Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(81,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.81");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.l (of order \(4\), degree \(2\), not 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: | \(80\) |
Relative dimension: | \(40\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 81.1 | ||
Character | \(\chi\) | \(=\) | 320.81 |
Dual form | 320.6.l.a.241.1 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −21.2511 | − | 21.2511i | −1.36326 | − | 1.36326i | −0.869725 | − | 0.493536i | \(-0.835704\pi\) |
−0.493536 | − | 0.869725i | \(-0.664296\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −17.6777 | + | 17.6777i | −0.316228 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 169.621i | 1.30838i | 0.756330 | + | 0.654191i | \(0.226991\pi\) | ||||
−0.756330 | + | 0.654191i | \(0.773009\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 660.222i | 2.71696i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −379.002 | + | 379.002i | −0.944408 | + | 0.944408i | −0.998534 | − | 0.0541263i | \(-0.982763\pi\) |
0.0541263 | + | 0.998534i | \(0.482763\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.8362 | + | 10.8362i | 0.0177836 | + | 0.0177836i | 0.715943 | − | 0.698159i | \(-0.245997\pi\) |
−0.698159 | + | 0.715943i | \(0.745997\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 751.341 | 0.862202 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1788.05 | −1.50057 | −0.750286 | − | 0.661114i | \(-0.770084\pi\) | ||||
−0.750286 | + | 0.661114i | \(0.770084\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1092.33 | + | 1092.33i | 0.694174 | + | 0.694174i | 0.963148 | − | 0.268973i | \(-0.0866843\pi\) |
−0.268973 | + | 0.963148i | \(0.586684\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3604.64 | − | 3604.64i | 1.78367 | − | 1.78367i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2097.19i | 0.826642i | 0.910585 | + | 0.413321i | \(0.135631\pi\) | ||||
−0.910585 | + | 0.413321i | \(0.864369\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 625.000i | − | 0.200000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8866.44 | − | 8866.44i | 2.34067 | − | 2.34067i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 100.133 | + | 100.133i | 0.0221096 | + | 0.0221096i | 0.718075 | − | 0.695966i | \(-0.245023\pi\) |
−0.695966 | + | 0.718075i | \(0.745023\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3154.58 | −0.589573 | −0.294787 | − | 0.955563i | \(-0.595249\pi\) | ||||
−0.294787 | + | 0.955563i | \(0.595249\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16108.4 | 2.57495 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2998.50 | − | 2998.50i | −0.413747 | − | 0.413747i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7283.15 | − | 7283.15i | 0.874611 | − | 0.874611i | −0.118360 | − | 0.992971i | \(-0.537764\pi\) |
0.992971 | + | 0.118360i | \(0.0377637\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 460.565i | − | 0.0484874i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13081.0i | 1.21529i | 0.794208 | + | 0.607646i | \(0.207886\pi\) | ||||
−0.794208 | + | 0.607646i | \(0.792114\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1355.74 | + | 1355.74i | −0.111817 | + | 0.111817i | −0.760801 | − | 0.648985i | \(-0.775194\pi\) |
0.648985 | + | 0.760801i | \(0.275194\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11671.2 | − | 11671.2i | −0.859179 | − | 0.859179i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −18498.7 | −1.22151 | −0.610754 | − | 0.791820i | \(-0.709134\pi\) | ||||
−0.610754 | + | 0.791820i | \(0.709134\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11964.3 | −0.711862 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 37998.0 | + | 37998.0i | 2.04567 | + | 2.04567i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10148.2 | + | 10148.2i | −0.496247 | + | 0.496247i | −0.910267 | − | 0.414021i | \(-0.864124\pi\) |
0.414021 | + | 0.910267i | \(0.364124\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 13399.7i | − | 0.597296i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 46426.4i | − | 1.89268i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5697.28 | + | 5697.28i | −0.213077 | + | 0.213077i | −0.805573 | − | 0.592496i | \(-0.798143\pi\) |
0.592496 | + | 0.805573i | \(0.298143\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −16810.4 | − | 16810.4i | −0.578434 | − | 0.578434i | 0.356037 | − | 0.934472i | \(-0.384128\pi\) |
−0.934472 | + | 0.356037i | \(0.884128\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −111987. | −3.55482 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −383.119 | −0.0112473 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8866.04 | − | 8866.04i | −0.241292 | − | 0.241292i | 0.576093 | − | 0.817384i | \(-0.304577\pi\) |
−0.817384 | + | 0.576093i | \(0.804577\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 44567.6 | − | 44567.6i | 1.12693 | − | 1.12693i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 23103.9i | 0.543925i | 0.962308 | + | 0.271962i | \(0.0876726\pi\) | ||||
−0.962308 | + | 0.271962i | \(0.912327\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 134.268i | 0.00294894i | 0.999999 | + | 0.00147447i | \(0.000469338\pi\) | ||||
−0.999999 | + | 0.00147447i | \(0.999531\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13282.0 | + | 13282.0i | −0.272652 | + | 0.272652i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −64286.6 | − | 64286.6i | −1.23565 | − | 1.23565i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 26974.0 | 0.486270 | 0.243135 | − | 0.969993i | \(-0.421824\pi\) | ||||
0.243135 | + | 0.969993i | \(0.421824\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −216410. | −3.66492 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 20245.8 | + | 20245.8i | 0.322581 | + | 0.322581i | 0.849757 | − | 0.527175i | \(-0.176749\pi\) |
−0.527175 | + | 0.849757i | \(0.676749\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 31608.5 | − | 31608.5i | 0.474522 | − | 0.474522i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 4255.86i | − | 0.0602823i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 101494.i | 1.35821i | 0.734041 | + | 0.679105i | \(0.237632\pi\) | ||||
−0.734041 | + | 0.679105i | \(0.762368\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1838.05 | + | 1838.05i | −0.0232678 | + | 0.0232678i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 67038.5 | + | 67038.5i | 0.803743 | + | 0.803743i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −38619.6 | −0.439034 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −47842.6 | −0.516280 | −0.258140 | − | 0.966107i | \(-0.583110\pi\) | ||||
−0.258140 | + | 0.966107i | \(0.583110\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −250225. | − | 250225.i | −2.56592 | − | 2.56592i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −95106.3 | + | 95106.3i | −0.927696 | + | 0.927696i | −0.997557 | − | 0.0698605i | \(-0.977745\pi\) |
0.0698605 | + | 0.997557i | \(0.477745\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 25847.2i | 0.240060i | 0.992770 | + | 0.120030i | \(0.0382991\pi\) | ||||
−0.992770 | + | 0.120030i | \(0.961701\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 127443.i | 1.12809i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 110256. | − | 110256.i | 0.930985 | − | 0.930985i | −0.0667822 | − | 0.997768i | \(-0.521273\pi\) |
0.997768 | + | 0.0667822i | \(0.0212733\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −73554.2 | − | 73554.2i | −0.592982 | − | 0.592982i | 0.345454 | − | 0.938436i | \(-0.387725\pi\) |
