Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,8,Mod(1,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(119.955849786\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 286x - 1680 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(19.3129\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −368.444 | −1.31819 | −0.659093 | − | 0.752062i | \(-0.729059\pi\) | ||||
−0.659093 | + | 0.752062i | \(0.729059\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1058.71 | 1.16663 | 0.583314 | − | 0.812246i | \(-0.301756\pi\) | ||||
0.583314 | + | 0.812246i | \(0.301756\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4728.97 | −1.07125 | −0.535626 | − | 0.844455i | \(-0.679924\pi\) | ||||
−0.535626 | + | 0.844455i | \(0.679924\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5522.34 | −0.697142 | −0.348571 | − | 0.937282i | \(-0.613333\pi\) | ||||
−0.348571 | + | 0.937282i | \(0.613333\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9947.99 | 0.761055 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 28487.5 | 1.40632 | 0.703159 | − | 0.711033i | \(-0.251772\pi\) | ||||
0.703159 | + | 0.711033i | \(0.251772\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −12644.8 | −0.422935 | −0.211467 | − | 0.977385i | \(-0.567824\pi\) | ||||
−0.211467 | + | 0.977385i | \(0.567824\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −28585.1 | −0.673554 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −16997.8 | −0.291304 | −0.145652 | − | 0.989336i | \(-0.546528\pi\) | ||||
−0.145652 | + | 0.989336i | \(0.546528\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 57626.0 | 0.737612 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 75684.6 | 0.576255 | 0.288128 | − | 0.957592i | \(-0.406967\pi\) | ||||
0.288128 | + | 0.957592i | \(0.406967\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 69384.1 | 0.418306 | 0.209153 | − | 0.977883i | \(-0.432929\pi\) | ||||
0.209153 | + | 0.977883i | \(0.432929\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 127682. | 0.618488 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −390074. | −1.53783 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 29223.4 | 0.0948472 | 0.0474236 | − | 0.998875i | \(-0.484899\pi\) | ||||
0.0474236 | + | 0.998875i | \(0.484899\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 149103. | 0.402495 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 295928. | 0.670568 | 0.335284 | − | 0.942117i | \(-0.391168\pi\) | ||||
0.335284 | + | 0.942117i | \(0.391168\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −16387.0 | −0.0314310 | −0.0157155 | − | 0.999877i | \(-0.505003\pi\) | ||||
−0.0157155 | + | 0.999877i | \(0.505003\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −268596. | −0.439395 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 68148.4 | 0.0957444 | 0.0478722 | − | 0.998853i | \(-0.484756\pi\) | ||||
0.0478722 | + | 0.998853i | \(0.484756\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 297318. | 0.361023 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −769163. | −0.811938 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.85505e6 | 1.71155 | 0.855777 | − | 0.517346i | \(-0.173080\pi\) | ||||
0.855777 | + | 0.517346i | \(0.173080\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.74236e6 | 1.41211 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 341409. | 0.244181 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.75215e6 | 1.74458 | 0.872289 | − | 0.488991i | \(-0.162635\pi\) | ||||
0.872289 | + | 0.488991i | \(0.162635\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.77198e6 | −0.999547 | −0.499774 | − | 0.866156i | \(-0.666583\pi\) | ||||
−0.499774 | + | 0.866156i | \(0.666583\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 771798. | 0.388876 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.03467e6 | 0.918963 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.76825e6 | 1.12446 | 0.562230 | − | 0.826981i | \(-0.309943\pi\) | ||||
0.562230 | + | 0.826981i | \(0.309943\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 458941. | 0.168184 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.66235e6 | 1.54597 | 0.772985 | − | 0.634425i | \(-0.218763\pi\) | ||||
0.772985 | + | 0.634425i | \(0.218763\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.38405e6 | −1.92073 | −0.960364 | − | 0.278748i | \(-0.910081\pi\) | ||||
−0.960364 | + | 0.278748i | \(0.910081\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.55590e6 | −0.425861 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.00659e6 | −1.24975 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.32391e6 | −1.67128 | −0.835638 | − | 0.549281i | \(-0.814902\pi\) | ||||
−0.835638 | + | 0.549281i | \(0.814902\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.05313e6 | 0.586100 | 0.293050 | − | 0.956097i | \(-0.405330\pi\) | ||||
0.293050 | + | 0.956097i | \(0.405330\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.04961e7 | −1.85379 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.04349e6 | −0.332701 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.79581e6 | −1.32255 | −0.661273 | − | 0.750145i | \(-0.729984\pi\) | ||||
−0.661273 | + | 0.750145i | \(0.729984\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.84654e6 | −0.813307 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.87337e6 | −0.241509 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.65889e6 | 0.557506 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.84797e6 | 0.761835 | 0.380917 | − | 0.924609i | \(-0.375608\pi\) | ||||
0.380917 | + | 0.924609i | \(0.375608\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.44742e6 | −0.357084 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.01398e7 | 0.979274 | 0.489637 | − | 0.871926i | \(-0.337129\pi\) | ||||
0.489637 | + | 0.871926i | \(0.337129\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.54107e7 | −1.38961 | −0.694803 | − | 0.719200i | \(-0.744509\pi\) | ||||
−0.694803 | + | 0.719200i | \(0.744509\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.05320e7 | 0.887868 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.22867e6 | −0.570447 | −0.285224 | − | 0.958461i | \(-0.592068\pi\) | ||||
−0.285224 | + | 0.958461i | \(0.592068\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.12169e7 | −0.829625 | −0.414812 | − | 0.909907i | \(-0.636153\pi\) | ||||
−0.414812 | + | 0.909907i | \(0.636153\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −789031. | −0.0547600 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.49419e7 | −0.974162 | −0.487081 | − | 0.873357i | \(-0.661938\pi\) | ||||
