Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,8,Mod(193,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.193");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(119.955849786\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 449x^{6} + 50632x^{4} + 69129x^{2} + 18225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.4 | ||
Root | \(-14.6646i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.8.d.d.193.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 27.0000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 344.306i | 1.23183i | 0.787814 | + | 0.615913i | \(0.211213\pi\) | ||||
−0.787814 | + | 0.615913i | \(0.788787\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1669.75 | 1.83995 | 0.919977 | − | 0.391972i | \(-0.128207\pi\) | ||||
0.919977 | + | 0.391972i | \(0.128207\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −729.000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2282.14i | − 0.516974i | −0.966015 | − | 0.258487i | \(-0.916776\pi\) | ||||
0.966015 | − | 0.258487i | \(-0.0832239\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 11526.9i | − 1.45516i | −0.686022 | − | 0.727581i | \(-0.740645\pi\) | ||||
0.686022 | − | 0.727581i | \(-0.259355\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9296.26 | 0.711195 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −17243.9 | −0.851264 | −0.425632 | − | 0.904896i | \(-0.639948\pi\) | ||||
−0.425632 | + | 0.904896i | \(0.639948\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14550.2i | 0.486666i | 0.969943 | + | 0.243333i | \(0.0782407\pi\) | ||||
−0.969943 | + | 0.243333i | \(0.921759\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 45083.1i | − 1.06230i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −40886.4 | −0.700698 | −0.350349 | − | 0.936619i | \(-0.613937\pi\) | ||||
−0.350349 | + | 0.936619i | \(0.613937\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −40421.6 | −0.517397 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19683.0i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 159495.i | − 1.21438i | −0.794558 | − | 0.607188i | \(-0.792297\pi\) | ||||
0.794558 | − | 0.607188i | \(-0.207703\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −171754. | −1.03548 | −0.517739 | − | 0.855539i | \(-0.673226\pi\) | ||||
−0.517739 | + | 0.855539i | \(0.673226\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −61617.9 | −0.298475 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 574903.i | 2.26651i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 9029.61i | − 0.0293064i | −0.999893 | − | 0.0146532i | \(-0.995336\pi\) | ||||
0.999893 | − | 0.0146532i | \(-0.00466443\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −311227. | −0.840138 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −735509. | −1.66665 | −0.833325 | − | 0.552784i | \(-0.813565\pi\) | ||||
−0.833325 | + | 0.552784i | \(0.813565\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 280634.i | − 0.538271i | −0.963102 | − | 0.269135i | \(-0.913262\pi\) | ||||
0.963102 | − | 0.269135i | \(-0.0867379\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 250999.i | − 0.410609i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −529498. | −0.743912 | −0.371956 | − | 0.928250i | \(-0.621313\pi\) | ||||
−0.371956 | + | 0.928250i | \(0.621313\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.96451e6 | 2.38543 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 465585.i | 0.491477i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 540438.i | − 0.498632i | −0.968422 | − | 0.249316i | \(-0.919794\pi\) | ||||
0.968422 | − | 0.249316i | \(-0.0802058\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 785756. | 0.636822 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 392855. | 0.280977 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 727412.i | − 0.461104i | −0.973060 | − | 0.230552i | \(-0.925947\pi\) | ||||
0.973060 | − | 0.230552i | \(-0.0740531\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.21789e6i | 1.25108i | 0.780193 | + | 0.625539i | \(0.215121\pi\) | ||||
−0.780193 | + | 0.625539i | \(0.784879\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.21724e6 | −0.613318 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.96878e6 | 1.79251 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 2.59799e6i | − 1.05530i | −0.849462 | − | 0.527649i | \(-0.823074\pi\) | ||||
0.849462 | − | 0.527649i | \(-0.176926\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.10393e6i | 0.404548i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −524418. | −0.173889 | −0.0869447 | − | 0.996213i | \(-0.527710\pi\) | ||||
−0.0869447 | + | 0.996213i | \(0.527710\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.37636e6 | 0.414097 | 0.207049 | − | 0.978331i | \(-0.433614\pi\) | ||||
0.207049 | + | 0.978331i | \(0.433614\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.09138e6i | 0.298719i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 3.81060e6i | − 0.951208i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.61970e6 | 1.51058 | 0.755290 | − | 0.655391i | \(-0.227496\pi\) | ||||
0.755290 | + | 0.655391i | \(0.227496\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.38593e6i | 1.22589i | 0.790126 | + | 0.612944i | \(0.210015\pi\) | ||||
−0.790126 | + | 0.612944i | \(0.789985\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 5.93718e6i | − 1.04861i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.30636e6 | −0.701120 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.60915e6 | −1.44484 | −0.722420 | − | 0.691454i | \(-0.756970\pi\) | ||||
−0.722420 | + | 0.691454i | \(0.756970\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 1.92470e7i | − 2.67743i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.63736e6i | 0.597834i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.00971e6 | −0.599488 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.87790e6 | −1.09891 | −0.549457 | − | 0.835522i | \(-0.685165\pi\) | ||||
−0.549457 | + | 0.835522i | \(0.685165\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.66368e6i | 0.172325i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1.59806e7i | − 1.54336i | −0.636008 | − | 0.771682i | \(-0.719415\pi\) | ||||
0.636008 | − | 0.771682i | \(-0.280585\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.40912e7 | 1.27062 | 0.635312 | − | 0.772255i | \(-0.280871\pi\) | ||||
0.635312 | + | 0.772255i | \(0.280871\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.55224e7 | 1.30857 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 2.31609e7i | − 1.82773i | −0.406018 | − | 0.913865i | \(-0.633083\pi\) | ||||
