Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,8,Mod(3,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.3");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.e (of order \(4\), degree \(2\), 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: | \(6.24770050968\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{4}]$ |
Embedding invariants
Embedding label | 7.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 20.7 |
Dual form | 20.8.e.a.3.1 |
$q$-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 \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.00000 | − | 8.00000i | −0.707107 | − | 0.707107i | ||||
\(3\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(4\) | 128.000i | 1.00000i | ||||||||
\(5\) | 278.000 | + | 29.0000i | 0.994603 | + | 0.103754i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | 1024.00 | − | 1024.00i | 0.707107 | − | 0.707107i | ||||
\(9\) | − | 2187.00i | − | 1.00000i | ||||||
\(10\) | −1992.00 | − | 2456.00i | −0.629926 | − | 0.776655i | ||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11003.0 | − | 11003.0i | 1.38902 | − | 1.38902i | 0.561643 | − | 0.827379i | \(-0.310169\pi\) |
0.827379 | − | 0.561643i | \(-0.189831\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −16384.0 | −1.00000 | ||||||||
\(17\) | 17139.0 | + | 17139.0i | 0.846086 | + | 0.846086i | 0.989642 | − | 0.143557i | \(-0.0458539\pi\) |
−0.143557 | + | 0.989642i | \(0.545854\pi\) | |||||||
\(18\) | −17496.0 | + | 17496.0i | −0.707107 | + | 0.707107i | ||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | −3712.00 | + | 35584.0i | −0.103754 | + | 0.994603i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 76443.0 | + | 16124.0i | 0.978470 | + | 0.206387i | ||||
\(26\) | −176048. | −1.96437 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 120844.i | − | 0.920094i | −0.887895 | − | 0.460047i | \(-0.847833\pi\) | ||
0.887895 | − | 0.460047i | \(-0.152167\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 131072. | + | 131072.i | 0.707107 | + | 0.707107i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 274224.i | − | 1.19655i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 279936. | 1.00000 | ||||||||
\(37\) | 157829. | + | 157829.i | 0.512249 | + | 0.512249i | 0.915215 | − | 0.402966i | \(-0.132021\pi\) |
−0.402966 | + | 0.915215i | \(0.632021\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 314368. | − | 254976.i | 0.776655 | − | 0.629926i | ||||
\(41\) | −882568. | −1.99988 | −0.999942 | − | 0.0107974i | \(-0.996563\pi\) | ||||
−0.999942 | + | 0.0107974i | \(0.996563\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 63423.0 | − | 607986.i | 0.103754 | − | 0.994603i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 823543.i | 1.00000i | ||||||||
\(50\) | −482552. | − | 740536.i | −0.545945 | − | 0.837821i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.40838e6 | + | 1.40838e6i | 1.38902 | + | 1.38902i | ||||
\(53\) | −1.40691e6 | + | 1.40691e6i | −1.29808 | + | 1.29808i | −0.368413 | + | 0.929662i | \(0.620099\pi\) |
−0.929662 | + | 0.368413i | \(0.879901\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −966752. | + | 966752.i | −0.650605 | + | 0.650605i | ||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 532572. | 0.300417 | 0.150208 | − | 0.988654i | \(-0.452006\pi\) | ||||
0.150208 | + | 0.988654i | \(0.452006\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 2.09715e6i | − | 1.00000i | ||||||
\(65\) | 3.37792e6 | − | 2.73975e6i | 1.52564 | − | 1.23741i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(68\) | −2.19379e6 | + | 2.19379e6i | −0.846086 | + | 0.846086i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | −2.23949e6 | − | 2.23949e6i | −0.707107 | − | 0.707107i | ||||
\(73\) | 4.64401e6 | − | 4.64401e6i | 1.39722 | − | 1.39722i | 0.589305 | − | 0.807911i | \(-0.299402\pi\) |
0.807911 | − | 0.589305i | \(-0.200598\pi\) | |||||||
\(74\) | − | 2.52526e6i | − | 0.724429i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | −4.55475e6 | − | 475136.i | −0.994603 | − | 0.103754i | ||||
\(81\) | −4.78297e6 | −1.00000 | ||||||||
\(82\) | 7.06054e6 | + | 7.06054e6i | 1.41413 | + | 1.41413i | ||||
\(83\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.26761e6 | + | 5.26167e6i | 0.753735 | + | 0.929304i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.56210e6i | 1.43777i | 0.695131 | + | 0.718883i | \(0.255346\pi\) | ||||
−0.695131 | + | 0.718883i | \(0.744654\pi\) | |||||||
