Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,10,Mod(16,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.16");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.b (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: | \(8.75560921479\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 122690 x^{10} + 5157152560 x^{8} + 87983684680032 x^{6} + \cdots + 20\!\cdots\!28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{17}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 16.10 | ||
Root | \(225.146i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 17.16 |
Dual form | 17.10.b.a.16.9 |
$q$-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 \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 25.8215 | 1.14116 | 0.570580 | − | 0.821242i | \(-0.306718\pi\) | ||||
0.570580 | + | 0.821242i | \(0.306718\pi\) | |||||||
\(3\) | 225.146i | 1.60479i | 0.596792 | + | 0.802396i | \(0.296442\pi\) | ||||
−0.596792 | + | 0.802396i | \(0.703558\pi\) | |||||||
\(4\) | 154.751 | 0.302248 | ||||||||
\(5\) | 96.4328i | 0.0690017i | 0.999405 | + | 0.0345009i | \(0.0109841\pi\) | ||||
−0.999405 | + | 0.0345009i | \(0.989016\pi\) | |||||||
\(6\) | 5813.61i | 1.83133i | ||||||||
\(7\) | 1385.77i | 0.218148i | 0.994034 | + | 0.109074i | \(0.0347885\pi\) | ||||
−0.994034 | + | 0.109074i | \(0.965211\pi\) | |||||||
\(8\) | −9224.72 | −0.796248 | ||||||||
\(9\) | −31007.8 | −1.57536 | ||||||||
\(10\) | 2490.04i | 0.0787420i | ||||||||
\(11\) | 33833.7i | 0.696759i | 0.937354 | + | 0.348379i | \(0.113268\pi\) | ||||
−0.937354 | + | 0.348379i | \(0.886732\pi\) | |||||||
\(12\) | 34841.5i | 0.485045i | ||||||||
\(13\) | 138558. | 1.34551 | 0.672755 | − | 0.739866i | \(-0.265111\pi\) | ||||
0.672755 | + | 0.739866i | \(0.265111\pi\) | |||||||
\(14\) | 35782.8i | 0.248942i | ||||||||
\(15\) | −21711.5 | −0.110733 | ||||||||
\(16\) | −317429. | −1.21089 | ||||||||
\(17\) | 177982. | + | 294805.i | 0.516840 | + | 0.856082i | ||||
\(18\) | −800668. | −1.79774 | ||||||||
\(19\) | 429726. | 0.756484 | 0.378242 | − | 0.925707i | \(-0.376529\pi\) | ||||
0.378242 | + | 0.925707i | \(0.376529\pi\) | |||||||
\(20\) | 14923.1i | 0.0208556i | ||||||||
\(21\) | −312001. | −0.350082 | ||||||||
\(22\) | 873638.i | 0.795114i | ||||||||
\(23\) | − | 352831.i | − | 0.262901i | −0.991323 | − | 0.131450i | \(-0.958037\pi\) | ||
0.991323 | − | 0.131450i | \(-0.0419634\pi\) | |||||||
\(24\) | − | 2.07691e6i | − | 1.27781i | ||||||
\(25\) | 1.94383e6 | 0.995239 | ||||||||
\(26\) | 3.57778e6 | 1.53544 | ||||||||
\(27\) | − | 2.54973e6i | − | 0.923330i | ||||||
\(28\) | 214449.i | 0.0659347i | ||||||||
\(29\) | − | 508224.i | − | 0.133433i | −0.997772 | − | 0.0667166i | \(-0.978748\pi\) | ||
0.997772 | − | 0.0667166i | \(-0.0212523\pi\) | |||||||
\(30\) | −560623. | −0.126365 | ||||||||
\(31\) | − | 8.73026e6i | − | 1.69785i | −0.528513 | − | 0.848925i | \(-0.677250\pi\) | ||
0.528513 | − | 0.848925i | \(-0.322750\pi\) | |||||||
\(32\) | −3.47343e6 | −0.585577 | ||||||||
\(33\) | −7.61753e6 | −1.11815 | ||||||||
\(34\) | 4.59577e6 | + | 7.61232e6i | 0.589798 | + | 0.976927i | ||||
\(35\) | −133634. | −0.0150526 | ||||||||
\(36\) | −4.79848e6 | −0.476148 | ||||||||
\(37\) | 1.62218e7i | 1.42295i | 0.702710 | + | 0.711476i | \(0.251973\pi\) | ||||
−0.702710 | + | 0.711476i | \(0.748027\pi\) | |||||||
\(38\) | 1.10962e7 | 0.863270 | ||||||||
\(39\) | 3.11958e7i | 2.15926i | ||||||||
\(40\) | − | 889565.i | − | 0.0549424i | ||||||
\(41\) | − | 1.12435e7i | − | 0.621406i | −0.950507 | − | 0.310703i | \(-0.899436\pi\) | ||
0.950507 | − | 0.310703i | \(-0.100564\pi\) | |||||||
\(42\) | −8.05635e6 | −0.399500 | ||||||||
\(43\) | −2.43795e7 | −1.08747 | −0.543735 | − | 0.839257i | \(-0.682990\pi\) | ||||
−0.543735 | + | 0.839257i | \(0.682990\pi\) | |||||||
\(44\) | 5.23579e6i | 0.210594i | ||||||||
\(45\) | − | 2.99017e6i | − | 0.108702i | ||||||
\(46\) | − | 9.11064e6i | − | 0.300012i | ||||||
\(47\) | −1.11673e7 | −0.333817 | −0.166909 | − | 0.985972i | \(-0.553379\pi\) | ||||
−0.166909 | + | 0.985972i | \(0.553379\pi\) | |||||||
\(48\) | − | 7.14678e7i | − | 1.94323i | ||||||
\(49\) | 3.84332e7 | 0.952412 | ||||||||
\(50\) | 5.01925e7 | 1.13573 | ||||||||
\(51\) | −6.63743e7 | + | 4.00720e7i | −1.37383 | + | 0.829421i | ||||
\(52\) | 2.14420e7 | 0.406677 | ||||||||
\(53\) | 3.54297e7 | 0.616774 | 0.308387 | − | 0.951261i | \(-0.400211\pi\) | ||||
0.308387 | + | 0.951261i | \(0.400211\pi\) | |||||||
\(54\) | − | 6.58378e7i | − | 1.05367i | ||||||
\(55\) | −3.26268e6 | −0.0480775 | ||||||||
\(56\) | − | 1.27834e7i | − | 0.173700i | ||||||
\(57\) | 9.67510e7i | 1.21400i | ||||||||
\(58\) | − | 1.31231e7i | − | 0.152269i | ||||||
\(59\) | 5.03437e7 | 0.540893 | 0.270446 | − | 0.962735i | \(-0.412829\pi\) | ||||
0.270446 | + | 0.962735i | \(0.412829\pi\) | |||||||
\(60\) | −3.35987e6 | −0.0334689 | ||||||||
\(61\) | 1.53033e8i | 1.41515i | 0.706639 | + | 0.707574i | \(0.250211\pi\) | ||||
−0.706639 | + | 0.707574i | \(0.749789\pi\) | |||||||
\(62\) | − | 2.25429e8i | − | 1.93752i | ||||||
\(63\) | − | 4.29697e7i | − | 0.343661i | ||||||
\(64\) | 7.28341e7 | 0.542656 | ||||||||
\(65\) | 1.33615e7i | 0.0928425i | ||||||||
\(66\) | −1.96696e8 | −1.27599 | ||||||||
\(67\) | −2.44023e8 | −1.47943 | −0.739713 | − | 0.672922i | \(-0.765039\pi\) | ||||
−0.739713 | + | 0.672922i | \(0.765039\pi\) | |||||||
\(68\) | 2.75429e7 | + | 4.56214e7i | 0.156214 | + | 0.258749i | ||||
\(69\) | 7.94386e7 | 0.421901 | ||||||||
\(70\) | −3.45063e6 | −0.0171774 | ||||||||
\(71\) | − | 3.78713e8i | − | 1.76867i | −0.466850 | − | 0.884337i | \(-0.654611\pi\) | ||
0.466850 | − | 0.884337i | \(-0.345389\pi\) | |||||||
\(72\) | 2.86038e8 | 1.25437 | ||||||||
\(73\) | 1.38738e7i | 0.0571798i | 0.999591 | + | 0.0285899i | \(0.00910169\pi\) | ||||
−0.999591 | + | 0.0285899i | \(0.990898\pi\) | |||||||
\(74\) | 4.18871e8i | 1.62382i | ||||||||
\(75\) | 4.37645e8i | 1.59715i | ||||||||
\(76\) | 6.65004e7 | 0.228646 | ||||||||
\(77\) | −4.68858e7 | −0.151996 | ||||||||
\(78\) | 8.05523e8i | 2.46407i | ||||||||
\(79\) | − | 5.65164e8i | − | 1.63250i | −0.577700 | − | 0.816250i | \(-0.696049\pi\) | ||
0.577700 | − | 0.816250i | \(-0.303951\pi\) | |||||||
\(80\) | − | 3.06105e7i | − | 0.0835537i | ||||||
\(81\) | −3.62648e7 | −0.0936057 | ||||||||
\(82\) | − | 2.90325e8i | − | 0.709124i | ||||||
\(83\) | −5.68408e8 | −1.31465 | −0.657323 | − | 0.753609i | \(-0.728311\pi\) | ||||
−0.657323 | + | 0.753609i | \(0.728311\pi\) | |||||||
\(84\) | −4.82825e7 | −0.105811 | ||||||||
\(85\) | −2.84289e7 | + | 1.71633e7i | −0.0590711 | + | 0.0356629i | ||||
\(86\) | −6.29517e8 | −1.24098 | ||||||||
\(87\) | 1.14425e8 | 0.214133 | ||||||||
\(88\) | − | 3.12106e8i | − | 0.554792i | ||||||
\(89\) | 2.61194e8 | 0.441275 | 0.220637 | − | 0.975356i | \(-0.429186\pi\) | ||||
0.220637 | + | 0.975356i | \(0.429186\pi\) | |||||||
\(90\) | − | 7.72106e7i | − | 0.124047i | ||||||
\(91\) | 1.92010e8i | 0.293520i | ||||||||
\(92\) | − | 5.46009e7i | − | 0.0794611i | ||||||
\(93\) | 1.96558e9 | 2.72470 | ||||||||
\(94\) | −2.88357e8 | −0.380939 | ||||||||
\(95\) | 4.14396e7i | 0.0521987i | ||||||||
\(96\) | − | 7.82030e8i | − | 0.939730i | ||||||
\(97\) | − | 1.04492e9i | − | 1.19842i | −0.800590 | − | 0.599212i | \(-0.795481\pi\) | ||
0.800590 | − | 0.599212i | \(-0.204519\pi\) | |||||||
\(98\) | 9.92405e8 | 1.08685 | ||||||||
\(99\) | − | 1.04911e9i | − | 1.09764i | ||||||
\(100\) | 3.00809e8 | 0.300809 | ||||||||
\(101\) | 2.97630e7 | 0.0284597 | 0.0142299 | − | 0.999899i | \(-0.495470\pi\) | ||||
0.0142299 | + | 0.999899i | \(0.495470\pi\) | |||||||
\(102\) | −1.71388e9 | + | 1.03472e9i | −1.56776 | + | 0.946503i | ||||
\(103\) | 1.60523e9 | 1.40530 | 0.702650 | − | 0.711536i | \(-0.252000\pi\) | ||||
0.702650 | + | 0.711536i | \(0.252000\pi\) | |||||||
\(104\) | −1.27816e9 | −1.07136 | ||||||||
\(105\) | − | 3.00872e7i | − | 0.0241562i | ||||||
\(106\) | 9.14849e8 | 0.703838 | ||||||||
\(107\) | 2.35483e9i | 1.73673i | 0.495925 | + | 0.868365i | \(0.334829\pi\) | ||||
−0.495925 | + | 0.868365i | \(0.665171\pi\) | |||||||
