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 | 161.17 | ||
Character | \(\chi\) | \(=\) | 576.161 |
Dual form | 576.7.h.b.161.20 |
$q$-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 | ||||||||
\(5\) | 83.0572 | 0.664457 | 0.332229 | − | 0.943199i | \(-0.392199\pi\) | ||||
0.332229 | + | 0.943199i | \(0.392199\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 37.1638 | 0.108349 | 0.0541747 | − | 0.998531i | \(-0.482747\pi\) | ||||
0.0541747 | + | 0.998531i | \(0.482747\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1959.80 | −1.47243 | −0.736214 | − | 0.676748i | \(-0.763388\pi\) | ||||
−0.736214 | + | 0.676748i | \(0.763388\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4306.41i | − 1.96013i | −0.198675 | − | 0.980065i | \(-0.563664\pi\) | ||||
0.198675 | − | 0.980065i | \(-0.436336\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 7855.72i | − 1.59897i | −0.600688 | − | 0.799483i | \(-0.705107\pi\) | ||||
0.600688 | − | 0.799483i | \(-0.294893\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 6114.84i | − 0.891507i | −0.895156 | − | 0.445753i | \(-0.852936\pi\) | ||||
0.895156 | − | 0.445753i | \(-0.147064\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 15556.2i | 1.27856i | 0.768975 | + | 0.639279i | \(0.220767\pi\) | ||||
−0.768975 | + | 0.639279i | \(0.779233\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8726.51 | −0.558497 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1668.36 | 0.0684061 | 0.0342030 | − | 0.999415i | \(-0.489111\pi\) | ||||
0.0342030 | + | 0.999415i | \(0.489111\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 27871.2 | 0.935558 | 0.467779 | − | 0.883846i | \(-0.345054\pi\) | ||||
0.467779 | + | 0.883846i | \(0.345054\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3086.72 | 0.0719935 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 52355.1i | 1.03360i | 0.856105 | + | 0.516802i | \(0.172878\pi\) | ||||
−0.856105 | + | 0.516802i | \(0.827122\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 51807.9i | 0.751699i | 0.926681 | + | 0.375850i | \(0.122649\pi\) | ||||
−0.926681 | + | 0.375850i | \(0.877351\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 135857.i | 1.70874i | 0.519664 | + | 0.854371i | \(0.326057\pi\) | ||||
−0.519664 | + | 0.854371i | \(0.673943\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 93610.2i | − 0.901633i | −0.892617 | − | 0.450816i | \(-0.851133\pi\) | ||||
0.892617 | − | 0.450816i | \(-0.148867\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −116268. | −0.988260 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −104925. | −0.704773 | −0.352387 | − | 0.935854i | \(-0.614630\pi\) | ||||
−0.352387 | + | 0.935854i | \(0.614630\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −162776. | −0.978366 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −176394. | −0.858870 | −0.429435 | − | 0.903098i | \(-0.641287\pi\) | ||||
−0.429435 | + | 0.903098i | \(0.641287\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 926.866i | 0.00408345i | 0.999998 | + | 0.00204173i | \(0.000649902\pi\) | ||||
−0.999998 | + | 0.00204173i | \(0.999350\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 357678.i | − 1.30242i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 163928.i | − 0.545039i | −0.962150 | − | 0.272520i | \(-0.912143\pi\) | ||||
0.962150 | − | 0.272520i | \(-0.0878570\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 610911.i | 1.70688i | 0.521190 | + | 0.853441i | \(0.325488\pi\) | ||||
−0.521190 | + | 0.853441i | \(0.674512\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 333300. | 0.856774 | 0.428387 | − | 0.903595i | \(-0.359082\pi\) | ||||
0.428387 | + | 0.903595i | \(0.359082\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −72833.8 | −0.159537 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 605169. | 1.22743 | 0.613713 | − | 0.789529i | \(-0.289675\pi\) | ||||
0.613713 | + | 0.789529i | \(0.289675\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 486745. | 0.851270 | 0.425635 | − | 0.904895i | \(-0.360051\pi\) | ||||
0.425635 | + | 0.904895i | \(0.360051\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 652474.i | − 1.06245i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 826800.i | 1.17282i | 0.810015 | + | 0.586409i | \(0.199459\pi\) | ||||
−0.810015 | + | 0.586409i | \(0.800541\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 160043.i | − 0.212379i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 507882.i | − 0.592368i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.11632e6 | −1.22313 | −0.611565 | − | 0.791194i | \(-0.709460\pi\) | ||||
−0.611565 | + | 0.791194i | \(0.709460\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 153614. | 0.149096 | 0.0745481 | − | 0.997217i | \(-0.476249\pi\) | ||||
0.0745481 | + | 0.997217i | \(0.476249\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.73563e6 | −1.58835 | −0.794173 | − | 0.607692i | \(-0.792096\pi\) | ||||
−0.794173 | + | 0.607692i | \(0.792096\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.41074e6 | 1.15159 | 0.575793 | − | 0.817596i | \(-0.304694\pi\) | ||||
