Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [200,10,Mod(49,200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("200.49");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 200 = 2^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 200.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(103.007167233\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 8) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 200.49 |
Dual form | 200.10.c.b.49.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/200\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 60.0000i | − 0.427667i | −0.976870 | − | 0.213833i | \(-0.931405\pi\) | ||||
0.976870 | − | 0.213833i | \(-0.0685950\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4344.00i | 0.683831i | 0.939731 | + | 0.341915i | \(0.111076\pi\) | ||||
−0.939731 | + | 0.341915i | \(0.888924\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 16083.0 | 0.817101 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 93644.0 | 1.92847 | 0.964235 | − | 0.265049i | \(-0.0853881\pi\) | ||||
0.964235 | + | 0.265049i | \(0.0853881\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 12242.0i | − 0.118880i | −0.998232 | − | 0.0594398i | \(-0.981069\pi\) | ||||
0.998232 | − | 0.0594398i | \(-0.0189314\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 319598.i | 0.928077i | 0.885815 | + | 0.464038i | \(0.153600\pi\) | ||||
−0.885815 | + | 0.464038i | \(0.846400\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 553516. | 0.974404 | 0.487202 | − | 0.873289i | \(-0.338018\pi\) | ||||
0.487202 | + | 0.873289i | \(0.338018\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 260640. | 0.292452 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 712936.i | − 0.531221i | −0.964080 | − | 0.265611i | \(-0.914426\pi\) | ||||
0.964080 | − | 0.265611i | \(-0.0855735\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 2.14596e6i | − 0.777114i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.07584e6 | −0.545007 | −0.272504 | − | 0.962155i | \(-0.587852\pi\) | ||||
−0.272504 | + | 0.962155i | \(0.587852\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.42045e6 | −1.24864 | −0.624321 | − | 0.781168i | \(-0.714624\pi\) | ||||
−0.624321 | + | 0.781168i | \(0.714624\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 5.61864e6i | − 0.824743i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.81978e7i | 1.59628i | 0.602470 | + | 0.798142i | \(0.294183\pi\) | ||||
−0.602470 | + | 0.798142i | \(0.705817\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −734520. | −0.0508409 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.03383e6 | 0.499281 | 0.249640 | − | 0.968339i | \(-0.419688\pi\) | ||||
0.249640 | + | 0.968339i | \(0.419688\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.95947e7i | 0.874040i | 0.899452 | + | 0.437020i | \(0.143966\pi\) | ||||
−0.899452 | + | 0.437020i | \(0.856034\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.84842e7i | 0.552535i | 0.961081 | + | 0.276267i | \(0.0890976\pi\) | ||||
−0.961081 | + | 0.276267i | \(0.910902\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.14833e7 | 0.532375 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.91759e7 | 0.396908 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.02558e7i | 0.178536i | 0.996008 | + | 0.0892682i | \(0.0284528\pi\) | ||||
−0.996008 | + | 0.0892682i | \(0.971547\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 3.32110e7i | − 0.416720i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.21667e8 | −1.30719 | −0.653593 | − | 0.756847i | \(-0.726739\pi\) | ||||
−0.653593 | + | 0.756847i | \(0.726739\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.59490e7 | −0.424905 | −0.212452 | − | 0.977171i | \(-0.568145\pi\) | ||||
−0.212452 | + | 0.977171i | \(0.568145\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.98646e7i | 0.558759i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 5.05354e7i | − 0.306379i | −0.988197 | − | 0.153190i | \(-0.951045\pi\) | ||||
0.988197 | − | 0.153190i | \(-0.0489545\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.27762e7 | −0.227186 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.67045e8 | 1.24716 | 0.623579 | − | 0.781760i | \(-0.285678\pi\) | ||||
0.623579 | + | 0.781760i | \(0.285678\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 1.76213e8i | − 0.726250i | −0.931740 | − | 0.363125i | \(-0.881710\pi\) | ||||
0.931740 | − | 0.363125i | \(-0.118290\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.06790e8i | 1.31875i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.69686e8 | 0.778997 | 0.389499 | − | 0.921027i | \(-0.372648\pi\) | ||||
0.389499 | + | 0.921027i | \(0.372648\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.87804e8 | 0.484755 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 2.27033e8i | − 0.525094i | −0.964919 | − | 0.262547i | \(-0.915438\pi\) | ||||
0.964919 | − | 0.262547i | \(-0.0845624\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.24550e8i | 0.233082i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.21416e7 | −0.121880 | −0.0609398 | − | 0.998141i | \(-0.519410\pi\) | ||||
−0.0609398 | + | 0.998141i | \(0.519410\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.31792e7 | 0.0812935 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.85227e8i | 0.534003i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 2.28777e8i | − 0.262385i | −0.991357 | − | 0.131192i | \(-0.958119\pi\) | ||||
0.991357 | − | 0.131192i | \(-0.0418806\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.50608e9 | 1.57575 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.03256e8 | −0.768082 | −0.384041 | − | 0.923316i | \(-0.625468\pi\) | ||||
−0.384041 | + | 0.923316i | \(0.625468\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.81726e8i | 0.684363i | 0.939634 | + | 0.342182i | \(0.111166\pi\) | ||||
