Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,10,Mod(193,384)]
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([0, 1, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.193");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.d (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: | \(197.773761087\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 13062x^{6} + 45211107x^{4} + 45928424926x^{2} + 852972309225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.5 | ||
Root | \(90.8862i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.10.d.a.193.4 |
$q$-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 | ||||||||
\(3\) | 81.0000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 2178.24i | − 1.55862i | −0.626636 | − | 0.779312i | \(-0.715569\pi\) | ||||
0.626636 | − | 0.779312i | \(-0.284431\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7658.16 | −1.20554 | −0.602772 | − | 0.797913i | \(-0.705937\pi\) | ||||
−0.602772 | + | 0.797913i | \(0.705937\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6561.00 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 61495.3i | 1.26641i | 0.773984 | + | 0.633205i | \(0.218261\pi\) | ||||
−0.773984 | + | 0.633205i | \(0.781739\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 28283.5i | 0.274655i | 0.990526 | + | 0.137328i | \(0.0438513\pi\) | ||||
−0.990526 | + | 0.137328i | \(0.956149\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 176438. | 0.899872 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 193168. | 0.560939 | 0.280470 | − | 0.959863i | \(-0.409510\pi\) | ||||
0.280470 | + | 0.959863i | \(0.409510\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 366846.i | − 0.645792i | −0.946434 | − | 0.322896i | \(-0.895344\pi\) | ||||
0.946434 | − | 0.322896i | \(-0.104656\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 620311.i | − 0.696021i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −820746. | −0.611553 | −0.305776 | − | 0.952103i | \(-0.598916\pi\) | ||||
−0.305776 | + | 0.952103i | \(0.598916\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.79162e6 | −1.42931 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 531441.i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 4.44100e6i | − 1.16598i | −0.812481 | − | 0.582988i | \(-0.801884\pi\) | ||||
0.812481 | − | 0.582988i | \(-0.198116\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.59982e6 | 0.505609 | 0.252805 | − | 0.967517i | \(-0.418647\pi\) | ||||
0.252805 | + | 0.967517i | \(0.418647\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.98112e6 | −0.731163 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.66813e7i | 1.87899i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.14501e7i | 1.88157i | 0.338999 | + | 0.940787i | \(0.389912\pi\) | ||||
−0.338999 | + | 0.940787i | \(0.610088\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.29096e6 | −0.158572 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.15678e7 | −1.74468 | −0.872341 | − | 0.488898i | \(-0.837399\pi\) | ||||
−0.872341 | + | 0.488898i | \(0.837399\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.42768e6i | 0.420530i | 0.977644 | + | 0.210265i | \(0.0674327\pi\) | ||||
−0.977644 | + | 0.210265i | \(0.932567\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.42915e7i | 0.519541i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.59591e7 | 1.07490 | 0.537450 | − | 0.843295i | \(-0.319388\pi\) | ||||
0.537450 | + | 0.843295i | \(0.319388\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.82938e7 | 0.453337 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.56466e7i | 0.323859i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.97195e7i | 0.691453i | 0.938335 | + | 0.345726i | \(0.112367\pi\) | ||||
−0.938335 | + | 0.345726i | \(0.887633\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.33952e8 | 1.97386 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.97145e7 | 0.372848 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.36289e7i | 1.00595i | 0.864301 | + | 0.502975i | \(0.167761\pi\) | ||||
−0.864301 | + | 0.502975i | \(0.832239\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 3.86390e7i | − 0.357308i | −0.983912 | − | 0.178654i | \(-0.942826\pi\) | ||||
0.983912 | − | 0.178654i | \(-0.0571742\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.02452e7 | 0.401848 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.16083e7 | 0.428084 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.80133e8i | 1.09209i | 0.837757 | + | 0.546043i | \(0.183866\pi\) | ||||
−0.837757 | + | 0.546043i | \(0.816134\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 6.64805e7i | − 0.353080i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.54189e8 | −0.720097 | −0.360049 | − | 0.932934i | \(-0.617240\pi\) | ||||
−0.360049 | + | 0.932934i | \(0.617240\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.79531e8 | −1.56421 | −0.782105 | − | 0.623147i | \(-0.785854\pi\) | ||||
−0.782105 | + | 0.623147i | \(0.785854\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 2.26121e8i | − 0.825212i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 4.70940e8i | − 1.52671i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.21268e8 | 1.50570 | 0.752851 | − | 0.658190i | \(-0.228678\pi\) | ||||
0.752851 | + | 0.658190i | \(0.228678\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.93034e8i | 1.37160i | 0.727790 | + | 0.685801i | \(0.240548\pi\) | ||||
−0.727790 | + | 0.685801i | \(0.759452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 4.20768e8i | − 0.874294i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.59721e8 | 0.673176 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.05828e8 | 0.178790 | 0.0893952 | − | 0.995996i | \(-0.471507\pi\) | ||||
0.0893952 | + | 0.995996i | \(0.471507\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 2.16599e8i | − 0.331109i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.10585e8i | 0.291914i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.99080e8 | −1.00655 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.91252e8 | 0.334038 | 0.167019 | − | 0.985954i | \(-0.446586\pi\) | ||||
0.167019 | + | 0.985954i | \(0.446586\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 4.03470e8i | − 0.422137i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1.38250e9i | − 1.32197i | −0.750401 | − | 0.660983i | \(-0.770140\pi\) | ||||
0.750401 | − | 0.660983i | \(-0.229860\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.22223e8 | −0.457181 | −0.228591 | − | 0.973523i | \(-0.573412\pi\) | ||||
−0.228591 | + | 0.973523i | \(0.573412\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.35119e9 | −1.08484 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 2.56206e9i | − 1.88957i | −0.327695 | − | 0.944784i | \(-0.606272\pi\) | ||||
