 | − | 0.381385i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.0000i | 1.30189i | 0.759125 | + | 0.650945i | \(0.225627\pi\) | ||||
−0.759125 | + | 0.650945i | \(0.774373\pi\) | |||||||
\(60\) | 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 | ||||||||
\(65\) | −4.00000 | + | 4.89898i | −0.496139 | + | 0.607644i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.79796 | 1.19701 | 0.598506 | − | 0.801119i | \(-0.295761\pi\) | ||||
0.598506 | + | 0.801119i | \(0.295761\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.8564 | 1.64445 | 0.822226 | − | 0.569160i | \(-0.192732\pi\) | ||||
0.822226 | + | 0.569160i | \(0.192732\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.79796i | 1.14676i | 0.819288 | + | 0.573382i | \(0.194369\pi\) | ||||
−0.819288 | + | 0.573382i | \(0.805631\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.65685 | 0.644658 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.46410 | −0.389742 | −0.194871 | − | 0.980829i | \(-0.562429\pi\) | ||||
−0.194871 | + | 0.980829i | \(0.562429\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.79796 | 1.07547 | 0.537733 | − | 0.843115i | \(-0.319281\pi\) | ||||
0.537733 | + | 0.843115i | \(0.319281\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.48528 | − | 6.92820i | −0.920358 | − | 0.751469i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.0000 | −1.69600 | −0.847998 | − | 0.529999i | \(-0.822192\pi\) | ||||
−0.847998 | + | 0.529999i | \(0.822192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 8.00000i | − | 0.838628i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.46410i | 0.344691i | 0.985037 | + | 0.172345i | \(0.0551346\pi\) | ||||
−0.985037 | + | 0.172345i | \(0.944865\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.1421i | 1.39347i | 0.717331 | + | 0.696733i | \(0.245364\pi\) | ||||
−0.717331 | + | 0.696733i | \(0.754636\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.5959 | 1.89441 | 0.947204 | − | 0.320630i | \(-0.103895\pi\) | ||||
0.947204 | + | 0.320630i | \(0.103895\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.92820i | − | 0.663602i | −0.943349 | − | 0.331801i | \(-0.892344\pi\) | ||
0.943349 | − | 0.331801i | \(-0.107656\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.6969i | 1.38257i | 0.722581 | + | 0.691286i | \(0.242955\pi\) | ||||
−0.722581 | + | 0.691286i | \(0.757045\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.79796 | + | 8.00000i | 0.913664 | + | 0.746004i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.8564 | 1.27021 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.89949 | + | 5.19615i | 0.885438 | + | 0.464758i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.82843i | 0.250982i | 0.992095 | + | 0.125491i | \(0.0400507\pi\) | ||||
−0.992095 | + | 0.125491i | \(0.959949\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.0000i | 1.22319i | 0.791173 | + | 0.611593i | \(0.209471\pi\) | ||||
−0.791173 | + | 0.611593i | \(0.790529\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.89898i | 0.418548i | 0.977857 | + | 0.209274i | \(0.0671101\pi\) | ||||
−0.977857 | + | 0.209274i | \(0.932890\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000i | 0.678551i | 0.940687 | + | 0.339276i | \(0.110182\pi\) | ||||
−0.940687 | + | 0.339276i | \(0.889818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.65685i | 0.473050i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | − | 4.89898i | −0.498273 | − | 0.406838i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.3923i | 0.851371i | 0.904871 | + | 0.425685i | \(0.139967\pi\) | ||||
−0.904871 | + | 0.425685i | \(0.860033\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.3205 | 1.40952 | 0.704761 | − | 0.709444i | \(-0.251054\pi\) | ||||
0.704761 | + | 0.709444i | \(0.251054\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.89898 | + | 6.00000i | −0.393496 | + | 0.481932i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.7990 | −1.58013 | −0.790066 | − | 0.613022i | \(-0.789954\pi\) | ||||
−0.790066 | + | 0.613022i | \(0.789954\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.0000 | −1.26098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 22.6274i | − | 1.75096i | −0.483252 | − | 0.875481i | \(-0.660545\pi\) | ||
0.483252 | − | 0.875481i | \(-0.339455\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.48528 | −0.645124 | −0.322562 | − | 0.946548i | \(-0.604544\pi\) | ||||
−0.322562 | + | 0.946548i | \(0.604544\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.8564 | + | 2.82843i | −1.04745 | + | 0.213809i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.0000i | 1.04641i | 0.852207 | + | 0.523205i | \(0.175264\pi\) | ||||
