Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,9,Mod(127,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.127");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.g (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: | \(78.2166931317\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{8} - 342x^{6} + 43937x^{4} - 2512824x^{2} + 53993104 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{40}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.1 | ||
Root | \(9.62695 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 192.127 |
Dual form | 192.9.g.f.127.5 |
$q$-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 \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(133\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − 46.7654i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −455.790 | −0.729264 | −0.364632 | − | 0.931152i | \(-0.618805\pi\) | ||||
−0.364632 | + | 0.931152i | \(0.618805\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1689.76i | − 0.703775i | −0.936042 | − | 0.351887i | \(-0.885540\pi\) | ||||
0.936042 | − | 0.351887i | \(-0.114460\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2187.00 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6803.31i | 0.464675i | 0.972635 | + | 0.232338i | \(0.0746374\pi\) | ||||
−0.972635 | + | 0.232338i | \(0.925363\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15357.7 | 0.537716 | 0.268858 | − | 0.963180i | \(-0.413354\pi\) | ||||
0.268858 | + | 0.963180i | \(0.413354\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 21315.2i | 0.421041i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −93787.7 | −1.12292 | −0.561462 | − | 0.827503i | \(-0.689761\pi\) | ||||
−0.561462 | + | 0.827503i | \(0.689761\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14546.9i | 0.111623i | 0.998441 | + | 0.0558117i | \(0.0177746\pi\) | ||||
−0.998441 | + | 0.0558117i | \(0.982225\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −79022.4 | −0.406325 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 336401.i | 1.20212i | 0.799205 | + | 0.601058i | \(0.205254\pi\) | ||||
−0.799205 | + | 0.601058i | \(0.794746\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −182880. | −0.468174 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 102276.i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10707.6 | 0.0151391 | 0.00756953 | − | 0.999971i | \(-0.497591\pi\) | ||||
0.00756953 | + | 0.999971i | \(0.497591\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 740903.i | − 0.802259i | −0.916021 | − | 0.401130i | \(-0.868618\pi\) | ||||
0.916021 | − | 0.401130i | \(-0.131382\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 318159. | 0.268280 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 770177.i | 0.513238i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.33541e6 | 0.712540 | 0.356270 | − | 0.934383i | \(-0.384048\pi\) | ||||
0.356270 | + | 0.934383i | \(0.384048\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 718209.i | − 0.310451i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.17759e6 | −1.12451 | −0.562253 | − | 0.826965i | \(-0.690065\pi\) | ||||
−0.562253 | + | 0.826965i | \(0.690065\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00670e6i | 1.17196i | 0.810325 | + | 0.585981i | \(0.199291\pi\) | ||||
−0.810325 | + | 0.585981i | \(0.800709\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 996813. | 0.243088 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 1.57345e6i | − 0.322450i | −0.986918 | − | 0.161225i | \(-0.948456\pi\) | ||||
0.986918 | − | 0.161225i | \(-0.0515445\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.90950e6 | 0.504701 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.38601e6i | 0.648320i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.67006e6 | 0.972065 | 0.486033 | − | 0.873941i | \(-0.338444\pi\) | ||||
0.486033 | + | 0.873941i | \(0.338444\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 3.10088e6i | − 0.338871i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 680289. | 0.0644457 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.53199e7i | 1.26430i | 0.774848 | + | 0.632148i | \(0.217827\pi\) | ||||
−0.774848 | + | 0.632148i | \(0.782173\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.93832e7 | 1.39993 | 0.699965 | − | 0.714178i | \(-0.253199\pi\) | ||||
0.699965 | + | 0.714178i | \(0.253199\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.69551e6i | 0.234592i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.99990e6 | −0.392137 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 1.37063e7i | − 0.680176i | −0.940394 | − | 0.340088i | \(-0.889543\pi\) | ||||
0.940394 | − | 0.340088i | \(-0.110457\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.57319e7 | 0.694042 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 1.95800e7i | − 0.770510i | −0.922810 | − | 0.385255i | \(-0.874113\pi\) | ||||
0.922810 | − | 0.385255i | \(-0.125887\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.69806e7 | −1.30221 | −0.651107 | − | 0.758986i | \(-0.725695\pi\) | ||||
−0.651107 | + | 0.758986i | \(0.725695\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.55247e6i | 0.270300i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.14960e7 | 0.327027 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 6.14961e7i | − 1.57884i | −0.613851 | − | 0.789422i | \(-0.710381\pi\) | ||||
0.613851 | − | 0.789422i | \(-0.289619\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.78297e6 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.79749e7i | 0.378751i | 0.981905 | + | 0.189375i | \(0.0606463\pi\) | ||||
−0.981905 | + | 0.189375i | \(0.939354\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.27475e7 | 0.818908 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 500744.i | − 0.00874055i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.04735e7 | 1.12322 | 0.561611 | − | 0.827401i | \(-0.310182\pi\) | ||||
0.561611 | + | 0.827401i | \(0.310182\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 2.59509e7i | − 0.378431i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.46486e7 | −0.463185 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 6.63031e6i | − 0.0814029i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.04776e8 | 1.18351 | 0.591757 | − | 0.806116i | \(-0.298434\pi\) | ||||
0.591757 | + | 0.806116i | \(0.298434\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 1.48788e7i | − 0.154892i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.62286e7 | 0.540346 | 0.270173 | − | 0.962812i | \(-0.412919\pi\) | ||||
0.270173 | + | 0.962812i | \(0.412919\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.22106e8i | 1.08490i | 0.840090 | + | 0.542448i | \(0.182502\pi\) | ||||
