Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,8,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, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.193");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
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: | \(119.955849786\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} - 1020 x^{14} + 7280 x^{13} + 388150 x^{12} - 2423904 x^{11} - 70542796 x^{10} + \cdots + 694045717832241 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{108}\cdot 3^{28} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.6 | ||
Root | \(-18.4308 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.8.d.f.193.11 |
$q$-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 | ||||||||
\(3\) | − 27.0000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 183.972i | 0.658199i | 0.944295 | + | 0.329099i | \(0.106745\pi\) | ||||
−0.944295 | + | 0.329099i | \(0.893255\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −284.564 | −0.313572 | −0.156786 | − | 0.987633i | \(-0.550113\pi\) | ||||
−0.156786 | + | 0.987633i | \(0.550113\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −729.000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 5594.99i | − 1.26743i | −0.773566 | − | 0.633716i | \(-0.781529\pi\) | ||||
0.773566 | − | 0.633716i | \(-0.218471\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 14239.5i | − 1.79760i | −0.438358 | − | 0.898800i | \(-0.644440\pi\) | ||||
0.438358 | − | 0.898800i | \(-0.355560\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4967.25 | 0.380011 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6689.16 | 0.330218 | 0.165109 | − | 0.986275i | \(-0.447202\pi\) | ||||
0.165109 | + | 0.986275i | \(0.447202\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 25535.9i | − 0.854109i | −0.904226 | − | 0.427054i | \(-0.859551\pi\) | ||||
0.904226 | − | 0.427054i | \(-0.140449\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7683.23i | 0.181041i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −38266.6 | −0.655802 | −0.327901 | − | 0.944712i | \(-0.606341\pi\) | ||||
−0.327901 | + | 0.944712i | \(0.606341\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 44279.3 | 0.566775 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19683.0i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 159373.i | 1.21345i | 0.794911 | + | 0.606726i | \(0.207518\pi\) | ||||
−0.794911 | + | 0.606726i | \(0.792482\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 315025. | 1.89924 | 0.949620 | − | 0.313405i | \(-0.101470\pi\) | ||||
0.949620 | + | 0.313405i | \(0.101470\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −151065. | −0.731752 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 52351.8i | − 0.206392i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 445274.i | 1.44518i | 0.691278 | + | 0.722589i | \(0.257048\pi\) | ||||
−0.691278 | + | 0.722589i | \(0.742952\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −384467. | −1.03785 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 298003. | 0.675268 | 0.337634 | − | 0.941277i | \(-0.390373\pi\) | ||||
0.337634 | + | 0.941277i | \(0.390373\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 112165.i | 0.215138i | 0.994198 | + | 0.107569i | \(0.0343066\pi\) | ||||
−0.994198 | + | 0.107569i | \(0.965693\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 134116.i | − 0.219400i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −444602. | −0.624639 | −0.312320 | − | 0.949977i | \(-0.601106\pi\) | ||||
−0.312320 | + | 0.949977i | \(0.601106\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −742566. | −0.901673 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 180607.i | − 0.190651i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 677212.i | − 0.624826i | −0.949946 | − | 0.312413i | \(-0.898863\pi\) | ||||
0.949946 | − | 0.312413i | \(-0.101137\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.02932e6 | 0.834222 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −689469. | −0.493120 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 1.80472e6i | − 1.14401i | −0.820251 | − | 0.572004i | \(-0.806166\pi\) | ||||
0.820251 | − | 0.572004i | \(-0.193834\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 513377.i | − 0.289589i | −0.989462 | − | 0.144795i | \(-0.953748\pi\) | ||||
0.989462 | − | 0.144795i | \(-0.0462521\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 207447. | 0.104524 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.61967e6 | 1.18318 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 3.66168e6i | − 1.48737i | −0.668530 | − | 0.743685i | \(-0.733076\pi\) | ||||
0.668530 | − | 0.743685i | \(-0.266924\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.03320e6i | 0.378627i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.21898e6 | −1.06737 | −0.533684 | − | 0.845684i | \(-0.679193\pi\) | ||||
−0.533684 | + | 0.845684i | \(0.679193\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.10349e6 | −0.933727 | −0.466864 | − | 0.884329i | \(-0.654616\pi\) | ||||
−0.466864 | + | 0.884329i | \(0.654616\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 1.19554e6i | − 0.327227i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.59213e6i | 0.397431i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 520868. | 0.118859 | 0.0594296 | − | 0.998232i | \(-0.481072\pi\) | ||||
0.0594296 | + | 0.998232i | \(0.481072\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.29441e6i | 0.440451i | 0.975449 | + | 0.220226i | \(0.0706793\pi\) | ||||
−0.975449 | + | 0.220226i | \(0.929321\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.23062e6i | 0.217349i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.30308e6 | 0.700587 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.41532e6 | −1.11497 | −0.557487 | − | 0.830186i | \(-0.688234\pi\) | ||||
−0.557487 | + | 0.830186i | \(0.688234\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.05205e6i | 0.563676i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 8.50569e6i | − 1.09653i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.69789e6 | 0.562173 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.06744e6 | 0.341252 | 0.170626 | − | 0.985336i | \(-0.445421\pi\) | ||||
0.170626 | + | 0.985336i | \(0.445421\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.07874e6i | 0.422477i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1.40466e7i | − 1.35659i | −0.734791 | − | 0.678294i | \(-0.762720\pi\) | ||||
0.734791 | − | 0.678294i | \(-0.237280\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.49402e7 | −1.34719 | −0.673593 | − | 0.739103i | \(-0.735250\pi\) | ||||