−0.938436 | + | 0.345454i | \(0.887725\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −309550. | −2.38465 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 116163. | 0.855801 | 0.427901 | − | 0.903826i | \(-0.359253\pi\) | ||||
0.427901 | + | 0.903826i | \(0.359253\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −37073.4 | − | 37073.4i | −0.261407 | − | 0.261407i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7154.32 | + | 7154.32i | −0.0483174 | + | 0.0483174i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 303290.i | − | 1.96332i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 126234.i | − | 0.783812i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 277986. | − | 277986.i | 1.65676 | − | 1.65676i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11048.5 | + | 11048.5i | 0.0632456 | + | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 206963. | 1.13863 | 0.569317 | − | 0.822118i | \(-0.307208\pi\) | ||||
0.569317 | + | 0.822118i | \(0.307208\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 57622.2 | 0.304871 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 138422. | + | 138422.i | 0.704738 | + | 0.704738i | 0.965424 | − | 0.260685i | \(-0.0839485\pi\) |
−0.260685 | + | 0.965424i | \(0.583949\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −185282. | + | 185282.i | −0.908245 | + | 0.908245i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 313476.i | 1.48037i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 230300.i | − | 1.04831i | −0.851621 | − | 0.524157i | \(-0.824380\pi\) | ||
0.851621 | − | 0.524157i | \(-0.175620\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −32332.2 | + | 32332.2i | −0.141938 | + | 0.141938i | −0.774505 | − | 0.632568i | \(-0.782001\pi\) |
0.632568 | + | 0.774505i | \(0.282001\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 393118. | + | 393118.i | 1.66523 | + | 1.66523i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8213.91 | −0.0335900 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3540.22 | −0.0139833 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 254254. | + | 254254.i | 0.970454 | + | 0.970454i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 142412. | − | 142412.i | 0.525510 | − | 0.525510i | −0.393720 | − | 0.919230i | \(-0.628812\pi\) |
0.919230 | + | 0.393720i | \(0.128812\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 101751.i | − | 0.363158i | −0.983376 | − | 0.181579i | \(-0.941879\pi\) | ||
0.983376 | − | 0.181579i | \(-0.0581208\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.18051e6i | − | 4.07700i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 55765.7 | − | 55765.7i | 0.186440 | − | 0.186440i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −35410.6 | − | 35410.6i | −0.114653 | − | 0.114653i | 0.647453 | − | 0.762106i | \(-0.275834\pi\) |
−0.762106 | + | 0.647453i | \(0.775834\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 431320. | 1.35303 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −355727. | −1.08156 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −301633. | − | 301633.i | −0.889221 | − | 0.889221i | 0.105227 | − | 0.994448i | \(-0.466443\pi\) |
−0.994448 | + | 0.105227i | \(0.966443\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −284760. | + | 284760.i | −0.814270 | + | 0.814270i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 157537.i | 0.437111i | 0.975824 | + | 0.218556i | \(0.0701345\pi\) | ||||
−0.975824 | + | 0.218556i | \(0.929865\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 371058.i | − | 0.999367i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −721178. | + | 721178.i | −1.88605 | + | 1.88605i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 35638.7 | + | 35638.7i | 0.0905329 | + | 0.0905329i | 0.750923 | − | 0.660390i | \(-0.229609\pi\) |
−0.660390 | + | 0.750923i | \(0.729609\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 106013. | 0.261676 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 242147. | 0.580960 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −63778.3 | − | 63778.3i | −0.148779 | − | 0.148779i | 0.628794 | − | 0.777572i | \(-0.283549\pi\) |
−0.777572 | + | 0.628794i | \(0.783549\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −370078. | + | 370078.i | −0.839647 | + | 0.839647i | −0.988812 | − | 0.149166i | \(-0.952341\pi\) |
0.149166 | + | 0.988812i | \(0.452341\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 714482.i | 1.57711i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 257498.i | 0.553152i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 677673. | − | 677673.i | 1.41715 | − | 1.41715i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.50393e6 | + | 1.50393e6i | 3.06249 | + | 3.06249i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −168330. | −0.333870 | −0.166935 | − | 0.985968i | \(-0.553387\pi\) | ||||
−0.166935 | + | 0.985968i | \(0.553387\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −541728. | −1.04686 | −0.523429 | − | 0.852069i | \(-0.675347\pi\) | ||||
−0.523429 | + | 0.852069i | \(0.675347\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8141.71 | + | 8141.71i | 0.0153331 | + | 0.0153331i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 585746. | − | 585746.i | 1.07534 | − | 1.07534i | 0.0784142 | − | 0.996921i | \(-0.475014\pi\) |
0.996921 | − | 0.0784142i | \(-0.0249857\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 127714.i | − | 0.228615i | −0.993445 | − | 0.114307i | \(-0.963535\pi\) | ||
0.993445 | − | 0.114307i | \(-0.0364649\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 376827.i | 0.657887i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16984.6 | + | 16984.6i | −0.0289278 | + | 0.0289278i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −231241. | − | 231241.i | −0.384309 | − | 0.384309i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.38461e6 | −2.24596 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −827988. | −1.31117 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −644768. | − | 644768.i | −0.997005 | − | 0.997005i | 0.00299074 | − | 0.999996i | \(-0.499048\pi\) |
−0.999996 | + | 0.00299074i | \(0.999048\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 490983. | − | 490983.i | 0.741511 | − | 0.741511i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 47932.8i | − | 0.0707191i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 535084.i | − | 0.771387i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2853.35 | − | 2853.35i | 0.00402017 | − | 0.00402017i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19375.7 | − | 19375.7i | −0.0266856 | − | 0.0266856i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.44076e6 | 1.94013 | 0.970064 | − | 0.242851i | \(-0.0780825\pi\) | ||||
0.970064 | + | 0.242851i | \(0.0780825\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 412639. | 0.543393 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −517029. | − | 517029.i | −0.665963 | − | 0.665963i | 0.290816 | − | 0.956779i | \(-0.406073\pi\) |
−0.956779 | + | 0.290816i | \(0.906073\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −920463. | + | 920463.i | −1.15989 | + | 1.15989i | −0.175394 | + | 0.984498i | \(0.556120\pi\) |
−0.984498 | + | 0.175394i | \(0.943880\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.73233e6i | 3.36902i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.24039e6i | 1.49682i | 0.663238 | + | 0.748409i | \(0.269182\pi\) | ||||
