Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [416,2,Mod(209,416)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(416, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("416.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 416 = 2^{5} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 416.b (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: | \(3.32177672409\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 104) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 416.209 |
Dual form | 416.2.b.b.209.3 |
$q$-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 \(\left(\mathbb{Z}/416\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(287\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 2.00000i | − 1.15470i | −0.816497 | − | 0.577350i | \(-0.804087\pi\) | ||||
0.816497 | − | 0.577350i | \(-0.195913\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.46410i | 1.54919i | 0.632456 | + | 0.774597i | \(0.282047\pi\) | ||||
−0.632456 | + | 0.774597i | \(0.717953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.26795 | 0.479240 | 0.239620 | − | 0.970867i | \(-0.422977\pi\) | ||||
0.239620 | + | 0.970867i | \(0.422977\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.73205i | 1.42677i | 0.700774 | + | 0.713384i | \(0.252838\pi\) | ||||
−0.700774 | + | 0.713384i | \(0.747162\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.92820 | 1.78885 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.46410 | 1.32524 | 0.662620 | − | 0.748956i | \(-0.269445\pi\) | ||||
0.662620 | + | 0.748956i | \(0.269445\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 0.732051i | − 0.167944i | −0.996468 | − | 0.0839720i | \(-0.973239\pi\) | ||||
0.996468 | − | 0.0839720i | \(-0.0267606\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 2.53590i | − 0.553378i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.00000 | −1.40000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 4.00000i | − 0.769800i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000i | 0.371391i | 0.982607 | + | 0.185695i | \(0.0594537\pi\) | ||||
−0.982607 | + | 0.185695i | \(0.940546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.73205 | 1.20911 | 0.604556 | − | 0.796563i | \(-0.293351\pi\) | ||||
0.604556 | + | 0.796563i | \(0.293351\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.46410 | 1.64749 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.39230i | 0.742435i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 8.92820i | − 1.46779i | −0.679264 | − | 0.733894i | \(-0.737701\pi\) | ||||
0.679264 | − | 0.733894i | \(-0.262299\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.92820 | 1.39435 | 0.697176 | − | 0.716900i | \(-0.254440\pi\) | ||||
0.697176 | + | 0.716900i | \(0.254440\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.535898i | 0.0817237i | 0.999165 | + | 0.0408619i | \(0.0130104\pi\) | ||||
−0.999165 | + | 0.0408619i | \(0.986990\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 3.46410i | − 0.516398i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.73205 | −0.981971 | −0.490985 | − | 0.871168i | \(-0.663363\pi\) | ||||
−0.490985 | + | 0.871168i | \(0.663363\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.39230 | −0.770329 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 10.9282i | − 1.53025i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 2.92820i | − 0.402220i | −0.979569 | − | 0.201110i | \(-0.935545\pi\) | ||||
0.979569 | − | 0.201110i | \(-0.0644548\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.3923 | −2.21034 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.46410 | −0.193925 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.1962i | 1.32743i | 0.747987 | + | 0.663713i | \(0.231020\pi\) | ||||
−0.747987 | + | 0.663713i | \(0.768980\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.92820i | 0.374918i | 0.982272 | + | 0.187459i | \(0.0600252\pi\) | ||||
−0.982272 | + | 0.187459i | \(0.939975\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.26795 | −0.159747 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.46410 | −0.429669 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 0.732051i | − 0.0894342i | −0.999000 | − | 0.0447171i | \(-0.985761\pi\) | ||||
0.999000 | − | 0.0447171i | \(-0.0142386\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.00000i | 0.963087i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.19615 | 0.972704 | 0.486352 | − | 0.873763i | \(-0.338327\pi\) | ||||
0.486352 | + | 0.873763i | \(0.338327\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.46410 | −0.873607 | −0.436804 | − | 0.899557i | \(-0.643889\pi\) | ||||
−0.436804 | + | 0.899557i | \(0.643889\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14.0000i | 1.61658i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.00000i | 0.683763i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.46410 | −0.614759 | −0.307380 | − | 0.951587i | \(-0.599452\pi\) | ||||
−0.307380 | + | 0.951587i | \(0.599452\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 3.26795i | − 0.358704i | −0.983785 | − | 0.179352i | \(-0.942600\pi\) | ||||
0.983785 | − | 0.179352i | \(-0.0574001\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.9282i | 2.05305i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.00000 | 0.428845 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.3205 | −1.83597 | −0.917985 | − | 0.396615i | \(-0.870185\pi\) | ||||
−0.917985 | + | 0.396615i | \(0.870185\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.26795i | 0.132917i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 13.4641i | − 1.39616i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.53590 | 0.260178 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.39230 | 0.649040 | 0.324520 | − | 0.945879i | \(-0.394797\pi\) | ||||
0.324520 | + | 0.945879i | \(0.394797\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 4.73205i | − 0.475589i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 12.0000i | − 1.19404i | −0.802225 | − | 0.597022i | \(-0.796350\pi\) | ||||
0.802225 | − | 0.597022i | \(-0.203650\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.92820 | −0.682656 | −0.341328 | − | 0.939944i | \(-0.610877\pi\) | ||||
−0.341328 | + | 0.939944i | \(0.610877\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.78461 | 0.857290 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 4.92820i | − 0.476427i | −0.971213 | − | 0.238214i | \(-0.923438\pi\) | ||||
0.971213 | − | 0.238214i | \(-0.0765619\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 2.00000i | − 0.191565i | −0.995402 | − | 0.0957826i | \(-0.969465\pi\) | ||||
