Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [112,7,Mod(17,112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(112, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("112.17");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.s (of order \(6\), 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: | \(25.7660573654\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 285x^{6} + 282x^{5} + 62091x^{4} + 29260x^{3} + 4838750x^{2} + 2401000x + 294122500 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 33.1 | ||
Root | \(-4.86132 + 8.42006i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 112.33 |
Dual form | 112.7.s.c.17.1 |
$q$-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 \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(85\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −27.6101 | + | 15.9407i | −1.02260 | + | 0.590397i | −0.914855 | − | 0.403782i | \(-0.867695\pi\) |
−0.107742 | + | 0.994179i | \(0.534362\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 111.836 | + | 64.5687i | 0.894691 | + | 0.516550i | 0.875474 | − | 0.483265i | \(-0.160549\pi\) |
0.0192168 | + | 0.999815i | \(0.493883\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −298.743 | − | 168.528i | −0.870971 | − | 0.491335i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 143.713 | − | 248.917i | 0.197136 | − | 0.341450i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1189.23 | + | 2059.81i | 0.893487 | + | 1.54756i | 0.835666 | + | 0.549237i | \(0.185082\pi\) |
0.0578204 | + | 0.998327i | \(0.481585\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 820.701i | 0.373555i | 0.982402 | + | 0.186778i | \(0.0598044\pi\) | ||||
−0.982402 | + | 0.186778i | \(0.940196\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4117.09 | −1.21988 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2284.02 | + | 1318.68i | −0.464894 | + | 0.268406i | −0.714100 | − | 0.700044i | \(-0.753164\pi\) |
0.249206 | + | 0.968450i | \(0.419830\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4814.93 | + | 2779.90i | 0.701987 | + | 0.405292i | 0.808087 | − | 0.589063i | \(-0.200503\pi\) |
−0.106100 | + | 0.994355i | \(0.533836\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10934.8 | − | 109.096i | 1.18073 | − | 0.0117801i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5696.37 | − | 9866.40i | 0.468182 | − | 0.810914i | −0.531157 | − | 0.847273i | \(-0.678243\pi\) |
0.999339 | + | 0.0363589i | \(0.0115759\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 525.743 | + | 910.614i | 0.0336476 | + | 0.0582793i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 14078.0i | − | 0.715238i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −32822.6 | −1.34579 | −0.672897 | − | 0.739736i | \(-0.734950\pi\) | ||||
−0.672897 | + | 0.739736i | \(0.734950\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −40622.4 | + | 23453.4i | −1.36358 | + | 0.787263i | −0.990098 | − | 0.140375i | \(-0.955169\pi\) |
−0.373481 | + | 0.927638i | \(0.621836\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −65669.6 | − | 37914.4i | −1.82735 | − | 1.05502i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −22528.7 | − | 38137.0i | −0.525450 | − | 0.889493i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10862.8 | + | 18814.9i | −0.214454 | + | 0.371446i | −0.953104 | − | 0.302644i | \(-0.902131\pi\) |
0.738649 | + | 0.674090i | \(0.235464\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −13082.5 | − | 22659.6i | −0.220546 | − | 0.381996i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 85846.0i | − | 1.24557i | −0.782392 | − | 0.622786i | \(-0.786001\pi\) | ||
0.782392 | − | 0.622786i | \(-0.213999\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −113977. | −1.43355 | −0.716774 | − | 0.697305i | \(-0.754382\pi\) | ||||
−0.716774 | + | 0.697305i | \(0.754382\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 32144.6 | − | 18558.7i | 0.352752 | − | 0.203662i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −33367.3 | − | 19264.6i | −0.321387 | − | 0.185553i | 0.330624 | − | 0.943763i | \(-0.392741\pi\) |
−0.652011 | + | 0.758210i | \(0.726074\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 60845.6 | + | 100693.i | 0.517179 | + | 0.855877i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 42041.4 | − | 72817.9i | 0.316932 | − | 0.548943i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −16620.4 | − | 28787.3i | −0.111638 | − | 0.193363i | 0.804793 | − | 0.593556i | \(-0.202276\pi\) |
−0.916431 | + | 0.400193i | \(0.868943\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 307149.i | 1.84612i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −177254. | −0.957133 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 289901. | − | 167374.i | 1.41154 | − | 0.814953i | 0.416007 | − | 0.909361i | \(-0.363429\pi\) |
0.995534 | + | 0.0944082i | \(0.0300959\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −145845. | − | 84203.9i | −0.642544 | − | 0.370973i | 0.143050 | − | 0.989716i | \(-0.454309\pi\) |
−0.785594 | + | 0.618742i | \(0.787642\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −84882.6 | + | 50142.7i | −0.339467 | + | 0.200533i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −52991.6 | + | 91784.1i | −0.192960 | + | 0.334216i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −161261. | − | 279312.i | −0.536173 | − | 0.928679i | −0.999106 | − | 0.0422855i | \(-0.986536\pi\) |
0.462932 | − | 0.886394i | \(-0.346797\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 363217.i | 1.10565i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −325510. | −0.909473 | −0.454737 | − | 0.890626i | \(-0.650267\pi\) | ||||
−0.454737 | + | 0.890626i | \(0.650267\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 93404.3 | − | 53927.0i | 0.240103 | − | 0.138624i | −0.375121 | − | 0.926976i | \(-0.622399\pi\) |
0.615224 | + | 0.788352i | \(0.289065\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −29031.7 | − | 16761.4i | −0.0688158 | − | 0.0397308i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8138.93 | − | 815772.i | −0.0178277 | − | 1.78688i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −169525. | + | 293625.i | −0.343836 | + | 0.595542i | −0.985142 | − | 0.171744i | \(-0.945060\pi\) |
0.641305 | + | 0.767286i | \(0.278393\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 329180. | + | 570157.i | 0.619411 | + | 1.07285i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 224674.i | 0.392934i | 0.980510 | + | 0.196467i | \(0.0629468\pi\) | ||||
−0.980510 | + | 0.196467i | \(0.937053\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −340582. | −0.554581 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 906235. | − | 523215.i | 1.37620 | − | 0.794552i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 331888. | + | 191615.i | 0.470783 | + | 0.271807i | 0.716568 | − | 0.697518i | \(-0.245712\pi\) |
−0.245784 | + | 0.969325i | \(0.579045\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 138311. | − | 245178.i | 0.183541 | − | 0.325355i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 747726. | − | 1.29510e6i | 0.929595 | − | 1.61011i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 358989. | + | 621787.i | 0.418707 | + | 0.725222i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 32664.1i | 0.0357895i | 0.999840 | + | 0.0178948i | \(0.00569638\pi\) | ||||
−0.999840 | + | 0.0178948i | \(0.994304\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 683629. | 0.704555 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −433003. | + | 249994.i | −0.420268 | + | 0.242642i | −0.695192 | − | 0.718824i | \(-0.744681\pi\) |
0.274924 | + | 0.961466i | \(0.411347\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −386249. | − | 223001.i | −0.353472 | − | 0.204077i | 0.312741 | − | 0.949838i | \(-0.398753\pi\) |
−0.666214 | + | 0.745761i | \(0.732086\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.22995e6 | + | 693844.i | 1.06248 | + | 0.599369i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −944735. | + | 1.63633e6i | −0.771186 | + | 1.33573i | 0.165728 | + | 0.986171i | \(0.447003\pi\) |