\(90\) | −5.37127e6 | + | 4.35650e6i | −0.776655 | + | 0.629926i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.06929e7 | − | 1.06929e7i | −1.18958 | − | 1.18958i | −0.977185 | − | 0.212392i | \(-0.931875\pi\) |
−0.212392 | − | 0.977185i | \(-0.568125\pi\) | |||||||
\(98\) | 6.58834e6 | − | 6.58834e6i | 0.707107 | − | 0.707107i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.06387e6 | + | 9.78470e6i | −0.206387 | + | 0.978470i | ||||
\(101\) | −1.33042e7 | −1.28488 | −0.642442 | − | 0.766334i | \(-0.722079\pi\) | ||||
−0.642442 | + | 0.766334i | \(0.722079\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(104\) | − | 2.25341e7i | − | 1.96437i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.25105e7 | 1.83576 | ||||||||
\(107\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.41162e7i | 1.78368i | 0.452352 | + | 0.891839i | \(0.350585\pi\) | ||||
−0.452352 | + | 0.891839i | \(0.649415\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.74590e6 | − | 9.74590e6i | 0.635400 | − | 0.635400i | −0.314017 | − | 0.949417i | \(-0.601675\pi\) |
0.949417 | + | 0.314017i | \(0.101675\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.54680e7 | 0.920094 | ||||||||
\(117\) | −2.40636e7 | − | 2.40636e7i | −1.38902 | − | 1.38902i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.94872e7 | 1.00000 | ||||||||
\(122\) | −4.26058e6 | − | 4.26058e6i | −0.212427 | − | 0.212427i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.07836e7 | + | 6.69932e6i | 0.951776 | + | 0.306793i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(128\) | −1.67772e7 | + | 1.67772e7i | −0.707107 | + | 0.707107i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.89413e7 | − | 5.10539e6i | −1.95377 | − | 0.203811i | ||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.51007e7 | 1.19655 | ||||||||
\(137\) | 3.62213e6 | + | 3.62213e6i | 0.120349 | + | 0.120349i | 0.764716 | − | 0.644367i | \(-0.222879\pi\) |
−0.644367 | + | 0.764716i | \(0.722879\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.58318e7i | 1.00000i | ||||||||
\(145\) | 3.50448e6 | − | 3.35946e7i | 0.0954630 | − | 0.915128i | ||||
\(146\) | −7.43042e7 | −1.97596 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.02021e7 | + | 2.02021e7i | −0.512249 | + | 0.512249i | ||||
\(149\) | 7.31577e7i | 1.81179i | 0.423502 | + | 0.905895i | \(0.360801\pi\) | ||||
−0.423502 | + | 0.905895i | \(0.639199\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.74830e7 | − | 3.74830e7i | 0.846086 | − | 0.846086i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.86842e7 | + | 2.86842e7i | 0.591554 | + | 0.591554i | 0.938051 | − | 0.346497i | \(-0.112629\pi\) |
−0.346497 | + | 0.938051i | \(0.612629\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.26369e7 | + | 4.02391e7i | 0.629926 | + | 0.776655i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.82638e7 | + | 3.82638e7i | 0.707107 | + | 0.707107i | ||||
\(163\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(164\) | − | 1.12969e8i | − | 1.99988i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.79384e8i | − | 2.85877i | ||||||
\(170\) | 7.95250e6 | − | 7.62343e7i | 0.124146 | − | 1.19009i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.24761e7 | + | 9.24761e7i | −1.35790 | + | 1.35790i | −0.481400 | + | 0.876501i | \(0.659871\pi\) |
−0.876501 | + | 0.481400i | \(0.840129\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.64968e7 | − | 7.64968e7i | 1.01665 | − | 1.01665i | ||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 7.78222e7 | + | 8.11814e6i | 0.994603 | + | 0.103754i | ||||
\(181\) | −1.45860e8 | −1.82836 | −0.914180 | − | 0.405309i | \(-0.867164\pi\) | ||||
−0.914180 | + | 0.405309i | \(0.867164\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.92994e7 | + | 4.84535e7i | 0.456336 | + | 0.562632i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.22647e7 | + | 3.22647e7i | −0.323056 | + | 0.323056i | −0.849938 | − | 0.526883i | \(-0.823361\pi\) |
0.526883 | + | 0.849938i | \(0.323361\pi\) | |||||||
\(194\) | 1.71086e8i | 1.68232i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.05414e8 | −1.00000 | ||||||||
\(197\) | 1.45581e8 | + | 1.45581e8i | 1.35667 | + | 1.35667i | 0.877989 | + | 0.478681i | \(0.158885\pi\) |