−0.487081 | + | 0.873357i | \(0.661938\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.26275e6 | 0.383992 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.02579e6 | −0.232381 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.01599e7 | 1.64065 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.87595e6 | 0.147582 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.99006e6 | −0.387153 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.55274e6 | 0.345875 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.92110e7 | 1.26542 | 0.632709 | − | 0.774390i | \(-0.281943\pi\) | ||||
0.632709 | + | 0.774390i | \(0.281943\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 442448. | 0.0181467 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.38297e7 | −0.537481 | −0.268741 | − | 0.963213i | \(-0.586607\pi\) | ||||
−0.268741 | + | 0.963213i | \(0.586607\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.33871e7 | −0.493408 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.25208e6 | 0.253685 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.59943e7 | −1.86047 | −0.930233 | − | 0.366969i | \(-0.880395\pi\) | ||||
−0.930233 | + | 0.366969i | \(0.880395\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.22397e7 | −1.64987 | −0.824934 | − | 0.565229i | \(-0.808788\pi\) | ||||
−0.824934 | + | 0.565229i | \(0.808788\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.84001e6 | −0.0552780 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.61150e7 | 0.746816 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.78855e7 | −0.759611 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.02759e6 | −0.208437 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.62977e7 | 0.403622 | 0.201811 | − | 0.979424i | \(-0.435317\pi\) | ||||
0.201811 | + | 0.979424i | \(0.435317\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.71334e7 | 0.404971 | 0.202486 | − | 0.979285i | \(-0.435098\pi\) | ||||
0.202486 | + | 0.979285i | \(0.435098\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.07674e7 | 0.468772 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.55641e7 | −0.551404 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.35265e7 | 1.72257 | 0.861283 | − | 0.508126i | \(-0.169662\pi\) | ||||
0.861283 | + | 0.508126i | \(0.169662\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.00864e7 | −0.988166 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.79957e7 | −0.339843 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.70834e7 | −1.21327 | −0.606637 | − | 0.794979i | \(-0.707482\pi\) | ||||
−0.606637 | + | 0.794979i | \(0.707482\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.70437e7 | −0.815282 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.88943e7 | 0.978510 | 0.489255 | − | 0.872141i | \(-0.337269\pi\) | ||||
0.489255 | + | 0.872141i | \(0.337269\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.22523e7 | −0.513992 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.21804e6 | −0.140978 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.79040e7 | −0.850250 | −0.425125 | − | 0.905135i | \(-0.639770\pi\) | ||||
−0.425125 | + | 0.905135i | \(0.639770\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.10090e7 | 0.860520 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.43081e7 | −1.00723 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.73524e7 | 0.617102 | 0.308551 | − | 0.951208i | \(-0.400156\pi\) | ||||
0.308551 | + | 0.951208i | \(0.400156\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.33152e8 | −1.66907 | −0.834534 | − | 0.550957i | \(-0.814263\pi\) | ||||
−0.834534 | + | 0.550957i | \(0.814263\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.78433e7 | 0.577089 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.07672e7 | −0.125026 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.34717e8 | −1.50652 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.08385e7 | −0.224518 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.13177e7 | −0.948283 | −0.474142 | − | 0.880449i | \(-0.657242\pi\) | ||||
−0.474142 | + | 0.880449i | \(0.657242\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.06396e8 | −1.06530 | −0.532651 | − | 0.846335i | \(-0.678804\pi\) | ||||
−0.532651 | + | 0.846335i | \(0.678804\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.49362e7 | −0.530564 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.91262e8 | −1.78236 | −0.891182 | − | 0.453646i | \(-0.850123\pi\) | ||||
−0.891182 | + | 0.453646i | \(0.850123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.13489e7 | 0.371945 | 0.185972 | − | 0.982555i | \(-0.440457\pi\) | ||||
0.185972 | + | 0.982555i | \(0.440457\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.47429e7 | −0.649208 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.01279e7 | 0.672276 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.09033e8 | −0.883933 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.23914e7 | −0.0971012 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.97967e7 | 0.453070 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.48974e7 | 0.402312 | 0.201156 | − | 0.979559i | \(-0.435530\pi\) | ||||
0.201156 | + | 0.979559i | \(0.435530\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.25884e8 | −0.892566 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.03768e6 | 0.0414319 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.34574e7 | 0.488008 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.72369e8 | 1.10893 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.57318e8 | −0.980404 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.22016e8 | 0.736799 | 0.368399 | − | 0.929668i | \(-0.379906\pi\) | ||||
0.368399 | + | 0.929668i | \(0.379906\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.20093e7 | 0.245871 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.33351e8 | −1.89152 | −0.945762 | − | 0.324861i | \(-0.894683\pi\) | ||||
−0.945762 | + | 0.324861i | \(0.894683\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.28881e7 | −0.0709193 | −0.0354597 | − | 0.999371i | \(-0.511290\pi\) | ||||
−0.0354597 | + | 0.999371i | \(0.511290\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.35178e8 | 0.721546 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.67790e8 | −1.90482 | −0.952411 | − | 0.304817i | \(-0.901405\pi\) | ||||