0.995402 | − | 0.0957826i | \(-0.0305354\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.8564 | −1.69486 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.53590 | 0.238557 | 0.119279 | − | 0.992861i | \(-0.461942\pi\) | ||||
0.119279 | + | 0.992861i | \(0.461942\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 13.8564i | − 1.29212i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 1.00000i | − 0.0924500i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.92820 | 0.635107 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.3923 | −1.03566 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 17.8564i | − 1.61006i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 6.92820i | − 0.619677i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000 | 0.354943 | 0.177471 | − | 0.984126i | \(-0.443208\pi\) | ||||
0.177471 | + | 0.984126i | \(0.443208\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.07180 | 0.0943664 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 19.8564i | − 1.73486i | −0.497557 | − | 0.867431i | \(-0.665770\pi\) | ||||
0.497557 | − | 0.867431i | \(-0.334230\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 0.928203i | − 0.0804854i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.8564 | 1.19257 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.9282 | 1.10453 | 0.552265 | − | 0.833668i | \(-0.313763\pi\) | ||||
0.552265 | + | 0.833668i | \(0.313763\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000i | 0.848189i | 0.905618 | + | 0.424094i | \(0.139408\pi\) | ||||
−0.905618 | + | 0.424094i | \(0.860592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.4641i | 1.13388i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.73205 | −0.395714 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.92820 | −0.575356 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.7846i | 0.889500i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 12.9282i | − 1.05912i | −0.848273 | − | 0.529560i | \(-0.822357\pi\) | ||||
0.848273 | − | 0.529560i | \(-0.177643\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.12436 | 0.579772 | 0.289886 | − | 0.957061i | \(-0.406383\pi\) | ||||
0.289886 | + | 0.957061i | \(0.406383\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.46410 | −0.441746 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.3205i | 1.87315i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 16.9282i | − 1.35102i | −0.737352 | − | 0.675509i | \(-0.763924\pi\) | ||||
0.737352 | − | 0.675509i | \(-0.236076\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.85641 | −0.464443 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.07180 | −0.399714 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 16.7321i | − 1.31056i | −0.755388 | − | 0.655278i | \(-0.772552\pi\) | ||||
0.755388 | − | 0.655278i | \(-0.227448\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 32.7846i | 2.55228i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.66025 | 0.438004 | 0.219002 | − | 0.975724i | \(-0.429720\pi\) | ||||
0.219002 | + | 0.975724i | \(0.429720\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.732051i | 0.0559813i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.92820i | 0.526742i | 0.964695 | + | 0.263371i | \(0.0848343\pi\) | ||||
−0.964695 | + | 0.263371i | \(0.915166\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.87564 | −0.670936 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 20.3923 | 1.53278 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.3923i | 0.776757i | 0.921500 | + | 0.388379i | \(0.126965\pi\) | ||||
−0.921500 | + | 0.388379i | \(0.873035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 8.92820i | − 0.663628i | −0.943345 | − | 0.331814i | \(-0.892339\pi\) | ||||
0.943345 | − | 0.331814i | \(-0.107661\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.85641 | 0.432918 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 30.9282 | 2.27389 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 25.8564i | 1.89081i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 5.07180i | − 0.368919i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.5359 | 1.05178 | 0.525890 | − | 0.850552i | \(-0.323732\pi\) | ||||
0.525890 | + | 0.850552i | \(0.323732\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.60770 | −0.115724 | −0.0578622 | − | 0.998325i | \(-0.518428\pi\) | ||||
−0.0578622 | + | 0.998325i | \(0.518428\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.92820i | 0.496139i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 3.07180i | − 0.218856i | −0.993995 | − | 0.109428i | \(-0.965098\pi\) | ||||
0.993995 | − | 0.109428i | \(-0.0349020\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.7846 | −1.18983 | −0.594915 | − | 0.803789i | \(-0.702814\pi\) | ||||
−0.594915 | + | 0.803789i | \(0.702814\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.46410 | −0.103270 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.53590i | 0.177985i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 30.9282i | 2.16012i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.46410 | 0.239617 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.85641i | 0.540857i | 0.962740 | + | 0.270429i | \(0.0871654\pi\) | ||||
−0.962740 | + | 0.270429i | \(0.912835\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 16.3923i | − 1.12318i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.85641 | −0.126606 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.53590 | 0.579455 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.9282i | 1.00875i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.46410i | 0.367555i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.196152 | 0.0131353 | 0.00656767 | − | 0.999978i | \(-0.497909\pi\) | ||||
0.00656767 | + | 0.999978i | \(0.497909\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.00000 | 0.466667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2.87564i | − 0.190863i | −0.995436 | − | 0.0954316i | \(-0.969577\pi\) | ||||
0.995436 | − | 0.0954316i | \(-0.0304231\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 5.32051i | − 0.351589i | −0.984427 | − | 0.175795i | \(-0.943751\pi\) | ||||
0.984427 | − | 0.175795i | \(-0.0562494\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.0000 | 0.789542 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.9282 | 1.10900 | 0.554502 | − | 0.832183i | \(-0.312909\pi\) | ||||
