Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(289,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.289");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.f (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: | \(51.3228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 289.10 | ||
Character | \(\chi\) | \(=\) | 320.289 |
Dual form | 320.6.f.d.289.11 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −11.4004 | −0.731337 | −0.365668 | − | 0.930745i | \(-0.619160\pi\) | ||||
−0.365668 | + | 0.930745i | \(0.619160\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 32.3114 | − | 45.6177i | 0.578004 | − | 0.816034i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 121.355i | − | 0.936076i | −0.883708 | − | 0.468038i | \(-0.844961\pi\) | ||
0.883708 | − | 0.468038i | \(-0.155039\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −113.031 | −0.465147 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 625.005i | − | 1.55741i | −0.627393 | − | 0.778703i | \(-0.715878\pi\) | ||
0.627393 | − | 0.778703i | \(-0.284122\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −924.688 | −1.51753 | −0.758764 | − | 0.651366i | \(-0.774196\pi\) | ||||
−0.758764 | + | 0.651366i | \(0.774196\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −368.363 | + | 520.060i | −0.422716 | + | 0.596795i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1325.51i | − | 1.11240i | −0.831049 | − | 0.556199i | \(-0.812259\pi\) | ||
0.831049 | − | 0.556199i | \(-0.187741\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1135.08i | 0.721342i | 0.932693 | + | 0.360671i | \(0.117452\pi\) | ||||
−0.932693 | + | 0.360671i | \(0.882548\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1383.49i | 0.684586i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3055.36i | 1.20432i | 0.798375 | + | 0.602160i | \(0.205693\pi\) | ||||
−0.798375 | + | 0.602160i | \(0.794307\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1036.94 | − | 2947.94i | −0.331822 | − | 0.943342i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4058.90 | 1.07152 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 8232.27i | − | 1.81771i | −0.417113 | − | 0.908855i | \(-0.636958\pi\) | ||
0.417113 | − | 0.908855i | \(-0.363042\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1985.84 | −0.371141 | −0.185571 | − | 0.982631i | \(-0.559413\pi\) | ||||
−0.185571 | + | 0.982631i | \(0.559413\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7125.31i | 1.13899i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5535.91 | − | 3921.14i | −0.763869 | − | 0.541056i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9681.82 | 1.16266 | 0.581330 | − | 0.813668i | \(-0.302532\pi\) | ||||
0.581330 | + | 0.813668i | \(0.302532\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10541.8 | 1.10982 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −15897.7 | −1.47698 | −0.738491 | − | 0.674264i | \(-0.764461\pi\) | ||||
−0.738491 | + | 0.674264i | \(0.764461\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 18727.8 | 1.54460 | 0.772299 | − | 0.635259i | \(-0.219107\pi\) | ||||
0.772299 | + | 0.635259i | \(0.219107\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3652.18 | + | 5156.20i | −0.268857 | + | 0.379575i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5162.47i | 0.340889i | 0.985367 | + | 0.170444i | \(0.0545203\pi\) | ||||
−0.985367 | + | 0.170444i | \(0.945480\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2080.07 | 0.123762 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 15111.4i | 0.813538i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5659.20 | −0.276736 | −0.138368 | − | 0.990381i | \(-0.544186\pi\) | ||||
−0.138368 | + | 0.990381i | \(0.544186\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −28511.3 | − | 20194.8i | −1.27090 | − | 0.900187i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 12940.3i | − | 0.527544i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 28693.0i | 1.07311i | 0.843864 | + | 0.536557i | \(0.180275\pi\) | ||||
−0.843864 | + | 0.536557i | \(0.819725\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2410.34i | 0.0829382i | 0.999140 | + | 0.0414691i | \(0.0132038\pi\) | ||||
−0.999140 | + | 0.0414691i | \(0.986796\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13716.8i | 0.435413i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −29878.0 | + | 42182.1i | −0.877138 | + | 1.23835i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 45886.3 | 1.24881 | 0.624405 | − | 0.781101i | \(-0.285342\pi\) | ||||
0.624405 | + | 0.781101i | \(0.285342\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 34832.3i | − | 0.880764i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5535.02 | −0.130309 | −0.0651544 | − | 0.997875i | \(-0.520754\pi\) | ||||
−0.0651544 | + | 0.997875i | \(0.520754\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 58819.4i | 1.29185i | 0.763399 | + | 0.645927i | \(0.223529\pi\) | ||||
−0.763399 | + | 0.645927i | \(0.776471\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11821.6 | + | 33607.8i | 0.242674 | + | 0.689901i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −75847.2 | −1.45785 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −79344.3 | −1.43037 | −0.715185 | − | 0.698935i | \(-0.753657\pi\) | ||||
−0.715185 | + | 0.698935i | \(0.753657\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −18806.6 | −0.318492 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −102859. | −1.63888 | −0.819441 | − | 0.573164i | \(-0.805716\pi\) | ||||
−0.819441 | + | 0.573164i | \(0.805716\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −60466.7 | − | 42829.1i | −0.907755 | − | 0.642971i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 93851.2i | 1.32936i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −95263.4 | −1.27483 | −0.637413 | − | 0.770522i | \(-0.719996\pi\) | ||||
−0.637413 | + | 0.770522i | \(0.719996\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 112215.i | 1.42052i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 22639.3 | 0.271429 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 51779.6 | + | 36675.9i | 0.588639 | + | 0.416939i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 55240.6i | 0.596113i | 0.954548 | + | 0.298057i | \(0.0963384\pi\) | ||||
−0.954548 | + | 0.298057i | \(0.903662\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 70644.7i | 0.724422i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 104507.i | − | 1.01940i | −0.860353 | − | 0.509699i | \(-0.829757\pi\) | ||
0.860353 | − | 0.509699i | \(-0.170243\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16103.7i | 0.149566i | 0.997200 | + | 0.0747832i | \(0.0238265\pi\) | ||||
−0.997200 | + | 0.0747832i | \(0.976174\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 63111.7 | + | 44702.6i | 0.558646 | + | 0.395694i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 156165. | 1.31863 | 0.659317 | − | 0.751865i | \(-0.270845\pi\) | ||||
0.659317 | + | 0.751865i | \(0.270845\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 64503.2i | 0.520014i | 0.965607 | + | 0.260007i | \(0.0837249\pi\) | ||||
