Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,7,Mod(161,576)]
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([0, 1, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.161");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(132.511152165\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.28 | ||
Character | \(\chi\) | \(=\) | 576.161 |
Dual form | 576.7.h.b.161.25 |
$q$-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 | ||||||||
\(5\) | 108.406 | 0.867244 | 0.433622 | − | 0.901095i | \(-0.357235\pi\) | ||||
0.433622 | + | 0.901095i | \(0.357235\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −167.464 | −0.488234 | −0.244117 | − | 0.969746i | \(-0.578498\pi\) | ||||
−0.244117 | + | 0.969746i | \(0.578498\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1016.29 | 0.763551 | 0.381776 | − | 0.924255i | \(-0.375313\pi\) | ||||
0.381776 | + | 0.924255i | \(0.375313\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2272.52i | − 1.03438i | −0.855872 | − | 0.517188i | \(-0.826979\pi\) | ||||
0.855872 | − | 0.517188i | \(-0.173021\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 865.606i | − 0.176187i | −0.996112 | − | 0.0880934i | \(-0.971923\pi\) | ||||
0.996112 | − | 0.0880934i | \(-0.0280774\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 8674.42i | − 1.26468i | −0.774692 | − | 0.632339i | \(-0.782095\pi\) | ||||
0.774692 | − | 0.632339i | \(-0.217905\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7261.66i | 0.596832i | 0.954436 | + | 0.298416i | \(0.0964583\pi\) | ||||
−0.954436 | + | 0.298416i | \(0.903542\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3873.24 | −0.247888 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −21010.9 | −0.861491 | −0.430746 | − | 0.902473i | \(-0.641749\pi\) | ||||
−0.430746 | + | 0.902473i | \(0.641749\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 12998.3 | 0.436316 | 0.218158 | − | 0.975913i | \(-0.429995\pi\) | ||||
0.218158 | + | 0.975913i | \(0.429995\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −18154.1 | −0.423418 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 3255.75i | − 0.0642755i | −0.999483 | − | 0.0321378i | \(-0.989768\pi\) | ||||
0.999483 | − | 0.0321378i | \(-0.0102315\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 112661.i | 1.63464i | 0.576186 | + | 0.817318i | \(0.304540\pi\) | ||||
−0.576186 | + | 0.817318i | \(0.695460\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 59336.4i | − 0.746304i | −0.927770 | − | 0.373152i | \(-0.878277\pi\) | ||||
0.927770 | − | 0.373152i | \(-0.121723\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 117122.i | − 1.12809i | −0.825744 | − | 0.564045i | \(-0.809245\pi\) | ||||
0.825744 | − | 0.564045i | \(-0.190755\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −89604.7 | −0.761628 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11719.7 | −0.0787208 | −0.0393604 | − | 0.999225i | \(-0.512532\pi\) | ||||
−0.0393604 | + | 0.999225i | \(0.512532\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 110171. | 0.662185 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −47019.2 | −0.228939 | −0.114469 | − | 0.993427i | \(-0.536517\pi\) | ||||
−0.114469 | + | 0.993427i | \(0.536517\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 35243.8i | − 0.155272i | −0.996982 | − | 0.0776359i | \(-0.975263\pi\) | ||||
0.996982 | − | 0.0776359i | \(-0.0247372\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 246354.i | − 0.897056i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 123187.i | − 0.409581i | −0.978806 | − | 0.204791i | \(-0.934349\pi\) | ||||
0.978806 | − | 0.204791i | \(-0.0656513\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 184149.i | 0.514511i | 0.966343 | + | 0.257255i | \(0.0828182\pi\) | ||||
−0.966343 | + | 0.257255i | \(0.917182\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −294641. | −0.757398 | −0.378699 | − | 0.925520i | \(-0.623628\pi\) | ||||
−0.378699 | + | 0.925520i | \(0.623628\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −170192. | −0.372792 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −404395. | −0.820209 | −0.410105 | − | 0.912039i | \(-0.634508\pi\) | ||||
−0.410105 | + | 0.912039i | \(0.634508\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 43028.4 | 0.0752525 | 0.0376263 | − | 0.999292i | \(-0.488020\pi\) | ||||
0.0376263 | + | 0.999292i | \(0.488020\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 93836.5i | − 0.152797i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 308883.i | − 0.438151i | −0.975708 | − | 0.219076i | \(-0.929696\pi\) | ||||
0.975708 | − | 0.219076i | \(-0.0703041\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 380567.i | 0.505017i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 940355.i | − 1.09678i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.21046e6 | 1.32628 | 0.663139 | − | 0.748496i | \(-0.269224\pi\) | ||||
0.663139 | + | 0.748496i | \(0.269224\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12652.2 | −0.0122801 | −0.00614006 | − | 0.999981i | \(-0.501954\pi\) | ||||
−0.00614006 | + | 0.999981i | \(0.501954\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.15864e6 | −1.06032 | −0.530158 | − | 0.847899i | \(-0.677867\pi\) | ||||