0.406018 | − | 0.913865i | \(-0.366917\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 2.10486e6i | − 0.155679i | −0.996966 | − | 0.0778395i | \(-0.975198\pi\) | ||||
0.996966 | − | 0.0778395i | \(-0.0248022\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −243799. | −0.0169201 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.30926e7 | −1.50556 | −0.752780 | − | 0.658272i | \(-0.771288\pi\) | ||||
−0.752780 | + | 0.658272i | \(0.771288\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1.40774e7i | − 0.863139i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.40312e6i | 0.485054i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.87929e7 | −1.56629 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.42790e7 | 0.732738 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.98587e7i | 0.962240i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.29815e7i | 0.594483i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.56266e7 | −1.97654 | −0.988269 | − | 0.152724i | \(-0.951195\pi\) | ||||
−0.988269 | + | 0.152724i | \(0.951195\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.57712e6 | −0.310771 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.78031e7i | 0.691904i | 0.938252 | + | 0.345952i | \(0.112444\pi\) | ||||
−0.938252 | + | 0.345952i | \(0.887556\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.42951e7i | 0.895443i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.77698e6 | −0.237065 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.05756e6 | 0.101591 | 0.0507953 | − | 0.998709i | \(-0.483824\pi\) | ||||
0.0507953 | + | 0.998709i | \(0.483824\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.22305e7i | 1.64958i | 0.565441 | + | 0.824789i | \(0.308706\pi\) | ||||
−0.565441 | + | 0.824789i | \(0.691294\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.42964e7i | 0.429498i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.63061e7 | −0.752280 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.49150e7 | 1.49590 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 5.30417e7i | − 1.37723i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 2.81604e6i | − 0.0697407i | −0.999392 | − | 0.0348703i | \(-0.988898\pi\) | ||||
0.999392 | − | 0.0348703i | \(-0.0111018\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.76673e7 | −1.36305 | −0.681523 | − | 0.731797i | \(-0.738682\pi\) | ||||
−0.681523 | + | 0.731797i | \(0.738682\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.25708e7 | 0.283755 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 5.91360e7i | − 1.27553i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.17674e7i | 1.89252i | 0.323412 | + | 0.946258i | \(0.395170\pi\) | ||||
−0.323412 | + | 0.946258i | \(0.604830\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.45918e7 | −0.287885 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.82698e7 | −1.28925 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 9.20744e7i | − 1.66526i | −0.553829 | − | 0.832630i | \(-0.686834\pi\) | ||||
0.553829 | − | 0.832630i | \(-0.313166\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 2.12154e7i | − 0.367670i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.62432e7 | 0.269875 | 0.134938 | − | 0.990854i | \(-0.456917\pi\) | ||||
0.134938 | + | 0.990854i | \(0.456917\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.01211e7 | −1.11749 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 1.06071e7i | − 0.162222i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 4.74152e7i | − 0.696236i | −0.937451 | − | 0.348118i | \(-0.886821\pi\) | ||||
0.937451 | − | 0.348118i | \(-0.113179\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.74939e7 | −0.951987 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.96401e7 | −0.266218 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 8.00081e7i | − 1.04267i | −0.853351 | − | 0.521337i | \(-0.825433\pi\) | ||||
0.853351 | − | 0.521337i | \(-0.174567\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1.96745e7i | − 0.246620i | −0.992368 | − | 0.123310i | \(-0.960649\pi\) | ||||
0.992368 | − | 0.123310i | \(-0.0393509\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.98829e7 | 0.722311 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.10895e6 | 0.0361004 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.93530e7i | 0.440081i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.28656e7i | 0.354099i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.78405e7 | −0.912174 | −0.456087 | − | 0.889935i | \(-0.650749\pi\) | ||||
−0.456087 | + | 0.889935i | \(0.650749\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.29628e8 | 1.29792 | 0.648959 | − | 0.760824i | \(-0.275205\pi\) | ||||
0.648959 | + | 0.760824i | \(0.275205\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 1.07157e8i | − 1.03490i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.21765e8i | − 1.13472i | −0.823469 | − | 0.567362i | \(-0.807964\pi\) | ||||
0.823469 | − | 0.567362i | \(-0.192036\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.43807e8 | −1.29359 | −0.646793 | − | 0.762665i | \(-0.723890\pi\) | ||||
−0.646793 | + | 0.762665i | \(0.723890\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.01457e7 | −0.609277 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 2.66315e8i | − 2.23440i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 2.53240e8i | − 2.05302i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.98062e7 | 0.233566 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.32056e7 | 0.251593 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1.17120e8i | − 0.858303i | −0.903233 | − | 0.429152i | \(-0.858813\pi\) | ||||
0.903233 | − | 0.429152i | \(-0.141187\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.41593e7i | 0.100395i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.66240e7 | 0.663056 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.86785e8 | −1.90523 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 3.71617e7i | − 0.239079i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.98769e8i | 1.23873i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.15918e8 | −1.90769 | −0.953844 | − | 0.300301i | \(-0.902913\pi\) | ||||
−0.953844 | + | 0.300301i | \(0.902913\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.94674e7 | 0.172466 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.46937e7i | 0.367089i | 0.983011 | + | 0.183545i | \(0.0587572\pi\) | ||||
−0.983011 | + | 0.183545i | \(0.941243\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 2.06223e8i | − 1.13478i | −0.823448 | − | 0.567392i | \(-0.807952\pi\) | ||||
