Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,8,Mod(1,192)]
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([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.a (trivial) |
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: | yes |
Analytic conductor: | \(59.9779248930\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{46}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 46 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 96) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-6.78233\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 192.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −423.552 | −1.51535 | −0.757673 | − | 0.652635i | \(-0.773664\pi\) | ||||
−0.757673 | + | 0.652635i | \(0.773664\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1228.66 | −1.35390 | −0.676951 | − | 0.736028i | \(-0.736699\pi\) | ||||
−0.676951 | + | 0.736028i | \(0.736699\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2781.31 | 0.630050 | 0.315025 | − | 0.949083i | \(-0.397987\pi\) | ||||
0.315025 | + | 0.949083i | \(0.397987\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3729.10 | −0.470763 | −0.235382 | − | 0.971903i | \(-0.575634\pi\) | ||||
−0.235382 | + | 0.971903i | \(0.575634\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −11435.9 | −0.874885 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −11630.2 | −0.574138 | −0.287069 | − | 0.957910i | \(-0.592681\pi\) | ||||
−0.287069 | + | 0.957910i | \(0.592681\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −45178.2 | −1.51109 | −0.755546 | − | 0.655096i | \(-0.772628\pi\) | ||||
−0.755546 | + | 0.655096i | \(0.772628\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −33173.7 | −0.781675 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −27729.3 | −0.475217 | −0.237608 | − | 0.971361i | \(-0.576363\pi\) | ||||
−0.237608 | + | 0.971361i | \(0.576363\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 101271. | 1.29627 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 210915. | 1.60589 | 0.802943 | − | 0.596056i | \(-0.203266\pi\) | ||||
0.802943 | + | 0.596056i | \(0.203266\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −172577. | −1.04044 | −0.520221 | − | 0.854031i | \(-0.674151\pi\) | ||||
−0.520221 | + | 0.854031i | \(0.674151\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 75095.4 | 0.363760 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 520399. | 2.05163 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 269522. | 0.874757 | 0.437379 | − | 0.899277i | \(-0.355907\pi\) | ||||
0.437379 | + | 0.899277i | \(0.355907\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −100686. | −0.271795 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −379673. | −0.860332 | −0.430166 | − | 0.902750i | \(-0.641545\pi\) | ||||
−0.430166 | + | 0.902750i | \(0.641545\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.03330e6 | 1.98192 | 0.990960 | − | 0.134154i | \(-0.0428318\pi\) | ||||
0.990960 | + | 0.134154i | \(0.0428318\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −308769. | −0.505115 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 624148. | 0.876890 | 0.438445 | − | 0.898758i | \(-0.355529\pi\) | ||||
0.438445 | + | 0.898758i | \(0.355529\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 686051. | 0.833049 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −314016. | −0.331479 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.84130e6 | −1.69886 | −0.849431 | − | 0.527699i | \(-0.823055\pi\) | ||||
−0.849431 | + | 0.527699i | \(0.823055\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.17803e6 | −0.954744 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.21981e6 | −0.872429 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.74738e6 | 1.74155 | 0.870776 | − | 0.491679i | \(-0.163617\pi\) | ||||
0.870776 | + | 0.491679i | \(0.163617\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.70188e6 | 1.52409 | 0.762046 | − | 0.647523i | \(-0.224195\pi\) | ||||
0.762046 | + | 0.647523i | \(0.224195\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −895690. | −0.451300 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.57947e6 | 0.713369 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 989057. | 0.401753 | 0.200877 | − | 0.979617i | \(-0.435621\pi\) | ||||
0.200877 | + | 0.979617i | \(0.435621\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −748691. | −0.274366 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.30668e6 | −1.09645 | −0.548224 | − | 0.836331i | \(-0.684696\pi\) | ||||
−0.548224 | + | 0.836331i | \(0.684696\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.10275e6 | −0.331779 | −0.165889 | − | 0.986144i | \(-0.553049\pi\) | ||||
−0.165889 | + | 0.986144i | \(0.553049\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.73432e6 | 0.748402 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.41727e6 | −0.853026 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.02881e6 | 1.83213 | 0.916065 | − | 0.401031i | \(-0.131348\pi\) | ||||
0.916065 | + | 0.401031i | \(0.131348\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.55645e6 | −0.682722 | −0.341361 | − | 0.939932i | \(-0.610888\pi\) | ||||
−0.341361 | + | 0.939932i | \(0.610888\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.92600e6 | 0.870018 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.69471e6 | 0.927159 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.21527e6 | −0.784172 | −0.392086 | − | 0.919928i | \(-0.628247\pi\) | ||||
−0.392086 | + | 0.919928i | \(0.628247\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.58178e6 | 0.637367 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.65959e6 | −0.600700 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.91353e7 | 2.28983 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.07452e6 | −0.787038 | −0.393519 | − | 0.919316i | \(-0.628743\pi\) | ||||
−0.393519 | + | 0.919316i | \(0.628743\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.02758e6 | 0.210017 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.27236e6 | 0.605768 | 0.302884 | − | 0.953027i | \(-0.402051\pi\) | ||||
0.302884 | + | 0.953027i | \(0.402051\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.22232e7 | 1.10219 | 0.551093 | − | 0.834444i | \(-0.314211\pi\) | ||||
0.551093 | + | 0.834444i | \(0.314211\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.40508e7 | 1.18451 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.74065e6 | 0.689764 | 0.344882 | − | 0.938646i | \(-0.387919\pi\) | ||||