−0.936914 | + | 0.349561i | \(0.886331\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 960930. | + | 1.66438e6i | 0.742014 | + | 1.28521i | 0.951577 | + | 0.307411i | \(0.0994626\pi\) |
−0.209563 | + | 0.977795i | \(0.567204\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 692640.i | − | 0.506453i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −472481. | −0.327453 | −0.163726 | − | 0.986506i | \(-0.552351\pi\) | ||||
−0.163726 | + | 0.986506i | \(0.552351\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.27412e6 | − | 735614.i | 0.837756 | − | 0.483678i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 204287. | + | 117945.i | 0.127551 | + | 0.0736413i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 904570. | − | 9024.86i | 0.536786 | − | 0.00535550i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.94276e6 | + | 3.36496e6i | −1.09664 | + | 1.89943i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.36845e6 | + | 2.37022e6i | 0.735381 | + | 1.27372i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.88199e6i | − | 0.963577i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 632211. | 0.308639 | 0.154319 | − | 0.988021i | \(-0.450681\pi\) | ||||
0.154319 | + | 0.988021i | \(0.450681\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.14692e6 | − | 1.81688e6i | 1.46594 | − | 0.846362i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −111928. | − | 64621.5i | −0.0497879 | − | 0.0287451i | 0.474899 | − | 0.880040i | \(-0.342484\pi\) |
−0.524687 | + | 0.851295i | \(0.675818\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −969934. | − | 1.64193e6i | −0.412275 | − | 0.697908i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 909001. | − | 1.57444e6i | 0.369456 | − | 0.639917i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 798004. | + | 1.38218e6i | 0.310344 | + | 0.537532i | 0.978437 | − | 0.206546i | \(-0.0662224\pi\) |
−0.668093 | + | 0.744078i | \(0.732889\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 688428.i | 0.256339i | 0.991752 | + | 0.128169i | \(0.0409101\pi\) | ||||
−0.991752 | + | 0.128169i | \(0.959090\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.22837e6 | 0.438199 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.69049e6 | + | 976002.i | −0.578101 | + | 0.333767i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.67075e6 | − | 2.11931e6i | −1.20407 | − | 0.695170i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.28507e6 | − | 1.81023e6i | −1.03417 | − | 0.569876i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −316745. | + | 548619.i | −0.0957527 | + | 0.165849i | −0.909923 | − | 0.414778i | \(-0.863859\pi\) |
0.814170 | + | 0.580627i | \(0.197192\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.24696e6 | − | 2.15980e6i | −0.362178 | − | 0.627311i | 0.626141 | − | 0.779710i | \(-0.284633\pi\) |
−0.988319 | + | 0.152399i | \(0.951300\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 758044.i | 0.211651i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.05741e6 | −1.62664 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.23038e6 | − | 1.28771e6i | 0.576342 | − | 0.332751i | −0.183336 | − | 0.983050i | \(-0.558690\pi\) |
0.759678 | + | 0.650299i | \(0.225356\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 917781. | + | 529881.i | 0.228322 | + | 0.131822i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.36451e6 | + | 1.98752e6i | −0.806203 | + | 0.476248i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −437858. | + | 758391.i | −0.101104 | + | 0.175118i | −0.912140 | − | 0.409879i | \(-0.865571\pi\) |
0.811036 | + | 0.584997i | \(0.198904\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.89617e6 | − | 8.48041e6i | −1.08994 | − | 1.88784i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 4.20699e6i | − | 0.903280i | −0.892200 | − | 0.451640i | \(-0.850839\pi\) | ||
0.892200 | − | 0.451640i | \(-0.149161\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.15326e6 | 0.860457 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.38393e6 | − | 799013.i | 0.276774 | − | 0.159796i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.28647e6 | − | 1.89744e6i | −0.634732 | − | 0.366463i | 0.147850 | − | 0.989010i | \(-0.452765\pi\) |
−0.782583 | + | 0.622547i | \(0.786098\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3598.11 | − | 360642.i | −0.000671368 | − | 0.0672918i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.33613e6 | + | 9.24245e6i | −0.962291 | + | 1.66674i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 662601. | + | 1.14766e6i | 0.115530 | + | 0.200103i | 0.917991 | − | 0.396600i | \(-0.129810\pi\) |
−0.802462 | + | 0.596704i | \(0.796477\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.90685e6i | − | 0.827499i | −0.910391 | − | 0.413749i | \(-0.864219\pi\) | ||
0.910391 | − | 0.413749i | \(-0.135781\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.36908e6 | 0.876085 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.42970e6 | + | 1.40279e6i | −0.383741 | + | 0.221553i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.43246e6 | − | 3.13643e6i | −0.830752 | − | 0.479635i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.37254e6 | + | 4.20571e6i | −0.351422 | + | 0.622952i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.15391e6 | + | 5.46273e6i | −0.452636 | + | 0.783989i | −0.998549 | − | 0.0538534i | \(-0.982850\pi\) |
0.545913 | + | 0.837842i | \(0.316183\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −437455. | − | 757694.i | −0.0608501 | − | 0.105395i | 0.833996 | − | 0.551771i | \(-0.186048\pi\) |
−0.894846 | + | 0.446376i | \(0.852714\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 3.37889e6i | − | 0.455691i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.85421e6 | −0.896518 | −0.448259 | − | 0.893904i | \(-0.647956\pi\) | ||||
−0.448259 | + | 0.893904i | \(0.647956\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.24491e6 | + | 4.76020e6i | −1.04623 | + | 0.604040i | −0.921591 | − | 0.388162i | \(-0.873110\pi\) |
−0.124637 | + | 0.992202i | \(0.539777\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.90487e6 | + | 5.14123e6i | 1.09658 | + | 0.633110i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.80551e6 | + | 5.53152e6i | 1.17215 | + | 0.661236i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.54297e6 | − | 9.60071e6i | 0.643400 | − | 1.11440i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.63728e6 | − | 2.83585e6i | −0.184591 | − | 0.319722i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.32238e7i | 1.44849i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.02482e7 | 1.09094 | 0.545469 | − | 0.838131i | \(-0.316351\pi\) | ||||
0.545469 | + | 0.838131i | \(0.316351\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.98738e6 | − | 5.18887e6i | 0.930025 | − | 0.536950i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.27468e7 | − | 7.35936e6i | −1.28258 | − | 0.740499i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.60882e7 | − | 160511.i | 1.57445 | − | 0.0157082i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.71927e6 | + | 2.97786e6i | −0.163686 | + | 0.283512i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.08224e6 | − | 1.87450e6i | −0.100265 | − | 0.173663i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.75966e6i | − | 0.158677i | −0.996848 | − | 0.0793385i | \(-0.974719\pi\) | ||
0.996848 | − | 0.0793385i | \(-0.0252808\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 302224. | 0.0265327 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.44566e6 | − | 4.87610e6i | 0.722031 | − | 0.416865i | −0.0934685 | − | 0.995622i | \(-0.529795\pi\) |
0.815500 | + | 0.578757i | \(0.196462\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.75825e7 | − | 1.01513e7i | −1.46411 | − | 0.845306i | −0.464915 | − | 0.885355i | \(-0.653915\pi\) |
−0.999198 | + | 0.0400494i | \(0.987248\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.32287e7 | + | 2.23938e7i | 1.07320 | + | 1.81674i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.71453e6 | − | 4.70171e6i | 0.214599 | − | 0.371696i | −0.738550 | − | 0.674199i | \(-0.764489\pi\) |
