Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,9,Mod(127,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, 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("384.127");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(156.433386263\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.16 | ||
Character | \(\chi\) | \(=\) | 384.127 |
Dual form | 384.9.g.a.127.15 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | −19.7383 | −0.0315813 | −0.0157906 | − | 0.999875i | \(-0.505027\pi\) | ||||
−0.0157906 | + | 0.999875i | \(0.505027\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 759.796i | 0.316450i | 0.987403 | + | 0.158225i | \(0.0505771\pi\) | ||||
−0.987403 | + | 0.158225i | \(0.949423\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2187.00 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 15847.0i | − 1.08237i | −0.840902 | − | 0.541187i | \(-0.817975\pi\) | ||||
0.840902 | − | 0.541187i | \(-0.182025\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −47667.3 | −1.66897 | −0.834483 | − | 0.551034i | \(-0.814234\pi\) | ||||
−0.834483 | + | 0.551034i | \(0.814234\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 923.068i | − 0.0182335i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −117951. | −1.41223 | −0.706117 | − | 0.708095i | \(-0.749555\pi\) | ||||
−0.706117 | + | 0.708095i | \(0.749555\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 196795.i | 1.51008i | 0.655678 | + | 0.755041i | \(0.272383\pi\) | ||||
−0.655678 | + | 0.755041i | \(0.727617\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −35532.1 | −0.182702 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 143587.i | − 0.513101i | −0.966531 | − | 0.256550i | \(-0.917414\pi\) | ||||
0.966531 | − | 0.256550i | \(-0.0825859\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −390235. | −0.999003 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 102276.i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.30803e6 | 1.84938 | 0.924690 | − | 0.380720i | \(-0.124324\pi\) | ||||
0.924690 | + | 0.380720i | \(0.124324\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.08127e6i | 1.17081i | 0.810740 | + | 0.585407i | \(0.199065\pi\) | ||||
−0.810740 | + | 0.585407i | \(0.800935\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 741092. | 0.624909 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 14997.1i | − 0.00999388i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.61456e6 | −1.39506 | −0.697528 | − | 0.716558i | \(-0.745717\pi\) | ||||
−0.697528 | + | 0.716558i | \(0.745717\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 2.22918e6i | − 0.963578i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 956143. | 0.338367 | 0.169183 | − | 0.985585i | \(-0.445887\pi\) | ||||
0.169183 | + | 0.985585i | \(0.445887\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 4.78185e6i | − 1.39869i | −0.714783 | − | 0.699346i | \(-0.753475\pi\) | ||||
0.714783 | − | 0.699346i | \(-0.246525\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 43167.6 | 0.0105271 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 2.03435e6i | − 0.416903i | −0.978033 | − | 0.208451i | \(-0.933158\pi\) | ||||
0.978033 | − | 0.208451i | \(-0.0668423\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.18751e6 | 0.899860 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 5.51603e6i | − 0.815353i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.50474e6 | 0.570908 | 0.285454 | − | 0.958392i | \(-0.407856\pi\) | ||||
0.285454 | + | 0.958392i | \(0.407856\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 312793.i | 0.0341827i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.20320e6 | −0.871846 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.40186e7i | 1.15690i | 0.815718 | + | 0.578449i | \(0.196342\pi\) | ||||
−0.815718 | + | 0.578449i | \(0.803658\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.05420e7 | −1.48362 | −0.741812 | − | 0.670608i | \(-0.766033\pi\) | ||||
−0.741812 | + | 0.670608i | \(0.766033\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 1.66167e6i | − 0.105483i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 940872. | 0.0527080 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.77586e7i | 1.37752i | 0.724989 | + | 0.688760i | \(0.241845\pi\) | ||||
−0.724989 | + | 0.688760i | \(0.758155\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.71488e6 | 0.296239 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 3.22968e7i | − 1.27094i | −0.772125 | − | 0.635471i | \(-0.780806\pi\) | ||||
0.772125 | − | 0.635471i | \(-0.219194\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.34885e7 | 0.827112 | 0.413556 | − | 0.910479i | \(-0.364287\pi\) | ||||
0.413556 | + | 0.910479i | \(0.364287\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 1.82495e7i | − 0.576774i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.20405e7 | 0.342517 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.08547e7i | 0.278683i | 0.990244 | + | 0.139341i | \(0.0444985\pi\) | ||||
−0.990244 | + | 0.139341i | \(0.955502\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.78297e6 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 7.99186e7i | − 1.68398i | −0.539497 | − | 0.841988i | \(-0.681386\pi\) | ||||
0.539497 | − | 0.841988i | \(-0.318614\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.32815e6 | 0.0446001 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.11706e7i | 1.06774i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.46098e7 | 1.18915 | 0.594574 | − | 0.804041i | \(-0.297321\pi\) | ||||
0.594574 | + | 0.804041i | \(0.297321\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 3.62174e7i | − 0.528144i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.05661e7 | −0.675970 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 3.88440e6i | − 0.0476903i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.73670e7 | −0.648001 | −0.324000 | − | 0.946057i | \(-0.605028\pi\) | ||||
−0.324000 | + | 0.946057i | \(0.605028\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.46575e7i | 0.360791i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.65501e7 | −0.927827 | −0.463914 | − | 0.885881i | \(-0.653555\pi\) | ||||
−0.463914 | + | 0.885881i | \(0.653555\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1.41970e8i | − 1.26138i | −0.776033 | − | 0.630692i | \(-0.782771\pi\) | ||||
0.776033 | − | 0.630692i | \(-0.217229\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 701343. | 0.00576997 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.39218e7i | 0.487656i | 0.969818 | + | 0.243828i | \(0.0784033\pi\) | ||||
−0.969818 | + | 0.243828i | \(0.921597\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.31267e8 | 0.929932 | 0.464966 | − | 0.885329i | \(-0.346067\pi\) | ||||