−0.663238 | + | 0.748409i | \(0.730818\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 327014. | − | 327014.i | 0.386275 | − | 0.386275i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −573228. | − | 573228.i | −0.662912 | − | 0.662912i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.34665e6 | −1.52496 | −0.762482 | − | 0.647009i | \(-0.776020\pi\) | ||||
−0.762482 | + | 0.647009i | \(0.776020\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 32567.7 | 0.0361197 | 0.0180599 | − | 0.999837i | \(-0.494251\pi\) | ||||
0.0180599 | + | 0.999837i | \(0.494251\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.44442e6 | + | 2.44442e6i | 2.65558 | + | 2.65558i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 211500. | − | 211500.i | 0.225111 | − | 0.225111i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23673.4i | 0.0246899i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 860492.i | − | 0.879525i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 292306. | − | 292306.i | 0.292856 | − | 0.292856i | −0.545351 | − | 0.838207i | \(-0.683604\pi\) |
0.838207 | + | 0.545351i | \(0.183604\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −794838. | − | 794838.i | −0.780687 | − | 0.780687i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.34343e6 | −1.29380 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.04416e6 | 0.986130 | 0.493065 | − | 0.869993i | \(-0.335877\pi\) | ||||
0.493065 | + | 0.869993i | \(0.335877\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.23537e6 | + | 1.23537e6i | 1.14432 | + | 1.14432i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −66109.7 | + | 66109.7i | −0.0600709 | + | 0.0600709i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 645063.i | − | 0.575059i | −0.957772 | − | 0.287530i | \(-0.907166\pi\) | ||
0.957772 | − | 0.287530i | \(-0.0928340\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 358792.i | − | 0.313854i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.15687e6 | − | 2.15687e6i | 1.85160 | − | 1.85160i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.50774e6 | + | 1.50774e6i | 1.27042 | + | 1.27042i | 0.945870 | + | 0.324547i | \(0.105212\pi\) |
0.324547 | + | 0.945870i | \(0.394788\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 52832.6 | 0.0436997 | 0.0218499 | − | 0.999761i | \(-0.493044\pi\) | ||||
0.0218499 | + | 0.999761i | \(0.493044\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 78121.4 | 0.0634401 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 236876. | + | 236876.i | 0.188882 | + | 0.188882i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 977130. | − | 977130.i | 0.765161 | − | 0.765161i | −0.212089 | − | 0.977250i | \(-0.568027\pi\) |
0.977250 | + | 0.212089i | \(0.0680267\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 2.08273e6i | − | 1.60185i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 581362.i | − | 0.439219i | −0.975588 | − | 0.219610i | \(-0.929522\pi\) | ||
0.975588 | − | 0.219610i | \(-0.0704783\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −590873. | + | 590873.i | −0.438559 | + | 0.438559i | −0.891527 | − | 0.452968i | \(-0.850365\pi\) |
0.452968 | + | 0.891527i | \(0.350365\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 820710. | + | 820710.i | 0.598519 | + | 0.598519i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.21881e6 | −1.59007 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.77726e6 | 1.25171 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.01671e6 | + | 1.01671e6i | 0.703825 | + | 0.703825i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.64681e6 | − | 1.64681e6i | 1.12066 | − | 1.12066i | 0.129016 | − | 0.991643i | \(-0.458818\pi\) |
0.991643 | − | 0.129016i | \(-0.0411818\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 201429.i | − | 0.134762i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.72080e6i | 4.42109i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −22725.6 | + | 22725.6i | −0.0147007 | + | 0.0147007i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −229963. | − | 229963.i | −0.146299 | − | 0.146299i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.04223e6 | 2.52938 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 594338. | 0.365834 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.06448e6 | + | 1.06448e6i | 0.644601 | + | 0.644601i | 0.951683 | − | 0.307082i | \(-0.0993525\pi\) |
−0.307082 | + | 0.951683i | \(0.599352\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 549282. | − | 549282.i | 0.327265 | − | 0.327265i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 938055.i | − | 0.549955i | −0.961451 | − | 0.274978i | \(-0.911330\pi\) | ||
0.961451 | − | 0.274978i | \(-0.0886705\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 851057.i | − | 0.491018i | −0.969394 | − | 0.245509i | \(-0.921045\pi\) | ||
0.969394 | − | 0.245509i | \(-0.0789551\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.97968e6 | − | 1.97968e6i | 1.12413 | − | 1.12413i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.34483e6 | − | 2.34483e6i | −1.31058 | − | 1.31058i | −0.920986 | − | 0.389595i | \(-0.872615\pi\) |
−0.389595 | − | 0.920986i | \(-0.627385\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −75900.9 | −0.0417609 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.68613e6 | −2.53835 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.95313e6 | − | 1.95313e6i | −1.04166 | − | 1.04166i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6772.65 | − | 6772.65i | 0.00355672 | − | 0.00355672i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.12622e6i | 1.61678i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 3.13776e6i | − | 1.59820i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.43713e6 | − | 2.43713e6i | 1.22267 | − | 1.22267i | 0.255992 | − | 0.966679i | \(-0.417598\pi\) |
0.966679 | − | 0.255992i | \(-0.0824021\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.80849e6 | + | 4.80849e6i | 2.37629 | + | 2.37629i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 313462. | 0.152606 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.39700e6 | 1.14972 | 0.574861 | − | 0.818251i | \(-0.305056\pi\) | ||||
0.574861 | + | 0.818251i | \(0.305056\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.46860e6 | − | 2.46860e6i | −1.16668 | − | 1.16668i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.19559e6 | − | 1.19559e6i | 0.556798 | − | 0.556798i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 821430.i | 0.376994i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.57570e6i | 0.712733i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.82591e6 | + | 2.82591e6i | −1.25989 | + | 1.25989i | −0.308751 | + | 0.951143i | \(0.599911\pi\) |
−0.951143 | + | 0.308751i | \(0.900089\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −724297. | − | 724297.i | −0.318312 | − | 0.318312i | 0.529806 | − | 0.848119i | \(-0.322265\pi\) |
−0.848119 | + | 0.529806i | \(0.822265\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 192158. | 0.0832511 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 714440. | 0.305161 | 0.152580 | − | 0.988291i | \(-0.451242\pi\) | ||||
0.152580 | + | 0.988291i | \(0.451242\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −408422. | − | 408422.i | −0.172004 | − | 0.172004i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.44526e6 | + | 6.44526e6i | −2.67652 | + | 2.67652i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 2.73797e6i | − | 1.12122i | −0.828078 | − | 0.560612i | \(-0.810566\pi\) | ||
