Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [81,9,Mod(80,81)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(81, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("81.80");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.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: | \(32.9976674150\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{16} + 1024 x^{14} + 419701 x^{12} + 88203292 x^{10} + 10121979748 x^{8} + 629108384896 x^{6} + \cdots + 16\!\cdots\!24 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{84} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 80.6 | ||
Root | \(5.78233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 81.80 |
Dual form | 81.9.b.b.80.11 |
$q$-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 \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 10.0153i | − 0.625956i | −0.949760 | − | 0.312978i | \(-0.898673\pi\) | ||||
0.949760 | − | 0.312978i | \(-0.101327\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 155.694 | 0.608179 | ||||||||
\(5\) | 594.387i | 0.951019i | 0.879711 | + | 0.475509i | \(0.157736\pi\) | ||||
−0.879711 | + | 0.475509i | \(0.842264\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4409.51 | 1.83653 | 0.918265 | − | 0.395965i | \(-0.129590\pi\) | ||||
0.918265 | + | 0.395965i | \(0.129590\pi\) | |||||||
\(8\) | − 4123.23i | − 1.00665i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5952.96 | 0.595296 | ||||||||
\(11\) | 3479.38i | 0.237646i | 0.992915 | + | 0.118823i | \(0.0379121\pi\) | ||||
−0.992915 | + | 0.118823i | \(0.962088\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −18263.0 | −0.639437 | −0.319718 | − | 0.947513i | \(-0.603588\pi\) | ||||
−0.319718 | + | 0.947513i | \(0.603588\pi\) | |||||||
\(14\) | − 44162.5i | − 1.14959i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1437.76 | −0.0219385 | ||||||||
\(17\) | 86637.8i | 1.03732i | 0.854981 | + | 0.518659i | \(0.173568\pi\) | ||||
−0.854981 | + | 0.518659i | \(0.826432\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 76109.5 | 0.584016 | 0.292008 | − | 0.956416i | \(-0.405677\pi\) | ||||
0.292008 | + | 0.956416i | \(0.405677\pi\) | |||||||
\(20\) | 92542.4i | 0.578390i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 34847.0 | 0.148756 | ||||||||
\(23\) | 524101.i | 1.87285i | 0.350863 | + | 0.936427i | \(0.385888\pi\) | ||||
−0.350863 | + | 0.936427i | \(0.614112\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 37329.5 | 0.0955636 | ||||||||
\(26\) | 182909.i | 0.400259i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 686534. | 1.11694 | ||||||||
\(29\) | − 775418.i | − 1.09634i | −0.836368 | − | 0.548168i | \(-0.815325\pi\) | ||||
0.836368 | − | 0.548168i | \(-0.184675\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −925425. | −1.00206 | −0.501031 | − | 0.865430i | \(-0.667046\pi\) | ||||
−0.501031 | + | 0.865430i | \(0.667046\pi\) | |||||||
\(32\) | − 1.04115e6i | − 0.992917i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 867703. | 0.649315 | ||||||||
\(35\) | 2.62095e6i | 1.74658i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 237767. | 0.126866 | 0.0634329 | − | 0.997986i | \(-0.479795\pi\) | ||||
0.0634329 | + | 0.997986i | \(0.479795\pi\) | |||||||
\(38\) | − 762259.i | − 0.365568i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.45080e6 | 0.957342 | ||||||||
\(41\) | 515887.i | 0.182566i | 0.995825 | + | 0.0912829i | \(0.0290968\pi\) | ||||
−0.995825 | + | 0.0912829i | \(0.970903\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.95836e6 | 1.15782 | 0.578910 | − | 0.815392i | \(-0.303478\pi\) | ||||
0.578910 | + | 0.815392i | \(0.303478\pi\) | |||||||
\(44\) | 541718.i | 0.144532i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.24903e6 | 1.17232 | ||||||||
\(47\) | − 5.32614e6i | − 1.09149i | −0.837950 | − | 0.545746i | \(-0.816246\pi\) | ||||
0.837950 | − | 0.545746i | \(-0.183754\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.36790e7 | 2.37285 | ||||||||
\(50\) | − 373866.i | − 0.0598186i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.84343e6 | −0.388892 | ||||||||
\(53\) | 1.30260e7i | 1.65085i | 0.564514 | + | 0.825424i | \(0.309064\pi\) | ||||
−0.564514 | + | 0.825424i | \(0.690936\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.06810e6 | −0.226006 | ||||||||
\(56\) | − 1.81814e7i | − 1.84874i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.76604e6 | −0.686258 | ||||||||
\(59\) | − 1.25431e7i | − 1.03513i | −0.855644 | − | 0.517566i | \(-0.826838\pi\) | ||||
0.855644 | − | 0.517566i | \(-0.173162\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.18844e7 | 0.858335 | 0.429167 | − | 0.903225i | \(-0.358807\pi\) | ||||
0.429167 | + | 0.903225i | \(0.358807\pi\) | |||||||
\(62\) | 9.26840e6i | 0.627246i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.07955e7 | −0.643460 | ||||||||
\(65\) | − 1.08553e7i | − 0.608116i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.35316e7 | 0.671504 | 0.335752 | − | 0.941950i | \(-0.391010\pi\) | ||||
0.335752 | + | 0.941950i | \(0.391010\pi\) | |||||||
\(68\) | 1.34890e7i | 0.630875i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.62496e7 | 1.09328 | ||||||||
\(71\) | − 133345.i | − 0.00524738i | −0.999997 | − | 0.00262369i | \(-0.999165\pi\) | ||||
0.999997 | − | 0.00262369i | \(-0.000835147\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.24749e7 | 1.84782 | 0.923910 | − | 0.382609i | \(-0.124974\pi\) | ||||
0.923910 | + | 0.382609i | \(0.124974\pi\) | |||||||
\(74\) | − 2.38130e6i | − 0.0794123i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.18498e7 | 0.355186 | ||||||||
\(77\) | 1.53424e7i | 0.436445i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.78499e7 | −1.22849 | −0.614246 | − | 0.789115i | \(-0.710540\pi\) | ||||
−0.614246 | + | 0.789115i | \(0.710540\pi\) | |||||||
\(80\) | − 854585.i | − 0.0208639i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.16676e6 | 0.114278 | ||||||||
\(83\) | 5.85268e7i | 1.23322i | 0.787267 | + | 0.616612i | \(0.211495\pi\) | ||||
−0.787267 | + | 0.616612i | \(0.788505\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.14963e7 | −0.986508 | ||||||||
\(86\) | − 3.96441e7i | − 0.724744i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.43463e7 | 0.239226 | ||||||||
\(89\) | 4.62606e7i | 0.737312i | 0.929566 | + | 0.368656i | \(0.120182\pi\) | ||||
−0.929566 | + | 0.368656i | \(0.879818\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.05307e7 | −1.17435 | ||||||||
\(92\) | 8.15994e7i | 1.13903i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.33428e7 | −0.683226 | ||||||||
\(95\) | 4.52385e7i | 0.555410i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.82391e7 | −0.996722 | −0.498361 | − | 0.866969i | \(-0.666065\pi\) | ||||
−0.498361 | + | 0.866969i | \(0.666065\pi\) | |||||||
\(98\) | − 1.36999e8i | − 1.48530i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.81198e6 | 0.0581198 | ||||||||
\(101\) | − 5.74015e7i | − 0.551617i | −0.961213 | − | 0.275809i | \(-0.911054\pi\) | ||||
0.961213 | − | 0.275809i | \(-0.0889456\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.89124e7 | −0.701126 | −0.350563 | − | 0.936539i | \(-0.614010\pi\) | ||||
