Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,4,Mod(575,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.575");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.c (of order \(2\), degree \(1\), 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: | \(33.9851001633\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 575.1 | ||
Root | \(1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.575 |
Dual form | 576.4.c.c.575.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 4.24264i | − 0.379473i | −0.981835 | − | 0.189737i | \(-0.939237\pi\) | ||||
0.981835 | − | 0.189737i | \(-0.0607634\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 13.8564i | − 0.748176i | −0.927393 | − | 0.374088i | \(-0.877956\pi\) | ||||
0.927393 | − | 0.374088i | \(-0.122044\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −58.7878 | −1.61138 | −0.805690 | − | 0.592338i | \(-0.798205\pi\) | ||||
−0.805690 | + | 0.592338i | \(0.798205\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −28.0000 | −0.597369 | −0.298685 | − | 0.954352i | \(-0.596548\pi\) | ||||
−0.298685 | + | 0.954352i | \(0.596548\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 97.5807i | 1.39216i | 0.717962 | + | 0.696082i | \(0.245075\pi\) | ||||
−0.717962 | + | 0.696082i | \(0.754925\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 110.851i | 1.33847i | 0.743049 | + | 0.669237i | \(0.233379\pi\) | ||||
−0.743049 | + | 0.669237i | \(0.766621\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 176.363 | 1.59888 | 0.799441 | − | 0.600745i | \(-0.205129\pi\) | ||||
0.799441 | + | 0.600745i | \(0.205129\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 107.000 | 0.856000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.24264i | 0.0271668i | 0.999908 | + | 0.0135834i | \(0.00432387\pi\) | ||||
−0.999908 | + | 0.0135834i | \(0.995676\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 124.708i | − 0.722521i | −0.932465 | − | 0.361261i | \(-0.882346\pi\) | ||||
0.932465 | − | 0.361261i | \(-0.117654\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −58.7878 | −0.283913 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 118.000 | 0.524299 | 0.262150 | − | 0.965027i | \(-0.415569\pi\) | ||||
0.262150 | + | 0.965027i | \(0.415569\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 190.919i | 0.727232i | 0.931549 | + | 0.363616i | \(0.118458\pi\) | ||||
−0.931549 | + | 0.363616i | \(0.881542\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 249.415i | − 0.884546i | −0.896880 | − | 0.442273i | \(-0.854172\pi\) | ||||
0.896880 | − | 0.442273i | \(-0.145828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −293.939 | −0.912242 | −0.456121 | − | 0.889918i | \(-0.650762\pi\) | ||||
−0.456121 | + | 0.889918i | \(0.650762\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 151.000 | 0.440233 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 700.036i | 1.81429i | 0.420820 | + | 0.907144i | \(0.361743\pi\) | ||||
−0.420820 | + | 0.907144i | \(0.638257\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 249.415i | 0.611476i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 587.878 | 1.29721 | 0.648603 | − | 0.761127i | \(-0.275354\pi\) | ||||
0.648603 | + | 0.761127i | \(0.275354\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 802.000 | 1.68337 | 0.841685 | − | 0.539969i | \(-0.181564\pi\) | ||||
0.841685 | + | 0.539969i | \(0.181564\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 118.794i | 0.226686i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 138.564i | − 0.252661i | −0.991988 | − | 0.126331i | \(-0.959680\pi\) | ||||
0.991988 | − | 0.126331i | \(-0.0403200\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −646.665 | −1.08092 | −0.540458 | − | 0.841371i | \(-0.681749\pi\) | ||||
−0.540458 | + | 0.841371i | \(0.681749\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 496.000 | 0.795238 | 0.397619 | − | 0.917551i | \(-0.369837\pi\) | ||||
0.397619 | + | 0.917551i | \(0.369837\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 814.587i | 1.20559i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1011.52i | 1.44056i | 0.693681 | + | 0.720282i | \(0.255988\pi\) | ||||
−0.693681 | + | 0.720282i | \(0.744012\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 58.7878 | 0.0777445 | 0.0388723 | − | 0.999244i | \(-0.487623\pi\) | ||||
0.0388723 | + | 0.999244i | \(0.487623\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 414.000 | 0.528289 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1124.30i | 1.33905i | 0.742789 | + | 0.669525i | \(0.233503\pi\) | ||||
−0.742789 | + | 0.669525i | \(0.766497\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 387.979i | 0.446937i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 470.302 | 0.507915 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −152.000 | −0.159106 | −0.0795529 | − | 0.996831i | \(-0.525349\pi\) | ||||
−0.0795529 | + | 0.996831i | \(0.525349\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 929.138i | 0.915373i | 0.889114 | + | 0.457687i | \(0.151322\pi\) | ||||
−0.889114 | + | 0.457687i | \(0.848678\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1759.76i | − 1.68344i | −0.539912 | − | 0.841722i | \(-0.681542\pi\) | ||||