−0.840090 | + | 0.542448i | \(0.817498\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.60176e7 | 0.296318 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.28826e6i | 0.0174570i | 0.999962 | + | 0.00872850i | \(0.00277840\pi\) | ||||
−0.999962 | + | 0.00872850i | \(0.997222\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.50447e8 | 1.06580 | 0.532901 | − | 0.846177i | \(-0.321102\pi\) | ||||
0.532901 | + | 0.846177i | \(0.321102\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 6.24512e7i | − 0.411385i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.57360e8 | 1.57844 | 0.789220 | − | 0.614111i | \(-0.210485\pi\) | ||||
0.789220 | + | 0.614111i | \(0.210485\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1.53328e8i | − 0.876660i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.35873e7 | −0.179239 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.58479e8i | 0.790285i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.68074e8 | 0.784077 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.48601e8i | 0.649234i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.61398e8 | 1.07069 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.20725e8i | 1.23287i | 0.787405 | + | 0.616436i | \(0.211424\pi\) | ||||
−0.787405 | + | 0.616436i | \(0.788576\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.87375e8 | 0.676633 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1.62608e8i | − 0.552149i | −0.961136 | − | 0.276075i | \(-0.910966\pi\) | ||||
0.961136 | − | 0.276075i | \(-0.0890337\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.45808e7 | 0.0785577 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 4.66163e7i | − 0.140347i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.73201e8 | 1.05940 | 0.529700 | − | 0.848185i | \(-0.322304\pi\) | ||||
0.529700 | + | 0.848185i | \(0.322304\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2.91334e8i | − 0.780428i | −0.920724 | − | 0.390214i | \(-0.872401\pi\) | ||||
0.920724 | − | 0.390214i | \(-0.127599\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.35831e7 | −0.186167 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.04483e8i | 0.249864i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.88041e6 | −0.0110404 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 1.36064e8i | − 0.291389i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00711e8 | −1.21877 | −0.609383 | − | 0.792876i | \(-0.708583\pi\) | ||||
−0.609383 | + | 0.792876i | \(0.708583\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.53985e8i | 1.06559i | 0.846244 | + | 0.532795i | \(0.178858\pi\) | ||||
−0.846244 | + | 0.532795i | \(0.821142\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.05114e8 | 0.374308 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.37696e8i | 0.585059i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.83548e8 | 1.61881 | 0.809407 | − | 0.587248i | \(-0.199789\pi\) | ||||
0.809407 | + | 0.587248i | \(0.199789\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 3.58693e8i | − 0.561222i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.68439e8 | 0.846019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 7.01240e6i | − 0.00993382i | −0.999988 | − | 0.00496691i | \(-0.998419\pi\) | ||||
0.999988 | − | 0.00496691i | \(-0.00158102\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.45014e8 | −0.195647 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 1.07398e9i | − 1.38079i | −0.723431 | − | 0.690396i | \(-0.757436\pi\) | ||||
0.723431 | − | 0.690396i | \(-0.242564\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.79871e8 | −0.710861 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 3.18140e7i | − 0.0372078i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.38472e7 | −0.0377867 | −0.0188933 | − | 0.999822i | \(-0.506014\pi\) | ||||
−0.0188933 | + | 0.999822i | \(0.506014\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.09025e8i | 0.329489i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.16442e8 | 0.729942 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.55294e9i | 1.51266i | 0.654188 | + | 0.756332i | \(0.273010\pi\) | ||||
−0.654188 | + | 0.756332i | \(0.726990\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.27084e9 | 1.18407 | 0.592033 | − | 0.805913i | \(-0.298325\pi\) | ||||
0.592033 | + | 0.805913i | \(0.298325\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 9.06462e8i | − 0.808249i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.08669e8 | −0.519630 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 6.38067e8i | − 0.521795i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.72822e8 | 0.135442 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.90488e8i | 0.293409i | 0.989180 | + | 0.146705i | \(0.0468667\pi\) | ||||
−0.989180 | + | 0.146705i | \(0.953133\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.80145e9 | −1.29836 | −0.649178 | − | 0.760637i | \(-0.724887\pi\) | ||||
−0.649178 | + | 0.760637i | \(0.724887\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.27353e8i | 0.226401i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.96764e8 | 0.396221 | 0.198110 | − | 0.980180i | \(-0.436520\pi\) | ||||
0.198110 | + | 0.980180i | \(0.436520\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 4.63439e8i | − 0.295516i | −0.989024 | − | 0.147758i | \(-0.952794\pi\) | ||||
0.989024 | − | 0.147758i | \(-0.0472056\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.40980e8 | −0.392700 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.80933e7i | − 0.0106545i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.44831e9 | 0.820062 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 7.35710e8i | − 0.400705i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.89668e7 | −0.0518686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 3.26587e9i | − 1.64767i | −0.566833 | − | 0.823833i | \(-0.691832\pi\) | ||||
0.566833 | − | 0.823833i | \(-0.308168\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.15664e8 | −0.444854 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 1.82622e9i | − 0.854670i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.25195e9 | −0.564610 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.72941e9i | 0.751834i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.44036e9 | −0.603814 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 8.00369e8i | − 0.323647i | −0.986820 | − | 0.161823i | \(-0.948263\pi\) | ||||
0.986820 | − | 0.161823i | \(-0.0517375\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.99959e8 | 0.156058 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.56089e9i | 1.34108i | 0.741872 | + | 0.670541i | \(0.233938\pi\) | ||||
−0.741872 | + | 0.670541i | \(0.766062\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.50719e9 | −0.548058 | −0.274029 | − | 0.961721i | \(-0.588356\pi\) | ||||