−0.350563 | + | 0.936539i | \(0.614010\pi\) | |||||||
\(104\) | 7.53024e7i | 0.643688i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.30459e8 | 1.03336 | ||||||||
\(107\) | − 2.50821e8i | − 1.91350i | −0.290907 | − | 0.956751i | \(-0.593957\pi\) | ||||
0.290907 | − | 0.956751i | \(-0.406043\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.76440e7 | −0.550050 | −0.275025 | − | 0.961437i | \(-0.588686\pi\) | ||||
−0.275025 | + | 0.961437i | \(0.588686\pi\) | |||||||
\(110\) | 2.07126e7i | 0.141470i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.33981e6 | −0.0402907 | ||||||||
\(113\) | − 6.15863e7i | − 0.377720i | −0.982004 | − | 0.188860i | \(-0.939521\pi\) | ||||
0.982004 | − | 0.188860i | \(-0.0604793\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.11519e8 | −1.78112 | ||||||||
\(116\) | − 1.20728e8i | − 0.666769i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.25622e8 | −0.647946 | ||||||||
\(119\) | 3.82030e8i | 1.90507i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.02253e8 | 0.943524 | ||||||||
\(122\) | − 1.19025e8i | − 0.537280i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.44083e8 | −0.609433 | ||||||||
\(125\) | 2.54370e8i | 1.04190i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.58325e8 | −1.37741 | −0.688703 | − | 0.725044i | \(-0.741819\pi\) | ||||
−0.688703 | + | 0.725044i | \(0.741819\pi\) | |||||||
\(128\) | − 1.58414e8i | − 0.590139i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.08719e8 | −0.380654 | ||||||||
\(131\) | − 1.87148e8i | − 0.635477i | −0.948178 | − | 0.317738i | \(-0.897077\pi\) | ||||
0.948178 | − | 0.317738i | \(-0.102923\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.35606e8 | 1.07256 | ||||||||
\(134\) | − 1.35523e8i | − 0.420332i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.57228e8 | 1.04421 | ||||||||
\(137\) | 1.50180e8i | 0.426314i | 0.977018 | + | 0.213157i | \(0.0683746\pi\) | ||||
−0.977018 | + | 0.213157i | \(0.931625\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.29964e8 | 0.348148 | 0.174074 | − | 0.984733i | \(-0.444307\pi\) | ||||
0.174074 | + | 0.984733i | \(0.444307\pi\) | |||||||
\(140\) | 4.08067e8i | 1.06223i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.33549e6 | −0.00328462 | ||||||||
\(143\) | − 6.35437e7i | − 0.151960i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.60898e8 | 1.04264 | ||||||||
\(146\) | − 5.25551e8i | − 1.15665i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.70189e7 | 0.0771571 | ||||||||
\(149\) | − 1.50916e8i | − 0.306188i | −0.988212 | − | 0.153094i | \(-0.951076\pi\) | ||||
0.988212 | − | 0.153094i | \(-0.0489238\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.71244e8 | 0.329388 | 0.164694 | − | 0.986345i | \(-0.447336\pi\) | ||||
0.164694 | + | 0.986345i | \(0.447336\pi\) | |||||||
\(152\) | − 3.13817e8i | − 0.587899i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.53658e8 | 0.273195 | ||||||||
\(155\) | − 5.50060e8i | − 0.952979i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.21868e8 | −1.18812 | −0.594059 | − | 0.804422i | \(-0.702475\pi\) | ||||
−0.594059 | + | 0.804422i | \(0.702475\pi\) | |||||||
\(158\) | 4.79230e8i | 0.768982i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.18845e8 | 0.944282 | ||||||||
\(161\) | 2.31103e9i | 3.43955i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.90963e8 | −0.270520 | −0.135260 | − | 0.990810i | \(-0.543187\pi\) | ||||
−0.135260 | + | 0.990810i | \(0.543187\pi\) | |||||||
\(164\) | 8.03205e7i | 0.111033i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.86163e8 | 0.771944 | ||||||||
\(167\) | − 5.59370e8i | − 0.719173i | −0.933112 | − | 0.359586i | \(-0.882918\pi\) | ||||
0.933112 | − | 0.359586i | \(-0.117082\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.82195e8 | −0.591121 | ||||||||
\(170\) | 5.15751e8i | 0.617510i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.16292e8 | 0.704162 | ||||||||
\(173\) | − 6.07138e8i | − 0.677802i | −0.940822 | − | 0.338901i | \(-0.889945\pi\) | ||||
0.940822 | − | 0.338901i | \(-0.110055\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.64605e8 | 0.175505 | ||||||||
\(176\) | − 5.00251e6i | − 0.00521359i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.63314e8 | 0.461525 | ||||||||
\(179\) | 4.18834e8i | 0.407971i | 0.978974 | + | 0.203986i | \(0.0653896\pi\) | ||||
−0.978974 | + | 0.203986i | \(0.934610\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.10216e9 | 1.02690 | 0.513451 | − | 0.858119i | \(-0.328367\pi\) | ||||
0.513451 | + | 0.858119i | \(0.328367\pi\) | |||||||
\(182\) | 8.06538e8i | 0.735088i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.16099e9 | 1.88531 | ||||||||
\(185\) | 1.41325e8i | 0.120652i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.01446e8 | −0.246515 | ||||||||
\(188\) | − 8.29247e8i | − 0.663823i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.53077e8 | 0.347662 | ||||||||
\(191\) | − 1.78725e9i | − 1.34293i | −0.741038 | − | 0.671463i | \(-0.765666\pi\) | ||||
0.741038 | − | 0.671463i | \(-0.234334\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.17286e8 | −0.516968 | −0.258484 | − | 0.966016i | \(-0.583223\pi\) | ||||
−0.258484 | + | 0.966016i | \(0.583223\pi\) | |||||||
\(194\) | 8.83741e8i | 0.623904i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.12973e9 | 1.44312 | ||||||||
\(197\) | − 1.81939e9i | − 1.20798i | −0.796992 | − | 0.603990i | \(-0.793577\pi\) | ||||
0.796992 | − | 0.603990i | \(-0.206423\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.90300e9 | −1.21346 | −0.606730 | − | 0.794908i | \(-0.707519\pi\) | ||||
−0.606730 | + | 0.794908i | \(0.707519\pi\) | |||||||
\(200\) | − 1.53918e8i | − 0.0961990i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.74893e8 | −0.345288 | ||||||||
\(203\) | − 3.41921e9i | − 2.01346i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.06637e8 | −0.173624 | ||||||||
\(206\) | 7.90331e8i | 0.438874i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.62577e7 | 0.0140283 | ||||||||
\(209\) | 2.64814e8i | 0.138789i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.59903e8 | 0.0806726 | 0.0403363 | − | 0.999186i | \(-0.487157\pi\) | ||||
0.0403363 | + | 0.999186i | \(0.487157\pi\) | |||||||
\(212\) | 2.02807e9i | 1.00401i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.51205e9 | −1.19777 | ||||||||
\(215\) | 2.35279e9i | 1.10111i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.08067e9 | −1.84032 | ||||||||
\(218\) | 7.77628e8i | 0.344307i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.21990e8 | −0.137452 | ||||||||
\(221\) | − 1.58226e9i | − 0.663299i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.13186e8 | −0.247955 | −0.123977 | − | 0.992285i | \(-0.539565\pi\) | ||||
−0.123977 | + | 0.992285i | \(0.539565\pi\) | |||||||
\(224\) | − 4.59096e9i | − 1.82352i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.16805e8 | −0.236436 | ||||||||
\(227\) | 2.96458e9i | 1.11650i | 0.829672 | + | 0.558251i | \(0.188527\pi\) | ||||