0.953148 | + | 0.302503i | \(0.0978223\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.48779e6 | − | 4.30897e6i | −0.191694 | − | 0.332025i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.08094e7i | − | 0.811999i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 920423. | 0.0674208 | 0.0337104 | − | 0.999432i | \(-0.489268\pi\) | ||||
0.0337104 | + | 0.999432i | \(0.489268\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.15894e7 | + | 1.24646e7i | −1.54237 | + | 0.890488i | −0.543681 | + | 0.839292i | \(0.682970\pi\) |
−0.998689 | + | 0.0511961i | \(0.983697\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.28949e6 | − | 5.36329e6i | −0.647401 | − | 0.373777i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 303128. | + | 1.51899e7i | 0.0206124 | + | 1.03289i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.28146e6 | + | 3.95161e6i | −0.151399 | + | 0.262231i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.58147e6 | − | 6.20329e6i | −0.231987 | − | 0.401813i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 9.00977e6i | − | 0.569761i | −0.958563 | − | 0.284880i | \(-0.908046\pi\) | ||
0.958563 | − | 0.284880i | \(-0.0919539\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.70972e7 | 1.67326 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.40351e6 | − | 5.42912e6i | 0.567113 | − | 0.327423i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.52035e7 | + | 8.77772e6i | 0.895659 | + | 0.517109i | 0.875789 | − | 0.482693i | \(-0.160341\pi\) |
0.0198699 | + | 0.999803i | \(0.493675\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.41600e6 | − | 3.79012e6i | 0.369288 | − | 0.218149i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.71701e6 | + | 8.17011e6i | −0.265305 | + | 0.459522i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.02078e6 | − | 6.96420e6i | −0.221026 | − | 0.382828i | 0.734094 | − | 0.679048i | \(-0.237607\pi\) |
−0.955120 | + | 0.296220i | \(0.904274\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.29263e6i | − | 0.230667i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.22179e7 | −0.641895 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.41178e7 | − | 8.15090e6i | 0.725286 | − | 0.418744i | −0.0914090 | − | 0.995813i | \(-0.529137\pi\) |
0.816695 | + | 0.577069i | \(0.195804\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.67932e7 | + | 1.54691e7i | 1.34622 | + | 0.777243i | 0.987712 | − | 0.156283i | \(-0.0499511\pi\) |
0.358511 | + | 0.933525i | \(0.383284\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 89535.1 | + | 8.97418e6i | 0.00440053 | + | 0.441069i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.25046e6 | + | 2.16586e6i | −0.0601273 | + | 0.104144i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.70800e6 | + | 1.16186e7i | 0.315612 | + | 0.546656i | 0.979567 | − | 0.201116i | \(-0.0644568\pi\) |
−0.663955 | + | 0.747772i | \(0.731123\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.34822e7i | 0.620793i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.17351e6 | −0.0528895 | −0.0264447 | − | 0.999650i | \(-0.508419\pi\) | ||||
−0.0264447 | + | 0.999650i | \(0.508419\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.44869e7 | − | 1.41375e7i | 1.08038 | − | 0.623756i | 0.149379 | − | 0.988780i | \(-0.452273\pi\) |
0.930998 | + | 0.365024i | \(0.118939\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.98235e7 | − | 1.14451e7i | −0.856338 | − | 0.494407i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.44675e7 | + | 2.56459e7i | −0.611993 | + | 1.08486i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.59095e6 | + | 1.48800e7i | −0.355916 | + | 0.616465i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −520689. | − | 901860.i | −0.0211300 | − | 0.0365982i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.58159e6i | 0.221899i | 0.993826 | + | 0.110949i | \(0.0353892\pi\) | ||||
−0.993826 | + | 0.110949i | \(0.964611\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.32286e7 | 1.68386 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.89981e7 | − | 1.67420e7i | 1.10688 | − | 0.639056i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.09736e6 | + | 4.67501e6i | 0.302921 | + | 0.174892i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.40499e7 | + | 1.92083e7i | 1.24858 | + | 0.704353i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.97017e6 | − | 1.38047e7i | 0.286510 | − | 0.496250i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.08739e7 | − | 1.88341e7i | −0.383252 | − | 0.663812i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.40807e7i | 1.52347i | 0.647891 | + | 0.761733i | \(0.275651\pi\) | ||||
−0.647891 | + | 0.761733i | \(0.724349\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.42192e7 | 0.481946 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.44238e7 | + | 1.41011e7i | −0.811956 | + | 0.468783i | −0.847635 | − | 0.530580i | \(-0.821974\pi\) |
0.0356786 | + | 0.999363i | \(0.488641\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.13461e6 | − | 2.96447e6i | −0.167446 | − | 0.0966750i | 0.413935 | − | 0.910306i | \(-0.364154\pi\) |
−0.581381 | + | 0.813631i | \(0.697487\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.27306e7 | + | 127013.i | −0.407303 | + | 0.00406365i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.26491e7 | + | 3.92294e7i | −0.711007 | + | 1.23150i | 0.253473 | + | 0.967342i | \(0.418427\pi\) |
−0.964480 | + | 0.264157i | \(0.914906\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.90336e7 | − | 6.76082e7i | −1.20245 | − | 2.08270i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 6.02390e7i | − | 1.82122i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.46632e7 | −0.435132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −747342. | + | 431478.i | −0.0217705 | + | 0.0125692i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.30628e7 | − | 3.06358e7i | −1.51756 | − | 0.876165i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.72162e6 | + | 1.13785e7i | 0.188750 | + | 0.319520i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.34507e7 | + | 5.79383e7i | −0.922404 | + | 1.59765i | −0.126719 | + | 0.991939i | \(0.540445\pi\) |
−0.795685 | + | 0.605711i | \(0.792889\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.12223e6 | + | 5.40786e6i | 0.0845536 | + | 0.146451i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 4.16497e7i | − | 1.10784i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.67215e7 | −0.959469 | −0.479735 | − | 0.877414i | \(-0.659267\pi\) | ||||
−0.479735 | + | 0.877414i | \(0.659267\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.30452e7 | − | 7.53168e6i | 0.334852 | − | 0.193327i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.66188e7 | − | 5.57829e7i | −2.43668 | − | 1.40682i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.20760e6 | − | 4.03355e7i | −0.0299254 | − | 0.999552i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.34524e7 | + | 4.06208e7i | −0.571124 | + | 0.989216i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.31773e7 | + | 5.74648e7i | 0.794059 | + | 1.37535i | 0.923435 | + | 0.383756i | \(0.125370\pi\) |
−0.129375 | + | 0.991596i | \(0.541297\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 9.44163e6i | − | 0.222111i | −0.993814 | − | 0.111056i | \(-0.964577\pi\) | ||
0.993814 | − | 0.111056i | \(-0.0354232\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.15539e7 | 0.267181 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.53150e6 | − | 5.50301e6i | 0.216689 | − | 0.125105i | −0.387727 | − | 0.921774i | \(-0.626740\pi\) |
0.604416 | + | 0.796669i | \(0.293406\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.64039e7 | − | 2.10178e7i | −0.813697 | − | 0.469788i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.48314e7 | + | 1.46687e7i | −0.545754 | + | 0.322393i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.73638e7 | + | 4.73954e7i | −0.591415 | + | 1.02436i | 0.402627 | + | 0.915364i | \(0.368097\pi\) |