−0.274029 | + | 0.961721i | \(0.588356\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 5.37614e8i | − 0.188809i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.73819e9 | −1.26835 | −0.634173 | − | 0.773191i | \(-0.718659\pi\) | ||||
−0.634173 | + | 0.773191i | \(0.718659\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.17164e8i | 0.235151i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.87589e9 | −0.911546 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.67896e9i | 1.43403i | 0.697058 | + | 0.717014i | \(0.254492\pi\) | ||||
−0.697058 | + | 0.717014i | \(0.745508\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.10707e9 | −1.21748 | −0.608742 | − | 0.793368i | \(-0.708326\pi\) | ||||
−0.608742 | + | 0.793368i | \(0.708326\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 2.23677e8i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.32612e9 | −0.368060 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.23407e8i | 0.0600217i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.40602e8 | 0.218672 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.48115e9i | 0.877057i | 0.898717 | + | 0.438529i | \(0.144500\pi\) | ||||
−0.898717 | + | 0.438529i | \(0.855500\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.28864e9 | −0.558594 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 1.99910e9i | − 0.472796i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.32719e9 | 0.762685 | 0.381342 | − | 0.924434i | \(-0.375462\pi\) | ||||
0.381342 | + | 0.924434i | \(0.375462\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 2.25653e9i | − 0.501468i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.34175e7 | −0.00504636 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.91281e9i | 1.02685i | 0.858135 | + | 0.513425i | \(0.171623\pi\) | ||||
−0.858135 | + | 0.513425i | \(0.828377\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.49594e9 | −0.708892 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 3.29572e9i | − 0.648493i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.37829e9 | −1.40912 | −0.704558 | − | 0.709646i | \(-0.748855\pi\) | ||||
−0.704558 | + | 0.709646i | \(0.748855\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.89984e9i | 0.723052i | 0.932362 | + | 0.361526i | \(0.117744\pi\) | ||||
−0.932362 | + | 0.361526i | \(0.882256\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.21360e9 | −0.218487 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1.24419e9i | − 0.217549i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.38474e9 | −1.59405 | −0.797027 | − | 0.603943i | \(-0.793595\pi\) | ||||
−0.797027 | + | 0.603943i | \(0.793595\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.62036e9i | 0.267420i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.48974e9 | 0.720106 | 0.360053 | − | 0.932932i | \(-0.382759\pi\) | ||||
0.360053 | + | 0.932932i | \(0.382759\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 5.99019e9i | − 0.933888i | −0.884287 | − | 0.466944i | \(-0.845355\pi\) | ||||
0.884287 | − | 0.466944i | \(-0.154645\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.10069e8 | −0.0469980 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.36937e9i | 0.791399i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.82037e9 | 0.260956 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 4.89987e9i | − 0.683302i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.09529e9 | −0.148613 | −0.0743066 | − | 0.997235i | \(-0.523674\pi\) | ||||
−0.0743066 | + | 0.997235i | \(0.523674\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 6.98267e9i | − 0.922006i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.95815e8 | −0.0894268 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.16636e9i | 0.646398i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.77038e9 | 0.824797 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 2.62955e9i | − 0.311969i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.83467e9 | −1.02092 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.16757e10i | − 1.31440i | −0.753714 | − | 0.657202i | \(-0.771740\pi\) | ||||
0.753714 | − | 0.657202i | \(-0.228260\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.71033e9 | 0.626365 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.41321e9i | 0.578647i | 0.957231 | + | 0.289323i | \(0.0934303\pi\) | ||||
−0.957231 | + | 0.289323i | \(0.906570\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.50436e10 | 1.56738 | 0.783691 | − | 0.621151i | \(-0.213335\pi\) | ||||
0.783691 | + | 0.621151i | \(0.213335\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 1.68438e9i | − 0.171079i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.36257e9 | −0.134934 | −0.0674672 | − | 0.997721i | \(-0.521492\pi\) | ||||
−0.0674672 | + | 0.997721i | \(0.521492\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.28470e7i | 0.00703475i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.07011e8 | 0.0100788 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.36432e9i | − 0.125344i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.80863e9 | −0.251745 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 7.03570e9i | − 0.615342i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.65876e9 | −0.226932 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.66087e10i | 1.38364i | 0.722069 | + | 0.691821i | \(0.243191\pi\) | ||||
−0.722069 | + | 0.691821i | \(0.756809\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.92055e9 | −0.237513 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.24720e9i | 0.496028i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.92166e9 | −0.148990 | −0.0744948 | − | 0.997221i | \(-0.523734\pi\) | ||||
−0.0744948 | + | 0.997221i | \(0.523734\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 1.20356e10i | − 0.911313i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.04060e9 | 0.372790 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.46575e10i | − 1.05897i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.17046e9 | −0.506140 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.88173e10i | 1.29789i | 0.760833 | + | 0.648947i | \(0.224791\pi\) | ||||
−0.760833 | + | 0.648947i | \(0.775209\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.56042e10 | −1.05182 | −0.525910 | − | 0.850540i | \(-0.676275\pi\) | ||||
−0.525910 | + | 0.850540i | \(0.676275\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.57072e9i | 0.103484i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.78029e9 | −0.436666 | −0.218333 | − | 0.975874i | \(-0.570062\pi\) | ||||
−0.218333 | + | 0.975874i | \(0.570062\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.92435e9i | 0.561906i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.41133e9 | 0.456271 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.33198e9i | 0.0801900i | 0.999196 | + | 0.0400950i | \(0.0127661\pi\) | ||||