0.327695 | − | 0.944784i | \(-0.393728\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.72077e8i | 0.320327i | 0.987090 | + | 0.160164i | \(0.0512022\pi\) | ||||
−0.987090 | + | 0.160164i | \(0.948798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.73746e9 | −1.08633 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.44729e8 | 0.545073 | 0.272536 | − | 0.962146i | \(-0.412138\pi\) | ||||
0.272536 | + | 0.962146i | \(0.412138\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.78779e9i | 0.953180i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 1.85568e8i | − 0.0915517i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.47931e9 | −0.676237 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.42372e9 | −0.603796 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 2.55699e9i | − 1.00729i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.82644e9i | 0.669132i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.56290e9 | 0.874209 | 0.437105 | − | 0.899411i | \(-0.356004\pi\) | ||||
0.437105 | + | 0.899411i | \(0.356004\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.63642e8 | −0.242793 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1.68489e9i | − 0.499863i | −0.968264 | − | 0.249931i | \(-0.919592\pi\) | ||||
0.968264 | − | 0.249931i | \(-0.0804081\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.80936e9i | 0.778531i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.15761e9 | −0.299957 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.71074e7 | 0.0138500 | 0.00692501 | − | 0.999976i | \(-0.497796\pi\) | ||||
0.00692501 | + | 0.999976i | \(0.497796\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 5.87092e9i | − 1.33395i | −0.745081 | − | 0.666974i | \(-0.767589\pi\) | ||||
0.745081 | − | 0.666974i | \(-0.232411\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.91269e9i | 0.620594i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.73930e9 | −0.347826 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.67357e9 | −1.81732 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.48180e9i | 0.261734i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 1.06329e10i | − 1.76731i | −0.468136 | − | 0.883656i | \(-0.655074\pi\) | ||||
0.468136 | − | 0.883656i | \(-0.344926\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.05058e9 | 0.634046 | 0.317023 | − | 0.948418i | \(-0.397317\pi\) | ||||
0.317023 | + | 0.948418i | \(0.397317\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.26738e9 | −0.186980 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 5.66303e9i | − 0.788054i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 5.91477e8i | − 0.0776944i | −0.999245 | − | 0.0388472i | \(-0.987631\pi\) | ||||
0.999245 | − | 0.0388472i | \(-0.0123686\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.21728e9 | −0.399210 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.28541e9 | 0.737254 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.71216e10i | 1.89977i | 0.312598 | + | 0.949886i | \(0.398801\pi\) | ||||
−0.312598 | + | 0.949886i | \(0.601199\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.08501e10i | 1.13961i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.79932e10 | 1.79013 | 0.895065 | − | 0.445936i | \(-0.147129\pi\) | ||||
0.895065 | + | 0.445936i | \(0.147129\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.80454e9 | 0.924565 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.40688e9i | 0.215264i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.65957e10i | − 1.40861i | −0.709900 | − | 0.704303i | \(-0.751260\pi\) | ||||
0.709900 | − | 0.704303i | \(-0.248740\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.13787e10 | 1.72310 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.58394e9 | −0.580785 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 1.76363e10i | − 1.28401i | −0.766701 | − | 0.642004i | \(-0.778103\pi\) | ||||
0.766701 | − | 0.642004i | \(-0.221897\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 4.78894e8i | − 0.0331654i | −0.999862 | − | 0.0165827i | \(-0.994721\pi\) | ||||
0.999862 | − | 0.0165827i | \(-0.00527868\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.12976e9 | 0.206292 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.67235e10 | 2.93267 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.18789e10i | 0.710380i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.06986e9i | 0.232007i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.02911e10 | 1.10320 | 0.551601 | − | 0.834108i | \(-0.314017\pi\) | ||||
0.551601 | + | 0.834108i | \(0.314017\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.29052e9 | 0.326346 | 0.163173 | − | 0.986597i | \(-0.447827\pi\) | ||||
0.163173 | + | 0.986597i | \(0.447827\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.99027e9i | 0.247154i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 6.17930e9i | − 0.292308i | −0.989262 | − | 0.146154i | \(-0.953310\pi\) | ||||
0.989262 | − | 0.146154i | \(-0.0466896\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.98276e10 | −0.896255 | −0.448128 | − | 0.893970i | \(-0.647909\pi\) | ||||
−0.448128 | + | 0.893970i | \(0.647909\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.45908e10 | −0.630516 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.40099e10i | 1.40564i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.87623e10i | 2.71930i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.38492e9 | 0.203851 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.25593e10 | 0.817838 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 5.37775e10i | − 1.86780i | −0.357539 | − | 0.933898i | \(-0.616384\pi\) | ||||
0.357539 | − | 0.933898i | \(-0.383616\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.24893e10i | − 0.415748i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.05358e10 | 0.655448 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.99098e10 | −0.609534 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 3.07420e10i | − 0.903097i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.46347e9i | 0.154065i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.21444e10 | 1.14122 | 0.570609 | − | 0.821222i | \(-0.306707\pi\) | ||||
0.570609 | + | 0.821222i | \(0.306707\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.83158e10 | 0.476436 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 6.21393e10i | − 1.55328i | −0.629944 | − | 0.776641i | \(-0.716922\pi\) | ||||
0.629944 | − | 0.776641i | \(-0.283078\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 2.28989e10i | − 0.550244i | −0.961409 | − | 0.275122i | \(-0.911282\pi\) | ||||
