Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5376,2,Mod(2689,5376)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5376, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5376.2689");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5376 = 2^{8} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5376.c (of order \(2\), degree \(1\), not 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: | \(42.9275761266\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 672) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2689.3 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5376.2689 |
Dual form | 5376.2.c.bh.2689.2 |
$q$-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 \(\left(\mathbb{Z}/5376\mathbb{Z}\right)^\times\).
\(n\) | \(1793\) | \(2815\) | \(4609\) | \(5125\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 3.46410i | − 1.54919i | −0.632456 | − | 0.774597i | \(-0.717953\pi\) | ||||
0.632456 | − | 0.774597i | \(-0.282047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 5.46410i | − 1.64749i | −0.566961 | − | 0.823744i | \(-0.691881\pi\) | ||||
0.566961 | − | 0.823744i | \(-0.308119\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.00000i | − 0.554700i | −0.960769 | − | 0.277350i | \(-0.910544\pi\) | ||||
0.960769 | − | 0.277350i | \(-0.0894562\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.46410 | 0.894427 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.46410 | 1.81031 | 0.905155 | − | 0.425081i | \(-0.139754\pi\) | ||||
0.905155 | + | 0.425081i | \(0.139754\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 6.92820i | − 1.58944i | −0.606977 | − | 0.794719i | \(-0.707618\pi\) | ||||
0.606977 | − | 0.794719i | \(-0.292382\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 1.00000i | − 0.218218i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.46410 | 1.13934 | 0.569672 | − | 0.821872i | \(-0.307070\pi\) | ||||
0.569672 | + | 0.821872i | \(0.307070\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.00000 | −1.40000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 8.92820i | − 1.65793i | −0.559304 | − | 0.828963i | \(-0.688931\pi\) | ||||
0.559304 | − | 0.828963i | \(-0.311069\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.92820 | −0.525921 | −0.262960 | − | 0.964807i | \(-0.584699\pi\) | ||||
−0.262960 | + | 0.964807i | \(0.584699\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.46410 | 0.951178 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.46410i | 0.585540i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.00000i | − 0.328798i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) | ||||
0.986394 | − | 0.164399i | \(-0.0525685\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.53590 | −0.708388 | −0.354194 | − | 0.935172i | \(-0.615245\pi\) | ||||
−0.354194 | + | 0.935172i | \(0.615245\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000i | 1.21999i | 0.792406 | + | 0.609994i | \(0.208828\pi\) | ||||
−0.792406 | + | 0.609994i | \(0.791172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.46410i | 0.516398i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.92820 | 0.427122 | 0.213561 | − | 0.976930i | \(-0.431494\pi\) | ||||
0.213561 | + | 0.976930i | \(0.431494\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.46410i | 1.04518i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 2.00000i | − 0.274721i | −0.990521 | − | 0.137361i | \(-0.956138\pi\) | ||||
0.990521 | − | 0.137361i | \(-0.0438619\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.9282 | −2.55228 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.92820 | 0.917663 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.9282i | 1.94349i | 0.236040 | + | 0.971743i | \(0.424150\pi\) | ||||
−0.236040 | + | 0.971743i | \(0.575850\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 4.92820i | − 0.630992i | −0.948927 | − | 0.315496i | \(-0.897829\pi\) | ||||
0.948927 | − | 0.315496i | \(-0.102171\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.92820 | −0.859338 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.9282i | 1.33509i | 0.744568 | + | 0.667546i | \(0.232655\pi\) | ||||
−0.744568 | + | 0.667546i | \(0.767345\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.46410i | 0.657801i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.53590 | 0.300956 | 0.150478 | − | 0.988613i | \(-0.451919\pi\) | ||||
0.150478 | + | 0.988613i | \(0.451919\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.928203 | 0.108638 | 0.0543190 | − | 0.998524i | \(-0.482701\pi\) | ||||
0.0543190 | + | 0.998524i | \(0.482701\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 7.00000i | − 0.808290i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.46410i | 0.622692i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.92820 | −0.329449 | −0.164724 | − | 0.986340i | \(-0.552673\pi\) | ||||
−0.164724 | + | 0.986340i | \(0.552673\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 4.00000i | − 0.439057i | −0.975606 | − | 0.219529i | \(-0.929548\pi\) | ||||
0.975606 | − | 0.219529i | \(-0.0704519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 25.8564i | − 2.80452i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.92820 | 0.957204 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.46410 | 0.367194 | 0.183597 | − | 0.983002i | \(-0.441226\pi\) | ||||
0.183597 | + | 0.983002i | \(0.441226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000i | 0.209657i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 2.92820i | − 0.303641i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −24.0000 | −2.46235 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.92820 | 0.500383 | 0.250192 | − | 0.968196i | \(-0.419506\pi\) | ||||
0.250192 | + | 0.968196i | \(0.419506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.46410i | 0.549163i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 8.53590i | − 0.849354i | −0.905345 | − | 0.424677i | \(-0.860388\pi\) | ||||
0.905345 | − | 0.424677i | \(-0.139612\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.92820 | 0.288524 | 0.144262 | − | 0.989539i | \(-0.453919\pi\) | ||||
0.144262 | + | 0.989539i | \(0.453919\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.46410 | −0.338062 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.39230i | 0.811315i | 0.914025 | + | 0.405657i | \(0.132957\pi\) | ||||
−0.914025 | + | 0.405657i | \(0.867043\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000i | 0.191565i | 0.995402 | + | 0.0957826i | \(0.0305354\pi\) | ||||