−0.999196 | + | 0.0400950i | \(0.987234\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.67720e10 | 0.987540 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 7.86003e9i | − 0.452687i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.68554e10 | 0.949658 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 1.87117e10i | − 1.03145i | −0.856754 | − | 0.515725i | \(-0.827523\pi\) | ||||
0.856754 | − | 0.515725i | \(-0.172477\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.94938e9 | 0.374835 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1.29606e10i | − 0.684115i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.69388e10 | 0.875081 | 0.437541 | − | 0.899199i | \(-0.355850\pi\) | ||||
0.437541 | + | 0.899199i | \(0.355850\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 1.22244e10i | − 0.618161i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.64444e8 | 0.00814053 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.28410e10i | 1.59169i | 0.605498 | + | 0.795847i | \(0.292974\pi\) | ||||
−0.605498 | + | 0.795847i | \(0.707026\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.49988e10 | 0.711799 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.74844e10i | 1.74203i | 0.491255 | + | 0.871016i | \(0.336538\pi\) | ||||
−0.491255 | + | 0.871016i | \(0.663462\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.23976e9 | −0.238489 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 8.76266e9i | − 0.390654i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.42667e10 | 1.93321 | 0.966604 | − | 0.256274i | \(-0.0824948\pi\) | ||||
0.966604 | + | 0.256274i | \(0.0824948\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 3.15503e10i | − 1.34988i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.60442e9 | −0.318783 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.80293e10i | 1.15139i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.16236e10 | 0.870495 | 0.435248 | − | 0.900311i | \(-0.356661\pi\) | ||||
0.435248 | + | 0.900311i | \(0.356661\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 1.14953e9i | − 0.0453553i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.59819e9 | 0.216506 | 0.108253 | − | 0.994123i | \(-0.465474\pi\) | ||||
0.108253 | + | 0.994123i | \(0.465474\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.13786e10i | − 0.431388i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.18003e9 | −0.0810293 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.08524e9i | 0.331100i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.03559e10 | 0.727440 | 0.363720 | − | 0.931508i | \(-0.381506\pi\) | ||||
0.363720 | + | 0.931508i | \(0.381506\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 1.74529e10i | − 0.611645i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.58871e10 | 0.889780 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 8.19277e9i | − 0.276209i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.36244e10 | −0.450580 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.45043e10i | 1.44393i | 0.691930 | + | 0.721965i | \(0.256761\pi\) | ||||
−0.691930 | + | 0.721965i | \(0.743239\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.02330e9 | −0.191737 | −0.0958685 | − | 0.995394i | \(-0.530563\pi\) | ||||
−0.0958685 | + | 0.995394i | \(0.530563\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.44114e9i | 0.107483i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.71519e10 | 0.525723 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3.27530e10i | − 0.985235i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.88620e9 | 0.144259 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.56553e10i | 1.03327i | 0.856205 | + | 0.516637i | \(0.172816\pi\) | ||||
−0.856205 | + | 0.516637i | \(0.827184\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.62137e10 | 1.31468 | 0.657338 | − | 0.753596i | \(-0.271682\pi\) | ||||
0.657338 | + | 0.753596i | \(0.271682\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.28234e8i | 0.00637417i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.89358e9 | −0.134184 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 3.76751e10i | − 1.01437i | −0.861837 | − | 0.507185i | \(-0.830686\pi\) | ||||
0.861837 | − | 0.507185i | \(-0.169314\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.36308e9 | −0.168234 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.34035e10i | 1.12696i | 0.826128 | + | 0.563482i | \(0.190539\pi\) | ||||
−0.826128 | + | 0.563482i | \(0.809461\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.21211e10 | −0.819126 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.80925e10i | 0.703655i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.97918e10 | 1.22510 | 0.612551 | − | 0.790431i | \(-0.290143\pi\) | ||||
0.612551 | + | 0.790431i | \(0.290143\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 2.16181e10i | − 0.522530i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.59073e10 | 0.615219 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.18282e10i | 0.275976i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.97522e9 | −0.114064 | −0.0570319 | − | 0.998372i | \(-0.518164\pi\) | ||||
−0.0570319 | + | 0.998372i | \(0.518164\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 9.59221e9i | − 0.216107i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.43202e10 | −0.538472 | −0.269236 | − | 0.963074i | \(-0.586771\pi\) | ||||
−0.269236 | + | 0.963074i | \(0.586771\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.95954e10i | 1.07924i | 0.841909 | + | 0.539619i | \(0.181432\pi\) | ||||
−0.841909 | + | 0.539619i | \(0.818568\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.57925e10 | 0.337784 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 8.32165e10i | − 1.74961i | −0.484474 | − | 0.874806i | \(-0.660989\pi\) | ||||
0.484474 | − | 0.874806i | \(-0.339011\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.31604e10 | −0.478691 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 4.59960e10i | − 0.934623i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.72589e10 | −0.544582 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 2.66034e9i | − 0.0522591i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.67744e10 | −0.324022 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.26328e10i | 0.809844i | 0.914351 | + | 0.404922i | \(0.132701\pi\) | ||||
−0.914351 | + | 0.404922i | \(0.867299\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.05089e10 | 0.383144 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 2.65833e10i | − 0.488449i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.77557e10 | −0.863094 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 6.66609e10i | − 1.18510i | −0.805533 | − | 0.592550i | \(-0.798121\pi\) | ||||