−0.673593 | + | 0.739103i | \(0.735250\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.41350e6 | −0.119161 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 3.93955e6i | − 0.310888i | −0.987845 | − | 0.155444i | \(-0.950319\pi\) | ||||
0.987845 | − | 0.155444i | \(-0.0496808\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 42469.4i | 0.00314111i | 0.999999 | + | 0.00157056i | \(0.000499924\pi\) | ||||
−0.999999 | + | 0.00157056i | \(0.999500\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.20224e7 | 0.834374 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.55574e7 | −1.66626 | −0.833129 | − | 0.553078i | \(-0.813453\pi\) | ||||
−0.833129 | + | 0.553078i | \(0.813453\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 7.03999e6i | − 0.431648i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.03806e7i | 0.599200i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.90349e6 | −0.103547 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.18167e7 | −0.606383 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 8.04607e6i | − 0.389866i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.25190e7i | 1.03125i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.68496e7 | 0.729924 | 0.364962 | − | 0.931023i | \(-0.381082\pi\) | ||||
0.364962 | + | 0.931023i | \(0.381082\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.02845e6 | 0.124210 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 421999.i | 0.0164007i | 0.999966 | + | 0.00820035i | \(0.00261028\pi\) | ||||
−0.999966 | + | 0.00820035i | \(0.997390\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.26659e6i | 0.267824i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.62112e6 | −0.126670 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.61817e7 | −1.53443 | −0.767217 | − | 0.641388i | \(-0.778359\pi\) | ||||
−0.767217 | + | 0.641388i | \(0.778359\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.34792e7i | 1.05736i | 0.848821 | + | 0.528680i | \(0.177313\pi\) | ||||
−0.848821 | + | 0.528680i | \(0.822687\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.20043e7i | 0.360636i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.96698e7 | −2.27834 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.93203e7 | −0.798693 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.00493e7i | 0.520581i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.65368e7i | 0.657198i | 0.944470 | + | 0.328599i | \(0.106576\pi\) | ||||
−0.944470 | + | 0.328599i | \(0.893424\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.94638e7 | 1.64187 | 0.820936 | − | 0.571021i | \(-0.193452\pi\) | ||||
0.820936 | + | 0.571021i | \(0.193452\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.87640e6 | −0.110073 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.79559e7i | 1.25008i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.41307e7i | 0.497646i | 0.968549 | + | 0.248823i | \(0.0800438\pi\) | ||||
−0.968549 | + | 0.248823i | \(0.919956\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.82847e7 | −0.360744 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.08893e7 | 0.205641 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1.36103e7i | − 0.246157i | −0.992397 | − | 0.123078i | \(-0.960723\pi\) | ||||
0.992397 | − | 0.123078i | \(-0.0392766\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 2.77917e7i | − 0.481638i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.38336e7 | 0.229841 | 0.114921 | − | 0.993375i | \(-0.463339\pi\) | ||||
0.114921 | + | 0.993375i | \(0.463339\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.40015e8 | −2.23137 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.86157e7i | 0.284703i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.04444e8i | − 1.53364i | −0.641862 | − | 0.766820i | \(-0.721838\pi\) | ||||
0.641862 | − | 0.766820i | \(-0.278162\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.26003e7 | −0.177724 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.87275e7 | −0.660493 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 7.08133e6i | − 0.0922846i | −0.998935 | − | 0.0461423i | \(-0.985307\pi\) | ||||
0.998935 | − | 0.0461423i | \(-0.0146928\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1.08452e8i | − 1.35945i | −0.733465 | − | 0.679727i | \(-0.762098\pi\) | ||||
0.733465 | − | 0.679727i | \(-0.237902\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.38612e7 | −0.167194 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.19180e7 | −0.951214 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3.74258e7i | − 0.418528i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 5.60107e6i | − 0.0603469i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.38858e7 | 0.974951 | 0.487476 | − | 0.873137i | \(-0.337918\pi\) | ||||
0.487476 | + | 0.873137i | \(0.337918\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.03956e8 | −1.04088 | −0.520439 | − | 0.853899i | \(-0.674232\pi\) | ||||
−0.520439 | + | 0.853899i | \(0.674232\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 7.07311e7i | − 0.683108i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.56759e8i | 1.46083i | 0.683002 | + | 0.730416i | \(0.260674\pi\) | ||||
−0.683002 | + | 0.730416i | \(0.739326\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.30545e7 | −0.297334 | −0.148667 | − | 0.988887i | \(-0.547498\pi\) | ||||
−0.148667 | + | 0.988887i | \(0.547498\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.88655e7 | −0.858734 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4.53519e7i | − 0.380504i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.48242e7i | 0.444461i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.78964e7 | 0.218601 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.42873e8 | −1.08252 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 7.58975e7i | − 0.556210i | −0.960551 | − | 0.278105i | \(-0.910294\pi\) | ||||
0.960551 | − | 0.278105i | \(-0.0897064\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.69125e7i | 0.616246i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.06352e7 | −0.141603 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.96449e7 | −0.595547 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.37941e7i | 0.539088i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 9.52503e7i | − 0.593600i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.24762e7 | −0.437652 | −0.218826 | − | 0.975764i | \(-0.570223\pi\) | ||||
−0.218826 | + | 0.975764i | \(0.570223\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.22796e7 | −0.188925 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 1.54924e8i | − 0.879077i | −0.898224 | − | 0.439539i | \(-0.855142\pi\) | ||||
0.898224 | − | 0.439539i | \(-0.144858\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 1.71007e8i | − 0.940998i | −0.882400 | − | 0.470499i | \(-0.844074\pi\) | ||||