−0.530158 | + | 0.847899i | \(0.677867\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 899526. | 0.734282 | 0.367141 | − | 0.930165i | \(-0.380337\pi\) | ||||
0.367141 | + | 0.930165i | \(0.380337\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.99024e6i | 1.53683i | 0.639950 | + | 0.768416i | \(0.278955\pi\) | ||||
−0.639950 | + | 0.768416i | \(0.721045\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 300140.i | − 0.208012i | −0.994577 | − | 0.104006i | \(-0.966834\pi\) | ||||
0.994577 | − | 0.104006i | \(-0.0331662\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 787204.i | 0.517599i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 144958.i | 0.0860204i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −738723. | −0.416990 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.11372e6 | −1.08222 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.52556e6 | 0.744765 | 0.372383 | − | 0.928079i | \(-0.378541\pi\) | ||||
0.372383 | + | 0.928079i | \(0.378541\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.64651e6 | 1.17722 | 0.588612 | − | 0.808415i | \(-0.299674\pi\) | ||||
0.588612 | + | 0.808415i | \(0.299674\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.45266e6i | 0.617459i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 1.92479e6i | − 0.748551i | −0.927318 | − | 0.374276i | \(-0.877891\pi\) | ||||
0.927318 | − | 0.374276i | \(-0.122109\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2.59236e6i | − 0.965276i | −0.875820 | − | 0.482638i | \(-0.839679\pi\) | ||||
0.875820 | − | 0.482638i | \(-0.160321\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 2.30953e6i | − 0.789799i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.27770e6 | −0.747123 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.38355e6 | −0.418252 | −0.209126 | − | 0.977889i | \(-0.567062\pi\) | ||||
−0.209126 | + | 0.977889i | \(0.567062\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.22138e6 | −1.80699 | −0.903495 | − | 0.428599i | \(-0.859007\pi\) | ||||
−0.903495 | + | 0.428599i | \(0.859007\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.40909e6 | 0.378393 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 369736.i | − 0.0955417i | −0.998858 | − | 0.0477709i | \(-0.984788\pi\) | ||||
0.998858 | − | 0.0477709i | \(-0.0152117\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 1.21607e6i | − 0.291394i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 5.02401e6i | − 1.16008i | −0.814588 | − | 0.580040i | \(-0.803037\pi\) | ||||
0.814588 | − | 0.580040i | \(-0.196963\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 7.12372e6i | − 1.52953i | −0.644311 | − | 0.764764i | \(-0.722856\pi\) | ||||
0.644311 | − | 0.764764i | \(-0.277144\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −337555. | −0.0699333 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.14826e6 | −1.76685 | −0.883426 | − | 0.468571i | \(-0.844769\pi\) | ||||
−0.883426 | + | 0.468571i | \(0.844769\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 648630. | 0.121027 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.71580e6 | −0.822235 | −0.411117 | − | 0.911582i | \(-0.634861\pi\) | ||||
−0.411117 | + | 0.911582i | \(0.634861\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.61763e6i | 0.272800i | 0.990654 | + | 0.136400i | \(0.0435532\pi\) | ||||
−0.990654 | + | 0.136400i | \(0.956447\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 352941.i | − 0.0557426i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 879704.i | − 0.134528i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 1.01300e7i | − 1.45381i | −0.686737 | − | 0.726906i | \(-0.740958\pi\) | ||||
0.686737 | − | 0.726906i | \(-0.259042\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.31577e7 | −1.83024 | −0.915120 | − | 0.403181i | \(-0.867904\pi\) | ||||
−0.915120 | + | 0.403181i | \(0.867904\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.11089e7 | −1.45302 | −0.726512 | − | 0.687154i | \(-0.758860\pi\) | ||||
−0.726512 | + | 0.687154i | \(0.758860\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.20132e6 | −1.16759 | −0.583795 | − | 0.811901i | \(-0.698433\pi\) | ||||
−0.583795 | + | 0.811901i | \(0.698433\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.51858e6 | 0.420609 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.22131e7i | 1.41763i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 8.81570e6i | − 0.965646i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1.58526e6i | − 0.168753i | −0.996434 | − | 0.0843766i | \(-0.973110\pi\) | ||||
0.996434 | − | 0.0843766i | \(-0.0268899\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 6.43239e6i | − 0.647228i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.17675e6 | −0.213024 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.96711e6 | −0.182243 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 60439.3 | 0.00545010 | 0.00272505 | − | 0.999996i | \(-0.499133\pi\) | ||||
0.00272505 | + | 0.999996i | \(0.499133\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.09366e7 | 1.78990 | 0.894952 | − | 0.446163i | \(-0.147210\pi\) | ||||
