Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,21,Mod(2,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 21, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.2");
S:= CuspForms(chi, 21);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 21 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.h (of order \(6\), 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: | \(53.2378906716\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 2.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.2 |
Dual form | 21.21.h.a.11.1 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | −29524.5 | − | 51137.9i | −0.500000 | − | 0.866025i | ||||
\(4\) | −524288. | − | 908093.i | −0.500000 | − | 0.866025i | ||||
\(5\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.22994e8 | − | 1.73395e8i | −0.789428 | − | 0.613843i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.74339e9 | + | 3.01964e9i | −0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | −3.09587e10 | + | 5.36220e10i | −0.500000 | + | 0.866025i | ||||
\(13\) | 3.81709e10 | 0.276885 | 0.138442 | − | 0.990370i | \(-0.455790\pi\) | ||||
0.138442 | + | 0.990370i | \(0.455790\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.49756e11 | + | 9.52205e11i | −0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.00291e12 | + | 1.03973e13i | −0.979097 | + | 1.69585i | −0.313404 | + | 0.949620i | \(0.601469\pi\) |
−0.665693 | + | 0.746226i | \(0.731864\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.28330e12 | + | 1.65229e13i | −0.136889 | + | 0.990586i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.76837e13 | − | 8.25906e13i | −0.500000 | − | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.05891e14 | 1.00000 | ||||||||
\(28\) | −4.05462e13 | + | 2.93408e14i | −0.136889 | + | 0.990586i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.22563e14 | − | 7.31900e14i | −0.515554 | − | 0.892966i | −0.999837 | − | 0.0180543i | \(-0.994253\pi\) |
0.484283 | − | 0.874911i | \(-0.339080\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.65616e15 | 1.00000 | ||||||||
\(37\) | 3.60548e14 | − | 6.24488e14i | 0.0749801 | − | 0.129869i | −0.826098 | − | 0.563527i | \(-0.809444\pi\) |
0.901078 | + | 0.433658i | \(0.142777\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.12698e15 | − | 1.95198e15i | −0.138442 | − | 0.239789i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.34394e15 | 0.0621862 | 0.0310931 | − | 0.999516i | \(-0.490101\pi\) | ||||
0.0310931 | + | 0.999516i | \(0.490101\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(48\) | 6.49251e16 | 1.00000 | ||||||||
\(49\) | 1.96603e16 | + | 7.73323e16i | 0.246394 | + | 0.969170i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.00126e16 | − | 3.46628e16i | −0.138442 | − | 0.239789i | ||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.08931e17 | 1.95819 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.93894e17 | − | 1.20186e18i | 0.972736 | − | 1.68483i | 0.285522 | − | 0.958372i | \(-0.407833\pi\) |
0.687213 | − | 0.726456i | \(-0.258834\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.12358e17 | − | 3.71066e17i | 0.926318 | − | 0.376743i | ||||
\(64\) | 1.15292e18 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.02793e18 | + | 1.78042e18i | 0.563915 | + | 0.976729i | 0.997150 | + | 0.0754482i | \(0.0240388\pi\) |
−0.433235 | + | 0.901281i | \(0.642628\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.38136e18 | + | 4.12464e18i | 0.554111 | + | 0.959748i | 0.997972 | + | 0.0636525i | \(0.0202749\pi\) |
−0.443861 | + | 0.896095i | \(0.646392\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.81568e18 | + | 4.87689e18i | −0.500000 | + | 0.866025i | ||||
\(76\) | 1.25890e19 | 1.95819 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.26142e18 | − | 1.25772e19i | 0.766921 | − | 1.32835i | −0.172303 | − | 0.985044i | \(-0.555121\pi\) |
0.939225 | − | 0.343303i | \(-0.111546\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.07883e18 | − | 1.05288e19i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 1.62014e19 | − | 6.58929e18i | 0.926318 | − | 0.376743i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.51188e18 | − | 6.61866e18i | −0.218581 | − | 0.169964i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.49519e19 | + | 4.32180e19i | −0.515554 | + | 0.892966i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.46702e20 | −1.98938 | −0.994690 | − | 0.102912i | \(-0.967184\pi\) | ||||