0.575793 | + | 0.817596i | \(0.304694\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 121880.i | − 0.0941137i | −0.998892 | − | 0.0470568i | \(-0.985016\pi\) | ||||
0.998892 | − | 0.0470568i | \(-0.0149842\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.38095e6i | 0.957069i | 0.878069 | + | 0.478534i | \(0.158832\pi\) | ||||
−0.878069 | + | 0.478534i | \(0.841168\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.29205e6i | 0.849547i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 291949.i | − 0.173247i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.06926e6 | 1.16805 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.02257e6 | −1.03555 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.04249e6 | −0.997124 | −0.498562 | − | 0.866854i | \(-0.666138\pi\) | ||||
−0.498562 | + | 0.866854i | \(0.666138\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.55809e6 | −0.693072 | −0.346536 | − | 0.938037i | \(-0.612642\pi\) | ||||
−0.346536 | + | 0.938037i | \(0.612642\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 227251.i | − 0.0965942i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 227489.i | − 0.0884707i | −0.999021 | − | 0.0442354i | \(-0.985915\pi\) | ||||
0.999021 | − | 0.0442354i | \(-0.0140851\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 1.83311e6i | − 0.682565i | −0.939961 | − | 0.341282i | \(-0.889139\pi\) | ||||
0.939961 | − | 0.341282i | \(-0.110861\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.43971e6i | 2.88615i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 138569. | 0.0454529 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.77808e6 | −1.74673 | −0.873363 | − | 0.487070i | \(-0.838065\pi\) | ||||
−0.873363 | + | 0.487070i | \(0.838065\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 479414. | 0.139245 | 0.0696226 | − | 0.997573i | \(-0.477821\pi\) | ||||
0.0696226 | + | 0.997573i | \(0.477821\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.31490e6 | 0.621638 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 5.54477e6i | − 1.43280i | −0.697692 | − | 0.716398i | \(-0.745789\pi\) | ||||
0.697692 | − | 0.716398i | \(-0.254211\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 578128.i | 0.138531i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.96511e6i | 0.453759i | 0.973923 | + | 0.226879i | \(0.0728523\pi\) | ||||
−0.973923 | + | 0.226879i | \(0.927148\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 2.09517e6i | − 0.449852i | −0.974376 | − | 0.224926i | \(-0.927786\pi\) | ||||
0.974376 | − | 0.224926i | \(-0.0722140\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.37183e7 | −2.84211 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 964175. | 0.186216 | 0.0931081 | − | 0.995656i | \(-0.470320\pi\) | ||||
0.0931081 | + | 0.995656i | \(0.470320\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −324311. | −0.0605128 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.77781e6 | 1.35612 | 0.678060 | − | 0.735007i | \(-0.262821\pi\) | ||||
0.678060 | + | 0.735007i | \(0.262821\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 5.24935e6i | − 0.885258i | −0.896705 | − | 0.442629i | \(-0.854046\pi\) | ||||
0.896705 | − | 0.442629i | \(-0.145954\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.34847e6i | 0.686786i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.53957e7i | 2.35436i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.21395e7i | 1.74221i | 0.491100 | + | 0.871103i | \(0.336595\pi\) | ||||
−0.491100 | + | 0.871103i | \(0.663405\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.06934e6 | 0.287846 | 0.143923 | − | 0.989589i | \(-0.454028\pi\) | ||||
0.143923 | + | 0.989589i | \(0.454028\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.58221e6 | −0.860940 | −0.430470 | − | 0.902605i | \(-0.641652\pi\) | ||||
−0.430470 | + | 0.902605i | \(0.641652\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.08503e7 | −1.37683 | −0.688416 | − | 0.725316i | \(-0.741694\pi\) | ||||
−0.688416 | + | 0.725316i | \(0.741694\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 62002.5 | 0.00741176 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.30301e6i | 0.499472i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.19839e7i | 1.31268i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1.29771e6i | − 0.138143i | −0.997612 | − | 0.0690715i | \(-0.977996\pi\) | ||||
0.997612 | − | 0.0690715i | \(-0.0220036\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.12839e7i | 1.13539i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.03580e6 | 0.101367 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.38299e7 | −3.13418 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.77428e6 | −0.701044 | −0.350522 | − | 0.936554i | \(-0.613996\pi\) | ||||
−0.350522 | + | 0.936554i | \(0.613996\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.27506e6 | 0.365481 | 0.182740 | − | 0.983161i | \(-0.441503\pi\) | ||||
0.182740 | + | 0.983161i | \(0.441503\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 8.38344e6i | − 0.698097i | −0.937105 | − | 0.349049i | \(-0.886505\pi\) | ||||
0.937105 | − | 0.349049i | \(-0.113495\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 4.76991e6i | − 0.377087i | −0.982065 | − | 0.188544i | \(-0.939623\pi\) | ||||