0.478681 | + | 0.877989i | \(0.341115\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 9.47886e7 | − | 6.17667e7i | 0.837821 | − | 0.545945i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.06434e8 | + | 1.06434e8i | 0.908550 | + | 0.908550i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.45354e8 | − | 2.55945e7i | −1.98909 | − | 0.207495i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.80273e8 | + | 1.80273e8i | −1.38902 | + | 1.38902i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | −1.80084e8 | − | 1.80084e8i | −1.29808 | − | 1.29808i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.92930e8 | − | 1.92930e8i | 1.26125 | − | 1.26125i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.77161e8 | 2.35046 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.52632e7 | − | 1.67181e8i | 0.206387 | − | 0.978470i | ||||
\(226\) | −1.55934e8 | −0.898592 | ||||||||
\(227\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.90890e8i | − | 1.60068i | −0.599547 | − | 0.800339i | \(-0.704653\pi\) | ||
0.599547 | − | 0.800339i | \(-0.295347\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.23744e8 | − | 1.23744e8i | −0.650605 | − | 0.650605i | ||||
\(233\) | 1.78471e7 | − | 1.78471e7i | 0.0924320 | − | 0.0924320i | −0.659379 | − | 0.751811i | \(-0.729181\pi\) |
0.751811 | + | 0.659379i | \(0.229181\pi\) | |||||||
\(234\) | 3.85017e8i | 1.96437i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.20719e8 | 1.93612 | 0.968061 | − | 0.250717i | \(-0.0806662\pi\) | ||||
0.968061 | + | 0.250717i | \(0.0806662\pi\) | |||||||
\(242\) | −1.55897e8 | − | 1.55897e8i | −0.707107 | − | 0.707107i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.81692e7i | 0.300417i | ||||||||
\(245\) | −2.38827e7 | + | 2.28945e8i | −0.103754 | + | 0.994603i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.12674e8 | − | 2.19863e8i | −0.456072 | − | 0.889943i | ||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.68435e8 | 1.00000 | ||||||||
\(257\) | −1.31406e8 | − | 1.31406e8i | −0.482893 | − | 0.482893i | 0.423161 | − | 0.906054i | \(-0.360920\pi\) |
−0.906054 | + | 0.423161i | \(0.860920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.50688e8 | + | 4.32374e8i | 1.23741 | + | 1.52564i | ||||
\(261\) | −2.64286e8 | −0.920094 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.31920e8 | + | 3.50320e8i | −1.42575 | + | 1.15639i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.80336e7i | 0.244427i | 0.992504 | + | 0.122213i | \(0.0389992\pi\) | ||||
−0.992504 | + | 0.122213i | \(0.961001\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | −2.80805e8 | − | 2.80805e8i | −0.846086 | − | 0.846086i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 5.79541e7i | − | 0.170199i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.61729e7 | + | 3.61729e7i | 0.102259 | + | 0.102259i | 0.756386 | − | 0.654126i | \(-0.226963\pi\) |
−0.654126 | + | 0.756386i | \(0.726963\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.88434e8 | −1.04435 | −0.522174 | − | 0.852839i | \(-0.674879\pi\) | ||||
−0.522174 | + | 0.852839i | \(0.674879\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.86654e8 | − | 2.86654e8i | 0.707107 | − | 0.707107i | ||||
\(289\) | 1.77152e8i | 0.431721i | ||||||||
\(290\) | −2.96793e8 | + | 2.40721e8i | −0.714596 | + | 0.579591i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.94434e8 | + | 5.94434e8i | 1.39722 | + | 1.39722i | ||||
\(293\) | −2.09198e7 | + | 2.09198e7i | −0.0485871 | + | 0.0485871i | −0.730983 | − | 0.682396i | \(-0.760938\pi\) |
0.682396 | + | 0.730983i | \(0.260938\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.23234e8 | 0.724429 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.85261e8 | − | 5.85261e8i | 1.28113 | − | 1.28113i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.48055e8 | + | 1.54446e7i | 0.298795 | + | 0.0311693i | ||||
\(306\) | −5.99728e8 | −1.19655 | ||||||||
\(307\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.11916e8 | − | 2.11916e8i | 0.390623 | − | 0.390623i | −0.484286 | − | 0.874910i | \(-0.660921\pi\) |
0.874910 | + | 0.484286i | \(0.160921\pi\) | |||||||
\(314\) | − | 4.58948e8i | − | 0.836583i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.95125e8 | − | 5.95125e8i | −1.04930 | − | 1.04930i | −0.998720 | − | 0.0505827i | \(-0.983892\pi\) |
−0.0505827 | − | 0.998720i | \(-0.516108\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 6.08174e7 | − | 5.83008e8i | 0.103754 | − | 0.994603i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | − | 6.12220e8i | − | 1.00000i | ||||||
\(325\) | 1.01851e9 | − | 6.63690e8i | 1.64579 | − | 1.07244i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.03750e8 | + | 9.03750e8i | −1.41413 | + | 1.41413i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.45172e8 | − | 3.45172e8i | 0.512249 | − | 0.512249i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.36651e8 | + | 9.36651e8i | 1.33313 | + | 1.33313i | 0.902553 | + | 0.430578i | \(0.141690\pi\) |