−0.952411 | + | 0.304817i | \(0.901405\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.51089e7 | −0.126209 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.97746e8 | 0.964912 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.50083e8 | 0.711113 | 0.355556 | − | 0.934655i | \(-0.384291\pi\) | ||||
0.355556 | + | 0.934655i | \(0.384291\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.57608e7 | −0.348646 | −0.174323 | − | 0.984689i | \(-0.555774\pi\) | ||||
−0.174323 | + | 0.984689i | \(0.555774\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.09545e8 | −0.475895 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.98287e7 | 0.294846 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.24345e7 | −0.338385 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.46051e8 | −0.982127 | −0.491063 | − | 0.871124i | \(-0.663392\pi\) | ||||
−0.491063 | + | 0.871124i | \(0.663392\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.03821e7 | 0.312060 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.83393e8 | 1.07028 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.21274e8 | 1.18062 | 0.590309 | − | 0.807177i | \(-0.299006\pi\) | ||||
0.590309 | + | 0.807177i | \(0.299006\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.09390e7 | 0.110651 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.51741e7 | 0.192085 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.79444e8 | 0.608254 | 0.304127 | − | 0.952632i | \(-0.401635\pi\) | ||||
0.304127 | + | 0.952632i | \(0.401635\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.83483e8 | −2.25614 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.37487e8 | 0.763572 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.19069e7 | 0.225236 | 0.112618 | − | 0.993638i | \(-0.464076\pi\) | ||||
0.112618 | + | 0.993638i | \(0.464076\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.37851e8 | 1.64161 | 0.820805 | − | 0.571209i | \(-0.193525\pi\) | ||||
0.820805 | + | 0.571209i | \(0.193525\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.57857e8 | 0.469563 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.72511e8 | −0.790169 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.21434e8 | 0.625986 | 0.312993 | − | 0.949755i | \(-0.398668\pi\) | ||||
0.312993 | + | 0.949755i | \(0.398668\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.05810e7 | 0.139435 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00421e8 | 0.538855 | 0.269428 | − | 0.963021i | \(-0.413166\pi\) | ||||
0.269428 | + | 0.963021i | \(0.413166\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.60104e8 | −1.46898 | −0.734490 | − | 0.678619i | \(-0.762579\pi\) | ||||
−0.734490 | + | 0.678619i | \(0.762579\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.25790e8 | −0.321876 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.13301e8 | 0.782304 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.01200e8 | 0.977729 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.84895e8 | −0.439845 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.99015e8 | −1.15898 | −0.579492 | − | 0.814978i | \(-0.696749\pi\) | ||||
−0.579492 | + | 0.814978i | \(0.696749\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.01401e9 | −2.29968 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.30802e7 | 0.206163 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.38678e7 | 0.203080 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.73490e7 | −0.0366684 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.73774e8 | −0.565384 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.52874e8 | 1.31759 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.21105e8 | 1.61963 | 0.809813 | − | 0.586689i | \(-0.199569\pi\) | ||||
0.809813 | + | 0.586689i | \(0.199569\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.16089e8 | 0.802290 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.43818e7 | −0.102516 | −0.0512581 | − | 0.998685i | \(-0.516323\pi\) | ||||
−0.0512581 | + | 0.998685i | \(0.516323\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.71990e8 | −1.23868 | −0.619338 | − | 0.785124i | \(-0.712599\pi\) | ||||
−0.619338 | + | 0.785124i | \(0.712599\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.84364e8 | −0.512611 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.49707e8 | −0.263958 | −0.131979 | − | 0.991253i | \(-0.542133\pi\) | ||||
−0.131979 | + | 0.991253i | \(0.542133\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.57910e8 | −0.617315 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.95174e8 | 0.329348 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.60218e8 | −0.594780 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.18230e8 | −0.514221 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.02857e8 | 0.478984 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.21492e7 | 0.111698 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.29194e8 | 0.347380 | 0.173690 | − | 0.984800i | \(-0.444431\pi\) | ||||
0.173690 | + | 0.984800i | \(0.444431\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.13038e7 | 0.0316157 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.01995e9 | −1.48225 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.68268e8 | −0.808814 | −0.404407 | − | 0.914579i | \(-0.632522\pi\) | ||||
−0.404407 | + | 0.914579i | \(0.632522\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.03431e8 | 0.562433 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.28115e8 | −0.448111 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.57118e8 | −0.745449 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.69094e8 | −0.221698 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.99189e8 | 0.384408 | 0.192204 | − | 0.981355i | \(-0.438436\pi\) | ||||
0.192204 | + | 0.981355i | \(0.438436\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.48423e9 | 1.86901 | 0.934503 | − | 0.355954i | \(-0.115844\pi\) | ||||
0.934503 | + | 0.355954i | \(0.115844\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.08696e8 | 0.134165 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.05417e8 | −0.732560 | −0.366280 | − | 0.930505i | \(-0.619369\pi\) | ||||
−0.366280 | + | 0.930505i | \(0.619369\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.71782e9 | −2.03787 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.14318e8 | −0.947230 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.74734e8 | 0.313388 | 0.156694 | − | 0.987647i | \(-0.449916\pi\) | ||||