0.805533 | − | 0.592550i | \(-0.201879\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.27938e8 | −0.00573530 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.56152e10i | 0.784845i | 0.919785 | + | 0.392422i | \(0.128363\pi\) | ||||
−0.919785 | + | 0.392422i | \(0.871637\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.00424e9 | −0.0170000 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.78163e9i | 0.112957i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.30855e10 | −0.542266 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 4.30599e10i | − 0.694497i | −0.937773 | − | 0.347249i | \(-0.887116\pi\) | ||||
0.937773 | − | 0.347249i | \(-0.112884\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.02249e10 | −0.797201 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 3.00633e10i | − 0.469639i | −0.972039 | − | 0.234819i | \(-0.924550\pi\) | ||||
0.972039 | − | 0.234819i | \(-0.0754499\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.56285e10 | −0.394055 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.71179e10i | 0.410416i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.28086e10 | −0.637763 | −0.318882 | − | 0.947795i | \(-0.603307\pi\) | ||||
−0.318882 | + | 0.947795i | \(0.603307\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.24884e10i | 0.916465i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.48779e9 | −0.0214819 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 5.56547e10i | − 0.791175i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.07047e10 | 0.149835 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.58288e9i | 0.0218162i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.00634e10 | 0.272304 | 0.136152 | − | 0.990688i | \(-0.456526\pi\) | ||||
0.136152 | + | 0.990688i | \(0.456526\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 4.87294e10i | − 0.651304i | −0.945490 | − | 0.325652i | \(-0.894416\pi\) | ||||
0.945490 | − | 0.325652i | \(-0.105584\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.44517e10 | 0.190231 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.94876e10i | 0.900876i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.48549e10 | −0.445083 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 3.35047e10i | − 0.421432i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.88005e10 | −0.604666 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 1.04296e9i | − 0.0127308i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.26238e10 | 0.873337 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.97942e10i | 0.234522i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.88063e10 | 0.803229 | 0.401614 | − | 0.915809i | \(-0.368449\pi\) | ||||
0.401614 | + | 0.915809i | \(0.368449\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 5.94313e10i | − 0.683621i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.85722e10 | −0.777252 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 8.25362e10i | − 0.921924i | −0.887420 | − | 0.460962i | \(-0.847504\pi\) | ||||
0.887420 | − | 0.460962i | \(-0.152496\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.23910e10 | −0.466643 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.55762e8i | 0.00168987i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.03914e11 | −1.11115 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.84646e10i | 0.300008i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.74890e9 | −0.0389478 | −0.0194739 | − | 0.999810i | \(-0.506199\pi\) | ||||
−0.0194739 | + | 0.999810i | \(0.506199\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.15338e10i | 0.630183i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.98394e10 | −0.301258 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.87145e10i | 0.584402i | 0.956357 | + | 0.292201i | \(0.0943876\pi\) | ||||
−0.956357 | + | 0.292201i | \(0.905612\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.17302e11 | −1.15110 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 8.08209e9i | − 0.0781972i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.06599e10 | −0.483299 | −0.241649 | − | 0.970364i | \(-0.577688\pi\) | ||||
−0.241649 | + | 0.970364i | \(0.577688\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.04586e11i | 1.92456i | 0.272067 | + | 0.962278i | \(0.412293\pi\) | ||||
−0.272067 | + | 0.962278i | \(0.587707\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.82613e10 | 0.169400 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 6.15212e10i | − 0.562799i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.83766e10 | −0.526667 | −0.263333 | − | 0.964705i | \(-0.584822\pi\) | ||||
−0.263333 | + | 0.964705i | \(0.584822\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.42456e10i | 0.749606i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.03733e10 | 0.266555 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.21818e10i | 0.451695i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.53088e10 | 0.130712 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.89365e11i | 1.59495i | 0.603349 | + | 0.797477i | \(0.293833\pi\) | ||||
−0.603349 | + | 0.797477i | \(0.706167\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.07778e10 | 0.0895508 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 2.79079e10i | − 0.228758i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.98001e10 | −0.160121 | −0.0800605 | − | 0.996790i | \(-0.525511\pi\) | ||||
−0.0800605 | + | 0.996790i | \(0.525511\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 7.22331e10i | − 0.576327i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.16729e10 | −0.170616 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 2.18765e11i | − 1.69930i | −0.527343 | − | 0.849652i | \(-0.676812\pi\) | ||||
0.527343 | − | 0.849652i | \(-0.323188\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.58060e11 | −1.97798 | −0.988992 | − | 0.147972i | \(-0.952725\pi\) | ||||
−0.988992 | + | 0.147972i | \(0.952725\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.99757e10i | 0.226725i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.66064e10 | −0.571799 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.74343e10i | 0.644061i | 0.946729 | + | 0.322030i | \(0.104365\pi\) | ||||
−0.946729 | + | 0.322030i | \(0.895635\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.46138e8 | −0.00615138 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 2.41646e10i | − 0.173387i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.79871e11 | 1.27385 | 0.636925 | − | 0.770926i | \(-0.280206\pi\) | ||||