−0.939634 | + | 0.342182i | \(0.888834\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.00756e9i | 0.743093i | 0.928414 | + | 0.371546i | \(0.121172\pi\) | ||||
−0.928414 | + | 0.371546i | \(0.878828\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.80692e8 | 0.326173 | 0.163086 | − | 0.986612i | \(-0.447855\pi\) | ||||
0.163086 | + | 0.986612i | \(0.447855\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.09187e9 | 0.682678 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 2.89781e9i | − 1.67193i | −0.548786 | − | 0.835963i | \(-0.684910\pi\) | ||||
0.548786 | − | 0.835963i | \(-0.315090\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 1.96888e8i | − 0.0971366i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.38833e9 | −0.634647 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.41125e9 | 2.71900 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 5.42030e8i | − 0.213526i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.24330e9i | 1.44740i | 0.690117 | + | 0.723698i | \(0.257559\pi\) | ||||
−0.690117 | + | 0.723698i | \(0.742441\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.17568e9 | 0.373798 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.89728e9 | 0.859546 | 0.429773 | − | 0.902937i | \(-0.358594\pi\) | ||||
0.429773 | + | 0.902937i | \(0.358594\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.40447e9i | 0.666327i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.35617e9i | 0.571432i | 0.958314 | + | 0.285716i | \(0.0922314\pi\) | ||||
−0.958314 | + | 0.285716i | \(0.907769\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.71527e9 | 0.616946 | 0.308473 | − | 0.951233i | \(-0.400182\pi\) | ||||
0.308473 | + | 0.951233i | \(0.400182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.10905e9 | 0.236301 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 1.14639e9i | − 0.229256i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 1.28900e9i | − 0.227679i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.67402e9 | −0.278242 | −0.139121 | − | 0.990275i | \(-0.544428\pi\) | ||||
−0.139121 | + | 0.990275i | \(0.544428\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.32709e9 | 0.833860 | 0.416930 | − | 0.908938i | \(-0.363106\pi\) | ||||
0.416930 | + | 0.908938i | \(0.363106\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.14009e9i | 0.758333i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.15835e10i | 1.52156i | 0.649008 | + | 0.760782i | \(0.275184\pi\) | ||||
−0.649008 | + | 0.760782i | \(0.724816\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.15346e8 | 0.0763541 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.09699e9 | 0.363265 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.48418e8i | 0.105234i | 0.998615 | + | 0.0526169i | \(0.0167562\pi\) | ||||
−0.998615 | + | 0.0526169i | \(0.983244\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.44718e10i | 1.43978i | 0.694087 | + | 0.719891i | \(0.255808\pi\) | ||||
−0.694087 | + | 0.719891i | \(0.744192\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.04546e10 | 0.985868 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.90220e9 | 0.796186 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.39886e10i | − 1.18732i | −0.804717 | − | 0.593658i | \(-0.797683\pi\) | ||||
0.804717 | − | 0.593658i | \(-0.202317\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.29999e9i | 0.559040i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.54924e9 | 0.331207 | 0.165604 | − | 0.986192i | \(-0.447043\pi\) | ||||
0.165604 | + | 0.986192i | \(0.447043\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.56484e10 | 1.08372 | 0.541859 | − | 0.840469i | \(-0.317721\pi\) | ||||
0.541859 | + | 0.840469i | \(0.317721\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.75694e9i | 0.181718i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.99284e10i | 1.78977i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.32205e9 | 0.531414 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.02052e10 | 1.09853 | 0.549267 | − | 0.835647i | \(-0.314907\pi\) | ||||
0.549267 | + | 0.835647i | \(0.314907\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 7.10827e9i | − 0.368770i | −0.982854 | − | 0.184385i | \(-0.940971\pi\) | ||||
0.982854 | − | 0.184385i | \(-0.0590294\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 2.25924e10i | − 1.06872i | −0.845257 | − | 0.534359i | \(-0.820553\pi\) | ||||
0.845257 | − | 0.534359i | \(-0.179447\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.55506e10 | −1.60697 | −0.803485 | − | 0.595325i | \(-0.797023\pi\) | ||||
−0.803485 | + | 0.595325i | \(0.797023\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.03213e9 | −0.131028 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 9.01744e9i | − 0.372693i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 1.14661e10i | − 0.434061i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.18335e10 | 1.87911 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.58480e9 | −0.193971 | −0.0969854 | − | 0.995286i | \(-0.530920\pi\) | ||||
−0.0969854 | + | 0.995286i | \(0.530920\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.60227e10i | − 0.533368i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 2.78904e10i | − 0.853859i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.05728e10 | −0.310593 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.91252e9 | 0.110329 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.74713e10i | 1.28546i | 0.766092 | + | 0.642731i | \(0.222199\pi\) | ||||
−0.766092 | + | 0.642731i | \(0.777801\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.37702e10i | 0.844146i | 0.906562 | + | 0.422073i | \(0.138697\pi\) | ||||
−0.906562 | + | 0.422073i | \(0.861303\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.28989e9 | −0.175171 | −0.0875854 | − | 0.996157i | \(-0.527915\pi\) | ||||
−0.0875854 | + | 0.996157i | \(0.527915\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.44074e10 | 0.563984 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.79739e10i | 1.51092i | 0.655197 | + | 0.755458i | \(0.272586\pi\) | ||||