0.554502 | + | 0.832183i | \(0.312909\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 23.3205i | − 1.52126i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.9282i | 0.709863i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.7321 | −1.21168 | −0.605838 | − | 0.795588i | \(-0.707162\pi\) | ||||
−0.605838 | + | 0.795588i | \(0.707162\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −30.3923 | −1.95774 | −0.978870 | − | 0.204482i | \(-0.934449\pi\) | ||||
−0.978870 | + | 0.204482i | \(0.934449\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.0000i | 0.641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 18.6795i | − 1.19339i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.732051 | 0.0465793 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.53590 | −0.414196 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 6.39230i | − 0.403479i | −0.979439 | − | 0.201739i | \(-0.935341\pi\) | ||||
0.979439 | − | 0.201739i | \(-0.0646594\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 18.9282i | − 1.19001i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 37.8564 | 2.37066 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.8564 | −1.48812 | −0.744061 | − | 0.668112i | \(-0.767103\pi\) | ||||
−0.744061 | + | 0.668112i | \(0.767103\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 11.3205i | − 0.703422i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 2.00000i | − 0.123797i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.3205 | 1.68465 | 0.842327 | − | 0.538966i | \(-0.181185\pi\) | ||||
0.842327 | + | 0.538966i | \(0.181185\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.1436 | 0.623116 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 34.6410i | 2.12000i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 7.85641i | − 0.479014i | −0.970895 | − | 0.239507i | \(-0.923014\pi\) | ||||
0.970895 | − | 0.239507i | \(-0.0769857\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.1962 | 1.22683 | 0.613414 | − | 0.789761i | \(-0.289796\pi\) | ||||
0.613414 | + | 0.789761i | \(0.289796\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.53590 | 0.153480 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 33.1244i | − 1.99747i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.85641i | 0.111541i | 0.998444 | + | 0.0557703i | \(0.0177615\pi\) | ||||
−0.998444 | + | 0.0557703i | \(0.982239\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.73205 | −0.403037 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.32051 | 0.556015 | 0.278007 | − | 0.960579i | \(-0.410326\pi\) | ||||
0.278007 | + | 0.960579i | \(0.410326\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 19.4641i | − 1.15702i | −0.815675 | − | 0.578510i | \(-0.803634\pi\) | ||||
0.815675 | − | 0.578510i | \(-0.196366\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 5.07180i | − 0.300427i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.3205 | 0.668228 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.8564 | 0.756259 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 12.7846i | − 0.749447i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32.9282i | 1.92369i | 0.273602 | + | 0.961843i | \(0.411785\pi\) | ||||
−0.273602 | + | 0.961843i | \(0.588215\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −35.3205 | −2.05644 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.9282 | 1.09833 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 4.00000i | − 0.231326i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.679492i | 0.0391653i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −24.0000 | −1.37876 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.1436 | −0.580820 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 0.732051i | − 0.0417803i | −0.999782 | − | 0.0208902i | \(-0.993350\pi\) | ||||
0.999782 | − | 0.0208902i | \(-0.00665003\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.8564i | 0.788263i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.07180 | −0.0607760 | −0.0303880 | − | 0.999538i | \(-0.509674\pi\) | ||||
−0.0303880 | + | 0.999538i | \(0.509674\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.392305 | 0.0221744 | 0.0110872 | − | 0.999939i | \(-0.496471\pi\) | ||||
0.0110872 | + | 0.999939i | \(0.496471\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 4.39230i | − 0.247478i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.46410i | 0.194563i | 0.995257 | + | 0.0972817i | \(0.0310148\pi\) | ||||
−0.995257 | + | 0.0972817i | \(0.968985\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.46410 | −0.529888 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.85641 | −0.550131 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 4.00000i | − 0.222566i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 7.00000i | − 0.388290i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.00000 | −0.221201 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.53590 | −0.470599 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 17.5167i | − 0.962803i | −0.876500 | − | 0.481401i | \(-0.840128\pi\) | ||||
0.876500 | − | 0.481401i | \(-0.159872\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.92820i | 0.489263i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.53590 | 0.138551 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.46410 | 0.0797547 | 0.0398773 | − | 0.999205i | \(-0.487303\pi\) | ||||
0.0398773 | + | 0.999205i | \(0.487303\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 5.07180i | − 0.275462i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 31.8564i | 1.72512i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.7128 | −0.848412 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −27.7128 | −1.49201 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.07180i | 0.379634i | 0.981819 | + | 0.189817i | \(0.0607895\pi\) | ||||
−0.981819 | + | 0.189817i | \(0.939211\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.60770i | 0.514288i | 0.966373 | + | 0.257144i | \(0.0827815\pi\) | ||||
−0.966373 | + | 0.257144i | \(0.917219\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.00000 | 0.213504 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.0718 | −0.589292 | −0.294646 | − | 0.955606i | \(-0.595202\pi\) | ||||
−0.294646 | + | 0.955606i | \(0.595202\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 28.3923i | 1.50691i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 13.8564i | − 0.733359i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.5167 | −1.66339 | −0.831693 | − | 0.555236i | \(-0.812628\pi\) | ||||