0.894952 | + | 0.446163i | \(0.147210\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.68612e6i | 0.806573i | 0.915074 | + | 0.403286i | \(0.132132\pi\) | ||||
−0.915074 | + | 0.403286i | \(0.867868\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 1.32063e7i | − 1.04403i | −0.852937 | − | 0.522014i | \(-0.825181\pi\) | ||||
0.852937 | − | 0.522014i | \(-0.174819\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 1.26966e7i | − 0.978329i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 2.45983e7i | − 1.80182i | −0.434006 | − | 0.900910i | \(-0.642900\pi\) | ||||
0.434006 | − | 0.900910i | \(-0.357100\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.47566e6 | 0.248305 | 0.124153 | − | 0.992263i | \(-0.460379\pi\) | ||||
0.124153 | + | 0.992263i | \(0.460379\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.71365e6 | −0.660517 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.97128e7 | −1.30815 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.98804e7 | 1.25720 | 0.628599 | − | 0.777729i | \(-0.283629\pi\) | ||||
0.628599 | + | 0.777729i | \(0.283629\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.37993e6i | 0.455712i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 2.06716e6i | − 0.121780i | −0.998144 | − | 0.0608898i | \(-0.980606\pi\) | ||||
0.998144 | − | 0.0608898i | \(-0.0193938\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 545221.i | 0.0313815i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.11532e7i | 0.613100i | 0.951855 | + | 0.306550i | \(0.0991746\pi\) | ||||
−0.951855 | + | 0.306550i | \(0.900825\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.27048e6 | −0.0682702 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.93896e7 | −1.50986 | −0.754930 | − | 0.655805i | \(-0.772329\pi\) | ||||
−0.754930 | + | 0.655805i | \(0.772329\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.42141e7 | −1.21663 | −0.608317 | − | 0.793694i | \(-0.708155\pi\) | ||||
−0.608317 | + | 0.793694i | \(0.708155\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.93632e6 | −0.189275 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.59678e7i | 1.22179i | 0.791712 | + | 0.610895i | \(0.209190\pi\) | ||||
−0.791712 | + | 0.610895i | \(0.790810\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 2.40037e7i | − 1.08183i | −0.841077 | − | 0.540916i | \(-0.818078\pi\) | ||||
0.841077 | − | 0.540916i | \(-0.181922\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.31588e7i | 0.580574i | 0.956940 | + | 0.290287i | \(0.0937508\pi\) | ||||
−0.956940 | + | 0.290287i | \(0.906249\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 1.88667e7i | − 0.798085i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.33883e7 | 0.968958 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.01348e7 | −1.59558 | −0.797790 | − | 0.602935i | \(-0.793998\pi\) | ||||
−0.797790 | + | 0.602935i | \(0.793998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.09714e6 | −0.198546 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.65023e7 | 0.617349 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.93672e6i | 0.364371i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 3.82062e6i | − 0.134659i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 6.27888e6i | − 0.217004i | −0.994096 | − | 0.108502i | \(-0.965395\pi\) | ||||
0.994096 | − | 0.108502i | \(-0.0346054\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 3.40106e7i | − 1.13066i | −0.824864 | − | 0.565332i | \(-0.808748\pi\) | ||||
0.824864 | − | 0.565332i | \(-0.191252\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.31466e7 | −1.08095 | −0.540476 | − | 0.841359i | \(-0.681756\pi\) | ||||
−0.540476 | + | 0.841359i | \(0.681756\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.78191e7 | 0.873305 | 0.436652 | − | 0.899630i | \(-0.356164\pi\) | ||||
0.436652 | + | 0.899630i | \(0.356164\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.13531e7 | −0.657792 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.50863e6 | −0.222820 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.80204e6i | 0.256409i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.96137e7i | 0.550772i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 4.84270e7i | − 1.33538i | −0.744442 | − | 0.667688i | \(-0.767284\pi\) | ||||
0.744442 | − | 0.667688i | \(-0.232716\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 1.33541e7i | − 0.355207i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.71914e7 | −0.971745 | −0.485873 | − | 0.874030i | \(-0.661498\pi\) | ||||
−0.485873 | + | 0.874030i | \(0.661498\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.32100e7 | 0.333150 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.47076e7 | 0.860086 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.33386e6 | 0.0797918 | 0.0398959 | − | 0.999204i | \(-0.487297\pi\) | ||||
0.0398959 | + | 0.999204i | \(0.487297\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 3.31165e7i | − 0.779056i | −0.921015 | − | 0.389528i | \(-0.872638\pi\) | ||||
0.921015 | − | 0.389528i | \(-0.127362\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 5.48754e7i | − 1.24754i | −0.781609 | − | 0.623769i | \(-0.785601\pi\) | ||||