0.882400 | − | 0.470499i | \(-0.155926\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.29875e7 | 0.229457 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.41003e7 | −0.435564 | −0.217782 | − | 0.975997i | \(-0.569882\pi\) | ||||
−0.217782 | + | 0.975997i | \(0.569882\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 8.17944e7i | − 0.411137i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.40634e7i | − 0.0686234i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.01887e7 | 0.285182 | 0.142591 | − | 0.989782i | \(-0.454457\pi\) | ||||
0.142591 | + | 0.989782i | \(0.454457\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.16773e8 | −0.997575 | −0.498788 | − | 0.866724i | \(-0.666221\pi\) | ||||
−0.498788 | + | 0.866724i | \(0.666221\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.43489e7i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.36612e8i | − 0.593480i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.63618e8 | −1.53535 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.19491e7 | 0.254295 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.90911e8i | 1.16119i | 0.814193 | + | 0.580594i | \(0.197180\pi\) | ||||
−0.814193 | + | 0.580594i | \(0.802820\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.14101e8i | 0.831184i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.32267e7 | 0.125486 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.97350e8 | −1.82766 | −0.913831 | − | 0.406095i | \(-0.866890\pi\) | ||||
−0.913831 | + | 0.406095i | \(0.866890\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.26709e8i | − 0.453167i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 1.16183e8i | − 0.404484i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.98800e8 | 1.69076 | 0.845378 | − | 0.534168i | \(-0.179375\pi\) | ||||
0.845378 | + | 0.534168i | \(0.179375\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.24588e8 | 0.411260 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.00214e8i | 0.643730i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.27422e7i | 0.290499i | 0.989395 | + | 0.145249i | \(0.0463984\pi\) | ||||
−0.989395 | + | 0.145249i | \(0.953602\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.16293e7 | −0.157581 | −0.0787905 | − | 0.996891i | \(-0.525106\pi\) | ||||
−0.0787905 | + | 0.996891i | \(0.525106\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.09405e8 | 0.325439 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 2.47742e8i | − 0.718348i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.92885e8i | 1.11067i | 0.831625 | + | 0.555337i | \(0.187411\pi\) | ||||
−0.831625 | + | 0.555337i | \(0.812589\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.29654e8 | −0.633080 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.37674e8 | −0.370152 | −0.185076 | − | 0.982724i | \(-0.559253\pi\) | ||||
−0.185076 | + | 0.982724i | \(0.559253\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 6.74922e7i | − 0.177011i | −0.996076 | − | 0.0885057i | \(-0.971791\pi\) | ||||
0.996076 | − | 0.0885057i | \(-0.0282091\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 1.26843e8i | − 0.324571i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.48008e7 | −0.211745 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.65594e8 | −0.890956 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 8.28208e7i | − 0.197022i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.45006e8i | 0.801289i | 0.916233 | + | 0.400645i | \(0.131214\pi\) | ||||
−0.916233 | + | 0.400645i | \(0.868786\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.32019e8 | 0.752984 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.10126e8 | 0.243917 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.44898e8i | 1.17887i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 3.19180e7i | − 0.0674611i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.79260e8 | −0.783226 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.44471e7 | 0.190607 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 9.09040e8i | − 1.79308i | −0.442968 | − | 0.896538i | \(-0.646074\pi\) | ||||
0.442968 | − | 0.896538i | \(-0.353926\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.03387e8i | 0.777798i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.17772e8 | −1.35308 | −0.676542 | − | 0.736404i | \(-0.736522\pi\) | ||||
−0.676542 | + | 0.736404i | \(0.736522\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.85927e7 | −0.163303 | −0.0816513 | − | 0.996661i | \(-0.526019\pi\) | ||||
−0.0816513 | + | 0.996661i | \(0.526019\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.81645e7i | 0.0687975i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.89237e8i | 0.862605i | 0.902207 | + | 0.431302i | \(0.141946\pi\) | ||||
−0.902207 | + | 0.431302i | \(0.858054\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.91692e8 | 1.53797 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.06368e8 | −0.179491 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.70814e8i | − 0.282042i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 6.30515e8i | − 1.01883i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.14667e6 | 0.00181352 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.26518e8 | 0.195869 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.88413e8i | 1.49810i | 0.662514 | + | 0.749050i | \(0.269489\pi\) | ||||
−0.662514 | + | 0.749050i | \(0.730511\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 3.24605e8i | − 0.481726i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.73648e8 | 0.978985 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.18765e9 | 1.69038 | 0.845188 | − | 0.534469i | \(-0.179488\pi\) | ||||
0.845188 | + | 0.534469i | \(0.179488\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.90050e8i | 0.962015i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 1.76256e9i | − 2.40716i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.45658e8 | 0.596311 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.90080e8 | −0.249212 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.37733e9i | 1.76964i | 0.465930 | + | 0.884821i | \(0.345720\pi\) | ||||
−0.465930 | + | 0.884821i | \(0.654280\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 3.14137e8i | − 0.395576i | −0.980245 | − | 0.197788i | \(-0.936624\pi\) | ||||
0.980245 | − | 0.197788i | \(-0.0633757\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.80276e8 | 0.345948 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.67291e8 | 0.807428 | 0.403714 | − | 0.914885i | \(-0.367719\pi\) | ||||
