Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,3,Mod(1025,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.1025");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.e (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: | \(62.7794529086\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 576) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1025.1 | ||
Root | \(-0.517638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.1025 |
Dual form | 2304.3.e.g.1025.3 |
$q$-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 \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 7.34847i | − 1.46969i | −0.678233 | − | 0.734847i | \(-0.737254\pi\) | ||||
0.678233 | − | 0.734847i | \(-0.262746\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.3923 | −1.48461 | −0.742307 | − | 0.670059i | \(-0.766269\pi\) | ||||
−0.742307 | + | 0.670059i | \(0.766269\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 8.48528i | − 0.771389i | −0.922627 | − | 0.385695i | \(-0.873962\pi\) | ||||
0.922627 | − | 0.385695i | \(-0.126038\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.3923 | 0.799408 | 0.399704 | − | 0.916644i | \(-0.369113\pi\) | ||||
0.399704 | + | 0.916644i | \(0.369113\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 21.2132i | − 1.24784i | −0.781490 | − | 0.623918i | \(-0.785540\pi\) | ||||
0.781490 | − | 0.623918i | \(-0.214460\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −20.0000 | −1.05263 | −0.526316 | − | 0.850289i | \(-0.676427\pi\) | ||||
−0.526316 | + | 0.850289i | \(0.676427\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 14.6969i | − 0.638997i | −0.947587 | − | 0.319499i | \(-0.896486\pi\) | ||||
0.947587 | − | 0.319499i | \(-0.103514\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −29.0000 | −1.16000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 36.7423i | − 1.26698i | −0.773752 | − | 0.633489i | \(-0.781622\pi\) | ||||
0.773752 | − | 0.633489i | \(-0.218378\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −51.9615 | −1.67618 | −0.838089 | − | 0.545533i | \(-0.816327\pi\) | ||||
−0.838089 | + | 0.545533i | \(0.816327\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 76.3675i | 2.18193i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 41.5692 | 1.12349 | 0.561746 | − | 0.827310i | \(-0.310130\pi\) | ||||
0.561746 | + | 0.827310i | \(0.310130\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 72.1249i | 1.75914i | 0.475766 | + | 0.879572i | \(0.342171\pi\) | ||||
−0.475766 | + | 0.879572i | \(0.657829\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 40.0000 | 0.930233 | 0.465116 | − | 0.885250i | \(-0.346013\pi\) | ||||
0.465116 | + | 0.885250i | \(0.346013\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 73.4847i | − 1.56350i | −0.623589 | − | 0.781752i | \(-0.714326\pi\) | ||||
0.623589 | − | 0.781752i | \(-0.285674\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 59.0000 | 1.20408 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 36.7423i | − 0.693252i | −0.938003 | − | 0.346626i | \(-0.887327\pi\) | ||||
0.938003 | − | 0.346626i | \(-0.112673\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −62.3538 | −1.13371 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 33.9411i | − 0.575273i | −0.957740 | − | 0.287637i | \(-0.907130\pi\) | ||||
0.957740 | − | 0.287637i | \(-0.0928695\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 76.3675i | − 1.17489i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −100.000 | −1.49254 | −0.746269 | − | 0.665645i | \(-0.768157\pi\) | ||||
−0.746269 | + | 0.665645i | \(0.768157\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 73.4847i | − 1.03500i | −0.855685 | − | 0.517498i | \(-0.826864\pi\) | ||||
0.855685 | − | 0.517498i | \(-0.173136\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −20.0000 | −0.273973 | −0.136986 | − | 0.990573i | \(-0.543742\pi\) | ||||
−0.136986 | + | 0.990573i | \(0.543742\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 88.1816i | 1.14522i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 51.9615 | 0.657741 | 0.328870 | − | 0.944375i | \(-0.393332\pi\) | ||||
0.328870 | + | 0.944375i | \(0.393332\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 127.279i | 1.53348i | 0.641955 | + | 0.766742i | \(0.278124\pi\) | ||||
−0.641955 | + | 0.766742i | \(0.721876\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −155.885 | −1.83394 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.7279i | 0.143010i | 0.997440 | + | 0.0715052i | \(0.0227802\pi\) | ||||
−0.997440 | + | 0.0715052i | \(0.977220\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −108.000 | −1.18681 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 146.969i | 1.54705i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 40.0000 | 0.412371 | 0.206186 | − | 0.978513i | \(-0.433895\pi\) | ||||
0.206186 | + | 0.978513i | \(0.433895\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 183.712i | 1.81893i | 0.415783 | + | 0.909464i | \(0.363508\pi\) | ||||
−0.415783 | + | 0.909464i | \(0.636492\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 93.5307 | 0.908065 | 0.454033 | − | 0.890985i | \(-0.349985\pi\) | ||||
