Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,8,Mod(1,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.a (trivial) |
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: | yes |
Analytic conductor: | \(59.9779248930\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{46}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 46 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 96) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(6.78233\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 192.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 227.552 | 0.814114 | 0.407057 | − | 0.913403i | \(-0.366555\pi\) | ||||
0.407057 | + | 0.913403i | \(0.366555\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 724.656 | 0.798525 | 0.399262 | − | 0.916837i | \(-0.369266\pi\) | ||||
0.399262 | + | 0.916837i | \(0.369266\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1125.31 | −0.254917 | −0.127458 | − | 0.991844i | \(-0.540682\pi\) | ||||
−0.127458 | + | 0.991844i | \(0.540682\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2426.90 | −0.306372 | −0.153186 | − | 0.988197i | \(-0.548953\pi\) | ||||
−0.153186 | + | 0.988197i | \(0.548953\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6143.90 | 0.470029 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 28738.2 | 1.41869 | 0.709347 | − | 0.704860i | \(-0.248990\pi\) | ||||
0.709347 | + | 0.704860i | \(0.248990\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 44674.2 | 1.49423 | 0.747117 | − | 0.664692i | \(-0.231437\pi\) | ||||
0.747117 | + | 0.664692i | \(0.231437\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 19565.7 | 0.461029 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −23822.7 | −0.408266 | −0.204133 | − | 0.978943i | \(-0.565438\pi\) | ||||
−0.204133 | + | 0.978943i | \(0.565438\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −26345.2 | −0.337218 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −11111.2 | −0.0845994 | −0.0422997 | − | 0.999105i | \(-0.513468\pi\) | ||||
−0.0422997 | + | 0.999105i | \(0.513468\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −84678.5 | −0.510514 | −0.255257 | − | 0.966873i | \(-0.582160\pi\) | ||||
−0.255257 | + | 0.966873i | \(0.582160\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −30383.4 | −0.147176 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 164897. | 0.650090 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 199202. | 0.646530 | 0.323265 | − | 0.946309i | \(-0.395220\pi\) | ||||
0.323265 | + | 0.946309i | \(0.395220\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −65526.2 | −0.176884 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 272733. | 0.618008 | 0.309004 | − | 0.951061i | \(-0.400004\pi\) | ||||
0.309004 | + | 0.951061i | \(0.400004\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 584037. | 1.12021 | 0.560107 | − | 0.828420i | \(-0.310760\pi\) | ||||
0.560107 | + | 0.828420i | \(0.310760\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 165885. | 0.271371 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.27056e6 | −1.78506 | −0.892532 | − | 0.450983i | \(-0.851073\pi\) | ||||
−0.892532 | + | 0.450983i | \(0.851073\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −298417. | −0.362358 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 775932. | 0.819083 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 371805. | 0.343044 | 0.171522 | − | 0.985180i | \(-0.445132\pi\) | ||||
0.171522 | + | 0.985180i | \(0.445132\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −256067. | −0.207531 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.20620e6 | 0.862697 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.79416e6 | 1.13731 | 0.568657 | − | 0.822575i | \(-0.307463\pi\) | ||||
0.568657 | + | 0.822575i | \(0.307463\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.22047e6 | −1.25253 | −0.626267 | − | 0.779608i | \(-0.715418\pi\) | ||||
−0.626267 | + | 0.779608i | \(0.715418\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 528274. | 0.266175 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −552245. | −0.249422 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.78620e6 | 1.53795 | 0.768974 | − | 0.639280i | \(-0.220768\pi\) | ||||
0.768974 | + | 0.639280i | \(0.220768\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −643213. | −0.235713 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.40108e6 | 1.45934 | 0.729668 | − | 0.683802i | \(-0.239675\pi\) | ||||
0.729668 | + | 0.683802i | \(0.239675\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.62913e6 | −1.39274 | −0.696369 | − | 0.717684i | \(-0.745202\pi\) | ||||
−0.696369 | + | 0.717684i | \(0.745202\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −711319. | −0.194693 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −815463. | −0.203557 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.37397e6 | 0.541727 | 0.270863 | − | 0.962618i | \(-0.412691\pi\) | ||||
0.270863 | + | 0.962618i | \(0.412691\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.76865e6 | 1.10739 | 0.553696 | − | 0.832719i | \(-0.313217\pi\) | ||||
0.553696 | + | 0.832719i | \(0.313217\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.53943e6 | 1.15498 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −300002. | −0.0488435 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.61090e6 | 0.242217 | 0.121108 | − | 0.992639i | \(-0.461355\pi\) | ||||
0.121108 | + | 0.992639i | \(0.461355\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.75866e6 | −0.244646 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.28632e6 | −0.294745 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.01657e7 | 1.21648 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −81667.2 | −0.00908546 | −0.00454273 | − | 0.999990i | \(-0.501446\pi\) | ||||
−0.00454273 | + | 0.999990i | \(0.501446\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −820352. | −0.0849722 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.09433e6 | −0.878307 | −0.439153 | − | 0.898412i | \(-0.644722\pi\) | ||||
−0.439153 | + | 0.898412i | \(0.644722\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.97220e7 | 1.77836 | 0.889181 | − | 0.457556i | \(-0.151275\pi\) | ||||
0.889181 | + | 0.457556i | \(0.151275\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.45221e6 | 0.375330 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.09689e6 | −0.638962 | −0.319481 | − | 0.947593i | \(-0.603509\pi\) | ||||
−0.319481 | + | 0.947593i | \(0.603509\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.90660e7 | 1.41016 | 0.705078 | − | 0.709130i | \(-0.250912\pi\) | ||||