0.961409 | − | 0.275122i | \(-0.0887182\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.81462e10 | 0.881449 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.44391e10 | −1.43234 | −0.716172 | − | 0.697923i | \(-0.754108\pi\) | ||||
−0.716172 | + | 0.697923i | \(0.754108\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 7.83277e10i | − 1.67537i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.22227e10i | 0.869318i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.85246e10 | −0.367246 | −0.183623 | − | 0.982997i | \(-0.558783\pi\) | ||||
−0.183623 | + | 0.982997i | \(0.558783\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.59459e10 | −1.64115 | −0.820575 | − | 0.571539i | \(-0.806347\pi\) | ||||
−0.820575 | + | 0.571539i | \(0.806347\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.48678e9i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3.98483e10i | − 0.706581i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.03757e10 | 0.177370 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.80357e10 | −0.791894 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.84815e10i | 0.611957i | 0.952038 | + | 0.305978i | \(0.0989835\pi\) | ||||
−0.952038 | + | 0.305978i | \(0.901016\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 5.04720e10i | − 0.774477i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.40822e10 | 0.504774 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.23429e11 | 1.76489 | 0.882447 | − | 0.470412i | \(-0.155895\pi\) | ||||
0.882447 | + | 0.470412i | \(0.155895\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.64268e11i | − 2.26832i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.91374e10i | 0.388659i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.36808e10 | −0.305207 | −0.152604 | − | 0.988287i | \(-0.548766\pi\) | ||||
−0.152604 | + | 0.988287i | \(0.548766\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.65188e10 | 1.07771 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.57204e9i | 0.103225i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.33379e10i | 0.621085i | 0.950560 | + | 0.310542i | \(0.100511\pi\) | ||||
−0.950560 | + | 0.310542i | \(0.899489\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.06039e11 | −1.19427 | −0.597137 | − | 0.802139i | \(-0.703695\pi\) | ||||
−0.597137 | + | 0.802139i | \(0.703695\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.75445e10 | 0.191166 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1.71671e11i | − 1.81009i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.39984e10i | 0.142863i | 0.997446 | + | 0.0714314i | \(0.0227567\pi\) | ||||
−0.997446 | + | 0.0714314i | \(0.977243\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.70574e10 | −0.168536 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.66573e10 | −0.924818 | −0.462409 | − | 0.886667i | \(-0.653015\pi\) | ||||
−0.462409 | + | 0.886667i | \(0.653015\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1.62302e11i | − 1.50413i | −0.659087 | − | 0.752066i | \(-0.729057\pi\) | ||||
0.659087 | − | 0.752066i | \(-0.270943\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 6.47255e10i | − 0.581130i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.41751e11 | 2.10329 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.12738e10 | −0.685347 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.35914e10i | 0.192857i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.22365e10i | 0.0969957i | 0.998823 | + | 0.0484979i | \(0.0154434\pi\) | ||||
−0.998823 | + | 0.0484979i | \(0.984557\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.03947e11 | 1.56790 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.26811e10 | 0.243721 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 2.32136e10i | − 0.167966i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 7.21987e10i | − 0.506967i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.11983e11 | 0.763237 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.41653e10 | −0.556908 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.03830e11i | 0.667116i | 0.942730 | + | 0.333558i | \(0.108249\pi\) | ||||
−0.942730 | + | 0.333558i | \(0.891751\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 4.23001e10i | − 0.263954i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.95717e10 | 0.118633 | 0.0593167 | − | 0.998239i | \(-0.481108\pi\) | ||||
0.0593167 | + | 0.998239i | \(0.481108\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.36501e11 | 1.39278 | 0.696391 | − | 0.717662i | \(-0.254788\pi\) | ||||
0.696391 | + | 0.717662i | \(0.254788\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 1.09446e11i | − 0.626330i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.54506e11i | − 0.859369i | −0.902979 | − | 0.429684i | \(-0.858625\pi\) | ||||
0.902979 | − | 0.429684i | \(-0.141375\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.73100e11 | 1.47660 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.07527e11 | 1.09094 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 7.08631e10i | − 0.362250i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 7.89567e10i | − 0.392567i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.82382e10 | −0.184941 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.75380e11 | −1.29584 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 4.67240e10i | − 0.213951i | −0.994262 | − | 0.106975i | \(-0.965883\pi\) | ||||
0.994262 | − | 0.106975i | \(-0.0341166\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 1.40734e11i | − 0.627191i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.92373e11 | 1.70215 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.64738e10 | −0.196279 | −0.0981394 | − | 0.995173i | \(-0.531289\pi\) | ||||
−0.0981394 | + | 0.995173i | \(0.531289\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.65231e10i | 0.314698i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.59876e11i | 0.640309i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.68938e11 | 0.659027 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.44811e11 | −0.550319 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1.67034e11i | − 0.618476i | −0.950985 | − | 0.309238i | \(-0.899926\pi\) | ||||
0.950985 | − | 0.309238i | \(-0.100074\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 4.14205e11i | − 1.49452i | −0.664534 | − | 0.747258i | \(-0.731370\pi\) | ||||
0.664534 | − | 0.747258i | \(-0.268630\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.50310e10 | 0.0528574 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.92533e11 | −1.34552 | −0.672759 | − | 0.739862i | \(-0.734891\pi\) | ||||
−0.672759 | + | 0.739862i | \(0.734891\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.35861e11i | 1.12236i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 1.19824e11i | − 0.390426i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.24918e11 | 1.66789 | 0.833943 | − | 0.551850i | \(-0.186078\pi\) | ||||