−0.965607 | + | 0.260007i | \(0.916275\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −110377. | −0.850296 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 51268.0i | 0.377703i | 0.982006 | + | 0.188851i | \(0.0604764\pi\) | ||||
−0.982006 | + | 0.188851i | \(0.939524\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 139378. | + | 98722.9i | 0.982766 | + | 0.696103i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 104518. | 0.705873 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −160857. | −1.04129 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −229580. | −1.42551 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 181240. | 1.08017 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −167983. | − | 47949.3i | −0.961593 | − | 0.274478i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 246962.i | − | 1.35869i | −0.733819 | − | 0.679345i | \(-0.762264\pi\) | ||
0.733819 | − | 0.679345i | \(-0.237736\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −213504. | −1.12962 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 24117.5i | 0.122787i | 0.998114 | + | 0.0613937i | \(0.0195545\pi\) | ||||
−0.998114 | + | 0.0613937i | \(0.980445\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 137747. | 0.675231 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 131149. | − | 185157.i | 0.619341 | − | 0.874393i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 132684.i | 0.603974i | 0.953312 | + | 0.301987i | \(0.0976500\pi\) | ||||
−0.953312 | + | 0.301987i | \(0.902350\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 96391.0i | − | 0.423155i | −0.977361 | − | 0.211577i | \(-0.932140\pi\) | ||
0.977361 | − | 0.211577i | \(-0.0678601\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 58854.3i | − | 0.249305i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 577935.i | 2.36341i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −375537. | − | 265996.i | −1.48331 | − | 1.05064i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −23713.7 | −0.0905119 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 204014.i | − | 0.752825i | −0.926452 | − | 0.376413i | \(-0.877158\pi\) | ||
0.926452 | − | 0.376413i | \(-0.122842\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 165135. | 0.589382 | 0.294691 | − | 0.955593i | \(-0.404783\pi\) | ||||
0.294691 | + | 0.955593i | \(0.404783\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 149823.i | 0.517429i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −64165.2 | + | 90589.2i | −0.214521 | + | 0.302864i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −380052. | −1.23054 | −0.615268 | − | 0.788318i | \(-0.710952\pi\) | ||||
−0.615268 | + | 0.788318i | \(0.710952\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 64517.1 | 0.202387 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 370781. | 1.12734 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 174832. | 0.515410 | 0.257705 | − | 0.966224i | \(-0.417034\pi\) | ||||
0.257705 | + | 0.966224i | \(0.417034\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 325040. | + | 230229.i | 0.929453 | + | 0.658340i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 64065.2i | 0.177759i | 0.996042 | + | 0.0888794i | \(0.0283286\pi\) | ||||
−0.996042 | + | 0.0888794i | \(0.971671\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 483754. | 1.30289 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 128298.i | − | 0.335530i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 303497. | 0.770974 | 0.385487 | − | 0.922713i | \(-0.374034\pi\) | ||||
0.385487 | + | 0.922713i | \(0.374034\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −357746. | + | 125838.i | −0.883040 | + | 0.310610i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 327112.i | − | 0.784808i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 95959.4i | 0.223849i | 0.993717 | + | 0.111924i | \(0.0357015\pi\) | ||||
−0.993717 | + | 0.111924i | \(0.964299\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 121991.i | 0.276779i | 0.990378 | + | 0.138389i | \(0.0441925\pi\) | ||||
−0.990378 | + | 0.138389i | \(0.955807\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 27478.9i | − | 0.0606557i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 312833. | − | 441662.i | 0.672023 | − | 0.948770i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −828450. | −1.73246 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 492565.i | − | 1.00302i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −185327. | −0.367582 | −0.183791 | − | 0.982965i | \(-0.558837\pi\) | ||||
−0.183791 | + | 0.982965i | \(0.558837\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 455781.i | 0.880771i | 0.897809 | + | 0.440386i | \(0.145158\pi\) | ||||
−0.897809 | + | 0.440386i | \(0.854842\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 340621. | − | 480893.i | 0.641483 | − | 0.905654i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −366599. | −0.673017 | −0.336508 | − | 0.941680i | \(-0.609246\pi\) | ||||
−0.336508 | + | 0.941680i | \(0.609246\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 414885. | 0.742669 | 0.371334 | − | 0.928499i | \(-0.378900\pi\) | ||||
0.371334 | + | 0.928499i | \(0.378900\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −523123. | −0.913300 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −999023. | −1.70151 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −513678. | + | 725217.i | −0.853702 | + | 1.20527i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 345349.i | − | 0.560186i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 709429. | 1.12342 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 42516.6i | − | 0.0657435i | −0.999460 | − | 0.0328717i | \(-0.989535\pi\) | ||
0.999460 | − | 0.0328717i | \(-0.0104653\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 63101.5 | 0.0952995 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 605122. | − | 854318.i | 0.892784 | − | 1.26044i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 240990.i | 0.347416i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 670565.i | − | 0.944780i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.22568e6i | 1.68810i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 252515.i | − | 0.340036i | −0.985441 | − | 0.170018i | \(-0.945617\pi\) | ||
0.985441 | − | 0.170018i | \(-0.0543826\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 117206. | + | 333208.i | 0.154346 | + | 0.438793i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 99603.1 | 0.128295 | 0.0641473 | − | 0.997940i | \(-0.479567\pi\) | ||||
0.0641473 | + | 0.997940i | \(0.479567\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 212126.i | − | 0.267303i | −0.991028 | − | 0.133652i | \(-0.957330\pi\) | ||
0.991028 | − | 0.133652i | \(-0.0426703\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 864689. | 1.06618 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.24877e6i | − | 1.50693i | −0.657487 | − | 0.753466i | \(-0.728380\pi\) | ||