0.454033 | + | 0.890985i | \(0.349985\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 169.706i | 1.58603i | 0.609200 | + | 0.793017i | \(0.291491\pi\) | ||||
−0.609200 | + | 0.793017i | \(0.708509\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −51.9615 | −0.476711 | −0.238356 | − | 0.971178i | \(-0.576608\pi\) | ||||
−0.238356 | + | 0.971178i | \(0.576608\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 63.6396i | 0.563182i | 0.959534 | + | 0.281591i | \(0.0908622\pi\) | ||||
−0.959534 | + | 0.281591i | \(0.909138\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −108.000 | −0.939130 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 220.454i | 1.85256i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 49.0000 | 0.404959 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 29.3939i | 0.235151i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.3923 | −0.0818292 | −0.0409146 | − | 0.999163i | \(-0.513027\pi\) | ||||
−0.0409146 | + | 0.999163i | \(0.513027\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 50.9117i | 0.388639i | 0.980938 | + | 0.194319i | \(0.0622498\pi\) | ||||
−0.980938 | + | 0.194319i | \(0.937750\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 207.846 | 1.56275 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 106.066i | − 0.774205i | −0.922037 | − | 0.387102i | \(-0.873476\pi\) | ||||
0.922037 | − | 0.387102i | \(-0.126524\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −172.000 | −1.23741 | −0.618705 | − | 0.785623i | \(-0.712342\pi\) | ||||
−0.618705 | + | 0.785623i | \(0.712342\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 88.1816i | − 0.616655i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −270.000 | −1.86207 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 110.227i | − 0.739779i | −0.929076 | − | 0.369889i | \(-0.879396\pi\) | ||||
0.929076 | − | 0.369889i | \(-0.120604\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 155.885 | 1.03235 | 0.516174 | − | 0.856484i | \(-0.327356\pi\) | ||||
0.516174 | + | 0.856484i | \(0.327356\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 381.838i | 2.46347i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −166.277 | −1.05909 | −0.529544 | − | 0.848282i | \(-0.677637\pi\) | ||||
−0.529544 | + | 0.848282i | \(0.677637\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 152.735i | 0.948665i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 160.000 | 0.981595 | 0.490798 | − | 0.871274i | \(-0.336705\pi\) | ||||
0.490798 | + | 0.871274i | \(0.336705\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 58.7878i | 0.352022i | 0.984388 | + | 0.176011i | \(0.0563195\pi\) | ||||
−0.984388 | + | 0.176011i | \(0.943680\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −61.0000 | −0.360947 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 36.7423i | − 0.212384i | −0.994346 | − | 0.106192i | \(-0.966134\pi\) | ||||
0.994346 | − | 0.106192i | \(-0.0338657\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 301.377 | 1.72215 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 50.9117i | 0.284423i | 0.989836 | + | 0.142211i | \(0.0454213\pi\) | ||||
−0.989836 | + | 0.142211i | \(0.954579\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −259.808 | −1.43540 | −0.717701 | − | 0.696352i | \(-0.754805\pi\) | ||||
−0.717701 | + | 0.696352i | \(0.754805\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 305.470i | − 1.65119i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −180.000 | −0.962567 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 293.939i | 1.53895i | 0.638679 | + | 0.769473i | \(0.279481\pi\) | ||||
−0.638679 | + | 0.769473i | \(0.720519\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0000 | −0.0518135 | −0.0259067 | − | 0.999664i | \(-0.508247\pi\) | ||||
−0.0259067 | + | 0.999664i | \(0.508247\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 22.0454i | − 0.111906i | −0.998433 | − | 0.0559528i | \(-0.982180\pi\) | ||||
0.998433 | − | 0.0559528i | \(-0.0178196\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 51.9615 | 0.261113 | 0.130557 | − | 0.991441i | \(-0.458324\pi\) | ||||
0.130557 | + | 0.991441i | \(0.458324\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 381.838i | 1.88097i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 530.008 | 2.58540 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 169.706i | 0.811989i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −172.000 | −0.815166 | −0.407583 | − | 0.913168i | \(-0.633628\pi\) | ||||
−0.407583 | + | 0.913168i | \(0.633628\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 293.939i | − 1.36716i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 540.000 | 2.48848 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 220.454i | − 0.997530i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.3923 | −0.0466023 | −0.0233011 | − | 0.999728i | \(-0.507418\pi\) | ||||
−0.0233011 | + | 0.999728i | \(0.507418\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 42.4264i | 0.186900i | 0.995624 | + | 0.0934502i | \(0.0297896\pi\) | ||||
−0.995624 | + | 0.0934502i | \(0.970210\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 259.808 | 1.13453 | 0.567266 | − | 0.823535i | \(-0.308001\pi\) | ||||