0.705078 | + | 0.709130i | \(0.250912\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.37846e6 | 0.373274 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.69299e7 | 1.10377 | 0.551886 | − | 0.833919i | \(-0.313908\pi\) | ||||
0.551886 | + | 0.833919i | \(0.313908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.42090e6 | −0.332375 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.76921e6 | −0.102124 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.08253e7 | 1.13286 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.82208e7 | −0.935018 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.36379e6 | 0.356807 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.37724e7 | −1.08865 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.91925e7 | 0.831418 | 0.415709 | − | 0.909498i | \(-0.363534\pi\) | ||||
0.415709 | + | 0.909498i | \(0.363534\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.57690e7 | 0.646756 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.48634e7 | 0.966298 | 0.483149 | − | 0.875538i | \(-0.339493\pi\) | ||||
0.483149 | + | 0.875538i | \(0.339493\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.23734e7 | 1.19318 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.47890e6 | 0.156676 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.43232e7 | −0.808164 | −0.404082 | − | 0.914723i | \(-0.632409\pi\) | ||||
−0.404082 | + | 0.914723i | \(0.632409\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.83111e7 | 1.20996 | 0.604982 | − | 0.796239i | \(-0.293180\pi\) | ||||
0.604982 | + | 0.796239i | \(0.293180\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.43052e7 | −1.03061 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.73101e6 | 0.0780994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.52837e6 | −0.0688735 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.05727e6 | −0.209207 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.80329e6 | 0.0694250 | 0.0347125 | − | 0.999397i | \(-0.488948\pi\) | ||||
0.0347125 | + | 0.999397i | \(0.488948\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.31756e7 | −1.02052 | −0.510258 | − | 0.860022i | \(-0.670450\pi\) | ||||
−0.510258 | + | 0.860022i | \(0.670450\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.09502e7 | 0.472898 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.92687e7 | −0.415616 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.86833e7 | 1.62268 | 0.811341 | − | 0.584573i | \(-0.198738\pi\) | ||||
0.811341 | + | 0.584573i | \(0.198738\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.00387e7 | 0.198056 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.72632e7 | −0.326011 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.04599e6 | 0.163606 | 0.0818031 | − | 0.996649i | \(-0.473932\pi\) | ||||
0.0818031 | + | 0.996649i | \(0.473932\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.91380e6 | −0.119818 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.02777e8 | −1.70761 | −0.853806 | − | 0.520592i | \(-0.825711\pi\) | ||||
−0.853806 | + | 0.520592i | \(0.825711\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.68587e7 | −0.906136 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.25675e7 | 0.498078 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.19796e8 | −1.75906 | −0.879532 | − | 0.475839i | \(-0.842145\pi\) | ||||
−0.879532 | + | 0.475839i | \(0.842145\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.90912e7 | −0.269277 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.84424e7 | 0.656628 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.07336e7 | 0.139882 | 0.0699408 | − | 0.997551i | \(-0.477719\pi\) | ||||
0.0699408 | + | 0.997551i | \(0.477719\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.57289e7 | −0.197162 | −0.0985812 | − | 0.995129i | \(-0.531430\pi\) | ||||
−0.0985812 | + | 0.995129i | \(0.531430\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.99526e7 | −0.723151 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.53289e7 | 0.526349 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.23394e7 | −0.361649 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.42634e7 | 0.153676 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.01986e8 | −1.05906 | −0.529532 | − | 0.848290i | \(-0.677632\pi\) | ||||
−0.529532 | + | 0.848290i | \(0.677632\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.34130e7 | −0.835186 | −0.417593 | − | 0.908634i | \(-0.637126\pi\) | ||||
−0.417593 | + | 0.908634i | \(0.637126\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.49106e7 | −0.144004 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.81982e7 | −0.542348 | −0.271174 | − | 0.962530i | \(-0.587412\pi\) | ||||
−0.271174 | + | 0.962530i | \(0.587412\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.61506e8 | −1.45279 | −0.726393 | − | 0.687280i | \(-0.758805\pi\) | ||||
−0.726393 | + | 0.687280i | \(0.758805\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.02227e8 | 0.887935 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.05178e6 | −0.0675547 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.20609e7 | 0.503129 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.73667e7 | −0.136089 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.02723e7 | −0.380905 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.74548e7 | −0.567623 | −0.283811 | − | 0.958880i | \(-0.591599\pi\) | ||||
−0.283811 | + | 0.958880i | \(0.591599\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.18829e8 | 0.842548 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.32899e8 | 0.911982 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.13627e7 | −0.407658 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.24987e8 | −0.804098 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.97447e7 | −0.434648 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.33465e7 | 0.563678 | 0.281839 | − | 0.959462i | \(-0.409056\pi\) | ||||
0.281839 | + | 0.959462i | \(0.409056\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.92056e7 | −0.112406 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.28306e7 | −0.243032 | −0.121516 | − | 0.992589i | \(-0.538776\pi\) | ||||
−0.121516 | + | 0.992589i | \(0.538776\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.81117e8 | 0.996630 | 0.498315 | − | 0.866996i | \(-0.333952\pi\) | ||||
0.498315 | + | 0.866996i | \(0.333952\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.20175e7 | −0.117524 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.73990e7 | −0.141902 | −0.0709512 | − | 0.997480i | \(-0.522603\pi\) | ||||