0.657487 | − | 0.753466i | \(-0.271620\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 235500. | + | 166807.i | 0.278177 | + | 0.197035i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 904558. | 1.04608 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.34898e6 | −1.52761 | −0.763803 | − | 0.645450i | \(-0.776670\pi\) | ||||
−0.763803 | + | 0.645450i | \(0.776670\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.34315e6 | 1.48964 | 0.744822 | − | 0.667264i | \(-0.232535\pi\) | ||||
0.744822 | + | 0.667264i | \(0.232535\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −771908. | −0.838591 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 67210.1 | − | 94888.1i | 0.0715352 | − | 0.100994i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.04959e6i | − | 1.09466i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.17264e6 | 1.19857 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 595167.i | − | 0.596286i | −0.954521 | − | 0.298143i | \(-0.903633\pi\) | ||
0.954521 | − | 0.298143i | \(-0.0963673\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.90961e6 | 1.87562 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 689345. | + | 488269.i | 0.663874 | + | 0.470228i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 78872.4i | − | 0.0744890i | −0.999306 | − | 0.0372445i | \(-0.988142\pi\) | ||
0.999306 | − | 0.0372445i | \(-0.0118580\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.17493e6i | − | 1.08834i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 930499.i | 0.845502i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 652871.i | − | 0.582020i | −0.956720 | − | 0.291010i | \(-0.906009\pi\) | ||
0.956720 | − | 0.291010i | \(-0.0939913\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −182857. | + | 258159.i | −0.159954 | + | 0.225826i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.08604e6 | 0.932327 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 153469.i | 0.129313i | 0.997908 | + | 0.0646563i | \(0.0205951\pi\) | ||||
−0.997908 | + | 0.0646563i | \(0.979405\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.17390e6 | 0.970972 | 0.485486 | − | 0.874244i | \(-0.338643\pi\) | ||||
0.485486 | + | 0.874244i | \(0.338643\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 1.27930e6i | − | 1.03888i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.84248e6 | + | 648095.i | −1.46917 | + | 0.516782i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 719910. | 0.563740 | 0.281870 | − | 0.959453i | \(-0.409045\pi\) | ||||
0.281870 | + | 0.959453i | \(0.409045\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 224460. | 0.172635 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2785.80 | −0.00210467 | −0.00105234 | − | 0.999999i | \(-0.500335\pi\) | ||||
−0.00105234 | + | 0.999999i | \(0.500335\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −342464. | −0.254185 | −0.127092 | − | 0.991891i | \(-0.540564\pi\) | ||||
−0.127092 | + | 0.991891i | \(0.540564\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −590308. | − | 418121.i | −0.430494 | − | 0.304923i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.92926e6i | 1.38257i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −337118. | −0.237431 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 629765.i | − | 0.435960i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.03747e6 | −1.38651 | −0.693255 | − | 0.720693i | \(-0.743824\pi\) | ||||
−0.693255 | + | 0.720693i | \(0.743824\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.30891e6 | + | 927112.i | 0.875698 | + | 0.620265i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.53683e6i | − | 1.66878i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 2.82525e6i | − | 1.82759i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 2.27270e6i | − | 1.44586i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.19143e6i | 0.745523i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 109954. | + | 77881.7i | 0.0676804 | + | 0.0479386i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −406791. | −0.246335 | −0.123167 | − | 0.992386i | \(-0.539305\pi\) | ||||
−0.123167 | + | 0.992386i | \(0.539305\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 183589.i | − | 0.109383i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.64556e6 | 0.964745 | 0.482372 | − | 0.875966i | \(-0.339775\pi\) | ||||
0.482372 | + | 0.875966i | \(0.339775\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.11949e6i | 1.22284i | 0.791305 | + | 0.611422i | \(0.209402\pi\) | ||||
−0.791305 | + | 0.611422i | \(0.790598\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 625728. | + | 443209.i | 0.355311 | + | 0.251670i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −526511. | −0.294279 | −0.147140 | − | 0.989116i | \(-0.547007\pi\) | ||||
−0.147140 | + | 0.989116i | \(0.547007\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.14521e6 | −2.83091 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.78035e6 | −0.964366 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.50455e6 | 0.802420 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 958849. | + | 2.72593e6i | 0.503549 | + | 1.43155i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 735363.i | − | 0.380305i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 626489. | 0.319098 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.72847e6i | 1.36883i | 0.729093 | + | 0.684415i | \(0.239942\pi\) | ||||
−0.729093 | + | 0.684415i | \(0.760058\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.09434e6 | −0.540808 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.48265e6 | − | 2.09323e6i | 0.721817 | − | 1.01907i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.14704e6i | − | 1.02983i | −0.857241 | − | 0.514916i | \(-0.827823\pi\) | ||
0.857241 | − | 0.514916i | \(-0.172177\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 584476.i | − | 0.276228i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.24116e6i | 0.578017i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.29203e6i | − | 1.05193i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.58897e6 | − | 1.12548e6i | −0.718733 | − | 0.509085i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 917072. | 0.408865 | 0.204432 | − | 0.978881i | \(-0.434465\pi\) | ||||
0.204432 | + | 0.978881i | \(0.434465\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.98463e6i | − | 1.75115i | −0.483078 | − | 0.875577i | \(-0.660481\pi\) | ||
0.483078 | − | 0.875577i | \(-0.339519\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.75321e6 | −1.62605 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.18612e6i | 0.506630i | 0.967384 | + | 0.253315i | \(0.0815210\pi\) | ||||
−0.967384 | + | 0.253315i | \(0.918479\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −178844. | + | 252495.i | −0.0753190 | + | 0.106336i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.83383e6 | 0.761533 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 265806. | 0.108850 | 0.0544249 | − | 0.998518i | \(-0.482667\pi\) | ||||