0.982065 | − | 0.188544i | \(-0.0603767\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 7.77500e6i | − 0.599096i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.88451e6i | 0.504289i | 0.967690 | + | 0.252144i | \(0.0811358\pi\) | ||||
−0.967690 | + | 0.252144i | \(0.918864\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.90446e6 | 0.136057 | 0.0680284 | − | 0.997683i | \(-0.478329\pi\) | ||||
0.0680284 | + | 0.997683i | \(0.478329\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.65688e6 | −0.656657 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.63330e7 | −1.74747 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.61930e6 | 0.481830 | 0.240915 | − | 0.970546i | \(-0.422553\pi\) | ||||
0.240915 | + | 0.970546i | \(0.422553\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 3.04871e7i | − 1.88258i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.21558e7i | 0.716115i | 0.933700 | + | 0.358058i | \(0.116561\pi\) | ||||
−0.933700 | + | 0.358058i | \(0.883439\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.94572e6i | 0.111990i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.70043e7i | 1.48445i | 0.670149 | + | 0.742226i | \(0.266230\pi\) | ||||
−0.670149 | + | 0.742226i | \(0.733770\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.71473e6 | −0.468292 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.21804e7 | 1.13949 | 0.569747 | − | 0.821820i | \(-0.307041\pi\) | ||||
0.569747 | + | 0.821820i | \(0.307041\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.95677e6 | 0.450032 | 0.225016 | − | 0.974355i | \(-0.427757\pi\) | ||||
0.225016 | + | 0.974355i | \(0.427757\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.71022e7 | 0.822346 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2.73042e7i | − 1.28466i | −0.766427 | − | 0.642332i | \(-0.777967\pi\) | ||||
0.766427 | − | 0.642332i | \(-0.222033\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.84445e7i | 1.73267i | 0.499466 | + | 0.866334i | \(0.333530\pi\) | ||||
−0.499466 | + | 0.866334i | \(0.666470\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.02032e7i | 0.891374i | 0.895189 | + | 0.445687i | \(0.147041\pi\) | ||||
−0.895189 | + | 0.445687i | \(0.852959\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.92538e6i | 0.0814462i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.75748e7 | −1.55669 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.25402e7 | −0.498541 | −0.249270 | − | 0.968434i | \(-0.580191\pi\) | ||||
−0.249270 | + | 0.968434i | \(0.580191\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.46508e7 | −0.570682 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.69914e7 | 2.50614 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.04896e6i | 0.185141i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 76982.8i | 0.00271328i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.56216e6i | 0.295916i | 0.988994 | + | 0.147958i | \(0.0472700\pi\) | ||||
−0.988994 | + | 0.147958i | \(0.952730\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.46955e7i | 1.15343i | 0.816944 | + | 0.576716i | \(0.195666\pi\) | ||||
−0.816944 | + | 0.576716i | \(0.804334\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.49394e7 | 1.13942 | 0.569708 | − | 0.821847i | \(-0.307056\pi\) | ||||
0.569708 | + | 0.821847i | \(0.307056\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.33835e7 | −1.67583 | −0.837913 | − | 0.545804i | \(-0.816224\pi\) | ||||
−0.837913 | + | 0.545804i | \(0.816224\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.26965e6 | −0.100723 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.80365e7 | −1.42549 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.75799e7i | 1.09473i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 3.47891e6i | − 0.0976913i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 3.32801e7i | − 0.917699i | −0.888514 | − | 0.458850i | \(-0.848262\pi\) | ||||
0.888514 | − | 0.458850i | \(-0.151738\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 1.36154e7i | − 0.362155i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.44209e7 | −0.376792 | −0.188396 | − | 0.982093i | \(-0.560329\pi\) | ||||
−0.188396 | + | 0.982093i | \(0.560329\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.46220e7 | −1.37754 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.69325e6 | −0.215427 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.05006e7 | −1.44801 | −0.724005 | − | 0.689795i | \(-0.757701\pi\) | ||||
−0.724005 | + | 0.689795i | \(0.757701\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 2.78673e7i | − 0.655569i | −0.944753 | − | 0.327785i | \(-0.893698\pi\) | ||||
0.944753 | − | 0.327785i | \(-0.106302\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 3.20925e7i | − 0.729591i | −0.931088 | − | 0.364796i | \(-0.881139\pi\) | ||||
0.931088 | − | 0.364796i | \(-0.118861\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.07406e7i | 1.13415i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 9.17808e6i | − 0.198367i | −0.995069 | − | 0.0991833i | \(-0.968377\pi\) | ||||