−0.0709512 | + | 0.997480i | \(0.522603\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.89119e8 | −1.45325 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.40972e7 | 0.312766 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.76036e7 | 0.367696 | 0.183848 | − | 0.982955i | \(-0.441145\pi\) | ||||
0.183848 | + | 0.982955i | \(0.441145\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.21193e8 | 1.93830 | 0.969150 | − | 0.246471i | \(-0.0792710\pi\) | ||||
0.969150 | + | 0.246471i | \(0.0792710\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.79054e7 | −0.295001 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.08420e8 | −0.457792 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.55754e8 | 0.639353 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.75375e8 | −1.89748 | −0.948741 | − | 0.316053i | \(-0.897642\pi\) | ||||
−0.948741 | + | 0.316053i | \(0.897642\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.68079e7 | 0.104074 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.76565e8 | 0.666827 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.12886e8 | −1.88476 | −0.942378 | − | 0.334551i | \(-0.891416\pi\) | ||||
−0.942378 | + | 0.334551i | \(0.891416\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.44353e8 | 0.516270 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.10005e6 | −0.0281998 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.07182e8 | −0.702275 | −0.351138 | − | 0.936324i | \(-0.614205\pi\) | ||||
−0.351138 | + | 0.936324i | \(0.614205\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.46048e7 | 0.279277 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.34944e7 | 0.139844 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.95082e7 | −0.123753 | −0.0618763 | − | 0.998084i | \(-0.519708\pi\) | ||||
−0.0618763 | + | 0.998084i | \(0.519708\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.60355e8 | 0.489430 | 0.244715 | − | 0.969595i | \(-0.421306\pi\) | ||||
0.244715 | + | 0.969595i | \(0.421306\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.74839e7 | −0.141246 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.96465e7 | 0.0859625 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.47081e8 | −1.82928 | −0.914638 | − | 0.404274i | \(-0.867524\pi\) | ||||
−0.914638 | + | 0.404274i | \(0.867524\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.17306e7 | −0.170171 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.78439e8 | −1.01748 | −0.508738 | − | 0.860922i | \(-0.669888\pi\) | ||||
−0.508738 | + | 0.860922i | \(0.669888\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.46034e8 | −1.16981 | −0.584905 | − | 0.811102i | \(-0.698868\pi\) | ||||
−0.584905 | + | 0.811102i | \(0.698868\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.74474e8 | 0.702334 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.97637e8 | 0.493495 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.15546e8 | 1.01269 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.20502e6 | −0.00524549 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.46621e8 | −1.26955 | −0.634775 | − | 0.772697i | \(-0.718907\pi\) | ||||
−0.634775 | + | 0.772697i | \(0.718907\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.08265e8 | 0.925903 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.21495e7 | −0.0490587 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.78152e7 | 0.125081 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.23226e8 | 0.894519 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.45547e8 | −0.507091 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.05271e8 | −1.01971 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.30513e8 | 1.24368 | 0.621842 | − | 0.783143i | \(-0.286385\pi\) | ||||
0.621842 | + | 0.783143i | \(0.286385\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.32493e8 | 1.02674 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.23661e8 | −0.610139 | −0.305069 | − | 0.952330i | \(-0.598680\pi\) | ||||
−0.305069 | + | 0.952330i | \(0.598680\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.60648e8 | 1.58643 | 0.793214 | − | 0.608943i | \(-0.208406\pi\) | ||||
0.793214 | + | 0.608943i | \(0.208406\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.20210e8 | 0.216697 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.23939e8 | −0.394840 | −0.197420 | − | 0.980319i | \(-0.563256\pi\) | ||||
−0.197420 | + | 0.980319i | \(0.563256\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.25035e7 | 0.0215658 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.18616e8 | −0.368905 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.28386e9 | 2.11986 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.39370e7 | 0.103314 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.14782e8 | 0.814154 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.20721e8 | −1.42542 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.12017e9 | 1.69780 | 0.848902 | − | 0.528550i | \(-0.177264\pi\) | ||||
0.848902 | + | 0.528550i | \(0.177264\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.45219e8 | 0.215510 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.61556e8 | 1.25207 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.53693e8 | 0.503410 | 0.251705 | − | 0.967804i | \(-0.419009\pi\) | ||||
0.251705 | + | 0.967804i | \(0.419009\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.57107e8 | 0.637263 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.52897e7 | 0.130138 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.13035e8 | −1.08788 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.46364e8 | −0.191897 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.88230e8 | 0.241845 | 0.120922 | − | 0.992662i | \(-0.461415\pi\) | ||||
0.120922 | + | 0.992662i | \(0.461415\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.58810e7 | 0.108145 | 0.0540727 | − | 0.998537i | \(-0.482780\pi\) | ||||
0.0540727 | + | 0.998537i | \(0.482780\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.77686e7 | −0.0589614 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.55346e7 | 0.0550973 | 0.0275487 | − | 0.999620i | \(-0.491230\pi\) | ||||
0.0275487 | + | 0.999620i | \(0.491230\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.00147e9 | 1.18807 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.62283e8 | 0.654058 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.01706e9 | −1.16015 | −0.580077 | − | 0.814562i | \(-0.696978\pi\) | ||||