0.833943 | + | 0.551850i | \(0.186078\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.88112e11 | 0.582953 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1.15321e11i | − 0.348602i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.26712e11i | 2.43801i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.29807e11 | 0.661250 | 0.330625 | − | 0.943762i | \(-0.392740\pi\) | ||||
0.330625 | + | 0.943762i | \(0.392740\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.07116e11 | 0.581561 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 3.04178e11i | − 0.833577i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 5.03584e10i | − 0.134704i | −0.997729 | − | 0.0673522i | \(-0.978545\pi\) | ||||
0.997729 | − | 0.0673522i | \(-0.0214551\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.47942e11 | −0.386323 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.25607e11 | 0.320241 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 4.42233e11i | − 1.10097i | −0.834846 | − | 0.550484i | \(-0.814443\pi\) | ||||
0.834846 | − | 0.550484i | \(-0.185557\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.07595e11i | 0.504725i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.96927e11 | 0.942576 | 0.471288 | − | 0.881979i | \(-0.343789\pi\) | ||||
0.471288 | + | 0.881979i | \(0.343789\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.02582e12 | −2.37957 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 6.18550e10i | − 0.140177i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.68232e11i | 1.70106i | 0.525929 | + | 0.850529i | \(0.323718\pi\) | ||||
−0.525929 | + | 0.850529i | \(0.676282\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.58542e11 | −0.343044 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.36476e11 | 0.288596 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 1.13545e12i | − 2.34682i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.41102e11i | 0.689172i | 0.938755 | + | 0.344586i | \(0.111981\pi\) | ||||
−0.938755 | + | 0.344586i | \(0.888019\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.27559e11 | −0.449485 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.83691e11 | 1.12728 | 0.563642 | − | 0.826019i | \(-0.309400\pi\) | ||||
0.563642 | + | 0.826019i | \(0.309400\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.35318e10i | 0.138868i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 9.37662e10i | − 0.173180i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.31908e12 | −2.38284 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.80713e11 | 1.37955 | 0.689773 | − | 0.724026i | \(-0.257710\pi\) | ||||
0.689773 | + | 0.724026i | \(0.257710\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.62570e9i | 0.00799631i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 7.17025e11i | − 1.21272i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.29177e12 | 2.13781 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.75544e11 | 0.770156 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.88488e11i | 0.932769i | 0.884582 | + | 0.466385i | \(0.154444\pi\) | ||||
−0.884582 | + | 0.466385i | \(0.845556\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.50950e11i | 0.389330i | 0.980870 | + | 0.194665i | \(0.0623620\pi\) | ||||
−0.980870 | + | 0.194665i | \(0.937638\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.35928e11 | −0.358300 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.39253e11 | −0.801756 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.95904e11i | 0.430750i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 1.40883e11i | − 0.200817i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.22079e12 | −1.70409 | −0.852046 | − | 0.523467i | \(-0.824638\pi\) | ||||
−0.852046 | + | 0.523467i | \(0.824638\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.85938e11 | 0.390909 | 0.195455 | − | 0.980713i | \(-0.437382\pi\) | ||||
0.195455 | + | 0.980713i | \(0.437382\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 7.83559e11i | − 1.04923i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.01088e11i | 0.394936i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.26567e11 | −0.548147 | −0.274073 | − | 0.961709i | \(-0.588371\pi\) | ||||
−0.274073 | + | 0.961709i | \(0.588371\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.20025e11 | −0.151112 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.78131e11i | 0.343109i | 0.985175 | + | 0.171555i | \(0.0548790\pi\) | ||||
−0.985175 | + | 0.171555i | \(0.945121\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 2.30518e11i | − 0.278667i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.61265e11 | 1.02036 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.47195e11 | 0.751496 | 0.375748 | − | 0.926722i | \(-0.377386\pi\) | ||||
0.375748 | + | 0.926722i | \(0.377386\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1.94127e12i | − 2.20948i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.28097e11i | 0.366067i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.71806e11 | −0.516074 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.87836e11 | 1.05940 | 0.529702 | − | 0.848184i | \(-0.322304\pi\) | ||||
0.529702 | + | 0.848184i | \(0.322304\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 1.02658e11i | − 0.107953i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 5.23286e11i | − 0.539616i | −0.962914 | − | 0.269808i | \(-0.913040\pi\) | ||||
0.962914 | − | 0.269808i | \(-0.0869603\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.21613e11 | −0.932039 | −0.466020 | − | 0.884774i | \(-0.654312\pi\) | ||||
−0.466020 | + | 0.884774i | \(0.654312\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.58705e11 | 0.454983 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.04570e11i | 0.101738i | 0.998705 | + | 0.0508689i | \(0.0161991\pi\) | ||||
−0.998705 | + | 0.0508689i | \(0.983801\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 1.37949e12i | − 1.31656i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.79097e10 | 0.0448569 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.79758e11 | −0.532563 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.02409e12i | 0.923036i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 2.60600e11i | − 0.230484i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.93040e12 | 1.67547 | 0.837737 | − | 0.546074i | \(-0.183878\pi\) | ||||
0.837737 | + | 0.546074i | \(0.183878\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.06683e11 | −0.516784 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.09118e11i | 0.425654i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 6.34417e11i | − 0.520639i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.28669e12 | −1.03656 | −0.518281 | − | 0.855210i | \(-0.673428\pi\) | ||||