−0.995402 | + | 0.0957826i | \(0.969465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.85641 | 0.739069 | 0.369534 | − | 0.929217i | \(-0.379517\pi\) | ||||
0.369534 | + | 0.929217i | \(0.379517\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 18.9282i | − 1.76506i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000i | 0.184900i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.46410 | −0.684233 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −18.8564 | −1.71422 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 4.53590i | − 0.408988i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92820i | 0.619677i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.9282 | 0.969721 | 0.484861 | − | 0.874591i | \(-0.338870\pi\) | ||||
0.484861 | + | 0.874591i | \(0.338870\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.00000 | −0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000i | 1.04844i | 0.851581 | + | 0.524222i | \(0.175644\pi\) | ||||
−0.851581 | + | 0.524222i | \(0.824356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.92820i | 0.600751i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.46410 | −0.298142 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.92820 | −0.421045 | −0.210522 | − | 0.977589i | \(-0.567516\pi\) | ||||
−0.210522 | + | 0.977589i | \(0.567516\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 9.85641i | − 0.836009i | −0.908445 | − | 0.418005i | \(-0.862730\pi\) | ||||
0.908445 | − | 0.418005i | \(-0.137270\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.92820i | 0.246599i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.9282 | −0.913862 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −30.9282 | −2.56845 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 18.0000i | − 1.47462i | −0.675556 | − | 0.737309i | \(-0.736096\pi\) | ||||
0.675556 | − | 0.737309i | \(-0.263904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.85641 | −0.476588 | −0.238294 | − | 0.971193i | \(-0.576588\pi\) | ||||
−0.238294 | + | 0.971193i | \(0.576588\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.46410 | −0.603437 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.1436i | 0.814753i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 12.9282i | − 1.03178i | −0.856654 | − | 0.515891i | \(-0.827461\pi\) | ||||
0.856654 | − | 0.515891i | \(-0.172539\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.00000 | 0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.46410 | −0.430632 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2.92820i | − 0.229355i | −0.993403 | − | 0.114677i | \(-0.963417\pi\) | ||||
0.993403 | − | 0.114677i | \(-0.0365834\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 18.9282i | − 1.47356i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.92820 | 0.226591 | 0.113296 | − | 0.993561i | \(-0.463859\pi\) | ||||
0.113296 | + | 0.993561i | \(0.463859\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.92820i | 0.529813i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.60770i | − 0.122231i | −0.998131 | − | 0.0611154i | \(-0.980534\pi\) | ||||
0.998131 | − | 0.0611154i | \(-0.0194658\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.00000 | 0.529150 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.9282 | −1.12207 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.53590i | 0.189542i | 0.995499 | + | 0.0947710i | \(0.0302119\pi\) | ||||
−0.995499 | + | 0.0947710i | \(0.969788\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 6.00000i | − 0.445976i | −0.974821 | − | 0.222988i | \(-0.928419\pi\) | ||||
0.974821 | − | 0.222988i | \(-0.0715812\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.92820 | 0.364303 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.92820 | −0.509372 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 40.7846i | − 2.98247i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000i | 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.53590 | −0.183491 | −0.0917456 | − | 0.995782i | \(-0.529245\pi\) | ||||
−0.0917456 | + | 0.995782i | \(0.529245\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.8564 | −0.853443 | −0.426721 | − | 0.904383i | \(-0.640332\pi\) | ||||
−0.426721 | + | 0.904383i | \(0.640332\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 6.92820i | − 0.496139i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.8564i | 1.41471i | 0.706858 | + | 0.707355i | \(0.250112\pi\) | ||||
−0.706858 | + | 0.707355i | \(0.749888\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.8564 | −1.54936 | −0.774680 | − | 0.632354i | \(-0.782089\pi\) | ||||
−0.774680 | + | 0.632354i | \(0.782089\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.9282 | −0.770816 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.92820i | 0.626637i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.7128i | 1.09743i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.46410 | −0.379781 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −37.8564 | −2.61858 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 16.0000i | − 1.10149i | −0.834675 | − | 0.550743i | \(-0.814345\pi\) | ||||
0.834675 | − | 0.550743i | \(-0.185655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.53590i | 0.173757i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 27.7128 | 1.89000 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.92820 | 0.198779 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.928203i | 0.0627222i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 14.9282i | − 1.00418i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0000 | 1.60716 | 0.803579 | − | 0.595198i | \(-0.202926\pi\) | ||||
0.803579 | + | 0.595198i | \(0.202926\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.00000 | 0.466667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 9.07180i | − 0.602116i | −0.953606 | − | 0.301058i | \(-0.902660\pi\) | ||||
0.953606 | − | 0.301058i | \(-0.0973398\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 0.143594i | − 0.00948893i | −0.999989 | − | 0.00474446i | \(-0.998490\pi\) | ||||
0.999989 | − | 0.00474446i | \(-0.00151022\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.46410 | −0.359511 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.928203 | 0.0608086 | 0.0304043 | − | 0.999538i | \(-0.490321\pi\) | ||||
0.0304043 | + | 0.999538i | \(0.490321\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 10.1436i | − 0.661695i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 2.92820i | − 0.190207i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.4641 | −1.38840 | −0.694199 | − | 0.719783i | \(-0.744241\pi\) | ||||