0.781609 | − | 0.623769i | \(-0.214399\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.99628e7i | 0.446207i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 4.05268e7i | − 0.875910i | −0.898997 | − | 0.437955i | \(-0.855703\pi\) | ||||
0.898997 | − | 0.437955i | \(-0.144297\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.81997e7 | −0.599409 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.19407e7 | −0.656849 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.17570e7 | 0.237848 | 0.118924 | − | 0.992903i | \(-0.462056\pi\) | ||||
0.118924 | + | 0.992903i | \(0.462056\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.96263e6 | 0.0384342 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 5.53125e6i | − 0.106585i | −0.998579 | − | 0.0532926i | \(-0.983028\pi\) | ||||
0.998579 | − | 0.0532926i | \(-0.0169716\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.77478e7i | 0.891105i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 5.25982e6i | − 0.0966169i | −0.998832 | − | 0.0483085i | \(-0.984617\pi\) | ||||
0.998832 | − | 0.0483085i | \(-0.0153830\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.04442e7i | 1.43185i | 0.698175 | + | 0.715927i | \(0.253996\pi\) | ||||
−0.698175 | + | 0.715927i | \(0.746004\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.84497e7 | −0.323301 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.65628e7 | −0.281375 | −0.140688 | − | 0.990054i | \(-0.544931\pi\) | ||||
−0.140688 | + | 0.990054i | \(0.544931\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.28574e6 | 0.105154 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.38387e7 | −0.711322 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.39116e7i | 0.382153i | 0.981575 | + | 0.191077i | \(0.0611979\pi\) | ||||
−0.981575 | + | 0.191077i | \(0.938802\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.47399e7i | 0.693845i | 0.937894 | + | 0.346922i | \(0.112773\pi\) | ||||
−0.937894 | + | 0.346922i | \(0.887227\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 2.95389e7i | − 0.451315i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 3.30877e6i | − 0.0490776i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.44529e7 | 1.23437 | 0.617184 | − | 0.786819i | \(-0.288273\pi\) | ||||
0.617184 | + | 0.786819i | \(0.288273\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.87403e6 | 0.111776 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.66452e6 | 0.0652623 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.18395e8 | −1.60950 | −0.804750 | − | 0.593614i | \(-0.797701\pi\) | ||||
−0.804750 | + | 0.593614i | \(0.797701\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 7.97937e7i | − 1.06936i | −0.845056 | − | 0.534678i | \(-0.820433\pi\) | ||||
0.845056 | − | 0.534678i | \(-0.179567\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.35270e6i | 0.0436745i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.90207e6i | 0.0758090i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.11850e7i | 0.639309i | 0.947534 | + | 0.319654i | \(0.103567\pi\) | ||||
−0.947534 | + | 0.319654i | \(0.896433\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.36319e7 | 0.783811 | 0.391906 | − | 0.920005i | \(-0.371816\pi\) | ||||
0.391906 | + | 0.920005i | \(0.371816\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.29907e7 | 0.754801 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.70188e6 | 0.114673 | 0.0573367 | − | 0.998355i | \(-0.481739\pi\) | ||||
0.0573367 | + | 0.998355i | \(0.481739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.59558e8 | 1.83530 | 0.917651 | − | 0.397387i | \(-0.130083\pi\) | ||||
0.917651 | + | 0.397387i | \(0.130083\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 3.34846e7i | − 0.379984i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.87088e7i | 1.09048i | 0.838281 | + | 0.545239i | \(0.183561\pi\) | ||||
−0.838281 | + | 0.545239i | \(0.816439\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.14496e8i | 1.24813i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.12555e7i | 0.437973i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.39206e7 | 0.669718 | 0.334859 | − | 0.942268i | \(-0.391311\pi\) | ||||
0.334859 | + | 0.942268i | \(0.391311\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.56965e8 | 1.60214 | 0.801068 | − | 0.598574i | \(-0.204266\pi\) | ||||
0.801068 | + | 0.598574i | \(0.204266\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.41552e7 | −0.142617 | −0.0713086 | − | 0.997454i | \(-0.522718\pi\) | ||||
−0.0713086 | + | 0.997454i | \(0.522718\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.88086e6 | −0.0577418 | −0.0288709 | − | 0.999583i | \(-0.509191\pi\) | ||||
−0.0288709 | + | 0.999583i | \(0.509191\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.06294e7i | 0.199971i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 6.03028e7i | − 0.569841i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.35982e7i | 0.313498i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.02069e8i | 1.83862i | 0.393531 | + | 0.919311i | \(0.371253\pi\) | ||||
−0.393531 | + | 0.919311i | \(0.628747\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.39876e6 | −0.0664850 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.31220e8 | 1.15021 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.07112e8 | 1.79316 | 0.896581 | − | 0.442881i | \(-0.146044\pi\) | ||||
