Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [896,2,Mod(223,896)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(896, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("896.223");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 896.j (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.15459602111\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 671.2 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 896.671 |
Dual form | 896.2.j.e.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 \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(645\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.44949 | − | 2.44949i | 1.09545 | − | 1.09545i | 0.100509 | − | 0.994936i | \(-0.467953\pi\) |
0.994936 | − | 0.100509i | \(-0.0320471\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | − | 2.44949i | 0.377964 | − | 0.925820i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 1.00000i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | − | 1.00000i | 0.301511 | − | 0.301511i | −0.540094 | − | 0.841605i | \(-0.681611\pi\) |
0.841605 | + | 0.540094i | \(0.181611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44949 | + | 2.44949i | 0.679366 | + | 0.679366i | 0.959857 | − | 0.280491i | \(-0.0904971\pi\) |
−0.280491 | + | 0.959857i | \(0.590497\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | 4.89898 | − | 4.89898i | 1.12390 | − | 1.12390i | 0.132754 | − | 0.991149i | \(-0.457618\pi\) |
0.991149 | − | 0.132754i | \(-0.0423820\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 7.00000i | − | 1.40000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | − | 3.00000i | 0.557086 | − | 0.557086i | −0.371391 | − | 0.928477i | \(-0.621119\pi\) |
0.928477 | + | 0.371391i | \(0.121119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.89898 | −0.879883 | −0.439941 | − | 0.898027i | \(-0.645001\pi\) | ||||
−0.439941 | + | 0.898027i | \(0.645001\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.55051 | − | 8.44949i | −0.600146 | − | 1.42822i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.00000 | − | 5.00000i | −0.821995 | − | 0.821995i | 0.164399 | − | 0.986394i | \(-0.447432\pi\) |
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.89898 | 0.765092 | 0.382546 | − | 0.923936i | \(-0.375047\pi\) | ||||
0.382546 | + | 0.923936i | \(0.375047\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00000 | + | 5.00000i | −0.762493 | + | 0.762493i | −0.976772 | − | 0.214280i | \(-0.931260\pi\) |
0.214280 | + | 0.976772i | \(0.431260\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.34847 | + | 7.34847i | 1.09545 | + | 1.09545i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.89898 | 0.714590 | 0.357295 | − | 0.933992i | \(-0.383699\pi\) | ||||
0.357295 | + | 0.933992i | \(0.383699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | − | 4.89898i | −0.714286 | − | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | + | 1.00000i | 0.137361 | + | 0.137361i | 0.772444 | − | 0.635083i | \(-0.219034\pi\) |
−0.635083 | + | 0.772444i | \(0.719034\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.89898i | − | 0.660578i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.89898 | − | 4.89898i | −0.637793 | − | 0.637793i | 0.312218 | − | 0.950011i | \(-0.398928\pi\) |
−0.950011 | + | 0.312218i | \(0.898928\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.44949 | − | 2.44949i | −0.313625 | − | 0.313625i | 0.532687 | − | 0.846312i | \(-0.321182\pi\) |
−0.846312 | + | 0.532687i | \(0.821182\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.34847 | + | 3.00000i | 0.925820 | + | 0.377964i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.0000 | 1.48842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.00000 | + | 5.00000i | 0.610847 | + | 0.610847i | 0.943167 | − | 0.332320i | \(-0.107831\pi\) |
−0.332320 | + | 0.943167i | \(0.607831\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.79796 | 1.14676 | 0.573382 | − | 0.819288i | \(-0.305631\pi\) | ||||
0.573382 | + | 0.819288i | \(0.305631\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.44949 | − | 3.44949i | −0.165185 | − | 0.393106i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000i | 0.450035i | 0.974355 | + | 0.225018i | \(0.0722440\pi\) | ||||
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0000 | + | 12.0000i | 1.30158 | + | 1.30158i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.44949 | − | 3.55051i | 0.885747 | − | 0.372195i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 24.0000i | − | 2.46235i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.89898i | 0.497416i | 0.968579 | + | 0.248708i | \(0.0800060\pi\) | ||||
−0.968579 | + | 0.248708i | \(0.919994\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.00000 | + | 3.00000i | 0.301511 | + | 0.301511i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.44949 | + | 2.44949i | −0.243733 | + | 0.243733i | −0.818393 | − | 0.574659i | \(-0.805135\pi\) |
0.574659 | + | 0.818393i | \(0.305135\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.79796i | − | 0.965422i | −0.875780 | − | 0.482711i | \(-0.839652\pi\) | ||
0.875780 | − | 0.482711i | \(-0.160348\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.00000 | − | 3.00000i | 0.290021 | − | 0.290021i | −0.547068 | − | 0.837088i | \(-0.684256\pi\) |
0.837088 | + | 0.547068i | \(0.184256\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | + | 7.00000i | −0.670478 | + | 0.670478i | −0.957826 | − | 0.287348i | \(-0.907226\pi\) |
0.287348 | + | 0.957826i | \(0.407226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00000 | 0.376288 | 0.188144 | − | 0.982141i | \(-0.439753\pi\) | ||||
0.188144 | + | 0.982141i | \(0.439753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.79796 | + | 9.79796i | −0.913664 | + | 0.913664i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.34847 | + | 7.34847i | −0.679366 | + | 0.679366i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.0000 | + | 4.89898i | 1.10004 | + | 0.449089i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000i | 0.818182i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.89898 | − | 4.89898i | −0.438178 | − | 0.438178i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.0000i | 1.59724i | 0.601834 | + | 0.798621i | \(0.294437\pi\) | ||||