\(108\) | − | 3.94572e8i | − | 0.279074i | ||||||
\(109\) | − | 1.68886e9i | − | 1.14597i | −0.819566 | − | 0.572985i | \(-0.805785\pi\) | ||
0.819566 | − | 0.572985i | \(-0.194215\pi\) | |||||||
\(110\) | −8.42473e7 | −0.0548642 | ||||||||
\(111\) | −3.65227e9 | −2.28354 | ||||||||
\(112\) | − | 4.39884e8i | − | 0.264154i | ||||||
\(113\) | 2.39661e9i | 1.38275i | 0.722496 | + | 0.691375i | \(0.242995\pi\) | ||||
−0.722496 | + | 0.691375i | \(0.757005\pi\) | |||||||
\(114\) | 2.49826e9i | 1.38537i | ||||||||
\(115\) | 3.40245e7 | 0.0181406 | ||||||||
\(116\) | − | 7.86480e7i | − | 0.0403299i | ||||||
\(117\) | −4.29638e9 | −2.11966 | ||||||||
\(118\) | 1.29995e9 | 0.617245 | ||||||||
\(119\) | −4.08533e8 | + | 2.46643e8i | −0.186752 | + | 0.112748i | ||||
\(120\) | 2.00282e8 | 0.0881712 | ||||||||
\(121\) | 1.21323e9 | 0.514527 | ||||||||
\(122\) | 3.95156e9i | 1.61491i | ||||||||
\(123\) | 2.53144e9 | 0.997227 | ||||||||
\(124\) | − | 1.35101e9i | − | 0.513171i | ||||||
\(125\) | 3.75794e8i | 0.137675i | ||||||||
\(126\) | − | 1.10954e9i | − | 0.392172i | ||||||
\(127\) | 4.20715e9 | 1.43506 | 0.717532 | − | 0.696526i | \(-0.245272\pi\) | ||||
0.717532 | + | 0.696526i | \(0.245272\pi\) | |||||||
\(128\) | 3.65909e9 | 1.20484 | ||||||||
\(129\) | − | 5.48896e9i | − | 1.74516i | ||||||
\(130\) | 3.45015e8i | 0.105948i | ||||||||
\(131\) | − | 1.46332e9i | − | 0.434129i | −0.976157 | − | 0.217064i | \(-0.930352\pi\) | ||
0.976157 | − | 0.217064i | \(-0.0696481\pi\) | |||||||
\(132\) | −1.17882e9 | −0.337959 | ||||||||
\(133\) | 5.95502e8i | 0.165025i | ||||||||
\(134\) | −6.30103e9 | −1.68826 | ||||||||
\(135\) | 2.45877e8 | 0.0637113 | ||||||||
\(136\) | −1.64184e9 | − | 2.71950e9i | −0.411533 | − | 0.681653i | ||||
\(137\) | −4.13890e9 | −1.00379 | −0.501894 | − | 0.864929i | \(-0.667363\pi\) | ||||
−0.501894 | + | 0.864929i | \(0.667363\pi\) | |||||||
\(138\) | 2.05122e9 | 0.481457 | ||||||||
\(139\) | − | 1.74238e9i | − | 0.395892i | −0.980213 | − | 0.197946i | \(-0.936573\pi\) | ||
0.980213 | − | 0.197946i | \(-0.0634271\pi\) | |||||||
\(140\) | −2.06800e7 | −0.00454960 | ||||||||
\(141\) | − | 2.51428e9i | − | 0.535708i | ||||||
\(142\) | − | 9.77895e9i | − | 2.01834i | ||||||
\(143\) | 4.68793e9i | 0.937496i | ||||||||
\(144\) | 9.84275e9 | 1.90759 | ||||||||
\(145\) | 4.90094e7 | 0.00920712 | ||||||||
\(146\) | 3.58243e8i | 0.0652514i | ||||||||
\(147\) | 8.65309e9i | 1.52842i | ||||||||
\(148\) | 2.51033e9i | 0.430084i | ||||||||
\(149\) | 4.80220e9 | 0.798183 | 0.399092 | − | 0.916911i | \(-0.369326\pi\) | ||||
0.399092 | + | 0.916911i | \(0.369326\pi\) | |||||||
\(150\) | 1.13007e10i | 1.82261i | ||||||||
\(151\) | 1.22756e9 | 0.192152 | 0.0960762 | − | 0.995374i | \(-0.469371\pi\) | ||||
0.0960762 | + | 0.995374i | \(0.469371\pi\) | |||||||
\(152\) | −3.96410e9 | −0.602349 | ||||||||
\(153\) | −5.51883e9 | − | 9.14126e9i | −0.814208 | − | 1.34864i | ||||
\(154\) | −1.21066e9 | −0.173452 | ||||||||
\(155\) | 8.41883e8 | 0.117155 | ||||||||
\(156\) | 4.82758e9i | 0.652632i | ||||||||
\(157\) | 1.72654e9 | 0.226792 | 0.113396 | − | 0.993550i | \(-0.463827\pi\) | ||||
0.113396 | + | 0.993550i | \(0.463827\pi\) | |||||||
\(158\) | − | 1.45934e10i | − | 1.86294i | ||||||
\(159\) | 7.97686e9i | 0.989794i | ||||||||
\(160\) | − | 3.34953e8i | − | 0.0404058i | ||||||
\(161\) | 4.88944e8 | 0.0573512 | ||||||||
\(162\) | −9.36411e8 | −0.106819 | ||||||||
\(163\) | − | 2.27451e9i | − | 0.252374i | −0.992006 | − | 0.126187i | \(-0.959726\pi\) | ||
0.992006 | − | 0.126187i | \(-0.0402739\pi\) | |||||||
\(164\) | − | 1.73995e9i | − | 0.187818i | ||||||
\(165\) | − | 7.34580e8i | − | 0.0771545i | ||||||
\(166\) | −1.46772e10 | −1.50022 | ||||||||
\(167\) | 1.42586e10i | 1.41857i | 0.704921 | + | 0.709286i | \(0.250982\pi\) | ||||
−0.704921 | + | 0.709286i | \(0.749018\pi\) | |||||||
\(168\) | 2.87812e9 | 0.278752 | ||||||||
\(169\) | 8.59384e9 | 0.810396 | ||||||||
\(170\) | −7.34078e8 | + | 4.43183e8i | −0.0674096 | + | 0.0406971i | ||||
\(171\) | −1.33248e10 | −1.19173 | ||||||||
\(172\) | −3.77275e9 | −0.328685 | ||||||||
\(173\) | − | 6.92744e9i | − | 0.587984i | −0.955808 | − | 0.293992i | \(-0.905016\pi\) | ||
0.955808 | − | 0.293992i | \(-0.0949839\pi\) | |||||||
\(174\) | 2.95462e9 | 0.244360 | ||||||||
\(175\) | 2.69370e9i | 0.217109i | ||||||||
\(176\) | − | 1.07398e10i | − | 0.843701i | ||||||
\(177\) | 1.13347e10i | 0.868020i | ||||||||
\(178\) | 6.74444e9 | 0.503565 | ||||||||
\(179\) | 1.32700e10 | 0.966120 | 0.483060 | − | 0.875587i | \(-0.339525\pi\) | ||||
0.483060 | + | 0.875587i | \(0.339525\pi\) | |||||||
\(180\) | − | 4.62731e8i | − | 0.0328550i | ||||||
\(181\) | 8.95066e9i | 0.619871i | 0.950758 | + | 0.309936i | \(0.100308\pi\) | ||||
−0.950758 | + | 0.309936i | \(0.899692\pi\) | |||||||
\(182\) | 4.95799e9i | 0.334953i | ||||||||
\(183\) | −3.44549e10 | −2.27102 | ||||||||
\(184\) | 3.25477e9i | 0.209334i | ||||||||
\(185\) | −1.56431e9 | −0.0981861 | ||||||||
\(186\) | 5.07544e10 | 3.10932 | ||||||||
\(187\) | −9.97436e9 | + | 6.02180e9i | −0.596483 | + | 0.360113i | ||||
\(188\) | −1.72815e9 | −0.100896 | ||||||||
\(189\) | 3.53334e9 | 0.201422 | ||||||||
\(190\) | 1.07003e9i | 0.0595671i | ||||||||
\(191\) | −2.10560e9 | −0.114479 | −0.0572394 | − | 0.998360i | \(-0.518230\pi\) | ||||
−0.0572394 | + | 0.998360i | \(0.518230\pi\) | |||||||
\(192\) | 1.63983e10i | 0.870851i | ||||||||
\(193\) | 5.10730e9i | 0.264962i | 0.991186 | + | 0.132481i | \(0.0422944\pi\) | ||||
−0.991186 | + | 0.132481i | \(0.957706\pi\) | |||||||
\(194\) | − | 2.69815e10i | − | 1.36760i | ||||||
\(195\) | −3.00830e9 | −0.148993 | ||||||||
\(196\) | 5.94758e9 | 0.287864 | ||||||||
\(197\) | − | 1.85517e10i | − | 0.877578i | −0.898590 | − | 0.438789i | \(-0.855408\pi\) | ||
0.898590 | − | 0.438789i | \(-0.144592\pi\) | |||||||
\(198\) | − | 2.70896e10i | − | 1.25259i | ||||||
\(199\) | − | 1.37208e10i | − | 0.620211i | −0.950702 | − | 0.310105i | \(-0.899636\pi\) | ||
0.950702 | − | 0.310105i | \(-0.100364\pi\) | |||||||
\(200\) | −1.79312e10 | −0.792456 | ||||||||
\(201\) | − | 5.49407e10i | − | 2.37417i | ||||||
\(202\) | 7.68527e8 | 0.0324771 | ||||||||
\(203\) | 7.04282e8 | 0.0291082 | ||||||||
\(204\) | −1.02715e10 | + | 6.20117e9i | −0.415238 | + | 0.250691i | ||||
\(205\) | 1.08425e9 | 0.0428781 | ||||||||
\(206\) | 4.14494e10 | 1.60367 | ||||||||
\(207\) | 1.09405e10i | 0.414163i | ||||||||
\(208\) | −4.39823e10 | −1.62927 | ||||||||
\(209\) | 1.45392e10i | 0.527087i | ||||||||
\(210\) | − | 7.76896e8i | − | 0.0275662i | ||||||
\(211\) | − | 6.12032e9i | − | 0.212570i | −0.994336 | − | 0.106285i | \(-0.966104\pi\) | ||
0.994336 | − | 0.106285i | \(-0.0338957\pi\) | |||||||
\(212\) | 5.48278e9 | 0.186419 | ||||||||
\(213\) | 8.52658e10 | 2.83835 | ||||||||
\(214\) | 6.08053e10i | 1.98189i | ||||||||
\(215\) | − | 2.35099e9i | − | 0.0750373i | ||||||
\(216\) | 2.35205e10i | 0.735199i | ||||||||
\(217\) | 1.20982e10 | 0.370382 | ||||||||
\(218\) | − | 4.36088e10i | − | 1.30774i | ||||||
\(219\) | −3.12363e9 | −0.0917617 | ||||||||
\(220\) | −5.04902e8 | −0.0145313 | ||||||||
\(221\) | 2.46609e10 | + | 4.08477e10i | 0.695414 | + | 1.15187i | ||||
\(222\) | −9.43071e10 | −2.60589 | ||||||||
\(223\) | −6.31228e9 | −0.170928 | −0.0854642 | − | 0.996341i | \(-0.527237\pi\) | ||||
−0.0854642 | + | 0.996341i | \(0.527237\pi\) | |||||||
\(224\) | − | 4.81339e9i | − | 0.127742i | ||||||
\(225\) | −6.02737e10 | −1.56786 | ||||||||
\(226\) | 6.18840e10i | 1.57794i | ||||||||
\(227\) | 5.43032e10i | 1.35740i | 0.734413 | + | 0.678702i | \(0.237457\pi\) | ||||
−0.734413 | + | 0.678702i | \(0.762543\pi\) | |||||||
\(228\) | 1.49723e10i | 0.366929i | ||||||||
\(229\) | −1.03751e10 | −0.249306 | −0.124653 | − | 0.992200i | \(-0.539782\pi\) | ||||
−0.124653 | + | 0.992200i | \(0.539782\pi\) | |||||||
\(230\) | 8.78564e8 | 0.0207013 | ||||||||
\(231\) | − | 1.05562e10i | − | 0.243923i | ||||||
\(232\) | 4.68822e9i | 0.106246i | ||||||||
\(233\) | − | 5.93158e10i | − | 1.31846i | −0.751939 | − | 0.659232i | \(-0.770881\pi\) | ||