−0.518281 | + | 0.855210i | \(0.673428\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.38685e12 | −1.09683 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.58967e12i | 1.23436i | 0.786823 | + | 0.617179i | \(0.211724\pi\) | ||||
−0.786823 | + | 0.617179i | \(0.788276\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 8.57860e11i | − 0.654042i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.78857e11 | −0.657953 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.18080e12 | 0.868109 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.27745e12i | 0.922344i | 0.887311 | + | 0.461172i | \(0.152571\pi\) | ||||
−0.887311 | + | 0.461172i | \(0.847429\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.45745e12i | 1.03353i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.40613e11 | −0.167596 | −0.0837979 | − | 0.996483i | \(-0.526705\pi\) | ||||
−0.0837979 | + | 0.996483i | \(0.526705\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.01143e12 | −2.06045 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.94168e11i | 0.533798i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.46994e11i | 0.361204i | 0.983556 | + | 0.180602i | \(0.0578046\pi\) | ||||
−0.983556 | + | 0.180602i | \(0.942195\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.90651e12 | 1.88572 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.94957e11 | −0.124283 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.13753e12i | 0.712574i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.21131e12i | 1.36127i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.34426e12 | 0.813259 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.49243e12 | 1.48202 | 0.741009 | − | 0.671495i | \(-0.234347\pi\) | ||||
0.741009 | + | 0.671495i | \(0.234347\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.54454e12i | 0.902697i | 0.892348 | + | 0.451349i | \(0.149057\pi\) | ||||
−0.892348 | + | 0.451349i | \(0.850943\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.73167e12i | 0.994829i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.02202e11 | 0.283616 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.12753e12 | −0.626004 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 6.14299e11i | − 0.335316i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 8.92846e11i | − 0.479186i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.58079e12 | −2.94513 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.42854e12 | 0.741322 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.12498e12i | 0.574110i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.66468e11i | 0.234118i | 0.993125 | + | 0.117059i | \(0.0373466\pi\) | ||||
−0.993125 | + | 0.117059i | \(0.962653\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.87904e10 | 0.0191481 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.02830e12 | 0.499269 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1.63835e12i | − 0.782462i | −0.920293 | − | 0.391231i | \(-0.872049\pi\) | ||||
0.920293 | − | 0.391231i | \(-0.127951\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.53511e11i | 0.119103i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.62916e12 | −0.752978 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.99195e12 | −1.81519 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.78460e12i | 1.69318i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 6.77404e11i | − 0.298194i | −0.988823 | − | 0.149097i | \(-0.952363\pi\) | ||||
0.988823 | − | 0.149097i | \(-0.0476367\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.66647e11 | −0.115501 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.62194e11 | −0.410138 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.75360e12i | 1.15508i | 0.816361 | + | 0.577542i | \(0.195988\pi\) | ||||
−0.816361 | + | 0.577542i | \(0.804012\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 2.05785e12i | − 0.849563i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.29659e11 | −0.133949 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.14461e12 | 0.857716 | 0.428858 | − | 0.903372i | \(-0.358916\pi\) | ||||
0.428858 | + | 0.903372i | \(0.358916\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.43875e12i | 1.35375i | 0.736098 | + | 0.676875i | \(0.236666\pi\) | ||||
−0.736098 | + | 0.676875i | \(0.763334\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.64358e12i | 0.636934i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.29121e12 | 0.874098 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.85300e12 | −1.07155 | −0.535773 | − | 0.844362i | \(-0.679980\pi\) | ||||
−0.535773 | + | 0.844362i | \(0.679980\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.09532e11i | 0.188416i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 4.54154e12i | − 1.65353i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.44256e12 | −0.875663 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.04212e11 | −0.142695 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.36076e10i | 0.00820691i | 0.999992 | + | 0.00410346i | \(0.00130617\pi\) | ||||
−0.999992 | + | 0.00410346i | \(0.998694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 9.53732e11i | − 0.326518i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.00523e11 | 0.168764 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.05586e12 | −0.682727 | −0.341364 | − | 0.939931i | \(-0.610889\pi\) | ||||
−0.341364 | + | 0.939931i | \(0.610889\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.22231e12i | 1.05400i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 1.60604e12i | − 0.517453i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.72088e12 | −1.81569 | −0.907846 | − | 0.419304i | \(-0.862274\pi\) | ||||
−0.907846 | + | 0.419304i | \(0.862274\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.10411e12 | 0.970516 | 0.485258 | − | 0.874371i | \(-0.338726\pi\) | ||||
0.485258 | + | 0.874371i | \(0.338726\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.18185e12i | − 0.364028i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.10121e12i | 0.941091i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.37507e12 | −0.411127 | −0.205564 | − | 0.978644i | \(-0.565903\pi\) | ||||
−0.205564 | + | 0.978644i | \(0.565903\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.75480e12 | −0.811544 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.01705e12i | 0.295227i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 6.69362e12i | − 1.91465i | −0.289016 | − | 0.957324i | \(-0.593328\pi\) | ||||
