Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [387,8,Mod(1,387)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(387, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("387.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 387 = 3^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 387.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: | \(120.893004862\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2 x^{10} - 977 x^{9} + 2592 x^{8} + 344686 x^{7} - 1160956 x^{6} - 53409536 x^{5} + 209758592 x^{4} + 3410917248 x^{3} - 14180732672 x^{2} + \cdots + 238240894976 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{4}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-5.14919\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 387.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.14919 | −0.278352 | −0.139176 | − | 0.990268i | \(-0.544445\pi\) | ||||
−0.139176 | + | 0.990268i | \(0.544445\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −118.083 | −0.922520 | ||||||||
\(5\) | 39.2891 | 0.140565 | 0.0702824 | − | 0.997527i | \(-0.477610\pi\) | ||||
0.0702824 | + | 0.997527i | \(0.477610\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 434.472 | 0.478760 | 0.239380 | − | 0.970926i | \(-0.423056\pi\) | ||||
0.239380 | + | 0.970926i | \(0.423056\pi\) | |||||||
\(8\) | 774.961 | 0.535137 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −123.729 | −0.0391265 | ||||||||
\(11\) | 6392.85 | 1.44817 | 0.724086 | − | 0.689710i | \(-0.242262\pi\) | ||||
0.724086 | + | 0.689710i | \(0.242262\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 442.964 | 0.0559200 | 0.0279600 | − | 0.999609i | \(-0.491099\pi\) | ||||
0.0279600 | + | 0.999609i | \(0.491099\pi\) | |||||||
\(14\) | −1368.23 | −0.133264 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12674.1 | 0.773564 | ||||||||
\(17\) | 26318.9 | 1.29926 | 0.649630 | − | 0.760250i | \(-0.274924\pi\) | ||||
0.649630 | + | 0.760250i | \(0.274924\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7748.98 | 0.259183 | 0.129592 | − | 0.991567i | \(-0.458633\pi\) | ||||
0.129592 | + | 0.991567i | \(0.458633\pi\) | |||||||
\(20\) | −4639.35 | −0.129674 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −20132.3 | −0.403101 | ||||||||
\(23\) | 58609.7 | 1.00444 | 0.502218 | − | 0.864741i | \(-0.332517\pi\) | ||||
0.502218 | + | 0.864741i | \(0.332517\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −76581.4 | −0.980242 | ||||||||
\(26\) | −1394.98 | −0.0155654 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −51303.5 | −0.441666 | ||||||||
\(29\) | −27040.0 | −0.205880 | −0.102940 | − | 0.994688i | \(-0.532825\pi\) | ||||
−0.102940 | + | 0.994688i | \(0.532825\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 100436. | 0.605514 | 0.302757 | − | 0.953068i | \(-0.402093\pi\) | ||||
0.302757 | + | 0.953068i | \(0.402093\pi\) | |||||||
\(32\) | −139108. | −0.750460 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −82883.2 | −0.361652 | ||||||||
\(35\) | 17070.0 | 0.0672969 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 358755. | 1.16437 | 0.582186 | − | 0.813055i | \(-0.302197\pi\) | ||||
0.582186 | + | 0.813055i | \(0.302197\pi\) | |||||||
\(38\) | −24403.0 | −0.0721441 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 30447.5 | 0.0752214 | ||||||||
\(41\) | 74304.4 | 0.168372 | 0.0841862 | − | 0.996450i | \(-0.473171\pi\) | ||||
0.0841862 | + | 0.996450i | \(0.473171\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 79507.0 | 0.152499 | ||||||||
\(44\) | −754884. | −1.33597 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −184573. | −0.279587 | ||||||||
\(47\) | −462198. | −0.649359 | −0.324680 | − | 0.945824i | \(-0.605257\pi\) | ||||
−0.324680 | + | 0.945824i | \(0.605257\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −634777. | −0.770788 | ||||||||
\(50\) | 241169. | 0.272852 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −52306.4 | −0.0515873 | ||||||||
\(53\) | −1.17404e6 | −1.08322 | −0.541612 | − | 0.840629i | \(-0.682186\pi\) | ||||
−0.541612 | + | 0.840629i | \(0.682186\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 251169. | 0.203562 | ||||||||
\(56\) | 336699. | 0.256202 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 85154.2 | 0.0573071 | ||||||||
\(59\) | −1.70392e6 | −1.08011 | −0.540055 | − | 0.841630i | \(-0.681596\pi\) | ||||
−0.540055 | + | 0.841630i | \(0.681596\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.64618e6 | 1.49267 | 0.746336 | − | 0.665570i | \(-0.231811\pi\) | ||||
0.746336 | + | 0.665570i | \(0.231811\pi\) | |||||||
\(62\) | −316293. | −0.168546 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.18420e6 | −0.564672 | ||||||||
\(65\) | 17403.6 | 0.00786038 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.11768e6 | −0.860199 | −0.430099 | − | 0.902782i | \(-0.641522\pi\) | ||||
−0.430099 | + | 0.902782i | \(0.641522\pi\) | |||||||
\(68\) | −3.10780e6 | −1.19859 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −53756.6 | −0.0187322 | ||||||||
\(71\) | 5.06201e6 | 1.67849 | 0.839246 | − | 0.543752i | \(-0.182997\pi\) | ||||
0.839246 | + | 0.543752i | \(0.182997\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 899577. | 0.270650 | 0.135325 | − | 0.990801i | \(-0.456792\pi\) | ||||
0.135325 | + | 0.990801i | \(0.456792\pi\) | |||||||
\(74\) | −1.12979e6 | −0.324105 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −915020. | −0.239102 | ||||||||
\(77\) | 2.77751e6 | 0.693327 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.05836e6 | −0.926095 | −0.463047 | − | 0.886333i | \(-0.653244\pi\) | ||||
−0.463047 | + | 0.886333i | \(0.653244\pi\) | |||||||
\(80\) | 497952. | 0.108736 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −233999. | −0.0468668 | ||||||||
\(83\) | 6.07269e6 | 1.16576 | 0.582878 | − | 0.812559i | \(-0.301926\pi\) | ||||
0.582878 | + | 0.812559i | \(0.301926\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.03404e6 | 0.182630 | ||||||||
\(86\) | −250383. | −0.0424483 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.95421e6 | 0.774970 | ||||||||
\(89\) | 3.93741e6 | 0.592033 | 0.296017 | − | 0.955183i | \(-0.404342\pi\) | ||||
0.296017 | + | 0.955183i | \(0.404342\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 192455. | 0.0267723 | ||||||||
\(92\) | −6.92079e6 | −0.926613 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.45555e6 | 0.180750 | ||||||||
\(95\) | 304450. | 0.0364320 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.24981e7 | −1.39041 | −0.695203 | − | 0.718813i | \(-0.744686\pi\) | ||||
−0.695203 | + | 0.718813i | \(0.744686\pi\) | |||||||
\(98\) | 1.99904e6 | 0.214550 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.04293e6 | 0.904293 | ||||||||
\(101\) | −8.38183e6 | −0.809495 | −0.404747 | − | 0.914429i | \(-0.632641\pi\) | ||||
−0.404747 | + | 0.914429i | \(0.632641\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.30426e7 | 1.17607 | 0.588036 | − | 0.808835i | \(-0.299902\pi\) | ||||