−0.994690 | + | 0.102912i | \(0.967184\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.00000e19 | + | 8.66025e19i | −0.500000 | + | 0.866025i | ||||
\(101\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.75304e19 | + | 1.68928e20i | −0.725718 | + | 1.25698i | 0.232960 | + | 0.972486i | \(0.425159\pi\) |
−0.958678 | + | 0.284494i | \(0.908174\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | −1.07946e20 | − | 1.86968e20i | −0.500000 | − | 0.866025i | ||||
\(109\) | −2.33087e20 | − | 4.03719e20i | −0.984587 | − | 1.70535i | −0.643759 | − | 0.765229i | \(-0.722626\pi\) |
−0.340828 | − | 0.940126i | \(-0.610707\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.25800e19 | −0.149960 | ||||||||
\(112\) | 2.87700e20 | − | 1.17011e20i | 0.926318 | − | 0.376743i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.65469e19 | + | 1.15263e20i | −0.138442 | + | 0.239789i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.36375e20 | + | 5.82619e20i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.43089e20 | + | 7.67453e20i | −0.515554 | + | 0.892966i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.77305e20 | 0.712122 | 0.356061 | − | 0.934463i | \(-0.384120\pi\) | ||||
0.356061 | + | 0.934463i | \(0.384120\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.96790e19 | − | 6.87261e19i | −0.0310931 | − | 0.0538548i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.14146e21 | − | 1.27767e21i | 1.81391 | − | 0.737737i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.21077e21 | 1.93533 | 0.967663 | − | 0.252248i | \(-0.0811698\pi\) | ||||
0.967663 | + | 0.252248i | \(0.0811698\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.91688e21 | − | 3.32013e21i | −0.500000 | − | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.37415e21 | − | 3.28858e21i | 0.716129 | − | 0.697968i | ||||
\(148\) | −7.56124e20 | −0.149960 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.11218e21 | + | 1.05866e22i | 0.991806 | + | 1.71786i | 0.606543 | + | 0.795050i | \(0.292556\pi\) |
0.385262 | + | 0.922807i | \(0.374111\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.18172e21 | + | 2.04680e21i | −0.138442 | + | 0.239789i | ||||
\(157\) | −6.89465e21 | − | 1.19419e22i | −0.757732 | − | 1.31243i | −0.944004 | − | 0.329933i | \(-0.892974\pi\) |
0.186272 | − | 0.982498i | \(-0.440359\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.31858e22 | + | 2.28385e22i | −0.995933 | + | 1.72501i | −0.419937 | + | 0.907553i | \(0.637948\pi\) |
−0.575996 | + | 0.817453i | \(0.695385\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.75479e22 | −0.923335 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.09308e22 | − | 3.62533e22i | −0.979097 | − | 1.69585i | ||||
\(172\) | −7.04609e20 | − | 1.22042e21i | −0.0310931 | − | 0.0538548i | ||||
\(173\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.68766e21 | + | 2.66853e22i | −0.136889 | + | 0.990586i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.95296e22 | 1.04746 | 0.523730 | − | 0.851885i | \(-0.324540\pi\) | ||||
0.523730 | + | 0.851885i | \(0.324540\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.19475e22 | −1.94547 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.59125e22 | − | 3.57006e22i | −0.789428 | − | 0.613843i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | −3.40394e22 | − | 5.89580e22i | −0.500000 | − | 0.866025i | ||||
\(193\) | 6.62234e22 | + | 1.14702e23i | 0.923504 | + | 1.59956i | 0.793950 | + | 0.607983i | \(0.208021\pi\) |
0.129554 | + | 0.991572i | \(0.458646\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.99172e22 | − | 5.83978e22i | 0.716129 | − | 0.697968i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.57463e22 | + | 1.31197e23i | 0.777734 | + | 1.34707i | 0.933245 | + | 0.359240i | \(0.116964\pi\) |
−0.155511 | + | 0.987834i | \(0.549703\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.06980e22 | − | 1.05132e23i | 0.563915 | − | 0.976729i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.09847e22 | + | 3.63465e22i | −0.138442 | + | 0.239789i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.17102e23 | 1.24119 | 0.620595 | − | 0.784131i | \(-0.286891\pi\) | ||||