0.344882 | + | 0.938646i | \(0.387919\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.57044e6 | −0.412000 | −0.206000 | − | 0.978552i | \(-0.566045\pi\) | ||||
−0.206000 | + | 0.978552i | \(0.566045\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.27708e6 | 0.505041 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.25206e7 | 0.816302 | 0.408151 | − | 0.912914i | \(-0.366174\pi\) | ||||
0.408151 | + | 0.912914i | \(0.366174\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.17448e7 | 0.720117 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.71852e6 | −0.156921 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.42895e7 | 0.777327 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.17515e7 | −0.603037 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.02512e7 | −0.496713 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.80360e6 | −0.448953 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.60536e7 | 0.695438 | 0.347719 | − | 0.937599i | \(-0.386956\pi\) | ||||
0.347719 | + | 0.937599i | \(0.386956\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.78991e7 | 1.14426 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.53592e7 | −0.596923 | −0.298462 | − | 0.954422i | \(-0.596474\pi\) | ||||
−0.298462 | + | 0.954422i | \(0.596474\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.55084e7 | 2.04587 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.33677e6 | −0.291628 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.09949e7 | 0.697576 | 0.348788 | − | 0.937202i | \(-0.386593\pi\) | ||||
0.348788 | + | 0.937202i | \(0.386593\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.99151e7 | −1.26062 | −0.630312 | − | 0.776342i | \(-0.717073\pi\) | ||||
−0.630312 | + | 0.776342i | \(0.717073\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.68520e7 | 0.506273 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.03718e7 | −0.296605 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.93335e7 | −2.43347 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.85234e7 | 0.480961 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.79531e7 | −1.43524 | −0.717621 | − | 0.696434i | \(-0.754769\pi\) | ||||
−0.717621 | + | 0.696434i | \(0.754769\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.00182e7 | −0.236793 | −0.118397 | − | 0.992966i | \(-0.537775\pi\) | ||||
−0.118397 | + | 0.992966i | \(0.537775\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.47843e6 | −0.191379 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.30955e7 | 1.57663 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.88494e7 | −0.388732 | −0.194366 | − | 0.980929i | \(-0.562265\pi\) | ||||
−0.194366 | + | 0.980929i | \(0.562265\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.97150e7 | −0.980839 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.40698e7 | 0.643396 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.98770e7 | 1.44466 | 0.722329 | − | 0.691550i | \(-0.243072\pi\) | ||||
0.722329 | + | 0.691550i | \(0.243072\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.18068e7 | −0.551221 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.20039e7 | −0.365587 | −0.182794 | − | 0.983151i | \(-0.558514\pi\) | ||||
−0.182794 | + | 0.983151i | \(0.558514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.88423e7 | −0.778382 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.29349e7 | −0.503697 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.83727e7 | −1.00397 | −0.501986 | − | 0.864876i | \(-0.667397\pi\) | ||||
−0.501986 | + | 0.864876i | \(0.667397\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.24427e8 | −1.75502 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.41793e7 | 1.00549 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.95976e7 | 0.776682 | 0.388341 | − | 0.921516i | \(-0.373048\pi\) | ||||
0.388341 | + | 0.921516i | \(0.373048\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.51283e8 | 1.89634 | 0.948168 | − | 0.317769i | \(-0.102934\pi\) | ||||
0.948168 | + | 0.317769i | \(0.102934\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.29507e7 | 0.879935 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.14156e8 | −1.32556 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.23472e7 | −0.361736 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.41836e7 | −0.260558 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.66555e6 | 0.0899869 | 0.0449935 | − | 0.998987i | \(-0.485673\pi\) | ||||
0.0449935 | + | 0.998987i | \(0.485673\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.51312e8 | 1.51504 | 0.757520 | − | 0.652812i | \(-0.226411\pi\) | ||||
0.757520 | + | 0.652812i | \(0.226411\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.26457e7 | 0.411864 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.77091e7 | −0.910549 | −0.455274 | − | 0.890351i | \(-0.650459\pi\) | ||||
−0.455274 | + | 0.890351i | \(0.650459\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.19522e7 | −0.287419 | −0.143709 | − | 0.989620i | \(-0.545903\pi\) | ||||
−0.143709 | + | 0.989620i | \(0.545903\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.67045e7 | 0.231952 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.59142e8 | −2.17421 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.60811e8 | 1.30370 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.02147e7 | −0.158406 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.25654e8 | −0.952064 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.47789e7 | −0.254875 | −0.127437 | − | 0.991847i | \(-0.540675\pi\) | ||||
−0.127437 | + | 0.991847i | \(0.540675\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.92804e7 | −0.633035 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.37656e8 | −3.00329 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.12038e8 | 1.40866 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.97743e7 | −0.191552 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.33703e7 | 0.270283 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.06077e7 | −0.124441 | −0.0622204 | − | 0.998062i | \(-0.519818\pi\) | ||||
−0.0622204 | + | 0.998062i | \(0.519818\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.38267e7 | 0.432090 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.38134e8 | −1.35124 | −0.675619 | − | 0.737251i | \(-0.736123\pi\) | ||||
−0.675619 | + | 0.737251i | \(0.736123\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.34105e7 | 0.293902 | 0.146951 | − | 0.989144i | \(-0.453054\pi\) | ||||
0.146951 | + | 0.989144i | \(0.453054\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.22664e7 | −0.492495 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.32484e8 | −1.20406 | −0.602028 | − | 0.798475i | \(-0.705640\pi\) | ||||