−0.831693 | + | 0.555236i | \(0.812628\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.4641 | 0.971795 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.7846i | 1.19588i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 25.8564i | − 1.35339i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.2487 | 1.16137 | 0.580687 | − | 0.814127i | \(-0.302784\pi\) | ||||
0.580687 | + | 0.814127i | \(0.302784\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.92820 | −0.464784 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 3.71281i | − 0.192760i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 14.7846i | − 0.765518i | −0.923848 | − | 0.382759i | \(-0.874974\pi\) | ||||
0.923848 | − | 0.382759i | \(-0.125026\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.8564 | −0.715542 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.00000 | −0.103005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 14.5885i | − 0.749359i | −0.927154 | − | 0.374679i | \(-0.877753\pi\) | ||||
0.927154 | − | 0.374679i | \(-0.122247\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 8.00000i | − 0.409852i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.3397 | 0.528336 | 0.264168 | − | 0.964477i | \(-0.414903\pi\) | ||||
0.264168 | + | 0.964477i | \(0.414903\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.7846 | −1.05928 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 0.535898i | − 0.0272412i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.00000i | 0.101404i | 0.998714 | + | 0.0507020i | \(0.0161459\pi\) | ||||
−0.998714 | + | 0.0507020i | \(0.983854\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.8564 | −1.10533 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −39.7128 | −2.00325 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 18.9282i | − 0.952381i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 4.53590i | − 0.227650i | −0.993501 | − | 0.113825i | \(-0.963690\pi\) | ||||
0.993501 | − | 0.113825i | \(-0.0363104\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.85641 | −0.0929366 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.53590 | 0.226512 | 0.113256 | − | 0.993566i | \(-0.463872\pi\) | ||||
0.113256 | + | 0.993566i | \(0.463872\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.73205i | 0.335347i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 38.1051i | − 1.89346i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 42.2487 | 2.09419 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.9282 | 0.639259 | 0.319629 | − | 0.947543i | \(-0.396442\pi\) | ||||
0.319629 | + | 0.947543i | \(0.396442\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 25.8564i | − 1.27540i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.9282i | 0.636155i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.3205 | 0.555702 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.0000 | 0.979404 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.7846i | 1.50393i | 0.659205 | + | 0.751963i | \(0.270893\pi\) | ||||
−0.659205 | + | 0.751963i | \(0.729107\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.2487i | 1.18181i | 0.806741 | + | 0.590905i | \(0.201229\pi\) | ||||
−0.806741 | + | 0.590905i | \(0.798771\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.73205 | 0.327324 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −38.2487 | −1.85534 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.71281i | 0.179676i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.46410i | 0.456931i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −39.1244 | −1.88455 | −0.942277 | − | 0.334835i | \(-0.891320\pi\) | ||||
−0.942277 | + | 0.334835i | \(0.891320\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.78461 | −0.326048 | −0.163024 | − | 0.986622i | \(-0.552125\pi\) | ||||
−0.163024 | + | 0.986622i | \(0.552125\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.8564i | 0.664364i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.92820i | 0.140075i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.92820 | −0.139756 | −0.0698778 | − | 0.997556i | \(-0.522261\pi\) | ||||
−0.0698778 | + | 0.997556i | \(0.522261\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.39230 | 0.256776 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.0000i | 1.42534i | 0.701498 | + | 0.712672i | \(0.252515\pi\) | ||||
−0.701498 | + | 0.712672i | \(0.747485\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 60.0000i | − 2.84427i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −25.8564 | −1.22297 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.6077 | 0.830959 | 0.415479 | − | 0.909603i | \(-0.363614\pi\) | ||||
0.415479 | + | 0.909603i | \(0.363614\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 42.2487i | 1.98941i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 14.2487i | − 0.669463i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.39230 | −0.205914 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.0000 | −0.654892 | −0.327446 | − | 0.944870i | \(-0.606188\pi\) | ||||
−0.327446 | + | 0.944870i | \(0.606188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 21.8564i | − 1.02017i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.9282i | 0.974724i | 0.873200 | + | 0.487362i | \(0.162041\pi\) | ||||
−0.873200 | + | 0.487362i | \(0.837959\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.66025 | −0.0771585 | −0.0385793 | − | 0.999256i | \(-0.512283\pi\) | ||||
−0.0385793 | + | 0.999256i | \(0.512283\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 46.6410 | 2.16293 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 36.2487i | − 1.67739i | −0.544601 | − | 0.838695i | \(-0.683319\pi\) | ||||
0.544601 | − | 0.838695i | \(-0.316681\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 0.928203i | − 0.0428604i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −33.8564 | −1.56002 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.53590 | −0.116601 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.12436i | 0.235122i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.92820i | 0.134073i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.2679 | −0.971757 | −0.485879 | − | 0.874026i | \(-0.661500\pi\) | ||||
−0.485879 | + | 0.874026i | \(0.661500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.92820 | 0.407091 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.1436i | 0.461549i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.1436i | 1.00549i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 42.4449 | 1.92336 | 0.961680 | − | 0.274174i | \(-0.0884043\pi\) | ||||
0.961680 | + | 0.274174i | \(0.0884043\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −33.4641 | −1.51330 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.2487i | 1.09433i | 0.837025 | + | 0.547165i | \(0.184293\pi\) | ||||