0.620595 | + | 0.784131i | \(0.286891\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.26792e22 | + | 2.36480e23i | −0.141148 | + | 1.02140i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.40617e23 | − | 2.43556e23i | 0.554111 | − | 0.959748i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.12862e23 | 1.35755 | 0.678776 | − | 0.734345i | \(-0.262511\pi\) | ||||
0.678776 | + | 0.734345i | \(0.262511\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.32526e23 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(228\) | −3.71684e23 | − | 6.43776e23i | −0.979097 | − | 1.69585i | ||||
\(229\) | 1.76002e22 | − | 3.04845e22i | 0.0443776 | − | 0.0768642i | −0.842983 | − | 0.537940i | \(-0.819203\pi\) |
0.887361 | + | 0.461075i | \(0.152536\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.57560e23 | −1.53384 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.59376e23 | + | 1.14207e24i | 0.997614 | + | 1.72792i | 0.558597 | + | 0.829440i | \(0.311340\pi\) |
0.439017 | + | 0.898479i | \(0.355327\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.58949e23 | + | 6.21718e23i | −0.500000 | + | 0.866025i | ||||
\(244\) | −1.45520e24 | −1.94547 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.29137e23 | + | 3.96876e23i | −0.271097 | + | 0.469554i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | −8.15301e23 | − | 6.33961e23i | −0.789428 | − | 0.613843i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.04463e23 | − | 1.04696e24i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.88683e23 | + | 7.67396e22i | −0.138911 | + | 0.0564965i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.07786e24 | − | 1.86690e24i | 0.563915 | − | 0.976729i | ||||
\(269\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.79147e23 | + | 3.10292e23i | −0.0838528 | + | 0.145237i | −0.904902 | − | 0.425620i | \(-0.860056\pi\) |
0.821049 | + | 0.570858i | \(0.193389\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.71557e22 | + | 6.30693e23i | −0.0379026 | + | 0.274278i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.02984e24 | − | 1.78374e24i | −0.387233 | − | 0.670707i | 0.604843 | − | 0.796345i | \(-0.293236\pi\) |
−0.992076 | + | 0.125637i | \(0.959902\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.94677e24 | 1.03111 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.63926e24 | + | 2.83928e24i | 0.497488 | + | 0.861675i | 0.999996 | − | 0.00289763i | \(-0.000922346\pi\) |
−0.502507 | + | 0.864573i | \(0.667589\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.03212e24 | + | 3.51973e24i | −0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.33130e24 | + | 7.50202e24i | 0.994690 | + | 1.72285i | ||||
\(292\) | 2.49704e24 | − | 4.32500e24i | 0.554111 | − | 0.959748i | ||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5.90490e24 | 1.00000 | ||||||||
\(301\) | −2.99689e23 | − | 2.33032e23i | −0.0490915 | − | 0.0381725i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.60027e24 | − | 1.14320e25i | −0.979097 | − | 1.69585i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.17417e24 | 1.09916 | 0.549579 | − | 0.835442i | \(-0.314788\pi\) | ||||
0.549579 | + | 0.835442i | \(0.314788\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.15181e25 | 1.45144 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.85581e24 | − | 1.53387e25i | 0.981261 | − | 1.69959i | 0.323764 | − | 0.946138i | \(-0.395052\pi\) |
0.657497 | − | 0.753457i | \(-0.271615\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.52283e25 | −1.53384 | ||||||||
\(317\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −6.37412e24 | + | 1.10403e25i | −0.500000 | + | 0.866025i | ||||
\(325\) | −1.82013e24 | − | 3.15256e24i | −0.138442 | − | 0.239789i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.37636e25 | + | 2.38392e25i | −0.984587 | + | 1.70535i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.34605e25 | + | 2.33143e25i | −0.852671 | + | 1.47687i | 0.0261172 | + | 0.999659i | \(0.491686\pi\) |