0.430578 | + | 0.902553i | \(0.358310\pi\) | |||||||
\(338\) | −1.43507e9 | + | 1.43507e9i | −2.02145 | + | 2.02145i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.73494e8 | + | 5.46254e8i | −0.929304 | + | 0.753735i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.47962e9 | 1.92036 | ||||||||
\(347\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.08394e8i | 0.640194i | 0.947385 | + | 0.320097i | \(0.103715\pi\) | ||||
−0.947385 | + | 0.320097i | \(0.896285\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.73037e8 | + | 7.73037e8i | −0.935382 | + | 0.935382i | −0.998035 | − | 0.0626535i | \(-0.980044\pi\) |
0.0626535 | + | 0.998035i | \(0.480044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.22395e9 | −1.43777 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | −5.57633e8 | − | 6.87523e8i | −0.629926 | − | 0.776655i | ||||
\(361\) | −8.93872e8 | −1.00000 | ||||||||
\(362\) | 1.16688e9 | + | 1.16688e9i | 1.29285 | + | 1.29285i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.42571e9 | − | 1.15636e9i | 1.53464 | − | 1.24471i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.93018e9i | 1.99988i | ||||||||
\(370\) | 7.32327e7 | − | 7.02023e8i | 0.0751621 | − | 0.720519i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.36984e8 | − | 3.36984e8i | 0.336223 | − | 0.336223i | −0.518720 | − | 0.854944i | \(-0.673591\pi\) |
0.854944 | + | 0.518720i | \(0.173591\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.32965e9 | − | 1.32965e9i | −1.27803 | − | 1.27803i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.16235e8 | 0.456870 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.36868e9 | − | 1.36868e9i | 1.18958 | − | 1.18958i | ||||
\(389\) | − | 1.94162e9i | − | 1.67240i | −0.548422 | − | 0.836202i | \(-0.684771\pi\) | ||
0.548422 | − | 0.836202i | \(-0.315229\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 8.43308e8 | + | 8.43308e8i | 0.707107 | + | 0.707107i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 2.32930e9i | − | 1.91862i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.76230e8 | + | 3.76230e8i | 0.301777 | + | 0.301777i | 0.841709 | − | 0.539932i | \(-0.181550\pi\) |
−0.539932 | + | 0.841709i | \(0.681550\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.25244e9 | − | 2.64176e8i | −0.978470 | − | 0.206387i | ||||
\(401\) | −8.84817e8 | −0.685248 | −0.342624 | − | 0.939473i | \(-0.611316\pi\) | ||||
−0.342624 | + | 0.939473i | \(0.611316\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | − | 1.70294e9i | − | 1.28488i | ||||||
\(405\) | −1.32967e9 | − | 1.38706e8i | −0.994603 | − | 0.103754i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.38968e9i | 1.72706i | 0.504296 | + | 0.863531i | \(0.331752\pi\) | ||||
−0.504296 | + | 0.863531i | \(0.668248\pi\) | |||||||
\(410\) | 1.75808e9 | + | 2.16759e9i | 1.25978 | + | 1.55322i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.88437e9 | 1.96437 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.61988e9 | −1.71117 | −0.855586 | − | 0.517661i | \(-0.826803\pi\) | ||||
−0.855586 | + | 0.517661i | \(0.826803\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.88135e9i | 1.83576i | ||||||||
\(425\) | 1.03381e9 | + | 1.58651e9i | 0.653248 | + | 1.00249i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.76483e8 | − | 8.76483e8i | 0.518843 | − | 0.518843i | −0.398378 | − | 0.917221i | \(-0.630427\pi\) |
0.917221 | + | 0.398378i | \(0.130427\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.08688e9 | −1.78368 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.80109e9 | 1.00000 | ||||||||
\(442\) | −3.01729e9 | − | 3.01729e9i | −1.66203 | − | 1.66203i | ||||
\(443\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.77301e8 | + | 2.65826e9i | −0.149173 | + | 1.43001i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 2.71111e9i | − | 1.41346i | −0.707481 | − | 0.706732i | \(-0.750168\pi\) | ||
0.707481 | − | 0.706732i | \(-0.249832\pi\) | |||||||
\(450\) | −1.61955e9 | + | 1.05534e9i | −0.837821 | + | 0.545945i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.24748e9 | + | 1.24748e9i | 0.635400 | + | 0.635400i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.48649e9 | − | 2.48649e9i | −1.21865 | − | 1.21865i | −0.968104 | − | 0.250548i | \(-0.919389\pi\) |
−0.250548 | − | 0.968104i | \(-0.580611\pi\) | |||||||
\(458\) | −2.32712e9 | + | 2.32712e9i | −1.13185 | + | 1.13185i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.07657e9 | 1.93795 | 0.968974 | − | 0.247164i | \(-0.0794988\pi\) | ||||