0.588036 | + | 0.808835i | \(0.299902\pi\) | |||||||
\(104\) | 343280. | 0.0299248 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.69728e6 | 0.301517 | ||||||||
\(107\) | 8.79724e6 | 0.694230 | 0.347115 | − | 0.937823i | \(-0.387161\pi\) | ||||
0.347115 | + | 0.937823i | \(0.387161\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.73854e7 | −1.28585 | −0.642927 | − | 0.765927i | \(-0.722280\pi\) | ||||
−0.642927 | + | 0.765927i | \(0.722280\pi\) | |||||||
\(110\) | −790979. | −0.0566618 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.50652e6 | 0.370352 | ||||||||
\(113\) | 7.28232e6 | 0.474783 | 0.237391 | − | 0.971414i | \(-0.423708\pi\) | ||||
0.237391 | + | 0.971414i | \(0.423708\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.30272e6 | 0.141188 | ||||||||
\(116\) | 3.19296e6 | 0.189929 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.36598e6 | 0.300650 | ||||||||
\(119\) | 1.14348e7 | 0.622035 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.13813e7 | 1.09720 | ||||||||
\(122\) | −8.33331e6 | −0.415488 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.18598e7 | −0.558599 | ||||||||
\(125\) | −6.07827e6 | −0.278352 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.14216e6 | 0.396037 | 0.198018 | − | 0.980198i | \(-0.436549\pi\) | ||||
0.198018 | + | 0.980198i | \(0.436549\pi\) | |||||||
\(128\) | 2.15351e7 | 0.907637 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −54807.4 | −0.00218795 | ||||||||
\(131\) | 3.19287e7 | 1.24089 | 0.620443 | − | 0.784251i | \(-0.286953\pi\) | ||||
0.620443 | + | 0.784251i | \(0.286953\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.36671e6 | 0.124087 | ||||||||
\(134\) | 6.66899e6 | 0.239438 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.03961e7 | 0.695282 | ||||||||
\(137\) | −1.07371e7 | −0.356750 | −0.178375 | − | 0.983963i | \(-0.557084\pi\) | ||||
−0.178375 | + | 0.983963i | \(0.557084\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.67775e6 | −0.242483 | −0.121242 | − | 0.992623i | \(-0.538688\pi\) | ||||
−0.121242 | + | 0.992623i | \(0.538688\pi\) | |||||||
\(140\) | −2.01567e6 | −0.0620827 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.59413e7 | −0.467211 | ||||||||
\(143\) | 2.83180e6 | 0.0809817 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.06238e6 | −0.0289395 | ||||||||
\(146\) | −2.83294e6 | −0.0753360 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.23627e7 | −1.07416 | ||||||||
\(149\) | 5.77368e7 | 1.42988 | 0.714942 | − | 0.699184i | \(-0.246453\pi\) | ||||
0.714942 | + | 0.699184i | \(0.246453\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.59611e7 | −0.377263 | −0.188632 | − | 0.982048i | \(-0.560405\pi\) | ||||
−0.188632 | + | 0.982048i | \(0.560405\pi\) | |||||||
\(152\) | 6.00516e6 | 0.138699 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.74691e6 | −0.192989 | ||||||||
\(155\) | 3.94604e6 | 0.0851139 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.56041e7 | 1.14672 | 0.573361 | − | 0.819303i | \(-0.305639\pi\) | ||||
0.573361 | + | 0.819303i | \(0.305639\pi\) | |||||||
\(158\) | 1.27805e7 | 0.257780 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.46543e6 | −0.105488 | ||||||||
\(161\) | 2.54643e7 | 0.480884 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.30748e7 | −0.236472 | −0.118236 | − | 0.992986i | \(-0.537724\pi\) | ||||
−0.118236 | + | 0.992986i | \(0.537724\pi\) | |||||||
\(164\) | −8.77405e6 | −0.155327 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.91241e7 | −0.324490 | ||||||||
\(167\) | −4.97944e7 | −0.827319 | −0.413660 | − | 0.910432i | \(-0.635750\pi\) | ||||
−0.413660 | + | 0.910432i | \(0.635750\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.25523e7 | −0.996873 | ||||||||
\(170\) | −3.25640e6 | −0.0508355 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.38839e6 | −0.140683 | ||||||||
\(173\) | −9.03870e7 | −1.32722 | −0.663612 | − | 0.748077i | \(-0.730978\pi\) | ||||
−0.663612 | + | 0.748077i | \(0.730978\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.32724e7 | −0.469301 | ||||||||
\(176\) | 8.10234e7 | 1.12025 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.23997e7 | −0.164794 | ||||||||
\(179\) | 1.32357e8 | 1.72489 | 0.862447 | − | 0.506147i | \(-0.168931\pi\) | ||||
0.862447 | + | 0.506147i | \(0.168931\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.38366e7 | −0.173441 | −0.0867207 | − | 0.996233i | \(-0.527639\pi\) | ||||
−0.0867207 | + | 0.996233i | \(0.527639\pi\) | |||||||
\(182\) | −606079. | −0.00745211 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.54203e7 | 0.537511 | ||||||||
\(185\) | 1.40951e7 | 0.163670 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.68253e8 | 1.88155 | ||||||||
\(188\) | 5.45775e7 | 0.599047 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −958772. | −0.0101409 | ||||||||
\(191\) | −3.54814e7 | −0.368455 | −0.184227 | − | 0.982884i | \(-0.558978\pi\) | ||||
−0.184227 | + | 0.982884i | \(0.558978\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.17213e8 | 1.17361 | 0.586807 | − | 0.809727i | \(-0.300385\pi\) | ||||
0.586807 | + | 0.809727i | \(0.300385\pi\) | |||||||
\(194\) | 3.93588e7 | 0.387022 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.49562e7 | 0.711068 | ||||||||
\(197\) | 3.73724e7 | 0.348272 | 0.174136 | − | 0.984722i | \(-0.444287\pi\) | ||||
0.174136 | + | 0.984722i | \(0.444287\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.42971e8 | 1.28606 | 0.643031 | − | 0.765840i | \(-0.277677\pi\) | ||||
0.643031 | + | 0.765840i | \(0.277677\pi\) | |||||||
\(200\) | −5.93476e7 | −0.524564 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.63960e7 | 0.225324 | ||||||||
\(203\) | −1.17481e7 | −0.0985672 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.91935e6 | 0.0236672 | ||||||||
\(206\) | −4.10736e7 | −0.327362 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.61416e6 | 0.0432577 | ||||||||
\(209\) | 4.95380e7 | 0.375342 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.59039e8 | 1.16551 | 0.582754 | − | 0.812648i | \(-0.301975\pi\) | ||||
0.582754 | + | 0.812648i | \(0.301975\pi\) | |||||||
\(212\) | 1.38634e8 | 0.999295 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.77042e7 | −0.193240 | ||||||||
\(215\) | 3.12375e6 | 0.0214359 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.36367e7 | 0.289896 | ||||||||
\(218\) | 5.47499e7 | 0.357920 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.96587e7 | −0.187790 | ||||||||
\(221\) | 1.16583e7 | 0.0726546 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.10300e7 | −0.247762 | −0.123881 | − | 0.992297i | \(-0.539534\pi\) | ||||
−0.123881 | + | 0.992297i | \(0.539534\pi\) | |||||||
\(224\) | −6.04385e7 | −0.359291 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.29334e7 | −0.132157 | ||||||||
\(227\) | −4.91817e7 | −0.279070 | −0.139535 | − | 0.990217i | \(-0.544561\pi\) | ||||