−0.878789 | + | 0.477211i | \(0.841648\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.25715e24 | + | 2.17745e24i | 0.0749801 | + | 0.129869i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.44779e25 | − | 1.12577e25i | −0.789428 | − | 0.613843i | ||||
\(337\) | −3.46628e25 | −1.83470 | −0.917348 | − | 0.398086i | \(-0.869675\pi\) | ||||
−0.917348 | + | 0.398086i | \(0.869675\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.02493e24 | − | 2.06536e25i | 0.400408 | − | 0.916337i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.20209e24 | 0.343267 | 0.171634 | − | 0.985161i | \(-0.445095\pi\) | ||||
0.171634 | + | 0.985161i | \(0.445095\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.85905e24 | 0.276885 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.32748e25 | − | 9.22747e25i | −1.41726 | − | 2.45477i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.97252e25 | 1.00000 | ||||||||
\(364\) | −1.54769e24 | + | 1.11997e25i | −0.0379026 | + | 0.274278i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.22629e25 | + | 3.85604e25i | 0.502250 | + | 0.869923i | 0.999997 | + | 0.00260049i | \(0.000827762\pi\) |
−0.497746 | + | 0.867323i | \(0.665839\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.23279e25 | 1.03111 | ||||||||
\(373\) | −4.35481e25 | + | 7.54275e25i | −0.835374 | + | 1.44691i | 0.0583519 | + | 0.998296i | \(0.481415\pi\) |
−0.893726 | + | 0.448614i | \(0.851918\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.22146e26 | 1.99750 | 0.998751 | − | 0.0499685i | \(-0.0159121\pi\) | ||||
0.998751 | + | 0.0499685i | \(0.0159121\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.29495e25 | − | 3.97498e25i | −0.356061 | − | 0.616716i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.34301e24 | + | 4.05821e24i | −0.0310931 | + | 0.0538548i | ||||
\(388\) | 7.69140e25 | + | 1.33219e26i | 0.994690 | + | 1.72285i | ||||
\(389\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.31510e25 | − | 1.44022e26i | 0.854993 | − | 1.48089i | −0.0216588 | − | 0.999765i | \(-0.506895\pi\) |
0.876652 | − | 0.481126i | \(-0.159772\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.58087e26 | − | 1.22925e26i | −1.54585 | − | 1.20202i | ||||
\(400\) | 1.04858e26 | 1.00000 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.61296e25 | − | 2.79373e25i | −0.142749 | − | 0.247249i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.23612e26 | + | 2.14102e26i | 0.943685 | + | 1.63451i | 0.758363 | + | 0.651832i | \(0.225999\pi\) |
0.185321 | + | 0.982678i | \(0.440667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.04536e26 | 1.45144 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.53845e26 | − | 2.66468e26i | −0.967663 | − | 1.67604i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.42656e26 | −1.95901 | −0.979507 | − | 0.201410i | \(-0.935448\pi\) | ||||
−0.979507 | + | 0.201410i | \(0.935448\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.63131e26 | + | 1.47689e26i | −1.80212 | + | 0.732944i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | −1.13190e26 | + | 1.96051e26i | −0.500000 | + | 0.866025i | ||||
\(433\) | 1.96482e26 | 0.848096 | 0.424048 | − | 0.905640i | \(-0.360609\pi\) | ||||
0.424048 | + | 0.905640i | \(0.360609\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.44410e26 | + | 4.23330e26i | −0.984587 | + | 1.70535i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.27020e26 | − | 2.20005e26i | 0.477780 | − | 0.827539i | −0.521896 | − | 0.853009i | \(-0.674775\pi\) |
0.999676 | + | 0.0254706i | \(0.00810842\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.67792e26 | − | 7.54533e25i | −0.962523 | − | 0.271202i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | 2.23242e25 | + | 3.86666e25i | 0.0749801 | + | 0.129869i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.57094e26 | − | 1.99911e26i | −0.789428 | − | 0.613843i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.60918e26 | − | 6.25128e26i | 0.991806 | − | 1.71786i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.42274e26 | + | 5.92837e26i | −0.861415 | + | 1.49201i | 0.00914856 | + | 0.999958i | \(0.497088\pi\) |
−0.870563 | + | 0.492056i | \(0.836245\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.51579e26 | 0.555730 | 0.277865 | − | 0.960620i | \(-0.410373\pi\) | ||||