−0.994042 | + | 0.108997i | \(0.965236\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.06726e6 | − | 1.39729e7i | −0.171476 | − | 0.297006i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 1.23876e8i | − | 2.58980i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.39280e7 | 0.286424 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.26059e7 | − | 4.76926e7i | 1.67114 | − | 0.964834i | 0.704140 | − | 0.710061i | \(-0.251333\pi\) |
0.967001 | − | 0.254773i | \(-0.0820007\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.13686e7 | − | 1.23371e7i | −0.425301 | − | 0.245548i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 113747. | + | 1.14010e7i | 0.00222751 | + | 0.223265i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.11254e7 | − | 3.65902e7i | 0.407078 | − | 0.705081i | −0.587483 | − | 0.809237i | \(-0.699881\pi\) |
0.994561 | + | 0.104156i | \(0.0332142\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.00002e7 | + | 5.19619e7i | 0.568893 | + | 0.985351i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.69375e7i | − | 0.502728i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.92437e7 | −0.537173 | −0.268587 | − | 0.963256i | \(-0.586557\pi\) | ||||
−0.268587 | + | 0.963256i | \(0.586557\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.74554e7 | + | 1.00779e7i | −0.315613 | + | 0.182219i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.53968e7 | − | 1.46629e7i | −0.452047 | − | 0.260989i | 0.256647 | − | 0.966505i | \(-0.417382\pi\) |
−0.708694 | + | 0.705516i | \(0.750715\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.17631e7 | − | 9.17584e7i | 0.907065 | − | 1.60792i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.63799e7 | + | 2.83709e7i | −0.282605 | + | 0.489486i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.20331e7 | + | 9.01241e7i | 0.883957 | + | 1.53106i | 0.846904 | + | 0.531746i | \(0.178464\pi\) |
0.0370533 | + | 0.999313i | \(0.488203\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.00468e7i | 0.502652i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.12045e6 | 0.0678840 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.79180e7 | + | 2.18920e7i | −0.615254 | + | 0.355217i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.06717e7 | + | 3.50288e7i | 0.969649 | + | 0.559827i | 0.899129 | − | 0.437683i | \(-0.144201\pi\) |
0.0705197 | + | 0.997510i | \(0.477534\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.29535e7 | + | 2.98723e7i | 0.833634 | + | 0.470273i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.84740e7 | + | 6.66389e7i | −0.596670 | + | 1.03346i | 0.396639 | + | 0.917975i | \(0.370177\pi\) |
−0.993309 | + | 0.115488i | \(0.963157\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.92482e7 | − | 3.33388e7i | −0.294086 | − | 0.509372i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.50190e7i | 1.27983i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.16733e7 | −0.766449 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.50627e7 | − | 2.02435e7i | 0.512479 | − | 0.295880i | −0.221373 | − | 0.975189i | \(-0.571054\pi\) |
0.733852 | + | 0.679309i | \(0.237721\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.40660e7 | − | 2.54415e7i | −0.634714 | − | 0.366452i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.14813e8 | + | 1.14549e6i | −1.62983 | + | 0.0162607i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.45069e7 | + | 2.51268e7i | −0.202970 | + | 0.351554i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.09740e7 | − | 1.90076e7i | −0.151342 | − | 0.262131i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.02960e7i | 0.683741i | 0.939747 | + | 0.341870i | \(0.111060\pi\) | ||||
−0.939747 | + | 0.341870i | \(0.888940\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.61043e6 | 0.0215822 | 0.0107911 | − | 0.999942i | \(-0.496565\pi\) | ||||
0.0107911 | + | 0.999942i | \(0.496565\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.59061e6 | + | 5.53714e6i | −0.126714 | + | 0.0731584i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.40162e6 | − | 1.38658e6i | −0.0312851 | − | 0.0180624i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.93796e7 | + | 4.97343e7i | 0.377365 | + | 0.638811i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.11163e7 | − | 5.38951e7i | 0.394109 | − | 0.682617i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.45151e7 | + | 5.97819e7i | 0.431099 | + | 0.746686i | 0.996968 | − | 0.0778092i | \(-0.0247925\pi\) |
−0.565869 | + | 0.824495i | \(0.691459\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 7.91462e7i | − | 0.974915i | −0.873147 | − | 0.487457i | \(-0.837924\pi\) | ||
0.873147 | − | 0.487457i | \(-0.162076\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.35133e8 | 1.64170 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.48552e7 | − | 3.16707e7i | 0.657315 | − | 0.379501i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.09035e7 | − | 1.20687e7i | −0.247073 | − | 0.142648i | 0.371350 | − | 0.928493i | \(-0.378895\pi\) |
−0.618423 | + | 0.785845i | \(0.712228\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.38085e7 | − | 674680.i | 0.394195 | − | 0.00786651i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.35504e7 | − | 4.07904e7i | 0.270886 | − | 0.469188i | −0.698203 | − | 0.715900i | \(-0.746017\pi\) |
0.969089 | + | 0.246712i | \(0.0793500\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.47447e7 | + | 4.28591e7i | 0.280804 | + | 0.486366i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 2.01966e7i | − | 0.226128i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.69720e6 | −0.0518920 | −0.0259460 | − | 0.999663i | \(-0.508260\pi\) | ||||
−0.0259460 | + | 0.999663i | \(0.508260\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.76826e8 | − | 1.02091e8i | 1.92760 | − | 1.11290i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.88575e7 | + | 3.97549e7i | 0.740724 | + | 0.427657i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.12991e7 | − | 1.84893e7i | 0.332275 | − | 0.196285i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.91484e7 | + | 1.02448e8i | −0.619718 | + | 1.07338i | 0.369819 | + | 0.929104i | \(0.379420\pi\) |
−0.989537 | + | 0.144280i | \(0.953914\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.85644e7 | + | 3.21545e7i | 0.191975 | + | 0.332510i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.71817e8i | 1.75373i | 0.480733 | + | 0.876867i | \(0.340371\pi\) | ||||
−0.480733 | + | 0.876867i | \(0.659629\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.58717e7 | −0.462170 | −0.231085 | − | 0.972934i | \(-0.574228\pi\) | ||||
−0.231085 | + | 0.972934i | \(0.574228\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.67246e8 | − | 9.65595e7i | 1.66340 | − | 0.960364i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.12372e7 | − | 6.48779e6i | −0.110333 | − | 0.0637010i | 0.443818 | − | 0.896117i | \(-0.353624\pi\) |
−0.554151 | + | 0.832416i | \(0.686957\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.10365e6 | + | 1.10620e8i | 0.0106982 | + | 1.07229i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.10541e7 | + | 7.11077e7i | −0.392910 | + | 0.680541i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.35545e8 | − | 2.34771e8i | −1.28086 | − | 2.21851i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.84605e6i | 0.0545484i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.55422e6 | −0.0880319 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.00019e7 | − | 1.15481e7i | 0.181997 | − | 0.105076i | −0.406233 | − | 0.913769i | \(-0.633158\pi\) |
0.588231 | + | 0.808693i | \(0.299825\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.54414e7 | − | 8.91507e6i | −0.138756 | − | 0.0801105i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.12121e7 | − | 1.08508e8i | 0.543246 | − | 0.962990i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.10908e6 | + | 3.65304e6i | −0.0184871 | + | 0.0320205i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.67086e7 | − | 2.89401e7i | −0.144661 | − | 0.250561i | 0.784585 | − | 0.620021i | \(-0.212876\pi\) |