−0.852207 | + | 0.523205i | \(0.824736\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.7846i | 1.54491i | 0.635071 | + | 0.772454i | \(0.280971\pi\) | ||||
−0.635071 | + | 0.772454i | \(0.719029\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00000 | + | 4.89898i | −0.294086 | + | 0.360180i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.79796 | −0.716498 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.8564 | −1.00261 | −0.501307 | − | 0.865269i | \(-0.667147\pi\) | ||||
−0.501307 | + | 0.865269i | \(0.667147\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.79796i | 0.705273i | 0.935760 | + | 0.352636i | \(0.114715\pi\) | ||||
−0.935760 | + | 0.352636i | \(0.885285\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.82843 | 0.201517 | 0.100759 | − | 0.994911i | \(-0.467873\pi\) | ||||
0.100759 | + | 0.994911i | \(0.467873\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.3923 | −0.736691 | −0.368345 | − | 0.929689i | \(-0.620076\pi\) | ||||
−0.368345 | + | 0.929689i | \(0.620076\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.79796 | 0.687682 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.3137 | − | 13.8564i | 0.790184 | − | 0.967773i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 8.00000i | − | 0.550743i | −0.961338 | − | 0.275371i | \(-0.911199\pi\) | ||
0.961338 | − | 0.275371i | \(-0.0888008\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.8564 | − | 16.9706i | 0.944999 | − | 1.15738i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 9.79796i | − | 0.665129i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.8564i | 0.932083i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 14.1421i | − | 0.947027i | −0.880786 | − | 0.473514i | \(-0.842985\pi\) | ||
0.880786 | − | 0.473514i | \(-0.157015\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.79796 | −0.650313 | −0.325157 | − | 0.945660i | \(-0.605417\pi\) | ||||
−0.325157 | + | 0.945660i | \(0.605417\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.92820i | − | 0.457829i | −0.973447 | − | 0.228914i | \(-0.926482\pi\) | ||
0.973447 | − | 0.228914i | \(-0.0735176\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.6969i | 0.962828i | 0.876493 | + | 0.481414i | \(0.159877\pi\) | ||||
−0.876493 | + | 0.481414i | \(0.840123\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.8564 | −0.896296 | −0.448148 | − | 0.893959i | \(-0.647916\pi\) | ||||
−0.448148 | + | 0.893959i | \(0.647916\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.0000 | 1.15948 | 0.579741 | − | 0.814801i | \(-0.303154\pi\) | ||||
0.579741 | + | 0.814801i | \(0.303154\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.41421 | − | 1.73205i | 0.0903508 | − | 0.110657i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.0000i | 0.883672i | 0.897096 | + | 0.441836i | \(0.145673\pi\) | ||||
−0.897096 | + | 0.441836i | \(0.854327\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.3137 | 0.711287 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.89898i | 0.305590i | 0.988258 | + | 0.152795i | \(0.0488274\pi\) | ||||
−0.988258 | + | 0.152795i | \(0.951173\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8.00000i | − | 0.497096i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 11.3137i | − | 0.697633i | −0.937191 | − | 0.348817i | \(-0.886584\pi\) | ||
0.937191 | − | 0.348817i | \(-0.113416\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | + | 14.6969i | −0.737154 | + | 0.902826i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 3.46410i | − | 0.211210i | −0.994408 | − | 0.105605i | \(-0.966322\pi\) | ||
0.994408 | − | 0.105605i | \(-0.0336779\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.1769 | 1.89386 | 0.946931 | − | 0.321436i | \(-0.104165\pi\) | ||||
0.946931 | + | 0.321436i | \(0.104165\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.79796 | − | 2.00000i | 0.590839 | − | 0.120605i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31.1127 | 1.86938 | 0.934690 | − | 0.355463i | \(-0.115677\pi\) | ||||
0.934690 | + | 0.355463i | \(0.115677\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.0000 | 0.954480 | 0.477240 | − | 0.878773i | \(-0.341637\pi\) | ||||
0.477240 | + | 0.878773i | \(0.341637\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.79796 | 0.582428 | 0.291214 | − | 0.956658i | \(-0.405941\pi\) | ||||
0.291214 | + | 0.956658i | \(0.405941\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.6274i | 1.33565i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.82843 | −0.165238 | −0.0826192 | − | 0.996581i | \(-0.526329\pi\) | ||||