−0.829672 | + | 0.558251i | \(0.811473\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.78965e9 | −1.37803 | −0.689013 | − | 0.724749i | \(-0.741956\pi\) | ||||
−0.689013 | + | 0.724749i | \(0.741956\pi\) | |||||||
\(230\) | 3.11995e9i | 1.11490i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.19723e9 | −1.10363 | ||||||||
\(233\) | − 3.76374e9i | − 1.27701i | −0.769616 | − | 0.638507i | \(-0.779552\pi\) | ||||
0.769616 | − | 0.638507i | \(-0.220448\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.16578e9 | 1.03803 | ||||||||
\(236\) | − 1.95288e9i | − 0.629545i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.82614e9 | 1.19249 | ||||||||
\(239\) | 5.29760e8i | 0.162363i | 0.996699 | + | 0.0811816i | \(0.0258694\pi\) | ||||
−0.996699 | + | 0.0811816i | \(0.974131\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.38906e8 | −0.248682 | −0.124341 | − | 0.992240i | \(-0.539682\pi\) | ||||
−0.124341 | + | 0.992240i | \(0.539682\pi\) | |||||||
\(242\) | − 2.02562e9i | − 0.590604i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.85032e9 | 0.522021 | ||||||||
\(245\) | 8.13060e9i | 2.25662i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.38998e9 | −0.373441 | ||||||||
\(248\) | 3.81574e9i | 1.00872i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.54759e9 | 0.652184 | ||||||||
\(251\) | 2.40283e9i | 0.605380i | 0.953089 | + | 0.302690i | \(0.0978847\pi\) | ||||
−0.953089 | + | 0.302690i | \(0.902115\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.82355e9 | −0.445076 | ||||||||
\(254\) | 3.58873e9i | 0.862195i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.35021e9 | −1.01286 | ||||||||
\(257\) | − 4.79378e9i | − 1.09887i | −0.835537 | − | 0.549434i | \(-0.814843\pi\) | ||||
0.835537 | − | 0.549434i | \(-0.185157\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.04844e9 | 0.232993 | ||||||||
\(260\) | − 1.69010e9i | − 0.369844i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.87434e9 | −0.397780 | ||||||||
\(263\) | − 2.24924e9i | − 0.470124i | −0.971980 | − | 0.235062i | \(-0.924471\pi\) | ||||
0.971980 | − | 0.235062i | \(-0.0755292\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.74247e9 | −1.56999 | ||||||||
\(266\) | − 3.36119e9i | − 0.671377i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.10678e9 | 0.408395 | ||||||||
\(269\) | 2.01512e9i | 0.384851i | 0.981312 | + | 0.192425i | \(0.0616353\pi\) | ||||
−0.981312 | + | 0.192425i | \(0.938365\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.85840e9 | −1.08618 | −0.543090 | − | 0.839675i | \(-0.682746\pi\) | ||||
−0.543090 | + | 0.839675i | \(0.682746\pi\) | |||||||
\(272\) | − 1.24564e8i | − 0.0227571i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.50410e9 | 0.266854 | ||||||||
\(275\) | 1.29883e8i | 0.0227103i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.81588e9 | −1.15772 | −0.578859 | − | 0.815427i | \(-0.696502\pi\) | ||||
−0.578859 | + | 0.815427i | \(0.696502\pi\) | |||||||
\(278\) | − 1.30163e9i | − 0.217925i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.08068e10 | 1.75819 | ||||||||
\(281\) | − 2.07175e9i | − 0.332286i | −0.986102 | − | 0.166143i | \(-0.946869\pi\) | ||||
0.986102 | − | 0.166143i | \(-0.0531314\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.61757e8 | 0.149941 | 0.0749704 | − | 0.997186i | \(-0.476114\pi\) | ||||
0.0749704 | + | 0.997186i | \(0.476114\pi\) | |||||||
\(284\) | − 2.07609e7i | − 0.00319135i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.36409e8 | −0.0951200 | ||||||||
\(287\) | 2.27481e9i | 0.335288i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.30347e8 | −0.0760272 | ||||||||
\(290\) | − 4.61603e9i | − 0.652644i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.17002e9 | 1.12381 | ||||||||
\(293\) | 1.21580e10i | 1.64965i | 0.565391 | + | 0.824823i | \(0.308725\pi\) | ||||
−0.565391 | + | 0.824823i | \(0.691275\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.45543e9 | 0.984429 | ||||||||
\(296\) | − 9.80369e8i | − 0.127709i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.51146e9 | −0.191660 | ||||||||
\(299\) | − 9.57163e9i | − 1.19757i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.74544e10 | 2.12637 | ||||||||
\(302\) | − 1.71506e9i | − 0.206182i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.09427e8 | −0.0128124 | ||||||||
\(305\) | 7.06391e9i | 0.816292i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.91035e9 | 0.552788 | 0.276394 | − | 0.961044i | \(-0.410860\pi\) | ||||
0.276394 | + | 0.961044i | \(0.410860\pi\) | |||||||
\(308\) | 2.38871e9i | 0.265437i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.50901e9 | −0.596523 | ||||||||
\(311\) | − 2.68957e9i | − 0.287502i | −0.989614 | − | 0.143751i | \(-0.954083\pi\) | ||||
0.989614 | − | 0.143751i | \(-0.0459165\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.13306e9 | −0.534809 | −0.267405 | − | 0.963584i | \(-0.586166\pi\) | ||||
−0.267405 | + | 0.963584i | \(0.586166\pi\) | |||||||
\(314\) | 7.22972e9i | 0.743709i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.44993e9 | −0.747144 | ||||||||
\(317\) | − 1.53801e10i | − 1.52308i | −0.648117 | − | 0.761540i | \(-0.724443\pi\) | ||||
0.648117 | − | 0.761540i | \(-0.275557\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.69797e9 | 0.260540 | ||||||||
\(320\) | − 6.41669e9i | − 0.611943i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.31456e10 | 2.15301 | ||||||||
\(323\) | 6.59396e9i | 0.605810i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.81747e8 | −0.0611068 | ||||||||
\(326\) | 1.91256e9i | 0.169334i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.12713e9 | 0.183780 | ||||||||
\(329\) | − 2.34857e10i | − 2.00456i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.40976e9 | −0.617294 | −0.308647 | − | 0.951177i | \(-0.599876\pi\) | ||||
−0.308647 | + | 0.951177i | \(0.599876\pi\) | |||||||
\(332\) | 9.11226e9i | 0.750022i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.60225e9 | −0.450170 | ||||||||
\(335\) | 8.04298e9i | 0.638613i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.70501e9 | 0.364788 | 0.182394 | − | 0.983226i | \(-0.441615\pi\) | ||||
0.182394 | + | 0.983226i | \(0.441615\pi\) | |||||||
\(338\) | 4.82933e9i | 0.370015i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.01767e9 | −0.599974 | ||||||||
\(341\) | − 3.21990e9i | − 0.238136i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.48977e10 | 2.52127 | ||||||||
\(344\) | − 1.63212e10i | − 1.16552i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.08066e9 | −0.424274 | ||||||||
\(347\) | 4.87208e9i | 0.336044i | 0.985783 | + | 0.168022i | \(0.0537380\pi\) | ||||
−0.985783 | + | 0.168022i | \(0.946262\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.37996e10 | 1.60423 | 0.802117 | − | 0.597168i | \(-0.203707\pi\) | ||||
0.802117 | + | 0.597168i | \(0.203707\pi\) | |||||||
\(350\) | − 1.64857e9i | − 0.109859i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.62255e9 | 0.235963 | ||||||||
\(353\) | − 7.90818e9i | − 0.509305i | −0.967033 | − | 0.254652i | \(-0.918039\pi\) | ||||
0.967033 | − | 0.254652i | \(-0.0819611\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.92583e7 | 0.00499035 | ||||||||