0.968974 | + | 0.247164i | \(0.0794988\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(464\) | 1.97991e9i | 0.920094i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.85554e8 | −0.130719 | ||||||||
\(467\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(468\) | 3.08014e9 | − | 3.08014e9i | 1.38902 | − | 1.38902i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.07691e9 | + | 3.07691e9i | 1.29808 | + | 1.29808i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.47318e9 | 1.42305 | ||||||||
\(482\) | −3.36575e9 | − | 3.36575e9i | −1.36904 | − | 1.36904i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.49436e9i | 1.00000i | ||||||||
\(485\) | −2.66252e9 | − | 3.28271e9i | −1.05973 | − | 1.30658i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(488\) | 5.45354e8 | − | 5.45354e8i | 0.212427 | − | 0.212427i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.02262e9 | − | 1.64050e9i | 0.776655 | − | 0.629926i | ||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.07115e9 | − | 2.07115e9i | 0.778478 | − | 0.778478i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | −8.57513e8 | + | 2.66030e9i | −0.306793 | + | 0.951776i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.69857e9 | − | 3.85822e8i | −1.27795 | − | 0.133311i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.84397e7i | 0.0129201i | 0.999979 | + | 0.00646007i | \(0.00205632\pi\) | ||||
−0.999979 | + | 0.00646007i | \(0.997944\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −2.14748e9 | − | 2.14748e9i | −0.707107 | − | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.10250e9i | 0.682914i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.53490e8 | − | 6.26449e9i | 0.203811 | − | 1.95377i | ||||
\(521\) | 2.38452e9 | 0.738701 | 0.369350 | − | 0.929290i | \(-0.379580\pi\) | ||||
0.369350 | + | 0.929290i | \(0.379580\pi\) | |||||||
\(522\) | 2.11429e9 | + | 2.11429e9i | 0.650605 | + | 0.650605i | ||||
\(523\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 3.40483e9i | − | 1.00000i | ||||||
\(530\) | 6.25792e9 | + | 6.52805e8i | 1.82585 | + | 0.190466i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.71090e9 | + | 9.71090e9i | −2.77788 | + | 2.77788i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.24269e8 | − | 6.24269e8i | 0.172836 | − | 0.172836i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.36235e9 | −1.99906 | −0.999530 | − | 0.0306534i | \(-0.990241\pi\) | ||||
−0.999530 | + | 0.0306534i | \(0.990241\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.49289e9i | 1.19655i | ||||||||
\(545\) | −6.99371e8 | + | 6.70431e9i | −0.185063 | + | 1.77405i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(548\) | −4.63633e8 | + | 4.63633e8i | −0.120349 | + | 0.120349i | ||||
\(549\) | − | 1.16473e9i | − | 0.300417i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 5.78766e8i | − | 0.144617i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.85686e9 | + | 2.85686e9i | 0.700480 | + | 0.700480i | 0.964513 | − | 0.264034i | \(-0.0850530\pi\) |
−0.264034 | + | 0.964513i | \(0.585053\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.10747e9 | + | 3.10747e9i | 0.738465 | + | 0.738465i | ||||
\(563\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.99199e9 | − | 2.42673e9i | 0.697896 | − | 0.566046i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 6.84617e9i | − | 1.55796i | −0.627052 | − | 0.778978i | \(-0.715738\pi\) | ||
0.627052 | − | 0.778978i | \(-0.284262\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.58647e9 | −1.00000 | ||||||||
\(577\) | 5.74586e9 | + | 5.74586e9i | 1.24520 | + | 1.24520i | 0.957814 | + | 0.287387i | \(0.0927867\pi\) |
0.287387 | + | 0.957814i | \(0.407213\pi\) | |||||||
\(578\) | 1.41722e9 | − | 1.41722e9i | 0.305273 | − | 0.305273i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.30011e9 | + | 4.48573e8i | 0.915128 | + | 0.0954630i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 9.51094e9i | − | 1.97596i | ||||||
\(585\) | −5.99183e9 | − | 7.38751e9i | −1.23741 | − | 1.52564i | ||||
\(586\) | 3.34717e8 | 0.0687126 | ||||||||
\(587\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.58587e9 | − | 2.58587e9i | −0.512249 | − | 0.512249i | ||||
\(593\) | 7.18075e9 | − | 7.18075e9i | 1.41409 | − | 1.41409i | 0.697829 | − | 0.716265i | \(-0.254150\pi\) |
0.716265 | − | 0.697829i | \(-0.245850\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.36418e9 | −1.81179 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.41174e9 | −0.265273 | −0.132637 | − | 0.991165i | \(-0.542344\pi\) | ||||