−0.837025 | + | 0.547165i | \(0.815707\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.9282i | 0.492182i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.3923 | 0.736779 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.3923 | 0.466159 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.26795i | 0.325358i | 0.986679 | + | 0.162679i | \(0.0520135\pi\) | ||||
−0.986679 | + | 0.162679i | \(0.947986\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 11.3205i | − 0.505763i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.5359 | −1.36153 | −0.680764 | − | 0.732503i | \(-0.738352\pi\) | ||||
−0.680764 | + | 0.732503i | \(0.738352\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 41.5692 | 1.84981 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.00000i | 0.0888231i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.3923i | 0.637928i | 0.947767 | + | 0.318964i | \(0.103335\pi\) | ||||
−0.947767 | + | 0.318964i | \(0.896665\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.46410 | −0.418667 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.92820 | −0.129283 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 24.0000i | − 1.05757i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 31.8564i | − 1.40104i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.8564 | 0.608229 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.1769 | −1.10302 | −0.551510 | − | 0.834168i | \(-0.685948\pi\) | ||||
−0.551510 | + | 0.834168i | \(0.685948\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 14.0000i | − 0.612177i | −0.952003 | − | 0.306089i | \(-0.900980\pi\) | ||||
0.952003 | − | 0.306089i | \(-0.0990204\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.7513i | 0.774730i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 36.7846 | 1.60236 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 10.1962i | − 0.442475i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.92820i | 0.386723i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.0718 | 0.738078 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.7846 | 0.896922 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 25.5167i | − 1.09908i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 3.07180i | − 0.132067i | −0.997817 | − | 0.0660334i | \(-0.978966\pi\) | ||||
0.997817 | − | 0.0660334i | \(-0.0210344\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.8564 | −0.766292 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.92820 | 0.296772 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.8564i | 0.506943i | 0.967343 | + | 0.253472i | \(0.0815725\pi\) | ||||
−0.967343 | + | 0.253472i | \(0.918428\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 2.92820i | − 0.124973i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.46410 | 0.0623728 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.92820 | −0.294617 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 61.8564i | − 2.62566i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.7846i | 1.47387i | 0.675963 | + | 0.736936i | \(0.263728\pi\) | ||||
−0.675963 | + | 0.736936i | \(0.736272\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.535898 | −0.0226661 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 51.7128 | 2.18332 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.46410i | 0.314574i | 0.987553 | + | 0.157287i | \(0.0502748\pi\) | ||||
−0.987553 | + | 0.157287i | \(0.949725\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.78461i | 0.369571i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.9474 | −0.585737 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.0000 | −0.586911 | −0.293455 | − | 0.955973i | \(-0.594805\pi\) | ||||
−0.293455 | + | 0.955973i | \(0.594805\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 2.67949i | − 0.112133i | −0.998427 | − | 0.0560666i | \(-0.982144\pi\) | ||||
0.998427 | − | 0.0560666i | \(-0.0178559\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 29.0718i | − 1.21449i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.0000 | 1.16768 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.07180 | −0.294403 | −0.147201 | − | 0.989107i | \(-0.547027\pi\) | ||||
−0.147201 | + | 0.989107i | \(0.547027\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.21539i | 0.133627i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 4.14359i | − 0.171905i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.8564 | 0.573874 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.46410 | 0.143223 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.33975i | 0.179120i | 0.995981 | + | 0.0895602i | \(0.0285462\pi\) | ||||
−0.995981 | + | 0.0895602i | \(0.971454\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 4.92820i | − 0.203063i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.14359 | −0.252714 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.85641 | −0.322624 | −0.161312 | − | 0.986903i | \(-0.551573\pi\) | ||||
−0.161312 | + | 0.986903i | \(0.551573\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.0000i | 0.983904i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 33.5692i | 1.37390i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 45.1769 | 1.84588 | 0.922939 | − | 0.384945i | \(-0.125780\pi\) | ||||
0.922939 | + | 0.384945i | \(0.125780\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.39230 | −0.179166 | −0.0895829 | − | 0.995979i | \(-0.528553\pi\) | ||||
−0.0895829 | + | 0.995979i | \(0.528553\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.732051i | 0.0298114i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 39.4641i | − 1.60444i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.32051 | −0.297130 | −0.148565 | − | 0.988903i | \(-0.547465\pi\) | ||||
−0.148565 | + | 0.988903i | \(0.547465\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.07180 | 0.205520 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 6.73205i | − 0.272350i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.6410i | 0.995241i | 0.867395 | + | 0.497621i | \(0.165793\pi\) | ||||
−0.867395 | + | 0.497621i | \(0.834207\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 61.8564 | 2.49429 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.3205 | 1.66350 | 0.831751 | − | 0.555150i | \(-0.187339\pi\) | ||||
0.831751 | + | 0.555150i | \(0.187339\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.5885i | 0.747133i | 0.927603 | + | 0.373567i | \(0.121865\pi\) | ||||