0.751939 | − | 0.659232i | \(-0.229119\pi\) | |||||||
\(234\) | −1.10939e11 | −2.41887 | ||||||||
\(235\) | − | 1.07690e9i | − | 0.0230340i | ||||||
\(236\) | 7.79073e9 | 0.163484 | ||||||||
\(237\) | 1.27245e11 | 2.61982 | ||||||||
\(238\) | −1.05489e10 | + | 6.36869e9i | −0.213114 | + | 0.128663i | ||||
\(239\) | −6.57143e10 | −1.30278 | −0.651388 | − | 0.758745i | \(-0.725813\pi\) | ||||
−0.651388 | + | 0.758745i | \(0.725813\pi\) | |||||||
\(240\) | 6.89184e9 | 0.134086 | ||||||||
\(241\) | − | 2.02970e10i | − | 0.387574i | −0.981044 | − | 0.193787i | \(-0.937923\pi\) | ||
0.981044 | − | 0.193787i | \(-0.0620771\pi\) | |||||||
\(242\) | 3.13274e10 | 0.587158 | ||||||||
\(243\) | − | 5.83511e10i | − | 1.07355i | ||||||
\(244\) | 2.36820e10i | 0.427725i | ||||||||
\(245\) | 3.70623e9i | 0.0657180i | ||||||||
\(246\) | 6.53655e10 | 1.13800 | ||||||||
\(247\) | 5.95420e10 | 1.01786 | ||||||||
\(248\) | 8.05342e10i | 1.35191i | ||||||||
\(249\) | − | 1.27975e11i | − | 2.10974i | ||||||
\(250\) | 9.70357e9i | 0.157109i | ||||||||
\(251\) | −8.71654e10 | −1.38616 | −0.693078 | − | 0.720863i | \(-0.743746\pi\) | ||||
−0.693078 | + | 0.720863i | \(0.743746\pi\) | |||||||
\(252\) | − | 6.64960e9i | − | 0.103871i | ||||||
\(253\) | 1.19376e10 | 0.183178 | ||||||||
\(254\) | 1.08635e11 | 1.63764 | ||||||||
\(255\) | −3.86426e9 | − | 6.40066e9i | −0.0572315 | − | 0.0947968i | ||||
\(256\) | 5.71921e10 | 0.832254 | ||||||||
\(257\) | −1.20306e10 | −0.172023 | −0.0860115 | − | 0.996294i | \(-0.527412\pi\) | ||||
−0.0860115 | + | 0.996294i | \(0.527412\pi\) | |||||||
\(258\) | − | 1.41733e11i | − | 1.99151i | ||||||
\(259\) | −2.24797e10 | −0.310414 | ||||||||
\(260\) | 2.06771e9i | 0.0280614i | ||||||||
\(261\) | 1.57589e10i | 0.210205i | ||||||||
\(262\) | − | 3.77851e10i | − | 0.495411i | ||||||
\(263\) | 3.51365e10 | 0.452853 | 0.226426 | − | 0.974028i | \(-0.427296\pi\) | ||||
0.226426 | + | 0.974028i | \(0.427296\pi\) | |||||||
\(264\) | 7.02695e10 | 0.890327 | ||||||||
\(265\) | 3.41659e9i | 0.0425585i | ||||||||
\(266\) | 1.53768e10i | 0.188321i | ||||||||
\(267\) | 5.88069e10i | 0.708154i | ||||||||
\(268\) | −3.77627e10 | −0.447153 | ||||||||
\(269\) | 8.30055e10i | 0.966544i | 0.875470 | + | 0.483272i | \(0.160552\pi\) | ||||
−0.875470 | + | 0.483272i | \(0.839448\pi\) | |||||||
\(270\) | 6.34893e9 | 0.0727048 | ||||||||
\(271\) | −5.57473e10 | −0.627858 | −0.313929 | − | 0.949446i | \(-0.601645\pi\) | ||||
−0.313929 | + | 0.949446i | \(0.601645\pi\) | |||||||
\(272\) | −5.64966e10 | − | 9.35797e10i | −0.625839 | − | 1.03662i | ||||
\(273\) | −4.32303e10 | −0.471038 | ||||||||
\(274\) | −1.06873e11 | −1.14548 | ||||||||
\(275\) | 6.57668e10i | 0.693441i | ||||||||
\(276\) | 1.22932e10 | 0.127519 | ||||||||
\(277\) | − | 1.84969e11i | − | 1.88773i | −0.330333 | − | 0.943864i | \(-0.607161\pi\) | ||
0.330333 | − | 0.943864i | \(-0.392839\pi\) | |||||||
\(278\) | − | 4.49910e10i | − | 0.451777i | ||||||
\(279\) | 2.70706e11i | 2.67472i | ||||||||
\(280\) | 1.23274e9 | 0.0119856 | ||||||||
\(281\) | −1.35823e11 | −1.29956 | −0.649778 | − | 0.760124i | \(-0.725138\pi\) | ||||
−0.649778 | + | 0.760124i | \(0.725138\pi\) | |||||||
\(282\) | − | 6.49225e10i | − | 0.611328i | ||||||
\(283\) | 5.85987e10i | 0.543062i | 0.962430 | + | 0.271531i | \(0.0875299\pi\) | ||||
−0.962430 | + | 0.271531i | \(0.912470\pi\) | |||||||
\(284\) | − | 5.86061e10i | − | 0.534577i | ||||||
\(285\) | −9.32997e9 | −0.0837681 | ||||||||
\(286\) | 1.21050e11i | 1.06983i | ||||||||
\(287\) | 1.55810e10 | 0.135558 | ||||||||
\(288\) | 1.07703e11 | 0.922493 | ||||||||
\(289\) | −5.52326e10 | + | 1.04940e11i | −0.465752 | + | 0.884915i | ||||
\(290\) | 1.26550e9 | 0.0105068 | ||||||||
\(291\) | 2.35260e11 | 1.92322 | ||||||||
\(292\) | 2.14698e9i | 0.0172825i | ||||||||
\(293\) | −5.48232e10 | −0.434571 | −0.217285 | − | 0.976108i | \(-0.569720\pi\) | ||||
−0.217285 | + | 0.976108i | \(0.569720\pi\) | |||||||
\(294\) | 2.23436e11i | 1.74418i | ||||||||
\(295\) | 4.85478e9i | 0.0373225i | ||||||||
\(296\) | − | 1.49641e11i | − | 1.13302i | ||||||
\(297\) | 8.62667e10 | 0.643338 | ||||||||
\(298\) | 1.24000e11 | 0.910855 | ||||||||
\(299\) | − | 4.88876e10i | − | 0.353735i | ||||||
\(300\) | 6.77259e10i | 0.482735i | ||||||||
\(301\) | − | 3.37845e10i | − | 0.237229i | ||||||
\(302\) | 3.16974e10 | 0.219277 | ||||||||
\(303\) | 6.70103e9i | 0.0456720i | ||||||||
\(304\) | −1.36407e11 | −0.916023 | ||||||||
\(305\) | −1.47574e10 | −0.0976477 | ||||||||
\(306\) | −1.42505e11 | − | 2.36041e11i | −0.929143 | − | 1.53901i | ||||
\(307\) | −1.88055e11 | −1.20826 | −0.604132 | − | 0.796884i | \(-0.706480\pi\) | ||||
−0.604132 | + | 0.796884i | \(0.706480\pi\) | |||||||
\(308\) | −7.25562e9 | −0.0459406 | ||||||||
\(309\) | 3.61411e11i | 2.25521i | ||||||||
\(310\) | 2.17387e10 | 0.133692 | ||||||||
\(311\) | − | 1.81717e11i | − | 1.10147i | −0.834679 | − | 0.550737i | \(-0.814347\pi\) | ||
0.834679 | − | 0.550737i | \(-0.185653\pi\) | |||||||
\(312\) | − | 2.87773e11i | − | 1.71931i | ||||||
\(313\) | − | 2.21549e11i | − | 1.30473i | −0.757905 | − | 0.652364i | \(-0.773777\pi\) | ||
0.757905 | − | 0.652364i | \(-0.226223\pi\) | |||||||
\(314\) | 4.45819e10 | 0.258807 | ||||||||
\(315\) | 4.14369e9 | 0.0237132 | ||||||||
\(316\) | − | 8.74597e10i | − | 0.493419i | ||||||
\(317\) | 2.66841e11i | 1.48418i | 0.670301 | + | 0.742089i | \(0.266165\pi\) | ||||
−0.670301 | + | 0.742089i | \(0.733835\pi\) | |||||||
\(318\) | 2.05975e11i | 1.12951i | ||||||||
\(319\) | 1.71951e10 | 0.0929708 | ||||||||
\(320\) | 7.02360e9i | 0.0374442i | ||||||||
\(321\) | −5.30181e11 | −2.78709 | ||||||||
\(322\) | 1.26253e10 | 0.0654469 | ||||||||
\(323\) | 7.64835e10 | + | 1.26685e11i | 0.390982 | + | 0.647613i | ||||
\(324\) | −5.61200e9 | −0.0282921 | ||||||||
\(325\) | 2.69333e11 | 1.33910 | ||||||||
\(326\) | − | 5.87314e10i | − | 0.287999i | ||||||
\(327\) | 3.80239e11 | 1.83904 | ||||||||
\(328\) | 1.03718e11i | 0.494793i | ||||||||
\(329\) | − | 1.54754e10i | − | 0.0728215i | ||||||
\(330\) | − | 1.89680e10i | − | 0.0880456i | ||||||
\(331\) | 3.46276e11 | 1.58561 | 0.792804 | − | 0.609476i | \(-0.208620\pi\) | ||||
0.792804 | + | 0.609476i | \(0.208620\pi\) | |||||||
\(332\) | −8.79617e10 | −0.397349 | ||||||||
\(333\) | − | 5.03001e11i | − | 2.24166i | ||||||
\(334\) | 3.68177e11i | 1.61882i | ||||||||
\(335\) | − | 2.35318e10i | − | 0.102083i | ||||||
\(336\) | 9.90381e10 | 0.423912 | ||||||||
\(337\) | − | 2.14440e11i | − | 0.905671i | −0.891594 | − | 0.452836i | \(-0.850412\pi\) | ||
0.891594 | − | 0.452836i | \(-0.149588\pi\) | |||||||
\(338\) | 2.21906e11 | 0.924792 | ||||||||
\(339\) | −5.39586e11 | −2.21903 | ||||||||
\(340\) | −4.39940e9 | + | 2.65604e9i | −0.0178541 | + | 0.0107790i | ||||
\(341\) | 2.95377e11 | 1.18299 | ||||||||
\(342\) | −3.44067e11 | −1.35996 | ||||||||
\(343\) | 1.09181e11i | 0.425914i | ||||||||
\(344\) | 2.24894e11 | 0.865896 | ||||||||
\(345\) | 7.66048e9i | 0.0291119i | ||||||||
\(346\) | − | 1.78877e11i | − | 0.670984i | ||||||
\(347\) | − | 2.25675e11i | − | 0.835603i | −0.908538 | − | 0.417801i | \(-0.862801\pi\) | ||
0.908538 | − | 0.417801i | \(-0.137199\pi\) | |||||||
\(348\) | 1.77073e10 | 0.0647211 | ||||||||
\(349\) | −3.13210e10 | −0.113011 | −0.0565055 | − | 0.998402i | \(-0.517996\pi\) | ||||
−0.0565055 | + | 0.998402i | \(0.517996\pi\) | |||||||
\(350\) | 6.95554e10i | 0.247756i | ||||||||
\(351\) | − | 3.53285e11i | − | 1.24235i | ||||||
\(352\) | − | 1.17519e11i | − | 0.408006i | ||||||
\(353\) | 1.67054e11 | 0.572625 | 0.286312 | − | 0.958136i | \(-0.407571\pi\) | ||||
0.286312 | + | 0.958136i | \(0.407571\pi\) | |||||||
\(354\) | 2.92679e11i | 0.990551i | ||||||||
\(355\) | 3.65204e10 | 0.122041 | ||||||||
\(356\) | 4.04201e10 | 0.133374 | ||||||||
\(357\) | −5.55307e10 | − | 9.19797e10i | −0.180936 | − | 0.299699i | ||||
\(358\) | 3.42650e11 | 1.10250 | ||||||||
\(359\) | −5.25130e11 | −1.66856 | −0.834280 | − | 0.551341i | \(-0.814116\pi\) | ||||
−0.834280 | + | 0.551341i | \(0.814116\pi\) | |||||||
\(360\) | 2.75834e10i | 0.0865540i | ||||||||