0.464966 | + | 0.885329i | \(0.346067\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 1.22271e8i | − 0.805436i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.49881e8 | 0.919246 | 0.459623 | − | 0.888114i | \(-0.347985\pi\) | ||||
0.459623 | + | 0.888114i | \(0.347985\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.83415e6i | 0.0162044i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.04248e8 | 0.556322 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 8.96188e7i | − 0.446901i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.67695e7 | −0.171533 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.47144e7i | 0.195356i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.54128e7 | 0.0631310 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 1.99191e8i | − 0.765695i | −0.923812 | − | 0.382848i | \(-0.874943\pi\) | ||||
0.923812 | − | 0.382848i | \(-0.125057\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.23625e8 | 0.807536 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.03185e8i | 1.02949i | 0.857343 | + | 0.514746i | \(0.172114\pi\) | ||||
−0.857343 | + | 0.514746i | \(0.827886\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.49524e8 | −0.477865 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.01875e6i | 0.00607782i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.76126e8 | −1.06770 | −0.533852 | − | 0.845578i | \(-0.679256\pi\) | ||||
−0.533852 | + | 0.845578i | \(0.679256\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2.37171e8i | − 0.635334i | −0.948202 | − | 0.317667i | \(-0.897101\pi\) | ||||
0.948202 | − | 0.317667i | \(-0.102899\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.51372e7 | 0.240699 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.55386e8i | 1.80644i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.58183e7 | −0.0584058 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.42596e8i | 0.519534i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.73173e8 | 1.77156 | 0.885779 | − | 0.464108i | \(-0.153625\pi\) | ||||
0.885779 | + | 0.464108i | \(0.153625\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.26207e6i | 0.00242758i | 0.999999 | + | 0.00121379i | \(0.000386362\pi\) | ||||
−0.999999 | + | 0.00121379i | \(0.999614\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.57959e8 | 0.470745 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 2.13424e7i | − 0.0369758i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.79730e8 | 0.954174 | 0.477087 | − | 0.878856i | \(-0.341693\pi\) | ||||
0.477087 | + | 0.878856i | \(0.341693\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.10666e8i | 0.329614i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.09096e8 | 0.162370 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.36798e9i | 1.93790i | 0.247264 | + | 0.968948i | \(0.420468\pi\) | ||||
−0.247264 | + | 0.968948i | \(0.579532\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.46279e7 | −0.0197354 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 9.31645e8i | − 1.19780i | −0.800824 | − | 0.598900i | \(-0.795605\pi\) | ||||
0.800824 | − | 0.598900i | \(-0.204395\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.45644e9 | 1.78545 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 4.30391e8i | − 0.503360i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.08081e8 | −0.678856 | −0.339428 | − | 0.940632i | \(-0.610233\pi\) | ||||
−0.339428 | + | 0.940632i | \(0.610233\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 2.96499e8i | − 0.316134i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.55583e8 | −0.667936 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.47872e8i | 0.144037i | 0.997403 | + | 0.0720184i | \(0.0229440\pi\) | ||||
−0.997403 | + | 0.0720184i | \(0.977056\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.89805e8 | 0.642705 | 0.321353 | − | 0.946960i | \(-0.395863\pi\) | ||||
0.321353 | + | 0.946960i | \(0.395863\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 9.60655e8i | − 0.856571i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.16069e7 | 0.0440576 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.86918e9i | 1.52856i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.77088e7 | 0.0609008 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 1.82722e9i | − 1.37296i | −0.727148 | − | 0.686481i | \(-0.759155\pi\) | ||||
0.727148 | − | 0.686481i | \(-0.240845\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.57534e8 | 0.329757 | 0.164879 | − | 0.986314i | \(-0.447277\pi\) | ||||
0.164879 | + | 0.986314i | \(0.447277\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.40002e7i | 0.0304310i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.22625e8 | 0.280601 | 0.140301 | − | 0.990109i | \(-0.455193\pi\) | ||||
0.140301 | + | 0.990109i | \(0.455193\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.66840e8i | 0.297684i | 0.988861 | + | 0.148842i | \(0.0475546\pi\) | ||||
−0.988861 | + | 0.148842i | \(0.952445\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.29814e9 | −0.795312 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.93837e8i | 0.585236i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.88726e7 | −0.0106860 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.14024e8i | 0.171034i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.11862e9 | 1.63447 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1.16847e9i | − 0.589505i | −0.955574 | − | 0.294753i | \(-0.904763\pi\) | ||||
0.955574 | − | 0.294753i | \(-0.0952373\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.51037e9 | 0.733779 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.43856e7i | 0.0441725i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.21545e8 | −0.370504 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.09845e9i | 0.477533i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.62242e9 | 2.35697 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.79628e8i | 0.234385i | 0.993109 | + | 0.117192i | \(0.0373894\pi\) | ||||
−0.993109 | + | 0.117192i | \(0.962611\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.53445e8 | 0.333001 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.62864e9i | 1.74321i | 0.490207 | + | 0.871606i | \(0.336921\pi\) | ||||
−0.490207 | + | 0.871606i | \(0.663079\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.38866e9 | 1.23221 | 0.616107 | − | 0.787663i | \(-0.288709\pi\) | ||||
0.616107 | + | 0.787663i | \(0.288709\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.63079e8i | 0.197752i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.20266e9 | 0.747351 | 0.373675 | − | 0.927560i | \(-0.378097\pi\) | ||||