0.403714 | + | 0.914885i | \(0.367719\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 5.92203e8i | − 0.702541i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.13943e7i | 0.0597828i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.01929e9 | −1.16269 | −0.581347 | − | 0.813656i | \(-0.697474\pi\) | ||||
−0.581347 | + | 0.813656i | \(0.697474\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.41791e8 | 0.270498 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.19051e8i | 0.350096i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 5.70955e8i | − 0.614578i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.63115e9 | −1.72252 | −0.861259 | − | 0.508167i | \(-0.830323\pi\) | ||||
−0.861259 | + | 0.508167i | \(0.830323\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.17244e8 | −0.225089 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.92710e8i | 0.195928i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.79337e8i | 0.977128i | 0.872528 | + | 0.488564i | \(0.162479\pi\) | ||||
−0.872528 | + | 0.488564i | \(0.837521\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.08012e8 | 0.595392 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.26940e9 | 2.18130 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 7.09025e7i | − 0.0668997i | −0.999440 | − | 0.0334498i | \(-0.989351\pi\) | ||||
0.999440 | − | 0.0334498i | \(-0.0106494\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 4.54940e8i | − 0.421422i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.89421e8 | −0.263230 | −0.131615 | − | 0.991301i | \(-0.542016\pi\) | ||||
−0.131615 | + | 0.991301i | \(0.542016\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.92908e8 | −0.261588 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 8.17680e7i | − 0.0717126i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.78931e9i | 1.54121i | 0.637314 | + | 0.770604i | \(0.280045\pi\) | ||||
−0.637314 | + | 0.770604i | \(0.719955\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.55972e8 | −0.216557 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.13940e7 | 0.00946894 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.58252e7i | 0.0782330i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.16405e8i | 0.334002i | 0.985957 | + | 0.167001i | \(0.0534083\pi\) | ||||
−0.985957 | + | 0.167001i | \(0.946592\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.96198e8 | 0.154628 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.22663e9 | 0.949965 | 0.474983 | − | 0.879995i | \(-0.342454\pi\) | ||||
0.474983 | + | 0.879995i | \(0.342454\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 4.48581e9i | − 3.41407i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.77703e7i | 0.0731332i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.49130e9 | 1.83166 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.90034e9 | 1.37341 | 0.686704 | − | 0.726937i | \(-0.259057\pi\) | ||||
0.686704 | + | 0.726937i | \(0.259057\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.24691e9i | 0.885905i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.13559e8i | 0.358728i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.22107e8 | −0.289904 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.03938e8 | 0.610467 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 9.70717e8i | − 0.644679i | −0.946624 | − | 0.322339i | \(-0.895531\pi\) | ||||
0.946624 | − | 0.322339i | \(-0.104469\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 1.33738e9i | − 0.873509i | −0.899581 | − | 0.436755i | \(-0.856128\pi\) | ||||
0.899581 | − | 0.436755i | \(-0.143872\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.24115e8 | 0.208213 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.96191e8 | 0.187159 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.46089e8i | 0.0908069i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.15109e9i | 1.31540i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.12208e9 | −1.87834 | −0.939169 | − | 0.343455i | \(-0.888403\pi\) | ||||
−0.939169 | + | 0.343455i | \(0.888403\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.31888e9 | 0.780724 | 0.390362 | − | 0.920661i | \(-0.372350\pi\) | ||||
0.390362 | + | 0.920661i | \(0.372350\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.91647e8i | 0.461125i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.77172e8i | 0.560126i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.36568e8 | −0.0770410 | −0.0385205 | − | 0.999258i | \(-0.512264\pi\) | ||||
−0.0385205 | + | 0.999258i | \(0.512264\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.41331e8 | 0.300558 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.12150e9i | 0.612894i | 0.951888 | + | 0.306447i | \(0.0991402\pi\) | ||||
−0.951888 | + | 0.306447i | \(0.900860\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1.36421e9i | − 0.733874i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.16493e8 | 0.379433 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.24802e8 | 0.169339 | 0.0846693 | − | 0.996409i | \(-0.473017\pi\) | ||||
0.0846693 | + | 0.996409i | \(0.473017\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1.66732e9i | − 0.855857i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 1.87552e9i | − 0.947935i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.45464e8 | −0.371011 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.60194e9 | −0.785126 | −0.392563 | − | 0.919725i | \(-0.628411\pi\) | ||||
−0.392563 | + | 0.919725i | \(0.628411\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.31663e8i | 0.0635504i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 1.41415e9i | − 0.672268i | −0.941814 | − | 0.336134i | \(-0.890880\pi\) | ||||
0.941814 | − | 0.336134i | \(-0.109120\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.32759e9 | 1.08986 | 0.544932 | − | 0.838480i | \(-0.316555\pi\) | ||||
0.544932 | + | 0.838480i | \(0.316555\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.56481e9 | 0.721732 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.69027e8i | 0.303973i | 0.988383 | + | 0.151986i | \(0.0485670\pi\) | ||||
−0.988383 | + | 0.151986i | \(0.951433\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.04198e9i | 0.466397i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.51529e8 | 0.287316 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.27560e8 | 0.272672 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1.13071e9i | − 0.484087i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.93688e8i | 0.208275i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.55573e9 | 1.06253 | 0.531265 | − | 0.847206i | \(-0.321717\pi\) | ||||