0.823448 | − | 0.567392i | \(-0.192048\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.02886e8 | −0.549180 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.20225e8 | 1.65848 | 0.829238 | − | 0.558895i | \(-0.188775\pi\) | ||||
0.829238 | + | 0.558895i | \(0.188775\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 1.82309e8i | − 0.916371i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.78732e8i | − 0.872134i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.24636e8 | −0.590540 | −0.295270 | − | 0.955414i | \(-0.595410\pi\) | ||||
−0.295270 | + | 0.955414i | \(0.595410\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.47831e8 | 1.14050 | 0.570251 | − | 0.821470i | \(-0.306846\pi\) | ||||
0.570251 | + | 0.821470i | \(0.306846\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.43489e7i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.76391e8i | 2.93844i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.67719e8 | 0.708177 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.72420e8 | 0.707767 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 1.73374e8i | − 0.692031i | −0.938229 | − | 0.346016i | \(-0.887534\pi\) | ||||
0.938229 | − | 0.346016i | \(-0.112466\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.33086e7i | 0.362243i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.60304e8 | −0.605415 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.68797e7 | 0.356014 | 0.178007 | − | 0.984029i | \(-0.443035\pi\) | ||||
0.178007 | + | 0.984029i | \(0.443035\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.50771e7i | − 0.0539225i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.16272e8i | 0.404792i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.23068e8 | −1.09509 | −0.547544 | − | 0.836777i | \(-0.684437\pi\) | ||||
−0.547544 | + | 0.836777i | \(0.684437\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.86076e8 | 0.614229 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.59447e8i | 0.834179i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 1.84244e8i | − 0.577112i | −0.957463 | − | 0.288556i | \(-0.906825\pi\) | ||||
0.957463 | − | 0.288556i | \(-0.0931752\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.62257e8 | 0.495235 | 0.247618 | − | 0.968858i | \(-0.420352\pi\) | ||||
0.247618 | + | 0.968858i | \(0.420352\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.19669e8 | −1.54582 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.22480e7i | 0.267481i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 9.60497e7i | − 0.271529i | −0.990741 | − | 0.135765i | \(-0.956651\pi\) | ||||
0.990741 | − | 0.135765i | \(-0.0433491\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.25209e8 | 0.345159 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.61577e8 | 0.972139 | 0.486070 | − | 0.873920i | \(-0.338430\pi\) | ||||
0.486070 | + | 0.873920i | \(0.338430\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3.43417e8i | − 0.900677i | −0.892858 | − | 0.450338i | \(-0.851303\pi\) | ||||
0.892858 | − | 0.450338i | \(-0.148697\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.35262e8i | 0.346114i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.22811e9 | −3.06656 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.12987e8 | −0.275350 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.66703e8i | 0.634458i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 2.82677e8i | − 0.656528i | −0.944586 | − | 0.328264i | \(-0.893536\pi\) | ||||
0.944586 | − | 0.328264i | \(-0.106464\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.50452e8 | 0.568000 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.49194e7 | 0.0994917 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.71293e8i | 1.01963i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 4.68587e8i | − 0.990394i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.31477e8 | −0.891062 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.63631e8 | −1.54111 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.57819e8i | 0.311296i | 0.987813 | + | 0.155648i | \(0.0497466\pi\) | ||||
−0.987813 | + | 0.155648i | \(0.950253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 3.80462e8i | − 0.733595i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.79231e8 | 1.09192 | 0.545960 | − | 0.837811i | \(-0.316165\pi\) | ||||
0.545960 | + | 0.837811i | \(0.316165\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.81032e7 | −0.162400 | −0.0812001 | − | 0.996698i | \(-0.525875\pi\) | ||||
−0.0812001 | + | 0.996698i | \(0.525875\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 4.19105e8i | − 0.755502i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.19161e8i | 0.210100i | 0.994467 | + | 0.105050i | \(0.0335002\pi\) | ||||
−0.994467 | + | 0.105050i | \(0.966500\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.63990e8 | −0.627801 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.25344e8 | −1.05524 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2.50902e8i | − 0.414281i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.65937e8i | 0.752896i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.68312e7 | −0.0898813 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.84126e8 | −1.36876 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 9.04996e8i | − 1.37167i | −0.727758 | − | 0.685834i | \(-0.759438\pi\) | ||||
0.727758 | − | 0.685834i | \(-0.240562\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.58258e6i | 0.00976881i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.94503e8 | 1.29994 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.49042e8 | 0.496790 | 0.248395 | − | 0.968659i | \(-0.420097\pi\) | ||||
0.248395 | + | 0.968659i | \(0.420097\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.23500e8i | 0.869236i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.91967e8i | 0.535315i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.90512e9 | 2.54913 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.80090e8 | −0.498334 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.41085e8i | 0.823688i | 0.911254 | + | 0.411844i | \(0.135115\pi\) | ||||
−0.911254 | + | 0.411844i | \(0.864885\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 4.06717e8i | − 0.512158i | −0.966656 | − | 0.256079i | \(-0.917569\pi\) | ||||
0.966656 | − | 0.256079i | \(-0.0824307\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.26884e8 | 0.280046 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.01273e8 | 1.09055 | 0.545274 | − | 0.838258i | \(-0.316426\pi\) | ||||
0.545274 | + | 0.838258i | \(0.316426\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 1.80560e8i | − 0.214202i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.77409e8i | 0.904296i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.69288e9 | 1.93106 | 0.965532 | − | 0.260285i | \(-0.0838164\pi\) | ||||