0.995069 | − | 0.0991833i | \(-0.0316230\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.65456e6 | 0.205216 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.76829e7 | 0.569290 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.02971e7 | −1.62443 | −0.812216 | − | 0.583357i | \(-0.801739\pi\) | ||||
−0.812216 | + | 0.583357i | \(0.801739\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.89940e6 | −0.0763618 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 2.61467e7i | − 0.503837i | −0.967748 | − | 0.251918i | \(-0.918939\pi\) | ||||
0.967748 | − | 0.251918i | \(-0.0810615\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 7.18462e6i | − 0.134085i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.11681e7i | 1.49097i | 0.666524 | + | 0.745483i | \(0.267781\pi\) | ||||
−0.666524 | + | 0.745483i | \(0.732219\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.20532e7i | 1.28250i | 0.767332 | + | 0.641250i | \(0.221584\pi\) | ||||
−0.767332 | + | 0.641250i | \(0.778416\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.04937e6 | −0.106005 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.30952e7 | 1.41165 | 0.705825 | − | 0.708386i | \(-0.250577\pi\) | ||||
0.705825 | + | 0.708386i | \(0.250577\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.22205e8 | 2.04437 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.02636e7 | 0.815572 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.67473e7i | 0.747111i | 0.927608 | + | 0.373555i | \(0.121861\pi\) | ||||
−0.927608 | + | 0.373555i | \(0.878139\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 4.29945e7i | − 0.666775i | −0.942790 | − | 0.333388i | \(-0.891808\pi\) | ||||
0.942790 | − | 0.333388i | \(-0.108192\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.20025e8i | − 1.83382i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 1.02606e8i | − 1.52191i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.10094e8 | −1.60914 | −0.804571 | − | 0.593857i | \(-0.797604\pi\) | ||||
−0.804571 | + | 0.593857i | \(0.797604\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.55547e6 | −0.0930580 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.04277e7 | 0.565633 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.89084e7 | 0.664877 | 0.332439 | − | 0.943125i | \(-0.392129\pi\) | ||||
0.332439 | + | 0.943125i | \(0.392129\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.81777e7i | 0.243608i | 0.992554 | + | 0.121804i | \(0.0388680\pi\) | ||||
−0.992554 | + | 0.121804i | \(0.961132\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.85530e7i | 0.893017i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 34445.9i | 0 0.000442439i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 3.09271e7i | − 0.386285i | −0.981171 | − | 0.193143i | \(-0.938132\pi\) | ||||
0.981171 | − | 0.193143i | \(-0.0618680\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.51429e7 | 0.679244 | 0.339622 | − | 0.940562i | \(-0.389701\pi\) | ||||
0.339622 | + | 0.940562i | \(0.389701\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.51238e7 | 1.13984 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.34146e8 | 1.58557 | 0.792784 | − | 0.609503i | \(-0.208631\pi\) | ||||
0.792784 | + | 0.609503i | \(0.208631\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.59880e7 | −0.183900 | −0.0919501 | − | 0.995764i | \(-0.529310\pi\) | ||||
−0.0919501 | + | 0.995764i | \(0.529310\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.86717e7i | 0.779287i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.72078e7i | 0.852947i | 0.904500 | + | 0.426473i | \(0.140244\pi\) | ||||
−0.904500 | + | 0.426473i | \(0.859756\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1.01533e8i | − 1.10682i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 1.32927e7i | − 0.141117i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.09149e8 | 1.14359 | 0.571796 | − | 0.820396i | \(-0.306247\pi\) | ||||
0.571796 | + | 0.820396i | \(0.306247\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.95186e7 | 0.811645 | 0.405822 | − | 0.913952i | \(-0.366985\pi\) | ||||
0.405822 | + | 0.913952i | \(0.366985\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.28884e7 | −0.734371 | −0.367185 | − | 0.930148i | \(-0.619679\pi\) | ||||
−0.367185 | + | 0.930148i | \(0.619679\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.96554e8 | −1.92988 | −0.964940 | − | 0.262470i | \(-0.915463\pi\) | ||||
−0.964940 | + | 0.262470i | \(0.915463\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 6.09218e6i | − 0.0590547i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 2.66253e8i | − 2.51600i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.33612e7i | 0.497903i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 2.05958e8i | − 1.87401i | −0.349320 | − | 0.937004i | \(-0.613587\pi\) | ||||
0.349320 | − | 0.937004i | \(-0.386413\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.25463e8 | 2.02600 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.27182e7 | −0.812718 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.47902e8 | −1.28052 | −0.640262 | − | 0.768157i | \(-0.721174\pi\) | ||||