−0.602028 | + | 0.798475i | \(0.705640\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.64359e8 | −1.32879 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.16778e8 | 1.05778 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.35251e8 | 1.11465 | 0.557326 | − | 0.830294i | \(-0.311827\pi\) | ||||
0.557326 | + | 0.830294i | \(0.311827\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.44508e8 | −1.58540 | −0.792701 | − | 0.609610i | \(-0.791326\pi\) | ||||
−0.792701 | + | 0.609610i | \(0.791326\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.90578e8 | −1.26236 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.68474e8 | 0.711367 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.60242e7 | −0.394170 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.57037e7 | −0.142513 | −0.0712567 | − | 0.997458i | \(-0.522701\pi\) | ||||
−0.0712567 | + | 0.997458i | \(0.522701\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.71238e7 | −0.299410 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.33002e8 | 0.502305 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.77388e8 | 0.651866 | 0.325933 | − | 0.945393i | \(-0.394322\pi\) | ||||
0.325933 | + | 0.945393i | \(0.394322\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.31149e8 | −1.18433 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.53757e8 | 0.535295 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.51237e8 | 0.851604 | 0.425802 | − | 0.904816i | \(-0.359992\pi\) | ||||
0.425802 | + | 0.904816i | \(0.359992\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.79885e8 | 2.57436 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.40812e8 | −0.452742 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.42878e8 | −1.07400 | −0.537002 | − | 0.843581i | \(-0.680443\pi\) | ||||
−0.537002 | + | 0.843581i | \(0.680443\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.49518e8 | 1.37200 | 0.686000 | − | 0.727601i | \(-0.259365\pi\) | ||||
0.686000 | + | 0.727601i | \(0.259365\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.23708e8 | 0.367984 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.81667e8 | 0.816716 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.29030e8 | 0.647461 | 0.323730 | − | 0.946149i | \(-0.395063\pi\) | ||||
0.323730 | + | 0.946149i | \(0.395063\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.25809e8 | −0.346814 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.49209e8 | −0.401165 | −0.200582 | − | 0.979677i | \(-0.564283\pi\) | ||||
−0.200582 | + | 0.979677i | \(0.564283\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.05047e8 | 1.06231 | 0.531157 | − | 0.847273i | \(-0.321757\pi\) | ||||
0.531157 | + | 0.847273i | \(0.321757\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.16653e8 | 1.32203 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.66487e8 | 1.16480 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.75077e8 | −0.670365 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.91012e8 | −0.454397 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.59019e7 | −0.129834 | −0.0649172 | − | 0.997891i | \(-0.520678\pi\) | ||||
−0.0649172 | + | 0.997891i | \(0.520678\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.16366e9 | −2.63905 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.47445e7 | 0.121253 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.03405e8 | 0.223715 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.26957e9 | −2.68333 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.69354e8 | 0.349740 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.14439e9 | −2.30953 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.13287e8 | 1.40695 | 0.703477 | − | 0.710718i | \(-0.251630\pi\) | ||||
0.703477 | + | 0.710718i | \(0.251630\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.30027e8 | 0.636347 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.32785e8 | −0.438827 | −0.219414 | − | 0.975632i | \(-0.570414\pi\) | ||||
−0.219414 | + | 0.975632i | \(0.570414\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.35376e8 | 0.249538 | 0.124769 | − | 0.992186i | \(-0.460181\pi\) | ||||
0.124769 | + | 0.992186i | \(0.460181\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.79371e8 | 0.683876 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.29613e8 | 0.933794 | 0.466897 | − | 0.884312i | \(-0.345372\pi\) | ||||
0.466897 | + | 0.884312i | \(0.345372\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.86621e8 | 1.01179 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.35997e8 | 0.398235 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.25432e8 | 0.867576 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.77651e8 | −0.610237 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.50402e8 | −0.237868 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.66863e8 | −1.18722 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.24935e8 | −1.40189 | −0.700944 | − | 0.713217i | \(-0.747238\pi\) | ||||
−0.700944 | + | 0.713217i | \(0.747238\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.96481e8 | 0.291586 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.18917e8 | −0.608795 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.02943e9 | 1.46518 | 0.732592 | − | 0.680668i | \(-0.238311\pi\) | ||||
0.732592 | + | 0.680668i | \(0.238311\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.38057e8 | 0.471292 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.79992e8 | −0.655531 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.68930e8 | 0.226036 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.17110e8 | 0.415760 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.00011e8 | 0.385464 | 0.192732 | − | 0.981251i | \(-0.438265\pi\) | ||||
0.192732 | + | 0.981251i | \(0.438265\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.43096e8 | 0.683893 | 0.341946 | − | 0.939719i | \(-0.388914\pi\) | ||||
0.341946 | + | 0.939719i | \(0.388914\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.33999e7 | −0.0905985 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.10616e8 | −0.375849 | −0.187924 | − | 0.982184i | \(-0.560176\pi\) | ||||
−0.187924 | + | 0.982184i | \(0.560176\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.40055e9 | 1.66150 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.85817e8 | 0.448790 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.00225e8 | 0.228395 | 0.114198 | − | 0.993458i | \(-0.463570\pi\) | ||||