0.965532 | + | 0.260285i | \(0.0838164\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.82164e8 | 0.763156 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 3.85533e8i | − 0.423046i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.73889e8i | 0.510096i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.61417e8 | −0.487262 | −0.243631 | − | 0.969868i | \(-0.578339\pi\) | ||||
−0.243631 | + | 0.969868i | \(0.578339\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.36186e8 | 0.555550 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 9.02394e8i | − 0.917461i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 6.51827e8i | − 0.650356i | −0.945653 | − | 0.325178i | \(-0.894576\pi\) | ||||
0.945653 | − | 0.325178i | \(-0.105424\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.50500e8 | 0.343225 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.83848e9 | −1.76711 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.31212e9i | 1.23804i | 0.785374 | + | 0.619021i | \(0.212471\pi\) | ||||
−0.785374 | + | 0.619021i | \(0.787529\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.23192e9i | 1.14115i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.86348e8 | −0.260434 | −0.130217 | − | 0.991486i | \(-0.541567\pi\) | ||||
−0.130217 | + | 0.991486i | \(0.541567\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.31201e9 | 1.17172 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.04582e8i | 0.179424i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.07035e8i | 0.436731i | 0.975867 | + | 0.218366i | \(0.0700725\pi\) | ||||
−0.975867 | + | 0.218366i | \(0.929927\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.05040e8 | 0.596479 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.80684e8 | 0.399471 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.27920e9i | 1.86077i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.17590e8i | 0.575585i | 0.957693 | + | 0.287793i | \(0.0929213\pi\) | ||||
−0.957693 | + | 0.287793i | \(0.907079\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.55968e8 | 0.516984 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.14391e8 | −0.166036 | −0.0830178 | − | 0.996548i | \(-0.526456\pi\) | ||||
−0.0830178 | + | 0.996548i | \(0.526456\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.97979e9i | 1.50679i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.82978e8i | 0.136870i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.06069e7 | −0.0151507 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.86290e8 | 0.495994 | 0.247997 | − | 0.968761i | \(-0.420228\pi\) | ||||
0.247997 | + | 0.968761i | \(0.420228\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 8.25542e7i | − 0.0586534i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1.21459e9i | − 0.848410i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.19871e9 | −1.51008 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.41022e9 | 0.952384 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 1.08929e9i | − 0.723428i | −0.932289 | − | 0.361714i | \(-0.882192\pi\) | ||||
0.932289 | − | 0.361714i | \(-0.117808\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 1.47613e9i | − 0.964136i | −0.876134 | − | 0.482068i | \(-0.839886\pi\) | ||||
0.876134 | − | 0.482068i | \(-0.160114\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.86004e8 | 0.247971 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.97027e8 | 0.440441 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.70330e9i | 2.30193i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.10264e8i | 0.434329i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.47143e8 | 0.0885256 | 0.0442628 | − | 0.999020i | \(-0.485906\pi\) | ||||
0.0442628 | + | 0.999020i | \(0.485906\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.31693e9 | 0.779572 | 0.389786 | − | 0.920905i | \(-0.372549\pi\) | ||||
0.389786 | + | 0.920905i | \(0.372549\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 1.48270e9i | − 0.863659i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 5.94904e8i | − 0.341006i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.94899e8 | 0.392009 | 0.196004 | − | 0.980603i | \(-0.437203\pi\) | ||||
0.196004 | + | 0.980603i | \(0.437203\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.43212e9 | −0.795144 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.53160e9i | 1.38351i | 0.722133 | + | 0.691754i | \(0.243162\pi\) | ||||
−0.722133 | + | 0.691754i | \(0.756838\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 3.30849e9i | − 1.77979i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.60330e7 | −0.0402648 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.62399e9 | −1.88940 | −0.944701 | − | 0.327934i | \(-0.893648\pi\) | ||||
−0.944701 | + | 0.327934i | \(0.893648\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.67854e9i | 0.861614i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.55702e9i | 0.786954i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.62686e9 | 3.29813 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.06640e9 | 1.01277 | 0.506383 | − | 0.862309i | \(-0.330982\pi\) | ||||
0.506383 | + | 0.862309i | \(0.330982\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 3.39412e8i | − 0.163826i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.53131e9i | 0.727966i | 0.931406 | + | 0.363983i | \(0.118583\pi\) | ||||
−0.931406 | + | 0.363983i | \(0.881417\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.09022e8 | −0.0978721 | −0.0489360 | − | 0.998802i | \(-0.515583\pi\) | ||||
−0.0489360 | + | 0.998802i | \(0.515583\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.59667e9 | −0.736428 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.40416e9i | 0.637979i | 0.947758 | + | 0.318989i | \(0.103343\pi\) | ||||
−0.947758 | + | 0.318989i | \(0.896657\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 4.33798e9i | − 1.94170i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.47772e9 | 1.09264 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.40447e8 | −0.278272 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 5.88142e8i | − 0.251799i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.93979e8i | 0.166211i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.95376e9 | −1.64375 | −0.821876 | − | 0.569666i | \(-0.807073\pi\) | ||||
−0.821876 | + | 0.569666i | \(0.807073\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.04083e8 | −0.0426456 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.84329e9i | 0.744351i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 3.40102e9i | − 1.35367i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.40238e7 | −0.0290416 | −0.0145208 | − | 0.999895i | \(-0.504622\pi\) | ||||