−0.655197 | + | 0.755458i | \(0.727414\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.61811e10i | − 0.333151i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.11283e10 | 0.617114 | 0.308557 | − | 0.951206i | \(-0.400154\pi\) | ||||
0.308557 | + | 0.951206i | \(0.400154\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.42372e10 | 0.271861 | 0.135931 | − | 0.990718i | \(-0.456598\pi\) | ||||
0.135931 | + | 0.990718i | \(0.456598\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 5.35072e10i | − 0.984428i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 6.77614e9i | − 0.115837i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.36220e10 | −0.224565 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.78389e10 | −0.919789 | −0.459894 | − | 0.887974i | \(-0.652113\pi\) | ||||
−0.459894 | + | 0.887974i | \(0.652113\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 6.67622e10i | − 1.02444i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.87176e10i | 0.267641i | 0.991006 | + | 0.133820i | \(0.0427245\pi\) | ||||
−0.991006 | + | 0.133820i | \(0.957276\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.90510e10 | −1.09159 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.33857e10 | −0.445326 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 2.80437e10i | − 0.361439i | −0.983535 | − | 0.180719i | \(-0.942157\pi\) | ||||
0.983535 | − | 0.180719i | \(-0.0578426\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.32850e9i | 0.0521238i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.46600e10 | 0.520036 | 0.260018 | − | 0.965604i | \(-0.416271\pi\) | ||||
0.260018 | + | 0.965604i | \(0.416271\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.03375e11 | −1.16427 | −0.582137 | − | 0.813090i | \(-0.697783\pi\) | ||||
−0.582137 | + | 0.813090i | \(0.697783\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 3.19075e9i | − 0.0347665i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.81403e11i | − 1.85133i | −0.378341 | − | 0.925666i | \(-0.623505\pi\) | ||||
0.378341 | − | 0.925666i | \(-0.376495\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.03260e11 | −1.02027 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.25487e11 | −1.20066 | −0.600332 | − | 0.799751i | \(-0.704965\pi\) | ||||
−0.600332 | + | 0.799751i | \(0.704965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.33561e11i | 1.23777i | 0.785481 | + | 0.618886i | \(0.212416\pi\) | ||||
−0.785481 | + | 0.618886i | \(0.787584\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.92430e10i | 0.341423i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.64450e10 | 0.138673 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.37266e10 | −0.112213 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 3.50635e9i | − 0.0277940i | −0.999903 | − | 0.0138970i | \(-0.995576\pi\) | ||||
0.999903 | − | 0.0138970i | \(-0.00442369\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 2.00956e11i | − 1.49864i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.72776e9 | −0.0631513 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.51195e10 | −0.597695 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.81954e10i | 0.328483i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.94357e11i | 1.89126i | 0.325246 | + | 0.945629i | \(0.394553\pi\) | ||||
−0.325246 | + | 0.945629i | \(0.605447\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.69035e10 | 0.292680 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.40305e10 | 0.145660 | 0.0728301 | − | 0.997344i | \(-0.476797\pi\) | ||||
0.0728301 | + | 0.997344i | \(0.476797\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 2.55229e11i | − 1.50308i | −0.659689 | − | 0.751539i | \(-0.729312\pi\) | ||||
0.659689 | − | 0.751539i | \(-0.270688\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2.30255e11i | − 1.28069i | −0.768089 | − | 0.640343i | \(-0.778792\pi\) | ||||
0.768089 | − | 0.640343i | \(-0.221208\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.94390e11 | −1.05103 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.04535e10 | 0.317796 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.76903e11i | 0.904322i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 2.88415e10i | − 0.139493i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.02953e10 | −0.377840 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.21212e11 | −0.555035 | −0.277518 | − | 0.960721i | \(-0.589512\pi\) | ||||
−0.277518 | + | 0.960721i | \(0.589512\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.92674e11i | 1.30432i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 2.52249e11i | − 1.06536i | −0.846318 | − | 0.532678i | \(-0.821186\pi\) | ||||
0.846318 | − | 0.532678i | \(-0.178814\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.73869e11 | −0.715027 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.01236e11 | −2.40797 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.68619e11i | 1.04789i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 2.99996e11i | − 1.11079i | −0.831585 | − | 0.555397i | \(-0.812566\pi\) | ||||
0.831585 | − | 0.555397i | \(-0.187434\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.25625e11 | 0.453275 | 0.226638 | − | 0.973979i | \(-0.427227\pi\) | ||||
0.226638 | + | 0.973979i | \(0.427227\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.62708e10 | −0.0923830 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 4.31672e11i | − 1.47968i | −0.672782 | − | 0.739841i | \(-0.734901\pi\) | ||||
0.672782 | − | 0.739841i | \(-0.265099\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.33000e10i | 0.271418i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.83615e11 | −0.583421 | −0.291711 | − | 0.956507i | \(-0.594224\pi\) | ||||