0.114198 | + | 0.993458i | \(0.463570\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.14719e9 | 1.28340 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.17290e8 | −0.348163 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.67073e8 | 0.502759 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.09899e8 | 0.749662 | 0.374831 | − | 0.927093i | \(-0.377701\pi\) | ||||
0.374831 | + | 0.927093i | \(0.377701\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.76782e8 | −0.286777 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.26232e9 | 2.30009 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.90313e8 | −0.189883 | −0.0949416 | − | 0.995483i | \(-0.530266\pi\) | ||||
−0.0949416 | + | 0.995483i | \(0.530266\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.64697e8 | −0.259203 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.86525e8 | −0.755993 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.52757e9 | 1.44133 | 0.720665 | − | 0.693284i | \(-0.243837\pi\) | ||||
0.720665 | + | 0.693284i | \(0.243837\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.33446e8 | 0.401511 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.22576e8 | −0.384334 | −0.192167 | − | 0.981362i | \(-0.561552\pi\) | ||||
−0.192167 | + | 0.981362i | \(0.561552\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.44739e9 | 1.29263 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.53275e8 | 0.660640 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.37610e8 | −0.721470 | −0.360735 | − | 0.932668i | \(-0.617474\pi\) | ||||
−0.360735 | + | 0.932668i | \(0.617474\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.22498e8 | 0.272840 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.14698e8 | −0.344634 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.40062e9 | −2.77631 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.46607e9 | 1.17595 | 0.587973 | − | 0.808881i | \(-0.299926\pi\) | ||||
0.587973 | + | 0.808881i | \(0.299926\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.49873e9 | 1.18118 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.61531e9 | 1.25098 | 0.625489 | − | 0.780233i | \(-0.284899\pi\) | ||||
0.625489 | + | 0.780233i | \(0.284899\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.43559e8 | 0.489802 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.25093e8 | −0.168372 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.49623e8 | 0.551141 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.00624e9 | −0.727230 | −0.363615 | − | 0.931549i | \(-0.618458\pi\) | ||||
−0.363615 | + | 0.931549i | \(0.618458\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.66862e8 | 0.402746 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.37558e9 | −2.35789 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.50634e9 | 1.03456 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.07771e9 | −0.727822 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.49577e8 | 0.232164 | 0.116082 | − | 0.993240i | \(-0.462967\pi\) | ||||
0.116082 | + | 0.993240i | \(0.462967\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.71712e8 | 0.504043 | 0.252022 | − | 0.967722i | \(-0.418905\pi\) | ||||
0.252022 | + | 0.967722i | \(0.418905\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.55004e8 | 0.292297 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.17781e9 | −0.744239 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.31968e9 | −2.06347 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.80039e8 | −0.171245 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.24587e9 | 1.35118 | 0.675592 | − | 0.737276i | \(-0.263888\pi\) | ||||
0.675592 | + | 0.737276i | \(0.263888\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.16044e8 | −0.0686937 | −0.0343468 | − | 0.999410i | \(-0.510935\pi\) | ||||
−0.0343468 | + | 0.999410i | \(0.510935\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.41200e9 | −1.40497 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.25276e9 | 0.718096 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.46503e9 | −1.39058 | −0.695290 | − | 0.718729i | \(-0.744724\pi\) | ||||
−0.695290 | + | 0.718729i | \(0.744724\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.00131e8 | 0.277683 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.71781e9 | −1.48527 | −0.742635 | − | 0.669696i | \(-0.766424\pi\) | ||||
−0.742635 | + | 0.669696i | \(0.766424\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.20894e9 | 1.18829 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.56474e9 | −0.828637 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.31427e9 | −1.72793 | −0.863964 | − | 0.503553i | \(-0.832026\pi\) | ||||
−0.863964 | + | 0.503553i | \(0.832026\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.05599e9 | −0.542052 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.70491e8 | −0.136713 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.94062e9 | −0.965831 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.13520e9 | −0.556374 | −0.278187 | − | 0.960527i | \(-0.589733\pi\) | ||||
−0.278187 | + | 0.960527i | \(0.589733\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.28918e8 | −0.110493 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.89698e9 | −0.901799 | −0.450900 | − | 0.892575i | \(-0.648897\pi\) | ||||
−0.450900 | + | 0.892575i | \(0.648897\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.13818e9 | −0.532940 | −0.266470 | − | 0.963843i | \(-0.585857\pi\) | ||||
−0.266470 | + | 0.963843i | \(0.585857\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.97358e9 | 0.910268 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.10626e9 | 0.956978 | 0.478489 | − | 0.878094i | \(-0.341185\pi\) | ||||
0.478489 | + | 0.878094i | \(0.341185\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.21521e9 | −0.543935 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.08935e8 | −0.224434 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.87393e9 | 1.24871 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.57524e9 | −1.95878 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.34231e9 | −0.566288 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.63874e8 | 0.0681295 | 0.0340648 | − | 0.999420i | \(-0.489155\pi\) | ||||
0.0340648 | + | 0.999420i | \(0.489155\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.00507e9 | −0.411804 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.19884e8 | 0.371465 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.99643e9 | 1.19263 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.01594e8 | 0.157556 | 0.0787781 | − | 0.996892i | \(-0.474898\pi\) | ||||