−0.0145208 | + | 0.999895i | \(0.504622\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.48601e9 | −0.961439 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 4.08459e9i | − 1.55727i | −0.627479 | − | 0.778634i | \(-0.715913\pi\) | ||||
0.627479 | − | 0.778634i | \(-0.284087\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.75031e9i | 1.03375i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.72816e8 | −0.212274 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.75644e8 | −0.319949 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.35811e9i | 1.20988i | 0.796270 | + | 0.604941i | \(0.206803\pi\) | ||||
−0.796270 | + | 0.604941i | \(0.793197\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 4.38565e8i | − 0.155812i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.31504e9 | −0.811093 | −0.405546 | − | 0.914074i | \(-0.632919\pi\) | ||||
−0.405546 | + | 0.914074i | \(0.632919\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.50222e9 | 1.90116 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.89327e9i | 0.645186i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 2.61529e9i | − 0.879039i | −0.898233 | − | 0.439520i | \(-0.855149\pi\) | ||||
0.898233 | − | 0.439520i | \(-0.144851\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.29817e9 | 0.761920 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.86391e8 | −0.0936589 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.85168e9i | 1.56519i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.20839e9i | 0.384583i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.28021e9 | −0.401972 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.75395e8 | 0.302168 | 0.151084 | − | 0.988521i | \(-0.451724\pi\) | ||||
0.151084 | + | 0.988521i | \(0.451724\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2.45790e9i | − 0.751291i | −0.926763 | − | 0.375646i | \(-0.877421\pi\) | ||||
0.926763 | − | 0.375646i | \(-0.122579\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.82233e9i | 0.549630i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.96171e9 | 0.881465 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.73313e9 | −0.509022 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.30284e8i | 0.153701i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.47814e9i | 2.42524i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.97444e9 | 2.25145 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.16022e9 | −0.601988 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 4.48329e9i | − 1.23321i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 1.30734e9i | − 0.354977i | −0.984123 | − | 0.177488i | \(-0.943203\pi\) | ||||
0.984123 | − | 0.177488i | \(-0.0567972\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.31211e8 | −0.142386 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.24715e8 | 0.191770 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 5.91915e9i | − 1.54634i | −0.634201 | − | 0.773168i | \(-0.718671\pi\) | ||||
0.634201 | − | 0.773168i | \(-0.281329\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 1.61684e9i | − 0.417026i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.32068e9 | 0.590995 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.10532e10 | 2.77940 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 8.39416e7i | − 0.0208426i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.93049e9i | 1.20892i | 0.796636 | + | 0.604459i | \(0.206611\pi\) | ||||
−0.796636 | + | 0.604459i | \(0.793389\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.23484e9 | −0.783271 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.06253e9 | 0.254081 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.84747e8i | 0.161715i | 0.996726 | + | 0.0808576i | \(0.0257659\pi\) | ||||
−0.996726 | + | 0.0808576i | \(0.974234\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 7.95092e9i | − 1.85459i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.87371e8 | 0.204439 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.26374e9 | −1.19785 | −0.598924 | − | 0.800806i | \(-0.704405\pi\) | ||||
−0.598924 | + | 0.800806i | \(0.704405\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 3.59028e9i | − 0.807053i | −0.914968 | − | 0.403527i | \(-0.867784\pi\) | ||||
0.914968 | − | 0.403527i | \(-0.132216\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.37169e9i | 0.526644i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.65269e9 | 0.362539 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.91183e9 | 0.847744 | 0.423872 | − | 0.905722i | \(-0.360671\pi\) | ||||
0.423872 | + | 0.905722i | \(0.360671\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 3.49995e9i | − 0.749353i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.06629e10i | 2.25558i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.23336e9 | −0.257780 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.89324e9 | −0.597502 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.88957e9i | 0.793721i | 0.917879 | + | 0.396860i | \(0.129900\pi\) | ||||
−0.917879 | + | 0.396860i | \(0.870100\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 2.49905e9i | − 0.503932i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.28765e9 | −0.655133 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.76138e9 | 0.937652 | 0.468826 | − | 0.883291i | \(-0.344677\pi\) | ||||
0.468826 | + | 0.883291i | \(0.344677\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 9.91357e9i | − 1.92939i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.88280e9i | 0.746852i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.22390e9 | −0.993118 | −0.496559 | − | 0.868003i | \(-0.665403\pi\) | ||||
−0.496559 | + | 0.868003i | \(0.665403\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.36008e9 | −1.57091 | −0.785453 | − | 0.618922i | \(-0.787570\pi\) | ||||
−0.785453 | + | 0.618922i | \(0.787570\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.89393e9i | 0.351766i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.91634e9i | 0.902606i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.78582e9 | 1.05004 | 0.525018 | − | 0.851091i | \(-0.324058\pi\) | ||||
0.525018 | + | 0.851091i | \(0.324058\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.19052e9 | −1.29003 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.10347e9i | 1.08251i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.73833e9i | − 0.304803i | −0.988319 | − | 0.152402i | \(-0.951299\pi\) | ||||