0.373675 | + | 0.927560i | \(0.378097\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.01546e7i | 0.0131663i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.07624e8 | −0.160897 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 4.26194e9i | − 1.30622i | −0.757264 | − | 0.653108i | \(-0.773465\pi\) | ||||
0.757264 | − | 0.653108i | \(-0.226535\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.80122e9 | 1.42326 | 0.711628 | − | 0.702556i | \(-0.247958\pi\) | ||||
0.711628 | + | 0.702556i | \(0.247958\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.23677e8i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.02393e8 | −0.0284187 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 9.38071e9i | − 2.52027i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.73742e9 | 0.972244 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 1.15369e9i | − 0.290667i | −0.989383 | − | 0.145333i | \(-0.953575\pi\) | ||||
0.989383 | − | 0.145333i | \(-0.0464255\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.27542e9 | −0.555366 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.08877e8i | 0.0257499i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.22177e8 | 0.142620 | 0.0713102 | − | 0.997454i | \(-0.477282\pi\) | ||||
0.0713102 | + | 0.997454i | \(0.477282\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.98653e9i | − 0.441465i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.86067e9 | −0.616460 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 2.82148e9i | − 0.589732i | −0.955539 | − | 0.294866i | \(-0.904725\pi\) | ||||
0.955539 | − | 0.294866i | \(-0.0952750\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.89159e7 | −0.0180300 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.48915e9i | 0.686555i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.33848e9 | −0.446605 | −0.223303 | − | 0.974749i | \(-0.571684\pi\) | ||||
−0.223303 | + | 0.974749i | \(0.571684\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 1.92807e9i | − 0.357475i | −0.983897 | − | 0.178737i | \(-0.942799\pi\) | ||||
0.983897 | − | 0.178737i | \(-0.0572012\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.69372e9 | 0.304924 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.18407e9i | 1.08129i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.15707e9 | 0.536248 | 0.268124 | − | 0.963384i | \(-0.413596\pi\) | ||||
0.268124 | + | 0.963384i | \(0.413596\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 2.36474e9i | − 0.390271i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.57086e9 | 0.412338 | 0.206169 | − | 0.978516i | \(-0.433900\pi\) | ||||
0.206169 | + | 0.978516i | \(0.433900\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1.59550e9i | − 0.248743i | −0.992236 | − | 0.124372i | \(-0.960308\pi\) | ||||
0.992236 | − | 0.124372i | \(-0.0396915\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.81656e8 | 0.0275340 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.26473e8i | 0.107076i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.93672e9 | 0.994404 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 2.68279e9i | − 0.374123i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.12015e9 | 0.559039 | 0.279520 | − | 0.960140i | \(-0.409825\pi\) | ||||
0.279520 | + | 0.960140i | \(0.409825\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 2.76702e8i | − 0.0365363i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.62077e9 | −0.208303 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.84439e9i | 0.856347i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.63323e9 | 0.442616 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 4.51520e9i | − 0.535681i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.05464e8 | 0.0468547 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.53448e10i | 1.72746i | 0.503954 | + | 0.863731i | \(0.331878\pi\) | ||||
−0.503954 | + | 0.863731i | \(0.668122\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.63928e9 | 0.728261 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.41711e9i | 0.899749i | 0.893092 | + | 0.449875i | \(0.148531\pi\) | ||||
−0.893092 | + | 0.449875i | \(0.851469\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.18210e9 | 0.539918 | 0.269959 | − | 0.962872i | \(-0.412990\pi\) | ||||
0.269959 | + | 0.962872i | \(0.412990\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.27986e7i | 0.00333129i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.31162e9 | −0.426976 | −0.213488 | − | 0.976946i | \(-0.568482\pi\) | ||||
−0.213488 | + | 0.976946i | \(0.568482\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 2.07284e10i | − 2.00172i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.98933e9 | −0.281548 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2.32122e10i | − 2.13259i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.86015e10 | 1.66730 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.13877e9i | 0.536896i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.54569e9 | 0.131929 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.84383e9i | 0.653456i | 0.945118 | + | 0.326728i | \(0.105946\pi\) | ||||
−0.945118 | + | 0.326728i | \(0.894054\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.71804e9 | 0.465018 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 5.47907e8i | − 0.0435039i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.60451e10 | 1.24401 | 0.622005 | − | 0.783013i | \(-0.286318\pi\) | ||||
0.622005 | + | 0.783013i | \(0.286318\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.00922e9i | 0.530727i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.71349e10 | 1.26726 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.32152e9i | 0.601210i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.32540e8 | −0.00935559 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.36821e10i | 0.943700i | 0.881679 | + | 0.471850i | \(0.156414\pi\) | ||||
−0.881679 | + | 0.471850i | \(0.843586\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.11356e10 | −1.42466 | −0.712332 | − | 0.701843i | \(-0.752361\pi\) | ||||
−0.712332 | + | 0.701843i | \(0.752361\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.87522e9i | 0.321193i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.47373e10 | 0.949112 | 0.474556 | − | 0.880225i | \(-0.342609\pi\) | ||||
0.474556 | + | 0.880225i | \(0.342609\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.37483e8i | 0.0401379i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.19106e9 | 0.258018 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 2.49699e10i | − 1.50328i | −0.659575 | − | 0.751638i | \(-0.729264\pi\) | ||||