0.0787781 | + | 0.996892i | \(0.474898\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.15668e9 | 0.834073 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.05766e9 | 0.784490 | 0.392245 | − | 0.919861i | \(-0.371699\pi\) | ||||
0.392245 | + | 0.919861i | \(0.371699\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.45299e9 | −0.922001 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.58783e8 | −0.318248 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.06277e9 | 1.48448 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.05327e8 | −0.290148 | −0.145074 | − | 0.989421i | \(-0.546342\pi\) | ||||
−0.145074 | + | 0.989421i | \(0.546342\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.94104e8 | −0.211072 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.32490e9 | −0.464189 | −0.232094 | − | 0.972693i | \(-0.574558\pi\) | ||||
−0.232094 | + | 0.972693i | \(0.574558\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.65667e9 | −0.917948 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.31874e9 | −0.449399 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.83357e9 | 0.952406 | 0.476203 | − | 0.879335i | \(-0.342013\pi\) | ||||
0.476203 | + | 0.879335i | \(0.342013\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.35490e9 | 0.449195 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.89242e8 | −0.290810 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.17716e9 | −1.67019 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.73595e9 | 0.552485 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.84606e9 | −0.579643 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.08648e8 | −0.0336580 | −0.0168290 | − | 0.999858i | \(-0.505357\pi\) | ||||
−0.0168290 | + | 0.999858i | \(0.505357\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.09356e9 | 1.55692 | 0.778458 | − | 0.627696i | \(-0.216002\pi\) | ||||
0.778458 | + | 0.627696i | \(0.216002\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.35954e9 | −1.01326 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.00711e9 | 0.597358 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.63591e9 | −0.774169 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.00284e9 | 0.580518 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.41584e9 | 0.405013 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.70212e9 | −1.04523 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.60914e9 | 0.448418 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.90812e9 | 0.524862 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.98616e9 | 1.08234 | 0.541171 | − | 0.840913i | \(-0.317981\pi\) | ||||
0.541171 | + | 0.840913i | \(0.317981\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.08464e9 | 1.09485 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.35937e9 | 0.624322 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.49694e9 | 1.17479 | 0.587397 | − | 0.809299i | \(-0.300153\pi\) | ||||
0.587397 | + | 0.809299i | \(0.300153\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.96967e9 | 0.508031 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.52876e9 | −2.42664 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.86464e9 | −2.48052 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.08222e9 | −0.765312 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.10617e9 | −1.49719 | −0.748593 | − | 0.663030i | \(-0.769270\pi\) | ||||
−0.748593 | + | 0.663030i | \(0.769270\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.85328e9 | −0.933016 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.73376e8 | −0.208848 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.38158e9 | −0.326284 | −0.163142 | − | 0.986603i | \(-0.552163\pi\) | ||||
−0.163142 | + | 0.986603i | \(0.552163\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.30313e9 | −1.23698 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.52958e8 | −0.150433 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.73612e9 | 1.98804 | 0.994021 | − | 0.109188i | \(-0.0348251\pi\) | ||||
0.994021 | + | 0.109188i | \(0.0348251\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.33535e9 | 0.300170 | 0.150085 | − | 0.988673i | \(-0.452045\pi\) | ||||
0.150085 | + | 0.988673i | \(0.452045\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.33970e8 | 0.0519540 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.80818e9 | −0.616009 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.50143e8 | 0.119223 | 0.0596115 | − | 0.998222i | \(-0.481014\pi\) | ||||
0.0596115 | + | 0.998222i | \(0.481014\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.08544e9 | 0.874709 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.36966e9 | 0.924338 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.12122e9 | −1.07037 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.15143e9 | 0.237790 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.96942e9 | 0.810017 | 0.405008 | − | 0.914313i | \(-0.367269\pi\) | ||||
0.405008 | + | 0.914313i | \(0.367269\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.79673e9 | 1.57220 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.63815e9 | −0.525706 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.66508e9 | 0.524830 | 0.262415 | − | 0.964955i | \(-0.415481\pi\) | ||||
0.262415 | + | 0.964955i | \(0.415481\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.05236e9 | −1.17792 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.62709e8 | −0.165941 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.20668e7 | −0.00229403 | −0.00114701 | − | 0.999999i | \(-0.500365\pi\) | ||||
−0.00114701 | + | 0.999999i | \(0.500365\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.12678e9 | 0.211728 | 0.105864 | − | 0.994381i | \(-0.466239\pi\) | ||||
0.105864 | + | 0.994381i | \(0.466239\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.21023e8 | 0.133918 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.97736e9 | 0.913809 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.33232e9 | 0.604765 | 0.302382 | − | 0.953187i | \(-0.402218\pi\) | ||||
0.302382 | + | 0.953187i | \(0.402218\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.99684e9 | −1.25528 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.32751e9 | −0.412808 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.28653e9 | −0.751612 | −0.375806 | − | 0.926698i | \(-0.622634\pi\) | ||||
−0.375806 | + | 0.926698i | \(0.622634\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.34190e9 | 0.752692 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.82726e9 | 0.655978 | 0.327989 | − | 0.944681i | \(-0.393629\pi\) | ||||