−0.139535 | + | 0.990217i | \(0.544561\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.27086e8 | −0.699315 | −0.349657 | − | 0.936878i | \(-0.613702\pi\) | ||||
−0.349657 | + | 0.936878i | \(0.613702\pi\) | |||||||
\(230\) | −7.25171e6 | −0.0393000 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.09550e7 | −0.110174 | ||||||||
\(233\) | 7.98934e7 | 0.413776 | 0.206888 | − | 0.978365i | \(-0.433666\pi\) | ||||
0.206888 | + | 0.978365i | \(0.433666\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.81593e7 | −0.0912771 | ||||||||
\(236\) | 2.01204e8 | 0.996423 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.60104e7 | −0.173144 | ||||||||
\(239\) | 1.85347e8 | 0.878199 | 0.439100 | − | 0.898438i | \(-0.355298\pi\) | ||||
0.439100 | + | 0.898438i | \(0.355298\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.85587e7 | 0.0854061 | 0.0427031 | − | 0.999088i | \(-0.486403\pi\) | ||||
0.0427031 | + | 0.999088i | \(0.486403\pi\) | |||||||
\(242\) | −6.73338e7 | −0.305407 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.12467e8 | −1.37702 | ||||||||
\(245\) | −2.49398e7 | −0.108346 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.43252e6 | 0.0144935 | ||||||||
\(248\) | 7.78341e7 | 0.324033 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.91416e7 | 0.0774799 | ||||||||
\(251\) | −1.86162e8 | −0.743075 | −0.371537 | − | 0.928418i | \(-0.621169\pi\) | ||||
−0.371537 | + | 0.928418i | \(0.621169\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.74683e8 | 1.45460 | ||||||||
\(254\) | −2.87904e7 | −0.110238 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.37598e7 | 0.312029 | ||||||||
\(257\) | 4.61094e8 | 1.69443 | 0.847214 | − | 0.531251i | \(-0.178278\pi\) | ||||
0.847214 | + | 0.531251i | \(0.178278\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.55869e8 | 0.557456 | ||||||||
\(260\) | −2.05507e6 | −0.00725136 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.00550e8 | −0.345403 | ||||||||
\(263\) | 4.24659e8 | 1.43945 | 0.719723 | − | 0.694261i | \(-0.244269\pi\) | ||||
0.719723 | + | 0.694261i | \(0.244269\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.61270e7 | −0.152263 | ||||||||
\(266\) | −1.06024e7 | −0.0345398 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.50061e8 | 0.793551 | ||||||||
\(269\) | 2.01202e7 | 0.0630230 | 0.0315115 | − | 0.999503i | \(-0.489968\pi\) | ||||
0.0315115 | + | 0.999503i | \(0.489968\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.31931e8 | 1.01311 | 0.506554 | − | 0.862208i | \(-0.330919\pi\) | ||||
0.506554 | + | 0.862208i | \(0.330919\pi\) | |||||||
\(272\) | 3.33567e8 | 1.00506 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.38131e7 | 0.0993020 | ||||||||
\(275\) | −4.89573e8 | −1.41956 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.27194e8 | −1.77306 | −0.886528 | − | 0.462674i | \(-0.846890\pi\) | ||||
−0.886528 | + | 0.462674i | \(0.846890\pi\) | |||||||
\(278\) | 2.41787e7 | 0.0674957 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.32286e7 | 0.0360130 | ||||||||
\(281\) | 5.46595e8 | 1.46958 | 0.734791 | − | 0.678294i | \(-0.237280\pi\) | ||||
0.734791 | + | 0.678294i | \(0.237280\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.74316e8 | 1.24398 | 0.621992 | − | 0.783023i | \(-0.286324\pi\) | ||||
0.621992 | + | 0.783023i | \(0.286324\pi\) | |||||||
\(284\) | −5.97736e8 | −1.54844 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.91789e6 | −0.0225414 | ||||||||
\(287\) | 3.22831e7 | 0.0806100 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.82345e8 | 0.688078 | ||||||||
\(290\) | 3.34563e6 | 0.00805536 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.06224e8 | −0.249680 | ||||||||
\(293\) | 2.61274e8 | 0.606820 | 0.303410 | − | 0.952860i | \(-0.401875\pi\) | ||||
0.303410 | + | 0.952860i | \(0.401875\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.69455e7 | −0.151825 | ||||||||
\(296\) | 2.78021e8 | 0.623099 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.81824e8 | −0.398011 | ||||||||
\(299\) | 2.59620e7 | 0.0561680 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.45435e7 | 0.0730103 | ||||||||
\(302\) | 5.02647e7 | 0.105012 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.82111e7 | 0.200495 | ||||||||
\(305\) | 1.03966e8 | 0.209817 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.32337e8 | 1.24728 | 0.623640 | − | 0.781711i | \(-0.285653\pi\) | ||||
0.623640 | + | 0.781711i | \(0.285653\pi\) | |||||||
\(308\) | −3.27976e8 | −0.639608 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.24268e7 | −0.0236916 | ||||||||
\(311\) | −9.11382e8 | −1.71806 | −0.859031 | − | 0.511923i | \(-0.828933\pi\) | ||||
−0.859031 | + | 0.511923i | \(0.828933\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.76864e8 | −0.879001 | −0.439501 | − | 0.898242i | \(-0.644845\pi\) | ||||
−0.439501 | + | 0.898242i | \(0.644845\pi\) | |||||||
\(314\) | −1.75108e8 | −0.319192 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.79221e8 | 0.854341 | ||||||||
\(317\) | −2.70951e8 | −0.477731 | −0.238865 | − | 0.971053i | \(-0.576775\pi\) | ||||
−0.238865 | + | 0.971053i | \(0.576775\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.72863e8 | −0.298150 | ||||||||
\(320\) | −4.65262e7 | −0.0793730 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.01919e7 | −0.133855 | ||||||||
\(323\) | 2.03945e8 | 0.336747 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.39228e7 | −0.0548151 | ||||||||
\(326\) | 4.11751e7 | 0.0658223 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.75830e7 | 0.0901023 | ||||||||
\(329\) | −2.00812e8 | −0.310888 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.79247e8 | −0.726376 | −0.363188 | − | 0.931716i | \(-0.618312\pi\) | ||||
−0.363188 | + | 0.931716i | \(0.618312\pi\) | |||||||
\(332\) | −7.17079e8 | −1.07543 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.56812e8 | 0.230286 | ||||||||
\(335\) | −8.32017e7 | −0.120914 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.14532e8 | −0.590002 | −0.295001 | − | 0.955497i | \(-0.595320\pi\) | ||||
−0.295001 | + | 0.955497i | \(0.595320\pi\) | |||||||
\(338\) | 1.96989e8 | 0.277481 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.22103e8 | −0.168480 | ||||||||
\(341\) | 6.42073e8 | 0.876888 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.33599e8 | −0.847784 | ||||||||
\(344\) | 6.16148e7 | 0.0816076 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.84646e8 | 0.369435 | ||||||||
\(347\) | 3.46330e7 | 0.0444976 | 0.0222488 | − | 0.999752i | \(-0.492917\pi\) | ||||
0.0222488 | + | 0.999752i | \(0.492917\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.29687e9 | −1.63308 | −0.816541 | − | 0.577287i | \(-0.804111\pi\) | ||||
−0.816541 | + | 0.577287i | \(0.804111\pi\) | |||||||
\(350\) | 1.04781e8 | 0.130631 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8.89297e8 | −1.08679 | ||||||||
\(353\) | −2.44931e8 | −0.296369 | −0.148184 | − | 0.988960i | \(-0.547343\pi\) | ||||