0.659575 | − | 0.751638i | \(-0.270736\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.17448e10 | −1.28034 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1.71954e9i | − 0.0990344i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.63623e8 | −0.0261212 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.11559e10i | 0.614951i | 0.951556 | + | 0.307475i | \(0.0994842\pi\) | ||||
−0.951556 | + | 0.307475i | \(0.900516\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.09108e9 | −0.112789 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.42268e9i | 0.180664i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.65556e10 | −1.88851 | −0.944253 | − | 0.329221i | \(-0.893214\pi\) | ||||
−0.944253 | + | 0.329221i | \(0.893214\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.20788e8i | 0.0364487i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.23504e10 | −3.08655 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.16949e9i | 0.105148i | 0.998617 | + | 0.0525740i | \(0.0167425\pi\) | ||||
−0.998617 | + | 0.0525740i | \(0.983257\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.31526e9 | 0.442074 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 8.10758e9i | − 0.376787i | −0.982094 | − | 0.188394i | \(-0.939672\pi\) | ||||
0.982094 | − | 0.188394i | \(-0.0603280\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.37659e8 | −0.0108171 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.04579e10i | 0.466231i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.73636e10 | 0.758300 | 0.379150 | − | 0.925335i | \(-0.376217\pi\) | ||||
0.379150 | + | 0.925335i | \(0.376217\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.69362e10i | 0.724618i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.41786e10 | −0.594377 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 2.14253e8i | − 0.00880115i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.49508e9 | −0.301727 | −0.150864 | − | 0.988555i | \(-0.548205\pi\) | ||||
−0.150864 | + | 0.988555i | \(0.548205\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 6.99255e9i | − 0.275895i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.17286e10 | 1.22708 | 0.613541 | − | 0.789663i | \(-0.289745\pi\) | ||||
0.613541 | + | 0.789663i | \(0.289745\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 5.15413e10i | − 1.95405i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.44076e7 | −0.00350903 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.14330e10i | 1.50997i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.02548e10 | 1.08119 | 0.540595 | − | 0.841283i | \(-0.318199\pi\) | ||||
0.540595 | + | 0.841283i | \(0.318199\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 1.75897e10i | − 0.616440i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.06512e10 | −0.366100 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.57746e9i | 0.0531821i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.10914e10 | 0.366810 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.95924e10i | 1.28456i | 0.766468 | + | 0.642282i | \(0.222012\pi\) | ||||
−0.766468 | + | 0.642282i | \(0.777988\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.41632e10 | 1.08750 | 0.543751 | − | 0.839247i | \(-0.317004\pi\) | ||||
0.543751 | + | 0.839247i | \(0.317004\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.44913e9i | 0.138968i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.60287e10 | 1.41083 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.56077e10i | − 0.469492i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.53259e10 | −1.04295 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.74352e10i | 1.37465i | 0.726351 | + | 0.687324i | \(0.241215\pi\) | ||||
−0.726351 | + | 0.687324i | \(0.758785\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.46150e10 | −0.984720 | −0.492360 | − | 0.870392i | \(-0.663866\pi\) | ||||
−0.492360 | + | 0.870392i | \(0.663866\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 1.20740e9i | − 0.0337206i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.82572e10 | 0.774823 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 3.47839e10i | − 0.936525i | −0.883589 | − | 0.468263i | \(-0.844880\pi\) | ||||
0.883589 | − | 0.468263i | \(-0.155120\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.13451e10 | −0.299953 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.71982e10i | 0.706196i | 0.935586 | + | 0.353098i | \(0.114872\pi\) | ||||
−0.935586 | + | 0.353098i | \(0.885128\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.47267e9 | −0.0375548 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.08343e10i | 1.02281i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.44839e10 | −1.58659 | −0.793297 | − | 0.608834i | \(-0.791637\pi\) | ||||
−0.793297 | + | 0.608834i | \(0.791637\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1.51520e10i | − 0.366239i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.90210e7 | −0.00140157 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.14870e8i | 0.0166794i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.83314e10 | −1.79586 | −0.897928 | − | 0.440143i | \(-0.854928\pi\) | ||||
−0.897928 | + | 0.440143i | \(0.854928\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.20636e10i | 0.271784i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.86144e10 | −1.74060 | −0.870299 | − | 0.492525i | \(-0.836074\pi\) | ||||
−0.870299 | + | 0.492525i | \(0.836074\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 3.70967e10i | − 0.807257i | −0.914923 | − | 0.403628i | \(-0.867749\pi\) | ||||
0.914923 | − | 0.403628i | \(-0.132251\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.98088e8 | 0.0213480 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 4.80694e10i | − 1.01065i | −0.862929 | − | 0.505325i | \(-0.831373\pi\) | ||||
0.862929 | − | 0.505325i | \(-0.168627\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.10909e10 | −0.435916 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.71113e10i | 0.550892i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.57782e10 | −1.51391 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 7.67965e10i | − 1.50857i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.85187e9 | −0.190303 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.39132e10i | 1.21408i | 0.794670 | + | 0.607042i | \(0.207644\pi\) | ||||
−0.794670 | + | 0.607042i | \(0.792356\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.24629e11 | 2.32830 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.10194e9i | 0.0937447i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.13233e9 | 0.0204647 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 2.04932e10i | − 0.364329i | −0.983268 | − | 0.182164i | \(-0.941690\pi\) | ||||