0.539912 | − | 0.841722i | \(-0.318458\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −940.604 | −0.849828 | −0.424914 | − | 0.905234i | \(-0.639696\pi\) | ||||
−0.424914 | + | 0.905234i | \(0.639696\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −628.000 | −0.551849 | −0.275924 | − | 0.961179i | \(-0.588984\pi\) | ||||
−0.275924 | + | 0.961179i | \(0.588984\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1243.09i | 1.03487i | 0.855722 | + | 0.517435i | \(0.173113\pi\) | ||||
−0.855722 | + | 0.517435i | \(0.826887\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 748.246i | − 0.606733i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1352.12 | 1.04158 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2125.00 | 1.59654 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 984.293i | − 0.704302i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 1621.20i | − 1.13274i | −0.824151 | − | 0.566371i | \(-0.808347\pi\) | ||||
0.824151 | − | 0.566371i | \(-0.191653\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −823.029 | −0.548919 | −0.274459 | − | 0.961599i | \(-0.588499\pi\) | ||||
−0.274459 | + | 0.961599i | \(0.588499\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1536.00 | 1.00141 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1607.96i | 1.00275i | 0.865229 | + | 0.501377i | \(0.167173\pi\) | ||||
−0.865229 | + | 0.501377i | \(0.832827\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2133.89i | 1.30211i | 0.759029 | + | 0.651057i | \(0.225674\pi\) | ||||
−0.759029 | + | 0.651057i | \(0.774326\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1646.06 | 0.962589 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.0000 | 0.0103091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 818.830i | 0.450209i | 0.974335 | + | 0.225104i | \(0.0722723\pi\) | ||||
−0.974335 | + | 0.225104i | \(0.927728\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3256.26i | 1.75490i | 0.479666 | + | 0.877451i | \(0.340758\pi\) | ||||
−0.479666 | + | 0.877451i | \(0.659242\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −529.090 | −0.274178 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1730.00 | −0.879421 | −0.439710 | − | 0.898140i | \(-0.644919\pi\) | ||||
−0.439710 | + | 0.898140i | \(0.644919\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 2443.76i | − 1.19624i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1635.06i | 0.785690i | 0.919605 | + | 0.392845i | \(0.128509\pi\) | ||||
−0.919605 | + | 0.392845i | \(0.871491\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1998.78 | −0.926171 | −0.463085 | − | 0.886314i | \(-0.653258\pi\) | ||||
−0.463085 | + | 0.886314i | \(0.653258\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1413.00 | −0.643150 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 2159.50i | − 0.949041i | −0.880245 | − | 0.474520i | \(-0.842622\pi\) | ||||
0.880245 | − | 0.474520i | \(-0.157378\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 1482.64i | − 0.640438i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2351.51 | 0.981900 | 0.490950 | − | 0.871188i | \(-0.336650\pi\) | ||||
0.490950 | + | 0.871188i | \(0.336650\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 620.000 | 0.254609 | 0.127305 | − | 0.991864i | \(-0.459367\pi\) | ||||
0.127305 | + | 0.991864i | \(0.459367\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 500.632i | − 0.198958i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 5736.55i | − 2.24331i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3644.84 | −1.38079 | −0.690396 | − | 0.723431i | \(-0.742564\pi\) | ||||
−0.690396 | + | 0.723431i | \(0.742564\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −946.000 | −0.352822 | −0.176411 | − | 0.984317i | \(-0.556449\pi\) | ||||
−0.176411 | + | 0.984317i | \(0.556449\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1913.43i | 0.692012i | 0.938232 | + | 0.346006i | \(0.112462\pi\) | ||||
−0.938232 | + | 0.346006i | \(0.887538\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 734.390i | 0.261605i | 0.991408 | + | 0.130803i | \(0.0417555\pi\) | ||||
−0.991408 | + | 0.130803i | \(0.958245\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 58.7878 | 0.0203256 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 810.000 | 0.275965 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 6516.70i | − 2.15679i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 360.267i | − 0.117544i | −0.998271 | − | 0.0587720i | \(-0.981282\pi\) | ||||
0.998271 | − | 0.0587720i | \(-0.0187185\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1058.18 | −0.335662 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1728.00 | −0.540573 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 2732.26i | − 0.831637i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3865.94i | 1.16091i | 0.814293 | + | 0.580454i | \(0.197125\pi\) | ||||
−0.814293 | + | 0.580454i | \(0.802875\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2763.02 | 0.807878 | 0.403939 | − | 0.914786i | \(-0.367641\pi\) | ||||
0.403939 | + | 0.914786i | \(0.367641\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −700.000 | −0.201997 | −0.100998 | − | 0.994887i | \(-0.532204\pi\) | ||||