\(356\) | 7.20250e9i | 0.448418i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.19474e9 | 0.255372 | ||||||||
\(359\) | − 7.90247e9i | − 0.475757i | −0.971295 | − | 0.237879i | \(-0.923548\pi\) | ||||
0.971295 | − | 0.237879i | \(-0.0764520\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.11909e10 | −0.658926 | ||||||||
\(362\) | − 1.10384e10i | − 0.642795i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.25381e10 | −0.714213 | ||||||||
\(365\) | 3.11904e10i | 1.75731i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.38911e10 | −0.765725 | −0.382863 | − | 0.923805i | \(-0.625062\pi\) | ||||
−0.382863 | + | 0.923805i | \(0.625062\pi\) | |||||||
\(368\) | − 7.53531e8i | − 0.0410875i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.41542e9 | 0.0755226 | ||||||||
\(371\) | 5.74382e10i | 3.03183i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.17709e10 | 1.12471 | 0.562356 | − | 0.826895i | \(-0.309895\pi\) | ||||
0.562356 | + | 0.826895i | \(0.309895\pi\) | |||||||
\(374\) | 3.01907e9i | 0.154307i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.19609e10 | −1.09875 | ||||||||
\(377\) | 1.41614e10i | 0.701038i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.86928e10 | −0.905975 | −0.452988 | − | 0.891517i | \(-0.649642\pi\) | ||||
−0.452988 | + | 0.891517i | \(0.649642\pi\) | |||||||
\(380\) | 7.04336e9i | 0.337789i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.78998e10 | −0.840612 | ||||||||
\(383\) | 1.48977e10i | 0.692347i | 0.938170 | + | 0.346174i | \(0.112519\pi\) | ||||
−0.938170 | + | 0.346174i | \(0.887481\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.11929e9 | −0.415067 | ||||||||
\(386\) | 7.18383e9i | 0.323599i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.37383e10 | −0.606186 | ||||||||
\(389\) | − 1.67875e10i | − 0.733140i | −0.930390 | − | 0.366570i | \(-0.880532\pi\) | ||||
0.930390 | − | 0.366570i | \(-0.119468\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.54070e10 | −1.94274 | ||||||||
\(392\) | − 5.64017e10i | − 2.38862i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.82217e10 | −0.756142 | ||||||||
\(395\) | − 2.84413e10i | − 1.16832i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.63950e10 | 1.46514 | 0.732570 | − | 0.680692i | \(-0.238321\pi\) | ||||
0.732570 | + | 0.680692i | \(0.238321\pi\) | |||||||
\(398\) | 1.90591e10i | 0.759573i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.36709e7 | −0.00209652 | ||||||||
\(401\) | 3.09381e9i | 0.119651i | 0.998209 | + | 0.0598255i | \(0.0190544\pi\) | ||||
−0.998209 | + | 0.0598255i | \(0.980946\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.69010e10 | 0.640755 | ||||||||
\(404\) | − 8.93706e9i | − 0.335482i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.42444e10 | −1.26033 | ||||||||
\(407\) | 8.27281e8i | 0.0301492i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.78841e9 | −0.206855 | −0.103427 | − | 0.994637i | \(-0.532981\pi\) | ||||
−0.103427 | + | 0.994637i | \(0.532981\pi\) | |||||||
\(410\) | 3.07106e9i | 0.108681i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.22862e10 | −0.426411 | ||||||||
\(413\) | − 5.53087e10i | − 1.90105i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.47875e10 | −1.17282 | ||||||||
\(416\) | 1.90144e10i | 0.634907i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.65219e9 | 0.0868759 | ||||||||
\(419\) | 2.41615e10i | 0.783914i | 0.919984 | + | 0.391957i | \(0.128202\pi\) | ||||
−0.919984 | + | 0.391957i | \(0.871798\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.16694e10 | 0.371468 | 0.185734 | − | 0.982600i | \(-0.440534\pi\) | ||||
0.185734 | + | 0.982600i | \(0.440534\pi\) | |||||||
\(422\) | − 1.60147e9i | − 0.0504975i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.37092e10 | 1.66182 | ||||||||
\(425\) | 3.23415e9i | 0.0991297i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.24042e10 | 1.57636 | ||||||||
\(428\) | − 3.90513e10i | − 1.16375i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.35639e10 | 0.689245 | ||||||||
\(431\) | − 6.44251e10i | − 1.86701i | −0.358568 | − | 0.933504i | \(-0.616735\pi\) | ||||
0.358568 | − | 0.933504i | \(-0.383265\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.35776e10 | −1.52416 | −0.762082 | − | 0.647480i | \(-0.775823\pi\) | ||||
−0.762082 | + | 0.647480i | \(0.775823\pi\) | |||||||
\(434\) | 4.08691e10i | 1.15196i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.20887e10 | −0.334529 | ||||||||
\(437\) | 3.98891e10i | 1.09378i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.27951e9 | −0.115222 | −0.0576111 | − | 0.998339i | \(-0.518348\pi\) | ||||
−0.0576111 | + | 0.998339i | \(0.518348\pi\) | |||||||
\(440\) | 8.52725e9i | 0.227509i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.58468e10 | −0.415196 | ||||||||
\(443\) | − 1.20749e10i | − 0.313522i | −0.987637 | − | 0.156761i | \(-0.949895\pi\) | ||||
0.987637 | − | 0.156761i | \(-0.0501052\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.74967e10 | −0.701198 | ||||||||
\(446\) | 6.14124e9i | 0.155209i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.76028e10 | −1.18173 | ||||||||
\(449\) | 3.17911e10i | 0.782205i | 0.920347 | + | 0.391103i | \(0.127906\pi\) | ||||
−0.920347 | + | 0.391103i | \(0.872094\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.79497e9 | −0.0433861 | ||||||||
\(452\) | − 9.58861e9i | − 0.229722i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.96911e10 | 0.698881 | ||||||||
\(455\) | − 4.78664e10i | − 1.11682i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.30400e9 | −0.190381 | −0.0951903 | − | 0.995459i | \(-0.530346\pi\) | ||||
−0.0951903 | + | 0.995459i | \(0.530346\pi\) | |||||||
\(458\) | 3.79544e10i | 0.862583i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.85016e10 | −1.08324 | ||||||||
\(461\) | − 3.19035e10i | − 0.706374i | −0.935553 | − | 0.353187i | \(-0.885098\pi\) | ||||
0.935553 | − | 0.353187i | \(-0.114902\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.75541e10 | 0.599601 | 0.299800 | − | 0.954002i | \(-0.403080\pi\) | ||||
0.299800 | + | 0.954002i | \(0.403080\pi\) | |||||||
\(464\) | 1.11486e9i | 0.0240519i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.76949e10 | −0.799354 | ||||||||
\(467\) | 2.60699e10i | 0.548114i | 0.961713 | + | 0.274057i | \(0.0883658\pi\) | ||||
−0.961713 | + | 0.274057i | \(0.911634\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.96675e10 | 1.23324 | ||||||||
\(470\) | − 3.17063e10i | − 0.649761i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.17180e10 | −1.04201 | ||||||||
\(473\) | 1.37726e10i | 0.275151i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.84113e9 | 0.0558106 | ||||||||
\(476\) | 5.94798e10i | 1.15862i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.30570e9 | 0.101632 | ||||||||
\(479\) | 2.22131e9i | 0.0421956i | 0.999777 | + | 0.0210978i | \(0.00671614\pi\) | ||||
−0.999777 | + | 0.0210978i | \(0.993284\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.34232e9 | −0.0811226 | ||||||||
\(482\) | 8.40188e9i | 0.155664i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.14895e10 | 0.573832 | ||||||||