0.983268 | − | 0.182164i | \(-0.0583103\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.39743e10 | −1.11884 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 9.60306e10i | − 1.65228i | −0.563464 | − | 0.826140i | \(-0.690532\pi\) | ||||
0.563464 | − | 0.826140i | \(-0.309468\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.54284e11 | −2.61176 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 6.84079e8i | − 0.0113942i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.45389e10 | 0.402189 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.03307e9i | 0.0166620i | 0.999965 | + | 0.00833099i | \(0.00265187\pi\) | ||||
−0.999965 | + | 0.00833099i | \(0.997348\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.35687e10 | 0.691550 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 2.88572e10i | − 0.450798i | −0.974267 | − | 0.225399i | \(-0.927632\pi\) | ||||
0.974267 | − | 0.225399i | \(-0.0723685\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.90573e9 | 0.0293020 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.81111e10i | 1.03083i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.12139e10 | −0.614005 | −0.307003 | − | 0.951709i | \(-0.599326\pi\) | ||||
−0.307003 | + | 0.951709i | \(0.599326\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.78465e10i | 0.261739i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.01274e10 | 0.290615 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.80224e9i | 0.0398361i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.22384e10 | −0.451244 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 2.84372e10i | − 0.391937i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.02598e10 | −0.953577 | −0.476789 | − | 0.879018i | \(-0.658199\pi\) | ||||
−0.476789 | + | 0.879018i | \(0.658199\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.04627e11i | − 1.39842i | −0.714918 | − | 0.699208i | \(-0.753536\pi\) | ||||
0.714918 | − | 0.699208i | \(-0.246464\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.38659e10 | 0.182520 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1.27537e11i | − 1.65346i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.76939e10 | 0.736728 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 3.06586e10i | − 0.385633i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.55768e10 | −0.564722 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 1.26171e9i | − 0.0154008i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.91529e9 | −0.0831597 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 8.22067e10i | − 0.973984i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.70512e10 | −0.199052 | −0.0995260 | − | 0.995035i | \(-0.531733\pi\) | ||||
−0.0995260 | + | 0.995035i | \(0.531733\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.22590e10i | 0.371066i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.59099e9 | −0.0293684 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 8.74356e10i | − 0.976650i | −0.872662 | − | 0.488325i | \(-0.837608\pi\) | ||||
0.872662 | − | 0.488325i | \(-0.162392\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.49254e10 | 0.494541 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.57415e11i | 2.79271i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.24736e9 | −0.0881890 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.41342e9i | 0.0254367i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.25190e10 | −0.337844 | −0.168922 | − | 0.985629i | \(-0.554029\pi\) | ||||
−0.168922 | + | 0.985629i | \(0.554029\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.27938e11i | 2.33437i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.74127e10 | −0.882517 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 2.12615e10i | − 0.211621i | −0.994386 | − | 0.105811i | \(-0.966256\pi\) | ||||
0.994386 | − | 0.105811i | \(-0.0337438\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.95839e9 | −0.0290309 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.63408e9i | 0.0351611i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.50487e11 | −1.43566 | −0.717830 | − | 0.696219i | \(-0.754864\pi\) | ||||
−0.717830 | + | 0.696219i | \(0.754864\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.23675e9i | 0.0492626i | 0.999697 | + | 0.0246313i | \(0.00784118\pi\) | ||||
−0.999697 | + | 0.0246313i | \(0.992159\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.54508e10 | 0.792679 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.60326e10i | 0.512589i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.74601e9 | 0.0698835 | 0.0349418 | − | 0.999389i | \(-0.488875\pi\) | ||||
0.0349418 | + | 0.999389i | \(0.488875\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.13968e10i | 0.190385i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.07218e10 | 0.532893 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 7.13868e10i | − 0.617936i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.05769e9 | −0.0175693 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.50562e11i | 1.26813i | 0.773279 | + | 0.634066i | \(0.218615\pi\) | ||||
−0.773279 | + | 0.634066i | \(0.781385\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.12789e11 | −1.76802 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.97642e10i | 0.162005i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.15664e10 | 0.336143 | 0.168071 | − | 0.985775i | \(-0.446246\pi\) | ||||
0.168071 | + | 0.985775i | \(0.446246\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.76892e9i | 0.0141137i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.18320e10 | −0.171868 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.23752e10i | 0.484512i | 0.970212 | + | 0.242256i | \(0.0778874\pi\) | ||||
−0.970212 | + | 0.242256i | \(0.922113\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.01687e11 | −0.779414 | −0.389707 | − | 0.920939i | \(-0.627424\pi\) | ||||
−0.389707 | + | 0.920939i | \(0.627424\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 6.07080e10i | − 0.459174i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.25768e8 | 0.00541722 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 2.50543e11i | − 1.84555i | −0.385334 | − | 0.922777i | \(-0.625914\pi\) | ||||
0.385334 | − | 0.922777i | \(-0.374086\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.64772e10 | −0.337886 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.69721e10i | 0.695796i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.28165e11 | −0.907667 | −0.453833 | − | 0.891087i | \(-0.649944\pi\) | ||||
−0.453833 | + | 0.891087i | \(0.649944\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 8.82585e8i | − 0.00616959i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.17897e11 | −0.813510 | −0.406755 | − | 0.913537i | \(-0.633340\pi\) | ||||