−0.100998 | + | 0.994887i | \(0.532204\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1964.34i | 0.552311i | 0.961113 | + | 0.276155i | \(0.0890604\pi\) | ||||
−0.961113 | + | 0.276155i | \(0.910940\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1247.08i | 0.346172i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 235.151 | 0.0636429 | 0.0318215 | − | 0.999494i | \(-0.489869\pi\) | ||||
0.0318215 | + | 0.999494i | \(0.489869\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6488.00 | −1.73414 | −0.867072 | − | 0.498182i | \(-0.834001\pi\) | ||||
−0.867072 | + | 0.498182i | \(0.834001\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 640.639i | − 0.167057i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 3103.84i | − 0.799564i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3586.05 | 0.901791 | 0.450896 | − | 0.892577i | \(-0.351105\pi\) | ||||
0.450896 | + | 0.892577i | \(0.351105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10368.0 | −2.57641 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 5316.03i | − 1.29029i | −0.764060 | − | 0.645145i | \(-0.776797\pi\) | ||||
0.764060 | − | 0.645145i | \(-0.223203\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1635.06i | − 0.392268i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5996.35 | 1.40590 | 0.702948 | − | 0.711241i | \(-0.251866\pi\) | ||||
0.702948 | + | 0.711241i | \(0.251866\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2970.00 | 0.688474 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 6520.94i | − 1.47802i | −0.673692 | − | 0.739012i | \(-0.735292\pi\) | ||||
0.673692 | − | 0.739012i | \(-0.264708\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 734.390i | − 0.164616i | −0.996607 | − | 0.0823081i | \(-0.973771\pi\) | ||||
0.996607 | − | 0.0823081i | \(-0.0262292\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6290.29 | −1.37934 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4124.00 | 0.894538 | 0.447269 | − | 0.894399i | \(-0.352397\pi\) | ||||
0.447269 | + | 0.894399i | \(0.352397\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1294.01i | 0.274711i | 0.990522 | + | 0.137356i | \(0.0438603\pi\) | ||||
−0.990522 | + | 0.137356i | \(0.956140\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7482.46i | 1.57168i | 0.618428 | + | 0.785841i | \(0.287770\pi\) | ||||
−0.618428 | + | 0.785841i | \(0.712230\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2645.45 | 0.544097 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4609.00 | −0.938123 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 3542.60i | − 0.706352i | −0.935557 | − | 0.353176i | \(-0.885102\pi\) | ||||
0.935557 | − | 0.353176i | \(-0.114898\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 2494.15i | − 0.492255i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4938.17 | −0.955123 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3456.00 | −0.661796 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 3402.60i | − 0.638794i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 249.415i | 0.0463677i | 0.999731 | + | 0.0231839i | \(0.00738031\pi\) | ||||
−0.999731 | + | 0.0231839i | \(0.992620\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2233.93 | −0.407315 | −0.203657 | − | 0.979042i | \(-0.565283\pi\) | ||||
−0.203657 | + | 0.979042i | \(0.565283\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7946.00 | 1.43493 | 0.717467 | − | 0.696592i | \(-0.245301\pi\) | ||||
0.717467 | + | 0.696592i | \(0.245301\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 8964.70i | − 1.58835i | −0.607688 | − | 0.794176i | \(-0.707903\pi\) | ||||
0.607688 | − | 0.794176i | \(-0.292097\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 249.415i | − 0.0437761i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10816.9 | −1.86338 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2996.00 | −0.511348 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4072.94i | 0.682517i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 1856.76i | − 0.308328i | −0.988045 | − | 0.154164i | \(-0.950732\pi\) | ||||
0.988045 | − | 0.154164i | \(-0.0492685\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −587.878 | −0.0958782 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1952.00 | −0.315526 | −0.157763 | − | 0.987477i | \(-0.550428\pi\) | ||||
−0.157763 | + | 0.987477i | \(0.550428\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7331.28i | 1.16426i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 6845.06i | − 1.07755i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5819.99 | 0.900384 | 0.450192 | − | 0.892932i | \(-0.351356\pi\) | ||||
0.450192 | + | 0.892932i | \(0.351356\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 226.000 | 0.0346633 | 0.0173317 | − | 0.999850i | \(-0.494483\pi\) | ||||
0.0173317 | + | 0.999850i | \(0.494483\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 1845.55i | − 0.278268i | −0.990274 | − | 0.139134i | \(-0.955568\pi\) | ||||
0.990274 | − | 0.139134i | \(-0.0444319\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2743.57i | 0.410179i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −58.7878 | −0.00864262 | −0.00432131 | − | 0.999991i | \(-0.501376\pi\) | ||||