0.828078 | − | 0.560612i | \(-0.189434\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 89743.0i | − | 0.0362437i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.68261e6 | + | 2.68261e6i | −1.06854 | + | 1.06854i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2373.55 | − | 2373.55i | −0.000932536 | − | 0.000932536i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.70699e6 | −0.661555 | −0.330777 | − | 0.943709i | \(-0.607311\pi\) | ||||
−0.330777 | + | 0.943709i | \(0.607311\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.63635e6 | −3.30190 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.72134e6 | − | 1.72134e6i | −0.649280 | − | 0.649280i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.59619e6 | − | 1.59619e6i | 0.594036 | − | 0.594036i | −0.344683 | − | 0.938719i | \(-0.612014\pi\) |
0.938719 | + | 0.344683i | \(0.112014\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 469588.i | − | 0.172440i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2170.12i | 0.000786377i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.12185e6 | + | 2.12185e6i | −0.758782 | + | 0.758782i | −0.976101 | − | 0.217319i | \(-0.930269\pi\) |
0.217319 | + | 0.976101i | \(0.430269\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.39820e6 | − | 4.39820e6i | −1.55225 | − | 1.55225i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.39113e6 | −1.18127 | −0.590633 | − | 0.806940i | \(-0.701122\pi\) | ||||
−0.590633 | + | 0.806940i | \(0.701122\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.27288e6 | 0.781491 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −895092. | − | 895092.i | −0.303802 | − | 0.303802i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.15607e6 | + | 4.15607e6i | −1.39254 | + | 1.39254i | −0.572958 | + | 0.819585i | \(0.694204\pi\) |
−0.819585 | + | 0.572958i | \(0.805796\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.74987e6i | − | 1.24044i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 5.88326e6i | − | 1.92149i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −476837. | + | 476837.i | −0.153772 | + | 0.153772i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.36699e6 | − | 3.36699e6i | −1.07217 | − | 1.07217i | −0.997184 | − | 0.0749888i | \(-0.976108\pi\) |
−0.0749888 | − | 0.997184i | \(-0.523892\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.87489e6 | 2.47635 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.35505e6 | 1.35248 | 0.676242 | − | 0.736680i | \(-0.263607\pi\) | ||||
0.676242 | + | 0.736680i | \(0.263607\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −34183.8 | − | 34183.8i | −0.0104848 | − | 0.0104848i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.82563e6 | − | 3.82563e6i | 1.15895 | − | 1.15895i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.52065e6i | 1.65198i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 377060.i | 0.111456i | 0.998446 | + | 0.0557279i | \(0.0177479\pi\) | ||||
−0.998446 | + | 0.0557279i | \(0.982252\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.89413e6 | + | 4.89413e6i | −1.42913 | + | 1.42913i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −966378. | − | 966378.i | −0.278786 | − | 0.278786i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −715796. | −0.204018 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.37419e6 | 0.386996 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 48525.8 | + | 48525.8i | 0.0135032 | + | 0.0135032i | 0.713826 | − | 0.700323i | \(-0.246961\pi\) |
−0.700323 | + | 0.713826i | \(0.746961\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.37804e6 | + | 1.37804e6i | −0.378929 | + | 0.378929i | −0.870716 | − | 0.491787i | \(-0.836344\pi\) |
0.491787 | + | 0.870716i | \(0.336344\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 1.22132e7i | − | 3.31879i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.11753e6i | 0.300114i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.85140e6 | − | 2.85140e6i | 0.756813 | − | 0.756813i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 174555. | + | 174555.i | 0.0457919 | + | 0.0457919i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.22831e6 | −0.318503 | −0.159251 | − | 0.987238i | \(-0.550908\pi\) | ||||
−0.159251 | + | 0.987238i | \(0.550908\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.43096e6 | −0.879418 | −0.439709 | − | 0.898140i | \(-0.644918\pi\) | ||||
−0.439709 | + | 0.898140i | \(0.644918\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 75233.7 | + | 75233.7i | 0.0190629 | + | 0.0190629i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.29081e6 | + | 2.29081e6i | −0.573834 | + | 0.573834i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.48221e6i | 0.862371i | 0.902263 | + | 0.431185i | \(0.141904\pi\) | ||||
−0.902263 | + | 0.431185i | \(0.858096\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 7.89907e6i | − | 1.93410i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.92993e6 | − | 2.92993e6i | 0.709330 | − | 0.709330i | −0.257064 | − | 0.966394i | \(-0.582755\pi\) |
0.966394 | + | 0.257064i | \(0.0827552\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.79418e6 | − | 1.79418e6i | −0.429504 | − | 0.429504i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.05283e6 | −1.43281 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.52284e6 | 1.52694 | 0.763469 | − | 0.645845i | \(-0.223495\pi\) | ||||
0.763469 | + | 0.645845i | \(0.223495\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.95771e6 | − | 4.95771e6i | −1.14773 | − | 1.14773i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.16232e6 | + | 2.16232e6i | −0.495079 | + | 0.495079i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 64985.0i | − | 0.0147158i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 260871.i | − | 0.0584299i | −0.999573 | − | 0.0292150i | \(-0.990699\pi\) | ||
0.999573 | − | 0.0292150i | \(-0.00930074\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.58536e7 | + | 1.58536e7i | −3.51234 | + | 3.51234i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.25443e6 | + | 4.25443e6i | 0.932372 | + | 0.932372i | 0.997854 | − | 0.0654817i | \(-0.0208584\pi\) |
−0.0654817 | + | 0.997854i | \(0.520858\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.35973e6 | 0.945163 | 0.472582 | − | 0.881287i | \(-0.343322\pi\) | ||||
0.472582 | + | 0.881287i | \(0.343322\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.37017e6 | −0.508332 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.89257e6 | − | 1.89257e6i | −0.401569 | − | 0.401569i | 0.477216 | − | 0.878786i | \(-0.341646\pi\) |
−0.878786 | + | 0.477216i | \(0.841646\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.50387e6 | − | 1.50387e6i | 0.315702 | − | 0.315702i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.50503e6i | 0.312603i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.02766e6i | − | 0.211201i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 682704. | − | 682704.i | 0.138835 | − | 0.138835i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.70004e6 | − | 6.70004e6i | −1.34828 | − | 1.34828i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.95775e6 | 0.788151 | 0.394075 | − | 0.919078i | \(-0.371065\pi\) | ||||
0.394075 | + | 0.919078i | \(0.371065\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 157844. | 0.0311075 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.55960e6 | + | 7.55960e6i | 1.47445 | + | 1.47445i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 845746. | − | 845746.i | 0.163262 | − | 0.163262i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 453914.i | 0.0867264i | 0.999059 | + | 0.0433632i | \(0.0138073\pi\) | ||||