−0.406755 | + | 0.913537i | \(0.633340\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 4.79933e10i | − 0.326902i | −0.986551 | − | 0.163451i | \(-0.947737\pi\) | ||||
0.986551 | − | 0.163451i | \(-0.0522626\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.46854e10 | −0.0987462 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.66882e10i | 0.376305i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.52131e11 | 0.997009 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.45843e11i | 0.943663i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.08390e11 | 1.97014 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 1.90637e11i | − 1.20251i | −0.799057 | − | 0.601256i | \(-0.794667\pi\) | ||||
0.799057 | − | 0.601256i | \(-0.205333\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.46439e10 | 0.340351 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.93170e9i | 0.0241816i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.47275e11 | −1.50183 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.06330e10i | 0.423647i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.61699e10 | 0.155014 | 0.0775069 | − | 0.996992i | \(-0.475304\pi\) | ||||
0.0775069 | + | 0.996992i | \(0.475304\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 6.78239e10i | − 0.396770i | −0.980124 | − | 0.198385i | \(-0.936430\pi\) | ||||
0.980124 | − | 0.198385i | \(-0.0635697\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.41398e9 | −0.0255030 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 2.04734e11i | − 1.16835i | −0.811628 | − | 0.584174i | \(-0.801419\pi\) | ||||
0.811628 | − | 0.584174i | \(-0.198581\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.22153e11 | 1.25220 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 3.84199e10i | − 0.213910i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.51233e10 | 0.0831753 | 0.0415876 | − | 0.999135i | \(-0.486758\pi\) | ||||
0.0415876 | + | 0.999135i | \(0.486758\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 5.98436e9i | − 0.0325126i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.13694e10 | −0.275704 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.16908e10i | 0.221054i | 0.993873 | + | 0.110527i | \(0.0352539\pi\) | ||||
−0.993873 | + | 0.110527i | \(0.964746\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.51774e11 | 1.84271 | 0.921357 | − | 0.388719i | \(-0.127082\pi\) | ||||
0.921357 | + | 0.388719i | \(0.127082\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.62934e11i | 1.36080i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.95135e9 | 0.0150916 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.87816e11i | − 0.948918i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.71065e10 | −0.135322 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.25530e11i | 1.60584i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.26006e11 | 0.614229 | 0.307115 | − | 0.951673i | \(-0.400637\pi\) | ||||
0.307115 | + | 0.951673i | \(0.400637\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.99117e10i | 0.192258i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.43623e11 | 0.683708 | 0.341854 | − | 0.939753i | \(-0.388945\pi\) | ||||
0.341854 | + | 0.939753i | \(0.388945\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 4.35872e10i | − 0.205060i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.16460e11 | −1.00644 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.24502e11i | 1.03166i | 0.856690 | + | 0.515831i | \(0.172517\pi\) | ||||
−0.856690 | + | 0.515831i | \(0.827483\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.42409e9 | 0.0337195 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.58472e11i | 0.711419i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.14729e11 | −0.952826 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1.36709e11i | − 0.599634i | −0.953997 | − | 0.299817i | \(-0.903074\pi\) | ||||
0.953997 | − | 0.299817i | \(-0.0969256\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.63326e10 | −0.114172 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.68135e9i | 0.0200647i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.12778e11 | −0.477853 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.03008e11i | 0.431483i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.04497e11 | 1.26099 | 0.630493 | − | 0.776195i | \(-0.282853\pi\) | ||||
0.630493 | + | 0.776195i | \(0.282853\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 5.14533e11i | − 2.10665i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.87785e9 | −0.00760157 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 7.33583e10i | − 0.293611i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.06434e11 | −0.421206 | −0.210603 | − | 0.977572i | \(-0.567543\pi\) | ||||
−0.210603 | + | 0.977572i | \(0.567543\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 2.37392e10i | − 0.0928942i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.55256e11 | 0.600745 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1.49100e10i | − 0.0570498i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.99311e11 | 0.754145 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 6.97035e10i | − 0.260819i | −0.991460 | − | 0.130410i | \(-0.958371\pi\) | ||||
0.991460 | − | 0.130410i | \(-0.0416292\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.07868e11 | 0.399165 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.24531e11i | 0.821717i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.10440e11 | −1.84754 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.36941e11i | 0.848207i | 0.905614 | + | 0.424104i | \(0.139411\pi\) | ||||
−0.905614 | + | 0.424104i | \(0.860589\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.04604e10 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.64025e11i | 1.97528i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.77173e11 | 1.30655 | 0.653274 | − | 0.757122i | \(-0.273395\pi\) | ||||
0.653274 | + | 0.757122i | \(0.273395\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 4.78843e9i | − 0.0164075i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.39891e11 | 1.49099 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 2.53030e11i | − 0.848387i | −0.905572 | − | 0.424193i | \(-0.860558\pi\) | ||||
0.905572 | − | 0.424193i | \(-0.139442\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.38692e11 | 1.45508 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.74065e10i | 0.0571159i | 0.999592 | + | 0.0285580i | \(0.00909152\pi\) | ||||