0.531265 | + | 0.847206i | \(0.321717\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.34048e9 | 2.59785 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 2.94011e8i | − 0.118727i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.64323e8i | 0.224611i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.14252e8 | 0.319453 | 0.159727 | − | 0.987161i | \(-0.448939\pi\) | ||||
0.159727 | + | 0.987161i | \(0.448939\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.67478e8 | −0.142119 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.42000e9i | 1.68514i | 0.538584 | + | 0.842572i | \(0.318960\pi\) | ||||
−0.538584 | + | 0.842572i | \(0.681040\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.06607e9i | 0.400703i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.50375e8 | −0.278074 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.16006e8 | 0.334696 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 5.22005e9i | − 1.88071i | −0.340188 | − | 0.940357i | \(-0.610491\pi\) | ||||
0.340188 | − | 0.940357i | \(-0.389509\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 3.73508e8i | − 0.132699i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.31577e9 | −1.86242 | −0.931212 | − | 0.364479i | \(-0.881247\pi\) | ||||
−0.931212 | + | 0.364479i | \(0.881247\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.58419e9 | 0.892904 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.78041e9i | 1.28828i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.25207e7i | 0.00756954i | 0.999993 | + | 0.00378477i | \(0.00120473\pi\) | ||||
−0.999993 | + | 0.00378477i | \(0.998795\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.83140e8 | 0.292790 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.02623e8 | 0.164373 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 2.74859e9i | − 0.886716i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.48754e9i | 0.791688i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.82000e9 | −0.885448 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.69906e9 | −0.836143 | −0.418071 | − | 0.908414i | \(-0.637294\pi\) | ||||
−0.418071 | + | 0.908414i | \(0.637294\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 5.30973e9i | − 1.62299i | −0.584357 | − | 0.811497i | \(-0.698653\pi\) | ||||
0.584357 | − | 0.811497i | \(-0.301347\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.40208e8i | 0.102609i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.10726e9 | 0.627162 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.94049e9 | −0.569924 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.31564e9i | 0.381336i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 4.24341e9i | − 1.21386i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.24767e8 | 0.204626 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.91196e8 | −0.0532805 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.15465e9i | 1.14281i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 2.01180e7i | − 0.00546255i | −0.999996 | − | 0.00273127i | \(-0.999131\pi\) | ||||
0.999996 | − | 0.00273127i | \(-0.000869393\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.92822e9 | −0.784881 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.81319e6 | −0.00206748 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 6.92319e8i | − 0.180863i | −0.995903 | − | 0.0904317i | \(-0.971175\pi\) | ||||
0.995903 | − | 0.0904317i | \(-0.0288247\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.74252e8i | 0.0965297i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.06974e9 | 1.03642 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.48220e8 | −0.0372709 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.21179e9i | 0.549184i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.79188e9i | 0.684549i | 0.939600 | + | 0.342274i | \(0.111197\pi\) | ||||
−0.939600 | + | 0.342274i | \(0.888803\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.59717e9 | 0.386732 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.01050e9 | −0.241638 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.93722e8i | 0.163835i | 0.996639 | + | 0.0819173i | \(0.0261043\pi\) | ||||
−0.996639 | + | 0.0819173i | \(0.973896\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 4.70185e9i | − 1.09673i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.51229e8 | −0.0348413 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.92736e9 | 1.12130 | 0.560649 | − | 0.828053i | \(-0.310552\pi\) | ||||
0.560649 | + | 0.828053i | \(0.310552\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 3.97256e9i | − 0.892984i | −0.894788 | − | 0.446492i | \(-0.852673\pi\) | ||||
0.894788 | − | 0.446492i | \(-0.147327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 2.53492e9i | − 0.562889i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.69442e9 | −0.371692 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.68322e9 | −1.23163 | −0.615814 | − | 0.787892i | \(-0.711173\pi\) | ||||
−0.615814 | + | 0.787892i | \(0.711173\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.80682e9i | 0.600951i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 6.52906e8i | − 0.138113i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.78899e9 | −0.791925 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.90974e9 | −0.394393 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.92999e9i | 1.00603i | 0.864277 | + | 0.503017i | \(0.167777\pi\) | ||||
−0.864277 | + | 0.503017i | \(0.832223\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 8.04445e9i | − 1.62216i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.23249e9 | 0.843412 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.08495e9 | −1.00137 | −0.500685 | − | 0.865629i | \(-0.666919\pi\) | ||||
−0.500685 | + | 0.865629i | \(0.666919\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 3.50190e8i | − 0.0681544i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.92470e8i | 0.171666i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.33152e9 | 0.633357 | 0.316679 | − | 0.948533i | \(-0.397432\pi\) | ||||
0.316679 | + | 0.948533i | \(0.397432\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.84837e9 | −1.09894 | −0.549470 | − | 0.835513i | \(-0.685170\pi\) | ||||
−0.549470 | + | 0.835513i | \(0.685170\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.66937e9i | 0.495790i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 2.17394e9i | − 0.399121i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.27070e9 | −1.68249 | −0.841244 | − | 0.540655i | \(-0.818176\pi\) | ||||
−0.841244 | + | 0.540655i | \(0.818176\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.22450e9 | −0.219684 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.33092e9i | 1.12285i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.35417e9i | 1.11416i | 0.830459 | + | 0.557080i | \(0.188078\pi\) | ||||