−0.0826192 | + | 0.996581i | \(0.526329\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.3205 | − | 14.1421i | −1.00844 | − | 0.823387i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 16.0000i | − | 0.925304i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.7128i | 1.59734i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.0000 | − | 9.79796i | −0.687118 | − | 0.561029i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.5959 | −1.11840 | −0.559199 | − | 0.829033i | \(-0.688891\pi\) | ||||
−0.559199 | + | 0.829033i | \(0.688891\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.8564 | 0.785725 | 0.392862 | − | 0.919597i | \(-0.371485\pi\) | ||||
0.392862 | + | 0.919597i | \(0.371485\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 29.3939i | − | 1.66144i | −0.556690 | − | 0.830720i | \(-0.687929\pi\) | ||
0.556690 | − | 0.830720i | \(-0.312071\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.82843 | 0.158860 | 0.0794301 | − | 0.996840i | \(-0.474690\pi\) | ||||
0.0794301 | + | 0.996840i | \(0.474690\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.92820 | −0.387905 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.82843 | − | 13.8564i | −0.156893 | − | 0.768615i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 24.0000i | − | 1.31916i | −0.751635 | − | 0.659580i | \(-0.770734\pi\) | ||
0.751635 | − | 0.659580i | \(-0.229266\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.8564 | + | 16.9706i | −0.757056 | + | 0.927201i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 9.79796i | − | 0.533729i | −0.963734 | − | 0.266864i | \(-0.914012\pi\) | ||
0.963734 | − | 0.266864i | \(-0.0859876\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.92820i | 0.375183i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.9706i | − | 0.916324i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.79796 | −0.525982 | −0.262991 | − | 0.964798i | \(-0.584709\pi\) | ||||
−0.262991 | + | 0.964798i | \(0.584709\pi\) | |||||||
\(348\) | 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 | ||||||||
\(353\) | − | 34.2929i | − | 1.82522i | −0.408826 | − | 0.912612i | \(-0.634062\pi\) | ||
0.408826 | − | 0.912612i | \(-0.365938\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.5959 | + | 24.0000i | −1.04004 | + | 1.27379i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.7128 | 1.46263 | 0.731313 | − | 0.682042i | \(-0.238908\pi\) | ||||
0.731313 | + | 0.682042i | \(0.238908\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.9706 | − | 13.8564i | −0.888280 | − | 0.725277i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.82843i | 0.147643i | 0.997271 | + | 0.0738213i | \(0.0235195\pi\) | ||||
−0.997271 | + | 0.0738213i | \(0.976481\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 24.0000i | − | 1.24602i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.7990 | −1.02515 | −0.512576 | − | 0.858642i | \(-0.671309\pi\) | ||||
−0.512576 | + | 0.858642i | \(0.671309\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.79796i | 0.504621i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.0000i | 1.64373i | 0.569683 | + | 0.821865i | \(0.307066\pi\) | ||||
−0.569683 | + | 0.821865i | \(0.692934\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.9706i | 0.867155i | 0.901116 | + | 0.433578i | \(0.142749\pi\) | ||||
−0.901116 | + | 0.433578i | \(0.857251\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00000 | + | 9.79796i | −0.407718 | + | 0.499350i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 24.2487i | − | 1.22946i | −0.788738 | − | 0.614729i | \(-0.789265\pi\) | ||
0.788738 | − | 0.614729i | \(-0.210735\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.7128 | 1.40150 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.89898 | − | 6.00000i | 0.246494 | − | 0.301893i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.1421 | −0.709773 | −0.354887 | − | 0.934909i | \(-0.615481\pi\) | ||||
−0.354887 | + | 0.934909i | \(0.615481\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.00000 | 0.399501 | 0.199750 | − | 0.979847i | \(-0.435987\pi\) | ||||
0.199750 | + | 0.979847i | \(0.435987\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.79796 | 0.488071 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.65685i | 0.280400i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.00000 | −0.0988936 | −0.0494468 | − | 0.998777i | \(-0.515746\pi\) | ||||
−0.0494468 | + | 0.998777i | \(0.515746\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.2843 | 1.39178 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.8564 | + | 16.9706i | −0.680184 | + | 0.833052i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 10.0000i | − | 0.488532i | −0.969708 | − | 0.244266i | \(-0.921453\pi\) | ||