−0.580077 | + | 0.814562i | \(0.696978\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.10191e9 | 1.23274 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.91963e8 | −0.539833 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.05337e9 | −1.13385 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.15304e8 | 0.966571 | 0.483286 | − | 0.875463i | \(-0.339443\pi\) | ||||
0.483286 | + | 0.875463i | \(0.339443\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.98822e8 | 0.206003 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.69430e8 | 0.273929 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.99424e8 | −0.697846 | −0.348923 | − | 0.937151i | \(-0.613452\pi\) | ||||
−0.348923 | + | 0.937151i | \(0.613452\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.41854e8 | −0.628531 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.69657e7 | 0.0259189 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.35218e9 | −1.27584 | −0.637921 | − | 0.770102i | \(-0.720205\pi\) | ||||
−0.637921 | + | 0.770102i | \(0.720205\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.18198e8 | 0.480019 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.69797e9 | 1.54431 | 0.772155 | − | 0.635435i | \(-0.219179\pi\) | ||||
0.772155 | + | 0.635435i | \(0.219179\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.85560e8 | −0.165719 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.25763e8 | 0.373405 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.88879e8 | 0.679496 | 0.339748 | − | 0.940516i | \(-0.389658\pi\) | ||||
0.339748 | + | 0.940516i | \(0.389658\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.84622e8 | −0.579204 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.71312e8 | 0.557892 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.40201e8 | 0.441028 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.19931e9 | −0.961978 | −0.480989 | − | 0.876727i | \(-0.659722\pi\) | ||||
−0.480989 | + | 0.876727i | \(0.659722\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.74081e8 | 0.688885 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.04006e9 | −0.805480 | −0.402740 | − | 0.915314i | \(-0.631942\pi\) | ||||
−0.402740 | + | 0.915314i | \(0.631942\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.05506e8 | 0.156407 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.20930e8 | 0.0904571 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.24165e8 | −0.164811 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.04909e8 | −0.292634 | −0.146317 | − | 0.989238i | \(-0.546742\pi\) | ||||
−0.146317 | + | 0.989238i | \(0.546742\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.56727e8 | −0.466594 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.30015e9 | 0.908173 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.31267e9 | 0.901543 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.03440e9 | 0.698573 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.46116e8 | −0.163452 | −0.0817261 | − | 0.996655i | \(-0.526043\pi\) | ||||
−0.0817261 | + | 0.996655i | \(0.526043\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.07285e9 | 0.700731 | 0.350365 | − | 0.936613i | \(-0.386057\pi\) | ||||
0.350365 | + | 0.936613i | \(0.386057\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.26241e8 | −0.595022 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.57113e8 | −0.478409 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.60907e9 | −1.00018 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.37374e7 | 0.0450907 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.24317e8 | 0.495934 | 0.247967 | − | 0.968768i | \(-0.420238\pi\) | ||||
0.247967 | + | 0.968768i | \(0.420238\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.40778e8 | −0.260923 | −0.130462 | − | 0.991453i | \(-0.541646\pi\) | ||||
−0.130462 | + | 0.991453i | \(0.541646\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.82660e7 | −0.0397642 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.06426e9 | −0.610045 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.43490e8 | 0.306596 | 0.153298 | − | 0.988180i | \(-0.451011\pi\) | ||||
0.153298 | + | 0.988180i | \(0.451011\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.17546e8 | −0.120786 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.85228e9 | −1.01226 | −0.506130 | − | 0.862457i | \(-0.668925\pi\) | ||||
−0.506130 | + | 0.862457i | \(0.668925\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.66564e8 | 0.197192 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.56888e7 | 0.0400825 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.41843e9 | 0.739515 | 0.369758 | − | 0.929128i | \(-0.379441\pi\) | ||||
0.369758 | + | 0.929128i | \(0.379441\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.06909e8 | −0.157541 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.16574e9 | −0.589195 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.00187e8 | −0.199170 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.89446e9 | −0.928493 | −0.464247 | − | 0.885706i | \(-0.653675\pi\) | ||||
−0.464247 | + | 0.885706i | \(0.653675\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.65654e8 | 0.273028 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.41152e9 | −1.62179 | −0.810895 | − | 0.585192i | \(-0.801019\pi\) | ||||
−0.810895 | + | 0.585192i | \(0.801019\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.75923e9 | 0.823736 | 0.411868 | − | 0.911244i | \(-0.364877\pi\) | ||||
0.411868 | + | 0.911244i | \(0.364877\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.20256e8 | −0.239956 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.76328e9 | −1.25550 | −0.627749 | − | 0.778416i | \(-0.716024\pi\) | ||||
−0.627749 | + | 0.778416i | \(0.716024\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.74369e9 | 1.22809 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.12445e9 | 0.936856 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.57224e8 | −0.285561 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.17695e9 | −0.503883 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.71046e8 | 0.114348 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.32149e8 | −0.387535 | −0.193767 | − | 0.981047i | \(-0.562071\pi\) | ||||
−0.193767 | + | 0.981047i | \(0.562071\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.83444e8 | −0.198079 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.66108e8 | −0.188222 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.85835e7 | −0.00739660 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.53986e9 | −1.38878 | −0.694392 | − | 0.719597i | \(-0.744326\pi\) | ||||