−0.291711 | + | 0.956507i | \(0.594224\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.63077e10 | −0.0505372 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 3.84675e11i | − 1.16282i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 3.77185e11i | − 1.08532i | −0.839953 | − | 0.542659i | \(-0.817418\pi\) | ||||
0.839953 | − | 0.542659i | \(-0.182582\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.45291e11 | 0.407963 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.45510e10 | −0.122089 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.69400e11i | 0.720623i | 0.932832 | + | 0.360312i | \(0.117330\pi\) | ||||
−0.932832 | + | 0.360312i | \(0.882670\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.54124e10i | 0.0647903i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.04102e11 | 0.508124 | 0.254062 | − | 0.967188i | \(-0.418233\pi\) | ||||
0.254062 | + | 0.967188i | \(0.418233\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.54598e11 | 0.619003 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 4.10631e10i | − 0.0975117i | −0.998811 | − | 0.0487559i | \(-0.984474\pi\) | ||||
0.998811 | − | 0.0487559i | \(-0.0155256\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.15142e11i | 0.714179i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.86342e11 | 0.634032 | 0.317016 | − | 0.948420i | \(-0.397319\pi\) | ||||
0.317016 | + | 0.948420i | \(0.397319\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.27853e11 | 0.493014 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 1.73837e11i | − 0.367599i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 3.73016e11i | − 0.753651i | −0.926284 | − | 0.376826i | \(-0.877016\pi\) | ||||
0.926284 | − | 0.376826i | \(-0.122984\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.44268e11 | 0.284966 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.70676e11 | 0.909018 | 0.454509 | − | 0.890742i | \(-0.349815\pi\) | ||||
0.454509 | + | 0.890742i | \(0.349815\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.85991e10i | 0.148438i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.70411e12i | 3.07838i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.60520e11 | 1.52057 | 0.760284 | − | 0.649590i | \(-0.225060\pi\) | ||||
0.760284 | + | 0.649590i | \(0.225060\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.41370e11 | 0.244382 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 5.28520e11i | − 0.893894i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 1.62916e11i | − 0.263847i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.46565e11 | −1.34183 | −0.670914 | − | 0.741535i | \(-0.734098\pi\) | ||||
−0.670914 | + | 0.741535i | \(0.734098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.27835e11 | −0.353468 | −0.176734 | − | 0.984259i | \(-0.556553\pi\) | ||||
−0.176734 | + | 0.984259i | \(0.556553\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.97281e11i | 0.451477i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.99602e11i | − 0.290563i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.87834e10 | −0.0980451 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.47351e11 | −0.903633 | −0.451817 | − | 0.892111i | \(-0.649224\pi\) | ||||
−0.451817 | + | 0.892111i | \(0.649224\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.69898e11i | 0.779114i | 0.921002 | + | 0.389557i | \(0.127372\pi\) | ||||
−0.921002 | + | 0.389557i | \(0.872628\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3.94621e11i | − 0.517624i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.98042e11 | −0.768496 | −0.384248 | − | 0.923230i | \(-0.625539\pi\) | ||||
−0.384248 | + | 0.923230i | \(0.625539\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.45515e11 | 0.435005 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.10867e11i | 0.383494i | 0.981444 | + | 0.191747i | \(0.0614152\pi\) | ||||
−0.981444 | + | 0.191747i | \(0.938585\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.00441e11i | 0.118995i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.47114e11 | −0.867517 | −0.433759 | − | 0.901029i | \(-0.642813\pi\) | ||||
−0.433759 | + | 0.901029i | \(0.642813\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.45964e11 | 0.962848 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 3.19625e11i | − 0.356615i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.54275e12i | 1.65452i | 0.561819 | + | 0.827260i | \(0.310102\pi\) | ||||
−0.561819 | + | 0.827260i | \(0.689898\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.85845e11 | 0.721221 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.62766e12 | 1.67846 | 0.839230 | − | 0.543777i | \(-0.183006\pi\) | ||||
0.839230 | + | 0.543777i | \(0.183006\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 1.11591e12i | − 1.12854i | −0.825592 | − | 0.564268i | \(-0.809158\pi\) | ||||
0.825592 | − | 0.564268i | \(-0.190842\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.30194e11i | 0.515832i | 0.966167 | + | 0.257916i | \(0.0830358\pi\) | ||||
−0.966167 | + | 0.257916i | \(0.916964\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.19526e11 | 0.209512 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.95008e11 | 0.650722 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.83493e12i | 1.68556i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.64943e11i | 0.145882i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.10019e12 | 1.82284 | 0.911422 | − | 0.411473i | \(-0.134986\pi\) | ||||
0.911422 | + | 0.411473i | \(0.134986\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.22777e11 | 0.189766 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.85820e11i | − 0.155357i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.05307e12i | 0.848351i | 0.905580 | + | 0.424176i | \(0.139436\pi\) | ||||
−0.905580 | + | 0.424176i | \(0.860564\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.69051e10 | 0.0450050 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.10556e12 | 1.63494 | 0.817470 | − | 0.575971i | \(-0.195376\pi\) | ||||