−0.00432131 | + | 0.999991i | \(0.501376\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5429.00 | −0.791515 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 2104.35i | − 0.301772i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2480.30i | 0.352780i | 0.984320 | + | 0.176390i | \(0.0564421\pi\) | ||||
−0.984320 | + | 0.176390i | \(0.943558\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9699.98 | 1.35741 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5338.00 | 0.740995 | 0.370498 | − | 0.928833i | \(-0.379187\pi\) | ||||
0.370498 | + | 0.928833i | \(0.379187\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 118.794i | − 0.0162286i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 5376.29i | − 0.728658i | −0.931270 | − | 0.364329i | \(-0.881298\pi\) | ||||
0.931270 | − | 0.364329i | \(-0.118702\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6349.08 | 0.847057 | 0.423528 | − | 0.905883i | \(-0.360791\pi\) | ||||
0.423528 | + | 0.905883i | \(0.360791\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3456.00 | 0.457491 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11238.8i | 1.46485i | 0.680847 | + | 0.732426i | \(0.261612\pi\) | ||||
−0.680847 | + | 0.732426i | \(0.738388\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17209.7i | 2.22591i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4291.51 | 0.546656 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 466.000 | 0.0589115 | 0.0294558 | − | 0.999566i | \(-0.490623\pi\) | ||||
0.0294558 | + | 0.999566i | \(0.490623\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 7403.41i | − 0.921966i | −0.887409 | − | 0.460983i | \(-0.847497\pi\) | ||||
0.887409 | − | 0.460983i | \(-0.152503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3491.81i | 0.431612i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6936.95 | −0.844845 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4024.00 | 0.486489 | 0.243244 | − | 0.969965i | \(-0.421788\pi\) | ||||
0.243244 | + | 0.969965i | \(0.421788\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 8145.87i | − 0.970538i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 249.415i | − 0.0295020i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15108.5 | 1.76157 | 0.880783 | − | 0.473520i | \(-0.157017\pi\) | ||||
0.880783 | + | 0.473520i | \(0.157017\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8540.00 | 0.988632 | 0.494316 | − | 0.869282i | \(-0.335419\pi\) | ||||
0.494316 | + | 0.869282i | \(0.335419\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10441.1i | 1.19169i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 11112.8i | − 1.25946i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16049.1 | −1.79363 | −0.896817 | − | 0.442403i | \(-0.854126\pi\) | ||||
−0.896817 | + | 0.442403i | \(0.854126\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11266.0 | −1.25037 | −0.625184 | − | 0.780477i | \(-0.714976\pi\) | ||||
−0.625184 | + | 0.780477i | \(0.714976\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19550.1i | 2.14006i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 6110.68i | − 0.664343i | −0.943219 | − | 0.332172i | \(-0.892219\pi\) | ||||
0.943219 | − | 0.332172i | \(-0.107781\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13580.0 | −1.45644 | −0.728221 | − | 0.685342i | \(-0.759653\pi\) | ||||
−0.728221 | + | 0.685342i | \(0.759653\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4770.00 | 0.508134 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 547.301i | 0.0575250i | 0.999586 | + | 0.0287625i | \(0.00915665\pi\) | ||||
−0.999586 | + | 0.0287625i | \(0.990843\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 11223.7i | − 1.17185i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1646.06 | 0.169601 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15784.0 | 1.61563 | 0.807817 | − | 0.589434i | \(-0.200649\pi\) | ||||
0.807817 | + | 0.589434i | \(0.200649\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18620.9i | 1.88127i | 0.339424 | + | 0.940634i | \(0.389768\pi\) | ||||
−0.339424 | + | 0.940634i | \(0.610232\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 8244.56i | − 0.827554i | −0.910378 | − | 0.413777i | \(-0.864209\pi\) | ||||
0.910378 | − | 0.413777i | \(-0.135791\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2057.57 | 0.203882 | 0.101941 | − | 0.994790i | \(-0.467495\pi\) | ||||
0.101941 | + | 0.994790i | \(0.467495\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1920.00 | −0.189035 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14662.6i | 1.42534i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11861.1i | 1.14573i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2175.15 | −0.207484 | −0.103742 | − | 0.994604i | \(-0.533082\pi\) | ||||
−0.103742 | + | 0.994604i | \(0.533082\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3304.00 | −0.313200 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 644.881i | 0.0603764i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11708.7i | 1.08947i | 0.838609 | + | 0.544733i | \(0.183369\pi\) | ||||
−0.838609 | + | 0.544733i | \(0.816631\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1646.06 | −0.151294 | −0.0756472 | − | 0.997135i | \(-0.524102\pi\) | ||||