0.0544249 | + | 0.998518i | \(0.482667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.18770e6 | 0.479666 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.61731e6 | 1.04253 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.68320e6 | + | 1.90054e6i | 1.05420 | + | 0.746697i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.89812e6i | 1.89830i | 0.314827 | + | 0.949149i | \(0.398053\pi\) | ||||
−0.314827 | + | 0.949149i | \(0.601947\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.79693e6 | 0.687013 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 686769.i | 0.259045i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.42717e6 | −1.64761 | −0.823804 | − | 0.566875i | \(-0.808152\pi\) | ||||
−0.823804 | + | 0.566875i | \(0.808152\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.91508e6 | + | 546642.i | 0.703248 | + | 0.200736i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.61227e6i | 2.75842i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.97522e6i | 1.77916i | 0.456784 | + | 0.889578i | \(0.349001\pi\) | ||||
−0.456784 | + | 0.889578i | \(0.650999\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.81547e6i | 0.993660i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 994461.i | − | 0.346410i | −0.984886 | − | 0.173205i | \(-0.944588\pi\) | ||
0.984886 | − | 0.173205i | \(-0.0554124\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.45073e6 | + | 3.45997e6i | −0.842644 | + | 1.18965i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.11681e6 | −0.718465 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 5.89205e6i | − | 1.97421i | −0.160087 | − | 0.987103i | \(-0.551177\pi\) | ||
0.160087 | − | 0.987103i | \(-0.448823\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.04990e6 | 1.33968 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 274949.i | − | 0.0897989i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.56373e6 | + | 3.61950e6i | −0.826760 | + | 1.16723i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.76823e6 | −0.563071 | −0.281535 | − | 0.959551i | \(-0.590844\pi\) | ||||
−0.281535 | + | 0.959551i | \(0.590844\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.57037e6 | −0.493821 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.32752e6 | −1.65449 | −0.827245 | − | 0.561841i | \(-0.810093\pi\) | ||||
−0.827245 | + | 0.561841i | \(0.810093\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.83628e6 | 0.563217 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −607669. | + | 857914.i | −0.184090 | + | 0.259900i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 6.05119e6i | − | 1.81073i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.40082e6 | −0.414070 | −0.207035 | − | 0.978334i | \(-0.566381\pi\) | ||||
−0.207035 | + | 0.978334i | \(0.566381\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 1.51266e6i | − | 0.441709i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.48203e6 | 1.00452 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.32353e6 | + | 4.69219e6i | −0.947281 | + | 1.33738i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.09890e6i | 0.309469i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 461773.i | 0.128497i | 0.997934 | + | 0.0642486i | \(0.0204650\pi\) | ||||
−0.997934 | + | 0.0642486i | \(0.979535\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 820398.i | − | 0.225590i | −0.993618 | − | 0.112795i | \(-0.964020\pi\) | ||
0.993618 | − | 0.112795i | \(-0.0359803\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 583517.i | − | 0.158563i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.90753e6 | + | 1.37448e6i | −1.04937 | + | 0.369118i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 292506. | 0.0776364 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 6.58869e6i | − | 1.72845i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.53969e6 | −1.43646 | −0.718229 | − | 0.695807i | \(-0.755047\pi\) | ||||
−0.718229 | + | 0.695807i | \(0.755047\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 360822.i | 0.0924854i | 0.998930 | + | 0.0462427i | \(0.0147248\pi\) | ||||
−0.998930 | + | 0.0462427i | \(0.985275\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.28127e6 | + | 3.03247e6i | 1.08480 | + | 0.768374i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.46806e6 | −0.868727 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.40731e6 | −1.58677 | −0.793386 | − | 0.608719i | \(-0.791684\pi\) | ||||
−0.793386 | + | 0.608719i | \(0.791684\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −235112. | −0.0575676 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.55001e6 | 0.375253 | 0.187627 | − | 0.982240i | \(-0.439920\pi\) | ||||
0.187627 | + | 0.982240i | \(0.439920\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.07810e6 | + | 4.34569e6i | −0.736855 | + | 1.04030i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.32584e6i | 0.550569i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.15790e6 | 1.67560 | 0.837799 | − | 0.545979i | \(-0.183842\pi\) | ||||
0.837799 | + | 0.545979i | \(0.183842\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.93615e6i | 2.30026i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.88261e6 | −0.431036 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.11899e6 | + | 3.62583e6i | 1.15919 | + | 0.821067i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.20570e6i | 0.941994i | 0.882135 | + | 0.470997i | \(0.156106\pi\) | ||||
−0.882135 | + | 0.470997i | \(0.843894\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 5.38010e6i | − | 1.19195i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.81134e6i | 0.616114i | 0.951368 | + | 0.308057i | \(0.0996788\pi\) | ||||
−0.951368 | + | 0.308057i | \(0.900321\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.18515e6i | 0.473728i | 0.971543 | + | 0.236864i | \(0.0761197\pi\) | ||||
−0.971543 | + | 0.236864i | \(0.923880\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 731509. | − | 1.03275e6i | 0.156887 | − | 0.221495i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.77798e6 | 0.801617 | 0.400809 | − | 0.916162i | \(-0.368729\pi\) | ||||
0.400809 | + | 0.916162i | \(0.368729\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 5.56851e6i | − | 1.16898i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.33275e6 | 0.899936 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.17050e7i | − | 2.40557i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.34614e6 | − | 1.17701e6i | 0.680472 | − | 0.239357i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 639663. | 0.128723 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.16313e6 | −1.62562 | −0.812808 | − | 0.582531i | \(-0.802062\pi\) | ||||
−0.812808 | + | 0.582531i | \(0.802062\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.95266e6 | −1.76437 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.22706e6 | −0.824462 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.51995e6 | + | 1.78490e6i | 0.486449 | + | 0.344556i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.47312e6i | 0.281459i | 0.990048 | + | 0.140730i | \(0.0449448\pi\) | ||||
−0.990048 | + | 0.140730i | \(0.955055\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.99316e6 | −0.376938 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.25498e6i | 0.234926i | 0.993077 | + | 0.117463i | \(0.0374762\pi\) | ||||