−0.601834 | + | 0.798621i | \(0.705563\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.79796 | + | 9.79796i | −0.856052 | + | 0.856052i | −0.990870 | − | 0.134819i | \(-0.956955\pi\) |
0.134819 | + | 0.990870i | \(0.456955\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.10102 | − | 16.8990i | −0.615737 | − | 1.46533i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 8.00000i | − | 0.683486i | −0.939793 | − | 0.341743i | \(-0.888983\pi\) | ||
0.939793 | − | 0.341743i | \(-0.111017\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.89898 | − | 4.89898i | −0.415526 | − | 0.415526i | 0.468132 | − | 0.883658i | \(-0.344927\pi\) |
−0.883658 | + | 0.468132i | \(0.844927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.89898 | 0.409673 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 14.6969i | − | 1.22051i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.00000 | − | 3.00000i | −0.245770 | − | 0.245770i | 0.573462 | − | 0.819232i | \(-0.305600\pi\) |
−0.819232 | + | 0.573462i | \(0.805600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.6969 | −1.18818 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.0000 | + | 12.0000i | −0.963863 | + | 0.963863i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.2474 | − | 12.2474i | −0.977453 | − | 0.977453i | 0.0222985 | − | 0.999751i | \(-0.492902\pi\) |
−0.999751 | + | 0.0222985i | \(0.992902\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.00000 | + | 9.79796i | −0.315244 | + | 0.772187i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.00000 | − | 1.00000i | −0.0783260 | − | 0.0783260i | 0.666858 | − | 0.745184i | \(-0.267639\pi\) |
−0.745184 | + | 0.666858i | \(0.767639\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.5959i | 1.51638i | 0.652035 | + | 0.758189i | \(0.273915\pi\) | ||||
−0.652035 | + | 0.758189i | \(0.726085\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.00000i | − | 0.0769231i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.6969 | + | 14.6969i | 1.12390 | + | 1.12390i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.44949 | + | 2.44949i | 0.186231 | + | 0.186231i | 0.794065 | − | 0.607833i | \(-0.207961\pi\) |
−0.607833 | + | 0.794065i | \(0.707961\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.1464 | − | 7.00000i | −1.29615 | − | 0.529150i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.00000 | + | 3.00000i | 0.224231 | + | 0.224231i | 0.810277 | − | 0.586047i | \(-0.199317\pi\) |
−0.586047 | + | 0.810277i | \(0.699317\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.44949 | + | 2.44949i | −0.182069 | + | 0.182069i | −0.792257 | − | 0.610188i | \(-0.791094\pi\) |
0.610188 | + | 0.792257i | \(0.291094\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −24.4949 | −1.80090 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.89898 | + | 4.89898i | 0.358249 | + | 0.358249i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.0000i | 1.44715i | 0.690246 | + | 0.723575i | \(0.257502\pi\) | ||||
−0.690246 | + | 0.723575i | \(0.742498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.0000 | −1.15171 | −0.575853 | − | 0.817554i | \(-0.695330\pi\) | ||||
−0.575853 | + | 0.817554i | \(0.695330\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.0000 | + | 15.0000i | 1.06871 | + | 1.06871i | 0.997459 | + | 0.0712470i | \(0.0226979\pi\) |
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.79796i | 0.694559i | 0.937762 | + | 0.347279i | \(0.112894\pi\) | ||||
−0.937762 | + | 0.347279i | \(0.887106\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.34847 | − | 10.3485i | −0.305203 | − | 0.726320i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.0000 | − | 12.0000i | 0.838116 | − | 0.838116i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 12.0000i | − | 0.834058i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 9.79796i | − | 0.677739i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.00000 | + | 1.00000i | 0.0688428 | + | 0.0688428i | 0.740690 | − | 0.671847i | \(-0.234499\pi\) |
−0.671847 | + | 0.740690i | \(0.734499\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 24.4949i | 1.67054i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.89898 | + | 12.0000i | −0.332564 | + | 0.814613i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0000 | + | 12.0000i | −0.807207 | + | 0.807207i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.79796 | −0.656120 | −0.328060 | − | 0.944657i | \(-0.606395\pi\) | ||||
−0.328060 | + | 0.944657i | \(0.606395\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 21.0000 | 1.40000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.5959 | − | 19.5959i | 1.30063 | − | 1.30063i | 0.372658 | − | 0.927969i | \(-0.378446\pi\) |
0.927969 | − | 0.372658i | \(-0.121554\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.34847 | − | 7.34847i | 0.485601 | − | 0.485601i | −0.421314 | − | 0.906915i | \(-0.638431\pi\) |
0.906915 | + | 0.421314i | \(0.138431\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.00000i | 0.262049i | 0.991379 | + | 0.131024i | \(0.0418266\pi\) | ||||
−0.991379 | + | 0.131024i | \(0.958173\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.0000 | − | 12.0000i | 0.782794 | − | 0.782794i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.0000i | 0.905585i | 0.891616 | + | 0.452792i | \(0.149572\pi\) | ||||
−0.891616 | + | 0.452792i | \(0.850428\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 24.4949i | − | 1.57786i | −0.614486 | − | 0.788928i | \(-0.710637\pi\) | ||
0.614486 | − | 0.788928i | \(-0.289363\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −24.2474 | + | 0.247449i | −1.54911 | + | 0.0158089i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.0000 | 1.52708 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.6969 | + | 14.6969i | 0.927663 | + | 0.927663i | 0.997555 | − | 0.0698920i | \(-0.0222655\pi\) |