0.289016 | − | 0.957324i | \(-0.406672\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.56974e12 | −1.56999 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.17726e11 | 0.116040 | 0.0580201 | − | 0.998315i | \(-0.481521\pi\) | ||||
0.0580201 | + | 0.998315i | \(0.481521\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 6.34992e12i | − 1.73844i | −0.494423 | − | 0.869221i | \(-0.664621\pi\) | ||||
0.494423 | − | 0.869221i | \(-0.335379\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.36178e11i | 0.117693i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.10445e11 | −0.215540 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.47394e12 | −0.386385 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.82730e12i | 0.472179i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.14348e12i | 1.05545i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.73127e12 | −1.18808 | −0.594040 | − | 0.804435i | \(-0.702468\pi\) | ||||
−0.594040 | + | 0.804435i | \(0.702468\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.35598e12 | 1.07837 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 5.58263e12i | − 1.36256i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.17411e11i | 0.124511i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.01163e12 | 0.240032 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.90673e12 | 0.914014 | 0.457007 | − | 0.889463i | \(-0.348921\pi\) | ||||
0.457007 | + | 0.889463i | \(0.348921\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.06347e12i | 0.476046i | 0.971260 | + | 0.238023i | \(0.0764993\pi\) | ||||
−0.971260 | + | 0.238023i | \(0.923501\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.66340e12i | 0.378423i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.14405e12 | −0.929728 | −0.464864 | − | 0.885382i | \(-0.653897\pi\) | ||||
−0.464864 | + | 0.885382i | \(0.653897\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.75773e12 | −1.27394 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 1.61269e12i | − 0.351915i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 8.11599e12i | − 1.74676i | −0.487044 | − | 0.873378i | \(-0.661925\pi\) | ||||
0.487044 | − | 0.873378i | \(-0.338075\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.67010e12 | −0.779098 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.49011e12 | 0.521403 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 8.57180e11i | − 0.177047i | −0.996074 | − | 0.0885234i | \(-0.971785\pi\) | ||||
0.996074 | − | 0.0885234i | \(-0.0282148\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.57325e12i | 0.320546i | 0.987073 | + | 0.160273i | \(0.0512375\pi\) | ||||
−0.987073 | + | 0.160273i | \(0.948762\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.42541e11 | −0.0889494 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.11948e12 | 1.21344 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.64493e12i | 0.713055i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.41370e12i | 0.658882i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.37612e12 | 0.452498 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.91142e12 | 0.922867 | 0.461434 | − | 0.887175i | \(-0.347335\pi\) | ||||
0.461434 | + | 0.887175i | \(0.347335\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.48358e12i | 0.275071i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.67942e12i | 0.856137i | 0.903746 | + | 0.428069i | \(0.140806\pi\) | ||||
−0.903746 | + | 0.428069i | \(0.859194\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.23045e12 | −0.402697 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.03329e12 | 0.896787 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.92535e12i | 1.04189i | 0.853591 | + | 0.520944i | \(0.174420\pi\) | ||||
−0.853591 | + | 0.520944i | \(0.825580\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1.24394e11i | − 0.0215870i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.85481e12 | 0.317683 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.12341e12 | −0.189911 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.43776e12i | 0.740479i | 0.928936 | + | 0.370239i | \(0.120724\pi\) | ||||
−0.928936 | + | 0.370239i | \(0.879276\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.08984e12i | 0.508905i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.27883e13 | −2.07912 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.09789e12 | −0.978661 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 5.21956e12i | − 0.826965i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.55720e12i | 1.49486i | 0.664343 | + | 0.747428i | \(0.268712\pi\) | ||||
−0.664343 | + | 0.747428i | \(0.731288\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.86888e12 | 1.21511 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.34454e12 | 0.967273 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.05874e13i | 1.59369i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 5.67373e12i | − 0.843258i | −0.906769 | − | 0.421629i | \(-0.861459\pi\) | ||||
0.906769 | − | 0.421629i | \(-0.138541\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.42004e12 | −0.501901 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.13379e12 | −0.309207 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.78862e12i | 0.542130i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1.50049e12i | − 0.212030i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.80229e11 | 0.0530598 | 0.0265299 | − | 0.999648i | \(-0.491554\pi\) | ||||
0.0265299 | + | 0.999648i | \(0.491554\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.99927e12 | 0.551152 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 6.96161e12i | − 0.947518i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.23976e13i | 1.66654i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.32242e13 | 1.75576 | 0.877880 | − | 0.478881i | \(-0.158957\pi\) | ||||
0.877880 | + | 0.478881i | \(0.158957\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.82430e11 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.82113e12i | 0.235892i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.53563e13i | − 1.96480i | −0.186797 | − | 0.982399i | \(-0.559811\pi\) | ||||
0.186797 | − | 0.982399i | \(-0.440189\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.22771e12 | 0.407945 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.10773e13 | −1.38303 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.82404e12i | 0.841669i | 0.907137 | + | 0.420835i | \(0.138263\pi\) | ||||
−0.907137 | + | 0.420835i | \(0.861737\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.40430e11i | 0.102405i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.28798e12 | 0.756940 | 0.378470 | − | 0.925614i | \(-0.376450\pi\) | ||||