−0.993077 | + | 0.117463i | \(0.962524\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.09119e7 | −2.02202 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.22265e6 | + | 2.28263e6i | 0.591153 | + | 0.418719i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 671700.i | 0.121979i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 8.05328e6i | − | 1.44784i | −0.689882 | − | 0.723921i | \(-0.742338\pi\) | ||
0.689882 | − | 0.723921i | \(-0.257662\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 730370.i | − | 0.130002i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 3.77386e6i | − | 0.665067i | −0.943091 | − | 0.332534i | \(-0.892096\pi\) | ||
0.943091 | − | 0.332534i | \(-0.107904\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.76739e6 | − | 3.37679e6i | −0.831863 | − | 0.589217i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.51500e6 | −0.952852 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 1.29923e6i | − | 0.222276i | −0.993805 | − | 0.111138i | \(-0.964550\pi\) | ||
0.993805 | − | 0.111138i | \(-0.0354496\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.13800e6 | 1.20927 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.60716e6i | 0.772929i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 734615. | + | 520335.i | 0.122051 | + | 0.0864500i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.22657e6 | 0.530902 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.45999e6 | −0.563841 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.28934e6 | 0.530903 | 0.265451 | − | 0.964124i | \(-0.414479\pi\) | ||||
0.265451 | + | 0.964124i | \(0.414479\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.50676e6 | 0.400736 | 0.200368 | − | 0.979721i | \(-0.435786\pi\) | ||||
0.200368 | + | 0.979721i | \(0.435786\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.07846e6 | − | 1.43460e6i | 0.645799 | − | 0.227161i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.63224e6i | 0.412857i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.89885e6 | −0.450388 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 3.24319e6i | − | 0.499156i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.47004e7 | 2.24136 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.04591e6 | − | 7.12389e6i | 0.762176 | − | 1.07605i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 1.09398e6i | − | 0.163709i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.30006e6i | − | 0.192748i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 1.88877e6i | − | 0.277451i | −0.990331 | − | 0.138725i | \(-0.955699\pi\) | ||
0.990331 | − | 0.138725i | \(-0.0443005\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1.39075e6i | − | 0.202418i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.94249e6 | + | 2.08419e6i | 0.424349 | + | 0.300571i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.65871e6 | 0.951529 | 0.475764 | − | 0.879573i | \(-0.342172\pi\) | ||||
0.475764 | + | 0.879573i | \(0.342172\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 272443.i | − | 0.0385784i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.34425e6 | 1.31119 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.62880e6i | 1.33893i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.56643e6 | + | 5.03513e6i | −0.491475 | + | 0.693870i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.92957e6 | 0.400098 | 0.200049 | − | 0.979786i | \(-0.435890\pi\) | ||||
0.200049 | + | 0.979786i | \(0.435890\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.73174e7 | −2.34397 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.44467e6 | 1.26701 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.54089e6 | 1.00266 | 0.501328 | − | 0.865257i | \(-0.332845\pi\) | ||||
0.501328 | + | 0.865257i | \(0.332845\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.33872e6 | + | 1.65654e6i | 0.308218 | + | 0.218314i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.28227e6i | 0.298132i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.78696e6 | 1.00829 | 0.504147 | − | 0.863618i | \(-0.331807\pi\) | ||||
0.504147 | + | 0.863618i | \(0.331807\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 2.28912e6i | − | 0.293817i | −0.989150 | − | 0.146909i | \(-0.953068\pi\) | ||
0.989150 | − | 0.146909i | \(-0.0469324\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.11280e6 | 0.268827 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.00702e6 | − | 3.16823e6i | 1.13609 | − | 0.399620i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.37541e7i | − | 1.71986i | −0.510415 | − | 0.859928i | \(-0.670508\pi\) | ||
0.510415 | − | 0.859928i | \(-0.329492\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 5.19609e6i | − | 0.644140i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.24824e7i | 1.53412i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.53703e6i | 0.430990i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.37713e6 | − | 4.76787e6i | 0.407998 | − | 0.576016i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.03428e7 | −1.23892 | −0.619462 | − | 0.785027i | \(-0.712649\pi\) | ||||
−0.619462 | + | 0.785027i | \(0.712649\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2.25408e6i | − | 0.267720i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.17938e6 | 0.492202 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1.02755e6i | − | 0.119995i | −0.998199 | − | 0.0599976i | \(-0.980891\pi\) | ||
0.998199 | − | 0.0599976i | \(-0.0191093\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.19751e6 | + | 7.33790e6i | −0.601870 | + | 0.849727i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.72986e6 | −0.543141 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.71137e6 | 0.422636 | 0.211318 | − | 0.977417i | \(-0.432224\pi\) | ||||
0.211318 | + | 0.977417i | \(0.432224\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.30716e6 | −0.486412 | −0.243206 | − | 0.969975i | \(-0.578199\pi\) | ||||
−0.243206 | + | 0.969975i | \(0.578199\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.18656e6 | −0.580880 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.41807e6 | + | 1.04729e7i | −0.823953 | + | 1.16327i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.70813e7i | − | 1.88170i | −0.338828 | − | 0.940848i | \(-0.610031\pi\) | ||
0.338828 | − | 0.940848i | \(-0.389969\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.13893e7 | 1.24438 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 4.77367e6i | − | 0.517308i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.80249e6 | 0.193741 | 0.0968705 | − | 0.995297i | \(-0.469117\pi\) | ||||
0.0968705 | + | 0.995297i | \(0.469117\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.85614e6 | − | 8.26777e6i | 0.624343 | − | 0.881456i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.48312e6i | − | 0.791353i | −0.918390 | − | 0.395676i | \(-0.870510\pi\) | ||
0.918390 | − | 0.395676i | \(-0.129490\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.03953e7i | − | 1.09047i | −0.838284 | − | 0.545233i | \(-0.816441\pi\) | ||