−0.640262 | + | 0.768157i | \(0.721174\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.18634e7 | −0.269183 | −0.134592 | − | 0.990901i | \(-0.542972\pi\) | ||||
−0.134592 | + | 0.990901i | \(0.542972\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.31061e7i | − 0.109379i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.27038e7i | 0.184940i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 1.10011e8i | − 0.885386i | −0.896673 | − | 0.442693i | \(-0.854023\pi\) | ||||
0.896673 | − | 0.442693i | \(-0.145977\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 3.58001e7i | − 0.281307i | −0.990059 | − | 0.140653i | \(-0.955080\pi\) | ||||
0.990059 | − | 0.140653i | \(-0.0449203\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.27587e7 | 0.0990680 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.16724e8 | 1.64344 | 0.821720 | − | 0.569892i | \(-0.193015\pi\) | ||||
0.821720 | + | 0.569892i | \(0.193015\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.23867e7 | 0.0928309 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.44156e8 | −1.05539 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.83457e8i | 1.32759i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 1.01755e8i | − 0.719518i | −0.933045 | − | 0.359759i | \(-0.882859\pi\) | ||||
0.933045 | − | 0.359759i | \(-0.117141\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.10857e8i | − 0.774920i | −0.921887 | − | 0.387460i | \(-0.873353\pi\) | ||||
0.921887 | − | 0.387460i | \(-0.126647\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 2.18948e8i | − 1.49593i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.39596e7 | −0.634709 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.23106e8 | 1.47343 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.17172e8 | 0.765179 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.27862e8 | 1.45514 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.47693e8i | 0.932756i | 0.884586 | + | 0.466378i | \(0.154441\pi\) | ||||
−0.884586 | + | 0.466378i | \(0.845559\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 1.01230e7i | − 0.0625345i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.41332e7i | 0.514050i | 0.966405 | + | 0.257025i | \(0.0827423\pi\) | ||||
−0.966405 | + | 0.257025i | \(0.917258\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 1.02017e7i | − 0.0609845i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.24904e7 | 0.132991 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.09820e7 | 0.295020 | 0.147510 | − | 0.989061i | \(-0.452874\pi\) | ||||
0.147510 | + | 0.989061i | \(0.452874\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.85055e8 | 3.34936 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.51243e8 | −0.847521 | −0.423761 | − | 0.905774i | \(-0.639290\pi\) | ||||
−0.423761 | + | 0.905774i | \(0.639290\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.14698e8i | 0.635931i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.34052e8i | 0.727671i | 0.931463 | + | 0.363836i | \(0.118533\pi\) | ||||
−0.931463 | + | 0.363836i | \(0.881467\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 8.15488e7i | − 0.438035i | −0.975721 | − | 0.219018i | \(-0.929715\pi\) | ||||
0.975721 | − | 0.219018i | \(-0.0702852\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 1.35751e8i | − 0.714070i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.66709e6 | 0.00867826 | 0.00433913 | − | 0.999991i | \(-0.498619\pi\) | ||||
0.00433913 | + | 0.999991i | \(0.498619\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.80893e7 | 0.0922346 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.05631e8 | 1.03773 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.33311e8 | 0.659098 | 0.329549 | − | 0.944138i | \(-0.393103\pi\) | ||||
0.329549 | + | 0.944138i | \(0.393103\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1.70428e8i | − 0.834056i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 2.62556e8i | − 1.25910i | −0.776962 | − | 0.629548i | \(-0.783240\pi\) | ||||
0.776962 | − | 0.629548i | \(-0.216760\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 2.42484e7i | − 0.115115i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.70406e7i | 0.125816i | 0.998019 | + | 0.0629081i | \(0.0200375\pi\) | ||||
−0.998019 | + | 0.0629081i | \(0.979963\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.33675e8 | −0.615782 | −0.307891 | − | 0.951422i | \(-0.599623\pi\) | ||||
−0.307891 | + | 0.951422i | \(0.599623\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.71867e8 | 0.776117 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.25106e8 | −0.559387 | −0.279693 | − | 0.960089i | \(-0.590233\pi\) | ||||
−0.279693 | + | 0.960089i | \(0.590233\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.03124e8 | −1.76732 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.23831e6i | − 0.00537588i | −0.999996 | − | 0.00268794i | \(-0.999144\pi\) | ||||
0.999996 | − | 0.00268794i | \(-0.000855599\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 4.35967e7i | − 0.185608i | −0.995684 | − | 0.0928042i | \(-0.970417\pi\) | ||||
0.995684 | − | 0.0928042i | \(-0.0295831\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.54527e8i | 1.49478i | 0.664386 | + | 0.747390i | \(0.268693\pi\) | ||||