−0.0698920 | + | 0.997555i | \(0.522265\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | + | 4.00000i | −0.251478 | + | 0.251478i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 29.3939i | 1.83354i | 0.399416 | + | 0.916770i | \(0.369213\pi\) | ||||
−0.399416 | + | 0.916770i | \(0.630787\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.2474 | + | 7.24745i | −1.07170 | + | 0.450335i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.00000 | + | 9.00000i | 0.557086 | + | 0.557086i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.0000 | 1.60323 | 0.801614 | − | 0.597841i | \(-0.203975\pi\) | ||||
0.801614 | + | 0.597841i | \(0.203975\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.89898 | 0.300942 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.34847 | − | 7.34847i | −0.448044 | − | 0.448044i | 0.446660 | − | 0.894704i | \(-0.352613\pi\) |
−0.894704 | + | 0.446660i | \(0.852613\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.3939 | −1.78555 | −0.892775 | − | 0.450502i | \(-0.851245\pi\) | ||||
−0.892775 | + | 0.450502i | \(0.851245\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.00000 | − | 7.00000i | −0.422116 | − | 0.422116i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.00000 | − | 5.00000i | −0.300421 | − | 0.300421i | 0.540758 | − | 0.841178i | \(-0.318138\pi\) |
−0.841178 | + | 0.540758i | \(0.818138\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 14.6969i | − | 0.879883i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.0000i | 1.19310i | 0.802576 | + | 0.596550i | \(0.203462\pi\) | ||||
−0.802576 | + | 0.596550i | \(0.796538\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.6969 | − | 14.6969i | −0.873642 | − | 0.873642i | 0.119225 | − | 0.992867i | \(-0.461959\pi\) |
−0.992867 | + | 0.119225i | \(0.961959\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.89898 | − | 12.0000i | 0.289178 | − | 0.708338i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.2474 | − | 12.2474i | 0.715504 | − | 0.715504i | −0.252177 | − | 0.967681i | \(-0.581147\pi\) |
0.967681 | + | 0.252177i | \(0.0811467\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.0000 | −1.39733 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.79796 | − | 9.79796i | −0.566631 | − | 0.566631i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.24745 | + | 17.2474i | 0.417736 | + | 0.994126i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.0000 | −0.687118 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.89898 | + | 4.89898i | −0.279600 | + | 0.279600i | −0.832949 | − | 0.553350i | \(-0.813349\pi\) |
0.553350 | + | 0.832949i | \(0.313349\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 24.4949i | − | 1.38898i | −0.719503 | − | 0.694489i | \(-0.755630\pi\) | ||
0.719503 | − | 0.694489i | \(-0.244370\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.6969 | −0.830720 | −0.415360 | − | 0.909657i | \(-0.636344\pi\) | ||||
−0.415360 | + | 0.909657i | \(0.636344\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 25.3485 | − | 10.6515i | 1.42822 | − | 0.600146i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.0000 | + | 13.0000i | −0.730153 | + | 0.730153i | −0.970650 | − | 0.240497i | \(-0.922690\pi\) |
0.240497 | + | 0.970650i | \(0.422690\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 6.00000i | − | 0.335936i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.0000 | + | 24.0000i | 1.33540 | + | 1.33540i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.1464 | − | 17.1464i | 0.951113 | − | 0.951113i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.89898 | − | 12.0000i | 0.270089 | − | 0.661581i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.0000 | + | 19.0000i | −1.04433 | + | 1.04433i | −0.0453639 | + | 0.998971i | \(0.514445\pi\) |
−0.998971 | + | 0.0453639i | \(0.985555\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.0000 | − | 15.0000i | 0.821995 | − | 0.821995i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 24.4949 | 1.33830 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.0000 | 1.52526 | 0.762629 | − | 0.646837i | \(-0.223908\pi\) | ||||
0.762629 | + | 0.646837i | \(0.223908\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.89898 | + | 4.89898i | −0.265295 | + | 0.265295i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.00000 | − | 3.00000i | 0.161048 | − | 0.161048i | −0.621983 | − | 0.783031i | \(-0.713673\pi\) |
0.783031 | + | 0.621983i | \(0.213673\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.34847 | − | 7.34847i | −0.393355 | − | 0.393355i | 0.482527 | − | 0.875881i | \(-0.339719\pi\) |
−0.875881 | + | 0.482527i | \(0.839719\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.79796i | 0.521493i | 0.965407 | + | 0.260746i | \(0.0839686\pi\) | ||||
−0.965407 | + | 0.260746i | \(0.916031\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.89898 | + | 4.89898i | −0.260011 | + | 0.260011i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.0000 | −1.05556 | −0.527780 | − | 0.849381i | \(-0.676975\pi\) | ||||
−0.527780 | + | 0.849381i | \(0.676975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 29.0000i | − | 1.52632i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.0000 | − | 24.0000i | 1.25622 | − | 1.25622i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.3939 | 1.53435 | 0.767174 | − | 0.641439i | \(-0.221662\pi\) | ||||
0.767174 | + | 0.641439i | \(0.221662\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.6969i | 0.765092i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.44949 | − | 1.44949i | 0.179089 | − | 0.0752538i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0000 | + | 11.0000i | 0.569558 | + | 0.569558i | 0.932005 | − | 0.362446i | \(-0.118058\pi\) |
−0.362446 | + | 0.932005i | \(0.618058\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.6969 | 0.756931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.0000 | + | 23.0000i | −1.18143 | + | 1.18143i | −0.202057 | + | 0.979374i | \(0.564763\pi\) |