0.156694 | + | 0.987647i | \(0.449916\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.33982e8 | −0.821126 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.76507e7 | −0.0852064 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.35216e9 | 2.53188 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.66951e8 | −0.915511 | −0.457755 | − | 0.889078i | \(-0.651346\pi\) | ||||
−0.457755 | + | 0.889078i | \(0.651346\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.15732e8 | 0.223523 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.96396e9 | 1.99675 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.09365e8 | −0.508216 | −0.254108 | − | 0.967176i | \(-0.581782\pi\) | ||||
−0.254108 | + | 0.967176i | \(0.581782\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.03924e8 | −0.199691 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.17956e8 | −0.401732 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.85372e8 | 0.929743 | 0.464871 | − | 0.885378i | \(-0.346101\pi\) | ||||
0.464871 | + | 0.885378i | \(0.346101\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.88698e8 | −0.730590 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.47060e8 | −0.315652 | −0.157826 | − | 0.987467i | \(-0.550449\pi\) | ||||
−0.157826 | + | 0.987467i | \(0.550449\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.84465e9 | 1.64741 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.19461e7 | −0.0104770 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.19819e8 | −0.706146 | −0.353073 | − | 0.935596i | \(-0.614863\pi\) | ||||
−0.353073 | + | 0.935596i | \(0.614863\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.84226e8 | −0.409665 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.73402e8 | 0.310315 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.69845e9 | 2.20305 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.57699e9 | 1.26492 | 0.632460 | − | 0.774593i | \(-0.282045\pi\) | ||||
0.632460 | + | 0.774593i | \(0.282045\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.61452e8 | 0.284869 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.99350e8 | 0.464168 | 0.232084 | − | 0.972696i | \(-0.425446\pi\) | ||||
0.232084 | + | 0.972696i | \(0.425446\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.83162e8 | −0.291619 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.95806e8 | −0.146465 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.38196e8 | −0.101605 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.08431e8 | −0.295180 | −0.147590 | − | 0.989049i | \(-0.547152\pi\) | ||||
−0.147590 | + | 0.989049i | \(0.547152\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.51185e9 | 1.07414 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.91372e9 | 2.03527 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.12491e9 | −0.772589 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.41047e9 | 0.952552 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.46270e9 | 0.971417 | 0.485708 | − | 0.874121i | \(-0.338562\pi\) | ||||
0.485708 | + | 0.874121i | \(0.338562\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.76741e8 | −0.115438 | −0.0577191 | − | 0.998333i | \(-0.518383\pi\) | ||||
−0.0577191 | + | 0.998333i | \(0.518383\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.96802e7 | 0.0319148 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.64162e9 | 1.03732 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.87600e9 | −1.16610 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.05104e8 | −0.431174 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.56757e9 | 0.943099 | 0.471549 | − | 0.881840i | \(-0.343695\pi\) | ||||
0.471549 | + | 0.881840i | \(0.343695\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.75419e9 | 1.63037 | 0.815185 | − | 0.579201i | \(-0.196635\pi\) | ||||
0.815185 | + | 0.579201i | \(0.196635\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.52910e8 | 0.438562 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.14934e8 | 0.123202 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.51524e8 | 0.311128 | 0.155564 | − | 0.987826i | \(-0.450281\pi\) | ||||
0.155564 | + | 0.987826i | \(0.450281\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.16745e8 | 0.120341 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.80168e9 | −0.984610 | −0.492305 | − | 0.870423i | \(-0.663845\pi\) | ||||
−0.492305 | + | 0.870423i | \(0.663845\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.24076e9 | 1.74336 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.40039e8 | −0.233032 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.05710e8 | 0.211521 | 0.105760 | − | 0.994392i | \(-0.466272\pi\) | ||||
0.105760 | + | 0.994392i | \(0.466272\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.39943e9 | −0.718348 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.62602e8 | −0.233810 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.15412e9 | 1.07209 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.68101e9 | 0.823877 | 0.411939 | − | 0.911212i | \(-0.364852\pi\) | ||||
0.411939 | + | 0.911212i | \(0.364852\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.60720e8 | −0.270646 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.11400e9 | −1.00497 | −0.502484 | − | 0.864586i | \(-0.667580\pi\) | ||||
−0.502484 | + | 0.864586i | \(0.667580\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.49558e9 | −1.16852 | −0.584261 | − | 0.811566i | \(-0.698616\pi\) | ||||
−0.584261 | + | 0.811566i | \(0.698616\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.90232e8 | 0.318353 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.80333e9 | 1.27369 | 0.636847 | − | 0.770990i | \(-0.280238\pi\) | ||||
0.636847 | + | 0.770990i | \(0.280238\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.93077e9 | 1.31183 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.25522e9 | −0.994524 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.74934e7 | 0.0336706 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.28667e8 | −0.311962 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.35233e9 | 0.570518 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.17285e8 | 0.0487605 | 0.0243803 | − | 0.999703i | \(-0.492239\pi\) | ||||
0.0243803 | + | 0.999703i | \(0.492239\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.61381e8 | −0.0661220 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.85884e8 | 0.196209 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.52309e9 | −1.00424 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.37486e9 | −0.539393 | −0.269697 | − | 0.962945i | \(-0.586923\pi\) | ||||