−0.0756472 | + | 0.997135i | \(0.524102\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −414.000 | −0.0378207 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8960.46i | 0.808715i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 2992.98i | − 0.268506i | −0.990947 | − | 0.134253i | \(-0.957137\pi\) | ||||
0.990947 | − | 0.134253i | \(-0.0428634\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9112.10 | 0.807731 | 0.403865 | − | 0.914818i | \(-0.367666\pi\) | ||||
0.403865 | + | 0.914818i | \(0.367666\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3942.00 | 0.347360 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 12384.3i | − 1.07843i | −0.842167 | − | 0.539217i | \(-0.818720\pi\) | ||||
0.842167 | − | 0.539217i | \(-0.181280\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 6872.78i | − 0.594978i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7466.04 | −0.638822 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17280.0 | 1.46997 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3882.02i | 0.326438i | 0.986590 | + | 0.163219i | \(0.0521877\pi\) | ||||
−0.986590 | + | 0.163219i | \(0.947812\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15574.6i | 1.30216i | 0.759009 | + | 0.651080i | \(0.225684\pi\) | ||||
−0.759009 | + | 0.651080i | \(0.774316\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12169.1 | 1.00587 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18937.0 | 1.55642 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 5345.73i | − 0.434426i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3990.65i | 0.322487i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8876.95 | −0.709383 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11188.0 | −0.889112 | −0.444556 | − | 0.895751i | \(-0.646639\pi\) | ||||
−0.444556 | + | 0.895751i | \(0.646639\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2664.38i | 0.209412i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21588.3i | 1.68747i | 0.536757 | + | 0.843737i | \(0.319649\pi\) | ||||
−0.536757 | + | 0.843737i | \(0.680351\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −470.302 | −0.0363621 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14016.0 | 1.07780 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16346.9i | 1.24352i | 0.783208 | + | 0.621760i | \(0.213582\pi\) | ||||
−0.783208 | + | 0.621760i | \(0.786418\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6983.63i | 0.528401i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21692.7 | −1.62387 | −0.811934 | − | 0.583749i | \(-0.801585\pi\) | ||||
−0.811934 | + | 0.583749i | \(0.801585\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5274.00 | 0.392706 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9414.42i | 0.693626i | 0.937934 | + | 0.346813i | \(0.112736\pi\) | ||||
−0.937934 | + | 0.346813i | \(0.887264\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 10364.6i | − 0.759623i | −0.925064 | − | 0.379811i | \(-0.875989\pi\) | ||||
0.925064 | − | 0.379811i | \(-0.124011\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18870.9 | 1.36864 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9406.00 | −0.678643 | −0.339321 | − | 0.940670i | \(-0.610197\pi\) | ||||
−0.339321 | + | 0.940670i | \(0.610197\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 814.587i | − 0.0581665i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 41153.5i | − 2.92351i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21986.6 | 1.54597 | 0.772985 | − | 0.634424i | \(-0.218763\pi\) | ||||
0.772985 | + | 0.634424i | \(0.218763\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13824.0 | 0.967076 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13419.5i | 0.929295i | 0.885496 | + | 0.464647i | \(0.153819\pi\) | ||||
−0.885496 | + | 0.464647i | \(0.846181\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 5736.55i | − 0.395253i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6878.17 | −0.469172 | −0.234586 | − | 0.972095i | \(-0.575374\pi\) | ||||
−0.234586 | + | 0.972095i | \(0.575374\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6086.00 | 0.413067 | 0.206533 | − | 0.978440i | \(-0.433782\pi\) | ||||
0.206533 | + | 0.978440i | \(0.433782\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 9015.61i | − 0.605846i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7967.43i | 0.532765i | 0.963867 | + | 0.266382i | \(0.0858284\pi\) | ||||
−0.963867 | + | 0.266382i | \(0.914172\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8230.29 | 0.544946 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20438.0 | −1.34663 | −0.673314 | − | 0.739357i | \(-0.735130\pi\) | ||||
−0.673314 | + | 0.739357i | \(0.735130\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3568.06i | 0.232812i | 0.993202 | + | 0.116406i | \(0.0371373\pi\) | ||||
−0.993202 | + | 0.116406i | \(0.962863\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 1884.47i | − 0.122364i | −0.998127 | − | 0.0611820i | \(-0.980513\pi\) | ||||
0.998127 | − | 0.0611820i | \(-0.0194870\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15578.8 | 1.00185 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9199.00 | 0.588736 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11514.5i | 0.729911i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9491.64i | 0.598821i | 0.954124 | + | 0.299411i | \(0.0967900\pi\) | ||||