\(361\) | −1.38024e11 | −0.427731 | ||||||||
\(362\) | 2.31120e11i | 0.707373i | ||||||||
\(363\) | 2.73154e11i | 0.825709i | ||||||||
\(364\) | 2.97137e10i | 0.0887157i | ||||||||
\(365\) | −1.33789e9 | −0.00394551 | ||||||||
\(366\) | −8.89677e11 | −2.59160 | ||||||||
\(367\) | − | 9.23982e10i | − | 0.265868i | −0.991125 | − | 0.132934i | \(-0.957560\pi\) | ||
0.991125 | − | 0.132934i | \(-0.0424399\pi\) | |||||||
\(368\) | 1.11999e11i | 0.318345i | ||||||||
\(369\) | 3.48637e11i | 0.978936i | ||||||||
\(370\) | −4.03929e10 | −0.112046 | ||||||||
\(371\) | 4.90975e10i | 0.134548i | ||||||||
\(372\) | 3.04176e11 | 0.823533 | ||||||||
\(373\) | 1.27208e11 | 0.340272 | 0.170136 | − | 0.985421i | \(-0.445579\pi\) | ||||
0.170136 | + | 0.985421i | \(0.445579\pi\) | |||||||
\(374\) | −2.57553e11 | + | 1.55492e11i | −0.680682 | + | 0.410947i | ||||
\(375\) | −8.46085e10 | −0.220940 | ||||||||
\(376\) | 1.03015e11 | 0.265801 | ||||||||
\(377\) | − | 7.04185e10i | − | 0.179536i | ||||||
\(378\) | 9.12363e10 | 0.229855 | ||||||||
\(379\) | − | 4.08652e11i | − | 1.01737i | −0.860954 | − | 0.508683i | \(-0.830132\pi\) | ||
0.860954 | − | 0.508683i | \(-0.169868\pi\) | |||||||
\(380\) | 6.41282e9i | 0.0157769i | ||||||||
\(381\) | 9.47223e11i | 2.30298i | ||||||||
\(382\) | −5.43697e10 | −0.130639 | ||||||||
\(383\) | 2.61140e11 | 0.620123 | 0.310062 | − | 0.950716i | \(-0.399650\pi\) | ||||
0.310062 | + | 0.950716i | \(0.399650\pi\) | |||||||
\(384\) | 8.23829e11i | 1.93351i | ||||||||
\(385\) | − | 4.52133e9i | − | 0.0104880i | ||||||
\(386\) | 1.31878e11i | 0.302364i | ||||||||
\(387\) | 7.55955e11 | 1.71316 | ||||||||
\(388\) | − | 1.61702e11i | − | 0.362221i | ||||||
\(389\) | −3.51283e11 | −0.777829 | −0.388914 | − | 0.921274i | \(-0.627150\pi\) | ||||
−0.388914 | + | 0.921274i | \(0.627150\pi\) | |||||||
\(390\) | −7.76789e10 | −0.170025 | ||||||||
\(391\) | 1.04017e11 | − | 6.27977e10i | 0.225064 | − | 0.135878i | ||||
\(392\) | −3.54536e11 | −0.758355 | ||||||||
\(393\) | 3.29461e11 | 0.696686 | ||||||||
\(394\) | − | 4.79033e11i | − | 1.00146i | ||||||
\(395\) | 5.45004e10 | 0.112645 | ||||||||
\(396\) | − | 1.62350e11i | − | 0.331760i | ||||||
\(397\) | 4.17307e11i | 0.843137i | 0.906797 | + | 0.421569i | \(0.138520\pi\) | ||||
−0.906797 | + | 0.421569i | \(0.861480\pi\) | |||||||
\(398\) | − | 3.54291e11i | − | 0.707760i | ||||||
\(399\) | −1.34075e11 | −0.264831 | ||||||||
\(400\) | −6.17026e11 | −1.20513 | ||||||||
\(401\) | 4.93060e11i | 0.952248i | 0.879378 | + | 0.476124i | \(0.157959\pi\) | ||||
−0.879378 | + | 0.476124i | \(0.842041\pi\) | |||||||
\(402\) | − | 1.41865e12i | − | 2.70931i | ||||||
\(403\) | − | 1.20965e12i | − | 2.28447i | ||||||
\(404\) | 4.60585e9 | 0.00860189 | ||||||||
\(405\) | − | 3.49711e9i | − | 0.00645895i | ||||||
\(406\) | 1.81856e10 | 0.0332171 | ||||||||
\(407\) | −5.48842e11 | −0.991454 | ||||||||
\(408\) | 6.12284e11 | − | 3.69653e11i | 1.09391 | − | 0.660425i | ||||
\(409\) | 2.79374e11 | 0.493663 | 0.246831 | − | 0.969058i | \(-0.420611\pi\) | ||||
0.246831 | + | 0.969058i | \(0.420611\pi\) | |||||||
\(410\) | 2.79969e10 | 0.0489308 | ||||||||
\(411\) | − | 9.31857e11i | − | 1.61087i | ||||||
\(412\) | 2.48410e11 | 0.424748 | ||||||||
\(413\) | 6.97649e10i | 0.117995i | ||||||||
\(414\) | 2.82500e11i | 0.472626i | ||||||||
\(415\) | − | 5.48132e10i | − | 0.0907129i | ||||||
\(416\) | −4.81272e11 | −0.787900 | ||||||||
\(417\) | 3.92291e11 | 0.635325 | ||||||||
\(418\) | 3.75424e11i | 0.601491i | ||||||||
\(419\) | − | 4.89354e10i | − | 0.0775640i | −0.999248 | − | 0.0387820i | \(-0.987652\pi\) | ||
0.999248 | − | 0.0387820i | \(-0.0123478\pi\) | |||||||
\(420\) | − | 4.65601e9i | − | 0.00730117i | ||||||
\(421\) | 9.73572e11 | 1.51042 | 0.755211 | − | 0.655481i | \(-0.227534\pi\) | ||||
0.755211 | + | 0.655481i | \(0.227534\pi\) | |||||||
\(422\) | − | 1.58036e11i | − | 0.242577i | ||||||
\(423\) | 3.46274e11 | 0.525882 | ||||||||
\(424\) | −3.26829e11 | −0.491105 | ||||||||
\(425\) | 3.45966e11 | + | 5.73050e11i | 0.514380 | + | 0.852006i | ||||
\(426\) | 2.20169e12 | 3.23902 | ||||||||
\(427\) | −2.12070e11 | −0.308712 | ||||||||
\(428\) | 3.64412e11i | 0.524923i | ||||||||
\(429\) | −1.05547e12 | −1.50449 | ||||||||
\(430\) | − | 6.07061e10i | − | 0.0856296i | ||||||
\(431\) | 3.60887e11i | 0.503760i | 0.967758 | + | 0.251880i | \(0.0810489\pi\) | ||||
−0.967758 | + | 0.251880i | \(0.918951\pi\) | |||||||
\(432\) | 8.09356e11i | 1.11805i | ||||||||
\(433\) | −1.32088e12 | −1.80579 | −0.902895 | − | 0.429862i | \(-0.858562\pi\) | ||||
−0.902895 | + | 0.429862i | \(0.858562\pi\) | |||||||
\(434\) | 3.12393e11 | 0.422666 | ||||||||
\(435\) | 1.10343e10i | 0.0147755i | ||||||||
\(436\) | − | 2.61352e11i | − | 0.346367i | ||||||
\(437\) | − | 1.51621e11i | − | 0.198880i | ||||||
\(438\) | −8.06570e10 | −0.104715 | ||||||||
\(439\) | − | 4.29288e11i | − | 0.551643i | −0.961209 | − | 0.275822i | \(-0.911050\pi\) | ||
0.961209 | − | 0.275822i | \(-0.0889499\pi\) | |||||||
\(440\) | 3.00973e10 | 0.0382816 | ||||||||
\(441\) | −1.19173e12 | −1.50039 | ||||||||
\(442\) | 6.36781e11 | + | 1.05475e12i | 0.793579 | + | 1.31446i | ||||
\(443\) | −9.88207e11 | −1.21908 | −0.609538 | − | 0.792757i | \(-0.708645\pi\) | ||||
−0.609538 | + | 0.792757i | \(0.708645\pi\) | |||||||
\(444\) | −5.65191e11 | −0.690195 | ||||||||
\(445\) | 2.51877e10i | 0.0304487i | ||||||||
\(446\) | −1.62993e11 | −0.195057 | ||||||||
\(447\) | 1.08120e12i | 1.28092i | ||||||||
\(448\) | 1.00932e11i | 0.118379i | ||||||||
\(449\) | − | 5.27610e11i | − | 0.612639i | −0.951929 | − | 0.306319i | \(-0.900902\pi\) | ||
0.951929 | − | 0.306319i | \(-0.0990975\pi\) | |||||||
\(450\) | −1.55636e12 | −1.78918 | ||||||||
\(451\) | 3.80410e11 | 0.432970 | ||||||||
\(452\) | 3.70877e11i | 0.417933i | ||||||||
\(453\) | 2.76380e11i | 0.308365i | ||||||||
\(454\) | 1.40219e12i | 1.54902i | ||||||||
\(455\) | −1.85161e10 | −0.0202534 | ||||||||
\(456\) | − | 8.92501e11i | − | 0.966645i | ||||||
\(457\) | 1.13024e11 | 0.121213 | 0.0606064 | − | 0.998162i | \(-0.480697\pi\) | ||||
0.0606064 | + | 0.998162i | \(0.480697\pi\) | |||||||
\(458\) | −2.67901e11 | −0.284498 | ||||||||
\(459\) | 7.51673e11 | − | 4.53806e11i | 0.790446 | − | 0.477214i | ||||
\(460\) | 5.26532e9 | 0.00548295 | ||||||||
\(461\) | 1.11660e12 | 1.15145 | 0.575725 | − | 0.817643i | \(-0.304720\pi\) | ||||
0.575725 | + | 0.817643i | \(0.304720\pi\) | |||||||
\(462\) | − | 2.72576e11i | − | 0.278355i | ||||||
\(463\) | −3.92248e11 | −0.396685 | −0.198343 | − | 0.980133i | \(-0.563556\pi\) | ||||
−0.198343 | + | 0.980133i | \(0.563556\pi\) | |||||||
\(464\) | 1.61325e11i | 0.161573i | ||||||||
\(465\) | 1.89547e11i | 0.188009i | ||||||||
\(466\) | − | 1.53162e12i | − | 1.50458i | ||||||
\(467\) | 1.59510e11 | 0.155189 | 0.0775946 | − | 0.996985i | \(-0.475276\pi\) | ||||
0.0775946 | + | 0.996985i | \(0.475276\pi\) | |||||||
\(468\) | −6.64868e11 | −0.640662 | ||||||||
\(469\) | − | 3.38160e11i | − | 0.322734i | ||||||
\(470\) | − | 2.78071e10i | − | 0.0262855i | ||||||
\(471\) | 3.88724e11i | 0.363955i | ||||||||
\(472\) | −4.64406e11 | −0.430684 | ||||||||
\(473\) | − | 8.24850e11i | − | 0.757705i | ||||||
\(474\) | 3.28565e12 | 2.98964 | ||||||||
\(475\) | 8.35312e11 | 0.752883 | ||||||||
\(476\) | −6.32209e10 | + | 3.81682e10i | −0.0564455 | + | 0.0340777i | ||||
\(477\) | −1.09860e12 | −0.971640 | ||||||||
\(478\) | −1.69684e12 | −1.48668 | ||||||||
\(479\) | 4.37040e11i | 0.379325i | 0.981849 | + | 0.189662i | \(0.0607393\pi\) | ||||
−0.981849 | + | 0.189662i | \(0.939261\pi\) | |||||||
\(480\) | 7.54134e10 | 0.0648429 | ||||||||
\(481\) | 2.24766e12i | 1.91460i | ||||||||
\(482\) | − | 5.24099e11i | − | 0.442284i | ||||||
\(483\) | 1.10084e11i | 0.0920367i | ||||||||
\(484\) | 1.87748e11 | 0.155515 | ||||||||
\(485\) | 1.00765e11 | 0.0826933 | ||||||||
\(486\) | − | 1.50672e12i | − | 1.22509i | ||||||
\(487\) | 1.05048e12i | 0.846270i | 0.906067 | + | 0.423135i | \(0.139070\pi\) | ||||
−0.906067 | + | 0.423135i | \(0.860930\pi\) | |||||||