0.988319 | − | 0.152402i | \(-0.0487007\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.83748e9 | −1.18531 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.44016e9 | −0.761028 | −0.380514 | − | 0.924775i | \(-0.624253\pi\) | ||||
−0.380514 | + | 0.924775i | \(0.624253\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.64970e9i | 0.279568i | 0.990182 | + | 0.139784i | \(0.0446408\pi\) | ||||
−0.990182 | + | 0.139784i | \(0.955359\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 8.04766e8i | − 0.134849i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.60448e10 | −2.65844 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.62755e9 | −1.24970 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 8.96551e8i | − 0.145258i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.55706e8i | 0.0249475i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.28962e9 | −0.521246 | −0.260623 | − | 0.965441i | \(-0.583928\pi\) | ||||
−0.260623 | + | 0.965441i | \(0.583928\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.16223e9 | −0.495541 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.57095e10i | − 2.43475i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 2.26447e10i | − 3.47119i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.82300e8 | 0.0579631 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.66402e9 | 1.14935 | 0.574677 | − | 0.818381i | \(-0.305128\pi\) | ||||
0.574677 | + | 0.818381i | \(0.305128\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.16781e7i | − 0.00173234i | −1.00000 | 0.000866170i | \(-0.999724\pi\) | |||||
1.00000 | 0.000866170i | \(-0.000275710\pi\) | ||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 2.60885e9i | − 0.382816i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.10751e9 | −0.160762 | −0.0803811 | − | 0.996764i | \(-0.525614\pi\) | ||||
−0.0803811 | + | 0.996764i | \(0.525614\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.66006e9 | −0.238379 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.74321e9i | 1.09999i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 5.58523e9i | − 0.784955i | −0.919762 | − | 0.392477i | \(-0.871618\pi\) | ||||
0.919762 | − | 0.392477i | \(-0.128382\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.12971e9 | −0.852306 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.00337e9 | −0.138032 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.10525e9i | 0.967120i | 0.875311 | + | 0.483560i | \(0.160657\pi\) | ||||
−0.875311 | + | 0.483560i | \(0.839343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 3.08453e9i | − 0.415416i | −0.978191 | − | 0.207708i | \(-0.933400\pi\) | ||||
0.978191 | − | 0.207708i | \(-0.0666005\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.36676e9 | 0.715179 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.36495e9 | −1.10303 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.52116e9i | 0.850911i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.52979e9i | 1.10140i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.06153e9 | 0.646775 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.17552e10 | 1.48655 | 0.743273 | − | 0.668988i | \(-0.233272\pi\) | ||||
0.743273 | + | 0.668988i | \(0.233272\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 7.95619e8i | − 0.0995731i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.23386e9i | 0.524416i | 0.965011 | + | 0.262208i | \(0.0844507\pi\) | ||||
−0.965011 | + | 0.262208i | \(0.915549\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.64936e10 | −2.02195 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.74673e9 | 0.211939 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.23179e9i | 0.388124i | 0.980989 | + | 0.194062i | \(0.0621663\pi\) | ||||
−0.980989 | + | 0.194062i | \(0.937834\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.05274e9i | 0.125142i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.56803e9 | −0.655168 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.22958e9 | −0.725590 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 2.19695e9i | − 0.253307i | −0.991947 | − | 0.126653i | \(-0.959576\pi\) | ||||
0.991947 | − | 0.126653i | \(-0.0404236\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.77793e9i | 0.317069i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.79833e10 | −2.03199 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.26830e10 | 1.41876 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 8.64607e9i | − 0.957522i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.54482e9i | 0.607959i | 0.952679 | + | 0.303980i | \(0.0983155\pi\) | ||||
−0.952679 | + | 0.303980i | \(0.901684\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.31382e8 | 0.0142624 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.92235e9 | −0.529067 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 2.66836e10i | − 2.83972i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1.08253e10i | − 1.14071i | −0.821397 | − | 0.570357i | \(-0.806805\pi\) | ||||
0.821397 | − | 0.570357i | \(-0.193195\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.82576e9 | −0.503527 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.02240e9 | 0.725558 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 9.05734e9i | − 0.926679i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.36516e9i | 0.340948i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.08562e10 | 1.08925 | 0.544623 | − | 0.838681i | \(-0.316673\pi\) | ||||
0.544623 | + | 0.838681i | \(0.316673\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.35287e10 | 2.33789 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 6.69144e9i | − 0.658469i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.44704e9i | 0.628315i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.04714e10 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.87420e8 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.83922e9i | 0.458210i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.93042e10i | 1.81045i | 0.424931 | + | 0.905226i | \(0.360298\pi\) | ||||
−0.424931 | + | 0.905226i | \(0.639702\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.82626e10 | 1.69651 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.92898e9 | −0.545562 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 2.64009e9i | − 0.240637i | −0.992735 | − | 0.120319i | \(-0.961608\pi\) | ||||
0.992735 | − | 0.120319i | \(-0.0383916\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 4.52840e9i | − 0.408866i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.00716e10 | 1.79523 | 0.897617 | − | 0.440777i | \(-0.145297\pi\) | ||||