0.567266 | + | 0.823535i | \(0.308001\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 106.066i | 0.455219i | 0.973752 | + | 0.227609i | \(0.0730910\pi\) | ||||
−0.973752 | + | 0.227609i | \(0.926909\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −540.000 | −2.29787 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 146.969i | − 0.614935i | −0.951559 | − | 0.307467i | \(-0.900519\pi\) | ||||
0.951559 | − | 0.307467i | \(-0.0994815\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 140.000 | 0.580913 | 0.290456 | − | 0.956888i | \(-0.406193\pi\) | ||||
0.290456 | + | 0.956888i | \(0.406193\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 433.560i | − 1.76963i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −207.846 | −0.841482 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 246.073i | 0.980371i | 0.871618 | + | 0.490186i | \(0.163071\pi\) | ||||
−0.871618 | + | 0.490186i | \(0.836929\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −124.708 | −0.492916 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.2132i | 0.0825416i | 0.999148 | + | 0.0412708i | \(0.0131406\pi\) | ||||
−0.999148 | + | 0.0412708i | \(0.986859\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −432.000 | −1.66795 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 88.1816i | 0.335291i | 0.985847 | + | 0.167646i | \(0.0536165\pi\) | ||||
−0.985847 | + | 0.167646i | \(0.946384\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −270.000 | −1.01887 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 110.227i | − 0.409766i | −0.978786 | − | 0.204883i | \(-0.934319\pi\) | ||||
0.978786 | − | 0.204883i | \(-0.0656814\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −467.654 | −1.72566 | −0.862830 | − | 0.505495i | \(-0.831310\pi\) | ||||
−0.862830 | + | 0.505495i | \(0.831310\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 246.073i | 0.894811i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 322.161 | 1.16304 | 0.581519 | − | 0.813533i | \(-0.302459\pi\) | ||||
0.581519 | + | 0.813533i | \(0.302459\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 140.007i | − 0.498246i | −0.968472 | − | 0.249123i | \(-0.919858\pi\) | ||||
0.968472 | − | 0.249123i | \(-0.0801424\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 80.0000 | 0.282686 | 0.141343 | − | 0.989961i | \(-0.454858\pi\) | ||||
0.141343 | + | 0.989961i | \(0.454858\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 749.544i | − 2.61165i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −161.000 | −0.557093 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 315.984i | 1.07844i | 0.842164 | + | 0.539222i | \(0.181282\pi\) | ||||
−0.842164 | + | 0.539222i | \(0.818718\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −249.415 | −0.845476 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 152.735i | − 0.510820i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −415.692 | −1.38104 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 380.000 | 1.23779 | 0.618893 | − | 0.785476i | \(-0.287582\pi\) | ||||
0.618893 | + | 0.785476i | \(0.287582\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 146.969i | 0.472570i | 0.971684 | + | 0.236285i | \(0.0759300\pi\) | ||||
−0.971684 | + | 0.236285i | \(0.924070\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −310.000 | −0.990415 | −0.495208 | − | 0.868775i | \(-0.664908\pi\) | ||||
−0.495208 | + | 0.868775i | \(0.664908\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 242.499i | 0.764983i | 0.923959 | + | 0.382491i | \(0.124934\pi\) | ||||
−0.923959 | + | 0.382491i | \(0.875066\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −311.769 | −0.977333 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 424.264i | 1.31351i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −301.377 | −0.927313 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 763.675i | 2.32120i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 500.000 | 1.51057 | 0.755287 | − | 0.655394i | \(-0.227497\pi\) | ||||
0.755287 | + | 0.655394i | \(0.227497\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 734.847i | 2.19357i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 100.000 | 0.296736 | 0.148368 | − | 0.988932i | \(-0.452598\pi\) | ||||
0.148368 | + | 0.988932i | \(0.452598\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 440.908i | 1.29299i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −103.923 | −0.302983 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 42.4264i | 0.122266i | 0.998130 | + | 0.0611332i | \(0.0194714\pi\) | ||||
−0.998130 | + | 0.0611332i | \(0.980529\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 207.846 | 0.595548 | 0.297774 | − | 0.954636i | \(-0.403756\pi\) | ||||
0.297774 | + | 0.954636i | \(0.403756\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 615.183i | − 1.74273i | −0.490637 | − | 0.871364i | \(-0.663236\pi\) | ||||
0.490637 | − | 0.871364i | \(-0.336764\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −540.000 | −1.52113 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 514.393i | − 1.43285i | −0.697665 | − | 0.716425i | \(-0.745777\pi\) | ||||