−0.830459 | + | 0.557080i | \(0.811922\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.48025e9 | 0.256610 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.20833e9 | 1.06409 | 0.532043 | − | 0.846718i | \(-0.321425\pi\) | ||||
0.532043 | + | 0.846718i | \(0.321425\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 4.14645e9i | − 0.702682i | −0.936248 | − | 0.351341i | \(-0.885726\pi\) | ||||
0.936248 | − | 0.351341i | \(-0.114274\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 7.53202e8i | − 0.126209i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.11013e9 | 0.349624 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.83545e8 | −0.111992 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.85757e9i | 0.624996i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.97851e9i | 0.477223i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.67069e9 | −0.423176 | −0.211588 | − | 0.977359i | \(-0.567864\pi\) | ||||
−0.211588 | + | 0.977359i | \(0.567864\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.04923e9 | −0.321128 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.09986e9i | 0.480435i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.05738e10i | 1.62085i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.34664e9 | 0.355790 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.26474e9 | −1.38941 | −0.694705 | − | 0.719295i | \(-0.744465\pi\) | ||||
−0.694705 | + | 0.719295i | \(0.744465\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 6.02904e9i | − 0.894354i | −0.894445 | − | 0.447177i | \(-0.852429\pi\) | ||||
0.894445 | − | 0.447177i | \(-0.147571\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.57150e8i | 0.0817547i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.87910e9 | 1.43401 | 0.717005 | − | 0.697068i | \(-0.245512\pi\) | ||||
0.717005 | + | 0.697068i | \(0.245512\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.00974e10 | −1.44995 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.42041e9i | 0.343839i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.01069e10i | 1.42044i | 0.703980 | + | 0.710220i | \(0.251405\pi\) | ||||
−0.703980 | + | 0.710220i | \(0.748595\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.76361e7 | −0.0107949 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.26244e9 | 0.311242 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.18052e9i | 0.977366i | 0.872461 | + | 0.488683i | \(0.162523\pi\) | ||||
−0.872461 | + | 0.488683i | \(0.837477\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.28840e10i | 1.73518i | 0.497277 | + | 0.867592i | \(0.334333\pi\) | ||||
−0.497277 | + | 0.867592i | \(0.665667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.57176e9 | −0.342715 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.33685e9 | −0.176282 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 6.09868e9i | − 0.795784i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.95686e9i | 0.252678i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.87234e9 | −0.367035 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.98882e9 | −0.630877 | −0.315439 | − | 0.948946i | \(-0.602152\pi\) | ||||
−0.315439 | + | 0.948946i | \(0.602152\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.71549e8i | 0.109076i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1.13046e10i | − 1.40021i | −0.714040 | − | 0.700105i | \(-0.753137\pi\) | ||||
0.714040 | − | 0.700105i | \(-0.246863\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.72882e8 | −0.107007 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.18294e9 | −0.507535 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.06414e10i | − 1.27798i | −0.769214 | − | 0.638991i | \(-0.779352\pi\) | ||||
0.769214 | − | 0.638991i | \(-0.220648\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 8.49615e9i | − 1.00996i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.61718e9 | −0.543286 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.64317e9 | −1.12319 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1.57441e10i | − 1.81529i | −0.419743 | − | 0.907643i | \(-0.637880\pi\) | ||||
0.419743 | − | 0.907643i | \(-0.362120\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.16066e9i | − 0.132477i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.15924e9 | −0.695953 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.99339e9 | 0.222986 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.27071e9i | 0.251473i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 4.43950e9i | − 0.486767i | −0.969930 | − | 0.243384i | \(-0.921743\pi\) | ||||
0.969930 | − | 0.243384i | \(-0.0782574\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.13705e10 | 1.23434 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.20845e9 | −0.237370 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.99717e9i | 0.425387i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1.36199e10i | − 1.43520i | −0.696457 | − | 0.717599i | \(-0.745241\pi\) | ||||
0.696457 | − | 0.717599i | \(-0.254759\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.79713e8 | −0.0396198 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.20550e10 | −1.24552 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1.46570e10i | − 1.49960i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1.62510e9i | − 0.164650i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.21125e9 | 0.924204 | 0.462102 | − | 0.886827i | \(-0.347095\pi\) | ||||
0.462102 | + | 0.886827i | \(0.347095\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.25146e9 | 0.422439 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.85287e9i | 0.575950i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.05693e9i | 0.687754i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.19112e9 | 0.308015 | 0.154008 | − | 0.988070i | \(-0.450782\pi\) | ||||
0.154008 | + | 0.988070i | \(0.450782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.87420e8 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.50287e8i | 0.0710423i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 6.29300e9i | − 0.590193i | −0.955467 | − | 0.295097i | \(-0.904648\pi\) | ||||
0.955467 | − | 0.295097i | \(-0.0953518\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.68851e9 | −0.342646 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.04871e10 | −1.88514 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 7.41064e9i | − 0.675461i | −0.941243 | − | 0.337730i | \(-0.890341\pi\) | ||||
0.941243 | − | 0.337730i | \(-0.109659\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.81769e9i | 0.886433i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.34972e10 | −1.20721 | −0.603605 | − | 0.797283i | \(-0.706270\pi\) | ||||