−0.269697 | + | 0.962945i | \(0.586923\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.81125e9 | 0.700484 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.33074e8 | −0.0888606 | −0.0444303 | − | 0.999012i | \(-0.514147\pi\) | ||||
−0.0444303 | + | 0.999012i | \(0.514147\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.15607e9 | 0.810397 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.27018e9 | 0.470703 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.93607e9 | 1.80357 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.97141e7 | 0.0323228 | 0.0161614 | − | 0.999869i | \(-0.494855\pi\) | ||||
0.0161614 | + | 0.999869i | \(0.494855\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.59014e9 | −0.564943 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.47433e9 | −0.866901 | −0.433450 | − | 0.901177i | \(-0.642704\pi\) | ||||
−0.433450 | + | 0.901177i | \(0.642704\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.73594e9 | −1.29086 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.70811e8 | 0.296754 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.68523e8 | 0.0566430 | 0.0283215 | − | 0.999599i | \(-0.490984\pi\) | ||||
0.0283215 | + | 0.999599i | \(0.490984\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.75884e9 | −2.24078 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.48887e8 | 0.0813938 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.67798e9 | 1.83176 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.22272e8 | −0.102566 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.56341e9 | 0.490892 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.41709e9 | −0.748792 | −0.374396 | − | 0.927269i | \(-0.622150\pi\) | ||||
−0.374396 | + | 0.927269i | \(0.622150\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.40312e8 | 0.287419 | 0.143710 | − | 0.989620i | \(-0.454097\pi\) | ||||
0.143710 | + | 0.989620i | \(0.454097\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.64724e9 | −0.496821 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.97658e9 | 0.588271 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.11590e9 | −0.915142 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.00632e9 | 0.581526 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.63422e9 | −0.467482 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.66336e9 | 0.751955 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.27852e9 | −0.356284 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.40601e9 | −0.386747 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.65125e8 | 0.0719879 | 0.0359939 | − | 0.999352i | \(-0.488540\pi\) | ||||
0.0359939 | + | 0.999352i | \(0.488540\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.59511e9 | 0.963636 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.13281e9 | 1.09360 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.41977e8 | 0.167712 | 0.0838559 | − | 0.996478i | \(-0.473276\pi\) | ||||
0.0838559 | + | 0.996478i | \(0.473276\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.29177e9 | −0.333182 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.57015e8 | −0.243718 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.75388e9 | −1.94976 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.90714e8 | 0.0721839 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.92485e9 | −0.717152 | −0.358576 | − | 0.933501i | \(-0.616738\pi\) | ||||
−0.358576 | + | 0.933501i | \(0.616738\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.04944e7 | 0.0219119 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.63735e9 | 0.869790 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.62455e9 | −1.32834 | −0.664169 | − | 0.747583i | \(-0.731214\pi\) | ||||
−0.664169 | + | 0.747583i | \(0.731214\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.50525e9 | 1.28413 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.62640e8 | 0.129625 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.48615e9 | −1.93116 | −0.965579 | − | 0.260111i | \(-0.916241\pi\) | ||||
−0.965579 | + | 0.260111i | \(0.916241\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.42789e9 | 1.22013 | 0.610063 | − | 0.792353i | \(-0.291144\pi\) | ||||
0.610063 | + | 0.792353i | \(0.291144\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.46558e9 | 0.547492 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.79516e8 | −0.214869 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.80138e9 | −1.90737 | −0.953686 | − | 0.300803i | \(-0.902745\pi\) | ||||
−0.953686 | + | 0.300803i | \(0.902745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.87268e9 | 0.615053 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.23237e9 | 0.683761 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.77248e9 | −1.83351 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.48328e9 | 0.306321 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.50790e8 | 0.0715836 | 0.0357918 | − | 0.999359i | \(-0.488605\pi\) | ||||
0.0357918 | + | 0.999359i | \(0.488605\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.77345e8 | −0.176916 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.16407e9 | 1.02905 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.34103e9 | 1.24873 | 0.624364 | − | 0.781133i | \(-0.285358\pi\) | ||||
0.624364 | + | 0.781133i | \(0.285358\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.11122e10 | −2.16268 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.11642e9 | −0.214742 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.85447e9 | 0.542664 | 0.271332 | − | 0.962486i | \(-0.412536\pi\) | ||||
0.271332 | + | 0.962486i | \(0.412536\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.22420e9 | 0.605844 | 0.302922 | − | 0.953015i | \(-0.402038\pi\) | ||||
0.302922 | + | 0.953015i | \(0.402038\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.01806e9 | 0.374820 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.05963e9 | −0.194540 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.25547e8 | 0.149824 | 0.0749120 | − | 0.997190i | \(-0.476132\pi\) | ||||
0.0749120 | + | 0.997190i | \(0.476132\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.16345e9 | −0.388139 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.76339e8 | −0.0667475 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.26909e9 | −0.222526 | −0.111263 | − | 0.993791i | \(-0.535490\pi\) | ||||
−0.111263 | + | 0.993791i | \(0.535490\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.94389e9 | 0.510339 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.08847e10 | 1.86560 | 0.932802 | − | 0.360389i | \(-0.117356\pi\) | ||||