−0.694199 | + | 0.719783i | \(0.744241\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.9282 | −1.09044 | −0.545221 | − | 0.838293i | \(-0.683554\pi\) | ||||
−0.545221 | + | 0.838293i | \(0.683554\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3.46410i | − 0.221313i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.8564 | −0.881662 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.00000 | 0.253490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.9282i | 1.44722i | 0.690212 | + | 0.723608i | \(0.257517\pi\) | ||||
−0.690212 | + | 0.723608i | \(0.742483\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 29.8564i | − 1.87706i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 25.8564 | 1.61919 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.53590 | 0.282942 | 0.141471 | − | 0.989942i | \(-0.454817\pi\) | ||||
0.141471 | + | 0.989942i | \(0.454817\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.00000i | 0.124274i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.92820i | 0.552642i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.39230 | −0.517492 | −0.258746 | − | 0.965945i | \(-0.583309\pi\) | ||||
−0.258746 | + | 0.965945i | \(0.583309\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.92820 | −0.425596 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.46410i | 0.212000i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.46410i | 0.211210i | 0.994408 | + | 0.105605i | \(0.0336779\pi\) | ||||
−0.994408 | + | 0.105605i | \(0.966322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9282 | 0.663841 | 0.331921 | − | 0.943307i | \(-0.392303\pi\) | ||||
0.331921 | + | 0.943307i | \(0.392303\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.00000 | −0.121046 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 38.2487i | 2.30648i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.8564i | 1.67373i | 0.547410 | + | 0.836865i | \(0.315614\pi\) | ||||
−0.547410 | + | 0.836865i | \(0.684386\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.92820 | 0.175307 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.928203 | 0.0553720 | 0.0276860 | − | 0.999617i | \(-0.491186\pi\) | ||||
0.0276860 | + | 0.999617i | \(0.491186\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.07180i | 0.0637117i | 0.999492 | + | 0.0318559i | \(0.0101417\pi\) | ||||
−0.999492 | + | 0.0318559i | \(0.989858\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 24.0000i | − 1.42164i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.53590 | 0.267746 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 38.7128 | 2.27722 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.92820i | 0.288896i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.4641i | 1.37079i | 0.728173 | + | 0.685394i | \(0.240370\pi\) | ||||
−0.728173 | + | 0.685394i | \(0.759630\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 51.7128 | 3.01084 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.46410 | −0.317059 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 10.9282i | − 0.631994i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 8.00000i | − 0.461112i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.53590 | 0.490375 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.0718 | −0.977528 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.07180i | 0.517755i | 0.965910 | + | 0.258877i | \(0.0833526\pi\) | ||||
−0.965910 | + | 0.258877i | \(0.916647\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.92820i | 0.166580i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.07180 | 0.287595 | 0.143798 | − | 0.989607i | \(-0.454069\pi\) | ||||
0.143798 | + | 0.989607i | \(0.454069\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 3.46410i | − 0.195180i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 27.8564i | − 1.56457i | −0.622920 | − | 0.782286i | \(-0.714054\pi\) | ||||
0.622920 | − | 0.782286i | \(-0.285946\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −48.7846 | −2.73141 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.39230 | −0.468413 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 51.7128i | − 2.87738i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.0000i | 0.776580i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.00000 | −0.110600 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.92820 | −0.161437 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 24.0000i | − 1.31916i | −0.751635 | − | 0.659580i | \(-0.770734\pi\) | ||||
0.751635 | − | 0.659580i | \(-0.229266\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.00000i | 0.109599i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 37.8564 | 2.06832 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.8564 | −1.08165 | −0.540824 | − | 0.841136i | \(-0.681887\pi\) | ||||
−0.540824 | + | 0.841136i | \(0.681887\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.85641i | 0.426701i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0000i | 0.866449i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.9282 | 1.01906 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.3205i | 0.607717i | 0.952717 | + | 0.303858i | \(0.0982750\pi\) | ||||
−0.952717 | + | 0.303858i | \(0.901725\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.7846i | 1.64786i | 0.566690 | + | 0.823931i | \(0.308224\pi\) | ||||
−0.566690 | + | 0.823931i | \(0.691776\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.4641 | 0.823071 | 0.411536 | − | 0.911394i | \(-0.364993\pi\) | ||||
0.411536 | + | 0.911394i | \(0.364993\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 8.78461i | − 0.466239i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 7.46410i | − 0.395042i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.3205 | −1.44192 | −0.720961 | − | 0.692976i | \(-0.756299\pi\) | ||||
−0.720961 | + | 0.692976i | \(0.756299\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −29.0000 | −1.52632 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 18.8564i | − 0.989705i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 3.21539i | − 0.168301i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.00000 | −0.417597 | −0.208798 | − | 0.977959i | \(-0.566955\pi\) | ||||
−0.208798 | + | 0.977959i | \(0.566955\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.53590 | 0.236129 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.00000i | 0.103835i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.0000i | 1.55334i | 0.629907 | + | 0.776671i | \(0.283093\pi\) | ||||