−0.603605 | + | 0.797283i | \(0.706270\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.88202e9 | −0.432567 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1.67262e9i | − 0.146817i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.12105e9i | 0.0974855i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.51489e9 | −0.302811 | −0.151406 | − | 0.988472i | \(-0.548380\pi\) | ||||
−0.151406 | + | 0.988472i | \(0.548380\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.85461e9 | 0.670413 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.27794e10i | 1.08068i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1.76869e10i | − 1.48189i | −0.671567 | − | 0.740944i | \(-0.734378\pi\) | ||||
0.671567 | − | 0.740944i | \(-0.265622\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.78073e9 | 0.479884 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.31006e9 | −0.436770 | −0.218385 | − | 0.975863i | \(-0.570079\pi\) | ||||
−0.218385 | + | 0.975863i | \(0.570079\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.20853e7i | 0 0.000984964i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 8.97121e8i | − 0.0724496i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.56984e10 | −2.05647 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.07584e10 | −0.853114 | −0.426557 | − | 0.904461i | \(-0.640274\pi\) | ||||
−0.426557 | + | 0.904461i | \(0.640274\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.34284e10i | 1.05520i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.62681e9i | 0.360291i | 0.983640 | + | 0.180146i | \(0.0576569\pi\) | ||||
−0.983640 | + | 0.180146i | \(0.942343\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.39491e10 | 1.07644 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.42114e9 | −0.261636 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 7.60976e9i | − 0.576753i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.80102e10i | 1.35282i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.13695e9 | −0.233529 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.43937e9 | −0.327550 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.11869e9i | 0.520581i | 0.965530 | + | 0.260291i | \(0.0838184\pi\) | ||||
−0.965530 | + | 0.260291i | \(0.916182\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 1.34676e10i | − 0.976159i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.27272e9 | 0.522491 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.31024e9 | −0.520566 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 3.36388e9i | − 0.237441i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.53742e10i | − 1.07569i | −0.843043 | − | 0.537846i | \(-0.819238\pi\) | ||||
0.843043 | − | 0.537846i | \(-0.180762\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.97402e9 | −0.206267 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.40577e9 | 0.371658 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.73640e10i | 1.18344i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.00333e9i | 0.135353i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.50404e9 | 0.167720 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.11744e10 | 1.40602 | 0.703008 | − | 0.711182i | \(-0.251840\pi\) | ||||
0.703008 | + | 0.711182i | \(0.251840\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1.97139e10i | − 1.29778i | −0.760883 | − | 0.648889i | \(-0.775234\pi\) | ||||
0.760883 | − | 0.648889i | \(-0.224766\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.39399e9i | 0.0909794i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.50392e9 | 0.162020 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.86422e9 | 0.183751 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 2.95394e9i | − 0.187892i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.39351e10i | 1.50951i | 0.656009 | + | 0.754753i | \(0.272243\pi\) | ||||
−0.656009 | + | 0.754753i | \(0.727757\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.42443e10 | 1.51604 | 0.758020 | − | 0.652231i | \(-0.226167\pi\) | ||||
0.758020 | + | 0.652231i | \(0.226167\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.68903e9 | −0.414738 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1.22177e10i | − 0.751137i | −0.926795 | − | 0.375568i | \(-0.877448\pi\) | ||||
0.926795 | − | 0.375568i | \(-0.122552\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.53509e10i | 1.54544i | 0.634747 | + | 0.772720i | \(0.281105\pi\) | ||||
−0.634747 | + | 0.772720i | \(0.718895\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.06079e10 | 0.641248 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.96715e9 | −0.297748 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.54500e9i | 0.151281i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.20065e9i | 0.365509i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.80130e10 | −1.05298 | −0.526488 | − | 0.850182i | \(-0.676492\pi\) | ||||
−0.526488 | + | 0.850182i | \(0.676492\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.14999e9 | −0.472467 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.71720e9i | 0.213707i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 2.57589e10i | − 1.46868i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.36261e9 | 0.190145 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.82229e9 | −0.102198 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1.70391e10i | − 0.947750i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1.29463e10i | − 0.714207i | −0.934065 | − | 0.357104i | \(-0.883764\pi\) | ||||
0.934065 | − | 0.357104i | \(-0.116236\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.42476e9 | −0.187391 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.35856e10 | 1.28001 | 0.640006 | − | 0.768370i | \(-0.278932\pi\) | ||||
0.640006 | + | 0.768370i | \(0.278932\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1.37171e10i | − 0.738391i | −0.929352 | − | 0.369196i | \(-0.879633\pi\) | ||||
0.929352 | − | 0.369196i | \(-0.120367\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.28962e9i | 0.122251i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.29995e10 | 1.21809 | 0.609046 | − | 0.793135i | \(-0.291552\pi\) | ||||
0.609046 | + | 0.793135i | \(0.291552\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.92148e10 | 1.00944 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.87103e9i | 0.514394i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 2.91425e9i | − 0.150646i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.21406e10 | −2.67370 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.23616e9 | −0.113751 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 6.40809e9i | − 0.323370i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 2.42484e10i | − 1.21390i | −0.794739 | − | 0.606952i | \(-0.792392\pi\) | ||||