−0.954124 | + | 0.299411i | \(0.903210\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6878.17 | −0.429845 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4228.00 | −0.262982 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 16363.9i | − 1.00832i | −0.863610 | − | 0.504161i | \(-0.831802\pi\) | ||||
0.863610 | − | 0.504161i | \(-0.168198\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 24193.3i | − 1.48381i | −0.670505 | − | 0.741905i | \(-0.733922\pi\) | ||||
0.670505 | − | 0.741905i | \(-0.266078\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14520.6 | −0.882323 | −0.441161 | − | 0.897428i | \(-0.645433\pi\) | ||||
−0.441161 | + | 0.897428i | \(0.645433\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −34560.0 | −2.09029 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4187.49i | 0.250948i | 0.992097 | + | 0.125474i | \(0.0400452\pi\) | ||||
−0.992097 | + | 0.125474i | \(0.959955\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3491.81i | 0.208300i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4115.14 | −0.243252 | −0.121626 | − | 0.992576i | \(-0.538811\pi\) | ||||
−0.121626 | + | 0.992576i | \(0.538811\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22438.0 | 1.32033 | 0.660164 | − | 0.751121i | \(-0.270487\pi\) | ||||
0.660164 | + | 0.751121i | \(0.270487\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 6516.70i | − 0.380010i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 748.246i | 0.0434366i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −47147.8 | −2.71255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18962.0 | 1.08608 | 0.543040 | − | 0.839707i | \(-0.317273\pi\) | ||||
0.543040 | + | 0.839707i | \(0.317273\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 2278.30i | − 0.129338i | −0.997907 | − | 0.0646692i | \(-0.979401\pi\) | ||||
0.997907 | − | 0.0646692i | \(-0.0205992\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2106.17i | 0.119039i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11581.2 | 0.648817 | 0.324408 | − | 0.945917i | \(-0.394835\pi\) | ||||
0.324408 | + | 0.945917i | \(0.394835\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6822.00 | 0.380519 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 19601.0i | − 1.08380i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11722.5i | 0.645363i | 0.946508 | + | 0.322681i | \(0.104584\pi\) | ||||
−0.946508 | + | 0.322681i | \(0.895416\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9053.31 | 0.494118 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18630.0 | −1.01243 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 9601.10i | − 0.517302i | −0.965971 | − | 0.258651i | \(-0.916722\pi\) | ||||
0.965971 | − | 0.258651i | \(-0.0832779\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13080.4i | 0.701762i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12874.5 | 0.684860 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14572.0 | −0.771880 | −0.385940 | − | 0.922524i | \(-0.626123\pi\) | ||||
−0.385940 | + | 0.922524i | \(0.626123\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 21993.8i | − 1.15523i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 6983.63i | − 0.365277i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9817.55 | −0.509225 | −0.254613 | − | 0.967043i | \(-0.581948\pi\) | ||||
−0.254613 | + | 0.967043i | \(0.581948\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24384.0 | −1.25951 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 453.963i | 0.0232548i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33047.5i | 1.68592i | 0.537975 | + | 0.842961i | \(0.319189\pi\) | ||||
−0.537975 | + | 0.842961i | \(0.680811\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24338.1 | 1.23143 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28636.0 | −1.44297 | −0.721483 | − | 0.692432i | \(-0.756539\pi\) | ||||
−0.721483 | + | 0.692432i | \(0.756539\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8145.87i | 0.407133i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1496.49i | 0.0744917i | 0.999306 | + | 0.0372458i | \(0.0118585\pi\) | ||||
−0.999306 | + | 0.0372458i | \(0.988142\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13050.9 | 0.644402 | 0.322201 | − | 0.946671i | \(-0.395577\pi\) | ||||
0.322201 | + | 0.946671i | \(0.395577\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3474.00 | 0.170842 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13033.4i | 0.635821i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8244.56i | 0.400597i | 0.979735 | + | 0.200298i | \(0.0641912\pi\) | ||||
−0.979735 | + | 0.200298i | \(0.935809\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13815.1 | 0.665939 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17740.0 | −0.851745 | −0.425873 | − | 0.904783i | \(-0.640033\pi\) | ||||
−0.425873 | + | 0.904783i | \(0.640033\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 17254.8i | − 0.821927i | −0.911652 | − | 0.410964i | \(-0.865192\pi\) | ||||