0.969708 | − | 0.244266i | \(-0.0785470\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.6410i | 1.68830i | 0.536107 | + | 0.844150i | \(0.319894\pi\) | ||||
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.0000 | − | 4.89898i | 1.16417 | − | 0.237635i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.5959 | 0.948313 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.7128 | −1.33488 | −0.667440 | − | 0.744664i | \(-0.732610\pi\) | ||||
−0.667440 | + | 0.744664i | \(0.732610\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 19.5959i | − | 0.941720i | −0.882208 | − | 0.470860i | \(-0.843944\pi\) | ||
0.882208 | − | 0.470860i | \(-0.156056\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.3923 | −0.495998 | −0.247999 | − | 0.968760i | \(-0.579773\pi\) | ||||
−0.247999 | + | 0.968760i | \(0.579773\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.3939 | −1.39655 | −0.698273 | − | 0.715832i | \(-0.746048\pi\) | ||||
−0.698273 | + | 0.715832i | \(0.746048\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.6274 | − | 27.7128i | 1.07264 | − | 1.31371i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.00000 | 0.377543 | 0.188772 | − | 0.982021i | \(-0.439549\pi\) | ||||
0.188772 | + | 0.982021i | \(0.439549\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 16.0000i | − | 0.753411i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.8564 | + | 11.3137i | 0.649598 | + | 0.530395i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 39.1918i | 1.83332i | 0.399672 | + | 0.916658i | \(0.369124\pi\) | ||||
−0.399672 | + | 0.916658i | \(0.630876\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 31.1769i | − | 1.45205i | −0.687666 | − | 0.726027i | \(-0.741365\pi\) | ||
0.687666 | − | 0.726027i | \(-0.258635\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.82843i | 0.131448i | 0.997838 | + | 0.0657241i | \(0.0209357\pi\) | ||||
−0.997838 | + | 0.0657241i | \(0.979064\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.79796 | 0.453395 | 0.226698 | − | 0.973965i | \(-0.427207\pi\) | ||||
0.226698 | + | 0.973965i | \(0.427207\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 27.7128i | − | 1.27966i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 19.5959i | − | 0.901021i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −41.5692 | −1.89935 | −0.949673 | − | 0.313243i | \(-0.898585\pi\) | ||||
−0.949673 | + | 0.313243i | \(0.898585\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.00000 | 0.364769 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.82843i | 0.128168i | 0.997944 | + | 0.0640841i | \(0.0204126\pi\) | ||||
−0.997944 | + | 0.0640841i | \(0.979587\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 22.0000i | − | 0.992846i | −0.868081 | − | 0.496423i | \(-0.834646\pi\) | ||
0.868081 | − | 0.496423i | \(-0.165354\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.9706 | −0.764316 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 39.1918i | − | 1.75799i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 24.0000i | − | 1.07439i | −0.843459 | − | 0.537194i | \(-0.819484\pi\) | ||
0.843459 | − | 0.537194i | \(-0.180516\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 33.9411i | − | 1.51336i | −0.653785 | − | 0.756680i | \(-0.726820\pi\) | ||
0.653785 | − | 0.756680i | \(-0.273180\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.00000 | − | 4.89898i | −0.266996 | − | 0.218002i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.3923i | 0.460631i | 0.973116 | + | 0.230315i | \(0.0739758\pi\) | ||||
−0.973116 | + | 0.230315i | \(0.926024\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.7128 | 1.22594 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.4949 | − | 20.0000i | −1.07937 | − | 0.881305i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.00000 | 0.350486 | 0.175243 | − | 0.984525i | \(-0.443929\pi\) | ||||
0.175243 | + | 0.984525i | \(0.443929\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 39.1918 | 1.71374 | 0.856870 | − | 0.515533i | \(-0.172406\pi\) | ||||
0.856870 | + | 0.515533i | \(0.172406\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.9706i | 0.739249i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.00000 | −0.391304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.6274 | −0.980102 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27.7128 | + | 33.9411i | −1.19813 | + | 1.46740i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 2.00000i | − | 0.0861461i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.6410i | 1.48933i | 0.667436 | + | 0.744667i | \(0.267392\pi\) | ||||