−0.999592 | + | 0.0285580i | \(0.990908\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.72349e10 | −0.0559480 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.74782e11i | 0.561325i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.85675e10 | −0.154319 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 4.54672e11i | − 1.42935i | −0.699457 | − | 0.714675i | \(-0.746575\pi\) | ||||
0.699457 | − | 0.714675i | \(-0.253425\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.39529e10 | 0.167817 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 2.49110e7i | 0 7.66661e-5i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.54282e11 | −1.68790 | −0.843952 | − | 0.536419i | \(-0.819777\pi\) | ||||
−0.843952 | + | 0.536419i | \(0.819777\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 1.06411e11i | − 0.320641i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.46497e10 | 0.252399 | 0.126199 | − | 0.992005i | \(-0.459722\pi\) | ||||
0.126199 | + | 0.992005i | \(0.459722\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.97364e10i | 0.294277i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.09167e9 | −0.0148667 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 6.68227e11i | − 1.93082i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.61130e11 | 0.460756 | 0.230378 | − | 0.973101i | \(-0.426004\pi\) | ||||
0.230378 | + | 0.973101i | \(0.426004\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.90963e10i | 0.0823419i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.45092e11 | 1.52669 | 0.763346 | − | 0.645990i | \(-0.223555\pi\) | ||||
0.763346 | + | 0.645990i | \(0.223555\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 4.21950e11i | − 1.16965i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.29008e10 | 0.254880 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.88164e11i | 0.510961i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.11808e11 | −1.37563 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 1.33780e11i | − 0.355914i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.14429e10 | −0.0301340 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.18854e11i | 1.09185i | 0.837833 | + | 0.545926i | \(0.183822\pi\) | ||||
−0.837833 | + | 0.545926i | \(0.816178\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.31948e11 | 0.340482 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.13879e11i | 0.290895i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.79183e11 | 2.47612 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 4.15818e9i | − 0.0104096i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.31554e11 | 1.31739 | 0.658694 | − | 0.752411i | \(-0.271109\pi\) | ||||
0.658694 | + | 0.752411i | \(0.271109\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.39954e11i | 0.588764i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.63172e11 | −0.396382 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 3.72223e11i | − 0.895244i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.15338e9 | −0.00512787 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 1.09360e11i | − 0.257848i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.98989e11 | −0.931466 | −0.465733 | − | 0.884925i | \(-0.654209\pi\) | ||||
−0.465733 | + | 0.884925i | \(0.654209\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1.83588e10i | − 0.0424385i | −0.999775 | − | 0.0212192i | \(-0.993245\pi\) | ||||
0.999775 | − | 0.0212192i | \(-0.00675480\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.01668e10 | 0.206388 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 2.70017e10i | − 0.0612012i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.41046e11 | 2.11214 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.92075e10i | 0.176048i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.50902e11 | 0.332141 | 0.166070 | − | 0.986114i | \(-0.446892\pi\) | ||||
0.166070 | + | 0.986114i | \(0.446892\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 5.25782e11i | − 1.14606i | −0.819535 | − | 0.573029i | \(-0.805768\pi\) | ||||
0.819535 | − | 0.573029i | \(-0.194232\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.89200e11 | −0.624285 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1.65875e11i | − 0.354617i | −0.984155 | − | 0.177309i | \(-0.943261\pi\) | ||||
0.984155 | − | 0.177309i | \(-0.0567390\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.36343e11 | −0.288678 | −0.144339 | − | 0.989528i | \(-0.546106\pi\) | ||||
−0.144339 | + | 0.989528i | \(0.546106\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.47642e11i | 0.309603i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.11873e11 | −1.27081 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.83891e10i | 0.0378281i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.10588e11 | 0.225323 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.41586e11i | 1.29481i | 0.762145 | + | 0.647406i | \(0.224146\pi\) | ||||
−0.762145 | + | 0.647406i | \(0.775854\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.21070e12 | 2.42021 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.20227e11i | 0.238063i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.87477e10 | −0.0563867 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 2.79373e10i | − 0.0542814i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.46142e10 | 0.143612 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.75415e11i | 0.715804i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.03535e9 | −0.0132889 | −0.00664446 | − | 0.999978i | \(-0.502115\pi\) | ||||
−0.00664446 | + | 0.999978i | \(0.502115\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.49519e9i | 0.0158968i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.30808e11 | 0.798657 | 0.399328 | − | 0.916808i | \(-0.369243\pi\) | ||||
0.399328 | + | 0.916808i | \(0.369243\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 7.05962e11i | − 1.29661i | −0.761382 | − | 0.648304i | \(-0.775479\pi\) | ||||
0.761382 | − | 0.648304i | \(-0.224521\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.39738e10 | −0.0618203 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 3.49784e11i | − 0.630604i | −0.948991 | − | 0.315302i | \(-0.897894\pi\) | ||||
0.948991 | − | 0.315302i | \(-0.102106\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.20025e10 | 0.0214391 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.24398e11i | 0.574119i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.72015e11 | 0.301639 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1.32318e12i | − 2.29904i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.25462e11 | 0.216000 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.17106e10i | 0.0199778i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.02015e11 | 0.848631 | 0.424315 | − | 0.905514i | \(-0.360515\pi\) | ||||