−0.148184 | + | 0.988960i | \(0.547343\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.98882e8 | 0.235937 | ||||||||
\(356\) | −4.64940e8 | −0.546163 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.16819e8 | −0.480128 | ||||||||
\(359\) | −1.89464e8 | −0.216121 | −0.108060 | − | 0.994144i | \(-0.534464\pi\) | ||||
−0.108060 | + | 0.994144i | \(0.534464\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.33825e8 | −0.932824 | ||||||||
\(362\) | 4.35740e7 | 0.0482777 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.27256e7 | −0.0246980 | ||||||||
\(365\) | 3.53435e7 | 0.0380439 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.82269e8 | −0.509282 | −0.254641 | − | 0.967036i | \(-0.581957\pi\) | ||||
−0.254641 | + | 0.967036i | \(0.581957\pi\) | |||||||
\(368\) | 7.42824e8 | 0.776996 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.43883e7 | −0.0455578 | ||||||||
\(371\) | −5.10088e8 | −0.518604 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.14493e9 | −1.14235 | −0.571176 | − | 0.820828i | \(-0.693512\pi\) | ||||
−0.571176 | + | 0.820828i | \(0.693512\pi\) | |||||||
\(374\) | −5.29860e8 | −0.523733 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.58185e8 | −0.347496 | ||||||||
\(377\) | −1.19778e7 | −0.0115128 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.22401e9 | 1.15491 | 0.577454 | − | 0.816423i | \(-0.304046\pi\) | ||||
0.577454 | + | 0.816423i | \(0.304046\pi\) | |||||||
\(380\) | −3.59503e7 | −0.0336093 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.11738e8 | 0.102560 | ||||||||
\(383\) | −1.02057e9 | −0.928210 | −0.464105 | − | 0.885780i | \(-0.653624\pi\) | ||||
−0.464105 | + | 0.885780i | \(0.653624\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.09126e8 | 0.0974574 | ||||||||
\(386\) | −3.69126e8 | −0.326678 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.47580e9 | 1.28268 | ||||||||
\(389\) | 5.65923e7 | 0.0487454 | 0.0243727 | − | 0.999703i | \(-0.492241\pi\) | ||||
0.0243727 | + | 0.999703i | \(0.492241\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.54254e9 | 1.30502 | ||||||||
\(392\) | −4.91928e8 | −0.412477 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.17693e8 | −0.0969422 | ||||||||
\(395\) | −1.59449e8 | −0.130176 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.60632e8 | −0.770532 | −0.385266 | − | 0.922806i | \(-0.625890\pi\) | ||||
−0.385266 | + | 0.922806i | \(0.625890\pi\) | |||||||
\(398\) | −4.50243e8 | −0.357978 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.70598e8 | −0.758279 | ||||||||
\(401\) | −1.62607e9 | −1.25931 | −0.629656 | − | 0.776874i | \(-0.716804\pi\) | ||||
−0.629656 | + | 0.776874i | \(0.716804\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.44896e7 | 0.0338603 | ||||||||
\(404\) | 9.89748e8 | 0.746775 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.69971e7 | 0.0274364 | ||||||||
\(407\) | 2.29347e9 | 1.68621 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.13080e9 | −0.817247 | −0.408623 | − | 0.912703i | \(-0.633991\pi\) | ||||
−0.408623 | + | 0.912703i | \(0.633991\pi\) | |||||||
\(410\) | −9.19359e6 | −0.00658782 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.54010e9 | −1.08495 | ||||||||
\(413\) | −7.40306e8 | −0.517114 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.38590e8 | 0.163864 | ||||||||
\(416\) | −6.16199e7 | −0.0419657 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.56005e8 | −0.104477 | ||||||||
\(419\) | 5.90861e7 | 0.0392406 | 0.0196203 | − | 0.999808i | \(-0.493754\pi\) | ||||
0.0196203 | + | 0.999808i | \(0.493754\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.62456e9 | 1.71423 | 0.857116 | − | 0.515124i | \(-0.172254\pi\) | ||||
0.857116 | + | 0.515124i | \(0.172254\pi\) | |||||||
\(422\) | −5.00845e8 | −0.324421 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.09837e8 | −0.579673 | ||||||||
\(425\) | −2.01554e9 | −1.27359 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.14969e9 | 0.714632 | ||||||||
\(428\) | −1.03880e9 | −0.640441 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.83730e6 | −0.00596673 | ||||||||
\(431\) | 5.24926e8 | 0.315811 | 0.157906 | − | 0.987454i | \(-0.449526\pi\) | ||||
0.157906 | + | 0.987454i | \(0.449526\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.25218e9 | 1.33320 | 0.666600 | − | 0.745415i | \(-0.267749\pi\) | ||||
0.666600 | + | 0.745415i | \(0.267749\pi\) | |||||||
\(434\) | −1.37420e8 | −0.0806931 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.05291e9 | 1.18623 | ||||||||
\(437\) | 4.54166e8 | 0.260333 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.75255e8 | 0.211690 | 0.105845 | − | 0.994383i | \(-0.466245\pi\) | ||||
0.105845 | + | 0.994383i | \(0.466245\pi\) | |||||||
\(440\) | 1.94646e8 | 0.108933 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.67143e7 | −0.0202235 | ||||||||
\(443\) | −5.78363e7 | −0.0316073 | −0.0158036 | − | 0.999875i | \(-0.505031\pi\) | ||||
−0.0158036 | + | 0.999875i | \(0.505031\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.54697e8 | 0.0832190 | ||||||||
\(446\) | 1.29211e8 | 0.0689650 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.14503e8 | −0.270343 | ||||||||
\(449\) | −7.38749e8 | −0.385154 | −0.192577 | − | 0.981282i | \(-0.561685\pi\) | ||||
−0.192577 | + | 0.981282i | \(0.561685\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.75016e8 | 0.243832 | ||||||||
\(452\) | −8.59915e8 | −0.437997 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.54883e8 | 0.0776797 | ||||||||
\(455\) | 7.56139e6 | 0.00376324 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.98291e9 | −0.971845 | −0.485922 | − | 0.874002i | \(-0.661516\pi\) | ||||
−0.485922 | + | 0.874002i | \(0.661516\pi\) | |||||||
\(458\) | 4.00217e8 | 0.194656 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.71911e8 | −0.130249 | ||||||||
\(461\) | −1.72573e9 | −0.820389 | −0.410195 | − | 0.911998i | \(-0.634539\pi\) | ||||
−0.410195 | + | 0.911998i | \(0.634539\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.52996e9 | 1.65286 | 0.826429 | − | 0.563040i | \(-0.190368\pi\) | ||||
0.826429 | + | 0.563040i | \(0.190368\pi\) | |||||||
\(464\) | −3.42707e8 | −0.159261 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.51600e8 | −0.115175 | ||||||||
\(467\) | −3.16059e9 | −1.43602 | −0.718009 | − | 0.696034i | \(-0.754946\pi\) | ||||
−0.718009 | + | 0.696034i | \(0.754946\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.20073e8 | −0.411829 | ||||||||
\(470\) | 5.71871e7 | 0.0254071 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.32047e9 | −0.578007 | ||||||||
\(473\) | 5.08276e8 | 0.220844 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.93428e8 | −0.254062 | ||||||||
\(476\) | −1.35025e9 | −0.573840 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.83693e8 | −0.244448 | ||||||||
\(479\) | 1.20495e9 | 0.500950 | 0.250475 | − | 0.968123i | \(-0.419413\pi\) | ||||