0.636925 | + | 0.770926i | \(0.280206\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 6.77309e10i | − 0.473463i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.01331e11 | 0.699202 | 0.349601 | − | 0.936899i | \(-0.386317\pi\) | ||||
0.349601 | + | 0.936899i | \(0.386317\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.04565e11i | 0.712234i | 0.934441 | + | 0.356117i | \(0.115900\pi\) | ||||
−0.934441 | + | 0.356117i | \(0.884100\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.44057e10 | −0.231347 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 1.19084e11i | − 0.790496i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.77050e10 | −0.312639 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.62822e9i | 0.0299464i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.25245e11 | −0.800128 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.38666e11i | 0.874687i | 0.899295 | + | 0.437344i | \(0.144081\pi\) | ||||
−0.899295 | + | 0.437344i | \(0.855919\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.52730e11 | −0.951280 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.46183e11i | − 0.899089i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.46833e10 | 0.271386 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.28214e10i | 0.256837i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.29564e10 | −0.372913 | −0.186457 | − | 0.982463i | \(-0.559700\pi\) | ||||
−0.186457 | + | 0.982463i | \(0.559700\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.36211e11i | − 0.796834i | −0.917204 | − | 0.398417i | \(-0.869560\pi\) | ||||
0.917204 | − | 0.398417i | \(-0.130440\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.54037e10 | −0.493444 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 2.53047e11i | − 1.44405i | −0.691864 | − | 0.722027i | \(-0.743210\pi\) | ||||
0.691864 | − | 0.722027i | \(-0.256790\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.04226e11 | −0.587487 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.85480e10i | 0.325978i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.08800e10 | 0.444824 | 0.222412 | − | 0.974953i | \(-0.428607\pi\) | ||||
0.222412 | + | 0.974953i | \(0.428607\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.41151e10i | 0.402663i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.08765e10 | 0.434071 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 8.97635e10i | − 0.475946i | −0.971272 | − | 0.237973i | \(-0.923517\pi\) | ||||
0.971272 | − | 0.237973i | \(-0.0764830\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.12878e11 | 0.591296 | 0.295648 | − | 0.955297i | \(-0.404464\pi\) | ||||
0.295648 | + | 0.955297i | \(0.404464\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.73592e10i | 0.348612i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.12037e10 | −0.0572893 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.60204e9i | 0.0181989i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.74296e10 | −0.186857 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.31870e11i | 0.650513i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.26871e10 | 0.0618444 | 0.0309222 | − | 0.999522i | \(-0.490156\pi\) | ||||
0.0309222 | + | 0.999522i | \(0.490156\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 1.87043e10i | − 0.0901001i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.20385e11 | 0.573082 | 0.286541 | − | 0.958068i | \(-0.407495\pi\) | ||||
0.286541 | + | 0.958068i | \(0.407495\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 1.77046e11i | − 0.832927i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.66526e11 | 0.774274 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 8.09582e10i | − 0.372030i | −0.982547 | − | 0.186015i | \(-0.940443\pi\) | ||||
0.982547 | − | 0.186015i | \(-0.0595573\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.70101e11 | −0.772583 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.04844e10i | 0.316422i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.17795e11 | 0.522695 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 5.81335e10i | − 0.254985i | −0.991840 | − | 0.127492i | \(-0.959307\pi\) | ||||
0.991840 | − | 0.127492i | \(-0.0406928\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.51417e10 | −0.109009 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.32787e11i | 0.569138i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.98018e11 | 1.26273 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.74818e11i | 0.732280i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.42599e10 | 0.0590531 | 0.0295266 | − | 0.999564i | \(-0.490600\pi\) | ||||
0.0295266 | + | 0.999564i | \(0.490600\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.94261e10i | 0.0795361i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.35384e10 | 0.135765 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 9.50131e10i | − 0.380282i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.59144e11 | 1.42130 | 0.710648 | − | 0.703548i | \(-0.248402\pi\) | ||||
0.710648 | + | 0.703548i | \(0.248402\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.34492e11i | 0.526281i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.49241e11 | 0.964409 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 4.76225e10i | − 0.182217i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.18813e11 | 0.827937 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1.87449e11i | − 0.701404i | −0.936487 | − | 0.350702i | \(-0.885943\pi\) | ||||
0.936487 | − | 0.350702i | \(-0.114057\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.06330e11 | 0.763522 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.92068e11i | 0.702915i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.95821e9 | −0.00708772 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.12950e11i | 0.404341i | 0.979350 | + | 0.202171i | \(0.0647996\pi\) | ||||
−0.979350 | + | 0.202171i | \(0.935200\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.04604e10 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 3.75779e11i | − 1.31602i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.07098e11 | −0.717397 | −0.358699 | − | 0.933453i | \(-0.616779\pi\) | ||||
−0.358699 | + | 0.933453i | \(0.616779\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.20166e10i | 0.212500i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.32483e10 | 0.316061 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.08051e10i | 0.170345i | 0.996366 | + | 0.0851726i | \(0.0271442\pi\) | ||||
−0.996366 | + | 0.0851726i | \(0.972856\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.04477e10 | 0.0346535 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 5.69279e10i | − 0.186797i | −0.995629 | − | 0.0933985i | \(-0.970227\pi\) | ||||