0.838284 | − | 0.545233i | \(-0.183559\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.24014e7i | 1.29045i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.15606e7i | 1.19333i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.61512e6 | + | 6.11370e6i | −0.779788 | + | 0.626043i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.08778e6 | −0.821600 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.28333e7i | − | 1.29334i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.37210e7 | −1.37187 | −0.685933 | − | 0.727665i | \(-0.740606\pi\) | ||||
−0.685933 | + | 0.727665i | \(0.740606\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 484707.i | 0.0480806i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.12658e7 | − | 7.97969e6i | −1.10874 | − | 0.785329i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.92342e6 | −0.187813 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 625627. | 0.0606127 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.05003e6 | 0.773843 | 0.386921 | − | 0.922113i | \(-0.373538\pi\) | ||||
0.386921 | + | 0.922113i | \(0.373538\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.53306e7 | −1.46228 | −0.731140 | − | 0.682227i | \(-0.761011\pi\) | ||||
−0.731140 | + | 0.682227i | \(0.761011\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.89863e6 | + | 9.73958e6i | −0.652926 | + | 0.921809i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.55551e6i | 0.240003i | 0.992774 | + | 0.120002i | \(0.0382900\pi\) | ||||
−0.992774 | + | 0.120002i | \(0.961710\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.79333e7 | 1.67128 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 2.74739e6i | − | 0.254078i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.03839e7 | −0.952969 | −0.476484 | − | 0.879183i | \(-0.658089\pi\) | ||||
−0.476484 | + | 0.879183i | \(0.658089\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.10018e6 | + | 779270.i | 0.100199 | + | 0.0709716i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 6.64840e6i | − | 0.600902i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.63129e7i | − | 1.46325i | −0.681708 | − | 0.731625i | \(-0.738762\pi\) | ||
0.681708 | − | 0.731625i | \(-0.261238\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 9.87139e6i | − | 0.878769i | −0.898299 | − | 0.439385i | \(-0.855197\pi\) | ||
0.898299 | − | 0.439385i | \(-0.144803\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 1.39733e7i | − | 1.23457i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.45079e6 | − | 6.28368e6i | 0.390286 | − | 0.551011i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.51525e7 | 2.18910 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.87877e6i | 0.248681i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.50648e6 | 0.129168 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 2.67399e6i | − | 0.227574i | −0.993505 | − | 0.113787i | \(-0.963702\pi\) | ||
0.993505 | − | 0.113787i | \(-0.0362981\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.20885e6 | − | 1.19654e7i | −0.355552 | − | 1.01081i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.18547e6 | 0.770247 | 0.385123 | − | 0.922865i | \(-0.374159\pi\) | ||||
0.385123 | + | 0.922865i | \(0.374159\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.70370e6 | 0.558007 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.13552e6 | −0.0938265 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.63593e7 | −1.34188 | −0.670941 | − | 0.741511i | \(-0.734109\pi\) | ||||
−0.670941 | + | 0.741511i | \(0.734109\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.05275e6 | + | 4.28722e6i | 0.492863 | + | 0.349100i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.41832e6i | 0.195489i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.23299e6 | 0.419954 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.12037e7i | 0.892623i | 0.894878 | + | 0.446311i | \(0.147263\pi\) | ||||
−0.894878 | + | 0.446311i | \(0.852737\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.57306e6 | 0.678114 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.39713e6 | − | 3.11453e6i | −0.345309 | − | 0.244585i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.10726e7i | 1.64299i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.42365e7i | 1.10207i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.26088e6i | − | 0.0969122i | −0.998825 | − | 0.0484561i | \(-0.984570\pi\) | ||
0.998825 | − | 0.0484561i | \(-0.0154301\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.09896e7i | 0.838676i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.68479e6 | − | 1.90167e6i | −0.203441 | − | 0.144099i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.26825e7 | −0.954234 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 6.78380e6i | − | 0.506824i | −0.967358 | − | 0.253412i | \(-0.918447\pi\) | ||
0.967358 | − | 0.253412i | \(-0.0815528\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.96834e6 | 0.665332 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 6.06743e6i | − | 0.446973i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.63640e7 | + | 1.86739e7i | 1.92862 | + | 1.36606i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.53789e7 | 1.11719 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.05951e7 | 0.764332 | 0.382166 | − | 0.924094i | \(-0.375178\pi\) | ||||
0.382166 | + | 0.924094i | \(0.375178\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.95426e6 | 0.140005 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.53125e7 | −1.08943 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.42683e7 | + | 8.53640e6i | −1.71472 | + | 0.603156i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.24737e7i | 0.875307i | 0.899144 | + | 0.437653i | \(0.144190\pi\) | ||||
−0.899144 | + | 0.437653i | \(0.855810\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.33701e7 | 0.931784 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 2.48239e7i | − | 1.71821i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.45429e7 | 1.68720 | 0.843599 | − | 0.536974i | \(-0.180433\pi\) | ||||
0.843599 | + | 0.536974i | \(0.180433\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −766223. | + | 1.08176e6i | −0.0523163 | + | 0.0738608i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2.86792e7i | − | 1.94490i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.22999e7i | 0.828495i | 0.910164 | + | 0.414247i | \(0.135955\pi\) | ||||
−0.910164 | + | 0.414247i | \(0.864045\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.19658e7i | 0.800562i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.22075e7i | 0.811249i | 0.914040 | + | 0.405625i | \(0.132946\pi\) | ||||
−0.914040 | + | 0.405625i | \(0.867054\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.30664e6 | − | 6.59198e6i | −0.614331 | − | 0.435136i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.16262e7 | 0.762321 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1.89513e7i | − | 1.23434i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.31871e6 | 0.602915 | 0.301457 | − | 0.953480i | \(-0.402527\pi\) | ||||