0.327989 | + | 0.944681i | \(0.393629\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.89529e9 | −0.321187 | −0.160594 | − | 0.987021i | \(-0.551341\pi\) | ||||
−0.160594 | + | 0.987021i | \(0.551341\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.45796e8 | −0.0914555 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.40777e9 | 1.06169 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.75948e9 | −0.615953 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.39267e9 | −0.549674 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.13459e9 | −0.502232 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.20090e10 | 1.90285 | 0.951424 | − | 0.307882i | \(-0.0996203\pi\) | ||||
0.951424 | + | 0.307882i | \(0.0996203\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.39029e8 | −0.147152 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.79951e9 | −1.05383 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.55836e9 | −0.392169 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.41057e9 | −0.365483 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.33728e9 | 0.500484 | 0.250242 | − | 0.968183i | \(-0.419490\pi\) | ||||
0.250242 | + | 0.968183i | \(0.419490\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.80682e9 | 1.15807 | 0.579037 | − | 0.815302i | \(-0.303429\pi\) | ||||
0.579037 | + | 0.815302i | \(0.303429\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.18167e10 | −1.73395 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.81228e9 | 0.698531 | 0.349265 | − | 0.937024i | \(-0.386431\pi\) | ||||
0.349265 | + | 0.937024i | \(0.386431\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.64132e9 | 1.09727 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.72503e9 | 0.813288 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.16908e9 | 0.585927 | 0.292964 | − | 0.956124i | \(-0.405359\pi\) | ||||
0.292964 | + | 0.956124i | \(0.405359\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.50541e9 | 0.904545 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.03907e8 | −0.110593 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.02165e10 | 1.39060 | 0.695299 | − | 0.718721i | \(-0.255272\pi\) | ||||
0.695299 | + | 0.718721i | \(0.255272\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.41924e9 | −0.191139 | −0.0955697 | − | 0.995423i | \(-0.530467\pi\) | ||||
−0.0955697 | + | 0.995423i | \(0.530467\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.17100e9 | 0.156048 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.35107e10 | −3.10020 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.84853e9 | −0.763144 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.56408e8 | −0.0718459 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.51476e9 | 0.960255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.90621e9 | 1.12626 | 0.563132 | − | 0.826367i | \(-0.309596\pi\) | ||||
0.563132 | + | 0.826367i | \(0.309596\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.99332e9 | 0.249467 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.21191e9 | 0.397834 | 0.198917 | − | 0.980016i | \(-0.436258\pi\) | ||||
0.198917 | + | 0.980016i | \(0.436258\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.69215e9 | 1.06557 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.42963e9 | −0.780137 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.49063e10 | 1.79018 | 0.895091 | − | 0.445883i | \(-0.147110\pi\) | ||||
0.895091 | + | 0.445883i | \(0.147110\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.89242e9 | −1.05707 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.44208e9 | 0.169684 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.86639e9 | 0.799762 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.38129e9 | 0.389860 | 0.194930 | − | 0.980817i | \(-0.437552\pi\) | ||||
0.194930 | + | 0.980817i | \(0.437552\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.49119e9 | −0.284342 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.69061e10 | 1.91028 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.41568e9 | 0.493950 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.27706e9 | −0.695162 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.19330e10 | 1.30839 | 0.654195 | − | 0.756326i | \(-0.273008\pi\) | ||||
0.654195 | + | 0.756326i | \(0.273008\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.21765e10 | −1.32184 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.13769e9 | −0.767178 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.70657e9 | −0.820150 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.92709e9 | −0.203068 | −0.101534 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101534 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.85300e9 | 0.610710 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.78546e9 | 0.494436 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.39299e9 | 0.449458 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.35179e9 | 0.643545 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.16235e9 | −0.517960 | −0.258980 | − | 0.965883i | \(-0.583386\pi\) | ||||
−0.258980 | + | 0.965883i | \(0.583386\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.50181e10 | −1.49225 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.30171e9 | −0.915333 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.13596e10 | 2.08166 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.38758e10 | 1.33933 | 0.669667 | − | 0.742662i | \(-0.266437\pi\) | ||||
0.669667 | + | 0.742662i | \(0.266437\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.20175e10 | −1.13790 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.26388e9 | −0.306104 | −0.153052 | − | 0.988218i | \(-0.548910\pi\) | ||||
−0.153052 | + | 0.988218i | \(0.548910\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.84561e9 | −0.728822 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.75088e9 | 0.253125 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.49185e8 | −0.0500568 | −0.0250284 | − | 0.999687i | \(-0.507968\pi\) | ||||
−0.0250284 | + | 0.999687i | \(0.507968\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.54880e9 | 0.410708 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.11208e10 | 0.994663 | 0.497332 | − | 0.867561i | \(-0.334313\pi\) | ||||
0.497332 | + | 0.867561i | \(0.334313\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.45462e10 | 2.17489 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.59265e9 | −0.227574 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.07392e10 | −0.933872 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.06853e9 | −0.436659 | −0.218329 | − | 0.975875i | \(-0.570061\pi\) | ||||