0.995629 | − | 0.0933985i | \(-0.0297731\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.73798e11 | 0.888803 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 3.93111e10i | − 0.126250i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.86661e9 | 0.0122858 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.75630e10i | 0.0866497i | 0.999061 | + | 0.0433248i | \(0.0137950\pi\) | ||||
−0.999061 | + | 0.0433248i | \(0.986205\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.62797e11 | 0.506369 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 2.52501e11i | − 0.777097i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.84625e11 | −0.866743 | −0.433371 | − | 0.901215i | \(-0.642676\pi\) | ||||
−0.433371 | + | 0.901215i | \(0.642676\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.07029e11i | 0.322504i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.24323e11 | 0.967028 | 0.483514 | − | 0.875337i | \(-0.339360\pi\) | ||||
0.483514 | + | 0.875337i | \(0.339360\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 2.54219e11i | − 0.750085i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.34887e10 | −0.272969 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.35279e11i | 0.679833i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.03018e11 | 1.15244 | 0.576221 | − | 0.817294i | \(-0.304527\pi\) | ||||
0.576221 | + | 0.817294i | \(0.304527\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 1.55597e11i | − 0.440336i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.04590e11 | 0.853097 | 0.426548 | − | 0.904465i | \(-0.359729\pi\) | ||||
0.426548 | + | 0.904465i | \(0.359729\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.35497e11i | 0.375597i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.05528e11 | −0.289522 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 4.62239e10i | − 0.125521i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.33209e11 | 0.358037 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.09513e9i | 0.00291352i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.48292e11 | −1.18054 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.85835e11i | 1.52713i | 0.645730 | + | 0.763565i | \(0.276553\pi\) | ||||
−0.645730 | + | 0.763565i | \(0.723447\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.29749e11 | 0.592852 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 4.34878e11i | − 1.11087i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.97682e11 | 0.752765 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.63489e11i | 0.409279i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.31674e11 | −1.06985 | −0.534925 | − | 0.844900i | \(-0.679660\pi\) | ||||
−0.534925 | + | 0.844900i | \(0.679660\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.47570e11i | 0.362086i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.54126e11 | −0.374408 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2.51590e11i | − 0.605107i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.59089e11 | −0.616971 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.45049e11i | 0.813554i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.05205e10 | −0.0245608 | −0.0122804 | − | 0.999925i | \(-0.503909\pi\) | ||||
−0.0122804 | + | 0.999925i | \(0.503909\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.65876e11i | 1.07693i | 0.842648 | + | 0.538464i | \(0.180995\pi\) | ||||
−0.842648 | + | 0.538464i | \(0.819005\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.82377e11 | 0.417454 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.19618e9i | 0.00724438i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.82850e10 | −0.130818 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.67546e10i | 0.126144i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.66593e11 | 1.24709 | 0.623546 | − | 0.781786i | \(-0.285691\pi\) | ||||
0.623546 | + | 0.781786i | \(0.285691\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 4.94664e10i | − 0.107823i | −0.998546 | − | 0.0539114i | \(-0.982831\pi\) | ||||
0.998546 | − | 0.0539114i | \(-0.0171689\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.81851e10 | −0.125602 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 3.83529e11i | − 0.819928i | −0.912102 | − | 0.409964i | \(-0.865541\pi\) | ||||
0.912102 | − | 0.409964i | \(-0.134459\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.61549e11 | 1.18897 | 0.594483 | − | 0.804108i | \(-0.297357\pi\) | ||||
0.594483 | + | 0.804108i | \(0.297357\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.38881e11i | 0.920328i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.72875e11 | −0.566740 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.89507e11i | 1.00696i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.57765e10 | 0.154395 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 2.21865e11i | − 0.447755i | −0.974617 | − | 0.223877i | \(-0.928129\pi\) | ||||
0.974617 | − | 0.223877i | \(-0.0718715\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.00132e11 | −0.999771 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 2.09965e11i | − 0.415753i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.64300e11 | 0.518405 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 2.84005e11i | − 0.551814i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.80134e11 | −0.539181 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.49235e11i | 0.856556i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.73278e11 | −0.516189 | −0.258095 | − | 0.966120i | \(-0.583095\pi\) | ||||
−0.258095 | + | 0.966120i | \(0.583095\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.45005e10i | 0.0271343i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.78664e11 | 0.516605 | 0.258302 | − | 0.966064i | \(-0.416837\pi\) | ||||
0.258302 | + | 0.966064i | \(0.416837\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.77264e11i | 0.509239i | 0.967041 | + | 0.254619i | \(0.0819502\pi\) | ||||
−0.967041 | + | 0.254619i | \(0.918050\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.51101e11 | 0.456915 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 8.42997e11i | − 1.51979i | −0.650047 | − | 0.759894i | \(-0.725251\pi\) | ||||
0.650047 | − | 0.759894i | \(-0.274749\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.54272e10 | 0.0275565 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 8.51302e10i | − 0.150663i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.18377e11 | 0.733650 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 2.10498e11i | − 0.365742i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.29144e11 | −0.394505 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 4.41701e11i | − 0.753522i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.59168e11 | 0.269066 | 0.134533 | − | 0.990909i | \(-0.457047\pi\) | ||||