0.277865 | + | 0.960620i | \(0.410373\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(468\) | 1.39559e26 | 0.276885 | ||||||||
\(469\) | 7.94954e25 | − | 5.75260e26i | 0.154388 | − | 1.11721i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.07122e26 | + | 7.05157e26i | −0.757732 | + | 1.31243i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.14496e27 | 1.95819 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.37625e25 | − | 2.38373e25i | 0.0207609 | − | 0.0359588i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.05429e26 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.50068e26 | − | 1.12595e27i | −0.866302 | − | 1.50048i | −0.865748 | − | 0.500480i | \(-0.833157\pi\) |
−0.000554074 | − | 1.00000i | \(-0.500176\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.55721e27 | 1.99187 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.29225e26 | 1.03111 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.76001e26 | + | 1.17087e27i | −0.706223 | + | 1.22321i | 0.260025 | + | 0.965602i | \(0.416269\pi\) |
−0.966248 | + | 0.257613i | \(0.917064\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.18094e26 | + | 8.97366e26i | 0.461667 | + | 0.799631i | ||||
\(508\) | −4.07532e26 | − | 7.05866e26i | −0.356061 | − | 0.616716i | ||||
\(509\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.84164e26 | − | 1.33269e27i | 0.151704 | − | 1.09779i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.23595e27 | + | 2.14072e27i | −0.979097 | + | 1.69585i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.16065e25 | + | 7.20645e25i | −0.0310931 | + | 0.0538548i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.27221e26 | + | 3.93558e26i | −0.148399 | + | 0.257035i | −0.930636 | − | 0.365946i | \(-0.880745\pi\) |
0.782237 | + | 0.622981i | \(0.214079\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.47351e27 | − | 5.99292e26i | 0.926318 | − | 0.376743i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.58078e26 | − | 1.48623e27i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.80727e27 | − | 2.18288e27i | −1.54585 | − | 1.20202i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.34276e27 | + | 2.32573e27i | −0.625210 | + | 1.08290i | 0.363290 | + | 0.931676i | \(0.381654\pi\) |
−0.988500 | + | 0.151220i | \(0.951680\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.16709e27 | − | 2.02146e27i | −0.523730 | − | 0.907126i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.59721e26 | −0.191699 | −0.0958497 | − | 0.995396i | \(-0.530557\pi\) | ||||
−0.0958497 | + | 0.995396i | \(0.530557\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.41946e27 | + | 4.19063e27i | 0.972736 | + | 1.68483i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.80007e27 | + | 1.54553e27i | −1.42083 | + | 0.577865i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.73194e27 | − | 4.73187e27i | −0.967663 | − | 1.67604i | ||||
\(557\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.12992e25 | 0.0172184 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.70111e26 | + | 3.40191e27i | −0.136889 | + | 0.990586i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.68287e25 | − | 1.33071e26i | −0.0208527 | − | 0.0361180i | 0.855411 | − | 0.517950i | \(-0.173305\pi\) |
−0.876263 | + | 0.481832i | \(0.839971\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.00999e27 | + | 3.48141e27i | −0.500000 | + | 0.866025i | ||||
\(577\) | 3.33936e27 | + | 5.78394e27i | 0.816404 | + | 1.41405i | 0.908315 | + | 0.418286i | \(0.137369\pi\) |
−0.0919114 | + | 0.995767i | \(0.529298\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.91043e27 | − | 6.77306e27i | 0.923504 | − | 1.59956i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(588\) | −4.75537e27 | − | 1.33988e27i | −0.962523 | − | 0.271202i | ||||
\(589\) | 1.01464e28 | 2.01911 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.96427e26 | + | 6.86632e26i | 0.0749801 | + | 0.129869i | ||||
\(593\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.47275e27 | − | 7.74702e27i | 0.777734 | − | 1.34707i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.35173e27 | 1.52106 | 0.760531 | − | 0.649301i | \(-0.224939\pi\) | ||||