−0.979374 | + | 0.202057i | \(0.935237\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.6969 | 0.750978 | 0.375489 | − | 0.926827i | \(-0.377475\pi\) | ||||
0.375489 | + | 0.926827i | \(0.377475\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.0000 | − | 4.89898i | −0.611577 | − | 0.249675i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.0000 | − | 15.0000i | −0.762493 | − | 0.762493i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.0000 | − | 13.0000i | −0.659126 | − | 0.659126i | 0.296047 | − | 0.955173i | \(-0.404331\pi\) |
−0.955173 | + | 0.296047i | \(0.904331\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 19.5959i | − | 0.991008i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.79796 | + | 9.79796i | 0.492989 | + | 0.492989i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.2474 | + | 12.2474i | 0.614682 | + | 0.614682i | 0.944162 | − | 0.329481i | \(-0.106874\pi\) |
−0.329481 | + | 0.944162i | \(0.606874\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.00000 | −0.399501 | −0.199750 | − | 0.979847i | \(-0.564013\pi\) | ||||
−0.199750 | + | 0.979847i | \(0.564013\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.0000 | − | 12.0000i | −0.597763 | − | 0.597763i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −22.0454 | + | 22.0454i | −1.09545 | + | 1.09545i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.0000 | −0.495682 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.4949 | 1.21119 | 0.605597 | − | 0.795771i | \(-0.292934\pi\) | ||||
0.605597 | + | 0.795771i | \(0.292934\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.8990 | + | 7.10102i | −0.831544 | + | 0.349418i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.89898 | − | 4.89898i | 0.239331 | − | 0.239331i | −0.577242 | − | 0.816573i | \(-0.695871\pi\) |
0.816573 | + | 0.577242i | \(0.195871\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.0000 | − | 11.0000i | −0.536107 | − | 0.536107i | 0.386276 | − | 0.922383i | \(-0.373761\pi\) |
−0.922383 | + | 0.386276i | \(0.873761\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.6969i | 0.714590i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 34.2929 | 1.66345 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.44949 | + | 3.55051i | −0.408899 | + | 0.171821i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.0000i | 0.481683i | 0.970564 | + | 0.240842i | \(0.0774234\pi\) | ||||
−0.970564 | + | 0.240842i | \(0.922577\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 14.6969i | − | 0.706290i | −0.935569 | − | 0.353145i | \(-0.885112\pi\) | ||
0.935569 | − | 0.353145i | \(-0.114888\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.5959 | + | 19.5959i | −0.937400 | + | 0.937400i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 14.6969i | − | 0.701447i | −0.936479 | − | 0.350723i | \(-0.885936\pi\) | ||
0.936479 | − | 0.350723i | \(-0.114064\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.6969 | − | 15.0000i | 0.699854 | − | 0.714286i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.00000 | − | 5.00000i | 0.237557 | − | 0.237557i | −0.578281 | − | 0.815838i | \(-0.696276\pi\) |
0.815838 | + | 0.578281i | \(0.196276\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.0000 | 0.471929 | 0.235965 | − | 0.971762i | \(-0.424175\pi\) | ||||
0.235965 | + | 0.971762i | \(0.424175\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.89898 | − | 4.89898i | 0.230684 | − | 0.230684i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.0000 | − | 29.3939i | 0.562569 | − | 1.37801i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 18.0000i | − | 0.842004i | −0.907060 | − | 0.421002i | \(-0.861678\pi\) | ||
0.907060 | − | 0.421002i | \(-0.138322\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.0454 | + | 22.0454i | 1.02676 | + | 1.02676i | 0.999632 | + | 0.0271249i | \(0.00863520\pi\) |
0.0271249 | + | 0.999632i | \(0.491365\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.00000i | − | 0.185896i | −0.995671 | − | 0.0929479i | \(-0.970371\pi\) | ||
0.995671 | − | 0.0929479i | \(-0.0296290\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.5959 | − | 19.5959i | 0.906791 | − | 0.906791i | −0.0892209 | − | 0.996012i | \(-0.528438\pi\) |
0.996012 | + | 0.0892209i | \(0.0284377\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.2474 | − | 7.24745i | 0.796413 | − | 0.334656i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.0000i | 0.459800i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −34.2929 | − | 34.2929i | −1.57346 | − | 1.57346i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.00000 | + | 3.00000i | −0.137361 | + | 0.137361i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.4949 | −1.11920 | −0.559600 | − | 0.828763i | \(-0.689045\pi\) | ||||
−0.559600 | + | 0.828763i | \(0.689045\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 24.4949i | − | 1.11687i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.0000 | + | 12.0000i | 0.544892 | + | 0.544892i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0000 | 0.543772 | 0.271886 | − | 0.962329i | \(-0.412353\pi\) | ||||
0.271886 | + | 0.962329i | \(0.412353\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.0000 | − | 11.0000i | 0.496423 | − | 0.496423i | −0.413900 | − | 0.910323i | \(-0.635834\pi\) |
0.910323 | + | 0.413900i | \(0.135834\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.6969 | + | 14.6969i | 0.661917 | + | 0.661917i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.6969 | 0.660578 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.00000 | + | 4.89898i | −0.0897123 | + | 0.219749i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.0000 | + | 23.0000i | 1.02962 | + | 1.02962i | 0.999548 | + | 0.0300737i | \(0.00957421\pi\) |
0.0300737 | + | 0.999548i | \(0.490426\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.6969i | 0.655304i | 0.944798 | + | 0.327652i | \(0.106257\pi\) | ||||
−0.944798 | + | 0.327652i | \(0.893743\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0000i | 0.533993i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.34847 | − | 7.34847i | −0.325715 | − | 0.325715i | 0.525239 | − | 0.850955i | \(-0.323976\pi\) |