0.911652 | − | 0.410964i | \(-0.134808\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8701.82i | 0.412880i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16460.6 | −0.774911 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17038.0 | −0.798967 | −0.399484 | − | 0.916740i | \(-0.630811\pi\) | ||||
−0.399484 | + | 0.916740i | \(0.630811\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 38739.6i | − 1.80254i | −0.433256 | − | 0.901271i | \(-0.642635\pi\) | ||||
0.433256 | − | 0.901271i | \(-0.357365\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 13343.7i | − 0.618478i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21163.6 | −0.973382 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38016.0 | 1.74177 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7339.77i | 0.333717i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3103.84i | 0.140584i | 0.997526 | + | 0.0702921i | \(0.0223931\pi\) | ||||
−0.997526 | + | 0.0702921i | \(0.977607\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17224.8 | 0.774265 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22456.0 | −1.00559 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1098.84i | 0.0488370i | 0.999702 | + | 0.0244185i | \(0.00777341\pi\) | ||||
−0.999702 | + | 0.0244185i | \(0.992227\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 28682.8i | − 1.26999i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −29158.7 | −1.28143 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10368.0 | −0.453943 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 38739.6i | − 1.68357i | −0.539811 | − | 0.841786i | \(-0.681504\pi\) | ||||
0.539811 | − | 0.841786i | \(-0.318496\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 34419.3i | − 1.49029i | −0.666902 | − | 0.745145i | \(-0.732380\pi\) | ||||
0.666902 | − | 0.745145i | \(-0.267620\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6936.95 | 0.298148 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27648.0 | 1.18394 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 35387.9i | − 1.50432i | −0.658982 | − | 0.752159i | \(-0.729013\pi\) | ||||
0.658982 | − | 0.752159i | \(-0.270987\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 11708.7i | − 0.495915i | −0.968771 | − | 0.247958i | \(-0.920241\pi\) | ||||
0.968771 | − | 0.247958i | \(-0.0797594\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31392.7 | −1.31999 | −0.659994 | − | 0.751271i | \(-0.729441\pi\) | ||||
−0.659994 | + | 0.751271i | \(0.729441\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43444.0 | −1.82011 | −0.910056 | − | 0.414486i | \(-0.863961\pi\) | ||||
−0.910056 | + | 0.414486i | \(0.863961\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14734.7i | 0.612877i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8480.12i | 0.351457i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15343.6 | −0.631371 | −0.315685 | − | 0.948864i | \(-0.602234\pi\) | ||||
−0.315685 | + | 0.948864i | \(0.602234\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24371.0 | 0.999262 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5994.85i | 0.244058i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 29444.9i | − 1.19450i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20810.9 | 0.838293 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4870.00 | 0.195481 | 0.0977407 | − | 0.995212i | \(-0.468838\pi\) | ||||
0.0977407 | + | 0.995212i | \(0.468838\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 9414.42i | − 0.375251i | −0.982241 | − | 0.187626i | \(-0.939921\pi\) | ||||
0.982241 | − | 0.187626i | \(-0.0600792\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16600.0i | 0.659353i | 0.944094 | + | 0.329676i | \(0.106940\pi\) | ||||
−0.944094 | + | 0.329676i | \(0.893060\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36095.7 | 1.42377 | 0.711884 | − | 0.702297i | \(-0.247842\pi\) | ||||
0.711884 | + | 0.702297i | \(0.247842\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9162.00 | −0.360136 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 59464.9i | − 2.32130i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3879.79i | 0.150932i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13638.8 | −0.526942 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19954.0 | 0.768300 | 0.384150 | − | 0.923271i | \(-0.374495\pi\) | ||||
0.384150 | + | 0.923271i | \(0.374495\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 8744.08i | − 0.334388i | −0.985924 | − | 0.167194i | \(-0.946529\pi\) | ||||
0.985924 | − | 0.167194i | \(-0.0534706\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30068.4i | 1.14596i | 0.819570 | + | 0.572980i | \(0.194213\pi\) | ||||
−0.819570 | + | 0.572980i | \(0.805787\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28100.5 | 1.06372 | 0.531862 | − | 0.846831i | \(-0.321492\pi\) | ||||
0.531862 | + | 0.846831i | \(0.321492\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22464.0 | −0.847490 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 32583.5i | − 1.22101i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 9976.61i | − 0.372605i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 529.090 | 0.0196286 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −68310.0 | −2.52579 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 2630.44i | − 0.0966173i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1136.23i | − 0.0415962i | −0.999784 | − | 0.0207981i | \(-0.993379\pi\) | ||||