0.250475 | + | 0.968123i | \(0.419413\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.58916e8 | 0.0651117 | ||||||||
\(482\) | −5.84450e7 | −0.0237730 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.52476e9 | −1.01219 | ||||||||
\(485\) | −4.91037e8 | −0.195442 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.76020e9 | −0.690576 | −0.345288 | − | 0.938497i | \(-0.612219\pi\) | ||||
−0.345288 | + | 0.938497i | \(0.612219\pi\) | |||||||
\(488\) | 2.05068e9 | 0.798784 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.85402e7 | 0.0301582 | ||||||||
\(491\) | 3.34075e9 | 1.27368 | 0.636839 | − | 0.770997i | \(-0.280242\pi\) | ||||
0.636839 | + | 0.770997i | \(0.280242\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.11664e8 | −0.267492 | ||||||||
\(494\) | −1.08097e7 | −0.00403430 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.27293e9 | 0.468404 | ||||||||
\(497\) | 2.19930e9 | 0.803595 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.65908e9 | −1.31832 | −0.659159 | − | 0.752004i | \(-0.729087\pi\) | ||||
−0.659159 | + | 0.752004i | \(0.729087\pi\) | |||||||
\(500\) | 7.17738e8 | 0.256786 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.86259e8 | 0.206836 | ||||||||
\(503\) | 9.88140e7 | 0.0346203 | 0.0173101 | − | 0.999850i | \(-0.494490\pi\) | ||||
0.0173101 | + | 0.999850i | \(0.494490\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.29314e8 | −0.113786 | ||||||||
\(506\) | −1.17995e9 | −0.404889 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.07953e9 | −0.365352 | ||||||||
\(509\) | 3.29148e9 | 1.10632 | 0.553158 | − | 0.833076i | \(-0.313422\pi\) | ||||
0.553158 | + | 0.833076i | \(0.313422\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.90841e8 | 0.129577 | ||||||||
\(512\) | −3.02027e9 | −0.994491 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.45207e9 | −0.471647 | ||||||||
\(515\) | 5.12431e8 | 0.165314 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.95476e9 | −0.940384 | ||||||||
\(518\) | −4.90861e8 | −0.155169 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.34871e7 | 0.00420638 | ||||||||
\(521\) | −1.48897e9 | −0.461267 | −0.230634 | − | 0.973041i | \(-0.574080\pi\) | ||||
−0.230634 | + | 0.973041i | \(0.574080\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.83188e9 | 1.78259 | 0.891297 | − | 0.453420i | \(-0.149796\pi\) | ||||
0.891297 | + | 0.453420i | \(0.149796\pi\) | |||||||
\(524\) | −3.77023e9 | −1.14474 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.33733e9 | −0.400673 | ||||||||
\(527\) | 2.64337e9 | 0.786720 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.02763e7 | 0.00889216 | ||||||||
\(530\) | 1.45263e8 | 0.0423827 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.97550e8 | −0.114472 | ||||||||
\(533\) | 3.29142e7 | 0.00941538 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.45635e8 | 0.0975843 | ||||||||
\(536\) | −1.64112e9 | −0.460324 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.33623e7 | −0.0175426 | ||||||||
\(539\) | −4.05803e9 | −1.11623 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.86680e9 | 1.04993 | 0.524966 | − | 0.851123i | \(-0.324078\pi\) | ||||
0.524966 | + | 0.851123i | \(0.324078\pi\) | |||||||
\(542\) | −1.04532e9 | −0.282001 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.66117e9 | −0.975043 | ||||||||
\(545\) | −6.83056e8 | −0.180746 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.69733e9 | 0.965901 | 0.482950 | − | 0.875648i | \(-0.339565\pi\) | ||||
0.482950 | + | 0.875648i | \(0.339565\pi\) | |||||||
\(548\) | 1.26786e9 | 0.329109 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.54176e9 | 0.395136 | ||||||||
\(551\) | −2.09533e8 | −0.0533607 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.76324e9 | −0.443378 | ||||||||
\(554\) | 1.97515e9 | 0.493534 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.06608e8 | 0.223696 | ||||||||
\(557\) | −2.06821e9 | −0.507110 | −0.253555 | − | 0.967321i | \(-0.581600\pi\) | ||||
−0.253555 | + | 0.967321i | \(0.581600\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.52188e7 | 0.00852771 | ||||||||
\(560\) | 2.16346e8 | 0.0520584 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.72133e9 | −0.409061 | ||||||||
\(563\) | −3.92675e9 | −0.927372 | −0.463686 | − | 0.886000i | \(-0.653473\pi\) | ||||
−0.463686 | + | 0.886000i | \(0.653473\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.86115e8 | 0.0667377 | ||||||||
\(566\) | −1.49371e9 | −0.346265 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.92286e9 | 0.898223 | ||||||||
\(569\) | 3.55278e9 | 0.808491 | 0.404245 | − | 0.914651i | \(-0.367534\pi\) | ||||
0.404245 | + | 0.914651i | \(0.367534\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.16477e8 | 0.0261828 | 0.0130914 | − | 0.999914i | \(-0.495833\pi\) | ||||
0.0130914 | + | 0.999914i | \(0.495833\pi\) | |||||||
\(572\) | −3.34386e8 | −0.0747072 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.01666e8 | −0.0224380 | ||||||||
\(575\) | −4.48841e9 | −0.984590 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.38024e9 | 1.38268 | 0.691340 | − | 0.722529i | \(-0.257021\pi\) | ||||
0.691340 | + | 0.722529i | \(0.257021\pi\) | |||||||
\(578\) | −8.89159e8 | −0.191528 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.25448e8 | 0.0266973 | ||||||||
\(581\) | 2.63841e9 | 0.558118 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.50547e9 | −1.56869 | ||||||||
\(584\) | 6.97137e8 | 0.144835 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.22803e8 | −0.168910 | ||||||||
\(587\) | 3.91131e9 | 0.798157 | 0.399079 | − | 0.916917i | \(-0.369330\pi\) | ||||
0.399079 | + | 0.916917i | \(0.369330\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.78278e8 | 0.156939 | ||||||||
\(590\) | 2.10824e8 | 0.0422609 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.54689e9 | 0.900716 | ||||||||
\(593\) | 9.01946e9 | 1.77619 | 0.888094 | − | 0.459661i | \(-0.152029\pi\) | ||||
0.888094 | + | 0.459661i | \(0.152029\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.49263e8 | 0.0874362 | ||||||||
\(596\) | −6.81771e9 | −1.31910 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.17593e7 | −0.0156345 | ||||||||
\(599\) | −3.06365e9 | −0.582432 | −0.291216 | − | 0.956657i | \(-0.594060\pi\) | ||||
−0.291216 | + | 0.956657i | \(0.594060\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.13537e9 | 0.777059 | 0.388529 | − | 0.921436i | \(-0.372983\pi\) | ||||
0.388529 | + | 0.921436i | \(0.372983\pi\) | |||||||
\(602\) | −1.08784e8 | −0.0203225 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.88473e9 | 0.348033 | ||||||||
\(605\) | 8.40052e8 | 0.154228 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.50688e9 | −0.636445 | −0.318222 | − | 0.948016i | \(-0.603086\pi\) | ||||
−0.318222 | + | 0.948016i | \(0.603086\pi\) | |||||||
\(608\) | −1.07795e9 | −0.194507 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.27408e8 | −0.0584030 | ||||||||