\(485\) | − 5.24482e10i | − 0.947902i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.62519e10 | 1.53339 | 0.766696 | − | 0.642011i | \(-0.221900\pi\) | ||||
0.766696 | + | 0.642011i | \(0.221900\pi\) | |||||||
\(488\) | − 4.90020e10i | − 0.864042i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.14304e10 | 1.41254 | ||||||||
\(491\) | − 4.40442e9i | − 0.0757814i | −0.999282 | − | 0.0378907i | \(-0.987936\pi\) | ||||
0.999282 | − | 0.0378907i | \(-0.0120639\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.71805e10 | 1.13725 | ||||||||
\(494\) | 1.39211e10i | 0.233758i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.33054e9 | 0.0219837 | ||||||||
\(497\) | − 5.87985e8i | − 0.00963697i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.77040e10 | −0.446829 | −0.223414 | − | 0.974724i | \(-0.571720\pi\) | ||||
−0.223414 | + | 0.974724i | \(0.571720\pi\) | |||||||
\(500\) | 3.96039e10i | 0.633663i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.40650e10 | 0.378941 | ||||||||
\(503\) | 2.37306e10i | 0.370712i | 0.982671 | + | 0.185356i | \(0.0593438\pi\) | ||||
−0.982671 | + | 0.185356i | \(0.940656\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.41187e10 | 0.524598 | ||||||||
\(506\) | 1.82633e10i | 0.278598i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.57890e10 | −0.837709 | ||||||||
\(509\) | 3.83002e10i | 0.570597i | 0.958439 | + | 0.285299i | \(0.0920928\pi\) | ||||
−0.958439 | + | 0.285299i | \(0.907907\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.31388e11 | 3.39358 | ||||||||
\(512\) | 3.01455e9i | 0.0438674i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.80111e10 | −0.687843 | ||||||||
\(515\) | − 4.69045e10i | − 0.666784i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.85316e10 | 0.259389 | ||||||||
\(518\) | − 1.05004e10i | − 0.145843i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.47588e10 | −0.612160 | ||||||||
\(521\) | 1.29094e11i | 1.75208i | 0.482238 | + | 0.876040i | \(0.339824\pi\) | ||||
−0.482238 | + | 0.876040i | \(0.660176\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.37220e11 | 1.83405 | 0.917024 | − | 0.398831i | \(-0.130584\pi\) | ||||
0.917024 | + | 0.398831i | \(0.130584\pi\) | |||||||
\(524\) | − 2.91378e10i | − 0.386484i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.25268e10 | −0.294277 | ||||||||
\(527\) | − 8.01767e10i | − 1.03946i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.96371e11 | −2.50758 | ||||||||
\(530\) | 7.75431e10i | 0.982742i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.22518e10 | 0.652311 | ||||||||
\(533\) | − 9.42163e9i | − 0.116739i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.49085e11 | 1.81978 | ||||||||
\(536\) | − 5.57938e10i | − 0.675969i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.01820e10 | 0.240900 | ||||||||
\(539\) | 4.75944e10i | 0.563898i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.71547e10 | −0.900686 | −0.450343 | − | 0.892856i | \(-0.648698\pi\) | ||||
−0.450343 | + | 0.892856i | \(0.648698\pi\) | |||||||
\(542\) | 5.86735e10i | 0.679900i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.02028e10 | 1.02997 | ||||||||
\(545\) | − 4.61506e10i | − 0.523108i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.33068e10 | −0.595434 | −0.297717 | − | 0.954654i | \(-0.596225\pi\) | ||||
−0.297717 | + | 0.954654i | \(0.596225\pi\) | |||||||
\(548\) | 2.33821e10i | 0.259276i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.30082e9 | 0.0142157 | ||||||||
\(551\) | − 5.90167e10i | − 0.640278i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.10995e11 | −2.25616 | ||||||||
\(554\) | 6.82631e10i | 0.724681i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.02346e10 | 0.211736 | ||||||||
\(557\) | − 1.56229e11i | − 1.62309i | −0.584291 | − | 0.811544i | \(-0.698627\pi\) | ||||
0.584291 | − | 0.811544i | \(-0.301373\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.22912e10 | −0.740352 | ||||||||
\(560\) | − 3.76830e9i | − 0.0383172i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.07492e10 | −0.207996 | ||||||||
\(563\) | 4.85065e10i | 0.482799i | 0.970426 | + | 0.241399i | \(0.0776064\pi\) | ||||
−0.970426 | + | 0.241399i | \(0.922394\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.66061e10 | 0.359219 | ||||||||
\(566\) | − 9.63228e9i | − 0.0938563i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.49811e8 | −0.00528227 | ||||||||
\(569\) | − 4.85523e10i | − 0.463192i | −0.972812 | − | 0.231596i | \(-0.925605\pi\) | ||||
0.972812 | − | 0.231596i | \(-0.0743947\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.65482e11 | 1.55670 | 0.778351 | − | 0.627830i | \(-0.216057\pi\) | ||||
0.778351 | + | 0.627830i | \(0.216057\pi\) | |||||||
\(572\) | − 9.89337e9i | − 0.0924188i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.27829e10 | 0.209875 | ||||||||
\(575\) | 1.95644e10i | 0.178977i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.25738e11 | −1.13439 | −0.567194 | − | 0.823584i | \(-0.691971\pi\) | ||||
−0.567194 | + | 0.823584i | \(0.691971\pi\) | |||||||
\(578\) | 5.31158e9i | 0.0475897i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.17590e10 | 0.634110 | ||||||||
\(581\) | 2.58074e11i | 2.26486i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.53223e10 | −0.392318 | ||||||||
\(584\) | − 2.16366e11i | − 1.86011i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.21766e11 | 1.03261 | ||||||||
\(587\) | 6.82411e10i | 0.574769i | 0.957815 | + | 0.287385i | \(0.0927858\pi\) | ||||
−0.957815 | + | 0.287385i | \(0.907214\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.04336e10 | −0.585220 | ||||||||
\(590\) | − 7.46683e10i | − 0.616209i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.41851e8 | −0.00278324 | ||||||||
\(593\) | − 2.22279e10i | − 0.179755i | −0.995953 | − | 0.0898774i | \(-0.971352\pi\) | ||||
0.995953 | − | 0.0898774i | \(-0.0286475\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.27074e11 | −1.81175 | ||||||||
\(596\) | − 2.34966e10i | − 0.186218i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.58627e10 | −0.749627 | ||||||||
\(599\) | − 2.13320e11i | − 1.65701i | −0.559984 | − | 0.828503i | \(-0.689193\pi\) | ||||
0.559984 | − | 0.828503i | \(-0.310807\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.49960e10 | 0.268238 | 0.134119 | − | 0.990965i | \(-0.457180\pi\) | ||||
0.134119 | + | 0.990965i | \(0.457180\pi\) | |||||||
\(602\) | − 1.74811e11i | − 1.33101i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.66617e10 | 0.200327 | ||||||||
\(605\) | 1.20216e11i | 0.897309i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.10769e11 | −0.815951 | −0.407975 | − | 0.912993i | \(-0.633765\pi\) | ||||
−0.407975 | + | 0.912993i | \(0.633765\pi\) | |||||||
\(608\) | − 7.92413e10i | − 0.579879i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.07471e10 | 0.510963 | ||||||||
\(611\) | 9.72710e10i | 0.697940i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.84434e10 | −0.343078 | −0.171539 | − | 0.985177i | \(-0.554874\pi\) | ||||
−0.171539 | + | 0.985177i | \(0.554874\pi\) | |||||||