0.760531 | + | 0.649301i | \(0.224939\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.16831e27 | −1.12783 | ||||||||
\(604\) | 6.40908e27 | − | 1.11009e28i | 0.991806 | − | 1.71786i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.50384e27 | − | 6.06883e27i | 0.516009 | − | 0.893754i | −0.483818 | − | 0.875169i | \(-0.660750\pi\) |
0.999827 | − | 0.0185856i | \(-0.00591632\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.50699e27 | + | 7.80633e27i | 0.601564 | + | 1.04194i | 0.992584 | + | 0.121557i | \(0.0387887\pi\) |
−0.391021 | + | 0.920382i | \(0.627878\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.73768e27 | + | 1.34021e28i | 0.936923 | + | 1.62280i | 0.771168 | + | 0.636632i | \(0.219673\pi\) |
0.165756 | + | 0.986167i | \(0.446994\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.47825e27 | 0.276885 | ||||||||
\(625\) | −4.54747e27 | + | 7.87646e27i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.22957e27 | + | 1.25220e28i | −0.757732 | + | 1.31243i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.59436e28 | −1.59328 | −0.796642 | − | 0.604452i | \(-0.793392\pi\) | ||||
−0.796642 | + | 0.604452i | \(0.793392\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.40982e27 | − | 1.11021e28i | −0.620595 | − | 1.07490i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.50452e26 | + | 2.95184e27i | 0.0682227 | + | 0.268348i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.25078e28 | −1.86304 | −0.931522 | − | 0.363685i | \(-0.881518\pi\) | ||||
−0.931522 | + | 0.363685i | \(0.881518\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.30579e28 | − | 5.31080e27i | 0.955133 | − | 0.388463i | ||||
\(652\) | 2.76526e28 | 1.99187 | ||||||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.66066e28 | −1.10822 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.58023e28 | − | 2.73703e28i | −0.992440 | − | 1.71896i | −0.602506 | − | 0.798114i | \(-0.705831\pi\) |
−0.389934 | − | 0.920843i | \(-0.627502\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.21895e28 | − | 2.11129e28i | −0.678776 | − | 1.17567i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.75672e28 | −1.97087 | −0.985435 | − | 0.170055i | \(-0.945606\pi\) | ||||
−0.985435 | + | 0.170055i | \(0.945606\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.81765e27 | − | 1.70047e28i | −0.500000 | − | 0.866025i | ||||
\(676\) | 9.20018e27 | + | 1.59352e28i | 0.461667 | + | 0.799631i | ||||
\(677\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.27136e28 | + | 2.54374e28i | 1.57047 | + | 1.22117i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(684\) | −2.19476e28 | + | 3.80143e28i | −0.979097 | + | 1.69585i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.07855e27 | −0.0887552 | ||||||||
\(688\) | −7.38836e26 | + | 1.27970e27i | −0.0310931 | + | 0.0538548i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.05088e28 | + | 1.82018e28i | −0.423421 | + | 0.733387i | −0.996272 | − | 0.0862731i | \(-0.972504\pi\) |
0.572850 | + | 0.819660i | \(0.305838\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.61662e28 | − | 1.06421e28i | 0.926318 | − | 0.376743i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.32867e27 | + | 7.49748e27i | 0.146826 | + | 0.254309i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.97659e28 | − | 3.42356e28i | 0.615821 | − | 1.06663i | −0.374418 | − | 0.927260i | \(-0.622158\pi\) |
0.990240 | − | 0.139374i | \(-0.0445090\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.53190e28 | + | 4.38538e28i | 0.766921 | + | 1.32835i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.10400e28 | − | 2.07585e28i | 1.34449 | − | 0.546819i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.89355e28 | − | 6.74382e28i | 0.997614 | − | 1.72792i | ||||
\(724\) | −2.07249e28 | − | 3.58966e28i | −0.523730 | − | 0.907126i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.68811e28 | −1.37919 | −0.689595 | − | 0.724196i | \(-0.742211\pi\) | ||||
−0.689595 | + | 0.724196i | \(0.742211\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.23912e28 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 4.29641e28 | + | 7.44160e28i | 0.972736 | + | 1.68483i | ||||
\(733\) | 3.81996e28 | − | 6.61636e28i | 0.853137 | − | 1.47768i | −0.0252259 | − | 0.999682i | \(-0.508031\pi\) |