−0.850955 | + | 0.525239i | \(0.823976\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.79796 | − | 24.0000i | 0.433436 | − | 1.06170i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.0000 | − | 24.0000i | −1.05757 | − | 1.05757i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.89898 | − | 4.89898i | 0.215457 | − | 0.215457i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.89898 | 0.214628 | 0.107314 | − | 0.994225i | \(-0.465775\pi\) | ||||
0.107314 | + | 0.994225i | \(0.465775\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.6969 | − | 14.6969i | −0.642652 | − | 0.642652i | 0.308554 | − | 0.951207i | \(-0.400155\pi\) |
−0.951207 | + | 0.308554i | \(0.900155\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 24.0000i | − | 1.04546i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.6969 | − | 14.6969i | 0.637793 | − | 0.637793i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000 | + | 12.0000i | 0.519778 | + | 0.519778i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 14.6969i | − | 0.635404i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.89898 | + | 0.101021i | −0.426379 | + | 0.00435126i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.0000 | − | 29.0000i | 1.24681 | − | 1.24681i | 0.289685 | − | 0.957122i | \(-0.406449\pi\) |
0.957122 | − | 0.289685i | \(-0.0935507\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 34.2929i | 1.46894i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.00000 | − | 5.00000i | −0.213785 | − | 0.213785i | 0.592088 | − | 0.805873i | \(-0.298304\pi\) |
−0.805873 | + | 0.592088i | \(0.798304\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.34847 | − | 7.34847i | 0.313625 | − | 0.313625i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 29.3939i | − | 1.25222i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.79796 | + | 4.00000i | 0.416652 | + | 0.170097i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.00000 | + | 3.00000i | −0.127114 | + | 0.127114i | −0.767802 | − | 0.640688i | \(-0.778649\pi\) |
0.640688 | + | 0.767802i | \(0.278649\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.4949 | −1.03602 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.4949 | + | 24.4949i | −1.03234 | + | 1.03234i | −0.0328775 | + | 0.999459i | \(0.510467\pi\) |
−0.999459 | + | 0.0328775i | \(0.989533\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.79796 | − | 9.79796i | 0.412203 | − | 0.412203i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.00000 | + | 22.0454i | −0.377964 | + | 0.925820i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 14.0000i | − | 0.586911i | −0.955973 | − | 0.293455i | \(-0.905195\pi\) | ||
0.955973 | − | 0.293455i | \(-0.0948052\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.0000 | − | 31.0000i | 1.29731 | − | 1.29731i | 0.367146 | − | 0.930163i | \(-0.380335\pi\) |
0.930163 | − | 0.367146i | \(-0.119665\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.0000i | 1.16768i | ||||||||
\(576\) | 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 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.00000 | 0.0828315 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 36.0000i | 1.48842i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.4949 | + | 24.4949i | 1.01101 | + | 1.01101i | 0.999939 | + | 0.0110739i | \(0.00352501\pi\) |
0.0110739 | + | 0.999939i | \(0.496475\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.0000 | + | 24.0000i | −0.988903 | + | 0.988903i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 39.1918i | − | 1.60942i | −0.593671 | − | 0.804708i | \(-0.702322\pi\) | ||
0.593671 | − | 0.804708i | \(-0.297678\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 41.3939 | − | 17.3939i | 1.69698 | − | 0.713079i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.0000 | −0.408589 | −0.204294 | − | 0.978909i | \(-0.565490\pi\) | ||||
−0.204294 | + | 0.978909i | \(0.565490\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.5959 | −0.799334 | −0.399667 | − | 0.916660i | \(-0.630874\pi\) | ||||
−0.399667 | + | 0.916660i | \(0.630874\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.0000 | + | 15.0000i | −0.610847 | + | 0.610847i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.0454 | + | 22.0454i | 0.896273 | + | 0.896273i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.3939 | 1.19306 | 0.596530 | − | 0.802591i | \(-0.296546\pi\) | ||||
0.596530 | + | 0.802591i | \(0.296546\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.0000 | + | 12.0000i | 0.485468 | + | 0.485468i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.0000 | − | 19.0000i | −0.767403 | − | 0.767403i | 0.210246 | − | 0.977649i | \(-0.432574\pi\) |
−0.977649 | + | 0.210246i | \(0.932574\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.00000i | 0.0805170i | 0.999189 | + | 0.0402585i | \(0.0128181\pi\) | ||||
−0.999189 | + | 0.0402585i | \(0.987182\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.89898 | − | 4.89898i | −0.196907 | − | 0.196907i | 0.601766 | − | 0.798673i | \(-0.294464\pi\) |
−0.798673 | + | 0.601766i | \(0.794464\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.4949 | − | 24.4949i | 0.976676 | − | 0.976676i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.0000 | 0.716569 | 0.358284 | − | 0.933613i | \(-0.383362\pi\) | ||||
0.358284 | + | 0.933613i | \(0.383362\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 44.0908 | + | 44.0908i | 1.74969 | + | 1.74969i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.247449 | − | 24.2474i | −0.00980428 | − | 0.960719i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 6.00000i | − | 0.237356i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.0000 | 1.26392 | 0.631962 | − | 0.774999i | \(-0.282250\pi\) | ||||
0.631962 | + | 0.774999i | \(0.282250\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.5959i | 0.770395i | 0.922834 | + | 0.385198i | \(0.125867\pi\) | ||||