−0.629907 | + | 0.776671i | \(0.716907\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.92820 | −0.357771 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.8564 | −0.919652 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.00000i | 0.410932i | 0.978664 | + | 0.205466i | \(0.0658711\pi\) | ||||
−0.978664 | + | 0.205466i | \(0.934129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.9282i | 0.559869i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.7128 | 1.00728 | 0.503639 | − | 0.863914i | \(-0.331994\pi\) | ||||
0.503639 | + | 0.863914i | \(0.331994\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.9282 | 0.964671 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 8.00000i | − 0.406663i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 26.7846i | − 1.35803i | −0.734123 | − | 0.679017i | \(-0.762406\pi\) | ||||
0.734123 | − | 0.679017i | \(-0.237594\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.7846 | 2.06257 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.0000 | −0.605320 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.1436i | 0.510380i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.7846i | 1.54504i | 0.634993 | + | 0.772518i | \(0.281003\pi\) | ||||
−0.634993 | + | 0.772518i | \(0.718997\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.92820 | −0.346844 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.92820 | −0.445853 | −0.222927 | − | 0.974835i | \(-0.571561\pi\) | ||||
−0.222927 | + | 0.974835i | \(0.571561\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.85641i | 0.291728i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 3.46410i | − 0.172133i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.9282 | −0.541691 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.92820 | 0.441471 | 0.220736 | − | 0.975334i | \(-0.429154\pi\) | ||||
0.220736 | + | 0.975334i | \(0.429154\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 4.92820i | − 0.243090i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 14.9282i | − 0.734569i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.8564 | −0.680184 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.85641 | 0.482670 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.9282i | 1.51094i | 0.655182 | + | 0.755471i | \(0.272592\pi\) | ||||
−0.655182 | + | 0.755471i | \(0.727408\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 31.8564i | − 1.55259i | −0.630372 | − | 0.776293i | \(-0.717098\pi\) | ||||
0.630372 | − | 0.776293i | \(-0.282902\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.92820 | −0.142374 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −52.2487 | −2.53443 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.92820i | 0.238492i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 10.9282i | − 0.527619i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −38.2487 | −1.84238 | −0.921188 | − | 0.389118i | \(-0.872780\pi\) | ||||
−0.921188 | + | 0.389118i | \(0.872780\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.143594 | −0.00690067 | −0.00345033 | − | 0.999994i | \(-0.501098\pi\) | ||||
−0.00345033 | + | 0.999994i | \(0.501098\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 30.9282i | − 1.48289i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 37.8564i | − 1.81092i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.8564 | −0.661330 | −0.330665 | − | 0.943748i | \(-0.607273\pi\) | ||||
−0.330665 | + | 0.943748i | \(0.607273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.60770i | 0.361453i | 0.983533 | + | 0.180726i | \(0.0578448\pi\) | ||||
−0.983533 | + | 0.180726i | \(0.942155\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 12.0000i | − 0.568855i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.0000 | 0.851371 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.8564 | −0.937082 | −0.468541 | − | 0.883442i | \(-0.655220\pi\) | ||||
−0.468541 | + | 0.883442i | \(0.655220\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.7846i | 1.16706i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 5.85641i | − 0.275158i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.92820 | 0.324799 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.7128 | 0.828570 | 0.414285 | − | 0.910147i | \(-0.364032\pi\) | ||||
0.414285 | + | 0.910147i | \(0.364032\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 7.46410i | − 0.348394i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 35.1769i | − 1.63835i | −0.573542 | − | 0.819176i | \(-0.694431\pi\) | ||||
0.573542 | − | 0.819176i | \(-0.305569\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.78461 | 0.408255 | 0.204128 | − | 0.978944i | \(-0.434564\pi\) | ||||
0.204128 | + | 0.978944i | \(0.434564\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.1436 | −0.470398 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 20.7846i | − 0.961797i | −0.876776 | − | 0.480899i | \(-0.840311\pi\) | ||||
0.876776 | − | 0.480899i | \(-0.159689\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 10.9282i | − 0.504618i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.9282 | 0.595700 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 43.7128 | 2.00992 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 48.4974i | 2.22521i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000i | 0.0915737i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.9282 | 0.864852 | 0.432426 | − | 0.901670i | \(-0.357658\pi\) | ||||
0.432426 | + | 0.901670i | \(0.357658\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | −0.182384 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 5.46410i | − 0.248625i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 17.0718i | − 0.775190i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.7128 | 1.25579 | 0.627894 | − | 0.778299i | \(-0.283917\pi\) | ||||
0.627894 | + | 0.778299i | \(0.283917\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.92820 | 0.132418 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.4641i | 0.607626i | 0.952732 | + | 0.303813i | \(0.0982599\pi\) | ||||
−0.952732 | + | 0.303813i | \(0.901740\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 66.6410i | − 3.00136i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 18.9282 | 0.850759 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.53590 | −0.113751 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.85641i | 0.262169i | 0.991371 | + | 0.131084i | \(0.0418459\pi\) | ||||