−0.999059 | + | 0.0433632i | \(0.986193\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.28201e7i | 2.42448i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.41878e6 | − | 5.41878e6i | 1.01437 | − | 1.01437i | 0.0144777 | − | 0.999895i | \(-0.495391\pi\) |
0.999895 | − | 0.0144777i | \(-0.00460855\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −179042. | − | 179042.i | −0.0331770 | − | 0.0331770i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.84680e6 | 1.62283 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.91890e6 | −0.711661 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.16769e6 | − | 5.16769e6i | −0.929063 | − | 0.929063i | 0.0685828 | − | 0.997645i | \(-0.478152\pi\) |
−0.997645 | + | 0.0685828i | \(0.978152\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.34785e6 | − | 3.34785e6i | 0.595897 | − | 0.595897i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.19408e6i | 1.62027i | 0.586240 | + | 0.810137i | \(0.300607\pi\) | ||||
−0.586240 | + | 0.810137i | \(0.699393\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 3.36252e6i | − | 0.586727i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.88541e6 | + | 7.88541e6i | −1.36240 | + | 1.36240i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −913921. | − | 913921.i | −0.156356 | − | 0.156356i | 0.624594 | − | 0.780950i | \(-0.285265\pi\) |
−0.780950 | + | 0.624594i | \(0.785265\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22774.7 | −0.00385833 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.93701e7 | 3.24967 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −456918. | − | 456918.i | −0.0759137 | − | 0.0759137i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.01104e6 | − | 7.01104e6i | 1.15360 | − | 1.15360i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 1.51473e6i | − | 0.246840i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.10507e6i | 1.14676i | 0.819288 | + | 0.573382i | \(0.194369\pi\) | ||||
−0.819288 | + | 0.573382i | \(0.805631\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.26173e6 | − | 5.26173e6i | 0.841152 | − | 0.841152i | −0.147857 | − | 0.989009i | \(-0.547238\pi\) |
0.989009 | + | 0.147857i | \(0.0472376\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.25290e6 | − | 2.25290e6i | −0.356733 | − | 0.356733i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.64055e6 | 0.884697 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.03815e6 | 0.316663 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.76147e6 | − | 3.76147e6i | −0.578923 | − | 0.578923i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −141749. | + | 141749.i | −0.0216123 | + | 0.0216123i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.89814e6i | 0.588807i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.71072e6i | 0.405648i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.53448e6 | − | 4.53448e6i | 0.672288 | − | 0.672288i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.53164e6 | − | 1.53164e6i | −0.224989 | − | 0.224989i | 0.585606 | − | 0.810596i | \(-0.300857\pi\) |
−0.810596 | + | 0.585606i | \(0.800857\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.57292e7 | 2.28932 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.60053e6 | 0.375035 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.29041e6 | + | 3.29041e6i | 0.470198 | + | 0.470198i | 0.901979 | − | 0.431780i | \(-0.142114\pi\) |
−0.431780 | + | 0.901979i | \(0.642114\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.10986e7 | − | 1.10986e7i | 1.57159 | − | 1.57159i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 218755.i | 0.0306958i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.57535e6i | 0.636226i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.47213e6 | − | 5.47213e6i | 0.754091 | − | 0.754091i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −712454. | − | 712454.i | −0.0973014 | − | 0.0973014i | 0.656780 | − | 0.754082i | \(-0.271918\pi\) |
−0.754082 | + | 0.656780i | \(0.771918\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29382.3 | −0.00397701 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.88027e7 | −3.86390 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 368542. | + | 368542.i | 0.0490023 | + | 0.0490023i | 0.731183 | − | 0.682181i | \(-0.238968\pi\) |
−0.682181 | + | 0.731183i | \(0.738968\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.05350e6 | + | 2.05350e6i | −0.270628 | + | 0.270628i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 3.67077e7i | − | 4.79512i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 2.45410e6i | − | 0.317769i | −0.987297 | − | 0.158884i | \(-0.949210\pi\) | ||
0.987297 | − | 0.158884i | \(-0.0507897\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.20689e6 | + | 2.20689e6i | −0.283263 | + | 0.283263i | −0.834409 | − | 0.551146i | \(-0.814191\pi\) |
0.551146 | + | 0.834409i | \(0.314191\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.57720e6 | + | 3.57720e6i | 0.455152 | + | 0.455152i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.31074e6 | 0.165328 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.03399e6 | 0.879553 | 0.439777 | − | 0.898107i | \(-0.355058\pi\) | ||||
0.439777 | + | 0.898107i | \(0.355058\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.15123e7 | + | 1.15123e7i | 1.42714 | + | 1.42714i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.43411e6 | + | 3.43411e6i | −0.422059 | + | 0.422059i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 7.69234e6i | − | 0.937319i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 252944.i | − | 0.0305586i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.32556e6 | + | 5.32556e6i | −0.637926 | + | 0.637926i | −0.950043 | − | 0.312118i | \(-0.898962\pi\) |
0.312118 | + | 0.950043i | \(0.398962\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.44584e6 | − | 3.44584e6i | −0.409267 | − | 0.409267i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.48955e7 | −2.93193 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.24117e6 | 0.962392 | 0.481196 | − | 0.876613i | \(-0.340203\pi\) | ||||
0.481196 | + | 0.876613i | \(0.340203\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.36146e6 | + | 5.36146e6i | 0.620856 | + | 0.620856i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.71406e6 | + | 2.71406e6i | −0.311662 | + | 0.311662i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 5.71298e6i | − | 0.650572i | −0.945616 | − | 0.325286i | \(-0.894539\pi\) | ||
0.945616 | − | 0.325286i | \(-0.105461\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.26506e6i | 0.707521i | 0.935336 | + | 0.353761i | \(0.115097\pi\) | ||||
−0.935336 | + | 0.353761i | \(0.884903\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.85355e6 | − | 5.85355e6i | 0.655581 | − | 0.655581i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.23152e6 | + | 2.23152e6i | 0.247863 | + | 0.247863i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.00536e7 | −1.10752 | −0.553760 | − | 0.832676i | \(-0.686807\pi\) | ||||
−0.553760 | + | 0.832676i | \(0.686807\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 721883. | 0.0788722 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −200456. | − | 200456.i | −0.0217228 | − | 0.0217228i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.73964e6 | + | 8.73964e6i | −0.939382 | + | 0.939382i | −0.998265 | − | 0.0588831i | \(-0.981246\pi\) |
0.0588831 | + | 0.998265i | \(0.481246\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.82828e6i | 1.04783i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.44012e7i | 1.52295i | 0.648194 | + | 0.761475i | \(0.275525\pi\) | ||||