0.932802 | + | 0.360389i | \(0.117356\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.60725e9 | −0.950239 | −0.475119 | − | 0.879921i | \(-0.657595\pi\) | ||||
−0.475119 | + | 0.879921i | \(0.657595\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.34568e8 | 0.0560614 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.31219e9 | −1.54292 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.28479e9 | −1.19354 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.61451e9 | −0.261580 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.32501e8 | 0.133385 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.03140e9 | −0.480330 | −0.240165 | − | 0.970732i | \(-0.577202\pi\) | ||||
−0.240165 | + | 0.970732i | \(0.577202\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.48223e9 | −0.232275 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.07626e10 | −1.66806 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.64189e9 | −0.251685 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.39886e9 | 0.515323 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.88737e9 | 0.283045 | 0.141522 | − | 0.989935i | \(-0.454800\pi\) | ||||
0.141522 | + | 0.989935i | \(0.454800\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.23016e10 | −1.82483 | −0.912417 | − | 0.409263i | \(-0.865786\pi\) | ||||
−0.912417 | + | 0.409263i | \(0.865786\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.63017e8 | −0.0239207 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.68136e9 | 0.824683 | 0.412342 | − | 0.911029i | \(-0.364711\pi\) | ||||
0.412342 | + | 0.911029i | \(0.364711\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.30148e10 | −1.86888 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.98335e9 | −0.281751 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.38850e9 | −1.31947 | −0.659736 | − | 0.751497i | \(-0.729332\pi\) | ||||
−0.659736 | + | 0.751497i | \(0.729332\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.09547e9 | 0.708500 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.65397e9 | −0.640243 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.88229e9 | −0.528432 | −0.264216 | − | 0.964463i | \(-0.585113\pi\) | ||||
−0.264216 | + | 0.964463i | \(0.585113\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.30387e9 | −0.444957 | −0.222478 | − | 0.974938i | \(-0.571415\pi\) | ||||
−0.222478 | + | 0.974938i | \(0.571415\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.24758e9 | 0.566036 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.93240e9 | 0.650403 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.28647e9 | −0.167865 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.29442e9 | −0.425391 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.37961e9 | 1.07077 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.44280e9 | 0.435371 | 0.217685 | − | 0.976019i | \(-0.430149\pi\) | ||||
0.217685 | + | 0.976019i | \(0.430149\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.13425e9 | −0.141954 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.59211e10 | −1.97202 | −0.986012 | − | 0.166677i | \(-0.946696\pi\) | ||||
−0.986012 | + | 0.166677i | \(0.946696\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.24999e9 | 0.888778 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.00049e9 | 1.09207 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.17757e9 | 0.861995 | 0.430997 | − | 0.902353i | \(-0.358162\pi\) | ||||
0.430997 | + | 0.902353i | \(0.358162\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.06308e10 | 2.45244 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.47979e8 | 0.0409453 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.02442e10 | −1.19320 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.18199e10 | −1.36282 | −0.681411 | − | 0.731901i | \(-0.738633\pi\) | ||||
−0.681411 | + | 0.731901i | \(0.738633\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.64981e9 | −0.416585 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.92474e10 | 2.17483 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.43026e9 | 0.943032 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.93033e9 | 1.09975 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.79765e9 | −0.964614 | −0.482307 | − | 0.876002i | \(-0.660201\pi\) | ||||
−0.482307 | + | 0.876002i | \(0.660201\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.69523e8 | −0.0401142 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.77940e8 | 0.0728667 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.07351e10 | 1.14245 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.09495e9 | −0.431506 | −0.215753 | − | 0.976448i | \(-0.569221\pi\) | ||||
−0.215753 | + | 0.976448i | \(0.569221\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.33913e9 | −0.557092 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.17938e9 | −0.121854 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.62190e9 | −0.984441 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.05224e9 | −0.410561 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.16329e10 | 1.16718 | 0.583589 | − | 0.812049i | \(-0.301648\pi\) | ||||
0.583589 | + | 0.812049i | \(0.301648\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.63154e10 | −1.62116 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.04554e9 | 0.201291 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.36140e9 | 0.425053 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.69867e10 | −1.63960 | −0.819799 | − | 0.572651i | \(-0.805915\pi\) | ||||
−0.819799 | + | 0.572651i | \(0.805915\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.66824e8 | −0.0442020 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.28036e9 | −0.307650 | −0.153825 | − | 0.988098i | \(-0.549159\pi\) | ||||
−0.153825 | + | 0.988098i | \(0.549159\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.95772e9 | 0.274758 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.30910e10 | −1.20458 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.76555e10 | 1.60926 | 0.804628 | − | 0.593779i | \(-0.202365\pi\) | ||||
0.804628 | + | 0.593779i | \(0.202365\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.88538e9 | −0.170229 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.33458e9 | 0.745458 | 0.372729 | − | 0.927940i | \(-0.378422\pi\) | ||||
0.372729 | + | 0.927940i | \(0.378422\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.00480e9 | −0.532049 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.22573e9 | 0.195367 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.65305e9 | −0.665500 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.15928e10 | 0.998729 | 0.499365 | − | 0.866392i | \(-0.333567\pi\) | ||||