−0.929246 | + | 0.369460i | \(0.879543\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 2.79190e7i | − | 0.238767i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.96184e8 | −1.65737 | −0.828686 | − | 0.559714i | \(-0.810911\pi\) | ||||
−0.828686 | + | 0.559714i | \(0.810911\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.49674e7 | − | 4.32825e7i | 0.625651 | − | 0.361220i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.64546e7 | + | 4.41411e7i | 0.630359 | + | 0.363938i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.72439e7 | + | 5.48576e7i | 0.792124 | + | 0.446856i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.63697e7 | − | 8.03147e7i | 0.373192 | − | 0.646388i | −0.616862 | − | 0.787071i | \(-0.711597\pi\) |
0.990055 | + | 0.140683i | \(0.0449298\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.70625e7 | + | 1.16156e8i | 0.533294 | + | 0.923692i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.26998e8i | 0.997914i | 0.866627 | + | 0.498957i | \(0.166283\pi\) | ||||
−0.866627 | + | 0.498957i | \(0.833717\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.45673e7 | −0.501347 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.14672e8 | + | 6.62059e7i | −0.879900 | + | 0.508011i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.24437e8 | − | 7.18438e7i | −0.943619 | − | 0.544799i | −0.0525259 | − | 0.998620i | \(-0.516727\pi\) |
−0.891093 | + | 0.453821i | \(0.850061\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.69921e7 | + | 369069.i | −0.277234 | + | 0.00276595i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.91355e7 | − | 6.77847e7i | 0.289881 | − | 0.502088i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.87978e7 | − | 4.98792e7i | −0.210832 | − | 0.365172i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 9.16404e7i | − | 0.663156i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.20986e8 | 0.865434 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.12128e8 | + | 6.47370e7i | −0.792866 | + | 0.457761i | −0.840971 | − | 0.541081i | \(-0.818015\pi\) |
0.0481045 | + | 0.998842i | \(0.484682\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.11656e8 | + | 1.22200e8i | 1.47954 | + | 0.854210i | 0.999732 | − | 0.0231657i | \(-0.00737454\pi\) |
0.479804 | + | 0.877376i | \(0.340708\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.84823e6 | + | 9.90001e6i | 0.0404154 | + | 0.0684160i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.18550e7 | − | 1.07136e8i | 0.422613 | − | 0.731987i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.12076e6 | + | 1.57976e7i | 0.0616118 | + | 0.106715i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 9.62151e7i | − | 0.642628i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.04539e7 | 0.465290 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.11311e8 | + | 1.22001e8i | −1.37995 | + | 0.796712i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.65890e7 | − | 2.11247e7i | −0.236280 | − | 0.136417i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.35049e8 | + | 2.45078e8i | −0.862432 | + | 1.56508i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.21709e6 | − | 3.84011e6i | 0.0140020 | − | 0.0242522i | −0.858939 | − | 0.512077i | \(-0.828876\pi\) |
0.872942 | + | 0.487825i | \(0.162210\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.82187e7 | + | 1.35479e8i | 0.488553 | + | 0.846198i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.48184e8i | 1.53315i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.96292e7 | 0.486531 | 0.243265 | − | 0.969960i | \(-0.421781\pi\) | ||||
0.243265 | + | 0.969960i | \(0.421781\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.19196e7 | + | 2.42023e7i | −0.253338 | + | 0.146265i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.58038e8 | − | 9.12434e7i | −0.944729 | − | 0.545440i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.00128e8 | − | 5.91488e7i | 0.592082 | − | 0.349761i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.47229e7 | − | 7.74624e7i | 0.261608 | − | 0.453119i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.46346e7 | − | 2.53478e7i | −0.0846865 | − | 0.146681i | 0.820571 | − | 0.571544i | \(-0.193656\pi\) |
−0.905258 | + | 0.424863i | \(0.860322\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.35411e7i | − | 0.535509i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.99988e8 | 1.13270 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.62041e8 | + | 9.35545e7i | −0.908030 | + | 0.524251i | −0.879797 | − | 0.475350i | \(-0.842321\pi\) |
−0.0282330 | + | 0.999601i | \(0.508988\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.28405e7 | − | 3.05075e7i | −0.292969 | − | 0.169146i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.25286e6 | − | 2.25806e8i | −0.0123591 | − | 1.23876i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.18400e7 | + | 5.51485e7i | −0.172837 | + | 0.299362i | −0.939410 | − | 0.342794i | \(-0.888627\pi\) |
0.766574 | + | 0.642156i | \(0.221960\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.74210e7 | − | 1.34097e8i | −0.415863 | − | 0.720296i | 0.579655 | − | 0.814862i | \(-0.303187\pi\) |
−0.995519 | + | 0.0945655i | \(0.969854\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 2.01102e8i | − | 1.06894i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.19793e7 | 0.0630127 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.73237e8 | + | 1.57754e8i | −1.42237 | + | 0.821205i | −0.996501 | − | 0.0835798i | \(-0.973365\pi\) |
−0.425868 | + | 0.904785i | \(0.640031\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.41564e7 | + | 1.39467e7i | 0.124450 | + | 0.0718514i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.78639e7 | − | 6.71199e7i | 0.193062 | − | 0.342234i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.95309e7 | − | 6.84696e7i | 0.199495 | − | 0.345535i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.52311e7 | + | 2.63811e7i | 0.0760789 | + | 0.131772i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.57952e7i | 0.275856i | 0.990442 | + | 0.137928i | \(0.0440443\pi\) | ||||
−0.990442 | + | 0.137928i | \(0.955956\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.60792e8 | −1.27629 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.89246e8 | − | 1.09261e8i | 0.916776 | − | 0.529301i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.39874e8 | + | 1.38491e8i | 1.15032 | + | 0.664137i | 0.948965 | − | 0.315381i | \(-0.102132\pi\) |
0.201354 | + | 0.979518i | \(0.435466\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.01747e8 | + | 5.73976e7i | 0.483024 | + | 0.272485i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.51762e8 | − | 2.62859e8i | 0.713247 | − | 1.23538i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.32594e7 | − | 1.61530e8i | −0.433923 | − | 0.751576i | 0.563284 | − | 0.826263i | \(-0.309538\pi\) |
−0.997207 | + | 0.0746871i | \(0.976204\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2.43621e8i | − | 1.12226i | −0.827729 | − | 0.561128i | \(-0.810368\pi\) | ||
0.827729 | − | 0.561128i | \(-0.189632\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.27009e7 | −0.422797 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.34542e8 | + | 2.50883e8i | −1.96230 | + | 1.13294i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.01650e7 | − | 5.20568e7i | −0.403155 | − | 0.232762i | 0.284689 | − | 0.958620i | \(-0.408110\pi\) |
−0.687844 | + | 0.725858i | \(0.741443\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.58908e8 | + | 3.58081e6i | −1.58903 | + | 0.0158537i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.58105e7 | − | 2.73846e7i | 0.0693142 | − | 0.120056i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.42147e8 | − | 2.46207e8i | −0.617103 | − | 1.06885i | −0.990012 | − | 0.140986i | \(-0.954973\pi\) |
0.372909 | − | 0.927868i | \(-0.378361\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.53436e8i | 1.51944i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.78930e8 | −0.761776 | −0.380888 | − | 0.924621i | \(-0.624382\pi\) | ||||
−0.380888 | + | 0.924621i | \(0.624382\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.04695e8 | + | 1.18181e8i | −0.863048 | + | 0.498281i | −0.865032 | − | 0.501717i | \(-0.832702\pi\) |