0.896581 | + | 0.442881i | \(0.146044\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.77240e7 | −0.234214 | −0.117107 | − | 0.993119i | \(-0.537362\pi\) | ||||
−0.117107 | + | 0.993119i | \(0.537362\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.81872e7i | 0.151783i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 3.08384e7i | − 0.251202i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.20361e8i | 0.968690i | 0.874877 | + | 0.484345i | \(0.160942\pi\) | ||||
−0.874877 | + | 0.484345i | \(0.839058\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.35139e7i | 0.734805i | 0.930062 | + | 0.367402i | \(0.119753\pi\) | ||||
−0.930062 | + | 0.367402i | \(0.880247\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.37157e6 | −0.0106499 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.78114e7 | −0.210896 | −0.105448 | − | 0.994425i | \(-0.533628\pi\) | ||||
−0.105448 | + | 0.994425i | \(0.533628\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.93418e7 | 0.369787 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.25602e8 | −0.919552 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1.19029e8i | − 0.861354i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 1.21387e7i | − 0.0858336i | −0.999079 | − | 0.0429168i | \(-0.986335\pi\) | ||||
0.999079 | − | 0.0429168i | \(-0.0136650\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 6.09328e6i | − 0.0425938i | −0.999773 | − | 0.0212969i | \(-0.993220\pi\) | ||||
0.999773 | − | 0.0212969i | \(-0.00677952\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1.12514e7i | − 0.0768732i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.53042e7 | 0.643791 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.56024e8 | 1.69083 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.75136e7 | 0.636801 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.10641e7 | −0.581542 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 1.95052e8i | − 1.23185i | −0.787804 | − | 0.615926i | \(-0.788782\pi\) | ||||
0.787804 | − | 0.615926i | \(-0.211218\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.15753e8i | 1.33281i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.88786e8i | 1.15347i | 0.816930 | + | 0.576737i | \(0.195674\pi\) | ||||
−0.816930 | + | 0.576737i | \(0.804326\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.82257e8i | 1.08951i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.77217e7 | 0.400454 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.27981e8 | 0.740594 | 0.370297 | − | 0.928913i | \(-0.379256\pi\) | ||||
0.370297 | + | 0.928913i | \(0.379256\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.34843e8 | −0.771959 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.03932e8 | −1.70314 | −0.851571 | − | 0.524239i | \(-0.824350\pi\) | ||||
−0.851571 | + | 0.524239i | \(0.824350\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 3.25369e7i | − 0.180397i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.54208e8i | 0.837087i | 0.908197 | + | 0.418543i | \(0.137459\pi\) | ||||
−0.908197 | + | 0.418543i | \(0.862541\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 1.81493e8i | − 0.974880i | −0.873156 | − | 0.487440i | \(-0.837931\pi\) | ||||
0.873156 | − | 0.487440i | \(-0.162069\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 2.81262e7i | − 0.147947i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.73075e7 | 0.194209 | 0.0971044 | − | 0.995274i | \(-0.469042\pi\) | ||||
0.0971044 | + | 0.995274i | \(0.469042\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.20572e6 | −0.0367408 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.19106e7 | −0.0601074 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.23294e8 | 0.609576 | 0.304788 | − | 0.952420i | \(-0.401414\pi\) | ||||
0.304788 | + | 0.952420i | \(0.401414\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1.12753e8i | − 0.551799i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.26663e7i | 0.252562i | 0.991994 | + | 0.126281i | \(0.0403042\pi\) | ||||
−0.991994 | + | 0.126281i | \(0.959696\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.57143e7i | 0.0746007i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.67475e8i | 0.779237i | 0.920976 | + | 0.389619i | \(0.127393\pi\) | ||||
−0.920976 | + | 0.389619i | \(0.872607\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.04027e7 | −0.232183 | −0.116091 | − | 0.993239i | \(-0.537037\pi\) | ||||
−0.116091 | + | 0.993239i | \(0.537037\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.00816e7 | −0.361632 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.13800e8 | 1.85023 | 0.925113 | − | 0.379693i | \(-0.123970\pi\) | ||||
0.925113 | + | 0.379693i | \(0.123970\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.66162e8 | −1.16687 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 4.18881e8i | − 1.81848i | −0.416268 | − | 0.909242i | \(-0.636662\pi\) | ||||
0.416268 | − | 0.909242i | \(-0.363338\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.43886e8i | 1.03832i | 0.854677 | + | 0.519161i | \(0.173755\pi\) | ||||