−0.991371 | + | 0.131084i | \(0.958154\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.92820i | 0.130822i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.0000 | −0.713405 | −0.356702 | − | 0.934218i | \(-0.616099\pi\) | ||||
−0.356702 | + | 0.934218i | \(0.616099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.5692 | −1.31581 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.00000i | 0.399704i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 8.24871i | − 0.365618i | −0.983148 | − | 0.182809i | \(-0.941481\pi\) | ||||
0.983148 | − | 0.182809i | \(-0.0585189\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.928203 | −0.0410613 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.92820 | −0.305888 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 10.1436i | − 0.446980i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 16.0000i | − 0.703679i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.60770 | 0.0705700 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.60770 | −0.420921 | −0.210460 | − | 0.977602i | \(-0.567496\pi\) | ||||
−0.210460 | + | 0.977602i | \(0.567496\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 28.0000i | − 1.22435i | −0.790721 | − | 0.612177i | \(-0.790294\pi\) | ||||
0.790721 | − | 0.612177i | \(-0.209706\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.00000i | 0.305505i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.8564 | −0.952080 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.85641 | 0.298105 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 14.9282i | − 0.647829i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.07180i | 0.392943i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.0718 | 1.25688 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.53590 | −0.109432 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 5.46410i | − 0.235356i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 19.8564i | − 0.853694i | −0.904324 | − | 0.426847i | \(-0.859624\pi\) | ||||
0.904324 | − | 0.426847i | \(-0.140376\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.00000 | 0.257485 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.92820 | 0.296772 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 2.92820i | − 0.125201i | −0.998039 | − | 0.0626005i | \(-0.980061\pi\) | ||||
0.998039 | − | 0.0626005i | \(-0.0199394\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.92820i | 0.210331i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −61.8564 | −2.63517 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.92820 | 0.124520 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 6.92820i | − 0.294086i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.8564i | 1.34980i | 0.737910 | + | 0.674900i | \(0.235813\pi\) | ||||
−0.737910 | + | 0.674900i | \(0.764187\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.7846 | 1.72193 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 46.9282i | 1.97779i | 0.148623 | + | 0.988894i | \(0.452516\pi\) | ||||
−0.148623 | + | 0.988894i | \(0.547484\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 27.2154i | − 1.14496i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.0718 | 0.464154 | 0.232077 | − | 0.972697i | \(-0.425448\pi\) | ||||
0.232077 | + | 0.972697i | \(0.425448\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.7846i | 1.03720i | 0.855016 | + | 0.518602i | \(0.173547\pi\) | ||||
−0.855016 | + | 0.518602i | \(0.826453\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 2.53590i | − 0.105939i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −38.2487 | −1.59508 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.85641 | −0.160544 | −0.0802722 | − | 0.996773i | \(-0.525579\pi\) | ||||
−0.0802722 | + | 0.996773i | \(0.525579\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 11.8564i | − 0.492735i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.00000i | 0.165948i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.9282 | −0.452600 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.92820 | 0.286446 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 20.7846i | − 0.857873i | −0.903335 | − | 0.428936i | \(-0.858888\pi\) | ||||
0.903335 | − | 0.428936i | \(-0.141112\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.2872i | 0.835919i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.8564 | −0.816783 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.4641 | 0.635035 | 0.317517 | − | 0.948252i | \(-0.397151\pi\) | ||||
0.317517 | + | 0.948252i | \(0.397151\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 25.8564i | 1.06001i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 21.8564i | − 0.894523i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.60770 | −0.310842 | −0.155421 | − | 0.987848i | \(-0.549673\pi\) | ||||
−0.155421 | + | 0.987848i | \(0.549673\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.5692 | 1.61406 | 0.807031 | − | 0.590509i | \(-0.201073\pi\) | ||||
0.807031 | + | 0.590509i | \(0.201073\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 10.9282i | − 0.445031i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 65.3205i | 2.65566i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.8564 | 0.562414 | 0.281207 | − | 0.959647i | \(-0.409265\pi\) | ||||
0.281207 | + | 0.959647i | \(0.409265\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.92820 | −0.361789 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 5.85641i | − 0.236925i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.143594i | 0.00579969i | 0.999996 | + | 0.00289984i | \(0.000923050\pi\) | ||||
−0.999996 | + | 0.00289984i | \(0.999077\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.7128 | −0.633602 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.7846 | 0.917274 | 0.458637 | − | 0.888624i | \(-0.348338\pi\) | ||||
0.458637 | + | 0.888624i | \(0.348338\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.00000i | 0.160774i | 0.996764 | + | 0.0803868i | \(0.0256155\pi\) | ||||
−0.996764 | + | 0.0803868i | \(0.974384\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 5.46410i | − 0.219267i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.46410 | −0.138786 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 37.8564i | − 1.51184i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 14.9282i | − 0.595226i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.0718 | 0.520380 | 0.260190 | − | 0.965557i | \(-0.416215\pi\) | ||||