−0.648194 | + | 0.761475i | \(0.724475\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.63486e6 | − | 8.63486e6i | 0.905792 | − | 0.905792i | −0.0901369 | − | 0.995929i | \(-0.528730\pi\) |
0.995929 | + | 0.0901369i | \(0.0287305\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.85946e7 | + | 1.85946e7i | 1.93490 | + | 1.93490i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.72156e7 | −1.77706 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −390625. | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.75957e7 | + | 1.75957e7i | 1.78746 | + | 1.78746i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.30226e7 | + | 1.30226e7i | −1.31242 | + | 1.31242i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.80181e7i | 1.80150i | 0.434334 | + | 0.900752i | \(0.356984\pi\) | ||||
−0.434334 | + | 0.900752i | \(0.643016\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.74041e7i | 2.71836i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.65863e6 | + | 3.65863e6i | −0.360067 | + | 0.360067i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −129648. | − | 129648.i | −0.0126595 | − | 0.0126595i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.52537e7 | −1.47782 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.76428e6 | 0.650245 | 0.325122 | − | 0.945672i | \(-0.394595\pi\) | ||||
0.325122 | + | 0.945672i | \(0.394595\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.24694e7 | − | 1.24694e7i | −1.18937 | − | 1.18937i | −0.977240 | − | 0.212134i | \(-0.931959\pi\) |
−0.212134 | − | 0.977240i | \(-0.568041\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.01863e6 | + | 1.01863e6i | −0.0964086 | + | 0.0964086i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.76781e7i | 1.66025i | 0.557574 | + | 0.830127i | \(0.311732\pi\) | ||||
−0.557574 | + | 0.830127i | \(0.688268\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 4.31856e6i | − | 0.402464i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.13711e7 | + | 1.13711e7i | −1.05160 | + | 1.05160i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.23084e6 | − | 6.23084e6i | −0.571826 | − | 0.571826i | 0.360812 | − | 0.932638i | \(-0.382499\pi\) |
−0.932638 | + | 0.360812i | \(0.882499\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.89397e6 | −0.445716 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −88646.7 | −0.00801215 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.26417e6 | + | 7.26417e6i | 0.651587 | + | 0.651587i | 0.953375 | − | 0.301788i | \(-0.0975834\pi\) |
−0.301788 | + | 0.953375i | \(0.597583\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.99304e6 | + | 4.99304e6i | −0.444489 | + | 0.444489i | −0.893518 | − | 0.449028i | \(-0.851770\pi\) |
0.449028 | + | 0.893518i | \(0.351770\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 823512.i | 0.0727589i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 6.55069e6i | − | 0.574425i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −209997. | + | 209997.i | −0.0182767 | + | 0.0182767i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.06178e7 | − | 3.06178e7i | −2.64490 | − | 2.64490i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.27424e7 | 1.09256 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.16798e7 | 0.994028 | 0.497014 | − | 0.867742i | \(-0.334430\pi\) | ||||
0.497014 | + | 0.867742i | \(0.334430\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.54153e6 | − | 5.54153e6i | −0.468134 | − | 0.468134i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.60241e6 | + | 6.60241e6i | −0.553645 | + | 0.553645i | −0.927491 | − | 0.373846i | \(-0.878039\pi\) |
0.373846 | + | 0.927491i | \(0.378039\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 8.11511e6i | − | 0.675492i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.19749e7i | 1.81576i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −851589. | + | 851589.i | −0.0698519 | + | 0.0698519i | −0.741170 | − | 0.671318i | \(-0.765729\pi\) |
0.671318 | + | 0.741170i | \(0.265729\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.07116e6 | + | 4.07116e6i | 0.331506 | + | 0.331506i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.91218e7 | 3.16247 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −219936. | −0.0176501 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.38682e6 | + | 2.38682e6i | 0.190163 | + | 0.190163i | 0.795766 | − | 0.605604i | \(-0.207068\pi\) |
−0.605604 | + | 0.795766i | \(0.707068\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.24435e7 | − | 4.24435e7i | 3.35720 | − | 3.35720i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 1.14311e6i | − | 0.0897693i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2.33894e7i | − | 1.82363i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.63597e7 | − | 2.63597e7i | 2.04055 | − | 2.04055i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.80021e6 | − | 9.80021e6i | −0.753252 | − | 0.753252i | 0.221833 | − | 0.975085i | \(-0.428796\pi\) |
−0.975085 | + | 0.221833i | \(0.928796\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.59112e7 | 1.21426 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.38988e7 | −1.05319 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.61320e7 | − | 1.61320e7i | −1.21378 | − | 1.21378i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.08067e6 | − | 7.08067e6i | 0.529004 | − | 0.529004i | −0.391272 | − | 0.920275i | \(-0.627965\pi\) |
0.920275 | + | 0.391272i | \(0.127965\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.78088e7i | 1.32118i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 6.61575e6i | − | 0.487366i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 145203. | − | 145203.i | 0.0106221 | − | 0.0106221i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.86178e7 | + | 2.86178e7i | 2.07893 | + | 2.07893i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.03907e7 | −1.47099 | −0.735495 | − | 0.677531i | \(-0.763050\pi\) | ||||
−0.735495 | + | 0.677531i | \(0.763050\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.38422e6 | −0.314090 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −692100. | − | 692100.i | −0.0492406 | − | 0.0492406i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 62582.9 | − | 62582.9i | 0.00442191 | − | 0.00442191i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 6.88695e6i | − | 0.483271i | −0.970367 | − | 0.241636i | \(-0.922316\pi\) | ||
0.970367 | − | 0.241636i | \(-0.0776838\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 5.13056e7i | − | 3.57558i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.42414e6 | − | 2.42414e6i | 0.167789 | − | 0.167789i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.97843e6 | + | 8.97843e6i | 0.617221 | + | 0.617221i | 0.944818 | − | 0.327597i | \(-0.106239\pi\) |
−0.327597 | + | 0.944818i | \(0.606239\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.98925e6 | −0.613769 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.72049e6 | 0.455756 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.28144e7 | + | 1.28144e7i | 0.863153 | + | 0.863153i | 0.991703 | − | 0.128550i | \(-0.0410322\pi\) |
−0.128550 | + | 0.991703i | \(0.541032\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 503087. | − | 503087.i | 0.0336587 | − | 0.0336587i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.59231e7i | 1.05817i | 0.848568 | + | 0.529087i | \(0.177465\pi\) | ||||