−0.854677 | + | 0.519161i | \(0.826245\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 6.06565e7i | − 0.255744i | −0.991791 | − | 0.127872i | \(-0.959185\pi\) | ||||
0.991791 | − | 0.127872i | \(-0.0408146\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.17269e7i | 0.213920i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.68619e8 | −0.690664 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.81819e6 | −0.0113245 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.14374e8 | 0.455239 | 0.227619 | − | 0.973750i | \(-0.426906\pi\) | ||||
0.227619 | + | 0.973750i | \(0.426906\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.65380e8 | 0.645893 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.03629e8i | 0.787809i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 2.66320e8i | − 1.01118i | −0.862773 | − | 0.505592i | \(-0.831274\pi\) | ||||
0.862773 | − | 0.505592i | \(-0.168726\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.18317e8i | − 0.445056i | −0.974926 | − | 0.222528i | \(-0.928569\pi\) | ||||
0.974926 | − | 0.222528i | \(-0.0714310\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.63390e8i | 0.972491i | 0.873822 | + | 0.486246i | \(0.161634\pi\) | ||||
−0.873822 | + | 0.486246i | \(0.838366\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.77850e7 | −0.174806 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.96726e8 | 1.42479 | 0.712396 | − | 0.701778i | \(-0.247610\pi\) | ||||
0.712396 | + | 0.701778i | \(0.247610\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.86896e8 | 1.02094 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.73867e8 | −0.607520 | −0.303760 | − | 0.952749i | \(-0.598242\pi\) | ||||
−0.303760 | + | 0.952749i | \(0.598242\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.86993e8i | 1.33998i | 0.742369 | + | 0.669991i | \(0.233702\pi\) | ||||
−0.742369 | + | 0.669991i | \(0.766298\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.57476e8i | 0.535487i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.52574e8i | − 0.514166i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 3.58178e7i | − 0.118558i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.44017e8 | 0.472463 | 0.236231 | − | 0.971697i | \(-0.424088\pi\) | ||||
0.236231 | + | 0.971697i | \(0.424088\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.59250e7 | −0.309148 | −0.154574 | − | 0.987981i | \(-0.549400\pi\) | ||||
−0.154574 | + | 0.987981i | \(0.549400\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.02708e8 | −0.647534 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.27860e8 | 1.65675 | 0.828374 | − | 0.560176i | \(-0.189266\pi\) | ||||
0.828374 | + | 0.560176i | \(0.189266\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 2.08658e8i | − 0.649177i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.66333e7i | 0.0814269i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.54597e8i | 1.68091i | 0.541884 | + | 0.840453i | \(0.317711\pi\) | ||||
−0.541884 | + | 0.840453i | \(0.682289\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 2.81027e8i | − 0.837130i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.75199e7 | 0.288002 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.17969e8 | −0.342463 | −0.171232 | − | 0.985231i | \(-0.554775\pi\) | ||||
−0.171232 | + | 0.985231i | \(0.554775\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.82417e7 | −0.0812878 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.11879e6 | 0.00599557 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 8.62629e7i | − 0.242039i | −0.992650 | − | 0.121020i | \(-0.961384\pi\) | ||||
0.992650 | − | 0.121020i | \(-0.0386164\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.43892e7i | 0.260408i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 2.50366e8i | − 0.684948i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 8.41415e7i | − 0.226372i | −0.993574 | − | 0.113186i | \(-0.963894\pi\) | ||||
0.993574 | − | 0.113186i | \(-0.0361057\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.94030e8 | 0.517682 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.13803e7 | 0.213553 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.23120e8 | −1.88195 | −0.940973 | − | 0.338483i | \(-0.890086\pi\) | ||||
−0.940973 | + | 0.338483i | \(0.890086\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.13619e7 | −0.131489 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.34884e7i | 0.110423i | 0.998475 | + | 0.0552117i | \(0.0175834\pi\) | ||||
−0.998475 | + | 0.0552117i | \(0.982417\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 1.25193e8i | − 0.312736i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.17057e8i | 1.03338i | 0.856171 | + | 0.516692i | \(0.172837\pi\) | ||||
−0.856171 | + | 0.516692i | \(0.827163\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 2.30520e8i | − 0.562009i | −0.959706 | − | 0.281004i | \(-0.909332\pi\) | ||||
0.959706 | − | 0.281004i | \(-0.0906676\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.49985e8 | −0.362726 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.50639e8 | −0.358501 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.46588e8 | −0.346081 | −0.173041 | − | 0.984915i | \(-0.555359\pi\) | ||||