−0.664386 | + | 0.747390i | \(0.731307\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.07271e7i | 0.127074i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.16370e7 | −0.129585 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.11288e8 | 1.65270 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.25768e8 | −1.29664 | −0.648322 | − | 0.761367i | \(-0.724529\pi\) | ||||
−0.648322 | + | 0.761367i | \(0.724529\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.69644e8 | −0.662547 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.00697e8i | 1.93712i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 5.13127e8i | − 1.94828i | −0.225954 | − | 0.974138i | \(-0.572550\pi\) | ||||
0.225954 | − | 0.974138i | \(-0.427450\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 4.59513e8i | − 1.72848i | −0.503077 | − | 0.864242i | \(-0.667799\pi\) | ||||
0.503077 | − | 0.864242i | \(-0.332201\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 2.56031e8i | − 0.945323i | −0.881244 | − | 0.472662i | \(-0.843293\pi\) | ||||
0.881244 | − | 0.472662i | \(-0.156707\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.45697e8 | 1.26462 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.52625e8 | −1.62555 | −0.812773 | − | 0.582580i | \(-0.802043\pi\) | ||||
−0.812773 | + | 0.582580i | \(0.802043\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.29410e8 | −0.460516 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.27984e8 | −0.796613 | −0.398306 | − | 0.917252i | \(-0.630402\pi\) | ||||
−0.398306 | + | 0.917252i | \(0.630402\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 1.28280e8i | − 0.444177i | −0.975027 | − | 0.222089i | \(-0.928713\pi\) | ||||
0.975027 | − | 0.222089i | \(-0.0712874\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 1.88748e7i | − 0.0641827i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.59533e7i | 0.0874611i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 1.81647e6i | − 0.00601259i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.51573e8 | −0.497253 | −0.248627 | − | 0.968599i | \(-0.579979\pi\) | ||||
−0.248627 | + | 0.968599i | \(0.579979\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.60675e8 | −1.48467 | −0.742333 | − | 0.670031i | \(-0.766281\pi\) | ||||
−0.742333 | + | 0.670031i | \(0.766281\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.14867e7 | −0.132525 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.03627e8 | 0.325245 | 0.162623 | − | 0.986688i | \(-0.448005\pi\) | ||||
0.162623 | + | 0.986688i | \(0.448005\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1.88946e7i | − 0.0587850i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.51848e8i | 1.38145i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 5.59603e7i | − 0.169608i | −0.996398 | − | 0.0848039i | \(-0.972974\pi\) | ||||
0.996398 | − | 0.0848039i | \(-0.0270264\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 1.52253e8i | − 0.453535i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.06988e8 | 1.20194 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.95564e8 | 1.14832 | 0.574159 | − | 0.818744i | \(-0.305329\pi\) | ||||
0.574159 | + | 0.818744i | \(0.305329\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.20144e8 | 0.921465 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.70888e6 | 0.0161545 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.41424e7i | 0.208031i | 0.994576 | + | 0.104015i | \(0.0331691\pi\) | ||||
−0.994576 | + | 0.104015i | \(0.966831\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.33570e8i | 1.19616i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.00978e8i | 1.91772i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.26454e8i | 1.41636i | 0.706032 | + | 0.708180i | \(0.250483\pi\) | ||||
−0.706032 | + | 0.708180i | \(0.749517\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.45026e7 | −0.172096 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.45589e7 | −0.0382046 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.60552e8 | 0.678096 | 0.339048 | − | 0.940769i | \(-0.389895\pi\) | ||||
0.339048 | + | 0.940769i | \(0.389895\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.06725e9 | 2.73222 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.52419e8i | − 0.387014i | −0.981099 | − | 0.193507i | \(-0.938014\pi\) | ||||
0.981099 | − | 0.193507i | \(-0.0619861\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.21266e8i | 0.802531i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 7.15919e8i | − 1.77391i | −0.461860 | − | 0.886953i | \(-0.652818\pi\) | ||||
0.461860 | − | 0.886953i | \(-0.347182\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 4.70029e8i | − 1.14593i | −0.819580 | − | 0.572965i | \(-0.805793\pi\) | ||||
0.819580 | − | 0.572965i | \(-0.194207\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.79911e8 | −1.16062 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.24286e7 | 0.124774 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.67972e8 | −0.632659 | −0.316329 | − | 0.948649i | \(-0.602450\pi\) | ||||