−0.848568 | + | 0.529087i | \(0.822535\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.03502e6i | 0.332362i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.33667e7 | + | 1.33667e7i | −0.876442 | + | 0.876442i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.87017e7 | + | 1.87017e7i | 1.21808 | + | 1.21808i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.14541e7 | 1.38807 | 0.694034 | − | 0.719942i | \(-0.255832\pi\) | ||||
0.694034 | + | 0.719942i | \(0.255832\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.24237e7 | −0.798478 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.79872e6 | + | 1.79872e6i | 0.114841 | + | 0.114841i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.08813e7 | − | 1.08813e7i | 0.690145 | − | 0.690145i | −0.272119 | − | 0.962264i | \(-0.587724\pi\) |
0.962264 | + | 0.272119i | \(0.0877244\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.37824e7i | 2.12856i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.31444e6i | 0.144872i | 0.997373 | + | 0.0724361i | \(0.0230773\pi\) | ||||
−0.997373 | + | 0.0724361i | \(0.976923\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.24763e7 | − | 1.24763e7i | 0.775846 | − | 0.775846i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.08686e7 | + | 2.08686e7i | 1.28926 | + | 1.28926i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −123474. | −0.00757857 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.53993e7 | 1.54884 | 0.774418 | − | 0.632675i | \(-0.218043\pi\) | ||||
0.774418 | + | 0.632675i | \(0.218043\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.21896e7 | − | 2.21896e7i | −1.34435 | − | 1.34435i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.08318e7 | + | 2.08318e7i | −1.25394 | + | 1.25394i | −0.300004 | + | 0.953938i | \(0.596988\pi\) |
−0.953938 | + | 0.300004i | \(0.903012\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.97162e6i | 0.117915i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 5.25062e7i | − | 3.12003i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.42887e7 | + | 1.42887e7i | −0.843625 | + | 0.843625i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.75640e6 | − | 8.75640e6i | −0.513687 | − | 0.513687i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.77564e6 | 0.103502 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.25196e6 | 0.0725128 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.60181e6 | + | 7.60181e6i | 0.437502 | + | 0.437502i | 0.891171 | − | 0.453668i | \(-0.149885\pi\) |
−0.453668 | + | 0.891171i | \(0.649885\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.37083e7 | + | 1.37083e7i | −0.783956 | + | 0.783956i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.97037e7i | 1.11971i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 364324.i | − | 0.0205733i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.62473e6 | + | 7.62473e6i | −0.427865 | + | 0.427865i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.04958e7 | − | 1.04958e7i | −0.585290 | − | 0.585290i | 0.351062 | − | 0.936352i | \(-0.385821\pi\) |
−0.936352 | + | 0.351062i | \(0.885821\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.30765e7 | 1.83296 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.70088e7 | −3.69021 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −50887.8 | − | 50887.8i | −0.00278500 | − | 0.00278500i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.28842e6 | − | 6.28842e6i | 0.342020 | − | 0.342020i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 6.40824e7i | − | 3.46382i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.72728e7i | 1.46507i | 0.680730 | + | 0.732535i | \(0.261663\pi\) | ||||
−0.680730 | + | 0.732535i | \(0.738337\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.24393e6 | + | 4.24393e6i | −0.226577 | + | 0.226577i | −0.811261 | − | 0.584684i | \(-0.801218\pi\) |
0.584684 | + | 0.811261i | \(0.301218\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.12275e6 | − | 1.12275e6i | −0.0595742 | − | 0.0595742i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.06643e7 | 0.562393 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.96183e6 | −0.155241 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.21352e6 | − | 1.21352e6i | −0.0632176 | − | 0.0632176i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.18846e6 | − | 3.18846e6i | 0.165091 | − | 0.165091i | −0.619727 | − | 0.784818i | \(-0.712757\pi\) |
0.784818 | + | 0.619727i | \(0.212757\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 9.67709e6i | − | 0.498018i | −0.968501 | − | 0.249009i | \(-0.919895\pi\) | ||
0.968501 | − | 0.249009i | \(-0.0801049\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1.00678e7i | − | 0.514990i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.33843e7 | + | 1.33843e7i | −0.680504 | + | 0.680504i | −0.960114 | − | 0.279609i | \(-0.909795\pi\) |
0.279609 | + | 0.960114i | \(0.409795\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.72004e7 | + | 1.72004e7i | 0.869264 | + | 0.869264i | 0.992391 | − | 0.123127i | \(-0.0392921\pi\) |
−0.123127 | + | 0.992391i | \(0.539292\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.15303e7 | −2.08623 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.13927e7 | 1.06820 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.78489e6 | − | 2.78489e6i | −0.138227 | − | 0.138227i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.79699e7 | + | 2.79699e7i | −1.38000 | + | 1.38000i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.95196e6i | 0.439049i | 0.975607 | + | 0.219525i | \(0.0704506\pi\) | ||||
−0.975607 | + | 0.219525i | \(0.929549\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 2.04911e7i | − | 0.999022i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.23546e7 | + | 1.23546e7i | −0.598770 | + | 0.598770i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.55944e6 | + | 6.55944e6i | 0.316028 | + | 0.316028i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.14119e7 | 1.02553 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.51134e7 | 1.19574 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.52741e7 | + | 1.52741e7i | 0.722990 | + | 0.722990i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.60428e6 | + | 9.60428e6i | −0.451952 | + | 0.451952i | −0.896002 | − | 0.444050i | \(-0.853541\pi\) |
0.444050 | + | 0.896002i | \(0.353541\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 2.54975e7i | − | 1.19284i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 2.01049e7i | − | 0.935080i | −0.883972 | − | 0.467540i | \(-0.845140\pi\) | ||
0.883972 | − | 0.467540i | \(-0.154860\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.69138e7 | − | 1.69138e7i | 0.782092 | − | 0.782092i | −0.198092 | − | 0.980184i | \(-0.563474\pi\) |
0.980184 | + | 0.198092i | \(0.0634743\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.71522e7 | + | 4.71522e7i | 2.16767 | + | 2.16767i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.27514e7 | −1.03987 | −0.519937 | − | 0.854205i | \(-0.674044\pi\) | ||||
−0.519937 | + | 0.854205i | \(0.674044\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.26002e6 | −0.0572581 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.77687e7 | − | 3.77687e7i | −1.70641 | − | 1.70641i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.02232e7 | + | 1.02232e7i | −0.459237 | + | 0.459237i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 192149.i | − | 0.00858208i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 3.15867e7i | − | 1.40271i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.87406e6 | + | 1.87406e6i | −0.0827493 | + | 0.0827493i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.21674e6 | − | 3.21674e6i | −0.141227 | − | 0.141227i | 0.632959 | − | 0.774186i | \(-0.281840\pi\) |