−0.922834 | + | 0.385198i | \(0.874133\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.79796 | −0.384604 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.0000 | + | 15.0000i | −0.586995 | + | 0.586995i | −0.936817 | − | 0.349821i | \(-0.886242\pi\) |
0.349821 | + | 0.936817i | \(0.386242\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 48.0000i | 1.87552i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.3939i | 1.14676i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.0000 | − | 27.0000i | −1.05177 | − | 1.05177i | −0.998585 | − | 0.0531861i | \(-0.983062\pi\) |
−0.0531861 | − | 0.998585i | \(-0.516938\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.44949 | + | 2.44949i | −0.0952741 | + | 0.0952741i | −0.753137 | − | 0.657863i | \(-0.771460\pi\) |
0.657863 | + | 0.753137i | \(0.271460\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −58.7878 | − | 24.0000i | −2.27969 | − | 0.930680i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.0000 | + | 12.0000i | −0.464642 | + | 0.464642i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.89898 | −0.189123 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.00000 | −0.231283 | −0.115642 | − | 0.993291i | \(-0.536892\pi\) | ||||
−0.115642 | + | 0.993291i | \(0.536892\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.34847 | + | 7.34847i | −0.282425 | + | 0.282425i | −0.834075 | − | 0.551651i | \(-0.813998\pi\) |
0.551651 | + | 0.834075i | \(0.313998\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0000 | + | 4.89898i | 0.460518 | + | 0.188006i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.0000 | + | 25.0000i | −0.956598 | + | 0.956598i | −0.999097 | − | 0.0424981i | \(-0.986468\pi\) |
0.0424981 | + | 0.999097i | \(0.486468\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.5959 | − | 19.5959i | −0.748722 | − | 0.748722i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.89898i | 0.186636i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.79796 | + | 9.79796i | −0.372732 | + | 0.372732i | −0.868471 | − | 0.495739i | \(-0.834897\pi\) |
0.495739 | + | 0.868471i | \(0.334897\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.3485 | − | 4.34847i | 0.393106 | − | 0.165185i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −24.0000 | −0.910372 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.0000i | 0.909065i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.0000 | − | 29.0000i | 1.09531 | − | 1.09531i | 0.100364 | − | 0.994951i | \(-0.467999\pi\) |
0.994951 | − | 0.100364i | \(-0.0320008\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −48.9898 | −1.84769 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.55051 | + | 8.44949i | 0.133531 | + | 0.317776i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.0000 | − | 23.0000i | −0.863783 | − | 0.863783i | 0.127992 | − | 0.991775i | \(-0.459147\pi\) |
−0.991775 | + | 0.127992i | \(0.959147\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.0000 | −0.450035 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.5959 | 0.733873 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | − | 12.0000i | 0.448775 | − | 0.448775i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.4949 | −0.913506 | −0.456753 | − | 0.889594i | \(-0.650988\pi\) | ||||
−0.456753 | + | 0.889594i | \(0.650988\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0000 | − | 9.79796i | −0.893807 | − | 0.364895i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.0000 | − | 21.0000i | −0.779920 | − | 0.779920i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.5959i | 0.726772i | 0.931639 | + | 0.363386i | \(0.118379\pi\) | ||||
−0.931639 | + | 0.363386i | \(0.881621\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.4949 | − | 24.4949i | −0.905977 | − | 0.905977i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.0454 | − | 22.0454i | −0.814266 | − | 0.814266i | 0.171005 | − | 0.985270i | \(-0.445299\pi\) |
−0.985270 | + | 0.171005i | \(0.945299\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.0000 | 0.368355 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.0000 | − | 17.0000i | −0.625355 | − | 0.625355i | 0.321541 | − | 0.946896i | \(-0.395799\pi\) |
−0.946896 | + | 0.321541i | \(0.895799\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.00000 | −0.146746 | −0.0733729 | − | 0.997305i | \(-0.523376\pi\) | ||||
−0.0733729 | + | 0.997305i | \(0.523376\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.6969 | −0.538454 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.34847 | − | 10.3485i | −0.158890 | − | 0.378125i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 10.0000i | − | 0.364905i | −0.983215 | − | 0.182453i | \(-0.941596\pi\) | ||
0.983215 | − | 0.182453i | \(-0.0584036\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −29.3939 | + | 29.3939i | −1.06975 | + | 1.06975i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.00000 | + | 5.00000i | 0.181728 | + | 0.181728i | 0.792108 | − | 0.610380i | \(-0.208983\pi\) |
−0.610380 | + | 0.792108i | \(0.708983\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −44.0908 | −1.59829 | −0.799145 | − | 0.601138i | \(-0.794714\pi\) | ||||
−0.799145 | + | 0.601138i | \(0.794714\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.1464 | + | 24.1464i | 0.367325 | + | 0.874159i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −36.0000 | + | 36.0000i | −1.30158 | + | 1.30158i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 24.0000i | − | 0.866590i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 34.2929i | − | 1.23663i | −0.785930 | − | 0.618316i | \(-0.787815\pi\) | ||
0.785930 | − | 0.618316i | \(-0.212185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.2474 | + | 12.2474i | −0.440510 | + | 0.440510i | −0.892183 | − | 0.451673i | \(-0.850827\pi\) |
0.451673 | + | 0.892183i | \(0.350827\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34.2929i | 1.23184i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.0000 | − | 24.0000i | 0.859889 | − | 0.859889i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.00000 | + | 2.00000i | −0.0715656 | + | 0.0715656i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −60.0000 | −2.14149 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.89898 | + | 4.89898i | −0.174630 | + | 0.174630i | −0.789010 | − | 0.614380i | \(-0.789406\pi\) |