0.00198390 | + | 0.999998i | \(0.499369\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.38900e8 | − | 8.01937e7i | −0.579997 | − | 0.334862i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.68565e7 | − | 1.13176e8i | −0.276490 | − | 0.468048i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.29732e8 | − | 2.24703e8i | 0.531383 | − | 0.920383i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.10796e8 | − | 3.65110e8i | −0.855185 | − | 1.48122i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 5.72980e7i | − | 0.230244i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.51341e8 | −0.602378 | −0.301189 | − | 0.953564i | \(-0.597384\pi\) | ||||
−0.301189 | + | 0.953564i | \(0.597384\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.82954e8 | + | 1.63364e8i | −1.11559 | + | 0.644087i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.07041e7 | + | 4.08211e7i | 0.276136 | + | 0.159427i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.26389e7 | + | 4.99360e7i | −0.319717 | + | 0.193195i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.67799e7 | + | 8.10252e7i | −0.179290 | + | 0.310540i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.15332e8 | + | 1.99760e8i | 0.437899 | + | 0.758463i | 0.997527 | − | 0.0702803i | \(-0.0223894\pi\) |
−0.559628 | + | 0.828744i | \(0.689056\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.68539e8i | − | 0.633967i | −0.948431 | − | 0.316983i | \(-0.897330\pi\) | ||
0.948431 | − | 0.316983i | \(-0.102670\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.69254e8 | 1.74875 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.43881e8 | − | 8.30696e7i | 0.531239 | − | 0.306711i | −0.210282 | − | 0.977641i | \(-0.567438\pi\) |
0.741521 | + | 0.670930i | \(0.234105\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.89518e8 | + | 3.98093e8i | 2.52239 | + | 1.45630i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.41638e8 | + | 2.60889e8i | −1.60075 | + | 0.945612i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.18804e8 | − | 2.05775e8i | 0.426670 | − | 0.739014i | −0.569905 | − | 0.821711i | \(-0.693020\pi\) |
0.996575 | + | 0.0826970i | \(0.0263534\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.34506e6 | − | 1.44541e7i | −0.0296965 | − | 0.0514359i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 3.09999e7i | − | 0.109311i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.19568e8 | 1.11662 | 0.558312 | − | 0.829631i | \(-0.311449\pi\) | ||||
0.558312 | + | 0.829631i | \(0.311449\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.66423e8 | − | 2.11554e8i | 1.26876 | − | 0.732517i | 0.294004 | − | 0.955804i | \(-0.405012\pi\) |
0.974753 | + | 0.223287i | \(0.0716787\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.97617e7 | + | 3.45034e7i | 0.205061 | + | 0.118392i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.45687e6 | − | 2.46254e8i | −0.00835444 | − | 0.837373i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.86969e8 | + | 3.23840e8i | −0.630076 | + | 1.09132i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.80502e7 | + | 4.85844e7i | 0.0936824 | + | 0.162263i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 4.00551e8i | − | 1.32584i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.60395e8 | −0.854256 | −0.427128 | − | 0.904191i | \(-0.640475\pi\) | ||||
−0.427128 | + | 0.904191i | \(0.640475\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.28197e7 | − | 7.40144e6i | 0.0416836 | − | 0.0240660i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.43309e8 | − | 1.40475e8i | −0.784139 | − | 0.452723i | 0.0537564 | − | 0.998554i | \(-0.482881\pi\) |
−0.837895 | + | 0.545831i | \(0.816214\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.50482e6 | − | 9.75817e6i | 0.0175846 | − | 0.0311716i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.55457e8 | + | 2.69260e8i | −0.492231 | + | 0.852570i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.08581e8 | + | 1.88068e8i | 0.340794 | + | 0.590272i | 0.984580 | − | 0.174933i | \(-0.0559709\pi\) |
−0.643787 | + | 0.765205i | \(0.722638\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.06105e8i | 0.641233i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.47274e8 | 1.99626 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.36258e7 | − | 1.36403e7i | 0.0722318 | − | 0.0417031i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.52106e8 | + | 2.61024e8i | 1.37027 | + | 0.791126i | 0.990962 | − | 0.134144i | \(-0.0428285\pi\) |
0.379309 | + | 0.925270i | \(0.376162\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.04229e8 | − | 1.15211e8i | −0.613647 | − | 0.346173i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.44509e7 | + | 7.69913e7i | −0.132412 | + | 0.229344i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.13204e8 | + | 1.96074e8i | 0.334319 | + | 0.579058i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.73086e8i | 0.506794i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.81338e8 | 1.10702 | 0.553511 | − | 0.832842i | \(-0.313288\pi\) | ||||
0.553511 | + | 0.832842i | \(0.313288\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.04607e8 | + | 6.03948e7i | −0.301088 | + | 0.173833i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.37376e8 | + | 7.93142e7i | 0.392052 | + | 0.226352i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.71488e8 | − | 1.71093e6i | 0.485260 | − | 0.00484142i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.19766e8 | + | 2.07441e8i | −0.336043 | + | 0.582043i | −0.983685 | − | 0.179902i | \(-0.942422\pi\) |
0.647642 | + | 0.761945i | \(0.275755\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.87256e7 | + | 8.43953e7i | 0.135565 | + | 0.234806i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.34396e8i | 1.47433i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.52077e8 | −0.689628 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.54130e7 | + | 1.46722e7i | −0.0689443 | + | 0.0398050i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.18017e8 | + | 2.41342e8i | 1.12462 | + | 0.649302i | 0.942577 | − | 0.333988i | \(-0.108394\pi\) |
0.182047 | + | 0.983290i | \(0.441728\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.78072e7 | + | 1.31714e8i | 0.207594 | + | 0.351419i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.97390e8 | − | 6.88299e8i | 1.05148 | − | 1.82122i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.72562e7 | − | 2.98887e7i | −0.0452827 | − | 0.0784319i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.49464e8i | 1.43000i | 0.699124 | + | 0.715000i | \(0.253574\pi\) | ||||
−0.699124 | + | 0.715000i | \(0.746426\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.37966e8 | −0.356115 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.60326e8 | − | 1.50299e8i | 0.666447 | − | 0.384774i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.09314e8 | + | 2.94053e8i | 1.29322 | + | 0.746643i | 0.979224 | − | 0.202780i | \(-0.0649977\pi\) |
0.313999 | + | 0.949423i | \(0.398331\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.50507e8 | − | 4.14562e8i | −0.630895 | − | 1.04407i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.83553e8 | − | 6.64334e8i | 0.958127 | − | 1.65952i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.92818e8 | + | 6.80381e8i | 0.973325 | + | 1.68585i | 0.685354 | + | 0.728210i | \(0.259648\pi\) |
0.287972 | + | 0.957639i | \(0.407019\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 1.45473e8i | − | 0.357542i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.34716e8 | −1.30364 | −0.651819 | − | 0.758375i | \(-0.725994\pi\) | ||||
−0.651819 | + | 0.758375i | \(0.725994\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.08472e7 | + | 4.09037e7i | −0.171338 | + | 0.0989221i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.59253e7 | + | 3.22885e7i | 0.134167 | + | 0.0774616i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.58000e8 | − | 3.29628e8i | 1.32797 | − | 0.784473i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.36530e8 | − | 5.82887e8i | 0.794518 | − | 1.37615i | −0.128626 | − | 0.991693i | \(-0.541057\pi\) |