0.378470 | + | 0.925614i | \(0.376450\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.31610e13 | −2.75458 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 3.89089e12i | − 0.457200i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.96207e13i | 2.27796i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.19773e13 | 1.37397 | 0.686986 | − | 0.726671i | \(-0.258933\pi\) | ||||
0.686986 | + | 0.726671i | \(0.258933\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.11700e12 | −0.353313 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 8.82315e12i | − 0.988240i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 5.00435e12i | − 0.553881i | −0.960887 | − | 0.276940i | \(-0.910680\pi\) | ||||
0.960887 | − | 0.276940i | \(-0.0893205\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.08823e12 | 0.447144 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.44206e12 | 0.263952 | 0.131976 | − | 0.991253i | \(-0.457868\pi\) | ||||
0.131976 | + | 0.991253i | \(0.457868\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 3.61524e12i | − 0.386168i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.76066e12i | 0.291431i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.64815e12 | −0.276289 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.52460e12 | 0.879034 | 0.439517 | − | 0.898234i | \(-0.355150\pi\) | ||||
0.439517 | + | 0.898234i | \(0.355150\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.99776e12i | 1.01896i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.84609e12i | 0.588922i | 0.955664 | + | 0.294461i | \(0.0951401\pi\) | ||||
−0.955664 | + | 0.294461i | \(0.904860\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.25769e12 | −0.722672 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.33057e13 | 1.30962 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.15805e13i | 1.12670i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 9.48190e12i | − 0.911939i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.36013e12 | −0.224392 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.28838e12 | −0.121096 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.32719e13i | 1.23324i | 0.787262 | + | 0.616618i | \(0.211498\pi\) | ||||
−0.787262 | + | 0.616618i | \(0.788502\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 1.91814e12i | − 0.176211i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.23489e12 | −0.657109 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.09285e12 | 0.0981363 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.00802e12i | 0.622219i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.02632e12i | 0.177887i | 0.996037 | + | 0.0889436i | \(0.0283491\pi\) | ||||
−0.996037 | + | 0.0889436i | \(0.971651\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.94616e12 | 0.602954 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.94335e11 | −0.0595968 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2.33394e13i | − 1.98093i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.36911e13i | − 1.14910i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.32037e12 | −0.358584 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.71860e12 | −0.305219 | −0.152609 | − | 0.988287i | \(-0.548768\pi\) | ||||
−0.152609 | + | 0.988287i | \(0.548768\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 8.32783e12i | − 0.675987i | −0.941149 | − | 0.337993i | \(-0.890252\pi\) | ||||
0.941149 | − | 0.337993i | \(-0.109748\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 8.58916e12i | − 0.689515i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.72951e13 | 2.96103 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.45851e12 | 0.271575 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.42111e12i | 0.110370i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 3.72889e12i | − 0.286441i | −0.989691 | − | 0.143220i | \(-0.954254\pi\) | ||||
0.989691 | − | 0.143220i | \(-0.0457458\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.95662e12 | −0.376605 | −0.188303 | − | 0.982111i | \(-0.560299\pi\) | ||||
−0.188303 | + | 0.982111i | \(0.560299\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.39054e13 | 1.04506 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.05532e12i | 0.152794i | 0.997077 | + | 0.0763968i | \(0.0243416\pi\) | ||||
−0.997077 | + | 0.0763968i | \(0.975658\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.49719e12i | 0.330709i | 0.986234 | + | 0.165354i | \(0.0528768\pi\) | ||||
−0.986234 | + | 0.165354i | \(0.947123\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.13387e12 | −0.0824818 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.53378e12 | 0.254294 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 3.91936e13i | − 2.79014i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 1.38165e12i | − 0.0973045i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.05888e12 | 0.631169 | 0.315585 | − | 0.948897i | \(-0.397799\pi\) | ||||
0.315585 | + | 0.948897i | \(0.397799\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.21531e12 | −0.359499 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 7.82924e12i | − 0.533944i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 2.13567e13i | − 1.44105i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.09031e13 | 0.727903 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.31465e13 | 0.868411 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1.76051e13i | − 1.15068i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 2.43668e13i | − 1.57589i | −0.615743 | − | 0.787947i | \(-0.711144\pi\) | ||||
0.615743 | − | 0.787947i | \(-0.288856\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.24276e12 | 0.335516 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.54772e13 | 0.980117 | 0.490059 | − | 0.871689i | \(-0.336975\pi\) | ||||
0.490059 | + | 0.871689i | \(0.336975\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1.56032e12i | − 0.0977790i | −0.998804 | − | 0.0488895i | \(-0.984432\pi\) | ||||
0.998804 | − | 0.0488895i | \(-0.0155682\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.95818e13i | 1.21434i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.09332e13 | −0.670962 | −0.335481 | − | 0.942047i | \(-0.608899\pi\) | ||||
−0.335481 | + | 0.942047i | \(0.608899\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.61496e13 | −2.19549 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 6.58318e12i | − 0.395685i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.20555e13i | 1.90684i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.09478e12 | −0.299947 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.91090e12 | −0.111346 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1.39872e13i | − 0.806668i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1.51832e13i | − 0.866693i | −0.901227 | − | 0.433347i | \(-0.857333\pi\) | ||||