0.697665 | − | 0.716425i | \(-0.254223\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.0000 | 0.108033 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 146.969i | 0.402656i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −218.238 | −0.594655 | −0.297328 | − | 0.954776i | \(-0.596095\pi\) | ||||
−0.297328 | + | 0.954776i | \(0.596095\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 381.838i | 1.02921i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −665.108 | −1.78313 | −0.891565 | − | 0.452893i | \(-0.850392\pi\) | ||||
−0.891565 | + | 0.452893i | \(0.850392\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 381.838i | − 1.01283i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −92.0000 | −0.242744 | −0.121372 | − | 0.992607i | \(-0.538729\pi\) | ||||
−0.121372 | + | 0.992607i | \(0.538729\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 146.969i | − 0.383732i | −0.981421 | − | 0.191866i | \(-0.938546\pi\) | ||||
0.981421 | − | 0.191866i | \(-0.0614539\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 648.000 | 1.68312 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 257.196i | − 0.661173i | −0.943776 | − | 0.330587i | \(-0.892753\pi\) | ||||
0.943776 | − | 0.330587i | \(-0.107247\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −311.769 | −0.797364 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 381.838i | − 0.966678i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −41.5692 | −0.104708 | −0.0523542 | − | 0.998629i | \(-0.516672\pi\) | ||||
−0.0523542 | + | 0.998629i | \(0.516672\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 224.860i | − 0.560748i | −0.959891 | − | 0.280374i | \(-0.909542\pi\) | ||||
0.959891 | − | 0.280374i | \(-0.0904585\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −540.000 | −1.33995 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 352.727i | − 0.866650i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −368.000 | −0.899756 | −0.449878 | − | 0.893090i | \(-0.648532\pi\) | ||||
−0.449878 | + | 0.893090i | \(0.648532\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 352.727i | 0.854059i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 935.307 | 2.25375 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 432.749i | 1.03281i | 0.856343 | + | 0.516407i | \(0.172731\pi\) | ||||
−0.856343 | + | 0.516407i | \(0.827269\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −51.9615 | −0.123424 | −0.0617120 | − | 0.998094i | \(-0.519656\pi\) | ||||
−0.0617120 | + | 0.998094i | \(0.519656\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 615.183i | 1.44749i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 367.423i | − 0.852491i | −0.904608 | − | 0.426245i | \(-0.859836\pi\) | ||||
0.904608 | − | 0.426245i | \(-0.140164\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −470.000 | −1.08545 | −0.542725 | − | 0.839910i | \(-0.682607\pi\) | ||||
−0.542725 | + | 0.839910i | \(0.682607\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 293.939i | 0.672629i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 155.885 | 0.355090 | 0.177545 | − | 0.984113i | \(-0.443184\pi\) | ||||
0.177545 | + | 0.984113i | \(0.443184\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 551.543i | − 1.24502i | −0.782612 | − | 0.622509i | \(-0.786113\pi\) | ||||
0.782612 | − | 0.622509i | \(-0.213887\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 93.5307 | 0.210181 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 691.550i | − 1.54020i | −0.637922 | − | 0.770101i | \(-0.720206\pi\) | ||||
0.637922 | − | 0.770101i | \(-0.279794\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 612.000 | 1.35698 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 793.635i | 1.74425i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −680.000 | −1.48796 | −0.743982 | − | 0.668199i | \(-0.767065\pi\) | ||||
−0.743982 | + | 0.668199i | \(0.767065\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 330.681i | 0.717313i | 0.933470 | + | 0.358656i | \(0.116765\pi\) | ||||
−0.933470 | + | 0.358656i | \(0.883235\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −322.161 | −0.695813 | −0.347907 | − | 0.937529i | \(-0.613107\pi\) | ||||
−0.347907 | + | 0.937529i | \(0.613107\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 466.690i | − 0.999337i | −0.866217 | − | 0.499669i | \(-0.833455\pi\) | ||||
0.866217 | − | 0.499669i | \(-0.166545\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1039.23 | 2.21584 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 339.411i | − 0.717571i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 580.000 | 1.22105 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 220.454i | − 0.460238i | −0.973162 | − | 0.230119i | \(-0.926088\pi\) | ||||
0.973162 | − | 0.230119i | \(-0.0739116\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 432.000 | 0.898129 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 293.939i | − 0.606059i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 633.931 | 1.30171 | 0.650853 | − | 0.759204i | \(-0.274412\pi\) | ||||
0.650853 | + | 0.759204i | \(0.274412\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 220.617i | − 0.449322i | −0.974437 | − | 0.224661i | \(-0.927872\pi\) | ||||