0.260190 | + | 0.965557i | \(0.416215\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.0000 | 0.635943 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 37.8564i | − 1.50229i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 2.00000i | − 0.0792429i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.53590 | −0.100319 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.7846 | 1.37391 | 0.686955 | − | 0.726700i | \(-0.258947\pi\) | ||||
0.686955 | + | 0.726700i | \(0.258947\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.7846i | 1.13515i | 0.823320 | + | 0.567577i | \(0.192119\pi\) | ||||
−0.823320 | + | 0.567577i | \(0.807881\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 27.7128i | 1.09119i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.9282 | −0.744144 | −0.372072 | − | 0.928204i | \(-0.621353\pi\) | ||||
−0.372072 | + | 0.928204i | \(0.621353\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 81.5692 | 3.20187 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.92820i | 0.114765i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.07180i | 0.276741i | 0.990381 | + | 0.138370i | \(0.0441864\pi\) | ||||
−0.990381 | + | 0.138370i | \(0.955814\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 41.5692 | 1.62424 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.928203 | −0.0362127 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.4641i | 0.836123i | 0.908419 | + | 0.418061i | \(0.137290\pi\) | ||||
−0.908419 | + | 0.418061i | \(0.862710\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 14.7846i | − 0.575055i | −0.957772 | − | 0.287527i | \(-0.907167\pi\) | ||||
0.957772 | − | 0.287527i | \(-0.0928332\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 14.9282 | 0.579763 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24.0000 | 0.930680 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 48.7846i | − 1.88895i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.0000i | 0.927894i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.9282 | −1.03955 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.14359 | 0.159724 | 0.0798619 | − | 0.996806i | \(-0.474552\pi\) | ||||
0.0798619 | + | 0.996806i | \(0.474552\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.00000i | 0.269430i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 22.3923i | − 0.860606i | −0.902684 | − | 0.430303i | \(-0.858407\pi\) | ||||
0.902684 | − | 0.430303i | \(-0.141593\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.92820 | −0.189127 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.07180 | 0.347632 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 30.2487i | − 1.15743i | −0.815528 | − | 0.578717i | \(-0.803553\pi\) | ||||
0.815528 | − | 0.578717i | \(-0.196447\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.0718i | 0.652280i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.143594 | 0.00547844 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.00000 | −0.152388 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 14.1436i | − 0.538048i | −0.963134 | − | 0.269024i | \(-0.913299\pi\) | ||||
0.963134 | − | 0.269024i | \(-0.0867010\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 5.46410i | − 0.207564i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −34.1436 | −1.29514 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33.8564 | −1.28240 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.928203i | 0.0351079i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.6410i | 1.53499i | 0.641055 | + | 0.767495i | \(0.278497\pi\) | ||||
−0.641055 | + | 0.767495i | \(0.721503\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.8564 | −0.522604 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.1436 | 0.382030 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.53590i | 0.321025i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 37.7128i | − 1.41633i | −0.706045 | − | 0.708167i | \(-0.749522\pi\) | ||||
0.706045 | − | 0.708167i | \(-0.250478\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.92820 | 0.109816 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.0000 | −0.599205 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37.8564i | 1.41575i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 21.4641i | − 0.801592i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.8564 | −0.516757 | −0.258378 | − | 0.966044i | \(-0.583188\pi\) | ||||
−0.258378 | + | 0.966044i | \(0.583188\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.92820 | −0.109052 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 16.9282i | − 0.629567i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 62.4974i | 2.32110i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.9282 | 1.29542 | 0.647708 | − | 0.761889i | \(-0.275728\pi\) | ||||
0.647708 | + | 0.761889i | \(0.275728\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 59.7128i | 2.20856i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 49.7128i | 1.83618i | 0.396367 | + | 0.918092i | \(0.370271\pi\) | ||||
−0.396367 | + | 0.918092i | \(0.629729\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.46410 | 0.127775 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 59.7128 | 2.19955 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 50.9282i | − 1.87342i | −0.350101 | − | 0.936712i | \(-0.613853\pi\) | ||||
0.350101 | − | 0.936712i | \(-0.386147\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 13.8564i | − 0.509028i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.3923 | 1.18836 | 0.594179 | − | 0.804333i | \(-0.297477\pi\) | ||||
0.594179 | + | 0.804333i | \(0.297477\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −62.3538 | −2.28447 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.00000i | 0.146352i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 8.39230i | − 0.306648i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.7128 | 1.01125 | 0.505627 | − | 0.862752i | \(-0.331261\pi\) | ||||
0.505627 | + | 0.862752i | \(0.331261\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.9282 | −0.835550 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.2872i | 0.738326i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 26.0000i | − 0.944986i | −0.881334 | − | 0.472493i | \(-0.843354\pi\) | ||||
0.881334 | − | 0.472493i | \(-0.156646\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 29.8564 | 1.08372 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.5359 | −0.744426 | −0.372213 | − | 0.928147i | \(-0.621401\pi\) | ||||