0.301457 | + | 0.953480i | \(0.402527\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.78515e6i | 0.436086i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.33575e6 | − | 7.53307e6i | 0.340665 | − | 0.480955i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.47661e7 | −0.936542 | −0.468271 | − | 0.883585i | \(-0.655123\pi\) | ||||
−0.468271 | + | 0.883585i | \(0.655123\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.17704e7 | −1.37171 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.04414e6 | −0.315737 | −0.157868 | − | 0.987460i | \(-0.550462\pi\) | ||||
−0.157868 | + | 0.987460i | \(0.550462\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.82776e6 | 0.486773 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.83459e6 | + | 4.84100e6i | 0.422239 | + | 0.299076i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 2.65321e7i | − | 1.62848i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.04383e7 | −1.85612 | −0.928058 | − | 0.372435i | \(-0.878523\pi\) | ||||
−0.928058 | + | 0.372435i | \(0.878523\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 899177.i | 0.0544765i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.30104e7 | 1.38508 | 0.692540 | − | 0.721380i | \(-0.256492\pi\) | ||||
0.692540 | + | 0.721380i | \(0.256492\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.05920e6 | + | 5.85413e6i | 0.123153 | + | 0.350113i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.33947e7i | 0.795941i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1.80451e7i | − | 1.06541i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.45942e6i | 0.202944i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 3.34139e7i | − | 1.94770i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.22800e7 | + | 1.73371e7i | −0.711255 | + | 1.00416i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.52083e6 | 0.317737 | 0.158868 | − | 0.987300i | \(-0.449215\pi\) | ||||
0.158868 | + | 0.987300i | \(0.449215\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.44300e6i | 0.425653i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.22160e6 | 0.353558 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2.22882e6i | − | 0.125861i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.08464e6 | − | 2.94312e6i | 0.116980 | − | 0.165154i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.26506e7 | −1.26309 | −0.631544 | − | 0.775340i | \(-0.717578\pi\) | ||||
−0.631544 | + | 0.775340i | \(0.717578\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.84290e6 | 0.379204 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.07677e7 | 0.592981 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.67624e7 | 2.01194 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.19805e7 | − | 1.69142e7i | 0.651605 | − | 0.919944i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 1.74961e6i | − | 0.0945711i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.69128e7 | −0.908538 | −0.454269 | − | 0.890865i | \(-0.650100\pi\) | ||||
−0.454269 | + | 0.890865i | \(0.650100\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.76752e7i | 0.943651i | 0.881692 | + | 0.471825i | \(0.156405\pi\) | ||||
−0.881692 | + | 0.471825i | \(0.843595\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.33829e7 | −0.710107 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.64909e6 | − | 7.97545e6i | 0.297909 | − | 0.420592i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.12575e7i | 1.11418i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 1.26837e7i | − | 0.660751i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.02203e7i | − | 0.529182i | −0.964361 | − | 0.264591i | \(-0.914763\pi\) | ||
0.964361 | − | 0.264591i | \(-0.0852369\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.30139e7i | 1.69901i | 0.527577 | + | 0.849507i | \(0.323100\pi\) | ||||
−0.527577 | + | 0.849507i | \(0.676900\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.10050e7 | − | 7.38855e6i | 1.07446 | − | 0.377941i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.06482e7 | −1.04983 | −0.524915 | − | 0.851155i | \(-0.675903\pi\) | ||||
−0.524915 | + | 0.851155i | \(0.675903\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 8.92770e6i | − | 0.451184i | −0.974222 | − | 0.225592i | \(-0.927568\pi\) | ||
0.974222 | − | 0.225592i | \(-0.0724316\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.20727e6 | −0.412284 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 2.75716e6i | − | 0.137673i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.92251e6 | + | 2.07004e6i | 0.145057 | + | 0.102745i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.06030e6 | −0.397683 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.73576e7 | −1.83220 | −0.916102 | − | 0.400946i | \(-0.868681\pi\) | ||||
−0.916102 | + | 0.400946i | \(0.868681\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.72591e7 | −2.30407 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31759.3 | 0.00153923 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.56308e7 | − | 2.20677e7i | 0.753077 | − | 1.06320i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.78606e7i | 1.33439i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.90423e6 | 0.185894 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.95814e7i | 1.40022i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.98231e7 | −1.40340 | −0.701698 | − | 0.712475i | \(-0.747574\pi\) | ||||
−0.701698 | + | 0.712475i | \(0.747574\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.85268e6 | − | 4.14551e6i | −0.273804 | − | 0.193938i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.38305e7i | − | 0.643257i | −0.946866 | − | 0.321628i | \(-0.895770\pi\) | ||
0.946866 | − | 0.321628i | \(-0.104230\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.84721e7i | 1.77895i | 0.456988 | + | 0.889473i | \(0.348928\pi\) | ||||
−0.456988 | + | 0.889473i | \(0.651072\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 2.19944e7i | − | 1.01112i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.55372e7i | 1.16720i | 0.812040 | + | 0.583602i | \(0.198357\pi\) | ||||
−0.812040 | + | 0.583602i | \(0.801643\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.80643e6 | − | 1.38448e7i | 0.445626 | − | 0.629140i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.84329e6 | 0.173642 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.95906e7i | 2.22767i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.24305e7 | −1.89510 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 6.24388e6i | − | 0.277280i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.81887e6 | + | 2.03856e7i | −0.256932 | + | 0.900124i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.81524e7 | −0.796958 | −0.398479 | − | 0.917177i | \(-0.630462\pi\) | ||||
−0.398479 | + | 0.917177i | \(0.630462\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.32280e7 | 1.01401 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.81238e6 | 0.252298 | 0.126149 | − | 0.992011i | \(-0.459738\pi\) | ||||
0.126149 | + | 0.992011i | \(0.459738\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.03320e7 | 0.877563 | 0.438782 | − | 0.898594i | \(-0.355410\pi\) | ||||