0.974437 | − | 0.224661i | \(-0.0721275\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −779.423 | −1.58098 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 763.675i | 1.53657i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −640.000 | −1.28257 | −0.641283 | − | 0.767305i | \(-0.721597\pi\) | ||||
−0.641283 | + | 0.767305i | \(0.721597\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 73.4847i | 0.146093i | 0.997329 | + | 0.0730464i | \(0.0232721\pi\) | ||||
−0.997329 | + | 0.0730464i | \(0.976728\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1350.00 | 2.67327 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 624.620i | − 1.22715i | −0.789636 | − | 0.613576i | \(-0.789731\pi\) | ||||
0.789636 | − | 0.613576i | \(-0.210269\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 207.846 | 0.406744 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 687.308i | − 1.33458i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −623.538 | −1.20607 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 861.256i | 1.65308i | 0.562876 | + | 0.826541i | \(0.309695\pi\) | ||||
−0.562876 | + | 0.826541i | \(0.690305\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.0000 | −0.0382409 | −0.0191205 | − | 0.999817i | \(-0.506087\pi\) | ||||
−0.0191205 | + | 0.999817i | \(0.506087\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1102.27i | 2.09159i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 313.000 | 0.591682 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 749.544i | 1.40627i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1247.08 | 2.33098 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 500.632i | − 0.928816i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 363.731 | 0.672330 | 0.336165 | − | 0.941803i | \(-0.390870\pi\) | ||||
0.336165 | + | 0.941803i | \(0.390870\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 381.838i | 0.700620i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 760.000 | 1.38940 | 0.694698 | − | 0.719301i | \(-0.255538\pi\) | ||||
0.694698 | + | 0.719301i | \(0.255538\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 734.847i | 1.33366i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −540.000 | −0.976492 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 992.043i | − 1.78105i | −0.454937 | − | 0.890524i | \(-0.650338\pi\) | ||||
0.454937 | − | 0.890524i | \(-0.349662\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 415.692 | 0.743635 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 212.132i | − 0.376789i | −0.982093 | − | 0.188394i | \(-0.939672\pi\) | ||||
0.982093 | − | 0.188394i | \(-0.0603283\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 467.654 | 0.827706 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 479.418i | − 0.842563i | −0.906930 | − | 0.421282i | \(-0.861580\pi\) | ||||
0.906930 | − | 0.421282i | \(-0.138420\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −280.000 | −0.490368 | −0.245184 | − | 0.969477i | \(-0.578848\pi\) | ||||
−0.245184 | + | 0.969477i | \(0.578848\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 426.211i | 0.741237i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −650.000 | −1.12652 | −0.563258 | − | 0.826281i | \(-0.690452\pi\) | ||||
−0.563258 | + | 0.826281i | \(0.690452\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 1322.72i | − 2.27663i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −311.769 | −0.534767 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 678.823i | 1.15643i | 0.815886 | + | 0.578213i | \(0.196250\pi\) | ||||
−0.815886 | + | 0.578213i | \(0.803750\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1039.23 | 1.76440 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 445.477i | 0.751226i | 0.926777 | + | 0.375613i | \(0.122568\pi\) | ||||
−0.926777 | + | 0.375613i | \(0.877432\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1620.00 | 2.72269 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 367.423i | − 0.613395i | −0.951807 | − | 0.306697i | \(-0.900776\pi\) | ||||
0.951807 | − | 0.306697i | \(-0.0992240\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 490.000 | 0.815308 | 0.407654 | − | 0.913137i | \(-0.366347\pi\) | ||||
0.407654 | + | 0.913137i | \(0.366347\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 360.075i | − 0.595165i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 322.161 | 0.530744 | 0.265372 | − | 0.964146i | \(-0.414505\pi\) | ||||
0.265372 | + | 0.964146i | \(0.414505\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 763.675i | − 1.24988i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −374.123 | −0.610315 | −0.305157 | − | 0.952302i | \(-0.598709\pi\) | ||||
−0.305157 | + | 0.952302i | \(0.598709\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 784.889i | − 1.27210i | −0.771646 | − | 0.636052i | \(-0.780566\pi\) | ||||
0.771646 | − | 0.636052i | \(-0.219434\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1112.00 | 1.79645 | 0.898223 | − | 0.439540i | \(-0.144859\pi\) | ||||
0.898223 | + | 0.439540i | \(0.144859\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 132.272i | − 0.212315i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −509.000 | −0.814400 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 881.816i | − 1.40193i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −987.269 | −1.56461 | −0.782305 | − | 0.622896i | \(-0.785956\pi\) | ||||