−0.667436 | + | 0.744667i | \(0.732608\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.0000 | + | 9.79796i | 0.514024 | + | 0.419698i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.79796 | −0.418930 | −0.209465 | − | 0.977816i | \(-0.567172\pi\) | ||||
−0.209465 | + | 0.977816i | \(0.567172\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.79796i | 0.416652i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −42.4264 | −1.79766 | −0.898832 | − | 0.438293i | \(-0.855583\pi\) | ||||
−0.898832 | + | 0.438293i | \(0.855583\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.7128 | −1.17213 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.3939 | −1.23880 | −0.619402 | − | 0.785074i | \(-0.712625\pi\) | ||||
−0.619402 | + | 0.785074i | \(0.712625\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25.4558 | − | 20.7846i | −1.07094 | − | 0.874415i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 40.0000 | 1.67689 | 0.838444 | − | 0.544988i | \(-0.183466\pi\) | ||||
0.838444 | + | 0.544988i | \(0.183466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 24.0000i | − | 1.00437i | −0.864761 | − | 0.502184i | \(-0.832530\pi\) | ||
0.864761 | − | 0.502184i | \(-0.167470\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −27.7128 | + | 5.65685i | −1.15570 | + | 0.235907i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.3939i | 1.22368i | 0.790980 | + | 0.611842i | \(0.209571\pi\) | ||||
−0.790980 | + | 0.611842i | \(0.790429\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 27.7128i | − | 1.14972i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.9706i | 0.702849i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.1918 | −1.61762 | −0.808810 | − | 0.588070i | \(-0.799888\pi\) | ||||
−0.808810 | + | 0.588070i | \(0.799888\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.6969i | 0.603531i | 0.953382 | + | 0.301765i | \(0.0975760\pi\) | ||||
−0.953382 | + | 0.301765i | \(0.902424\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.5959 | + | 24.0000i | −0.803354 | + | 0.983904i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.0000 | 0.734235 | 0.367118 | − | 0.930175i | \(-0.380345\pi\) | ||||
0.367118 | + | 0.930175i | \(0.380345\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.89949 | + | 12.1244i | −0.402472 | + | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.82843i | − | 0.114802i | −0.998351 | − | 0.0574012i | \(-0.981719\pi\) | ||
0.998351 | − | 0.0574012i | \(-0.0182814\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.1421 | −0.571195 | −0.285598 | − | 0.958350i | \(-0.592192\pi\) | ||||
−0.285598 | + | 0.958350i | \(0.592192\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 34.2929i | − | 1.38058i | −0.723534 | − | 0.690289i | \(-0.757483\pi\) | ||
0.723534 | − | 0.690289i | \(-0.242517\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.0000i | 1.60774i | 0.594808 | + | 0.803868i | \(0.297228\pi\) | ||||
−0.594808 | + | 0.803868i | \(0.702772\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 45.2548i | 1.81310i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.0000 | + | 9.79796i | −0.920000 | + | 0.391918i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.8564i | 0.552491i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.1051 | 1.51694 | 0.758470 | − | 0.651707i | \(-0.225947\pi\) | ||||
0.758470 | + | 0.651707i | \(0.225947\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.89898 | − | 4.00000i | −0.194410 | − | 0.158735i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.82843 | −0.112066 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.0000 | 1.57991 | 0.789953 | − | 0.613168i | \(-0.210105\pi\) | ||||
0.789953 | + | 0.613168i | \(0.210105\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.5959 | −0.772788 | −0.386394 | − | 0.922334i | \(-0.626279\pi\) | ||||
−0.386394 | + | 0.922334i | \(0.626279\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 33.9411i | − | 1.33436i | −0.744895 | − | 0.667182i | \(-0.767500\pi\) | ||
0.744895 | − | 0.667182i | \(-0.232500\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.0000 | −0.785069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.7990 | −0.774794 | −0.387397 | − | 0.921913i | \(-0.626626\pi\) | ||||
−0.387397 | + | 0.921913i | \(0.626626\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.2487 | − | 19.7990i | −0.947476 | − | 0.773611i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 46.0000i | − | 1.79191i | −0.444149 | − | 0.895953i | \(-0.646494\pi\) | ||
0.444149 | − | 0.895953i | \(-0.353506\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.7846i | 0.808428i | 0.914665 | + | 0.404214i | \(0.132455\pi\) | ||||