−0.132637 | + | 0.991165i | \(0.542344\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.41743e9 | + | 5.65128e8i | 0.994603 | + | 0.103754i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.06088e9 | − | 1.30800e9i | −0.189240 | − | 0.233320i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.79782e9 | + | 4.79782e9i | 0.846086 | + | 0.846086i | ||||
\(613\) | 1.60192e9 | − | 1.60192e9i | 0.280885 | − | 0.280885i | −0.552577 | − | 0.833462i | \(-0.686355\pi\) |
0.833462 | + | 0.552577i | \(0.186355\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.64897e9 | − | 4.64897e9i | −0.796817 | − | 0.796817i | 0.185776 | − | 0.982592i | \(-0.440520\pi\) |
−0.982592 | + | 0.185776i | \(0.940520\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.58355e9 | + | 2.46513e9i | 0.914809 | + | 0.403888i | ||||
\(626\) | −3.39065e9 | −0.552425 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.67158e9 | + | 3.67158e9i | −0.591554 | + | 0.591554i | ||||
\(629\) | 5.41006e9i | 0.866812i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.52200e9i | 1.48394i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.06144e9 | + | 9.06144e9i | 1.38902 | + | 1.38902i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.15061e9 | + | 4.17753e9i | −0.776655 | + | 0.629926i | ||||
\(641\) | 1.19487e10 | 1.79192 | 0.895959 | − | 0.444136i | \(-0.146489\pi\) | ||||
0.895959 | + | 0.444136i | \(0.146489\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(648\) | −4.89776e9 | + | 4.89776e9i | −0.707107 | + | 0.707107i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.34576e10 | − | 2.83860e9i | −1.92208 | − | 0.405422i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.87957e9 | + | 9.87957e9i | −1.38849 | + | 1.38849i | −0.559983 | + | 0.828504i | \(0.689192\pi\) |
−0.828504 | + | 0.559983i | \(0.810808\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.44600e10 | 1.99988 | ||||||||
\(657\) | −1.01565e10 | − | 1.01565e10i | −1.39722 | − | 1.39722i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.48051e10 | −1.99392 | −0.996958 | − | 0.0779394i | \(-0.975166\pi\) | ||||
−0.996958 | + | 0.0779394i | \(0.975166\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.52275e9 | −0.724429 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.47042e9 | − | 9.47042e9i | 1.19761 | − | 1.19761i | 0.222734 | − | 0.974879i | \(-0.428502\pi\) |
0.974879 | − | 0.222734i | \(-0.0714982\pi\) | |||||||
\(674\) | − | 1.49864e10i | − | 1.88533i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.29611e10 | 2.85877 | ||||||||
\(677\) | −5.63649e9 | − | 5.63649e9i | −0.698149 | − | 0.698149i | 0.265862 | − | 0.964011i | \(-0.414343\pi\) |
−0.964011 | + | 0.265862i | \(0.914343\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 9.75799e9 | + | 1.01792e9i | 1.19009 | + | 0.124146i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.01910e8 | + | 1.11199e9i | 0.107213 | + | 0.132186i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.09604e10i | 3.60611i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | −1.18369e10 | − | 1.18369e10i | −1.35790 | − | 1.35790i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.51263e10 | − | 1.51263e10i | −1.69207 | − | 1.69207i | ||||
\(698\) | 4.06715e9 | − | 4.06715e9i | 0.452685 | − | 0.452685i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.35144e9 | 0.477111 | 0.238556 | − | 0.971129i | \(-0.423326\pi\) | ||||
0.238556 | + | 0.971129i | \(0.423326\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.23686e10 | 1.32283 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 9.48757e9i | − | 0.999754i | −0.866096 | − | 0.499877i | \(-0.833379\pi\) | ||
0.866096 | − | 0.499877i | \(-0.166621\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.79159e9 | + | 9.79159e9i | 1.01665 | + | 1.01665i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | −1.03912e9 | + | 9.96124e9i | −0.103754 | + | 0.994603i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 7.15097e9 | + | 7.15097e9i | 0.707107 | + | 0.707107i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 1.86701e10i | − | 1.82836i | ||||||
\(725\) | 1.94849e9 | − | 9.23768e9i | 0.189896 | − | 0.900285i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.04604e10i | 1.00000i | ||||||||
\(730\) | −2.06566e10 | − | 2.15482e9i | −1.96530 | − | 0.205013i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.99048e9 | − | 3.99048e9i | 0.374250 | − | 0.374250i | −0.494773 | − | 0.869022i | \(-0.664749\pi\) |
0.869022 | + | 0.494773i | \(0.164749\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 1.54414e10 | − | 1.54414e10i | 1.41413 | − | 1.41413i | ||||