0.134533 | + | 0.990909i | \(0.457047\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.12215e10i | 0.0858019i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.76086e11 | 0.458290 | 0.229145 | − | 0.973392i | \(-0.426407\pi\) | ||||
0.229145 | + | 0.973392i | \(0.426407\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.01305e11i | 1.15362i | 0.816877 | + | 0.576811i | \(0.195703\pi\) | ||||
−0.816877 | + | 0.576811i | \(0.804297\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.26547e11 | −0.532320 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.11458e11i | 1.14936i | 0.818379 | + | 0.574678i | \(0.194873\pi\) | ||||
−0.818379 | + | 0.574678i | \(0.805127\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.41949e11 | 0.867664 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.25400e10i | 0.0516306i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.28888e10 | 0.0359929 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 7.07814e11i | − 1.10313i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.41607e11 | 0.373198 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 7.93328e9i | − 0.0121455i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.19357e11 | −1.09155 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 3.16619e11i | − 0.476197i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.79236e11 | −0.863497 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.42602e10i | 0.0801774i | 0.999196 | + | 0.0400887i | \(0.0127641\pi\) | ||||
−0.999196 | + | 0.0400887i | \(0.987236\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.22972e11 | −0.180115 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 7.14023e11i | − 1.03667i | −0.855179 | − | 0.518333i | \(-0.826553\pi\) | ||||
0.855179 | − | 0.518333i | \(-0.173447\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.22289e11 | −0.175996 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.13157e11i | 0.589427i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.74769e11 | −0.388589 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.58012e11i | 0.221527i | 0.993847 | + | 0.110764i | \(0.0353296\pi\) | ||||
−0.993847 | + | 0.110764i | \(0.964670\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.46018e11 | −0.758872 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 3.00704e11i | − 0.414316i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.44221e11 | −0.333593 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 2.67046e11i | − 0.361632i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.26528e12 | −1.69873 | −0.849365 | − | 0.527805i | \(-0.823015\pi\) | ||||
−0.849365 | + | 0.527805i | \(0.823015\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.23241e10i | 0.0563364i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.53151e11 | 0.334082 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.90824e11i | 0.380526i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.74824e11 | −0.875452 | −0.437726 | − | 0.899108i | \(-0.644216\pi\) | ||||
−0.437726 | + | 0.899108i | \(0.644216\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 7.03520e11i | − 0.904928i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.19026e11 | −0.406881 | −0.203441 | − | 0.979087i | \(-0.565212\pi\) | ||||
−0.203441 | + | 0.979087i | \(0.565212\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.06894e12i | − 1.35179i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.87706e10 | −0.0987726 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 6.73069e11i | − 0.836873i | −0.908246 | − | 0.418437i | \(-0.862578\pi\) | ||||
0.908246 | − | 0.418437i | \(-0.137422\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.67937e11 | −0.700222 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.37212e10i | 0.0779044i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.41655e11 | −0.656676 | −0.328338 | − | 0.944560i | \(-0.606489\pi\) | ||||
−0.328338 | + | 0.944560i | \(0.606489\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1.77980e11i | − 0.213973i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.40672e9 | 0.00406152 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 6.30621e11i | − 0.745580i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.03953e11 | 0.356380 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 5.00441e9i | − 0.00581900i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.21084e11 | 0.946844 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.61996e12i | 1.85267i | 0.376697 | + | 0.926336i | \(0.377060\pi\) | ||||
−0.376697 | + | 0.926336i | \(0.622940\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.38027e10 | −0.0723676 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.73599e11i | 0.645255i | 0.946526 | + | 0.322627i | \(0.104566\pi\) | ||||
−0.946526 | + | 0.322627i | \(0.895434\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.92286e11 | −0.549245 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.31346e11i | 0.145345i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.32544e11 | 0.145473 | 0.0727366 | − | 0.997351i | \(-0.476827\pi\) | ||||
0.0727366 | + | 0.997351i | \(0.476827\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.79453e11i | 0.521934i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.29027e11 | −0.355268 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.02796e12i | 1.10093i | 0.834857 | + | 0.550466i | \(0.185550\pi\) | ||||
−0.834857 | + | 0.550466i | \(0.814450\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.71999e11 | −0.288950 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.24338e11i | 0.131019i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.34786e12 | −1.40883 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.84738e11i | 0.502588i | 0.967911 | + | 0.251294i | \(0.0808561\pi\) | ||||
−0.967911 | + | 0.251294i | \(0.919144\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.76712e11 | 0.798846 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.11231e11i | 0.215509i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.70160e11 | −0.981890 | −0.490945 | − | 0.871191i | \(-0.663348\pi\) | ||||
−0.490945 | + | 0.871191i | \(0.663348\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.36581e11i | 0.137128i |
(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 | 192.9.g.f.127.1 | 8 | ||
4.3 | odd | 2 | inner | 192.9.g.f.127.5 | 8 | ||
8.3 | odd | 2 | 96.9.g.a.31.4 | ✓ | 8 | ||
8.5 | even | 2 | 96.9.g.a.31.8 | yes | 8 | ||
24.5 | odd | 2 | 288.9.g.f.127.1 | 8 | |||
24.11 | even | 2 | 288.9.g.f.127.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.9.g.a.31.4 | ✓ | 8 | 8.3 | odd | 2 | ||
96.9.g.a.31.8 | yes | 8 | 8.5 | even | 2 | ||
192.9.g.f.127.1 | 8 | 1.1 | even | 1 | trivial | ||
192.9.g.f.127.5 | 8 | 4.3 | odd | 2 | inner | ||
288.9.g.f.127.1 | 8 | 24.5 | odd | 2 | |||
288.9.g.f.127.2 | 8 | 24.11 | even | 2 |