\(488\) | − | 1.41169e12i | − | 1.12681i | ||||||
\(489\) | 5.12097e11 | 0.405007 | ||||||||
\(490\) | 9.57004e10i | 0.0749948i | ||||||||
\(491\) | 1.77945e12 | 1.38172 | 0.690859 | − | 0.722990i | \(-0.257233\pi\) | ||||
0.690859 | + | 0.722990i | \(0.257233\pi\) | |||||||
\(492\) | 3.91742e11 | 0.301410 | ||||||||
\(493\) | 1.49827e11 | − | 9.04548e10i | 0.114230 | − | 0.0689637i | ||||
\(494\) | 1.53746e12 | 1.16154 | ||||||||
\(495\) | 1.01168e11 | 0.0757393 | ||||||||
\(496\) | 2.77123e12i | 2.05592i | ||||||||
\(497\) | 5.24810e11 | 0.385832 | ||||||||
\(498\) | − | 3.30451e12i | − | 2.40755i | ||||||
\(499\) | − | 1.14978e12i | − | 0.830162i | −0.909785 | − | 0.415081i | \(-0.863753\pi\) | ||
0.909785 | − | 0.415081i | \(-0.136247\pi\) | |||||||
\(500\) | 5.81544e10i | 0.0416119i | ||||||||
\(501\) | −3.21026e12 | −2.27651 | ||||||||
\(502\) | −2.25074e12 | −1.58183 | ||||||||
\(503\) | − | 1.33344e12i | − | 0.928788i | −0.885629 | − | 0.464394i | \(-0.846272\pi\) | ||
0.885629 | − | 0.464394i | \(-0.153728\pi\) | |||||||
\(504\) | 3.96383e11i | 0.273639i | ||||||||
\(505\) | 2.87013e9i | 0.00196377i | ||||||||
\(506\) | 3.08247e11 | 0.209036 | ||||||||
\(507\) | 1.93487e12i | 1.30052i | ||||||||
\(508\) | 6.51059e11 | 0.433744 | ||||||||
\(509\) | −2.18589e12 | −1.44344 | −0.721721 | − | 0.692185i | \(-0.756648\pi\) | ||||
−0.721721 | + | 0.692185i | \(0.756648\pi\) | |||||||
\(510\) | −9.97809e10 | − | 1.65275e11i | −0.0653103 | − | 0.108178i | ||||
\(511\) | −1.92259e10 | −0.0124737 | ||||||||
\(512\) | −3.96666e11 | −0.255100 | ||||||||
\(513\) | − | 1.09568e12i | − | 0.698484i | ||||||
\(514\) | −3.10647e11 | −0.196306 | ||||||||
\(515\) | 1.54797e11i | 0.0969681i | ||||||||
\(516\) | − | 8.49421e11i | − | 0.527472i | ||||||
\(517\) | − | 3.77832e11i | − | 0.232590i | ||||||
\(518\) | −5.80459e11 | −0.354232 | ||||||||
\(519\) | 1.55969e12 | 0.943592 | ||||||||
\(520\) | − | 1.23256e11i | − | 0.0739256i | ||||||
\(521\) | 9.81356e11i | 0.583521i | 0.956491 | + | 0.291761i | \(0.0942411\pi\) | ||||
−0.956491 | + | 0.291761i | \(0.905759\pi\) | |||||||
\(522\) | 4.06918e11i | 0.239878i | ||||||||
\(523\) | 1.01562e11 | 0.0593572 | 0.0296786 | − | 0.999559i | \(-0.490552\pi\) | ||||
0.0296786 | + | 0.999559i | \(0.490552\pi\) | |||||||
\(524\) | − | 2.26450e11i | − | 0.131214i | ||||||
\(525\) | −6.06476e11 | −0.348415 | ||||||||
\(526\) | 9.07277e11 | 0.516778 | ||||||||
\(527\) | 2.57373e12 | − | 1.55383e12i | 1.45350 | − | 0.877518i | ||||
\(528\) | 2.41802e12 | 1.35396 | ||||||||
\(529\) | 1.67666e12 | 0.930883 | ||||||||
\(530\) | 8.82214e10i | 0.0485660i | ||||||||
\(531\) | −1.56105e12 | −0.852099 | ||||||||
\(532\) | 9.21544e10i | 0.0498785i | ||||||||
\(533\) | − | 1.55788e12i | − | 0.836107i | ||||||
\(534\) | 1.51848e12i | 0.808117i | ||||||||
\(535\) | −2.27083e11 | −0.119837 | ||||||||
\(536\) | 2.25104e12 | 1.17799 | ||||||||
\(537\) | 2.98768e12i | 1.55042i | ||||||||
\(538\) | 2.14333e12i | 1.10298i | ||||||||
\(539\) | 1.30034e12i | 0.663601i | ||||||||
\(540\) | 3.80497e10 | 0.0192566 | ||||||||
\(541\) | 2.29392e12i | 1.15131i | 0.817694 | + | 0.575653i | \(0.195252\pi\) | ||||
−0.817694 | + | 0.575653i | \(0.804748\pi\) | |||||||
\(542\) | −1.43948e12 | −0.716487 | ||||||||
\(543\) | −2.01521e12 | −0.994765 | ||||||||
\(544\) | −6.18209e11 | − | 1.02399e12i | −0.302650 | − | 0.501302i | ||||
\(545\) | 1.62861e11 | 0.0790739 | ||||||||
\(546\) | −1.11627e12 | −0.537531 | ||||||||
\(547\) | 4.31625e10i | 0.0206140i | 0.999947 | + | 0.0103070i | \(0.00328088\pi\) | ||||
−0.999947 | + | 0.0103070i | \(0.996719\pi\) | |||||||
\(548\) | −6.40498e11 | −0.303393 | ||||||||
\(549\) | − | 4.74522e12i | − | 2.22937i | ||||||
\(550\) | 1.69820e12i | 0.791328i | ||||||||
\(551\) | − | 2.18397e11i | − | 0.100940i | ||||||
\(552\) | −7.32798e11 | −0.335938 | ||||||||
\(553\) | 7.83189e11 | 0.356126 | ||||||||
\(554\) | − | 4.77618e12i | − | 2.15420i | ||||||
\(555\) | − | 3.52198e11i | − | 0.157568i | ||||||
\(556\) | − | 2.69635e11i | − | 0.119658i | ||||||
\(557\) | −1.26017e12 | −0.554730 | −0.277365 | − | 0.960765i | \(-0.589461\pi\) | ||||
−0.277365 | + | 0.960765i | \(0.589461\pi\) | |||||||
\(558\) | 6.99003e12i | 3.05229i | ||||||||
\(559\) | −3.37798e12 | −1.46320 | ||||||||
\(560\) | 4.24192e10 | 0.0182271 | ||||||||
\(561\) | −1.35578e12 | − | 2.24569e12i | −0.577907 | − | 0.957231i | ||||
\(562\) | −3.50716e12 | −1.48300 | ||||||||
\(563\) | 1.57680e12 | 0.661436 | 0.330718 | − | 0.943730i | \(-0.392709\pi\) | ||||
0.330718 | + | 0.943730i | \(0.392709\pi\) | |||||||
\(564\) | − | 3.89087e11i | − | 0.161916i | ||||||
\(565\) | −2.31111e11 | −0.0954121 | ||||||||
\(566\) | 1.51311e12i | 0.619721i | ||||||||
\(567\) | − | 5.02547e10i | − | 0.0204199i | ||||||
\(568\) | 3.49352e12i | 1.40830i | ||||||||
\(569\) | 4.44023e12 | 1.77583 | 0.887913 | − | 0.460012i | \(-0.152155\pi\) | ||||
0.887913 | + | 0.460012i | \(0.152155\pi\) | |||||||
\(570\) | −2.40914e11 | −0.0955928 | ||||||||
\(571\) | 2.59026e11i | 0.101972i | 0.998699 | + | 0.0509860i | \(0.0162364\pi\) | ||||
−0.998699 | + | 0.0509860i | \(0.983764\pi\) | |||||||
\(572\) | 7.25461e11i | 0.283356i | ||||||||
\(573\) | − | 4.74067e11i | − | 0.183715i | ||||||
\(574\) | 4.02324e11 | 0.154694 | ||||||||
\(575\) | − | 6.85842e11i | − | 0.261649i | ||||||
\(576\) | −2.25842e12 | −0.854878 | ||||||||
\(577\) | 2.66713e12 | 1.00173 | 0.500867 | − | 0.865524i | \(-0.333015\pi\) | ||||
0.500867 | + | 0.865524i | \(0.333015\pi\) | |||||||
\(578\) | −1.42619e12 | + | 2.70972e12i | −0.531498 | + | 1.00983i | ||||
\(579\) | −1.14989e12 | −0.425209 | ||||||||
\(580\) | 7.58425e9 | 0.00278283 | ||||||||
\(581\) | − | 7.87685e11i | − | 0.286787i | ||||||
\(582\) | 6.07477e12 | 2.19471 | ||||||||
\(583\) | 1.19872e12i | 0.429743i | ||||||||
\(584\) | − | 1.27982e11i | − | 0.0455293i | ||||||
\(585\) | − | 4.14312e11i | − | 0.146260i | ||||||
\(586\) | −1.41562e12 | −0.495915 | ||||||||
\(587\) | −4.82084e12 | −1.67591 | −0.837956 | − | 0.545738i | \(-0.816249\pi\) | ||||
−0.837956 | + | 0.545738i | \(0.816249\pi\) | |||||||
\(588\) | 1.33907e12i | 0.461962i | ||||||||
\(589\) | − | 3.75162e12i | − | 1.28440i | ||||||
\(590\) | 1.25358e11i | 0.0425910i | ||||||||
\(591\) | 4.17684e12 | 1.40833 | ||||||||
\(592\) | − | 5.14925e12i | − | 1.72304i | ||||||
\(593\) | 2.49924e12 | 0.829968 | 0.414984 | − | 0.909829i | \(-0.363787\pi\) | ||||
0.414984 | + | 0.909829i | \(0.363787\pi\) | |||||||
\(594\) | 2.22754e12 | 0.734152 | ||||||||
\(595\) | −2.37845e10 | − | 3.93960e10i | −0.00777977 | − | 0.0128862i | ||||
\(596\) | 7.43145e11 | 0.241249 | ||||||||
\(597\) | 3.08918e12 | 0.995310 | ||||||||
\(598\) | − | 1.26235e12i | − | 0.403669i | ||||||
\(599\) | −3.23334e12 | −1.02620 | −0.513098 | − | 0.858330i | \(-0.671502\pi\) | ||||
−0.513098 | + | 0.858330i | \(0.671502\pi\) | |||||||
\(600\) | − | 4.03715e12i | − | 1.27173i | ||||||
\(601\) | − | 5.50244e12i | − | 1.72036i | −0.509988 | − | 0.860181i | \(-0.670350\pi\) | ||
0.509988 | − | 0.860181i | \(-0.329650\pi\) | |||||||
\(602\) | − | 8.72367e11i | − | 0.270717i | ||||||
\(603\) | 7.56660e12 | 2.33063 | ||||||||
\(604\) | 1.89966e11 | 0.0580776 | ||||||||
\(605\) | 1.16995e11i | 0.0355032i | ||||||||
\(606\) | 1.73031e11i | 0.0521191i | ||||||||
\(607\) | 3.65674e12i | 1.09331i | 0.837357 | + | 0.546657i | \(0.184100\pi\) | ||||
−0.837357 | + | 0.546657i | \(0.815900\pi\) | |||||||
\(608\) | −1.49262e12 | −0.442980 | ||||||||
\(609\) | 1.58566e11i | 0.0467125i | ||||||||
\(610\) | −3.81060e11 | −0.111432 | ||||||||
\(611\) | −1.54732e12 | −0.449155 | ||||||||
\(612\) | −8.54043e11 | − | 1.41462e12i | −0.246093 | − | 0.407622i | ||||
\(613\) | 1.17726e12 | 0.336743 | 0.168372 | − | 0.985724i | \(-0.446149\pi\) | ||||
0.168372 | + | 0.985724i | \(0.446149\pi\) | |||||||
\(614\) | −4.85586e12 | −1.37882 | ||||||||
\(615\) | 2.44114e11i | 0.0688104i | ||||||||
\(616\) | 4.32508e11 | 0.121027 | ||||||||
\(617\) | 3.74523e12i | 1.04039i | 0.854048 | + | 0.520194i | \(0.174141\pi\) | ||||
−0.854048 | + | 0.520194i | \(0.825859\pi\) | |||||||