−0.927603 | + | 0.373567i | \(0.878135\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.0000i | 0.642058i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.9615 | −0.879870 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 6.92820i | − 0.276686i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 48.7846i | − 1.94517i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.0526 | 1.67409 | 0.837043 | − | 0.547137i | \(-0.184282\pi\) | ||||
0.837043 | + | 0.547137i | \(0.184282\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.7128 | 0.624528 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.8564i | 0.549875i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 5.39230i | − 0.213651i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.19615 | −0.324235 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.2487 | −0.878771 | −0.439386 | − | 0.898299i | \(-0.644804\pi\) | ||||
−0.439386 | + | 0.898299i | \(0.644804\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.7321i | 0.502103i | 0.967974 | + | 0.251052i | \(0.0807764\pi\) | ||||
−0.967974 | + | 0.251052i | \(0.919224\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.71281i | 0.146192i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.8564 | −1.48829 | −0.744144 | − | 0.668019i | \(-0.767143\pi\) | ||||
−0.744144 | + | 0.668019i | \(0.767143\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.2487 | −1.89393 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 17.0718i | − 0.669096i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 3.07180i | − 0.120209i | −0.998192 | − | 0.0601043i | \(-0.980857\pi\) | ||||
0.998192 | − | 0.0601043i | \(-0.0191433\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 68.7846 | 2.68764 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.46410 | 0.291202 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 14.0000i | − 0.545363i | −0.962104 | − | 0.272681i | \(-0.912090\pi\) | ||||
0.962104 | − | 0.272681i | \(-0.0879105\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.3205i | 0.673690i | 0.941560 | + | 0.336845i | \(0.109360\pi\) | ||||
−0.941560 | + | 0.336845i | \(0.890640\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.9282 | 0.424416 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.21539 | 0.124687 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 8.00000i | − 0.309761i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 0.392305i | − 0.0151674i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.8564 | −0.534921 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.1769 | 1.27888 | 0.639438 | − | 0.768843i | \(-0.279167\pi\) | ||||
0.639438 | + | 0.768843i | \(0.279167\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 28.0000i | 1.07772i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.0718i | 0.809855i | 0.914349 | + | 0.404927i | \(0.132703\pi\) | ||||
−0.914349 | + | 0.404927i | \(0.867297\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.10512 | 0.311046 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.75129 | −0.220390 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.8038i | 0.681245i | 0.940200 | + | 0.340623i | \(0.110638\pi\) | ||||
−0.940200 | + | 0.340623i | \(0.889362\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 44.7846i | 1.71113i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.6410 | −0.405980 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.92820 | 0.111556 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.8372i | 1.24918i | 0.780951 | + | 0.624592i | \(0.214735\pi\) | ||||
−0.780951 | + | 0.624592i | \(0.785265\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 6.00000i | − 0.227921i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −34.6410 | −1.31401 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 48.7846 | 1.84785 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 33.8564i | − 1.28057i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 40.6410i | − 1.53499i | −0.641055 | − | 0.767495i | \(-0.721503\pi\) | ||||
0.641055 | − | 0.767495i | \(-0.278497\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.53590 | −0.246506 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −46.6410 | −1.75660 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 15.2154i | − 0.572234i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.3205i | 1.10115i | 0.834784 | + | 0.550577i | \(0.185592\pi\) | ||||
−0.834784 | + | 0.550577i | \(0.814408\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.46410 | 0.204920 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26.9282 | −1.00847 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 16.3923i | − 0.613037i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 37.4641i | 1.39912i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.9282 | −1.15343 | −0.576714 | − | 0.816946i | \(-0.695665\pi\) | ||||
−0.576714 | + | 0.816946i | \(0.695665\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.78461 | −0.327156 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 60.7846i | 2.26060i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 14.0000i | − 0.519947i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.9282 | 0.850360 | 0.425180 | − | 0.905109i | \(-0.360211\pi\) | ||||
0.425180 | + | 0.905109i | \(0.360211\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.92820i | 0.108304i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.3205i | 1.37846i | 0.724541 | + | 0.689232i | \(0.242052\pi\) | ||||
−0.724541 | + | 0.689232i | \(0.757948\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −37.3590 | −1.37801 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.46410 | 0.127602 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 39.7654i | − 1.46279i | −0.681953 | − | 0.731396i | \(-0.738869\pi\) | ||||
0.681953 | − | 0.731396i | \(-0.261131\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 1.46410i | − 0.0537851i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.1962 | 1.18116 | 0.590581 | − | 0.806978i | \(-0.298899\pi\) | ||||
0.590581 | + | 0.806978i | \(0.298899\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 44.7846 | 1.64078 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.26795i | 0.119568i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 6.24871i | − 0.228323i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.07180 | −0.0391104 | −0.0195552 | − | 0.999809i | \(-0.506225\pi\) | ||||
−0.0195552 | + | 0.999809i | \(0.506225\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.7846 | −0.465897 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.6795i | 0.898179i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.7846i | 1.48234i | 0.671316 | + | 0.741171i | \(0.265729\pi\) | ||||