0.897617 | + | 0.440777i | \(0.145297\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.69578e8 | 0.0859084 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 4.65534e9i | − 0.408629i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 3.86728e10i | − 3.36294i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.78345e10 | −1.53646 | −0.768229 | − | 0.640175i | \(-0.778862\pi\) | ||||
−0.768229 | + | 0.640175i | \(0.778862\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.68110e9 | −0.399545 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 1.98552e10i | − 1.67904i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.59023e9i | 0.217021i | 0.994095 | + | 0.108511i | \(0.0346082\pi\) | ||||
−0.994095 | + | 0.108511i | \(0.965392\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.51933e9 | 0.209141 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.47456e10 | 1.21287 | 0.606436 | − | 0.795132i | \(-0.292599\pi\) | ||||
0.606436 | + | 0.795132i | \(0.292599\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 3.51458e9i | − 0.286442i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.32820e9i | 0.349536i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.38482e9 | −0.670980 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.16839e9 | 0.171947 | 0.0859737 | − | 0.996297i | \(-0.472600\pi\) | ||||
0.0859737 | + | 0.996297i | \(0.472600\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 2.61575e9i | − 0.205545i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.19037e10i | 1.70565i | 0.522198 | + | 0.852824i | \(0.325112\pi\) | ||||
−0.522198 | + | 0.852824i | \(0.674888\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.94258e9 | 0.535753 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.07083e8 | −0.0311322 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.07018e10i | − 0.811101i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.19680e9i | 0.0898963i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.13933e9 | 0.233707 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.15961e10 | −2.33125 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.86968e9i | 0.721758i | 0.932613 | + | 0.360879i | \(0.117523\pi\) | ||||
−0.932613 | + | 0.360879i | \(0.882477\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.72284e9i | 0.632249i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.85588e10 | −2.77016 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.55654e10 | 1.82052 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 5.02405e9i | − 0.354625i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.69316e10i | 1.18466i | 0.805695 | + | 0.592331i | \(0.201792\pi\) | ||||
−0.805695 | + | 0.592331i | \(0.798208\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.13060e9 | 0.633265 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.00507e9 | 0.481614 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 3.14105e9i | − 0.214077i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 2.35057e10i | − 1.58814i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.97459e9 | −0.333196 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.74007e8 | −0.0381151 | −0.0190576 | − | 0.999818i | \(-0.506067\pi\) | ||||
−0.0190576 | + | 0.999818i | \(0.506067\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.00117e10i | 1.31738i | 0.752415 | + | 0.658689i | \(0.228889\pi\) | ||||
−0.752415 | + | 0.658689i | \(0.771111\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 4.38095e9i | − 0.285924i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.17018e10 | 2.05131 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.08328e9 | 0.261958 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.40311e10i | 0.892477i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 8.15447e9i | − 0.514274i | −0.966375 | − | 0.257137i | \(-0.917221\pi\) | ||||
0.966375 | − | 0.257137i | \(-0.0827791\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.80708e9 | −0.613254 | −0.306627 | − | 0.951830i | \(-0.599200\pi\) | ||||
−0.306627 | + | 0.951830i | \(0.599200\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.49070e9 | 0.154430 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.05065e10i | 0.645937i | 0.946410 | + | 0.322969i | \(0.104681\pi\) | ||||
−0.946410 | + | 0.322969i | \(0.895319\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1.45134e10i | − 0.884766i | −0.896826 | − | 0.442383i | \(-0.854133\pi\) | ||||
0.896826 | − | 0.442383i | \(-0.145867\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.59334e9 | −0.156767 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.38757e10 | −2.03063 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.59262e9i | 0.332439i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 3.38063e9i | − 0.199278i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.98293e9 | −0.115915 | −0.0579576 | − | 0.998319i | \(-0.518459\pi\) | ||||
−0.0579576 | + | 0.998319i | \(0.518459\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.18867e9 | −0.474709 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 9.76257e9i | − 0.561265i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 2.41431e10i | − 1.37656i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.38423e10 | 1.34820 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.27225e9 | −0.520006 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.69188e8i | 0.0205350i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 7.37240e9i | − 0.406712i | −0.979105 | − | 0.203356i | \(-0.934815\pi\) | ||||
0.979105 | − | 0.203356i | \(-0.0651849\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.65208e9 | 0.199829 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.41520e10 | −1.31075 | −0.655374 | − | 0.755304i | \(-0.727489\pi\) | ||||
−0.655374 | + | 0.755304i | \(0.727489\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 3.64471e10i | − 1.96195i | −0.194145 | − | 0.980973i | \(-0.562193\pi\) | ||||
0.194145 | − | 0.980973i | \(-0.437807\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.31590e10i | 1.77048i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.59737e9 | 0.243485 | 0.121742 | − | 0.992562i | \(-0.461152\pi\) | ||||
0.121742 | + | 0.992562i | \(0.461152\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.63253e10 | 0.857642 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.05064e9i | 0.158973i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.51071e10i | − 0.780930i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.99468e10 | −1.53563 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.20099e9 | 0.366305 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.16758e10i | 1.09382i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.57473e10i | 0.788327i | 0.919040 | + | 0.394164i | \(0.128966\pi\) | ||||