0.499365 | + | 0.866392i | \(0.333567\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.64338e9 | 0.567031 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.31270e9 | −0.533827 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.07716e10 | 1.74034 | 0.870170 | − | 0.492751i | \(-0.164009\pi\) | ||||
0.870170 | + | 0.492751i | \(0.164009\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.17032e9 | −0.180168 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.33390e9 | 0.520985 | 0.260492 | − | 0.965476i | \(-0.416115\pi\) | ||||
0.260492 | + | 0.965476i | \(0.416115\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.18755e10 | −0.967864 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.65162e9 | −0.617929 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.51983e10 | −1.21622 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.52316e9 | −0.517268 | −0.258634 | − | 0.965975i | \(-0.583272\pi\) | ||||
−0.258634 | + | 0.965975i | \(0.583272\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.67439e9 | −0.681630 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.77839e9 | −0.527835 | −0.263918 | − | 0.964545i | \(-0.585015\pi\) | ||||
−0.263918 | + | 0.964545i | \(0.585015\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.99832e9 | 0.308547 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.35353e8 | −0.0638846 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.74195e9 | −0.283607 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.20481e10 | −1.65612 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.48970e9 | −0.110900 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.07748e10 | −2.27066 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.82358e9 | 0.206485 | 0.103242 | − | 0.994656i | \(-0.467078\pi\) | ||||
0.103242 | + | 0.994656i | \(0.467078\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.84500e9 | −0.351175 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.58191e10 | −1.13649 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.78546e9 | 0.696827 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.84540e10 | 1.30259 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.30653e9 | −0.371284 | −0.185642 | − | 0.982617i | \(-0.559436\pi\) | ||||
−0.185642 | + | 0.982617i | \(0.559436\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.94138e9 | 0.134647 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.41215e9 | −0.440849 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.01899e10 | 2.05759 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.63041e9 | 0.447976 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.94149e9 | −0.130040 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.64448e9 | −0.441206 | −0.220603 | − | 0.975364i | \(-0.570803\pi\) | ||||
−0.220603 | + | 0.975364i | \(0.570803\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.83502e10 | −1.20800 | −0.604000 | − | 0.796984i | \(-0.706427\pi\) | ||||
−0.604000 | + | 0.796984i | \(0.706427\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.45220e10 | −0.947784 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.47165e10 | 1.59932 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.07209e8 | 0.0132933 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.26213e9 | −0.271102 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.10009e10 | 0.693788 | 0.346894 | − | 0.937904i | \(-0.387236\pi\) | ||||
0.346894 | + | 0.937904i | \(0.387236\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.35279e10 | −0.845926 | −0.422963 | − | 0.906147i | \(-0.639010\pi\) | ||||
−0.422963 | + | 0.906147i | \(0.639010\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.35780e9 | 0.456204 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.77028e9 | −0.108836 | −0.0544181 | − | 0.998518i | \(-0.517330\pi\) | ||||
−0.0544181 | + | 0.998518i | \(0.517330\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.54339e9 | −0.520822 | −0.260411 | − | 0.965498i | \(-0.583858\pi\) | ||||
−0.260411 | + | 0.965498i | \(0.583858\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.97871e9 | −0.361413 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.46986e9 | 0.507713 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.16992e10 | −1.28986 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.36569e9 | −0.0805030 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.23734e10 | 0.723307 | 0.361653 | − | 0.932313i | \(-0.382212\pi\) | ||||
0.361653 | + | 0.932313i | \(0.382212\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.15217e10 | −0.667930 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.41138e9 | −0.311108 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.18832e10 | 0.677537 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.04479e9 | 0.172173 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.51228e10 | 0.848117 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.96734e8 | −0.0276293 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.67180e10 | −0.922282 | −0.461141 | − | 0.887327i | \(-0.652560\pi\) | ||||
−0.461141 | + | 0.887327i | \(0.652560\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.39633e9 | 0.185835 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.33011e9 | 0.180728 | 0.0903642 | − | 0.995909i | \(-0.471197\pi\) | ||||
0.0903642 | + | 0.995909i | \(0.471197\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.10846e10 | 0.596682 | 0.298341 | − | 0.954459i | \(-0.403567\pi\) | ||||
0.298341 | + | 0.954459i | \(0.403567\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.45914e9 | −0.451664 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.94912e10 | −1.56191 | −0.780954 | − | 0.624589i | \(-0.785266\pi\) | ||||
−0.780954 | + | 0.624589i | \(0.785266\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.13344e10 | 1.12079 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.08324e10 | −0.564492 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.46345e10 | 1.79036 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.52872e10 | −0.783909 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.99217e9 | 0.253945 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.99615e9 | 0.403508 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.29461e9 | −0.164932 | −0.0824660 | − | 0.996594i | \(-0.526280\pi\) | ||||