\(611\) | −2.04737e8 | −0.0363122 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.51080e9 | −0.440251 | −0.220125 | − | 0.975472i | \(-0.570647\pi\) | ||||
−0.220125 | + | 0.975472i | \(0.570647\pi\) | |||||||
\(614\) | −1.99135e9 | −0.347183 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.15246e9 | 0.371025 | ||||||||
\(617\) | 8.91772e9 | 1.52847 | 0.764233 | − | 0.644941i | \(-0.223118\pi\) | ||||
0.764233 | + | 0.644941i | \(0.223118\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.01712e10 | −1.72368 | −0.861838 | − | 0.507183i | \(-0.830687\pi\) | ||||
−0.861838 | + | 0.507183i | \(0.830687\pi\) | |||||||
\(620\) | −4.65959e8 | −0.0785193 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.87012e9 | 0.478226 | ||||||||
\(623\) | 1.71069e9 | 0.283442 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.74411e9 | 0.941115 | ||||||||
\(626\) | 1.50174e9 | 0.244672 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.56588e9 | −1.05787 | ||||||||
\(629\) | 9.44203e9 | 1.51282 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.57149e9 | −1.35817 | −0.679084 | − | 0.734061i | \(-0.737623\pi\) | ||||
−0.679084 | + | 0.734061i | \(0.737623\pi\) | |||||||
\(632\) | −3.14507e9 | −0.495588 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.53276e8 | 0.132977 | ||||||||
\(635\) | 3.59187e8 | 0.0556688 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.81184e8 | −0.0431025 | ||||||||
\(638\) | 5.44378e8 | 0.0829905 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.46094e8 | 0.127582 | ||||||||
\(641\) | −3.31058e9 | −0.496479 | −0.248240 | − | 0.968699i | \(-0.579852\pi\) | ||||
−0.248240 | + | 0.968699i | \(0.579852\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.42873e9 | −0.508622 | −0.254311 | − | 0.967122i | \(-0.581849\pi\) | ||||
−0.254311 | + | 0.967122i | \(0.581849\pi\) | |||||||
\(644\) | −3.00689e9 | −0.443626 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.42260e8 | −0.0937340 | ||||||||
\(647\) | −2.83989e8 | −0.0412228 | −0.0206114 | − | 0.999788i | \(-0.506561\pi\) | ||||
−0.0206114 | + | 0.999788i | \(0.506561\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.08929e10 | −1.56418 | ||||||||
\(650\) | 1.06829e8 | 0.0152579 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.54391e9 | 0.218150 | ||||||||
\(653\) | −3.48386e8 | −0.0489626 | −0.0244813 | − | 0.999700i | \(-0.507793\pi\) | ||||
−0.0244813 | + | 0.999700i | \(0.507793\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.25445e9 | 0.174425 | ||||||||
\(656\) | 9.41739e8 | 0.130247 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.32395e8 | 0.0865361 | ||||||||
\(659\) | 9.43143e9 | 1.28375 | 0.641873 | − | 0.766811i | \(-0.278158\pi\) | ||||
0.641873 | + | 0.766811i | \(0.278158\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.05208e10 | 1.41692 | 0.708458 | − | 0.705753i | \(-0.249391\pi\) | ||||
0.708458 | + | 0.705753i | \(0.249391\pi\) | |||||||
\(662\) | 1.50924e9 | 0.202188 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.70610e9 | 0.623840 | ||||||||
\(665\) | 1.32275e8 | 0.0174422 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.58481e9 | −0.206793 | ||||||||
\(668\) | 5.87986e9 | 0.763219 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.62018e8 | 0.0336565 | ||||||||
\(671\) | 1.69166e10 | 2.16164 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.80231e8 | −0.0354376 | −0.0177188 | − | 0.999843i | \(-0.505640\pi\) | ||||
−0.0177188 | + | 0.999843i | \(0.505640\pi\) | |||||||
\(674\) | 1.30544e9 | 0.164228 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.38634e9 | 0.919636 | ||||||||
\(677\) | 3.28856e9 | 0.407329 | 0.203664 | − | 0.979041i | \(-0.434715\pi\) | ||||
0.203664 | + | 0.979041i | \(0.434715\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.43006e9 | −0.665672 | ||||||||
\(680\) | 8.01344e8 | 0.0977322 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.02201e9 | −0.244083 | ||||||||
\(683\) | 2.54212e9 | 0.305298 | 0.152649 | − | 0.988280i | \(-0.451220\pi\) | ||||
0.152649 | + | 0.988280i | \(0.451220\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.21849e8 | −0.0501465 | ||||||||
\(686\) | 1.99532e9 | 0.235982 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.00768e9 | 0.117967 | ||||||||
\(689\) | −5.20058e8 | −0.0605738 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.50328e10 | 1.73328 | 0.866638 | − | 0.498937i | \(-0.166276\pi\) | ||||
0.866638 | + | 0.498937i | \(0.166276\pi\) | |||||||
\(692\) | 1.06731e10 | 1.22439 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.09066e8 | −0.0123860 | ||||||||
\(695\) | −3.01651e8 | −0.0340846 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.95561e9 | 0.218760 | ||||||||
\(698\) | 4.08410e9 | 0.454571 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.92890e9 | 0.432940 | ||||||||
\(701\) | 3.96542e9 | 0.434787 | 0.217393 | − | 0.976084i | \(-0.430245\pi\) | ||||
0.217393 | + | 0.976084i | \(0.430245\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.77999e9 | 0.301786 | ||||||||
\(704\) | −7.57043e9 | −0.817742 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.71335e8 | 0.0824947 | ||||||||
\(707\) | −3.64167e9 | −0.387554 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.82480e9 | 0.929914 | 0.464957 | − | 0.885333i | \(-0.346070\pi\) | ||||
0.464957 | + | 0.885333i | \(0.346070\pi\) | |||||||
\(710\) | −6.26317e8 | −0.0656734 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.05134e9 | 0.316819 | ||||||||
\(713\) | 5.88654e9 | 0.608200 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.11259e8 | 0.0113832 | ||||||||
\(716\) | −1.56291e10 | −1.59125 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.96659e8 | 0.0601576 | ||||||||
\(719\) | 1.63954e10 | 1.64501 | 0.822507 | − | 0.568755i | \(-0.192575\pi\) | ||||
0.822507 | + | 0.568755i | \(0.192575\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.66664e9 | 0.563056 | ||||||||
\(722\) | 2.62587e9 | 0.259653 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.63386e9 | 0.160003 | ||||||||
\(725\) | 2.07076e9 | 0.201812 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.74182e9 | −0.457693 | −0.228847 | − | 0.973462i | \(-0.573495\pi\) | ||||
−0.228847 | + | 0.973462i | \(0.573495\pi\) | |||||||
\(728\) | 1.49145e8 | 0.0143268 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.11304e8 | −0.0105896 | ||||||||
\(731\) | 2.09254e9 | 0.198135 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.56780e10 | −1.47037 | −0.735184 | − | 0.677868i | \(-0.762904\pi\) | ||||
−0.735184 | + | 0.677868i | \(0.762904\pi\) | |||||||
\(734\) | 1.51876e9 | 0.141760 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.15309e9 | −0.753789 | ||||||||
\(737\) | −1.35380e10 | −1.24572 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.09854e10 | 1.91277 | 0.956383 | − | 0.292116i | \(-0.0943594\pi\) | ||||
0.956383 | + | 0.292116i | \(0.0943594\pi\) | |||||||