−0.914665 | + | 0.404214i | \(0.867545\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.5959 | 0.758757 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.8564 | −0.534921 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 19.5959i | − | 0.755367i | −0.925935 | − | 0.377684i | \(-0.876721\pi\) | ||
0.925935 | − | 0.377684i | \(-0.123279\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.7990 | −0.760937 | −0.380468 | − | 0.924794i | \(-0.624237\pi\) | ||||
−0.380468 | + | 0.924794i | \(0.624237\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.79796 | 0.374908 | 0.187454 | − | 0.982273i | \(-0.439976\pi\) | ||||
0.187454 | + | 0.982273i | \(0.439976\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.48528 | − | 6.92820i | −0.324206 | − | 0.264713i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.0000 | 0.914327 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.8564 | − | 11.3137i | −0.525603 | − | 0.429153i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 39.1918i | − | 1.48450i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.3205i | 0.654187i | 0.944992 | + | 0.327093i | \(0.106069\pi\) | ||||
−0.944992 | + | 0.327093i | \(0.893931\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.79796 | 0.368490 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 6.92820i | − | 0.260194i | −0.991501 | − | 0.130097i | \(-0.958471\pi\) | ||
0.991501 | − | 0.130097i | \(-0.0415289\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 19.5959i | − | 0.733873i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.79796 | − | 8.00000i | −0.366423 | − | 0.299183i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.7128 | −1.03351 | −0.516757 | − | 0.856132i | \(-0.672861\pi\) | ||||
−0.516757 | + | 0.856132i | \(0.672861\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40.0000 | 1.48968 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.9706 | − | 3.46410i | 0.630271 | − | 0.128654i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.1421i | 0.524503i | 0.965000 | + | 0.262251i | \(0.0844650\pi\) | ||||
−0.965000 | + | 0.262251i | \(0.915535\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 48.0000i | − | 1.77534i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.7990 | 0.731292 | 0.365646 | − | 0.930754i | \(-0.380848\pi\) | ||||
0.365646 | + | 0.930754i | \(0.380848\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.5959i | 0.721825i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 24.0000i | − | 0.882854i | −0.897297 | − | 0.441427i | \(-0.854472\pi\) | ||
0.897297 | − | 0.441427i | \(-0.145528\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.9706i | 0.622590i | 0.950313 | + | 0.311295i | \(0.100763\pi\) | ||||
−0.950313 | + | 0.311295i | \(0.899237\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0000 | − | 14.6969i | −0.659469 | − | 0.538454i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 55.4256i | − | 2.02521i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.1769 | 1.13766 | 0.568831 | − | 0.822455i | \(-0.307396\pi\) | ||||
0.568831 | + | 0.822455i | \(0.307396\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.4949 | + | 30.0000i | −0.891461 | + | 1.09181i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.1127 | 1.13081 | 0.565405 | − | 0.824813i | \(-0.308720\pi\) | ||||
0.565405 | + | 0.824813i | \(0.308720\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.00000 | −0.290000 | −0.145000 | − | 0.989432i | \(-0.546318\pi\) | ||||
−0.145000 | + | 0.989432i | \(0.546318\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.5959 | −0.709420 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.2843i | 1.02129i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.00000 | 0.216366 | 0.108183 | − | 0.994131i | \(-0.465497\pi\) | ||||
0.108183 | + | 0.994131i | \(0.465497\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.1127 | −1.11905 | −0.559523 | − | 0.828815i | \(-0.689016\pi\) | ||||
−0.559523 | + | 0.828815i | \(0.689016\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.46410 | − | 16.9706i | −0.124434 | − | 0.609601i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.7128i | 0.991642i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.0000 | − | 34.2929i | 0.999363 | − | 1.22396i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.5959 | 0.698519 | 0.349260 | − | 0.937026i | \(-0.386433\pi\) | ||||
0.349260 | + | 0.937026i | \(0.386433\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 41.5692 | 1.47803 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.5959i | 0.695871i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.4264 | 1.50282 | 0.751410 | − | 0.659835i | \(-0.229374\pi\) | ||||