−0.316329 | + | 0.948649i | \(0.602450\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.98188e7 | 0.0925225 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1.90775e8i | − 0.439778i | −0.975525 | − | 0.219889i | \(-0.929431\pi\) | ||||
0.975525 | − | 0.219889i | \(-0.0705695\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.63151e8i | 0.370200i | 0.982720 | + | 0.185100i | \(0.0592608\pi\) | ||||
−0.982720 | + | 0.185100i | \(0.940739\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 4.52953e6i | − 0.0101972i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.59623e8i | 1.68350i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.52840e8 | −0.775888 | −0.387944 | − | 0.921683i | \(-0.626815\pi\) | ||||
−0.387944 | + | 0.921683i | \(0.626815\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.92662e8 | 0.417116 | 0.208558 | − | 0.978010i | \(-0.433123\pi\) | ||||
0.208558 | + | 0.978010i | \(0.433123\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.43218e8 | −0.522506 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.16797e8 | 0.670145 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1.19727e9i | − 2.51326i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 4.60533e8i | − 0.952032i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.39654e8i | − 0.286503i | −0.989686 | − | 0.143252i | \(-0.954244\pi\) | ||||
0.989686 | − | 0.143252i | \(-0.0457558\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.13215e7i | 0.103698i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.99146e6 | 0.00800410 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.74248e8 | −0.739239 | −0.369619 | − | 0.929183i | \(-0.620512\pi\) | ||||
−0.369619 | + | 0.929183i | \(0.620512\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.35376e8 | −1.44168 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.53201e8 | −1.26154 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.80177e7i | 0.0920479i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 8.07376e8i | − 1.52486i | −0.647071 | − | 0.762430i | \(-0.724006\pi\) | ||||
0.647071 | − | 0.762430i | \(-0.275994\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.75232e8i | 1.26587i | 0.774204 | + | 0.632937i | \(0.218151\pi\) | ||||
−0.774204 | + | 0.632937i | \(0.781849\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.63217e8i | 0.301503i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.30744e8 | 1.52335 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.61450e8 | −0.833865 | −0.416932 | − | 0.908938i | \(-0.636895\pi\) | ||||
−0.416932 | + | 0.908938i | \(0.636895\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.57228e8 | −0.640835 | −0.320418 | − | 0.947276i | \(-0.603823\pi\) | ||||
−0.320418 | + | 0.947276i | \(0.603823\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.57478e8 | 1.33922 | 0.669612 | − | 0.742711i | \(-0.266460\pi\) | ||||
0.669612 | + | 0.742711i | \(0.266460\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.96526e8i | 0.344950i | 0.985014 | + | 0.172475i | \(0.0551764\pi\) | ||||
−0.985014 | + | 0.172475i | \(0.944824\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.13368e8i | 1.58020i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1.74019e8i | − 0.298907i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.04024e9i | 1.76136i | 0.473711 | + | 0.880680i | \(0.342914\pi\) | ||||
−0.473711 | + | 0.880680i | \(0.657086\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.92040e8 | −0.995321 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.13941e9 | −1.88846 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.69018e7 | 0.126557 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.14447e8 | −1.32152 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 6.97415e8i | − 1.12368i | −0.827244 | − | 0.561842i | \(-0.810093\pi\) | ||||
0.827244 | − | 0.561842i | \(-0.189907\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.24118e8i | 0.832696i | 0.909205 | + | 0.416348i | \(0.136690\pi\) | ||||
−0.909205 | + | 0.416348i | \(0.863310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.07319e8i | 0.169315i | 0.996410 | + | 0.0846575i | \(0.0269796\pi\) | ||||
−0.996410 | + | 0.0846575i | \(0.973020\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.28624e8i | 0.355705i | 0.984057 | + | 0.177852i | \(0.0569150\pi\) | ||||
−0.984057 | + | 0.177852i | \(0.943085\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.00816e7 | 0.123733 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.18601e9 | −1.80730 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.05939e8 | −1.06835 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.51664e7 | −0.112202 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.54337e8i | 0.821818i | 0.911676 | + | 0.410909i | \(0.134789\pi\) | ||||
−0.911676 | + | 0.410909i | \(0.865211\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.17732e9i | 1.72174i | 0.508824 | + | 0.860870i | \(0.330080\pi\) | ||||
−0.508824 | + | 0.860870i | \(0.669920\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.67777e8i | 1.11520i | 0.830109 | + | 0.557600i | \(0.188278\pi\) | ||||
−0.830109 | + | 0.557600i | \(0.811722\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.89440e8i | 0.987929i | 0.869482 | + | 0.493964i | \(0.164453\pi\) | ||||