−0.173041 | + | 0.984915i | \(0.555359\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.74432e8 | −1.56710 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.22315e8i | 1.43457i | 0.696778 | + | 0.717286i | \(0.254616\pi\) | ||||
−0.696778 | + | 0.717286i | \(0.745384\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 7.99870e8i | − 1.81495i | −0.420102 | − | 0.907477i | \(-0.638006\pi\) | ||||
0.420102 | − | 0.907477i | \(-0.361994\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 3.33295e8i | − 0.750334i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.06852e8i | 0.236809i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.96019e8 | 0.650940 | 0.325470 | − | 0.945552i | \(-0.394478\pi\) | ||||
0.325470 | + | 0.945552i | \(0.394478\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.14258e8 | −1.32988 | −0.664939 | − | 0.746897i | \(-0.731543\pi\) | ||||
−0.664939 | + | 0.746897i | \(0.731543\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.03456e7 | −0.108157 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.77267e8 | 2.06729 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.87148e8i | 0.392855i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 4.00814e7i | − 0.0828580i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.58778e8i | 0.736040i | 0.929818 | + | 0.368020i | \(0.119964\pi\) | ||||
−0.929818 | + | 0.368020i | \(0.880036\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.02628e7i | 0.101559i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.00923e7 | −0.160609 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.16661e8 | −0.427963 | −0.213981 | − | 0.976838i | \(-0.568643\pi\) | ||||
−0.213981 | + | 0.976838i | \(0.568643\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.01381e8 | −0.198755 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.99439e8 | −0.578312 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.31829e8i | − 0.252710i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 8.25793e8i | − 1.55964i | −0.626001 | − | 0.779822i | \(-0.715309\pi\) | ||||
0.626001 | − | 0.779822i | \(-0.284691\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.72696e6i | 0.0163606i | 0.999967 | + | 0.00818032i | \(0.00260391\pi\) | ||||
−0.999967 | + | 0.00818032i | \(0.997396\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 5.44631e8i | − 1.00607i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.14709e8 | −0.943834 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.19753e8 | −0.216400 | −0.108200 | − | 0.994129i | \(-0.534509\pi\) | ||||
−0.108200 | + | 0.994129i | \(0.534509\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.19710e8 | −0.752921 | −0.376460 | − | 0.926433i | \(-0.622859\pi\) | ||||
−0.376460 | + | 0.926433i | \(0.622859\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.01240e9 | 1.78993 | 0.894964 | − | 0.446138i | \(-0.147201\pi\) | ||||
0.894964 | + | 0.446138i | \(0.147201\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.27028e7i | 0.0398488i | 0.999801 | + | 0.0199244i | \(0.00634256\pi\) | ||||
−0.999801 | + | 0.0199244i | \(0.993657\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.75624e7i | 0.134189i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 7.72250e8i | − 1.32647i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 5.45149e8i | − 0.923058i | −0.887125 | − | 0.461529i | \(-0.847301\pi\) | ||||
0.887125 | − | 0.461529i | \(-0.152699\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.53365e8 | −0.257833 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.65928e7 | −0.0606492 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.23710e8 | 0.203589 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.36421e7 | 0.0383617 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.55247e8i | 0.733499i | 0.930320 | + | 0.366750i | \(0.119529\pi\) | ||||
−0.930320 | + | 0.366750i | \(0.880471\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.98993e8i | 0.792778i | 0.918083 | + | 0.396389i | \(0.129737\pi\) | ||||
−0.918083 | + | 0.396389i | \(0.870263\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 9.96593e8i | − 1.57231i | −0.618029 | − | 0.786155i | \(-0.712069\pi\) | ||||
0.618029 | − | 0.786155i | \(-0.287931\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 9.23182e8i | − 1.43633i | −0.695871 | − | 0.718167i | \(-0.744982\pi\) | ||||
0.695871 | − | 0.718167i | \(-0.255018\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.91722e8 | −1.53229 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.10981e8 | −0.626272 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.79945e8 | −0.423661 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.53972e8 | 0.528378 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.38117e8i | 1.09427i | 0.837043 | + | 0.547137i | \(0.184282\pi\) | ||||
−0.837043 | + | 0.547137i | \(0.815718\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 3.10844e6i | − 0.00454584i | −0.999997 | − | 0.00227292i | \(-0.999277\pi\) | ||||
0.999997 | − | 0.00227292i | \(-0.000723494\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.69574e8i | 0.972560i | 0.873803 | + | 0.486280i | \(0.161647\pi\) | ||||