−0.372213 | + | 0.928147i | \(0.621401\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 2.00000i | − 0.0724049i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 25.8564i | 0.934840i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 29.8564 | 1.07805 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.8564 | 1.14877 | 0.574386 | − | 0.818585i | \(-0.305241\pi\) | ||||
0.574386 | + | 0.818585i | \(0.305241\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.53590i | 0.163356i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.3205i | 1.05459i | 0.849684 | + | 0.527293i | \(0.176793\pi\) | ||||
−0.849684 | + | 0.527293i | \(0.823207\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.4974 | 0.736289 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.00000 | −0.0717496 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 31.4256i | 1.12594i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 13.8564i | − 0.495821i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.92820 | −0.319068 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −44.7846 | −1.59843 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 31.7128i | − 1.13044i | −0.824940 | − | 0.565220i | \(-0.808791\pi\) | ||||
0.824940 | − | 0.565220i | \(-0.191209\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 8.39230i | − 0.298774i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.85641 | −0.279342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.85641 | −0.350011 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 6.92820i | − 0.245718i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.3923i | 0.509802i | 0.966967 | + | 0.254901i | \(0.0820428\pi\) | ||||
−0.966967 | + | 0.254901i | \(0.917957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.8564 | 0.773224 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.46410 | −0.122398 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 5.07180i | − 0.178980i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.9282i | 0.667132i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.46410 | −0.121942 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.0000 | 1.33601 | 0.668004 | − | 0.744157i | \(-0.267149\pi\) | ||||
0.668004 | + | 0.744157i | \(0.267149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 45.5692i | − 1.60015i | −0.599899 | − | 0.800076i | \(-0.704793\pi\) | ||||
0.599899 | − | 0.800076i | \(-0.295207\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.9282i | 0.383269i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.1436 | −0.355315 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 55.4256 | 1.93910 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 2.00000i | − 0.0698857i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 39.8564i | − 1.39100i | −0.718527 | − | 0.695499i | \(-0.755183\pi\) | ||||
0.718527 | − | 0.695499i | \(-0.244817\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.9282 | −1.21752 | −0.608760 | − | 0.793354i | \(-0.708333\pi\) | ||||
−0.608760 | + | 0.793354i | \(0.708333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −38.2487 | −1.33165 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 25.1769i | − 0.875487i | −0.899100 | − | 0.437744i | \(-0.855778\pi\) | ||||
0.899100 | − | 0.437744i | \(-0.144222\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.7128i | 1.17089i | 0.810711 | + | 0.585447i | \(0.199081\pi\) | ||||
−0.810711 | + | 0.585447i | \(0.800919\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.8564 | −0.966328 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.46410 | 0.258616 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 10.1436i | − 0.351034i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.92820i | 0.101214i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.92820 | 0.101093 | 0.0505464 | − | 0.998722i | \(-0.483904\pi\) | ||||
0.0505464 | + | 0.998722i | \(0.483904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −50.7128 | −1.74872 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.928203i | 0.0319690i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 31.1769i | − 1.07252i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.8564 | 0.647914 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.07180 | −0.0367840 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 10.9282i | − 0.374614i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.9282i | 1.26440i | 0.774806 | + | 0.632199i | \(0.217847\pi\) | ||||
−0.774806 | + | 0.632199i | \(0.782153\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 24.0000 | 0.820783 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.17691 | 0.245159 | 0.122579 | − | 0.992459i | \(-0.460883\pi\) | ||||
0.122579 | + | 0.992459i | \(0.460883\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.0718i | 0.855439i | 0.903912 | + | 0.427719i | \(0.140683\pi\) | ||||
−0.903912 | + | 0.427719i | \(0.859317\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.53590i | 0.154583i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.53590 | 0.0863230 | 0.0431615 | − | 0.999068i | \(-0.486257\pi\) | ||||
0.0431615 | + | 0.999068i | \(0.486257\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.56922 | −0.189359 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 38.7128i | 1.31476i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.0000i | 0.542763i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.8564 | 0.740576 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.92820 | −0.166794 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 6.92820i | − 0.234216i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 35.8564i | − 1.21078i | −0.795927 | − | 0.605392i | \(-0.793016\pi\) | ||||
0.795927 | − | 0.605392i | \(-0.206984\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.4641 | −0.791425 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.3205 | 0.718306 | 0.359153 | − | 0.933279i | \(-0.383066\pi\) | ||||
0.359153 | + | 0.933279i | \(0.383066\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.5692i | 1.66814i | 0.551661 | + | 0.834069i | \(0.313994\pi\) | ||||
−0.551661 | + | 0.834069i | \(0.686006\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 51.7128i | 1.73831i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.0718 | −0.438908 | −0.219454 | − | 0.975623i | \(-0.570428\pi\) | ||||