0.817470 | + | 0.575971i | \(0.195376\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 6.63434e11i | − 0.505809i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.16004e12i | 0.852845i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.88807e11 | −0.208523 | −0.104262 | − | 0.994550i | \(-0.533248\pi\) | ||||
−0.104262 | + | 0.994550i | \(0.533248\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.68305e11 | 0.615747 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.17681e11i | 0.360584i | 0.983613 | + | 0.180292i | \(0.0577042\pi\) | ||||
−0.983613 | + | 0.180292i | \(0.942296\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 6.27278e11i | − 0.421623i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.01747e11 | −0.397360 | −0.198680 | − | 0.980064i | \(-0.563665\pi\) | ||||
−0.198680 | + | 0.980064i | \(0.563665\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.65471e11 | 0.496632 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 1.18782e12i | − 0.757223i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.73093e12i | 1.06555i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.39316e11 | −0.507776 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.67285e11 | −0.0994691 | −0.0497345 | − | 0.998762i | \(-0.515838\pi\) | ||||
−0.0497345 | + | 0.998762i | \(0.515838\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.57966e12i | − 0.923222i | −0.887083 | − | 0.461611i | \(-0.847272\pi\) | ||||
0.887083 | − | 0.461611i | \(-0.152728\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 2.05196e12i | − 1.15884i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.29287e12 | 0.717804 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.95676e12 | −1.06810 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.10592e11i | − 0.0593543i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 2.72954e11i | − 0.141646i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.01178e12 | 1.02667 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.08736e12 | −1.54953 | −0.774765 | − | 0.632250i | \(-0.782132\pi\) | ||||
−0.774765 | + | 0.632250i | \(0.782132\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 9.38904e11i | − 0.463470i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 2.62136e11i | − 0.125194i | −0.998039 | − | 0.0625969i | \(-0.980062\pi\) | ||||
0.998039 | − | 0.0625969i | \(-0.0199383\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.38997e11 | −0.347190 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.14901e12 | −0.531057 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.17151e12i | 0.532702i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 3.64238e11i | − 0.160338i | −0.996781 | − | 0.0801691i | \(-0.974454\pi\) | ||||
0.996781 | − | 0.0801691i | \(-0.0255460\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.39879e11 | 0.103906 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.79571e12 | 0.765425 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.04052e12i | 1.27544i | 0.770267 | + | 0.637721i | \(0.220123\pi\) | ||||
−0.770267 | + | 0.637721i | \(0.779877\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.15821e11i | 0.331491i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.35845e11 | 0.294294 | 0.147147 | − | 0.989115i | \(-0.452991\pi\) | ||||
0.147147 | + | 0.989115i | \(0.452991\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.44618e12 | 0.569324 | 0.284662 | − | 0.958628i | \(-0.408119\pi\) | ||||
0.284662 | + | 0.958628i | \(0.408119\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 1.21231e12i | − 0.469806i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.26945e12i | 0.852371i | 0.904636 | + | 0.426186i | \(0.140143\pi\) | ||||
−0.904636 | + | 0.426186i | \(0.859857\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.26496e11 | −0.157711 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.86229e11 | 0.359075 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.60391e11i | 0.344302i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 3.41977e12i | − 1.18885i | −0.804153 | − | 0.594423i | \(-0.797381\pi\) | ||||
0.804153 | − | 0.594423i | \(-0.202619\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.55382e12 | −1.21668 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.35554e12 | −0.457056 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 1.32482e12i | − 0.439959i | −0.975505 | − | 0.219979i | \(-0.929401\pi\) | ||||
0.975505 | − | 0.219979i | \(-0.0705990\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.13303e12i | 0.687248i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.19936e12 | 1.33279 | 0.666395 | − | 0.745599i | \(-0.267836\pi\) | ||||
0.666395 | + | 0.745599i | \(0.267836\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.05682e12 | 0.330418 | 0.165209 | − | 0.986259i | \(-0.447170\pi\) | ||||
0.165209 | + | 0.986259i | \(0.447170\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 8.12761e11i | − 0.250343i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 5.97096e12i | − 1.78523i | −0.450816 | − | 0.892617i | \(-0.648867\pi\) | ||||
0.450816 | − | 0.892617i | \(-0.351133\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.41046e11 | −0.159388 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.26283e11 | 0.0656851 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.80650e12i | 0.802774i | 0.915909 | + | 0.401387i | \(0.131472\pi\) | ||||
−0.915909 | + | 0.401387i | \(0.868528\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 1.48302e12i | − 0.411968i | −0.978555 | − | 0.205984i | \(-0.933961\pi\) | ||||
0.978555 | − | 0.205984i | \(-0.0660394\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.53469e12 | −0.420158 | −0.210079 | − | 0.977684i | \(-0.567372\pi\) | ||||
−0.210079 | + | 0.977684i | \(0.567372\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.52993e12 | −0.412819 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 3.13383e11i | − 0.0833450i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 3.11001e12i | − 0.803632i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.81597e12 | −1.48147 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.43498e12 | −1.11368 | −0.556839 | − | 0.830620i | \(-0.687986\pi\) | ||||