\(740\) | −1.66439e9 | −0.150989 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.60636e9 | 0.144354 | ||||||||
\(743\) | −1.57915e10 | −1.41242 | −0.706209 | − | 0.708004i | \(-0.749596\pi\) | ||||
−0.706209 | + | 0.708004i | \(0.749596\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.26842e9 | 0.200991 | ||||||||
\(746\) | 3.60562e9 | 0.317976 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.98677e10 | −1.73577 | ||||||||
\(749\) | 3.82215e9 | 0.332370 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.46937e10 | 1.26588 | 0.632939 | − | 0.774201i | \(-0.281848\pi\) | ||||
0.632939 | + | 0.774201i | \(0.281848\pi\) | |||||||
\(752\) | −5.85792e9 | −0.502321 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.77203e7 | 0.00320461 | ||||||||
\(755\) | −6.27098e8 | −0.0530299 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.22699e9 | 0.689295 | 0.344648 | − | 0.938732i | \(-0.387998\pi\) | ||||
0.344648 | + | 0.938732i | \(0.387998\pi\) | |||||||
\(758\) | −3.85464e9 | −0.321471 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.35937e8 | 0.0194961 | ||||||||
\(761\) | −2.23002e10 | −1.83427 | −0.917133 | − | 0.398581i | \(-0.869503\pi\) | ||||
−0.917133 | + | 0.398581i | \(0.869503\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.55346e9 | −0.615616 | ||||||||
\(764\) | 4.18974e9 | 0.339907 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.21397e9 | 0.258369 | ||||||||
\(767\) | −7.54777e8 | −0.0603997 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.62540e10 | 1.28890 | 0.644448 | − | 0.764648i | \(-0.277087\pi\) | ||||
0.644448 | + | 0.764648i | \(0.277087\pi\) | |||||||
\(770\) | −3.43658e8 | −0.0271274 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.38408e10 | −1.08268 | ||||||||
\(773\) | 1.29767e10 | 1.01050 | 0.505248 | − | 0.862974i | \(-0.331401\pi\) | ||||
0.505248 | + | 0.862974i | \(0.331401\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.69154e9 | −0.593550 | ||||||||
\(776\) | −9.68552e9 | −0.744058 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.78220e8 | −0.0135684 | ||||||||
\(779\) | 5.75783e8 | 0.0436393 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.23607e10 | 2.43074 | ||||||||
\(782\) | −4.85776e9 | −0.363256 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.04521e9 | −0.596254 | ||||||||
\(785\) | 2.18463e9 | 0.161189 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.18344e10 | −0.865436 | −0.432718 | − | 0.901529i | \(-0.642445\pi\) | ||||
−0.432718 | + | 0.901529i | \(0.642445\pi\) | |||||||
\(788\) | −4.41302e9 | −0.321288 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.02136e8 | 0.0362348 | ||||||||
\(791\) | 3.16396e9 | 0.227307 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.17216e9 | 0.0834701 | ||||||||
\(794\) | 3.02522e9 | 0.214479 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.68824e10 | −1.18642 | ||||||||
\(797\) | 5.74935e8 | 0.0402267 | 0.0201134 | − | 0.999798i | \(-0.493597\pi\) | ||||
0.0201134 | + | 0.999798i | \(0.493597\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.21645e10 | −0.843687 | ||||||||
\(800\) | 1.06531e10 | 0.735632 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.12080e9 | 0.350532 | ||||||||
\(803\) | 5.75086e9 | 0.391948 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.00047e9 | 0.0675954 | ||||||||
\(806\) | −1.40106e8 | −0.00942508 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.49559e9 | −0.433191 | ||||||||
\(809\) | −1.85697e10 | −1.23306 | −0.616532 | − | 0.787330i | \(-0.711463\pi\) | ||||
−0.616532 | + | 0.787330i | \(0.711463\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.35102e10 | −0.889384 | −0.444692 | − | 0.895683i | \(-0.646687\pi\) | ||||
−0.444692 | + | 0.895683i | \(0.646687\pi\) | |||||||
\(812\) | 1.38725e9 | 0.0909303 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.22256e9 | −0.469360 | ||||||||
\(815\) | −5.13697e8 | −0.0332396 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.16098e8 | 0.0395251 | ||||||||
\(818\) | 3.56110e9 | 0.227482 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.44724e8 | −0.0218335 | ||||||||
\(821\) | 2.18113e10 | 1.37557 | 0.687783 | − | 0.725917i | \(-0.258584\pi\) | ||||
0.687783 | + | 0.725917i | \(0.258584\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.25550e10 | 1.41040 | 0.705202 | − | 0.709006i | \(-0.250856\pi\) | ||||
0.705202 | + | 0.709006i | \(0.250856\pi\) | |||||||
\(824\) | 1.01075e10 | 0.629359 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.33137e9 | 0.143940 | ||||||||
\(827\) | 2.31862e10 | 1.42548 | 0.712739 | − | 0.701430i | \(-0.247455\pi\) | ||||
0.712739 | + | 0.701430i | \(0.247455\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.89637e10 | 1.76568 | 0.882842 | − | 0.469671i | \(-0.155627\pi\) | ||||
0.882842 | + | 0.469671i | \(0.155627\pi\) | |||||||
\(830\) | −7.51366e8 | −0.0456119 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.24559e8 | −0.0315764 | ||||||||
\(833\) | −1.67066e10 | −1.00145 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.95638e9 | −0.116292 | ||||||||
\(836\) | −5.84958e9 | −0.346260 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.86073e8 | −0.0109227 | ||||||||
\(839\) | 9.53603e9 | 0.557444 | 0.278722 | − | 0.960372i | \(-0.410089\pi\) | ||||
0.278722 | + | 0.960372i | \(0.410089\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.65187e10 | −0.957613 | ||||||||
\(842\) | −8.26525e9 | −0.477160 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.87798e10 | −1.07521 | ||||||||
\(845\) | −2.45762e9 | −0.140125 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.28957e9 | 0.525296 | ||||||||
\(848\) | −1.48799e10 | −0.837942 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.34731e9 | 0.354506 | ||||||||
\(851\) | 2.10265e10 | 1.16954 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.23351e10 | 1.23216 | 0.616078 | − | 0.787685i | \(-0.288721\pi\) | ||||
0.616078 | + | 0.787685i | \(0.288721\pi\) | |||||||
\(854\) | −3.62059e9 | −0.198919 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.81752e9 | 0.371508 | ||||||||
\(857\) | 2.98724e10 | 1.62120 | 0.810602 | − | 0.585598i | \(-0.199140\pi\) | ||||
0.810602 | + | 0.585598i | \(0.199140\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.94294e10 | −1.04588 | −0.522941 | − | 0.852369i | \(-0.675165\pi\) | ||||
−0.522941 | + | 0.852369i | \(0.675165\pi\) | |||||||
\(860\) | −3.68861e8 | −0.0197751 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.65309e9 | −0.0879067 | ||||||||
\(863\) | −2.20900e10 | −1.16992 | −0.584962 | − | 0.811060i | \(-0.698891\pi\) | ||||
−0.584962 | + | 0.811060i | \(0.698891\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.55122e9 | −0.186561 | ||||||||
\(866\) | −7.09255e9 | −0.371099 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.15273e9 | −0.267435 | ||||||||
\(869\) | −2.59445e10 | −1.34114 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.38057e8 | −0.0481023 | ||||||||