−0.0824660 | + | 0.996594i | \(0.526280\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.34734e10 | 0.669139 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.93619e10 | 0.953966 | 0.476983 | − | 0.878913i | \(-0.341730\pi\) | ||||
0.476983 | + | 0.878913i | \(0.341730\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.16110e9 | −0.105636 | −0.0528181 | − | 0.998604i | \(-0.516820\pi\) | ||||
−0.0528181 | + | 0.998604i | \(0.516820\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.73784e10 | 1.32772 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.57751e10 | 1.72127 | 0.860633 | − | 0.509226i | \(-0.170068\pi\) | ||||
0.860633 | + | 0.509226i | \(0.170068\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.09259e10 | 1.47627 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.51317e9 | −0.119028 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.61721e8 | −0.0404936 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.74467e10 | −0.813454 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.53443e9 | −0.117248 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.25131e9 | 0.241051 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.28458e10 | 2.40699 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.68423e8 | 0.0211705 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.90592e10 | 2.20014 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.96026e10 | −0.872347 | −0.436173 | − | 0.899863i | \(-0.643667\pi\) | ||||
−0.436173 | + | 0.899863i | \(0.643667\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.39191e9 | 0.326425 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.00474e10 | −1.31672 | −0.658359 | − | 0.752704i | \(-0.728749\pi\) | ||||
−0.658359 | + | 0.752704i | \(0.728749\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.44381e10 | −0.627861 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.76276e10 | −0.760710 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.46416e10 | −0.627041 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.48018e10 | −1.05409 | −0.527046 | − | 0.849837i | \(-0.676701\pi\) | ||||
−0.527046 | + | 0.849837i | \(0.676701\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.21698e10 | −0.935091 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.57471e10 | −1.07776 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.68403e9 | 0.0699604 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.12344e10 | −0.463202 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.43504e10 | −0.996438 | −0.498219 | − | 0.867051i | \(-0.666012\pi\) | ||||
−0.498219 | + | 0.867051i | \(0.666012\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.75952e9 | −0.152689 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.46831e9 | 0.0591877 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.96355e10 | 1.98587 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.85512e10 | −1.92802 | −0.964011 | − | 0.265864i | \(-0.914343\pi\) | ||||
−0.964011 | + | 0.265864i | \(0.914343\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.81437e10 | 0.715150 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.87097e10 | 1.12322 | 0.561610 | − | 0.827402i | \(-0.310182\pi\) | ||||
0.561610 | + | 0.827402i | \(0.310182\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.03014e9 | −0.195339 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.67783e9 | 0.295956 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.85339e10 | 1.85703 | 0.928517 | − | 0.371290i | \(-0.121084\pi\) | ||||
0.928517 | + | 0.371290i | \(0.121084\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.52549e10 | 1.33902 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.04209e9 | 0.152396 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.62731e9 | −0.210608 | −0.105304 | − | 0.994440i | \(-0.533582\pi\) | ||||
−0.105304 | + | 0.994440i | \(0.533582\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.36454e10 | 1.25001 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.66357e9 | 0.356407 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.92816e10 | −2.17047 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.26985e10 | −0.825020 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.26970e9 | −0.190149 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.92008e10 | 1.40427 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.43610e10 | −0.510732 | −0.255366 | − | 0.966844i | \(-0.582196\pi\) | ||||
−0.255366 | + | 0.966844i | \(0.582196\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.72589e9 | 0.343397 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.71664e9 | −0.130281 | −0.0651407 | − | 0.997876i | \(-0.520750\pi\) | ||||
−0.0651407 | + | 0.997876i | \(0.520750\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.53066e10 | −1.92478 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.59222e9 | 0.296886 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.35573e10 | 0.465096 | 0.232548 | − | 0.972585i | \(-0.425294\pi\) | ||||
0.232548 | + | 0.972585i | \(0.425294\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.15951e10 | 1.41678 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.17715e9 | −0.276542 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.75077e9 | −0.260260 | −0.130130 | − | 0.991497i | \(-0.541539\pi\) | ||||
−0.130130 | + | 0.991497i | \(0.541539\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.04693e10 | 2.34949 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.94803e9 | −0.0644890 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.78543e8 | 0.00915597 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.43046e10 | 1.44608 | 0.723039 | − | 0.690808i | \(-0.242745\pi\) | ||||
0.723039 | + | 0.690808i | \(0.242745\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.18824e9 | −0.200560 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.52348e10 | −0.490292 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.71271e9 | −0.118647 | −0.0593236 | − | 0.998239i | \(-0.518894\pi\) | ||||
−0.0593236 | + | 0.998239i | \(0.518894\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.75204e8 | −0.0182533 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 384.8.a.i.1.1 | ✓ | 3 | |
4.3 | odd | 2 | 384.8.a.k.1.1 | yes | 3 | ||
8.3 | odd | 2 | 384.8.a.j.1.3 | yes | 3 | ||
8.5 | even | 2 | 384.8.a.l.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.8.a.i.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
384.8.a.j.1.3 | yes | 3 | 8.3 | odd | 2 | ||
384.8.a.k.1.1 | yes | 3 | 4.3 | odd | 2 | ||
384.8.a.l.1.3 | yes | 3 | 8.5 | even | 2 |