−0.218329 | + | 0.975875i | \(0.570061\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.64001e8 | −0.0822801 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.24322e9 | 0.358824 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.64424e9 | −0.472901 | −0.236450 | − | 0.971644i | \(-0.575984\pi\) | ||||
−0.236450 | + | 0.971644i | \(0.575984\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.08234e9 | −0.172865 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.57769e10 | 1.29770 | 0.648850 | − | 0.760916i | \(-0.275250\pi\) | ||||
0.648850 | + | 0.760916i | \(0.275250\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.84416e9 | 0.557807 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.59105e9 | 0.290006 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.02453e10 | −0.819859 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.05126e10 | 0.833616 | 0.416808 | − | 0.908994i | \(-0.363149\pi\) | ||||
0.416808 | + | 0.908994i | \(0.363149\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.78947e9 | 0.376355 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.70533e9 | 0.366405 | 0.183203 | − | 0.983075i | \(-0.441354\pi\) | ||||
0.183203 | + | 0.983075i | \(0.441354\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.74771e10 | −1.34870 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.94103e9 | −0.683776 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.71529e10 | 1.30004 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.19691e9 | −0.690818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.15144e9 | 0.309053 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.98372e9 | 0.589063 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.07916e10 | −1.52046 | −0.760232 | − | 0.649652i | \(-0.774915\pi\) | ||||
−0.760232 | + | 0.649652i | \(0.774915\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.78339e9 | 0.491674 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.53835e10 | −1.10519 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.00756e10 | −0.717487 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.10569e10 | 1.48631 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.09035e10 | −0.762890 | −0.381445 | − | 0.924392i | \(-0.624573\pi\) | ||||
−0.381445 | + | 0.924392i | \(0.624573\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.25897e9 | −0.503456 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.80193e9 | −0.261391 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.06710e9 | −0.209037 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.44303e10 | −0.974968 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.25769e9 | −0.620077 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.20873e10 | −0.802620 | −0.401310 | − | 0.915942i | \(-0.631445\pi\) | ||||
−0.401310 | + | 0.915942i | \(0.631445\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.39636e10 | 0.919229 | 0.459615 | − | 0.888118i | \(-0.347988\pi\) | ||||
0.459615 | + | 0.888118i | \(0.347988\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.21370e10 | 0.792125 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.38320e10 | −2.18915 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.66825e10 | −2.99486 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.34012e9 | 0.212456 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.90599e9 | −0.435537 | −0.217769 | − | 0.976000i | \(-0.569878\pi\) | ||||
−0.217769 | + | 0.976000i | \(0.569878\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.31839e9 | 0.0824413 | 0.0412206 | − | 0.999150i | \(-0.486875\pi\) | ||||
0.0412206 | + | 0.999150i | \(0.486875\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.60500e9 | 0.471531 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.16284e10 | −0.714907 | −0.357454 | − | 0.933931i | \(-0.616355\pi\) | ||||
−0.357454 | + | 0.933931i | \(0.616355\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.53849e10 | −0.937893 | −0.468947 | − | 0.883226i | \(-0.655366\pi\) | ||||
−0.468947 | + | 0.883226i | \(0.655366\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.18382e9 | 0.373812 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.97892e9 | −0.478285 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.31978e9 | 0.553991 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.39684e9 | −0.200233 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.92329e9 | −0.287799 | −0.143899 | − | 0.989592i | \(-0.545964\pi\) | ||||
−0.143899 | + | 0.989592i | \(0.545964\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.72353e10 | 1.57887 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.02864e9 | −0.231613 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.06872e10 | 1.17952 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.44385e10 | 0.816452 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.09363e10 | 0.613327 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.47365e9 | −0.415699 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.54820e9 | 0.416411 | 0.208205 | − | 0.978085i | \(-0.433238\pi\) | ||||
0.208205 | + | 0.978085i | \(0.433238\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.39496e10 | 0.763275 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.27814e10 | −0.693656 | −0.346828 | − | 0.937929i | \(-0.612741\pi\) | ||||
−0.346828 | + | 0.937929i | \(0.612741\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.33691e10 | 0.719657 | 0.359829 | − | 0.933018i | \(-0.382835\pi\) | ||||
0.359829 | + | 0.933018i | \(0.382835\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.25952e10 | 0.672500 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.25958e9 | −0.490404 | −0.245202 | − | 0.969472i | \(-0.578854\pi\) | ||||
−0.245202 | + | 0.969472i | \(0.578854\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.89594e10 | 1.52136 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.42707e9 | −0.387036 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.23306e10 | 1.15433 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.68830e9 | −0.189131 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.15733e9 | −0.262346 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.20452e10 | 0.607837 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.40971e10 | −0.705717 | −0.352859 | − | 0.935677i | \(-0.614790\pi\) | ||||
−0.352859 | + | 0.935677i | \(0.614790\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.50935e9 | −0.0749600 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.97871e10 | 0.974914 | 0.487457 | − | 0.873147i | \(-0.337925\pi\) | ||||