−0.694392 | + | 0.719597i | \(0.744326\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.44242e8 | 0.0944581 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.04042e9 | −1.54043 | −0.770213 | − | 0.637786i | \(-0.779850\pi\) | ||||
−0.770213 | + | 0.637786i | \(0.779850\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.19315e8 | −0.120021 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.86673e8 | −0.0691771 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.18927e9 | 1.16532 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.83149e9 | 0.659860 | 0.329930 | − | 0.944005i | \(-0.392975\pi\) | ||||
0.329930 | + | 0.944005i | \(0.392975\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.77498e9 | −0.985890 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.44153e9 | −1.20577 | −0.602884 | − | 0.797829i | \(-0.705982\pi\) | ||||
−0.602884 | + | 0.797829i | \(0.705982\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.06943e9 | −0.715042 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.53518e9 | −0.523158 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.73694e8 | 0.192827 | 0.0964136 | − | 0.995341i | \(-0.469263\pi\) | ||||
0.0964136 | + | 0.995341i | \(0.469263\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.35453e9 | −1.11214 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.79321e8 | 0.287566 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.48777e9 | 1.44779 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.42978e9 | 0.455043 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.23450e9 | −1.01560 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.83121e9 | 0.877081 | 0.438540 | − | 0.898712i | \(-0.355496\pi\) | ||||
0.438540 | + | 0.898712i | \(0.355496\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.02759e9 | −0.925426 | −0.462713 | − | 0.886508i | \(-0.653124\pi\) | ||||
−0.462713 | + | 0.886508i | \(0.653124\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.15461e8 | −0.155467 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.43351e9 | −0.724262 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.83730e9 | −0.833319 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.30795e9 | 0.379104 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.61895e8 | −0.189341 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.84246e9 | −0.520188 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.89808e8 | 0.0807606 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.35812e8 | 0.0923711 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.46669e9 | 1.21282 | 0.606408 | − | 0.795153i | \(-0.292610\pi\) | ||||
0.606408 | + | 0.795153i | \(0.292610\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.24681e8 | −0.113832 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.33851e9 | 1.14803 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.49405e9 | −0.390311 | −0.195155 | − | 0.980772i | \(-0.562521\pi\) | ||||
−0.195155 | + | 0.980772i | \(0.562521\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.61872e9 | −0.417511 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.96382e8 | −0.126411 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.72031e9 | 0.432582 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.22388e9 | 0.303888 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.02645e9 | 1.23245 | 0.616224 | − | 0.787571i | \(-0.288662\pi\) | ||||
0.616224 | + | 0.787571i | \(0.288662\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.41740e9 | −0.343202 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.73165e8 | −0.208798 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.95585e9 | 1.17041 | 0.585206 | − | 0.810885i | \(-0.301014\pi\) | ||||
0.585206 | + | 0.810885i | \(0.301014\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.85243e9 | 0.898597 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.85112e8 | 0.0887250 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.06899e9 | −0.470831 | −0.235415 | − | 0.971895i | \(-0.575645\pi\) | ||||
−0.235415 | + | 0.971895i | \(0.575645\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.84156e9 | 0.413961 | 0.206980 | − | 0.978345i | \(-0.433636\pi\) | ||||
0.206980 | + | 0.978345i | \(0.433636\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.75361e9 | −0.611451 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.27613e8 | 0.137675 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.22939e9 | −1.13328 | −0.566638 | − | 0.823967i | \(-0.691756\pi\) | ||||
−0.566638 | + | 0.823967i | \(0.691756\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.25215e9 | −0.482195 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.18029e9 | 0.884280 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.18396e8 | −0.0874475 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.02586e8 | −0.0831407 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.29340e9 | −0.672065 | −0.336033 | − | 0.941850i | \(-0.609085\pi\) | ||||
−0.336033 | + | 0.941850i | \(0.609085\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.78294e9 | −0.762827 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.57135e9 | −0.313125 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.35508e8 | 0.0463783 | 0.0231892 | − | 0.999731i | \(-0.492618\pi\) | ||||
0.0231892 | + | 0.999731i | \(0.492618\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.73884e9 | 0.922279 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.36065e9 | −0.838766 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.02534e8 | 0.0194928 | 0.00974639 | − | 0.999953i | \(-0.496898\pi\) | ||||
0.00974639 | + | 0.999953i | \(0.496898\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.48675e9 | 0.467275 | 0.233637 | − | 0.972324i | \(-0.424937\pi\) | ||||
0.233637 | + | 0.972324i | \(0.424937\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.76014e9 | 0.512649 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.14619e9 | −0.761211 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.87128e9 | 0.521092 | 0.260546 | − | 0.965461i | \(-0.416097\pi\) | ||||
0.260546 | + | 0.965461i | \(0.416097\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.17398e8 | −0.0390027 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.08353e9 | 0.546894 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.52444e9 | −1.31936 | −0.659679 | − | 0.751547i | \(-0.729308\pi\) | ||||
−0.659679 | + | 0.751547i | \(0.729308\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.67564e9 | 0.290482 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.34114e8 | 0.108685 | 0.0543425 | − | 0.998522i | \(-0.482694\pi\) | ||||
0.0543425 | + | 0.998522i | \(0.482694\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.81321e9 | 0.815675 | 0.407838 | − | 0.913054i | \(-0.366283\pi\) | ||||