\(618\) | 9.33217e12i | 2.57356i | ||||||||
\(619\) | − | 6.72874e12i | − | 1.84215i | −0.389381 | − | 0.921077i | \(-0.627311\pi\) | ||
0.389381 | − | 0.921077i | \(-0.372689\pi\) | |||||||
\(620\) | 1.30282e11 | 0.0354097 | ||||||||
\(621\) | −8.99623e11 | −0.242744 | ||||||||
\(622\) | − | 4.69221e12i | − | 1.25696i | ||||||
\(623\) | 3.61956e11i | 0.0962631i | ||||||||
\(624\) | − | 9.90244e12i | − | 2.61464i | ||||||
\(625\) | 3.76030e12 | 0.985739 | ||||||||
\(626\) | − | 5.72073e12i | − | 1.48891i | ||||||
\(627\) | −3.27345e12 | −0.845865 | ||||||||
\(628\) | 2.67184e11 | 0.0685475 | ||||||||
\(629\) | −4.78226e12 | + | 2.88718e12i | −1.21816 | + | 0.735439i | ||||
\(630\) | 1.06996e11 | 0.0270605 | ||||||||
\(631\) | −4.61439e12 | −1.15873 | −0.579365 | − | 0.815068i | \(-0.696700\pi\) | ||||
−0.579365 | + | 0.815068i | \(0.696700\pi\) | |||||||
\(632\) | 5.21348e12i | 1.29987i | ||||||||
\(633\) | 1.37797e12 | 0.341131 | ||||||||
\(634\) | 6.89024e12i | 1.69369i | ||||||||
\(635\) | 4.05707e11i | 0.0990218i | ||||||||
\(636\) | 1.23443e12i | 0.299163i | ||||||||
\(637\) | 5.32524e12 | 1.28148 | ||||||||
\(638\) | 4.44003e11 | 0.106095 | ||||||||
\(639\) | 1.17430e13i | 2.78629i | ||||||||
\(640\) | 3.52856e11i | 0.0831357i | ||||||||
\(641\) | 7.42031e12i | 1.73605i | 0.496524 | + | 0.868023i | \(0.334609\pi\) | ||||
−0.496524 | + | 0.868023i | \(0.665391\pi\) | |||||||
\(642\) | −1.36901e13 | −3.18052 | ||||||||
\(643\) | − | 6.05336e12i | − | 1.39652i | −0.715845 | − | 0.698260i | \(-0.753958\pi\) | ||
0.715845 | − | 0.698260i | \(-0.246042\pi\) | |||||||
\(644\) | 7.56644e10 | 0.0173343 | ||||||||
\(645\) | 5.29316e11 | 0.120419 | ||||||||
\(646\) | 1.97492e12 | + | 3.27121e12i | 0.446173 | + | 0.739030i | ||||
\(647\) | −4.28077e12 | −0.960402 | −0.480201 | − | 0.877159i | \(-0.659436\pi\) | ||||
−0.480201 | + | 0.877159i | \(0.659436\pi\) | |||||||
\(648\) | 3.34532e11 | 0.0745333 | ||||||||
\(649\) | 1.70331e12i | 0.376872i | ||||||||
\(650\) | 6.95458e12 | 1.52813 | ||||||||
\(651\) | 2.72385e12i | 0.594387i | ||||||||
\(652\) | − | 3.51983e11i | − | 0.0762793i | ||||||
\(653\) | 2.02322e12i | 0.435445i | 0.976011 | + | 0.217723i | \(0.0698629\pi\) | ||||
−0.976011 | + | 0.217723i | \(0.930137\pi\) | |||||||
\(654\) | 9.81835e12 | 2.09864 | ||||||||
\(655\) | 1.41112e11 | 0.0299556 | ||||||||
\(656\) | 3.56902e12i | 0.752457i | ||||||||
\(657\) | − | 4.30196e11i | − | 0.0900787i | ||||||
\(658\) | − | 3.99598e11i | − | 0.0831011i | ||||||
\(659\) | −2.09148e12 | −0.431985 | −0.215993 | − | 0.976395i | \(-0.569299\pi\) | ||||
−0.215993 | + | 0.976395i | \(0.569299\pi\) | |||||||
\(660\) | − | 1.13677e11i | − | 0.0233198i | ||||||
\(661\) | −3.66578e12 | −0.746895 | −0.373448 | − | 0.927651i | \(-0.621824\pi\) | ||||
−0.373448 | + | 0.927651i | \(0.621824\pi\) | |||||||
\(662\) | 8.94136e12 | 1.80943 | ||||||||
\(663\) | −9.19669e12 | + | 5.55230e12i | −1.84851 | + | 1.11599i | ||||
\(664\) | 5.24341e12 | 1.04678 | ||||||||
\(665\) | −5.74259e10 | −0.0113870 | ||||||||
\(666\) | − | 1.29882e13i | − | 2.55809i | ||||||
\(667\) | −1.79317e11 | −0.0350797 | ||||||||
\(668\) | 2.20652e12i | 0.428760i | ||||||||
\(669\) | − | 1.42118e12i | − | 0.274305i | ||||||
\(670\) | − | 6.07626e11i | − | 0.116493i | ||||||
\(671\) | −5.17769e12 | −0.986017 | ||||||||
\(672\) | 1.08372e12 | 0.205000 | ||||||||
\(673\) | − | 4.12814e12i | − | 0.775686i | −0.921725 | − | 0.387843i | \(-0.873220\pi\) | ||
0.921725 | − | 0.387843i | \(-0.126780\pi\) | |||||||
\(674\) | − | 5.53716e12i | − | 1.03352i | ||||||
\(675\) | − | 4.95622e12i | − | 0.918933i | ||||||
\(676\) | 1.32990e12 | 0.244940 | ||||||||
\(677\) | − | 3.86753e12i | − | 0.707594i | −0.935322 | − | 0.353797i | \(-0.884890\pi\) | ||
0.935322 | − | 0.353797i | \(-0.115110\pi\) | |||||||
\(678\) | −1.39329e13 | −2.53226 | ||||||||
\(679\) | 1.44802e12 | 0.261434 | ||||||||
\(680\) | 2.62249e11 | − | 1.58327e11i | 0.0470352 | − | 0.0283965i | ||||
\(681\) | −1.22262e13 | −2.17835 | ||||||||
\(682\) | 7.62708e12 | 1.34998 | ||||||||
\(683\) | 6.60671e12i | 1.16170i | 0.814012 | + | 0.580848i | \(0.197279\pi\) | ||||
−0.814012 | + | 0.580848i | \(0.802721\pi\) | |||||||
\(684\) | −2.06203e12 | −0.360199 | ||||||||
\(685\) | − | 3.99126e11i | − | 0.0692631i | ||||||
\(686\) | 2.81921e12i | 0.486037i | ||||||||
\(687\) | − | 2.33591e12i | − | 0.400084i | ||||||
\(688\) | 7.73876e12 | 1.31681 | ||||||||
\(689\) | 4.90907e12 | 0.829875 | ||||||||
\(690\) | 1.97805e11i | 0.0332213i | ||||||||
\(691\) | − | 8.12202e12i | − | 1.35523i | −0.735417 | − | 0.677615i | \(-0.763014\pi\) | ||
0.735417 | − | 0.677615i | \(-0.236986\pi\) | |||||||
\(692\) | − | 1.07203e12i | − | 0.177717i | ||||||
\(693\) | 1.45382e12 | 0.239449 | ||||||||
\(694\) | − | 5.82726e12i | − | 0.953557i | ||||||
\(695\) | 1.68023e11 | 0.0273172 | ||||||||
\(696\) | −1.05553e12 | −0.170503 | ||||||||
\(697\) | 3.31465e12 | − | 2.00115e12i | 0.531974 | − | 0.321168i | ||||
\(698\) | −8.08755e11 | −0.128964 | ||||||||
\(699\) | 1.33547e13 | 2.11586 | ||||||||
\(700\) | 4.16852e11i | 0.0656207i | ||||||||
\(701\) | 6.09018e12 | 0.952574 | 0.476287 | − | 0.879290i | \(-0.341982\pi\) | ||||
0.476287 | + | 0.879290i | \(0.341982\pi\) | |||||||
\(702\) | − | 9.12236e12i | − | 1.41772i | ||||||
\(703\) | 6.97091e12i | 1.07644i | ||||||||
\(704\) | 2.46425e12i | 0.378101i | ||||||||
\(705\) | 2.42459e11 | 0.0369647 | ||||||||
\(706\) | 4.31358e12 | 0.653457 | ||||||||
\(707\) | 4.12448e10i | 0.00620843i | ||||||||
\(708\) | 1.75405e12i | 0.262357i | ||||||||
\(709\) | 1.24847e12i | 0.185553i | 0.995687 | + | 0.0927767i | \(0.0295743\pi\) | ||||
−0.995687 | + | 0.0927767i | \(0.970426\pi\) | |||||||
\(710\) | 9.43011e11 | 0.139269 | ||||||||
\(711\) | 1.75245e13i | 2.57177i | ||||||||
\(712\) | −2.40944e12 | −0.351364 | ||||||||
\(713\) | −3.08031e12 | −0.446366 | ||||||||
\(714\) | −1.43389e12 | − | 2.37505e12i | −0.206478 | − | 0.342004i | ||||
\(715\) | −4.52071e11 | −0.0646888 | ||||||||
\(716\) | 2.05354e12 | 0.292007 | ||||||||
\(717\) | − | 1.47953e13i | − | 2.09068i | ||||||
\(718\) | −1.35596e13 | −1.90409 | ||||||||
\(719\) | 4.85534e12i | 0.677547i | 0.940868 | + | 0.338774i | \(0.110012\pi\) | ||||
−0.940868 | + | 0.338774i | \(0.889988\pi\) | |||||||
\(720\) | 9.49164e11i | 0.131627i | ||||||||
\(721\) | 2.22448e12i | 0.306563i | ||||||||
\(722\) | −3.56398e12 | −0.488110 | ||||||||
\(723\) | 4.56979e12 | 0.621976 | ||||||||
\(724\) | 1.38512e12i | 0.187355i | ||||||||
\(725\) | − | 9.87898e11i | − | 0.132798i | ||||||
\(726\) | 7.05324e12i | 0.942267i | ||||||||
\(727\) | 3.36183e12 | 0.446345 | 0.223173 | − | 0.974779i | \(-0.428359\pi\) | ||||
0.223173 | + | 0.974779i | \(0.428359\pi\) | |||||||
\(728\) | − | 1.77124e12i | − | 0.233715i | ||||||
\(729\) | 1.24237e13 | 1.62921 | ||||||||
\(730\) | −3.45464e10 | −0.00450246 | ||||||||
\(731\) | −4.33912e12 | − | 7.18722e12i | −0.562049 | − | 0.930964i | ||||
\(732\) | −5.33192e12 | −0.686410 | ||||||||
\(733\) | −1.02897e13 | −1.31654 | −0.658271 | − | 0.752781i | \(-0.728712\pi\) | ||||
−0.658271 | + | 0.752781i | \(0.728712\pi\) | |||||||
\(734\) | − | 2.38586e12i | − | 0.303398i | ||||||
\(735\) | −8.34442e11 | −0.105464 | ||||||||
\(736\) | 1.22554e12i | 0.153949i | ||||||||
\(737\) | − | 8.25619e12i | − | 1.03080i | ||||||
\(738\) | 9.00233e12i | 1.11712i | ||||||||
\(739\) | −1.10714e12 | −0.136553 | −0.0682766 | − | 0.997666i | \(-0.521750\pi\) | ||||
−0.0682766 | + | 0.997666i | \(0.521750\pi\) | |||||||
\(740\) | −2.42078e11 | −0.0296765 | ||||||||
\(741\) | 1.34056e13i | 1.63345i | ||||||||
\(742\) | 1.26777e12i | 0.153541i | ||||||||
\(743\) | − | 5.80468e12i | − | 0.698761i | −0.936981 | − | 0.349380i | \(-0.886392\pi\) | ||
0.936981 | − | 0.349380i | \(-0.113608\pi\) | |||||||
\(744\) | −1.81320e13 | −2.16953 | ||||||||
\(745\) | 4.63090e11i | 0.0550760i | ||||||||
\(746\) | 3.28471e12 | 0.388305 | ||||||||
\(747\) | 1.76251e13 | 2.07104 | ||||||||
\(748\) | −1.54354e12 | + | 9.31878e11i | −0.180285 | + | 0.108843i | ||||