−0.556839 | + | 0.830620i | \(0.687986\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.35088e11i | 0.0829549i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 2.62998e11i | − 0.0632886i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.29488e12 | 1.01905 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.56257e12 | −1.06745 | −0.533725 | − | 0.845658i | \(-0.679208\pi\) | ||||
−0.533725 | + | 0.845658i | \(0.679208\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 3.32818e12i | − 0.767818i | −0.923371 | − | 0.383909i | \(-0.874578\pi\) | ||||
0.923371 | − | 0.383909i | \(-0.125422\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 2.31374e12i | − 0.519093i | −0.965731 | − | 0.259547i | \(-0.916427\pi\) | ||||
0.965731 | − | 0.259547i | \(-0.0835731\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.13933e13 | −2.52087 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.67343e12 | −0.365167 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.03697e12i | 1.51453i | 0.653110 | + | 0.757263i | \(0.273464\pi\) | ||||
−0.653110 | + | 0.757263i | \(0.726536\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 2.83404e12i | − 0.593419i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.20320e12 | −0.455060 | −0.227530 | − | 0.973771i | \(-0.573065\pi\) | ||||
−0.227530 | + | 0.973771i | \(0.573065\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.29570e12 | −1.48648 | −0.743242 | − | 0.669022i | \(-0.766713\pi\) | ||||
−0.743242 | + | 0.669022i | \(0.766713\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 2.34751e11i | − 0.0471842i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.47994e12i | 0.289519i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.84828e12 | 0.549749 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.30284e12 | −0.819416 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 4.47079e12i | − 0.840073i | −0.907507 | − | 0.420036i | \(-0.862017\pi\) | ||||
0.907507 | − | 0.420036i | \(-0.137983\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.42095e12i | 0.625890i | 0.949771 | + | 0.312945i | \(0.101316\pi\) | ||||
−0.949771 | + | 0.312945i | \(0.898684\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.93805e11 | 0.179427 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.02621e12 | 0.361013 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 9.18730e12i | − 1.61546i | −0.589556 | − | 0.807728i | \(-0.700697\pi\) | ||||
0.589556 | − | 0.807728i | \(-0.299303\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.37394e11i | 0.0749147i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.25551e11 | 0.0212243 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.88811e12 | −0.315047 | −0.157524 | − | 0.987515i | \(-0.550351\pi\) | ||||
−0.157524 | + | 0.987515i | \(0.550351\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.54240e12i | 1.07755i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.88720e12i | 0.463371i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.07843e12 | 0.646169 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.61907e12 | 0.253242 | 0.126621 | − | 0.991951i | \(-0.459587\pi\) | ||||
0.126621 | + | 0.991951i | \(0.459587\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.00727e13i | 1.55542i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 3.48934e12i | − 0.525238i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.06375e13 | 1.58099 | 0.790497 | − | 0.612466i | \(-0.209822\pi\) | ||||
0.790497 | + | 0.612466i | \(0.209822\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.33735e12 | 0.636520 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.57737e12i | 0.663305i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1.86770e12i | − 0.263919i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.32770e13 | −1.85276 | −0.926380 | − | 0.376589i | \(-0.877097\pi\) | ||||
−0.926380 | + | 0.376589i | \(0.877097\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.39582e12 | −0.467989 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 8.54230e11i | − 0.116266i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 2.60017e12i | − 0.345221i | −0.984990 | − | 0.172611i | \(-0.944780\pi\) | ||||
0.984990 | − | 0.172611i | \(-0.0552202\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.86117e11 | 0.0637481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.26244e12 | −0.811176 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.14818e13i | − 1.46906i | −0.678574 | − | 0.734532i | \(-0.737402\pi\) | ||||
0.678574 | − | 0.734532i | \(-0.262598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 4.73234e12i | − 0.590843i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.75984e12 | 0.957090 | 0.478545 | − | 0.878063i | \(-0.341164\pi\) | ||||
0.478545 | + | 0.878063i | \(0.341164\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.06569e11 | −0.0495395 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 2.58115e12i | − 0.310717i | −0.987858 | − | 0.155358i | \(-0.950347\pi\) | ||||
0.987858 | − | 0.155358i | \(-0.0496532\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 3.65136e12i | − 0.429055i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.37683e12 | −0.508150 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.39208e12 | −0.962697 | −0.481349 | − | 0.876529i | \(-0.659853\pi\) | ||||
−0.481349 | + | 0.876529i | \(0.659853\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.47033e12i | 0.393363i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 8.15875e12i | − 0.903009i | −0.892269 | − | 0.451505i | \(-0.850887\pi\) | ||||
0.892269 | − | 0.451505i | \(-0.149113\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.00573e12 | −0.438121 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.27433e12 | −0.678167 | −0.339083 | − | 0.940756i | \(-0.610117\pi\) | ||||