0.438782 | + | 0.898594i | \(0.355410\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.49221e7 | − | 1.05695e7i | −0.640430 | − | 0.453622i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 4.47254e6i | − | 0.190873i | −0.995435 | − | 0.0954367i | \(-0.969575\pi\) | ||
0.995435 | − | 0.0954367i | \(-0.0304248\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.99700e7 | −1.27184 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.17542e7i | 0.496021i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.85980e6 | −0.245897 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.37744e6 | + | 3.10059e6i | 0.182668 | + | 0.129386i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.22090e7i | 1.33658i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.63479e7i | 0.674627i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.50132e6i | 0.307840i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.59097e7i | 1.05741i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.56496e6 | + | 3.94172e6i | 0.225861 | + | 0.159979i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.68122e7 | −0.678590 | −0.339295 | − | 0.940680i | \(-0.610188\pi\) | ||||
−0.339295 | + | 0.940680i | \(0.610188\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.18126e7i | 0.474170i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.07181e7 | 0.827092 | 0.413546 | − | 0.910483i | \(-0.364290\pi\) | ||||
0.413546 | + | 0.910483i | \(0.364290\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.42875e7i | 2.55240i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.25352e6 | − | 887883.i | −0.0494971 | − | 0.0350593i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.92677e6 | 0.114938 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.97985e7 | −0.773293 | −0.386646 | − | 0.922228i | \(-0.626367\pi\) | ||||
−0.386646 | + | 0.922228i | \(0.626367\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.63759e6 | 0.180154 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.11817e6 | 0.197747 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.00395e7 | − | 2.85415e7i | −0.385796 | − | 1.09679i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 1.82022e6i | − | 0.0695703i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.51767e7 | 0.576951 | 0.288476 | − | 0.957487i | \(-0.406852\pi\) | ||||
0.288476 | + | 0.957487i | \(0.406852\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.36104e6i | 0.0892750i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.87600e7 | −0.705553 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.67684e7 | + | 3.77920e7i | −1.00137 | + | 1.41374i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.05634e7i | 1.50934i | 0.656107 | + | 0.754668i | \(0.272202\pi\) | ||||
−0.656107 | + | 0.754668i | \(0.727798\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 2.41631e7i | − | 0.894311i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 2.90077e7i | − | 1.06792i | −0.845509 | − | 0.533961i | \(-0.820703\pi\) | ||
0.845509 | − | 0.533961i | \(-0.179297\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.85732e7i | − | 1.77876i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.24697e7 | − | 1.59155e7i | −0.818498 | − | 0.579750i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.60988e6 | 0.130803 | 0.0654015 | − | 0.997859i | \(-0.479167\pi\) | ||||
0.0654015 | + | 0.997859i | \(0.479167\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 5.43896e7i | − | 1.96042i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.00245e6 | 0.215217 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.49602e7i | 0.533587i | 0.963754 | + | 0.266794i | \(0.0859642\pi\) | ||||
−0.963754 | + | 0.266794i | \(0.914036\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.98817e6 | + | 8.45418e6i | −0.212464 | + | 0.299960i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.86575e7 | 2.07035 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.61019e7 | 0.565366 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.46856e7 | −0.862254 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.76514e7 | −0.613358 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.07917e7 | + | 1.47269e7i | 0.718739 | + | 0.509090i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1.66472e7i | − | 0.572499i | −0.958155 | − | 0.286250i | \(-0.907591\pi\) | ||
0.958155 | − | 0.286250i | \(-0.0924087\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.71525e7 | −0.586839 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 2.76119e7i | − | 0.939828i | −0.882712 | − | 0.469914i | \(-0.844285\pi\) | ||
0.882712 | − | 0.469914i | \(-0.155715\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.16975e7 | −0.396105 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.09313e7 | − | 3.10767e7i | −0.368264 | − | 1.04694i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 3.13860e7i | − | 1.05196i | −0.850497 | − | 0.525981i | \(-0.823698\pi\) | ||
0.850497 | − | 0.525981i | \(-0.176302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.95401e7i | 1.98542i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 7.29084e6i | − | 0.241883i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 3.95095e7i | − | 1.30412i | −0.758167 | − | 0.652060i | \(-0.773905\pi\) | ||
0.758167 | − | 0.652060i | \(-0.226095\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.18453e7 | + | 1.67234e7i | −0.389007 | + | 0.549204i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.14223e6 | −0.233368 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.72201e7i | 1.86019i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.11347e7 | −0.360159 | −0.180080 | − | 0.983652i | \(-0.557636\pi\) | ||||
−0.180080 | + | 0.983652i | \(0.557636\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 3.11057e7i | − | 1.00107i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.34055e7 | − | 1.89261e7i | 0.429266 | − | 0.606043i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.32149e7 | −0.421044 | −0.210522 | − | 0.977589i | \(-0.567516\pi\) | ||||
−0.210522 | + | 0.977589i | \(0.567516\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.92975e7 | 1.24581 |
(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 | 320.6.f.d.289.10 | yes | 32 | |
4.3 | odd | 2 | inner | 320.6.f.d.289.23 | yes | 32 | |
5.4 | even | 2 | inner | 320.6.f.d.289.21 | yes | 32 | |
8.3 | odd | 2 | inner | 320.6.f.d.289.9 | ✓ | 32 | |
8.5 | even | 2 | inner | 320.6.f.d.289.24 | yes | 32 | |
20.19 | odd | 2 | inner | 320.6.f.d.289.12 | yes | 32 | |
40.19 | odd | 2 | inner | 320.6.f.d.289.22 | yes | 32 | |
40.29 | even | 2 | inner | 320.6.f.d.289.11 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.6.f.d.289.9 | ✓ | 32 | 8.3 | odd | 2 | inner | |
320.6.f.d.289.10 | yes | 32 | 1.1 | even | 1 | trivial | |
320.6.f.d.289.11 | yes | 32 | 40.29 | even | 2 | inner | |
320.6.f.d.289.12 | yes | 32 | 20.19 | odd | 2 | inner | |
320.6.f.d.289.21 | yes | 32 | 5.4 | even | 2 | inner | |
320.6.f.d.289.22 | yes | 32 | 40.19 | odd | 2 | inner | |
320.6.f.d.289.23 | yes | 32 | 4.3 | odd | 2 | inner | |
320.6.f.d.289.24 | yes | 32 | 8.5 | even | 2 | inner |