0.999784 | − | 0.0207981i | \(-0.00662072\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39387.8 | 1.43247 | 0.716233 | − | 0.697862i | \(-0.245865\pi\) | ||||
0.716233 | + | 0.697862i | \(0.245865\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3456.00 | −0.125276 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11404.2i | 0.410688i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5861.26i | 0.210386i | 0.994452 | + | 0.105193i | \(0.0335461\pi\) | ||||
−0.994452 | + | 0.105193i | \(0.966454\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18106.6 | 0.645706 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12626.0 | 0.448800 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6614.28i | 0.233592i | 0.993156 | + | 0.116796i | \(0.0372624\pi\) | ||||
−0.993156 | + | 0.116796i | \(0.962738\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16738.5i | 0.589241i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −24338.1 | −0.851275 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21610.0 | −0.753434 | −0.376717 | − | 0.926328i | \(-0.622947\pi\) | ||||
−0.376717 | + | 0.926328i | \(0.622947\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50865.0i | 1.76212i | 0.473007 | + | 0.881059i | \(0.343168\pi\) | ||||
−0.473007 | + | 0.881059i | \(0.656832\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33671.1i | 1.16276i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22927.2 | −0.786731 | −0.393366 | − | 0.919382i | \(-0.628689\pi\) | ||||
−0.393366 | + | 0.919382i | \(0.628689\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13888.0 | −0.475051 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 8981.67i | − 0.305294i | −0.988281 | − | 0.152647i | \(-0.951220\pi\) | ||||
0.988281 | − | 0.152647i | \(-0.0487797\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15463.7i | 0.523974i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22280.6 | 0.750236 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14239.0 | 0.477963 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4013.54i | 0.133886i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 983.805i | − 0.0327167i | −0.999866 | − | 0.0163583i | \(-0.994793\pi\) | ||||
0.999866 | − | 0.0163583i | \(-0.00520725\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12639.4 | −0.417731 | −0.208865 | − | 0.977944i | \(-0.566977\pi\) | ||||
−0.208865 | + | 0.977944i | \(0.566977\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29568.0 | 0.974210 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31501.6i | 1.03155i | 0.856724 | + | 0.515776i | \(0.172496\pi\) | ||||
−0.856724 | + | 0.515776i | \(0.827504\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 66095.1i | − 2.15772i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56318.7 | −1.82735 | −0.913676 | − | 0.406444i | \(-0.866769\pi\) | ||||
−0.913676 | + | 0.406444i | \(0.866769\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8118.00 | 0.262600 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 43987.7i | − 1.41428i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5473.28i | 0.175443i | 0.996145 | + | 0.0877217i | \(0.0279586\pi\) | ||||
−0.996145 | + | 0.0877217i | \(0.972041\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3115.75 | 0.0992723 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22858.0 | 0.726098 | 0.363049 | − | 0.931770i | \(-0.381736\pi\) | ||||
0.363049 | + | 0.931770i | \(0.381736\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 576.4.c.c.575.1 | 4 | ||
3.2 | odd | 2 | inner | 576.4.c.c.575.3 | 4 | ||
4.3 | odd | 2 | inner | 576.4.c.c.575.2 | 4 | ||
8.3 | odd | 2 | 144.4.c.b.143.4 | yes | 4 | ||
8.5 | even | 2 | 144.4.c.b.143.3 | yes | 4 | ||
12.11 | even | 2 | inner | 576.4.c.c.575.4 | 4 | ||
16.3 | odd | 4 | 2304.4.f.f.1151.1 | 8 | |||
16.5 | even | 4 | 2304.4.f.f.1151.8 | 8 | |||
16.11 | odd | 4 | 2304.4.f.f.1151.6 | 8 | |||
16.13 | even | 4 | 2304.4.f.f.1151.3 | 8 | |||
24.5 | odd | 2 | 144.4.c.b.143.1 | ✓ | 4 | ||
24.11 | even | 2 | 144.4.c.b.143.2 | yes | 4 | ||
48.5 | odd | 4 | 2304.4.f.f.1151.4 | 8 | |||
48.11 | even | 4 | 2304.4.f.f.1151.2 | 8 | |||
48.29 | odd | 4 | 2304.4.f.f.1151.7 | 8 | |||
48.35 | even | 4 | 2304.4.f.f.1151.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.4.c.b.143.1 | ✓ | 4 | 24.5 | odd | 2 | ||
144.4.c.b.143.2 | yes | 4 | 24.11 | even | 2 | ||
144.4.c.b.143.3 | yes | 4 | 8.5 | even | 2 | ||
144.4.c.b.143.4 | yes | 4 | 8.3 | odd | 2 | ||
576.4.c.c.575.1 | 4 | 1.1 | even | 1 | trivial | ||
576.4.c.c.575.2 | 4 | 4.3 | odd | 2 | inner | ||
576.4.c.c.575.3 | 4 | 3.2 | odd | 2 | inner | ||
576.4.c.c.575.4 | 4 | 12.11 | even | 2 | inner | ||
2304.4.f.f.1151.1 | 8 | 16.3 | odd | 4 | |||
2304.4.f.f.1151.2 | 8 | 48.11 | even | 4 | |||
2304.4.f.f.1151.3 | 8 | 16.13 | even | 4 | |||
2304.4.f.f.1151.4 | 8 | 48.5 | odd | 4 | |||
2304.4.f.f.1151.5 | 8 | 48.35 | even | 4 | |||
2304.4.f.f.1151.6 | 8 | 16.11 | odd | 4 | |||
2304.4.f.f.1151.7 | 8 | 48.29 | odd | 4 | |||
2304.4.f.f.1151.8 | 8 | 16.5 | even | 4 |