\(749\) | −3.26326e12 | −0.378864 | ||||||||
\(750\) | −2.18472e12 | −0.252128 | ||||||||
\(751\) | 8.01566e12i | 0.919517i | 0.888044 | + | 0.459758i | \(0.152064\pi\) | ||||
−0.888044 | + | 0.459758i | \(0.847936\pi\) | |||||||
\(752\) | 3.54483e12 | 0.404218 | ||||||||
\(753\) | − | 1.96249e13i | − | 2.22449i | ||||||
\(754\) | − | 1.81831e12i | − | 0.204879i | ||||||
\(755\) | 1.18377e11i | 0.0132588i | ||||||||
\(756\) | 5.46788e11 | 0.0608794 | ||||||||
\(757\) | −4.40521e12 | −0.487568 | −0.243784 | − | 0.969829i | \(-0.578389\pi\) | ||||
−0.243784 | + | 0.969829i | \(0.578389\pi\) | |||||||
\(758\) | − | 1.05520e13i | − | 1.16098i | ||||||
\(759\) | 2.68770e12i | 0.293963i | ||||||||
\(760\) | − | 3.82269e11i | − | 0.0415631i | ||||||
\(761\) | −1.23860e13 | −1.33875 | −0.669377 | − | 0.742923i | \(-0.733439\pi\) | ||||
−0.669377 | + | 0.742923i | \(0.733439\pi\) | |||||||
\(762\) | 2.44587e13i | 2.62807i | ||||||||
\(763\) | 2.34037e12 | 0.249991 | ||||||||
\(764\) | −3.25843e11 | −0.0346009 | ||||||||
\(765\) | 8.81517e11 | − | 5.32196e11i | 0.0930581 | − | 0.0561818i | ||||
\(766\) | 6.74302e12 | 0.707660 | ||||||||
\(767\) | 6.97553e12 | 0.727776 | ||||||||
\(768\) | 1.28766e13i | 1.33560i | ||||||||
\(769\) | −1.34212e13 | −1.38396 | −0.691978 | − | 0.721919i | \(-0.743260\pi\) | ||||
−0.691978 | + | 0.721919i | \(0.743260\pi\) | |||||||
\(770\) | − | 1.16748e11i | − | 0.0119685i | ||||||
\(771\) | − | 2.70863e12i | − | 0.276061i | ||||||
\(772\) | 7.90359e11i | 0.0800842i | ||||||||
\(773\) | 3.10743e12 | 0.313036 | 0.156518 | − | 0.987675i | \(-0.449973\pi\) | ||||
0.156518 | + | 0.987675i | \(0.449973\pi\) | |||||||
\(774\) | 1.95199e13 | 1.95499 | ||||||||
\(775\) | − | 1.69701e13i | − | 1.68977i | ||||||
\(776\) | 9.63910e12i | 0.954243i | ||||||||
\(777\) | − | 5.06121e12i | − | 0.498150i | ||||||
\(778\) | −9.07066e12 | −0.887628 | ||||||||
\(779\) | − | 4.83163e12i | − | 0.470084i | ||||||
\(780\) | −4.65537e11 | −0.0450327 | ||||||||
\(781\) | 1.28133e13 | 1.23234 | ||||||||
\(782\) | 2.68586e12 | − | 1.62153e12i | 0.256835 | − | 0.155058i | ||||
\(783\) | −1.29583e12 | −0.123203 | ||||||||
\(784\) | −1.21998e13 | −1.15327 | ||||||||
\(785\) | 1.66495e11i | 0.0156491i | ||||||||
\(786\) | 8.50718e12 | 0.795031 | ||||||||
\(787\) | 4.60263e12i | 0.427681i | 0.976869 | + | 0.213840i | \(0.0685973\pi\) | ||||
−0.976869 | + | 0.213840i | \(0.931403\pi\) | |||||||
\(788\) | − | 2.87089e12i | − | 0.265246i | ||||||
\(789\) | 7.91084e12i | 0.726735i | ||||||||
\(790\) | 1.40728e12 | 0.128546 | ||||||||
\(791\) | −3.32115e12 | −0.301644 | ||||||||
\(792\) | 9.67772e12i | 0.873997i | ||||||||
\(793\) | 2.12040e13i | 1.90410i | ||||||||
\(794\) | 1.07755e13i | 0.962155i | ||||||||
\(795\) | −7.69231e11 | −0.0682975 | ||||||||
\(796\) | − | 2.12330e12i | − | 0.187457i | ||||||
\(797\) | 1.39540e13 | 1.22500 | 0.612502 | − | 0.790469i | \(-0.290163\pi\) | ||||
0.612502 | + | 0.790469i | \(0.290163\pi\) | |||||||
\(798\) | −3.46202e12 | −0.302215 | ||||||||
\(799\) | −1.98759e12 | − | 3.29219e12i | −0.172530 | − | 0.285775i | ||||
\(800\) | −6.75175e12 | −0.582789 | ||||||||
\(801\) | −8.09906e12 | −0.695165 | ||||||||
\(802\) | 1.27316e13i | 1.08667i | ||||||||
\(803\) | −4.69402e11 | −0.0398405 | ||||||||
\(804\) | − | 8.50212e12i | − | 0.717588i | ||||||
\(805\) | 4.71502e10i | 0.00395733i | ||||||||
\(806\) | − | 3.12349e13i | − | 2.60695i | ||||||
\(807\) | −1.86884e13 | −1.55110 | ||||||||
\(808\) | −2.74556e11 | −0.0226610 | ||||||||
\(809\) | − | 2.10896e13i | − | 1.73101i | −0.500896 | − | 0.865507i | \(-0.666996\pi\) | ||
0.500896 | − | 0.865507i | \(-0.333004\pi\) | |||||||
\(810\) | − | 9.03008e10i | − | 0.00737070i | ||||||
\(811\) | 3.64082e12i | 0.295533i | 0.989022 | + | 0.147766i | \(0.0472084\pi\) | ||||
−0.989022 | + | 0.147766i | \(0.952792\pi\) | |||||||
\(812\) | 1.08988e11 | 0.00879787 | ||||||||
\(813\) | − | 1.25513e13i | − | 1.00758i | ||||||
\(814\) | −1.41719e13 | −1.13141 | ||||||||
\(815\) | 2.19338e11 | 0.0174142 | ||||||||
\(816\) | 2.10691e13 | − | 1.27200e13i | 1.66357 | − | 1.00434i | ||||
\(817\) | −1.04765e13 | −0.822655 | ||||||||
\(818\) | 7.21385e12 | 0.563349 | ||||||||
\(819\) | − | 5.95380e12i | − | 0.462399i | ||||||
\(820\) | 1.67788e11 | 0.0129598 | ||||||||
\(821\) | 1.79752e13i | 1.38080i | 0.723429 | + | 0.690399i | \(0.242565\pi\) | ||||
−0.723429 | + | 0.690399i | \(0.757435\pi\) | |||||||
\(822\) | − | 2.40620e13i | − | 1.83826i | ||||||
\(823\) | − | 4.92718e12i | − | 0.374368i | −0.982325 | − | 0.187184i | \(-0.940064\pi\) | ||
0.982325 | − | 0.187184i | \(-0.0599361\pi\) | |||||||
\(824\) | −1.48078e13 | −1.11897 | ||||||||
\(825\) | −1.48071e13 | −1.11283 | ||||||||
\(826\) | 1.80144e12i | 0.134651i | ||||||||
\(827\) | 5.12459e12i | 0.380964i | 0.981691 | + | 0.190482i | \(0.0610051\pi\) | ||||
−0.981691 | + | 0.190482i | \(0.938995\pi\) | |||||||
\(828\) | 1.69305e12i | 0.125180i | ||||||||
\(829\) | 1.91602e13 | 1.40898 | 0.704490 | − | 0.709714i | \(-0.251176\pi\) | ||||
0.704490 | + | 0.709714i | \(0.251176\pi\) | |||||||
\(830\) | − | 1.41536e12i | − | 0.103518i | ||||||
\(831\) | 4.16450e13 | 3.02941 | ||||||||
\(832\) | 1.00918e13 | 0.730149 | ||||||||
\(833\) | 6.84043e12 | + | 1.13303e13i | 0.492245 | + | 0.815342i | ||||
\(834\) | 1.01295e13 | 0.725008 | ||||||||
\(835\) | −1.37499e12 | −0.0978839 | ||||||||
\(836\) | 2.24995e12i | 0.159311i | ||||||||
\(837\) | −2.22598e13 | −1.56768 | ||||||||
\(838\) | − | 1.26359e12i | − | 0.0885130i | ||||||
\(839\) | 9.27849e12i | 0.646470i | 0.946319 | + | 0.323235i | \(0.104770\pi\) | ||||
−0.946319 | + | 0.323235i | \(0.895230\pi\) | |||||||
\(840\) | 2.77546e11i | 0.0192343i | ||||||||
\(841\) | 1.42489e13 | 0.982196 | ||||||||
\(842\) | 2.51391e13 | 1.72364 | ||||||||
\(843\) | − | 3.05800e13i | − | 2.08552i | ||||||
\(844\) | − | 9.47124e11i | − | 0.0642489i | ||||||
\(845\) | 8.28729e11i | 0.0559187i | ||||||||
\(846\) | 8.94132e12 | 0.600116 | ||||||||
\(847\) | 1.68126e12i | 0.112243i | ||||||||
\(848\) | −1.12464e13 | −0.746848 | ||||||||
\(849\) | −1.31933e13 | −0.871501 | ||||||||
\(850\) | 8.93338e12 | + | 1.47970e13i | 0.586990 | + | 0.972276i | ||||
\(851\) | 5.72354e12 | 0.374095 | ||||||||
\(852\) | 1.31949e13 | 0.857886 | ||||||||
\(853\) | 1.45073e13i | 0.938244i | 0.883133 | + | 0.469122i | \(0.155429\pi\) | ||||
−0.883133 | + | 0.469122i | \(0.844571\pi\) | |||||||
\(854\) | −5.47596e12 | −0.352289 | ||||||||
\(855\) | − | 1.28495e12i | − | 0.0822317i | ||||||
\(856\) | − | 2.17226e13i | − | 1.38287i | ||||||
\(857\) | 6.75756e12i | 0.427933i | 0.976841 | + | 0.213967i | \(0.0686384\pi\) | ||||
−0.976841 | + | 0.213967i | \(0.931362\pi\) | |||||||
\(858\) | −2.72538e13 | −1.71686 | ||||||||
\(859\) | −6.20315e11 | −0.0388726 | −0.0194363 | − | 0.999811i | \(-0.506187\pi\) | ||||
−0.0194363 | + | 0.999811i | \(0.506187\pi\) | |||||||
\(860\) | − | 3.63817e11i | − | 0.0226799i | ||||||
\(861\) | 3.50800e12i | 0.217543i | ||||||||
\(862\) | 9.31866e12i | 0.574871i | ||||||||
\(863\) | 1.36639e12 | 0.0838542 | 0.0419271 | − | 0.999121i | \(-0.486650\pi\) | ||||
0.0419271 | + | 0.999121i | \(0.486650\pi\) | |||||||
\(864\) | 8.85631e12i | 0.540681i | ||||||||
\(865\) | 6.68033e11 | 0.0405719 | ||||||||
\(866\) | −3.41071e13 | −2.06070 | ||||||||
\(867\) | −2.36269e13 | − | 1.24354e13i | −1.42010 | − | 0.747435i | ||||
\(868\) | 1.87220e12 | 0.111947 | ||||||||
\(869\) | 1.91216e13 | 1.13746 | ||||||||
\(870\) | 2.84922e11i | 0.0168612i | ||||||||
\(871\) | −3.38113e13 | −1.99058 | ||||||||
\(872\) | 1.55792e13i | 0.912476i | ||||||||
\(873\) | 3.24007e13i | 1.88795i | ||||||||
\(874\) | − | 3.91507e12i | − | 0.226954i | ||||||
\(875\) | −5.20765e11 | −0.0300335 | ||||||||
\(876\) | −4.83385e11 | −0.0277348 | ||||||||
\(877\) | 1.47910e13i | 0.844304i | 0.906525 | + | 0.422152i | \(0.138725\pi\) | ||||
−0.906525 | + | 0.422152i | \(0.861275\pi\) | |||||||
\(878\) | − | 1.10849e13i | − | 0.629514i | ||||||
\(879\) | − | 1.23432e13i | − | 0.697396i | ||||||
\(880\) | 1.03567e12 | 0.0582168 | ||||||||