0.923145 | − | 0.384453i | \(-0.125610\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.43622e8 | + | 2.48761e8i | 0.336385 | + | 0.582636i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 3.22059e8i | − | 0.748332i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.17395e8 | −0.962188 | −0.481094 | − | 0.876669i | \(-0.659760\pi\) | ||||
−0.481094 | + | 0.876669i | \(0.659760\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.48156e8 | + | 4.31948e8i | −1.71107 | + | 0.987885i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.96918e8 | − | 2.29161e8i | −0.900631 | − | 0.519980i | −0.0232261 | − | 0.999730i | \(-0.507394\pi\) |
−0.877405 | + | 0.479751i | \(0.840727\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.57647e6 | − | 6.59165e8i | −0.0148054 | − | 1.48395i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.89459e7 | + | 8.47768e7i | −0.109328 | + | 0.189362i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.37364e8 | + | 2.37922e8i | 0.304430 | + | 0.527288i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.67013e8i | 1.02695i | 0.858104 | + | 0.513475i | \(0.171642\pi\) | ||||
−0.858104 | + | 0.513475i | \(0.828358\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.59692e8 | −1.22120 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.73930e7 | + | 2.73624e7i | −0.102607 | + | 0.0592400i | −0.550425 | − | 0.834884i | \(-0.685534\pi\) |
0.447819 | + | 0.894124i | \(0.352201\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.27139e7 | − | 2.46609e7i | −0.0917623 | − | 0.0529790i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.16729e8 | + | 2.06921e8i | −0.248838 | + | 0.441105i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.38643e8 | − | 4.13342e8i | 0.504820 | − | 0.874375i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.87107e8 | − | 6.70489e8i | −0.812602 | − | 1.40747i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.62077e8i | 0.962563i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.32584e8 | 0.687530 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.05483e8 | + | 1.76371e8i | −0.626704 | + | 0.361828i | −0.779475 | − | 0.626434i | \(-0.784514\pi\) |
0.152770 | + | 0.988262i | \(0.451181\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.22029e8 | + | 1.28188e8i | 0.452041 | + | 0.260986i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.41150e8 | + | 7.96262e7i | 0.285202 | + | 0.160889i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.91062e7 | − | 1.19695e8i | 0.138579 | − | 0.240026i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.84275e7 | + | 1.18520e8i | 0.136185 | + | 0.235879i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 6.57525e8i | − | 1.29879i | −0.760453 | − | 0.649393i | \(-0.775023\pi\) | ||
0.760453 | − | 0.649393i | \(-0.224977\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.01616e8 | 0.199214 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.53928e7 | − | 5.50751e7i | 0.185617 | − | 0.107166i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.22159e8 | + | 1.28263e8i | 0.429058 | + | 0.247717i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.04606e8 | + | 5.03444e6i | −0.967309 | + | 0.00965081i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.59862e8 | + | 4.50095e8i | −0.494450 | + | 0.856413i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.44264e8 | + | 5.96282e8i | 0.650198 | + | 1.12618i | 0.983075 | + | 0.183206i | \(0.0586475\pi\) |
−0.332876 | + | 0.942971i | \(0.608019\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 4.12718e8i | − | 0.773732i | −0.922136 | − | 0.386866i | \(-0.873558\pi\) | ||
0.922136 | − | 0.386866i | \(-0.126442\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.86353e8 | −1.83553 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.79368e7 | + | 5.65438e7i | −0.180914 | + | 0.104451i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.48792e8 | − | 3.16845e8i | −1.00633 | − | 0.581006i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.11522e7 | − | 6.96632e7i | −0.0749102 | − | 0.126810i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.98839e8 | − | 3.44399e8i | 0.359312 | − | 0.622347i | −0.628534 | − | 0.777782i | \(-0.716345\pi\) |
0.987846 | + | 0.155435i | \(0.0496780\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.08211e8 | − | 1.87427e8i | −0.194121 | − | 0.336228i | 0.752491 | − | 0.658603i | \(-0.228852\pi\) |
−0.946612 | + | 0.322375i | \(0.895519\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 7.97329e7i | − | 0.141996i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.58785e8 | −0.811134 | −0.405567 | − | 0.914065i | \(-0.632926\pi\) | ||||
−0.405567 | + | 0.914065i | \(0.632926\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.95641e8 | − | 4.01628e8i | 1.22102 | − | 0.704954i | 0.255881 | − | 0.966708i | \(-0.417634\pi\) |
0.965135 | + | 0.261754i | \(0.0843010\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.70417e8 | − | 2.13861e8i | −0.645488 | − | 0.372673i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.71755e8 | − | 1.49749e8i | −0.470156 | − | 0.259077i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.71640e8 | − | 4.70495e8i | 0.466589 | − | 0.808156i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.30177e8 | + | 5.71884e8i | 0.563081 | + | 0.975284i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.09867e9i | 1.86030i | 0.367185 | + | 0.930148i | \(0.380322\pi\) | ||||
−0.367185 | + | 0.930148i | \(0.619678\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.82497e8 | 0.811160 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.24009e7 | − | 1.87066e7i | 0.0540846 | − | 0.0312258i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.64485e8 | + | 2.68171e8i | 0.769842 | + | 0.444469i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.14748e9 | − | 6.77848e8i | 1.88840 | − | 1.11553i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.50725e8 | + | 7.80679e8i | −0.736527 | + | 1.27570i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.23757e8 | + | 2.14353e8i | 0.200807 | + | 0.347808i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.99416e8i | 1.44915i | 0.689196 | + | 0.724575i | \(0.257964\pi\) | ||||
−0.689196 | + | 0.724575i | \(0.742036\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.06365e8 | 0.330170 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.09008e8 | − | 4.67081e8i | 1.28532 | − | 0.742078i | 0.307501 | − | 0.951548i | \(-0.400507\pi\) |
0.977815 | + | 0.209470i | \(0.0671738\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.89837e8 | − | 2.25073e8i | −0.615041 | − | 0.355094i | 0.159895 | − | 0.987134i | \(-0.448884\pi\) |
−0.774936 | + | 0.632040i | \(0.782218\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.36546e6 | − | 9.38708e8i | −0.0146730 | − | 1.47069i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.32956e8 | − | 4.03492e8i | 0.362445 | − | 0.627773i | −0.625918 | − | 0.779889i | \(-0.715275\pi\) |
0.988363 | + | 0.152116i | \(0.0486087\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.45031e8 | − | 4.24406e8i | −0.378593 | − | 0.655742i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 5.47783e8i | − | 0.840527i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.06416e8 | −1.22885 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.29232e8 | − | 1.32347e8i | 0.346913 | − | 0.200290i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.13067e6 | + | 4.69424e6i | 0.0122203 | + | 0.00705542i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.17167e8 | + | 5.62230e8i | −0.473439 | + | 0.839247i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.87763e8 | + | 3.25216e8i | −0.278363 | + | 0.482140i | −0.970978 | − | 0.239168i | \(-0.923125\pi\) |
0.692615 | + | 0.721308i | \(0.256459\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.89745e7 | − | 1.54108e8i | −0.131008 | − | 0.226913i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.74362e8i | 0.986201i | 0.869972 | + | 0.493101i | \(0.164137\pi\) | ||||