0.614380 | + | 0.789010i | \(0.289406\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.00000 | − | 9.79796i | 0.142224 | − | 0.348375i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 12.0000i | − | 0.426132i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.2474 | + | 12.2474i | 0.433827 | + | 0.433827i | 0.889928 | − | 0.456101i | \(-0.150754\pi\) |
−0.456101 | + | 0.889928i | \(0.650754\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000i | 0.849059i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.79796 | − | 9.79796i | 0.345762 | − | 0.345762i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.2020 | + | 33.7980i | 0.500556 | + | 1.19122i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 46.0000i | 1.61727i | 0.588308 | + | 0.808637i | \(0.299794\pi\) | ||||
−0.588308 | + | 0.808637i | \(0.700206\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.6969 | + | 14.6969i | 0.516079 | + | 0.516079i | 0.916383 | − | 0.400303i | \(-0.131095\pi\) |
−0.400303 | + | 0.916383i | \(0.631095\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.89898 | −0.171604 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 48.9898i | 1.71394i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.6515 | + | 25.3485i | 0.372195 | + | 0.885747i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.0000 | + | 19.0000i | 0.663105 | + | 0.663105i | 0.956111 | − | 0.293006i | \(-0.0946556\pi\) |
−0.293006 | + | 0.956111i | \(0.594656\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.00000 | 0.209147 | 0.104573 | − | 0.994517i | \(-0.466652\pi\) | ||||
0.104573 | + | 0.994517i | \(0.466652\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.0000 | − | 33.0000i | 1.14752 | − | 1.14752i | 0.160484 | − | 0.987038i | \(-0.448695\pi\) |
0.987038 | − | 0.160484i | \(-0.0513055\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.34847 | − | 7.34847i | −0.255223 | − | 0.255223i | 0.567885 | − | 0.823108i | \(-0.307762\pi\) |
−0.823108 | + | 0.567885i | \(0.807762\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.0000 | − | 24.4949i | 0.831551 | − | 0.848698i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 48.0000 | + | 48.0000i | 1.66111 | + | 1.66111i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.79796i | 0.338263i | 0.985593 | + | 0.169132i | \(0.0540963\pi\) | ||||
−0.985593 | + | 0.169132i | \(0.945904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0000i | 0.379310i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.44949 | − | 2.44949i | −0.0842650 | − | 0.0842650i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.0454 | + | 9.00000i | 0.757489 | + | 0.309244i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.0000 | + | 20.0000i | 0.685591 | + | 0.685591i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.2474 | + | 12.2474i | −0.419345 | + | 0.419345i | −0.884978 | − | 0.465633i | \(-0.845827\pi\) |
0.465633 | + | 0.884978i | \(0.345827\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 72.0000 | 2.46235 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.89898 | −0.167346 | −0.0836730 | − | 0.996493i | \(-0.526665\pi\) | ||||
−0.0836730 | + | 0.996493i | \(0.526665\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.3939 | − | 29.3939i | −1.00291 | − | 1.00291i | −0.999996 | − | 0.00291037i | \(-0.999074\pi\) |
−0.00291037 | − | 0.999996i | \(-0.500926\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 4.00000i | − | 0.136162i | −0.997680 | − | 0.0680808i | \(-0.978312\pi\) | ||
0.997680 | − | 0.0680808i | \(-0.0216876\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0000 | 0.408012 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.00000 | + | 4.00000i | 0.135691 | + | 0.135691i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.4949i | 0.829978i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.6969 | −0.497416 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16.8990 | + | 7.10102i | −0.571290 | + | 0.240058i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.0000 | + | 13.0000i | −0.438979 | + | 0.438979i | −0.891668 | − | 0.452689i | \(-0.850465\pi\) |
0.452689 | + | 0.891668i | \(0.350465\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 48.9898i | − | 1.65051i | −0.564762 | − | 0.825254i | \(-0.691032\pi\) | ||
0.564762 | − | 0.825254i | \(-0.308968\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.0000 | − | 31.0000i | −1.04323 | − | 1.04323i | −0.999022 | − | 0.0442108i | \(-0.985923\pi\) |
−0.0442108 | − | 0.999022i | \(-0.514077\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.5959i | 0.657967i | 0.944336 | + | 0.328983i | \(0.106706\pi\) | ||||
−0.944336 | + | 0.328983i | \(0.893294\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 44.0908 | + | 18.0000i | 1.47876 | + | 0.603701i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.00000 | + | 9.00000i | −0.301511 | + | 0.301511i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.0000 | − | 24.0000i | 0.803129 | − | 0.803129i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.6969 | 0.491264 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.6969 | + | 14.6969i | −0.490170 | + | 0.490170i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.89898 | + | 4.89898i | −0.163209 | + | 0.163209i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.0000i | 0.398893i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.00000 | + | 7.00000i | −0.232431 | + | 0.232431i | −0.813707 | − | 0.581276i | \(-0.802554\pi\) |
0.581276 | + | 0.813707i | \(0.302554\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.34847 | − | 7.34847i | −0.243733 | − | 0.243733i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 50.0000i | − | 1.65657i | −0.560304 | − | 0.828287i | \(-0.689316\pi\) | ||