0.407838 | + | 0.913054i | \(0.366283\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.68902e8 | −0.0785709 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.16735e9 | 0.193416 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.35123e9 | −0.549066 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.35735e9 | −0.219916 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.72472e9 | 0.917228 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.35568e9 | 0.531714 | 0.265857 | − | 0.964012i | \(-0.414345\pi\) | ||||
0.265857 | + | 0.964012i | \(0.414345\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.09128e9 | −0.327717 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.36730e9 | 0.676869 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.24228e8 | 0.111016 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.20839e9 | 0.486445 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.01582e10 | 1.52339 | 0.761696 | − | 0.647935i | \(-0.224367\pi\) | ||||
0.761696 | + | 0.647935i | \(0.224367\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.05703e9 | −0.750165 | −0.375083 | − | 0.926991i | \(-0.622386\pi\) | ||||
−0.375083 | + | 0.926991i | \(0.622386\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.58827e9 | 0.526533 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.05626e10 | 1.53323 | 0.766613 | − | 0.642109i | \(-0.221940\pi\) | ||||
0.766613 | + | 0.642109i | \(0.221940\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.01899e9 | −0.289920 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.65679e9 | −0.235361 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.19593e8 | −0.0870784 | −0.0435392 | − | 0.999052i | \(-0.513863\pi\) | ||||
−0.0435392 | + | 0.999052i | \(0.513863\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.65771e9 | 0.786677 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.37464e9 | −0.464246 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.32359e9 | −0.860725 | −0.430363 | − | 0.902656i | \(-0.641614\pi\) | ||||
−0.430363 | + | 0.902656i | \(0.641614\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.81233e9 | −1.32150 | −0.660750 | − | 0.750606i | \(-0.729761\pi\) | ||||
−0.660750 | + | 0.750606i | \(0.729761\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.88311e9 | −0.250944 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.36662e9 | 0.971388 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.64698e8 | 0.0345391 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.52036e9 | 0.325440 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.49871e9 | 0.319292 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.37509e10 | −1.73892 | −0.869458 | − | 0.494006i | \(-0.835532\pi\) | ||||
−0.869458 | + | 0.494006i | \(0.835532\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.18552e8 | −0.0648976 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.30590e9 | 1.02879 | 0.514395 | − | 0.857553i | \(-0.328017\pi\) | ||||
0.514395 | + | 0.857553i | \(0.328017\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.91806e7 | −0.00725496 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.15643e9 | −0.140315 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.10499e9 | −0.252800 | −0.126400 | − | 0.991979i | \(-0.540342\pi\) | ||||
−0.126400 | + | 0.991979i | \(0.540342\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.53480e9 | −0.657938 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.89015e9 | 0.575405 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.02331e8 | −0.105099 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.48072e9 | −0.516624 | −0.258312 | − | 0.966061i | \(-0.583166\pi\) | ||||
−0.258312 | + | 0.966061i | \(0.583166\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.94472e8 | −0.0678524 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.71775e9 | 0.985049 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.83786e9 | 0.876764 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.39774e8 | −0.0819274 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.62398e10 | 1.78060 | 0.890300 | − | 0.455374i | \(-0.150494\pi\) | ||||
0.890300 | + | 0.455374i | \(0.150494\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.89920e9 | 0.966067 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.80622e9 | −0.839032 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.59026e9 | −0.701350 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.62447e9 | −0.908805 | −0.454403 | − | 0.890796i | \(-0.650147\pi\) | ||||
−0.454403 | + | 0.890796i | \(0.650147\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.73062e9 | 0.180576 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.01727e9 | 0.208425 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.21447e8 | 0.0635818 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.09530e9 | 0.212289 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.97175e9 | −0.298168 | −0.149084 | − | 0.988825i | \(-0.547633\pi\) | ||||
−0.149084 | + | 0.988825i | \(0.547633\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.42916e10 | 1.42007 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.13722e10 | 1.11908 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.92726e8 | 0.0285284 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.52769e10 | 1.47457 | 0.737284 | − | 0.675583i | \(-0.236108\pi\) | ||||
0.737284 | + | 0.675583i | \(0.236108\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.67842e10 | 1.58924 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.55786e9 | 0.239891 | 0.119945 | − | 0.992780i | \(-0.461728\pi\) | ||||
0.119945 | + | 0.992780i | \(0.461728\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.83345e9 | −0.170319 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.26065e9 | −0.392048 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.76099e9 | 0.525099 | 0.262550 | − | 0.964919i | \(-0.415437\pi\) | ||||
0.262550 | + | 0.964919i | \(0.415437\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.92733e9 | −0.264306 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.79171e9 | −0.786344 | −0.393172 | − | 0.919465i | \(-0.628622\pi\) | ||||
−0.393172 | + | 0.919465i | \(0.628622\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.37894e8 | 0.0565199 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.20535e9 | 0.369130 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.86746e9 | −0.510227 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.14505e9 | −0.529402 | −0.264701 | − | 0.964330i | \(-0.585273\pi\) | ||||