\(739\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(740\) | −6.20205e9 | + | 5.03033e9i | −0.562632 | + | 0.456336i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.12157e9 | + | 2.03378e10i | −0.187980 | + | 1.80201i | ||||
\(746\) | −5.39174e9 | −0.475492 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.12743e10i | 1.80741i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.96360e8 | − | 3.96360e8i | −0.0332089 | − | 0.0332089i | 0.690307 | − | 0.723516i | \(-0.257475\pi\) |
−0.723516 | + | 0.690307i | \(0.757475\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.99861e10 | −1.64392 | −0.821961 | − | 0.569543i | \(-0.807120\pi\) | ||||
−0.821961 | + | 0.569543i | \(0.807120\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.15073e10 | − | 9.33327e9i | 0.929304 | − | 0.753735i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2.25801e8i | − | 0.0179054i | −0.999960 | − | 0.00895271i | \(-0.997150\pi\) | ||
0.999960 | − | 0.00895271i | \(-0.00284977\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.12988e9 | − | 4.12988e9i | −0.323056 | − | 0.323056i | ||||
\(773\) | 1.13946e10 | − | 1.13946e10i | 0.887299 | − | 0.887299i | −0.106964 | − | 0.994263i | \(-0.534113\pi\) |
0.994263 | + | 0.106964i | \(0.0341129\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.18990e10 | −1.68232 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.55330e10 | + | 1.55330e10i | −1.18257 | + | 1.18257i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 1.34929e10i | − | 1.00000i | ||||||
\(785\) | 7.14237e9 | + | 8.80606e9i | 0.526985 | + | 0.649737i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(788\) | −1.86344e10 | + | 1.86344e10i | −1.35667 | + | 1.35667i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.85989e9 | − | 5.85989e9i | 0.417285 | − | 0.417285i | ||||
\(794\) | − | 6.01968e9i | − | 0.426778i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.82397e10 | + | 1.82397e10i | 1.27619 | + | 1.27619i | 0.942785 | + | 0.333400i | \(0.108196\pi\) |
0.333400 | + | 0.942785i | \(0.391804\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 7.90613e9 | + | 1.21329e10i | 0.545945 | + | 0.837821i | ||||
\(801\) | 2.09123e10 | 1.43777 | ||||||||
\(802\) | 7.07853e9 | + | 7.07853e9i | 0.484544 | + | 0.484544i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.36235e10 | + | 1.36235e10i | −0.908550 | + | 0.908550i | ||||
\(809\) | − | 9.86925e9i | − | 0.655336i | −0.944793 | − | 0.327668i | \(-0.893737\pi\) | ||
0.944793 | − | 0.327668i | \(-0.106263\pi\) | |||||||
\(810\) | 9.52767e9 | + | 1.17470e10i | 0.629926 | + | 0.776655i | ||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 1.91174e10 | − | 1.91174e10i | 1.22122 | − | 1.22122i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.27609e9 | − | 3.14053e10i | 0.207495 | − | 1.98909i | ||||
\(821\) | −1.32726e10 | −0.837059 | −0.418530 | − | 0.908203i | \(-0.637454\pi\) | ||||
−0.418530 | + | 0.908203i | \(0.637454\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 2.59446e10i | − | 1.58163i | −0.612052 | − | 0.790817i | \(-0.709656\pi\) | ||
0.612052 | − | 0.790817i | \(-0.290344\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.30750e10 | − | 2.30750e10i | −1.38902 | − | 1.38902i | ||||
\(833\) | −1.41147e10 | + | 1.41147e10i | −0.846086 | + | 0.846086i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.64660e9 | 0.153427 | ||||||||
\(842\) | 2.09590e10 | + | 2.09590e10i | 1.20998 | + | 1.20998i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.20212e9 | − | 4.98686e10i | 0.296607 | − | 2.84334i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.30508e10 | − | 2.30508e10i | 1.29808 | − | 1.29808i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.42159e9 | − | 2.09625e10i | 0.246952 | − | 1.17078i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.69291e10 | + | 1.69291e10i | −0.933926 | + | 0.933926i | −0.997948 | − | 0.0640220i | \(-0.979607\pi\) |
0.0640220 | + | 0.997948i | \(0.479607\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.51299e9 | − | 4.51299e9i | −0.244924 | − | 0.244924i | 0.573960 | − | 0.818884i | \(-0.305407\pi\) |
−0.818884 | + | 0.573960i | \(0.805407\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.83902e10 | + | 2.30265e10i | −1.49146 | + | 1.20969i | ||||
\(866\) | −1.40237e10 | −0.733754 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 2.46950e10 | + | 2.46950e10i | 1.26125 | + | 1.26125i | ||||
\(873\) | −2.33853e10 | + | 2.33853e10i | −1.18958 | + | 1.18958i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.26128e10 | + | 2.26128e10i | 1.13203 | + | 1.13203i | 0.989840 | + | 0.142187i | \(0.0454134\pi\) |