0.560304 | − | 0.828287i | \(-0.310684\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.2020 | + | 33.7980i | 0.468993 | + | 1.11611i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.0000 | 0.329870 | 0.164935 | − | 0.986304i | \(-0.447259\pi\) | ||||
0.164935 | + | 0.986304i | \(0.447259\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.89898 | − | 4.89898i | −0.161252 | − | 0.161252i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35.0000 | + | 35.0000i | −1.15079 | + | 1.15079i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 29.3939 | 0.965422 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 34.2929i | − | 1.12511i | −0.826759 | − | 0.562556i | \(-0.809818\pi\) | ||
0.826759 | − | 0.562556i | \(-0.190182\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −48.4949 | + | 0.494897i | −1.58936 | + | 0.0162196i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.0000 | 0.784884 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.3939 | −0.960256 | −0.480128 | − | 0.877198i | \(-0.659410\pi\) | ||||
−0.480128 | + | 0.877198i | \(0.659410\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.9444 | − | 26.9444i | −0.878362 | − | 0.878362i | 0.115003 | − | 0.993365i | \(-0.463312\pi\) |
−0.993365 | + | 0.115003i | \(0.963312\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.5959 | −0.638131 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.0000 | − | 15.0000i | −0.487435 | − | 0.487435i | 0.420061 | − | 0.907496i | \(-0.362009\pi\) |
−0.907496 | + | 0.420061i | \(0.862009\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0000 | + | 24.0000i | 0.779073 | + | 0.779073i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 16.0000i | − | 0.518291i | −0.965838 | − | 0.259145i | \(-0.916559\pi\) | ||
0.965838 | − | 0.259145i | \(-0.0834409\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48.9898 | + | 48.9898i | 1.58527 | + | 1.58527i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.5959 | − | 8.00000i | −0.632785 | − | 0.258333i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.00000 | −0.225806 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.00000 | + | 9.00000i | 0.290021 | + | 0.290021i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −39.1918 | + | 39.1918i | −1.26163 | + | 1.26163i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.0000 | −0.900419 | −0.450210 | − | 0.892923i | \(-0.648651\pi\) | ||||
−0.450210 | + | 0.892923i | \(0.648651\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.79796 | − | 9.79796i | −0.314431 | − | 0.314431i | 0.532192 | − | 0.846624i | \(-0.321368\pi\) |
−0.846624 | + | 0.532192i | \(0.821368\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.8990 | + | 7.10102i | −0.541756 | + | 0.227648i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.0000 | 1.21573 | 0.607864 | − | 0.794041i | \(-0.292027\pi\) | ||||
0.607864 | + | 0.794041i | \(0.292027\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21.0000 | − | 21.0000i | −0.670478 | − | 0.670478i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 9.79796i | − | 0.312506i | −0.987717 | − | 0.156253i | \(-0.950058\pi\) | ||
0.987717 | − | 0.156253i | \(-0.0499416\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 73.4847 | 2.34142 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.0000 | − | 20.0000i | 0.635963 | − | 0.635963i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 60.0000i | 1.90596i | 0.303029 | + | 0.952981i | \(0.402002\pi\) | ||||
−0.303029 | + | 0.952981i | \(0.597998\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.0000 | + | 24.0000i | 0.760851 | + | 0.760851i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.34847 | + | 7.34847i | −0.232728 | + | 0.232728i | −0.813831 | − | 0.581102i | \(-0.802622\pi\) |
0.581102 | + | 0.813831i | \(0.302622\pi\) | |||||||
\(998\) | 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 | 896.2.j.e.671.2 | 4 | ||
4.3 | odd | 2 | 896.2.j.b.671.2 | 4 | |||
7.6 | odd | 2 | inner | 896.2.j.e.671.1 | 4 | ||
8.3 | odd | 2 | 112.2.j.a.27.1 | ✓ | 4 | ||
8.5 | even | 2 | 448.2.j.b.335.1 | 4 | |||
16.3 | odd | 4 | inner | 896.2.j.e.223.1 | 4 | ||
16.5 | even | 4 | 112.2.j.a.83.2 | yes | 4 | ||
16.11 | odd | 4 | 448.2.j.b.111.2 | 4 | |||
16.13 | even | 4 | 896.2.j.b.223.1 | 4 | |||
28.27 | even | 2 | 896.2.j.b.671.1 | 4 | |||
56.3 | even | 6 | 784.2.w.d.411.2 | 8 | |||
56.11 | odd | 6 | 784.2.w.d.411.1 | 8 | |||
56.13 | odd | 2 | 448.2.j.b.335.2 | 4 | |||
56.19 | even | 6 | 784.2.w.d.619.1 | 8 | |||
56.27 | even | 2 | 112.2.j.a.27.2 | yes | 4 | ||
56.51 | odd | 6 | 784.2.w.d.619.2 | 8 | |||
112.5 | odd | 12 | 784.2.w.d.227.1 | 8 | |||
112.13 | odd | 4 | 896.2.j.b.223.2 | 4 | |||
112.27 | even | 4 | 448.2.j.b.111.1 | 4 | |||
112.37 | even | 12 | 784.2.w.d.227.2 | 8 | |||
112.53 | even | 12 | 784.2.w.d.19.1 | 8 | |||
112.69 | odd | 4 | 112.2.j.a.83.1 | yes | 4 | ||
112.83 | even | 4 | inner | 896.2.j.e.223.2 | 4 | ||
112.101 | odd | 12 | 784.2.w.d.19.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.j.a.27.1 | ✓ | 4 | 8.3 | odd | 2 | ||
112.2.j.a.27.2 | yes | 4 | 56.27 | even | 2 | ||
112.2.j.a.83.1 | yes | 4 | 112.69 | odd | 4 | ||
112.2.j.a.83.2 | yes | 4 | 16.5 | even | 4 | ||
448.2.j.b.111.1 | 4 | 112.27 | even | 4 | |||
448.2.j.b.111.2 | 4 | 16.11 | odd | 4 | |||
448.2.j.b.335.1 | 4 | 8.5 | even | 2 | |||
448.2.j.b.335.2 | 4 | 56.13 | odd | 2 | |||
784.2.w.d.19.1 | 8 | 112.53 | even | 12 | |||
784.2.w.d.19.2 | 8 | 112.101 | odd | 12 | |||
784.2.w.d.227.1 | 8 | 112.5 | odd | 12 | |||
784.2.w.d.227.2 | 8 | 112.37 | even | 12 | |||
784.2.w.d.411.1 | 8 | 56.11 | odd | 6 | |||
784.2.w.d.411.2 | 8 | 56.3 | even | 6 | |||
784.2.w.d.619.1 | 8 | 56.19 | even | 6 | |||
784.2.w.d.619.2 | 8 | 56.51 | odd | 6 | |||
896.2.j.b.223.1 | 4 | 16.13 | even | 4 | |||
896.2.j.b.223.2 | 4 | 112.13 | odd | 4 | |||
896.2.j.b.671.1 | 4 | 28.27 | even | 2 | |||
896.2.j.b.671.2 | 4 | 4.3 | odd | 2 | |||
896.2.j.e.223.1 | 4 | 16.3 | odd | 4 | inner | ||
896.2.j.e.223.2 | 4 | 112.83 | even | 4 | inner | ||
896.2.j.e.671.1 | 4 | 7.6 | odd | 2 | inner | ||
896.2.j.e.671.2 | 4 | 1.1 | even | 1 | trivial |