−0.339083 | + | 0.940756i | \(0.610117\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.08813e12i | 0.223047i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.48944e12i | 0.155398i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.12027e12 | −0.631106 | −0.315553 | − | 0.948908i | \(-0.602190\pi\) | ||||
−0.315553 | + | 0.948908i | \(0.602190\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.12306e12 | 0.114461 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 6.62875e12i | − 0.667765i | −0.942615 | − | 0.333883i | \(-0.891641\pi\) | ||||
0.942615 | − | 0.333883i | \(-0.108359\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.74306e12i | 0.466836i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.00037e12 | 0.486501 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.50071e13 | 2.40511 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.45467e12i | 0.423533i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.19503e13i | − 1.11043i | −0.831706 | − | 0.555216i | \(-0.812636\pi\) | ||||
0.831706 | − | 0.555216i | \(-0.187364\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.68262e12 | −0.154575 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.25881e13 | 1.14331 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.62507e11i | 0.0505125i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.18887e13i | 1.04369i | 0.853041 | + | 0.521844i | \(0.174756\pi\) | ||||
−0.853041 | + | 0.521844i | \(0.825244\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.90751e12 | −0.512795 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.16025e12 | −0.0995879 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.65013e13i | − 1.40055i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 2.67960e12i | − 0.222402i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.68063e13 | 1.37944 | 0.689722 | − | 0.724074i | \(-0.257733\pi\) | ||||
0.689722 | + | 0.724074i | \(0.257733\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.98473e13 | 1.61104 | 0.805521 | − | 0.592567i | \(-0.201886\pi\) | ||||
0.805521 | + | 0.592567i | \(0.201886\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.20252e12i | 0.497922i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.08460e13i | 0.851668i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.55282e11 | 0.0664250 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.83992e12 | 0.371787 | 0.185893 | − | 0.982570i | \(-0.440482\pi\) | ||||
0.185893 | + | 0.982570i | \(0.440482\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.41664e12i | 0.639499i | 0.947502 | + | 0.319749i | \(0.103599\pi\) | ||||
−0.947502 | + | 0.319749i | \(0.896401\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.16658e13i | 1.61064i | 0.592839 | + | 0.805321i | \(0.298007\pi\) | ||||
−0.592839 | + | 0.805321i | \(0.701993\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.67734e12 | 0.270420 | 0.135210 | − | 0.990817i | \(-0.456829\pi\) | ||||
0.135210 | + | 0.990817i | \(0.456829\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.08842e13 | −0.791754 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.86601e12i | 0.494085i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.37780e13i | 0.970337i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.46942e13 | 1.02381 | 0.511903 | − | 0.859043i | \(-0.328941\pi\) | ||||
0.511903 | + | 0.859043i | \(0.328941\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.01980e13 | −0.702967 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.52924e12i | 0.513484i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.78505e13i | 1.85933i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.01366e12 | 0.529354 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.29738e13 | 0.847979 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1.99845e13i | − 1.29248i | −0.763136 | − | 0.646238i | \(-0.776341\pi\) | ||||
0.763136 | − | 0.646238i | \(-0.223659\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 2.11989e13i | − 1.34245i | −0.741252 | − | 0.671226i | \(-0.765768\pi\) | ||||
0.741252 | − | 0.671226i | \(-0.234232\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.51809e13 | −1.57798 | −0.788992 | − | 0.614404i | \(-0.789397\pi\) | ||||
−0.788992 | + | 0.614404i | \(0.789397\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.35458e12 | 0.146016 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.15905e13i | 1.32500i | 0.749064 | + | 0.662498i | \(0.230504\pi\) | ||||
−0.749064 | + | 0.662498i | \(0.769496\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 9.86700e11i | − 0.0593061i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.52544e13 | 1.50227 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.18655e11 | −0.0364222 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 3.67941e12i | − 0.214395i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 2.63182e13i | − 1.50230i | −0.660129 | − | 0.751152i | \(-0.729498\pi\) | ||||
0.660129 | − | 0.751152i | \(-0.270502\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.10381e11 | −0.0118866 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.23513e12 | 0.236851 | 0.118425 | − | 0.992963i | \(-0.462215\pi\) | ||||
0.118425 | + | 0.992963i | \(0.462215\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.56557e13i | − 1.42024i | −0.704081 | − | 0.710119i | \(-0.748641\pi\) | ||||
0.704081 | − | 0.710119i | \(-0.251359\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.14044e13i | 1.70347i | 0.523973 | + | 0.851735i | \(0.324449\pi\) | ||||
−0.523973 | + | 0.851735i | \(0.675551\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.84329e13 | −0.989774 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.75867e13 | 0.934836 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.02313e13i | 0.538392i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.23666e11i | 0.0270077i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.33278e13 | 0.680519 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.27772e12 | −0.165695 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.10717e12i | 0.255615i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.87001e13i | 1.89880i | 0.314070 | + | 0.949400i | \(0.398307\pi\) | ||||