−0.219454 | + | 0.975623i | \(0.570428\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.9282 | −0.366520 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 5.46410i | − 0.183054i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 20.2872i | − 0.678885i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.78461 | 0.293637 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.9282 | 0.364882 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.1436i | 0.871938i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 14.9282i | − 0.497331i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.00000 | 0.266223 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.7846 | −0.690904 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 11.7128i | − 0.388918i | −0.980911 | − | 0.194459i | \(-0.937705\pi\) | ||||
0.980911 | − | 0.194459i | \(-0.0622951\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.53590i | 0.283118i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.1769 | 1.09920 | 0.549600 | − | 0.835428i | \(-0.314780\pi\) | ||||
0.549600 | + | 0.835428i | \(0.314780\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.8564 | −0.723341 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 17.0718i | − 0.564376i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 12.0000i | − 0.396275i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.0000 | −1.31948 | −0.659739 | − | 0.751495i | \(-0.729333\pi\) | ||||
−0.659739 | + | 0.751495i | \(0.729333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.07180 | −0.298926 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 5.07180i | − 0.166940i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.0000i | 0.460317i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.92820 | −0.0961748 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.3923 | 1.12837 | 0.564187 | − | 0.825647i | \(-0.309190\pi\) | ||||
0.564187 | + | 0.825647i | \(0.309190\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 6.92820i | − 0.227063i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.07180i | 0.166043i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −141.282 | −4.62042 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.0000 | −0.849383 | −0.424691 | − | 0.905338i | \(-0.639617\pi\) | ||||
−0.424691 | + | 0.905338i | \(0.639617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0000i | 0.456873i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.4641i | 1.41689i | 0.705766 | + | 0.708445i | \(0.250603\pi\) | ||||
−0.705766 | + | 0.708445i | \(0.749397\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.7846 | −0.807098 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.46410 | 0.112687 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 22.2487i | − 0.722986i | −0.932375 | − | 0.361493i | \(-0.882267\pi\) | ||||
0.932375 | − | 0.361493i | \(-0.117733\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 1.85641i | − 0.0602615i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.8564 | 0.903306 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.0000 | 0.712650 | 0.356325 | − | 0.934362i | \(-0.384030\pi\) | ||||
0.356325 | + | 0.934362i | \(0.384030\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.78461i | 0.284263i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 48.7846i | − 1.57698i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.92820 | 0.159140 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.4256 | −0.723407 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 8.39230i | − 0.270438i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 41.0718i | 1.32215i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.0718 | 0.677623 | 0.338812 | − | 0.940854i | \(-0.389975\pi\) | ||||
0.338812 | + | 0.940854i | \(0.389975\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 51.7128 | 1.66125 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.8564i | 0.829772i | 0.909873 | + | 0.414886i | \(0.136178\pi\) | ||||
−0.909873 | + | 0.414886i | \(0.863822\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.85641i | 0.315982i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.0000 | −0.448359 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −58.4974 | −1.87150 | −0.935749 | − | 0.352666i | \(-0.885275\pi\) | ||||
−0.935749 | + | 0.352666i | \(0.885275\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 18.9282i | − 0.604948i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 2.00000i | − 0.0638551i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51.7128 | 1.64938 | 0.824691 | − | 0.565583i | \(-0.191349\pi\) | ||||
0.824691 | + | 0.565583i | \(0.191349\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 68.7846 | 2.19166 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 2.92820i | − 0.0932057i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 43.7128i | 1.38999i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.0000 | 1.27064 | 0.635321 | − | 0.772248i | \(-0.280868\pi\) | ||||
0.635321 | + | 0.772248i | \(0.280868\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.0000 | 0.761617 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 75.7128i | 2.40026i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.9282i | 1.42289i | 0.702742 | + | 0.711445i | \(0.251959\pi\) | ||||
−0.702742 | + | 0.711445i | \(0.748041\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.00000 | −0.0632772 |
(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 | 5376.2.c.bh.2689.3 | 4 | ||
4.3 | odd | 2 | 5376.2.c.bn.2689.1 | 4 | |||
8.3 | odd | 2 | 5376.2.c.bn.2689.4 | 4 | |||
8.5 | even | 2 | inner | 5376.2.c.bh.2689.2 | 4 | ||
16.3 | odd | 4 | 672.2.a.j.1.1 | yes | 2 | ||
16.5 | even | 4 | 1344.2.a.v.1.2 | 2 | |||
16.11 | odd | 4 | 1344.2.a.u.1.2 | 2 | |||
16.13 | even | 4 | 672.2.a.i.1.1 | ✓ | 2 | ||
48.5 | odd | 4 | 4032.2.a.bs.1.1 | 2 | |||
48.11 | even | 4 | 4032.2.a.br.1.1 | 2 | |||
48.29 | odd | 4 | 2016.2.a.t.1.2 | 2 | |||
48.35 | even | 4 | 2016.2.a.s.1.2 | 2 | |||
112.13 | odd | 4 | 4704.2.a.bn.1.2 | 2 | |||
112.27 | even | 4 | 9408.2.a.dx.1.1 | 2 | |||
112.69 | odd | 4 | 9408.2.a.do.1.1 | 2 | |||
112.83 | even | 4 | 4704.2.a.bm.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.a.i.1.1 | ✓ | 2 | 16.13 | even | 4 | ||
672.2.a.j.1.1 | yes | 2 | 16.3 | odd | 4 | ||
1344.2.a.u.1.2 | 2 | 16.11 | odd | 4 | |||
1344.2.a.v.1.2 | 2 | 16.5 | even | 4 | |||
2016.2.a.s.1.2 | 2 | 48.35 | even | 4 | |||
2016.2.a.t.1.2 | 2 | 48.29 | odd | 4 | |||
4032.2.a.br.1.1 | 2 | 48.11 | even | 4 | |||
4032.2.a.bs.1.1 | 2 | 48.5 | odd | 4 | |||
4704.2.a.bm.1.2 | 2 | 112.83 | even | 4 | |||
4704.2.a.bn.1.2 | 2 | 112.13 | odd | 4 | |||
5376.2.c.bh.2689.2 | 4 | 8.5 | even | 2 | inner | ||
5376.2.c.bh.2689.3 | 4 | 1.1 | even | 1 | trivial | ||
5376.2.c.bn.2689.1 | 4 | 4.3 | odd | 2 | |||
5376.2.c.bn.2689.4 | 4 | 8.3 | odd | 2 | |||
9408.2.a.do.1.1 | 2 | 112.69 | odd | 4 | |||
9408.2.a.dx.1.1 | 2 | 112.27 | even | 4 |