\(881\) | 1.90695e12i | 0.106647i | 0.998577 | + | 0.0533234i | \(0.0169814\pi\) | ||||
−0.998577 | + | 0.0533234i | \(0.983019\pi\) | |||||||
\(882\) | −3.07723e13 | −1.71218 | ||||||||
\(883\) | 9.34392e12 | 0.517256 | 0.258628 | − | 0.965977i | \(-0.416730\pi\) | ||||
0.258628 | + | 0.965977i | \(0.416730\pi\) | |||||||
\(884\) | 3.81629e12 | + | 6.32121e12i | 0.210187 | + | 0.348149i | ||||
\(885\) | −1.09304e12 | −0.0598949 | ||||||||
\(886\) | −2.55170e13 | −1.39116 | ||||||||
\(887\) | 6.67058e12i | 0.361832i | 0.983499 | + | 0.180916i | \(0.0579063\pi\) | ||||
−0.983499 | + | 0.180916i | \(0.942094\pi\) | |||||||
\(888\) | 3.36911e13 | 1.81826 | ||||||||
\(889\) | 5.83015e12i | 0.313056i | ||||||||
\(890\) | 6.50385e11i | 0.0347469i | ||||||||
\(891\) | − | 1.22697e12i | − | 0.0652206i | ||||||
\(892\) | −9.76830e11 | −0.0516627 | ||||||||
\(893\) | −4.79889e12 | −0.252528 | ||||||||
\(894\) | 2.79182e13i | 1.46173i | ||||||||
\(895\) | 1.27966e12i | 0.0666639i | ||||||||
\(896\) | 5.07066e12i | 0.262832i | ||||||||
\(897\) | 1.10069e13 | 0.567672 | ||||||||
\(898\) | − | 1.36237e13i | − | 0.699119i | ||||||
\(899\) | −4.43692e12 | −0.226550 | ||||||||
\(900\) | −9.32740e12 | −0.473881 | ||||||||
\(901\) | 6.30586e12 | + | 1.04449e13i | 0.318774 | + | 0.528009i | ||||
\(902\) | 9.82277e12 | 0.494088 | ||||||||
\(903\) | 7.60645e12 | 0.380704 | ||||||||
\(904\) | − | 2.21080e13i | − | 1.10101i | ||||||
\(905\) | −8.63138e11 | −0.0427722 | ||||||||
\(906\) | 7.13655e12i | 0.351893i | ||||||||
\(907\) | 2.25953e13i | 1.10863i | 0.832308 | + | 0.554313i | \(0.187019\pi\) | ||||
−0.832308 | + | 0.554313i | \(0.812981\pi\) | |||||||
\(908\) | 8.40347e12i | 0.410272i | ||||||||
\(909\) | −9.22885e11 | −0.0448343 | ||||||||
\(910\) | −4.78113e11 | −0.0231124 | ||||||||
\(911\) | 2.70620e13i | 1.30175i | 0.759186 | + | 0.650873i | \(0.225597\pi\) | ||||
−0.759186 | + | 0.650873i | \(0.774403\pi\) | |||||||
\(912\) | − | 3.07115e13i | − | 1.47003i | ||||||
\(913\) | − | 1.92314e13i | − | 0.915992i | ||||||
\(914\) | 2.91846e12 | 0.138323 | ||||||||
\(915\) | − | 3.32258e12i | − | 0.156704i | ||||||
\(916\) | −1.60555e12 | −0.0753521 | ||||||||
\(917\) | 2.02783e12 | 0.0947042 | ||||||||
\(918\) | 1.94093e13 | − | 1.17180e13i | 0.902026 | − | 0.544578i | ||||
\(919\) | 1.59897e13 | 0.739468 | 0.369734 | − | 0.929138i | \(-0.379449\pi\) | ||||
0.369734 | + | 0.929138i | \(0.379449\pi\) | |||||||
\(920\) | −3.13866e11 | −0.0144444 | ||||||||
\(921\) | − | 4.23398e13i | − | 1.93901i | ||||||
\(922\) | 2.88324e13 | 1.31399 | ||||||||
\(923\) | − | 5.24738e13i | − | 2.37977i | ||||||
\(924\) | − | 1.63357e12i | − | 0.0737250i | ||||||
\(925\) | 3.15323e13i | 1.41618i | ||||||||
\(926\) | −1.01284e13 | −0.452682 | ||||||||
\(927\) | −4.97745e13 | −2.21385 | ||||||||
\(928\) | 1.76528e12i | 0.0781354i | ||||||||
\(929\) | 9.00625e12i | 0.396710i | 0.980130 | + | 0.198355i | \(0.0635599\pi\) | ||||
−0.980130 | + | 0.198355i | \(0.936440\pi\) | |||||||
\(930\) | 4.89438e12i | 0.214548i | ||||||||
\(931\) | 1.65157e13 | 0.720485 | ||||||||
\(932\) | − | 9.17916e12i | − | 0.398503i | ||||||
\(933\) | 4.09129e13 | 1.76764 | ||||||||
\(934\) | 4.11879e12 | 0.177096 | ||||||||
\(935\) | −5.80699e11 | − | 9.61855e11i | −0.0248484 | − | 0.0411583i | ||||
\(936\) | 3.96329e13 | 1.68777 | ||||||||
\(937\) | −4.00157e13 | −1.69591 | −0.847954 | − | 0.530071i | \(-0.822165\pi\) | ||||
−0.847954 | + | 0.530071i | \(0.822165\pi\) | |||||||
\(938\) | − | 8.73180e12i | − | 0.368291i | ||||||
\(939\) | 4.98809e13 | 2.09382 | ||||||||
\(940\) | − | 1.66651e11i | − | 0.00696196i | ||||||
\(941\) | − | 2.42260e13i | − | 1.00723i | −0.863928 | − | 0.503615i | \(-0.832003\pi\) | ||
0.863928 | − | 0.503615i | \(-0.167997\pi\) | |||||||
\(942\) | 1.00374e13i | 0.415331i | ||||||||
\(943\) | −3.96707e12 | −0.163368 | ||||||||
\(944\) | −1.59805e13 | −0.654964 | ||||||||
\(945\) | 3.40730e11i | 0.0138985i | ||||||||
\(946\) | − | 2.12989e13i | − | 0.864663i | ||||||
\(947\) | − | 3.52100e13i | − | 1.42263i | −0.702875 | − | 0.711313i | \(-0.748101\pi\) | ||
0.702875 | − | 0.711313i | \(-0.251899\pi\) | |||||||
\(948\) | 1.96912e13 | 0.791835 | ||||||||
\(949\) | 1.92233e12i | 0.0769360i | ||||||||
\(950\) | 2.15690e13 | 0.859160 | ||||||||
\(951\) | −6.00782e13 | −2.38180 | ||||||||
\(952\) | 3.76860e12 | − | 2.27521e12i | 0.148701 | − | 0.0897750i | ||||
\(953\) | 9.99226e12 | 0.392415 | 0.196208 | − | 0.980562i | \(-0.437137\pi\) | ||||
0.196208 | + | 0.980562i | \(0.437137\pi\) | |||||||
\(954\) | −2.83674e13 | −1.10880 | ||||||||
\(955\) | − | 2.03049e11i | − | 0.00789923i | ||||||
\(956\) | −1.01693e13 | −0.393761 | ||||||||
\(957\) | 3.87141e12i | 0.149199i | ||||||||
\(958\) | 1.12850e13i | 0.432870i | ||||||||
\(959\) | − | 5.73557e12i | − | 0.218974i | ||||||
\(960\) | −1.58134e12 | −0.0600902 | ||||||||
\(961\) | −4.97778e13 | −1.88270 | ||||||||
\(962\) | 5.80379e13i | 2.18486i | ||||||||
\(963\) | − | 7.30180e13i | − | 2.73597i | ||||||
\(964\) | − | 3.14097e12i | − | 0.117143i | ||||||
\(965\) | −4.92511e11 | −0.0182828 | ||||||||
\(966\) | 2.84253e12i | 0.105029i | ||||||||
\(967\) | 3.17277e12 | 0.116686 | 0.0583431 | − | 0.998297i | \(-0.481418\pi\) | ||||
0.0583431 | + | 0.998297i | \(0.481418\pi\) | |||||||
\(968\) | −1.11917e13 | −0.409691 | ||||||||
\(969\) | −2.85227e13 | + | 1.72200e13i | −1.03928 | + | 0.627444i | ||||
\(970\) | 2.60190e12 | 0.0943664 | ||||||||
\(971\) | 2.55138e13 | 0.921061 | 0.460531 | − | 0.887644i | \(-0.347659\pi\) | ||||
0.460531 | + | 0.887644i | \(0.347659\pi\) | |||||||
\(972\) | − | 9.02989e12i | − | 0.324477i | ||||||
\(973\) | 2.41455e12 | 0.0863630 | ||||||||
\(974\) | 2.71251e13i | 0.965730i | ||||||||
\(975\) | 6.06392e13i | 2.14898i | ||||||||
\(976\) | − | 4.85772e13i | − | 1.71359i | ||||||
\(977\) | −4.02976e12 | −0.141499 | −0.0707496 | − | 0.997494i | \(-0.522539\pi\) | ||||
−0.0707496 | + | 0.997494i | \(0.522539\pi\) | |||||||
\(978\) | 1.32231e13 | 0.462178 | ||||||||
\(979\) | 8.83718e12i | 0.307462i | ||||||||
\(980\) | 5.73541e11i | 0.0198631i | ||||||||
\(981\) | 5.23676e13i | 1.80531i | ||||||||
\(982\) | 4.59481e13 | 1.57676 | ||||||||
\(983\) | 9.84380e12i | 0.336258i | 0.985765 | + | 0.168129i | \(0.0537724\pi\) | ||||
−0.985765 | + | 0.168129i | \(0.946228\pi\) | |||||||
\(984\) | −2.33518e13 | −0.794040 | ||||||||
\(985\) | 1.78899e12 | 0.0605544 | ||||||||
\(986\) | 3.86876e12 | − | 2.33568e12i | 0.130354 | − | 0.0786986i | ||||
\(987\) | 3.48422e12 | 0.116863 | ||||||||
\(988\) | 9.21417e12 | 0.307645 | ||||||||
\(989\) | 8.60186e12i | 0.285897i | ||||||||
\(990\) | 2.61232e12 | 0.0864307 | ||||||||
\(991\) | 7.10324e12i | 0.233951i | 0.993135 | + | 0.116976i | \(0.0373199\pi\) | ||||
−0.993135 | + | 0.116976i | \(0.962680\pi\) | |||||||
\(992\) | 3.03240e13i | 0.994222i | ||||||||
\(993\) | 7.79626e13i | 2.54457i | ||||||||
\(994\) | 1.35514e13 | 0.440297 | ||||||||
\(995\) | 1.32313e12 | 0.0427956 | ||||||||
\(996\) | − | 1.98042e13i | − | 0.637663i | ||||||
\(997\) | 3.04471e13i | 0.975928i | 0.872864 | + | 0.487964i | \(0.162260\pi\) | ||||
−0.872864 | + | 0.487964i | \(0.837740\pi\) | |||||||
\(998\) | − | 2.96891e13i | − | 0.947348i | ||||||
\(999\) | 4.13611e13 | 1.31385 |
(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 | 17.10.b.a.16.10 | yes | 12 | |
3.2 | odd | 2 | 153.10.d.b.118.3 | 12 | |||
4.3 | odd | 2 | 272.10.b.c.33.1 | 12 | |||
17.4 | even | 4 | 289.10.a.c.1.4 | 12 | |||
17.13 | even | 4 | 289.10.a.c.1.3 | 12 | |||
17.16 | even | 2 | inner | 17.10.b.a.16.9 | ✓ | 12 | |
51.50 | odd | 2 | 153.10.d.b.118.4 | 12 | |||
68.67 | odd | 2 | 272.10.b.c.33.12 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.b.a.16.9 | ✓ | 12 | 17.16 | even | 2 | inner | |
17.10.b.a.16.10 | yes | 12 | 1.1 | even | 1 | trivial | |
153.10.d.b.118.3 | 12 | 3.2 | odd | 2 | |||
153.10.d.b.118.4 | 12 | 51.50 | odd | 2 | |||
272.10.b.c.33.1 | 12 | 4.3 | odd | 2 | |||
272.10.b.c.33.12 | 12 | 68.67 | odd | 2 | |||
289.10.a.c.1.3 | 12 | 17.13 | even | 4 | |||
289.10.a.c.1.4 | 12 | 17.4 | even | 4 |