\(614\) | − 4.91786e10i | − 0.346021i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.32601e10 | 0.439347 | ||||||||
\(617\) | − 7.67452e10i | − 0.529554i | −0.964310 | − | 0.264777i | \(-0.914702\pi\) | ||||
0.964310 | − | 0.264777i | \(-0.0852984\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.11915e11 | −1.44344 | −0.721721 | − | 0.692184i | \(-0.756648\pi\) | ||||
−0.721721 | + | 0.692184i | \(0.756648\pi\) | |||||||
\(620\) | − 8.56410e10i | − 0.579582i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.69368e10 | −0.179964 | ||||||||
\(623\) | 2.03987e11i | 1.35410i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.36613e11 | −0.895304 | ||||||||
\(626\) | 5.14091e10i | 0.334767i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.12391e11 | −0.722589 | ||||||||
\(629\) | 2.05996e10i | 0.131600i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.44761e10 | −0.0913130 | −0.0456565 | − | 0.998957i | \(-0.514538\pi\) | ||||
−0.0456565 | + | 0.998957i | \(0.514538\pi\) | |||||||
\(632\) | 1.97296e11i | 1.23666i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.54036e11 | −0.953381 | ||||||||
\(635\) | − 2.12983e11i | − 1.30994i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.49819e11 | −1.51728 | ||||||||
\(638\) | − 2.70210e10i | − 0.163087i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.41593e10 | 0.561233 | ||||||||
\(641\) | 2.38883e10i | 0.141499i | 0.997494 | + | 0.0707494i | \(0.0225390\pi\) | ||||
−0.997494 | + | 0.0707494i | \(0.977461\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.51535e11 | 0.886480 | 0.443240 | − | 0.896403i | \(-0.353829\pi\) | ||||
0.443240 | + | 0.896403i | \(0.353829\pi\) | |||||||
\(644\) | 3.59813e11i | 2.09187i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.60404e10 | 0.379210 | ||||||||
\(647\) | − 1.51614e11i | − 0.865208i | −0.901584 | − | 0.432604i | \(-0.857595\pi\) | ||||
0.901584 | − | 0.432604i | \(-0.142405\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.36420e10 | 0.245995 | ||||||||
\(650\) | 6.82790e9i | 0.0382502i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.97319e10 | −0.164525 | ||||||||
\(653\) | 1.82933e11i | 1.00610i | 0.864258 | + | 0.503048i | \(0.167788\pi\) | ||||
−0.864258 | + | 0.503048i | \(0.832212\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.11238e11 | 0.604350 | ||||||||
\(656\) | − 7.41722e8i | − 0.00400521i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.35216e11 | −1.25477 | ||||||||
\(659\) | 2.97761e11i | 1.57880i | 0.613881 | + | 0.789398i | \(0.289607\pi\) | ||||
−0.613881 | + | 0.789398i | \(0.710393\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.11919e11 | 0.586270 | 0.293135 | − | 0.956071i | \(-0.405301\pi\) | ||||
0.293135 | + | 0.956071i | \(0.405301\pi\) | |||||||
\(662\) | 7.42109e10i | 0.386399i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.41320e11 | 1.24142 | ||||||||
\(665\) | 1.99480e11i | 1.02003i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.06397e11 | 2.05328 | ||||||||
\(668\) | − 8.70905e10i | − 0.437386i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.05528e10 | 0.399743 | ||||||||
\(671\) | 4.13502e10i | 0.203980i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.67096e10 | −0.227691 | −0.113845 | − | 0.993498i | \(-0.536317\pi\) | ||||
−0.113845 | + | 0.993498i | \(0.536317\pi\) | |||||||
\(674\) | − 4.71220e10i | − 0.228341i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.50749e10 | −0.359507 | ||||||||
\(677\) | − 1.71821e11i | − 0.817941i | −0.912548 | − | 0.408970i | \(-0.865888\pi\) | ||||
0.912548 | − | 0.408970i | \(-0.134112\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.89091e11 | −1.83051 | ||||||||
\(680\) | 2.12332e11i | 0.993068i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.22483e10 | −0.149063 | ||||||||
\(683\) | − 6.74141e10i | − 0.309790i | −0.987931 | − | 0.154895i | \(-0.950496\pi\) | ||||
0.987931 | − | 0.154895i | \(-0.0495040\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.92650e10 | −0.405433 | ||||||||
\(686\) | − 3.49510e11i | − 1.57821i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.69116e9 | −0.0254008 | ||||||||
\(689\) | − 2.37893e11i | − 1.05561i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.86155e10 | 0.300961 | 0.150481 | − | 0.988613i | \(-0.451918\pi\) | ||||
0.150481 | + | 0.988613i | \(0.451918\pi\) | |||||||
\(692\) | − 9.45277e10i | − 0.412225i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.87953e10 | 0.210349 | ||||||||
\(695\) | 7.72488e10i | 0.331095i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.46953e10 | −0.189379 | ||||||||
\(698\) | − 2.38360e11i | − 1.00418i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.56280e10 | 0.106739 | ||||||||
\(701\) | 3.47803e11i | 1.44033i | 0.693804 | + | 0.720164i | \(0.255934\pi\) | ||||
−0.693804 | + | 0.720164i | \(0.744066\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.80963e10 | 0.0740916 | ||||||||
\(704\) | − 3.75615e10i | − 0.152916i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.92027e10 | −0.318802 | ||||||||
\(707\) | − 2.53113e11i | − 1.01306i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.64810e11 | −1.04797 | −0.523986 | − | 0.851727i | \(-0.675555\pi\) | ||||
−0.523986 | + | 0.851727i | \(0.675555\pi\) | |||||||
\(710\) | − 7.93795e8i | − 0.00312374i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.90743e11 | 0.742215 | ||||||||
\(713\) | − 4.85016e11i | − 1.87671i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.77695e10 | 0.144517 | ||||||||
\(716\) | 6.52098e10i | 0.248120i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.91456e10 | −0.297803 | ||||||||
\(719\) | 2.48269e11i | 0.928981i | 0.885578 | + | 0.464491i | \(0.153763\pi\) | ||||
−0.885578 | + | 0.464491i | \(0.846237\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.47965e11 | −1.28764 | ||||||||
\(722\) | 1.12080e11i | 0.412458i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.71599e11 | 0.624540 | ||||||||
\(725\) | − 2.89460e10i | − 0.104770i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.95500e11 | 1.05784 | 0.528921 | − | 0.848671i | \(-0.322597\pi\) | ||||
0.528921 | + | 0.848671i | \(0.322597\pi\) | |||||||
\(728\) | 3.32047e11i | 1.18215i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.12380e11 | 1.10000 | ||||||||
\(731\) | 3.42943e11i | 1.20103i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.27907e11 | 1.48229 | 0.741146 | − | 0.671344i | \(-0.234283\pi\) | ||||
0.741146 | + | 0.671344i | \(0.234283\pi\) | |||||||
\(734\) | 1.39124e11i | 0.479310i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.45667e11 | 1.85959 | ||||||||
\(737\) | 4.70814e10i | 0.159580i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.19830e10 | −0.0401781 | −0.0200890 | − | 0.999798i | \(-0.506395\pi\) | ||||
−0.0200890 | + | 0.999798i | \(0.506395\pi\) | |||||||
\(740\) | 2.20035e10i | 0.0733779i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.75260e11 | 1.89779 | ||||||||
\(743\) | − 2.77564e11i | − 0.910769i | −0.890295 | − | 0.455384i | \(-0.849502\pi\) | ||||
0.890295 | − | 0.455384i | \(-0.150498\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.97022e10 | 0.291191 | ||||||||