0.424315 | + | 0.905514i | \(0.360515\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.92680e11i | 0.322761i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.95986e11 | −0.325328 | −0.162664 | − | 0.986682i | \(-0.552009\pi\) | ||||
−0.162664 | + | 0.986682i | \(0.552009\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 6.69240e11i | − 1.10088i | −0.834876 | − | 0.550439i | \(-0.814460\pi\) | ||||
0.834876 | − | 0.550439i | \(-0.185540\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.29401e10 | 0.0210943 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.04570e11i | 0.815130i | 0.913176 | + | 0.407565i | \(0.133622\pi\) | ||||
−0.913176 | + | 0.407565i | \(0.866378\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.51345e11 | 0.242304 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 7.57959e10i | − 0.120264i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.00351e11 | 0.629557 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 2.91874e9i | − 0.00454887i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.20080e11 | −0.494412 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.41434e12i | 2.16528i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.31340e11 | −0.806256 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.69909e11i | 0.255544i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.36156e10 | −0.0202974 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1.07760e11i | − 0.159232i | −0.996826 | − | 0.0796158i | \(-0.974631\pi\) | ||||
0.996826 | − | 0.0796158i | \(-0.0253693\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.11155e11 | 0.309276 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 3.44029e11i | − 0.499485i | −0.968312 | − | 0.249742i | \(-0.919654\pi\) | ||||
0.968312 | − | 0.249742i | \(-0.0803459\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.26647e12 | −1.82269 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.89617e10i | 0.0270516i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.30359e11 | −0.325782 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 6.25848e11i | − 0.877419i | −0.898629 | − | 0.438709i | \(-0.855436\pi\) | ||||
0.898629 | − | 0.438709i | \(-0.144564\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.17606e11 | −0.997350 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.53950e12i | 2.12116i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.02029e12 | 1.39366 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.10488e11i | 0.420461i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.19959e11 | −0.161054 | −0.0805269 | − | 0.996752i | \(-0.525660\pi\) | ||||
−0.0805269 | + | 0.996752i | \(0.525660\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.02088e12i | 1.35886i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.93629e11 | −0.519470 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 3.68943e10i | − 0.0482740i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.81236e11 | −0.235118 | −0.117559 | − | 0.993066i | \(-0.537507\pi\) | ||||
−0.117559 | + | 0.993066i | \(0.537507\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.42343e11i | 0.311722i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.59055e11 | 0.457934 | 0.228967 | − | 0.973434i | \(-0.426465\pi\) | ||||
0.228967 | + | 0.973434i | \(0.426465\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.37289e11i | − 0.173616i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.53384e9 | −0.00192332 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.42565e12i | − 1.77260i | −0.463109 | − | 0.886302i | \(-0.653266\pi\) | ||||
0.463109 | − | 0.886302i | \(-0.346734\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.11963e12 | −1.38042 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 2.01635e11i | − 0.246515i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.01220e12 | 1.22715 | 0.613573 | − | 0.789638i | \(-0.289732\pi\) | ||||
0.613573 | + | 0.789638i | \(0.289732\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.60663e10i | 0.0433598i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.69372e11 | 1.15569 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 2.85779e11i | − 0.337875i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.16257e11 | −0.370805 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 1.39797e11i | − 0.162552i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.03094e9 | −0.0104141 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.29366e12i | 1.47950i | 0.672881 | + | 0.739750i | \(0.265056\pi\) | ||||
−0.672881 | + | 0.739750i | \(0.734944\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.08553e12 | 1.23125 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 3.23711e11i | − 0.364150i | −0.983285 | − | 0.182075i | \(-0.941719\pi\) | ||||
0.983285 | − | 0.182075i | \(-0.0582813\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.80201e11 | 0.201051 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.69905e11i | 0.962617i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.69052e11 | 0.405050 | 0.202525 | − | 0.979277i | \(-0.435085\pi\) | ||||
0.202525 | + | 0.979277i | \(0.435085\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1.18234e12i | − 1.28710i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.87082e11 | −0.309977 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.92111e11i | 0.634146i | 0.948401 | + | 0.317073i | \(0.102700\pi\) | ||||
−0.948401 | + | 0.317073i | \(0.897300\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.34189e9 | −0.00886175 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.22849e10i | 0.0761691i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.86610e11 | −0.717670 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.22630e11i | 0.230828i | 0.993317 | + | 0.115414i | \(0.0368195\pi\) | ||||
−0.993317 | + | 0.115414i | \(0.963181\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.66820e11 | −0.377273 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 9.21463e9i | − 0.00940125i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.32972e11 | −0.235788 | −0.117894 | − | 0.993026i | \(-0.537614\pi\) | ||||
−0.117894 | + | 0.993026i | \(0.537614\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.67406e11i | 0.268479i |
(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 | 384.9.g.a.127.16 | yes | 32 | |
4.3 | odd | 2 | inner | 384.9.g.a.127.15 | ✓ | 32 | |
8.3 | odd | 2 | 384.9.g.b.127.18 | yes | 32 | ||
8.5 | even | 2 | 384.9.g.b.127.17 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.9.g.a.127.15 | ✓ | 32 | 4.3 | odd | 2 | inner | |
384.9.g.a.127.16 | yes | 32 | 1.1 | even | 1 | trivial | |
384.9.g.b.127.17 | yes | 32 | 8.5 | even | 2 | ||
384.9.g.b.127.18 | yes | 32 | 8.3 | odd | 2 |