−0.919040 | + | 0.394164i | \(0.871034\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.63227e9 | −0.379047 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.30534e10 | 1.13584 | 0.567922 | − | 0.823082i | \(-0.307748\pi\) | ||||
0.567922 | + | 0.823082i | \(0.307748\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.63512e9i | 0.275449i | 0.990471 | + | 0.137724i | \(0.0439788\pi\) | ||||
−0.990471 | + | 0.137724i | \(0.956021\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 6.76222e9i | − 0.327935i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.11246e10 | 0.535245 | 0.267623 | − | 0.963524i | \(-0.413762\pi\) | ||||
0.267623 | + | 0.963524i | \(0.413762\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.61848e10 | −3.63674 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 1.21282e9i | − 0.0574415i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 7.70429e9i | − 0.362036i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.75473e10 | 1.28439 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.27249e10 | 0.588683 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.73939e10i | 1.25746i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.31926e9i | 0.424468i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.26519e10 | −0.571804 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.77404e9 | 0.303793 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.73698e9i | 0.344307i | 0.985070 | + | 0.172154i | \(0.0550725\pi\) | ||||
−0.985070 | + | 0.172154i | \(0.944927\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.16499e10i | 0.514455i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.03842e10 | 0.455051 | 0.227526 | − | 0.973772i | \(-0.426936\pi\) | ||||
0.227526 | + | 0.973772i | \(0.426936\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.45736e10 | 0.633752 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.06180e10i | 0.889761i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.97266e10i | 1.27307i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.08020e9 | −0.343414 | −0.171707 | − | 0.985148i | \(-0.554928\pi\) | ||||
−0.171707 | + | 0.985148i | \(0.554928\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.26110e9 | 0.179727 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.04491e9i | 0.253037i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.64992e8i | 0.0151631i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.02725e10 | −0.423541 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.28931e10 | 0.527598 | 0.263799 | − | 0.964578i | \(-0.415024\pi\) | ||||
0.263799 | + | 0.964578i | \(0.415024\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.85839e10i | 1.16091i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1.56392e10i | − 0.630420i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.35495e10 | −0.542104 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.17106e9 | −0.284770 | −0.142385 | − | 0.989811i | \(-0.545477\pi\) | ||||
−0.142385 | + | 0.989811i | \(0.545477\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.37879e9i | 0.0937618i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.40976e9i | 0.0942781i | 0.998888 | + | 0.0471391i | \(0.0150104\pi\) | ||||
−0.998888 | + | 0.0471391i | \(0.984990\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.00723e10 | 1.16782 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.13158e10 | −0.436189 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.20590e10i | 1.60929i | 0.593758 | + | 0.804644i | \(0.297644\pi\) | ||||
−0.593758 | + | 0.804644i | \(0.702356\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 1.58652e10i | − 0.602578i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.21734e9 | 0.121301 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.79027e10 | 1.04429 | 0.522145 | − | 0.852857i | \(-0.325132\pi\) | ||||
0.522145 | + | 0.852857i | \(0.325132\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 3.02440e10i | − 1.12364i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.82772e9i | 0.362461i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.10535e9 | 0.186922 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.98684e9 | 0.0722155 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.68843e10i | 0.609243i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.46316e10i | 1.59881i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.50078e10 | 0.889371 | 0.444686 | − | 0.895687i | \(-0.353315\pi\) | ||||
0.444686 | + | 0.895687i | \(0.353315\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.77435e9 | −0.239185 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.65828e10i | 1.28236i | 0.767391 | + | 0.641179i | \(0.221554\pi\) | ||||
−0.767391 | + | 0.641179i | \(0.778446\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.72117e10i | 3.03515i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.25803e10 | 0.434685 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.86412e10 | 0.982563 | 0.491281 | − | 0.871001i | \(-0.336529\pi\) | ||||
0.491281 | + | 0.871001i | \(0.336529\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.19295e10i | 0.746945i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.53444e9i | 0.0518930i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.81805e10 | −1.28205 | −0.641024 | − | 0.767521i | \(-0.721490\pi\) | ||||
−0.641024 | + | 0.767521i | \(0.721490\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.19244e10 | 1.39778 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.38714e10i | 0.790256i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.14741e10i | 0.377165i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.06103e10 | 0.672709 | 0.336354 | − | 0.941736i | \(-0.390806\pi\) | ||||
0.336354 | + | 0.941736i | \(0.390806\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.44349e10 | −0.791932 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 4.95137e10i | − 1.59347i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 2.00020e10i | − 0.639204i | −0.947552 | − | 0.319602i | \(-0.896451\pi\) | ||||
0.947552 | − | 0.319602i | \(-0.103549\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.77730e8 | 0.00564002 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 384.8.d.d.193.4 | yes | 8 | |
4.3 | odd | 2 | 384.8.d.c.193.8 | yes | 8 | ||
8.3 | odd | 2 | 384.8.d.c.193.1 | ✓ | 8 | ||
8.5 | even | 2 | inner | 384.8.d.d.193.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.8.d.c.193.1 | ✓ | 8 | 8.3 | odd | 2 | ||
384.8.d.c.193.8 | yes | 8 | 4.3 | odd | 2 | ||
384.8.d.d.193.4 | yes | 8 | 1.1 | even | 1 | trivial | |
384.8.d.d.193.5 | yes | 8 | 8.5 | even | 2 | inner |