\(746\) | − 2.18042e11i | − 0.704020i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.69332e10 | −0.149925 | ||||||||
\(749\) | − 1.10600e12i | − 3.51421i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.44914e10 | 0.0455566 | 0.0227783 | − | 0.999741i | \(-0.492749\pi\) | ||||
0.0227783 | + | 0.999741i | \(0.492749\pi\) | |||||||
\(752\) | 7.65770e9i | 0.0239457i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.41831e11 | 0.438819 | ||||||||
\(755\) | 1.01785e11i | 0.313254i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.94269e11 | 0.591590 | 0.295795 | − | 0.955251i | \(-0.404415\pi\) | ||||
0.295795 | + | 0.955251i | \(0.404415\pi\) | |||||||
\(758\) | 1.87213e11i | 0.567100i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.86529e11 | 0.559103 | ||||||||
\(761\) | 4.48052e11i | 1.33595i | 0.744185 | + | 0.667974i | \(0.232838\pi\) | ||||
−0.744185 | + | 0.667974i | \(0.767162\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.42372e11 | −1.01018 | ||||||||
\(764\) | − 2.78264e11i | − 0.816740i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.49205e11 | 0.433379 | ||||||||
\(767\) | 2.29073e11i | 0.661901i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.27389e11 | 0.650225 | 0.325113 | − | 0.945675i | \(-0.394598\pi\) | ||||
0.325113 | + | 0.945675i | \(0.394598\pi\) | |||||||
\(770\) | 9.13324e10i | 0.259814i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.11677e11 | −0.314409 | ||||||||
\(773\) | 3.48003e11i | 0.974686i | 0.873211 | + | 0.487343i | \(0.162034\pi\) | ||||
−0.873211 | + | 0.487343i | \(0.837966\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.45457e10 | −0.0957605 | ||||||||
\(776\) | 3.63831e11i | 1.00335i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.68131e11 | −0.458913 | ||||||||
\(779\) | 3.92639e10i | 0.106621i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.63956e8 | 0.00124702 | ||||||||
\(782\) | 4.54764e11i | 1.21607i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.96671e10 | −0.0520566 | ||||||||
\(785\) | − 4.29069e11i | − 1.12992i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.54239e11 | 0.662741 | 0.331370 | − | 0.943501i | \(-0.392489\pi\) | ||||
0.331370 | + | 0.943501i | \(0.392489\pi\) | |||||||
\(788\) | − 2.83267e11i | − 0.734669i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.84848e11 | −0.731316 | ||||||||
\(791\) | − 2.71565e11i | − 0.693695i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.17044e11 | −0.548851 | ||||||||
\(794\) | − 3.64506e11i | − 0.917113i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.96285e11 | −0.738002 | ||||||||
\(797\) | − 5.53726e11i | − 1.37234i | −0.727442 | − | 0.686169i | \(-0.759291\pi\) | ||||
0.727442 | − | 0.686169i | \(-0.240709\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.61445e11 | 1.13222 | ||||||||
\(800\) | − 3.88656e10i | − 0.0948866i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.09854e10 | 0.0748962 | ||||||||
\(803\) | 1.82580e11i | 0.439128i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.37365e12 | −3.27108 | ||||||||
\(806\) | − 1.69268e11i | − 0.401084i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.36680e11 | −0.555285 | ||||||||
\(809\) | − 1.00027e11i | − 0.233519i | −0.993160 | − | 0.116759i | \(-0.962749\pi\) | ||||
0.993160 | − | 0.116759i | \(-0.0372506\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.06002e10 | 0.209433 | 0.104717 | − | 0.994502i | \(-0.466606\pi\) | ||||
0.104717 | + | 0.994502i | \(0.466606\pi\) | |||||||
\(812\) | − 5.32351e11i | − 1.22454i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.28546e9 | 0.0188720 | ||||||||
\(815\) | − 1.13506e11i | − 0.257270i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.01269e11 | 0.676185 | ||||||||
\(818\) | 5.79726e10i | 0.129482i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.77415e10 | −0.105594 | ||||||||
\(821\) | 6.19591e11i | 1.36374i | 0.731472 | + | 0.681871i | \(0.238834\pi\) | ||||
−0.731472 | + | 0.681871i | \(0.761166\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.63723e10 | 0.0792813 | 0.0396407 | − | 0.999214i | \(-0.487379\pi\) | ||||
0.0396407 | + | 0.999214i | \(0.487379\pi\) | |||||||
\(824\) | 3.25374e11i | 0.705788i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.53933e11 | −1.18997 | ||||||||
\(827\) | − 6.85214e10i | − 0.146489i | −0.997314 | − | 0.0732444i | \(-0.976665\pi\) | ||||
0.997314 | − | 0.0732444i | \(-0.0233353\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.13133e11 | −1.29819 | −0.649093 | − | 0.760709i | \(-0.724851\pi\) | ||||
−0.649093 | + | 0.760709i | \(0.724851\pi\) | |||||||
\(830\) | 3.48407e11i | 0.734133i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.97157e11 | 0.411452 | ||||||||
\(833\) | 1.18512e12i | 2.46139i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.32482e11 | 0.683947 | ||||||||
\(836\) | 4.12299e10i | 0.0844087i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.41985e11 | 0.490695 | ||||||||
\(839\) | 3.69496e11i | 0.745697i | 0.927892 | + | 0.372848i | \(0.121619\pi\) | ||||
−0.927892 | + | 0.372848i | \(0.878381\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.01027e11 | −0.201954 | ||||||||
\(842\) | − 1.16873e11i | − 0.232522i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.48959e10 | 0.0490634 | ||||||||
\(845\) | − 2.86610e11i | − 0.562167i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.91836e11 | 1.73281 | ||||||||
\(848\) | − 1.87282e10i | − 0.0362171i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.23909e10 | 0.0620508 | ||||||||
\(851\) | 1.24614e11i | 0.237601i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.05380e11 | 0.387937 | 0.193969 | − | 0.981008i | \(-0.437864\pi\) | ||||
0.193969 | + | 0.981008i | \(0.437864\pi\) | |||||||
\(854\) | − 5.24844e11i | − 0.986730i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.03419e12 | −1.92623 | ||||||||
\(857\) | 5.65349e11i | 1.04808i | 0.851694 | + | 0.524039i | \(0.175575\pi\) | ||||
−0.851694 | + | 0.524039i | \(0.824425\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.34065e10 | 0.116456 | 0.0582279 | − | 0.998303i | \(-0.481455\pi\) | ||||
0.0582279 | + | 0.998303i | \(0.481455\pi\) | |||||||
\(860\) | 3.66316e11i | 0.669671i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.45236e11 | −1.16866 | ||||||||
\(863\) | − 7.20037e11i | − 1.29811i | −0.760742 | − | 0.649055i | \(-0.775165\pi\) | ||||
0.760742 | − | 0.649055i | \(-0.224835\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.60875e11 | 0.644602 | ||||||||
\(866\) | 5.36596e11i | 0.954060i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.35336e11 | −1.11924 | ||||||||
\(869\) | − 1.66488e11i | − 0.291947i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.47126e11 | −0.429384 | ||||||||
\(872\) | 3.20145e11i | 0.553707i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.99501e11 | 0.684655 | ||||||||
\(875\) | 1.12165e12i | 1.91348i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.86955e11 | 0.823171 | 0.411586 | − | 0.911371i | \(-0.364975\pi\) | ||||
0.411586 | + | 0.911371i | \(0.364975\pi\) | |||||||