0.487457 | + | 0.873147i | \(0.337925\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.39322e10 | −1.65863 | −0.829314 | − | 0.558782i | \(-0.811269\pi\) | ||||
−0.829314 | + | 0.558782i | \(0.811269\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.14188e10 | −1.52366 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.05047e10 | 1.46769 | 0.733846 | − | 0.679316i | \(-0.237724\pi\) | ||||
0.733846 | + | 0.679316i | \(0.237724\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.97243e10 | −0.941554 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.47810e9 | 0.0700056 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.81978e10 | −1.32506 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.52427e10 | −1.17694 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.79195e9 | 0.129162 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.63992e10 | −1.67083 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.14147e10 | 0.975382 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.42783e10 | −1.54922 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.40762e10 | −2.87360 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.76417e9 | 0.301016 | 0.150508 | − | 0.988609i | \(-0.451909\pi\) | ||||
0.150508 | + | 0.988609i | \(0.451909\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.57255e9 | 0.201923 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.14881e10 | −0.503424 | −0.251712 | − | 0.967802i | \(-0.580994\pi\) | ||||
−0.251712 | + | 0.967802i | \(0.580994\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.89160e9 | −0.430149 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.08984e10 | −1.33341 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.88711e10 | 0.808175 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.87986e10 | −1.64897 | −0.824483 | − | 0.565887i | \(-0.808534\pi\) | ||||
−0.824483 | + | 0.565887i | \(0.808534\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.92587e10 | 0.812305 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.23310e10 | 0.516168 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.72948e10 | 1.13392 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.91072e9 | 0.367395 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.14694e10 | 1.69696 | 0.848482 | − | 0.529224i | \(-0.177517\pi\) | ||||
0.848482 | + | 0.529224i | \(0.177517\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.09945e10 | −1.25881 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.28519e9 | −0.253357 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.37007e10 | 0.548155 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.25279e10 | 0.497497 | 0.248748 | − | 0.968568i | \(-0.419981\pi\) | ||||
0.248748 | + | 0.968568i | \(0.419981\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.65515e9 | 0.144071 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.90647e10 | −1.52834 | −0.764171 | − | 0.645014i | \(-0.776852\pi\) | ||||
−0.764171 | + | 0.645014i | \(0.776852\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.05281e10 | 0.408844 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.02430e10 | 0.394836 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.55171e10 | −0.593726 | −0.296863 | − | 0.954920i | \(-0.595941\pi\) | ||||
−0.296863 | + | 0.954920i | \(0.595941\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.11228e9 | 0.156189 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.42995e10 | 0.539126 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.71024e10 | −1.38860 | −0.694299 | − | 0.719687i | \(-0.744285\pi\) | ||||
−0.694299 | + | 0.719687i | \(0.744285\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.67031e9 | −0.136361 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.58388e10 | 0.584157 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.57955e10 | −0.944449 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.27038e9 | 0.0825214 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.37193e9 | 0.229921 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.40887e10 | −2.29581 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.56321e10 | 0.911574 | 0.455787 | − | 0.890089i | \(-0.349358\pi\) | ||||
0.455787 | + | 0.890089i | \(0.349358\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.41867e10 | 0.500895 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.08869e10 | −1.78377 | −0.891884 | − | 0.452264i | \(-0.850616\pi\) | ||||
−0.891884 | + | 0.452264i | \(0.850616\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.90420e10 | 1.70676 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.01966e10 | −0.352320 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.68684e10 | 0.578686 | 0.289343 | − | 0.957225i | \(-0.406563\pi\) | ||||
0.289343 | + | 0.957225i | \(0.406563\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.45053e10 | −0.494068 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.06085e9 | −0.137333 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.61062e10 | 0.540825 | 0.270412 | − | 0.962745i | \(-0.412840\pi\) | ||||
0.270412 | + | 0.962745i | \(0.412840\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.13849e10 | 1.37980 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.07053e10 | −0.685443 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.86527e10 | −0.941842 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.98303e9 | 0.130004 | 0.0650019 | − | 0.997885i | \(-0.479295\pi\) | ||||
0.0650019 | + | 0.997885i | \(0.479295\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.49732e10 | −0.809380 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.35334e10 | 0.435538 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.19886e10 | 1.34183 | 0.670917 | − | 0.741533i | \(-0.265901\pi\) | ||||
0.670917 | + | 0.741533i | \(0.265901\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.30499e9 | 0.168347 |
(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 | 192.8.a.t.1.1 | 2 | ||
3.2 | odd | 2 | 576.8.a.bn.1.2 | 2 | |||
4.3 | odd | 2 | 192.8.a.q.1.1 | 2 | |||
8.3 | odd | 2 | 96.8.a.h.1.2 | yes | 2 | ||
8.5 | even | 2 | 96.8.a.e.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 576.8.a.bo.1.2 | 2 | |||
24.5 | odd | 2 | 288.8.a.g.1.1 | 2 | |||
24.11 | even | 2 | 288.8.a.h.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.8.a.e.1.2 | ✓ | 2 | 8.5 | even | 2 | ||
96.8.a.h.1.2 | yes | 2 | 8.3 | odd | 2 | ||
192.8.a.q.1.1 | 2 | 4.3 | odd | 2 | |||
192.8.a.t.1.1 | 2 | 1.1 | even | 1 | trivial | ||
288.8.a.g.1.1 | 2 | 24.5 | odd | 2 | |||
288.8.a.h.1.1 | 2 | 24.11 | even | 2 | |||
576.8.a.bn.1.2 | 2 | 3.2 | odd | 2 | |||
576.8.a.bo.1.2 | 2 | 12.11 | even | 2 |