0.901227 | − | 0.433347i | \(-0.142667\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.91156e11 | −0.0560005 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.87715e13 | 1.60905 | 0.804527 | − | 0.593916i | \(-0.202419\pi\) | ||||
0.804527 | + | 0.593916i | \(0.202419\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.30013e13i | − 1.27329i | −0.771155 | − | 0.636647i | \(-0.780321\pi\) | ||||
0.771155 | − | 0.636647i | \(-0.219679\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.65197e13i | 0.905225i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.27341e13 | 0.690735 | 0.345367 | − | 0.938468i | \(-0.387754\pi\) | ||||
0.345367 | + | 0.938468i | \(0.387754\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.96271e13 | −1.05390 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.64717e12i | 0.140712i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.31914e13i | − 0.694162i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.84161e13 | −2.00129 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.88030e12 | 0.0969752 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1.15458e13i | − 0.589528i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.67255e12i | 0.387863i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.84809e12 | 0.292698 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.04315e12 | −0.0516924 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 2.44366e12i | − 0.119897i | −0.998201 | − | 0.0599484i | \(-0.980906\pi\) | ||||
0.998201 | − | 0.0599484i | \(-0.0190936\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.07061e12i | 0.440655i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.69051e12 | 0.177523 | 0.0887613 | − | 0.996053i | \(-0.471709\pi\) | ||||
0.0887613 | + | 0.996053i | \(0.471709\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.64688e13 | −1.73701 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 6.81739e12i | − 0.321531i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.29032e13i | 0.602607i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.04045e13 | 0.481173 | 0.240587 | − | 0.970628i | \(-0.422660\pi\) | ||||
0.240587 | + | 0.970628i | \(0.422660\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.41025e12 | −0.385160 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 4.36100e12i | − 0.197778i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 5.98805e13i | − 2.68935i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.42631e12 | 0.152394 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.78338e13 | −1.66652 | −0.833258 | − | 0.552885i | \(-0.813527\pi\) | ||||
−0.833258 | + | 0.552885i | \(0.813527\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 6.71100e12i | − 0.292761i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.58531e12i | 0.0684930i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.58752e13 | 1.10721 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.67680e12 | −0.325351 | −0.162675 | − | 0.986680i | \(-0.552012\pi\) | ||||
−0.162675 | + | 0.986680i | \(0.552012\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.91566e13i | 0.804123i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.98175e12i | 0.0823941i | 0.999151 | + | 0.0411970i | \(0.0131171\pi\) | ||||
−0.999151 | + | 0.0411970i | \(0.986883\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.59091e13 | 1.06696 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.86514e12 | 0.361612 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.68460e13i | − 0.680647i | −0.940308 | − | 0.340324i | \(-0.889463\pi\) | ||||
0.940308 | − | 0.340324i | \(-0.110537\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 1.07345e13i | − 0.429618i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.25150e13 | 0.496157 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.24737e13 | 0.882585 | 0.441293 | − | 0.897363i | \(-0.354520\pi\) | ||||
0.441293 | + | 0.897363i | \(0.354520\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 4.41989e13i | − 1.71948i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.21211e13i | 0.852518i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.37338e11 | −0.0166968 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.96806e13 | −0.744359 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.68097e13i | 0.629856i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1.37023e13i | − 0.508651i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.69178e13 | −1.35774 | −0.678871 | − | 0.734258i | \(-0.737530\pi\) | ||||
−0.678871 | + | 0.734258i | \(0.737530\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.73991e12 | 0.209145 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1.73104e13i | − 0.624913i | −0.949932 | − | 0.312456i | \(-0.898848\pi\) | ||||
0.949932 | − | 0.312456i | \(-0.101152\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.49604e13i | 1.60813i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.39549e12 | 0.226649 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.58899e13 | 0.909085 | 0.454543 | − | 0.890725i | \(-0.349803\pi\) | ||||
0.454543 | + | 0.890725i | \(0.349803\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.50790e12i | 0.226422i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 3.09730e12i | − 0.106776i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.22442e13 | 0.759848 | 0.379924 | − | 0.925018i | \(-0.375950\pi\) | ||||
0.379924 | + | 0.925018i | \(0.375950\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.34600e13 | −0.455599 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 2.23058e13i | − 0.748154i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 7.73774e12i | − 0.257176i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.85698e13 | 1.27033 | 0.635165 | − | 0.772377i | \(-0.280932\pi\) | ||||
0.635165 | + | 0.772377i | \(0.280932\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.78465e12 | 0.123525 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.31894e13i | 1.39693i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.29804e13i | 0.416062i | 0.978122 | + | 0.208031i | \(0.0667056\pi\) | ||||
−0.978122 | + | 0.208031i | \(0.933294\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.13995e13 | 0.362109 |
(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 | 384.10.d.a.193.5 | yes | 8 | |
4.3 | odd | 2 | 384.10.d.b.193.1 | yes | 8 | ||
8.3 | odd | 2 | 384.10.d.b.193.8 | yes | 8 | ||
8.5 | even | 2 | inner | 384.10.d.a.193.4 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.10.d.a.193.4 | ✓ | 8 | 8.5 | even | 2 | inner | |
384.10.d.a.193.5 | yes | 8 | 1.1 | even | 1 | trivial | |
384.10.d.b.193.1 | yes | 8 | 4.3 | odd | 2 | ||
384.10.d.b.193.8 | yes | 8 | 8.3 | odd | 2 |