0.751410 | + | 0.659835i | \(0.229374\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.5959 | −0.691525 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.6274 | − | 27.7128i | 0.797512 | − | 0.976748i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.00000 | −0.281265 | −0.140633 | − | 0.990062i | \(-0.544914\pi\) | ||||
−0.140633 | + | 0.990062i | \(0.544914\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 32.0000i | − | 1.12367i | −0.827249 | − | 0.561836i | \(-0.810095\pi\) | ||
0.827249 | − | 0.561836i | \(-0.189905\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 10.3923i | − | 0.362694i | −0.983419 | − | 0.181347i | \(-0.941954\pi\) | ||
0.983419 | − | 0.181347i | \(-0.0580457\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 48.0833i | − | 1.67608i | −0.545611 | − | 0.838039i | \(-0.683702\pi\) | ||
0.545611 | − | 0.838039i | \(-0.316298\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.5959 | −0.681417 | −0.340708 | − | 0.940169i | \(-0.610667\pi\) | ||||
−0.340708 | + | 0.940169i | \(0.610667\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 34.6410i | − | 1.20313i | −0.798823 | − | 0.601566i | \(-0.794544\pi\) | ||
0.798823 | − | 0.601566i | \(-0.205456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 4.89898i | − | 0.169740i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 39.1918 | + | 32.0000i | 1.35629 | + | 1.10741i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.0000 | 0.586207 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.07107 | − | 8.66025i | 0.243252 | − | 0.297922i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 19.7990i | − | 0.680301i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 16.0000i | − | 0.548473i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.7990 | 0.677905 | 0.338952 | − | 0.940804i | \(-0.389927\pi\) | ||||
0.338952 | + | 0.940804i | \(0.389927\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 24.4949i | − | 0.836730i | −0.908279 | − | 0.418365i | \(-0.862603\pi\) | ||
0.908279 | − | 0.418365i | \(-0.137397\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.0000i | 1.09183i | 0.837842 | + | 0.545913i | \(0.183817\pi\) | ||||
−0.837842 | + | 0.545913i | \(0.816183\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.3137i | 0.385123i | 0.981285 | + | 0.192562i | \(0.0616795\pi\) | ||||
−0.981285 | + | 0.192562i | \(0.938320\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0000 | − | 14.6969i | 0.408012 | − | 0.499711i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 6.92820i | − | 0.235023i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.7128 | 0.939013 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14.6969 | − | 28.0000i | 0.496847 | − | 0.946573i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.82843 | 0.0955092 | 0.0477546 | − | 0.998859i | \(-0.484793\pi\) | ||||
0.0477546 | + | 0.998859i | \(0.484793\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.0000 | −0.539054 | −0.269527 | − | 0.962993i | \(-0.586867\pi\) | ||||
−0.269527 | + | 0.962993i | \(0.586867\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.5959 | −0.659455 | −0.329728 | − | 0.944076i | \(-0.606957\pi\) | ||||
−0.329728 | + | 0.944076i | \(0.606957\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.3137i | 0.379877i | 0.981796 | + | 0.189939i | \(0.0608289\pi\) | ||||
−0.981796 | + | 0.189939i | \(0.939171\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.00000 | 0.268311 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.2487 | − | 19.7990i | −0.810545 | − | 0.661807i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.0000i | 0.400222i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.5692i | 1.38487i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −36.0000 | − | 29.3939i | −1.19668 | − | 0.977086i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −48.9898 | −1.62668 | −0.813340 | − | 0.581789i | \(-0.802353\pi\) | ||||
−0.813340 | + | 0.581789i | \(0.802353\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.7128 | −0.918166 | −0.459083 | − | 0.888393i | \(-0.651822\pi\) | ||||
−0.459083 | + | 0.888393i | \(0.651822\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.5959i | 0.648530i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 39.5980 | 1.30764 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.1051 | −1.25697 | −0.628486 | − | 0.777821i | \(-0.716325\pi\) | ||||
−0.628486 | + | 0.777821i | \(0.716325\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 39.1918 | 1.29001 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.82843 | − | 13.8564i | −0.0929981 | − | 0.455596i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.00000 | 0.262471 | 0.131236 | − | 0.991351i | \(-0.458106\pi\) | ||||