−0.264701 | + | 0.964330i | \(0.585273\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.28351e10 | −1.09551 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.82470e9 | −0.830816 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.09591e9 | −0.594528 | −0.297264 | − | 0.954795i | \(-0.596074\pi\) | ||||
−0.297264 | + | 0.954795i | \(0.596074\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.23814e8 | 0.0600871 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.44986e10 | −1.19256 | −0.596280 | − | 0.802776i | \(-0.703355\pi\) | ||||
−0.596280 | + | 0.802776i | \(0.703355\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.38163e10 | 1.12604 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.76725e9 | 0.384993 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.35425e9 | −0.348441 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.48341e10 | 1.17630 | 0.588151 | − | 0.808751i | \(-0.299856\pi\) | ||||
0.588151 | + | 0.808751i | \(0.299856\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.38479e10 | −1.08816 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.64984e10 | 1.28473 | 0.642366 | − | 0.766398i | \(-0.277953\pi\) | ||||
0.642366 | + | 0.766398i | \(0.277953\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.23087e9 | 0.172154 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.89753e9 | 0.298069 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.21841e10 | 0.923449 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.95259e9 | −0.372009 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.18701e8 | −0.0162812 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.79045e10 | 1.32105 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.05010e9 | −0.296179 | −0.148090 | − | 0.988974i | \(-0.547312\pi\) | ||||
−0.148090 | + | 0.988974i | \(0.547312\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.59392e9 | −0.405459 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.22683e10 | 0.881390 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.38884e9 | 0.383742 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.28433e9 | 0.161240 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.61834e9 | −0.113231 | −0.0566156 | − | 0.998396i | \(-0.518031\pi\) | ||||
−0.0566156 | + | 0.998396i | \(0.518031\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.65137e10 | −2.53246 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.17435e9 | 0.0807390 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.20921e9 | 0.355032 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.92828e9 | −0.265410 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.06672e9 | −0.0714486 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.32510e10 | −0.879889 | −0.439945 | − | 0.898025i | \(-0.645002\pi\) | ||||
−0.439945 | + | 0.898025i | \(0.645002\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.29612e9 | 0.348646 | 0.174323 | − | 0.984689i | \(-0.444226\pi\) | ||||
0.174323 | + | 0.984689i | \(0.444226\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.32959e9 | 0.282573 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.05843e9 | 0.133194 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.60914e10 | 1.67386 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.28207e9 | −0.0815486 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.34687e10 | 0.849425 | 0.424712 | − | 0.905328i | \(-0.360375\pi\) | ||||
0.424712 | + | 0.905328i | \(0.360375\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.91545e9 | −0.369903 | −0.184952 | − | 0.982748i | \(-0.559213\pi\) | ||||
−0.184952 | + | 0.982748i | \(0.559213\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.00455e8 | 0.0496305 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.16343e9 | 0.133007 | 0.0665033 | − | 0.997786i | \(-0.478816\pi\) | ||||
0.0665033 | + | 0.997786i | \(0.478816\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.03884e9 | −0.0633301 | −0.0316650 | − | 0.999499i | \(-0.510081\pi\) | ||||
−0.0316650 | + | 0.999499i | \(0.510081\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.74712e10 | −1.05613 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.57598e9 | −0.514075 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.33871e10 | −1.39019 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.66673e9 | −0.0982484 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.96059e10 | −1.73066 | −0.865329 | − | 0.501205i | \(-0.832890\pi\) | ||||
−0.865329 | + | 0.501205i | \(0.832890\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.71264e10 | −0.992843 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.02179e10 | −0.587440 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.29383e10 | −0.737698 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.32038e10 | −0.746635 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.20429e10 | −0.675391 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.74554e9 | −0.263956 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.48670e10 | −0.820163 | −0.410082 | − | 0.912049i | \(-0.634500\pi\) | ||||
−0.410082 | + | 0.912049i | \(0.634500\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.41078e9 | 0.405492 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.25984e8 | 0.0393998 | 0.0196999 | − | 0.999806i | \(-0.493729\pi\) | ||||
0.0196999 | + | 0.999806i | \(0.493729\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.14667e9 | 0.492365 | 0.246182 | − | 0.969224i | \(-0.420824\pi\) | ||||
0.246182 | + | 0.969224i | \(0.420824\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.33621e9 | 0.284919 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.17870e10 | −1.68349 | −0.841746 | − | 0.539873i | \(-0.818472\pi\) | ||||
−0.841746 | + | 0.539873i | \(0.818472\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.72599e10 | −1.43208 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.12197e10 | 0.584677 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.67145e9 | −0.138095 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.18871e9 | −0.471185 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.95354e7 | −0.00302849 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.72268e10 | −0.869313 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.37560e10 | 1.68987 | 0.844933 | − | 0.534873i | \(-0.179640\pi\) | ||||
0.844933 | + | 0.534873i | \(0.179640\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.47588e10 | −0.732975 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.35501e10 | −0.667617 | −0.333809 | − | 0.942641i | \(-0.608334\pi\) | ||||