0.794739 | − | 0.606952i | \(-0.207608\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.31515e9 | 0.462625 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.91329e9 | 0.242079 | 0.121039 | − | 0.992648i | \(-0.461377\pi\) | ||||
0.121039 | + | 0.992648i | \(0.461377\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.82033e10i | 1.37860i | 0.724478 | + | 0.689298i | \(0.242081\pi\) | ||||
−0.724478 | + | 0.689298i | \(0.757919\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 8.96451e9i | − 0.434735i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.26085e10 | 0.606640 | 0.303320 | − | 0.952889i | \(-0.401905\pi\) | ||||
0.303320 | + | 0.952889i | \(0.401905\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.79480e9 | −0.228883 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 2.97340e9i | − 0.140826i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.13533e10i | 0.533510i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.30277e9 | 0.0607416 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.47122e10 | 0.680621 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.02067e10i | 2.30464i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 4.52998e9i | − 0.206329i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.61786e8 | −0.0389487 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.99522e10 | 0.894791 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 2.92782e10i | − 1.30292i | −0.758681 | − | 0.651462i | \(-0.774156\pi\) | ||||
0.758681 | − | 0.651462i | \(-0.225844\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.02400e10i | 0.452196i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.95238e9 | −0.129377 | −0.0646887 | − | 0.997905i | \(-0.520605\pi\) | ||||
−0.0646887 | + | 0.997905i | \(0.520605\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.28372e10 | 0.558242 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 2.55007e9i | − 0.110047i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1.20086e8i | − 0.00514279i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.90924e10 | −0.811441 | −0.405720 | − | 0.913997i | \(-0.632979\pi\) | ||||
−0.405720 | + | 0.913997i | \(0.632979\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.45441e10 | −1.03523 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.58367e10i | 1.91870i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.97164e10i | 0.819090i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.08914e10 | 0.449062 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.96279e10 | 0.803192 | 0.401596 | − | 0.915817i | \(-0.368456\pi\) | ||||
0.401596 | + | 0.915817i | \(0.368456\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.89621e10i | 0.770127i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.93798e10i | 0.781204i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.88530e9 | 0.275475 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.31934e8 | −0.00523924 | −0.00261962 | − | 0.999997i | \(-0.500834\pi\) | ||||
−0.00261962 | + | 0.999997i | \(0.500834\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.39200e9i | 0.0942828i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.52276e10i | 1.37822i | 0.724655 | + | 0.689112i | \(0.241999\pi\) | ||||
−0.724655 | + | 0.689112i | \(0.758001\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.14036e10 | −0.442842 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.03044e9 | 0.0397202 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.17267e10i | − 0.448696i | −0.974509 | − | 0.224348i | \(-0.927975\pi\) | ||||
0.974509 | − | 0.224348i | \(-0.0720253\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.41921e10i | 1.67847i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.32094e10 | 0.498025 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.67093e10 | 0.999627 | 0.499813 | − | 0.866133i | \(-0.333402\pi\) | ||||
0.499813 | + | 0.866133i | \(0.333402\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.72724e10i | 0.641712i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 2.40757e10i | − 0.887946i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.31416e10 | 0.481155 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.17284e10 | 2.60711 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.87193e9i | 0.103629i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1.91250e10i | − 0.685104i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.16153e10 | 1.12436 | 0.562179 | − | 0.827015i | \(-0.309963\pi\) | ||||
0.562179 | + | 0.827015i | \(0.309963\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.61197e9 | −0.162837 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 5.58741e10i | − 1.95859i | −0.202444 | − | 0.979294i | \(-0.564888\pi\) | ||||
0.202444 | − | 0.979294i | \(-0.435112\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 9.52696e9i | − 0.331558i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.70239e10 | −0.588224 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.53125e10 | −0.868369 | −0.434184 | − | 0.900824i | \(-0.642963\pi\) | ||||
−0.434184 | + | 0.900824i | \(0.642963\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.14886e10i | 1.41315i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 3.09602e7i | − 0.00104704i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.54874e10 | −1.86319 | −0.931595 | − | 0.363497i | \(-0.881583\pi\) | ||||
−0.931595 | + | 0.363497i | \(0.881583\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.88393e10 | −0.961518 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 3.41598e9i | − 0.113085i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 4.29216e9i | − 0.141088i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.49201e10 | 0.486982 | 0.243491 | − | 0.969903i | \(-0.421707\pi\) | ||||
0.243491 | + | 0.969903i | \(0.421707\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.66872e10 | 0.864928 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 6.08110e9i | − 0.195705i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.99025e9i | 0.159474i | 0.996816 | + | 0.0797369i | \(0.0254080\pi\) | ||||
−0.996816 | + | 0.0797369i | \(0.974592\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.76433e9 | −0.278125 |
(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 | 384.8.d.f.193.6 | yes | 16 | |
4.3 | odd | 2 | inner | 384.8.d.f.193.14 | yes | 16 | |
8.3 | odd | 2 | inner | 384.8.d.f.193.3 | ✓ | 16 | |
8.5 | even | 2 | inner | 384.8.d.f.193.11 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.8.d.f.193.3 | ✓ | 16 | 8.3 | odd | 2 | inner | |
384.8.d.f.193.6 | yes | 16 | 1.1 | even | 1 | trivial | |
384.8.d.f.193.11 | yes | 16 | 8.5 | even | 2 | inner | |
384.8.d.f.193.14 | yes | 16 | 4.3 | odd | 2 | inner |