0.131236 | + | 0.991351i | \(0.458106\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.8564 | − | 16.9706i | 0.453153 | − | 0.554997i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19.5959i | − | 0.640171i | −0.947389 | − | 0.320085i | \(-0.896288\pi\) | ||
0.947389 | − | 0.320085i | \(-0.103712\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 38.1051i | − | 1.24219i | −0.783735 | − | 0.621096i | \(-0.786688\pi\) | ||
0.783735 | − | 0.621096i | \(-0.213312\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45.2548i | 1.47370i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.5959 | −0.636782 | −0.318391 | − | 0.947960i | \(-0.603142\pi\) | ||||
−0.318391 | + | 0.947960i | \(0.603142\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.7128i | 0.899596i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 4.89898i | − | 0.158694i | −0.996847 | − | 0.0793468i | \(-0.974717\pi\) | ||
0.996847 | − | 0.0793468i | \(-0.0252834\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.5959 | − | 24.0000i | 0.634109 | − | 0.776622i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.8564 | 0.447447 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.0000 | −0.612903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.9706 | − | 13.8564i | −0.546302 | − | 0.446054i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 48.0833i | − | 1.54625i | −0.634252 | − | 0.773127i | \(-0.718692\pi\) | ||
0.634252 | − | 0.773127i | \(-0.281308\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.0000i | 1.47621i | 0.674686 | + | 0.738105i | \(0.264279\pi\) | ||||
−0.674686 | + | 0.738105i | \(0.735721\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.6274 | 0.725402 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.4949i | 0.783661i | 0.920037 | + | 0.391831i | \(0.128158\pi\) | ||||
−0.920037 | + | 0.391831i | \(0.871842\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 32.0000i | − | 1.02272i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.9706i | 0.541277i | 0.962681 | + | 0.270638i | \(0.0872348\pi\) | ||||
−0.962681 | + | 0.270638i | \(0.912765\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.00000 | + | 4.89898i | −0.127451 | + | 0.156094i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 55.4256i | 1.76243i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.2487 | 0.770286 | 0.385143 | − | 0.922857i | \(-0.374152\pi\) | ||||
0.385143 | + | 0.922857i | \(0.374152\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.6969 | − | 18.0000i | 0.465924 | − | 0.570638i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48.0833 | −1.52281 | −0.761406 | − | 0.648275i | \(-0.775491\pi\) | ||||
−0.761406 | + | 0.648275i | \(0.775491\pi\) | |||||||
\(998\) | 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 | 2880.2.d.f.289.3 | yes | 8 | |
3.2 | odd | 2 | 2880.2.d.h.289.5 | yes | 8 | ||
4.3 | odd | 2 | inner | 2880.2.d.f.289.4 | yes | 8 | |
5.4 | even | 2 | inner | 2880.2.d.f.289.8 | yes | 8 | |
8.3 | odd | 2 | inner | 2880.2.d.f.289.6 | yes | 8 | |
8.5 | even | 2 | inner | 2880.2.d.f.289.5 | yes | 8 | |
12.11 | even | 2 | 2880.2.d.h.289.6 | yes | 8 | ||
15.14 | odd | 2 | 2880.2.d.h.289.2 | yes | 8 | ||
20.19 | odd | 2 | inner | 2880.2.d.f.289.7 | yes | 8 | |
24.5 | odd | 2 | 2880.2.d.h.289.3 | yes | 8 | ||
24.11 | even | 2 | 2880.2.d.h.289.4 | yes | 8 | ||
40.19 | odd | 2 | inner | 2880.2.d.f.289.1 | ✓ | 8 | |
40.29 | even | 2 | inner | 2880.2.d.f.289.2 | yes | 8 | |
60.59 | even | 2 | 2880.2.d.h.289.1 | yes | 8 | ||
120.29 | odd | 2 | 2880.2.d.h.289.8 | yes | 8 | ||
120.59 | even | 2 | 2880.2.d.h.289.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2880.2.d.f.289.1 | ✓ | 8 | 40.19 | odd | 2 | inner | |
2880.2.d.f.289.2 | yes | 8 | 40.29 | even | 2 | inner | |
2880.2.d.f.289.3 | yes | 8 | 1.1 | even | 1 | trivial | |
2880.2.d.f.289.4 | yes | 8 | 4.3 | odd | 2 | inner | |
2880.2.d.f.289.5 | yes | 8 | 8.5 | even | 2 | inner | |
2880.2.d.f.289.6 | yes | 8 | 8.3 | odd | 2 | inner | |
2880.2.d.f.289.7 | yes | 8 | 20.19 | odd | 2 | inner | |
2880.2.d.f.289.8 | yes | 8 | 5.4 | even | 2 | inner | |
2880.2.d.h.289.1 | yes | 8 | 60.59 | even | 2 | ||
2880.2.d.h.289.2 | yes | 8 | 15.14 | odd | 2 | ||
2880.2.d.h.289.3 | yes | 8 | 24.5 | odd | 2 | ||
2880.2.d.h.289.4 | yes | 8 | 24.11 | even | 2 | ||
2880.2.d.h.289.5 | yes | 8 | 3.2 | odd | 2 | ||
2880.2.d.h.289.6 | yes | 8 | 12.11 | even | 2 | ||
2880.2.d.h.289.7 | yes | 8 | 120.59 | even | 2 | ||
2880.2.d.h.289.8 | yes | 8 | 120.29 | odd | 2 |