−0.333809 | + | 0.942641i | \(0.608334\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.32363e9 | 0.162461 | 0.0812307 | − | 0.996695i | \(-0.474115\pi\) | ||||
0.0812307 | + | 0.996695i | \(0.474115\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.10232e10 | 0.534570 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.18728e10 | 1.05238 | 0.526190 | − | 0.850367i | \(-0.323620\pi\) | ||||
0.526190 | + | 0.850367i | \(0.323620\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.39080e10 | 0.663908 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.98036e8 | −0.0283241 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.67614e10 | −2.66731 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.44245e9 | 0.113880 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.56101e9 | 0.0722158 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.40878e8 | 0.0431891 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.06850e10 | 0.486674 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.14271e10 | 0.516451 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.57915e9 | −0.160513 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.92742e10 | −1.30275 | −0.651373 | − | 0.758757i | \(-0.725807\pi\) | ||||
−0.651373 | + | 0.758757i | \(0.725807\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.62977e9 | −0.292769 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.06839e9 | 0.309747 | 0.154873 | − | 0.987934i | \(-0.450503\pi\) | ||||
0.154873 | + | 0.987934i | \(0.450503\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.49153e9 | −0.282292 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.36423e10 | −0.588728 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.80174e10 | 0.771613 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.15970e10 | 1.34289 | 0.671446 | − | 0.741054i | \(-0.265674\pi\) | ||||
0.671446 | + | 0.741054i | \(0.265674\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.70239e10 | 0.718041 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.06810e10 | −0.447100 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.24802e9 | −0.218022 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.43773e10 | 0.592787 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.01061e10 | 1.64118 | 0.820589 | − | 0.571519i | \(-0.193646\pi\) | ||||
0.820589 | + | 0.571519i | \(0.193646\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.33315e10 | −0.541448 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.73884e9 | −0.352264 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.35890e9 | −0.294423 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.56498e10 | 0.621470 | 0.310735 | − | 0.950497i | \(-0.399425\pi\) | ||||
0.310735 | + | 0.950497i | \(0.399425\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.32375e10 | 0.915925 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.90172e9 | −0.309142 | −0.154571 | − | 0.987982i | \(-0.549400\pi\) | ||||
−0.154571 | + | 0.987982i | \(0.549400\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.49723e9 | −0.252312 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.24566e9 | 0.125110 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.04304e10 | −1.92960 | −0.964800 | − | 0.262985i | \(-0.915293\pi\) | ||||
−0.964800 | + | 0.262985i | \(0.915293\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.12344e10 | 0.426696 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.04634e9 | −0.227961 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.01845e10 | −1.87821 | −0.939107 | − | 0.343626i | \(-0.888345\pi\) | ||||
−0.939107 | + | 0.343626i | \(0.888345\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.32070e10 | −0.862199 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.37595e8 | 0.0124510 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.76260e10 | −0.645339 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.03422e10 | −0.739376 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.90264e9 | −0.212987 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.89808e10 | −0.679937 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.67558e10 | 0.951535 | 0.475767 | − | 0.879571i | \(-0.342170\pi\) | ||||
0.475767 | + | 0.879571i | \(0.342170\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.46641e10 | 1.22390 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.60085e10 | 1.26223 | 0.631115 | − | 0.775690i | \(-0.282598\pi\) | ||||
0.631115 | + | 0.775690i | \(0.282598\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.77623e10 | 0.966186 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.72630e9 | 0.0596485 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.09028e10 | 0.717089 | 0.358544 | − | 0.933513i | \(-0.383273\pi\) | ||||
0.358544 | + | 0.933513i | \(0.383273\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.81277e9 | −0.0617451 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.38991e10 | 0.470052 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.52039e10 | 1.51788 | 0.758942 | − | 0.651158i | \(-0.225716\pi\) | ||||
0.758942 | + | 0.651158i | \(0.225716\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.32431e10 | −0.441533 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.48595e10 | −0.822966 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.39133e10 | −0.457345 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.67128e10 | −0.545495 | −0.272747 | − | 0.962086i | \(-0.587932\pi\) | ||||
−0.272747 | + | 0.962086i | \(0.587932\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.02447e10 | 0.980227 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.67509e10 | −1.18273 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.89725e9 | 0.284330 | 0.142165 | − | 0.989843i | \(-0.454594\pi\) | ||||
0.142165 | + | 0.989843i | \(0.454594\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.92090e9 | 0.124425 |
(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 | 192.8.a.t.1.2 | 2 | ||
3.2 | odd | 2 | 576.8.a.bn.1.1 | 2 | |||
4.3 | odd | 2 | 192.8.a.q.1.2 | 2 | |||
8.3 | odd | 2 | 96.8.a.h.1.1 | yes | 2 | ||
8.5 | even | 2 | 96.8.a.e.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 576.8.a.bo.1.1 | 2 | |||
24.5 | odd | 2 | 288.8.a.g.1.2 | 2 | |||
24.11 | even | 2 | 288.8.a.h.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.8.a.e.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
96.8.a.h.1.1 | yes | 2 | 8.3 | odd | 2 | ||
192.8.a.q.1.2 | 2 | 4.3 | odd | 2 | |||
192.8.a.t.1.2 | 2 | 1.1 | even | 1 | trivial | ||
288.8.a.g.1.2 | 2 | 24.5 | odd | 2 | |||
288.8.a.h.1.2 | 2 | 24.11 | even | 2 | |||
576.8.a.bn.1.1 | 2 | 3.2 | odd | 2 | |||
576.8.a.bo.1.1 | 2 | 12.11 | even | 2 |