−0.782305 | + | 0.622896i | \(0.785956\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 76.3675i | 0.120264i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 613.146 | 0.962553 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 97.5807i | 0.152232i | 0.997099 | + | 0.0761160i | \(0.0242519\pi\) | ||||
−0.997099 | + | 0.0761160i | \(0.975748\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −80.0000 | −0.124417 | −0.0622084 | − | 0.998063i | \(-0.519814\pi\) | ||||
−0.0622084 | + | 0.998063i | \(0.519814\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 514.393i | − 0.795043i | −0.917593 | − | 0.397522i | \(-0.869870\pi\) | ||||
0.917593 | − | 0.397522i | \(-0.130130\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −288.000 | −0.443760 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1080.22i | 1.65425i | 0.562018 | + | 0.827125i | \(0.310025\pi\) | ||||
−0.562018 | + | 0.827125i | \(0.689975\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 374.123 | 0.571180 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 712.764i | − 1.08158i | −0.841156 | − | 0.540792i | \(-0.818125\pi\) | ||||
0.841156 | − | 0.540792i | \(-0.181875\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1247.08 | 1.88665 | 0.943326 | − | 0.331868i | \(-0.107679\pi\) | ||||
0.943326 | + | 0.331868i | \(0.107679\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 1527.35i | − 2.29677i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −540.000 | −0.809595 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −50.0000 | −0.0742942 | −0.0371471 | − | 0.999310i | \(-0.511827\pi\) | ||||
−0.0371471 | + | 0.999310i | \(0.511827\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 169.015i | 0.249653i | 0.992179 | + | 0.124826i | \(0.0398374\pi\) | ||||
−0.992179 | + | 0.124826i | \(0.960163\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −415.692 | −0.612212 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 42.4264i | − 0.0621177i | −0.999518 | − | 0.0310589i | \(-0.990112\pi\) | ||||
0.999518 | − | 0.0310589i | \(-0.00988793\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −779.423 | −1.13784 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 381.838i | − 0.554191i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 400.000 | 0.578871 | 0.289436 | − | 0.957197i | \(-0.406532\pi\) | ||||
0.289436 | + | 0.957197i | \(0.406532\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1263.94i | 1.81861i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1530.00 | 2.19512 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 992.043i | 1.41518i | 0.706622 | + | 0.707592i | \(0.250218\pi\) | ||||
−0.706622 | + | 0.707592i | \(0.749782\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −831.384 | −1.18262 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1909.19i | − 2.70041i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1195.12 | −1.68563 | −0.842817 | − | 0.538200i | \(-0.819105\pi\) | ||||
−0.842817 | + | 0.538200i | \(0.819105\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 763.675i | 1.07107i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −648.000 | −0.906294 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 661.362i | − 0.919836i | −0.887961 | − | 0.459918i | \(-0.847879\pi\) | ||||
0.887961 | − | 0.459918i | \(-0.152121\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −972.000 | −1.34813 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1065.53i | 1.46969i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 93.5307 | 0.128653 | 0.0643265 | − | 0.997929i | \(-0.479510\pi\) | ||||
0.0643265 | + | 0.997929i | \(0.479510\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 848.528i | − 1.16078i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −613.146 | −0.836488 | −0.418244 | − | 0.908335i | \(-0.637354\pi\) | ||||
−0.418244 | + | 0.908335i | \(0.637354\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 848.528i | 1.15133i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 920.000 | 1.24493 | 0.622463 | − | 0.782649i | \(-0.286132\pi\) | ||||
0.622463 | + | 0.782649i | \(0.286132\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1175.76i | − 1.58244i | −0.611530 | − | 0.791221i | \(-0.709446\pi\) | ||||
0.611530 | − | 0.791221i | \(-0.290554\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −810.000 | −1.08725 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1763.63i | − 2.35465i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −51.9615 | −0.0691898 | −0.0345949 | − | 0.999401i | \(-0.511014\pi\) | ||||
−0.0345949 | + | 0.999401i | \(0.511014\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 1145.51i | − 1.51724i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −405.300 | −0.535403 | −0.267701 | − | 0.963502i | \(-0.586264\pi\) | ||||
−0.267701 | + | 0.963502i | \(0.586264\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 1030.96i | − 1.35475i | −0.735640 | − | 0.677373i | \(-0.763118\pi\) | ||||