−0.671316 | + | 0.741171i | \(0.734271\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −37.8564 | −1.37410 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.7846 | 0.680942 | 0.340471 | − | 0.940255i | \(-0.389414\pi\) | ||||
0.340471 | + | 0.940255i | \(0.389414\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 2.53590i | − 0.0918057i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 18.9282i | − 0.684351i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.1962 | −0.368162 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.4641 | 1.13462 | 0.567312 | − | 0.823503i | \(-0.307983\pi\) | ||||
0.567312 | + | 0.823503i | \(0.307983\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 47.7128i | 1.71833i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.4641i | 0.987815i | 0.869514 | + | 0.493908i | \(0.164432\pi\) | ||||
−0.869514 | + | 0.493908i | \(0.835568\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −47.1244 | −1.69276 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −22.6410 | −0.812242 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 6.53590i | − 0.234173i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.7846i | 1.38782i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.00000 | 0.285897 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 58.6410 | 2.09299 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.1244i | 1.03817i | 0.854722 | + | 0.519086i | \(0.173727\pi\) | ||||
−0.854722 | + | 0.519086i | \(0.826273\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 54.6410i | − 1.94527i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.21539 | 0.114326 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.92820 | −0.103984 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 20.2872i | − 0.719512i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 30.0000i | − 1.06265i | −0.847167 | − | 0.531327i | \(-0.821693\pi\) | ||||
0.847167 | − | 0.531327i | \(-0.178307\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.7846 | −1.30135 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.3205 | 0.611990 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 35.3205i | − 1.24643i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 17.5692i | − 0.619234i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.7128 | −0.553117 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.46410 | −0.192108 | −0.0960538 | − | 0.995376i | \(-0.530622\pi\) | ||||
−0.0960538 | + | 0.995376i | \(0.530622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 21.4115i | − 0.751861i | −0.926648 | − | 0.375930i | \(-0.877323\pi\) | ||||
0.926648 | − | 0.375930i | \(-0.122677\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 40.3923i | − 1.41662i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 57.9615 | 2.03030 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.392305 | 0.0137250 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 1.26795i | − 0.0443057i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 48.2487i | − 1.68389i | −0.539562 | − | 0.841946i | \(-0.681410\pi\) | ||||
0.539562 | − | 0.841946i | \(-0.318590\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.0000 | −0.697156 | −0.348578 | − | 0.937280i | \(-0.613335\pi\) | ||||
−0.348578 | + | 0.937280i | \(0.613335\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −66.2487 | −2.30648 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 8.73205i | − 0.303643i | −0.988408 | − | 0.151822i | \(-0.951486\pi\) | ||||
0.988408 | − | 0.151822i | \(-0.0485139\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 28.7846i | − 0.999731i | −0.866103 | − | 0.499865i | \(-0.833383\pi\) | ||||
0.866103 | − | 0.499865i | \(-0.166617\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.71281 | 0.128796 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29.4641 | −1.02087 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.6077i | 0.678552i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 26.9282i | − 0.930775i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.9808 | 0.724336 | 0.362168 | − | 0.932113i | \(-0.382037\pi\) | ||||
0.362168 | + | 0.932113i | \(0.382037\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 18.6410i | − 0.642031i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 3.46410i | − 0.119169i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.4449 | −0.496331 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −38.9282 | −1.33601 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.7128i | 1.22422i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 55.1769i | − 1.88922i | −0.328193 | − | 0.944611i | \(-0.606440\pi\) | ||||
0.328193 | − | 0.944611i | \(-0.393560\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.53590 | −0.0867259 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.85641 | −0.268370 | −0.134185 | − | 0.990956i | \(-0.542842\pi\) | ||||
−0.134185 | + | 0.990956i | \(0.542842\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 18.0000i | − 0.614152i | −0.951685 | − | 0.307076i | \(-0.900649\pi\) | ||||
0.951685 | − | 0.307076i | \(-0.0993506\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 22.6410i | − 0.771604i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.26795 | −0.0431615 | −0.0215807 | − | 0.999767i | \(-0.506870\pi\) | ||||
−0.0215807 | + | 0.999767i | \(0.506870\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.0000 | −0.816024 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 25.7128i | − 0.873253i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 25.8564i | − 0.877119i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.732051 | 0.0248046 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.39230 | −0.216347 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 8.78461i | − 0.296974i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 23.4641i | − 0.792326i | −0.918180 | − | 0.396163i | \(-0.870341\pi\) | ||||
0.918180 | − | 0.396163i | \(-0.129659\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 65.8564 | 2.22128 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.7128 | −1.13581 | −0.567907 | − | 0.823093i | \(-0.692247\pi\) | ||||
−0.567907 | + | 0.823093i | \(0.692247\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 31.4641i | − 1.05885i | −0.848356 | − | 0.529426i | \(-0.822407\pi\) | ||||
0.848356 | − | 0.529426i | \(-0.177593\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 70.6410i | 2.37457i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30.2487 | −1.01565 | −0.507826 | − | 0.861460i | \(-0.669551\pi\) | ||||