\(878\) | 4.28606e10i | 0.0721240i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.97342e9 | 0.00495822 | ||||||||
\(881\) | − 1.10625e12i | − 1.83633i | −0.396196 | − | 0.918166i | \(-0.629670\pi\) | ||||
0.396196 | − | 0.918166i | \(-0.370330\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.45262e10 | 0.122593 | 0.0612966 | − | 0.998120i | \(-0.480476\pi\) | ||||
0.0612966 | + | 0.998120i | \(0.480476\pi\) | |||||||
\(884\) | − 2.46348e11i | − 0.403405i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.20933e11 | −0.196251 | ||||||||
\(887\) | − 1.15964e12i | − 1.87338i | −0.350153 | − | 0.936692i | \(-0.613870\pi\) | ||||
0.350153 | − | 0.936692i | \(-0.386130\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.58004e12 | −2.52965 | ||||||||
\(890\) | 2.75387e11i | 0.438919i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.54693e10 | −0.150801 | ||||||||
\(893\) | − 4.05370e11i | − 0.637449i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.48949e11 | −0.387988 | ||||||||
\(896\) | − 6.98529e11i | − 1.08381i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.18397e11 | 0.489626 | ||||||||
\(899\) | 7.17591e11i | 1.09860i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.12854e12 | −1.71245 | ||||||||
\(902\) | 1.79771e10i | 0.0271578i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.53935e11 | −0.380232 | ||||||||
\(905\) | 6.55107e11i | 0.976602i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.26174e12 | 1.86440 | 0.932201 | − | 0.361941i | \(-0.117886\pi\) | ||||
0.932201 | + | 0.361941i | \(0.117886\pi\) | |||||||
\(908\) | 4.61567e11i | 0.679034i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.79396e11 | −0.699083 | ||||||||
\(911\) | − 7.43367e11i | − 1.07927i | −0.841899 | − | 0.539635i | \(-0.818562\pi\) | ||||
0.841899 | − | 0.539635i | \(-0.181438\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.03637e11 | −0.293071 | ||||||||
\(914\) | 8.31670e10i | 0.119170i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.90025e11 | −0.838086 | ||||||||
\(917\) | − 8.25230e11i | − 1.16707i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.99130e10 | −0.126055 | −0.0630276 | − | 0.998012i | \(-0.520076\pi\) | ||||
−0.0630276 | + | 0.998012i | \(0.520076\pi\) | |||||||
\(920\) | 1.28446e12i | 1.79296i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.19523e11 | −0.442159 | ||||||||
\(923\) | 2.43527e9i | 0.00335536i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.87572e9 | 0.0121237 | ||||||||
\(926\) | − 2.75962e11i | − 0.375323i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.07325e11 | −1.08857 | ||||||||
\(929\) | − 8.58727e11i | − 1.15290i | −0.817132 | − | 0.576451i | \(-0.804437\pi\) | ||||
0.817132 | − | 0.576451i | \(-0.195563\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.04110e12 | 1.38578 | ||||||||
\(932\) | − 5.85991e11i | − 0.776653i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.61097e11 | 0.343095 | ||||||||
\(935\) | − 1.79175e11i | − 0.234440i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.25416e11 | 0.162702 | 0.0813512 | − | 0.996685i | \(-0.474076\pi\) | ||||
0.0813512 | + | 0.996685i | \(0.474076\pi\) | |||||||
\(938\) | − 5.97588e11i | − 0.771952i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.92893e11 | 0.631308 | ||||||||
\(941\) | 1.01295e12i | 1.29191i | 0.763377 | + | 0.645954i | \(0.223540\pi\) | ||||
−0.763377 | + | 0.645954i | \(0.776460\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.70377e11 | −0.341919 | ||||||||
\(944\) | 1.80339e10i | 0.0227092i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.37937e11 | 0.172233 | ||||||||
\(947\) | − 2.99006e11i | − 0.371774i | −0.982571 | − | 0.185887i | \(-0.940484\pi\) | ||||
0.982571 | − | 0.185887i | \(-0.0595159\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.58346e11 | −1.18156 | ||||||||
\(950\) | − 2.84548e10i | − 0.0349350i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.57520e12 | 1.91773 | ||||||||
\(953\) | − 9.57954e11i | − 1.16138i | −0.814126 | − | 0.580688i | \(-0.802783\pi\) | ||||
0.814126 | − | 0.580688i | \(-0.197217\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.06232e12 | 1.27715 | ||||||||
\(956\) | 8.24804e10i | 0.0987460i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.22471e10 | 0.0264126 | ||||||||
\(959\) | 6.62220e11i | 0.782939i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.51989e9 | 0.00412701 | ||||||||
\(962\) | 4.34896e10i | 0.0507792i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.30612e11 | −0.151243 | ||||||||
\(965\) | − 4.26345e11i | − 0.491646i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.18590e12 | 1.35626 | 0.678131 | − | 0.734941i | \(-0.262790\pi\) | ||||
0.678131 | + | 0.734941i | \(0.262790\pi\) | |||||||
\(968\) | − 8.33936e11i | − 0.949798i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.25284e11 | −0.593345 | ||||||||
\(971\) | − 5.47759e10i | − 0.0616187i | −0.999525 | − | 0.0308093i | \(-0.990192\pi\) | ||||
0.999525 | − | 0.0308093i | \(-0.00980847\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.73077e11 | 0.639384 | ||||||||
\(974\) | − 8.63838e11i | − 0.959835i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.70869e10 | −0.0188305 | ||||||||
\(977\) | 9.25105e11i | 1.01534i | 0.861551 | + | 0.507672i | \(0.169494\pi\) | ||||
−0.861551 | + | 0.507672i | \(0.830506\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.60958e11 | −0.175219 | ||||||||
\(980\) | 1.26589e12i | 1.37243i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.41116e10 | −0.0474358 | ||||||||
\(983\) | − 5.78240e11i | − 0.619290i | −0.950852 | − | 0.309645i | \(-0.899790\pi\) | ||||
0.950852 | − | 0.309645i | \(-0.100210\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.08142e12 | 1.14881 | ||||||||
\(986\) | − 6.72832e11i | − 0.711867i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.16412e11 | −0.227119 | ||||||||
\(989\) | 2.07458e12i | 2.16843i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.41284e11 | −0.146487 | −0.0732435 | − | 0.997314i | \(-0.523335\pi\) | ||||
−0.0732435 | + | 0.997314i | \(0.523335\pi\) | |||||||
\(992\) | 9.63505e11i | 0.994963i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.88884e9 | −0.00603231 | ||||||||
\(995\) | − 1.13112e12i | − 1.15402i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.24199e12 | −1.25700 | −0.628502 | − | 0.777808i | \(-0.716332\pi\) | ||||
−0.628502 | + | 0.777808i | \(0.716332\pi\) | |||||||
\(998\) | 2.77464e11i | 0.279695i | ||||||||
\(999\) | 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 | 81.9.b.b.80.6 | ✓ | 16 | |
3.2 | odd | 2 | inner | 81.9.b.b.80.11 | yes | 16 | |
9.2 | odd | 6 | 81.9.d.g.53.11 | 32 | |||
9.4 | even | 3 | 81.9.d.g.26.11 | 32 | |||
9.5 | odd | 6 | 81.9.d.g.26.6 | 32 | |||
9.7 | even | 3 | 81.9.d.g.53.6 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
81.9.b.b.80.6 | ✓ | 16 | 1.1 | even | 1 | trivial | |
81.9.b.b.80.11 | yes | 16 | 3.2 | odd | 2 | inner | |
81.9.d.g.26.6 | 32 | 9.5 | odd | 6 | |||
81.9.d.g.26.11 | 32 | 9.4 | even | 3 | |||
81.9.d.g.53.6 | 32 | 9.7 | even | 3 | |||
81.9.d.g.53.11 | 32 | 9.2 | odd | 6 |