−0.314070 | + | 0.949400i | \(0.601693\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.29188e13 | −0.627601 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.73436e13 | 0.834269 | 0.417135 | − | 0.908845i | \(-0.363034\pi\) | ||||
0.417135 | + | 0.908845i | \(0.363034\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 2.12602e13i | − 1.01263i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.25858e13i | 0.587784i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.75232e12 | 0.0810387 | 0.0405194 | − | 0.999179i | \(-0.487099\pi\) | ||||
0.0405194 | + | 0.999179i | \(0.487099\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.76614e13 | 0.808829 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 3.26916e12i | − 0.148262i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.25725e13i | 0.559194i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.99977e13 | 0.880865 | 0.440432 | − | 0.897786i | \(-0.354825\pi\) | ||||
0.440432 | + | 0.897786i | \(0.354825\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.18913e13 | 0.518749 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1.44183e12i | − 0.0622940i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 4.62137e12i | − 0.195859i | −0.995193 | − | 0.0979293i | \(-0.968778\pi\) | ||||
0.995193 | − | 0.0979293i | \(-0.0312219\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.53138e13 | −0.642816 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.64959e13 | 0.685838 | 0.342919 | − | 0.939365i | \(-0.388584\pi\) | ||||
0.342919 | + | 0.939365i | \(0.388584\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 6.44055e12i | − 0.265228i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.99606e13i | − 0.806490i | −0.915092 | − | 0.403245i | \(-0.867882\pi\) | ||||
0.915092 | − | 0.403245i | \(-0.132118\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.15720e12 | −0.0863363 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.38153e13 | −0.547707 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 8.83087e12i | − 0.346805i | −0.984851 | − | 0.173402i | \(-0.944524\pi\) | ||||
0.984851 | − | 0.173402i | \(-0.0554761\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.16634e13i | 0.449491i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.02352e13 | −0.390763 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.47825e13 | 0.559105 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.62046e13i | 0.607182i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 2.03562e13i | − 0.748647i | −0.927298 | − | 0.374323i | \(-0.877875\pi\) | ||||
0.927298 | − | 0.374323i | \(-0.122125\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.06142e13 | 0.386748 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.66888e12 | 0.276851 | 0.138425 | − | 0.990373i | \(-0.455796\pi\) | ||||
0.138425 | + | 0.990373i | \(0.455796\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.17951e13i | 0.421886i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 6.23017e12i | − 0.218763i | −0.994000 | − | 0.109382i | \(-0.965113\pi\) | ||||
0.994000 | − | 0.109382i | \(-0.0348871\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.75563e12 | −0.235041 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.73097e12 | 0.266516 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.22800e13i | 1.78585i | 0.450207 | + | 0.892924i | \(0.351350\pi\) | ||||
−0.450207 | + | 0.892924i | \(0.648650\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.81772e12i | 0.161590i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.39698e13 | 0.464308 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.73672e13 | −1.23072 | −0.615359 | − | 0.788247i | \(-0.710989\pi\) | ||||
−0.615359 | + | 0.788247i | \(0.710989\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.27273e12i | 0.237370i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 3.66230e13i | − 1.17389i | −0.809628 | − | 0.586943i | \(-0.800331\pi\) | ||||
0.809628 | − | 0.586943i | \(-0.199669\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.90517e13 | 1.24049 |
(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 | 200.10.c.b.49.1 | 2 | ||
4.3 | odd | 2 | 400.10.c.g.49.2 | 2 | |||
5.2 | odd | 4 | 8.10.a.a.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 200.10.a.b.1.1 | 1 | |||
5.4 | even | 2 | inner | 200.10.c.b.49.2 | 2 | ||
15.2 | even | 4 | 72.10.a.e.1.1 | 1 | |||
20.3 | even | 4 | 400.10.a.d.1.1 | 1 | |||
20.7 | even | 4 | 16.10.a.c.1.1 | 1 | |||
20.19 | odd | 2 | 400.10.c.g.49.1 | 2 | |||
35.27 | even | 4 | 392.10.a.b.1.1 | 1 | |||
40.27 | even | 4 | 64.10.a.d.1.1 | 1 | |||
40.37 | odd | 4 | 64.10.a.f.1.1 | 1 | |||
60.47 | odd | 4 | 144.10.a.n.1.1 | 1 | |||
80.27 | even | 4 | 256.10.b.c.129.1 | 2 | |||
80.37 | odd | 4 | 256.10.b.i.129.2 | 2 | |||
80.67 | even | 4 | 256.10.b.c.129.2 | 2 | |||
80.77 | odd | 4 | 256.10.b.i.129.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.10.a.a.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
16.10.a.c.1.1 | 1 | 20.7 | even | 4 | |||
64.10.a.d.1.1 | 1 | 40.27 | even | 4 | |||
64.10.a.f.1.1 | 1 | 40.37 | odd | 4 | |||
72.10.a.e.1.1 | 1 | 15.2 | even | 4 | |||
144.10.a.n.1.1 | 1 | 60.47 | odd | 4 | |||
200.10.a.b.1.1 | 1 | 5.3 | odd | 4 | |||
200.10.c.b.49.1 | 2 | 1.1 | even | 1 | trivial | ||
200.10.c.b.49.2 | 2 | 5.4 | even | 2 | inner | ||
256.10.b.c.129.1 | 2 | 80.27 | even | 4 | |||
256.10.b.c.129.2 | 2 | 80.67 | even | 4 | |||
256.10.b.i.129.1 | 2 | 80.77 | odd | 4 | |||
256.10.b.i.129.2 | 2 | 80.37 | odd | 4 | |||
392.10.a.b.1.1 | 1 | 35.27 | even | 4 | |||
400.10.a.d.1.1 | 1 | 20.3 | even | 4 | |||
400.10.c.g.49.1 | 2 | 20.19 | odd | 2 | |||
400.10.c.g.49.2 | 2 | 4.3 | odd | 2 |