−0.873803 | + | 0.486280i | \(0.838353\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 2.58571e8i | − 0.370517i | −0.982690 | − | 0.185259i | \(-0.940688\pi\) | ||||
0.982690 | − | 0.185259i | \(-0.0593123\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.55478e8 | −0.363620 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.01596e9 | −1.42667 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.11218e8 | −0.713078 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.73106e8 | −0.375883 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.01447e7i | 0.0138696i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.75360e8i | 0.236584i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1.18881e9i | − 1.59328i | −0.604456 | − | 0.796639i | \(-0.706609\pi\) | ||||
0.604456 | − | 0.796639i | \(-0.293391\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 8.70158e8i | − 1.15091i | −0.817832 | − | 0.575457i | \(-0.804824\pi\) | ||||
0.817832 | − | 0.575457i | \(-0.195176\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.37292e7 | 0.0574591 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.43195e8 | −0.574761 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.37383e8 | 1.20773 | 0.603866 | − | 0.797086i | \(-0.293626\pi\) | ||||
0.603866 | + | 0.797086i | \(0.293626\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.18483e8 | 0.532198 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.26103e7i | 0.0159331i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 2.13347e7i | − 0.0266096i | −0.999911 | − | 0.0133048i | \(-0.995765\pi\) | ||||
0.999911 | − | 0.0133048i | \(-0.00423518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.77269e8i | 0.963213i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 9.53648e7i | − 0.116668i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.68741e8 | 1.17758 | 0.588788 | − | 0.808288i | \(-0.299605\pi\) | ||||
0.588788 | + | 0.808288i | \(0.299605\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.60277e8 | −1.15246 | −0.576232 | − | 0.817286i | \(-0.695478\pi\) | ||||
−0.576232 | + | 0.817286i | \(0.695478\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.18104e8 | −0.975604 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.72326e8 | −1.14489 | −0.572443 | − | 0.819945i | \(-0.694004\pi\) | ||||
−0.572443 | + | 0.819945i | \(0.694004\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.69578e8i | 0.783434i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 1.62051e8i | − 0.187228i | −0.995609 | − | 0.0936142i | \(-0.970158\pi\) | ||||
0.995609 | − | 0.0936142i | \(-0.0298420\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1.09814e9i | − 1.26081i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.22333e8i | 0.365468i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.18548e8 | −0.809628 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.42637e9 | −1.58727 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.00115e8 | −0.442492 | −0.221246 | − | 0.975218i | \(-0.571012\pi\) | ||||
−0.221246 | + | 0.975218i | \(0.571012\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.04286e9 | 1.13912 | 0.569560 | − | 0.821950i | \(-0.307114\pi\) | ||||
0.569560 | + | 0.821950i | \(0.307114\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.34128e8i | 0.471281i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 1.20778e9i | − 1.29511i | −0.762021 | − | 0.647553i | \(-0.775793\pi\) | ||||
0.762021 | − | 0.647553i | \(-0.224207\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 3.13914e8i | − 0.334551i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 7.86498e8i | − 0.828013i | −0.910274 | − | 0.414007i | \(-0.864129\pi\) | ||||
0.910274 | − | 0.414007i | \(-0.135871\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.20427e9 | −1.26013 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.30881e8 | 0.445418 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.16459e9 | −1.19661 | −0.598304 | − | 0.801269i | \(-0.704159\pi\) | ||||
−0.598304 | + | 0.801269i | \(0.704159\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.97473e8 | −1.01259 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 5.86089e8i | − 0.591396i | −0.955281 | − | 0.295698i | \(-0.904448\pi\) | ||||
0.955281 | − | 0.295698i | \(-0.0955522\pi\) | |||||||
\(998\) | 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 | 576.7.h.b.161.28 | yes | 32 | |
3.2 | odd | 2 | inner | 576.7.h.b.161.6 | yes | 32 | |
4.3 | odd | 2 | inner | 576.7.h.b.161.27 | yes | 32 | |
8.3 | odd | 2 | inner | 576.7.h.b.161.8 | yes | 32 | |
8.5 | even | 2 | inner | 576.7.h.b.161.7 | yes | 32 | |
12.11 | even | 2 | inner | 576.7.h.b.161.5 | ✓ | 32 | |
24.5 | odd | 2 | inner | 576.7.h.b.161.25 | yes | 32 | |
24.11 | even | 2 | inner | 576.7.h.b.161.26 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.7.h.b.161.5 | ✓ | 32 | 12.11 | even | 2 | inner | |
576.7.h.b.161.6 | yes | 32 | 3.2 | odd | 2 | inner | |
576.7.h.b.161.7 | yes | 32 | 8.5 | even | 2 | inner | |
576.7.h.b.161.8 | yes | 32 | 8.3 | odd | 2 | inner | |
576.7.h.b.161.25 | yes | 32 | 24.5 | odd | 2 | inner | |
576.7.h.b.161.26 | yes | 32 | 24.11 | even | 2 | inner | |
576.7.h.b.161.27 | yes | 32 | 4.3 | odd | 2 | inner | |
576.7.h.b.161.28 | yes | 32 | 1.1 | even | 1 | trivial |