−0.507826 | + | 0.861460i | \(0.669551\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.07180 | 0.170103 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 52.0526i | − 1.74383i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.92820i | 0.164916i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.0000 | −1.20335 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.00000 | −0.267112 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.4641i | 0.449053i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 16.0000i | − 0.533037i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.35898 | 0.0452242 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30.9282 | 1.02809 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 22.1051i | − 0.733988i | −0.930223 | − | 0.366994i | \(-0.880387\pi\) | ||||
0.930223 | − | 0.366994i | \(-0.119613\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.0000i | 0.398015i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.32051 | −0.110013 | −0.0550067 | − | 0.998486i | \(-0.517518\pi\) | ||||
−0.0550067 | + | 0.998486i | \(0.517518\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.4641 | 0.511787 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20.2872i | 0.670674i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 25.1769i | − 0.831415i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.3205 | 1.16512 | 0.582558 | − | 0.812789i | \(-0.302052\pi\) | ||||
0.582558 | + | 0.812789i | \(0.302052\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.46410 | −0.0482438 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.19615i | 0.269780i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 62.4974i | 2.05490i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.92820 | 0.227552 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.5359 | 0.673761 | 0.336880 | − | 0.941547i | \(-0.390628\pi\) | ||||
0.336880 | + | 0.941547i | \(0.390628\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.94744i | 0.129372i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.14359i | 0.0701781i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −89.5692 | −2.92923 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.7128 | −0.447978 | −0.223989 | − | 0.974592i | \(-0.571908\pi\) | ||||
−0.223989 | + | 0.974592i | \(0.571908\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 0.784610i | − 0.0256048i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.2487i | 1.05128i | 0.850708 | + | 0.525639i | \(0.176174\pi\) | ||||
−0.850708 | + | 0.525639i | \(0.823826\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35.7128 | −1.16297 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17.5692 | 0.571527 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.4449i | 1.57425i | 0.616796 | + | 0.787123i | \(0.288430\pi\) | ||||
−0.616796 | + | 0.787123i | \(0.711570\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 7.46410i | − 0.242295i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.92820 | 0.224662 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31.8564 | −1.03193 | −0.515965 | − | 0.856610i | \(-0.672567\pi\) | ||||
−0.515965 | + | 0.856610i | \(0.672567\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 50.3538i | 1.62941i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.9282i | 0.611862i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.3923 | 0.529335 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.3205 | 0.461952 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.92820i | 0.158809i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 5.56922i | − 0.179280i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.98076 | 0.288802 | 0.144401 | − | 0.989519i | \(-0.453875\pi\) | ||||
0.144401 | + | 0.989519i | \(0.453875\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.00000 | −0.256997 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.1436i | 0.518073i | 0.965868 | + | 0.259036i | \(0.0834049\pi\) | ||||
−0.965868 | + | 0.259036i | \(0.916595\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.6795i | 0.406486i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.0000 | −0.448359 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −58.3923 | −1.86814 | −0.934068 | − | 0.357096i | \(-0.883767\pi\) | ||||
−0.934068 | + | 0.357096i | \(0.883767\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 81.9615i | − 2.61950i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000i | 0.0638551i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.1962 | −0.516577 | −0.258289 | − | 0.966068i | \(-0.583159\pi\) | ||||
−0.258289 | + | 0.966068i | \(0.583159\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.6410 | 0.339051 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17.0718i | 0.543401i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 2.14359i | − 0.0681623i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.67949 | 0.275713 | 0.137857 | − | 0.990452i | \(-0.455979\pi\) | ||||
0.137857 | + | 0.990452i | \(0.455979\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −35.0333 | −1.11175 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 58.1436i | − 1.84328i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.5692i | 1.06315i | 0.847012 | + | 0.531574i | \(0.178399\pi\) | ||||
−0.847012 | + | 0.531574i | \(0.821601\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −35.7128 | −1.12990 |
(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 | 416.2.b.b.209.2 | 4 | ||
3.2 | odd | 2 | 3744.2.g.b.1873.1 | 4 | |||
4.3 | odd | 2 | 104.2.b.b.53.1 | ✓ | 4 | ||
8.3 | odd | 2 | 104.2.b.b.53.2 | yes | 4 | ||
8.5 | even | 2 | inner | 416.2.b.b.209.3 | 4 | ||
12.11 | even | 2 | 936.2.g.b.469.4 | 4 | |||
16.3 | odd | 4 | 3328.2.a.n.1.2 | 2 | |||
16.5 | even | 4 | 3328.2.a.m.1.1 | 2 | |||
16.11 | odd | 4 | 3328.2.a.bd.1.1 | 2 | |||
16.13 | even | 4 | 3328.2.a.bc.1.2 | 2 | |||
24.5 | odd | 2 | 3744.2.g.b.1873.3 | 4 | |||
24.11 | even | 2 | 936.2.g.b.469.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
104.2.b.b.53.1 | ✓ | 4 | 4.3 | odd | 2 | ||
104.2.b.b.53.2 | yes | 4 | 8.3 | odd | 2 | ||
416.2.b.b.209.2 | 4 | 1.1 | even | 1 | trivial | ||
416.2.b.b.209.3 | 4 | 8.5 | even | 2 | inner | ||
936.2.g.b.469.3 | 4 | 24.11 | even | 2 | |||
936.2.g.b.469.4 | 4 | 12.11 | even | 2 | |||
3328.2.a.m.1.1 | 2 | 16.5 | even | 4 | |||
3328.2.a.n.1.2 | 2 | 16.3 | odd | 4 | |||
3328.2.a.bc.1.2 | 2 | 16.13 | even | 4 | |||
3328.2.a.bd.1.1 | 2 | 16.11 | odd | 4 | |||
3744.2.g.b.1873.1 | 4 | 3.2 | odd | 2 | |||
3744.2.g.b.1873.3 | 4 | 24.5 | odd | 2 |