0.735640 | − | 0.677373i | \(-0.236882\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 540.000 | 0.707733 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 352.727i | − 0.459878i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 890.000 | 1.15735 | 0.578674 | − | 0.815559i | \(-0.303571\pi\) | ||||
0.578674 | + | 0.815559i | \(0.303571\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 933.256i | 1.20732i | 0.797243 | + | 0.603658i | \(0.206291\pi\) | ||||
−0.797243 | + | 0.603658i | \(0.793709\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1506.88 | 1.94437 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1442.50i | − 1.85173i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −623.538 | −0.798384 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1221.88i | 1.55654i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 100.000 | 0.127065 | 0.0635324 | − | 0.997980i | \(-0.479763\pi\) | ||||
0.0635324 | + | 0.997980i | \(0.479763\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 661.362i | − 0.836109i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 404.166i | 0.507109i | 0.967321 | + | 0.253554i | \(0.0815997\pi\) | ||||
−0.967321 | + | 0.253554i | \(0.918400\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1558.85 | −1.95100 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 169.706i | 0.211340i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1122.37 | 1.39425 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1090.36i | 1.34779i | 0.738829 | + | 0.673893i | \(0.235379\pi\) | ||||
−0.738829 | + | 0.673893i | \(0.764621\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 772.000 | 0.951911 | 0.475956 | − | 0.879469i | \(-0.342102\pi\) | ||||
0.475956 | + | 0.879469i | \(0.342102\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1175.76i | − 1.44264i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −800.000 | −0.979192 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 477.650i | 0.581791i | 0.956755 | + | 0.290896i | \(0.0939532\pi\) | ||||
−0.956755 | + | 0.290896i | \(0.906047\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1132.76 | −1.37638 | −0.688190 | − | 0.725530i | \(-0.741595\pi\) | ||||
−0.688190 | + | 0.725530i | \(0.741595\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 763.675i | 0.923428i | 0.887029 | + | 0.461714i | \(0.152765\pi\) | ||||
−0.887029 | + | 0.461714i | \(0.847235\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 363.731 | 0.438758 | 0.219379 | − | 0.975640i | \(-0.429597\pi\) | ||||
0.219379 | + | 0.975640i | \(0.429597\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1251.58i | − 1.50250i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 432.000 | 0.517365 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 808.332i | − 0.963447i | −0.876323 | − | 0.481723i | \(-0.840011\pi\) | ||||
0.876323 | − | 0.481723i | \(-0.159989\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −509.000 | −0.605232 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 448.257i | 0.530481i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −509.223 | −0.601208 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 610.940i | − 0.717909i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −997.661 | −1.16959 | −0.584796 | − | 0.811181i | \(-0.698825\pi\) | ||||
−0.584796 | + | 0.811181i | \(0.698825\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 572.756i | − 0.668327i | −0.942515 | − | 0.334164i | \(-0.891546\pi\) | ||||
0.942515 | − | 0.334164i | \(-0.108454\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 568.000 | 0.661234 | 0.330617 | − | 0.943765i | \(-0.392743\pi\) | ||||
0.330617 | + | 0.943765i | \(0.392743\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 823.029i | 0.953683i | 0.878989 | + | 0.476842i | \(0.158218\pi\) | ||||
−0.878989 | + | 0.476842i | \(0.841782\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −270.000 | −0.312139 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 440.908i | − 0.507374i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1039.23 | −1.19315 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 305.470i | − 0.349109i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.5692 | −0.0473993 | −0.0236997 | − | 0.999719i | \(-0.507545\pi\) | ||||
−0.0236997 | + | 0.999719i | \(0.507545\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 12.7279i | − 0.0144471i | −0.999974 | − | 0.00722357i | \(-0.997701\pi\) | ||||
0.999974 | − | 0.00722357i | \(-0.00229935\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 520.000 | 0.588901 | 0.294451 | − | 0.955667i | \(-0.404863\pi\) | ||||
0.294451 | + | 0.955667i | \(0.404863\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 88.1816i | − 0.0994156i | −0.998764 | − | 0.0497078i | \(-0.984171\pi\) | ||||
0.998764 | − | 0.0497078i | \(-0.0158290\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 108.000 | 0.121485 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1469.69i | 1.64579i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 374.123 | 0.418014 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1909.19i | 2.12368i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −779.423 | −0.865064 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1909.19i | 2.10960i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.0000 | 0.0441014 | 0.0220507 | − | 0.999757i | \(-0.492980\pi\) | ||||