−0.869972 | + | 0.493101i | \(0.835863\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.23657e9 | −1.79612 | −0.898061 | − | 0.439871i | \(-0.855024\pi\) | ||||
−0.898061 | + | 0.439871i | \(0.855024\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.19355e9 | + | 6.89094e8i | −1.72191 | + | 0.994143i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.15490e8 | − | 2.39883e8i | −0.595374 | − | 0.343739i | 0.171846 | − | 0.985124i | \(-0.445027\pi\) |
−0.767219 | + | 0.641385i | \(0.778360\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.88868e8 | − | 1.06545e8i | −0.268815 | − | 0.151645i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.82943e8 | + | 1.35610e9i | −1.10687 | + | 1.91716i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.07108e8 | − | 1.85516e8i | −0.150406 | − | 0.260511i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.71133e8i | 0.238707i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.98092e8 | −0.413022 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.33333e9 | − | 7.69799e8i | 1.83510 | − | 1.05949i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.59226e7 | + | 4.38339e7i | 0.103800 | + | 0.0599289i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.24632e9 | + | 1.24344e7i | −1.69264 | + | 0.0168874i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.16829e8 | − | 5.48765e8i | 0.427444 | − | 0.740355i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.16162e6 | − | 3.74403e6i | −0.00289705 | − | 0.00501784i | 0.864573 | − | 0.502507i | \(-0.167589\pi\) |
−0.867470 | + | 0.497489i | \(0.834255\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.43709e8i | 0.191334i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.54738e8 | 0.601459 | 0.300730 | − | 0.953709i | \(-0.402770\pi\) | ||||
0.300730 | + | 0.953709i | \(0.402770\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.62786e8 | + | 2.67190e8i | −0.608090 | + | 0.351081i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.00458e8 | + | 3.46675e8i | 0.783825 | + | 0.452542i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.25471e7 | + | 3.81682e7i | 0.0292403 | + | 0.0494987i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.08907e8 | + | 5.35042e8i | −0.397998 | + | 0.689353i | −0.993479 | − | 0.114017i | \(-0.963628\pi\) |
0.595481 | + | 0.803369i | \(0.296962\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.02677e8 | − | 1.21707e9i | −0.899450 | − | 1.55789i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 2.67147e8i | − | 0.339738i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.28441e7 | −0.0288635 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.11018e8 | + | 6.40960e7i | −0.139365 | + | 0.0804622i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.08765e8 | − | 3.51471e8i | −0.759282 | − | 0.438371i | 0.0697562 | − | 0.997564i | \(-0.477778\pi\) |
−0.829038 | + | 0.559193i | \(0.811111\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.30507e7 | + | 6.53975e8i | 0.0161727 | + | 0.810423i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.49563e8 | − | 7.78666e8i | 0.553536 | − | 0.958752i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.05031e8 | − | 7.01534e8i | −0.495511 | − | 0.858250i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.35920e8i | − | 0.286779i | −0.989666 | − | 0.143389i | \(-0.954200\pi\) | ||
0.989666 | − | 0.143389i | \(-0.0458001\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.89023e8 | 0.228306 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.18894e8 | + | 1.84114e8i | −0.382717 | + | 0.220962i | −0.679000 | − | 0.734139i | \(-0.737586\pi\) |
0.296283 | + | 0.955100i | \(0.404253\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.46991e8 | − | 4.89010e8i | −1.01005 | − | 0.583154i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.36894e8 | + | 3.17159e8i | −0.636199 | + | 0.375822i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.01831e8 | − | 5.22786e8i | 0.355397 | − | 0.615566i | −0.631789 | − | 0.775141i | \(-0.717679\pi\) |
0.987186 | + | 0.159575i | \(0.0510123\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.42579e7 | + | 7.66569e7i | 0.0517836 | + | 0.0896918i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1.44417e9i | − | 1.67910i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.87119e8 | 0.331729 | 0.165864 | − | 0.986149i | \(-0.446959\pi\) | ||||
0.165864 | + | 0.986149i | \(0.446959\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.05443e8 | + | 4.07288e8i | −0.809938 | + | 0.467618i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.15544e9 | + | 1.24445e9i | 2.45924 | + | 1.41984i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.46143e6 | − | 5.47404e8i | −0.00619228 | − | 0.620657i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.56367e8 | − | 1.13686e9i | 0.739566 | − | 1.28097i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.71541e8 | + | 4.70322e8i | 0.304058 | + | 0.526643i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1.12984e8i | − | 0.125728i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.68357e8 | 0.849735 | 0.424868 | − | 0.905256i | \(-0.360321\pi\) | ||||
0.424868 | + | 0.905256i | \(0.360321\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.04853e8 | − | 2.33742e8i | 0.444965 | − | 0.256901i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.15458e8 | + | 4.13070e8i | 0.781496 | + | 0.451197i | 0.836960 | − | 0.547264i | \(-0.184331\pi\) |
−0.0554643 | + | 0.998461i | \(0.517664\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.16019e8 | − | 2.05663e8i | 0.125948 | − | 0.223264i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.37561e7 | − | 2.38263e7i | 0.0148417 | − | 0.0257065i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.17857e8 | + | 7.23750e8i | 0.448068 | + | 0.776077i | 0.998260 | − | 0.0589610i | \(-0.0187788\pi\) |
−0.550192 | + | 0.835038i | \(0.685445\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.11500e8i | 0.971423i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.52390e8 | 0.585112 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.91250e8 | + | 1.10418e8i | −0.201345 | + | 0.116247i | −0.597283 | − | 0.802031i | \(-0.703753\pi\) |
0.395938 | + | 0.918277i | \(0.370420\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.66550e8 | − | 4.42568e8i | −0.802106 | − | 0.463096i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.66966e8 | − | 2.07014e8i | −0.381658 | − | 0.215303i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.49256e8 | + | 1.12454e9i | −0.671161 | + | 1.16249i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.64147e8 | − | 6.30721e8i | −0.374158 | − | 0.648061i | 0.616042 | − | 0.787713i | \(-0.288735\pi\) |
−0.990201 | + | 0.139652i | \(0.955402\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 2.13291e9i | − | 2.17834i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.22944e9 | −1.24807 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.47059e8 | + | 8.49047e7i | −0.148391 | + | 0.0856735i | −0.572357 | − | 0.820005i | \(-0.693971\pi\) |
0.423966 | + | 0.905678i | \(0.360638\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.64876e8 | + | 1.52926e8i | 0.265672 | + | 0.153386i |
(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 | 112.7.s.c.33.1 | 8 | ||
4.3 | odd | 2 | 14.7.d.a.5.2 | yes | 8 | ||
7.3 | odd | 6 | inner | 112.7.s.c.17.1 | 8 | ||
12.11 | even | 2 | 126.7.n.c.19.3 | 8 | |||
28.3 | even | 6 | 14.7.d.a.3.2 | ✓ | 8 | ||
28.11 | odd | 6 | 98.7.d.c.31.1 | 8 | |||
28.19 | even | 6 | 98.7.b.c.97.5 | 8 | |||
28.23 | odd | 6 | 98.7.b.c.97.8 | 8 | |||
28.27 | even | 2 | 98.7.d.c.19.1 | 8 | |||
84.59 | odd | 6 | 126.7.n.c.73.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.7.d.a.3.2 | ✓ | 8 | 28.3 | even | 6 | ||
14.7.d.a.5.2 | yes | 8 | 4.3 | odd | 2 | ||
98.7.b.c.97.5 | 8 | 28.19 | even | 6 | |||
98.7.b.c.97.8 | 8 | 28.23 | odd | 6 | |||
98.7.d.c.19.1 | 8 | 28.27 | even | 2 | |||
98.7.d.c.31.1 | 8 | 28.11 | odd | 6 | |||
112.7.s.c.17.1 | 8 | 7.3 | odd | 6 | inner | ||
112.7.s.c.33.1 | 8 | 1.1 | even | 1 | trivial | ||
126.7.n.c.19.3 | 8 | 12.11 | even | 2 | |||
126.7.n.c.73.3 | 8 | 84.59 | odd | 6 |