0.878363 | − | 0.477995i | \(-0.158636\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.03430e28 | + | 1.79145e28i | 0.212912 | + | 0.368775i | 0.952625 | − | 0.304148i | \(-0.0983719\pi\) |
−0.739713 | + | 0.672923i | \(0.765039\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.70606e28 | 0.542194 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.09672e28 | − | 3.63162e28i | 0.367401 | − | 0.636357i | −0.621758 | − | 0.783210i | \(-0.713581\pi\) |
0.989158 | + | 0.146853i | \(0.0469144\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.34811e27 | + | 6.04102e28i | −0.136889 | + | 0.990586i | ||||
\(757\) | −1.12972e29 | −1.82816 | −0.914078 | − | 0.405540i | \(-0.867084\pi\) | ||||
−0.914078 | + | 0.405540i | \(0.867084\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.80260e28 | + | 1.30443e29i | −0.269559 | + | 1.95064i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −3.56929e28 | + | 6.18220e28i | −0.500000 | + | 0.866025i | ||||
\(769\) | −1.37032e29 | −1.89478 | −0.947388 | − | 0.320088i | \(-0.896287\pi\) | ||||
−0.947388 | + | 0.320088i | \(0.896287\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.94403e28 | − | 1.20274e29i | 0.923504 | − | 1.59956i | ||||
\(773\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.02987e28 | + | 6.97994e28i | −0.515554 | + | 0.892966i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.49508e27 | + | 7.38318e27i | 0.118383 | + | 0.0920520i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.44445e28 | − | 2.37932e28i | −0.962523 | − | 0.271202i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.99832e28 | − | 5.19324e28i | −0.328950 | − | 0.569758i | 0.653354 | − | 0.757053i | \(-0.273361\pi\) |
−0.982304 | + | 0.187294i | \(0.940028\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.64866e28 | − | 4.58761e28i | 0.269336 | − | 0.466503i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.94258e28 | − | 1.37570e29i | 0.777734 | − | 1.34707i | ||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.27293e29 | −1.12783 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.12623e29 | −1.72743 | −0.863717 | − | 0.503977i | \(-0.831870\pi\) | ||||
−0.863717 | + | 0.503977i | \(0.831870\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.11570e28 | 0.167706 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.06752e27 | + | 1.39734e28i | −0.0608863 | + | 0.105458i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.48256e28 | − | 1.41639e28i | 0.256483 | − | 0.104315i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.09228e29 | + | 1.89189e29i | 0.766189 | + | 1.32708i | 0.939616 | + | 0.342232i | \(0.111183\pi\) |
−0.173426 | + | 0.984847i | \(0.555484\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.16819e29 | + | 2.02336e29i | 0.762023 | + | 1.31986i | 0.941806 | + | 0.336157i | \(0.109127\pi\) |
−0.179783 | + | 0.983706i | \(0.557539\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.08111e28 | + | 1.05328e29i | −0.387233 | + | 0.670707i | ||||
\(832\) | 4.40081e28 | 0.276885 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.70019e28 | − | 1.50692e29i | −0.515554 | − | 0.892966i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.76995e29 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.13824e29 | − | 1.97149e29i | −0.620595 | − | 1.07490i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.76033e29 | − | 7.15945e28i | 0.926318 | − | 0.376743i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.67966e28 | − | 1.67657e29i | 0.497488 | − | 0.861675i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.91602e29 | 1.92024 | 0.960118 | − | 0.279597i | \(-0.0902007\pi\) | ||||
0.960118 | + | 0.279597i | \(0.0902007\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.09983e29 | + | 3.63701e29i | −0.959959 | + | 1.66270i | −0.237369 | + | 0.971420i | \(0.576285\pi\) |
−0.722589 | + | 0.691277i | \(0.757048\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.39989e29 | 1.00000 | ||||||||
\(868\) | 2.31879e29 | − | 9.43077e28i | 0.955133 | − | 0.388463i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.92369e28 | + | 6.79602e28i | 0.156139 | + | 0.270442i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.55759e29 | − | 4.42987e29i | 0.994690 | − | 1.72285i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.94895e29 | −1.10822 | ||||||||