−0.774186 | + | 0.632959i | \(0.781840\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.99930e7 | −3.05550 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −697833. | −0.0302909 | −0.0151454 | − | 0.999885i | \(-0.504821\pi\) | ||||
−0.0151454 | + | 0.999885i | \(0.504821\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.47676e7 | − | 1.47676e7i | −0.637396 | − | 0.637396i | 0.312517 | − | 0.949912i | \(-0.398828\pi\) |
−0.949912 | + | 0.312517i | \(0.898828\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.28060e6 | + | 4.28060e6i | −0.183716 | + | 0.183716i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 4.01033e7i | − | 1.71148i | −0.517407 | − | 0.855739i | \(-0.673103\pi\) | ||
0.517407 | − | 0.855739i | \(-0.326897\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.51053e7i | 1.48977i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.20198e7 | − | 8.20198e7i | 3.46118 | − | 3.46118i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.02066e7 | − | 2.02066e7i | −0.847939 | − | 0.847939i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.25490e6 | 0.0940959 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 965891. | 0.0400818 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −315877. | − | 315877.i | −0.0130352 | − | 0.0130352i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.81454e7 | − | 1.81454e7i | 0.744654 | − | 0.744654i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.77394e6i | 0.398887i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.30842e7i | − | 0.531039i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.44283e6 | − | 6.44283e6i | 0.260051 | − | 0.260051i | −0.565024 | − | 0.825075i | \(-0.691133\pi\) |
0.825075 | + | 0.565024i | \(0.191133\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.27913e7 | − | 6.27913e7i | −2.52052 | − | 2.52052i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.92036e7 | −1.56506 | −0.782529 | − | 0.622615i | \(-0.786070\pi\) | ||||
−0.782529 | + | 0.622615i | \(0.786070\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.53464e7 | −0.609297 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.26304e7 | − | 1.26304e7i | −0.498727 | − | 0.498727i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.34793e7 | + | 2.34793e7i | −0.922067 | + | 0.922067i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.32181e7i | 1.68802i | 0.536329 | + | 0.844009i | \(0.319811\pi\) | ||||
−0.536329 | + | 0.844009i | \(0.680189\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 4.52428e7i | − | 1.75752i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −250359. | + | 250359.i | −0.00967295 | + | 0.00967295i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.55197e6 | − | 4.55197e6i | −0.174922 | − | 0.174922i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.70649e7 | −0.652234 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.47191e7 | −1.31986 | −0.659932 | − | 0.751325i | \(-0.729415\pi\) | ||||
−0.659932 | + | 0.751325i | \(0.729415\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.30689e7 | − | 1.30689e7i | −0.494156 | − | 0.494156i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.99347e7 | + | 1.99347e7i | −0.749733 | + | 0.749733i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.39594e7i | 0.896285i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.99327e7i | 0.741681i | 0.928697 | + | 0.370841i | \(0.120930\pi\) | ||||
−0.928697 | + | 0.370841i | \(0.879070\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.80859e7 | + | 1.80859e7i | −0.669386 | + | 0.669386i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.11958e7 | − | 1.11958e7i | −0.412173 | − | 0.412173i | 0.470322 | − | 0.882495i | \(-0.344138\pi\) |
−0.882495 | + | 0.470322i | \(0.844138\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.74333e7 | −1.00461 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.31721e7 | −1.93689 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.31901e7 | + | 3.31901e7i | 1.20264 | + | 1.20264i | 0.973362 | + | 0.229274i | \(0.0736353\pi\) |
0.229274 | + | 0.973362i | \(0.426365\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1454.96 | + | 1454.96i | −5.24428e−5 | + | 5.24428e-5i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.96608e7i | 3.57333i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.12435e6i | 0.147104i | 0.997291 | + | 0.0735519i | \(0.0234335\pi\) | ||||
−0.997291 | + | 0.0735519i | \(0.976567\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.97567e6 | − | 2.97567e6i | 0.105579 | − | 0.105579i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.61298e6 | + | 1.61298e6i | 0.0569310 | + | 0.0569310i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.90636e7 | 1.37160 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.86777e7 | −0.652403 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.27935e7 | + | 7.27935e7i | 2.52945 | + | 2.52945i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.57648e6 | − | 9.57648e6i | 0.331045 | − | 0.331045i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.73044e7i | 1.62680i | 0.581701 | + | 0.813402i | \(0.302387\pi\) | ||||
−0.581701 | + | 0.813402i | \(0.697613\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.30126e7i | 2.84010i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.52640e7 | − | 1.52640e7i | 0.519540 | − | 0.519540i | −0.397892 | − | 0.917432i | \(-0.630258\pi\) |
0.917432 | + | 0.397892i | \(0.130258\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.48421e6 | − | 5.48421e6i | −0.185709 | − | 0.185709i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −287853. | −0.00969749 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.77866e6 | 0.327750 | 0.163875 | − | 0.986481i | \(-0.447601\pi\) | ||||
0.163875 | + | 0.986481i | \(0.447601\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.84666e7 | − | 3.84666e7i | −1.28270 | − | 1.28270i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.85621e7 | − | 4.85621e7i | 1.61111 | − | 1.61111i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 2.52814e7i | − | 0.834483i | −0.908796 | − | 0.417242i | \(-0.862997\pi\) | ||
0.908796 | − | 0.417242i | \(-0.137003\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.07092e7i | 0.680102i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.66811e7 | + | 6.66811e7i | −2.17876 | + | 2.17876i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.84325e6 | − | 2.84325e6i | −0.0924324 | − | 0.0924324i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.21126e7 | −1.03870 | −0.519352 | − | 0.854560i | \(-0.673827\pi\) | ||||
−0.519352 | + | 0.854560i | \(0.673827\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.03584e8 | −3.33364 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.25768e6 | + | 2.25768e6i | 0.0722944 | + | 0.0722944i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.63140e7 | − | 3.63140e7i | 1.15701 | − | 1.15701i | 0.171891 | − | 0.985116i | \(-0.445012\pi\) |
0.985116 | − | 0.171891i | \(-0.0549876\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 1.29151e8i | − | 4.09435i |
(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.l.a.81.1 | 80 | ||
4.3 | odd | 2 | 80.6.l.a.61.35 | yes | 80 | ||
16.5 | even | 4 | inner | 320.6.l.a.241.1 | 80 | ||
16.11 | odd | 4 | 80.6.l.a.21.35 | ✓ | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.6.l.a.21.35 | ✓ | 80 | 16.11 | odd | 4 | ||
80.6.l.a.61.35 | yes | 80 | 4.3 | odd | 2 | ||
320.6.l.a.81.1 | 80 | 1.1 | even | 1 | trivial | ||
320.6.l.a.241.1 | 80 | 16.5 | even | 4 | inner |