0.0220507 | + | 0.999757i | \(0.492980\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1175.76i | − 1.29062i | −0.763921 | − | 0.645310i | \(-0.776728\pi\) | ||||
0.763921 | − | 0.645310i | \(-0.223272\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1080.00 | 1.18291 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 529.090i | − 0.576979i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1714.73 | −1.86587 | −0.932933 | − | 0.360051i | \(-0.882759\pi\) | ||||
−0.932933 | + | 0.360051i | \(0.882759\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 763.675i | − 0.827384i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1205.51 | −1.30325 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 1412.80i | − 1.52077i | −0.649470 | − | 0.760387i | \(-0.725009\pi\) | ||||
0.649470 | − | 0.760387i | \(-0.274991\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1180.00 | −1.26745 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1322.72i | 1.41468i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 470.000 | 0.501601 | 0.250800 | − | 0.968039i | \(-0.419306\pi\) | ||||
0.250800 | + | 0.968039i | \(0.419306\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 624.620i | 0.663783i | 0.943318 | + | 0.331892i | \(0.107687\pi\) | ||||
−0.943318 | + | 0.331892i | \(0.892313\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1060.02 | 1.12409 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 339.411i | − 0.358407i | −0.983812 | − | 0.179203i | \(-0.942648\pi\) | ||||
0.983812 | − | 0.179203i | \(-0.0573520\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −207.846 | −0.219016 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 530.330i | − 0.556485i | −0.960511 | − | 0.278242i | \(-0.910248\pi\) | ||||
0.960511 | − | 0.278242i | \(-0.0897519\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2160.00 | 2.26178 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1102.27i | 1.14940i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1739.00 | 1.80957 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 73.4847i | 0.0761499i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1028.84 | −1.06395 | −0.531974 | − | 0.846761i | \(-0.678550\pi\) | ||||
−0.531974 | + | 0.846761i | \(0.678550\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1603.72i | − 1.65162i | −0.563952 | − | 0.825808i | \(-0.690720\pi\) | ||||
0.563952 | − | 0.825808i | \(-0.309280\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1787.48 | 1.83708 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1378.86i | 1.41132i | 0.708551 | + | 0.705659i | \(0.249349\pi\) | ||||
−0.708551 | + | 0.705659i | \(0.750651\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 108.000 | 0.110317 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 440.908i | − 0.448533i | −0.974528 | − | 0.224267i | \(-0.928001\pi\) | ||||
0.974528 | − | 0.224267i | \(-0.0719986\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −162.000 | −0.164467 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 587.878i | − 0.594416i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −467.654 | −0.471901 | −0.235950 | − | 0.971765i | \(-0.575820\pi\) | ||||
−0.235950 | + | 0.971765i | \(0.575820\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 381.838i | − 0.383756i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 249.415 | 0.250166 | 0.125083 | − | 0.992146i | \(-0.460080\pi\) | ||||
0.125083 | + | 0.992146i | \(0.460080\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2304.3.e.g.1025.1 | 4 | ||
3.2 | odd | 2 | inner | 2304.3.e.g.1025.3 | 4 | ||
4.3 | odd | 2 | 2304.3.e.j.1025.2 | 4 | |||
8.3 | odd | 2 | inner | 2304.3.e.g.1025.4 | 4 | ||
8.5 | even | 2 | 2304.3.e.j.1025.3 | 4 | |||
12.11 | even | 2 | 2304.3.e.j.1025.4 | 4 | |||
16.3 | odd | 4 | 576.3.h.b.161.2 | yes | 8 | ||
16.5 | even | 4 | 576.3.h.b.161.7 | yes | 8 | ||
16.11 | odd | 4 | 576.3.h.b.161.5 | yes | 8 | ||
16.13 | even | 4 | 576.3.h.b.161.4 | yes | 8 | ||
24.5 | odd | 2 | 2304.3.e.j.1025.1 | 4 | |||
24.11 | even | 2 | inner | 2304.3.e.g.1025.2 | 4 | ||
48.5 | odd | 4 | 576.3.h.b.161.3 | yes | 8 | ||
48.11 | even | 4 | 576.3.h.b.161.1 | ✓ | 8 | ||
48.29 | odd | 4 | 576.3.h.b.161.8 | yes | 8 | ||
48.35 | even | 4 | 576.3.h.b.161.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.3.h.b.161.1 | ✓ | 8 | 48.11 | even | 4 | ||
576.3.h.b.161.2 | yes | 8 | 16.3 | odd | 4 | ||
576.3.h.b.161.3 | yes | 8 | 48.5 | odd | 4 | ||
576.3.h.b.161.4 | yes | 8 | 16.13 | even | 4 | ||
576.3.h.b.161.5 | yes | 8 | 16.11 | odd | 4 | ||
576.3.h.b.161.6 | yes | 8 | 48.35 | even | 4 | ||
576.3.h.b.161.7 | yes | 8 | 16.5 | even | 4 | ||
576.3.h.b.161.8 | yes | 8 | 48.29 | odd | 4 | ||
2304.3.e.g.1025.1 | 4 | 1.1 | even | 1 | trivial | ||
2304.3.e.g.1025.2 | 4 | 24.11 | even | 2 | inner | ||
2304.3.e.g.1025.3 | 4 | 3.2 | odd | 2 | inner | ||
2304.3.e.g.1025.4 | 4 | 8.3 | odd | 2 | inner | ||
2304.3.e.j.1025.1 | 4 | 24.5 | odd | 2 | |||
2304.3.e.j.1025.2 | 4 | 4.3 | odd | 2 | |||
2304.3.e.j.1025.3 | 4 | 8.5 | even | 2 | |||
2304.3.e.j.1025.4 | 4 | 12.11 | even | 2 |