0.142187 | + | 0.989840i | \(0.454587\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.03243e10 | 1.49408 | 0.747041 | − | 0.664778i | \(-0.231474\pi\) | ||||
0.747041 | + | 0.664778i | \(0.231474\pi\) | |||||||
\(882\) | −1.44087e10 | − | 1.44087e10i | −0.707107 | − | 0.707107i | ||||
\(883\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(884\) | 4.82766e10i | 2.35046i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 2.34845e10 | − | 1.90477e10i | 1.11665 | − | 0.905685i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.16889e10 | + | 2.16889e10i | −0.999471 | + | 0.999471i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 2.13991e10 | + | 4.51369e9i | 0.978470 | + | 0.206387i | ||||
\(901\) | −4.82260e10 | −2.19657 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 1.99596e10i | − | 0.898592i | ||||||
\(905\) | −4.05491e10 | − | 4.22994e9i | −1.81849 | − | 0.189699i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.90963e10i | 1.28488i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 3.97838e10i | 1.72343i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.72339e10 | 1.60068 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.26126e10 | − | 3.26126e10i | −1.37034 | − | 1.37034i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.52009e9 | + | 1.46098e10i | 0.395499 | + | 0.606942i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.58393e10 | − | 1.58393e10i | 0.650605 | − | 0.650605i | ||||
\(929\) | − | 1.43415e10i | − | 0.586866i | −0.955980 | − | 0.293433i | \(-0.905202\pi\) | ||
0.955980 | − | 0.293433i | \(-0.0947978\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.28443e9 | + | 2.28443e9i | 0.0924320 | + | 0.0924320i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.92822e10 | −1.96437 | ||||||||
\(937\) | 2.45467e10 | + | 2.45467e10i | 0.974776 | + | 0.974776i | 0.999690 | − | 0.0249138i | \(-0.00793112\pi\) |
−0.0249138 | + | 0.999690i | \(0.507931\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.49808e10 | 1.36857 | 0.684283 | − | 0.729217i | \(-0.260115\pi\) | ||||
0.684283 | + | 0.729217i | \(0.260115\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.02196e11i | − | 3.88153i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.92270e10 | − | 2.92270e10i | 1.09385 | − | 1.09385i | 0.0987400 | − | 0.995113i | \(-0.468519\pi\) |
0.995113 | − | 0.0987400i | \(-0.0314812\pi\) | |||||||
\(954\) | − | 4.92305e10i | − | 1.83576i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.75126e10 | 1.00000 | ||||||||
\(962\) | −2.77855e10 | − | 2.77855e10i | −1.00625 | − | 1.00625i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.38520e10i | 1.93612i | ||||||||
\(965\) | −9.90527e9 | + | 8.03391e9i | −0.354830 | + | 0.287794i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(968\) | 1.99549e10 | − | 1.99549e10i | 0.707107 | − | 0.707107i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.96148e9 | + | 4.75618e10i | −0.174546 | + | 1.67324i | ||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.72566e9 | −0.300417 | ||||||||
\(977\) | −4.09613e10 | − | 4.09613e10i | −1.40522 | − | 1.40522i | −0.782246 | − | 0.622970i | \(-0.785926\pi\) |
−0.622970 | − | 0.782246i | \(-0.714074\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −2.93050e10 | − | 3.05699e9i | −0.994603 | − | 0.103754i | ||||
\(981\) | 5.27422e10 | 1.78368 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.62498e10 | + | 4.46935e10i | 1.20859 | + | 1.49011i | ||||
\(986\) | −3.31383e10 | −1.10093 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.32398e10 | + | 2.32398e10i | 0.742676 | + | 0.742676i | 0.973092 | − | 0.230416i | \(-0.0740087\pi\) |
−0.230416 | + | 0.973092i | \(0.574009\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 20.8.e.a.7.1 | yes | 2 | |
4.3 | odd | 2 | CM | 20.8.e.a.7.1 | yes | 2 | |
5.2 | odd | 4 | 100.8.e.c.43.1 | 2 | |||
5.3 | odd | 4 | inner | 20.8.e.a.3.1 | ✓ | 2 | |
5.4 | even | 2 | 100.8.e.c.7.1 | 2 | |||
20.3 | even | 4 | inner | 20.8.e.a.3.1 | ✓ | 2 | |
20.7 | even | 4 | 100.8.e.c.43.1 | 2 | |||
20.19 | odd | 2 | 100.8.e.c.7.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.8.e.a.3.1 | ✓ | 2 | 5.3 | odd | 4 | inner | |
20.8.e.a.3.1 | ✓ | 2 | 20.3 | even | 4 | inner | |
20.8.e.a.7.1 | yes | 2 | 1.1 | even | 1 | trivial | |
20.8.e.a.7.1 | yes | 2 | 4.3 | odd | 2 | CM | |
100.8.e.c.7.1 | 2 | 5.4 | even | 2 | |||
100.8.e.c.7.1 | 2 | 20.19 | odd | 2 | |||
100.8.e.c.43.1 | 2 | 5.2 | odd | 4 | |||
100.8.e.c.43.1 | 2 | 20.7 | even | 4 |