\(872\) | −1.34730e10 | −0.688108 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.43025e9 | −0.0724642 | ||||||||
\(875\) | −2.64083e9 | −0.133264 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.02430e10 | −1.51400 | −0.757001 | − | 0.653413i | \(-0.773336\pi\) | ||||
−0.757001 | + | 0.653413i | \(0.773336\pi\) | |||||||
\(878\) | −1.18175e9 | −0.0589243 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.18333e9 | 0.157468 | ||||||||
\(881\) | 2.28024e10 | 1.12348 | 0.561739 | − | 0.827314i | \(-0.310132\pi\) | ||||
0.561739 | + | 0.827314i | \(0.310132\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.29419e10 | −1.61023 | −0.805113 | − | 0.593122i | \(-0.797895\pi\) | ||||
−0.805113 | + | 0.593122i | \(0.797895\pi\) | |||||||
\(884\) | −1.37664e9 | −0.0670253 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.82138e8 | 0.00879795 | ||||||||
\(887\) | −2.72521e9 | −0.131119 | −0.0655597 | − | 0.997849i | \(-0.520883\pi\) | ||||
−0.0655597 | + | 0.997849i | \(0.520883\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.97201e9 | 0.189607 | ||||||||
\(890\) | −4.87171e8 | −0.0231642 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.84493e9 | 0.228565 | ||||||||
\(893\) | −3.58156e9 | −0.168303 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.20020e9 | 0.242459 | ||||||||
\(896\) | 9.35640e9 | 0.434541 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.32646e9 | 0.107208 | ||||||||
\(899\) | −2.71580e9 | −0.124663 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.08995e10 | −1.40739 | ||||||||
\(902\) | −1.49592e9 | −0.0678711 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.64351e9 | 0.254074 | ||||||||
\(905\) | −5.43625e8 | −0.0243798 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.55130e9 | 0.291542 | 0.145771 | − | 0.989318i | \(-0.453434\pi\) | ||||
0.145771 | + | 0.989318i | \(0.453434\pi\) | |||||||
\(908\) | 5.80751e9 | 0.257448 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.38123e7 | −0.00104750 | ||||||||
\(911\) | 2.40723e10 | 1.05488 | 0.527440 | − | 0.849592i | \(-0.323152\pi\) | ||||
0.527440 | + | 0.849592i | \(0.323152\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.88218e10 | 1.68821 | ||||||||
\(914\) | 6.24457e9 | 0.270515 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.50066e10 | 0.645132 | ||||||||
\(917\) | 1.38721e10 | 0.594087 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.57146e10 | 1.94290 | 0.971450 | − | 0.237244i | \(-0.0762441\pi\) | ||||
0.971450 | + | 0.237244i | \(0.0762441\pi\) | |||||||
\(920\) | 1.78452e9 | 0.0755551 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.43466e9 | 0.228357 | ||||||||
\(923\) | 2.24229e9 | 0.0938612 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.74739e10 | −1.14137 | ||||||||
\(926\) | −1.11165e10 | −0.460076 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.76149e9 | 0.154505 | ||||||||
\(929\) | 3.25677e10 | 1.33270 | 0.666349 | − | 0.745640i | \(-0.267856\pi\) | ||||
0.666349 | + | 0.745640i | \(0.267856\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.91888e9 | −0.199775 | ||||||||
\(932\) | −9.43402e9 | −0.381717 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.95332e9 | 0.399718 | ||||||||
\(935\) | 6.61048e9 | 0.264480 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.92369e10 | −1.55814 | −0.779069 | − | 0.626938i | \(-0.784308\pi\) | ||||
−0.779069 | + | 0.626938i | \(0.784308\pi\) | |||||||
\(938\) | 2.89748e9 | 0.114633 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.14430e9 | 0.0842049 | ||||||||
\(941\) | −3.07063e10 | −1.20133 | −0.600667 | − | 0.799499i | \(-0.705098\pi\) | ||||
−0.600667 | + | 0.799499i | \(0.705098\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.35496e9 | 0.169119 | ||||||||
\(944\) | −2.15956e10 | −0.835534 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.60066e9 | −0.0614723 | ||||||||
\(947\) | −4.74031e10 | −1.81377 | −0.906883 | − | 0.421382i | \(-0.861545\pi\) | ||||
−0.906883 | + | 0.421382i | \(0.861545\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.98480e8 | 0.0151348 | ||||||||
\(950\) | 1.86882e9 | 0.0707187 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.86153e9 | 0.332874 | ||||||||
\(953\) | −4.93561e10 | −1.84721 | −0.923604 | − | 0.383347i | \(-0.874771\pi\) | ||||
−0.923604 | + | 0.383347i | \(0.874771\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.39403e9 | −0.0517918 | ||||||||
\(956\) | −2.18863e10 | −0.810157 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.79462e9 | −0.139440 | ||||||||
\(959\) | −4.66495e9 | −0.170798 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.74252e10 | −0.633353 | ||||||||
\(962\) | −5.00456e8 | −0.0181239 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.19147e9 | −0.0787889 | ||||||||
\(965\) | 4.60519e9 | 0.164969 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.84804e9 | −0.243542 | −0.121771 | − | 0.992558i | \(-0.538857\pi\) | ||||
−0.121771 | + | 0.992558i | \(0.538857\pi\) | |||||||
\(968\) | 1.65697e10 | 0.587152 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.54637e9 | 0.0544017 | ||||||||
\(971\) | −4.01610e8 | −0.0140779 | −0.00703894 | − | 0.999975i | \(-0.502241\pi\) | ||||
−0.00703894 | + | 0.999975i | \(0.502241\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.33576e9 | −0.116091 | ||||||||
\(974\) | 5.54322e9 | 0.192223 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.35378e10 | 1.15468 | ||||||||
\(977\) | −3.71330e10 | −1.27388 | −0.636940 | − | 0.770913i | \(-0.719800\pi\) | ||||
−0.636940 | + | 0.770913i | \(0.719800\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.51713e10 | 0.857365 | ||||||||
\(980\) | 2.94496e9 | 0.0999511 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.05207e10 | −0.354530 | ||||||||
\(983\) | −1.12625e10 | −0.378179 | −0.189089 | − | 0.981960i | \(-0.560554\pi\) | ||||
−0.189089 | + | 0.981960i | \(0.560554\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.46832e9 | 0.0489548 | ||||||||
\(986\) | 2.24116e9 | 0.0744568 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.05321e8 | −0.0133706 | ||||||||
\(989\) | 4.65988e9 | 0.153175 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.74895e10 | 1.55003 | 0.775015 | − | 0.631943i | \(-0.217743\pi\) | ||||
0.775015 | + | 0.631943i | \(0.217743\pi\) | |||||||
\(992\) | −1.39715e10 | −0.454414 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.92602e9 | −0.223682 | ||||||||
\(995\) | 5.61719e9 | 0.180775 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.12122e10 | 0.358310 | 0.179155 | − | 0.983821i | \(-0.442664\pi\) | ||||
0.179155 | + | 0.983821i | \(0.442664\pi\) | |||||||
\(998\) | 1.15231e10 | 0.366956 | ||||||||
\(999\) | 0 | 0 |
(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 | 387.8.a.b.1.5 | 11 | ||
3.2 | odd | 2 | 43.8.a.a.1.7 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.8.a.a.1.7 | ✓ | 11 | 3.2 | odd | 2 | ||
387.8.a.b.1.5 | 11 | 1.1 | even | 1 | trivial |