\(877\) | −2.53965e29 | + | 4.39880e29i | −0.943579 | + | 1.63433i | −0.185006 | + | 0.982737i | \(0.559231\pi\) |
−0.758572 | + | 0.651589i | \(0.774103\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.73662e29 | 1.64385 | 0.821923 | − | 0.569598i | \(-0.192901\pi\) | ||||
0.821923 | + | 0.569598i | \(0.192901\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.73334e29 | − | 1.34781e29i | −0.562169 | − | 0.437131i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.16459e29 | − | 3.74917e29i | −0.678776 | − | 1.17567i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −1.74339e29 | − | 3.01964e29i | −0.500000 | − | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.06861e27 | + | 2.22057e28i | −0.00851263 | + | 0.0616008i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.30665e29 | + | 3.99524e29i | 0.612222 | + | 1.06040i | 0.990865 | + | 0.134857i | \(0.0430576\pi\) |
−0.378643 | + | 0.925543i | \(0.623609\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | −3.89739e29 | + | 6.75048e29i | −0.979097 | + | 1.69585i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.69104e28 | −0.0887552 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.06521e29 | + | 7.04115e29i | −0.946080 | + | 1.63866i | −0.192505 | + | 0.981296i | \(0.561661\pi\) |
−0.753575 | + | 0.657362i | \(0.771672\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.41338e29 | − | 4.18010e29i | −0.549579 | − | 0.951898i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.87691e28 | −0.149960 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.40068e29 | − | 5.89014e29i | −0.725718 | − | 1.25698i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.22069e29 | − | 2.59803e29i | −1.88481 | − | 0.531065i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.63063e29 | 1.84612 | 0.923058 | − | 0.384662i | \(-0.125682\pi\) | ||||
0.923058 | + | 0.384662i | \(0.125682\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.04585e30 | −1.96252 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(948\) | 4.49608e29 | + | 7.78744e29i | 0.766921 | + | 1.32835i | ||||
\(949\) | 9.08987e28 | + | 1.57441e29i | 0.153425 | + | 0.265740i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.12230e28 | + | 3.67594e28i | −0.0315917 | + | 0.0547185i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.91406e29 | − | 1.19755e30i | 0.997614 | − | 1.72792i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.01403e30 | −1.41836 | −0.709178 | − | 0.705030i | \(-0.750934\pi\) | ||||
−0.709178 | + | 0.705030i | \(0.750934\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(972\) | 7.52771e29 | 1.00000 | ||||||||
\(973\) | −1.16197e30 | − | 9.03524e29i | −1.52780 | − | 1.18799i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.07477e29 | + | 1.86156e29i | −0.138442 | + | 0.239789i | ||||
\(976\) | 7.62945e29 | + | 1.32146e30i | 0.972736 | + | 1.68483i | ||||
\(977\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.62545e30 | 1.96917 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.80534e29 | 0.542194 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.26523e29 | − | 1.08517e30i | −0.685804 | − | 1.18785i | −0.973183 | − | 0.230031i | \(-0.926117\pi\) |
0.287379 | − | 0.957817i | \(-0.407216\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.58966e30 | 1.70534 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.52214e29 | − | 7.83258e29i | −0.466007 | − | 0.807148i | 0.533239 | − | 0.845964i | \(-0.320975\pi\) |
−0.999246 | + | 0.0388167i | \(0.987641\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.42337e28 | − | 1.28576e29i | 0.0749801 | − | 0.129869i |
(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 | 21.21.h.a.2.1 | ✓ | 2 | |
3.2 | odd | 2 | CM | 21.21.h.a.2.1 | ✓ | 2 | |
7.4 | even | 3 | inner | 21.21.h.a.11.1 | yes | 2 | |
21.11 | odd | 6 | inner | 21.21.h.a.11.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.21.h.a.2.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
21.21.h.a.2.1 | ✓ | 2 | 3.2 | odd | 2 | CM | |
21.21.h.a.11.1 | yes | 2 | 7.4 | even | 3 | inner | |
21.21.h.a.11.1 | yes | 2 | 21.11 | odd | 6 | inner |