−0.869482 | + | 0.493964i | \(0.835547\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.59069e7 | −0.108038 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.72412e8 | −0.803811 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.46003e8 | 0.901084 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.64991e7 | 0.0639978 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.24258e8i | 1.12691i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 4.35996e8i | − 0.588216i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.13153e8i | 0.419696i | 0.977734 | + | 0.209848i | \(0.0672969\pi\) | ||||
−0.977734 | + | 0.209848i | \(0.932703\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 7.81208e8i | − 1.03326i | −0.856207 | − | 0.516632i | \(-0.827185\pi\) | ||||
0.856207 | − | 0.516632i | \(-0.172815\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.53924e8 | −1.25343 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.79045e7 | −0.0750939 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.24800e8 | −0.676157 | −0.338078 | − | 0.941118i | \(-0.609777\pi\) | ||||
−0.338078 | + | 0.941118i | \(0.609777\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.63083e9 | 3.34571 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 4.56878e8i | − 0.577264i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 6.73499e8i | − 0.840021i | −0.907519 | − | 0.420010i | \(-0.862026\pi\) | ||||
0.907519 | − | 0.420010i | \(-0.137974\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.10960e8i | 0.881041i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.27872e9i | 1.56437i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.46278e9 | −1.77812 | −0.889060 | − | 0.457790i | \(-0.848641\pi\) | ||||
−0.889060 | + | 0.457790i | \(0.848641\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.46136e9 | 1.75384 | 0.876920 | − | 0.480637i | \(-0.159595\pi\) | ||||
0.876920 | + | 0.480637i | \(0.159595\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.05934e8 | −0.961091 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.23223e8 | −1.08707 | −0.543534 | − | 0.839387i | \(-0.682914\pi\) | ||||
−0.543534 | + | 0.839387i | \(0.682914\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 1.43532e9i | − 1.67939i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.21757e9i | 1.40675i | 0.710820 | + | 0.703374i | \(0.248324\pi\) | ||||
−0.710820 | + | 0.703374i | \(0.751676\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.00827e9i | 1.15762i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 8.45438e6i | − 0.00958575i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.10700e8 | −0.124732 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.71874e8 | 0.191261 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.22852e8 | 0.135863 | 0.0679317 | − | 0.997690i | \(-0.478360\pi\) | ||||
0.0679317 | + | 0.997690i | \(0.478360\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.16709e9 | 1.27481 | 0.637405 | − | 0.770529i | \(-0.280008\pi\) | ||||
0.637405 | + | 0.770529i | \(0.280008\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 6.81253e7i | − 0.0739554i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 3.31100e8i | − 0.355038i | −0.984117 | − | 0.177519i | \(-0.943193\pi\) | ||||
0.984117 | − | 0.177519i | \(-0.0568071\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1.62037e9i | − 1.72689i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.27161e8i | 0.976100i | 0.872816 | + | 0.488050i | \(0.162292\pi\) | ||||
−0.872816 | + | 0.488050i | \(0.837708\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.46700e8 | −0.572058 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.11342e9 | −2.18472 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.96968e8 | 0.613381 | 0.306691 | − | 0.951809i | \(-0.400778\pi\) | ||||
0.306691 | + | 0.951809i | \(0.400778\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.01192e8 | −0.914846 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.50998e9i | − 1.52365i | −0.647782 | − | 0.761826i | \(-0.724303\pi\) | ||||
0.647782 | − | 0.761826i | \(-0.275697\pi\) | |||||||
\(998\) | 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.161.17 | yes | 32 | |
3.2 | odd | 2 | inner | 576.7.h.b.161.15 | yes | 32 | |
4.3 | odd | 2 | inner | 576.7.h.b.161.19 | yes | 32 | |
8.3 | odd | 2 | inner | 576.7.h.b.161.16 | yes | 32 | |
8.5 | even | 2 | inner | 576.7.h.b.161.14 | yes | 32 | |
12.11 | even | 2 | inner | 576.7.h.b.161.13 | ✓ | 32 | |
24.5 | odd | 2 | inner | 576.7.h.b.161.20 | yes | 32 | |
24.11 | even | 2 | inner | 576.7.h.b.161.18 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.7.h.b.161.13 | ✓ | 32 | 12.11 | even | 2 | inner | |
576.7.h.b.161.14 | yes | 32 | 8.5 | even | 2 | inner | |
576.7.h.b.161.15 | yes | 32 | 3.2 | odd | 2 | inner | |
576.7.h.b.161.16 | yes | 32 | 8.3 | odd | 2 | inner | |
576.7.h.b.161.17 | yes | 32 | 1.1 | even | 1 | trivial | |
576.7.h.b.161.18 | yes | 32 | 24.11 | even | 2 | inner | |
576.7.h.b.161.19 | yes | 32 | 4.3 | odd | 2 | inner | |
576.7.h.b.161.20 | yes | 32 | 24.5 | odd | 2 | inner |